Finite Group Databasebeta

← #34448722

Subgroups — #34448722

Order 20224.

2110 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099115C211yesmaximal, characteristic
2#23766485C211yesmaximal, characteristic
3#23766483C211yesmaximal, characteristic
4#23766481C212yesmaximal
5#23766480C211yesmaximal, characteristic
6#23766478C212yesmaximal
7#23766356C212yesmaximal, complemented
8#23766354C212yesmaximal, complemented
9#23766354C212yesmaximal, complemented
10#23766353C212yesmaximal, complemented
11#23766145C212yesmaximal, complemented
12#23766143C212yesmaximal, complemented
13#23766019C212yesmaximal
14#23765957C212yesmaximal, complemented
15C4×#14579151C212yesmaximal, complemented
16C2×#19098427C211yesmaximal, characteristic
17#23765755C212yesmaximal
18C4×#14579117C211yesmaximal, characteristic
19C79×#2368C211yesmaximal, characteristic
20#19099115C4116yescomplemented
21C2×#14579160C2211yescharacteristic
22C2×#14579159C2211yescharacteristic
23C2×#14579151C2212yes—
24C2×#14579140C2211yescharacteristic
25C2×#14579138C2212yes—
26C2×Q8×Dic79C2211yescharacteristic
27C2×#14579126C2212yes—
28C2×#14579126C2211yescharacteristic
29C2×#14579117C2211yescharacteristic
30C2×#14579117C2212yes—
31C2×#14579117C2211yescharacteristic
32C22×Dic79⋊C4C2212yes—
33C22×C4×Dic79C2211yescharacteristic
34#19098470C2212yes—
35#19098469C2212yes—
36#19098468C2212yes—
37#19098467C2212yes—
38#19098467C2212yes—
39#19098467C2212yes—
40#19098467C2212yes—
41#19098460C2212yes—
42#19098460C2212yes—
43#19098458C2212yes—
44#19098458C2212yes—
45#19098450C2212yes—
46#19098450C2212yes—
47#19098449C2212yes—
48#19098449C2212yes—
49#19098448C2212yes—
50#19098448C2212yes—
51#19098447C2212yes—
52#19098447C2212yes—
53#19098446C2212yes—
54#19098446C2212yes—
55#19098445C2212yes—
56#19098445C2212yes—
57#19098444C2212yes—
58#19098444C2212yes—
59#19098438C2212yes—
60#19098436C2212yes—
61#19098435C2212yes—
62#19098432C2212yes—
63#19098432C2212yes—
64#19098427C2212yes—
65#19098427C2212yes—
66#19098427C2211yescharacteristic
67#19098427C2211yescharacteristic
68#19098427C2212yes—
69#19098427C2212yes—
70#19098427C2211yescharacteristic
71#19098427C2211yescharacteristic
72C4⋊C4×Dic79C2212yes—
73C4⋊C4×Dic79C2212yes—
74C4×Dic79⋊C4C2212yes—
75C4×Dic79⋊C4C2212yes—
76C4×Dic79⋊C4C2212yes—
77C4×Dic79⋊C4C2212yes—
78C4×Dic79⋊C4C2212yes—
79C4×Dic79⋊C4C2212yes—
80C4×Dic79⋊C4C2212yes—
81C4×C4⋊Dic79C2212yes—
82#19098414C2212yes—
83#19098414C2212yes—
84#19098414C2212yes—
85#19098414C2212yes—
86#19098414C2212yes—
87#19098414C2212yes—
88#19098414C2212yes—
