Finite Group Databasebeta

← #36718979

Subgroups — #36718979

Order 22784.

2500 conjugacy classes of subgroups.

The subgroup lattice has 1560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19152274C211yesmaximal, characteristic
2#26023439C211yesmaximal, characteristic, complemented
3#26023439C211yesmaximal, characteristic, complemented
4#26023421C211yesmaximal, characteristic, complemented
5#26023394C211yesmaximal, characteristic, complemented
6#26023258C211yesmaximal, characteristic, complemented
7#26023255C211yesmaximal, characteristic, complemented
8#26023246C211yesmaximal, characteristic, complemented
9#26023244C211yesmaximal, characteristic, complemented
10#26023231C211yesmaximal, characteristic
11#26023150C211yesmaximal, characteristic, complemented
12#26023148C211yesmaximal, characteristic, complemented
13#26023114C211yesmaximal, characteristic, complemented
14#26023110C211yesmaximal, characteristic, complemented
15#26023103C211yesmaximal, characteristic, complemented
16#26023034C211yesmaximal, characteristic, complemented
17#26023024C211yesmaximal, characteristic, complemented
18#26022982C211yesmaximal, characteristic, complemented
19#26022980C211yesmaximal, characteristic, complemented
20#26022961C211yesmaximal, characteristic, complemented
21#26022923C211yesmaximal, characteristic, complemented
22#26022922C211yesmaximal, characteristic, complemented
23#26022918C211yesmaximal, characteristic, complemented
24#26022880C211yesmaximal, characteristic, complemented
25#26022879C211yesmaximal, characteristic, complemented
26#26022872C211yesmaximal, characteristic, complemented
27#26022871C211yesmaximal, characteristic, complemented
28#26022751C211yesmaximal, characteristic
29C2×#19151473C211yesmaximal, characteristic, complemented
30C2×#19151470C211yesmaximal, characteristic, complemented
31C89×#2342C211yesmaximal, characteristic, complemented
32C24×Dic89C2211yescharacteristic
33#19152274C4116yescomplemented
34C2×#15668005C2211yescharacteristic
35C2×#15668005C2211yescharacteristic
36C2×#15667998C2211yescharacteristic
37C2×#15667996C2211yescharacteristic
38C2×#15667995C2211yescharacteristic
39C2×#15667994C2211yescharacteristic
40C2×#15667991C2211yescharacteristic
41C2×#15667989C2211yescharacteristic
42C2×#15667981C2211yescharacteristic
43C2×C4×Dic178C2211yescharacteristic, complemented
44C2×C4×C22⋊D89C2211yescharacteristic
45C2×C4×C22⋊D89C2211yescharacteristic
46C2×#15667972C2211yescharacteristic
47C2×#15667972C2211yescharacteristic
48C2×#15667972C2211yescharacteristic
49C2×#15667972C2211yescharacteristic
50C2×#15667972C2211yescharacteristic
51C2×#15667971C2211yescharacteristic
52C2×#15667968C2211yescharacteristic
53C2×#15667968C2211yescharacteristic
54C22×C4⋊Dic89C2211yescharacteristic
55C22×C4⋊Dic89C2211yescharacteristic
56C22×#13083553C2211yescharacteristic
57C22×#13083553C2211yescharacteristic
58C2×C4⋊C4×D89C2211yescharacteristic, complemented
59C22×C22⋊Dic89C2211yescharacteristic
60C22×C22⋊Dic89C2211yescharacteristic
61#19151504C2211yescharacteristic, complemented
62#19151502C2211yescharacteristic, complemented
63#19151502C2211yescharacteristic, complemented
64#19151498C2211yescharacteristic
65#19151496C2211yescharacteristic, complemented
66#19151496C2211yescharacteristic, complemented
67#19151496C2211yescharacteristic, complemented
68#19151496C2211yescharacteristic, complemented
69#19151496C2211yescharacteristic, complemented
70#19151495C2211yescharacteristic, complemented
71#19151495C2211yescharacteristic, complemented
72#19151495C2211yescharacteristic, complemented
73#19151495C2211yescharacteristic, complemented
74#19151495C2211yescharacteristic, complemented
75#19151495C2211yescharacteristic, complemented
76#19151493C2211yescharacteristic, complemented
77#19151493C2211yescharacteristic, complemented
78#19151493C2211yescharacteristic, complemented
79#19151492C2211yescharacteristic
80#19151492C2211yescharacteristic
81#19151492C2211yescharacteristic
82#19151490C2211yescharacteristic, complemented
83#19151490C2211yescharacteristic, complemented
84#19151489C2211yescharacteristic, complemented
85#19151489C2211yescharacteristic, complemented
86#19151489C2211yescharacteristic, complemented
87#19151488C2211yescharacteristic, complemented
88#19151486C2211yescharacteristic
89#19151486C2211yescharacteristic
90#19151486C2211yescharacteristic
91#19151485C2211yescharacteristic, complemented
92#19151485C2211yescharacteristic, complemented
93#19151485C2211yescharacteristic, complemented
94#19151485C2211yescharacteristic, complemented
95#19151483C2211yescharacteristic, complemented
96#19151483C2211yescharacteristic, complemented
97#19151483C2211yescharacteristic, complemented
98#19151483C2211yescharacteristic, complemented
99#19151482C2211yescharacteristic, complemented
100#19151482C2211yescharacteristic, complemented
101#19151482C2211yescharacteristic, complemented
102#19151481C2211yescharacteristic, complemented
103#19151481C2211yescharacteristic, complemented
