Finite Group Databasebeta

← #7679788

Subgroups — #7679788

Order 512.

4442 conjugacy classes of subgroups.

The subgroup lattice has 1059 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59870C212yesmaximal, complemented
2#59869C212yesmaximal, complemented
3#59665C212yesmaximal, complemented
4#59664C214yesmaximal
5#59456C212yesmaximal, complemented
6#59325C214yesmaximal
7#45426C214yesmaximal, complemented
8#45164C214yesmaximal, complemented
9#43557C218yesmaximal
10#39182C212yesmaximal, complemented
11#39182C214yesmaximal, complemented
12#39181C212yesmaximal, complemented
13#39177C214yesmaximal, complemented
14#36535C212yesmaximal, complemented
15#36447C212yesmaximal, complemented
16#35627C212yesmaximal
17#35566C212yesmaximal
18#35286C211yesmaximal, characteristic
19#35265C212yesmaximal
20C2×#2571C211yesmaximal, characteristic
21#34938C211yesmaximal, characteristic
22#34215C212yesmaximal
23#34214C211yesmaximal, characteristic
24#34213C211yesmaximal, characteristic
25#34145C211yesmaximal, characteristic
26C4×#544C211yesmaximal, characteristic
27C2×#544C2211yescharacteristic
28C2×#533C2212yes—
29C2×#533C2211yescharacteristic
30#2864C2214yes—
31#2859C2212yes—
32#2859C2214yes—
33#2859C2212yes—
34#2809C2218yes—
35#2805C2218yes—
36#2805C2218yes—
37#2805C2218yes—
38#2799C2218yes—
39#2791C2218yes—
40#2774C2218yes—
41#2774C2218yes—
42#2755C2218yes—
43#2755C2218yes—
44#2755C2218yes—
45#2713C2218yes—
46#2647C2214yes—
47#2647C2214yes—
48#2647C2214yes—
49#2590C2218yes—
50#2590C2218yes—
51#2588C2218yes—
52#2585C2218yes—
53#2584C2214yes—
54#2584C2214yes—
55#2581C2214yes—
56#2581C2214yes—
57#2571C2214yes—
58#2571C2212yes—
59#2571C2214yes—
60#2571C2214yes—
61#2571C2212yes—
62#2571C2212yes—
63#2571C2212yes—
64#2571C2212yes—
65#2571C2214yes—
66#2571C2212yes—
67#2570C2214yes—
68#2570C2214yes—
69#2568C2218yes—
70#2568C2214yes—
71#2567C2214yes—
72#2565C2214yes—
73#2552C2214yes—
74#2552C2212yes—
75#2552C2211yescharacteristic
76#2552C2212yes—
77#2552C2211yescharacteristic
78#2551C2211yescharacteristic
79#2551C2214yes—
80#2551C2211yescharacteristic
81#2550C2212yes—
82#2550C2214yes—
83#2550C2212yes—
84#2550C2218yes—
85#2550C2214yes—
86#2550C2214yes—
87#2549C2214yes—
88#2549C2218yes—
89#2546C2214yes—
90#2546C2214yes—
91#2520C2218yes—
92#2511C2218yes—
93#2509C2214yes—
94#2509C2214yes—
95#2509C2214yes—
96#2509C2214yes—
97#2508C2214yes—
98#2508C2218yes—
99#2508C2218yes—
100#2508C2214yes—
101#2508C2214yes—
102#2508C2214yes—
103#2508C2214yes—
104#2507C2214yes—
105#2506C2214yes—
106#2506C2214yes—
107#2506C2218yes—
108#2505C2218yes—
109#2505C2218yes—
110#2505C2218yes—
111#2473C2218yes—
112#2453C2214yes—
113#2453C2218yes—
114#2451C2214yes—
115#2442C2214yes—
116#2442C2214yes—
117#2440C2212yes—
118#2440C2218yes—
119#2440C2212yes—
120#2399C2214yes—
121C2×#400C2214yes—
122#2370C2214yes—
123#2370C2212yes—
124#2370C2212yes—
125#2370C2214yes—
126#2369C2211yescharacteristic
127#2369C2212yes—
128#2369C2211yescharacteristic
129#2368C2218yes—
130#2368C2214yes—
131#2368C2218yes—