89C22⋊C4×Dic79C2211yescharacteristic
90C22⋊C4×Dic79C2212yes—
91C22⋊C4×Dic79C2211yescharacteristic
92C22⋊C4×Dic79C2212yes—
93C4×C22⋊Dic79C2212yes—
94C4×C22⋊Dic79C2211yescharacteristic
95#19098408C2212yes—
96C2×C79⋊#95C2212yes—
97C2×C79⋊#95C2211yescharacteristic
98C42×Dic79C2212yes—
99C2×C22⋊Q8×C79C2211yescharacteristic
100#391×C79C2212yes—
101#387×C79C2212yes—
102#387×C79C2212yes—
103#385×C79C2212yes—
104C4×C4⋊C4×C79C2212yes—
105C4×C22⋊C4×C79C2212yes—
106C4×C22⋊C4×C79C2211yescharacteristic
107C2×#95×C79C2211yescharacteristic
108C22×Dic158C2311yescharacteristic
109C22×Dic158C2312yes—
110C23×Dic79C2312yes—
111C23×Dic79C2311yescharacteristic
112C23×Dic79C2311yescharacteristic
113#14579160C2×C418yescomplemented
114#14579159C2×C418yescomplemented
115#14579151C2×C4116yescomplemented
116#14579140C2×C418yes—
117#14579138C2×C4116yes—
118Q8×Dic79C2×C418yescomplemented
119#14579126C2×C4116yescomplemented
120#14579126C2×C418yescomplemented
121#14579117—24no—
122#14579117C2×C4116yes—
123#14579117Q818yescomplemented
124C2×C4⋊Dic79C2312yes—
125C2×C4⋊Dic79C2312yes—
126C2×C4⋊Dic79C2312yes—
127C2×C4⋊Dic79C2311yescharacteristic
128C2×Dic79⋊C4—28no—
129C2×Dic79⋊C4C2312yes—
130C2×Dic79⋊C4C2312yes—
131C2×Dic79⋊C4C2312yes—
132C2×Dic79⋊C4C2312yes—
133C2×Dic79⋊C4C2312yes—
134C2×Dic79⋊C4C2312yes—
135C2×Dic79⋊C4C2312yes—
136C2×Dic79⋊C4C2312yes—
137C2×Dic79⋊C4C2312yes—
138C2×Dic79⋊C4C2312yes—
139C2×Dic79⋊C4C2312yes—
140C2×Dic79⋊C4C2312yes—
141C2×Dic79⋊C4C2312yes—
142C2×Dic79⋊C4C2312yes—
143C2×Dic79⋊C4C2312yes—
144C2×C22⋊Dic79C2311yescharacteristic
145C2×C22⋊Dic79C2312yes—
146C2×C22⋊Dic79C2311yescharacteristic
147C2×C4×Dic79C2×C418yes—
148C2×C4×Dic79C2312yes—
149C2×C4×Dic79C2312yes—
150C2×C4×Dic79C2312yes—
151C2×C4×Dic79C2312yes—
152C2×C4×Dic79C2312yes—
153C2×C4×Dic79C2312yes—
154C2×C4×Dic79C2312yes—
155C2×C4×Dic79C2312yes—
156C2×C4×Dic79C2312yes—
157C2×C4×Dic79C2312yes—
158C2×C4×Dic79C2311yescharacteristic
159C2×C4×Dic79C2311yescharacteristic
160C2×C4×Dic79C2311yescharacteristic
161C2×C4×Dic79C2312yes—
162C2×C4×Dic79C2312yes—
163C2×C4×Dic79C2311yescharacteristic
164C2×C4×Dic79C2312yes—
165C79⋊#95C2312yes—
166C79⋊#95C2312yes—
167C79⋊#95C2311yescharacteristic
168C79⋊#95C2311yescharacteristic
169C79⋊#95C2312yes—
170C79⋊#95C2312yes—
171C79⋊#95C2312yes—
172C79⋊#95C2312yes—
173C79⋊#95C2312yes—
174C79⋊#95C2312yes—
175C79⋊#95C2312yes—
176C79⋊#95C2312yes—
177C79⋊#95C2312yes—
178C79⋊#95C2312yes—
179C79⋊#95C2312yes—
180C79⋊#95C2312yes—
181C79⋊#95C2312yes—
182C79⋊#95C2312yes—
183C79⋊#95C2312yes—
184C79⋊#95C2312yes—
