Finite Group Databasebeta

← #34451349

Subgroups — #34451349

Order 20224.

1990 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099094C211yesmaximal, characteristic
2#23766568C211yesmaximal, characteristic, complemented
3#23766563C211yesmaximal, characteristic, complemented
4#23766557C211yesmaximal, characteristic
5#23766535C212yesmaximal, complemented
6#23766533C212yesmaximal, complemented
7#23766362C212yesmaximal, complemented
8#23766338C212yesmaximal, complemented
9#23766282C212yesmaximal, complemented
10#23766258C212yesmaximal, complemented
11#23766209C212yesmaximal, complemented
12#23766203C212yesmaximal, complemented
13#23766176C212yesmaximal, complemented
14#23766172C212yesmaximal, complemented
15#23766037C212yesmaximal, complemented
16#23766026C212yesmaximal, complemented
17#23765795C211yesmaximal, characteristic, complemented
18#23765791C211yesmaximal, characteristic, complemented
19C79×#2377C211yesmaximal, characteristic
20#19099094C4116yescomplemented
21C2×#14579154C2212yes—
22C2×#14579152C2211yescharacteristic
23C2×#14579148C2211yescharacteristic
24C2×#14579142C2212yes—
25C2×#14579140C2211yescharacteristic
26C2×#14579126C2211yescharacteristic
27C2×D4×Dic79C2211yescharacteristic
28C2×D4×Dic79C2212yes—
29C2×#14579117C2212yes—
30C22×C4×Dic79C2211yescharacteristic
31#19098467C2212yes—
32#19098467C2212yes—
33#19098466C2212yes—
34#19098461C2212yes—
35#19098460C2212yes—
36#19098459C2212yes—
37#19098458C2212yes—
38#19098457C2212yes—
39#19098457C2212yes—
40#19098457C2212yes—
41#19098457C2212yes—
42#19098457C2212yes—
43#19098456C2212yes—
44#19098451C2212yes—
45#19098451C2212yes—
46#19098451C2212yes—
47#19098451C2212yes—
48#19098451C2212yes—
49#19098450C2212yes—
50#19098450C2212yes—
51#19098450C2212yes—
52#19098449C2212yes—
53#19098448C2212yes—
54#19098448C2212yes—
55#19098446C2212yes—
56#19098446C2212yes—
57#19098444C2212yes—
58#19098444C2212yes—
59#19098444C2212yes—
60#19098443C2212yes—
61#19098443C2212yes—
62#19098438C2212yes—
63#19098436C2212yes—
64#19098435C2212yes—
65#19098430C2212yes—
66#19098430C2212yes—
67#19098430C2212yes—
68#19098428C2212yes—
69#19098427C2212yes—
70#19098427C2211yescharacteristic
71#19098427C2211yescharacteristic
72#19098426C2211yescharacteristic
73#19098424C2211yescharacteristic
74#19098424C2211yescharacteristic
75#19098424C2212yes—
76#19098423C2211yescharacteristic
77#19098421C2212yes—
78#19098421C2212yes—
79C4⋊C4×Dic79C2212yes—
80C4⋊C4×Dic79C2212yes—
81C4×Dic79⋊C4C2212yes—
82C4×Dic79⋊C4C2212yes—
83#19098414C2212yes—
84#19098414C2212yes—
