Finite Group Databasebeta

← #7717468

Subgroups — #7717468

Order 512.

4076 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51795C214yesmaximal, complemented
2#51795C214yesmaximal, complemented
3#51606C214yesmaximal, complemented
4#51603C214yesmaximal, complemented
5#44753C214yesmaximal, complemented
6#44737C214yesmaximal, complemented
7#44667C214yesmaximal, complemented
8#44639C214yesmaximal, complemented
9#39175C214yesmaximal
10#38103C214yesmaximal
11#38103C214yesmaximal
12#36752C212yesmaximal
13#36751C212yesmaximal
14#36425C214yesmaximal
15#35304C212yesmaximal
16#35159C212yesmaximal
17#35120C211yesmaximal, characteristic
18#35015C212yesmaximal
19#34638C211yesmaximal, characteristic
20#34378C212yesmaximal
21C2×#2371C211yesmaximal, characteristic
22C22×#125C2211yescharacteristic
23#2857C2212yes—
24#2857C2212yes—
25#2855C2214yes—
26#2855C2214yes—
27#2851C2214yes—
28#2851C2212yes—
29#2851C2212yes—
30#2806C2214yes—
31#2806C2214yes—
32#2806C2214yes—
33#2805C2214yes—
34#2805C2214yes—
35#2805C2214yes—
36#2805C2214yes—
37#2802C2214yes—
38#2802C2214yes—
39#2802C2214yes—
40#2802C2214yes—
41#2802C2214yes—
42#2802C2214yes—
43#2802C2214yes—
44#2792C2214yes—
45#2792C2214yes—
46#2792C2214yes—
47#2792C2214yes—
48#2791C2214yes—
49#2791C2214yes—
50#2791C2214yes—
51#2791C2214yes—
52#2791C2214yes—
53#2774C2214yes—
54#2774C2214yes—
55#2774C2214yes—
56#2774C2214yes—
57#2774C2214yes—
58#2755C2214yes—
59#2755C2214yes—
60#2755C2214yes—
61#2755C2214yes—
62#2755C2214yes—
63#2755C2214yes—
64#2734C2214yes—
65#2726C2214yes—
66#2726C2214yes—
67#2713C2214yes—
68#2713C2214yes—
69#2713C2214yes—
70#2660C2212yes—
71#2660C2212yes—
72#2659C2212yes—
73#2647C2214yes—
74#2647C2214yes—
75#2647C2212yes—
76#2647C2212yes—
77#2646C2214yes—
78#2646C2214yes—
79#2646C2211yescharacteristic
80#2646C2211yescharacteristic
81#2646C2212yes—
82#2646C2211yescharacteristic
83#2646C2211yescharacteristic
84#2627C2214yes—
85#2612C2214yes—
86#2612C2214yes—
87#2612C2214yes—
88#2612C2214yes—
89#2606C2214yes—
90#2606C2214yes—
91#2605C2214yes—
92#2605C2214yes—
93#2590C2214yes—
94#2590C2214yes—
95#2590C2214yes—
96#2590C2214yes—
97#2590C2214yes—
98#2590C2214yes—
99#2590C2214yes—
100#2588C2214yes—
101#2588C2214yes—
102#2588C2214yes—
103#2588C2214yes—
104#2588C2214yes—
105#2588C2214yes—
106#2588C2214yes—
107#2586C2214yes—
108#2586C2214yes—
109#2586C2214yes—
110#2586C2214yes—
111#2585C2214yes—
112#2585C2214yes—
113#2585C2214yes—
114#2585C2214yes—
115#2585C2214yes—
116#2585C2214yes—
117#2584C2214yes—
118#2569C2214yes—
119#2569C2214yes—
120#2550C2214yes—
121#2549C2214yes—
122#2549C2214yes—
123#2520C2214yes—
124#2520C2214yes—
125#2520C2214yes—
126#2520C2214yes—
127#2520C2214yes—
128#2511C2214yes—
129#2511C2214yes—
130#2511C2214yes—
131#2511C2214yes—
132#2509C2214yes—
133#2509C2214yes—
134#2509C2214yes—
135#2508C2214yes—
136#2508C2214yes—
137#2507C2214yes—
138#2507C2214yes—
139#2507C2214yes—
140#2507C2214yes—
141#2507C2214yes—
142#2507C2214yes—
143#2506C2214yes—
144#2506C2214yes—
145#2462C2214yes—
146#2451C2214yes—
147#2446C2214yes—
148#2446C2214yes—
149#2442C2214yes—
150#2440C2214yes—
