Finite Group Databasebeta

← C79×#18974 #34130663

Subgroups — C79×#18974 #34130663

Order 20224.

930 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C79×#3546C211yesmaximal, characteristic
2C79×#3254C211yesmaximal, characteristic, complemented
3C79×#3248C211yesmaximal, characteristic, complemented
4C79×#3228C211yesmaximal, characteristic, complemented
5C79×#1654C211yesmaximal, characteristic, complemented
6C79×#1652C211yesmaximal, characteristic, complemented
7C79×#1650C211yesmaximal, characteristic, complemented
8C79×#1647C211yesmaximal, characteristic, complemented
9C79×#1642C211yesmaximal, characteristic, complemented
10C79×#1641C211yesmaximal, characteristic, complemented
11C79×#1639C211yesmaximal, characteristic, complemented
12C79×#1639C211yesmaximal, characteristic, complemented
13C79×#1547C211yesmaximal, characteristic, complemented
14C79×#1495C211yesmaximal, characteristic, complemented
15C79×#1480C211yesmaximal, characteristic, complemented
16#560×C79—22no—
17#556×C79C2211yescharacteristic
18#553×C79—21no—
19#550×C79—21no—
20#550×C79C2211yescharacteristic
21#547×C79C2211yescharacteristic
22#546×C79—21no—
23#546×C79—21no—
24D42×C79C2211yescharacteristic
25#542×C79—21no—
26#538×C79—22no—
27#537×C79—21no—
28#535×C79—21no—
29#535×C79—21no—
30#533×C79C2211yescharacteristic, complemented
31#532×C79C2211yescharacteristic
32#532×C79C2211yescharacteristic
33#529×C79C2211yescharacteristic
34#500×C79C2211yescharacteristic, complemented
35#498×C79C2211yescharacteristic, complemented
36#486×C79C2211yescharacteristic
37#486×C79C2211yescharacteristic
38#482×C79—22no—
39#479×C79—21no—
40#478×C79—22no—
41#477×C79—21no—
42#475×C79C2211yescharacteristic, complemented
43#474×C79C2211yescharacteristic
44#474×C79C2211yescharacteristic
45#474×C79C2211yescharacteristic, complemented
46#468×C79—21no—
47#468×C79—21no—
48#467×C79—21no—
49#465×C79—21no—
50#464×C79—21no—
51#462×C79C2211yescharacteristic, complemented
52#461×C79C2211yescharacteristic
53#461×C79C2211yescharacteristic
54#461×C79C2211yescharacteristic, complemented
55#460×C79—21no—
56#431×C79C2211yescharacteristic, complemented
57#423×C79C2211yescharacteristic, complemented
58C2×C4⋊C8×C79C2211yescharacteristic, complemented
59#332×C79C2211yescharacteristic, complemented
60#332×C79C2211yescharacteristic, complemented
61#331×C79C2211yescharacteristic
62#331×C79C2211yescharacteristic
63Q8⋊C8×C79C2211yescharacteristic, complemented
64Q8⋊C8×C79C2211yescharacteristic, complemented
65D4⋊C8×C79C2211yescharacteristic
66D4⋊C8×C79C2211yescharacteristic
67D4⋊C8×C79C2211yescharacteristic
68D4⋊C8×C79C2211yescharacteristic
69D4⋊C8×C79C2211yescharacteristic, complemented
70D4⋊C8×C79C2211yescharacteristic, complemented
71C2×#41×C79—21no—
72C2×#41×C79—21no—
73C2×#41×C79—21no—
74C2×#41×C79—21no—
75C22×D4×C79—21no—
76C22×D4×C79—21no—
77C2×Q16×C79—21no—
78C2×SD16×C79—21no—
79C2×SD16×C79—21no—
80C2×SD16×C79—21no—
81C2×M16×C79—21no—
82C22×C8×C79—21no—
83C4⋊Q8×C79D411yescharacteristic
84C4⋊Q8×C79C2311yescharacteristic
85C4⋊Q8×C79C2311yescharacteristic
86C4⋊Q8×C79C2311yescharacteristic
87#127×C79—22no—
88#127×C79—21no—
89#127×C79D411yescharacteristic
