Finite Group Databasebeta

← #36715860

Subgroups — #36715860

Order 22784.

2546 conjugacy classes of subgroups.

The subgroup lattice has 1606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19152181C211yesmaximal, characteristic
2#26023384C211yesmaximal, characteristic, complemented
3#26023378C211yesmaximal, characteristic, complemented
4#26023365C211yesmaximal, characteristic, complemented
5#26023359C211yesmaximal, characteristic, complemented
6#26023333C211yesmaximal, characteristic, complemented
7#26023318C211yesmaximal, characteristic, complemented
8#26023300C211yesmaximal, characteristic, complemented
9#26023296C211yesmaximal, characteristic, complemented
10#26023285C211yesmaximal, characteristic, complemented
11#26023263C211yesmaximal, characteristic, complemented
12#26023252C211yesmaximal, characteristic, complemented
13#26023237C211yesmaximal, characteristic, complemented
14#26023232C211yesmaximal, characteristic, complemented
15#26023232C211yesmaximal, characteristic, complemented
16#26023228C211yesmaximal, characteristic, complemented
17#26023228C211yesmaximal, characteristic, complemented
18#26023062C211yesmaximal, characteristic, complemented
19#26023038C211yesmaximal, characteristic, complemented
20#26023023C211yesmaximal, characteristic, complemented
21#26023014C211yesmaximal, characteristic, complemented
22#26022800C211yesmaximal, characteristic, complemented
23#26022791C211yesmaximal, characteristic, complemented
24#26022769C211yesmaximal, characteristic, complemented
25#26022758C211yesmaximal, characteristic, complemented
26#26022691C211yesmaximal, characteristic, complemented
27C2×#19151487C211yesmaximal, characteristic, complemented
28#26022610C211yesmaximal, characteristic, complemented
29#26022604C211yesmaximal, characteristic, complemented
30C4×D4×Dic89C211yesmaximal, characteristic, complemented
31C89×#2318C211yesmaximal, characteristic, complemented
32#19152181C4116yescomplemented
33C2×#15668007C2211yescharacteristic
34C2×#15668006C2211yescharacteristic
35C2×#15668000C2211yescharacteristic
36C2×#15667998C2211yescharacteristic
37C2×#15667997C2211yescharacteristic
38C2×#15667995C2211yescharacteristic
39C2×#15667989C2211yescharacteristic
40C2×#15667986C2211yescharacteristic
41C2×#15667985C2211yescharacteristic
42C2×#15667984C2211yescharacteristic
43C2×#15667982C2211yescharacteristic
44C2×#15667980C2211yescharacteristic
45C2×#15667977C2211yescharacteristic, complemented
46C2×D4×Dic89C2211yescharacteristic
47C2×D4×Dic89C2211yescharacteristic
48C2×#15667974C2211yescharacteristic
49C2×#15667974C2211yescharacteristic
50C2×C4×C22⋊D89C2211yescharacteristic
51C2×C4×C22⋊D89C2211yescharacteristic
52C2×C4×C22⋊D89C2211yescharacteristic
53C2×#15667972C2211yescharacteristic
54C2×#15667972C2211yescharacteristic
55C2×#15667972C2211yescharacteristic, complemented
56C2×#15667969C2211yescharacteristic, complemented
57C22×#13083553C2211yescharacteristic
58C22×#13083551C2211yescharacteristic
59C22×#13083551C2211yescharacteristic
60C22×#13083551C2211yescharacteristic
61C2×C22⋊C4×D89C2211yescharacteristic
62C2×C22⋊C4×D89C2211yescharacteristic
63C22×C4×Dic89C2211yescharacteristic
64C22×C4×Dic89C2211yescharacteristic, complemented
65#19151503C2211yescharacteristic, complemented
66#19151502C2211yescharacteristic, complemented
67#19151502C2211yescharacteristic, complemented
68#19151499C2211yescharacteristic
69#19151499C2211yescharacteristic
70#19151498C2211yescharacteristic
71#19151498C2211yescharacteristic
72#19151498C2211yescharacteristic, complemented
73#19151495C2211yescharacteristic, complemented
74#19151494C2211yescharacteristic, complemented
75#19151493C2211yescharacteristic, complemented
76#19151493C2211yescharacteristic, complemented
77#19151492C2211yescharacteristic, complemented
78#19151490C2211yescharacteristic
79#19151490C2211yescharacteristic
80#19151490C2211yescharacteristic, complemented
81#19151488C2211yescharacteristic
82#19151488C2211yescharacteristic
83#19151487C2211yescharacteristic
84#19151487C2211yescharacteristic
85#19151487C2211yescharacteristic
86#19151487C2211yescharacteristic
87#19151487C2211yescharacteristic
88#19151487C2211yescharacteristic
89#19151487C2211yescharacteristic
90#19151487C2211yescharacteristic
91#19151487C2211yescharacteristic
92#19151487C2211yescharacteristic
93#19151487C2211yescharacteristic
94#19151487C2211yescharacteristic
95#19151487C2211yescharacteristic, complemented
96#19151487C2211yescharacteristic, complemented
97#19151487C2211yescharacteristic, complemented
98#19151486C2211yescharacteristic, complemented
99#19151485C2211yescharacteristic, complemented
100#19151483C2211yescharacteristic, complemented
101#19151483C2211yescharacteristic, complemented
102#19151480C2211yescharacteristic, complemented
103#19151480C2211yescharacteristic, complemented
104#19151480C2211yescharacteristic, complemented
105#19151480C2211yescharacteristic, complemented
106#19151480C2211yescharacteristic, complemented
107#19151479C2211yescharacteristic, complemented
108#19151479C2211yescharacteristic, complemented
109#19151476C2211yescharacteristic
110#19151476C2211yescharacteristic
111#19151476C2211yescharacteristic
112#19151476C2211yescharacteristic
113#19151475C2211yescharacteristic
114#19151475C2211yescharacteristic
115#19151475C2211yescharacteristic
116#19151475C2211yescharacteristic
117#19151475C2211yescharacteristic, complemented
118#19151474C2211yescharacteristic
