Finite Group Databasebeta

← #34257070

Subgroups — #34257070

Order 20224.

862 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777286C211yesmaximal, characteristic
2#23772066C211yesmaximal, characteristic
3#23762137C211yesmaximal, characteristic, complemented
4#23762131C211yesmaximal, characteristic, complemented
5#23762128C211yesmaximal, characteristic, complemented
6#23762116C211yesmaximal, characteristic, complemented
7#23762111C211yesmaximal, characteristic, complemented
8#23762108C211yesmaximal, characteristic, complemented
9#23762101C211yesmaximal, characteristic, complemented
10#23762098C211yesmaximal, characteristic, complemented
11#23762091C211yesmaximal, characteristic, complemented
12#23762086C211yesmaximal, characteristic, complemented
13#23762064C211yesmaximal, characteristic, complemented
14#23762058C211yesmaximal, characteristic, complemented
15C79×#2989C211yesmaximal, characteristic
16#19099291—21no—
17#19099291C412yes—
18#19099283—21no—
19#19099283C412yes—
20#19099253—21no—
21#19099253—21no—
22#19099253C412yes—
23#19099253C412yes—
24#19099175—21no—
25#19099175—21no—
26#19099134—21no—
27#19099120C2211yescharacteristic
28#19099120C2211yescharacteristic
29#19099120C2211yescharacteristic
30#19099120C2211yescharacteristic
31#19099120C2211yescharacteristic
32C2×#14579161C2211yescharacteristic
33#19099040—21no—
34#19098624—21no—
35#19098624—21no—
36#19098620C2211yescharacteristic
37#19098620C2211yescharacteristic
38#19098616C2211yescharacteristic
39#19098616C2211yescharacteristic
40#19098587C2211yescharacteristic
41C2×C4⋊(C79⋊C8)C2211yescharacteristic
42#19098530—21no—
43#19098519—21no—
44#19098311C2211yescharacteristic
45#19098311C2211yescharacteristic
46#19098311C2211yescharacteristic
47#19098311C2211yescharacteristic
48#19098310C2211yescharacteristic
49#19098310C2211yescharacteristic
50#19098310C2211yescharacteristic
51#19098310C2211yescharacteristic
52#19098308C2211yescharacteristic
53#19098308C2211yescharacteristic
54#19098308C2211yescharacteristic
55#19098308C2211yescharacteristic
56#19098308C2211yescharacteristic
57#19098308C2211yescharacteristic
58#19098308C2211yescharacteristic
59#19098308C2211yescharacteristic
60C4×#41×C79C2211yescharacteristic
61#446×C79—21no—
62#436×C79—21no—
63#435×C79—21no—
64#435×C79—21no—
65#432×C79C2211yescharacteristic
66#432×C79C2211yescharacteristic
67#431×C79C2211yescharacteristic
68#423×C79C2211yescharacteristic
69#423×C79C2211yescharacteristic
70C2×C4⋊C8×C79C2211yescharacteristic
71C22×Dic158—21no—
72C2×#11929608—21no—
73C22×C79⋊C8—21no—
74#14579161—21no—
75#14579161—21no—
76#14579161C2×C412yes—
77#14579161C2311yescharacteristic
78#14579161C2311yescharacteristic
79#14579161C2311yescharacteristic
80#14579161C2311yescharacteristic
81#14579159—22no—
82#14579154—22no—
83#14579154—22no—
84#14579154—22no—
85#14579154—22no—
86#14579153—21no—
87#14579153—21no—
88#14579153—21no—