90#127×C79C2311yescharacteristic
91#126×C79—22no—
92#126×C79—22no—
93#126×C79—21no—
94#125×C79—21no—
95#125×C79D411yescharacteristic
96#124×C79—22no—
97#124×C79—21no—
98#124×C79—21no—
99#124×C79—21no—
100#124×C79D411yescharacteristic
101#123×C79—22no—
102#123×C79—22no—
103#123×C79—21no—
104#123×C79—22no—
105C22⋊Q8×C79—22no—
106C22⋊Q8×C79—21no—
107C22⋊Q8×C79—21no—
108C22⋊Q8×C79—21no—
109C22⋊Q8×C79—21no—
110C22⋊Q8×C79D411yescharacteristic
111#121×C79—22no—
112#121×C79—22no—
113#121×C79—22no—
114#121×C79—22no—
115#121×C79—22no—
116#121×C79—21no—
117#121×C79—22no—
118#121×C79—21no—
119#121×C79—21no—
120#121×C79—21no—
121#121×C79—21no—
122#121×C79—21no—
123#121×C79D411yescharacteristic
124#121×C79D411yescharacteristic
125#121×C79D411yescharacteristic
126#121×C79D412yes—
127#120×C79—22no—
128#120×C79—22no—
129#120×C79—22no—
130#120×C79—22no—
131C4×Q8×C79—21no—
132C4×Q8×C79—21no—
133C4×Q8×C79—21no—
134C4×Q8×C79C2311yescharacteristic
135C4×D4×C79—22no—
136C4×D4×C79—21no—
137C4×D4×C79—21no—
138C4×D4×C79—21no—
139C4×D4×C79—21no—
140C4×D4×C79D412yes—
141C4×D4×C79C2311yescharacteristic
142C4×D4×C79C2311yescharacteristic
143C4×D4×C79C2311yescharacteristic
144#117×C79—21no—
145#117×C79—21no—
146#117×C79—21no—
147C2×C4⋊C4×C79—21no—
148C2×C22⋊C4×C79—22no—
149C2×C42×C79C2311yescharacteristic
150#107×C79—21no—
151#107×C79—21no—
152#107×C79—21no—
153#107×C79—22no—
154#106×C79—21no—
155#106×C79—22no—
156C4⋊C8×C79—21no—
157C4⋊C8×C79—21no—
158C4⋊C8×C79—21no—
159C4⋊C8×C79C2311yescharacteristic
160C4⋊C8×C79C2311yescharacteristic
161C4⋊C8×C79C2311yescharacteristic
162C4⋊C8×C79C2311yescharacteristic
163#103×C79—21no—
164#103×C79—21no—
165#103×C79—21no—
166#103×C79—21no—
167#103×C79—21no—
168#102×C79—21no—
169#102×C79—21no—
170#102×C79—21no—
171#102×C79—22no—
172#102×C79—22no—
173C22⋊C8×C79—21no—
174C4×C8×C79C2311yescharacteristic
175C4×C8×C79C2311yescharacteristic
176C24×C79—22no—
177#41×C79—81no—
178#41×C79—81no—
179#41×C79—81no—
180#41×C79—81no—
181#41×C79—81no—
182#41×C79—81no—
183#41×C79—81no—
184#41×C79—81no—
185C2×Q8×C79—21no—
186C2×Q8×C79—21no—
187C2×Q8×C79—21no—
188C2×Q8×C79—21no—
189C2×Q8×C79C2×D411yescharacteristic
190C2×D4×C79—22no—
191C2×D4×C79—22no—
192C2×D4×C79—22no—
193C2×D4×C79—22no—
194C2×D4×C79—22no—
195C2×D4×C79—21no—
196C2×D4×C79—21no—
197C2×D4×C79—22no—
198C2×D4×C79—21no—
199C2×D4×C79—21no—
200C2×D4×C79—21no—
201C2×D4×C79—21no—
202C2×D4×C79—21no—
203C2×D4×C79—81no—
204C2×D4×C79—81no—
205C2×D4×C79—81no—
206C2×D4×C79—81no—
207C2×D4×C79C2×D411yescharacteristic
208C2×D4×C79C2×D411yescharacteristic
209C2×D4×C79C2×D411yescharacteristic
210C2×D4×C79C2×D412yes—
211C22×C4×C79—22no—
212C22×C4×C79—22no—
213C22×C4×C79—21no—
214C22×C4×C79—21no—
215C22×C4×C79—21no—
216C22×C4×C79—22no—
217C22×C4×C79C2×D411yescharacteristic
218C22×C4×C79C2×D411yescharacteristic
219C22×C4×C79C2×D411yescharacteristic
220Q16×C79—81no—
221SD16×C79—81no—
222SD16×C79—81no—
223SD16×C79—81no—
224M16×C79—81no—
225C2×C8×C79—21no—
226C2×C8×C79—21no—
227C2×C8×C79—21no—
228C2×C8×C79—21no—
229C2×C8×C79—21no—
230C2×C8×C79—21no—
231C2×C8×C79—81no—
232C4⋊C4×C79—22no—
233C4⋊C4×C79—22no—
234C4⋊C4×C79—21no—
235C4⋊C4×C79—21no—