119#19151474C2211yescharacteristic
120#19151474C2211yescharacteristic, complemented
121#19151472C2211yescharacteristic
122#19151472C2211yescharacteristic
123#19151472C2211yescharacteristic, complemented
124#19151470C2211yescharacteristic
125#19151470C2211yescharacteristic
126#19151470C2211yescharacteristic, complemented
127#19151469C2211yescharacteristic
128#19151469C2211yescharacteristic
129C4⋊C4×Dic89C2211yescharacteristic, complemented
130C4⋊C4×Dic89C2211yescharacteristic, complemented
131C4⋊C4×Dic89C2211yescharacteristic, complemented
132C4×#13083553C2211yescharacteristic, complemented
133C4×C4⋊Dic89C2211yescharacteristic, complemented
134#19151449C2211yescharacteristic, complemented
135#19151449C2211yescharacteristic, complemented
136#19151449C2211yescharacteristic, complemented
137#19151449C2211yescharacteristic, complemented
138#19151449C2211yescharacteristic, complemented
139#19151449C2211yescharacteristic, complemented
140C22⋊C4×Dic89C2211yescharacteristic
141C22⋊C4×Dic89C2211yescharacteristic
142C22⋊C4×Dic89C2211yescharacteristic
143C22⋊C4×Dic89C2211yescharacteristic
144C22⋊C4×Dic89C2211yescharacteristic, complemented
145C22⋊C4×Dic89C2211yescharacteristic, complemented
146C22⋊C4×Dic89C2211yescharacteristic, complemented
147C4×#13083551C2211yescharacteristic
148C4×#13083551C2211yescharacteristic
149C4×#13083551C2211yescharacteristic
150C4×#13083551C2211yescharacteristic
151C4×#13083551C2211yescharacteristic, complemented
152C4×C22⋊Dic89C2211yescharacteristic
153C4×C22⋊Dic89C2211yescharacteristic
154C4×C22⋊Dic89C2211yescharacteristic
155C4×C22⋊Dic89C2211yescharacteristic, complemented
156#19151445C2211yescharacteristic
157#19151445C2211yescharacteristic
158#19151445C2211yescharacteristic
159#19151445C2211yescharacteristic
160#19151445C2211yescharacteristic
161#19151445C2211yescharacteristic
162#19151445C2211yescharacteristic
163#19151445C2211yescharacteristic
164#19151445C2211yescharacteristic, complemented
165#19151445C2211yescharacteristic, complemented
166#19151445C2211yescharacteristic, complemented
167#19151445C2211yescharacteristic, complemented
168#19151444C2211yescharacteristic, complemented
169#19151443C2211yescharacteristic, complemented
170C2×#15667919C2211yescharacteristic
171#95×D89C2211yescharacteristic, complemented
172C42×Dic89C2211yescharacteristic, complemented
173C2×C4×D4×C89C2211yescharacteristic
174#388×C89C2211yescharacteristic, complemented
175#388×C89C2211yescharacteristic, complemented
176#387×C89C2211yescharacteristic, complemented
177#387×C89C2211yescharacteristic, complemented
178#386×C89C2211yescharacteristic
179#386×C89C2211yescharacteristic
180#385×C89C2211yescharacteristic
181#385×C89C2211yescharacteristic
182#383×C89C2211yescharacteristic, complemented
183#382×C89C2211yescharacteristic, complemented
184#381×C89C2211yescharacteristic, complemented
185#380×C89C2211yescharacteristic, complemented
186C4×C22⋊C4×C89C2211yescharacteristic
187C2×#95×C89C2211yescharacteristic
188C24×D89C2311yescharacteristic
189C22×Dic178C2311yescharacteristic
190C22×D356C2311yescharacteristic
191C22×D356C2311yescharacteristic
192C22×C22⋊D89C2311yescharacteristic
193C22×C22⋊D89C2311yescharacteristic
194C22×C22⋊D89C2311yescharacteristic
195C22×C22⋊D89C2311yescharacteristic
196C23×Dic89C2311yescharacteristic
197C23×Dic89C2311yescharacteristic
198C23×Dic89C2311yescharacteristic
199C23×Dic89C2311yescharacteristic
200C23×Dic89C2311yescharacteristic
201C22×C4×D89C2311yescharacteristic
202C22×C4×D89C2311yescharacteristic
203C22×C4×D89C2311yescharacteristic
204C22×C4×D89C2311yescharacteristic
205C22×C4×D89C2311yescharacteristic
206C22×C4×D89C2311yescharacteristic
207C22×C4×D89C2311yescharacteristic
208#15668007C2×C418yescomplemented
209#15668006C2×C418yescomplemented
210#15668000C2×C418yescomplemented
211#15667998C2×C418yescomplemented
212#15667997C2×C418yescomplemented
213#15667995C2×C418yescomplemented
214#15667989C2×C418yescomplemented
215#15667986C2×C418yescomplemented
216#15667985C2×C418yescomplemented
217#15667984C2×C418yescomplemented
218#15667982C2×C418yescomplemented
219#15667980C2×C418yescomplemented
220#15667977—42no—
221D4×Dic89—24no—
222D4×Dic89—24no—
223#15667974—42no—
224#15667974—42no—
225C4×C22⋊D89—24no—
226C4×C22⋊D89—24no—
227C4×C22⋊D89C2×C418yescomplemented
228#15667972—42no—
229#15667972—42no—
230#15667972—42no—
231#15667969—42no—
232C2×C4⋊Dic89C2311yescharacteristic
233C2×C4⋊Dic89C2311yescharacteristic
234C2×C4⋊Dic89C2311yescharacteristic
235C2×#13083553—42no—
236C2×#13083553C2311yescharacteristic
237C2×#13083553C2311yescharacteristic
238C2×#13083553C2311yescharacteristic
239C2×#13083553C2311yescharacteristic
240C2×#13083553C2311yescharacteristic
241C2×#13083553C2311yescharacteristic
242C2×#13083553C2311yescharacteristic
243C2×#13083553C2311yescharacteristic
244C2×#13083553C2311yescharacteristic
245C2×#13083553C2311yescharacteristic
246C2×#13083553C2311yescharacteristic
247C2×#13083553C2311yescharacteristic
248C2×#13083553C2311yescharacteristic
249C2×#13083553C2311yescharacteristic
250C2×C22⋊Dic89C2311yescharacteristic
251C2×C22⋊Dic89C2311yescharacteristic
252C2×C22⋊Dic89C2311yescharacteristic
253C2×C22⋊Dic89C2311yescharacteristic
254C2×C22⋊Dic89C2311yescharacteristic
255C2×C22⋊Dic89C2311yescharacteristic
256C2×#13083551—42no—
257C2×#13083551—42no—
258C2×#13083551C2×C418yescomplemented
259C2×#13083551C2311yescharacteristic
260C2×#13083551C2311yescharacteristic
