Finite Group Databasebeta

← #35152852

Subgroups — #35152852

Order 20224.

1996 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23772405C214yesmaximal, complemented
2#23772396C214yesmaximal, complemented
3#23772367C212yesmaximal, complemented
4#23772367C214yesmaximal, complemented
5#41×C79⋊C8C212yesmaximal, complemented
6#23772349C212yesmaximal, complemented
7#23772144C212yesmaximal, complemented
8#23772127C214yesmaximal, complemented
9#23772044C212yesmaximal, complemented
10C2×#19098616C211yesmaximal, characteristic, complemented
11C4×#14579168C212yesmaximal, complemented
12C2×C4×#11929608C211yesmaximal, characteristic, complemented
13C79×#3444C211yesmaximal, characteristic
14C2×#14579168C2214yes—
15C22×#11929608C2212yes—
16#19098694C2218yescomplemented
17#19098694C2214yescomplemented
18Q8×C79⋊C8C2214yescomplemented
19#19098641C2218yes—
20#19098641C2214yescomplemented
21#19098635C2218yes—
22#19098635C2218yes—
23#19098635C2218yescomplemented
24D4×C79⋊C8C2218yes—
25D4×C79⋊C8C2214yescomplemented
26#19098624C2218yescomplemented
27#19098616C2211yescharacteristic
28#19098616C2211yescharacteristic
29#19098616C2212yes—
30#19098616C2212yes—
31#19098616C2212yes—
32#19098616C2214yescomplemented
33#19098616C2214yescomplemented
34#19098590C2214yes—
35C2×C4⋊(C79⋊C8)C2212yes—
36#19098530C2214yes—
37C2×C22⋊(C79⋊C8)C2212yes—
38#19098519C2214yes—
39#19098519C2218yescomplemented
40C4×#11929608C2211yescharacteristic
41C4×#11929608C2211yescharacteristic
42C4×#11929608C2212yes—
43C4×#11929608C2212yes—
44C4×#11929608C2212yes—
45C4×#11929608C2214yescomplemented
46C2×#14579072C2212yes—
47C2×C4×C79⋊C8C2212yes—
48C2×C4×C79⋊C8C2212yes—
49C2×C4×C79⋊C8C2214yescomplemented
50#533×C79C411yescharacteristic
51#533×C79C411yescharacteristic
52#533×C79C2211yescharacteristic
53#532×C79C411yescharacteristic
54#532×C79C411yescharacteristic
55#532×C79C2211yescharacteristic
56#529×C79C412yes—
57#529×C79C412yes—
58#529×C79C412yes—
59#529×C79C412yes—
60#529×C79C2212yes—
61#529×C79C2212yes—
62#525×C79C412yes—
63#525×C79C412yes—
64#525×C79C2212yes—
65C4×#41×C79C2212yes—
66C4×#41×C79C2212yes—
67C4×#41×C79C2212yes—
68C22×C42×C79C2211yescharacteristic
69#14579168—216no—
70C2×#11929608—28no—
71C2×#11929608C2314yes—
72C2×#11929608C2318yes—
73C2×#11929608C2312yes—
74C2×#11929608C2312yes—
75C22×C79⋊C8C2314yes—
76C22×C79⋊C8C2318yes—
77C22×C79⋊C8C2314yes—
78C4⋊(C79⋊C8)C2318yes—
79C4⋊(C79⋊C8)C2318yes—
80C4⋊(C79⋊C8)C2312yes—
81C4⋊(C79⋊C8)C2314yes—
82C4⋊(C79⋊C8)C2312yes—
83C22⋊(C79⋊C8)C2318yes—
84C22⋊(C79⋊C8)C2318yes—
85C22⋊(C79⋊C8)C2312yes—
86C22⋊(C79⋊C8)C2312yes—
87C22⋊(C79⋊C8)C2314yes—
88#14579072C2312yes—
89#14579072C2318yes—
