Finite Group Databasebeta

← C89×#36887 #36414735

Subgroups — C89×#36887 #36414735

Order 22784.

2090 conjugacy classes of subgroups.

The subgroup lattice has 1670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#2849C211yesmaximal, characteristic, complemented
2C89×#2847C211yesmaximal, characteristic, complemented
3C89×#2778C211yesmaximal, characteristic, complemented
4C89×#2768C211yesmaximal, characteristic, complemented
5C89×#2753C211yesmaximal, characteristic, complemented
6C89×#2746C211yesmaximal, characteristic, complemented
7C89×#2739C211yesmaximal, characteristic, complemented
8C89×#2714C211yesmaximal, characteristic, complemented
9C89×#2709C211yesmaximal, characteristic, complemented
10C89×#2705C211yesmaximal, characteristic, complemented
11C89×#2699C211yesmaximal, characteristic, complemented
12C89×#2691C211yesmaximal, characteristic, complemented
13C89×#2685C211yesmaximal, characteristic, complemented
14C89×#2678C211yesmaximal, characteristic, complemented
15C89×#2678C211yesmaximal, characteristic, complemented
16C89×#2671C211yesmaximal, characteristic, complemented
17C89×#2671C211yesmaximal, characteristic, complemented
18C89×#2669C211yesmaximal, characteristic, complemented
19C89×#2636C211yesmaximal, characteristic, complemented
20C89×#2635C211yesmaximal, characteristic, complemented
21C89×#2576C211yesmaximal, characteristic, complemented
22C89×#2559C211yesmaximal, characteristic, complemented
23C89×#2554C211yesmaximal, characteristic, complemented
24C89×#2553C211yesmaximal, characteristic, complemented
25C89×#2468C211yesmaximal, characteristic, complemented
26C89×#2464C211yesmaximal, characteristic, complemented
27C89×#2428C211yesmaximal, characteristic, complemented
28C89×#2420C211yesmaximal, characteristic, complemented
29C89×#2335C211yesmaximal, characteristic, complemented
30C89×#2333C211yesmaximal, characteristic, complemented
31C4×#120×C89C211yesmaximal, characteristic, complemented
32C24×C4×C89C2211yescharacteristic
33C2×#127×C89C2211yescharacteristic
34C2×#126×C89C2211yescharacteristic
35C2×#126×C89C2211yescharacteristic, complemented
36C2×#126×C89C2211yescharacteristic, complemented
37C2×#123×C89C2211yescharacteristic
38C2×#123×C89C2211yescharacteristic
39C2×#123×C89C2211yescharacteristic
40C2×#123×C89C2211yescharacteristic
41C2×#121×C89C2211yescharacteristic
42C2×#121×C89C2211yescharacteristic
43C2×#121×C89C2211yescharacteristic
44C2×#121×C89C2211yescharacteristic
45C2×#121×C89C2211yescharacteristic
46C2×#121×C89C2211yescharacteristic
47C2×#121×C89C2211yescharacteristic
48C2×#121×C89C2211yescharacteristic, complemented
49C2×#121×C89C2211yescharacteristic, complemented
50C2×#120×C89C2211yescharacteristic
51C2×#120×C89C2211yescharacteristic
52C2×#120×C89C2211yescharacteristic
53C2×#120×C89C2211yescharacteristic
54C2×C4×D4×C89C2211yescharacteristic
55C2×C4×D4×C89C2211yescharacteristic
56C2×C4×D4×C89C2211yescharacteristic
57#401×C89C2211yescharacteristic, complemented
58#400×C89C2211yescharacteristic, complemented
59#400×C89C2211yescharacteristic, complemented
60#400×C89C2211yescharacteristic, complemented
61#399×C89C2211yescharacteristic
62#399×C89C2211yescharacteristic, complemented
63#399×C89C2211yescharacteristic, complemented
64#398×C89C2211yescharacteristic, complemented
65#398×C89C2211yescharacteristic, complemented
66#398×C89C2211yescharacteristic, complemented
67#398×C89C2211yescharacteristic, complemented
68#398×C89C2211yescharacteristic, complemented
69#397×C89C2211yescharacteristic
70#397×C89C2211yescharacteristic
71#397×C89C2211yescharacteristic, complemented
72#397×C89C2211yescharacteristic, complemented
73#396×C89C2211yescharacteristic
74#396×C89C2211yescharacteristic
75#396×C89C2211yescharacteristic
76#396×C89C2211yescharacteristic, complemented
77#394×C89C2211yescharacteristic
78#394×C89C2211yescharacteristic
79#394×C89C2211yescharacteristic
80#394×C89C2211yescharacteristic
81#394×C89C2211yescharacteristic
82#394×C89C2211yescharacteristic
83#394×C89C2211yescharacteristic
84#394×C89C2211yescharacteristic
85#394×C89C2211yescharacteristic
86#394×C89C2211yescharacteristic
87#394×C89C2211yescharacteristic, complemented
88#394×C89C2211yescharacteristic, complemented
89#394×C89C2211yescharacteristic, complemented
90#394×C89C2211yescharacteristic, complemented
91#394×C89C2211yescharacteristic, complemented
92#394×C89C2211yescharacteristic, complemented
93#394×C89C2211yescharacteristic, complemented
94#394×C89C2211yescharacteristic, complemented
95#394×C89C2211yescharacteristic, complemented
96#392×C89C2211yescharacteristic
97#392×C89C2211yescharacteristic
98#392×C89C2211yescharacteristic
99#392×C89C2211yescharacteristic
100#392×C89C2211yescharacteristic
101#392×C89C2211yescharacteristic
102#392×C89C2211yescharacteristic
103#392×C89C2211yescharacteristic
104#392×C89C2211yescharacteristic, complemented
105#390×C89C2211yescharacteristic
106#390×C89C2211yescharacteristic
107#390×C89C2211yescharacteristic
108#390×C89C2211yescharacteristic
109#390×C89C2211yescharacteristic
110#390×C89C2211yescharacteristic
111#390×C89C2211yescharacteristic, complemented
112#390×C89C2211yescharacteristic, complemented
113#389×C89C2211yescharacteristic, complemented
114#389×C89C2211yescharacteristic, complemented
115#389×C89C2211yescharacteristic, complemented
116#388×C89C2211yescharacteristic
117#388×C89C2211yescharacteristic
118#388×C89C2211yescharacteristic
119#388×C89C2211yescharacteristic
120#388×C89C2211yescharacteristic
121#388×C89C2211yescharacteristic
122#388×C89C2211yescharacteristic
123#388×C89C2211yescharacteristic, complemented
124#388×C89C2211yescharacteristic, complemented
125#388×C89C2211yescharacteristic, complemented
126#388×C89C2211yescharacteristic, complemented
127#388×C89C2211yescharacteristic, complemented
128#388×C89C2211yescharacteristic, complemented
129#388×C89C2211yescharacteristic, complemented
130#388×C89C2211yescharacteristic, complemented
131#387×C89C2211yescharacteristic, complemented
132#387×C89C2211yescharacteristic, complemented
133#387×C89C2211yescharacteristic, complemented
134#387×C89C2211yescharacteristic, complemented
135#387×C89C2211yescharacteristic, complemented
136#387×C89C2211yescharacteristic, complemented
137#386×C89C2211yescharacteristic
138#386×C89C2211yescharacteristic
139#386×C89C2211yescharacteristic
140#386×C89C2211yescharacteristic
141#386×C89C2211yescharacteristic
142#386×C89C2211yescharacteristic
143#386×C89C2211yescharacteristic
144#386×C89C2211yescharacteristic
