Finite Group Databasebeta

← #35173992

Subgroups — #35173992

Order 20224.

2044 conjugacy classes of subgroups.

The subgroup lattice has 1866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777054C211yesmaximal, characteristic, complemented
2#23775732C211yesmaximal, characteristic, complemented
3#23775647C211yesmaximal, characteristic, complemented
4#23775520C211yesmaximal, characteristic, complemented
5#23775505C211yesmaximal, characteristic, complemented
6#23775460C211yesmaximal, characteristic, complemented
7#23775400C211yesmaximal, characteristic, complemented
8#23775333C211yesmaximal, characteristic, complemented
9#23775281C211yesmaximal, characteristic, complemented
10#23775137C211yesmaximal, characteristic, complemented
11#23775126C211yesmaximal, characteristic, complemented
12#23775062C211yesmaximal, characteristic, complemented
13#23775053C211yesmaximal, characteristic, complemented
14#23774986C211yesmaximal, characteristic, complemented
15#23774986C211yesmaximal, characteristic, complemented
16#23774971C211yesmaximal, characteristic, complemented
17#23774951C211yesmaximal, characteristic, complemented
18#23774488C211yesmaximal, characteristic, complemented
19#23774466C211yesmaximal, characteristic, complemented
20#23774267C211yesmaximal, characteristic, complemented
21#23774246C211yesmaximal, characteristic, complemented
22#23774237C211yesmaximal, characteristic, complemented
23#23774181C211yesmaximal, characteristic, complemented
24#23773695C211yesmaximal, characteristic, complemented
25#23773623C211yesmaximal, characteristic, complemented
26#23772712C211yesmaximal, characteristic, complemented
27#23772693C211yesmaximal, characteristic, complemented
28#23772658C211yesmaximal, characteristic, complemented
29#23772616C211yesmaximal, characteristic, complemented
30#23772448C211yesmaximal, characteristic, complemented
31C79×#3541C211yesmaximal, characteristic, complemented
32C2×#14579208C2211yescharacteristic
33C22×#11929624C2211yescharacteristic
34C2×#14579192C2211yescharacteristic
35C2×#14579192C2211yescharacteristic
36C2×#14579192C2211yescharacteristic, complemented
37C2×#14579191C2211yescharacteristic, complemented
38C2×#14579181C2211yescharacteristic
39C2×#14579181C2211yescharacteristic
40C2×#14579181C2211yescharacteristic, complemented
41C22×#11929614C2211yescharacteristic, complemented
42#19099234C2211yescharacteristic
43#19099234C2211yescharacteristic
44#19099234C2211yescharacteristic
45#19099234C2211yescharacteristic
46#19099231—21no—
47#19099231—21no—
48#19099223—21no—
49#19099223—21no—
50#19099222C2211yescharacteristic
51#19099222C2211yescharacteristic
52#19099222C2211yescharacteristic
53#19099222C2211yescharacteristic
54#19099132C2211yescharacteristic
55#19099128—21no—
56#19099128—21no—
57#19099127C2211yescharacteristic
58#19099074C2211yescharacteristic
59#19099071—21no—
60#19099071—21no—
61#19099040C2211yescharacteristic
62#19098955C2211yescharacteristic, complemented
63#19098953C2211yescharacteristic, complemented
64#19098945C2211yescharacteristic, complemented
65#19098937C2211yescharacteristic, complemented
66#19098929C2211yescharacteristic, complemented
67#19098925C2211yescharacteristic, complemented
68#19098920C2211yescharacteristic, complemented
69#19098911C2211yescharacteristic, complemented
70#19098904C2211yescharacteristic, complemented
71#19098901C2211yescharacteristic
72#19098901C2211yescharacteristic
73#19098901C2211yescharacteristic
74#19098893C2211yescharacteristic, complemented
75#19098887C2211yescharacteristic, complemented
76#19098887C2211yescharacteristic, complemented
77#19098887C2211yescharacteristic, complemented
78#19098884C2211yescharacteristic
79#19098881C2211yescharacteristic, complemented
80#19098876C2211yescharacteristic, complemented
81#19098876C2211yescharacteristic, complemented
82#19098867C2211yescharacteristic, complemented
83#19098867C2211yescharacteristic, complemented
84#19098855C2211yescharacteristic, complemented
85#19098845C2211yescharacteristic, complemented
86#19098819C2211yescharacteristic, complemented
87#19098814C2211yescharacteristic, complemented
88#19098814C2211yescharacteristic, complemented
89#19098811C2211yescharacteristic, complemented
90#19098811C2211yescharacteristic, complemented
91#19098811C2211yescharacteristic, complemented
92#19098811C2211yescharacteristic, complemented
93#19098807C2211yescharacteristic, complemented
94#19098802C2211yescharacteristic, complemented
95#19098802C2211yescharacteristic, complemented
96#19098797C2211yescharacteristic, complemented
97#19098794C2211yescharacteristic, complemented
98#19098794C2211yescharacteristic, complemented
99#19098794C2211yescharacteristic, complemented
100#19098794C2211yescharacteristic, complemented
101#19098794C2211yescharacteristic, complemented
102#19098785C2211yescharacteristic, complemented
103#19098785C2211yescharacteristic, complemented
104#19098785C2211yescharacteristic, complemented
105#19098782C2211yescharacteristic, complemented
106#19098782C2211yescharacteristic, complemented
107#19098778C2211yescharacteristic, complemented
108#19098770C2211yescharacteristic, complemented
109#19098770C2211yescharacteristic, complemented
110#19098763C2211yescharacteristic, complemented
111#19098763C2211yescharacteristic, complemented
112#19098763C2211yescharacteristic, complemented
113#19098758C2211yescharacteristic, complemented
114#19098725C2211yescharacteristic, complemented
115#19098723C2211yescharacteristic
116#19098723C2211yescharacteristic
117#19098723C2211yescharacteristic
118#19098723C2211yescharacteristic
119#19098723C2211yescharacteristic
120#19098723C2211yescharacteristic
121#19098723C2211yescharacteristic
122#19098723C2211yescharacteristic
123#19098723C2211yescharacteristic
124#19098723C2211yescharacteristic, complemented
125#19098723C2211yescharacteristic, complemented
126#19098723C2211yescharacteristic, complemented
127#19098719C2211yescharacteristic, complemented
128#19098718C2211yescharacteristic
129#19098718C2211yescharacteristic
130#19098718C2211yescharacteristic
131#19098718C2211yescharacteristic, complemented
132#19098718C2211yescharacteristic, complemented