261C2×#13083551C2311yescharacteristic
262C2×#13083551C2311yescharacteristic
263C2×#13083551C2311yescharacteristic
264C2×#13083551C2311yescharacteristic
265C2×#13083551C2311yescharacteristic
266C2×#13083551C2311yescharacteristic
267C2×#13083551C2311yescharacteristic
268C2×#13083551C2311yescharacteristic
269C2×#13083551C2311yescharacteristic
270C2×#13083551C2311yescharacteristic
271C2×#13083551C2311yescharacteristic
272C2×#13083551C2311yescharacteristic
273C2×#13083551C2311yescharacteristic
274C2×#13083551C2311yescharacteristic
275C2×#13083551C2311yescharacteristic
276C2×#13083551C2311yescharacteristic
277C2×#13083551C2311yescharacteristic
278C2×#13083551C2311yescharacteristic
279C2×#13083551C2311yescharacteristic
280C2×#13083551C2311yescharacteristic
281C2×#13083551C2311yescharacteristic
282C2×#13083551C2311yescharacteristic
283C2×#13083551C2311yescharacteristic
284C2×#13083551C2311yescharacteristic
285C2×#13083551C2311yescharacteristic
286C2×#13083551C2311yescharacteristic
287C22⋊C4×D89—24no—
288C22⋊C4×D89—24no—
289C2×C4×Dic89—42no—
290C2×C4×Dic89—42no—
291C2×C4×Dic89C2311yescharacteristic
292C2×C4×Dic89C2311yescharacteristic
293C2×C4×Dic89C2311yescharacteristic
294C2×C4×Dic89C2311yescharacteristic
295C2×C4×Dic89C2311yescharacteristic
296C2×C4×Dic89C2311yescharacteristic
297C2×C4×Dic89C2311yescharacteristic
298C2×C4×Dic89C2311yescharacteristic
299C2×C4×Dic89C2311yescharacteristic
300C2×C4×Dic89C2311yescharacteristic
301C2×C4×Dic89C2311yescharacteristic
302C2×C4×Dic89C2311yescharacteristic
303C2×C4×Dic89C2311yescharacteristic
304C2×C4×Dic89C2311yescharacteristic
305C2×C4×Dic89C2311yescharacteristic
306C2×C4×Dic89C2311yescharacteristic
307C2×C4×Dic89C2311yescharacteristic
308C2×C4×Dic89C2311yescharacteristic
309C2×C4×Dic89C2311yescharacteristic
310C2×C4×Dic89C2311yescharacteristic
311C2×C4×Dic89C2311yescharacteristic
312C2×C4×Dic89C2311yescharacteristic
313C2×C4×Dic89C2311yescharacteristic
314#15667919C2311yescharacteristic
315#15667919C2311yescharacteristic
316#15667919C2311yescharacteristic
317#15667919C2311yescharacteristic
318#15667919C2311yescharacteristic
319#15667919C2311yescharacteristic
320#15667919C2311yescharacteristic
321#15667919C2311yescharacteristic
322#15667919C2311yescharacteristic
323#15667919C2311yescharacteristic
324#15667919C2311yescharacteristic
325#15667919C2311yescharacteristic
326#15667919C2311yescharacteristic
327#15667919C2311yescharacteristic
328#15667919C2311yescharacteristic
329#15667919C2311yescharacteristic
330#15667919C2311yescharacteristic
331#15667919C2311yescharacteristic
332#15667919C2311yescharacteristic
333#15667919C2311yescharacteristic
334#15667919C2311yescharacteristic
335#15667919C2311yescharacteristic
336#15667919C2311yescharacteristic
337#15667919C2311yescharacteristic
338#15667919C2311yescharacteristic
339#15667919C2311yescharacteristic
340C22×D4×C89C2311yescharacteristic
341C23×C4×C89C2311yescharacteristic
342C23×C4×C89C2311yescharacteristic
343C23×C4×C89C2311yescharacteristic
344C23×C4×C89C2311yescharacteristic
345C4×D4×C89C2×C418yescomplemented
346C2×C4⋊C4×C89C2311yescharacteristic
347C2×C4⋊C4×C89C2311yescharacteristic
348C2×C4⋊C4×C89C2311yescharacteristic
349C2×C4⋊C4×C89C2311yescharacteristic
350C2×C4⋊C4×C89C2311yescharacteristic
351C2×C22⋊C4×C89C2311yescharacteristic
352C2×C22⋊C4×C89C2311yescharacteristic
353C2×C22⋊C4×C89C2311yescharacteristic
354C2×C22⋊C4×C89C2311yescharacteristic
355C2×C22⋊C4×C89C2311yescharacteristic
356C2×C22⋊C4×C89C2311yescharacteristic
357C2×C22⋊C4×C89C2311yescharacteristic
358C2×C22⋊C4×C89C2311yescharacteristic
359C2×C42×C89C2311yescharacteristic
360C2×C42×C89C2311yescharacteristic
361C2×C42×C89C2311yescharacteristic
362#95×C89C2311yescharacteristic
363#95×C89C2311yescharacteristic
364#95×C89C2311yescharacteristic
365#95×C89C2311yescharacteristic
366#95×C89C2311yescharacteristic
367#95×C89C2311yescharacteristic
368#95×C89C2311yescharacteristic
369#95×C89C2311yescharacteristic
370#95×C89C2311yescharacteristic
371#95×C89C2311yescharacteristic
372#95×C89C2311yescharacteristic
373#95×C89C2311yescharacteristic
374#95×C89C2311yescharacteristic
375#95×C89C2311yescharacteristic
376C23×D89—22no—
377C23×D89—22no—
378C23×D89—41no—
379C23×D89—41no—
380C23×D89—41no—
381C23×D89—41no—
382C23×D89C22×C414yes—
383C23×D89C2411yescharacteristic
384C23×D89C2411yescharacteristic
385C23×D89C2411yescharacteristic
386C2×Dic178—41no—
387C2×Dic178—41no—
388C2×Dic178C22×C414yes—
389C2×D356—41no—
390C2×D356—41no—
391C2×D356—41no—
392C2×D356—41no—
393C2×D356C22×C414yes—
394C2×D356C22×C414yes—
395C2×C22⋊D89—22no—
396C2×C22⋊D89—22no—
397C2×C22⋊D89—41no—
398C2×C22⋊D89—41no—
399C2×C22⋊D89—41no—
400C2×C22⋊D89—41no—
401C2×C22⋊D89—41no—
402C2×C22⋊D89—41no—
403C2×C22⋊D89C22×C414yes—
404C2×C22⋊D89C22×C414yes—
405C2×C22⋊D89C22×C414yes—
406C2×C22⋊D89C22×C414yes—
407C22×Dic89—22no—
408C22×Dic89—22no—
409C22×Dic89—22no—
410C22×Dic89—22no—
411C22×Dic89—22no—
412C22×Dic89—22no—
413C22×Dic89—22no—
414C22×Dic89—22no—
415C22×Dic89—41no—
416C22×Dic89—41no—
417C22×Dic89—41no—
418C22×Dic89—41no—
419C22×Dic89—41no—
420C22×Dic89—41no—
421C22×Dic89C22×C414yes—
422C22×Dic89C2411yescharacteristic
423C22×Dic89C2411yescharacteristic
424C22×Dic89C2411yescharacteristic
425C22×Dic89C2411yescharacteristic
426C22×Dic89C2411yescharacteristic
427C22×Dic89C2411yescharacteristic
428C22×Dic89C2411yescharacteristic
429C22×Dic89C2411yescharacteristic
430C22×Dic89C2411yescharacteristic
431C22×Dic89C2411yescharacteristic
