Finite Group Databasebeta

← #35152807

Subgroups — #35152807

Order 20224.

1962 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23776692C211yesmaximal, characteristic
2#23772410C214yesmaximal, complemented
3#23772408C214yesmaximal, complemented
4#23772395C214yesmaximal, complemented
5#23772388C214yesmaximal, complemented
6#23772339C211yesmaximal, characteristic, complemented
7#23772338C211yesmaximal, characteristic, complemented
8#23772116C211yesmaximal, characteristic, complemented
9#23772115C211yesmaximal, characteristic, complemented
10#23772095C211yesmaximal, characteristic, complemented
11#23772094C211yesmaximal, characteristic, complemented
12#23772090C211yesmaximal, characteristic, complemented
13#23772050C211yesmaximal, characteristic, complemented
14#23772047C211yesmaximal, characteristic, complemented
15#23772029C211yesmaximal, characteristic, complemented
16#23771827C211yesmaximal, characteristic, complemented
17#23771826C211yesmaximal, characteristic, complemented
18C22×#14579071C211yesmaximal, characteristic, complemented
19C79×#2929C211yesmaximal, characteristic, complemented
20C2×#14579169C2211yescharacteristic
21C2×#14579168C2211yescharacteristic
22C2×#14579167C2211yescharacteristic
23C23×C79⋊C8C2211yescharacteristic
24#19099116C2211yescharacteristic
25#19099115C412yes—
26#19099109C2211yescharacteristic
27#19099108C412yes—
28#19099099C412yes—
29#19099094C412yes—
30#19099093C2214yes—
31#19099090C414yes—
32#19099074C2211yescharacteristic
33#19099069C414yes—
34#41×Dic79C2211yescharacteristic
35#19099031C2211yescharacteristic
36C4×#11929623C2214yes—
37C22×C4×Dic79C2211yescharacteristic
38#19098693C2214yescomplemented
39#19098692C2214yescomplemented
40#19098691C2214yescomplemented
41#19098690C2214yescomplemented
42#19098637C2214yescomplemented
43#19098635C2214yes—
44#19098634C2214yes—
45#19098634C2214yescomplemented
46#19098632C2214yescomplemented
47#19098631C2214yes—
48#19098631C2214yescomplemented
49D4×C79⋊C8C2214yes—
50C8×C22⋊D79C2214yes—
51(C22⋊D79)⋊C8C2214yes—
52#19098623C2214yescomplemented
53#19098621C2214yescomplemented
54#19098619C2214yescomplemented
55#19098617C2214yes—
56#19098617C2214yescomplemented
57#19098613C2214yes—
58#19098591C2211yescharacteristic
59#19098590C2211yescharacteristic
60#19098589C2211yescharacteristic
61#19098586C2211yescharacteristic
62#19098586C2211yescharacteristic
63#19098531C2211yescharacteristic
64#19098530C2211yescharacteristic
65#19098529C2211yescharacteristic
66#19098527C2211yescharacteristic
67#19098521C2211yescharacteristic
68#19098521C2212yescomplemented
69#19098520C2212yescomplemented
70#19098519C2211yescharacteristic
71#19098518C2211yescharacteristic
72#19098518C2212yescomplemented
73#19098517C2212yescomplemented
74M16×Dic79C2211yescharacteristic
75M16×Dic79C2211yescharacteristic