132#2365C2211yescharacteristic
133#2365C2212yes—
134#2365C2211yescharacteristic
135#2360C2212yes—
136#2360C2214yes—
137#2360C2214yes—
138#2360C2212yes—
139#2355C2212yes—
140#2355C2214yes—
141#2355C2212yes—
142#2355C2212yes—
143#2355C2214yes—
144#2355C2214yes—
145#2355C2214yes—
146#2355C2214yes—
147#2355C2214yes—
148#2351C2214yes—
149Q8×C4⋊C4C2212yes—
150Q8×C4⋊C4C2212yes—
151Q8×C4⋊C4C2212yes—
152Q8×C4⋊C4C2214yes—
153#2331C2214yes—
154#2331C2214yes—
155#2331C2212yes—
156#2331C2212yes—
157#2330C2212yes—
158#2330C2212yes—
159#2330C2214yes—
160#2329C2214yes—
161#2329C2214yes—
162#2317C2211yescharacteristic
163#2317C2212yes—
164#2317C2211yescharacteristic
165#2317C2212yes—
166#2317C2212yes—
167#2316C2212yes—
168#2316C2211yescharacteristic
169C4×C4⋊Q8C2212yes—
170C4×C4⋊Q8C2212yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2212yes—
174C4×C4⋊Q8C2212yes—
175C4×#125C2214yes—
176C4×#125C2212yes—
177C4×#125C2214yes—
178C4×#125C2212yes—
179C4×C22⋊Q8C2214yes—
180C4×C22⋊Q8C2214yes—
181#2296C2212yes—
182#2296C2212yes—
183#2295C2214yes—
184#2295C2212yes—
185C2×#389C2212yes—
186C2×#389C2212yes—
187#2285C2211yescharacteristic
188C2×#384C2211yescharacteristic
189C2×#382C2212yes—
190C2×#382C2212yes—
191#2274C2212yes—
192#2274C2212yes—
193C42×Q8C2212yes—
194C4×#117C2211yescharacteristic
195C4×#117C2211yescharacteristic
196C4×#117C2212yes—
197C2×C4×C4⋊C4C2211yescharacteristic
198C2×C4×C4⋊C4C2211yescharacteristic
199#544—28no—
200#533—216no—
201#533Q8116yescomplemented
202C2×C4⋊Q8C2312yes—
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2318yes—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#125C2312yes—
212C2×#125C2312yes—
213C2×#125C2312yes—
214C2×#125C2312yes—
215C2×#125C2314yes—
216C2×#125C2314yes—
217C2×#125C2318yes—
218C2×#125C2312yes—
219C2×C22⋊Q8C2314yes—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2312yes—
224C2×C4×Q8C2314yes—
225C2×C4×Q8C2314yes—
226C2×C4×Q8C2314yes—
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2314yes—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2312yes—
234C2×#117C2311yescharacteristic
235C2×#117C2311yescharacteristic
236C2×#117C2311yescharacteristic
237C2×#117C2312yes—
238C2×#117C2312yes—
239C2×#117C2311yescharacteristic
240C22×C4⋊C4C2311yescharacteristic
241C22×C4⋊C4C2312yes—
242C22×C4⋊C4C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2312yes—
246C22×C4⋊C4C2312yes—
247C22×C4⋊C4C2314yes—
248C22×C42C2312yes—
249C22×C42C2312yes—
250C22×C42C2311yescharacteristic
251#400C2318yes—
252#400C2318yes—
253#400C2318yes—
254#400C2318yes—
255#400C2318yes—
256#400C2318yes—
257#400C2318yes—
258#400C2318yes—
259#400C2318yes—
260#400C2318yes—
261#400C2318yes—
262#400C2318yes—
263#400C2318yes—
264#400C2318yes—
265#400C2318yes—
266#400C2318yes—
267#398C2318yes—
268#398C2318yes—
269#398C2318yes—
270#398C2318yes—
271#398C2318yes—
272#398C2318yes—
273#398C2314yes—
274#398C2314yes—
275#398C2318yes—
276#398C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2314yes—
280#398C2314yes—
281#398C2318yes—
282#398C2318yes—