185C79⋊#95C2312yes—
186C79⋊#95C2312yes—
187C22×Q8×C79C2311yescharacteristic
188C23×C4×C79C2312yes—
189C23×C4×C79C2311yescharacteristic
190C22⋊Q8×C79C2×C418yes—
191C2×C4⋊C4×C79C2312yes—
192C2×C4⋊C4×C79C2312yes—
193C2×C4⋊C4×C79C2312yes—
194C2×C4⋊C4×C79C2311yescharacteristic
195C2×C22⋊C4×C79C2311yescharacteristic
196C2×C22⋊C4×C79C2312yes—
197C2×C22⋊C4×C79C2311yescharacteristic
198C2×C42×C79C2312yes—
199C2×C42×C79C2312yes—
200C2×C42×C79C2312yes—
201#95×C79C2312yes—
202#95×C79C2311yescharacteristic
203#95×C79C2312yes—
204#95×C79C2312yes—
205#95×C79C2312yes—
206#95×C79C2311yescharacteristic
207#95×C79C2312yes—
208#95×C79C2312yes—
209C2×Dic158—42no—
210C2×Dic158—42no—
211C2×Dic158—42no—
212C2×Dic158C22×C418yes—
213C2×Dic158C22×C414yes—
214C22×Dic79—24no—
215C22×Dic79—42no—
216C22×Dic79—42no—
217C22×Dic79—42no—
218C22×Dic79C22×C414yes—
219C22×Dic79C22×C414yes—
220C22×Dic79C2×Q814yes—
221C22×Dic79#4114yes—
222C22×Dic79C2412yes—
223C22×Dic79C2412yes—
224C22×Dic79C2412yes—
225C22×Dic79C2411yescharacteristic
226C22×Dic79C2412yes—
227C22×Dic79C2412yes—
228C22×Dic79C2411yescharacteristic
229C22×Dic79C2412yes—
230C22×Dic79C2411yescharacteristic
231C22×Dic79C2411yescharacteristic
232C4⋊Dic79—42no—
233C4⋊Dic79—42no—
234C4⋊Dic79C22×C418yes—
235C4⋊Dic79C22×C414yes—
236Dic79⋊C4—24no—
237Dic79⋊C4—24no—
238Dic79⋊C4—24no—
239Dic79⋊C4—24no—
240Dic79⋊C4—24no—
241Dic79⋊C4—42no—
242Dic79⋊C4—42no—
243Dic79⋊C4—42no—
244Dic79⋊C4—42no—
245Dic79⋊C4C22×C418yes—
246Dic79⋊C4C22×C418yes—
247Dic79⋊C4C22×C418yes—
248Dic79⋊C4C22×C418yes—
249Dic79⋊C4C22×C418yes—
250Dic79⋊C4C2×Q818yes—
251C22⋊Dic79—22no—
252C22⋊Dic79C22×C418yes—
253C22⋊Dic79C2×Q814yes—
254C4×Dic79—24no—
255C4×Dic79—42no—
256C4×Dic79—42no—
257C4×Dic79—42no—
258C4×Dic79—42no—
259C4×Dic79—42no—
260C4×Dic79—42no—
261C4×Dic79—42no—
262C4×Dic79—42no—
263C4×Dic79—42no—
264C4×Dic79C22×C414yes—
265C4×Dic79C22×C414yes—
266C4×Dic79C22×C414yes—
267C4×Dic79C22×C414yes—
268C4×Dic79C22×C418yes—
269C4×Dic79C22×C418yes—
270C4×Dic79C2×Q818yes—
271C24×C79C2411yescharacteristic
272C2×Q8×C79—42no—
273C2×Q8×C79C22×C414yes—
274C22×C4×C79—24no—
275C22×C4×C79—42no—
276C22×C4×C79—42no—
277C22×C4×C79—42no—
278C22×C4×C79C22×C414yes—
279C22×C4×C79C2412yes—
280C22×C4×C79C2412yes—
281C22×C4×C79C2412yes—
282C22×C4×C79C2411yescharacteristic
283C22×C4×C79C2412yes—
284C22×C4×C79C2411yescharacteristic
285C22×C4×C79C2412yes—
286C22×C4×C79C2412yes—
287C4⋊C4×C79—42no—
288C4⋊C4×C79—42no—
289C4⋊C4×C79C22×C418yes—
290C4⋊C4×C79C22×C414yes—
291C22⋊C4×C79—22no—
292C22⋊C4×C79C22×C418yes—
293C22⋊C4×C79C2×Q814yes—