90#14579072C2314yes—
91#14579072C2312yes—
92C4×C79⋊C8C2314yes—
93C4×C79⋊C8C2318yes—
94C4×C79⋊C8C2314yes—
95C4×C79⋊C8C2312yes—
96C4×C79⋊C8C2312yes—
97C4×C79⋊C8C2312yes—
98C4×C79⋊C8C2312yes—
99C2×#41×C79C2×C412yes—
100C2×#41×C79C2×C412yes—
101C2×#41×C79C2312yes—
102C23×C4×C79C2×C411yescharacteristic
103C23×C4×C79C2×C411yescharacteristic
104C23×C4×C79C2311yescharacteristic
105C4⋊Q8×C79C2×C411yescharacteristic
106C4⋊Q8×C79C2×C411yescharacteristic
107C4⋊Q8×C79C2×C411yescharacteristic
108#127×C79C2×C411yescharacteristic
109#126×C79C2×C414yes—
110#126×C79C2×C414yes—
111#125×C79C2×C412yes—
112#125×C79C2×C412yes—
113#125×C79C2×C412yes—
114#124×C79C2×C412yes—
115#124×C79C2×C412yes—
116#124×C79C2×C412yes—
117#123×C79C2×C414yes—
118#123×C79C2×C414yes—
119#123×C79C2×C414yes—
120C22⋊Q8×C79C2×C412yes—
121C22⋊Q8×C79C2×C412yes—
122C22⋊Q8×C79C2×C412yes—
123C22⋊Q8×C79C2×C412yes—
124C22⋊Q8×C79C2×C412yes—
125C22⋊Q8×C79C2×C412yes—
126#121×C79C2×C412yes—
127#121×C79C2×C412yes—
128#121×C79C2×C412yes—
129#121×C79C2×C412yes—
130#121×C79C2×C412yes—
131#121×C79C2×C412yes—
132#120×C79C2×C414yes—
133C4×Q8×C79C2×C412yes—
134C4×Q8×C79C2×C412yes—
135C4×Q8×C79C2×C412yes—
136C4×Q8×C79C2×C412yes—
137C4×Q8×C79C2312yes—
138C4×Q8×C79C2312yes—
139C4×D4×C79C2×C414yes—
140C4×D4×C79C2×C414yes—
141C4×D4×C79C2×C414yes—
142C4×D4×C79C2×C414yes—
143C4×D4×C79C2×C412yes—
144C4×D4×C79C2×C412yes—
145C4×D4×C79C2×C412yes—
146C4×D4×C79C2×C412yes—
147C4×D4×C79C2314yes—
148C4×D4×C79C2312yes—
149C4×D4×C79C2314yes—
150C4×D4×C79C2312yes—
151#117×C79C2×C412yes—
152#117×C79C2×C412yes—
153#117×C79C2×C414yes—
154#117×C79C2×C414yes—
155#117×C79C2314yes—
156#117×C79C2312yes—
157C2×C42×C79C2×C411yescharacteristic
158C2×C42×C79C2×C411yescharacteristic
159C2×C42×C79C2×C411yescharacteristic
160C2×C42×C79C2×C411yescharacteristic
161C2×C42×C79C2×C411yescharacteristic
162C2×C42×C79C2×C411yescharacteristic
163C2×C42×C79C2311yescharacteristic
164C2×C42×C79C2311yescharacteristic
165C2×C42×C79C2311yescharacteristic
166C2×C42×C79C2311yescharacteristic
167C2×C42×C79C2311yescharacteristic
168C2×C42×C79C2311yescharacteristic
169C2×C42×C79C2314yes—
170#11929608—28no—
171#11929608—216no—
172#11929608—24no—
173#11929608#4118yescomplemented
174C2×C79⋊C8—28no—
175C2×C79⋊C8—216no—
176C2×C79⋊C8—28no—
177C2×C79⋊C8C2414yes—
178C2×C79⋊C8C2414yes—
179C2×C79⋊C8C2414yes—
180C2×C79⋊C8C2414yes—
181C24×C79C22×C411yescharacteristic
182#41×C79—28no—
183#41×C79—28no—
184#41×C79—44no—
185C2×Q8×C79C22×C412yes—
186C2×Q8×C79C22×C412yes—
187C2×Q8×C79C22×C412yes—
188C2×D4×C79C22×C414yes—
189C2×D4×C79C22×C412yes—
190C2×D4×C79C22×C414yes—
191C2×D4×C79C22×C412yes—
192C2×D4×C79C22×C414yes—
193C2×D4×C79C22×C412yes—