151#2438C2214yes—
152#2438C2214yes—
153#2438C2214yes—
154#2438C2214yes—
155#2438C2214yes—
156#2438C2214yes—
157#2402C2214yes—
158#2402C2214yes—
159#2382C2214yes—
160#2382C2214yes—
161#2371C2214yes—
162#2371C2214yes—
163#2371C2214yes—
164#2371C2214yes—
165#2370C2214yes—
166#2370C2214yes—
167#2370C2214yes—
168#2370C2214yes—
169#2369C2214yes—
170#2355C2214yes—
171#2345C2214yes—
172#2344C2214yes—
173#2344C2214yes—
174#2344C2214yes—
175#2336C2214yes—
176#2336C2214yes—
177#2331C2212yes—
178#2331C2212yes—
179#2330C2214yes—
180#2330C2214yes—
181#2330C2212yes—
182#2330C2212yes—
183#2329C2214yes—
184#2329C2214yes—
185#2317C2214yes—
186#2316C2212yes—
187#2316C2212yes—
188#2313C2212yes—
189#2313C2212yes—
190C4×C22⋊Q8C2214yes—
191#2296C2214yes—
192#2296C2214yes—
193C2×#387C2212yes—
194C2×#387C2212yes—
195C2×#387C2212yes—
196C2×#387C2212yes—
197#2285C2212yes—
198#2283C2212yes—
199C2×C4×C4⋊C4C2212yes—
200C2×C4×C4⋊C4C2212yes—
201C2×#376C2211yescharacteristic
202C2×#376C2211yescharacteristic
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2314yes—
206C2×#125Q8116yescomplemented
207C2×#125C2314yes—
208C2×#125C2312yes—
209C2×#125C2312yes—
210C2×#125C2314yes—
211C2×#125C2314yes—
212C2×#125C2314yes—
213C2×C22⋊Q8C2314yes—
214C2×C22⋊Q8C2314yes—
215C2×C22⋊Q8C2314yes—
216C2×C4×Q8C2314yes—
217C2×#117C2314yes—
218C2×#117C2314yes—
219C2×#117C2314yes—
220C22×C4⋊C4C2312yes—
221C22×C4⋊C4C2312yes—
222C22×C4⋊C4C2312yes—
223C22×C4⋊C4C2312yes—
224C22×C4⋊C4C2311yescharacteristic
225C22×C4⋊C4C2311yescharacteristic
226C22×C42C2312yes—
227C22×C42C2312yes—
228C22×C42C2312yes—
229C22×C42C2312yes—
230C22×C42C2311yescharacteristic
231#400C2314yes—
232#400C2314yes—
233#400C2314yes—
234#400C2314yes—
235#400C2314yes—
236#400C2314yes—
237#400C2314yes—
238#400C2314yes—
239#400C2314yes—
240#400C2314yes—
241#400C2314yes—
242#400C2314yes—
243#400C2314yes—
244#400C2314yes—
245#400C2314yes—
246#400C2314yes—
247#400C2314yes—
248#400C2314yes—
249#400C2314yes—
250#400C2314yes—
251#400C2314yes—
252#400C2314yes—
253#400C2314yes—
254#400C2314yes—
255#400C2314yes—
256#400C2314yes—
257#400C2314yes—
258#400C2314yes—
259#398C2314yes—
260#398C2314yes—
261#398C2314yes—
262#398C2314yes—
263#398C2314yes—
264#398C2314yes—
265#398C2314yes—
266#398C2314yes—
267#398C2314yes—
268#398C2314yes—
269#398C2314yes—
270#398C2314yes—
271#398C2314yes—
272#398C2314yes—
273#398C2314yes—
274#398C2314yes—
275#398C2314yes—
276#398C2314yes—
277#398C2314yes—
278#398C2314yes—
279#398C2314yes—
280#398C2314yes—
281#398C2314yes—
282#398C2314yes—
283#398C2314yes—
284#398C2314yes—
285#398C2314yes—
286#398C2314yes—
287#398C2314yes—
288#398C2314yes—
289#398C2314yes—
290#398C2314yes—
291#398C2314yes—
292#398C2314yes—
293#398C2314yes—
294#398C2314yes—
295#398C2314yes—
296#398C2314yes—
297#398C2314yes—
298#398C2314yes—
299#398C2314yes—
300#398C2314yes—
301#398C2314yes—
302#398C2314yes—
303#395C2314yes—
304#395C2314yes—
305#395C2314yes—
306#395C2314yes—
307#395C2314yes—
308#395C2314yes—
309#395C2314yes—
310#395C2314yes—
311#395C2314yes—
312#395C2314yes—
313#395C2314yes—
314#395C2314yes—
315#395C2314yes—