145#386×C89C2211yescharacteristic
146#386×C89C2211yescharacteristic
147#386×C89C2211yescharacteristic
148#386×C89C2211yescharacteristic
149#386×C89C2211yescharacteristic
150#386×C89C2211yescharacteristic
151#386×C89C2211yescharacteristic
152#386×C89C2211yescharacteristic
153#386×C89C2211yescharacteristic, complemented
154#386×C89C2211yescharacteristic, complemented
155#386×C89C2211yescharacteristic, complemented
156#386×C89C2211yescharacteristic, complemented
157#385×C89C2211yescharacteristic
158#385×C89C2211yescharacteristic
159#385×C89C2211yescharacteristic
160#385×C89C2211yescharacteristic
161#385×C89C2211yescharacteristic
162#385×C89C2211yescharacteristic
163#385×C89C2211yescharacteristic
164#385×C89C2211yescharacteristic, complemented
165#385×C89C2211yescharacteristic, complemented
166#385×C89C2211yescharacteristic, complemented
167#382×C89C2211yescharacteristic, complemented
168#382×C89C2211yescharacteristic, complemented
169#381×C89C2211yescharacteristic
170#381×C89C2211yescharacteristic
171#381×C89C2211yescharacteristic, complemented
172#381×C89C2211yescharacteristic, complemented
173#380×C89C2211yescharacteristic
174#380×C89C2211yescharacteristic
175#380×C89C2211yescharacteristic
176#380×C89C2211yescharacteristic, complemented
177#380×C89C2211yescharacteristic, complemented
178#379×C89C2211yescharacteristic
179#379×C89C2211yescharacteristic
180C4×C4⋊C4×C89C2211yescharacteristic, complemented
181C4×C22⋊C4×C89C2211yescharacteristic
182C4×C22⋊C4×C89C2211yescharacteristic
183C4×C22⋊C4×C89C2211yescharacteristic
184C4×C22⋊C4×C89C2211yescharacteristic, complemented
185C4×C22⋊C4×C89C2211yescharacteristic, complemented
186C4×C22⋊C4×C89C2211yescharacteristic, complemented
187C25×C89C2311yescharacteristic
188C22×D4×C89C2311yescharacteristic
189C22×D4×C89C2311yescharacteristic
190C22×D4×C89C2311yescharacteristic
191C22×D4×C89C2311yescharacteristic
192C22×D4×C89C2311yescharacteristic
193C22×D4×C89C2311yescharacteristic
194C22×D4×C89C2311yescharacteristic
195C22×D4×C89C2311yescharacteristic
196C22×D4×C89C2311yescharacteristic
197C22×D4×C89C2311yescharacteristic
198C22×D4×C89C2311yescharacteristic
199C22×D4×C89C2311yescharacteristic
200C22×D4×C89C2311yescharacteristic
201C22×D4×C89C2311yescharacteristic
202C22×D4×C89C2311yescharacteristic
203C22×D4×C89C2311yescharacteristic
204C22×D4×C89C2311yescharacteristic
205C22×D4×C89C2311yescharacteristic
206C23×C4×C89—42no—
207C23×C4×C89—42no—
208C23×C4×C89—42no—
209C23×C4×C89C2311yescharacteristic
210C23×C4×C89C2311yescharacteristic
211C23×C4×C89C2311yescharacteristic
212C23×C4×C89C2311yescharacteristic
213C23×C4×C89C2311yescharacteristic
214C23×C4×C89C2311yescharacteristic
215C23×C4×C89C2311yescharacteristic
216C23×C4×C89C2311yescharacteristic
217C23×C4×C89C2311yescharacteristic
218C23×C4×C89C2311yescharacteristic
219#127×C89—42no—
220#126×C89—42no—
221#126×C89—42no—
222#126×C89—42no—
223#123×C89—24no—
224#123×C89—42no—
225#123×C89—42no—
226#123×C89—42no—
227#121×C89—24no—
228#121×C89—42no—
229#121×C89—42no—
230#121×C89—42no—
231#121×C89—42no—
232#121×C89—42no—
233#121×C89—42no—
234#121×C89—42no—
235#121×C89—42no—
236#120×C89—24no—
237#120×C89—42no—
238#120×C89—42no—
239#120×C89—42no—
240C4×D4×C89—42no—
241C4×D4×C89—42no—
242C4×D4×C89—42no—
243C2×C4⋊C4×C89C2311yescharacteristic
244C2×C4⋊C4×C89C2311yescharacteristic
245C2×C4⋊C4×C89C2311yescharacteristic
246C2×C4⋊C4×C89C2311yescharacteristic
247C2×C4⋊C4×C89C2311yescharacteristic
248C2×C4⋊C4×C89C2311yescharacteristic
249C2×C4⋊C4×C89C2311yescharacteristic
250C2×C4⋊C4×C89C2311yescharacteristic
251C2×C4⋊C4×C89C2311yescharacteristic
252C2×C4⋊C4×C89C2311yescharacteristic
253C2×C4⋊C4×C89C2311yescharacteristic
254C2×C4⋊C4×C89C2311yescharacteristic
255C2×C4⋊C4×C89C2311yescharacteristic
256C2×C4⋊C4×C89C2311yescharacteristic
257C2×C4⋊C4×C89C2311yescharacteristic
258C2×C4⋊C4×C89C2311yescharacteristic
259C2×C4⋊C4×C89C2311yescharacteristic
260C2×C4⋊C4×C89C2311yescharacteristic
261C2×C4⋊C4×C89C2311yescharacteristic
262C2×C4⋊C4×C89C2311yescharacteristic
263C2×C4⋊C4×C89C2311yescharacteristic
264C2×C4⋊C4×C89C2311yescharacteristic
265C2×C4⋊C4×C89C2311yescharacteristic
266C2×C4⋊C4×C89C2311yescharacteristic
267C2×C4⋊C4×C89C2311yescharacteristic
268C2×C4⋊C4×C89C2311yescharacteristic
269C2×C22⋊C4×C89C2311yescharacteristic
270C2×C22⋊C4×C89C2311yescharacteristic
271C2×C22⋊C4×C89C2311yescharacteristic
272C2×C22⋊C4×C89C2311yescharacteristic
273C2×C22⋊C4×C89C2311yescharacteristic
274C2×C22⋊C4×C89C2311yescharacteristic
275C2×C22⋊C4×C89C2311yescharacteristic
276C2×C22⋊C4×C89C2311yescharacteristic
277C2×C22⋊C4×C89C2311yescharacteristic
278C2×C22⋊C4×C89C2311yescharacteristic
279C2×C22⋊C4×C89C2311yescharacteristic
280C2×C22⋊C4×C89C2311yescharacteristic
281C2×C22⋊C4×C89C2311yescharacteristic
282C2×C22⋊C4×C89C2311yescharacteristic
283C2×C22⋊C4×C89C2311yescharacteristic
284C2×C22⋊C4×C89C2311yescharacteristic
285C2×C22⋊C4×C89C2311yescharacteristic
286C2×C22⋊C4×C89C2311yescharacteristic
287C2×C22⋊C4×C89C2311yescharacteristic
288C2×C22⋊C4×C89C2311yescharacteristic
289C2×C22⋊C4×C89C2311yescharacteristic
290C2×C22⋊C4×C89C2311yescharacteristic
291C2×C22⋊C4×C89C2311yescharacteristic
292C2×C22⋊C4×C89C2311yescharacteristic
293C2×C22⋊C4×C89C2311yescharacteristic
294C2×C22⋊C4×C89C2311yescharacteristic
295C2×C22⋊C4×C89C2311yescharacteristic
296C2×C22⋊C4×C89C2311yescharacteristic
297C2×C22⋊C4×C89C2311yescharacteristic
298C2×C22⋊C4×C89C2311yescharacteristic
299C2×C22⋊C4×C89C2311yescharacteristic
300C2×C22⋊C4×C89C2311yescharacteristic
301C2×C22⋊C4×C89C2311yescharacteristic
302C2×C22⋊C4×C89C2311yescharacteristic
303C2×C22⋊C4×C89C2311yescharacteristic
304C2×C22⋊C4×C89C2311yescharacteristic
305C2×C22⋊C4×C89C2311yescharacteristic
306C2×C22⋊C4×C89C2311yescharacteristic
307C2×C22⋊C4×C89C2311yescharacteristic
308C2×C22⋊C4×C89C2311yescharacteristic
309C2×C22⋊C4×C89C2311yescharacteristic
310C2×C22⋊C4×C89C2311yescharacteristic
311C2×C22⋊C4×C89C2311yescharacteristic
312C2×C22⋊C4×C89C2311yescharacteristic
313C2×C22⋊C4×C89C2311yescharacteristic
314C2×C22⋊C4×C89C2311yescharacteristic
315C2×C22⋊C4×C89C2311yescharacteristic
316C2×C22⋊C4×C89C2311yescharacteristic
317C2×C22⋊C4×C89C2311yescharacteristic
318C2×C22⋊C4×C89C2311yescharacteristic
319C2×C22⋊C4×C89C2311yescharacteristic
320C2×C22⋊C4×C89C2311yescharacteristic
321C2×C22⋊C4×C89C2311yescharacteristic
322C2×C22⋊C4×C89C2311yescharacteristic
323C2×C22⋊C4×C89C2311yescharacteristic
324C2×C22⋊C4×C89C2311yescharacteristic
325C2×C42×C89C2311yescharacteristic
326C2×C42×C89C2311yescharacteristic