76M16×Dic79C2212yescomplemented
77C4×#11929607C2212yescomplemented
78C2×#14579071C2211yescharacteristic
79C2×#14579071C2211yescharacteristic
80C2×#14579071C2211yescharacteristic
81C2×#14579071C2211yescharacteristic
82C2×#14579071C2212yes—
83C2×#14579071C2212yes—
84C2×#14579071C2212yes—
85C2×#14579071C2212yes—
86C2×#14579071C2212yescomplemented
87#97×D79C2212yescomplemented
88C2×#131×C79C2211yescharacteristic
89C23×C8×C79C2211yescharacteristic
90#525×C79C2211yescharacteristic
91#435×C79C2214yes—
92C8×D4×C79C2214yes—
93#424×C79C2211yescharacteristic
94#408×C79C2211yescharacteristic
95#407×C79C2211yescharacteristic
96#405×C79C2211yescharacteristic
97C2×#11929624C2311yescharacteristic
98C2×#11929623C2×C414yes—
99C23×Dic79C2×C412yes—
100#14579169—24no—
101#14579168—24no—
102#14579167—24no—
103C2×#11929608C2312yes—
104C2×#11929608C2311yescharacteristic
105C2×#11929608C2311yescharacteristic
106C2×#11929607C2312yes—
107C2×#11929607C2312yes—
108C22×C79⋊C8—24no—
109C22×C79⋊C8C2312yes—
110C22×C79⋊C8C2312yes—
111C22×C79⋊C8C2312yes—
112C22×C79⋊C8C2311yescharacteristic
113C22×C79⋊C8C2311yescharacteristic
114C2×C8×D79C2312yes—
115C2×C8×D79C2312yes—
116#14579160C2×C412yes—
117#14579159C2×C411yescharacteristic
118#14579157C2×C411yescharacteristic
119#14579156C2×C414yes—
120#14579154C2×C414yes—
121#14579152C2×C412yes—
122#14579151C2×C414yes—
123#14579150C2×C411yescharacteristic
124#14579148C2×C411yescharacteristic
125#14579147C2×C414yes—
126#14579145C2×C414yes—
127#14579144C2×C412yes—
128#14579142C2×C414yes—
129#14579140C2×C412yes—
130#14579138C2×C414yes—
131#14579138C2×C414yes—
132#14579135C2×C412yes—
133#14579133C2×C414yes—
134#14579133C2×C414yes—
135#14579130C2×C412yes—
136Q8×Dic79C2×C412yes—
137C4×Dic158C2314yes—
138#14579126C2×C414yes—
139#14579126C2×C412yes—
140D4×Dic79C2×C414yes—
141D4×Dic79C2×C414yes—
142D4×Dic79C2×C412yes—
143#14579123C2×C412yes—
144C4×C22⋊D79C2314yes—
145C4×C22⋊D79C2314yes—
146(C22⋊D79)⋊C4C2×C414yes—
147(C22⋊D79)⋊C4C2×C414yes—
148(C22⋊D79)⋊C4C2×C414yes—
149#14579120C2311yescharacteristic
150#14579120C2312yes—
151#14579119C2×C414yes—
152#14579118C2312yes—
153#14579117C2×C414yes—
154#14579117C2×C414yes—
155C2×C4×Dic79C2×C412yes—
156C2×C4×Dic79C2×C412yes—
157C2×C4×Dic79C2×C412yes—
158C2×C4×Dic79C2311yescharacteristic
159C2×C4×Dic79C2312yes—
160C2×C4×Dic79C2312yes—
161C2×C4×Dic79C2311yescharacteristic
162C2×C4×Dic79C2312yes—
163C42×D79C2312yes—
164C4⋊(C79⋊C8)C2314yes—
165Dic79⋊C8C2314yes—
166Dic79⋊C8C2314yes—
167Dic79⋊C8C2314yes—
168Dic79⋊C8C2314yes—
169C22⋊(C79⋊C8)C2314yes—
170C22⋊(C79⋊C8)C2314yes—
171(C2×D79)⋊C8C2314yes—
172(C2×D79)⋊C8C2314yes—
173#14579072C2312yes—
174#14579071C2312yes—
175#14579071C2312yes—
176#14579071C2312yes—
177#14579071C2312yes—
178#14579071C2312yes—
179#14579071C2312yes—
