Finite Group Databasebeta

← #34304632

Subgroups — #34304632

Order 20224.

1122 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098635C211yesmaximal, characteristic
2#23766349C211yesmaximal, characteristic
3#23764370C211yesmaximal, characteristic, complemented
4#23764358C211yesmaximal, characteristic, complemented
5#23763834C211yesmaximal, characteristic, complemented
6#23763824C211yesmaximal, characteristic, complemented
7#23763713C211yesmaximal, characteristic, complemented
8#23763713C211yesmaximal, characteristic, complemented
9#23763495C211yesmaximal, characteristic, complemented
10#23763490C211yesmaximal, characteristic, complemented
11#23763405C211yesmaximal, characteristic, complemented
12#23763230C211yesmaximal, characteristic, complemented
13#23763119C211yesmaximal, characteristic, complemented
14#23763116C211yesmaximal, characteristic, complemented
15C2×#552×C79C211yesmaximal, characteristic
16C22×#11929608C2211yescharacteristic
17C23×C79⋊C8C2211yescharacteristic
18C2×#14579120C2211yescharacteristic
19C2×#14579120C2211yescharacteristic
20#19098635—24no—
21C2×C4⋊(C79⋊C8)C2211yescharacteristic
22C2×#14579085C2211yescharacteristic
23C2×#14579085C2211yescharacteristic
24C2×#14579085C2211yescharacteristic
25C2×#14579085C2211yescharacteristic
26C2×C22⋊(C79⋊C8)C2211yescharacteristic
27C2×C22⋊(C79⋊C8)C2211yescharacteristic
28C2×#14579072C2211yescharacteristic
29#19098466—21no—
30#19098456—21no—
31#19098456—21no—
32#19098433C2211yescharacteristic
33#19098423C2211yescharacteristic
34#19098423C2211yescharacteristic
35C4⋊C4×Dic79—21no—
36C4×C4⋊Dic79C2211yescharacteristic
37#19098325C2211yescharacteristic
38#19098325C2211yescharacteristic
39#19098325C2211yescharacteristic
40#19098325C2211yescharacteristic
41#19098325C2211yescharacteristic
42#19098325C2211yescharacteristic
43#19098325C2211yescharacteristic
44#19098325C2211yescharacteristic
45#19098325C2211yescharacteristic
46#19098325C2211yescharacteristic
47#19098325C2211yescharacteristic
48#19098325C2211yescharacteristic
49#552×C79—24no—
50#552×C79C418yescomplemented
51C2×#126×C79—21no—
52C2×#125×C79—21no—
53C2×#125×C79C2211yescharacteristic
54C2×#123×C79—21no—
55C2×C22⋊Q8×C79C2211yescharacteristic
56C2×C22⋊Q8×C79C2211yescharacteristic
57C2×C4×Q8×C79C2211yescharacteristic
58C2×C4×D4×C79C2211yescharacteristic
59C2×#117×C79—21no—
60C2×#117×C79C2211yescharacteristic
61C22×C4⋊C4×C79C2211yescharacteristic
62C2×#11929608—22no—
63C2×#11929608—22no—
64C2×#11929608—41no—
65C22×C79⋊C8—22no—
66C22×C79⋊C8—22no—
67C22×C79⋊C8—41no—
68C22×C79⋊C8C2311yescharacteristic
69C22×C79⋊C8C2311yescharacteristic
70C22×C79⋊C8C2311yescharacteristic