294C42×C79—42no—
295C42×C79—42no—
296C42×C79—42no—
297C23×C79—22no—
298C23×C79—22no—
299C23×C79C23×C412yes—
300C23×C79C22×Q812yes—
301C23×C79C2×#4112yes—
302C23×C79C2511yescharacteristic
303Q8×C79—44no—
304C2×C4×C79—22no—
305C2×C4×C79—22no—
306C2×C4×C79—22no—
307C2×C4×C79—22no—
308C2×C4×C79—22no—
309C2×C4×C79—22no—
310C2×C4×C79—22no—
311C2×C4×C79—22no—
312C2×C4×C79—22no—
313C2×C4×C79—22no—
314C2×C4×C79—22no—
315C2×C4×C79—22no—
316C2×C4×C79—22no—
317C2×C4×C79—22no—
318C2×C4×C79—22no—
319C2×C4×C79—22no—
320C2×C4×C79—22no—
321C2×C4×C79—44no—
322C2×C4×C79—84no—
323C2×C4×C79C23×C412yes—
324C2×C4×C79C23×C412yes—
325C2×C4×C79C23×C414yes—
326C2×C4×C79C23×C414yes—
327C2×C4×C79C22×Q814yes—
328C2×Dic79—22no—
329C2×Dic79—22no—
330C2×Dic79—22no—
331C2×Dic79—22no—
332C2×Dic79—22no—
333C2×Dic79—22no—
334C2×Dic79—22no—
335C2×Dic79—22no—
336C2×Dic79—22no—
337C2×Dic79—22no—
338C2×Dic79—22no—
339C2×Dic79—22no—
340C2×Dic79—22no—
341C2×Dic79—22no—
342C2×Dic79—22no—
343C2×Dic79—22no—
344C2×Dic79—22no—
345C2×Dic79—44no—
346C2×Dic79—84no—
347C2×Dic79C4×Q8116yes—
348C2×Dic79C23×C412yes—
349C2×Dic79C23×C412yes—
350C2×Dic79C23×C414yes—
351C2×Dic79C23×C414yes—
352C2×Dic79C23×C412yes—
353C2×Dic79C23×C412yes—
354C2×Dic79C22×Q814yes—
355C2×Dic79C22×Q812yes—
356C2×Dic79C22×Q812yes—
357C2×Dic79C2×#4112yes—
358C2×Dic79C2×#4112yes—
359Dic158—48no—
360Dic158—44no—
361C22×C79—22no—
362C22×C79—22no—
363C22×C79—24no—
364C22×C79—24no—
365C22×C79C2×C4×Q814yes—
366C22×C79C24×C411yescharacteristic
367C22×C79C23×Q811yescharacteristic
368C22×C79C22×#4111yescharacteristic
369C22×C79#58512yes—
370C22×C79#58512yes—
371C4×C79—22no—
372C4×C79—22no—
373C4×C79—24no—
374C4×C79—24no—
375C4×C79—24no—
376C4×C79—42no—
377C4×C79—42no—
378C4×C79—42no—
379Dic79—22no—
380Dic79—24no—
381Dic79—24no—
382Dic79—22no—
383Dic79—24no—
384Dic79—42no—
385Dic79—42no—
386Dic79—42no—
387Dic79C2×C4×Q814yes—
388Dic79C2×C4×Q814yes—
389#34215—791nomaximal, Sylow
390C2×C79—24no—
391C2×C79C22×C4×Q811yescharacteristic
392C2×C79#342811yescharacteristic
393C2×C79#342811yescharacteristic
394C2×C79#350412yes—
395C2×C79#351012yes—
396C2×#533—791no—
397#2368—792no—
398#2368—792no—
399#2368—791no—
400#2368—791no—
401#2368—791no—
402#2368D7911yescharacteristic
403#2355—792no—
404#2355—792no—
405#2355—792no—
406#2355—792no—
407#2331—792no—
408#2331—792no—
409#2317—792no—
410C4×#125—792no—
411C4×#125—792no—
412C2×#382—791no—
413#2274—792no—
414C4×#117—791no—
415C79#3421511yescharacteristic, complemented, Sylow
416#533—7916no—
417C2×C4⋊Q8—791no—
418C2×C4⋊Q8—791no—