133#19098718C2211yescharacteristic, complemented
134#19098713C2211yescharacteristic
135#19098713C2211yescharacteristic
136#19098713C2211yescharacteristic
137#19098708C2211yescharacteristic, complemented
138#19098708C2211yescharacteristic, complemented
139#19098708C2211yescharacteristic, complemented
140#19098706C2211yescharacteristic
141#19098706C2211yescharacteristic
142#19098706C2211yescharacteristic
143#19098706C2211yescharacteristic, complemented
144#19098702C2211yescharacteristic, complemented
145#19098702C2211yescharacteristic, complemented
146#19098702C2211yescharacteristic, complemented
147#19098701C2211yescharacteristic
148#19098701C2211yescharacteristic, complemented
149#19098696C2211yescharacteristic
150#19098668C2211yescharacteristic, complemented
151#19098668C2211yescharacteristic, complemented
152#19098668C2211yescharacteristic, complemented
153#19098663C2211yescharacteristic, complemented
154C4×#11929614C2211yescharacteristic, complemented
155C4×#11929614C2211yescharacteristic, complemented
156C4×#11929614C2211yescharacteristic, complemented
157C4×#11929612C2211yescharacteristic, complemented
158#19098641C2211yescharacteristic, complemented
159#19098641C2211yescharacteristic, complemented
160#19098635C2211yescharacteristic, complemented
161#19098635C2211yescharacteristic, complemented
162#19098635C2211yescharacteristic, complemented
163#19098635C2211yescharacteristic, complemented
164D4×C79⋊C8C2211yescharacteristic, complemented
165D4×C79⋊C8C2211yescharacteristic, complemented
166#19098624C2211yescharacteristic
167#19098624C2211yescharacteristic
168#19098571C2211yescharacteristic, complemented
169#19098562C2211yescharacteristic
170#19098562C2211yescharacteristic
171#19098562C2211yescharacteristic, complemented
172#19098557C2211yescharacteristic
173#19098557C2211yescharacteristic
174#19098557C2211yescharacteristic, complemented
175C2×#14579084C2211yescharacteristic, complemented
176#19098530C2211yescharacteristic
177#19098530C2211yescharacteristic
178#19098527C2211yescharacteristic
179C2×C22⋊(C79⋊C8)C2211yescharacteristic
180#563×C79—21no—
181#562×C79—21no—
182#556×C79C2211yescharacteristic, complemented
183#554×C79—21no—
184#554×C79C2211yescharacteristic, complemented
185#553×C79—21no—
186#553×C79C2211yescharacteristic, complemented
187#552×C79C2211yescharacteristic, complemented
188D4×Q8×C79C2211yescharacteristic, complemented
189#548×C79C2211yescharacteristic, complemented
190#548×C79C2211yescharacteristic, complemented
191#547×C79C2211yescharacteristic, complemented
192#542×C79—21no—
193#542×C79C2211yescharacteristic
194#541×C79C2211yescharacteristic
195#539×C79—21no—
196#538×C79—21no—
197#538×C79—21no—
198#537×C79C2211yescharacteristic
199#536×C79C2211yescharacteristic
200#525×C79C2211yescharacteristic
201#525×C79C2211yescharacteristic
202C2×C22⋊Q8×C79C2211yescharacteristic
203#14579208—42no—
204#14579208—42no—
205C2×#11929624—21no—
206C2×#11929624—21no—
207C2×#11929624—42no—
208C2×#11929624—42no—
209C2×#11929624C2311yescharacteristic
210C2×#11929624C2311yescharacteristic
211C2×#11929624C2311yescharacteristic
212C2×#11929624C2311yescharacteristic
213C2×#11929624C2311yescharacteristic
214C2×#11929624C2311yescharacteristic
215C2×#11929624C2311yescharacteristic
216C2×#11929623—21no—
217C2×#11929623—21no—
218C2×#11929623—21no—
219C22×Dic158C2311yescharacteristic
220C22×Dic158C2311yescharacteristic
221C22×Dic158C2311yescharacteristic
222C2×Q8×D79—21no—
223C22×D316C2311yescharacteristic
224C22×C22⋊D79—21no—
225C22×C4×D79—21no—
226#14579192—42no—
227#14579192—42no—
228#14579192—42no—
229#14579191—42no—
230#14579181—42no—
231#14579181—42no—
232#14579181—42no—
233C2×#11929614—42no—
234C2×#11929614C2311yescharacteristic
235C2×#11929614C2311yescharacteristic
236C2×#11929614C2311yescharacteristic
237C2×#11929614C2311yescharacteristic
238C2×#11929614C2311yescharacteristic
239C2×#11929614C2311yescharacteristic
240C2×#11929614C2311yescharacteristic
241C2×#11929614C2311yescharacteristic
242C2×#11929614C2311yescharacteristic
243C2×#11929612C2311yescharacteristic
244C2×#11929612C2311yescharacteristic
245C2×#11929612C2311yescharacteristic
246C2×#11929611C2311yescharacteristic
247C2×#11929611C2311yescharacteristic
248C2×#11929611C2311yescharacteristic
249C2×#11929611C2311yescharacteristic
250C2×#11929611C2311yescharacteristic
251C2×#11929611C2311yescharacteristic
252C2×#11929611C2311yescharacteristic
253C2×#11929611C2311yescharacteristic
254C2×#11929611C2311yescharacteristic
255C2×#11929609C2311yescharacteristic
256C2×#11929609C2311yescharacteristic
257C2×#11929609C2311yescharacteristic
258C2×#11929608C2311yescharacteristic
259C2×#11929608C2311yescharacteristic
260C2×#11929608C2311yescharacteristic
261C2×#11929608C2311yescharacteristic
262C22×C79⋊C8C2311yescharacteristic
263C22×C79⋊C8C2311yescharacteristic
264C22×C79⋊C8C2311yescharacteristic
265C22×C79⋊C8C2311yescharacteristic
266#14579158C2311yescharacteristic
267#14579158C2311yescharacteristic
268#14579157—21no—
269#14579157—21no—
270#14579157—21no—
271#14579157—21no—
272#14579157—21no—
273#14579150—21no—
274#14579149C2311yescharacteristic
275#14579149C2311yescharacteristic
276#14579147—21no—
277#14579147—21no—
278#14579147—21no—
279#14579147—21no—
280#14579144—21no—
281#14579140C2311yescharacteristic
282#14579140C2311yescharacteristic
283#14579139—21no—
284#14579139—21no—
285#14579139—21no—
286#14579139—21no—
287#14579136—21no—
288#14579136—21no—
289#14579135C2311yescharacteristic
290#14579135C2311yescharacteristic
291#14579135C2311yescharacteristic
292#14579135C2311yescharacteristic
293#14579135C2311yescharacteristic
294#14579135C2311yescharacteristic
295#14579134—21no—
296#14579134—21no—
297#14579134—21no—
298#14579134—21no—
299#14579134—21no—
300#14579134—21no—
301#14579134—21no—
302#14579134—21no—
303#14579133—21no—
304#14579133—21no—
305#14579133—21no—
306#14579133—21no—
307#14579131—21no—
308#14579131—21no—
309#14579130—21no—
310#14579129—21no—
311#14579129—21no—
312C4×Dic158C2311yescharacteristic
313C4×Dic158C2311yescharacteristic
314C4×Dic158C2311yescharacteristic
315C4×Dic158C2311yescharacteristic
316#14579126—21no—
317#14579126—21no—