236C4⋊C4×C79—21no—
237C4⋊C4×C79—21no—
238C4⋊C4×C79—21no—
239C4⋊C4×C79—21no—
240C4⋊C4×C79—21no—
241C4⋊C4×C79—21no—
242C4⋊C4×C79—21no—
243C4⋊C4×C79—21no—
244C4⋊C4×C79—41no—
245C4⋊C4×C79—41no—
246C4⋊C4×C79C2×D411yescharacteristic
247C4⋊C4×C79C2×D411yescharacteristic
248C4⋊C4×C79C2×D411yescharacteristic
249C4⋊C4×C79C2×D411yescharacteristic
250C4⋊C4×C79C2×D412yes—
251C22⋊C4×C79—22no—
252C22⋊C4×C79—22no—
253C22⋊C4×C79—22no—
254C22⋊C4×C79—22no—
255C22⋊C4×C79—22no—
256C22⋊C4×C79—21no—
257C22⋊C4×C79—21no—
258C22⋊C4×C79—21no—
259C22⋊C4×C79—21no—
260C22⋊C4×C79—21no—
261C22⋊C4×C79—21no—
262C22⋊C4×C79—22no—
263C22⋊C4×C79—22no—
264C22⋊C4×C79—21no—
265C22⋊C4×C79—21no—
266C22⋊C4×C79—21no—
267C22⋊C4×C79—41no—
268C42×C79—22no—
269C42×C79—21no—
270C42×C79—41no—
271C42×C79C2×D411yescharacteristic
272C42×C79C2×D411yescharacteristic
273C42×C79C2×D411yescharacteristic
274C42×C79C2411yescharacteristic
275C23×C79—21no—
276C23×C79—21no—
277C23×C79—22no—
278C23×C79—21no—
279C23×C79—82no—
280C23×C79—82no—
281C23×C79—82no—
282C23×C79#12011yescharacteristic
283Q8×C79—21no—
284Q8×C79—21no—
285Q8×C79—41no—
286Q8×C79—41no—
287Q8×C79—41no—
288Q8×C79—41no—
289Q8×C79—41no—
290Q8×C79—41no—
291Q8×C79—81no—
292D4×C79—21no—
293D4×C79—21no—
294D4×C79—21no—
295D4×C79—21no—
296D4×C79—21no—
297D4×C79—21no—
298D4×C79—42no—
299D4×C79—41no—
300D4×C79—41no—
301D4×C79—41no—
302D4×C79—41no—
303D4×C79—81no—
304D4×C79—81no—
305D4×C79—81no—
306D4×C79—81no—
307D4×C79—81no—
308D4×C79—82no—
309D4×C79—82no—
310D4×C79—82no—
311D4×C79—82no—
312D4×C79—82no—
313D4×C79—82no—
314C2×C4×C79—21no—
315C2×C4×C79—21no—
316C2×C4×C79—21no—
317C2×C4×C79—21no—
318C2×C4×C79—21no—
319C2×C4×C79—21no—
320C2×C4×C79—21no—
321C2×C4×C79—22no—
322C2×C4×C79—21no—
323C2×C4×C79—21no—
324C2×C4×C79—41no—
325C2×C4×C79—41no—
326C2×C4×C79—41no—
327C2×C4×C79—41no—
328C2×C4×C79—41no—
329C2×C4×C79—41no—
330C2×C4×C79—41no—
331C2×C4×C79—41no—
332C2×C4×C79—41no—
333C2×C4×C79—82no—
334C2×C4×C79—82no—
335C2×C4×C79—82no—
336C2×C4×C79#12011yescharacteristic
337C2×C4×C79#12011yescharacteristic
338C2×C4×C79#12011yescharacteristic
339C2×C4×C79C22×D411yescharacteristic
340C2×C4×C79C22×D411yescharacteristic
341C2×C4×C79C22×D411yescharacteristic
342C8×C79—41no—
343C8×C79—41no—
344C8×C79—41no—
345C8×C79—41no—
346C8×C79—41no—
347C8×C79—41no—
348C22×C79—21no—
349C22×C79—21no—
350C22×C79—21no—
351C22×C79—41no—
352C22×C79—41no—
353C22×C79—41no—
354C22×C79—41no—
355C22×C79—42no—
356C22×C79—42no—
357C22×C79—41no—
358C22×C79—41no—
359C22×C79—42no—
360C22×C79—41no—
361C22×C79—41no—
362C22×C79—41no—
363C22×C79—164no—
364C22×C79C2×#12011yescharacteristic
365C4×C79—21no—
366C4×C79—21no—
367C4×C79—21no—
368C4×C79—21no—
369C4×C79—41no—
370C4×C79—41no—
371C4×C79—41no—
372C4×C79—41no—
373C4×C79—42no—
374C4×C79—41no—
375C4×C79—81no—
376C4×C79—81no—
377C4×C79#57611yescharacteristic
378C4×C79#57611yescharacteristic
379C4×C79#57711yescharacteristic
380C4×C79#57711yescharacteristic
381#18974C7911yesmaximal, characteristic, direct product factor, Sylow
382C2×C79—41no—
383C2×C79—81no—
384C2×C79—82no—
385C2×C79—81no—
386C2×C79—81no—
387C2×C79#301211yescharacteristic
388C2×C79#301211yescharacteristic