432C22×Dic89C2411yescharacteristic
433C22×Dic89C2411yescharacteristic
434C22×Dic89C2411yescharacteristic
435C2×C4×D89—22no—
436C2×C4×D89—22no—
437C2×C4×D89—22no—
438C2×C4×D89—22no—
439C2×C4×D89—22no—
440C2×C4×D89—22no—
441C2×C4×D89—41no—
442C2×C4×D89—41no—
443C2×C4×D89—41no—
444C2×C4×D89—41no—
445C2×C4×D89—41no—
446C2×C4×D89—41no—
447C2×C4×D89—41no—
448C2×C4×D89—41no—
449C2×C4×D89—41no—
450C2×C4×D89—41no—
451C2×C4×D89—41no—
452C2×C4×D89—41no—
453C2×C4×D89—41no—
454C2×C4×D89—41no—
455C2×C4×D89C22×C414yes—
456C4⋊Dic89—22no—
457C4⋊Dic89—22no—
458C4⋊Dic89C22×C414yes—
459#13083553—22no—
460#13083553—22no—
461#13083553—22no—
462#13083553—22no—
463#13083553—22no—
464#13083553—22no—
465#13083553—41no—
466#13083553—41no—
467#13083553—41no—
468#13083553—41no—
469#13083553C22×C414yes—
470#13083553C22×C414yes—
471#13083553C22×C414yes—
472#13083553C22×C414yes—
473C22⋊Dic89—22no—
474C22⋊Dic89—22no—
475C22⋊Dic89C22×C414yes—
476C22⋊Dic89C22×C414yes—
477C22⋊Dic89#4114yes—
478C22⋊Dic89#4114yes—
479#13083551—22no—
480#13083551—22no—
481#13083551—22no—
482#13083551—22no—
483#13083551—22no—
484#13083551—22no—
485#13083551—22no—
486#13083551—22no—
487#13083551—22no—
488#13083551—22no—
489#13083551—22no—
490#13083551—22no—
491#13083551—41no—
492#13083551—41no—
493#13083551—41no—
494#13083551—41no—
495#13083551—41no—
496#13083551—41no—
497#13083551C22×C414yes—
498#13083551C22×C414yes—
499#13083551C22×C414yes—
500#13083551C22×C414yes—
501#13083551C22×C414yes—
502#13083551C22×C414yes—
503#13083551C22×C414yes—
504#13083551C22×C414yes—
505#13083551C22×C414yes—
506#13083551C22×C414yes—
507C4×Dic89—22no—
508C4×Dic89—22no—
509C4×Dic89—22no—
510C4×Dic89—22no—
511C4×Dic89—22no—
512C4×Dic89—22no—
513C4×Dic89—22no—
514C4×Dic89—22no—
515C4×Dic89—41no—
516C4×Dic89—41no—
517C4×Dic89—41no—
518C4×Dic89—41no—
519C4×Dic89—41no—
520C4×Dic89—41no—
521C4×Dic89—41no—
522C4×Dic89—41no—
523C4×Dic89—41no—
524C4×Dic89—41no—
525C4×Dic89—41no—
526C4×Dic89—41no—
527C4×Dic89—41no—
528C4×Dic89—41no—
529C4×Dic89C22×C414yes—
530C24×C89C2411yescharacteristic
531C24×C89C2411yescharacteristic
532C2×D4×C89—22no—
533C2×D4×C89—22no—
534C2×D4×C89C22×C414yes—
535C22×C4×C89—22no—
536C22×C4×C89—22no—
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×C89C22×C414yes—
546C22×C4×C89C22×C414yes—
547C22×C4×C89C2411yescharacteristic
548C22×C4×C89C2411yescharacteristic
549C22×C4×C89C2411yescharacteristic
550C22×C4×C89C2411yescharacteristic
551C22×C4×C89C2411yescharacteristic
552C22×C4×C89C2411yescharacteristic
553C22×C4×C89C2411yescharacteristic
554C22×C4×C89C2411yescharacteristic
555C22×C4×C89C2411yescharacteristic
556C22×C4×C89C2411yescharacteristic
557C22×C4×C89C2411yescharacteristic
558C22×C4×C89C2411yescharacteristic
559C22×C4×C89C2411yescharacteristic
560C4⋊C4×C89—41no—
561C4⋊C4×C89—41no—
562C4⋊C4×C89—41no—
563C4⋊C4×C89—41no—
564C4⋊C4×C89C22×C414yes—
565C22⋊C4×C89—22no—
566C22⋊C4×C89—22no—
567C22⋊C4×C89—41no—
568C22⋊C4×C89—41no—
569C22⋊C4×C89—41no—
570C22⋊C4×C89—41no—
571C22⋊C4×C89C22×C414yes—
572C22⋊C4×C89C22×C414yes—
573C42×C89—41no—
574C42×C89—41no—
575C42×C89C22×C414yes—
576C23×C89—21no—
577C23×C89—21no—
578C23×C89—21no—
579C23×C89—21no—
580C23×C89—21no—
581C23×C89—21no—
582C23×C89—21no—
583C23×C89—21no—
584C23×C89—21no—
585C23×C89—21no—
586C23×C89C23×C412yes—
587C23×C89C23×C412yes—
588C23×C89C2×#4112yes—
589C23×C89C2×#4112yes—
590C23×C89C2511yescharacteristic
591C22×D89—21no—
592C22×D89—21no—
593C22×D89—21no—
594C22×D89—21no—
595C22×D89—21no—
596C22×D89—21no—
597C22×D89—21no—
598C22×D89—21no—
599C22×D89—21no—
600C22×D89—21no—
601C22×D89—21no—
602C22×D89—21no—
603C22×D89—21no—
604C22×D89—21no—
605C22×D89—21no—
606C22×D89—21no—
607C22×D89—21no—
608C22×D89—21no—
609C22×D89—28no—
610C22×D89—44no—
611C22×D89—44no—
612C22×D89—82no—
613C22×D89—82no—
614C22×D89—82no—
615C22×D89—82no—
616C22×D89C23×C412yes—
617C22×D89C23×C412yes—
618C22×D89C23×C412yes—
619D4×C89—28no—
620C2×C4×C89—21no—
621C2×C4×C89—21no—
622C2×C4×C89—21no—
623C2×C4×C89—21no—
624C2×C4×C89—21no—
625C2×C4×C89—21no—
626C2×C4×C89—21no—
627C2×C4×C89—21no—
628C2×C4×C89—21no—
629C2×C4×C89—21no—
630C2×C4×C89—21no—
631C2×C4×C89—21no—
632C2×C4×C89—21no—
633C2×C4×C89—21no—
634C2×C4×C89—21no—
635C2×C4×C89—21no—
636C2×C4×C89—21no—
637C2×C4×C89—21no—
638C2×C4×C89—21no—
639C2×C4×C89—21no—
640C2×C4×C89—21no—
641C2×C4×C89—21no—
642C2×C4×C89—21no—
643C2×C4×C89—21no—
644C2×C4×C89—21no—
645C2×C4×C89—21no—
646C2×C4×C89—21no—
647C2×C4×C89—21no—
648C2×C4×C89—21no—
649C2×C4×C89—21no—
650C2×C4×C89—21no—
651C2×C4×C89—21no—
652C2×C4×C89—21no—
653C2×C4×C89—21no—
654C2×C4×C89—44no—
655C2×C4×C89—44no—
656C2×C4×C89—82no—
657C2×C4×C89—82no—
658C2×C4×C89C23×C412yes—
659C2×C4×C89C23×C412yes—
660C2×C4×C89C23×C412yes—
661C2×C4×C89C23×C412yes—
662C2×C4×C89C23×C412yes—
663C22⋊D89—28no—
664C22⋊D89—44no—
665C22⋊D89—44no—
666C22⋊D89—44no—
667C2×Dic89—21no—
668C2×Dic89—21no—
669C2×Dic89—21no—
670C2×Dic89—21no—
671C2×Dic89—21no—
672C2×Dic89—21no—
673C2×Dic89—21no—
674C2×Dic89—21no—
675C2×Dic89—21no—
676C2×Dic89—21no—
677C2×Dic89—21no—
678C2×Dic89—21no—
679C2×Dic89—21no—
680C2×Dic89—21no—
681C2×Dic89—21no—
682C2×Dic89—21no—
683C2×Dic89—21no—
684C2×Dic89—21no—
685C2×Dic89—21no—
686C2×Dic89—21no—
687C2×Dic89—21no—
688C2×Dic89—21no—
689C2×Dic89—21no—
690C2×Dic89—21no—
691C2×Dic89—21no—
692C2×Dic89—21no—
693C2×Dic89—21no—
694C2×Dic89—21no—
695C2×Dic89—44no—
696C2×Dic89—44no—
697C2×Dic89—44no—
698C2×Dic89—44no—
699C2×Dic89—44no—