71C22×C79⋊C8C2311yescharacteristic
72#14579120—22no—
73#14579120—22no—
74#14579120—41no—
75#14579120—41no—
76C2×C4⋊Dic79—21no—
77C2×C4⋊Dic79—21no—
78C2×C4⋊Dic79C2311yescharacteristic
79C2×C4⋊Dic79C2311yescharacteristic
80C2×C4⋊Dic79C2311yescharacteristic
81C2×C4⋊Dic79C2311yescharacteristic
82C2×C22⋊Dic79—21no—
83C2×C22⋊Dic79—21no—
84C2×C22⋊Dic79—21no—
85C2×C22⋊Dic79—21no—
86C2×C4×Dic79—21no—
87C2×C4×Dic79—21no—
88C2×C4×Dic79—21no—
89C4⋊(C79⋊C8)—22no—
90#14579085—22no—
91#14579085—22no—
92#14579085—41no—
93#14579085—41no—
94C22⋊(C79⋊C8)—22no—
95C22⋊(C79⋊C8)—22no—
96#14579072—22no—
97C79⋊#95—21no—
98C79⋊#95—21no—
99C79⋊#95—21no—
100C22×Q8×C79C2311yescharacteristic
101C22×D4×C79D411yescharacteristic
102C23×C4×C79—21no—
103C23×C4×C79C2311yescharacteristic
104C23×C4×C79C2311yescharacteristic
105#126×C79—28no—
106#125×C79—28no—
107#125×C79—22no—
108#125×C79C2×C414yes—
109#123×C79—28no—
110C22⋊Q8×C79—22no—
111C22⋊Q8×C79—22no—
112C22⋊Q8×C79C2×C414yes—
113C22⋊Q8×C79C2×C414yes—
114C4×Q8×C79—22no—
115C4×Q8×C79C2×C414yes—
116C4×D4×C79C2×C414yes—
117C4×D4×C79D414yes—
118#117×C79—22no—
119#117×C79—28no—
120#117×C79C2×C414yes—
121C2×C4⋊C4×C79—21no—
122C2×C4⋊C4×C79—22no—
123C2×C4⋊C4×C79—21no—
124C2×C4⋊C4×C79—21no—
125C2×C4⋊C4×C79—21no—
126C2×C4⋊C4×C79—21no—
127C2×C4⋊C4×C79—21no—
128C2×C4⋊C4×C79C2×C414yes—
129C2×C4⋊C4×C79D411yescharacteristic
130C2×C4⋊C4×C79C2311yescharacteristic
131C2×C4⋊C4×C79C2311yescharacteristic
132C2×C4⋊C4×C79C2311yescharacteristic
133C2×C22⋊C4×C79—21no—
134C2×C22⋊C4×C79—21no—
135C2×C22⋊C4×C79—21no—
136C2×C22⋊C4×C79D411yescharacteristic
137C2×C22⋊C4×C79D411yescharacteristic
138C2×C42×C79—21no—
139C2×C42×C79—21no—
140C2×C42×C79C2311yescharacteristic
141C22×Dic79—21no—
142C22×Dic79—21no—
143C22×Dic79—21no—
144C22×Dic79—21no—
145#11929608—44no—
146C2×C79⋊C8—21no—
147C2×C79⋊C8—21no—
148C2×C79⋊C8—21no—
149C2×C79⋊C8—21no—
150C2×C79⋊C8—21no—
151C2×C79⋊C8—21no—
152C2×C79⋊C8—21no—
153C2×C79⋊C8—21no—
154C2×C79⋊C8—21no—
155C2×C79⋊C8—21no—
156C2×C79⋊C8—21no—
157C2×C79⋊C8—44no—
158C2×C79⋊C8#4112yes—
159C4⋊Dic79—21no—
160C4⋊Dic79—21no—
161C4⋊Dic79—21no—
162C4⋊Dic79—21no—
163C4⋊Dic79—21no—
164C4⋊Dic79—21no—
165C4⋊Dic79—21no—
166C4⋊Dic79—42no—
167C4⋊Dic79—81no—
168C4⋊Dic79#4112yes—
169C22⋊Dic79—42no—
170C22⋊Dic79—42no—
171C22⋊Dic79—81no—
172C22⋊Dic79—81no—
173C4×Dic79—42no—
174C4×Dic79—42no—
175C4×Dic79—42no—
176C24×C79C2×D411yescharacteristic
177C24×C79C2×D411yescharacteristic
178C2×Q8×C79—21no—
179C2×Q8×C79—21no—
180C2×Q8×C79—21no—
181C2×Q8×C79—21no—
182C2×Q8×C79—21no—
183C2×Q8×C79C22×C412yes—
184C2×D4×C79—41no—
185C2×D4×C79—41no—
186C2×D4×C79C22⋊C414yes—
187C22×C4×C79—21no—
188C22×C4×C79—21no—
189C22×C4×C79—21no—
