Finite Group Databasebeta

← C79×#18107 #34129796

Subgroups — C79×#18107 #34129796

Order 20224.

1000 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C79×#3459C211yesmaximal, characteristic
2C79×#3091C212yesmaximal, complemented
3C79×#2395C211yesmaximal, characteristic, complemented
4C79×#1615C212yesmaximal, complemented
5C79×#1614C211yesmaximal, characteristic, complemented
6C79×#1613C211yesmaximal, characteristic, complemented
7C79×#1609C212yesmaximal, complemented
8C79×#1608C211yesmaximal, characteristic, complemented
9C79×#1607C211yesmaximal, characteristic, complemented
10C79×#1501C212yesmaximal, complemented
11C79×#1459C211yesmaximal, characteristic, complemented
12#543×C79C2211yescharacteristic
13#539×C79—22no—
14#539×C79C2212yes—
15#538×C79—22no—
16#538×C79—21no—
17#534×C79—21no—
18#534×C79C2211yescharacteristic
19#529×C79—22no—
20#529×C79—21no—
21#525×C79—22no—
22#525×C79C2212yes—
23C2×C4×D4×C79—21no—
24C2×C4×D4×C79C2211yescharacteristic
25C2×#117×C79C2211yescharacteristic, complemented
26#485×C79—22no—
27#484×C79C2212yescomplemented
28#483×C79C2212yescomplemented
29#482×C79—22no—
30#481×C79C2212yes—
31#480×C79C2212yes—
32#427×C79—22no—
33#416×C79—22no—
34C2×C22⋊C8×C79C2212yescomplemented
35#400×C79C2211yescharacteristic, complemented
36#399×C79C2211yescharacteristic
37#398×C79C2211yescharacteristic, complemented
38#397×C79—21no—
39#397×C79C2211yescharacteristic
40#394×C79—21no—
41C4×C4⋊C4×C79—21no—
42C4×C22⋊C4×C79—21no—
43C4×C22⋊C4×C79C2211yescharacteristic, complemented
44#328×C79C2212yescomplemented
45#328×C79C2212yescomplemented
46#327×C79C2212yes—
47#327×C79C2212yes—
48#324×C79C2212yescomplemented
49#323×C79C2211yescharacteristic
50#323×C79C2211yescharacteristic
51C2×#41×C79D412yes—
52C22×D4×C79—21no—
53C22×D4×C79D411yescharacteristic
54C23×C4×C79—21no—
55C23×C4×C79D411yescharacteristic
56C23×C4×C79C2311yescharacteristic
57C22×C8×C79—22no—
58#126×C79—22no—
59#126×C79—22no—
60#126×C79—22no—
61#125×C79—21no—
62#125×C79—22no—
63#124×C79—22no—
64#124×C79—21no—
65#123×C79—22no—
66#123×C79—22no—
67#123×C79—22no—
68#123×C79—22no—
69#123×C79—22no—
70#123×C79—22no—
71C22⋊Q8×C79—22no—
72C22⋊Q8×C79—22no—
73C22⋊Q8×C79—21no—
74C22⋊Q8×C79—22no—
75C22⋊Q8×C79D412yes—
76C22⋊Q8×C79C2312yes—
77#121×C79—22no—
78#121×C79—22no—
79#121×C79—22no—
80#121×C79—21no—
81#121×C79D412yes—
82#121×C79C2312yes—
83#120×C79—22no—
84#120×C79—22no—
85#120×C79—22no—
86C4×Q8×C79—21no—
87C4×D4×C79—22no—
88C4×D4×C79—22no—
89C4×D4×C79—21no—
90C4×D4×C79—22no—
91C4×D4×C79—22no—
92C4×D4×C79—22no—
93C4×D4×C79—22no—
94C4×D4×C79—22no—
95#117×C79—22no—
96#117×C79—22no—
97#117×C79—22no—
98#117×C79D412yes—
99C2×C4⋊C4×C79—21no—
100C2×C4⋊C4×C79—21no—
101C2×C4⋊C4×C79—21no—
102C2×C4⋊C4×C79C2311yescharacteristic
103C2×C4⋊C4×C79C2311yescharacteristic
104C2×C4⋊C4×C79C2311yescharacteristic
105C2×C22⋊C4×C79—21no—
106C2×C22⋊C4×C79—21no—
107C2×C22⋊C4×C79—21no—
108C2×C22⋊C4×C79—21no—
109C2×C22⋊C4×C79—21no—
110C2×C22⋊C4×C79—21no—
111C2×C22⋊C4×C79D411yescharacteristic
112C2×C22⋊C4×C79C2311yescharacteristic
113C2×C42×C79—21no—
114C2×C42×C79—21no—
115C2×C42×C79—21no—
116C2×C42×C79D411yescharacteristic
117#107×C79—22no—
118#107×C79—22no—
119#106×C79—22no—
