Finite Group Databasebeta

← #7658908

Subgroups — #7658908

Order 512.

4214 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42187C214yesmaximal, complemented
2#42183C214yesmaximal, complemented
3#42180C212yesmaximal
4#42005C214yesmaximal, complemented
5#42004C214yesmaximal, complemented
6#41997C212yesmaximal
7#40637C214yesmaximal, complemented
8#40633C214yesmaximal, complemented
9#40620C214yesmaximal, complemented
10#40616C214yesmaximal, complemented
11#37609C211yesmaximal, characteristic, complemented
12#37609C212yesmaximal, complemented
13#37563C212yesmaximal, complemented
14#37561C212yesmaximal, complemented
15#37561C212yesmaximal, complemented
16#36691C212yesmaximal, complemented
17C2×#2844C211yesmaximal, characteristic, complemented
18#36035C212yesmaximal, complemented
19#35962C214yesmaximal, complemented
20#35931C214yesmaximal, complemented
21#35743C212yesmaximal, complemented
22#34191C212yesmaximal
23#34189C211yesmaximal, characteristic
24C2×C4×#41C2211yescharacteristic
25#2845C2212yes—
26#2845C2212yes—
27#2845C2212yes—
28#2844C2214yes—
29#2844C2212yes—
30#2844C2211yescharacteristic
31#2844C2212yes—
32#2844C2214yes—
33#2844C2212yes—
34#2844C2211yescharacteristic
35#2844C2212yes—
36#2844C2211yescharacteristic
37#2844C2212yes—
38#2844C2211yescharacteristic
39#2843C2214yes—
40#2843C2214yes—
41#2841C2214yes—
42#2841C2214yes—
43#2841C2214yes—
44#2841C2214yes—
45#2811C2212yes—
46#2809C2212yes—
47#2806C2214yes—
48#2806C2214yes—
49#2805C2214yes—
50#2804C2212yes—
51#2799C2212yes—
52#2799C2214yes—
53#2799C2212yes—
54#2792C2214yes—
55#2791C2214yes—
56#2790C2214yes—
57#2788C2214yes—
58#2784C2212yes—
59#2784C2212yes—
60#2780C2214yes—
61#2774C2214yes—
62#2763C2214yes—
63#2755C2214yes—
64#2742C2214yes—
65#2729C2214yes—
66#2729C2214yes—
67#2720C2214yes—
68#2713C2214yes—
69#2713C2214yes—
70#2704C2214yes—
71#2692C2214yes—
72#2683C2212yes—
73#2666C2214yes—
74#2666C2214yes—
75#2666C2214yes—
76#2666C2214yes—
77#2666C2214yes—
78#2666C2214yes—
79#2666C2214yes—
80#2666C2214yes—
81#2666C2214yes—
82#2666C2214yes—
83#2665C2214yes—
84#2665C2214yes—
85#2665C2214yes—
86#2665C2214yes—
87#2665C2214yes—
88#2665C2214yes—
89#2660C2214yes—
90#2660C2214yes—
91#2659C2214yes—
92#2659C2214yes—
93#2647C2214yes—
94#2647C2214yes—
95#2646C2214yes—
96#2646C2214yes—
97#2627C2212yes—
98#2627C2214yes—
99#2627C2214yes—
100#2627C2212yes—
101#2612C2214yes—
102#2612C2212yes—
103#2612C2214yes—
104#2612C2212yes—
105#2605C2214yes—
106#2605C2214yes—
107#2605C2214yes—
108#2605C2214yes—
109#2605C2214yes—
110#2605C2214yes—
111#2590C2214yes—
112#2589C2214yes—
113#2588C2214yes—
114#2588C2214yes—
115#2588C2214yes—
116#2587C2214yes—
117#2586C2214yes—
118#2586C2214yes—
119#2586C2214yes—
120#2585C2214yes—
121#2579C2214yes—
122#2574C2214yes—
123#2570C2214yes—
124#2570C2214yes—
125#2569C2214yes—
126#2569C2214yes—
127#2569C2214yes—
128#2564C2214yes—
129#2556C2214yes—
130#2550C2214yes—
131#2550C2214yes—
132#2549C2214yes—
133#2549C2214yes—
134#2549C2214yes—
135#2549C2212yes—
136#2549C2212yes—
137#2520C2214yes—
138#2520C2214yes—
139#2511C2214yes—
140#2511C2214yes—
141#2505C2214yes—
142#2502C2212yes—
143#2497C2214yes—
144#2492C2214yes—
145#2473C2214yes—
146#2465C2214yes—