190C22×C4×C79—21no—
191C22×C4×C79—21no—
192C22×C4×C79—21no—
193C22×C4×C79—21no—
194C22×C4×C79—21no—
195C22×C4×C79—24no—
196C22×C4×C79—21no—
197C22×C4×C79—21no—
198C22×C4×C79—21no—
199C22×C4×C79—21no—
200C22×C4×C79—42no—
201C22×C4×C79—42no—
202C22×C4×C79C22×C412yes—
203C22×C4×C79C22×C412yes—
204C22×C4×C79C2×D411yescharacteristic
205C22×C4×C79C2×D411yescharacteristic
206C22×C4×C79C2×D411yescharacteristic
207C22×C4×C79C2×D411yescharacteristic
208C22×C4×C79C2×D412yes—
209C22×C4×C79C2×D412yes—
210C22×C4×C79C2411yescharacteristic
211C4⋊C4×C79—24no—
212C4⋊C4×C79—24no—
213C4⋊C4×C79—24no—
214C4⋊C4×C79—24no—
215C4⋊C4×C79—24no—
216C4⋊C4×C79—24no—
217C4⋊C4×C79—21no—
218C4⋊C4×C79—21no—
219C4⋊C4×C79—21no—
220C4⋊C4×C79C22⋊C414yes—
221C4⋊C4×C79C22×C412yes—
222C4⋊C4×C79C22×C412yes—
223C4⋊C4×C79C22×C412yes—
224C22⋊C4×C79—24no—
225C22⋊C4×C79—24no—
226C22⋊C4×C79—24no—
227C22⋊C4×C79C22⋊C414yes—
228C22⋊C4×C79C22⋊C414yes—
229C42×C79—24no—
230C42×C79—24no—
231C42×C79C22×C412yes—
232C42×C79C2×D412yes—
233C23×C79—21no—
234C23×C79—21no—
235C23×C79—21no—
236C23×C79—21no—
237C23×C79—21no—
238C23×C79—21no—
239C23×C79—21no—
240C23×C79—21no—
241C23×C79—21no—
242C23×C79—21no—
243C23×C79—21no—
244C23×C79—21no—
245C23×C79C2×C22⋊C412yes—
246C23×C79C2×C22⋊C412yes—
247C23×C79C22×D411yescharacteristic
248Q8×C79—22no—
249Q8×C79—22no—
250Q8×C79—41no—
251Q8×C79—41no—
252D4×C79—44no—
253C2×C4×C79—21no—
254C2×C4×C79—21no—
255C2×C4×C79—21no—
256C2×C4×C79—21no—
257C2×C4×C79—21no—
258C2×C4×C79—21no—
259C2×C4×C79—21no—
260C2×C4×C79—21no—
261C2×C4×C79—22no—
262C2×C4×C79—22no—
263C2×C4×C79—22no—
264C2×C4×C79—22no—
265C2×C4×C79—22no—
266C2×C4×C79—22no—
267C2×C4×C79—22no—
268C2×C4×C79—22no—
269C2×C4×C79—22no—
270C2×C4×C79—22no—
271C2×C4×C79—22no—
272C2×C4×C79—22no—
273C2×C4×C79—48no—
274C2×C4×C79—41no—
275C2×C4×C79—41no—
276C2×C4×C79—41no—
277C2×C4×C79—41no—
278C2×C4×C79—41no—
279C2×C4×C79—41no—
280C2×C4×C79—41no—
281C2×C4×C79—41no—
282C2×C4×C79C2×C22⋊C412yes—
283C2×C4×C79C2×C22⋊C412yes—
284C2×C4×C79C2×C22⋊C412yes—
285C2×C4×C79C2×C22⋊C412yes—
286C2×C4×C79C23×C411yescharacteristic
287C2×C4×C79C22×D411yescharacteristic
288C2×C4×C79C2×#4111yescharacteristic
289C2×C4×C79C2×#4111yescharacteristic
290C2×C4×C79H(5,𝔽2)11yescharacteristic
291C2×C4×C792−1+411yescharacteristic
292C2×Dic79—22no—
293C2×Dic79—41no—
294C2×Dic79—41no—
295C2×Dic79—41no—
296C2×Dic79—41no—
297C2×Dic79—41no—
298C2×Dic79—41no—
299C2×Dic79—41no—
300C2×Dic79—41no—
301C2×Dic79—41no—
302C2×Dic79—41no—
303C2×Dic79—41no—
304C79⋊C8—22no—
305C79⋊C8—41no—
306C79⋊C8—41no—
307C79⋊C8—41no—
308C22×C79—22no—
309C22×C79—22no—
310C22×C79—22no—
311C22×C79—22no—
312C22×C79—22no—
313C22×C79—22no—