419C2×#125—792no—
420C2×C22⋊Q8—791no—
421C2×C22⋊Q8—792no—
422C2×C22⋊Q8C2×D7911yescharacteristic
423C2×C4×Q8—791no—
424C2×C4×Q8—791no—
425C2×C4×Q8—792no—
426C2×#117—792no—
427C2×#117—791no—
428C2×#117—791no—
429C22×C4⋊C4—792no—
430C22×C42—791no—
431#391—792no—
432#391—792no—
433#391—792no—
434#391—792no—
435#391—792no—
436#391—792no—
437#391—792no—
438#391C2×D7912yes—
439#389—792no—
440#389—792no—
441#389—792no—
442#389—792no—
443#387—792no—
444#387—792no—
445#387—792no—
446#387—792no—
447#387—792no—
448#387—792no—
449#387—792no—
450#387—792no—
451#387—792no—
452#387—792no—
453#387—792no—
454#387—792no—
455#387—792no—
456#387—792no—
457#387C2×D7912yes—
458#387C2×D7912yes—
459#385—792no—
460#385—792no—
461#385—792no—
462#385C2×D7912yes—
463#384—792no—
464#384—792no—
465#382—791no—
466#382—791no—
467#382—792no—
468#382—792no—
469#382—792no—
470#382—792no—
471#382—791no—
472#382—791no—
473C4×C4⋊C4—792no—
474C4×C4⋊C4—792no—
475C4×C4⋊C4—792no—
476C4×C4⋊C4—792no—
477C4×C4⋊C4—792no—
478C4×C4⋊C4—792no—
479C4×C4⋊C4—792no—
480C4×C4⋊C4—792no—
481C4×C4⋊C4—792no—
482C4×C4⋊C4—792no—
483C4×C4⋊C4—792no—
484C4×C4⋊C4—792no—
485C4×C4⋊C4—792no—
486C4×C4⋊C4—792no—
487C4×C4⋊C4—792no—
488C4×C4⋊C4—792no—
489C4×C4⋊C4—792no—
490C4×C4⋊C4C2×D7912yes—
491C4×C22⋊C4—791no—
492C4×C22⋊C4—792no—
493C4×C22⋊C4—791no—
494C4×C22⋊C4—791no—
495C4×C22⋊C4—792no—
496C4×C22⋊C4—792no—
497C4×C22⋊C4C2×D7911yescharacteristic
498C4×C22⋊C4C2×D7912yes—
499#376—792no—
500C2×#95—792no—
501C2×#95—791no—
502C2×#95C2×D7911yescharacteristic
503C43—792no—
504C22×Q8—792no—
505C22×Q8—791no—
506C22×Q8C22×D7911yescharacteristic
507C23×C4—791no—
508C23×C4—792no—
509C23×C4—791no—
510C23×C4C22×D7912yes—
511C23×C4C22×D7911yescharacteristic
512C4⋊Q8—798no—
513C4⋊Q8—798no—
514#125—7916no—
515C22⋊Q8—798no—
516C22⋊Q8—7916no—
517C22⋊Q8C4×D7918yes—
518C4×Q8—798no—
519C4×Q8—798no—
520C4×Q8—7916no—
521#117—7916no—
522#117—798no—
523#117—1584no—
524C2×C4⋊C4—792no—
525C2×C4⋊C4—792no—
526C2×C4⋊C4—792no—
527C2×C4⋊C4—792no—
528C2×C4⋊C4—792no—
529C2×C4⋊C4—792no—
530C2×C4⋊C4—792no—
531C2×C4⋊C4—792no—
532C2×C4⋊C4—792no—
533C2×C4⋊C4—792no—
534C2×C4⋊C4—792no—
535C2×C4⋊C4—792no—
536C2×C4⋊C4—792no—
537C2×C4⋊C4—791no—
538C2×C4⋊C4—792no—
539C2×C4⋊C4—792no—
540C2×C4⋊C4—792no—
541C2×C4⋊C4—792no—
542C2×C4⋊C4—792no—
543C2×C4⋊C4—1588no—
544C2×C4⋊C4C22×D7912yes—
545C2×C4⋊C4C22×D7912yes—
546C2×C4⋊C4C22×D7912yes—
547C2×C4⋊C4C22×D7911yescharacteristic
548C2×C22⋊C4—792no—
549C2×C22⋊C4—791no—
550C2×C22⋊C4—791no—
551C2×C22⋊C4C22×D7911yescharacteristic
552C2×C22⋊C4C22×D7912yes—