147#2465C2214yes—
148#2462C2214yes—
149#2462C2214yes—
150#2451C2214yes—
151#2450C2214yes—
152#2450C2214yes—
153#2450C2214yes—
154#2449C2214yes—
155#2446C2214yes—
156#2442C2214yes—
157#2442C2214yes—
158#2440C2214yes—
159#2440C2214yes—
160#2438C2214yes—
161#2438C2214yes—
162#2438C2214yes—
163#2438C2214yes—
164#2434C2212yes—
165#2417C2214yes—
166#2409C2214yes—
167#2402C2214yes—
168#2402C2214yes—
169#2399C2214yes—
170#2399C2214yes—
171#2396C2214yes—
172#2396C2214yes—
173C2×#400C2214yes—
174C2×#400C2212yes—
175C2×#395C2212yes—
176C2×#395C2214yes—
177#2368C2214yes—
178#2368C2212yes—
179#2368C2212yes—
180#2360C2214yes—
181#2357C2214yes—
182#2356C2214yes—
183#2355C2212yes—
184#2355C2212yes—
185#2353C2214yes—
186#2353C2214yes—
187#2352C2212yes—
188#2352C2212yes—
189#2352C2212yes—
190#2352C2212yes—
191D4×C4⋊C4C2212yes—
192D4×C4⋊C4C2212yes—
193#2346C2214yes—
194#2345C2212yes—
195#2343C2214yes—
196#2343C2214yes—
197Q8×C22⋊C4C2212yes—
198#2339C2214yes—
199#2320C2214yes—
200#2318C2214yes—
201#2318C2214yes—
202#2314C2212yes—
203#2314C2212yes—
204#2311C2211yescharacteristic
205#2311C2211yescharacteristic
206#2285C2212yes—
207#2285C2211yescharacteristic
208#2283C2212yes—
209#2283C2212yes—
210#2283C2212yes—
211#2283C2212yes—
212#2283C2212yes—
213C2×#382C2211yescharacteristic
214C2×#382C2212yes—
215C2×#382C2212yes—
216#2275C2214yes—
217#2274C2211yescharacteristic
218#2274C2211yescharacteristic
219C22×#41C2311yescharacteristic
220C23×Q8C2312yes—
221C2×C4⋊Q8C2314yes—
222C2×C4⋊Q8C2314yes—
223C2×#125C2314yes—
224C2×#125C2314yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2314yes—
233C4×#41Q8116yescomplemented
234C2×C4×Q8C2314yes—
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2312yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2312yes—
240C2×C4×D4C2312yes—
241C2×C4×D4C2312yes—
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2312yes—
245C2×#117C2312yes—
246C2×#117C2311yescharacteristic
247C2×#117C2312yes—
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2312yes—
251C22×C4⋊C4C2312yes—
252C22×C4⋊C4C2312yes—
253C22×C4⋊C4C2312yes—
254C22×C4⋊C4C2312yes—
255C22×C4⋊C4C2314yes—
256C22×C42C2311yescharacteristic
257C22×C42C2312yes—
258#400C2314yes—
259#400C2312yes—
260#400C2314yes—
261#400C2314yes—
262#400C2314yes—
263#400C2314yes—
264#400C2314yes—
265#400C2312yes—
266#400C2314yes—
267#400C2314yes—
268#400C2312yes—
269#400C2312yes—
270#400C2314yes—
271#400C2314yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#400C2314yes—
276#400C2314yes—
277#400C2314yes—
278#400C2312yes—
279#400C2314yes—
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2312yes—
287#400C2312yes—
288#400C2314yes—
289#400C2314yes—
290#400C2312yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#399C2314yes—
295#399C2314yes—
296#398C2314yes—
297#398C2314yes—
298#398C2314yes—
299#398C2314yes—
300#398C2314yes—
301#398C2314yes—
302#398C2314yes—
303#398C2314yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#396C2314yes—
337#396C2314yes—
338#396C2314yes—
339#396C2314yes—
340#396C2314yes—
341#396C2314yes—
342#396C2314yes—
343#396C2314yes—
344#395C2314yes—
345#395C2314yes—
346#395C2312yes—
347#395C2314yes—
348#395C2314yes—
349#395C2314yes—