89#14579153C2×C412yes—
90#14579153C2×C412yes—
91#14579151—22no—
92#14579151—22no—
93#14579151—22no—
94#14579151—22no—
95#14579148—22no—
96#14579142—22no—
97#14579142—22no—
98#14579140—21no—
99#14579140—21no—
100#14579140—21no—
101#14579140—21no—
102#14579140—21no—
103#14579140—21no—
104#14579140—21no—
105#14579140C2×C412yes—
106#14579140C2×C412yes—
107#14579140C2×C412yes—
108C4×Dic158—21no—
109C4×Dic158—21no—
110C4×Dic158—21no—
111C4×Dic158—21no—
112C4×Dic158—21no—
113C4×Dic158—21no—
114C4×Dic158—21no—
115C4×Dic158C2×C412yes—
116C4×Dic158C2×C412yes—
117C4×Dic158C2×C412yes—
118#14579126—22no—
119#14579126—22no—
120#14579120—21no—
121#14579120—21no—
122#14579120—21no—
123#14579120C2×C412yes—
124#14579120C2×C412yes—
125#14579117—22no—
126#14579117—22no—
127C2×C4⋊Dic79—21no—
128C2×C4⋊Dic79C2×C412yes—
129C4⋊(C79⋊C8)—21no—
130C4⋊(C79⋊C8)—21no—
131C4⋊(C79⋊C8)C2311yescharacteristic
132C4⋊(C79⋊C8)C2311yescharacteristic
133C4⋊(C79⋊C8)C2311yescharacteristic
134C4⋊(C79⋊C8)C2311yescharacteristic
135C22⋊(C79⋊C8)—21no—
136C22⋊(C79⋊C8)—21no—
137C22⋊(C79⋊C8)—21no—
138C22⋊(C79⋊C8)—21no—
139#14579072—21no—
140#14579072—21no—
141C4×C79⋊C8—21no—
142C4×C79⋊C8—21no—
143C2×#41×C79D411yescharacteristic
144C2×M16×C79—21no—
145C2×M16×C79—21no—
146C22×C8×C79—21no—
147C4×Q8×C79C2×C411yescharacteristic
148C4×Q8×C79D411yescharacteristic
149C4×D4×C79C2×C411yescharacteristic
150C4×D4×C79C2×C411yescharacteristic
151C4×D4×C79C2×C411yescharacteristic
152C4×D4×C79D411yescharacteristic
153C4×D4×C79D411yescharacteristic
154C4×D4×C79D411yescharacteristic
155#117×C79D411yescharacteristic
156#117×C79D411yescharacteristic
157#117×C79D411yescharacteristic
158C2×C42×C79C2311yescharacteristic
159C2×C42×C79C2311yescharacteristic
160C2×C42×C79C2311yescharacteristic
161C4⋊C8×C79—21no—
162C4⋊C8×C79—21no—
163C4⋊C8×C79—21no—
164C4⋊C8×C79C2311yescharacteristic
165C4⋊C8×C79C2311yescharacteristic
166C4⋊C8×C79C2311yescharacteristic
167C4⋊C8×C79C2311yescharacteristic
168C22⋊C8×C79—21no—
169C22⋊C8×C79—21no—
170C22⋊C8×C79—21no—
171#97×C79—21no—
172#97×C79—21no—
173C4×C8×C79—21no—
174C2×Dic158—22no—
175C2×Dic158—21no—
176C2×Dic158—21no—
177C2×Dic158—21no—
178C2×Dic158—42no—
179C2×Dic158—42no—
180C2×Dic158C22×C412yes—
181C22×Dic79—22no—
182#11929608—42no—
183C2×C79⋊C8—21no—
184C2×C79⋊C8—21no—
185C2×C79⋊C8—21no—
186C2×C79⋊C8—21no—
187C2×C79⋊C8—42no—
188C4⋊Dic79—22no—
189C4⋊Dic79—22no—
190C4⋊Dic79—21no—
191C4⋊Dic79—21no—
192C4⋊Dic79—21no—
193C4⋊Dic79—21no—
194C4⋊Dic79—21no—
195C4⋊Dic79C22×C412yes—
196C4⋊Dic79C22×C412yes—
197C4⋊Dic79C22×C412yes—
198Dic79⋊C4—22no—
199Dic79⋊C4—22no—
200Dic79⋊C4—22no—
201Dic79⋊C4—22no—
202Dic79⋊C4—22no—
203Dic79⋊C4—22no—
204Dic79⋊C4—22no—
205Dic79⋊C4—22no—
206Dic79⋊C4—22no—
207Dic79⋊C4—22no—
208C22⋊Dic79—22no—
209C22⋊Dic79—22no—
210C22⋊Dic79—22no—
211C22⋊Dic79—22no—
212C22⋊Dic79—22no—
213C4×Dic79—22no—
214C4×Dic79—22no—
215C4×Dic79—22no—
216C4×Dic79—22no—