553C2×C22⋊C4C22×D7911yescharacteristic
554C2×C42—792no—
555C2×C42—792no—
556C2×C42—792no—
557C2×C42—792no—
558C2×C42—792no—
559C2×C42—792no—
560C2×C42—792no—
561C2×C42—792no—
562C2×C42—792no—
563C2×C42—798no—
564C2×C42—792no—
565C2×C42—792no—
566C2×C42—792no—
567C2×C42—791no—
568C2×C42—791no—
569C2×C42—791no—
570C2×C42—791no—
571C2×C42—792no—
572C2×C42C22×D7912yes—
573C2×C42C22×D7912yes—
574C2×C42C22×D7912yes—
575#95—792no—
576#95—792no—
577#95—791no—
578#95—791no—
579#95—792no—
580#95—792no—
581#95—792no—
582#95—792no—
583#95—792no—
584#95—792no—
585#95—792no—
586#95—792no—
587#95—792no—
588#95—792no—
589#95—792no—
590#95—792no—
591#95—792no—
592#95—792no—
593#95—792no—
594#95—792no—
595#95—792no—
596#95—792no—
597#95C22×D7911yescharacteristic
598#95C22×D7911yescharacteristic
599#95C22×D7912yes—
600#95C22×D7912yes—
601#95C22×D7912yes—
602#95C22×D7912yes—
603#95C22×D7912yes—
604#95C22×D7912yes—
605C24C23×D7911yescharacteristic
606C2×Q8—42no—
607C2×Q8—3162no—
608C2×Q8—3162no—
609C2×Q8—3162no—
610C2×Q8—798no—
611C2×Q8—794no—
612C2×Q8C2×C4×D7914yes—
613C22×C4—24no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—3162no—
618C22×C4—3162no—
619C22×C4—3162no—
620C22×C4—794no—
621C22×C4—794no—
622C22×C4—794no—
623C22×C4—791no—
624C22×C4—791no—
625C22×C4—794no—
626C22×C4—791no—
627C22×C4—792no—
628C22×C4—791no—
629C22×C4—792no—
630C22×C4—792no—
631C22×C4—792no—
632C22×C4—792no—
633C22×C4—792no—
634C22×C4—1584no—
635C22×C4C2×C4×D7914yes—
636C22×C4C23×D7912yes—
637C22×C4C23×D7912yes—
638C22×C4C23×D7912yes—
639C22×C4C23×D7912yes—
640C22×C4C23×D7911yescharacteristic
641C22×C4C23×D7911yescharacteristic
642C22×C4C23×D7912yes—
643C22×C4C23×D7912yes—
644C4⋊C4—42no—
645C4⋊C4—42no—
646C4⋊C4—3162no—
647C4⋊C4—3162no—
648C4⋊C4—3162no—
649C4⋊C4—3162no—
650C4⋊C4—3162no—
651C4⋊C4—3162no—
652C4⋊C4—798no—
653C4⋊C4—798no—
654C4⋊C4—798no—
655C4⋊C4—798no—
656C4⋊C4—798no—
657C4⋊C4—798no—
658C4⋊C4—798no—
659C4⋊C4—794no—
660C4⋊C4—1584no—
661C4⋊C4—1584no—
662C4⋊C4—1584no—
663C4⋊C4—1584no—
664C4⋊C4—1584no—
665C4⋊C4C2×C4×D7918yes—
666C4⋊C4C2×C4×D7914yes—
667C22⋊C4—22no—
668C22⋊C4—794no—
669C22⋊C4—798no—
670C22⋊C4—1582no—
671C22⋊C4C2×C4×D7918yes—
672C22⋊C4Q8×D7914yes—
673C42—42no—
674C42—42no—
675C42—42no—
676C42—3162no—
677C42—3162no—
678C42—3162no—
679C42—3162no—
680C42—3162no—
681C42—3162no—
682C42—3162no—
683C42—3162no—
684C42—3162no—
685C42—798no—
686C42—794no—
687C42—794no—
688C42—794no—
689C42—794no—
690C42—798no—
691C42—798no—
692C42—1584no—
693C23—22no—
694C23—22no—
695C23C22×C4×D7912yes—