180#14579071C2311yescharacteristic
181#14579071C2312yes—
182#14579071C2311yescharacteristic
183#14579071C2311yescharacteristic
184#14579071C2311yescharacteristic
185#14579071C2312yes—
186#14579071C2312yes—
187#14579071C2312yes—
188C4×C79⋊C8C2312yes—
189C8×Dic79C2312yes—
190C8×Dic79C2312yes—
191C8×Dic79C2312yes—
192C8×Dic79C2312yes—
193C2×#41×C79C2311yescharacteristic
194C23×C4×C79C2311yescharacteristic
195#131×C79—24no—
196C2×M16×C79C2311yescharacteristic
197C2×M16×C79C2312yes—
198C2×M16×C79C2311yescharacteristic
199C22×C8×C79—24no—
200C22×C8×C79C2312yes—
201C22×C8×C79C2311yescharacteristic
202C22×C8×C79C2312yes—
203C22×C8×C79C2312yes—
204C22×C8×C79C2311yescharacteristic
205#123×C79C2×C412yes—
206C22⋊Q8×C79C2×C412yes—
207#121×C79C2×C412yes—
208#120×C79C2×C412yes—
209C4×D4×C79C2314yes—
210#117×C79C2311yescharacteristic
211C4⋊C8×C79C2314yes—
212C22⋊C8×C79C2314yes—
213C22⋊C8×C79C2314yes—
214#97×C79C2312yes—
215C4×C8×C79C2312yes—
216#11929624—22no—
217#11929624—22no—
218#11929623—48no—
219C2×Dic158C22×C411yescharacteristic
220C2×Dic158C22×C414yes—
221C2×D316C22×C411yescharacteristic
222C2×C22⋊D79C22×C414yes—
223C2×C22⋊D79C22×C412yes—
224C2×C22⋊D79C22×C414yes—
225C22×Dic79—44no—
226C22×Dic79C22×C412yes—
227C22×Dic79C22×C412yes—
228C22×Dic79C22×C414yes—
229C22×Dic79C22×C412yes—
230C22×Dic79C22×C412yes—
231C22×Dic79C22×C412yes—
232C22×Dic79C22×C412yes—
233C2×C4×D79C22×C414yes—
234C2×C4×D79C2412yes—
235#11929608—24no—
236#11929608—22no—
237#11929608—22no—
238#11929607—24no—
239#11929607—24no—
240C2×C79⋊C8—24no—
241C2×C79⋊C8—24no—
242C2×C79⋊C8—24no—
243C2×C79⋊C8—22no—
244C2×C79⋊C8#4114yescomplemented
245C2×C79⋊C8C2412yes—
246C2×C79⋊C8C2412yes—
247C2×C79⋊C8C2412yes—
248C2×C79⋊C8C2411yescharacteristic
249C2×C79⋊C8C2411yescharacteristic
250C8×D79—24no—
251C8×D79—24no—
252C4⋊Dic79C22×C414yes—
253C4⋊Dic79C22×C412yes—
254C4⋊Dic79C22×C414yes—
255Dic79⋊C4C22×C414yes—
256Dic79⋊C4C22×C414yes—
257Dic79⋊C4C22×C414yes—
258Dic79⋊C4C22×C414yes—
259Dic79⋊C4C22×C414yes—
260C22⋊Dic79C22×C414yes—
261C22⋊Dic79C22×C414yes—
262C22⋊Dic79C22×C412yes—
263C22⋊Dic79C22×C414yes—
264(C2×D79)⋊C4C22×C414yes—
265(C2×D79)⋊C4C22×C414yes—
266(C2×D79)⋊C4C22×C414yes—
267C4×Dic79C22×C414yes—
268C4×Dic79C22×C412yes—
269C4×Dic79C22×C412yes—
270C4×Dic79C22×C412yes—
271C4×Dic79C22×C412yes—
272C4×Dic79C22×C411yescharacteristic
273C4×Dic79C22×C412yes—
274C4×Dic79C22×C411yescharacteristic
275C4×Dic79C22×C414yes—
276C4×Dic79C2411yescharacteristic
277C4×Dic79C2412yes—
278C4×Dic79C2411yescharacteristic
279C4×Dic79C2412yes—
280C24×C79C22×C411yescharacteristic
281#41×C79—22no—
282#41×C79—22no—
283C2×Q8×C79C22×C411yescharacteristic
284C2×D4×C79C22×C414yes—
285C2×D4×C79C22×C412yes—
286C2×D4×C79C22×C411yescharacteristic
287C22×C4×C79—22no—
288C22×C4×C79—22no—
289C22×C4×C79C22×C412yes—