327C2×C42×C89C2311yescharacteristic
328C2×C42×C89C2311yescharacteristic
329C2×C42×C89C2311yescharacteristic
330C2×C42×C89C2311yescharacteristic
331C2×C42×C89C2311yescharacteristic
332C2×C42×C89C2311yescharacteristic
333#95×C89C2311yescharacteristic
334#95×C89C2311yescharacteristic
335#95×C89C2311yescharacteristic
336#95×C89C2311yescharacteristic
337#95×C89C2311yescharacteristic
338#95×C89C2311yescharacteristic
339#95×C89C2311yescharacteristic
340#95×C89C2311yescharacteristic
341#95×C89C2311yescharacteristic
342#95×C89C2311yescharacteristic
343#95×C89C2311yescharacteristic
344#95×C89C2311yescharacteristic
345#95×C89C2311yescharacteristic
346#95×C89C2311yescharacteristic
347#95×C89C2311yescharacteristic
348#95×C89C2311yescharacteristic
349#95×C89C2311yescharacteristic
350#95×C89C2311yescharacteristic
351#95×C89C2311yescharacteristic
352#95×C89C2311yescharacteristic
353#95×C89C2311yescharacteristic
354#95×C89C2311yescharacteristic
355#95×C89C2311yescharacteristic
356#95×C89C2311yescharacteristic
357#95×C89C2311yescharacteristic
358#95×C89C2311yescharacteristic
359#95×C89C2311yescharacteristic
360#95×C89C2311yescharacteristic
361#95×C89C2311yescharacteristic
362#95×C89C2311yescharacteristic
363#95×C89C2311yescharacteristic
364#95×C89C2311yescharacteristic
365#95×C89C2311yescharacteristic
366#95×C89C2311yescharacteristic
367#95×C89C2311yescharacteristic
368#95×C89C2311yescharacteristic
369C24×C89—22no—
370C24×C89—22no—
371C24×C89—22no—
372C24×C89—41no—
373C24×C89—41no—
374C24×C89—41no—
375C24×C89—41no—
376C24×C89C2411yescharacteristic
377C24×C89C2411yescharacteristic
378C24×C89C2411yescharacteristic
379C24×C89C2411yescharacteristic
380C24×C89C2411yescharacteristic
381C24×C89C2411yescharacteristic
382C24×C89C2411yescharacteristic
383C2×D4×C89—22no—
384C2×D4×C89—22no—
385C2×D4×C89—22no—
386C2×D4×C89—22no—
387C2×D4×C89—22no—
388C2×D4×C89—22no—
389C2×D4×C89—22no—
390C2×D4×C89—22no—
391C2×D4×C89—22no—
392C2×D4×C89—22no—
393C2×D4×C89—22no—
394C2×D4×C89—22no—
395C2×D4×C89—22no—
396C2×D4×C89—22no—
397C2×D4×C89—22no—
398C2×D4×C89—22no—
399C2×D4×C89—41no—
400C2×D4×C89—41no—
401C2×D4×C89—41no—
402C2×D4×C89—41no—
403C2×D4×C89—41no—
404C2×D4×C89—41no—
405C2×D4×C89—41no—
406C2×D4×C89—41no—
407C2×D4×C89—41no—
408C2×D4×C89—41no—
409C2×D4×C89—41no—
410C2×D4×C89—41no—
411C2×D4×C89—41no—
412C2×D4×C89—41no—
413C2×D4×C89—41no—
414C2×D4×C89—41no—
415C2×D4×C89—41no—
416C2×D4×C89—41no—
417C2×D4×C89—41no—
418C2×D4×C89—41no—
419C2×D4×C89—41no—
420C2×D4×C89—41no—
421C2×D4×C89—41no—
422C2×D4×C89—41no—
423C2×D4×C89—41no—
424C2×D4×C89—41no—
425C2×D4×C89—41no—
426C2×D4×C89—41no—
427C2×D4×C89—41no—
428C2×D4×C89—41no—
429C2×D4×C89—41no—
430C2×D4×C89—41no—
431C2×D4×C89—41no—
432C2×D4×C89—41no—
433C2×D4×C89—41no—
434C2×D4×C89—41no—
435C2×D4×C89—41no—
436C2×D4×C89—41no—
437C22×C4×C89—22no—
438C22×C4×C89—22no—
439C22×C4×C89—22no—
440C22×C4×C89—22no—
441C22×C4×C89—22no—
442C22×C4×C89—22no—
443C22×C4×C89—22no—
444C22×C4×C89—22no—
445C22×C4×C89—22no—
446C22×C4×C89—22no—
447C22×C4×C89—22no—
448C22×C4×C89—41no—
449C22×C4×C89—41no—
450C22×C4×C89—41no—
451C22×C4×C89—41no—
452C22×C4×C89—41no—
453C22×C4×C89—41no—
454C22×C4×C89—41no—
455C22×C4×C89—41no—
456C22×C4×C89—41no—
457C22×C4×C89—41no—
458C22×C4×C89—41no—
459C22×C4×C89—41no—
460C22×C4×C89—41no—
461C22×C4×C89—41no—
462C22×C4×C89—41no—
463C22×C4×C89—41no—
464C22×C4×C89—41no—
465C22×C4×C89—41no—
466C22×C4×C89—41no—
467C22×C4×C89—416no—
468C22×C4×C89C2411yescharacteristic
469C22×C4×C89C2411yescharacteristic
470C22×C4×C89C2411yescharacteristic
471C22×C4×C89C2411yescharacteristic
472C22×C4×C89C2411yescharacteristic
473C22×C4×C89C2411yescharacteristic
474C22×C4×C89C2411yescharacteristic
475C22×C4×C89C2411yescharacteristic
476C22×C4×C89C2411yescharacteristic
477C22×C4×C89C2411yescharacteristic
478C22×C4×C89C2411yescharacteristic
479C22×C4×C89C2411yescharacteristic
480C22×C4×C89C2411yescharacteristic
481C22×C4×C89C2411yescharacteristic
482C22×C4×C89C2411yescharacteristic
483C22×C4×C89C2411yescharacteristic
484C22×C4×C89C2411yescharacteristic
485C22×C4×C89C2411yescharacteristic
486C22×C4×C89C2411yescharacteristic
487C22×C4×C89C2411yescharacteristic
488C22×C4×C89C2411yescharacteristic
489C22×C4×C89C2411yescharacteristic
490C22×C4×C89C2411yescharacteristic
491C22×C4×C89C2411yescharacteristic
492C4⋊C4×C89—22no—
493C4⋊C4×C89—22no—
494C4⋊C4×C89—22no—
495C4⋊C4×C89—22no—
496C4⋊C4×C89—22no—
497C4⋊C4×C89—22no—
498C4⋊C4×C89—22no—
499C4⋊C4×C89—41no—
500C4⋊C4×C89—41no—
501C4⋊C4×C89—41no—
502C4⋊C4×C89—41no—
503C4⋊C4×C89—41no—
504C4⋊C4×C89—41no—
505C4⋊C4×C89—41no—
506C4⋊C4×C89—41no—
507C4⋊C4×C89—41no—
508C4⋊C4×C89—41no—
509C4⋊C4×C89—41no—
510C4⋊C4×C89—41no—
511C4⋊C4×C89—41no—
512C4⋊C4×C89—41no—
513C4⋊C4×C89—41no—
514C4⋊C4×C89—41no—
515C4⋊C4×C89—41no—
516C4⋊C4×C89—41no—
517C4⋊C4×C89—41no—
518C22⋊C4×C89—22no—
519C22⋊C4×C89—22no—
520C22⋊C4×C89—22no—
521C22⋊C4×C89—22no—
522C22⋊C4×C89—22no—
523C22⋊C4×C89—22no—
524C22⋊C4×C89—22no—
525C22⋊C4×C89—22no—
526C22⋊C4×C89—22no—
527C22⋊C4×C89—22no—
528C22⋊C4×C89—22no—
529C22⋊C4×C89—22no—
530C22⋊C4×C89—22no—
531C22⋊C4×C89—22no—
532C22⋊C4×C89—22no—
533C22⋊C4×C89—22no—
534C22⋊C4×C89—41no—
535C22⋊C4×C89—41no—
536C22⋊C4×C89—41no—
537C22⋊C4×C89—41no—
538C22⋊C4×C89—41no—
539C22⋊C4×C89—41no—
540C22⋊C4×C89—41no—
541C22⋊C4×C89—41no—
542C22⋊C4×C89—41no—
543C22⋊C4×C89—41no—
544C22⋊C4×C89—41no—
545C22⋊C4×C89—41no—
546C22⋊C4×C89—41no—
547C22⋊C4×C89—41no—
548C22⋊C4×C89—41no—
549C22⋊C4×C89—41no—
550C22⋊C4×C89—41no—
551C22⋊C4×C89—41no—
552C22⋊C4×C89—41no—
553C22⋊C4×C89—41no—
554C22⋊C4×C89—41no—
555C22⋊C4×C89—41no—
556C22⋊C4×C89—41no—
557C22⋊C4×C89—41no—
558C22⋊C4×C89—41no—
559C22⋊C4×C89—41no—
560C22⋊C4×C89—41no—
561C22⋊C4×C89—41no—
562C22⋊C4×C89—41no—
563C22⋊C4×C89—41no—
564C22⋊C4×C89—41no—
565C22⋊C4×C89—41no—
566C22⋊C4×C89—41no—
567C22⋊C4×C89—41no—
568C22⋊C4×C89—41no—
569C22⋊C4×C89—41no—
570C22⋊C4×C89—41no—
571C22⋊C4×C89—41no—
572C22⋊C4×C89—41no—
573C22⋊C4×C89#4114yes—
574C42×C89—22no—
575C42×C89—41no—
576C42×C89—41no—
577C42×C89—41no—
578C42×C89—41no—
579C42×C89—41no—
580C42×C89—41no—
581C42×C89—41no—
582C23×C89—21no—
583C23×C89—21no—
584C23×C89—21no—
585C23×C89—21no—
586C23×C89—21no—
587C23×C89—21no—
588C23×C89—21no—
589C23×C89—21no—
590C23×C89—21no—
591C23×C89—21no—
592C23×C89—21no—
593C23×C89—21no—
594C23×C89—21no—
595C23×C89—21no—
596C23×C89—21no—
597C23×C89—21no—
598C23×C89—21no—
599C23×C89—21no—
600C23×C89—21no—
601C23×C89—21no—
602C23×C89—21no—
603C23×C89—21no—
604C23×C89—21no—
605C23×C89—21no—
606C23×C89—21no—
607C23×C89—21no—
608C23×C89—21no—