217C4×Dic79—22no—
218#41×C79—41no—
219#41×C79—41no—
220C2×Q8×C79C22⋊C411yescharacteristic
221C2×D4×C79C22⋊C411yescharacteristic
222C2×D4×C79C22⋊C411yescharacteristic
223C2×D4×C79C22⋊C411yescharacteristic
224C22×C4×C79C22×C411yescharacteristic
225C22×C4×C79C22×C411yescharacteristic
226C22×C4×C79C22×C411yescharacteristic
227C22×C4×C79C2×D411yescharacteristic
228C22×C4×C79C2×D411yescharacteristic
229C22×C4×C79C2×D411yescharacteristic
230C22×C4×C79C2×D411yescharacteristic
231C22×C4×C79C2×D411yescharacteristic
232C22×C4×C79C2×D411yescharacteristic
233M16×C79—81no—
234M16×C79—81no—
235C2×C8×C79—21no—
236C2×C8×C79—21no—
237C2×C8×C79—21no—
238C2×C8×C79—21no—
239C2×C8×C79—81no—
240C4⋊C4×C79C22⋊C411yescharacteristic
241C4⋊C4×C79C22⋊C411yescharacteristic
242C4⋊C4×C79C22⋊C411yescharacteristic
243C4⋊C4×C79C22⋊C411yescharacteristic
244C4⋊C4×C79C22⋊C411yescharacteristic
245C4⋊C4×C79C22⋊C411yescharacteristic
246C22⋊C4×C79C22⋊C411yescharacteristic
247C22⋊C4×C79C22⋊C411yescharacteristic
248C22⋊C4×C79C22⋊C411yescharacteristic
249C22⋊C4×C79C22⋊C411yescharacteristic
250C22⋊C4×C79C22⋊C411yescharacteristic
251C22⋊C4×C79C22⋊C411yescharacteristic
252C42×C79C22×C411yescharacteristic
253C42×C79C22×C411yescharacteristic
254C42×C79C22×C411yescharacteristic
255C42×C79C2×D411yescharacteristic
256C42×C79C2×D411yescharacteristic
257C42×C79C2×D411yescharacteristic
258C42×C79C2×D411yescharacteristic
259C42×C79C2×D411yescharacteristic
260C42×C79C2×D411yescharacteristic
261C42×C79C2411yescharacteristic
262C23×C79C2×C22⋊C411yescharacteristic
263C23×C79C2×C22⋊C411yescharacteristic
264C23×C79C2×C22⋊C411yescharacteristic
265Q8×C79—41no—
266D4×C79—41no—
267D4×C79—41no—
268D4×C79—41no—
269C2×C4×C79—21no—
270C2×C4×C79—21no—
271C2×C4×C79—21no—
272C2×C4×C79—21no—
273C2×C4×C79—21no—
274C2×C4×C79—21no—
275C2×C4×C79—21no—
276C2×C4×C79—21no—
277C2×C4×C79—21no—
278C2×C4×C79—21no—
279C2×C4×C79—21no—
280C2×C4×C79—21no—
281C2×C4×C79—41no—
282C2×C4×C79—41no—
283C2×C4×C79—41no—
284C2×C4×C79C2×C22⋊C411yescharacteristic
285C2×C4×C79C2×C22⋊C411yescharacteristic
286C2×C4×C79C2×C22⋊C411yescharacteristic
287C2×C4×C79C2×C22⋊C411yescharacteristic
288C2×C4×C79C2×C22⋊C411yescharacteristic
289C2×C4×C79C2×C22⋊C411yescharacteristic
290C2×C4×C79C2×C22⋊C411yescharacteristic
291C2×C4×C79C2×C22⋊C411yescharacteristic
292C2×C4×C79C2×C22⋊C411yescharacteristic
293C2×C4×C79C23×C411yescharacteristic
294C2×C4×C79C22×D411yescharacteristic
295C2×C4×C79C22×D411yescharacteristic
296C2×Dic79—22no—
297C2×Dic79—22no—
298C2×Dic79—22no—
299C2×Dic79—22no—
300C2×Dic79—44no—
301Dic158—44no—
302Dic158—41no—
303Dic158—41no—
304Dic158—41no—
305Dic158—41no—
306Dic158—41no—
307Dic158—41no—
308Dic158—42no—
309C8×C79—41no—
310C8×C79—41no—
311C8×C79—41no—
312C8×C79—41no—
313C79⋊C8—41no—
314C79⋊C8—41no—
315C79⋊C8—41no—
316C79⋊C8—41no—
317C22×C79—21no—
318C22×C79—21no—
319C22×C79—21no—
320C22×C79—21no—
321C22×C79—21no—
322C22×C79—21no—