696C23C2×Q8×D7912yes—
697C23#41×D7912yes—
698C23C24×D7911yescharacteristic
699Q8—44no—
700Q8—3164no—
701Q8—3168no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—44no—
720C2×C4—84no—
721C2×C4—3164no—
722C2×C4—7916no—
723C2×C4—792no—
724C2×C4—792no—
725C2×C4—792no—
726C2×C4—792no—
727C2×C4—792no—
728C2×C4—792no—
729C2×C4—792no—
730C2×C4—792no—
731C2×C4—794no—
732C2×C4—794no—
733C2×C4—794no—
734C2×C4—6324no—
735C2×C4—1582no—
736C2×C4—1582no—
737C2×C4—1582no—
738C2×C4—1582no—
739C2×C4—1582no—
740C2×C4—1582no—
741C2×C4—1582no—
742C2×C4—1582no—
743C2×C4—1582no—
744C2×C4—1582no—
745C2×C4—1582no—
746C2×C4—1582no—
747C2×C4—1582no—
748C2×C4—1582no—
749C2×C4—1582no—
750C2×C4—1582no—
751C2×C4—1582no—
752C2×C4C22×C4×D7912yes—
753C2×C4C22×C4×D7912yes—
754C2×C4C22×C4×D7914yes—
755C2×C4C22×C4×D7914yes—
756C2×C4C2×Q8×D7914yes—
757C22—24no—
758C22—22no—
759C22—22no—
760C22—24no—
761C22C4×Q8×D7914yes—
762C22C23×C4×D7911yescharacteristic
763C22C22×Q8×D7911yescharacteristic
764C22C2×#41×D7911yescharacteristic
765C22#1909939812yes—
766C22#1909939912yes—
767C4—22no—
768C4—22no—
769C4—24no—
770C4—24no—
771C4—24no—
772C4—42no—
773C4—42no—
774C4—42no—
775C4—3162no—
776C4—3162no—
777C4—3162no—
778C4—794no—
779C4—794no—
780C4—1584no—
781C4—1582no—
782C4—1582no—
783C4—1584no—
784C4—1584no—
785C2—24no—
786C2C2×C4×Q8×D7911yescharacteristic
787C2#2377659811yescharacteristic
788C2#2377659911yescharacteristic
789C2#2377722012yes—
790C2#2377728812yes—
subgroupG/H
center, FrattiniC23C24×D79
commutatorC22×C79C24×C4
FittingC79×#2368C2
socle, cosocleC23×C79C25
prime radicalC24×C79C24
hypercenter#2368D79
hypocenterC79#34215
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ #2368

Complements

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

NH ≅ G/Ntype
7. #23766356C2semidirect
8. #23766354C2semidirect
9. #23766354C2semidirect
10. #23766353C2semidirect
11. #23766145C2semidirect
12. #23766143C2semidirect
14. #23765957C2semidirect
15. C4×#14579151C2semidirect
20. #19099115C4semidirect
113. #14579160C2×C4semidirect
114. #14579159C2×C4semidirect
115. #14579151C2×C4semidirect
118. Q8×Dic79C2×C4semidirect
119. #14579126C2×C4semidirect
120. #14579126C2×C4semidirect
123. #14579117Q8semidirect
415. C79#34215semidirect

Maximal subgroups

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

subgroupindex
C2×#190991152
#237664852
#237664832
#237664812
#237664802
#237664782
#237663562
#237663542
#237663532
#237661452
#237661432
#237660192
#237659572
C4×#145791512
C2×#190984272
#237657552
C4×#145791172
C79×#23682
#3421579