609C23×C89—21no—
610C23×C89—21no—
611C23×C89—21no—
612C23×C89—21no—
613C23×C89—21no—
614C23×C89—21no—
615C23×C89—21no—
616C23×C89—21no—
617C23×C89—21no—
618C23×C89—21no—
619C23×C89—21no—
620C23×C89—21no—
621C23×C89—21no—
622C23×C89—21no—
623C23×C89—21no—
624C23×C89—21no—
625C23×C89—21no—
626C23×C89—21no—
627C23×C89—21no—
628C23×C89—44no—
629C23×C89—44no—
630C23×C89—44no—
631C23×C89—44no—
632C23×C89—44no—
633C23×C89—44no—
634C23×C89—44no—
635C23×C89C2×#4112yes—
636C23×C89H(5,𝔽2)12yes—
637C23×C89H(5,𝔽2)12yes—
638C23×C89C2511yescharacteristic
639D4×C89—44no—
640D4×C89—44no—
641D4×C89—44no—
642D4×C89—82no—
643D4×C89—82no—
644D4×C89—82no—
645D4×C89—82no—
646D4×C89—82no—
647D4×C89—82no—
648D4×C89—82no—
649D4×C89—82no—
650D4×C89—82no—
651D4×C89—82no—
652D4×C89—82no—
653D4×C89—82no—
654D4×C89—82no—
655D4×C89—82no—
656D4×C89—82no—
657C2×C4×C89—21no—
658C2×C4×C89—21no—
659C2×C4×C89—21no—
660C2×C4×C89—21no—
661C2×C4×C89—21no—
662C2×C4×C89—21no—
663C2×C4×C89—21no—
664C2×C4×C89—21no—
665C2×C4×C89—21no—
666C2×C4×C89—21no—
667C2×C4×C89—21no—
668C2×C4×C89—21no—
669C2×C4×C89—21no—
670C2×C4×C89—21no—
671C2×C4×C89—21no—
672C2×C4×C89—21no—
673C2×C4×C89—21no—
674C2×C4×C89—21no—
675C2×C4×C89—21no—
676C2×C4×C89—21no—
677C2×C4×C89—21no—
678C2×C4×C89—21no—
679C2×C4×C89—21no—
680C2×C4×C89—21no—
681C2×C4×C89—21no—
682C2×C4×C89—21no—
683C2×C4×C89—21no—
684C2×C4×C89—21no—
685C2×C4×C89—21no—
686C2×C4×C89—21no—
687C2×C4×C89—21no—
688C2×C4×C89—21no—
689C2×C4×C89—21no—
690C2×C4×C89—21no—
691C2×C4×C89—21no—
692C2×C4×C89—21no—
693C2×C4×C89—21no—
694C2×C4×C89—21no—
695C2×C4×C89—21no—
696C2×C4×C89—21no—
697C2×C4×C89—21no—
698C2×C4×C89—21no—
699C2×C4×C89—21no—
700C2×C4×C89—21no—
701C2×C4×C89—21no—
702C2×C4×C89—21no—
703C2×C4×C89—21no—
704C2×C4×C89—21no—
705C2×C4×C89—21no—
706C2×C4×C89—21no—
707C2×C4×C89—21no—
708C2×C4×C89—21no—
709C2×C4×C89—21no—
710C2×C4×C89—21no—
711C2×C4×C89—21no—
712C2×C4×C89—21no—
713C2×C4×C89—21no—
714C2×C4×C89—21no—
715C2×C4×C89—21no—
716C2×C4×C89—21no—
717C2×C4×C89—21no—
718C2×C4×C89—21no—
719C2×C4×C89—21no—
720C2×C4×C89—21no—
721C2×C4×C89—21no—
722C2×C4×C89—21no—
723C2×C4×C89—21no—
724C2×C4×C89—21no—
725C2×C4×C89—44no—
726C2×C4×C89—44no—
727C2×C4×C89—44no—
728C2×C4×C89—44no—
729C2×C4×C89—44no—
730C2×C4×C89—44no—
731C2×C4×C89—82no—
732C2×C4×C89—82no—
733C2×C4×C89—82no—
734C2×C4×C89—82no—
735C2×C4×C89C2×#4112yes—
736C2×C4×C89C2×#4112yes—
737C2×C4×C89H(5,𝔽2)12yes—
738C2×C4×C89H(5,𝔽2)12yes—
739C22×C89—22no—
740C22×C89—22no—
741C22×C89—22no—
742C22×C89—22no—
743C22×C89—22no—
744C22×C89—22no—
745C22×C89—22no—
746C22×C89—22no—
747C22×C89—22no—
748C22×C89—416no—
749C22×C89—41no—
750C22×C89—41no—
751C22×C89—41no—
752C22×C89—41no—
753C22×C89—41no—
754C22×C89—41no—
755C22×C89—41no—
756C22×C89—41no—
757C22×C89—41no—
758C22×C89—41no—
759C22×C89—41no—
760C22×C89—41no—
761C22×C89—41no—
762C22×C89—41no—
763C22×C89—41no—
764C22×C89—41no—
765C22×C89—41no—
766C22×C89—41no—
767C22×C89—41no—
768C22×C89—41no—
769C22×C89—41no—
770C22×C89—41no—
771C22×C89—41no—
772C22×C89—41no—
773C22×C89—41no—
774C22×C89—41no—
775C22×C89—41no—
776C22×C89—41no—
777C22×C89—41no—
778C22×C89—41no—
779C22×C89—41no—
780C22×C89—41no—
781C22×C89—41no—
782C22×C89—41no—
783C22×C89—41no—
784C22×C89—41no—
785C22×C89—41no—
786C22×C89—41no—
787C22×C89—41no—
788C22×C89—41no—
789C22×C89C22×#4111yescharacteristic
790C22×C89C2×H(5,𝔽2)11yescharacteristic
791C22×C89C2×H(5,𝔽2)11yescharacteristic
792C22×C89C2×H(5,𝔽2)11yescharacteristic
793C22×C89C2×H(5,𝔽2)11yescharacteristic
794C22×C89#58511yescharacteristic
795C22×C89#58511yescharacteristic
796C4×C89—22no—
797C4×C89—22no—
798C4×C89—22no—
799C4×C89—22no—
800C4×C89—41no—
801C4×C89—41no—
802C4×C89—41no—
803C4×C89—41no—
804C4×C89—41no—
805C4×C89—41no—
806C4×C89—41no—
807C4×C89—41no—
808C4×C89—41no—
809C4×C89—41no—
810C4×C89—41no—
811C4×C89—41no—
812C4×C89—41no—
813C4×C89—41no—
814C4×C89—41no—
815C4×C89—41no—
816C4×C89—41no—
817C4×C89—41no—
818C4×C89—41no—
819C4×C89—41no—
820#36887C8911yesmaximal, characteristic, direct product factor, Sylow
821C2×C89—42no—
822C2×C89—42no—
823C2×C89—42no—
824C2×C89—81no—
825C2×C89—81no—
826C2×C89—81no—
827C2×C89—81no—
828C2×C89#346011yescharacteristic
829C2×C89#351311yescharacteristic
830C2×C89#351911yescharacteristic
831C2×C89#353211yescharacteristic
832C2×C89#353411yescharacteristic
833C2×C89#353911yescharacteristic
834C2×C89#354211yescharacteristic
835#2849C2×C8911yescharacteristic, complemented
836#2847C2×C8911yescharacteristic, complemented
837#2778C2×C8911yescharacteristic, complemented
838#2768C2×C8911yescharacteristic, complemented
839#2753C2×C8911yescharacteristic, complemented
840#2746C2×C8911yescharacteristic, complemented
841#2739C2×C8911yescharacteristic, complemented
842#2714C2×C8911yescharacteristic, complemented
843#2709C2×C8911yescharacteristic, complemented
844#2705C2×C8911yescharacteristic, complemented
845#2699C2×C8911yescharacteristic, complemented
846#2691C2×C8911yescharacteristic, complemented
847#2685C2×C8911yescharacteristic, complemented
848#2678C2×C8911yescharacteristic, complemented
849#2678C2×C8911yescharacteristic, complemented
850#2671C2×C8911yescharacteristic, complemented
851#2671C2×C8911yescharacteristic, complemented
852#2669C2×C8911yescharacteristic, complemented
853#2636C2×C8911yescharacteristic, complemented
854#2635C2×C8911yescharacteristic, complemented
855#2576C2×C8911yescharacteristic, complemented
856#2559C2×C8911yescharacteristic, complemented
857#2554C2×C8911yescharacteristic, complemented
858#2553C2×C8911yescharacteristic, complemented
859#2468C2×C8911yescharacteristic, complemented
860#2464C2×C8911yescharacteristic, complemented
861#2428C2×C8911yescharacteristic, complemented
862#2420C2×C8911yescharacteristic, complemented
863#2335C2×C8911yescharacteristic, complemented
864#2333C2×C8911yescharacteristic, complemented
865C4×#120C2×C8911yescharacteristic, complemented
866C89#3688711yescharacteristic, direct product factor, Sylow
867C24×C4C22×C8911yescharacteristic
868C2×#127C22×C8911yescharacteristic
869C2×#126C22×C8911yescharacteristic
870C2×#126C22×C8911yescharacteristic, complemented
871C2×#126C22×C8911yescharacteristic, complemented
872C2×#123C22×C8911yescharacteristic
873C2×#123C22×C8911yescharacteristic
874C2×#123C22×C8911yescharacteristic
875C2×#123C22×C8911yescharacteristic
876C2×#121C22×C8911yescharacteristic
877C2×#121C22×C8911yescharacteristic
878C2×#121C22×C8911yescharacteristic
879C2×#121C22×C8911yescharacteristic
880C2×#121C22×C8911yescharacteristic
881C2×#121C22×C8911yescharacteristic