314C22×C79—41no—
315C22×C79—41no—
316C22×C79—41no—
317C22×C79—41no—
318C22×C79—41no—
319C22×C79—41no—
320C22×C79—41no—
321C22×C79—41no—
322C22×C79C22×C22⋊C411yescharacteristic
323C22×C79#54611yescharacteristic
324C22×C79#54711yescharacteristic
325C22×C79#57511yescharacteristic
326C22×C79#57511yescharacteristic
327C22×C79#57711yescharacteristic
328C22×C79#57811yescharacteristic
329C4×C79—22no—
330C4×C79—22no—
331C4×C79—22no—
332C4×C79—22no—
333C4×C79—42no—
334C4×C79—42no—
335C4×C79—42no—
336C4×C79—42no—
337C4×C79C4×#4111yescharacteristic
338C4×C79#52011yescharacteristic
339C4×C79#54611yescharacteristic
340C4×C79#54711yescharacteristic
341Dic79—42no—
342Dic79—81no—
343Dic79—81no—
344Dic79—81no—
345#22496—791nomaximal, Sylow
346C2×C79—42no—
347C2×C79—42no—
348C2×C79#233911yescharacteristic
349C2×C79#289611yescharacteristic
350C2×C79#289811yescharacteristic
351C2×C79#331511yescharacteristic
352C2×C79#331711yescharacteristic
353C2×C79#334811yescharacteristic
354C2×C79#334911yescharacteristic
355C2×#552D7911yescharacteristic
356C2×#435—791no—
357#2354—791no—
358#1992—791no—
359#1989—791no—
360#1894—791no—
361#1892—791no—
362#1873—791no—
363#1873—791no—
364#1825—791no—
365#1824—791no—
366#1803—791no—
367#1763—791no—
368#1736—791no—
369#1735—791no—
370C79#2249611yescharacteristic, complemented, Sylow
371C22×M16—791no—
372C23×C8—791no—
373#552—24no—
374#552Dic7918yescomplemented
375C2×#126—21no—
376C2×#125—21no—
377C2×#125C2×D7911yescharacteristic
378C2×#123—21no—
379C2×C22⋊Q8C2×D7911yescharacteristic
380C2×C22⋊Q8C2×D7911yescharacteristic
381C2×C4×Q8C2×D7911yescharacteristic
382C2×C4×D4C2×D7911yescharacteristic
383C2×#117—21no—
384C2×#117—791no—
385C2×#117—791no—
386C2×#117C2×D7911yescharacteristic
387C22×C4⋊C4C2×D7911yescharacteristic
388#435—1584no—
389C2×C4⋊C8—791no—
390C2×#103—791no—
391C2×#103—791no—
392C2×#103—791no—
393C2×#103—791no—
394C2×C22⋊C8—791no—
395C2×C22⋊C8—791no—
396C2×#97—791no—
397#390—1581no—
398#388—1581no—
399#388—1581no—
400#384—791no—
401#380—791no—
402#380—791no—
403C4×C4⋊C4—791no—
404C4×C4⋊C4—1581no—
405#340—791no—
406#340—791no—
407#340—791no—
408#340—791no—
409#340—791no—
410#340—791no—
411#340—791no—
412#340—791no—
413#340—791no—
414#340—791no—
415#340—791no—
416#340—791no—
417C22×Q8C22×D7911yescharacteristic
418C22×D4C22⋊D7911yescharacteristic
419C23×C4—21no—
420C23×C4C22×D7911yescharacteristic
421C23×C4C22×D7911yescharacteristic
422C2×M16—3161no—
423C2×M16—1582no—
424C2×M16—1582no—
425C22×C8—3161no—
426C22×C8—791no—
427C22×C8—791no—
428C22×C8—791no—
429C22×C8—791no—
430C22×C8—1582no—
431C22×C8—1582no—
432#126—28no—
433#125—28no—
434#125—22no—
435#125C2×Dic7914yes—
436#123—28no—