323C22×C79—21no—
324C22×C79—21no—
325C22×C79—21no—
326C22×C79C22×C22⋊C411yescharacteristic
327C4×C79—21no—
328C4×C79—21no—
329C4×C79—21no—
330C4×C79—21no—
331C4×C79—21no—
332C4×C79—21no—
333C4×C79—21no—
334C4×C79—21no—
335C4×C79—21no—
336C4×C79—21no—
337C4×C79#57511yescharacteristic
338C4×C79#57511yescharacteristic
339C4×C79#57711yescharacteristic
340C4×C79#57811yescharacteristic
341Dic79—42no—
342Dic79—42no—
343Dic79—42no—
344Dic79—42no—
345#17767—791nomaximal, Sylow
346C2×C79—41no—
347C2×C79—41no—
348C2×C79—41no—
349C2×C79#288911yescharacteristic
350C2×C79#289611yescharacteristic
351C2×C79#289811yescharacteristic
352#3509—791no—
353#2989D7911yescharacteristic
354#2925—791no—
355#1561—791no—
356#1559—791no—
357#1559—791no—
358#1556—791no—
359#1554—791no—
360#1554—791no—
361#1552—791no—
362#1552—791no—
363#1550—791no—
364#1549—791no—
365#1544—791no—
366#1542—791no—
367C79#1776711yescharacteristic, complemented, Sylow
368#557—792no—
369#557—1581no—
370#556—792no—
371#556—1581no—
372#552—792no—
373#552—792no—
374#552—1581no—
375#552—1581no—
376#541—1581no—
377#541—1581no—
378#536—1581no—
379#533—791no—
380#533—791no—
381#533—791no—
382#533—791no—
383#533—791no—
384C2×C4⋊Q8—791no—
385#519—1581no—
386C4×#41C2×D7911yescharacteristic
387#446—21no—
388#436—21no—
389#435—21no—
390#435—21no—
391#433—1581no—
392#433—1581no—
393#432—791no—
394#432—791no—
395#432C2×D7911yescharacteristic
396#432C2×D7911yescharacteristic
397#431—791no—
398#431—791no—
399#431C2×D7911yescharacteristic
400#423—791no—
401#423C2×D7911yescharacteristic
402#423C2×D7911yescharacteristic
403C2×C4⋊C8—791no—
404C2×C4⋊C8C2×D7911yescharacteristic
405#408—1581no—
406#405—1581no—
407#333—791no—
408#333—791no—
409#333—791no—
410#333—791no—
411#332—791no—
412#332—791no—
413#332—791no—
414#332—791no—
415#332—791no—
416#332—791no—
417#332—791no—
418#332—791no—
419#332—791no—
420#332—791no—
421#332—791no—
422#332—791no—
423C2×#41D31611yescharacteristic
424C22×Q8—1581no—
425C2×M16—21no—
426C2×M16—21no—
427C2×M16—1581no—
428C22×C8—21no—
429C22×C8—1581no—
430C4⋊Q8—792no—
431C4⋊Q8—791no—
432C4⋊Q8—791no—
433C4⋊Q8—791no—
434C4⋊Q8—791no—
435C4⋊Q8—1582no—
436C4⋊Q8—1581no—
437C4⋊Q8—1581no—
438#126—1582no—
439#126—1582no—
440#126—1582no—
441#126—1582no—
442#125—792no—
443#125—792no—
444#125—1582no—
445#125—1582no—
446#125—1582no—
447#125—1582no—
448#125—1581no—
449#125—1581no—
450#125—1581no—
451#124—1582no—
452#123—1582no—
453#123—1582no—
454C22⋊Q8—792no—
455C22⋊Q8—792no—
456C22⋊Q8—792no—
457C22⋊Q8—1581no—
458C22⋊Q8—1581no—
459C22⋊Q8—1581no—
460C22⋊Q8—1581no—
461C22⋊Q8—1581no—
462C22⋊Q8—1581no—
463C22⋊Q8—1581no—
464C4×Q8—792no—
465C4×Q8—792no—
466C4×Q8—792no—
467C4×Q8—1582no—
468C4×Q8—1582no—
469C4×Q8—1581no—
470C4×Q8—1581no—
471C4×Q8—1581no—
472C4×Q8—1581no—
473C4×Q8—1581no—
474C4×Q8—1581no—
475C4×Q8—1581no—
476C4×Q8C4×D7911yescharacteristic
477C4×Q8C22⋊D7911yescharacteristic
