Finite Group Databasebeta

← #34461355

Subgroups — #34461355

Order 20224.

1690 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23771750C211yesmaximal, characteristic
2#23771750C211yesmaximal, characteristic
3#23771737C212yesmaximal
4#23769373C211yesmaximal, characteristic
5#23769373C211yesmaximal, characteristic
6#23769217C212yesmaximal
7#23768864C212yesmaximal, complemented
8#23768862C212yesmaximal, complemented
9#23768834C212yesmaximal, complemented
10#23768832C212yesmaximal, complemented
11#23767974C212yesmaximal, complemented
12#23767926C212yesmaximal, complemented
13#23767238C212yesmaximal, complemented
14#23767175C212yesmaximal, complemented
15#23766128C212yesmaximal
16#23766003C211yesmaximal, characteristic
17C4×#14579138C212yesmaximal
18C2×C4⋊C4×Dic79C211yesmaximal, characteristic
19C79×#2313C211yesmaximal, characteristic
20C2×#14579160C2211yescharacteristic
21C2×#14579160C2211yescharacteristic
22C2×#14579138C2212yes—
23C2×#14579138C2212yes—
24C2×C4×Dic158C2212yes—
25C22×C4⋊Dic79C2211yescharacteristic
26C22×C4×Dic79C2211yescharacteristic
27C22×C4×Dic79C2211yescharacteristic
28C22×C4×Dic79C2211yescharacteristic
29#19098505C2212yes—
30#19098505C2212yes—
31#19098505C2212yes—
32#19098505C2212yes—
33#19098502C2212yes—
34#19098502C2212yes—
35#19098497C2212yes—
36#19098497C2212yes—
37#19098496C2212yes—
38#19098496C2212yes—
39#19098495C2212yes—
40#19098495C2212yes—
41#19098495C2212yes—
42#19098495C2212yes—
43#19098484C2212yes—
44#19098484C2212yes—
45#19098469C2212yes—
46#19098467C2212yes—
47#19098467C2212yes—
48#19098467C2212yes—
49#19098467C2212yes—
50#19098467C2212yes—
51#19098467C2212yes—
52#19098462C2211yescharacteristic
53#19098462C2211yescharacteristic
54#19098461C2212yes—
55#19098460C2212yes—
56#19098460C2212yes—
57#19098460C2212yes—
58#19098460C2212yes—
59#19098460C2212yes—
60#19098460C2212yes—
61#19098459C2211yescharacteristic
62#19098459C2211yescharacteristic
63#19098450C2212yes—
64#19098450C2212yes—
65#19098450C2212yes—
66#19098450C2212yes—
67#19098449C2212yes—
68#19098449C2212yes—
69#19098449C2212yes—
70#19098449C2212yes—
71#19098447C2212yes—
72#19098447C2212yes—
73#19098446C2212yes—
74#19098446C2212yes—
75#19098446C2212yes—
76#19098446C2212yes—
77#19098438C2212yes—
78#19098438C2212yes—
79#19098435C2212yes—
80#19098435C2212yes—
81#19098432C2211yescharacteristic
82#19098432C2211yescharacteristic
83#19098426C2212yes—
84#19098423C2211yescharacteristic
85#19098423C2211yescharacteristic
86#19098421C2212yes—
87#19098421C2212yes—
88C4⋊C4×Dic79C2212yes—
89C4⋊C4×Dic79C2212yes—
90C4⋊C4×Dic79C2212yes—
91C4⋊C4×Dic79C2212yes—
92C4×Dic79⋊C4C2212yes—
93C4×Dic79⋊C4C2212yes—
94C4×C4⋊Dic79C2212yes—
95C4×C22⋊Dic79C2212yes—
96C2×C79⋊#95C2211yescharacteristic
97C2×C79⋊#95C2211yescharacteristic