104#19151479C2211yescharacteristic, complemented
105#19151479C2211yescharacteristic, complemented
106#19151479C2211yescharacteristic, complemented
107#19151477C2211yescharacteristic
108#19151475C2211yescharacteristic
109#19151475C2211yescharacteristic
110#19151475C2211yescharacteristic
111#19151475C2211yescharacteristic
112#19151474C2211yescharacteristic
113#19151473C2211yescharacteristic
114#19151473C2211yescharacteristic
115#19151473C2211yescharacteristic
116#19151473C2211yescharacteristic
117#19151473C2211yescharacteristic
118#19151473C2211yescharacteristic
119#19151473C2211yescharacteristic
120#19151473C2211yescharacteristic
121#19151472C2211yescharacteristic, complemented
122#19151472C2211yescharacteristic, complemented
123#19151472C2211yescharacteristic, complemented
124#19151472C2211yescharacteristic, complemented
125#19151471C2211yescharacteristic
126#19151470C2211yescharacteristic
127#19151470C2211yescharacteristic
128#19151470C2211yescharacteristic
129#19151470C2211yescharacteristic
130#19151470C2211yescharacteristic
131#19151470C2211yescharacteristic
132#19151470C2211yescharacteristic
133#19151470C2211yescharacteristic
134#19151470C2211yescharacteristic
135#19151470C2211yescharacteristic
136#19151470C2211yescharacteristic
137#19151470C2211yescharacteristic
138#19151470C2211yescharacteristic
139#19151470C2211yescharacteristic
140#19151469C2211yescharacteristic, complemented
141#19151467C2211yescharacteristic, complemented
142#19151467C2211yescharacteristic, complemented
143#19151467C2211yescharacteristic, complemented
144#19151465C2211yescharacteristic, complemented
145#19151465C2211yescharacteristic, complemented
146#19151463C2211yescharacteristic, complemented
147#19151463C2211yescharacteristic, complemented
148#19151462C2211yescharacteristic, complemented
149#19151462C2211yescharacteristic, complemented
150#19151460C2211yescharacteristic, complemented
151#19151459C2211yescharacteristic
152#19151457C2211yescharacteristic, complemented
153#19151456C2211yescharacteristic
154#19151455C2211yescharacteristic, complemented
155C4⋊C4×Dic89C2211yescharacteristic, complemented
156C4×#13083553C2211yescharacteristic, complemented
157C4×C4⋊Dic89C2211yescharacteristic, complemented
158#19151449C2211yescharacteristic, complemented
159C22⋊C4×Dic89C2211yescharacteristic
160C22⋊C4×Dic89C2211yescharacteristic
161C22⋊C4×Dic89C2211yescharacteristic
162C22⋊C4×Dic89C2211yescharacteristic
163C22⋊C4×Dic89C2211yescharacteristic
164C22⋊C4×Dic89C2211yescharacteristic
165C22⋊C4×Dic89C2211yescharacteristic
166C4×#13083551C2211yescharacteristic, complemented
167C4×C22⋊Dic89C2211yescharacteristic
168#19151443C2211yescharacteristic, complemented
169C2×#15667919C2211yescharacteristic
170C2×#15667919C2211yescharacteristic
171C2×#15667919C2211yescharacteristic
172C2×#15667919C2211yescharacteristic
173C2×#117×C89C2211yescharacteristic
174C22×C22⋊C4×C89C2211yescharacteristic
175C22×C22⋊C4×C89C2211yescharacteristic
176#388×C89C2211yescharacteristic
177#388×C89C2211yescharacteristic
178#388×C89C2211yescharacteristic
179#388×C89C2211yescharacteristic
180#385×C89C2211yescharacteristic
181#385×C89C2211yescharacteristic
182#381×C89C2211yescharacteristic
183#380×C89C2211yescharacteristic
184#379×C89C2211yescharacteristic
185C4×C22⋊C4×C89C2211yescharacteristic
186C4×C22⋊C4×C89C2211yescharacteristic
187C4×C22⋊C4×C89C2211yescharacteristic
188C22×Dic178C2311yescharacteristic
189C22×C22⋊D89C2311yescharacteristic
190C22×C22⋊D89C2311yescharacteristic
191C22×C22⋊D89C2311yescharacteristic
192C23×Dic89—42no—
193C23×Dic89—42no—
194C23×Dic89—42no—
195C23×Dic89C2311yescharacteristic
196C23×Dic89C2311yescharacteristic
197C23×Dic89C2311yescharacteristic
198C23×Dic89C2311yescharacteristic
199C23×Dic89C2311yescharacteristic
200C23×Dic89C2311yescharacteristic
201C23×Dic89C2311yescharacteristic
202C23×Dic89C2311yescharacteristic
203C23×Dic89C2311yescharacteristic
204C23×Dic89C2311yescharacteristic
205C22×C4×D89C2311yescharacteristic
206C22×C4×D89C2311yescharacteristic
207C22×C4×D89C2311yescharacteristic
208#15668005C2×C418yescomplemented
209#15668005C2×C418yescomplemented
210#15667998C2×C418yescomplemented
211#15667996C2×C418yescomplemented
212#15667995C2×C418yescomplemented
213#15667994C2×C418yescomplemented
214#15667991C2×C418yescomplemented
215#15667989C2×C418yescomplemented
216#15667981C2×C418yes—
217C4×Dic178—42no—
218C4×C22⋊D89—42no—
219C4×C22⋊D89C2×C418yescomplemented
220#15667972—42no—
221#15667972—42no—
222#15667972—42no—
223#15667972—42no—
224#15667972C2×C418yescomplemented
225#15667971C2×C418yescomplemented
226#15667968—42no—
227#15667968C2×C418yescomplemented
228C2×C4⋊Dic89—42no—
229C2×C4⋊Dic89—42no—
230C2×C4⋊Dic89C2311yescharacteristic
231C2×C4⋊Dic89C2311yescharacteristic
232C2×C4⋊Dic89C2311yescharacteristic
233C2×C4⋊Dic89C2311yescharacteristic
234C2×C4⋊Dic89C2311yescharacteristic
235C2×C4⋊Dic89C2311yescharacteristic
236C2×C4⋊Dic89C2311yescharacteristic
237C2×C4⋊Dic89C2311yescharacteristic