478C4×D4C4×D7911yescharacteristic
479C4×D4C4×D7911yescharacteristic
480C4×D4C4×D7911yescharacteristic
481C4×D4C22⋊D7911yescharacteristic
482C4×D4C22⋊D7911yescharacteristic
483C4×D4C22⋊D7911yescharacteristic
484#117—792no—
485#117—792no—
486#117—1581no—
487#117—1581no—
488#117—1581no—
489#117—1582no—
490#117—1582no—
491#117D31611yescharacteristic
492#117D31611yescharacteristic
493#117D31611yescharacteristic
494C2×C4⋊C4—792no—
495C2×C4⋊C4—1581no—
496C2×C42C22×D7911yescharacteristic
497C2×C42C22×D7911yescharacteristic
498C2×C42C22×D7911yescharacteristic
499C4⋊C8—21no—
500C4⋊C8—21no—
501C4⋊C8—21no—
502C4⋊C8—791no—
503C4⋊C8—791no—
504C4⋊C8—791no—
505C4⋊C8—791no—
506C4⋊C8—1581no—
507C4⋊C8—1581no—
508C4⋊C8C22×D7911yescharacteristic
509C4⋊C8C22×D7911yescharacteristic
510C4⋊C8C22×D7911yescharacteristic
511C4⋊C8C22×D7911yescharacteristic
512C22⋊C8—21no—
513C22⋊C8—21no—
514C22⋊C8—21no—
515C22⋊C8—1581no—
516C22⋊C8—1581no—
517C22⋊C8—1581no—
518C22⋊C8—1581no—
519#97—21no—
520#97—21no—
521#97—1581no—
522#97—1581no—
523C4×C8—21no—
524C4×C8—1581no—
525C4×C8—1581no—
526#41—41no—
527#41—41no—
528C2×Q8—3162no—
529C2×Q8—3162no—
530C2×Q8—792no—
531C2×Q8—1582no—
532C2×Q8—1581no—
533C2×Q8—1581no—
534C2×Q8—1581no—
535C2×Q8(C2×D79)⋊C411yescharacteristic
536C2×D4(C2×D79)⋊C411yescharacteristic
537C2×D4(C2×D79)⋊C411yescharacteristic
538C2×D4(C2×D79)⋊C411yescharacteristic
539C22×C4—1582no—
540C22×C4C2×C4×D7911yescharacteristic
541C22×C4C2×C4×D7911yescharacteristic
542C22×C4C2×C4×D7911yescharacteristic
543C22×C4C2×C22⋊D7911yescharacteristic
544C22×C4C2×C22⋊D7911yescharacteristic
545C22×C4C2×C22⋊D7911yescharacteristic
546C22×C4C2×D31611yescharacteristic
547C22×C4C2×D31611yescharacteristic
548C22×C4C2×D31611yescharacteristic
549M16—81no—
550M16—81no—
551M16—3162no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—81no—
557C2×C8—3162no—
558C2×C8—1581no—
559C2×C8—1581no—
560C2×C8—1581no—
561C2×C8—1581no—
562C4⋊C4—792no—
563C4⋊C4—792no—
564C4⋊C4—792no—
565C4⋊C4—1582no—
566C4⋊C4—1582no—
567C4⋊C4—1582no—
568C4⋊C4—1582no—
569C4⋊C4—1582no—
570C4⋊C4—1582no—
571C4⋊C4—1582no—
572C4⋊C4—1582no—
573C4⋊C4—1582no—
574C4⋊C4—1582no—
575C4⋊C4—1582no—
576C4⋊C4—1582no—
577C4⋊C4—1581no—
578C4⋊C4—1581no—
579C4⋊C4—1581no—
580C4⋊C4—1581no—
581C4⋊C4—1581no—
582C4⋊C4(C2×D79)⋊C411yescharacteristic
583C4⋊C4(C2×D79)⋊C411yescharacteristic
584C4⋊C4(C2×D79)⋊C411yescharacteristic
585C4⋊C4(C2×D79)⋊C411yescharacteristic
586C4⋊C4(C2×D79)⋊C411yescharacteristic
587C4⋊C4(C2×D79)⋊C411yescharacteristic
588C22⋊C4—1582no—
589C22⋊C4—1582no—
590C22⋊C4—1582no—
591C22⋊C4—1582no—
592C22⋊C4—1582no—
593C22⋊C4(C2×D79)⋊C411yescharacteristic
594C22⋊C4(C2×D79)⋊C411yescharacteristic
595C22⋊C4(C2×D79)⋊C411yescharacteristic
596C22⋊C4(C2×D79)⋊C411yescharacteristic
597C22⋊C4(C2×D79)⋊C411yescharacteristic
598C22⋊C4(C2×D79)⋊C411yescharacteristic
599C42—1582no—
600C42—1582no—
601C42—1582no—
602C42—1582no—
603C42—1582no—