85#19098414C2212yes—
86C22⋊C4×Dic79C2211yescharacteristic
87C22⋊C4×Dic79C2212yes—
88C22⋊C4×Dic79C2211yescharacteristic
89C22⋊C4×Dic79C2212yes—
90C22⋊C4×Dic79C2212yes—
91C22⋊C4×Dic79C2212yes—
92C4×C22⋊Dic79C2212yes—
93C4×C22⋊Dic79C2212yes—
94#19098409C2212yes—
95#19098408C2211yescharacteristic
96#19098408C2211yescharacteristic
97#19098408C2212yes—
98C2×C79⋊#95C2212yes—
99C2×#121×C79C2211yescharacteristic
100#390×C79C2212yes—
101#388×C79C2212yes—
102#387×C79C2212yes—
103#386×C79C2212yes—
104#386×C79C2212yes—
105#385×C79C2212yes—
106#381×C79C2211yescharacteristic
107#380×C79C2211yescharacteristic
108C22×Dic158C2311yescharacteristic
109C23×Dic79C2312yes—
110C23×Dic79C2312yes—
111C23×Dic79C2311yescharacteristic
112C23×Dic79C2311yescharacteristic
113#14579154C2×C4116yescomplemented
114#14579152C2×C418yescomplemented
115#14579148C2×C418yes—
116#14579142C2×C4116yescomplemented
117#14579140C2×C418yescomplemented
118#14579126C2×C418yescomplemented
119D4×Dic79C2×C418yes—
120D4×Dic79C2×C4116yescomplemented
121#14579117C2×C4116yescomplemented
122C2×C4⋊Dic79C2312yes—
123C2×C4⋊Dic79C2312yes—
124C2×C4⋊Dic79C2311yescharacteristic
125C2×C4⋊Dic79C2312yes—
126C2×Dic79⋊C4C2312yes—
127C2×Dic79⋊C4C2312yes—
128C2×Dic79⋊C4C2312yes—
129C2×Dic79⋊C4C2312yes—
130C2×Dic79⋊C4C2312yes—
131C2×Dic79⋊C4C2312yes—
132C2×Dic79⋊C4C2312yes—
133C2×Dic79⋊C4C2312yes—
134C2×Dic79⋊C4C2312yes—
135C2×C22⋊Dic79C2312yes—
136C2×C22⋊Dic79C2312yes—
137C2×C22⋊Dic79C2312yes—
138C2×C22⋊Dic79C2311yescharacteristic
139C2×C22⋊Dic79C2311yescharacteristic
140C2×C22⋊Dic79C2312yes—
141C2×C22⋊Dic79C2312yes—
142C2×C22⋊Dic79C2312yes—
143C2×C22⋊Dic79C2312yes—
144C2×C22⋊Dic79C2312yes—
145C2×C4×Dic79C2×C418yescomplemented
146C2×C4×Dic79C2312yes—
147C2×C4×Dic79C2312yes—
148C2×C4×Dic79C2312yes—
149C2×C4×Dic79C2312yes—
150C2×C4×Dic79C2312yes—
151C2×C4×Dic79C2312yes—
152C2×C4×Dic79C2312yes—
153C2×C4×Dic79C2312yes—
154C2×C4×Dic79C2312yes—
155C2×C4×Dic79C2311yescharacteristic
156C2×C4×Dic79C2311yescharacteristic
157C2×C4×Dic79C2312yes—
158C2×C4×Dic79C2311yescharacteristic
159C2×C4×Dic79C2311yescharacteristic
160C79⋊#95C2312yes—
161C79⋊#95C2312yes—
162C79⋊#95C2312yes—
163C79⋊#95C2312yes—
164C79⋊#95C2312yes—
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—
184C22×D4×C79C2311yescharacteristic
185C22×D4×C79C2312yes—
186C23×C4×C79C2312yes—
187C23×C4×C79C2311yescharacteristic
188#121×C79C2×C418yes—
189C2×C4⋊C4×C79C2312yes—
190C2×C4⋊C4×C79C2312yes—
191C2×C4⋊C4×C79C2311yescharacteristic
192C2×C22⋊C4×C79C2312yes—
193C2×C22⋊C4×C79C2312yes—