238C2×C4⋊Dic89C2311yescharacteristic
239C2×C4⋊Dic89C2311yescharacteristic
240C2×C4⋊Dic89C2311yescharacteristic
241C2×#13083553—42no—
242C2×#13083553—42no—
243C2×#13083553C2311yescharacteristic
244C2×#13083553C2311yescharacteristic
245C2×#13083553C2311yescharacteristic
246C2×#13083553C2311yescharacteristic
247C2×#13083553C2311yescharacteristic
248C2×#13083553C2311yescharacteristic
249C2×#13083553C2311yescharacteristic
250C2×#13083553C2311yescharacteristic
251C2×#13083553C2311yescharacteristic
252C2×#13083553C2311yescharacteristic
253C2×#13083553C2311yescharacteristic
254C2×#13083553C2311yescharacteristic
255C2×#13083553C2311yescharacteristic
256C2×#13083553C2311yescharacteristic
257C2×#13083553C2311yescharacteristic
258C2×#13083553C2311yescharacteristic
259C2×#13083553C2311yescharacteristic
260C2×#13083553C2311yescharacteristic
261C2×#13083553C2311yescharacteristic
262C2×#13083553C2311yescharacteristic
263C2×#13083553C2311yescharacteristic
264C2×#13083553C2311yescharacteristic
265C2×#13083553C2311yescharacteristic
266C4⋊C4×D89—42no—
267C2×C22⋊Dic89—42no—
268C2×C22⋊Dic89C2×C418yescomplemented
269C2×C22⋊Dic89C2311yescharacteristic
270C2×C22⋊Dic89C2311yescharacteristic
271C2×C22⋊Dic89C2311yescharacteristic
272C2×C22⋊Dic89C2311yescharacteristic
273C2×C22⋊Dic89C2311yescharacteristic
274C2×C22⋊Dic89C2311yescharacteristic
275C2×C22⋊Dic89C2311yescharacteristic
276C2×C22⋊Dic89C2311yescharacteristic
277C2×C22⋊Dic89C2311yescharacteristic
278C2×C22⋊Dic89C2311yescharacteristic
279C2×C22⋊Dic89C2311yescharacteristic
280C2×#13083551C2311yescharacteristic
281C2×#13083551C2311yescharacteristic
282C2×#13083551C2311yescharacteristic
283C2×#13083551C2311yescharacteristic
284C2×#13083551C2311yescharacteristic
285C2×#13083551C2311yescharacteristic
286C2×#13083551C2311yescharacteristic
287C2×#13083551C2311yescharacteristic
288C2×#13083551C2311yescharacteristic
289C2×C4×Dic89C2311yescharacteristic
290C2×C4×Dic89C2311yescharacteristic
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
302#15667919C2311yescharacteristic
303#15667919C2311yescharacteristic
304#15667919C2311yescharacteristic
305#15667919C2311yescharacteristic
306#15667919C2311yescharacteristic
307#15667919C2311yescharacteristic
308#15667919C2311yescharacteristic
309#15667919C2311yescharacteristic
310#15667919C2311yescharacteristic
311#15667919C2311yescharacteristic
312#15667919C2311yescharacteristic
313#15667919C2311yescharacteristic
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
338C25×C89C2311yescharacteristic
339C23×C4×C89C2311yescharacteristic
340C23×C4×C89C2311yescharacteristic
341C23×C4×C89C2311yescharacteristic
342C23×C4×C89C2311yescharacteristic
343#117×C89—42no—
344C2×C4⋊C4×C89C2311yescharacteristic
345C2×C4⋊C4×C89C2311yescharacteristic
346C2×C4⋊C4×C89C2311yescharacteristic
347C2×C4⋊C4×C89C2311yescharacteristic
348C2×C22⋊C4×C89—42no—
349C2×C22⋊C4×C89C2×C418yescomplemented
350C2×C22⋊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×C22⋊C4×C89C2311yescharacteristic
360C2×C22⋊C4×C89C2311yescharacteristic
361C2×C22⋊C4×C89C2311yescharacteristic
362C2×C22⋊C4×C89C2311yescharacteristic
363C2×C22⋊C4×C89C2311yescharacteristic
364C2×C42×C89C2311yescharacteristic
365C2×C42×C89C2311yescharacteristic
366C2×C42×C89C2311yescharacteristic
367C2×C42×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×D89C2411yescharacteristic
377C2×Dic178—41no—
378C2×Dic178—41no—
379C2×Dic178C22×C414yescomplemented
380C2×C22⋊D89—22no—
381C2×C22⋊D89—22no—
382C2×C22⋊D89—22no—
383C2×C22⋊D89—22no—
384C2×C22⋊D89—41no—
385C2×C22⋊D89—41no—
386C2×C22⋊D89C22×C414yes—
387C2×C22⋊D89C22×C414yes—
388C2×C22⋊D89C22×C414yes—
389C22×Dic89—22no—
390C22×Dic89—22no—
391C22×Dic89—22no—
392C22×Dic89—22no—
393C22×Dic89—22no—
394C22×Dic89—22no—
395C22×Dic89—22no—
396C22×Dic89—22no—
397C22×Dic89—22no—
398C22×Dic89—22no—
399C22×Dic89—22no—
400C22×Dic89—41no—
401C22×Dic89—41no—
402C22×Dic89—41no—
403C22×Dic89—41no—
404C22×Dic89—41no—
405C22×Dic89—41no—
406C22×Dic89—41no—
407C22×Dic89—41no—
408C22×Dic89—41no—
409C22×Dic89—41no—
410C22×Dic89—41no—
411C22×Dic89—41no—
412C22×Dic89—41no—
413C22×Dic89—41no—
414C22×Dic89—41no—
415C22×Dic89—41no—
416C22×Dic89—41no—
417C22×Dic89—416no—
418C22×Dic89C22×C414yes—
419C22×Dic89C22×C414yes—
420C22×Dic89C2411yescharacteristic
421C22×Dic89C2411yescharacteristic
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—41no—
437C2×C4×D89—41no—
438C2×C4×D89—41no—
439C2×C4×D89—41no—
440C2×C4×D89—41no—
441C2×C4×D89—41no—
442C2×C4×D89—41no—
443C2×C4×D89C22×C414yescomplemented
444C4⋊Dic89—22no—
445C4⋊Dic89—22no—
446C4⋊Dic89—41no—
447C4⋊Dic89—41no—
448C4⋊Dic89—41no—
449C4⋊Dic89—41no—
450C4⋊Dic89—41no—
451C4⋊Dic89—41no—
452C4⋊Dic89C22×C414yescomplemented
453C4⋊Dic89C22×C414yescomplemented
454C4⋊Dic89C22×C414yescomplemented
455#13083553—22no—
456#13083553—22no—
457#13083553—41no—
458#13083553—41no—
459#13083553—41no—
460#13083553—41no—
461#13083553—41no—
462#13083553—41no—
463#13083553—41no—
464#13083553—41no—
465#13083553—41no—