389C2×C79#302211yescharacteristic
390#3546C2×C7911yescharacteristic
391#3254C2×C7911yescharacteristic, complemented
392#3248C2×C7911yescharacteristic, complemented
393#3228C2×C7911yescharacteristic, complemented
394#1654C2×C7911yescharacteristic, complemented
395#1652C2×C7911yescharacteristic, complemented
396#1650C2×C7911yescharacteristic, complemented
397#1647C2×C7911yescharacteristic, complemented
398#1642C2×C7911yescharacteristic, complemented
399#1641C2×C7911yescharacteristic, complemented
400#1639C2×C7911yescharacteristic, complemented
401#1639C2×C7911yescharacteristic, complemented
402#1547C2×C7911yescharacteristic, complemented
403#1495C2×C7911yescharacteristic, complemented
404#1480C2×C7911yescharacteristic, complemented
405C79#1897411yescharacteristic, direct product factor, Sylow
406#560—22no—
407#556C22×C7911yescharacteristic
408#553—21no—
409#550—21no—
410#550C22×C7911yescharacteristic
411#547C22×C7911yescharacteristic
412#546—21no—
413#546—21no—
414D42C22×C7911yescharacteristic
415#542—21no—
416#538—22no—
417#537—21no—
418#535—21no—
419#535—21no—
420#533C22×C7911yescharacteristic, complemented
421#532C22×C7911yescharacteristic
422#532C22×C7911yescharacteristic
423#529C22×C7911yescharacteristic
424#500C22×C7911yescharacteristic, complemented
425#498C22×C7911yescharacteristic, complemented
426#486C22×C7911yescharacteristic
427#486C22×C7911yescharacteristic
428#482—22no—
429#479—21no—
430#478—22no—
431#477—21no—
432#475C22×C7911yescharacteristic, complemented
433#474C22×C7911yescharacteristic
434#474C22×C7911yescharacteristic
435#474C22×C7911yescharacteristic, complemented
436#468—21no—
437#468—21no—
438#467—21no—
439#465—21no—
440#464—21no—
441#462C22×C7911yescharacteristic, complemented
442#461C22×C7911yescharacteristic
443#461C22×C7911yescharacteristic
444#461C22×C7911yescharacteristic, complemented
445#460—21no—
446#431C22×C7911yescharacteristic, complemented
447#423C22×C7911yescharacteristic, complemented
448C2×C4⋊C8C22×C7911yescharacteristic, complemented
449#332C22×C7911yescharacteristic, complemented
450#332C22×C7911yescharacteristic, complemented
451#331C22×C7911yescharacteristic
452#331C22×C7911yescharacteristic
453Q8⋊C8C22×C7911yescharacteristic, complemented
454Q8⋊C8C22×C7911yescharacteristic, complemented
455D4⋊C8C22×C7911yescharacteristic
456D4⋊C8C22×C7911yescharacteristic
457D4⋊C8C22×C7911yescharacteristic
458D4⋊C8C22×C7911yescharacteristic
459D4⋊C8C22×C7911yescharacteristic, complemented
460D4⋊C8C22×C7911yescharacteristic, complemented
461C2×#41—21no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—21no—
465C22×D4—21no—
466C22×D4—21no—
467C2×Q16—21no—
468C2×SD16—21no—
469C2×SD16—21no—
470C2×SD16—21no—
471C2×M16—21no—
472C22×C8—21no—
473C4⋊Q8D4×C7911yescharacteristic
474C4⋊Q8C23×C7911yescharacteristic
475C4⋊Q8C23×C7911yescharacteristic
476C4⋊Q8C23×C7911yescharacteristic
477#127—22no—
478#127—21no—
479#127D4×C7911yescharacteristic
480#127C23×C7911yescharacteristic
481#126—22no—
482#126—22no—
483#126—21no—
484#125—21no—
485#125D4×C7911yescharacteristic
486#124—22no—
487#124—21no—
488#124—21no—
489#124—21no—
490#124D4×C7911yescharacteristic