98C22×C4⋊C4×C79C2211yescharacteristic
99#387×C79C2212yes—
100#387×C79C2212yes—
101#387×C79C2212yes—
102#387×C79C2212yes—
103#381×C79C2212yes—
104#380×C79C2211yescharacteristic
105#380×C79C2211yescharacteristic
106C4×C22⋊C4×C79C2212yes—
107C22×Dic158C2312yes—
108C22×Dic158C2312yes—
109C23×Dic79C2311yescharacteristic
110C23×Dic79C2311yescharacteristic
111C23×Dic79C2311yescharacteristic
112C23×Dic79C2311yescharacteristic
113#14579160—42no—
114#14579160—42no—
115#14579138—28no—
116#14579138—28no—
117C4×Dic158—44no—
118C2×C4⋊Dic79—24no—
119C2×C4⋊Dic79C2312yes—
120C2×C4⋊Dic79C2312yes—
121C2×C4⋊Dic79C2312yes—
122C2×C4⋊Dic79C2312yes—
123C2×C4⋊Dic79C2312yes—
124C2×C4⋊Dic79C2311yescharacteristic
125C2×C4⋊Dic79C2311yescharacteristic
126C2×C4⋊Dic79C2311yescharacteristic
127C2×C4⋊Dic79C2311yescharacteristic
128C2×C4⋊Dic79C2312yes—
129C2×C4⋊Dic79C2312yes—
130C2×C4⋊Dic79C2312yes—
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×C22⋊Dic79C2312yes—
144C2×C22⋊Dic79C2312yes—
145C2×C4×Dic79—24no—
146C2×C4×Dic79—42no—
147C2×C4×Dic79—42no—
148C2×C4×Dic79C2312yes—
149C2×C4×Dic79C2311yescharacteristic
150C2×C4×Dic79C2311yescharacteristic
151C2×C4×Dic79C2312yes—
152C2×C4×Dic79C2312yes—
153C2×C4×Dic79C2312yes—
154C2×C4×Dic79C2312yes—
155C2×C4×Dic79C2312yes—
156C2×C4×Dic79C2311yescharacteristic
157C2×C4×Dic79C2311yescharacteristic
158C79⋊#95C2312yes—
159C79⋊#95C2312yes—
160C79⋊#95C2312yes—
161C79⋊#95C2312yes—
162C79⋊#95C2312yes—
163C79⋊#95C2312yes—
164C79⋊#95C2312yes—
165C79⋊#95C2312yes—
166C79⋊#95C2312yes—
167C79⋊#95C2312yes—
168C79⋊#95C2312yes—
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—
182C23×C4×C79C2311yescharacteristic
183C23×C4×C79C2311yescharacteristic
184C23×C4×C79C2311yescharacteristic
185C2×C4⋊C4×C79Q818yescomplemented
186C2×C4⋊C4×C79C2311yescharacteristic
187C2×C4⋊C4×C79C2311yescharacteristic
188C2×C4⋊C4×C79C2311yescharacteristic
189C2×C4⋊C4×C79C2311yescharacteristic
190C2×C4⋊C4×C79C2312yes—
191C2×C4⋊C4×C79C2312yes—
192C2×C22⋊C4×C79C2312yes—
193C2×C22⋊C4×C79C2312yes—
194C2×C42×C79C2312yes—
195C2×C42×C79C2312yes—
196#95×C79C2312yes—
197#95×C79C2312yes—
198#95×C79C2312yes—
199#95×C79C2312yes—
200#95×C79C2312yes—
201#95×C79C2312yes—
202#95×C79C2312yes—
203#95×C79C2312yes—
204C2×Dic158—24no—
205C2×Dic158—24no—
206C2×Dic158—24no—
207C2×Dic158—24no—
208C2×Dic158—42no—
209C2×Dic158—42no—
210C22×Dic79—22no—
211C22×Dic79—22no—
212C22×Dic79—22no—
213C22×Dic79—22no—
214C22×Dic79—41no—
215C22×Dic79—41no—
216C22×Dic79—41no—
217C22×Dic79—41no—
218C22×Dic79—41no—
219C22×Dic79—41no—
220C22×Dic79#4114yes—
221C22×Dic79#4114yes—
222C22×Dic79C2412yes—
223C22×Dic79C2412yes—
224C22×Dic79C2412yes—
225C22×Dic79C2412yes—
226C22×Dic79C2412yes—
227C22×Dic79C2412yes—
228C22×Dic79C2411yescharacteristic