604C42C2×C4×D7911yescharacteristic
605C42C2×C4×D7911yescharacteristic
606C42C2×C4×D7911yescharacteristic
607C42C2×C22⋊D7911yescharacteristic
608C42C2×C22⋊D7911yescharacteristic
609C42C2×C22⋊D7911yescharacteristic
610C42C2×D31611yescharacteristic
611C42C2×D31611yescharacteristic
612C42C2×D31611yescharacteristic
613C42C23×D7911yescharacteristic
614C23C2×(C2×D79)⋊C411yescharacteristic
615C23C2×(C2×D79)⋊C411yescharacteristic
616C23C2×(C2×D79)⋊C411yescharacteristic
617Q8—41no—
618Q8—3162no—
619Q8—3164no—
620Q8—3161no—
621Q8—3161no—
622Q8—3161no—
623Q8—3161no—
624Q8—3161no—
625Q8—3161no—
626D4—41no—
627D4—41no—
628D4—41no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—3164no—
645C2×C4—1582no—
646C2×C4—1582no—
647C2×C4—1582no—
648C2×C4—1582no—
649C2×C4C2×(C2×D79)⋊C411yescharacteristic
650C2×C4C2×(C2×D79)⋊C411yescharacteristic
651C2×C4C2×(C2×D79)⋊C411yescharacteristic
652C2×C4C2×(C2×D79)⋊C411yescharacteristic
653C2×C4C2×(C2×D79)⋊C411yescharacteristic
654C2×C4C2×(C2×D79)⋊C411yescharacteristic
655C2×C4C2×(C2×D79)⋊C411yescharacteristic
656C2×C4C2×(C2×D79)⋊C411yescharacteristic
657C2×C4C2×(C2×D79)⋊C411yescharacteristic
658C2×C4C22×C4×D7911yescharacteristic
659C2×C4C22×C22⋊D7911yescharacteristic
660C2×C4C22×D31611yescharacteristic
661C8—41no—
662C8—41no—
663C8—41no—
664C8—41no—
665C8—3161no—
666C8—3161no—
667C8—3161no—
668C8—3161no—
669C22—21no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—21no—
676C22—21no—
677C22—21no—
678C22C22×(C2×D79)⋊C411yescharacteristic
679C4—21no—
680C4—21no—
681C4—21no—
682C4—21no—
683C4—21no—
684C4—21no—
685C4—21no—
686C4—21no—
687C4—21no—
688C4—21no—
689C4—3162no—
690C4—3162no—
691C4—3162no—
692C4—3162no—
693C4#1909936311yescharacteristic
694C4#1909936311yescharacteristic
695C4#1909937411yescharacteristic
696C4#1909937811yescharacteristic
697C2—41no—
698C2—41no—
699C2—41no—
700C2#2377188211yescharacteristic
701C2#2377192011yescharacteristic
702C2#2377193011yescharacteristic
subgroupG/H
centerC22C22×(C2×D79)⋊C4
commutatorC2×C4×C79C23×C4
FrattiniC42C23×D79
FittingC79×#2989C2
socleC22×C79C22×C22⋊C4
prime radicalC2×#41×C79D4
cosocleC42×C79C24
hypercenter#2989D79
hypocenterC79#17767
LCSG ▷ C2×C4×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2989

Complements

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

NH ≅ G/Ntype
3. #23762137C2semidirect
4. #23762131C2semidirect
5. #23762128C2semidirect
6. #23762116C2semidirect
7. #23762111C2semidirect
8. #23762108C2semidirect
9. #23762101C2semidirect
10. #23762098C2semidirect
11. #23762091C2semidirect
12. #23762086C2semidirect
13. #23762064C2semidirect
14. #23762058C2semidirect
367. C79#17767semidirect

Maximal subgroups

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

subgroupindex
#237772862
#237720662
#237621372
#237621312
#237621282
#237621162
#237621112
#237621082
#237621012
#237620982
#237620912
#237620862
#237620642
#237620582
C79×#29892
#1776779