491#123—22no—
492#123—22no—
493#123—21no—
494#123—22no—
495C22⋊Q8—22no—
496C22⋊Q8—21no—
497C22⋊Q8—21no—
498C22⋊Q8—21no—
499C22⋊Q8—21no—
500C22⋊Q8D4×C7911yescharacteristic
501#121—22no—
502#121—22no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—21no—
507#121—22no—
508#121—21no—
509#121—21no—
510#121—21no—
511#121—21no—
512#121—21no—
513#121D4×C7911yescharacteristic
514#121D4×C7911yescharacteristic
515#121D4×C7911yescharacteristic
516#121D4×C7912yes—
517#120—22no—
518#120—22no—
519#120—22no—
520#120—22no—
521C4×Q8—21no—
522C4×Q8—21no—
523C4×Q8—21no—
524C4×Q8C23×C7911yescharacteristic
525C4×D4—22no—
526C4×D4—21no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4D4×C7912yes—
531C4×D4C23×C7911yescharacteristic
532C4×D4C23×C7911yescharacteristic
533C4×D4C23×C7911yescharacteristic
534#117—21no—
535#117—21no—
536#117—21no—
537C2×C4⋊C4—21no—
538C2×C22⋊C4—22no—
539C2×C42C23×C7911yescharacteristic
540#107—21no—
541#107—21no—
542#107—21no—
543#107—22no—
544#106—21no—
545#106—22no—
546C4⋊C8—21no—
547C4⋊C8—21no—
548C4⋊C8—21no—
549C4⋊C8C23×C7911yescharacteristic
550C4⋊C8C23×C7911yescharacteristic
551C4⋊C8C23×C7911yescharacteristic
552C4⋊C8C23×C7911yescharacteristic
553#103—21no—
554#103—21no—
555#103—21no—
556#103—21no—
557#103—21no—
558#102—21no—
559#102—21no—
560#102—21no—
561#102—22no—
562#102—22no—
563C22⋊C8—21no—
564C4×C8C23×C7911yescharacteristic
565C4×C8C23×C7911yescharacteristic
566C24—22no—
567#41—81no—
568#41—81no—
569#41—81no—
570#41—81no—
571#41—81no—
572#41—81no—
573#41—81no—
574#41—81no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8C2×D4×C7911yescharacteristic
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—22no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4—81no—
596C2×D4—81no—
597C2×D4C2×D4×C7911yescharacteristic
598C2×D4C2×D4×C7911yescharacteristic
599C2×D4C2×D4×C7911yescharacteristic
600C2×D4C2×D4×C7912yes—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4C2×D4×C7911yescharacteristic
608C22×C4C2×D4×C7911yescharacteristic
609C22×C4C2×D4×C7911yescharacteristic
610Q16—81no—
611SD16—81no—
612SD16—81no—
613SD16—81no—
614M16—81no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—81no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—41no—
635C4⋊C4—41no—
636C4⋊C4C2×D4×C7911yescharacteristic
637C4⋊C4C2×D4×C7911yescharacteristic
638C4⋊C4C2×D4×C7911yescharacteristic
639C4⋊C4C2×D4×C7911yescharacteristic
640C4⋊C4C2×D4×C7912yes—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—41no—
658C42—22no—
659C42—21no—
660C42—41no—
661C42C2×D4×C7911yescharacteristic
662C42C2×D4×C7911yescharacteristic
663C42C2×D4×C7911yescharacteristic
664C42C24×C7911yescharacteristic
665C23—21no—
666C23—21no—
667C23—22no—
668C23—21no—
669C23—82no—
670C23—82no—
671C23—82no—
672C23#120×C7911yescharacteristic
673Q8—21no—
674Q8—21no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678Q8—41no—
679Q8—41no—
680Q8—41no—
681Q8—81no—
682D4—21no—
683D4—21no—
684D4—21no—
685D4—21no—
686D4—21no—
687D4—21no—
688D4—42no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—81no—
694D4—81no—
695D4—81no—
696D4—81no—
697D4—81no—
698D4—82no—
699D4—82no—
700D4—82no—
701D4—82no—