283#395C2318yes—
284#395C2318yes—
285#395C2318yes—
286#395C2318yes—
287#395C2314yes—
288#395C2314yes—
289#395C2314yes—
290#395C2314yes—
291#391C2314yes—
292#391C2314yes—
293#391C2314yes—
294#391C2314yes—
295#391C2314yes—
296#391C2314yes—
297#391C2314yes—
298#391C2318yes—
299#391C2312yes—
300#391C2314yes—
301#391C2318yes—
302#391C2318yes—
303#391C2318yes—
304#391C2318yes—
305#391C2314yes—
306#391C2318yes—
307#391C2318yes—
308#391C2312yes—
309#391C2314yes—
310#389C2312yes—
311#389C2312yes—
312#389C2312yes—
313#389C2312yes—
314#389C2312yes—
315#389C2314yes—
316#389C2314yes—
317#389C2312yes—
318#389C2312yes—
319#389C2314yes—
320#389C2314yes—
321#389C2312yes—
322#389C2312yes—
323#389C2312yes—
324#389C2314yes—
325#389C2314yes—
326#389C2314yes—
327#389C2314yes—
328#389C2314yes—
329#389C2312yes—
330#389C2312yes—
331#389C2314yes—
332#389C2312yes—
333#389C2314yes—
334#389C2314yes—
335#389C2314yes—
336#389C2312yes—
337#389C2312yes—
338#389C2314yes—
339#389C2314yes—
340#389C2314yes—
341#389C2314yes—
342#389C2318yes—
343#389C2312yes—
344#389C2314yes—
345#389C2314yes—
346#389C2312yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2318yes—
352#389C2318yes—
353#389C2314yes—
354#389C2312yes—
355#389C2312yes—
356#389C2318yes—
357#389C2318yes—
358#389C2318yes—
359#389C2318yes—
360#389C2318yes—
361#389C2314yes—
362#389C2318yes—
363#389C2318yes—
364#389C2314yes—
365#389C2318yes—
366#389C2314yes—
367#389C2318yes—
368#389C2314yes—
369#389C2312yes—
370#389C2312yes—
371#389C2314yes—
372#389C2314yes—
373#389C2312yes—
374#387C2318yes—
375#387C2318yes—
376#387C2314yes—
377#387C2314yes—
378#387C2314yes—
379#387C2314yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2314yes—
392#387C2318yes—
393#387C2314yes—
394#387C2314yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2314yes—
401#387C2318yes—
402#387C2318yes—
403#387C2314yes—
404#387C2314yes—
405#387C2314yes—
406#387C2314yes—
407#385C2314yes—
408#385C2318yes—
409#385C2314yes—
410#385C2318yes—
411#385C2318yes—
412#385C2314yes—
413#385C2314yes—
414#385C2314yes—
415#385C2314yes—
416#384C2312yes—
417#384C2312yes—
418#384C2312yes—
419#384C2312yes—
420#384C2312yes—
421#384C2318yes—
422#384C2312yes—
423#384C2314yes—
424#384C2312yes—
425#384C2312yes—
426#384C2314yes—
427#384C2314yes—
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#382C2314yes—
431#382C2312yes—
432#382C2312yes—
433#382C2314yes—
434#382C2314yes—
435#382C2314yes—
436#382C2318yes—
437#382C2318yes—
438#382C2314yes—
439#382C2314yes—
440#382C2314yes—
441#382C2314yes—
442#382C2314yes—
443#382C2318yes—
444#382C2314yes—
445#382C2318yes—
446#382C2314yes—
447#382C2312yes—
448#380C2314yes—
449#380C2318yes—
450#380C2312yes—
451#380C2312yes—
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2312yes—
459C4×C4⋊C4C2318yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2314yes—
462C4×C4⋊C4C2318yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2318yes—
466C4×C4⋊C4C2318yes—
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2311yescharacteristic