194C2×C22⋊C4×C79C2311yescharacteristic
195C2×C22⋊C4×C79C2311yescharacteristic
196C2×C22⋊C4×C79C2312yes—
197C2×C22⋊C4×C79C2312yes—
198C2×C22⋊C4×C79C2312yes—
199C2×C42×C79C2312yes—
200#95×C79C2311yescharacteristic
201#95×C79C2311yescharacteristic
202#95×C79C2312yes—
203#95×C79C2312yes—
204#95×C79C2312yes—
205#95×C79C2312yes—
206C2×Dic158—42no—
207C2×Dic158C22×C414yes—
208C22×Dic79—41no—
209C22×Dic79—42no—
210C22×Dic79—41no—
211C22×Dic79—42no—
212C22×Dic79—42no—
213C22×Dic79—42no—
214C22×Dic79—42no—
215C22×Dic79—42no—
216C22×Dic79C22×C414yes—
217C22×Dic79C22×C414yes—
218C22×Dic79C22×C418yes—
219C22×Dic79C2412yes—
220C22×Dic79C2412yes—
221C22×Dic79C2412yes—
222C22×Dic79C2412yes—
223C22×Dic79C2412yes—
224C22×Dic79C2411yescharacteristic
225C22×Dic79C2411yescharacteristic
226C22×Dic79C2411yescharacteristic
227C22×Dic79C2412yes—
228C22×Dic79C2411yescharacteristic
229C4⋊Dic79—42no—
230C4⋊Dic79—42no—
231C4⋊Dic79C22×C414yes—
232C4⋊Dic79C22×C418yes—
233Dic79⋊C4—42no—
234Dic79⋊C4—42no—
235Dic79⋊C4—42no—
236Dic79⋊C4—42no—
237Dic79⋊C4—42no—
238Dic79⋊C4—42no—
239Dic79⋊C4C22×C418yes—
240Dic79⋊C4C22×C418yes—
241Dic79⋊C4C22×C418yes—
242C22⋊Dic79—41no—
243C22⋊Dic79—41no—
244C22⋊Dic79—42no—
245C22⋊Dic79—42no—
246C22⋊Dic79—42no—
247C22⋊Dic79—42no—
248C22⋊Dic79C22×C418yes—
249C22⋊Dic79C22×C418yes—
250C22⋊Dic79C22×C418yes—
251C22⋊Dic79C22×C418yes—
252C4×Dic79—42no—
253C4×Dic79—42no—
254C4×Dic79—42no—
255C4×Dic79—42no—
256C4×Dic79—42no—
257C4×Dic79—42no—
258C4×Dic79—42no—
259C4×Dic79—42no—
260C4×Dic79—42no—
261C4×Dic79C22×C414yes—
262C4×Dic79C22×C414yes—
263C4×Dic79C22×C414yes—
264C4×Dic79C22×C414yes—
265C4×Dic79C22×C418yes—
266C24×C79C2411yescharacteristic
267C24×C79C2412yes—
268C2×D4×C79—42no—
269C2×D4×C79—42no—
270C2×D4×C79—42no—
271C2×D4×C79C22×C414yes—
272C2×D4×C79C22×C418yes—
273C22×C4×C79—42no—
274C22×C4×C79—42no—
275C22×C4×C79—42no—
276C22×C4×C79—42no—
277C22×C4×C79C22×C414yes—
278C22×C4×C79C2412yes—
279C22×C4×C79C2412yes—
280C22×C4×C79C2412yes—
281C22×C4×C79C2412yes—
282C22×C4×C79C2411yescharacteristic
283C22×C4×C79C2412yes—
284C22×C4×C79C2411yescharacteristic
285C4⋊C4×C79—42no—
286C4⋊C4×C79—42no—
287C4⋊C4×C79C22×C414yes—
288C22⋊C4×C79—42no—
289C22⋊C4×C79—42no—
290C22⋊C4×C79—41no—
291C22⋊C4×C79—42no—
292C22⋊C4×C79—41no—
293C22⋊C4×C79—42no—
294C22⋊C4×C79C22×C418yes—
295C42×C79—42no—
296C23×C79—21no—
297C23×C79—22no—
298C23×C79—22no—
299C23×C79—22no—
300C23×C79—22no—
301C23×C79—21no—
302C23×C79—22no—
303C23×C79—22no—
304C23×C79—22no—
305C23×C79—22no—
306C23×C79C23×C414yes—