120#106×C79—22no—
121#103×C79—22no—
122#103×C79—22no—
123#102×C79—22no—
124#102×C79—22no—
125C22⋊C8×C79—22no—
126C22⋊C8×C79C2312yes—
127C22⋊C8×C79C2312yes—
128#95×C79—21no—
129#95×C79—21no—
130#95×C79—21no—
131#95×C79—21no—
132#95×C79C2311yescharacteristic
133#95×C79C2311yescharacteristic
134C24×C79—21no—
135C24×C79C2×D411yescharacteristic
136C24×C79C2×D411yescharacteristic
137#41×C79—44no—
138C2×Q8×C79—21no—
139C2×Q8×C79C2×D412yes—
140C2×D4×C79—22no—
141C2×D4×C79—22no—
142C2×D4×C79—22no—
143C2×D4×C79—22no—
144C2×D4×C79—21no—
145C2×D4×C79—22no—
146C2×D4×C79—22no—
147C2×D4×C79—41no—
148C2×D4×C79—42no—
149C2×D4×C79—42no—
150C2×D4×C79C2×D412yes—
151C22×C4×C79—21no—
152C22×C4×C79—21no—
153C22×C4×C79—21no—
154C22×C4×C79—21no—
155C22×C4×C79—22no—
156C22×C4×C79—21no—
157C22×C4×C79—22no—
158C22×C4×C79—21no—
159C22×C4×C79—21no—
160C22×C4×C79—21no—
161C22×C4×C79—21no—
162C22×C4×C79—42no—
163C22×C4×C79—42no—
164C22×C4×C79—82no—
165C22×C4×C79C2×D411yescharacteristic
166C22×C4×C79C2×D411yescharacteristic
167C22×C4×C79C2×D412yes—
168C22×C4×C79C2×D411yescharacteristic
169C22×C4×C79C2×D411yescharacteristic
170C22×C4×C79C2×D412yes—
171C22×C4×C79C2411yescharacteristic
172C2×C8×C79—22no—
173C2×C8×C79—22no—
174C2×C8×C79—44no—
175C4⋊C4×C79—22no—
176C4⋊C4×C79—22no—
177C4⋊C4×C79—22no—
178C4⋊C4×C79—21no—
179C4⋊C4×C79—21no—
180C4⋊C4×C79—22no—
181C4⋊C4×C79—22no—
182C4⋊C4×C79—22no—
183C4⋊C4×C79—22no—
184C4⋊C4×C79—22no—
185C4⋊C4×C79—22no—
186C4⋊C4×C79—42no—
187C4⋊C4×C79—42no—
188C4⋊C4×C79C2×D412yes—
189C4⋊C4×C79C2×D412yes—
190C22⋊C4×C79—22no—
191C22⋊C4×C79—22no—
192C22⋊C4×C79—22no—
193C22⋊C4×C79—22no—
194C22⋊C4×C79—22no—
195C22⋊C4×C79—22no—
196C22⋊C4×C79—22no—
197C22⋊C4×C79—22no—
198C22⋊C4×C79—22no—
199C22⋊C4×C79—22no—
200C22⋊C4×C79—22no—
201C22⋊C4×C79—22no—
202C22⋊C4×C79—42no—
203C22⋊C4×C79—42no—
204C22⋊C4×C79—42no—
205C22⋊C4×C79—42no—
206C42×C79—22no—
207C42×C79—21no—
208C42×C79—22no—
209C42×C79—21no—
210C42×C79—42no—
211C42×C79—41no—
212C42×C79—41no—
213C23×C79—21no—
214C23×C79—21no—
215C23×C79—21no—
216C23×C79—21no—
217C23×C79—22no—
218C23×C79—41no—
219C23×C79—41no—
220C23×C79—41no—
221C23×C79—41no—
222C23×C79—42no—
223C23×C79—81no—
224C23×C79—81no—
225C23×C79#12012yes—
226C23×C79#13512yes—
227C23×C79C22×D411yescharacteristic
228Q8×C79—42no—
229Q8×C79—81no—
230D4×C79—42no—
231D4×C79—44no—
232D4×C79—44no—
233D4×C79—42no—
234D4×C79—42no—
235D4×C79—82no—
236D4×C79—82no—
237D4×C79—81no—
238C2×C4×C79—22no—
239C2×C4×C79—24no—
240C2×C4×C79—22no—
241C2×C4×C79—21no—
242C2×C4×C79—22no—
243C2×C4×C79—21no—
244C2×C4×C79—22no—
245C2×C4×C79—21no—
246C2×C4×C79—22no—
247C2×C4×C79—21no—
248C2×C4×C79—21no—
249C2×C4×C79—42no—
250C2×C4×C79—41no—
251C2×C4×C79—41no—
252C2×C4×C79—42no—
253C2×C4×C79—41no—
254C2×C4×C79—42no—
255C2×C4×C79—44no—
256C2×C4×C79—41no—
257C2×C4×C79—41no—
258C2×C4×C79—41no—
259C2×C4×C79—41no—
260C2×C4×C79—41no—
261C2×C4×C79—41no—
262C2×C4×C79—41no—
263C2×C4×C79—41no—
264C2×C4×C79—41no—
265C2×C4×C79—41no—
266C2×C4×C79—41no—
267C2×C4×C79—81no—
268C2×C4×C79—81no—
269C2×C4×C79—82no—
270C2×C4×C79—81no—
271C2×C4×C79#12011yescharacteristic
272C2×C4×C79#12011yescharacteristic
273C2×C4×C79C22×D412yes—
274C8×C79—42no—
275C8×C79—42no—
276C22×C79—21no—