318#14579123—21no—
319#14579123—21no—
320#14579123—21no—
321#14579123—21no—
322C4×C22⋊D79—21no—
323C4×C22⋊D79—21no—
324(C22⋊D79)⋊C4—21no—
325(C22⋊D79)⋊C4—21no—
326(C22⋊D79)⋊C4—21no—
327(C22⋊D79)⋊C4—21no—
328#14579120C2311yescharacteristic
329#14579117—21no—
330#14579117—21no—
331#14579094C2311yescharacteristic
332#14579094C2311yescharacteristic
333#14579094C2311yescharacteristic
334#14579094C2311yescharacteristic
335#14579092C2311yescharacteristic
336#14579092C2311yescharacteristic
337#14579092C2311yescharacteristic
338#14579092C2311yescharacteristic
339C4⋊(C79⋊C8)C2311yescharacteristic
340C4⋊(C79⋊C8)C2311yescharacteristic
341C4⋊(C79⋊C8)C2311yescharacteristic
342C4⋊(C79⋊C8)C2311yescharacteristic
343#14579085C2311yescharacteristic
344#14579085C2311yescharacteristic
345#14579085C2311yescharacteristic
346#14579085C2311yescharacteristic
347#14579085C2311yescharacteristic
348#14579085C2311yescharacteristic
349#14579084C2311yescharacteristic
350#14579084C2311yescharacteristic
351#14579084C2311yescharacteristic
352#14579084C2311yescharacteristic
353#14579084C2311yescharacteristic
354#14579084C2311yescharacteristic
355#14579084C2311yescharacteristic
356#14579084C2311yescharacteristic
357#14579084C2311yescharacteristic
358#14579084C2311yescharacteristic
359#14579084C2311yescharacteristic
360#14579084C2311yescharacteristic
361#14579082C2311yescharacteristic
362#14579082C2311yescharacteristic
363#14579081C2311yescharacteristic
364#14579081C2311yescharacteristic
365#14579081C2311yescharacteristic
366#14579081C2311yescharacteristic
367#14579081C2311yescharacteristic
368#14579081C2311yescharacteristic
369#14579081C2311yescharacteristic
370#14579081C2311yescharacteristic
371#14579081C2311yescharacteristic
372#14579081C2311yescharacteristic
373#14579081C2311yescharacteristic
374#14579081C2311yescharacteristic
375C22⋊(C79⋊C8)C2311yescharacteristic
376C22⋊(C79⋊C8)C2311yescharacteristic
377C22⋊(C79⋊C8)C2311yescharacteristic
378C22⋊(C79⋊C8)C2311yescharacteristic
379C22⋊(C79⋊C8)C2311yescharacteristic
380C22⋊(C79⋊C8)C2311yescharacteristic
381C22⋊(C79⋊C8)C2311yescharacteristic
382C22⋊(C79⋊C8)C2311yescharacteristic
383C22⋊(C79⋊C8)C2311yescharacteristic
384C22⋊(C79⋊C8)C2311yescharacteristic
385C22⋊(C79⋊C8)C2311yescharacteristic
386C22⋊(C79⋊C8)C2311yescharacteristic
387#14579072C2311yescharacteristic
388#14579072C2311yescharacteristic
389C4×C79⋊C8C2311yescharacteristic
390C4×C79⋊C8C2311yescharacteristic
391C2×#41×C79C2311yescharacteristic
392C2×#41×C79C2311yescharacteristic
393C2×#41×C79C2311yescharacteristic
394C22×Q8×C79C2311yescharacteristic
395C22×Q8×C79C2311yescharacteristic
396C23×C4×C79C2311yescharacteristic
397C4⋊Q8×C79—21no—
398C4⋊Q8×C79—21no—
399C4⋊Q8×C79C2311yescharacteristic
400C4⋊Q8×C79C2311yescharacteristic
401#126×C79—21no—
402#126×C79—21no—
403#126×C79—21no—
404#126×C79—21no—
405#126×C79—21no—
406#126×C79—21no—
407#126×C79—21no—
408#125×C79—21no—
409#125×C79—21no—
410#125×C79—21no—
411#125×C79—21no—
412#125×C79C2311yescharacteristic
413#124×C79—21no—
414#124×C79—21no—
415#124×C79—21no—
416#124×C79—21no—
417#124×C79—21no—
418#124×C79C2311yescharacteristic
419#123×C79—21no—
420#123×C79—21no—
421#123×C79—21no—
422#123×C79—21no—
423#123×C79—21no—
424#123×C79—21no—
425#123×C79—21no—
426#123×C79—21no—
427#123×C79D411yescharacteristic
428#123×C79D411yescharacteristic
429C22⋊Q8×C79—21no—
430C22⋊Q8×C79—21no—
431C22⋊Q8×C79—21no—
432C22⋊Q8×C79—21no—
433C22⋊Q8×C79—21no—
434C22⋊Q8×C79—21no—
435C22⋊Q8×C79—21no—
436C22⋊Q8×C79—21no—
437C22⋊Q8×C79—21no—
438C22⋊Q8×C79—21no—
439C22⋊Q8×C79D411yescharacteristic
440C22⋊Q8×C79D411yescharacteristic
441C22⋊Q8×C79C2311yescharacteristic
442C22⋊Q8×C79C2311yescharacteristic
443C22⋊Q8×C79C2311yescharacteristic
444C22⋊Q8×C79C2311yescharacteristic
445C22⋊Q8×C79C2311yescharacteristic
446C22⋊Q8×C79C2311yescharacteristic
447C22⋊Q8×C79C2311yescharacteristic
448C22⋊Q8×C79C2311yescharacteristic
449C22⋊Q8×C79C2311yescharacteristic
450#121×C79—21no—
451#121×C79—21no—
452#121×C79—21no—
453#121×C79—21no—
454#121×C79—21no—
455#121×C79—21no—
456#121×C79—21no—
457#121×C79D411yescharacteristic
458#121×C79D411yescharacteristic
459#121×C79C2311yescharacteristic
460#121×C79C2311yescharacteristic
461#121×C79C2311yescharacteristic
462#120×C79—21no—
463#120×C79D411yescharacteristic
464#120×C79D411yescharacteristic
465C4×Q8×C79—21no—
466C4×Q8×C79C2311yescharacteristic
467C4×Q8×C79C2311yescharacteristic
468C4×Q8×C79C2311yescharacteristic
469C4×D4×C79—21no—
470C4×D4×C79—21no—
471C4×D4×C79—21no—
472C4×D4×C79—21no—
473C4×D4×C79—21no—
474C4×D4×C79—21no—
475C4×D4×C79—21no—
476C4×D4×C79C2311yescharacteristic
477C4×D4×C79C2311yescharacteristic
478C4×D4×C79C2311yescharacteristic
479C4×D4×C79C2311yescharacteristic
480C4×D4×C79C2311yescharacteristic
481#117×C79—21no—
482#117×C79C2311yescharacteristic
483#117×C79C2311yescharacteristic
484#117×C79C2311yescharacteristic
485C2×C4⋊C4×C79—21no—
486C2×C4⋊C4×C79—21no—
487C2×C4⋊C4×C79C2311yescharacteristic
488C2×C4⋊C4×C79C2311yescharacteristic
489C2×C22⋊C4×C79—21no—
490C23×D79—21no—
491#11929624—22no—
492#11929624—22no—
493#11929624—22no—
494#11929624—22no—
495#11929624—22no—
496#11929624—22no—
497#11929624—41no—
498#11929624—41no—
499#11929624—41no—
500#11929624—41no—
501#11929624—41no—
502#11929624—41no—
503#11929624—41no—
504#11929624—41no—
505#11929624—44no—
506#11929624—44no—
507#11929623—44no—
508#11929623—44no—
509#11929623—44no—
510C2×Dic158—22no—
511C2×Dic158—22no—
512C2×Dic158—22no—
513C2×Dic158—22no—
514C2×Dic158—21no—
515C2×Dic158—21no—
516C2×Dic158—21no—
517C2×Dic158—41no—
518C2×Dic158—41no—
519C2×Dic158C2411yescharacteristic
520C2×Dic158C2411yescharacteristic
521C2×Dic158C2411yescharacteristic
522Q8×D79—44no—
523C2×D316—21no—
524C2×D316—21no—
525C2×D316—21no—
526C2×D316—21no—
527C2×D316—21no—
528C2×D316—41no—
529C2×D316—41no—
530C2×D316C2411yescharacteristic
531C2×D316C2411yescharacteristic
532C2×D316C2411yescharacteristic
533C2×C22⋊D79—21no—
534C2×C22⋊D79—21no—
535C2×C22⋊D79—21no—
536C2×C22⋊D79—21no—
537C2×C22⋊D79—21no—
538C2×C22⋊D79—21no—
539C2×C22⋊D79—21no—
540C2×C22⋊D79—21no—
541C2×C22⋊D79—21no—
542C2×C22⋊D79—21no—
543C2×C22⋊D79—21no—
544C2×C22⋊D79—21no—