700C2×Dic89C23×C412yes—
701C2×Dic89C23×C412yes—
702C2×Dic89C23×C412yes—
703C2×Dic89C23×C412yes—
704C2×Dic89C23×C412yes—
705C2×Dic89C2×#4112yes—
706C2×Dic89C2×#4112yes—
707C2×Dic89C2×#4112yes—
708C2×Dic89C2×#4112yes—
709C2×Dic89H(5,𝔽2)12yes—
710C2×Dic89H(5,𝔽2)12yes—
711D356—44no—
712D356—44no—
713C4×D89—44no—
714C4×D89—82no—
715C4×D89—82no—
716C4×D89—82no—
717C4×D89—82no—
718C4×D89—82no—
719C4×D89—82no—
720Dic178—44no—
721C22×C89—22no—
722C22×C89—22no—
723C22×C89—22no—
724C22×C89—22no—
725C22×C89—22no—
726C22×C89—22no—
727C22×C89—22no—
728C22×C89—22no—
729C22×C89—22no—
730C22×C89—41no—
731C22×C89—41no—
732C22×C89—41no—
733C22×C89—41no—
734C22×C89C4×#4114yes—
735C22×C89C24×C411yescharacteristic
736C22×C89C22×#4111yescharacteristic
737C22×C89C22×#4111yescharacteristic
738C22×C89C2×H(5,𝔽2)11yescharacteristic
739C22×C89C2×H(5,𝔽2)11yescharacteristic
740C22×C89#58511yescharacteristic
741C22×C89#58511yescharacteristic
742C2×D89—22no—
743C2×D89—22no—
744C2×D89—22no—
745C2×D89—22no—
746C2×D89—22no—
747C2×D89—22no—
748C2×D89—22no—
749C2×D89—22no—
750C2×D89—22no—
751C2×D89—41no—
752C2×D89—41no—
753C2×D89—41no—
754C2×D89—41no—
755C2×D89—41no—
756C2×D89—41no—
757C2×D89—41no—
758C2×D89—41no—
759C2×D89—41no—
760C2×D89—41no—
761C2×D89—41no—
762C2×D89—41no—
763C2×D89—88no—
764C4×C89—22no—
765C4×C89—22no—
766C4×C89—22no—
767C4×C89—22no—
768C4×C89—22no—
769C4×C89—41no—
770C4×C89—41no—
771C4×C89—41no—
772C4×C89—41no—
773C4×C89—41no—
774C4×C89—41no—
775C4×C89—41no—
776C4×C89—41no—
777Dic89—22no—
778Dic89—22no—
779Dic89—22no—
780Dic89—22no—
781Dic89—22no—
782Dic89—22no—
783Dic89—22no—
784Dic89—22no—
785Dic89—22no—
786Dic89—22no—
787Dic89—22no—
788Dic89—41no—
789Dic89—41no—
790#34283—891nomaximal, Sylow
791C2×C89—24no—
792C2×C89—42no—
793C2×C89C2×C4×#4111yescharacteristic
794C2×C89C4×H(5,𝔽2)11yescharacteristic
795C2×C89C4×H(5,𝔽2)11yescharacteristic
796C2×C89#351311yescharacteristic
797C2×C89#351411yescharacteristic
798C2×C89#351911yescharacteristic
799C2×C89#352111yescharacteristic
800D89—42no—
801D89—42no—
802D89—42no—
803C2×#538—891no—
804#2374—891no—
805#2373—891no—
806#2373—891no—
807#2372—891no—
808#2368—891no—
809#2367—891no—
810#2364—891no—
811#2364—891no—
812#2363—891no—
813#2361—891no—
814#2360—891no—
815#2359—891no—
816#2358—891no—
817#2358—891no—
818#2358—891no—
819#2358—891no—
820#2337—891no—
821#2335—891no—
822#2334—891no—
823#2333—891no—
824#2318D8911yescharacteristic, complemented
825C4×#126—891no—
826C4×#124—891no—
827C4×#123—891no—
828C4×#121—891no—
829#2290—891no—
830C2×#388—891no—
831#2275—891no—
832#2273—891no—
833C42×D4—891no—
834C89#3428311yescharacteristic, complemented, Sylow
835#538—8916no—
836C2×#126—891no—
837C2×#126—891no—
838C2×#124—891no—
839C2×#124—891no—
840C2×#123—891no—
841C2×#123—891no—
842C2×C22⋊Q8—891no—
843C2×#121—891no—
844C2×#121—891no—
845C2×#121—891no—
846C2×#120—891no—
847C2×#120—891no—
848C2×C4×Q8—891no—
849C2×C4×D4—891no—
850C2×C4×D4—891no—
851C2×C4×D4—891no—
852C2×C4×D4—891no—
853C2×C4×D4—891no—
854C2×C4×D4—891no—
855C2×C4×D4—891no—
856C2×C4×D4—891no—
857C2×C4×D4—891no—
858C2×C4×D4—891no—
859C2×C4×D4C2×D8911yescharacteristic
860C2×#117—891no—
861C22×C4⋊C4—891no—
862C22×C22⋊C4—891no—
863C22×C22⋊C4—891no—
864C22×C22⋊C4—891no—
865C22×C22⋊C4—891no—
866C22×C22⋊C4—891no—
867C22×C42—891no—
868C22×C42—891no—
869#391—891no—
870#391—891no—
871#391—891no—
872#390—891no—
873#390—891no—
874#390—891no—
875#390—891no—
876#390—891no—
877#389—891no—
878#389—891no—
879#389—891no—
880#389—891no—
881#388—891no—
882#388—891no—
883#388—891no—
884#388—891no—
885#388—891no—
886#388—891no—
887#388—891no—
888#388—891no—
889#388—891no—
890#388—891no—
891#388—891no—
892#388—891no—
893#388—891no—
894#388—891no—
895#388—891no—
896#388—891no—
897#388—891no—
898#388—891no—
899#388—891no—
900#388—891no—
901#388—891no—
902#388—891no—
903#388C2×D8911yescharacteristic, complemented
904#388C2×D8911yescharacteristic, complemented
905#387—891no—
906#387—891no—
907#387—891no—
908#387—891no—
909#387—891no—
910#387—891no—
911#387—891no—
912#387—891no—
913#387—891no—
914#387—891no—
915#387C2×D8911yescharacteristic, complemented
916#387C2×D8911yescharacteristic, complemented
917#386—891no—
918#386—891no—
919#386—891no—
920#386—891no—
921#386—891no—
922#386—891no—
923#386—891no—
924#386—891no—
925#386—891no—
926#386—891no—
927#386—891no—
928#386—891no—
929#386C2×D8911yescharacteristic
930#386C2×D8911yescharacteristic
931#385—891no—
932#385—891no—
933#385—891no—
934#385—891no—
935#385—891no—
936#385—891no—
937#385—891no—
938#385—891no—
939#385C2×D8911yescharacteristic
940#385C2×D8911yescharacteristic
941#383C2×D8911yescharacteristic, complemented
942#382C2×D8911yescharacteristic, complemented
943#381C2×D8911yescharacteristic, complemented
944#380C2×D8911yescharacteristic, complemented
945C4×C4⋊C4—891no—
946C4×C4⋊C4—891no—
947C4×C4⋊C4—891no—
948C4×C4⋊C4—891no—
949C4×C4⋊C4—891no—
950C4×C4⋊C4—891no—
951C4×C4⋊C4—891no—
952C4×C4⋊C4—891no—
953C4×C4⋊C4—891no—
954C4×C4⋊C4—891no—
955C4×C4⋊C4—891no—
956C4×C22⋊C4—891no—
957C4×C22⋊C4—891no—
958C4×C22⋊C4—891no—
959C4×C22⋊C4—891no—
960C4×C22⋊C4—891no—
961C4×C22⋊C4—891no—
962C4×C22⋊C4—891no—
963C4×C22⋊C4—891no—
964C4×C22⋊C4—891no—
965C4×C22⋊C4—891no—
966C4×C22⋊C4—891no—
967C4×C22⋊C4—891no—
968C4×C22⋊C4—891no—
969C4×C22⋊C4—891no—
970C4×C22⋊C4—891no—
971C4×C22⋊C4—891no—
972C4×C22⋊C4—891no—
973C4×C22⋊C4—891no—
974C4×C22⋊C4—891no—
975C4×C22⋊C4—891no—
976C4×C22⋊C4—891no—
977C4×C22⋊C4—891no—