290C22×C4×C79C22×C411yescharacteristic
291C22×C4×C79C2412yes—
292C22×C4×C79C2412yes—
293C22×C4×C79C2411yescharacteristic
294M16×C79—24no—
295M16×C79—22no—
296M16×C79—22no—
297C2×C8×C79—24no—
298C2×C8×C79—24no—
299C2×C8×C79—24no—
300C2×C8×C79—22no—
301C2×C8×C79#4114yescomplemented
302C2×C8×C79C2412yes—
303C2×C8×C79C2412yes—
304C2×C8×C79C2412yes—
305C2×C8×C79C2411yescharacteristic
306C2×C8×C79C2411yescharacteristic
307C4⋊C4×C79C22×C412yes—
308C4⋊C4×C79C22×C414yes—
309C22⋊C4×C79C22×C412yes—
310C22⋊C4×C79C22×C414yes—
311C22⋊C4×C79C22×C414yes—
312C42×C79C2412yes—
313C23×C79—22no—
314C23×C79—24no—
315C23×C79C23×C412yes—
316C23×C79C23×C411yescharacteristic
317C23×C79C23×C412yes—
318C22×D79C23×C412yes—
319Q8×C79—22no—
320D4×C79—24no—
321D4×C79—28no—
322D4×C79—22no—
323C2×C4×C79—22no—
324C2×C4×C79—24no—
325C2×C4×C79—22no—
326C2×C4×C79—22no—
327C2×C4×C79—22no—
328C2×C4×C79—22no—
329C2×C4×C79C23×C412yes—
330C2×C4×C79C23×C412yes—
331C2×C4×C79C23×C414yes—
332C2×C4×C79C23×C411yescharacteristic
333C2×C4×C79C2×#4112yes—
334C2×C4×C79C2×#4112yes—
335C2×C4×C79C2511yescharacteristic
336C22⋊D79—24no—
337C22⋊D79—28no—
338C22⋊D79—44no—
339C2×Dic79—24no—
340C2×Dic79—24no—
341C2×Dic79—42no—
342C2×Dic79—42no—
343C2×Dic79—42no—
344C2×Dic79—42no—
345C2×Dic79—44no—
346C2×Dic79C23×C412yes—
347C2×Dic79C23×C412yes—
348C2×Dic79C23×C412yes—
349C2×Dic79C23×C412yes—
350C2×Dic79C23×C412yes—
351C2×Dic79C23×C414yes—
352D316—22no—
353C4×D79—22no—
354C4×D79—22no—
355C4×D79—44no—
356Dic158—22no—
357Dic158—44no—
358C8×C79—22no—
359C8×C79—22no—
360C8×C79—22no—
361C8×C79C2×#4112yes—
362C8×C79C2×#4112yes—
363C79⋊C8—22no—
364C79⋊C8—22no—
365C79⋊C8—22no—
366C79⋊C8C2×#4112yes—
367C79⋊C8C2×#4112yes—
368C22×C79—28no—
369C22×C79—22no—
370C22×C79—22no—
371C22×C79—22no—
372C22×C79—22no—
373C22×C79—24no—
374C22×C79C4×#4112yes—
375C22×C79#56814yes—
376C22×C79C24×C411yescharacteristic
377C2×D79—22no—
378C2×D79—24no—
379C4×C79—22no—
380C4×C79—22no—
381C4×C79—24no—
382C4×C79C4×#4112yes—
383C4×C79C22×#4111yescharacteristic
384C4×C79C22×#4111yescharacteristic
385Dic79—22no—
386Dic79—24no—
387Dic79—22no—
388Dic79—22no—
389Dic79—22no—
390Dic79—22no—
391#60207—791nomaximal, Sylow
392C2×C79—22no—
393C2×C79—24no—
394C2×C79—42no—
395C2×C79C2×C4×#4111yescharacteristic
396C2×C79C2×#56812yes—
397D79—42no—
398#3444—791no—
399#2970—794no—
400#2970—794no—
401#2968—794no—
402#2968—794no—
403#2961—791no—
404#2961—791no—
405#2932—791no—
406#2932—791no—
407#2929—791no—
408#2929—791no—
409#2929—791no—
410#2929D7911yescharacteristic, complemented
411#2923—791no—
412#2923—791no—
413#2920—791no—
414#2875—791no—
415#2875—791no—
416C22×#97—791no—
417C79#6020711yescharacteristic, complemented, Sylow
418C2×#131—791no—
419C2×#131—791no—
420C2×#131—791no—
421C2×#131C2×D7911yescharacteristic
422C23×C8—791no—
423C23×C8C2×D7911yescharacteristic