545C2×C22⋊D79—21no—
546C2×C22⋊D79—44no—
547C22×Dic79—21no—
548C22×Dic79—21no—
549C22×Dic79—21no—
550C2×C4×D79—21no—
551C2×C4×D79—21no—
552C2×C4×D79—21no—
553C2×C4×D79—21no—
554C2×C4×D79—21no—
555C2×C4×D79—21no—
556C2×C4×D79—21no—
557C2×C4×D79—44no—
558#11929614—22no—
559#11929614—22no—
560#11929614—22no—
561#11929614—22no—
562#11929614—22no—
563#11929614—22no—
564#11929614—41no—
565#11929614—41no—
566#11929614—41no—
567#11929612—22no—
568#11929612—22no—
569#11929612—41no—
570#11929611—41no—
571#11929611—41no—
572#11929611—41no—
573#11929611—41no—
574#11929611—41no—
575#11929611—41no—
576#11929611—41no—
577#11929611—41no—
578#11929611—41no—
579#11929609—41no—
580#11929609—41no—
581#11929609—41no—
582#11929608—41no—
583#11929608—41no—
584#11929608—41no—
585#11929608—41no—
586C2×C79⋊C8—41no—
587C2×C79⋊C8—41no—
588C2×C79⋊C8—41no—
589C2×C79⋊C8—41no—
590C2×C79⋊C8C2411yescharacteristic
591C2×C79⋊C8C2411yescharacteristic
592C2×C79⋊C8C2411yescharacteristic
593C2×C79⋊C8C2411yescharacteristic
594C2×C79⋊C8C2411yescharacteristic
595C2×C79⋊C8C2411yescharacteristic
596C2×C79⋊C8C2411yescharacteristic
597C2×C79⋊C8C2411yescharacteristic
598C4⋊Dic79C2411yescharacteristic
599C4⋊Dic79C2411yescharacteristic
600Dic79⋊C4—21no—
601Dic79⋊C4—21no—
602Dic79⋊C4—21no—
603Dic79⋊C4—21no—
604Dic79⋊C4—21no—
605Dic79⋊C4—21no—
606C22⋊Dic79—21no—
607C22⋊Dic79—21no—
608C22⋊Dic79—21no—
609(C2×D79)⋊C4—21no—
610(C2×D79)⋊C4—21no—
611(C2×D79)⋊C4—21no—
612(C2×D79)⋊C4—21no—
613(C2×D79)⋊C4—21no—
614(C2×D79)⋊C4—21no—
615(C2×D79)⋊C4—21no—
616(C2×D79)⋊C4—21no—
617(C2×D79)⋊C4—21no—
618(C2×D79)⋊C4—21no—
619C4×Dic79—21no—
620C4×Dic79—21no—
621C4×Dic79—21no—
622C4×Dic79—21no—
623C4×Dic79—21no—
624C24×C79C2×D411yescharacteristic
625#41×C79—41no—
626#41×C79—41no—
627#41×C79—41no—
628#41×C79—41no—
629#41×C79—41no—
630#41×C79—41no—
631C2×Q8×C79—21no—
632C2×Q8×C79—21no—
633C2×Q8×C79—21no—
634C2×Q8×C79—41no—
635C2×Q8×C79—41no—
636C2×Q8×C79—41no—
637C2×Q8×C79—41no—
638C2×Q8×C79C2×D411yescharacteristic
639C2×Q8×C79C2411yescharacteristic
640C2×Q8×C79C2411yescharacteristic
641C2×Q8×C79C2411yescharacteristic
642C2×D4×C79—21no—
643C2×D4×C79—21no—
644C2×D4×C79—21no—
645C2×D4×C79—21no—
646C2×D4×C79—21no—
647C2×D4×C79C2×D411yescharacteristic
648C2×D4×C79C2×D411yescharacteristic
649C2×D4×C79C2×D411yescharacteristic
650C2×D4×C79C2×D411yescharacteristic
651C2×D4×C79C2×D411yescharacteristic
652C2×D4×C79C2×D411yescharacteristic
653C2×D4×C79C2×D411yescharacteristic
654C2×D4×C79C2411yescharacteristic
655C22×C4×C79—21no—
656C22×C4×C79—21no—
657C22×C4×C79—21no—
658C22×C4×C79—21no—
659C22×C4×C79—21no—
660C22×C4×C79—21no—
661C22×C4×C79—21no—
662C22×C4×C79—41no—
663C22×C4×C79—41no—
664C22×C4×C79C2×D411yescharacteristic
665C22×C4×C79C2×D411yescharacteristic
666C22×C4×C79C2×D411yescharacteristic
667C22×C4×C79C2411yescharacteristic
668C22×C4×C79C2411yescharacteristic
669C22×C4×C79C2411yescharacteristic
670C22×C4×C79C2411yescharacteristic
671C22×C4×C79C2411yescharacteristic
672C4⋊C4×C79—21no—
673C4⋊C4×C79—21no—
674C4⋊C4×C79—21no—
675C4⋊C4×C79—21no—
676C4⋊C4×C79—21no—
677C4⋊C4×C79—21no—
678C4⋊C4×C79—21no—
679C4⋊C4×C79—21no—
680C4⋊C4×C79—21no—
681C4⋊C4×C79—21no—
682C4⋊C4×C79—21no—
683C4⋊C4×C79—21no—
684C4⋊C4×C79—21no—
685C4⋊C4×C79—21no—
686C4⋊C4×C79—21no—
687C4⋊C4×C79—21no—
688C4⋊C4×C79—21no—
689C4⋊C4×C79—21no—
690C4⋊C4×C79—21no—
691C4⋊C4×C79C2×D411yescharacteristic
692C4⋊C4×C79C2×D411yescharacteristic
693C4⋊C4×C79C2×D411yescharacteristic
694C4⋊C4×C79C2×D411yescharacteristic
695C4⋊C4×C79C2×D411yescharacteristic
696C4⋊C4×C79C2×D411yescharacteristic
697C4⋊C4×C79C2411yescharacteristic
698C4⋊C4×C79C2411yescharacteristic
699C4⋊C4×C79C2411yescharacteristic
700C4⋊C4×C79C2411yescharacteristic
701C22⋊C4×C79—21no—
702C22⋊C4×C79—21no—
703C22⋊C4×C79—21no—
704C22⋊C4×C79—21no—
705C22⋊C4×C79—21no—
706C22⋊C4×C79—21no—
707C22⋊C4×C79—21no—
708C22⋊C4×C79—21no—
709C22⋊C4×C79—21no—
710C22⋊C4×C79—21no—
711C22⋊C4×C79—21no—
712C22⋊C4×C79—21no—
713C22⋊C4×C79—21no—
714C22⋊C4×C79—21no—
715C22⋊C4×C79—21no—
716C22⋊C4×C79—21no—
717C22⋊C4×C79—21no—
718C22⋊C4×C79C2×D411yescharacteristic
719C22⋊C4×C79C2×D411yescharacteristic
720C22⋊C4×C79C2×D411yescharacteristic
721C22⋊C4×C79C2×D411yescharacteristic
722C22⋊C4×C79C2×D411yescharacteristic
723C22⋊C4×C79C2×D411yescharacteristic
724C22⋊C4×C79C2×D411yescharacteristic
725C22⋊C4×C79C2×D411yescharacteristic
726C22⋊C4×C79C2×D411yescharacteristic
727C22⋊C4×C79C2×D411yescharacteristic
728C42×C79—21no—
729C42×C79—21no—
730C42×C79—21no—
731C42×C79—21no—
732C42×C79—21no—
733C42×C79C2411yescharacteristic
734C42×C79C2411yescharacteristic
735C23×C79—21no—
736C23×C79—41no—
737C23×C79—41no—
738C23×C79—41no—
739C23×C79C22×D411yescharacteristic
740C23×C79C22×D411yescharacteristic
741C23×C79C22×D411yescharacteristic
742C23×C79C22×D411yescharacteristic
743C23×C79C22×D411yescharacteristic
744C22×D79—21no—
745C22×D79—21no—
746C22×D79—21no—
747C22×D79—42no—
748C22×D79—81no—
749C22×D79—81no—
750Q8×C79—21no—
751Q8×C79—21no—
752Q8×C79—21no—
753Q8×C79—21no—
754Q8×C79—21no—
755Q8×C79—21no—
756Q8×C79—41no—
757Q8×C79—81no—
758Q8×C79—81no—
759Q8×C79—81no—
760D4×C79—21no—
761D4×C79—21no—
762D4×C79—41no—
763D4×C79—41no—
764D4×C79—41no—
765D4×C79—41no—
766D4×C79—41no—
767D4×C79—41no—
768D4×C79—41no—
769D4×C79—42no—
770D4×C79—81no—
771D4×C79—81no—
772D4×C79—81no—
773D4×C79—81no—
774C2×C4×C79—21no—
775C2×C4×C79—21no—
776C2×C4×C79—21no—
777C2×C4×C79—21no—
778C2×C4×C79—21no—
779C2×C4×C79—21no—
780C2×C4×C79—21no—
781C2×C4×C79—21no—
782C2×C4×C79—21no—
783C2×C4×C79—21no—
784C2×C4×C79—21no—
785C2×C4×C79—21no—
786C2×C4×C79—21no—
787C2×C4×C79—21no—
788C2×C4×C79—21no—
789C2×C4×C79—21no—
790C2×C4×C79—21no—
791C2×C4×C79—41no—
792C2×C4×C79—41no—
793C2×C4×C79—41no—
794C2×C4×C79—81no—
795C2×C4×C79—81no—
796C2×C4×C79—81no—
797C2×C4×C79—81no—
798C2×C4×C79—81no—
799C2×C4×C79—81no—
800C2×C4×C79—81no—
801C2×C4×C79C22×D411yescharacteristic
802C2×C4×C79C22×D411yescharacteristic
803C2×C4×C79C22×D411yescharacteristic
804C2×C4×C79C22×D411yescharacteristic
805C2×C4×C79C22×D411yescharacteristic
806C2×C4×C79C22×D411yescharacteristic
807C2×C4×C79C22×D411yescharacteristic
808C2×C4×C79C22×D411yescharacteristic
809C2×C4×C79C22×D411yescharacteristic