978C4×C22⋊C4—891no—
979C4×C22⋊C4—891no—
980C4×C22⋊C4—891no—
981C4×C22⋊C4—891no—
982C4×C22⋊C4—891no—
983C4×C22⋊C4—891no—
984C4×C22⋊C4C2×D8911yescharacteristic
985#376—891no—
986#376—891no—
987C2×#95—891no—
988C2×#95—891no—
989C2×#95C2×D8911yescharacteristic
990C43—891no—
991C25—891no—
992C22×Q8—891no—
993C22×D4—891no—
994C22×D4—891no—
995C22×D4—891no—
996C22×D4—891no—
997C22×D4—891no—
998C22×D4—891no—
999C22×D4C22×D8911yescharacteristic
1000C23×C4—891no—
1001C23×C4—891no—
1002C23×C4—891no—
1003C23×C4—891no—
1004C23×C4—891no—
1005C23×C4—891no—
1006C23×C4—891no—
1007C23×C4—891no—
1008C23×C4—891no—
1009C23×C4—891no—
1010C23×C4—891no—
1011C23×C4—891no—
1012C23×C4C22×D8911yescharacteristic
1013C23×C4C22×D8911yescharacteristic
1014C23×C4C22×D8911yescharacteristic
1015C23×C4C22×D8911yescharacteristic
1016#126—898no—
1017#126—898no—
1018#124—898no—
1019#124—898no—
1020#123—898no—
1021#123—898no—
1022C22⋊Q8—898no—
1023#121—898no—
1024#121—898no—
1025#121—898no—
1026#120—898no—
1027#120—898no—
1028C4×Q8—3562no—
1029C4×D4—898no—
1030C4×D4—3562no—
1031C4×D4—3562no—
1032C4×D4—3562no—
1033C4×D4—3562no—
1034C4×D4—3562no—
1035C4×D4—1784no—
1036C4×D4—1784no—
1037C4×D4—1784no—
1038C4×D4—1784no—
1039C4×D4C4×D8918yescomplemented
1040#117—3562no—
1041C2×C4⋊C4—891no—
1042C2×C4⋊C4—891no—
1043C2×C4⋊C4—891no—
1044C2×C4⋊C4—891no—
1045C2×C4⋊C4—891no—
1046C2×C4⋊C4—891no—
1047C2×C4⋊C4—891no—
1048C2×C4⋊C4—891no—
1049C2×C4⋊C4—891no—
1050C2×C4⋊C4—891no—
1051C2×C4⋊C4—891no—
1052C2×C4⋊C4—891no—
1053C2×C4⋊C4—891no—
1054C2×C4⋊C4—891no—
1055C2×C4⋊C4—891no—
1056C2×C4⋊C4—891no—
1057C2×C4⋊C4—891no—
1058C2×C4⋊C4—3562no—
1059C2×C4⋊C4C22×D8911yescharacteristic
1060C2×C4⋊C4C22×D8911yescharacteristic
1061C2×C4⋊C4C22×D8911yescharacteristic
1062C2×C4⋊C4C22×D8911yescharacteristic
1063C2×C4⋊C4C22×D8911yescharacteristic
1064C2×C22⋊C4—891no—
1065C2×C22⋊C4—891no—
1066C2×C22⋊C4—891no—
1067C2×C22⋊C4—891no—
1068C2×C22⋊C4—898no—
1069C2×C22⋊C4—891no—
1070C2×C22⋊C4—891no—
1071C2×C22⋊C4—891no—
1072C2×C22⋊C4—891no—
1073C2×C22⋊C4—891no—
1074C2×C22⋊C4—891no—
1075C2×C22⋊C4—891no—
1076C2×C22⋊C4—891no—
1077C2×C22⋊C4—891no—
1078C2×C22⋊C4—891no—
1079C2×C22⋊C4—891no—
1080C2×C22⋊C4—891no—
1081C2×C22⋊C4—891no—
1082C2×C22⋊C4—891no—
1083C2×C22⋊C4—891no—
1084C2×C22⋊C4—891no—
1085C2×C22⋊C4—891no—
1086C2×C22⋊C4—891no—
1087C2×C22⋊C4—891no—
1088C2×C22⋊C4—891no—
1089C2×C22⋊C4—891no—
1090C2×C22⋊C4—891no—
1091C2×C22⋊C4—891no—
1092C2×C22⋊C4—891no—
1093C2×C22⋊C4—891no—
1094C2×C22⋊C4—891no—
1095C2×C22⋊C4—891no—
1096C2×C22⋊C4—891no—
1097C2×C22⋊C4—891no—
1098C2×C22⋊C4—891no—
1099C2×C22⋊C4—3562no—
1100C2×C22⋊C4—3562no—
1101C2×C22⋊C4—1784no—
1102C2×C22⋊C4—1784no—
1103C2×C22⋊C4C22×D8911yescharacteristic
1104C2×C22⋊C4C22×D8911yescharacteristic
1105C2×C22⋊C4C22×D8911yescharacteristic
1106C2×C22⋊C4C22×D8911yescharacteristic
1107C2×C22⋊C4C22×D8911yescharacteristic
1108C2×C22⋊C4C22×D8911yescharacteristic
1109C2×C22⋊C4C22×D8911yescharacteristic
1110C2×C22⋊C4C22×D8911yescharacteristic
1111C2×C42—891no—
1112C2×C42—891no—
1113C2×C42—891no—
1114C2×C42—891no—
1115C2×C42—891no—
1116C2×C42—891no—
1117C2×C42—891no—
1118C2×C42—891no—
1119C2×C42—891no—
1120C2×C42—891no—
1121C2×C42—891no—
1122C2×C42—891no—
1123C2×C42—891no—
1124C2×C42—891no—
1125C2×C42—891no—
1126C2×C42—891no—
1127C2×C42—891no—
1128C2×C42—891no—
1129C2×C42—891no—
1130C2×C42—891no—
1131C2×C42—891no—
1132C2×C42—891no—
1133C2×C42—891no—
1134C2×C42—3562no—
1135C2×C42—3562no—
1136C2×C42C22×D8911yescharacteristic
1137C2×C42C22×D8911yescharacteristic
1138C2×C42C22×D8911yescharacteristic
1139#95—891no—
1140#95—891no—
1141#95—891no—
1142#95—891no—
1143#95—891no—
1144#95—891no—
1145#95—891no—
1146#95—891no—
1147#95—891no—
1148#95—891no—
1149#95—891no—
1150#95—891no—
1151#95—891no—
1152#95—891no—
1153#95—891no—
1154#95—891no—
1155#95—891no—
1156#95—891no—
1157#95—891no—
1158#95—891no—
1159#95—891no—
1160#95—891no—
1161#95—891no—
1162#95—891no—
1163#95—891no—
1164#95—891no—
1165#95C22×D8911yescharacteristic
1166#95C22×D8911yescharacteristic
1167#95C22×D8911yescharacteristic
1168#95C22×D8911yescharacteristic
1169#95C22×D8911yescharacteristic
1170#95C22×D8911yescharacteristic
1171#95C22×D8911yescharacteristic
1172#95C22×D8911yescharacteristic
1173#95C22×D8911yescharacteristic
1174#95C22×D8911yescharacteristic
1175#95C22×D8911yescharacteristic
1176#95C22×D8911yescharacteristic
1177#95C22×D8911yescharacteristic
1178#95C22×D8911yescharacteristic
1179C24—894no—
1180C24—891no—
1181C24—891no—
1182C24—891no—
1183C24—3561no—
1184C24—3561no—
1185C24—3561no—
1186C24—3561no—
1187C24—1782no—
1188C24—1782no—
1189C24C23×D8911yescharacteristic
1190C24C23×D8911yescharacteristic
1191C2×Q8—894no—
1192C2×Q8—3561no—
1193C2×Q8—3561no—
1194C2×D4—22no—
1195C2×D4—22no—
1196C2×D4—894no—
1197C2×D4—894no—
1198C2×D4—894no—
1199C2×D4—894no—
1200C2×D4—894no—
1201C2×D4—894no—
1202C2×D4—3561no—
1203C2×D4—3561no—
1204C2×D4—3561no—
1205C2×D4—3561no—
1206C2×D4—3561no—
1207C2×D4—3561no—
1208C2×D4—3561no—
1209C2×D4—3561no—
1210C2×D4—3561no—
1211C2×D4—3561no—
1212C2×D4—1782no—
1213C2×D4—1782no—
1214C2×D4C2×C4×D8914yes—
1215C22×C4—22no—
1216C22×C4—22no—
1217C22×C4—41no—
1218C22×C4—41no—
1219C22×C4—41no—
1220C22×C4—41no—
1221C22×C4—41no—
1222C22×C4—41no—
1223C22×C4—41no—
1224C22×C4—41no—
1225C22×C4—894no—
1226C22×C4—891no—
1227C22×C4—891no—
1228C22×C4—891no—
1229C22×C4—891no—
1230C22×C4—891no—
1231C22×C4—891no—
1232C22×C4—891no—
1233C22×C4—891no—
1234C22×C4—891no—
1235C22×C4—891no—