277C22×C79—21no—
278C22×C79—22no—
279C22×C79—22no—
280C22×C79—22no—
281C22×C79—22no—
282C22×C79—42no—
283C22×C79—41no—
284C22×C79—41no—
285C22×C79—42no—
286C22×C79—42no—
287C22×C79—42no—
288C22×C79—81no—
289C22×C79—81no—
290C22×C79—81no—
291C22×C79—84no—
292C22×C79C2×#12011yescharacteristic
293C22×C79C2×#13511yescharacteristic
294C22×C79#57511yescharacteristic
295C4×C79—21no—
296C4×C79—22no—
297C4×C79—42no—
298C4×C79—41no—
299C4×C79—42no—
300C4×C79—41no—
301C4×C79—42no—
302C4×C79—41no—
303C4×C79—42no—
304C4×C79—81no—
305C4×C79—81no—
306C4×C79—81no—
307C4×C79#45812yes—
308#18107C7911yesmaximal, characteristic, direct product factor, Sylow
309C2×C79—21no—
310C2×C79—21no—
311C2×C79—42no—
312C2×C79—42no—
313C2×C79—82no—
314C2×C79#300211yescharacteristic
315C2×C79#301811yescharacteristic
316C2×C79C2×#45811yescharacteristic
317#3459C2×C7911yescharacteristic
318#3091C2×C7912yescomplemented
319#2395C2×C7911yescharacteristic, complemented
320#1615C2×C7912yescomplemented
321#1614C2×C7911yescharacteristic, complemented
322#1613C2×C7911yescharacteristic, complemented
323#1609C2×C7912yescomplemented
324#1608C2×C7911yescharacteristic, complemented
325#1607C2×C7911yescharacteristic, complemented
326#1501C2×C7912yescomplemented
327#1459C2×C7911yescharacteristic, complemented
328C79#1810711yescharacteristic, direct product factor, Sylow
329#543C22×C7911yescharacteristic
330#539—22no—
331#539C22×C7912yes—
332#538—22no—
333#538—21no—
334#534—21no—
335#534C22×C7911yescharacteristic
336#529—22no—
337#529—21no—
338#525—22no—
339#525C22×C7912yes—
340C2×C4×D4—21no—
341C2×C4×D4C22×C7911yescharacteristic
342C2×#117C22×C7911yescharacteristic, complemented
343#485—22no—
344#484C22×C7912yescomplemented
345#483C22×C7912yescomplemented
346#482—22no—
347#481C22×C7912yes—
348#480C22×C7912yes—
349#427—22no—
350#416—22no—
351C2×C22⋊C8C22×C7912yescomplemented
352#400C22×C7911yescharacteristic, complemented
353#399C22×C7911yescharacteristic
354#398C22×C7911yescharacteristic, complemented
355#397—21no—
356#397C22×C7911yescharacteristic
357#394—21no—
358C4×C4⋊C4—21no—
359C4×C22⋊C4—21no—
360C4×C22⋊C4C22×C7911yescharacteristic, complemented
361#328C22×C7912yescomplemented
362#328C22×C7912yescomplemented
363#327C22×C7912yes—
364#327C22×C7912yes—
365#324C22×C7912yescomplemented
366#323C22×C7911yescharacteristic
367#323C22×C7911yescharacteristic
368C2×#41D4×C7912yes—
369C22×D4—21no—
370C22×D4D4×C7911yescharacteristic
371C23×C4—21no—
372C23×C4D4×C7911yescharacteristic
373C23×C4C23×C7911yescharacteristic
374C22×C8—22no—
375#126—22no—
376#126—22no—
377#126—22no—
378#125—21no—
379#125—22no—
380#124—22no—
381#124—21no—
382#123—22no—
383#123—22no—
384#123—22no—
385#123—22no—
386#123—22no—
387#123—22no—
388C22⋊Q8—22no—
389C22⋊Q8—22no—
390C22⋊Q8—21no—
391C22⋊Q8—22no—
392C22⋊Q8D4×C7912yes—
393C22⋊Q8C23×C7912yes—
394#121—22no—
395#121—22no—
396#121—22no—
397#121—21no—
398#121D4×C7912yes—
399#121C23×C7912yes—
400#120—22no—
401#120—22no—
402#120—22no—
403C4×Q8—21no—
404C4×D4—22no—
405C4×D4—22no—
406C4×D4—21no—
407C4×D4—22no—
408C4×D4—22no—
409C4×D4—22no—
410C4×D4—22no—
411C4×D4—22no—
412#117—22no—
413#117—22no—
414#117—22no—
415#117D4×C7912yes—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4C23×C7911yescharacteristic