466#13083553—41no—
467#13083553—41no—
468#13083553—41no—
469#13083553—41no—
470#13083553—41no—
471#13083553—41no—
472#13083553—41no—
473#13083553C22×C414yescomplemented
474#13083553C22×C414yescomplemented
475#13083553C22×C414yescomplemented
476#13083553C22×C414yescomplemented
477#13083553C22×C414yescomplemented
478C22⋊Dic89—22no—
479C22⋊Dic89—22no—
480C22⋊Dic89—41no—
481C22⋊Dic89—41no—
482C22⋊Dic89C22×C414yes—
483C22⋊Dic89C22×C414yes—
484C22⋊Dic89C22×C414yes—
485C22⋊Dic89C22×C414yes—
486C22⋊Dic89C22×C414yes—
487C22⋊Dic89C22×C414yes—
488C22⋊Dic89C22×C414yes—
489#13083551—41no—
490#13083551—41no—
491#13083551—41no—
492#13083551—41no—
493#13083551—41no—
494#13083551—41no—
495#13083551C22×C414yescomplemented
496#13083551C22×C414yescomplemented
497#13083551C22×C414yescomplemented
498C4×Dic89—22no—
499C4×Dic89—41no—
500C4×Dic89—41no—
501C4×Dic89—41no—
502C4×Dic89—41no—
503C4×Dic89—41no—
504C4×Dic89—41no—
505C4×Dic89—41no—
506C4×Dic89—41no—
507C4×Dic89—41no—
508C4×Dic89C22×C414yescomplemented
509C4×Dic89C22×C414yescomplemented
510C4×Dic89C22×C414yescomplemented
511C24×C89—22no—
512C24×C89—22no—
513C24×C89—22no—
514C24×C89—22no—
515C24×C89—41no—
516C24×C89—41no—
517C24×C89C22×C414yes—
518C24×C89C2411yescharacteristic
519C24×C89C2411yescharacteristic
520C24×C89C2411yescharacteristic
521C22×C4×C89—22no—
522C22×C4×C89—22no—
523C22×C4×C89—22no—
524C22×C4×C89—22no—
525C22×C4×C89—41no—
526C22×C4×C89—41no—
527C22×C4×C89—41no—
528C22×C4×C89—41no—
529C22×C4×C89—41no—
530C22×C4×C89—41no—
531C22×C4×C89C22×C414yes—
532C22×C4×C89C22×C414yes—
533C22×C4×C89C2411yescharacteristic
534C22×C4×C89C2411yescharacteristic
535C22×C4×C89C2411yescharacteristic
536C22×C4×C89C2411yescharacteristic
537C22×C4×C89C2411yescharacteristic
538C22×C4×C89C2411yescharacteristic
539C22×C4×C89C2411yescharacteristic
540C22×C4×C89C2411yescharacteristic
541C22×C4×C89C2411yescharacteristic
542C22×C4×C89C2411yescharacteristic
543C22×C4×C89C2411yescharacteristic
544C22×C4×C89C2411yescharacteristic
545C4⋊C4×C89—41no—
546C4⋊C4×C89—41no—
547C4⋊C4×C89—41no—
548C4⋊C4×C89—41no—
549C22⋊C4×C89—22no—
550C22⋊C4×C89—22no—
551C22⋊C4×C89—22no—
552C22⋊C4×C89—22no—
553C22⋊C4×C89—22no—
554C22⋊C4×C89—22no—
555C22⋊C4×C89—41no—
556C22⋊C4×C89—41no—
557C22⋊C4×C89—41no—
558C22⋊C4×C89—41no—
559C22⋊C4×C89C22×C414yes—
560C22⋊C4×C89C22×C414yes—
561C22⋊C4×C89C22×C414yes—
562C22⋊C4×C89C22×C414yes—
563C42×C89—41no—
564C42×C89—41no—
565C42×C89—41no—
566C42×C89—41no—
567C23×C89—21no—
568C23×C89—21no—
569C23×C89—21no—
570C23×C89—21no—
571C23×C89—21no—
572C23×C89—21no—
573C23×C89—21no—
574C23×C89—21no—
575C23×C89—28no—
576C23×C89—28no—
577C23×C89—21no—
578C23×C89—21no—
579C23×C89—21no—
580C23×C89—21no—
581C23×C89—21no—
582C23×C89—21no—
583C23×C89—44no—
584C23×C89—44no—
585C23×C89—44no—
586C23×C89—44no—
587C23×C89—44no—
588C23×C89C23×C412yes—
589C23×C89C23×C412yes—
590C23×C89C23×C412yes—
591C23×C89H(5,𝔽2)12yes—
592C23×C89H(5,𝔽2)12yes—
593C23×C892−1+412yes—
594C23×C892−1+412yes—
595C23×C89C2511yescharacteristic
596C22×D89—21no—
597C22×D89—21no—
598C22×D89—21no—
599C22×D89—21no—
600C22×D89—21no—
601C22×D89—21no—
602C22×D89C23×C412yes—
603C2×C4×C89—28no—
604C2×C4×C89—21no—
605C2×C4×C89—21no—
606C2×C4×C89—21no—
607C2×C4×C89—21no—
608C2×C4×C89—21no—
609C2×C4×C89—21no—
610C2×C4×C89—21no—
611C2×C4×C89—21no—
612C2×C4×C89—21no—
613C2×C4×C89—21no—
614C2×C4×C89—21no—
615C2×C4×C89—21no—
616C2×C4×C89—21no—
617C2×C4×C89—21no—
618C2×C4×C89—21no—
619C2×C4×C89—21no—
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—44no—
637C2×C4×C89—82no—
638C2×C4×C89—82no—
639C2×C4×C89C23×C412yes—
640C2×C4×C89C23×C412yes—
641C2×C4×C89C23×C412yes—
642C2×C4×C89C23×C412yes—
643C22⋊D89—28no—
644C22⋊D89—28no—
645C22⋊D89—44no—
646C2×Dic89—28no—
647C2×Dic89—21no—
648C2×Dic89—21no—
649C2×Dic89—21no—
650C2×Dic89—21no—
651C2×Dic89—21no—
652C2×Dic89—21no—
653C2×Dic89—21no—
654C2×Dic89—21no—
655C2×Dic89—21no—
656C2×Dic89—21no—
657C2×Dic89—21no—
658C2×Dic89—21no—
659C2×Dic89—21no—
660C2×Dic89—21no—
661C2×Dic89—21no—
662C2×Dic89—21no—
663C2×Dic89—21no—
664C2×Dic89—21no—
665C2×Dic89—21no—
666C2×Dic89—21no—
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—44no—
685C2×Dic89—44no—
686C2×Dic89—44no—
687C2×Dic89—44no—
688C2×Dic89—44no—
689C2×Dic89—44no—
690C2×Dic89—44no—
691C2×Dic89—82no—
692C2×Dic89—82no—
693C2×Dic89C23×C412yes—
694C2×Dic89C23×C412yes—
695C2×Dic89C23×C412yes—
696C2×Dic89C23×C412yes—
697C2×Dic89C23×C412yes—
698C2×Dic89C23×C412yes—
699C2×Dic89C23×C412yes—
700C2×Dic89H(5,𝔽2)12yes—
701C4×D89—44no—
702C4×D89—82no—
703C4×D89—82no—
704Dic178—44no—
705C22×C89—22no—
706C22×C89—22no—
707C22×C89—22no—
708C22×C89—22no—
709C22×C89—22no—
710C22×C89—22no—
711C22×C89—22no—
712C22×C89—22no—
713C22×C89—22no—
714C22×C89—22no—
715C22×C89—22no—
716C22×C89—22no—
717C22×C89—22no—
718C22×C89—22no—
719C22×C89—22no—
720C22×C89—416no—
721C22×C89—41no—
722C22×C89—41no—
723C22×C89—41no—
724C22×C89—41no—
725C22×C89#52014yes—
726C22×C89#52014yes—
727C22×C89C24×C411yescharacteristic