882C2×#121C22×C8911yescharacteristic
883C2×#121C22×C8911yescharacteristic, complemented
884C2×#121C22×C8911yescharacteristic, complemented
885C2×#120C22×C8911yescharacteristic
886C2×#120C22×C8911yescharacteristic
887C2×#120C22×C8911yescharacteristic
888C2×#120C22×C8911yescharacteristic
889C2×C4×D4C22×C8911yescharacteristic
890C2×C4×D4C22×C8911yescharacteristic
891C2×C4×D4C22×C8911yescharacteristic
892#401C22×C8911yescharacteristic, complemented
893#400C22×C8911yescharacteristic, complemented
894#400C22×C8911yescharacteristic, complemented
895#400C22×C8911yescharacteristic, complemented
896#399C22×C8911yescharacteristic
897#399C22×C8911yescharacteristic, complemented
898#399C22×C8911yescharacteristic, complemented
899#398C22×C8911yescharacteristic, complemented
900#398C22×C8911yescharacteristic, complemented
901#398C22×C8911yescharacteristic, complemented
902#398C22×C8911yescharacteristic, complemented
903#398C22×C8911yescharacteristic, complemented
904#397C22×C8911yescharacteristic
905#397C22×C8911yescharacteristic
906#397C22×C8911yescharacteristic, complemented
907#397C22×C8911yescharacteristic, complemented
908#396C22×C8911yescharacteristic
909#396C22×C8911yescharacteristic
910#396C22×C8911yescharacteristic
911#396C22×C8911yescharacteristic, complemented
912#394C22×C8911yescharacteristic
913#394C22×C8911yescharacteristic
914#394C22×C8911yescharacteristic
915#394C22×C8911yescharacteristic
916#394C22×C8911yescharacteristic
917#394C22×C8911yescharacteristic
918#394C22×C8911yescharacteristic
919#394C22×C8911yescharacteristic
920#394C22×C8911yescharacteristic
921#394C22×C8911yescharacteristic
922#394C22×C8911yescharacteristic, complemented
923#394C22×C8911yescharacteristic, complemented
924#394C22×C8911yescharacteristic, complemented
925#394C22×C8911yescharacteristic, complemented
926#394C22×C8911yescharacteristic, complemented
927#394C22×C8911yescharacteristic, complemented
928#394C22×C8911yescharacteristic, complemented
929#394C22×C8911yescharacteristic, complemented
930#394C22×C8911yescharacteristic, complemented
931#392C22×C8911yescharacteristic
932#392C22×C8911yescharacteristic
933#392C22×C8911yescharacteristic
934#392C22×C8911yescharacteristic
935#392C22×C8911yescharacteristic
936#392C22×C8911yescharacteristic
937#392C22×C8911yescharacteristic
938#392C22×C8911yescharacteristic
939#392C22×C8911yescharacteristic, complemented
940#390C22×C8911yescharacteristic
941#390C22×C8911yescharacteristic
942#390C22×C8911yescharacteristic
943#390C22×C8911yescharacteristic
944#390C22×C8911yescharacteristic
945#390C22×C8911yescharacteristic
946#390C22×C8911yescharacteristic, complemented
947#390C22×C8911yescharacteristic, complemented
948#389C22×C8911yescharacteristic, complemented
949#389C22×C8911yescharacteristic, complemented
950#389C22×C8911yescharacteristic, complemented
951#388C22×C8911yescharacteristic
952#388C22×C8911yescharacteristic
953#388C22×C8911yescharacteristic
954#388C22×C8911yescharacteristic
955#388C22×C8911yescharacteristic
956#388C22×C8911yescharacteristic
957#388C22×C8911yescharacteristic
958#388C22×C8911yescharacteristic, complemented
959#388C22×C8911yescharacteristic, complemented
960#388C22×C8911yescharacteristic, complemented
961#388C22×C8911yescharacteristic, complemented
962#388C22×C8911yescharacteristic, complemented
963#388C22×C8911yescharacteristic, complemented
964#388C22×C8911yescharacteristic, complemented
965#388C22×C8911yescharacteristic, complemented
966#387C22×C8911yescharacteristic, complemented
967#387C22×C8911yescharacteristic, complemented
968#387C22×C8911yescharacteristic, complemented
969#387C22×C8911yescharacteristic, complemented
970#387C22×C8911yescharacteristic, complemented
971#387C22×C8911yescharacteristic, complemented
972#386C22×C8911yescharacteristic
973#386C22×C8911yescharacteristic
974#386C22×C8911yescharacteristic
975#386C22×C8911yescharacteristic
976#386C22×C8911yescharacteristic
977#386C22×C8911yescharacteristic
978#386C22×C8911yescharacteristic
979#386C22×C8911yescharacteristic
980#386C22×C8911yescharacteristic
981#386C22×C8911yescharacteristic
982#386C22×C8911yescharacteristic
983#386C22×C8911yescharacteristic
984#386C22×C8911yescharacteristic
985#386C22×C8911yescharacteristic
986#386C22×C8911yescharacteristic
987#386C22×C8911yescharacteristic
988#386C22×C8911yescharacteristic, complemented
989#386C22×C8911yescharacteristic, complemented
990#386C22×C8911yescharacteristic, complemented
991#386C22×C8911yescharacteristic, complemented
992#385C22×C8911yescharacteristic
993#385C22×C8911yescharacteristic
994#385C22×C8911yescharacteristic
995#385C22×C8911yescharacteristic
996#385C22×C8911yescharacteristic
997#385C22×C8911yescharacteristic
998#385C22×C8911yescharacteristic
999#385C22×C8911yescharacteristic, complemented
1000#385C22×C8911yescharacteristic, complemented
1001#385C22×C8911yescharacteristic, complemented
1002#382C22×C8911yescharacteristic, complemented
1003#382C22×C8911yescharacteristic, complemented
1004#381C22×C8911yescharacteristic
1005#381C22×C8911yescharacteristic
1006#381C22×C8911yescharacteristic, complemented
1007#381C22×C8911yescharacteristic, complemented
1008#380C22×C8911yescharacteristic
1009#380C22×C8911yescharacteristic
1010#380C22×C8911yescharacteristic
1011#380C22×C8911yescharacteristic, complemented
1012#380C22×C8911yescharacteristic, complemented
1013#379C22×C8911yescharacteristic
1014#379C22×C8911yescharacteristic
1015C4×C4⋊C4C22×C8911yescharacteristic, complemented
1016C4×C22⋊C4C22×C8911yescharacteristic
1017C4×C22⋊C4C22×C8911yescharacteristic
1018C4×C22⋊C4C22×C8911yescharacteristic
1019C4×C22⋊C4C22×C8911yescharacteristic, complemented
1020C4×C22⋊C4C22×C8911yescharacteristic, complemented
1021C4×C22⋊C4C22×C8911yescharacteristic, complemented
1022C25C23×C8911yescharacteristic
1023C22×D4C23×C8911yescharacteristic
1024C22×D4C23×C8911yescharacteristic
1025C22×D4C23×C8911yescharacteristic
1026C22×D4C23×C8911yescharacteristic
1027C22×D4C23×C8911yescharacteristic
1028C22×D4C23×C8911yescharacteristic
1029C22×D4C23×C8911yescharacteristic
1030C22×D4C23×C8911yescharacteristic
1031C22×D4C23×C8911yescharacteristic
1032C22×D4C23×C8911yescharacteristic
1033C22×D4C23×C8911yescharacteristic
1034C22×D4C23×C8911yescharacteristic
1035C22×D4C23×C8911yescharacteristic
1036C22×D4C23×C8911yescharacteristic
1037C22×D4C23×C8911yescharacteristic
1038C22×D4C23×C8911yescharacteristic
1039C22×D4C23×C8911yescharacteristic
1040C22×D4C23×C8911yescharacteristic
1041C23×C4—42no—
1042C23×C4—42no—