194C22×C4×C79—24no—
195C22×C4×C79—24no—
196C22×C4×C79—42no—
197C22×C4×C79C22×C411yescharacteristic
198C22×C4×C79C22×C411yescharacteristic
199C22×C4×C79C22×C411yescharacteristic
200C22×C4×C79C22×C411yescharacteristic
201C22×C4×C79C22×C411yescharacteristic
202C22×C4×C79C22×C411yescharacteristic
203C22×C4×C79C22×C411yescharacteristic
204C22×C4×C79C22×C411yescharacteristic
205C22×C4×C79C22×C411yescharacteristic
206C22×C4×C79C22×C411yescharacteristic
207C22×C4×C79C22×C411yescharacteristic
208C22×C4×C79C22×C414yes—
209C22×C4×C79C22×C414yes—
210C22×C4×C79C22×C411yescharacteristic
211C22×C4×C79C22×C411yescharacteristic
212C22×C4×C79C22×C411yescharacteristic
213C22×C4×C79C22×C411yescharacteristic
214C22×C4×C79C2411yescharacteristic
215C22×C4×C79C2411yescharacteristic
216C22×C4×C79C2414yes—
217C22×C4×C79C2411yescharacteristic
218C4⋊C4×C79C22×C412yes—
219C4⋊C4×C79C22×C412yes—
220C4⋊C4×C79C22×C414yes—
221C4⋊C4×C79C22×C414yes—
222C4⋊C4×C79C22×C412yes—
223C4⋊C4×C79C22×C412yes—
224C4⋊C4×C79C22×C414yes—
225C4⋊C4×C79C22×C414yes—
226C4⋊C4×C79C22×C412yes—
227C4⋊C4×C79C22×C412yes—
228C4⋊C4×C79C22×C414yes—
229C4⋊C4×C79C22×C414yes—
230C22⋊C4×C79C22×C414yes—
231C22⋊C4×C79C22×C414yes—
232C22⋊C4×C79C22×C414yes—
233C22⋊C4×C79C22×C414yes—
234C22⋊C4×C79C22×C414yes—
235C22⋊C4×C79C22×C414yes—
236C22⋊C4×C79C22×C414yes—
237C22⋊C4×C79C22×C414yes—
238C22⋊C4×C79C22×C414yes—
239C42×C79C22×C411yescharacteristic
240C42×C79C22×C411yescharacteristic
241C42×C79C22×C411yescharacteristic
242C42×C79C22×C411yescharacteristic
243C42×C79C22×C411yescharacteristic
244C42×C79C22×C411yescharacteristic
245C42×C79C22×C411yescharacteristic
246C42×C79C22×C411yescharacteristic
247C42×C79C22×C411yescharacteristic
248C42×C79C22×C411yescharacteristic
249C42×C79C22×C411yescharacteristic
250C42×C79C22×C411yescharacteristic
251C42×C79C22×C414yes—
252C42×C79C22×C414yes—
253C42×C79C2411yescharacteristic
254C42×C79C2411yescharacteristic
255C42×C79C2411yescharacteristic
256C42×C79C2414yes—
257C42×C79C2411yescharacteristic
258C23×C79—22no—
259C23×C79—22no—
260C23×C79—41no—
261C23×C79C23×C414yes—
262C23×C79C23×C411yescharacteristic
263C23×C79C23×C411yescharacteristic
264C23×C79C23×C411yescharacteristic
265Q8×C79—24no—
266Q8×C79—24no—
267Q8×C79—42no—
268D4×C79—28no—
269D4×C79—28no—
270D4×C79—24no—
271D4×C79—24no—
272D4×C79—42no—
273D4×C79—44no—
274C2×C4×C79—22no—
275C2×C4×C79—22no—
276C2×C4×C79—22no—
277C2×C4×C79—22no—
278C2×C4×C79—22no—
279C2×C4×C79—22no—
280C2×C4×C79—22no—
281C2×C4×C79—22no—
282C2×C4×C79—28no—
283C2×C4×C79—22no—
284C2×C4×C79—22no—
285C2×C4×C79—22no—
286C2×C4×C79—28no—
287C2×C4×C79—22no—
288C2×C4×C79—28no—
289C2×C4×C79—22no—