316#395C2314yes—
317#395C2314yes—
318#395C2314yes—
319#391C2314yes—
320#391C2314yes—
321#391C2314yes—
322#391C2314yes—
323#391C2314yes—
324#391C2314yes—
325#391C2314yes—
326#391C2314yes—
327#391C2314yes—
328#391C2314yes—
329#391C2314yes—
330#391C2314yes—
331#391C2314yes—
332#391C2314yes—
333#391C2314yes—
334#391C2314yes—
335#391C2314yes—
336#391C2314yes—
337#391C2314yes—
338#391C2314yes—
339#391C2314yes—
340#389C2314yes—
341#389C2314yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#389C2314yes—
377#389C2312yes—
378#389C2312yes—
379#389C2312yes—
380#389C2312yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2314yes—
385#389C2314yes—
386#389C2314yes—
387#389C2314yes—
388#389C2314yes—
389#389C2314yes—
390#389C2312yes—
391#389C2312yes—
392#389C2312yes—
393#389C2312yes—
394#389C2314yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#387C2314yes—
404#387C2314yes—
405#387C2314yes—
406#387C2314yes—
407#387C2314yes—
408#387C2314yes—
409#387C2314yes—
410#387C2314yes—
411#387C2314yes—
412#387C2314yes—
413#387C2314yes—
414#387C2314yes—
415#387C2314yes—
416#387C2314yes—
417#387C2314yes—
418#387C2314yes—
419#387C2314yes—
420#387C2314yes—
421#387C2314yes—
422#387C2314yes—
423#387C2314yes—
424#387C2314yes—
425#387C2314yes—
426#387C2314yes—
427#387C2314yes—
428#387C2314yes—
429#387C2314yes—
430#387C2314yes—
431#387C2314yes—
432#387C2314yes—
433#387C2314yes—
434#387C2314yes—
435#387C2314yes—
436#387C2314yes—
437#387C2314yes—
438#387C2314yes—
439#387C2314yes—
440#387C2314yes—
441#387C2314yes—
442#387C2314yes—
443#387C2314yes—
444#387C2314yes—
445#387C2314yes—
446#387C2314yes—
447#387C2314yes—
448#387C2314yes—
449#387C2314yes—
450#387C2314yes—
451#387C2314yes—
452#387C2314yes—
453#387C2314yes—
454#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#385C2314yes—
490#385C2314yes—
491#385C2314yes—
492#385C2314yes—
493#385C2314yes—
494#385C2314yes—
495#385C2314yes—
496#385C2314yes—
497#385C2314yes—
498#385C2314yes—
499#384C2314yes—
500#384C2314yes—
501#384C2312yes—
502#384C2312yes—
503#384C2312yes—
504#384C2312yes—
505#384C2314yes—
506#383C2314yes—
507#382C2314yes—
508#382C2314yes—
509#382C2312yes—
510#382C2312yes—
511#382C2314yes—
512#382C2314yes—
513#382C2314yes—
514#382C2312yes—
515#382C2312yes—
516#381C2314yes—
517#381C2314yes—
518#381C2314yes—
519#380C2312yes—
520#380C2312yes—
521#380C2312yes—
522#380C2314yes—
523#380C2314yes—
524#380C2314yes—
525#380C2314yes—
526#380C2314yes—
527#380C2312yes—
528#380C2314yes—
529C4×C4⋊C4C2314yes—
530C4×C4⋊C4C2314yes—
531C4×C4⋊C4C2314yes—
532C4×C4⋊C4C2314yes—
533C4×C4⋊C4C2314yes—
534C4×C4⋊C4C2314yes—
535C4×C4⋊C4C2314yes—
536C4×C4⋊C4C2314yes—
537C4×C4⋊C4C2314yes—
538C4×C4⋊C4C2314yes—
539C4×C4⋊C4C2314yes—
540C4×C4⋊C4C2314yes—
541C4×C4⋊C4C2312yes—
542C4×C4⋊C4C2314yes—
543C4×C4⋊C4C2312yes—
544C4×C4⋊C4C2312yes—
545C4×C4⋊C4C2314yes—
546C4×C4⋊C4C2314yes—
547C4×C4⋊C4C2314yes—
548C4×C4⋊C4C2312yes—
549C4×C4⋊C4C2314yes—
550C4×C4⋊C4C2314yes—
551C4×C4⋊C4C2314yes—
552C4×C4⋊C4C2314yes—
553C4×C4⋊C4C2314yes—
554C4×C4⋊C4C2314yes—
555C4×C4⋊C4C2314yes—
556C4×C4⋊C4C2314yes—
557C4×C4⋊C4C2314yes—
558C4×C4⋊C4C2314yes—