307C23×C79C23×C412yes—
308C23×C79C2511yescharacteristic
309D4×C79—44no—
310D4×C79—48no—
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—22no—
322C2×C4×C79—22no—
323C2×C4×C79—22no—
324C2×C4×C79—22no—
325C2×C4×C79—22no—
326C2×C4×C79—22no—
327C2×C4×C79—44no—
328C2×C4×C79—84no—
329C2×C4×C79C23×C412yes—
330C2×C4×C79C23×C412yes—
331C2×C4×C79C23×C414yes—
332C2×Dic79—22no—
333C2×Dic79—22no—
334C2×Dic79—22no—
335C2×Dic79—22no—
336C2×Dic79—22no—
337C2×Dic79—21no—
338C2×Dic79—21no—
339C2×Dic79—22no—
340C2×Dic79—21no—
341C2×Dic79—21no—
342C2×Dic79—22no—
343C2×Dic79—22no—
344C2×Dic79—22no—
345C2×Dic79—22no—
346C2×Dic79—22no—
347C2×Dic79—22no—
348C2×Dic79—22no—
349C2×Dic79—22no—
350C2×Dic79—22no—
351C2×Dic79—22no—
352C2×Dic79—22no—
353C2×Dic79—22no—
354C2×Dic79—44no—
355C2×Dic79—48no—
356C2×Dic79—44no—
357C2×Dic79—84no—
358C2×Dic79C23×C412yes—
359C2×Dic79C23×C412yes—
360C2×Dic79C23×C412yes—
361C2×Dic79C23×C412yes—
362C2×Dic79C23×C414yes—
363C2×Dic79C23×C414yes—
364Dic158—44no—
365C22×C79—22no—
366C22×C79—22no—
367C22×C79—24no—
368C22×C79—24no—
369C22×C79—22no—
370C22×C79—24no—
371C22×C79—42no—
372C22×C79—42no—
373C22×C79—42no—
374C22×C79—42no—
375C22×C79—42no—
376C22×C79—42no—
377C22×C79C24×C411yescharacteristic
378C22×C79#58511yescharacteristic
379C22×C79#58512yes—
380C22×C79#58512yes—
381C22×C79#58511yescharacteristic
382C4×C79—22no—
383C4×C79—22no—
384C4×C79—24no—
385C4×C79—42no—
386C4×C79—42no—
387C4×C79—42no—
388C4×C79—42no—
389Dic79—24no—
390Dic79—22no—
391Dic79—22no—
392Dic79—22no—
393Dic79—24no—
394Dic79—22no—
395Dic79—42no—
396Dic79—42no—
397Dic79—42no—
398Dic79—42no—
399#34387—791nomaximal, Sylow
400C2×C79—42no—
401C2×C79—44no—
402C2×C79#342811yescharacteristic
403C2×C79#342811yescharacteristic
404C2×C79#342811yescharacteristic
405C2×C79#356612yes—
406C2×C79#356612yes—
407C2×#529—791no—
408#2378—791no—
409#2378—791no—
410#2377—791no—
411#2377D7911yescharacteristic
412#2374—792no—
413#2374—792no—
414#2356—792no—
415#2353—792no—
416#2346—792no—
417#2343—792no—
418#2337—792no—
419#2336—792no—
420#2334—792no—
421#2334—792no—
422#2319—792no—
423#2318—792no—
424#2283—791no—
425#2283—791no—
426C79#3438711yescharacteristic, complemented, Sylow
427#529—7916no—
428C2×#126—792no—
429C2×#125—791no—
430C2×#124—791no—
431C2×#123—792no—
432C2×C22⋊Q8—791no—
433C2×#121C2×D7911yescharacteristic
434C2×C4×Q8—791no—
435C2×C4×D4—792no—
436C2×C4×D4—791no—
437C2×#117—792no—
438C22×C42—791no—
439#391—792no—
440#391—792no—
441#390—792no—
442#390C2×D7912yes—
443#389—792no—
444#389—792no—
445#389—792no—