437C22⋊Q8—22no—
438C22⋊Q8—22no—
439C22⋊Q8C2×Dic7914yes—
440C22⋊Q8C2×Dic7914yes—
441C4×Q8—22no—
442C4×Q8C2×Dic7914yes—
443C4×D4C2×Dic7914yes—
444C4×D4C22⋊D7914yes—
445#117—22no—
446#117—28no—
447#117—3161no—
448#117—3161no—
449#117—1582no—
450#117—1582no—
451#117C2×Dic7914yes—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—791no—
460C2×C4⋊C4—791no—
461C2×C4⋊C4—791no—
462C2×C4⋊C4—791no—
463C2×C4⋊C4—1581no—
464C2×C4⋊C4—1581no—
465C2×C4⋊C4C2×Dic7914yes—
466C2×C4⋊C4C22⋊D7911yescharacteristic
467C2×C4⋊C4C22×D7911yescharacteristic
468C2×C4⋊C4C22×D7911yescharacteristic
469C2×C4⋊C4C22×D7911yescharacteristic
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—1581no—
474C2×C22⋊C4—1581no—
475C2×C22⋊C4—1581no—
476C2×C22⋊C4—1581no—
477C2×C22⋊C4C22⋊D7911yescharacteristic
478C2×C22⋊C4C22⋊D7911yescharacteristic
479C2×C42—21no—
480C2×C42—21no—
481C2×C42—1581no—
482C2×C42—1581no—
483C2×C42—1581no—
484C2×C42C22×D7911yescharacteristic
485C4⋊C8—1582no—
486#103—3161no—
487#103—3161no—
488#103—1582no—
489#103—1582no—
490C22⋊C8—1582no—
491C22⋊C8—1582no—
492#97—1582no—
493#95—1581no—
494#95—1581no—
495#95—1581no—
496C24C2×C22⋊D7911yescharacteristic
497C24C2×C22⋊D7911yescharacteristic
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8C22×Dic7912yes—
504C2×D4—41no—
505C2×D4—41no—
506C2×D4C22⋊Dic7914yes—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—24no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—1581no—
523C22×C4—1581no—
524C22×C4—1581no—
525C22×C4—1581no—
526C22×C4C22×Dic7912yes—
527C22×C4C22×Dic7912yes—
528C22×C4C2×C22⋊D7911yescharacteristic
529C22×C4C2×C22⋊D7911yescharacteristic
530C22×C4C2×C22⋊D7911yescharacteristic
531C22×C4C2×C22⋊D7911yescharacteristic
532C22×C4C2×C22⋊D7912yes—
533C22×C4C2×C22⋊D7912yes—
534C22×C4C23×D7911yescharacteristic
535M16—3164no—
536C2×C8—3164no—
537C2×C8—792no—
538C2×C8—1581no—
539C2×C8—1581no—
540C2×C8—1581no—
541C2×C8—1581no—
542C2×C8—1581no—
543C2×C8—1581no—
544C2×C8—1581no—
545C2×C8—1581no—
546C2×C8—1581no—
547C2×C8—1581no—
548C2×C8—1581no—
549C4⋊C4—24no—
550C4⋊C4—24no—
551C4⋊C4—24no—
552C4⋊C4—24no—
553C4⋊C4—24no—
554C4⋊C4—24no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—3162no—
559C4⋊C4—792no—
560C4⋊C4—6321no—
561C4⋊C4—1581no—
562C4⋊C4—1581no—
563C4⋊C4—1581no—
564C4⋊C4—1581no—
565C4⋊C4—1581no—
566C4⋊C4—1581no—
567C4⋊C4—1581no—
568C4⋊C4C22⋊Dic7914yes—
569C4⋊C4C22×Dic7912yes—
570C4⋊C4C22×Dic7912yes—
571C4⋊C4C22×Dic7912yes—
572C22⋊C4—24no—
573C22⋊C4—24no—
574C22⋊C4—24no—
575C22⋊C4—3162no—
576C22⋊C4—3162no—
577C22⋊C4—6321no—
578C22⋊C4—6321no—
579C22⋊C4C22⋊Dic7914yes—
580C22⋊C4C22⋊Dic7914yes—
581C42—24no—
582C42—24no—
583C42—3162no—
584C42—3162no—