559C4×C4⋊C4C2314yes—
560C4×C4⋊C4C2314yes—
561C4×C22⋊C4C2314yes—
562C4×C22⋊C4C2314yes—
563C4×C22⋊C4C2314yes—
564#376C2314yes—
565#376C2312yes—
566#376C2312yes—
567#376C2314yes—
568#376C2312yes—
569#376C2314yes—
570#376C2312yes—
571C2×#95C2312yes—
572C2×#95C2312yes—
573C2×#95C2312yes—
574C2×#95C2312yes—
575C2×#95C2311yescharacteristic
576C2×#95C2311yescharacteristic
577C2×#95C2311yescharacteristic
578C2×#95C2311yescharacteristic
579C2×#95C2312yes—
580C2×#95C2312yes—
581C22×Q8C2414yes—
582C22×Q8C2414yes—
583C22×Q8C2414yes—
584C23×C4C2412yes—
585C23×C4C2412yes—
586C23×C4C2411yescharacteristic
587C23×C4C2412yes—
588C23×C4C2412yes—
589C23×C4C2412yes—
590C23×C4C2412yes—
591C23×C4C2411yescharacteristic
592C23×C4C2411yescharacteristic
593C4⋊Q8—44no—
594C4⋊Q8—44no—
595C4⋊Q8—48no—
596#125—48no—
597#125—44no—
598#125—44no—
599#125—48no—
600#125C2×Q8132yes—
601#125C2×Q8132yes—
602C22⋊Q8—48no—
603C22⋊Q8—48no—
604C22⋊Q8—48no—
605C4×Q8—48no—
606#117—48no—
607#117—48no—
608#117—48no—
609C2×C4⋊C4—44no—
610C2×C4⋊C4—44no—
611C2×C4⋊C4C2×Q8116yes—
612C2×C4⋊C4C2×Q818yes—
613C2×C4⋊C4C2×Q8116yes—
614C2×C4⋊C4C2×Q818yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C42—44no—
685C2×C42—44no—
686C2×C42—44no—
687C2×C42—44no—
688C2×C42C2×Q818yes—
689C2×C42C2414yes—
690C2×C42C2412yes—
691C2×C42C2412yes—
692C2×C42C2414yes—
693C2×C42C2414yes—
694C2×C42C2414yes—
695C2×C42C2414yes—
696C2×C42C2414yes—
697C2×C42C2414yes—
698C2×C42C2414yes—
699C2×C42C2414yes—
700C2×C42C2414yes—
701C2×C42C2414yes—
702C2×C42C2414yes—
703C2×C42C2412yes—
704C2×C42C2414yes—
705C2×C42C2412yes—
706C2×C42C2414yes—
707C2×C42C2414yes—
708C2×C42C2414yes—
709C2×C42C2414yes—
710C2×C42C2414yes—
711C2×C42C2412yes—
712C2×C42C2412yes—
713#95C2412yes—
714#95C2411yescharacteristic
715#95C2414yes—
716#95C2411yescharacteristic
717#95C2411yescharacteristic
718#95C2411yescharacteristic
719#95C2412yes—
720#95C2412yes—
721#95C2414yes—
722#95C2414yes—
723#95C2412yes—
724#95C2412yes—
725#95C2412yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2414yes—
780#95C2414yes—
781#95C2414yes—
782#95C2414yes—
783#95C2414yes—
784#95C2414yes—
785#95C2414yes—
786#95C2414yes—
787#95C2414yes—
788#95C2414yes—
789C24C2511yescharacteristic
790C2×Q8—28no—
791C2×Q8—44no—
792C2×Q8—44no—
793C2×Q8—44no—
794C2×Q8—44no—
795C2×Q8—44no—
796C2×Q8—44no—
797C2×Q8—44no—
798C2×Q8—44no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—41no—
812C22×C4—41no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—42no—
817C22×C4—42no—
818C22×C4—42no—
819C22×C4C22×Q814yes—
820C22×C4C22×Q818yes—
821C22×C4C22×Q814yes—
822C22×C4C22×Q814yes—
823C22×C4C22×Q818yes—
824C22×C4C2512yes—
825C22×C4C2514yes—
826C22×C4C2514yes—
827C22×C4C2514yes—
828C22×C4C2512yes—
829C22×C4C2514yes—
830C22×C4C2514yes—
831C22×C4C2514yes—
832C22×C4C2514yes—
833C22×C4C2512yes—
834C22×C4C2514yes—
835C22×C4C2514yes—
836C22×C4C2514yes—
837C22×C4C2512yes—
838C22×C4C2511yescharacteristic
839C22×C4C2514yes—
840C22×C4C2512yes—
841C22×C4C2514yes—
842C22×C4C2511yescharacteristic
843C22×C4C2512yes—
844C4⋊C4—28no—
845C4⋊C4—28no—
846C4⋊C4—28no—
847C4⋊C4—28no—