446#389—792no—
447#388—792no—
448#388—792no—
449#388—792no—
450#388—792no—
451#388—792no—
452#388—792no—
453#388—792no—
454#388—792no—
455#388—792no—
456#388—792no—
457#388—792no—
458#388C2×D7912yes—
459#387—792no—
460#387—792no—
461#387—792no—
462#387—792no—
463#387—792no—
464#387—792no—
465#387—792no—
466#387—792no—
467#387—792no—
468#387—792no—
469#387—792no—
470#387C2×D7912yes—
471#386—792no—
472#386—792no—
473#386C2×D7912yes—
474#386C2×D7912yes—
475#385—792no—
476#385—792no—
477#385—792no—
478#385C2×D7912yes—
479#383—792no—
480#383—792no—
481#383—792no—
482#382—792no—
483#382—792no—
484#382—791no—
485#382—791no—
486#381—791no—
487#381—791no—
488#381—791no—
489#381—792no—
490#381C2×D7911yescharacteristic
491#380—791no—
492#380—792no—
493#380—792no—
494#380C2×D7911yescharacteristic
495C4×C4⋊C4—792no—
496C4×C4⋊C4—792no—
497C4×C4⋊C4—792no—
498C4×C4⋊C4—792no—
499C4×C4⋊C4—792no—
500C4×C4⋊C4—792no—
501C4×C4⋊C4—792no—
502C4×C22⋊C4—792no—
503C4×C22⋊C4—792no—
504C4×C22⋊C4—792no—
505C4×C22⋊C4—792no—
506C4×C22⋊C4—792no—
507C4×C22⋊C4—792no—
508C4×C22⋊C4—791no—
509C4×C22⋊C4—791no—
510#376—792no—
511#376—791no—
512#376—791no—
513#376—792no—
514C2×#95—792no—
515C22×Q8—791no—
516C22×D4C22×D7912yes—
517C22×D4C22×D7911yescharacteristic
518C23×C4—792no—
519C23×C4—792no—
520C23×C4—791no—
521C23×C4—791no—
522C23×C4C22×D7912yes—
523C23×C4C22×D7911yescharacteristic
524#126—7916no—
525#125—798no—
526#124—798no—
527#123—7916no—
528C22⋊Q8—798no—
529#121C4×D7918yes—
530C4×Q8—798no—
531C4×D4—798no—
532C4×D4—7916no—
533#117—7916no—
534C2×C4⋊C4—792no—
535C2×C4⋊C4—792no—
536C2×C4⋊C4—792no—
537C2×C4⋊C4—792no—
538C2×C4⋊C4—792no—
539C2×C4⋊C4—792no—
540C2×C4⋊C4—792no—
541C2×C4⋊C4—792no—
542C2×C4⋊C4—792no—
543C2×C4⋊C4—792no—
544C2×C4⋊C4—791no—
545C2×C4⋊C4—792no—
546C2×C4⋊C4—792no—
547C2×C4⋊C4C22×D7912yes—
548C2×C4⋊C4C22×D7912yes—
549C2×C4⋊C4C22×D7911yescharacteristic
550C2×C22⋊C4—791no—
551C2×C22⋊C4—792no—
552C2×C22⋊C4—791no—
553C2×C22⋊C4—792no—
554C2×C22⋊C4—792no—
555C2×C22⋊C4—792no—
556C2×C22⋊C4—792no—
557C2×C22⋊C4—792no—
558C2×C22⋊C4—792no—
559C2×C22⋊C4—792no—
560C2×C22⋊C4C22×D7912yes—
561C2×C22⋊C4C22×D7912yes—
562C2×C22⋊C4C22×D7911yescharacteristic
563C2×C22⋊C4C22×D7911yescharacteristic
564C2×C22⋊C4C22×D7912yes—
565C2×C22⋊C4C22×D7912yes—
566C2×C22⋊C4C22×D7912yes—
567C2×C42—792no—
568C2×C42—792no—
569C2×C42—792no—
570C2×C42—792no—
571C2×C42—792no—
572C2×C42—792no—
573C2×C42—792no—
574C2×C42—792no—
575C2×C42—792no—
576C2×C42—798no—
577C2×C42—791no—
578C2×C42—792no—
579C2×C42—791no—
580C2×C42—791no—