424#533—792no—
425#533—791no—
426#532—791no—
427#532—792no—
428#529—794no—
429#529—792no—
430#529—792no—
431#529—794no—
432#525—791no—
433#525—794no—
434#525C2×D7911yescharacteristic
435C4×#41—791no—
436C4×#41—794no—
437C4×#41—791no—
438C22×C42—791no—
439#446—794no—
440#446—794no—
441#446—794no—
442#446—794no—
443#435—794no—
444#435—794no—
445#435—794no—
446#435—794no—
447#435—794no—
448#435—794no—
449#435—794no—
450#435C2×D7914yes—
451C8×D4—794no—
452C8×D4—794no—
453C8×D4—794no—
454C8×D4C2×D7914yes—
455#433—794no—
456#433—794no—
457#432—794no—
458#432—794no—
459#432—794no—
460#431—794no—
461#424—791no—
462#424—791no—
463#424—791no—
464#424C2×D7911yescharacteristic
465#423—791no—
466#423—791no—
467#408—791no—
468#408—791no—
469#408—791no—
470#408C2×D7911yescharacteristic
471#407—791no—
472#407C2×D7911yescharacteristic
473#405—791no—
474#405—792no—
475#405—791no—
476#405—792no—
477#405—791no—
478#405—792no—
479#405—792no—
480#405C2×D7911yescharacteristic
481C4×M16—791no—
482C4×M16—791no—
483C4×M16—792no—
484C4×M16—792no—
485C2×#97—791no—
486C2×#97—791no—
487C2×#97—791no—
488C2×#97—791no—
489C2×#97—792no—
490C2×#97—792no—
491C2×#97—792no—
492C2×#97—792no—
493C2×#97—792no—
494C2×#97—792no—
495C2×#41—794no—
496C2×#41—791no—
497C2×#41C22×D7911yescharacteristic
498C23×C4—792no—
499C23×C4C22×D7911yescharacteristic
500#131—24no—
501#131—1584no—
502#131—1584no—
503#131—1584no—
504C2×M16—791no—
505C2×M16—791no—
506C2×M16—792no—
507C2×M16—792no—
508C2×M16—792no—
509C2×M16C22×D7911yescharacteristic
510C2×M16C22×D7911yescharacteristic
511C2×M16C22×D7912yes—
512C22×C8—24no—
513C22×C8—791no—
514C22×C8—791no—
515C22×C8—792no—
516C22×C8—792no—
517C22×C8—792no—
518C22×C8—792no—
519C22×C8—792no—
520C22×C8—1584no—
521C22×C8C22×D7911yescharacteristic
522C22×C8C22×D7912yes—
523C22×C8C22×D7912yes—
524C22×C8C22×D7912yes—
525C22×C8C22×D7911yescharacteristic
526C4⋊Q8—791no—
527C4⋊Q8—792no—
528#127—791no—
529#126—794no—
530#126—794no—
531#125—794no—
532#125—792no—
533#124—791no—
534#124—791no—
535#124—794no—
536#123—794no—
537#123—792no—
538#123—794no—
539#123C4×D7912yes—
540C22⋊Q8—792no—
541C22⋊Q8—794no—
542C22⋊Q8—794no—
543C22⋊Q8C4×D7912yes—
544#121—794no—
545#121—794no—
546#121—792no—
547#121C4×D7912yes—
548#120—792no—
549#120C4×D7912yes—
550C4×Q8—792no—
551C4×Q8—794no—
552C4×Q8—792no—
553C4×Q8—794no—
554C4×D4—794no—
555C4×D4—794no—
556C4×D4—792no—
557C4×D4—794no—
558C4×D4—794no—
559C4×D4—792no—
560C4×D4—794no—
561C4×D4—794no—
562C4×D4—794no—
563C4×D4C22×D7914yes—
564#117—791no—
565#117—792no—
566#117—794no—
567#117—794no—
568#117—794no—
569#117—792no—
570#117C22×D7911yescharacteristic
571C2×C42—792no—
572C2×C42—792no—
573C2×C42—792no—
574C2×C42—792no—
575C2×C42—791no—
576C2×C42—792no—
577C2×C42—792no—
578C2×C42—791no—
579C2×C42—792no—