848C4⋊C4—44no—
849C4⋊C4—44no—
850C4⋊C4—44no—
851C4⋊C4—44no—
852C4⋊C4—44no—
853C4⋊C4—44no—
854C4⋊C4—44no—
855C4⋊C4—44no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C4⋊C4—44no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4—44no—
862C4⋊C4—44no—
863C4⋊C4—44no—
864C4⋊C4—44no—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C4⋊C4—44no—
870C4⋊C4—44no—
871C4⋊C4—44no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C4⋊C4—44no—
875C4⋊C4—44no—
876C4⋊C4—44no—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4—42no—
888C4⋊C4—42no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—42no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4C22×Q8116yes—
904C4⋊C4C22×Q8116yes—
905C4⋊C4C22×Q8116yes—
906C4⋊C4C22×Q8116yes—
907C4⋊C4C22×Q8116yes—
908C4⋊C4C22×Q8116yes—
909C22⋊C4—28no—
910C22⋊C4—28no—
911C22⋊C4—28no—
912C22⋊C4—28no—
913C42—28no—
914C42—24no—
915C42—24no—
916C42—44no—
917C42—42no—
918C42—42no—
919C42—44no—
920C42—44no—
921C42—44no—
922C42—44no—
923C42—44no—
924C42—44no—
925C42—44no—
926C42—44no—
927C42—44no—
928C42—44no—
929C42—44no—
930C42—44no—
931C42—44no—
932C42—44no—
933C42—44no—
934C42—44no—
935C42C22×Q818yes—
936C42C22×Q818yes—
937C23—22no—
938C23—21no—
939C23—21no—
940C23C23×Q812yes—
941C23#58514yes—
942C23C2611yescharacteristic
943Q8—88no—
944Q8—164no—
945Q8—164no—
946C2×C4—24no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—22no—
953C2×C4—24no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—28no—
959C2×C4—216no—
960C2×C4—24no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—22no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—22no—
993C2×C4—24no—
994C2×C4—22no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—22no—
999C2×C4—44no—
1000C2×C4—48no—
1001C2×C4—44no—
1002C2×C4—48no—
1003C2×C4—48no—
1004C2×C4—84no—
1005C2×C4—84no—
1006C2×C4C23×Q812yes—
1007C2×C4C23×Q812yes—
1008C2×C4C23×Q814yes—
1009C2×C4C23×Q814yes—
1010C2×C4C23×Q818yes—
1011C2×C4C23×Q818yes—
1012C2×C4#58514yes—
1013C22—22no—
1014C22—22no—
1015C22—24no—
1016C22—24no—
1017C22#350414yes—
1018C22C24×Q811yescharacteristic
1019C22C2×#58512yes—
1020C22C2×#58512yes—
1021C222−1+611yescharacteristic
1022C222−1+611yescharacteristic
1023C4—22no—
1024C4—28no—
1025C4—22no—
1026C4—28no—
1027C4—24no—
1028C4—24no—
1029C4—24no—
1030C4—44no—
1031C4—42no—
1032C4—44no—
1033C4—44no—
1034C4—44no—
1035C4—44no—
1036C4—44no—
1037C4—44no—
1038C4—44no—
1039C4—42no—
1040C4—42no—
1041C4—44no—
1042C4—44no—
1043C2—24no—
1044C2C2×#350411yescharacteristic
1045C2#6281311yescharacteristic
1046C2#6284911yescharacteristic
1047C2#6290912yes—
1048C2#6293412yes—
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. #51795C2semidirect
2. #51795C2semidirect
3. #51606C2semidirect
4. #51603C2semidirect
5. #44753C2semidirect
6. #44737C2semidirect
7. #44667C2semidirect
8. #44639C2semidirect
206. C2×#125Q8semidirect

Maximal subgroups

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

subgroupindex
#517952
#516062
#516032
#447532
#447372
#446672
#446392
#391752
#381032
#367522
#367512
#364252
#353042
#351592
#351202
#350152
#346382
#343782
C2×#23712