810C2×C4×C79C2511yescharacteristic
811C22⋊D79—42no—
812C22⋊D79—42no—
813C22⋊D79—42no—
814C22⋊D79—42no—
815C22⋊D79—42no—
816C22⋊D79—42no—
817C22⋊D79—42no—
818C22⋊D79—81no—
819C22⋊D79—81no—
820C22⋊D79—81no—
821C22⋊D79—81no—
822C22⋊D79—81no—
823C22⋊D79—81no—
824C2×Dic79—24no—
825C2×Dic79—21no—
826C2×Dic79—21no—
827C2×Dic79—21no—
828C2×Dic79—21no—
829C2×Dic79—21no—
830C2×Dic79—42no—
831C2×Dic79—42no—
832D316—21no—
833D316—21no—
834D316—21no—
835D316—21no—
836D316—21no—
837D316—21no—
838D316—42no—
839D316—81no—
840D316—81no—
841D316—81no—
842D316—81no—
843C4×D79—42no—
844C4×D79—42no—
845C4×D79—42no—
846C4×D79—42no—
847C4×D79—42no—
848C4×D79—42no—
849C4×D79—42no—
850Dic158—24no—
851Dic158—21no—
852Dic158—21no—
853Dic158—21no—
854Dic158—21no—
855Dic158—42no—
856Dic158—42no—
857Dic158H(5,𝔽2)12yes—
858Dic158H(5,𝔽2)12yes—
859C79⋊C8—21no—
860C79⋊C8—21no—
861C79⋊C8—21no—
862C79⋊C8—21no—
863C79⋊C8—21no—
864C79⋊C8—21no—
865C79⋊C8—21no—
866C79⋊C8—21no—
867C22×C79—21no—
868C22×C79—21no—
869C22×C79—21no—
870C22×C79—21no—
871C22×C79—21no—
872C22×C79—21no—
873C22×C79—21no—
874C22×C79—21no—
875C22×C79—21no—
876C22×C79—21no—
877C22×C79—21no—
878C22×C79—21no—
879C22×C79—21no—
880C22×C79—21no—
881C22×C79—21no—
882C22×C79—41no—
883C22×C79—41no—
884C22×C79—41no—
885C22×C79—82no—
886C22×C79C23×D411yescharacteristic
887C2×D79—41no—
888C2×D79—41no—
889C2×D79—41no—
890C2×D79—41no—
891C2×D79—41no—
892C2×D79—41no—
893C2×D79—41no—
894C2×D79—41no—
895C2×D79—41no—
896C2×D79—84no—
897C4×C79—21no—
898C4×C79—21no—
899C4×C79—21no—
900C4×C79—21no—
901C4×C79—21no—
902C4×C79—21no—
903C4×C79—21no—
904C4×C79—21no—
905C4×C79—21no—
906C4×C79—41no—
907C4×C79—41no—
908C4×C79—41no—
909C4×C79—41no—
910C4×C79—41no—
911C4×C79—41no—
912C4×C79—41no—
913C4×C79C2×H(5,𝔽2)11yescharacteristic
914C4×C79C2×H(5,𝔽2)11yescharacteristic
915Dic79—22no—
916Dic79—22no—
917Dic79—41no—
918Dic79—41no—
919Dic79—41no—
920#61615—791nomaximal, Sylow
921C2×C79—41no—
922C2×C79—41no—
923C2×C79—41no—
924C2×C79—41no—
925C2×C79—41no—
926C2×C79—81no—
927C2×C79#348411yescharacteristic
928C2×C79#358411yescharacteristic
929C2×C79#358611yescharacteristic
930D79—81no—
931D79—81no—
932D79—81no—
933#3541D7911yescharacteristic, complemented
934#3487—791no—
935#3333—791no—
936#3326—791no—
937#3317—791no—
938#3316—791no—
939#3313—791no—
940#3309—791no—
941#3304—791no—
942#3300—791no—
943#3285—791no—
944#3284—791no—
945#3278—791no—
946#3277—791no—
947#3271—791no—
948#3271—791no—
949#3270—791no—
950#3269—791no—
951#3224—791no—
952#3222—791no—
953#3200—791no—
954#3198—791no—
955#3197—791no—
956#3190—791no—
957#3127—791no—
958#3121—791no—
959#3013—791no—
960#3011—791no—
961#3007—791no—
962#3002—791no—
963#2976—791no—
964C79#6161511yescharacteristic, complemented, Sylow
965C2×2−1+4—791no—
966C22×#41—791no—
967C2×#137—791no—
968C2×#137—791no—
969C2×#137—791no—
970C2×#137—791no—
971C2×#135—791no—
972C2×#135—791no—
973C2×#135—791no—
974C22×Q16—791no—
975#563—21no—
976#562—21no—
977#556C2×D7911yescharacteristic, complemented
978#554—21no—
979#554C2×D7911yescharacteristic, complemented
980#553—21no—
981#553C2×D7911yescharacteristic, complemented
982#552C2×D7911yescharacteristic, complemented
983#550—791no—
984#550—791no—
985#550—791no—
986#550—791no—
987#550—1581no—
988#550—1581no—
989D4×Q8C2×D7911yescharacteristic, complemented
990#548—791no—
991#548—791no—
992#548—791no—
993#548—791no—
994#548—1581no—
995#548—1581no—
996#548C2×D7911yescharacteristic, complemented
997#548C2×D7911yescharacteristic, complemented
998#547C2×D7911yescharacteristic, complemented
999#542—21no—
1000#542C2×D7911yescharacteristic
1001#541C2×D7911yescharacteristic
1002#539—21no—
1003#538—21no—
1004#538—21no—
1005#537C2×D7911yescharacteristic
1006#536C2×D7911yescharacteristic
1007#535—791no—
1008#535—791no—
1009#535—1581no—
1010#535—1581no—
1011#525—791no—
1012#525—1581no—
1013#525—1581no—
1014#525C2×D7911yescharacteristic
1015#525C2×D7911yescharacteristic
1016C2×C22⋊Q8C2×D7911yescharacteristic
1017#519—791no—
1018#497—791no—
1019#496—791no—
1020#495—791no—
1021#492—791no—
1022#490—791no—
1023#489—791no—
1024#488—791no—
1025#486—791no—
1026#485—791no—
1027#485—791no—
1028#485—791no—
1029#485—791no—
1030#483—791no—
1031#482—791no—
1032#482—791no—
1033#482—791no—
1034#482—791no—
1035#481—791no—
1036#480—791no—
1037#480—791no—
1038#479—791no—
1039#479—791no—
1040#477—791no—
1041#475—791no—
1042#470—791no—
1043#469—791no—
1044#469—791no—
1045#468—791no—
1046#468—791no—
1047#468—791no—
1048#468—791no—
1049#468—791no—
1050#467—791no—
1051#467—791no—
1052#466—791no—
1053#465—791no—
1054#465—791no—
1055#465—791no—
1056#465—791no—
1057#465—791no—
1058#464—791no—
1059#464—791no—
1060#464—791no—
1061#464—791no—
1062#464—791no—
1063#463—791no—
1064#462—791no—
1065#462—791no—
1066#460—791no—
1067#460—791no—
1068#460—791no—
1069#459—791no—
1070#452—791no—
1071#452—791no—
1072#452—791no—
1073#452—791no—
1074#452—791no—
1075#452—791no—
1076#452—791no—
1077#452—791no—
1078#452—791no—
1079#452—791no—
1080#452—791no—
1081#452—791no—
1082#452—791no—
1083#451—791no—
1084#451—791no—
1085#451—791no—
1086#451—791no—
1087#451—791no—
1088#451—791no—
1089#451—791no—
1090#450—791no—
1091#450—791no—
1092#450—791no—
1093#449—791no—
1094#449—791no—
1095#449—791no—
1096#449—791no—
1097#449—791no—
1098#449—791no—
1099#449—791no—
1100#448—791no—
1101#448—791no—
1102#448—791no—
1103#448—791no—
1104#448—791no—
1105#447—791no—
1106#441—791no—
1107#441—791no—
1108#441—791no—
1109#440—791no—
1110C4×Q16—791no—
1111C4×Q16—791no—
1112C4×Q16—791no—
1113C4×SD16—791no—
1114#436—791no—
1115#436—791no—
1116#435—791no—
1117#435—791no—
1118#435—791no—
1119#435—791no—
1120C8×D4—791no—
1121C8×D4—791no—
1122#433—791no—
1123#433—791no—
1124#419—791no—
1125#417—791no—
1126#417—791no—
1127#417—791no—
1128#416—791no—
1129#416—791no—
1130#416—791no—
1131C2×#103—791no—
1132#408—791no—
1133#408—791no—
1134#407—791no—
1135C2×C22⋊C8—791no—
11362−1+4—3162no—
11372−1+4—3162no—
1138C2×#41—3162no—
1139C2×#41—3162no—
1140C2×#41—791no—
1141C2×#41—791no—
1142C2×#41—791no—
1143C2×#41—791no—
1144C2×#41—791no—
1145C2×#41—791no—
1146C2×#41—791no—
1147C2×#41—1581no—
1148C2×#41—1581no—