1043C23×C4—42no—
1044C23×C4C23×C8911yescharacteristic
1045C23×C4C23×C8911yescharacteristic
1046C23×C4C23×C8911yescharacteristic
1047C23×C4C23×C8911yescharacteristic
1048C23×C4C23×C8911yescharacteristic
1049C23×C4C23×C8911yescharacteristic
1050C23×C4C23×C8911yescharacteristic
1051C23×C4C23×C8911yescharacteristic
1052C23×C4C23×C8911yescharacteristic
1053C23×C4C23×C8911yescharacteristic
1054#127—42no—
1055#126—42no—
1056#126—42no—
1057#126—42no—
1058#123—24no—
1059#123—42no—
1060#123—42no—
1061#123—42no—
1062#121—24no—
1063#121—42no—
1064#121—42no—
1065#121—42no—
1066#121—42no—
1067#121—42no—
1068#121—42no—
1069#121—42no—
1070#121—42no—
1071#120—24no—
1072#120—42no—
1073#120—42no—
1074#120—42no—
1075C4×D4—42no—
1076C4×D4—42no—
1077C4×D4—42no—
1078C2×C4⋊C4C23×C8911yescharacteristic
1079C2×C4⋊C4C23×C8911yescharacteristic
1080C2×C4⋊C4C23×C8911yescharacteristic
1081C2×C4⋊C4C23×C8911yescharacteristic
1082C2×C4⋊C4C23×C8911yescharacteristic
1083C2×C4⋊C4C23×C8911yescharacteristic
1084C2×C4⋊C4C23×C8911yescharacteristic
1085C2×C4⋊C4C23×C8911yescharacteristic
1086C2×C4⋊C4C23×C8911yescharacteristic
1087C2×C4⋊C4C23×C8911yescharacteristic
1088C2×C4⋊C4C23×C8911yescharacteristic
1089C2×C4⋊C4C23×C8911yescharacteristic
1090C2×C4⋊C4C23×C8911yescharacteristic
1091C2×C4⋊C4C23×C8911yescharacteristic
1092C2×C4⋊C4C23×C8911yescharacteristic
1093C2×C4⋊C4C23×C8911yescharacteristic
1094C2×C4⋊C4C23×C8911yescharacteristic
1095C2×C4⋊C4C23×C8911yescharacteristic
1096C2×C4⋊C4C23×C8911yescharacteristic
1097C2×C4⋊C4C23×C8911yescharacteristic
1098C2×C4⋊C4C23×C8911yescharacteristic
1099C2×C4⋊C4C23×C8911yescharacteristic
1100C2×C4⋊C4C23×C8911yescharacteristic
1101C2×C4⋊C4C23×C8911yescharacteristic
1102C2×C4⋊C4C23×C8911yescharacteristic
1103C2×C4⋊C4C23×C8911yescharacteristic
1104C2×C22⋊C4C23×C8911yescharacteristic
1105C2×C22⋊C4C23×C8911yescharacteristic
1106C2×C22⋊C4C23×C8911yescharacteristic
1107C2×C22⋊C4C23×C8911yescharacteristic
1108C2×C22⋊C4C23×C8911yescharacteristic
1109C2×C22⋊C4C23×C8911yescharacteristic
1110C2×C22⋊C4C23×C8911yescharacteristic
1111C2×C22⋊C4C23×C8911yescharacteristic
1112C2×C22⋊C4C23×C8911yescharacteristic
1113C2×C22⋊C4C23×C8911yescharacteristic
1114C2×C22⋊C4C23×C8911yescharacteristic
1115C2×C22⋊C4C23×C8911yescharacteristic
1116C2×C22⋊C4C23×C8911yescharacteristic
1117C2×C22⋊C4C23×C8911yescharacteristic
1118C2×C22⋊C4C23×C8911yescharacteristic
1119C2×C22⋊C4C23×C8911yescharacteristic
1120C2×C22⋊C4C23×C8911yescharacteristic
1121C2×C22⋊C4C23×C8911yescharacteristic
1122C2×C22⋊C4C23×C8911yescharacteristic
1123C2×C22⋊C4C23×C8911yescharacteristic
1124C2×C22⋊C4C23×C8911yescharacteristic
1125C2×C22⋊C4C23×C8911yescharacteristic
1126C2×C22⋊C4C23×C8911yescharacteristic
1127C2×C22⋊C4C23×C8911yescharacteristic
1128C2×C22⋊C4C23×C8911yescharacteristic
1129C2×C22⋊C4C23×C8911yescharacteristic
1130C2×C22⋊C4C23×C8911yescharacteristic
1131C2×C22⋊C4C23×C8911yescharacteristic
1132C2×C22⋊C4C23×C8911yescharacteristic
1133C2×C22⋊C4C23×C8911yescharacteristic
1134C2×C22⋊C4C23×C8911yescharacteristic
1135C2×C22⋊C4C23×C8911yescharacteristic
1136C2×C22⋊C4C23×C8911yescharacteristic
1137C2×C22⋊C4C23×C8911yescharacteristic
1138C2×C22⋊C4C23×C8911yescharacteristic
1139C2×C22⋊C4C23×C8911yescharacteristic
1140C2×C22⋊C4C23×C8911yescharacteristic
1141C2×C22⋊C4C23×C8911yescharacteristic
1142C2×C22⋊C4C23×C8911yescharacteristic
1143C2×C22⋊C4C23×C8911yescharacteristic
1144C2×C22⋊C4C23×C8911yescharacteristic
1145C2×C22⋊C4C23×C8911yescharacteristic
1146C2×C22⋊C4C23×C8911yescharacteristic
1147C2×C22⋊C4C23×C8911yescharacteristic
1148C2×C22⋊C4C23×C8911yescharacteristic
1149C2×C22⋊C4C23×C8911yescharacteristic
1150C2×C22⋊C4C23×C8911yescharacteristic
1151C2×C22⋊C4C23×C8911yescharacteristic
1152C2×C22⋊C4C23×C8911yescharacteristic
1153C2×C22⋊C4C23×C8911yescharacteristic
1154C2×C22⋊C4C23×C8911yescharacteristic
1155C2×C22⋊C4C23×C8911yescharacteristic
1156C2×C22⋊C4C23×C8911yescharacteristic
1157C2×C22⋊C4C23×C8911yescharacteristic
1158C2×C22⋊C4C23×C8911yescharacteristic
1159C2×C22⋊C4C23×C8911yescharacteristic
1160C2×C42C23×C8911yescharacteristic
1161C2×C42C23×C8911yescharacteristic
1162C2×C42C23×C8911yescharacteristic
1163C2×C42C23×C8911yescharacteristic
1164C2×C42C23×C8911yescharacteristic
1165C2×C42C23×C8911yescharacteristic
1166C2×C42C23×C8911yescharacteristic
1167C2×C42C23×C8911yescharacteristic
1168#95C23×C8911yescharacteristic
1169#95C23×C8911yescharacteristic
1170#95C23×C8911yescharacteristic
1171#95C23×C8911yescharacteristic
1172#95C23×C8911yescharacteristic
1173#95C23×C8911yescharacteristic
1174#95C23×C8911yescharacteristic
1175#95C23×C8911yescharacteristic
1176#95C23×C8911yescharacteristic
1177#95C23×C8911yescharacteristic
1178#95C23×C8911yescharacteristic
1179#95C23×C8911yescharacteristic
1180#95C23×C8911yescharacteristic
1181#95C23×C8911yescharacteristic
1182#95C23×C8911yescharacteristic
1183#95C23×C8911yescharacteristic
1184#95C23×C8911yescharacteristic
1185#95C23×C8911yescharacteristic
1186#95C23×C8911yescharacteristic
1187#95C23×C8911yescharacteristic
1188#95C23×C8911yescharacteristic
1189#95C23×C8911yescharacteristic
1190#95C23×C8911yescharacteristic
1191#95C23×C8911yescharacteristic
1192#95C23×C8911yescharacteristic
1193#95C23×C8911yescharacteristic
1194#95C23×C8911yescharacteristic
1195#95C23×C8911yescharacteristic
1196#95C23×C8911yescharacteristic
1197#95C23×C8911yescharacteristic
1198#95C23×C8911yescharacteristic
1199#95C23×C8911yescharacteristic
1200#95C23×C8911yescharacteristic
1201#95C23×C8911yescharacteristic
1202#95C23×C8911yescharacteristic
1203#95C23×C8911yescharacteristic
1204C24—22no—
1205C24—22no—
1206C24—22no—
1207C24—41no—
1208C24—41no—
1209C24—41no—
1210C24—41no—
1211C24C24×C8911yescharacteristic
1212C24C24×C8911yescharacteristic
1213C24C24×C8911yescharacteristic
1214C24C24×C8911yescharacteristic
1215C24C24×C8911yescharacteristic
1216C24C24×C8911yescharacteristic
1217C24C24×C8911yescharacteristic
1218C2×D4—22no—
1219C2×D4—22no—
1220C2×D4—22no—
1221C2×D4—22no—
1222C2×D4—22no—
1223C2×D4—22no—
1224C2×D4—22no—
1225C2×D4—22no—
1226C2×D4—22no—
1227C2×D4—22no—
1228C2×D4—22no—
1229C2×D4—22no—
1230C2×D4—22no—
1231C2×D4—22no—
1232C2×D4—22no—
1233C2×D4—22no—
1234C2×D4—41no—
1235C2×D4—41no—
1236C2×D4—41no—
1237C2×D4—41no—
1238C2×D4—41no—
1239C2×D4—41no—
1240C2×D4—41no—
1241C2×D4—41no—
1242C2×D4—41no—
1243C2×D4—41no—
1244C2×D4—41no—
1245C2×D4—41no—
1246C2×D4—41no—
1247C2×D4—41no—
1248C2×D4—41no—
1249C2×D4—41no—
1250C2×D4—41no—
1251C2×D4—41no—
1252C2×D4—41no—
1253C2×D4—41no—
1254C2×D4—41no—
1255C2×D4—41no—