290C2×C4×C79—41no—
291C2×C4×C79—41no—
292C2×C4×C79—41no—
293C2×C4×C79#13114yescomplemented
294C2×C4×C79C23×C411yescharacteristic
295C2×C4×C79C23×C411yescharacteristic
296C2×C4×C79C23×C411yescharacteristic
297C2×C4×C79C23×C411yescharacteristic
298C2×C4×C79C23×C411yescharacteristic
299C2×C4×C79C23×C411yescharacteristic
300C2×C4×C79C23×C411yescharacteristic
301C2×C4×C79C23×C414yes—
302C2×C4×C79C23×C414yes—
303C2×C4×C79C23×C414yes—
304C2×C4×C79C23×C411yescharacteristic
305C2×C4×C79C23×C411yescharacteristic
306C2×C4×C79C23×C411yescharacteristic
307C2×C4×C79C23×C411yescharacteristic
308C2×C4×C79C2×#4114yes—
309C2×C4×C79C2511yescharacteristic
310C79⋊C8—24no—
311C79⋊C8—24no—
312C79⋊C8—24no—
313C79⋊C8C2×#4118yes—
314C22×C79—21no—
315C22×C79—21no—
316C22×C79—21no—
317C22×C79—21no—
318C22×C79—21no—
319C22×C79—24no—
320C22×C79—21no—
321C22×C79—24no—
322C22×C79—21no—
323C22×C79—24no—
324C22×C79—44no—
325C22×C79C4×#4112yes—
326C22×C79C2×#13112yes—
327C22×C79C24×C411yescharacteristic
328C4×C79—21no—
329C4×C79—21no—
330C4×C79—24no—
331C4×C79—21no—
332C4×C79—21no—
333C4×C79—24no—
334C4×C79—21no—
335C4×C79—21no—
336C4×C79—21no—
337C4×C79—24no—
338C4×C79C4×#4112yes—
339C4×C79C2×#13112yes—
340C4×C79C2×#13112yes—
341C4×C79#56812yes—
342C4×C79C22×#4112yes—
343#60210—791nomaximal, Sylow
344C2×C79—22no—
345C2×C79—22no—
346C2×C79—44no—
347C2×C79—41no—
348C2×C79C2×C4×#4111yescharacteristic
349C2×C79C22×#13111yescharacteristic
350C2×C79C2×#56811yescharacteristic
351#3444D7911yescharacteristic
352#2969—794no—
353#2968—794no—
354#2965—792no—
355#2965—794no—
356C8×#41—792no—
357#2962—792no—
358#2935—792no—
359#2933—794no—
360#2922—792no—
361C2×#431—791no—
362C4×#131—792no—
363C2×C4×M16—791no—
364C79#6021011yescharacteristic, complemented, Sylow
365C2×#131—794no—
366C22×M16—792no—
367#533Dic7911yescharacteristic
368#533Dic7911yescharacteristic
369#533C2×D7911yescharacteristic
370#532Dic7911yescharacteristic
371#532Dic7911yescharacteristic
372#532C2×D7911yescharacteristic
373#529Dic7912yes—
374#529Dic7912yes—
375#529Dic7912yes—
376#529Dic7912yes—
377#529C2×D7912yes—
378#529C2×D7912yes—
379#525Dic7912yes—
380#525Dic7912yes—
381#525C2×D7912yes—
382C4×#41C2×D7912yes—
383C4×#41C2×D7912yes—
384C4×#41C2×D7912yes—
385C22×C42C2×D7911yescharacteristic
386#446—798no—
387#446—794no—
388C8×Q8—794no—
389#436—798no—
390#436—794no—
391#435—798no—
392#435—798no—
393#435—798no—
394C8×D4—798no—
395C8×D4—794no—
396#433—798no—
397#431—791no—
398#431—792no—
399#431—791no—
400#431—792no—
401#431—792no—
402#431—794no—
403#431—794no—
404#424—794no—
405C2×C4⋊C8—792no—
406#408—794no—
407C2×C22⋊C8—792no—
408#405—794no—
409#405—798no—
410C4×M16—791no—