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2318yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2312yes—
503C4×C22⋊C4C2312yes—
504C4×C22⋊C4C2312yes—
505C4×C22⋊C4C2318yes—
506C4×C22⋊C4C2318yes—
507C4×C22⋊C4C2312yes—
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2314yes—
511#376C2312yes—
512#376C2312yes—
513#376C2314yes—
514C2×#95C2312yes—
515C2×#95C2312yes—
516C2×#95C2314yes—
517C2×#95C2314yes—
518C2×#95C2314yes—
519C43C2314yes—
520C43C2312yes—
521C43C2312yes—
522C22×Q8C2412yes—
523C22×Q8C2414yes—
524C22×Q8C2414yes—
525C22×Q8C2414yes—
526C22×Q8C2412yes—
527C23×C4C2411yescharacteristic
528C23×C4C2414yes—
529C23×C4C2412yes—
530C23×C4C2412yes—
531C23×C4C2412yes—
532C23×C4C2412yes—
533C23×C4C2411yescharacteristic
534C23×C4C2411yescharacteristic
535C4⋊Q8—28no—
536C4⋊Q8—28no—
537C4⋊Q8—28no—
538C4⋊Q8—28no—
539C4⋊Q8—44no—
540C4⋊Q8—44no—
541C4⋊Q8—88no—
542C4⋊Q8C2×Q818yes—
543C4⋊Q8C2×Q818yes—
544#125—28no—
545#125—28no—
546#125—28no—
547#125—28no—
548#125—48no—
549#125—88no—
550#125—84no—
551#125C2×Q8116yes—
552C22⋊Q8—216no—
553C22⋊Q8—216no—
554C22⋊Q8—216no—
555C22⋊Q8C2×Q8116yes—
556C22⋊Q8C2×Q8116yes—
557C4×Q8—216no—
558C4×Q8—216no—
559C4×Q8—48no—
560C4×Q8—48no—
561C4×Q8—44no—
562C4×Q8—48no—
563C4×Q8—44no—
564C4×Q8—84no—
565C4×Q8C2×Q8116yes—
566C4×Q8C2×Q8116yes—
567#117—28no—
568#117—24no—
569#117—24no—
570#117—24no—
571#117C2×Q8116yes—
572#117#4118yes—
573C2×C4⋊C4—24no—
574C2×C4⋊C4—28no—
575C2×C4⋊C4—24no—
576C2×C4⋊C4—42no—
577C2×C4⋊C4—42no—
578C2×C4⋊C4—44no—
579C2×C4⋊C4—82no—
580C2×C4⋊C4—84no—
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2418yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2418yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2412yes—
652C2×C22⋊C4C2412yes—
653C2×C22⋊C4C2412yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2412yes—
656C2×C42—28no—
657C2×C42—44no—
658C2×C42C2×Q818yes—
659C2×C42C2414yes—
660C2×C42C2412yes—
661C2×C42C2412yes—
662C2×C42C2412yes—
663C2×C42C2412yes—
664C2×C42C2412yes—
665C2×C42C2412yes—
666C2×C42C2412yes—
667C2×C42C2412yes—
668C2×C42C2414yes—
669C2×C42C2412yes—
670C2×C42C2412yes—
671C2×C42C2412yes—
672C2×C42C2412yes—
673C2×C42C2418yes—
674C2×C42C2414yes—
675C2×C42C2414yes—
676C2×C42C2418yes—
677C2×C42C2418yes—
678C2×C42C2414yes—
679C2×C42C2412yes—
680C2×C42C2414yes—
681C2×C42C2412yes—
682C2×C42C2412yes—
683C2×C42C2418yes—
684C2×C42C2414yes—
685C2×C42C2414yes—
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2412yes—
691#95C2412yes—
692#95C2418yes—
693#95C2418yes—
694#95C2414yes—
695#95C2414yes—
696#95C2412yes—
697#95C2412yes—
698#95C2412yes—
699#95C2418yes—
700#95C2418yes—
701#95C2418yes—
702#95C2418yes—
703#95C2412yes—
704#95C2412yes—
705#95C2412yes—
706#95C2412yes—
707#95C2412yes—
708#95C2412yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2412yes—
714#95C2412yes—
715#95C2418yes—
716#95C2418yes—
717#95C2418yes—
718#95C2418yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2418yes—
730#95C2414yes—
731#95C2418yes—
732#95C2414yes—
733#95C2418yes—