420C2×C4⋊C4C23×C7911yescharacteristic
421C2×C4⋊C4C23×C7911yescharacteristic
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4D4×C7911yescharacteristic
429C2×C22⋊C4C23×C7911yescharacteristic
430C2×C42—21no—
431C2×C42—21no—
432C2×C42—21no—
433C2×C42D4×C7911yescharacteristic
434#107—22no—
435#107—22no—
436#106—22no—
437#106—22no—
438#103—22no—
439#103—22no—
440#102—22no—
441#102—22no—
442C22⋊C8—22no—
443C22⋊C8C23×C7912yes—
444C22⋊C8C23×C7912yes—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95C23×C7911yescharacteristic
450#95C23×C7911yescharacteristic
451C24—21no—
452C24C2×D4×C7911yescharacteristic
453C24C2×D4×C7911yescharacteristic
454#41—44no—
455C2×Q8—21no—
456C2×Q8C2×D4×C7912yes—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—21no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—41no—
465C2×D4—42no—
466C2×D4—42no—
467C2×D4C2×D4×C7912yes—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—82no—
482C22×C4C2×D4×C7911yescharacteristic
483C22×C4C2×D4×C7911yescharacteristic
484C22×C4C2×D4×C7912yes—
485C22×C4C2×D4×C7911yescharacteristic
486C22×C4C2×D4×C7911yescharacteristic
487C22×C4C2×D4×C7912yes—
488C22×C4C24×C7911yescharacteristic
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—44no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—42no—
504C4⋊C4—42no—
505C4⋊C4C2×D4×C7912yes—
506C4⋊C4C2×D4×C7912yes—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—42no—
520C22⋊C4—42no—
521C22⋊C4—42no—
522C22⋊C4—42no—
523C42—22no—
524C42—22no—
525C42—21no—
526C42—21no—
527C42—42no—
528C42—41no—
529C42—41no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—22no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—42no—
540C23—81no—
541C23—81no—
542C23#120×C7912yes—
543C23#135×C7912yes—
544C23C22×D4×C7911yescharacteristic
545Q8—42no—
546Q8—81no—
547D4—42no—
548D4—44no—
549D4—44no—
550D4—42no—
551D4—42no—
552D4—82no—
553D4—82no—
554D4—81no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—42no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—42no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—44no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—81no—
585C2×C4—81no—
586C2×C4—82no—
587C2×C4—81no—
588C2×C4#120×C7911yescharacteristic
589C2×C4#120×C7911yescharacteristic
590C2×C4C22×D4×C7912yes—
591C8—42no—
592C8—42no—
593C22—21no—
594C22—21no—
595C22—22no—
596C22—22no—
597C22—22no—
598C22—22no—
599C22—42no—
600C22—41no—
601C22—41no—
602C22—42no—
603C22—42no—
604C22—42no—
605C22—81no—
606C22—81no—
607C22—81no—
608C22—84no—
609C22C2×#120×C7911yescharacteristic
610C22C2×#135×C7911yescharacteristic
611C22#575×C7911yescharacteristic
612C4—22no—
613C4—21no—
614C4—42no—
615C4—41no—
616C4—42no—
617C4—41no—
618C4—42no—
619C4—41no—
620C4—42no—
621C4—81no—
622C4—81no—
623C4—81no—
624C4#458×C7912yes—
625C2—21no—
626C2—21no—
627C2—42no—
628C2—42no—
629C2—82no—
630C2C79×#300211yescharacteristic
631C2C79×#301811yescharacteristic
632C2C2×#458×C7911yescharacteristic
subgroupG/H
centerC2×C4×C79#120
commutator, Frattini, cosocleC22×C4C24×C79
socleC22×C79C2×#120
prime radicalC79×#3459C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C79 ◁ C23×C4×C79 ◁ G