580C4⋊C8—794no—
581C4⋊C8—794no—
582C4⋊C8—794no—
583C4⋊C8—794no—
584C4⋊C8—794no—
585C4⋊C8C22×D7914yes—
586C22⋊C8—794no—
587C22⋊C8—794no—
588C22⋊C8—794no—
589C22⋊C8—794no—
590C22⋊C8C22×D7914yes—
591C22⋊C8C22×D7914yes—
592#97—791no—
593#97—791no—
594#97—791no—
595#97—791no—
596#97—792no—
597#97—792no—
598#97—792no—
599#97—792no—
600#97—792no—
601#97—792no—
602#97—792no—
603#97—792no—
604#97—792no—
605#97—792no—
606#97—792no—
607#97C22×D7912yes—
608C4×C8—792no—
609C4×C8—792no—
610C4×C8—792no—
611C4×C8—792no—
612C4×C8—792no—
613C4×C8C22×D7912yes—
614C24C2×C4×D7911yescharacteristic
615#41—22no—
616#41—22no—
617#41—3168no—
618#41—1582no—
619#41—1582no—
620C2×Q8—794no—
621C2×Q8—791no—
622C2×Q8C2×C4×D7911yescharacteristic
623C2×D4—794no—
624C2×D4—792no—
625C2×D4—794no—
626C2×D4—791no—
627C2×D4C2×C4×D7912yes—
628C2×D4C2×C4×D7911yescharacteristic
629C2×D4C2×C4×D7914yes—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—3164no—
633C22×C4—792no—
634C22×C4—792no—
635C22×C4—792no—
636C22×C4—792no—
637C22×C4—794no—
638C22×C4—794no—
639C22×C4—792no—
640C22×C4—792no—
641C22×C4—792no—
642C22×C4C2×C4×D7912yes—
643C22×C4C2×C4×D7911yescharacteristic
644C22×C4C23×D7912yes—
645C22×C4C23×D7912yes—
646C22×C4C23×D7911yescharacteristic
647M16—22no—
648M16—22no—
649M16—24no—
650M16—1584no—
651M16—1584no—
652M16—1582no—
653M16—1582no—
654M16—1584no—
655C2×C8—22no—
656C2×C8—24no—
657C2×C8—24no—
658C2×C8—24no—
659C2×C8—794no—
660C2×C8—791no—
661C2×C8—791no—
662C2×C8—792no—
663C2×C8—792no—
664C2×C8—792no—
665C2×C8—1584no—
666C2×C8—1584no—
667C2×C8—1584no—
668C2×C8—1584no—
669C2×C8—1582no—
670C2×C8—1584no—
671C2×C8#1192962314yescomplemented
672C2×C8C23×D7912yes—
673C2×C8C23×D7912yes—
674C2×C8C23×D7912yes—
675C2×C8C23×D7911yescharacteristic
676C2×C8C23×D7911yescharacteristic
677C4⋊C4—794no—
678C4⋊C4—794no—
679C4⋊C4—794no—
680C4⋊C4—794no—
681C4⋊C4—794no—
682C4⋊C4—792no—
683C4⋊C4—794no—
684C4⋊C4—794no—
685C4⋊C4C2×C4×D7914yes—
686C4⋊C4C2×C4×D7912yes—
687C22⋊C4—792no—
688C22⋊C4—794no—
689C22⋊C4—794no—
690C22⋊C4—794no—
691C22⋊C4—794no—
692C22⋊C4—794no—
693C22⋊C4—794no—
694C22⋊C4C2×C4×D7914yes—
695C22⋊C4C2×C4×D7914yes—
696C22⋊C4C2×C4×D7912yes—
697C42—791no—
698C42—792no—
699C42—791no—
700C42—792no—
701C42—792no—
702C42—792no—
703C42—792no—
704C42—791no—
705C42—792no—
706C42—792no—
707C42—791no—
708C42—794no—
709C42—794no—
710C42C23×D7912yes—
711C23—22no—
712C23—24no—
713C23—792no—
714C23C22×C4×D7912yes—
715C23C22×C4×D7911yescharacteristic
716C23C22×C4×D7912yes—
717Q8—22no—
718Q8—3164no—
719Q8—1582no—
720D4—24no—
721D4—28no—
722D4—22no—
723D4—3164no—
724D4—1584no—
725D4—1588no—
726D4—1582no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—3164no—
734C2×C4—3162no—
735C2×C4—3162no—
736C2×C4—3162no—
737C2×C4—3162no—
738C2×C4—3164no—
739C2×C4—792no—
740C2×C4—792no—