581C2×C42—791no—
582C2×C42C22×D7912yes—
583#95—792no—
584#95—792no—
585#95—792no—
586#95—792no—
587#95—792no—
588#95—792no—
589#95—792no—
590#95—791no—
591#95—791no—
592#95—792no—
593#95—792no—
594#95—792no—
595#95—792no—
596#95—792no—
597#95—792no—
598#95—792no—
599#95—792no—
600#95—792no—
601#95—792no—
602#95—792no—
603#95—792no—
604#95—792no—
605#95—792no—
606#95—792no—
607#95C22×D7912yes—
608#95C22×D7911yescharacteristic
609#95C22×D7911yescharacteristic
610#95C22×D7912yes—
611#95C22×D7912yes—
612#95C22×D7912yes—
613C24C23×D7911yescharacteristic
614C24C23×D7912yes—
615C2×Q8—3162no—
616C2×Q8—794no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4C2×C4×D7918yes—
621C2×D4C2×C4×D7914yes—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—3162no—
627C22×C4—3162no—
628C22×C4—3161no—
629C22×C4—3162no—
630C22×C4—3161no—
631C22×C4—3162no—
632C22×C4—3162no—
633C22×C4—3162no—
634C22×C4—794no—
635C22×C4—794no—
636C22×C4—798no—
637C22×C4—791no—
638C22×C4—791no—
639C22×C4—791no—
640C22×C4—792no—
641C22×C4—791no—
642C22×C4—792no—
643C22×C4—792no—
644C22×C4—792no—
645C22×C4—792no—
646C22×C4—792no—
647C22×C4C2×C4×D7914yes—
648C22×C4C23×D7912yes—
649C22×C4C23×D7912yes—
650C22×C4C23×D7912yes—
651C22×C4C23×D7912yes—
652C22×C4C23×D7911yescharacteristic
653C22×C4C23×D7912yes—
654C22×C4C23×D7911yescharacteristic
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4—3162no—
658C4⋊C4—3162no—
659C4⋊C4—3162no—
660C4⋊C4—3162no—
661C4⋊C4—3162no—
662C4⋊C4—3162no—
663C4⋊C4—3162no—
664C4⋊C4—3162no—
665C4⋊C4—798no—
666C4⋊C4—798no—
667C4⋊C4—798no—
668C4⋊C4—794no—
669C4⋊C4—798no—
670C4⋊C4C2×C4×D7914yes—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—41no—
674C22⋊C4—42no—
675C22⋊C4—41no—
676C22⋊C4—42no—
677C22⋊C4—3162no—
678C22⋊C4—3162no—
679C22⋊C4—3162no—
680C22⋊C4—3161no—
681C22⋊C4—3161no—
682C22⋊C4—3162no—
683C22⋊C4—798no—
684C22⋊C4—798no—
685C22⋊C4—798no—
686C22⋊C4—798no—
687C22⋊C4C2×C4×D7918yes—
688C42—42no—
689C42—3162no—
690C42—3162no—
691C42—3162no—
692C42—3162no—
693C42—3162no—
694C42—3162no—
695C42—3162no—
696C42—3162no—
697C42—3162no—
698C42—794no—
699C42—794no—
700C42—794no—
701C42—794no—
702C42—798no—
703C23—21no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—21no—
712C23—22no—
713C23C22×C4×D7914yes—
714C23C22×C4×D7912yes—
715C23C24×D7911yescharacteristic
716Q8—3164no—
717D4—44no—
718D4—48no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—44no—
736C2×C4—84no—
737C2×C4—3164no—
738C2×C4—3164no—
739C2×C4—3168no—
740C2×C4—792no—
741C2×C4—792no—
742C2×C4—792no—