411C4×M16—791no—
412C4×M16—792no—
413C4×M16—792no—
414C4×M16—792no—
415C4×M16—794no—
416C2×#97—792no—
417C2×C4×C8—792no—
418C2×C4×C8—792no—
419C2×C4×C8—794no—
420C2×#41C2×Dic7912yes—
421C2×#41C2×Dic7912yes—
422C2×#41C22×D7912yes—
423C23×C4C2×Dic7911yescharacteristic
424C23×C4C2×Dic7911yescharacteristic
425C23×C4C22×D7911yescharacteristic
426#131—15816no—
427C2×M16—792no—
428C2×M16—792no—
429C2×M16—794no—
430C2×M16—798no—
431C2×M16—1588no—
432C22×C8—794no—
433C22×C8—794no—
434C22×C8—798no—
435C4⋊Q8C2×Dic7911yescharacteristic
436C4⋊Q8C2×Dic7911yescharacteristic
437C4⋊Q8C2×Dic7911yescharacteristic
438#127C2×Dic7911yescharacteristic
439#126C2×Dic7914yes—
440#126C2×Dic7914yes—
441#125C2×Dic7912yes—
442#125C2×Dic7912yes—
443#125C2×Dic7912yes—
444#124C2×Dic7912yes—
445#124C2×Dic7912yes—
446#124C2×Dic7912yes—
447#123C2×Dic7914yes—
448#123C2×Dic7914yes—
449#123C2×Dic7914yes—
450C22⋊Q8C2×Dic7912yes—
451C22⋊Q8C2×Dic7912yes—
452C22⋊Q8C2×Dic7912yes—
453C22⋊Q8C2×Dic7912yes—
454C22⋊Q8C2×Dic7912yes—
455C22⋊Q8C2×Dic7912yes—
456#121C2×Dic7912yes—
457#121C2×Dic7912yes—
458#121C2×Dic7912yes—
459#121C2×Dic7912yes—
460#121C2×Dic7912yes—
461#121C2×Dic7912yes—
462#120C2×Dic7914yes—
463C4×Q8C2×Dic7912yes—
464C4×Q8C2×Dic7912yes—
465C4×Q8C2×Dic7912yes—
466C4×Q8C2×Dic7912yes—
467C4×Q8C22×D7912yes—
468C4×Q8C22×D7912yes—
469C4×D4C2×Dic7914yes—
470C4×D4C2×Dic7914yes—
471C4×D4C2×Dic7914yes—
472C4×D4C2×Dic7914yes—
473C4×D4C2×Dic7912yes—
474C4×D4C2×Dic7912yes—
475C4×D4C2×Dic7912yes—
476C4×D4C2×Dic7912yes—
477C4×D4C22×D7914yes—
478C4×D4C22×D7914yes—
479C4×D4C22×D7912yes—
480C4×D4C22×D7912yes—
481#117C2×Dic7912yes—
482#117C2×Dic7912yes—
483#117C2×Dic7914yes—
484#117C2×Dic7914yes—
485#117C22×D7912yes—
486#117C22×D7914yes—
487C2×C42C2×Dic7911yescharacteristic
488C2×C42C2×Dic7911yescharacteristic
489C2×C42C2×Dic7911yescharacteristic
490C2×C42C2×Dic7911yescharacteristic
491C2×C42C2×Dic7911yescharacteristic
492C2×C42C2×Dic7911yescharacteristic
493C2×C42C22×D7911yescharacteristic
494C2×C42C22×D7911yescharacteristic
495C2×C42C22×D7911yescharacteristic
496C2×C42C22×D7914yes—
497C2×C42C22×D7911yescharacteristic
498C2×C42C22×D7911yescharacteristic
499C2×C42C22×D7911yescharacteristic
500C4⋊C8—792no—
501C4⋊C8—794no—
502C4⋊C8—792no—
503C4⋊C8—798no—
504C4⋊C8—798no—
505C22⋊C8—792no—
506C22⋊C8—792no—
507C22⋊C8—794no—
508C22⋊C8—798no—
509C22⋊C8—798no—
510#97—792no—
511#97—792no—
512#97—794no—
513#97—798no—
514C4×C8—794no—
515C4×C8—794no—
516C4×C8—798no—
517C4×C8—792no—
518C4×C8—792no—
519C4×C8—792no—
520C4×C8—792no—
521C24C22×Dic7911yescharacteristic
522#41—28no—
523#41—28no—
524#41—44no—
525C2×Q8C22×Dic7912yes—
526C2×Q8C22×Dic7912yes—
527C2×Q8C22×Dic7912yes—