728C22×C89C2×H(5,𝔽2)11yescharacteristic
729C22×C89C2×H(5,𝔽2)11yescharacteristic
730C22×C89C2×H(5,𝔽2)11yescharacteristic
731C22×C89C2×2−1+411yescharacteristic
732C22×C89C2×2−1+411yescharacteristic
733C22×C89#58511yescharacteristic
734C2×D89—22no—
735C2×D89—22no—
736C2×D89—22no—
737C2×D89—41no—
738C2×D89—41no—
739C2×D89—41no—
740C2×D89—41no—
741C4×C89—22no—
742C4×C89—22no—
743C4×C89—22no—
744C4×C89—22no—
745C4×C89—41no—
746C4×C89—41no—
747C4×C89—41no—
748C4×C89—41no—
749C4×C89—41no—
750C4×C89—41no—
751C4×C89—41no—
752C4×C89—41no—
753Dic89—22no—
754Dic89—22no—
755Dic89—22no—
756Dic89—22no—
757Dic89—22no—
758Dic89—22no—
759Dic89—22no—
760Dic89—22no—
761Dic89—41no—
762Dic89—41no—
763Dic89—41no—
764Dic89—41no—
765Dic89—41no—
766Dic89—41no—
767Dic89—41no—
768#34457—891nomaximal, Sylow
769C2×C89—24no—
770C2×C89—24no—
771C2×C89—42no—
772C2×C89C2×#52011yescharacteristic
773C2×C89C2×#52011yescharacteristic
774C2×C89C4×H(5,𝔽2)11yescharacteristic
775C2×C89#353211yescharacteristic
776C2×C89#353511yescharacteristic
777C2×C89#353511yescharacteristic
778C2×C89#353811yescharacteristic
779D89—42no—
780C2×#551—891no—
781#2383—891no—
782#2383—891no—
783#2379—891no—
784#2376—891no—
785#2360—891no—
786#2360—891no—
787#2359—891no—
788#2359—891no—
789#2358—891no—
790D4×C4⋊C4—891no—
791D4×C4⋊C4—891no—
792#2343—891no—
793#2343—891no—
794#2342—891no—
795#2342D8911yescharacteristic, complemented
796#2334—891no—
797#2334—891no—
798#2329—891no—
799#2329—891no—
800#2326—891no—
801#2322—891no—
802#2322—891no—
803#2322—891no—
804#2318—891no—
805#2318—891no—
806#2317—891no—
807#2317—891no—
808C4×#120—891no—
809C2×#385—891no—
810C2×#385—891no—
811C89#3445711yescharacteristic, complemented, Sylow
812C24×C4—891no—
813#551—8916no—
814C2×#126—891no—
815C2×#126—891no—
816C2×#124—891no—
817C2×#123—891no—
818C2×#123—891no—
819C2×#123—891no—
820C2×C22⋊Q8—891no—
821C2×C22⋊Q8—891no—
822C2×#120—891no—
823C2×C4×Q8—891no—
824C2×C4×D4—891no—
825C2×C4×D4—891no—
826C2×C4×D4—891no—
827C2×C4×D4—891no—
828C2×C4×D4—891no—
829C2×C4×D4—891no—
830C2×C4×D4—891no—
831C2×#117—891no—
832C2×#117—891no—
833C2×#117—891no—
834C2×#117C2×D8911yescharacteristic
835C22×C4⋊C4—891no—
836C22×C4⋊C4—891no—
837C22×C4⋊C4—891no—
838C22×C4⋊C4—891no—
839C22×C4⋊C4—891no—
840C22×C22⋊C4—891no—
841C22×C22⋊C4—891no—
842C22×C22⋊C4C2×D8911yescharacteristic
843C22×C22⋊C4C2×D8911yescharacteristic
844#391—891no—
845#391—891no—
846#391—891no—
847#390—891no—
848#389—891no—
849#389—891no—
850#389—891no—
851#389—891no—
852#389—891no—
853#389—891no—
854#389—891no—
855#389—891no—
856#389—891no—
857#389—891no—
858#389—891no—
859#389—891no—
860#389—891no—
861#389—891no—
862#388—891no—
863#388—891no—
864#388—891no—
865#388—891no—
866#388—891no—
867#388—891no—
868#388—891no—
869#388—891no—
870#388—891no—
871#388—891no—
872#388—891no—
873#388—891no—
874#388C2×D8911yescharacteristic
875#388C2×D8911yescharacteristic
876#388C2×D8911yescharacteristic
877#388C2×D8911yescharacteristic
878#387—891no—
879#387—891no—
880#387—891no—
881#387—891no—
882#387—891no—
883#387—891no—
884#387—891no—
885#387—891no—
886#387—891no—
887#387—891no—
888#387—891no—
889#387—891no—
890#387—891no—
891#387—891no—
892#387—891no—
893#387—891no—
894#386—891no—
895#386—891no—
896#386—891no—
897#386—891no—
898#386—891no—
899#386—891no—
900#385—891no—
901#385—891no—
902#385—891no—
903#385—891no—
904#385—891no—
905#385—891no—
906#385—891no—
907#385—891no—
908#385—891no—
909#385—891no—
910#385—891no—
911#385—891no—
912#385—891no—
913#385—891no—
914#385—891no—
915#385—891no—
916#385—891no—
917#385—891no—
918#385—891no—
919#385—891no—
920#385—891no—
921#385—891no—
922#385—891no—
923#385—891no—
924#385—891no—
925#385—891no—
926#385—891no—
927#385—891no—
928#385C2×D8911yescharacteristic
929#385C2×D8911yescharacteristic
930#384—891no—
931#384—891no—
932#384—891no—
933#383—891no—
934#383—891no—
935#382—891no—
936#382—891no—
937#382—891no—
938#382—891no—
939#381—891no—
940#381—891no—
941#381C2×D8911yescharacteristic
942#380—891no—
943#380—891no—
944#380—891no—
945#380C2×D8911yescharacteristic
946#379C2×D8911yescharacteristic
947C4×C4⋊C4—891no—
948C4×C4⋊C4—891no—
949C4×C4⋊C4—891no—
950C4×C4⋊C4—891no—
951C4×C22⋊C4—891no—
952C4×C22⋊C4—891no—
953C4×C22⋊C4—891no—
954C4×C22⋊C4—891no—
955C4×C22⋊C4—891no—
956C4×C22⋊C4—891no—
957C4×C22⋊C4—891no—
958C4×C22⋊C4—891no—
959C4×C22⋊C4—891no—
960C4×C22⋊C4C2×D8911yescharacteristic
961C4×C22⋊C4C2×D8911yescharacteristic
962C4×C22⋊C4C2×D8911yescharacteristic
963#376—891no—
964C2×#95—891no—
965C2×#95—891no—
966C2×#95—891no—
967C2×#95—891no—
968C25C22×D8911yescharacteristic
969C22×Q8—891no—
970C22×D4—891no—
971C22×D4—891no—
972C22×D4—891no—
973C23×C4—891no—
974C23×C4—891no—
975C23×C4—891no—
976C23×C4—891no—
977C23×C4—891no—
978C23×C4—891no—
979C23×C4—891no—
980C23×C4—891no—
981C23×C4—891no—
982C23×C4—891no—
983C23×C4—891no—
984C23×C4—891no—
985C23×C4—891no—
986C23×C4—3562no—
987C23×C4—3562no—
988C23×C4—3562no—
989C23×C4C22×D8911yescharacteristic
990C23×C4C22×D8911yescharacteristic