229C22×Dic79C2411yescharacteristic
230C22×Dic79C2411yescharacteristic
231C22×Dic79C2411yescharacteristic
232C4⋊Dic79—24no—
233C4⋊Dic79—24no—
234C4⋊Dic79—24no—
235C4⋊Dic79—24no—
236C4⋊Dic79—41no—
237C4⋊Dic79—41no—
238C4⋊Dic79—42no—
239C4⋊Dic79—42no—
240C4⋊Dic79—42no—
241C4⋊Dic79—42no—
242C4⋊Dic79—41no—
243C4⋊Dic79—41no—
244Dic79⋊C4—24no—
245Dic79⋊C4—24no—
246Dic79⋊C4—24no—
247Dic79⋊C4—24no—
248Dic79⋊C4—24no—
249Dic79⋊C4—24no—
250Dic79⋊C4—42no—
251Dic79⋊C4—42no—
252Dic79⋊C4—42no—
253Dic79⋊C4—42no—
254Dic79⋊C4—42no—
255Dic79⋊C4—42no—
256C22⋊Dic79—24no—
257C22⋊Dic79—24no—
258C4×Dic79—24no—
259C4×Dic79—24no—
260C4×Dic79—24no—
261C4×Dic79—22no—
262C4×Dic79—22no—
263C4×Dic79—42no—
264C4×Dic79—41no—
265C4×Dic79—41no—
266C4×Dic79—42no—
267C4×Dic79—42no—
268C24×C79C2411yescharacteristic
269C22×C4×C79—22no—
270C22×C4×C79—22no—
271C22×C4×C79—41no—
272C22×C4×C79—41no—
273C22×C4×C79—41no—
274C22×C4×C79—41no—
275C22×C4×C79C2×Q814yes—
276C22×C4×C79C2×Q814yes—
277C22×C4×C79C2×Q814yes—
278C22×C4×C79C2412yes—
279C22×C4×C79C2412yes—
280C22×C4×C79C2412yes—
281C22×C4×C79C2412yes—
282C22×C4×C79C2412yes—
283C22×C4×C79C2412yes—
284C22×C4×C79C2411yescharacteristic
285C22×C4×C79C2411yescharacteristic
286C4⋊C4×C79—41no—
287C4⋊C4×C79—41no—
288C4⋊C4×C79—41no—
289C4⋊C4×C79—41no—
290C4⋊C4×C79C2×Q818yes—
291C4⋊C4×C79C2×Q818yes—
292C22⋊C4×C79—24no—
293C22⋊C4×C79—24no—
294C42×C79—42no—
295C42×C79—42no—
296C23×C79—21no—
297C23×C79—21no—
298C23×C79—21no—
299C23×C79—21no—
300C23×C79C22×Q812yes—
301C23×C79C2×#4112yes—
302C23×C79C2×#4112yes—
303C23×C79C2511yescharacteristic
304C2×C4×C79—28no—
305C2×C4×C79—22no—
306C2×C4×C79—22no—
307C2×C4×C79—22no—
308C2×C4×C79—21no—
309C2×C4×C79—21no—
310C2×C4×C79—22no—
311C2×C4×C79—21no—
312C2×C4×C79—21no—
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—44no—
326C2×C4×C79—44no—
327C2×C4×C79C22×Q814yes—
328C2×C4×C79C22×Q814yes—
329C2×C4×C79C22×Q812yes—
330C2×C4×C79C22×Q812yes—
331C2×Dic79—21no—
332C2×Dic79—21no—
333C2×Dic79—21no—
334C2×Dic79—21no—
335C2×Dic79—21no—
336C2×Dic79—21no—
337C2×Dic79—28no—
338C2×Dic79—22no—
339C2×Dic79—22no—
340C2×Dic79—22no—
341C2×Dic79—22no—
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—22no—
355C2×Dic79—22no—
356C2×Dic79—44no—
357C2×Dic79—44no—
358C2×Dic79—44no—
359C2×Dic79C2×#4112yes—
360C2×Dic79C2×#4112yes—
361C2×Dic79C2×#4112yes—
362C2×Dic79C2×#4112yes—
363C2×Dic79H(5,𝔽2)12yes—
364C2×Dic792−1+412yes—
365Dic158—48no—
366Dic158—84no—
367C22×C79—22no—
368C22×C79—22no—
369C22×C79—22no—
370C22×C79—22no—
371C22×C79—22no—
372C22×C79—22no—
373C22×C79#53314yes—
374C22×C79C23×Q811yescharacteristic
375C22×C79C22×#4111yescharacteristic
376C22×C79C22×#4111yescharacteristic
377C22×C79C2×H(5,𝔽2)11yescharacteristic
378C22×C79C2×2−1+411yescharacteristic