734#95C2418yes—
735#95C2418yes—
736#95C2418yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2418yes—
742#95C2418yes—
743C24C2511yescharacteristic
744C2×Q8—28no—
745C2×Q8—28no—
746C2×Q8—28no—
747C2×Q8—24no—
748C2×Q8—24no—
749C2×Q8—42no—
750C2×Q8—42no—
751C2×Q8—44no—
752C2×Q8—44no—
753C2×Q8—44no—
754C2×Q8—44no—
755C2×Q8—44no—
756C2×Q8—44no—
757C2×Q8C22×Q818yes—
758C2×Q8C22×Q818yes—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—24no—
762C22×C4—24no—
763C22×C4—24no—
764C22×C4—28no—
765C22×C4—24no—
766C22×C4—41no—
767C22×C4—41no—
768C22×C4—42no—
769C22×C4—42no—
770C22×C4—42no—
771C22×C4—42no—
772C22×C4—44no—
773C22×C4—42no—
774C22×C4—44no—
775C22×C4—42no—
776C22×C4—42no—
777C22×C4—42no—
778C22×C4C22×Q814yes—
779C22×C4C22×Q814yes—
780C22×C4C22×Q814yes—
781C22×C4C2×#4114yes—
782C22×C42−1+414yes—
783C22×C4C2514yes—
784C22×C4C2512yes—
785C22×C4C2512yes—
786C22×C4C2512yes—
787C22×C4C2512yes—
788C22×C4C2514yes—
789C22×C4C2518yes—
790C22×C4C2512yes—
791C22×C4C2512yes—
792C22×C4C2512yes—
793C22×C4C2512yes—
794C22×C4C2512yes—
795C22×C4C2514yes—
796C22×C4C2512yes—
797C22×C4C2514yes—
798C22×C4C2511yescharacteristic
799C22×C4C2514yes—
800C22×C4C2514yes—
801C22×C4C2511yescharacteristic
802C22×C4C2511yescharacteristic
803C22×C4C2512yes—
804C22×C4C2512yes—
805C22×C4C2511yescharacteristic
806C22×C4C2511yescharacteristic
807C22×C4C2511yescharacteristic
808C4⋊C4—24no—
809C4⋊C4—24no—
810C4⋊C4—22no—
811C4⋊C4—24no—
812C4⋊C4—24no—
813C4⋊C4—22no—
814C4⋊C4—28no—
815C4⋊C4—28no—
816C4⋊C4—28no—
817C4⋊C4—28no—
818C4⋊C4—28no—
819C4⋊C4—28no—
820C4⋊C4—28no—
821C4⋊C4—28no—
822C4⋊C4—28no—
823C4⋊C4—24no—
824C4⋊C4—24no—
825C4⋊C4—28no—
826C4⋊C4—28no—
827C4⋊C4—22no—
828C4⋊C4—22no—
829C4⋊C4—22no—
830C4⋊C4—22no—
831C4⋊C4—22no—
832C4⋊C4—22no—
833C4⋊C4—28no—
834C4⋊C4—22no—
835C4⋊C4—22no—
836C4⋊C4—24no—
837C4⋊C4—24no—
838C4⋊C4—42no—
839C4⋊C4—42no—
840C4⋊C4—44no—
841C4⋊C4—44no—
842C4⋊C4—44no—
843C4⋊C4—48no—
844C4⋊C4—48no—
845C4⋊C4—44no—
846C4⋊C4—42no—
847C4⋊C4—44no—
848C4⋊C4—44no—
849C4⋊C4—44no—
850C4⋊C4—44no—
851C4⋊C4—48no—
852C4⋊C4—44no—
853C4⋊C4—48no—
854C4⋊C4—44no—
855C4⋊C4—44no—
856C4⋊C4—44no—
857C4⋊C4—48no—
858C4⋊C4—48no—
859C4⋊C4—48no—
860C4⋊C4—42no—
861C4⋊C4—44no—
862C4⋊C4—48no—
863C4⋊C4—44no—
864C4⋊C4—48no—
865C4⋊C4—48no—
866C4⋊C4—44no—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C4⋊C4C22×Q818yes—
870C4⋊C4C22×Q818yes—
871C4⋊C4C22×Q8116yes—
872C4⋊C4C22×Q8116yes—
873C4⋊C4C22×Q818yes—
874C4⋊C4C22×Q818yes—
875C4⋊C4C2×#4114yes—
876C4⋊C4C2×#4114yes—
877C22⋊C4—24no—
878C22⋊C4—28no—
879C22⋊C4—24no—
880C22⋊C4—24no—
881C22⋊C4C22×Q8116yes—
882C22⋊C4C2×#4118yes—
883C42—24no—
884C42—24no—
885C42—24no—
886C42—24no—
887C42—28no—
888C42—24no—
889C42—24no—
890C42—24no—
891C42—28no—
892C42—24no—
893C42—24no—
894C42—24no—
895C42—24no—
896C42—44no—
897C42—44no—
898C42—48no—
899C42—42no—
900C42—42no—
901C42—48no—
902C42—48no—
903C42—44no—
904C42—44no—
905C42—42no—
906C42—48no—
907C42—44no—
908C42—42no—
909C42C22×Q814yes—
910C42C22×Q814yes—
911C42C22×Q814yes—
912C42C22×Q814yes—