991C23×C4C22×D8911yescharacteristic
992C23×C4C22×D8911yescharacteristic
993#126—898no—
994#126—898no—
995#124—898no—
996#123—898no—
997#123—898no—
998#123—898no—
999C22⋊Q8—898no—
1000C22⋊Q8—898no—
1001#120—898no—
1002C4×Q8—3562no—
1003C4×D4—898no—
1004C4×D4—898no—
1005C4×D4—3562no—
1006C4×D4—3562no—
1007C4×D4—3562no—
1008C4×D4—3562no—
1009C4×D4—3562no—
1010#117—42no—
1011#117—898no—
1012#117—898no—
1013#117—3562no—
1014C2×C4⋊C4—891no—
1015C2×C4⋊C4—891no—
1016C2×C4⋊C4—891no—
1017C2×C4⋊C4—891no—
1018C2×C4⋊C4—891no—
1019C2×C4⋊C4—891no—
1020C2×C4⋊C4—891no—
1021C2×C4⋊C4—891no—
1022C2×C4⋊C4—891no—
1023C2×C4⋊C4—891no—
1024C2×C4⋊C4—891no—
1025C2×C4⋊C4—891no—
1026C2×C4⋊C4—891no—
1027C2×C4⋊C4—891no—
1028C2×C4⋊C4—891no—
1029C2×C4⋊C4—891no—
1030C2×C4⋊C4—891no—
1031C2×C4⋊C4—891no—
1032C2×C4⋊C4—891no—
1033C2×C4⋊C4—891no—
1034C2×C4⋊C4—891no—
1035C2×C4⋊C4—891no—
1036C2×C4⋊C4—891no—
1037C2×C4⋊C4—891no—
1038C2×C4⋊C4—891no—
1039C2×C4⋊C4—891no—
1040C2×C4⋊C4—891no—
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—3562no—
1049C2×C4⋊C4—3562no—
1050C2×C4⋊C4—3562no—
1051C2×C4⋊C4—3562no—
1052C2×C4⋊C4—3562no—
1053C2×C4⋊C4C22×D8911yescharacteristic
1054C2×C4⋊C4C22×D8911yescharacteristic
1055C2×C4⋊C4C22×D8911yescharacteristic
1056C2×C4⋊C4C22×D8911yescharacteristic
1057C2×C22⋊C4—42no—
1058C2×C22⋊C4—898no—
1059C2×C22⋊C4—891no—
1060C2×C22⋊C4—891no—
1061C2×C22⋊C4—891no—
1062C2×C22⋊C4—891no—
1063C2×C22⋊C4—891no—
1064C2×C22⋊C4—891no—
1065C2×C22⋊C4—891no—
1066C2×C22⋊C4—891no—
1067C2×C22⋊C4—891no—
1068C2×C22⋊C4—891no—
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—3562no—
1080C2×C22⋊C4C4×D8918yescomplemented
1081C2×C22⋊C4C22×D8911yescharacteristic
1082C2×C22⋊C4C22×D8911yescharacteristic
1083C2×C22⋊C4C22×D8911yescharacteristic
1084C2×C22⋊C4C22×D8911yescharacteristic
1085C2×C22⋊C4C22×D8911yescharacteristic
1086C2×C22⋊C4C22×D8911yescharacteristic
1087C2×C22⋊C4C22×D8911yescharacteristic
1088C2×C22⋊C4C22×D8911yescharacteristic
1089C2×C22⋊C4C22×D8911yescharacteristic
1090C2×C22⋊C4C22×D8911yescharacteristic
1091C2×C22⋊C4C22×D8911yescharacteristic
1092C2×C22⋊C4C22×D8911yescharacteristic
1093C2×C22⋊C4C22×D8911yescharacteristic
1094C2×C22⋊C4C22×D8911yescharacteristic
1095C2×C42—891no—
1096C2×C42—891no—
1097C2×C42—891no—
1098C2×C42—891no—
1099C2×C42—891no—
1100C2×C42—891no—
1101C2×C42—891no—
1102C2×C42—891no—
1103C2×C42—891no—
1104C2×C42—891no—
1105C2×C42—891no—
1106C2×C42—891no—
1107C2×C42—891no—
1108C2×C42C22×D8911yescharacteristic
1109C2×C42C22×D8911yescharacteristic
1110C2×C42C22×D8911yescharacteristic
1111C2×C42C22×D8911yescharacteristic
1112#95—891no—
1113#95—891no—
1114#95—891no—
1115#95—891no—
1116#95—891no—
1117#95—891no—
1118#95—891no—
1119#95—891no—
1120#95—891no—
1121#95—891no—
1122#95—891no—
1123#95—891no—
1124#95—891no—
1125#95—891no—
1126#95—891no—
1127#95—891no—
1128#95—891no—
1129#95—891no—
1130#95—891no—
1131#95—891no—
1132#95—891no—
1133#95—891no—
1134#95—891no—
1135#95—891no—
1136#95—891no—
1137#95—891no—
1138#95—891no—
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#95C22×D8911yescharacteristic
1149#95C22×D8911yescharacteristic
1150#95C22×D8911yescharacteristic
1151#95C22×D8911yescharacteristic
1152#95C22×D8911yescharacteristic
1153#95C22×D8911yescharacteristic
1154#95C22×D8911yescharacteristic
1155#95C22×D8911yescharacteristic
1156C24—22no—
1157C24—22no—
1158C24—22no—
1159C24—22no—
1160C24—41no—
1161C24—41no—
1162C24—891no—
1163C24C2×C4×D8914yes—
1164C24C23×D8911yescharacteristic
1165C24C23×D8911yescharacteristic
1166C24C23×D8911yescharacteristic
1167C2×Q8—894no—
1168C2×Q8—3561no—
1169C2×Q8—3561no—
1170C2×D4—894no—
1171C2×D4—894no—
1172C2×D4—894no—
1173C2×D4—3561no—
1174C2×D4—3561no—
1175C2×D4—1782no—
1176C2×D4—1782no—
1177C2×D4—1782no—
1178C2×D4—1782no—
1179C22×C4—22no—
1180C22×C4—22no—
1181C22×C4—22no—
1182C22×C4—22no—
1183C22×C4—41no—
1184C22×C4—41no—
1185C22×C4—41no—
1186C22×C4—41no—
1187C22×C4—41no—
1188C22×C4—41no—
1189C22×C4—894no—
1190C22×C4—894no—
1191C22×C4—891no—
1192C22×C4—891no—
1193C22×C4—891no—
1194C22×C4—891no—
1195C22×C4—891no—
1196C22×C4—891no—
1197C22×C4—891no—
1198C22×C4—891no—
1199C22×C4—894no—
1200C22×C4—891no—
1201C22×C4—891no—
1202C22×C4—891no—
1203C22×C4—891no—
1204C22×C4—891no—
1205C22×C4—891no—
1206C22×C4—891no—
1207C22×C4—3561no—
1208C22×C4—3561no—
1209C22×C4—3561no—
1210C22×C4—3561no—
1211C22×C4—3561no—
1212C22×C4—3561no—
1213C22×C4—3561no—
1214C22×C4—35616no—
1215C22×C4—3561no—
1216C22×C4—3561no—
1217C22×C4—3561no—
1218C22×C4—3561no—
1219C22×C4—3561no—
1220C22×C4—3561no—
1221C22×C4—3561no—
1222C22×C4—3561no—
1223C22×C4—3561no—
1224C22×C4—3561no—
1225C22×C4—3561no—
1226C22×C4—3561no—
1227C22×C4—3561no—
1228C22×C4—3561no—
1229C22×C4—3561no—
1230C22×C4—3561no—
1231C22×C4—3561no—
1232C22×C4—1782no—
1233C22×C4—1782no—
1234C22×C4—1782no—
1235C22×C4—1782no—
1236C22×C4—1782no—
1237C22×C4—1782no—
1238C22×C4—1782no—
1239C22×C4—1782no—
1240C22×C4—1782no—
1241C22×C4—1782no—
1242C22×C4—1782no—
1243C22×C4—1782no—
1244C22×C4C2×C4×D8914yes—