379C22×C79#58511yescharacteristic
380C22×C79#58511yescharacteristic
381C4×C79—24no—
382C4×C79—24no—
383C4×C79—22no—
384C4×C79—22no—
385C4×C79—42no—
386C4×C79—42no—
387C4×C79—42no—
388C4×C79—42no—
389Dic79—22no—
390Dic79—22no—
391Dic79—22no—
392Dic79—42no—
393Dic79—42no—
394Dic79—42no—
395Dic79—42no—
396Dic79—42no—
397Dic79—42no—
398Dic79#53914yes—
399#35015—791nomaximal, Sylow
400C2×C79—24no—
401C2×C79C2×#53311yescharacteristic
402C2×C79C2×#53911yescharacteristic
403C2×C79#345511yescharacteristic
404C2×C79#350111yescharacteristic
405C2×C79#350211yescharacteristic
406C2×C79#350511yescharacteristic
407C2×C79#350711yescharacteristic
408#2857—791no—
409#2857—791no—
410#2855—792no—
411#2646—791no—
412#2646—791no—
413#2627—792no—
414#2590—792no—
415#2590—792no—
416#2588—792no—
417#2588—792no—
418#2511—792no—
419#2507—792no—
420#2451—792no—
421#2446—792no—
422#2329—792no—
423#2313—791no—
424#2313D7911yescharacteristic
425C4×C22⋊Q8—792no—
426C2×C4×C4⋊C4—791no—
427C79#3501511yescharacteristic, complemented, Sylow
428C2×C4⋊Q8—791no—
429C2×C4⋊Q8—791no—
430C2×C22⋊Q8—792no—
431C2×C22⋊Q8—792no—
432C2×C4×Q8—792no—
433C22×C4⋊C4—791no—
434C22×C4⋊C4C2×D7911yescharacteristic
435C22×C42—791no—
436C22×C42—791no—
437C22×C42—791no—
438#400—792no—
439#400—792no—
440#400—792no—
441#400—792no—
442#400—792no—
443#400—792no—
444#398—792no—
445#398—792no—
446#398—792no—
447#398—792no—
448#398—792no—
449#398—792no—
450#398—792no—
451#398—792no—
452#395—792no—
453#395—792no—
454#391—792no—
455#391—792no—
456#391—792no—
457#391—792no—
458#391—792no—
459#391—792no—
460#391—792no—
461#389—791no—
462#389—791no—
463#389—791no—
464#389—791no—
465#389—792no—
466#389—792no—
467#389—792no—
468#389—792no—
469#389—792no—
470#389—792no—
471#389—792no—
472#387—792no—
473#387—792no—
474#387—792no—
475#387—792no—
476#387—792no—
477#387—792no—
478#387—792no—
479#387—792no—
480#387—792no—
481#387—792no—
482#387—792no—
483#387—792no—
484#387—792no—
485#387—792no—
486#387C2×D7912yes—
487#387C2×D7912yes—
488#387C2×D7912yes—
489#387C2×D7912yes—
490#385—792no—
491#385—792no—
492#385—792no—
493#385—792no—
494#384—791no—
495#384—791no—
496#381—792no—
497#381C2×D7912yes—
498#380—791no—
499#380—791no—
500#380—792no—
501#380—792no—
502#380C2×D7911yescharacteristic
503#380C2×D7911yescharacteristic
504C4×C4⋊C4—792no—
505C4×C4⋊C4—792no—
506C4×C4⋊C4—792no—
507C4×C4⋊C4—792no—
508C4×C4⋊C4—792no—
509C4×C4⋊C4—792no—
510C4×C4⋊C4—792no—
511C4×C22⋊C4—792no—
512C4×C22⋊C4C2×D7912yes—
513C2×#95—791no—
514C2×#95—791no—
515C22×Q8—792no—
516C22×Q8—792no—
517C23×C4—791no—
518C23×C4—791no—
519C23×C4—791no—
520C23×C4—791no—
521C23×C4C22×D7911yescharacteristic
522C23×C4C22×D7911yescharacteristic
523C23×C4C22×D7911yescharacteristic
524C4⋊Q8—3162no—
525C4⋊Q8—3162no—
526C22⋊Q8—1588no—