585C42—3162no—
586C42C22×Dic7912yes—
587C42C2×C22⋊D7912yes—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23C2×C22⋊Dic7912yes—
601C23C2×C22⋊Dic7912yes—
602C23C22×C22⋊D7911yescharacteristic
603Q8—22no—
604Q8—22no—
605Q8—41no—
606Q8—41no—
607D4—44no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—48no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—3161no—
638C2×C4—3161no—
639C2×C4—3161no—
640C2×C4—3161no—
641C2×C4—3161no—
642C2×C4—3161no—
643C2×C4—3161no—
644C2×C4—3161no—
645C2×C4—3161no—
646C2×C4—3161no—
647C2×C4—3161no—
648C2×C4—1582no—
649C2×C4C2×C22⋊Dic7912yes—
650C2×C4C2×C22⋊Dic7912yes—
651C2×C4C2×C22⋊Dic7912yes—
652C2×C4C2×C22⋊Dic7912yes—
653C2×C4C23×Dic7911yescharacteristic
654C2×C4C22×C22⋊D7911yescharacteristic
655C2×C4#41×D7911yescharacteristic
656C2×C4#41×D7911yescharacteristic
657C2×C4#1457920711yescharacteristic
658C2×C4#1457920811yescharacteristic
659C8—3161no—
660C8—3161no—
661C8—3161no—
662C8—1582no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22C22×C22⋊Dic7911yescharacteristic
678C22#1909920111yescharacteristic
679C22#1909921211yescharacteristic
680C22#1909936111yescharacteristic
681C22#1909936111yescharacteristic
682C22#1909937111yescharacteristic
683C22#1909937811yescharacteristic
684C4—22no—
685C4—22no—
686C4—22no—
687C4—22no—
688C4—42no—
689C4—42no—
690C4—42no—
691C4—42no—
692C4—3162no—
693C4—6321no—
694C4—6321no—
695C4—6321no—
696C4#41×Dic7911yescharacteristic
697C4#1909904611yescharacteristic
698C4#1909920111yescharacteristic
699C4#1909921211yescharacteristic
700C2—42no—
701C2—42no—
702C2#2376623011yescharacteristic
703C2#2377191911yescharacteristic
704C2#2377193311yescharacteristic
705C2#2377549011yescharacteristic
706C2#2377552011yescharacteristic
707C2#2377590911yescharacteristic
708C2#2377593011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC2×#552×C79C2
socleC23×C79C22×D4
prime radicalC22×D4×C79D4
cosocleC22×C4×C79C24
hypercenterC2×#552D79
hypocenterC79#22496
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
3. #23764370C2semidirect
4. #23764358C2semidirect
5. #23763834C2semidirect
6. #23763824C2semidirect
7. #23763713C2semidirect
8. #23763713C2semidirect
9. #23763495C2semidirect
10. #23763490C2semidirect
11. #23763405C2semidirect
12. #23763230C2semidirect
13. #23763119C2semidirect
14. #23763116C2semidirect
50. #552×C79C4semidirect
370. C79#22496semidirect
374. #552Dic79semidirect

Maximal subgroups

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

subgroupindex
C2×#190986352
#237663492
#237643702
#237643582
#237638342
#237638242
#237637132
#237634952
#237634902
#237634052
#237632302
#237631192
#237631162
C2×#552×C792
#2249679