528C2×D4C22×Dic7914yes—
529C2×D4C22×Dic7912yes—
530C2×D4C22×Dic7914yes—
531C2×D4C22×Dic7912yes—
532C2×D4C22×Dic7914yes—
533C2×D4C22×Dic7912yes—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—42no—
537C22×C4C22×Dic7911yescharacteristic
538C22×C4C22×Dic7911yescharacteristic
539C22×C4C22×Dic7911yescharacteristic
540C22×C4C22×Dic7911yescharacteristic
541C22×C4C22×Dic7911yescharacteristic
542C22×C4C22×Dic7911yescharacteristic
543C22×C4C22×Dic7911yescharacteristic
544C22×C4C22×Dic7911yescharacteristic
545C22×C4C22×Dic7914yes—
546C22×C4C22×Dic7914yes—
547C22×C4C22×Dic7911yescharacteristic
548C22×C4C22×Dic7911yescharacteristic
549C22×C4C22×Dic7911yescharacteristic
550C22×C4C22×Dic7911yescharacteristic
551C22×C4C22×Dic7911yescharacteristic
552C22×C4C22×Dic7911yescharacteristic
553C22×C4C22×Dic7911yescharacteristic
554C22×C4C23×D7911yescharacteristic
555C22×C4C23×D7911yescharacteristic
556C22×C4C23×D7914yes—
557C22×C4C23×D7911yescharacteristic
558M16—798no—
559M16—1588no—
560M16—15816no—
561M16—1584no—
562C2×C8—794no—
563C2×C8—794no—
564C2×C8—794no—
565C2×C8—794no—
566C2×C8—1588no—
567C2×C8—15816no—
568C2×C8—1588no—
569C4⋊C4C22×Dic7912yes—
570C4⋊C4C22×Dic7912yes—
571C4⋊C4C22×Dic7914yes—
572C4⋊C4C22×Dic7914yes—
573C4⋊C4C22×Dic7912yes—
574C4⋊C4C22×Dic7912yes—
575C4⋊C4C22×Dic7914yes—
576C4⋊C4C22×Dic7914yes—
577C4⋊C4C22×Dic7912yes—
578C4⋊C4C22×Dic7912yes—
579C4⋊C4C22×Dic7914yes—
580C4⋊C4C22×Dic7914yes—
581C22⋊C4C22×Dic7914yes—
582C22⋊C4C22×Dic7914yes—
583C22⋊C4C22×Dic7914yes—
584C22⋊C4C22×Dic7914yes—
585C22⋊C4C22×Dic7914yes—
586C22⋊C4C22×Dic7914yes—
587C22⋊C4C22×Dic7914yes—
588C22⋊C4C22×Dic7914yes—
589C22⋊C4C22×Dic7914yes—
590C42C22×Dic7911yescharacteristic
591C42C22×Dic7911yescharacteristic
592C42C22×Dic7911yescharacteristic
593C42C22×Dic7911yescharacteristic
594C42C22×Dic7911yescharacteristic
595C42C22×Dic7911yescharacteristic
596C42C22×Dic7911yescharacteristic
597C42C22×Dic7911yescharacteristic
598C42C22×Dic7911yescharacteristic
599C42C22×Dic7911yescharacteristic
600C42C22×Dic7911yescharacteristic
601C42C22×Dic7911yescharacteristic
602C42C22×Dic7914yes—
603C42C22×Dic7914yes—
604C42C23×D7911yescharacteristic
605C42C23×D7911yescharacteristic
606C42C23×D7914yes—
607C42C23×D7911yescharacteristic
608C42C23×D7911yescharacteristic
609C23—22no—
610C23—22no—
611C23—41no—
612C23C23×Dic7914yes—
613C23C23×Dic7911yescharacteristic
614C23C23×Dic7911yescharacteristic
615C23C23×Dic7911yescharacteristic
616Q8—24no—
617Q8—24no—
618Q8—42no—
619D4—28no—
620D4—28no—
621D4—24no—
622D4—24no—
623D4—42no—
624D4—44no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—28no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—28no—