Complements

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

NH ≅ G/Ntype
2. C79×#3091C2semidirect
3. C79×#2395C2semidirect
4. C79×#1615C2semidirect
5. C79×#1614C2semidirect
6. C79×#1613C2semidirect
7. C79×#1609C2semidirect
8. C79×#1608C2semidirect
9. C79×#1607C2semidirect
10. C79×#1501C2semidirect
11. C79×#1459C2semidirect
25. C2×#117×C79C22semidirect
27. #484×C79C22semidirect
28. #483×C79C22semidirect
34. C2×C22⋊C8×C79C22semidirect
35. #400×C79C22semidirect
37. #398×C79C22semidirect
43. C4×C22⋊C4×C79C22semidirect
44. #328×C79C22semidirect
45. #328×C79C22semidirect
48. #324×C79C22semidirect
308. #18107C79direct (N × H)
318. #3091C2×C79semidirect
319. #2395C2×C79semidirect
320. #1615C2×C79semidirect
321. #1614C2×C79semidirect
322. #1613C2×C79semidirect
323. #1609C2×C79semidirect
324. #1608C2×C79semidirect
325. #1607C2×C79semidirect
326. #1501C2×C79semidirect
327. #1459C2×C79semidirect
328. C79#18107direct (N × H)
342. C2×#117C22×C79semidirect
344. #484C22×C79semidirect
345. #483C22×C79semidirect
351. C2×C22⋊C8C22×C79semidirect
352. #400C22×C79semidirect
354. #398C22×C79semidirect
360. C4×C22⋊C4C22×C79semidirect
361. #328C22×C79semidirect
362. #328C22×C79semidirect
365. #324C22×C79semidirect

Maximal subgroups

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

subgroupindex
C79×#34592
C79×#30912
C79×#23952
C79×#16152
C79×#16142
C79×#16132
C79×#16092
C79×#16082
C79×#16072
C79×#15012
C79×#14592
#1810779