1149C2×#41—1581no—
1150C2×#41—1581no—
1151C2×#41—1581no—
1152C2×#41C22×D7911yescharacteristic
1153C2×#41C22×D7911yescharacteristic
1154C2×#41C22×D7911yescharacteristic
1155C22×Q8—791no—
1156C22×Q8—791no—
1157C22×Q8—791no—
1158C22×Q8—1581no—
1159C22×Q8C22×D7911yescharacteristic
1160C22×Q8C22×D7911yescharacteristic
1161C22×D4—791no—
1162C22×D4—1581no—
1163C23×C4—1581no—
1164C23×C4C22×D7911yescharacteristic
1165#137—3162no—
1166#137—3162no—
1167#137—3162no—
1168#137—3162no—
1169#135—3162no—
1170#135—3162no—
1171#135—3162no—
1172C2×Q16—3162no—
1173C2×Q16—791no—
1174C2×Q16—791no—
1175C2×Q16—791no—
1176C2×Q16—791no—
1177C2×Q16—791no—
1178C2×Q16—791no—
1179C2×Q16—791no—
1180C2×Q16—791no—
1181C2×Q16—791no—
1182C2×SD16—791no—
1183C2×SD16—791no—
1184C2×SD16—791no—
1185C2×SD16—791no—
1186C2×SD16—791no—
1187C2×SD16—791no—
1188C2×SD16—791no—
1189C2×SD16—791no—
1190C2×SD16—791no—
1191C2×SD16—791no—
1192C2×SD16—791no—
1193C2×SD16—791no—
1194C2×D8—791no—
1195C2×D8—791no—
1196C2×D8—791no—
1197C2×M16—791no—
1198C2×M16—791no—
1199C2×M16—791no—
1200C2×M16—791no—
1201C22×C8—791no—
1202C22×C8—791no—
1203C22×C8—791no—
1204C22×C8—791no—
1205C4⋊Q8—21no—
1206C4⋊Q8—21no—
1207C4⋊Q8C22×D7911yescharacteristic
1208C4⋊Q8C22×D7911yescharacteristic
1209#127—791no—
1210#127—791no—
1211#127—1581no—
1212#127—1581no—
1213#127—1581no—
1214#127—1581no—
1215#127—1581no—
1216#126—21no—
1217#126—21no—
1218#126—21no—
1219#126—21no—
1220#126—21no—
1221#126—21no—
1222#126—21no—
1223#125—21no—
1224#125—21no—
1225#125—21no—
1226#125—21no—
1227#125C22×D7911yescharacteristic
1228#124—21no—
1229#124—21no—
1230#124—21no—
1231#124—21no—
1232#124—21no—
1233#124—791no—
1234#124—791no—
1235#124—1581no—
1236#124—1581no—
1237#124—1581no—
1238#124—1581no—
1239#124—1581no—
1240#124C22×D7911yescharacteristic
1241#123—21no—
1242#123—21no—
1243#123—21no—
1244#123—21no—
1245#123—21no—
1246#123—21no—
1247#123—21no—
1248#123—21no—
1249#123—1581no—
1250#123C22⋊D7911yescharacteristic
1251#123C22⋊D7911yescharacteristic
1252C22⋊Q8—21no—
1253C22⋊Q8—21no—
1254C22⋊Q8—21no—
1255C22⋊Q8—21no—
1256C22⋊Q8—21no—
1257C22⋊Q8—21no—
1258C22⋊Q8—21no—
1259C22⋊Q8—21no—
1260C22⋊Q8—21no—
1261C22⋊Q8—21no—
1262C22⋊Q8—791no—
1263C22⋊Q8—791no—
1264C22⋊Q8—1581no—
1265C22⋊Q8—1581no—
1266C22⋊Q8—1581no—
1267C22⋊Q8—1581no—
1268C22⋊Q8C22⋊D7911yescharacteristic
1269C22⋊Q8C22⋊D7911yescharacteristic
1270C22⋊Q8C22×D7911yescharacteristic
1271C22⋊Q8C22×D7911yescharacteristic
1272C22⋊Q8C22×D7911yescharacteristic
1273C22⋊Q8C22×D7911yescharacteristic
1274C22⋊Q8C22×D7911yescharacteristic
1275C22⋊Q8C22×D7911yescharacteristic
1276C22⋊Q8C22×D7911yescharacteristic
1277C22⋊Q8C22×D7911yescharacteristic
1278C22⋊Q8C22×D7911yescharacteristic
1279#121—21no—
1280#121—21no—
1281#121—21no—
1282#121—21no—
1283#121—21no—
1284#121—21no—
1285#121—21no—
1286#121—791no—
1287#121—791no—
1288#121—791no—
1289#121—791no—
1290#121—791no—
1291#121—791no—
1292#121—1581no—
1293#121—1581no—
1294#121—1581no—
1295#121—1581no—
1296#121—1581no—
1297#121—1581no—
1298#121—1581no—
1299#121—1581no—
1300#121—1581no—
1301#121—1581no—
1302#121—1581no—
1303#121—1581no—
1304#121—1581no—
1305#121—1581no—
1306#121C22⋊D7911yescharacteristic
1307#121C22⋊D7911yescharacteristic
1308#121C22×D7911yescharacteristic
1309#121C22×D7911yescharacteristic
1310#121C22×D7911yescharacteristic
1311#120—21no—
1312#120—1581no—
1313#120—1581no—
1314#120—1581no—
1315#120—1581no—
1316#120—1581no—
1317#120C22⋊D7911yescharacteristic
1318#120C22⋊D7911yescharacteristic
1319C4×Q8—21no—
1320C4×Q8—791no—
1321C4×Q8—791no—
1322C4×Q8—791no—
1323C4×Q8—791no—
1324C4×Q8—1581no—
1325C4×Q8—1581no—
1326C4×Q8C22×D7911yescharacteristic
1327C4×Q8C22×D7911yescharacteristic
1328C4×Q8C22×D7911yescharacteristic
1329C4×D4—21no—
1330C4×D4—21no—
1331C4×D4—21no—
1332C4×D4—21no—
1333C4×D4—21no—
1334C4×D4—21no—
1335C4×D4—21no—
1336C4×D4—1581no—
1337C4×D4—1581no—
1338C4×D4—1581no—
1339C4×D4—1581no—
1340C4×D4—1581no—
1341C4×D4—1581no—
1342C4×D4—1581no—
1343C4×D4—1581no—
1344C4×D4—1581no—
1345C4×D4—1581no—
1346C4×D4C22×D7911yescharacteristic
1347C4×D4C22×D7911yescharacteristic
1348C4×D4C22×D7911yescharacteristic
1349C4×D4C22×D7911yescharacteristic
1350C4×D4C22×D7911yescharacteristic
1351#117—21no—
1352#117—791no—
1353#117—1581no—
1354#117—1581no—
1355#117C22×D7911yescharacteristic
1356#117C22×D7911yescharacteristic
1357#117C22×D7911yescharacteristic
1358C2×C4⋊C4—21no—
1359C2×C4⋊C4—21no—
1360C2×C4⋊C4C22×D7911yescharacteristic
1361C2×C4⋊C4C22×D7911yescharacteristic
1362C2×C22⋊C4—21no—
1363#107—791no—
1364#107—791no—
1365#107—791no—
1366#107—791no—
1367#106—791no—
1368#106—791no—
1369#106—791no—
1370#106—791no—
1371C4⋊C8—791no—
1372C4⋊C8—791no—
1373C4⋊C8—791no—
1374C4⋊C8—791no—
1375#103—791no—
1376#103—791no—
1377#103—791no—
1378#103—791no—
1379#103—791no—
1380#103—791no—
1381#103—791no—
1382#103—791no—
1383#103—791no—
1384#103—791no—
1385#103—791no—
1386#103—791no—
1387#103—791no—
1388#103—791no—
1389#103—791no—
1390#103—791no—
1391#103—791no—
1392#103—791no—
1393#102—791no—
1394#102—791no—
1395#102—791no—
1396#102—791no—
1397#102—791no—
1398#102—791no—
1399#102—791no—
1400#102—791no—
1401#102—791no—
1402#102—791no—
1403#102—791no—
1404#102—791no—
1405#102—791no—
1406#102—791no—
1407C22⋊C8—791no—
1408C22⋊C8—791no—
1409C22⋊C8—791no—
1410C22⋊C8—791no—
1411C22⋊C8—791no—
1412C22⋊C8—791no—
1413C22⋊C8—791no—
1414C22⋊C8—791no—
1415C22⋊C8—791no—
1416C22⋊C8—791no—
1417C22⋊C8—791no—
1418C22⋊C8—791no—
1419#97—791no—
1420#97—791no—
1421C4×C8—791no—
1422C4×C8—791no—
1423C24—1581no—
1424C24C2×C22⋊D7911yescharacteristic
1425#41—41no—
1426#41—41no—
1427#41—41no—
1428#41—41no—
1429#41—41no—
1430#41—41no—
1431#41—3161no—
1432#41—3161no—
1433#41—3161no—
1434#41—3161no—
1435#41—3161no—
1436#41—3161no—
1437#41—3161no—
1438#41—3161no—
1439#41—3164no—
1440#41—3164no—
1441#41—3164no—
1442#41—3164no—
1443#41—3164no—
1444#41—1582no—
1445#41—1582no—
1446#41—1582no—
1447#41—1582no—
1448#41—1582no—
1449#41—1582no—
1450C2×Q8—21no—
1451C2×Q8—21no—
1452C2×Q8—21no—
1453C2×Q8—41no—
1454C2×Q8—41no—
1455C2×Q8—41no—
1456C2×Q8—41no—
1457C2×Q8—3161no—
1458C2×Q8—3161no—
1459C2×Q8—3164no—
1460C2×Q8—791no—
1461C2×Q8—791no—
1462C2×Q8—791no—