743C2×C4—792no—
744C2×C4—794no—
745C2×C4—794no—
746C2×C4—6324no—
747C2×C4—1582no—
748C2×C4—1582no—
749C2×C4—1582no—
750C2×C4—1582no—
751C2×C4—1582no—
752C2×C4—1582no—
753C2×C4—1582no—
754C2×C4—1582no—
755C2×C4—1582no—
756C2×C4—1582no—
757C2×C4—1582no—
758C2×C4—1582no—
759C2×C4—1582no—
760C2×C4—1582no—
761C2×C4—1582no—
762C2×C4—1582no—
763C2×C4—1581no—
764C2×C4—1582no—
765C2×C4—1581no—
766C2×C4—1582no—
767C2×C4—1581no—
768C2×C4—1581no—
769C2×C4C22×C4×D7912yes—
770C2×C4C22×C4×D7912yes—
771C2×C4C22×C4×D7914yes—
772C22—22no—
773C22—22no—
774C22—24no—
775C22—24no—
776C22—22no—
777C22—24no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22C23×C4×D7911yescharacteristic
785C22#1909939811yescharacteristic
786C22#1909939812yes—
787C22#1909939812yes—
788C22#1909940011yescharacteristic
789C4—22no—
790C4—22no—
791C4—24no—
792C4—42no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—3162no—
797C4—3162no—
798C4—3162no—
799C4—3162no—
800C4—1582no—
801C4—1582no—
802C4—1584no—
803C4—1582no—
804C4—1582no—
805C4—1584no—
806C2—42no—
807C2—44no—
808C2#2377659811yescharacteristic
809C2#2377659811yescharacteristic
810C2#2377660011yescharacteristic
811C2#2377805712yes—
812C2#2377807312yes—
subgroupG/H
center, FrattiniC23C24×D79
commutatorC22×C79C24×C4
FittingC79×#2377C2
socle, cosocleC23×C79C25
prime radicalC2×#121×C79C22
hypercenter#2377D79
hypocenterC79#34387
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ #2377

Complements

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

NH ≅ G/Ntype
2. #23766568C2semidirect
3. #23766563C2semidirect
5. #23766535C2semidirect
6. #23766533C2semidirect
7. #23766362C2semidirect
8. #23766338C2semidirect
9. #23766282C2semidirect
10. #23766258C2semidirect
11. #23766209C2semidirect
12. #23766203C2semidirect
13. #23766176C2semidirect
14. #23766172C2semidirect
15. #23766037C2semidirect
16. #23766026C2semidirect
17. #23765795C2semidirect
18. #23765791C2semidirect
20. #19099094C4semidirect
113. #14579154C2×C4semidirect
114. #14579152C2×C4semidirect
116. #14579142C2×C4semidirect
117. #14579140C2×C4semidirect
118. #14579126C2×C4semidirect
120. D4×Dic79C2×C4semidirect
121. #14579117C2×C4semidirect
145. C2×C4×Dic79C2×C4semidirect
426. C79#34387semidirect

Maximal subgroups

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

subgroupindex
C2×#190990942
#237665682
#237665632
#237665572
#237665352
#237665332
#237663622
#237663382
#237662822
#237662582
#237662092
#237662032
#237661762
#237661722
#237660372
#237660262
#237657952
#237657912
C79×#23772
#3438779