1256C2×D4—41no—
1257C2×D4—41no—
1258C2×D4—41no—
1259C2×D4—41no—
1260C2×D4—41no—
1261C2×D4—41no—
1262C2×D4—41no—
1263C2×D4—41no—
1264C2×D4—41no—
1265C2×D4—41no—
1266C2×D4—41no—
1267C2×D4—41no—
1268C2×D4—41no—
1269C2×D4—41no—
1270C2×D4—41no—
1271C2×D4—41no—
1272C22×C4—22no—
1273C22×C4—22no—
1274C22×C4—22no—
1275C22×C4—22no—
1276C22×C4—22no—
1277C22×C4—22no—
1278C22×C4—22no—
1279C22×C4—22no—
1280C22×C4—22no—
1281C22×C4—22no—
1282C22×C4—22no—
1283C22×C4—41no—
1284C22×C4—41no—
1285C22×C4—41no—
1286C22×C4—41no—
1287C22×C4—41no—
1288C22×C4—41no—
1289C22×C4—41no—
1290C22×C4—41no—
1291C22×C4—41no—
1292C22×C4—41no—
1293C22×C4—41no—
1294C22×C4—41no—
1295C22×C4—41no—
1296C22×C4—41no—
1297C22×C4—41no—
1298C22×C4—41no—
1299C22×C4—41no—
1300C22×C4—41no—
1301C22×C4—41no—
1302C22×C4—416no—
1303C22×C4C24×C8911yescharacteristic
1304C22×C4C24×C8911yescharacteristic
1305C22×C4C24×C8911yescharacteristic
1306C22×C4C24×C8911yescharacteristic
1307C22×C4C24×C8911yescharacteristic
1308C22×C4C24×C8911yescharacteristic
1309C22×C4C24×C8911yescharacteristic
1310C22×C4C24×C8911yescharacteristic
1311C22×C4C24×C8911yescharacteristic
1312C22×C4C24×C8911yescharacteristic
1313C22×C4C24×C8911yescharacteristic
1314C22×C4C24×C8911yescharacteristic
1315C22×C4C24×C8911yescharacteristic
1316C22×C4C24×C8911yescharacteristic
1317C22×C4C24×C8911yescharacteristic
1318C22×C4C24×C8911yescharacteristic
1319C22×C4C24×C8911yescharacteristic
1320C22×C4C24×C8911yescharacteristic
1321C22×C4C24×C8911yescharacteristic
1322C22×C4C24×C8911yescharacteristic
1323C22×C4C24×C8911yescharacteristic
1324C22×C4C24×C8911yescharacteristic
1325C22×C4C24×C8911yescharacteristic
1326C22×C4C24×C8911yescharacteristic
1327C4⋊C4—22no—
1328C4⋊C4—22no—
1329C4⋊C4—22no—
1330C4⋊C4—22no—
1331C4⋊C4—22no—
1332C4⋊C4—22no—
1333C4⋊C4—22no—
1334C4⋊C4—41no—
1335C4⋊C4—41no—
1336C4⋊C4—41no—
1337C4⋊C4—41no—
1338C4⋊C4—41no—
1339C4⋊C4—41no—
1340C4⋊C4—41no—
1341C4⋊C4—41no—
1342C4⋊C4—41no—
1343C4⋊C4—41no—
1344C4⋊C4—41no—
1345C4⋊C4—41no—
1346C4⋊C4—41no—
1347C4⋊C4—41no—
1348C4⋊C4—41no—
1349C4⋊C4—41no—
1350C4⋊C4—41no—
1351C4⋊C4—41no—
1352C4⋊C4—41no—
1353C22⋊C4—22no—
1354C22⋊C4—22no—
1355C22⋊C4—22no—
1356C22⋊C4—22no—
1357C22⋊C4—22no—
1358C22⋊C4—22no—
1359C22⋊C4—22no—
1360C22⋊C4—22no—
1361C22⋊C4—22no—
1362C22⋊C4—22no—
1363C22⋊C4—22no—
1364C22⋊C4—22no—
1365C22⋊C4—22no—
1366C22⋊C4—22no—
1367C22⋊C4—22no—
1368C22⋊C4—22no—
1369C22⋊C4—41no—
1370C22⋊C4—41no—
1371C22⋊C4—41no—
1372C22⋊C4—41no—
1373C22⋊C4—41no—
1374C22⋊C4—41no—
1375C22⋊C4—41no—
1376C22⋊C4—41no—
1377C22⋊C4—41no—
1378C22⋊C4—41no—
1379C22⋊C4—41no—
1380C22⋊C4—41no—
1381C22⋊C4—41no—
1382C22⋊C4—41no—
1383C22⋊C4—41no—
1384C22⋊C4—41no—
1385C22⋊C4—41no—
1386C22⋊C4—41no—
1387C22⋊C4—41no—
1388C22⋊C4—41no—
1389C22⋊C4—41no—
1390C22⋊C4—41no—
1391C22⋊C4—41no—
1392C22⋊C4—41no—
1393C22⋊C4—41no—
1394C22⋊C4—41no—
1395C22⋊C4—41no—
1396C22⋊C4—41no—
1397C22⋊C4—41no—
1398C22⋊C4—41no—
1399C22⋊C4—41no—
1400C22⋊C4—41no—
1401C22⋊C4—41no—
1402C22⋊C4—41no—
1403C22⋊C4—41no—
1404C22⋊C4—41no—
1405C22⋊C4—41no—
1406C22⋊C4—41no—
1407C22⋊C4—41no—
1408C22⋊C4#41×C8914yes—
1409C42—22no—
1410C42—41no—
1411C42—41no—
1412C42—41no—
1413C42—41no—
1414C42—41no—
1415C42—41no—
1416C42—41no—
1417C23—21no—
1418C23—21no—
1419C23—21no—
1420C23—21no—
1421C23—21no—
1422C23—21no—
1423C23—21no—
1424C23—21no—
1425C23—21no—
1426C23—21no—
1427C23—21no—
1428C23—21no—
1429C23—21no—
1430C23—21no—
1431C23—21no—
1432C23—21no—
1433C23—21no—
1434C23—21no—
1435C23—21no—
1436C23—21no—
1437C23—21no—
1438C23—21no—
1439C23—21no—
1440C23—21no—
1441C23—21no—
1442C23—21no—
1443C23—21no—
1444C23—21no—
1445C23—21no—
1446C23—21no—
1447C23—21no—
1448C23—21no—
1449C23—21no—
1450C23—21no—
1451C23—21no—
1452C23—21no—
1453C23—21no—
1454C23—21no—
1455C23—21no—
1456C23—21no—
1457C23—21no—
1458C23—21no—
1459C23—21no—
1460C23—21no—
1461C23—21no—
1462C23—21no—
1463C23—44no—
1464C23—44no—
1465C23—44no—
1466C23—44no—
1467C23—44no—
1468C23—44no—
1469C23—44no—
1470C23C2×#41×C8912yes—
1471C23H(5,𝔽2)×C8912yes—
1472C23H(5,𝔽2)×C8912yes—
1473C23C25×C8911yescharacteristic
1474D4—44no—
1475D4—44no—
1476D4—44no—
1477D4—82no—
1478D4—82no—
1479D4—82no—
1480D4—82no—
1481D4—82no—
1482D4—82no—
1483D4—82no—
1484D4—82no—
1485D4—82no—
1486D4—82no—
1487D4—82no—
1488D4—82no—
1489D4—82no—
1490D4—82no—
1491D4—82no—
1492C2×C4—21no—
1493C2×C4—21no—
1494C2×C4—21no—
1495C2×C4—21no—
1496C2×C4—21no—
1497C2×C4—21no—
1498C2×C4—21no—
1499C2×C4—21no—
1500C2×C4—21no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—21no—
1508C2×C4—21no—
1509C2×C4—21no—
1510C2×C4—21no—
1511C2×C4—21no—
1512C2×C4—21no—
1513C2×C4—21no—
1514C2×C4—21no—
1515C2×C4—21no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—21no—
1519C2×C4—21no—
1520C2×C4—21no—
1521C2×C4—21no—
1522C2×C4—21no—
1523C2×C4—21no—
1524C2×C4—21no—
1525C2×C4—21no—
1526C2×C4—21no—
1527C2×C4—21no—
1528C2×C4—21no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—21no—
1533C2×C4—21no—
1534C2×C4—21no—
1535C2×C4—21no—
1536C2×C4—21no—
1537C2×C4—21no—
1538C2×C4—21no—
1539C2×C4—21no—
1540C2×C4—21no—
1541C2×C4—21no—
1542C2×C4—21no—
1543C2×C4—21no—
1544C2×C4—21no—
1545C2×C4—21no—
1546C2×C4—21no—
1547C2×C4—21no—
1548C2×C4—21no—
1549C2×C4—21no—
1550C2×C4—21no—
1551C2×C4—21no—
1552C2×C4—21no—
1553C2×C4—21no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—21no—
1557C2×C4—21no—
1558C2×C4—21no—
1559C2×C4—21no—
1560C2×C4—44no—
1561C2×C4—44no—
1562C2×C4—44no—
1563C2×C4—44no—
1564C2×C4—44no—
1565C2×C4—44no—
1566C2×C4—82no—
1567C2×C4—82no—
1568C2×C4—82no—
1569C2×C4—82no—
1570C2×C4C2×#41×C8912yes—
1571C2×C4C2×#41×C8912yes—
1572C2×C4H(5,𝔽2)×C8912yes—
1573C2×C4H(5,𝔽2)×C8912yes—
1574C22—22no—
1575C22—22no—
1576C22—22no—
1577C22—22no—
1578C22—22no—
1579C22—22no—
1580C22—22no—
1581C22—22no—
1582C22—22no—
1583C22—416no—
1584C22—41no—
1585C22—41no—
1586C22—41no—
1587C22—41no—
1588C22—41no—
1589C22—41no—
1590C22—41no—
1591C22—41no—
1592C22—41no—
1593C22—41no—
1594C22—41no—
1595C22—41no—
1596C22—41no—
1597C22—41no—
1598C22—41no—
1599C22—41no—
1600C22—41no—
1601C22—41no—
1602C22—41no—
1603C22—41no—
1604C22—41no—
1605C22—41no—
1606C22—41no—
1607C22—41no—
1608C22—41no—
1609C22—41no—
1610C22—41no—
1611C22—41no—
1612C22—41no—
1613C22—41no—
1614C22—41no—
1615C22—41no—
1616C22—41no—
1617C22—41no—
1618C22—41no—
1619C22—41no—
1620C22—41no—
1621C22—41no—
1622C22—41no—
1623C22—41no—
1624C22C22×#41×C8911yescharacteristic
1625C22C2×H(5,𝔽2)×C8911yescharacteristic
1626C22C2×H(5,𝔽2)×C8911yescharacteristic
1627C22C2×H(5,𝔽2)×C8911yescharacteristic
1628C22C2×H(5,𝔽2)×C8911yescharacteristic