913C42C22×Q8116yes—
914C42C2×#4118yes—
915C23—21no—
916C23—21no—
917C23—21no—
918C23—21no—
919C23C23×Q812yes—
920C23C22×#4112yes—
921C23C2×2−1+412yes—
922C23C2611yescharacteristic
923Q8—216no—
924Q8—48no—
925Q8—88no—
926Q8—88no—
927Q8—88no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—21no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—21no—
934C2×C4—22no—
935C2×C4—24no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—24no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—22no—
942C2×C4—28no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—22no—
951C2×C4—24no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—24no—
957C2×C4—28no—
958C2×C4—24no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—24no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—24no—
969C2×C4—28no—
970C2×C4—24no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—28no—
977C2×C4—22no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—44no—
989C2×C4—84no—
990C2×C4—84no—
991C2×C4—84no—
992C2×C4—84no—
993C2×C4—88no—
994C2×C4#557116yes—
995C2×C4C23×Q812yes—
996C2×C4C23×Q812yes—
997C2×C4C23×Q812yes—
998C2×C4C23×Q818yes—
999C2×C4C23×Q818yes—
1000C2×C4C23×Q812yes—
1001C2×C4C23×Q812yes—
1002C2×C4C23×Q812yes—
1003C2×C4C22×#4114yes—
1004C2×C4C22×#4114yes—
1005C2×C4C22×#4112yes—
1006C2×C4C22×#4112yes—
1007C2×C4C2×2−1+412yes—
1008C2×C4C2×2−1+412yes—
1009C2×C4#58512yes—
1010C2×C4#58512yes—
1011C22—22no—
1012C22—22no—
1013C22—22no—
1014C22—22no—
1015C22—22no—
1016C22—22no—
1017C22C2×#55714yes—
1018C22C24×Q811yescharacteristic
1019C22C23×#4111yescharacteristic
1020C22C22×2−1+411yescharacteristic
1021C22C2×#58511yescharacteristic
1022C22C2×#58511yescharacteristic
1023C22H(7,𝔽2)11yescharacteristic
1024C222−1+611yescharacteristic
1025C4—24no—
1026C4—24no—
1027C4—22no—
1028C4—28no—
1029C4—22no—
1030C4—22no—
1031C4—28no—
1032C4—42no—
1033C4—44no—
1034C4—42no—
1035C4—44no—
1036C4—42no—
1037C4—42no—
1038C4—42no—
1039C4—42no—
1040C4—44no—
1041C4—42no—
1042C4—42no—
1043C4—44no—
1044C4—42no—
1045C4—42no—
1046C4—48no—
1047C4C2×#55714yes—
1048C4C2×#55714yes—
1049C4#350414yes—
1050C2—24no—
1051C2C22×#55711yescharacteristic
1052C2C2×#350411yescharacteristic
1053C2#6285411yescharacteristic
1054C2#6293211yescharacteristic
1055C2#6296211yescharacteristic
1056C2#6299411yescharacteristic
1057C2#6300911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC24C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59870C2semidirect
2. #59869C2semidirect
3. #59665C2semidirect
5. #59456C2semidirect
7. #45426C2semidirect
8. #45164C2semidirect
10. #39182C2semidirect
11. #39182C2semidirect
12. #39181C2semidirect
13. #39177C2semidirect
14. #36535C2semidirect
15. #36447C2semidirect
201. #533Q8semidirect

Maximal subgroups

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

subgroupindex
#598702
#598692
#596652
#596642
#594562
#593252
#454262
#451642
#435572
#391822
#391812
#391772
#365352
#364472
#356272
#355662
#352862
#352652
C2×#25712
#349382
#342152
#342142
#342132
#341452
C4×#5442