527C22⋊Q8—1588no—
528C4×Q8—3164no—
529C2×C4⋊C4—792no—
530C2×C4⋊C4—792no—
531C2×C4⋊C4—792no—
532C2×C4⋊C4—791no—
533C2×C4⋊C4—791no—
534C2×C4⋊C4—792no—
535C2×C4⋊C4—792no—
536C2×C4⋊C4—791no—
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—792no—
544C2×C4⋊C4—792no—
545C2×C4⋊C4—792no—
546C2×C4⋊C4—792no—
547C2×C4⋊C4—792no—
548C2×C4⋊C4—792no—
549C2×C4⋊C4—792no—
550C2×C4⋊C4—792no—
551C2×C4⋊C4—792no—
552C2×C4⋊C4—792no—
553C2×C4⋊C4—1584no—
554C2×C4⋊C4Dic15818yescomplemented
555C2×C4⋊C4C22×D7911yescharacteristic
556C2×C4⋊C4C22×D7911yescharacteristic
557C2×C4⋊C4C22×D7911yescharacteristic
558C2×C4⋊C4C22×D7911yescharacteristic
559C2×C4⋊C4C22×D7912yes—
560C2×C4⋊C4C22×D7912yes—
561C2×C22⋊C4—792no—
562C2×C22⋊C4—792no—
563C2×C22⋊C4C22×D7912yes—
564C2×C22⋊C4C22×D7912yes—
565C2×C42—3162no—
566C2×C42—3162no—
567C2×C42—792no—
568C2×C42—792no—
569C2×C42—792no—
570C2×C42—791no—
571C2×C42—791no—
572C2×C42—792no—
573C2×C42—791no—
574C2×C42—791no—
575C2×C42—792no—
576C2×C42—792no—
577C2×C42—1584no—
578C2×C42C22×D7912yes—
579C2×C42C22×D7912yes—
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#95—792no—
598#95—792no—
599#95—792no—
600#95—792no—
601#95—792no—
602#95—792no—
603#95—792no—
604#95C22×D7912yes—
605#95C22×D7912yes—
606#95C22×D7912yes—
607#95C22×D7912yes—
608#95C22×D7912yes—
609#95C22×D7912yes—
610#95C22×D7912yes—
611#95C22×D7912yes—
612C24C23×D7911yescharacteristic
613C2×Q8—3162no—
614C2×Q8—3162no—
615C2×Q8—1584no—
616C2×Q8—1584no—
617C2×Q8—1584no—
618C2×Q8—1584no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—41no—
622C22×C4—41no—
623C22×C4—41no—
624C22×C4—41no—
625C22×C4—3161no—
626C22×C4—3161no—
627C22×C4—3161no—
628C22×C4—3161no—
629C22×C4—3161no—
630C22×C4—3161no—
631C22×C4—794no—
632C22×C4—791no—
633C22×C4—794no—
634C22×C4—791no—
635C22×C4—791no—
636C22×C4—791no—
637C22×C4—792no—
638C22×C4—792no—
639C22×C4—792no—
640C22×C4—792no—
641C22×C4—792no—
642C22×C4—792no—
643C22×C4—1582no—
644C22×C4—1582no—
645C22×C4—1582no—
646C22×C4—1582no—
647C22×C4C2×Dic15814yes—
648C22×C4C2×Dic15814yes—
649C22×C4C2×Dic15814yes—
650C22×C4C23×D7912yes—
651C22×C4C23×D7912yes—
652C22×C4C23×D7912yes—
653C22×C4C23×D7912yes—
654C22×C4C23×D7912yes—
655C22×C4C23×D7912yes—
656C22×C4C23×D7911yescharacteristic
657C22×C4C23×D7911yescharacteristic
658C4⋊C4—41no—
659C4⋊C4—41no—
660C4⋊C4—41no—
661C4⋊C4—41no—
662C4⋊C4—3162no—
663C4⋊C4—3162no—
664C4⋊C4—3162no—
665C4⋊C4—3162no—
666C4⋊C4—3162no—
667C4⋊C4—3162no—
668C4⋊C4—3161no—
669C4⋊C4—3161no—
670C4⋊C4—3162no—
671C4⋊C4—3162no—
672C4⋊C4—3162no—
673C4⋊C4—3162no—
674C4⋊C4—3161no—
675C4⋊C4—3161no—
676C4⋊C4—1584no—
677C4⋊C4—1584no—
678C4⋊C4—1584no—
679C4⋊C4—1584no—
680C4⋊C4—1584no—
681C4⋊C4—1584no—
682C4⋊C4—1584no—
683C4⋊C4—1584no—
684C4⋊C4—1584no—
685C4⋊C4—1584no—