741C2×C4—792no—
742C2×C4—792no—
743C2×C4—794no—
744C2×C4—792no—
745C2×C4—1584no—
746C2×C4—1584no—
747C2×C4—1582no—
748C2×C4—1582no—
749C2×C4C22×C4×D7912yes—
750C2×C4C22×C4×D7912yes—
751C2×C4C22×C4×D7914yes—
752C2×C4C22×C4×D7911yescharacteristic
753C2×C4#41×D7912yes—
754C2×C4C2×#1192962312yes—
755C2×C4C24×D7911yescharacteristic
756C8—22no—
757C8—22no—
758C8—22no—
759C8—792no—
760C8—792no—
761C8—1582no—
762C8—1582no—
763C8—1582no—
764C8C2×#1192962312yes—
765C8C2×#1192962312yes—
766C22—28no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—24no—
771C22—22no—
772C22—1584no—
773C22—1582no—
774C22C4×#1192962312yes—
775C22#1909932814yes—
776C22C23×C4×D7911yescharacteristic
777C4—24no—
778C4—22no—
779C4—22no—
780C4—1582no—
781C4—1582no—
782C4—1582no—
783C4—1582no—
784C4—1584no—
785C4—1582no—
786C4C4×#1192962312yes—
787C4C2×#41×D7911yescharacteristic
788C4C22×#1192962311yescharacteristic
789C2—22no—
790C2—24no—
791C2—42no—
792C2—3162no—
793C2C2×C4×#1192962311yescharacteristic
794C2C2×#1909932812yes—
subgroupG/H
center, FrattiniC2×C4C24×D79
commutator, socleC22×C79C24×C4
FittingC79×#2929C2
prime radical#23776692C2
cosocleC2×C4×C79C25
hypercenter#2929D79
hypocenterC79#60207
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ #2929

Complements

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

NH ≅ G/Ntype
2. #23772410C2semidirect
3. #23772408C2semidirect
4. #23772395C2semidirect
5. #23772388C2semidirect
6. #23772339C2semidirect
7. #23772338C2semidirect
8. #23772116C2semidirect
9. #23772115C2semidirect
10. #23772095C2semidirect
11. #23772094C2semidirect
12. #23772090C2semidirect
13. #23772050C2semidirect
14. #23772047C2semidirect
15. #23772029C2semidirect
16. #23771827C2semidirect
17. #23771826C2semidirect
18. C22×#14579071C2semidirect
19. C79×#2929C2semidirect
38. #19098693C22semidirect
39. #19098692C22semidirect
40. #19098691C22semidirect
41. #19098690C22semidirect
42. #19098637C22semidirect
45. #19098634C22semidirect
46. #19098632C22semidirect
48. #19098631C22semidirect
52. #19098623C22semidirect
53. #19098621C22semidirect
54. #19098619C22semidirect
56. #19098617C22semidirect
68. #19098521C22semidirect
69. #19098520C22semidirect
72. #19098518C22semidirect
73. #19098517C22semidirect
76. M16×Dic79C22semidirect
77. C4×#11929607C22semidirect
86. C2×#14579071C22semidirect
87. #97×D79C22semidirect
244. C2×C79⋊C8#41semidirect
301. C2×C8×C79#41semidirect
410. #2929D79semidirect
417. C79#60207semidirect
671. C2×C8#11929623semidirect

Maximal subgroups

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

subgroupindex
#237766922
#237724102
#237724082
#237723952
#237723882
#237723392
#237723382
#237721162
#237721152
#237720952
#237720942
#237720902
#237720502
#237720472
#237720292
#237718272
#237718262
C22×#145790712
C79×#29292
#6020779