1245C22×C4C2×C4×D8914yes—
1246C22×C4C23×D8911yescharacteristic
1247C22×C4C23×D8911yescharacteristic
1248C22×C4C23×D8911yescharacteristic
1249C22×C4C23×D8911yescharacteristic
1250C22×C4C23×D8911yescharacteristic
1251C22×C4C23×D8911yescharacteristic
1252C22×C4C23×D8911yescharacteristic
1253C22×C4C23×D8911yescharacteristic
1254C22×C4C23×D8911yescharacteristic
1255C22×C4C23×D8911yescharacteristic
1256C22×C4C23×D8911yescharacteristic
1257C22×C4C23×D8911yescharacteristic
1258C4⋊C4—41no—
1259C4⋊C4—41no—
1260C4⋊C4—41no—
1261C4⋊C4—41no—
1262C4⋊C4—894no—
1263C4⋊C4—894no—
1264C4⋊C4—894no—
1265C4⋊C4—894no—
1266C4⋊C4—894no—
1267C4⋊C4—894no—
1268C4⋊C4—894no—
1269C4⋊C4—894no—
1270C4⋊C4—3561no—
1271C4⋊C4—3561no—
1272C4⋊C4—3561no—
1273C4⋊C4—3561no—
1274C4⋊C4—3561no—
1275C4⋊C4—3561no—
1276C4⋊C4—3561no—
1277C4⋊C4—3561no—
1278C4⋊C4—3561no—
1279C4⋊C4—3561no—
1280C4⋊C4—3561no—
1281C4⋊C4—3561no—
1282C4⋊C4—3561no—
1283C4⋊C4—3561no—
1284C4⋊C4—3561no—
1285C4⋊C4—3561no—
1286C4⋊C4—3561no—
1287C4⋊C4—3561no—
1288C4⋊C4—3561no—
1289C4⋊C4—3561no—
1290C4⋊C4—3561no—
1291C4⋊C4—3561no—
1292C4⋊C4—1782no—
1293C4⋊C4—1782no—
1294C4⋊C4—1782no—
1295C4⋊C4—1782no—
1296C22⋊C4—22no—
1297C22⋊C4—22no—
1298C22⋊C4—22no—
1299C22⋊C4—22no—
1300C22⋊C4—22no—
1301C22⋊C4—22no—
1302C22⋊C4—41no—
1303C22⋊C4—41no—
1304C22⋊C4—41no—
1305C22⋊C4—41no—
1306C22⋊C4—894no—
1307C22⋊C4—894no—
1308C22⋊C4—894no—
1309C22⋊C4—894no—
1310C22⋊C4—894no—
1311C22⋊C4—894no—
1312C22⋊C4—894no—
1313C22⋊C4—894no—
1314C22⋊C4—894no—
1315C22⋊C4—894no—
1316C22⋊C4—3561no—
1317C22⋊C4—3561no—
1318C22⋊C4—3561no—
1319C22⋊C4—3561no—
1320C22⋊C4—3561no—
1321C22⋊C4—3561no—
1322C22⋊C4—3561no—
1323C22⋊C4—3561no—
1324C22⋊C4—1782no—
1325C22⋊C4—1782no—
1326C22⋊C4C2×C4×D8914yes—
1327C22⋊C4C2×C4×D8914yes—
1328C22⋊C4C2×C4×D8914yes—
1329C22⋊C4C2×C4×D8914yes—
1330C42—41no—
1331C42—41no—
1332C42—41no—
1333C42—41no—
1334C42—894no—
1335C42—894no—
1336C42—894no—
1337C42—3561no—
1338C42—3561no—
1339C42—3561no—
1340C42—3561no—
1341C42—3561no—
1342C42—3561no—
1343C42—3561no—
1344C42—3561no—
1345C42—3561no—
1346C42—1782no—
1347C23—21no—
1348C23—21no—
1349C23—21no—
1350C23—21no—
1351C23—21no—
1352C23—21no—
1353C23—21no—
1354C23—21no—
1355C23—21no—
1356C23—21no—
1357C23—21no—
1358C23—21no—
1359C23—21no—
1360C23—21no—
1361C23—28no—
1362C23—28no—
1363C23—44no—
1364C23—44no—
1365C23—44no—
1366C23—44no—
1367C23—44no—
1368C23—892no—
1369C23—1781no—
1370C23—1781no—
1371C23—1781no—
1372C23—1781no—
1373C23—1781no—
1374C23—1781no—
1375C23C22×C4×D8912yes—
1376C23C22×C4×D8912yes—
1377C23C22×C4×D8912yes—
1378C23#1566805712yes—
1379C23#1566805812yes—
1380C23#1566805912yes—
1381C23#1566805912yes—
1382C23C24×D8911yescharacteristic
1383Q8—3564no—
1384D4—3564no—
1385D4—1788no—
1386D4—1788no—
1387C2×C4—21no—
1388C2×C4—21no—
1389C2×C4—21no—
1390C2×C4—21no—
1391C2×C4—21no—
1392C2×C4—21no—
1393C2×C4—21no—
1394C2×C4—21no—
1395C2×C4—28no—
1396C2×C4—21no—
1397C2×C4—21no—
1398C2×C4—21no—
1399C2×C4—21no—
1400C2×C4—21no—
1401C2×C4—21no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—21no—
1418C2×C4—21no—
1419C2×C4—21no—
1420C2×C4—44no—
1421C2×C4—82no—
1422C2×C4—82no—
1423C2×C4—892no—
1424C2×C4—892no—
1425C2×C4—892no—
1426C2×C4—892no—
1427C2×C4—892no—
1428C2×C4—892no—
1429C2×C4—892no—
1430C2×C4—892no—
1431C2×C4—3564no—
1432C2×C4—3564no—
1433C2×C4—3564no—
1434C2×C4—3564no—
1435C2×C4—3564no—
1436C2×C4—3564no—
1437C2×C4—3564no—
1438C2×C4—3564no—
1439C2×C4—1781no—
1440C2×C4—1781no—
1441C2×C4—1781no—
1442C2×C4—1781no—
1443C2×C4—1781no—
1444C2×C4—1781no—
1445C2×C4—1781no—
1446C2×C4—1781no—
1447C2×C4—1781no—
1448C2×C4—1781no—
1449C2×C4—1781no—
1450C2×C4—1781no—
1451C2×C4—1781no—
1452C2×C4—1781no—
1453C2×C4—1781no—
1454C2×C4—1781no—
1455C2×C4—1781no—
1456C2×C4—1781no—
1457C2×C4—1781no—
1458C2×C4—1781no—
1459C2×C4—1781no—
1460C2×C4—1781no—
1461C2×C4—1781no—
1462C2×C4—1781no—
1463C2×C4—1781no—
1464C2×C4—1781no—
1465C2×C4—1781no—
1466C2×C4—1781no—
1467C2×C4—1781no—
1468C2×C4—1781no—
1469C2×C4—1781no—
1470C2×C4—1781no—
1471C2×C4—1781no—
1472C2×C4—1781no—
1473C2×C4—1781no—
1474C2×C4—1781no—
1475C2×C4—1781no—
1476C2×C4—1788no—
1477C2×C4—7122no—
1478C2×C4—7122no—
1479C2×C4—7122no—
1480C2×C4—7122no—
1481C2×C4C22×C4×D8912yes—
1482C2×C4C22×C4×D8912yes—
1483C2×C4C22×C4×D8912yes—
1484C2×C4C22×C4×D8912yes—
1485C22—22no—
1486C22—22no—
1487C22—22no—
1488C22—22no—
1489C22—22no—
1490C22—22no—
1491C22—22no—
1492C22—22no—
1493C22—22no—
1494C22—22no—
1495C22—22no—
1496C22—22no—
1497C22—22no—
1498C22—22no—
1499C22—22no—
1500C22—416no—
1501C22—41no—
1502C22—41no—
1503C22—41no—
1504C22—41no—
1505C22—3561no—
1506C22—3561no—
1507C22—3561no—
1508C22—3561no—
1509C22—1782no—
1510C22—1782no—
1511C22—1782no—
1512C22#1915207714yes—
1513C22#1915207814yes—
1514C22C23×C4×D8911yescharacteristic
1515C22H(5,𝔽2)×D8911yescharacteristic
1516C22C2×#1566805711yescharacteristic
1517C22C2×#1566805811yescharacteristic
1518C22C2×#1566805911yescharacteristic
1519C22C2×#1566805911yescharacteristic
1520C22#1915243311yescharacteristic
1521C4—22no—