686C4⋊C4C2×Dic15818yes—
687C4⋊C4C2×Dic15818yes—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—1584no—
691C22⋊C4—1584no—
692C42—42no—
693C42—42no—
694C42—3162no—
695C42—3161no—
696C42—3161no—
697C42—3162no—
698C42—3162no—
699C42—1584no—
700C42—1582no—
701C42—1582no—
702C42—1584no—
703C42—1584no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23C22×Dic15812yes—
709C23#41×D7912yes—
710C23#41×D7912yes—
711C23C24×D7911yescharacteristic
712Q8—3168no—
713Q8—6324no—
714C2×C4—22no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—28no—
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—44no—
737C2×C4—3164no—
738C2×C4—3164no—
739C2×C4—3164no—
740C2×C4—792no—
741C2×C4—792no—
742C2×C4—792no—
743C2×C4—792no—
744C2×C4—792no—
745C2×C4—792no—
746C2×C4—1582no—
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—1582no—
764C2×C4—1588no—
765C2×C4—1581no—
766C2×C4—1581no—
767C2×C4—1581no—
768C2×C4—1581no—
769C2×C4—1581no—
770C2×C4—1581no—
771C2×C4C22×Dic15814yes—
772C2×C4C22×Dic15812yes—
773C2×C4C22×Dic15812yes—
774C2×C4C22×Dic15814yes—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22#1909911614yes—
782C22C23×Dic15811yescharacteristic
783C22C2×#41×D7911yescharacteristic
784C22C2×#41×D7911yescharacteristic
785C22H(5,𝔽2)×D7911yescharacteristic
786C222−1+4×D7911yescharacteristic
787C22#1909939811yescharacteristic
788C22#1909940011yescharacteristic
789C4—24no—
790C4—22no—
791C4—22no—
792C4—24no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—3162no—
798C4—3162no—
799C4—3162no—
800C4—3162no—
801C4—3162no—
802C4—3162no—
803C4—794no—
804C4—1582no—
805C4—1582no—
806C4—1582no—
807C2—24no—
808C2C2×#1909911611yescharacteristic
809C2#539×D7911yescharacteristic
810C2#2377678611yescharacteristic
811C2#2377719811yescharacteristic
812C2#2377720611yescharacteristic
813C2#2377723211yescharacteristic
814C2#2377726011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D79
commutator, socle, cosocleC23×C79C25
FittingC79×#2313C2
prime radicalC24×C79C24
hypercenter#2313D79
hypocenterC79#35015
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #2313

Complements

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

NH ≅ G/Ntype
7. #23768864C2semidirect
8. #23768862C2semidirect
9. #23768834C2semidirect
10. #23768832C2semidirect
11. #23767974C2semidirect
12. #23767926C2semidirect
13. #23767238C2semidirect
14. #23767175C2semidirect
185. C2×C4⋊C4×C79Q8semidirect
427. C79#35015semidirect
554. C2×C4⋊C4Dic158semidirect

Maximal subgroups

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

subgroupindex
#237717502
#237717372
#237693732
#237692172
#237688642
#237688622
#237688342
#237688322
#237679742
#237679262
#237672382
#237671752
#237661282
#237660032
C4×#145791382
C2×C4⋊C4×Dic792
C79×#23132
#3501579