1236C22×C4—891no—
1237C22×C4—894no—
1238C22×C4—891no—
1239C22×C4—891no—
1240C22×C4—3561no—
1241C22×C4—3561no—
1242C22×C4—3561no—
1243C22×C4—3561no—
1244C22×C4—3561no—
1245C22×C4—3561no—
1246C22×C4—3561no—
1247C22×C4—3561no—
1248C22×C4—3561no—
1249C22×C4—3561no—
1250C22×C4—3561no—
1251C22×C4—3561no—
1252C22×C4—3561no—
1253C22×C4—3561no—
1254C22×C4—3561no—
1255C22×C4—3561no—
1256C22×C4—3561no—
1257C22×C4—3561no—
1258C22×C4—3561no—
1259C22×C4—3561no—
1260C22×C4—1782no—
1261C22×C4—1782no—
1262C22×C4—1782no—
1263C22×C4—1782no—
1264C22×C4—1782no—
1265C22×C4—1782no—
1266C22×C4—1782no—
1267C22×C4—1782no—
1268C22×C4—1782no—
1269C22×C4—1782no—
1270C22×C4—1782no—
1271C22×C4—1782no—
1272C22×C4—1782no—
1273C22×C4—1782no—
1274C22×C4C2×C4×D8914yes—
1275C22×C4C2×C4×D8914yes—
1276C22×C4C23×D8911yescharacteristic
1277C22×C4C23×D8911yescharacteristic
1278C22×C4C23×D8911yescharacteristic
1279C22×C4C23×D8911yescharacteristic
1280C22×C4C23×D8911yescharacteristic
1281C22×C4C23×D8911yescharacteristic
1282C22×C4C23×D8911yescharacteristic
1283C22×C4C23×D8911yescharacteristic
1284C22×C4C23×D8911yescharacteristic
1285C22×C4C23×D8911yescharacteristic
1286C22×C4C23×D8911yescharacteristic
1287C22×C4C23×D8911yescharacteristic
1288C22×C4C23×D8911yescharacteristic
1289C4⋊C4—41no—
1290C4⋊C4—41no—
1291C4⋊C4—41no—
1292C4⋊C4—41no—
1293C4⋊C4—894no—
1294C4⋊C4—894no—
1295C4⋊C4—894no—
1296C4⋊C4—894no—
1297C4⋊C4—894no—
1298C4⋊C4—3561no—
1299C4⋊C4—3561no—
1300C4⋊C4—3561no—
1301C4⋊C4—3561no—
1302C4⋊C4—1782no—
1303C4⋊C4—1782no—
1304C4⋊C4—1782no—
1305C4⋊C4—1782no—
1306C4⋊C4—1782no—
1307C4⋊C4—1782no—
1308C4⋊C4—1782no—
1309C4⋊C4—1782no—
1310C4⋊C4C2×C4×D8914yes—
1311C22⋊C4—22no—
1312C22⋊C4—22no—
1313C22⋊C4—41no—
1314C22⋊C4—41no—
1315C22⋊C4—41no—
1316C22⋊C4—41no—
1317C22⋊C4—894no—
1318C22⋊C4—894no—
1319C22⋊C4—894no—
1320C22⋊C4—894no—
1321C22⋊C4—894no—
1322C22⋊C4—894no—
1323C22⋊C4—894no—
1324C22⋊C4—894no—
1325C22⋊C4—894no—
1326C22⋊C4—894no—
1327C22⋊C4—894no—
1328C22⋊C4—894no—
1329C22⋊C4—894no—
1330C22⋊C4—894no—
1331C22⋊C4—3561no—
1332C22⋊C4—3561no—
1333C22⋊C4—3561no—
1334C22⋊C4—3561no—
1335C22⋊C4—3561no—
1336C22⋊C4—3561no—
1337C22⋊C4—1782no—
1338C22⋊C4—1782no—
1339C22⋊C4—1782no—
1340C22⋊C4—1782no—
1341C22⋊C4—1782no—
1342C22⋊C4—1782no—
1343C22⋊C4—1782no—
1344C22⋊C4—1782no—
1345C22⋊C4—1782no—
1346C22⋊C4—1782no—
1347C22⋊C4—1782no—
1348C22⋊C4—1782no—
1349C22⋊C4—1782no—
1350C22⋊C4—1782no—
1351C22⋊C4C2×C4×D8914yes—
1352C22⋊C4C2×C4×D8914yes—
1353C42—41no—
1354C42—41no—
1355C42—894no—
1356C42—3561no—
1357C42—3561no—
1358C42—3561no—
1359C42—3561no—
1360C42—3561no—
1361C42—3561no—
1362C42—3561no—
1363C42—3561no—
1364C42—3561no—
1365C42—3561no—
1366C42—3561no—
1367C42—3561no—
1368C42—3561no—
1369C42—3561no—
1370C42—1782no—
1371C42—1782no—
1372C42—1782no—
1373C42—1782no—
1374C42—1782no—
1375C42—1782no—
1376C42—1782no—
1377C42—1782no—
1378C42C2×C4×D8914yes—
1379C23—21no—
1380C23—21no—
1381C23—21no—
1382C23—21no—
1383C23—21no—
1384C23—21no—
1385C23—21no—
1386C23—21no—
1387C23—21no—
1388C23—21no—
1389C23—892no—
1390C23—892no—
1391C23—892no—
1392C23—3564no—
1393C23—3564no—
1394C23—1781no—
1395C23—1781no—
1396C23—1781no—
1397C23—1781no—
1398C23—1781no—
1399C23—1781no—
1400C23—1781no—
1401C23—1781no—
1402C23—1781no—
1403C23—1781no—
1404C23—1781no—
1405C23—1781no—
1406C23—1781no—
1407C23—1781no—
1408C23—1781no—
1409C23—1781no—
1410C23—1781no—
1411C23—1781no—
1412C23—1788no—
1413C23—7122no—
1414C23—7122no—
1415C23—7122no—
1416C23—7122no—
1417C23C22×C4×D8912yes—
1418C23C22×C4×D8912yes—
1419C23#41×D8912yes—
1420C23#41×D8912yes—
1421C23C24×D8911yescharacteristic
1422Q8—3564no—
1423D4—28no—
1424D4—3564no—
1425D4—3564no—
1426D4—3564no—
1427D4—3564no—
1428D4—3564no—
1429D4—1788no—
1430C2×C4—21no—
1431C2×C4—21no—
1432C2×C4—21no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—21no—
1438C2×C4—21no—
1439C2×C4—21no—
1440C2×C4—21no—
1441C2×C4—21no—
1442C2×C4—21no—
1443C2×C4—21no—
1444C2×C4—21no—
1445C2×C4—21no—
1446C2×C4—21no—
1447C2×C4—21no—
1448C2×C4—21no—
1449C2×C4—21no—
1450C2×C4—21no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—21no—
1457C2×C4—21no—
1458C2×C4—21no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—44no—
1465C2×C4—44no—
1466C2×C4—82no—
1467C2×C4—82no—
1468C2×C4—892no—
1469C2×C4—892no—
1470C2×C4—892no—
1471C2×C4—892no—
1472C2×C4—892no—
1473C2×C4—892no—
1474C2×C4—892no—
1475C2×C4—892no—
1476C2×C4—892no—
1477C2×C4—892no—
1478C2×C4—892no—
1479C2×C4—3564no—
1480C2×C4—3564no—
1481C2×C4—3564no—
1482C2×C4—3564no—
1483C2×C4—3564no—
1484C2×C4—3564no—
1485C2×C4—1781no—
1486C2×C4—1781no—
1487C2×C4—1781no—
1488C2×C4—1781no—
1489C2×C4—1781no—
1490C2×C4—1781no—
1491C2×C4—1781no—
1492C2×C4—1781no—
1493C2×C4—1781no—
1494C2×C4—1781no—
1495C2×C4—1781no—
1496C2×C4—1781no—
1497C2×C4—1781no—
1498C2×C4—1781no—
1499C2×C4—1781no—
1500C2×C4—1781no—
1501C2×C4—1781no—
1502C2×C4—1781no—
1503C2×C4—1781no—
1504C2×C4—1781no—
1505C2×C4—1781no—
1506C2×C4—1781no—
1507C2×C4—1781no—
1508C2×C4—1781no—
1509C2×C4—1781no—
1510C2×C4—1781no—
1511C2×C4—1781no—
1512C2×C4—1781no—
1513C2×C4—7122no—
1514C2×C4—7122no—
1515C2×C4—7122no—
1516C2×C4—7122no—
1517C2×C4—7122no—
1518C2×C4—7122no—
1519C2×C4C22×C4×D8912yes—
1520C2×C4C22×C4×D8912yes—
1521C2×C4C22×C4×D8912yes—
1522C2×C4C22×C4×D8912yes—
1523C2×C4C22×C4×D8912yes—
1524C22—22no—
1525C22—22no—
1526C22—22no—
1527C22—22no—
1528C22—22no—
1529C22—22no—
1530C22—22no—
1531C22—22no—
1532C22—22no—
1533C22—41no—
1534C22—41no—
1535C22—41no—
1536C22—41no—