1629C22#585×C8911yescharacteristic
1630C22#585×C8911yescharacteristic
1631C4—22no—
1632C4—22no—
1633C4—22no—
1634C4—22no—
1635C4—41no—
1636C4—41no—
1637C4—41no—
1638C4—41no—
1639C4—41no—
1640C4—41no—
1641C4—41no—
1642C4—41no—
1643C4—41no—
1644C4—41no—
1645C4—41no—
1646C4—41no—
1647C4—41no—
1648C4—41no—
1649C4—41no—
1650C4—41no—
1651C4—41no—
1652C4—41no—
1653C4—41no—
1654C4—41no—
1655C2—42no—
1656C2—42no—
1657C2—42no—
1658C2—81no—
1659C2—81no—
1660C2—81no—
1661C2—81no—
1662C2C89×#346011yescharacteristic
1663C2C89×#351311yescharacteristic
1664C2C89×#351911yescharacteristic
1665C2C89×#353211yescharacteristic
1666C2C89×#353411yescharacteristic
1667C2C89×#353911yescharacteristic
1668C2C89×#354211yescharacteristic
subgroupG/H
center, socleC23×C89C25
commutator, Frattini, cosocleC23C25×C89
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C89 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C89×#2849C2semidirect
2. C89×#2847C2semidirect
3. C89×#2778C2semidirect
4. C89×#2768C2semidirect
5. C89×#2753C2semidirect
6. C89×#2746C2semidirect
7. C89×#2739C2semidirect
8. C89×#2714C2semidirect
9. C89×#2709C2semidirect
10. C89×#2705C2semidirect
11. C89×#2699C2semidirect
12. C89×#2691C2semidirect
13. C89×#2685C2semidirect
14. C89×#2678C2semidirect
15. C89×#2678C2semidirect
16. C89×#2671C2semidirect
17. C89×#2671C2semidirect
18. C89×#2669C2semidirect
19. C89×#2636C2semidirect
20. C89×#2635C2semidirect
21. C89×#2576C2semidirect
22. C89×#2559C2semidirect
23. C89×#2554C2semidirect
24. C89×#2553C2semidirect
25. C89×#2468C2semidirect
26. C89×#2464C2semidirect
27. C89×#2428C2semidirect
28. C89×#2420C2semidirect
29. C89×#2335C2semidirect
30. C89×#2333C2semidirect
31. C4×#120×C89C2semidirect
35. C2×#126×C89C22semidirect
36. C2×#126×C89C22semidirect
48. C2×#121×C89C22semidirect
49. C2×#121×C89C22semidirect
57. #401×C89C22semidirect
58. #400×C89C22semidirect
59. #400×C89C22semidirect
60. #400×C89C22semidirect
62. #399×C89C22semidirect
63. #399×C89C22semidirect
64. #398×C89C22semidirect
65. #398×C89C22semidirect
66. #398×C89C22semidirect
67. #398×C89C22semidirect
68. #398×C89C22semidirect
71. #397×C89C22semidirect
72. #397×C89C22semidirect
76. #396×C89C22semidirect
87. #394×C89C22semidirect
88. #394×C89C22semidirect
89. #394×C89C22semidirect
90. #394×C89C22semidirect
91. #394×C89C22semidirect
92. #394×C89C22semidirect
93. #394×C89C22semidirect
94. #394×C89C22semidirect
95. #394×C89C22semidirect
104. #392×C89C22semidirect
111. #390×C89C22semidirect
112. #390×C89C22semidirect
113. #389×C89C22semidirect
114. #389×C89C22semidirect
115. #389×C89C22semidirect
123. #388×C89C22semidirect
124. #388×C89C22semidirect
125. #388×C89C22semidirect
126. #388×C89C22semidirect
127. #388×C89C22semidirect
128. #388×C89C22semidirect
129. #388×C89C22semidirect
130. #388×C89C22semidirect
131. #387×C89C22semidirect
132. #387×C89C22semidirect
133. #387×C89C22semidirect
134. #387×C89C22semidirect
135. #387×C89C22semidirect
136. #387×C89C22semidirect
153. #386×C89C22semidirect
154. #386×C89C22semidirect
155. #386×C89C22semidirect
156. #386×C89C22semidirect
164. #385×C89C22semidirect
165. #385×C89C22semidirect
166. #385×C89C22semidirect
167. #382×C89C22semidirect
168. #382×C89C22semidirect
171. #381×C89C22semidirect
172. #381×C89C22semidirect
176. #380×C89C22semidirect
177. #380×C89C22semidirect
180. C4×C4⋊C4×C89C22semidirect
184. C4×C22⋊C4×C89C22semidirect
185. C4×C22⋊C4×C89C22semidirect
186. C4×C22⋊C4×C89C22semidirect
820. #36887C89direct (N × H)
835. #2849C2×C89semidirect
836. #2847C2×C89semidirect
837. #2778C2×C89semidirect
838. #2768C2×C89semidirect
839. #2753C2×C89semidirect
840. #2746C2×C89semidirect
841. #2739C2×C89semidirect
842. #2714C2×C89semidirect
843. #2709C2×C89semidirect
844. #2705C2×C89semidirect
845. #2699C2×C89semidirect
846. #2691C2×C89semidirect
847. #2685C2×C89semidirect
848. #2678C2×C89semidirect
849. #2678C2×C89semidirect
850. #2671C2×C89semidirect
851. #2671C2×C89semidirect
852. #2669C2×C89semidirect
853. #2636C2×C89semidirect
854. #2635C2×C89semidirect
855. #2576C2×C89semidirect
856. #2559C2×C89semidirect
857. #2554C2×C89semidirect
858. #2553C2×C89semidirect
859. #2468C2×C89semidirect
860. #2464C2×C89semidirect
861. #2428C2×C89semidirect
862. #2420C2×C89semidirect
863. #2335C2×C89semidirect
864. #2333C2×C89semidirect
865. C4×#120C2×C89semidirect
866. C89#36887direct (N × H)
870. C2×#126C22×C89semidirect
871. C2×#126C22×C89semidirect
883. C2×#121C22×C89semidirect
884. C2×#121C22×C89semidirect
892. #401C22×C89semidirect
893. #400C22×C89semidirect
894. #400C22×C89semidirect
895. #400C22×C89semidirect
897. #399C22×C89semidirect
898. #399C22×C89semidirect
899. #398C22×C89semidirect
900. #398C22×C89semidirect
901. #398C22×C89semidirect
902. #398C22×C89semidirect
903. #398C22×C89semidirect
906. #397C22×C89semidirect
907. #397C22×C89semidirect
911. #396C22×C89semidirect
922. #394C22×C89semidirect
923. #394C22×C89semidirect
924. #394C22×C89semidirect
925. #394C22×C89semidirect
926. #394C22×C89semidirect
927. #394C22×C89semidirect
928. #394C22×C89semidirect
929. #394C22×C89semidirect
930. #394C22×C89semidirect
939. #392C22×C89semidirect
946. #390C22×C89semidirect
947. #390C22×C89semidirect
948. #389C22×C89semidirect
949. #389C22×C89semidirect
950. #389C22×C89semidirect
958. #388C22×C89semidirect
959. #388C22×C89semidirect
960. #388C22×C89semidirect
961. #388C22×C89semidirect
962. #388C22×C89semidirect
963. #388C22×C89semidirect
964. #388C22×C89semidirect
965. #388C22×C89semidirect
966. #387C22×C89semidirect
967. #387C22×C89semidirect
968. #387C22×C89semidirect
969. #387C22×C89semidirect
970. #387C22×C89semidirect
971. #387C22×C89semidirect
988. #386C22×C89semidirect
989. #386C22×C89semidirect
990. #386C22×C89semidirect
991. #386C22×C89semidirect
999. #385C22×C89semidirect
1000. #385C22×C89semidirect
1001. #385C22×C89semidirect
1002. #382C22×C89semidirect
1003. #382C22×C89semidirect
1006. #381C22×C89semidirect
1007. #381C22×C89semidirect
1011. #380C22×C89semidirect
1012. #380C22×C89semidirect
1015. C4×C4⋊C4C22×C89semidirect
1019. C4×C22⋊C4C22×C89semidirect
1020. C4×C22⋊C4C22×C89semidirect
1021. C4×C22⋊C4C22×C89semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C89×#28492
C89×#28472
C89×#27782
C89×#27682
C89×#27532
C89×#27462
C89×#27392
C89×#27142
C89×#27092
C89×#27052
C89×#26992
C89×#26912
C89×#26852
C89×#26782
C89×#26712
C89×#26692
C89×#26362
C89×#26352
C89×#25762
C89×#25592
C89×#25542
C89×#25532
C89×#24682
C89×#24642
C89×#24282
C89×#24202
C89×#23352
C89×#23332
C4×#120×C892
#3688789