1522C4—22no—
1523C4—22no—
1524C4—22no—
1525C4—41no—
1526C4—41no—
1527C4—41no—
1528C4—41no—
1529C4—41no—
1530C4—41no—
1531C4—41no—
1532C4—41no—
1533C4—3561no—
1534C4—3561no—
1535C4—3561no—
1536C4—3561no—
1537C4—3561no—
1538C4—3561no—
1539C4—3561no—
1540C4—1782no—
1541C4—1782no—
1542C4—1782no—
1543C4—1782no—
1544C4—1782no—
1545C4—1782no—
1546C4—1782no—
1547C4—1782no—
1548C2—24no—
1549C2—24no—
1550C2—42no—
1551C2—3562no—
1552C2C2×#1915207711yescharacteristic
1553C2C2×#1915207811yescharacteristic
1554C2#2603345611yescharacteristic
1555C2#2603440111yescharacteristic
1556C2#2603444911yescharacteristic
1557C2#2603445711yescharacteristic
1558C2#2603449211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D89
commutatorC22×C89C24×C4
FittingC89×#2342C2
socle, cosocleC23×C89C25
prime radicalC2×#15667981C22
hypercenter#2342D89
hypocenterC89#34457
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ #2342

Complements

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

NH ≅ G/Ntype
2. #26023439C2semidirect
3. #26023439C2semidirect
4. #26023421C2semidirect
5. #26023394C2semidirect
6. #26023258C2semidirect
7. #26023255C2semidirect
8. #26023246C2semidirect
9. #26023244C2semidirect
11. #26023150C2semidirect
12. #26023148C2semidirect
13. #26023114C2semidirect
14. #26023110C2semidirect
15. #26023103C2semidirect
16. #26023034C2semidirect
17. #26023024C2semidirect
18. #26022982C2semidirect
19. #26022980C2semidirect
20. #26022961C2semidirect
21. #26022923C2semidirect
22. #26022922C2semidirect
23. #26022918C2semidirect
24. #26022880C2semidirect
25. #26022879C2semidirect
26. #26022872C2semidirect
27. #26022871C2semidirect
29. C2×#19151473C2semidirect
30. C2×#19151470C2semidirect
31. C89×#2342C2semidirect
33. #19152274C4semidirect
43. C2×C4×Dic178C22semidirect
58. C2×C4⋊C4×D89C22semidirect
61. #19151504C22semidirect
62. #19151502C22semidirect
63. #19151502C22semidirect
65. #19151496C22semidirect
66. #19151496C22semidirect
67. #19151496C22semidirect
68. #19151496C22semidirect
69. #19151496C22semidirect
70. #19151495C22semidirect
71. #19151495C22semidirect
72. #19151495C22semidirect
73. #19151495C22semidirect
74. #19151495C22semidirect
75. #19151495C22semidirect
76. #19151493C22semidirect
77. #19151493C22semidirect
78. #19151493C22semidirect
82. #19151490C22semidirect
83. #19151490C22semidirect
84. #19151489C22semidirect
85. #19151489C22semidirect
86. #19151489C22semidirect
87. #19151488C22semidirect
91. #19151485C22semidirect
92. #19151485C22semidirect
93. #19151485C22semidirect
94. #19151485C22semidirect
95. #19151483C22semidirect
96. #19151483C22semidirect
97. #19151483C22semidirect
98. #19151483C22semidirect
99. #19151482C22semidirect
100. #19151482C22semidirect
101. #19151482C22semidirect
102. #19151481C22semidirect
103. #19151481C22semidirect
104. #19151479C22semidirect
105. #19151479C22semidirect
106. #19151479C22semidirect
121. #19151472C22semidirect
122. #19151472C22semidirect
123. #19151472C22semidirect
124. #19151472C22semidirect
140. #19151469C22semidirect
141. #19151467C22semidirect
142. #19151467C22semidirect
143. #19151467C22semidirect
144. #19151465C22semidirect
145. #19151465C22semidirect
146. #19151463C22semidirect
147. #19151463C22semidirect
148. #19151462C22semidirect
149. #19151462C22semidirect
150. #19151460C22semidirect
152. #19151457C22semidirect
154. #19151455C22semidirect
155. C4⋊C4×Dic89C22semidirect
156. C4×#13083553C22semidirect
157. C4×C4⋊Dic89C22semidirect
158. #19151449C22semidirect
166. C4×#13083551C22semidirect
168. #19151443C22semidirect
208. #15668005C2×C4semidirect
209. #15668005C2×C4semidirect
210. #15667998C2×C4semidirect
211. #15667996C2×C4semidirect
212. #15667995C2×C4semidirect
213. #15667994C2×C4semidirect
214. #15667991C2×C4semidirect
215. #15667989C2×C4semidirect
219. C4×C22⋊D89C2×C4semidirect
224. #15667972C2×C4semidirect
225. #15667971C2×C4semidirect
227. #15667968C2×C4semidirect
268. C2×C22⋊Dic89C2×C4semidirect
349. C2×C22⋊C4×C89C2×C4semidirect
379. C2×Dic178C22×C4semidirect
443. C2×C4×D89C22×C4semidirect
452. C4⋊Dic89C22×C4semidirect
453. C4⋊Dic89C22×C4semidirect
454. C4⋊Dic89C22×C4semidirect
473. #13083553C22×C4semidirect
474. #13083553C22×C4semidirect
475. #13083553C22×C4semidirect
476. #13083553C22×C4semidirect
477. #13083553C22×C4semidirect
495. #13083551C22×C4semidirect
496. #13083551C22×C4semidirect
497. #13083551C22×C4semidirect
508. C4×Dic89C22×C4semidirect
509. C4×Dic89C22×C4semidirect
510. C4×Dic89C22×C4semidirect
795. #2342D89semidirect
811. C89#34457semidirect
1080. C2×C22⋊C4C4×D89semidirect

Maximal subgroups

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

subgroupindex
C2×#191522742
#260234392
#260234212
#260233942
#260232582
#260232552
#260232462
#260232442
#260232312
#260231502
#260231482
#260231142
#260231102
#260231032
#260230342
#260230242
#260229822
#260229802
#260229612
#260229232
#260229222
#260229182
#260228802
#260228792
#260228722
#260228712
#260227512
C2×#191514732
C2×#191514702
C89×#23422
#3445789