1463C2×Q8—1582no—
1464C2×Q8—1582no—
1465C2×Q8—1582no—
1466C2×Q8—1582no—
1467C2×Q8—1581no—
1468C2×Q8—1581no—
1469C2×Q8—1581no—
1470C2×Q8C2×C22⋊D7911yescharacteristic
1471C2×Q8C23×D7911yescharacteristic
1472C2×Q8C23×D7911yescharacteristic
1473C2×Q8C23×D7911yescharacteristic
1474C2×D4—21no—
1475C2×D4—21no—
1476C2×D4—21no—
1477C2×D4—21no—
1478C2×D4—21no—
1479C2×D4—3161no—
1480C2×D4—3161no—
1481C2×D4—3164no—
1482C2×D4—791no—
1483C2×D4—791no—
1484C2×D4—791no—
1485C2×D4—1581no—
1486C2×D4—1581no—
1487C2×D4—1581no—
1488C2×D4—1581no—
1489C2×D4—1581no—
1490C2×D4—1581no—
1491C2×D4—1581no—
1492C2×D4—1581no—
1493C2×D4—1581no—
1494C2×D4—1581no—
1495C2×D4—1581no—
1496C2×D4—1581no—
1497C2×D4—1581no—
1498C2×D4—1581no—
1499C2×D4—1581no—
1500C2×D4—1581no—
1501C2×D4—1581no—
1502C2×D4—1581no—
1503C2×D4C2×C22⋊D7911yescharacteristic
1504C2×D4C2×C22⋊D7911yescharacteristic
1505C2×D4C2×C22⋊D7911yescharacteristic
1506C2×D4C2×C22⋊D7911yescharacteristic
1507C2×D4C2×C22⋊D7911yescharacteristic
1508C2×D4C2×C22⋊D7911yescharacteristic
1509C2×D4C2×C22⋊D7911yescharacteristic
1510C2×D4C23×D7911yescharacteristic
1511C22×C4—21no—
1512C22×C4—21no—
1513C22×C4—21no—
1514C22×C4—21no—
1515C22×C4—21no—
1516C22×C4—21no—
1517C22×C4—21no—
1518C22×C4—41no—
1519C22×C4—41no—
1520C22×C4—3164no—
1521C22×C4—1581no—
1522C22×C4—1581no—
1523C22×C4—1581no—
1524C22×C4—1581no—
1525C22×C4—1581no—
1526C22×C4—1581no—
1527C22×C4—1581no—
1528C22×C4—1581no—
1529C22×C4—1581no—
1530C22×C4—1581no—
1531C22×C4C2×C22⋊D7911yescharacteristic
1532C22×C4C2×C22⋊D7911yescharacteristic
1533C22×C4C2×C22⋊D7911yescharacteristic
1534C22×C4C23×D7911yescharacteristic
1535C22×C4C23×D7911yescharacteristic
1536C22×C4C23×D7911yescharacteristic
1537C22×C4C23×D7911yescharacteristic
1538C22×C4C23×D7911yescharacteristic
1539Q16—3161no—
1540Q16—3161no—
1541Q16—3161no—
1542Q16—1582no—
1543Q16—1582no—
1544Q16—1582no—
1545Q16—1582no—
1546Q16—1582no—
1547Q16—1582no—
1548SD16—3161no—
1549SD16—3161no—
1550SD16—3161no—
1551SD16—3161no—
1552SD16—3161no—
1553SD16—3161no—
1554SD16—3161no—
1555SD16—3161no—
1556SD16—3161no—
1557SD16—3161no—
1558SD16—1582no—
1559SD16—1582no—
1560D8—3161no—
1561D8—3161no—
1562D8—3161no—
1563M16—3161no—
1564M16—3161no—
1565M16—3161no—
1566M16—3161no—
1567C2×C8—3161no—
1568C2×C8—3161no—
1569C2×C8—3161no—
1570C2×C8—3161no—
1571C2×C8—791no—
1572C2×C8—791no—
1573C2×C8—791no—
1574C2×C8—791no—
1575C2×C8—791no—
1576C2×C8—791no—
1577C2×C8—791no—
1578C2×C8—791no—
1579C4⋊C4—21no—
1580C4⋊C4—21no—
1581C4⋊C4—21no—
1582C4⋊C4—21no—
1583C4⋊C4—21no—
1584C4⋊C4—21no—
1585C4⋊C4—21no—
1586C4⋊C4—21no—
1587C4⋊C4—21no—
1588C4⋊C4—21no—
1589C4⋊C4—21no—
1590C4⋊C4—21no—
1591C4⋊C4—21no—
1592C4⋊C4—21no—
1593C4⋊C4—21no—
1594C4⋊C4—21no—
1595C4⋊C4—21no—
1596C4⋊C4—21no—
1597C4⋊C4—21no—
1598C4⋊C4—791no—
1599C4⋊C4—791no—
1600C4⋊C4—1581no—
1601C4⋊C4—1581no—
1602C4⋊C4—1581no—
1603C4⋊C4—1581no—
1604C4⋊C4—1581no—
1605C4⋊C4—1581no—
1606C4⋊C4C2×C22⋊D7911yescharacteristic
1607C4⋊C4C2×C22⋊D7911yescharacteristic
1608C4⋊C4C2×C22⋊D7911yescharacteristic
1609C4⋊C4C2×C22⋊D7911yescharacteristic
1610C4⋊C4C2×C22⋊D7911yescharacteristic
1611C4⋊C4C2×C22⋊D7911yescharacteristic
1612C4⋊C4C23×D7911yescharacteristic
1613C4⋊C4C23×D7911yescharacteristic
1614C4⋊C4C23×D7911yescharacteristic
1615C4⋊C4C23×D7911yescharacteristic
1616C22⋊C4—21no—
1617C22⋊C4—21no—
1618C22⋊C4—21no—
1619C22⋊C4—21no—
1620C22⋊C4—21no—
1621C22⋊C4—21no—
1622C22⋊C4—21no—
1623C22⋊C4—21no—
1624C22⋊C4—21no—
1625C22⋊C4—21no—
1626C22⋊C4—21no—
1627C22⋊C4—21no—
1628C22⋊C4—21no—
1629C22⋊C4—21no—
1630C22⋊C4—21no—
1631C22⋊C4—21no—
1632C22⋊C4—21no—
1633C22⋊C4—1581no—
1634C22⋊C4—1581no—
1635C22⋊C4—1581no—
1636C22⋊C4—1581no—
1637C22⋊C4—1581no—
1638C22⋊C4—1581no—
1639C22⋊C4—1581no—
1640C22⋊C4—1581no—
1641C22⋊C4—1581no—
1642C22⋊C4—1581no—
1643C22⋊C4—1581no—
1644C22⋊C4—1581no—
1645C22⋊C4—1581no—
1646C22⋊C4C2×C22⋊D7911yescharacteristic
1647C22⋊C4C2×C22⋊D7911yescharacteristic
1648C22⋊C4C2×C22⋊D7911yescharacteristic
1649C22⋊C4C2×C22⋊D7911yescharacteristic
1650C22⋊C4C2×C22⋊D7911yescharacteristic
1651C22⋊C4C2×C22⋊D7911yescharacteristic
1652C22⋊C4C2×C22⋊D7911yescharacteristic
1653C22⋊C4C2×C22⋊D7911yescharacteristic
1654C22⋊C4C2×C22⋊D7911yescharacteristic
1655C22⋊C4C2×C22⋊D7911yescharacteristic
1656C42—21no—
1657C42—21no—
1658C42—21no—
1659C42—21no—
1660C42—21no—
1661C42—1581no—
1662C42—1581no—
1663C42—1581no—
1664C42—1581no—
1665C42—1581no—
1666C42C23×D7911yescharacteristic
1667C42C23×D7911yescharacteristic
1668C23—21no—
1669C23—41no—
1670C23—41no—
1671C23—41no—
1672C23—3162no—
1673C23—6321no—
1674C23—6321no—
1675C23—1581no—
1676C23—1581no—
1677C23—1581no—
1678C23C22×C22⋊D7911yescharacteristic
1679C23C22×C22⋊D7911yescharacteristic
1680C23C22×C22⋊D7911yescharacteristic
1681C23C22×C22⋊D7911yescharacteristic
1682C23C22×C22⋊D7911yescharacteristic
1683Q8—21no—
1684Q8—21no—
1685Q8—21no—
1686Q8—21no—
1687Q8—21no—
1688Q8—21no—
1689Q8—41no—
1690Q8—81no—
1691Q8—81no—
1692Q8—81no—
1693Q8—3162no—
1694Q8—3162no—
1695Q8—792no—
1696Q8—792no—
1697Q8—1584no—
1698Q8—1581no—
1699Q8—1581no—
1700Q8—1581no—
1701Q8—1581no—
1702D4—21no—
1703D4—21no—
1704D4—41no—
1705D4—41no—
1706D4—41no—
1707D4—41no—
1708D4—41no—
1709D4—41no—
1710D4—41no—
1711D4—42no—
1712D4—81no—
1713D4—81no—
1714D4—81no—
1715D4—81no—
1716D4—3162no—
1717D4—3162no—
1718D4—3162no—
1719D4—3162no—
1720D4—3162no—
1721D4—3162no—
1722D4—3162no—
1723D4—3162no—
1724D4—6321no—
1725D4—6321no—
1726D4—6321no—
1727D4—6321no—
1728D4—6321no—
1729D4—6321no—
1730D4—6321no—
1731D4—6321no—
1732D4—6321no—
1733D4—6321no—
1734D4—1581no—
1735D4—1581no—
1736D4—1581no—
1737D4—1581no—
1738D4—1581no—
1739D4—1581no—
1740C2×C4—21no—
1741C2×C4—21no—
1742C2×C4—21no—
1743C2×C4—21no—
1744C2×C4—21no—
1745C2×C4—21no—
1746C2×C4—21no—
1747C2×C4—21no—
1748C2×C4—21no—
1749C2×C4—21no—
1750C2×C4—21no—
1751C2×C4—21no—
1752C2×C4—21no—
1753C2×C4—21no—
1754C2×C4—21no—
1755C2×C4—21no—
1756C2×C4—21no—
1757C2×C4—41no—
1758C2×C4—41no—
1759C2×C4—41no—
1760C2×C4—81no—
1761C2×C4—81no—
1762C2×C4—81no—
1763C2×C4—81no—
1764C2×C4—81no—
1765C2×C4—81no—
1766C2×C4—81no—
1767C2×C4—3162no—
1768C2×C4—3162no—
1769C2×C4—3162no—
1770C2×C4—3162no—
1771C2×C4—3162no—
1772C2×C4—3162no—
1773C2×C4—3162no—