638C2×C4—22no—
639C2×C4—28no—
640C2×C4—22no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4#1457916814yescomplemented
645C2×C4C23×Dic7911yescharacteristic
646C2×C4C23×Dic7911yescharacteristic
647C2×C4C23×Dic7911yescharacteristic
648C2×C4C23×Dic7911yescharacteristic
649C2×C4C23×Dic7911yescharacteristic
650C2×C4C23×Dic7911yescharacteristic
651C2×C4C23×Dic7911yescharacteristic
652C2×C4C23×Dic7914yes—
653C2×C4C23×Dic7914yes—
654C2×C4C23×Dic7914yes—
655C2×C4C23×Dic7911yescharacteristic
656C2×C4C23×Dic7911yescharacteristic
657C2×C4C23×Dic7911yescharacteristic
658C2×C4C23×Dic7911yescharacteristic
659C2×C4#41×D7914yes—
660C2×C4C24×D7911yescharacteristic
661C8—798no—
662C8—1584no—
663C8—1584no—
664C8—1584no—
665C22—21no—
666C22—21no—
667C22—21no—
668C22—21no—
669C22—21no—
670C22—24no—
671C22—21no—
672C22—24no—
673C22—21no—
674C22—24no—
675C22—44no—
676C22#41×Dic7912yes—
677C22C2×#1457916812yes—
678C22C24×Dic7911yescharacteristic
679C4—21no—
680C4—21no—
681C4—24no—
682C4—21no—
683C4—21no—
684C4—21no—
685C4—24no—
686C4—21no—
687C4—21no—
688C4—24no—
689C4#41×Dic7912yes—
690C4C2×#1457916812yes—
691C4C2×#1457916812yes—
692C4#1909933012yes—
693C4C2×#41×D7912yes—
694C2—22no—
695C2—22no—
696C2—41no—
697C2—44no—
698C2C2×#41×Dic7911yescharacteristic
699C2C22×#1457916811yescharacteristic
700C2C2×#1909933011yescharacteristic
subgroupG/H
centerC42C23×D79
commutator, socleC22×C79C24×C4
FrattiniC2×C4C24×D79
Fitting, prime radicalC79×#3444C2
cosocleC2×C4×C79C25
hypercenter#3444D79
hypocenterC79#60210
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C42 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. #23772405C2semidirect
2. #23772396C2semidirect
3. #23772367C2semidirect
4. #23772367C2semidirect
5. #41×C79⋊C8C2semidirect
6. #23772349C2semidirect
7. #23772144C2semidirect
8. #23772127C2semidirect
9. #23772044C2semidirect
10. C2×#19098616C2semidirect
11. C4×#14579168C2semidirect
12. C2×C4×#11929608C2semidirect
16. #19098694C22semidirect
17. #19098694C22semidirect
18. Q8×C79⋊C8C22semidirect
20. #19098641C22semidirect
23. #19098635C22semidirect
25. D4×C79⋊C8C22semidirect
26. #19098624C22semidirect
32. #19098616C22semidirect
33. #19098616C22semidirect
39. #19098519C22semidirect
45. C4×#11929608C22semidirect
49. C2×C4×C79⋊C8C22semidirect
173. #11929608#41semidirect
293. C2×C4×C79#131semidirect
364. C79#60210semidirect
644. C2×C4#14579168semidirect

Maximal subgroups

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

subgroupindex
#237724052
#237723962
#237723672
#41×C79⋊C82
#237723492
#237721442
#237721272
#237720442
C2×#190986162
C4×#145791682
C2×C4×#119296082
C79×#34442
#6021079