1537C22—3561no—
1538C22—3561no—
1539C22—3561no—
1540C22—3561no—
1541C22—3561no—
1542C22—3561no—
1543C22—3561no—
1544C22—3561no—
1545C22—3561no—
1546C22—3561no—
1547C22—3561no—
1548C22—3561no—
1549C22—1782no—
1550C22—1782no—
1551C22—1782no—
1552C22—1782no—
1553C22—1782no—
1554C22—1782no—
1555C22—1782no—
1556C22—1782no—
1557C22—1782no—
1558C22—7128no—
1559C22#1915206614yes—
1560C22C23×C4×D8911yescharacteristic
1561C22C2×#41×D8911yescharacteristic
1562C22C2×#41×D8911yescharacteristic
1563C22H(5,𝔽2)×D8911yescharacteristic
1564C22H(5,𝔽2)×D8911yescharacteristic
1565C22#1915243311yescharacteristic
1566C22#1915243511yescharacteristic
1567C4—22no—
1568C4—22no—
1569C4—22no—
1570C4—22no—
1571C4—22no—
1572C4—41no—
1573C4—41no—
1574C4—41no—
1575C4—41no—
1576C4—41no—
1577C4—41no—
1578C4—41no—
1579C4—41no—
1580C4—3561no—
1581C4—3561no—
1582C4—1782no—
1583C4—1782no—
1584C4—1782no—
1585C4—1782no—
1586C4—1782no—
1587C4—1782no—
1588C4—1782no—
1589C4—1782no—
1590C4—1782no—
1591C4—1782no—
1592C4—1782no—
1593C2—24no—
1594C2—42no—
1595C2—3562no—
1596C2—3562no—
1597C2—3562no—
1598C2C2×#1915206611yescharacteristic
1599C2#2603345611yescharacteristic
1600C2#2603345811yescharacteristic
1601C2#2603418211yescharacteristic
1602C2#2603420511yescharacteristic
1603C2#2603427611yescharacteristic
1604C2#2603431011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D89
commutatorC22×C89C24×C4
FittingC89×#2318C2
socle, cosocleC23×C89C25
prime radicalC2×#19152181C2
hypercenter#2318D89
hypocenterC89#34283
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ #2318

Complements

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

NH ≅ G/Ntype
2. #26023384C2semidirect
3. #26023378C2semidirect
4. #26023365C2semidirect
5. #26023359C2semidirect
6. #26023333C2semidirect
7. #26023318C2semidirect
8. #26023300C2semidirect
9. #26023296C2semidirect
10. #26023285C2semidirect
11. #26023263C2semidirect
12. #26023252C2semidirect
13. #26023237C2semidirect
14. #26023232C2semidirect
15. #26023232C2semidirect
16. #26023228C2semidirect
17. #26023228C2semidirect
18. #26023062C2semidirect
19. #26023038C2semidirect
20. #26023023C2semidirect
21. #26023014C2semidirect
22. #26022800C2semidirect
23. #26022791C2semidirect
24. #26022769C2semidirect
25. #26022758C2semidirect
26. #26022691C2semidirect
27. C2×#19151487C2semidirect
28. #26022610C2semidirect
29. #26022604C2semidirect
30. C4×D4×Dic89C2semidirect
31. C89×#2318C2semidirect
32. #19152181C4semidirect
45. C2×#15667977C22semidirect
55. C2×#15667972C22semidirect
56. C2×#15667969C22semidirect
64. C22×C4×Dic89C22semidirect
65. #19151503C22semidirect
66. #19151502C22semidirect
67. #19151502C22semidirect
72. #19151498C22semidirect
73. #19151495C22semidirect
74. #19151494C22semidirect
75. #19151493C22semidirect
76. #19151493C22semidirect
77. #19151492C22semidirect
80. #19151490C22semidirect
95. #19151487C22semidirect
96. #19151487C22semidirect
97. #19151487C22semidirect
98. #19151486C22semidirect
99. #19151485C22semidirect
100. #19151483C22semidirect
101. #19151483C22semidirect
102. #19151480C22semidirect
103. #19151480C22semidirect
104. #19151480C22semidirect
105. #19151480C22semidirect
106. #19151480C22semidirect
107. #19151479C22semidirect
108. #19151479C22semidirect
117. #19151475C22semidirect
120. #19151474C22semidirect
123. #19151472C22semidirect
126. #19151470C22semidirect
129. C4⋊C4×Dic89C22semidirect
130. C4⋊C4×Dic89C22semidirect
131. C4⋊C4×Dic89C22semidirect
132. C4×#13083553C22semidirect
133. C4×C4⋊Dic89C22semidirect
134. #19151449C22semidirect
135. #19151449C22semidirect
136. #19151449C22semidirect
137. #19151449C22semidirect
138. #19151449C22semidirect
139. #19151449C22semidirect
144. C22⋊C4×Dic89C22semidirect
145. C22⋊C4×Dic89C22semidirect
146. C22⋊C4×Dic89C22semidirect
151. C4×#13083551C22semidirect
155. C4×C22⋊Dic89C22semidirect
164. #19151445C22semidirect
165. #19151445C22semidirect
166. #19151445C22semidirect
167. #19151445C22semidirect
168. #19151444C22semidirect
169. #19151443C22semidirect
171. #95×D89C22semidirect
172. C42×Dic89C22semidirect
174. #388×C89C22semidirect
175. #388×C89C22semidirect
176. #387×C89C22semidirect
177. #387×C89C22semidirect
182. #383×C89C22semidirect
183. #382×C89C22semidirect
184. #381×C89C22semidirect
185. #380×C89C22semidirect
208. #15668007C2×C4semidirect
209. #15668006C2×C4semidirect
210. #15668000C2×C4semidirect
211. #15667998C2×C4semidirect
212. #15667997C2×C4semidirect
213. #15667995C2×C4semidirect
214. #15667989C2×C4semidirect
215. #15667986C2×C4semidirect
216. #15667985C2×C4semidirect
217. #15667984C2×C4semidirect
218. #15667982C2×C4semidirect
219. #15667980C2×C4semidirect
227. C4×C22⋊D89C2×C4semidirect
258. C2×#13083551C2×C4semidirect
345. C4×D4×C89C2×C4semidirect
824. #2318D89semidirect
834. C89#34283semidirect
903. #388C2×D89semidirect
904. #388C2×D89semidirect
915. #387C2×D89semidirect
916. #387C2×D89semidirect
941. #383C2×D89semidirect
942. #382C2×D89semidirect
943. #381C2×D89semidirect
944. #380C2×D89semidirect
1039. C4×D4C4×D89semidirect

Maximal subgroups

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

subgroupindex
C2×#191521812
#260233842
#260233782
#260233652
#260233592
#260233332
#260233182
#260233002
#260232962
#260232852
#260232632
#260232522
#260232372
#260232322
#260232282
#260230622
#260230382
#260230232
#260230142
#260228002
#260227912
#260227692
#260227582
#260226912
C2×#191514872
#260226102
#260226042
C4×D4×Dic892
C89×#23182
#3428389