1774C2×C4—3162no—
1775C2×C4—3162no—
1776C2×C4—1581no—
1777C2×C4—1581no—
1778C2×C4—1581no—
1779C2×C4—1584no—
1780C2×C4—1581no—
1781C2×C4—1581no—
1782C2×C4C22×C22⋊D7911yescharacteristic
1783C2×C4C22×C22⋊D7911yescharacteristic
1784C2×C4C22×C22⋊D7911yescharacteristic
1785C2×C4C22×C22⋊D7911yescharacteristic
1786C2×C4C22×C22⋊D7911yescharacteristic
1787C2×C4C22×C22⋊D7911yescharacteristic
1788C2×C4C22×C22⋊D7911yescharacteristic
1789C2×C4C22×C22⋊D7911yescharacteristic
1790C2×C4C22×C22⋊D7911yescharacteristic
1791C2×C4C24×D7911yescharacteristic
1792C8—1581no—
1793C8—1581no—
1794C8—1581no—
1795C8—1581no—
1796C8—1581no—
1797C8—1581no—
1798C8—1581no—
1799C8—1581no—
1800C22—21no—
1801C22—21no—
1802C22—21no—
1803C22—21no—
1804C22—21no—
1805C22—21no—
1806C22—21no—
1807C22—21no—
1808C22—21no—
1809C22—21no—
1810C22—21no—
1811C22—21no—
1812C22—21no—
1813C22—21no—
1814C22—21no—
1815C22—41no—
1816C22—41no—
1817C22—41no—
1818C22—82no—
1819C22—3161no—
1820C22—3161no—
1821C22—3161no—
1822C22—3161no—
1823C22—3161no—
1824C22—3161no—
1825C22—3161no—
1826C22—3161no—
1827C22—3161no—
1828C22—6324no—
1829C22C23×C22⋊D7911yescharacteristic
1830C4—21no—
1831C4—21no—
1832C4—21no—
1833C4—21no—
1834C4—21no—
1835C4—21no—
1836C4—21no—
1837C4—21no—
1838C4—21no—
1839C4—41no—
1840C4—41no—
1841C4—41no—
1842C4—41no—
1843C4—41no—
1844C4—41no—
1845C4—41no—
1846C4—3161no—
1847C4—3161no—
1848C4—3161no—
1849C4—1582no—
1850C4—1582no—
1851C4H(5,𝔽2)×D7911yescharacteristic
1852C4H(5,𝔽2)×D7911yescharacteristic
1853C2—41no—
1854C2—41no—
1855C2—41no—
1856C2—41no—
1857C2—41no—
1858C2—81no—
1859C2—6321no—
1860C2—6321no—
1861C2—6321no—
1862C2#2377703111yescharacteristic
1863C2#2377817111yescharacteristic
1864C2#2377818711yescharacteristic
subgroupG/H
centerC22C23×C22⋊D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC79×#3541C2
socleC22×C79C23×D4
hypercenter#3541D79
hypocenterC79#61615
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ #525 ◁ #3541

Complements

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

NH ≅ G/Ntype
1. #23777054C2semidirect
2. #23775732C2semidirect
3. #23775647C2semidirect
4. #23775520C2semidirect
5. #23775505C2semidirect
6. #23775460C2semidirect
7. #23775400C2semidirect
8. #23775333C2semidirect
9. #23775281C2semidirect
10. #23775137C2semidirect
11. #23775126C2semidirect
12. #23775062C2semidirect
13. #23775053C2semidirect
14. #23774986C2semidirect
15. #23774986C2semidirect
16. #23774971C2semidirect
17. #23774951C2semidirect
18. #23774488C2semidirect
19. #23774466C2semidirect
20. #23774267C2semidirect
21. #23774246C2semidirect
22. #23774237C2semidirect
23. #23774181C2semidirect
24. #23773695C2semidirect
25. #23773623C2semidirect
26. #23772712C2semidirect
27. #23772693C2semidirect
28. #23772658C2semidirect
29. #23772616C2semidirect
30. #23772448C2semidirect
31. C79×#3541C2semidirect
36. C2×#14579192C22semidirect
37. C2×#14579191C22semidirect
40. C2×#14579181C22semidirect
41. C22×#11929614C22semidirect
62. #19098955C22semidirect
63. #19098953C22semidirect
64. #19098945C22semidirect
65. #19098937C22semidirect
66. #19098929C22semidirect
67. #19098925C22semidirect
68. #19098920C22semidirect
69. #19098911C22semidirect
70. #19098904C22semidirect
74. #19098893C22semidirect
75. #19098887C22semidirect
76. #19098887C22semidirect
77. #19098887C22semidirect
79. #19098881C22semidirect
80. #19098876C22semidirect
81. #19098876C22semidirect
82. #19098867C22semidirect
83. #19098867C22semidirect
84. #19098855C22semidirect
85. #19098845C22semidirect
86. #19098819C22semidirect
87. #19098814C22semidirect
88. #19098814C22semidirect
89. #19098811C22semidirect
90. #19098811C22semidirect
91. #19098811C22semidirect
92. #19098811C22semidirect
93. #19098807C22semidirect
94. #19098802C22semidirect
95. #19098802C22semidirect
96. #19098797C22semidirect
97. #19098794C22semidirect
98. #19098794C22semidirect
99. #19098794C22semidirect
100. #19098794C22semidirect
101. #19098794C22semidirect
102. #19098785C22semidirect
103. #19098785C22semidirect
104. #19098785C22semidirect
105. #19098782C22semidirect
106. #19098782C22semidirect
107. #19098778C22semidirect
108. #19098770C22semidirect
109. #19098770C22semidirect
110. #19098763C22semidirect
111. #19098763C22semidirect
112. #19098763C22semidirect
113. #19098758C22semidirect
114. #19098725C22semidirect
124. #19098723C22semidirect
125. #19098723C22semidirect
126. #19098723C22semidirect
127. #19098719C22semidirect
131. #19098718C22semidirect
132. #19098718C22semidirect
133. #19098718C22semidirect
137. #19098708C22semidirect
138. #19098708C22semidirect
139. #19098708C22semidirect
143. #19098706C22semidirect
144. #19098702C22semidirect
145. #19098702C22semidirect
146. #19098702C22semidirect
148. #19098701C22semidirect
150. #19098668C22semidirect
151. #19098668C22semidirect
152. #19098668C22semidirect
153. #19098663C22semidirect
154. C4×#11929614C22semidirect
155. C4×#11929614C22semidirect
156. C4×#11929614C22semidirect
157. C4×#11929612C22semidirect
158. #19098641C22semidirect
159. #19098641C22semidirect
160. #19098635C22semidirect
161. #19098635C22semidirect
162. #19098635C22semidirect
163. #19098635C22semidirect
164. D4×C79⋊C8C22semidirect
165. D4×C79⋊C8C22semidirect
168. #19098571C22semidirect
171. #19098562C22semidirect
174. #19098557C22semidirect
175. C2×#14579084C22semidirect
182. #556×C79C22semidirect
184. #554×C79C22semidirect
186. #553×C79C22semidirect
187. #552×C79C22semidirect
188. D4×Q8×C79C22semidirect
189. #548×C79C22semidirect
190. #548×C79C22semidirect
191. #547×C79C22semidirect
933. #3541D79semidirect
964. C79#61615semidirect
977. #556C2×D79semidirect
979. #554C2×D79semidirect
981. #553C2×D79semidirect
982. #552C2×D79semidirect
989. D4×Q8C2×D79semidirect
996. #548C2×D79semidirect
997. #548C2×D79semidirect
998. #547C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237770542
#237757322
#237756472
#237755202
#237755052
#237754602
#237754002
#237753332
#237752812
#237751372
#237751262
#237750622
#237750532
#237749862
#237749712
#237749512
#237744882
#237744662
#237742672
#237742462
#237742372
#237741812
#237736952
#237736232
#237727122
#237726932
#237726582
#237726162
#237724482
C79×#35412
#6161579