702D4—82no—
703D4—82no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4—82no—
726C2×C4#120×C7911yescharacteristic
727C2×C4#120×C7911yescharacteristic
728C2×C4#120×C7911yescharacteristic
729C2×C4C22×D4×C7911yescharacteristic
730C2×C4C22×D4×C7911yescharacteristic
731C2×C4C22×D4×C7911yescharacteristic
732C8—41no—
733C8—41no—
734C8—41no—
735C8—41no—
736C8—41no—
737C8—41no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—42no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—42no—
751C22—41no—
752C22—41no—
753C22—164no—
754C22C2×#120×C7911yescharacteristic
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—41no—
764C4—42no—
765C4—81no—
766C4—81no—
767C4#576×C7911yescharacteristic
768C4#576×C7911yescharacteristic
769C4#577×C7911yescharacteristic
770C4#577×C7911yescharacteristic
771C2—41no—
772C2—81no—
773C2—81no—
774C2—82no—
775C2—81no—
776C2C79×#301211yescharacteristic
777C2C79×#301211yescharacteristic
778C2C79×#302211yescharacteristic
subgroupG/H
center, socleC22×C79C2×#120
commutator, Frattini, cosocleC42C24×C79
prime radicalC79×#3546C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C79 ◁ C2×C42×C79 ◁ G

Complements

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

NH ≅ G/Ntype
2. C79×#3254C2semidirect
3. C79×#3248C2semidirect
4. C79×#3228C2semidirect
5. C79×#1654C2semidirect
6. C79×#1652C2semidirect
7. C79×#1650C2semidirect
8. C79×#1647C2semidirect
9. C79×#1642C2semidirect
10. C79×#1641C2semidirect
11. C79×#1639C2semidirect
12. C79×#1639C2semidirect
13. C79×#1547C2semidirect
14. C79×#1495C2semidirect
15. C79×#1480C2semidirect
30. #533×C79C22semidirect
34. #500×C79C22semidirect
35. #498×C79C22semidirect
42. #475×C79C22semidirect
45. #474×C79C22semidirect
51. #462×C79C22semidirect
54. #461×C79C22semidirect
56. #431×C79C22semidirect
57. #423×C79C22semidirect
58. C2×C4⋊C8×C79C22semidirect
59. #332×C79C22semidirect
60. #332×C79C22semidirect
63. Q8⋊C8×C79C22semidirect
64. Q8⋊C8×C79C22semidirect
69. D4⋊C8×C79C22semidirect
70. D4⋊C8×C79C22semidirect
381. #18974C79direct (N × H)
391. #3254C2×C79semidirect
392. #3248C2×C79semidirect
393. #3228C2×C79semidirect
394. #1654C2×C79semidirect
395. #1652C2×C79semidirect
396. #1650C2×C79semidirect
397. #1647C2×C79semidirect
398. #1642C2×C79semidirect
399. #1641C2×C79semidirect
400. #1639C2×C79semidirect
401. #1639C2×C79semidirect
402. #1547C2×C79semidirect
403. #1495C2×C79semidirect
404. #1480C2×C79semidirect
405. C79#18974direct (N × H)
420. #533C22×C79semidirect
424. #500C22×C79semidirect
425. #498C22×C79semidirect
432. #475C22×C79semidirect
435. #474C22×C79semidirect
441. #462C22×C79semidirect
444. #461C22×C79semidirect
446. #431C22×C79semidirect
447. #423C22×C79semidirect
448. C2×C4⋊C8C22×C79semidirect
449. #332C22×C79semidirect
450. #332C22×C79semidirect
453. Q8⋊C8C22×C79semidirect
454. Q8⋊C8C22×C79semidirect
459. D4⋊C8C22×C79semidirect
460. D4⋊C8C22×C79semidirect

Maximal subgroups

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

subgroupindex
C79×#35462
C79×#32542
C79×#32482
C79×#32282
C79×#16542
C79×#16522
C79×#16502
C79×#16472
C79×#16422
C79×#16412
C79×#16392
C79×#15472
C79×#14952
C79×#14802
#1897479