350#395C2314yes—
351#395C2314yes—
352#395C2314yes—
353#395C2312yes—
354#395C2314yes—
355#395C2314yes—
356#395C2314yes—
357#395C2314yes—
358#395C2314yes—
359#395C2314yes—
360#395C2312yes—
361#395C2314yes—
362#395C2314yes—
363#395C2314yes—
364#395C2314yes—
365#395C2314yes—
366#395C2314yes—
367#395C2312yes—
368#395C2312yes—
369#395C2314yes—
370#395C2314yes—
371#395C2312yes—
372#395C2314yes—
373#395C2314yes—
374#395C2314yes—
375#395C2314yes—
376#395C2312yes—
377#395C2314yes—
378#395C2312yes—
379#395C2314yes—
380#393C2314yes—
381#393C2314yes—
382#393C2314yes—
383#393C2314yes—
384#393C2314yes—
385#393C2314yes—
386#391C2312yes—
387#391C2312yes—
388#391C2314yes—
389#391C2314yes—
390#391C2314yes—
391#391C2314yes—
392#391C2314yes—
393#391C2314yes—
394#391C2314yes—
395#391C2314yes—
396#391C2314yes—
397#391C2314yes—
398#391C2314yes—
399#391C2314yes—
400#391C2314yes—
401#391C2314yes—
402#391C2314yes—
403#391C2314yes—
404#391C2314yes—
405#391C2314yes—
406#391C2314yes—
407#391C2314yes—
408#391C2314yes—
409#391C2314yes—
410#391C2314yes—
411#391C2314yes—
412#390C2312yes—
413#390C2312yes—
414#389C2314yes—
415#389C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#388C2314yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#388C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
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#386C2314yes—
487#386C2314yes—
488#386C2314yes—
489#386C2314yes—
490#386C2314yes—
491#386C2314yes—
492#385C2314yes—
493#385C2314yes—
494#385C2314yes—
495#385C2314yes—
496#385C2314yes—
497#385C2314yes—
498#385C2314yes—
499#385C2314yes—
500#385C2314yes—
501#385C2314yes—
502#385C2314yes—
503#385C2314yes—
504#385C2314yes—
505#385C2314yes—
506#385C2314yes—
507#385C2314yes—
508#385C2314yes—
509#385C2314yes—
510#384C2312yes—
511#384C2314yes—
512#384C2314yes—
513#384C2312yes—
514#384C2312yes—
515#383C2314yes—
516#383C2314yes—
517#383C2314yes—
518#383C2314yes—
519#383C2314yes—
520#382C2311yescharacteristic
521#382C2311yescharacteristic
522#382C2314yes—
523#382C2314yes—
524#382C2314yes—
525#382C2314yes—
526#382C2314yes—
527#382C2311yescharacteristic
528#382C2312yes—
529#382C2312yes—
530#382C2312yes—
531#382C2311yescharacteristic
532#382C2312yes—
533#382C2314yes—
534#382C2312yes—
535#382C2312yes—
536#382C2314yes—
537#382C2312yes—
538#382C2312yes—
539#382C2312yes—
540#381C2314yes—
541#381C2314yes—
542#381C2314yes—
543#381C2314yes—
544#381C2314yes—
545#380C2312yes—
546#380C2314yes—
547#380C2312yes—
548#380C2312yes—
549#380C2312yes—
550#380C2312yes—
551#380C2312yes—
552#380C2312yes—
553#380C2312yes—
554#380C2314yes—
555#380C2314yes—
556#380C2314yes—
557#380C2314yes—
558#380C2314yes—
559#380C2312yes—
560#380C2312yes—
561#380C2314yes—
562#380C2312yes—
563#380C2312yes—
564#380C2314yes—
565#380C2314yes—
566C4×C4⋊C4C2312yes—
567C4×C4⋊C4C2312yes—
568C4×C4⋊C4C2312yes—
569C4×C4⋊C4C2312yes—
570C4×C4⋊C4C2312yes—
571C4×C4⋊C4C2314yes—
572C4×C4⋊C4C2314yes—
573C4×C4⋊C4C2314yes—
574C4×C4⋊C4C2314yes—
575C4×C4⋊C4C2314yes—
576C4×C4⋊C4C2314yes—
577C4×C4⋊C4C2314yes—
578C4×C4⋊C4C2314yes—
579C4×C4⋊C4C2314yes—
580C4×C4⋊C4C2314yes—
581C4×C4⋊C4C2314yes—
582C4×C4⋊C4C2314yes—
583C4×C4⋊C4C2314yes—
584C4×C4⋊C4C2312yes—
585C4×C4⋊C4C2312yes—
586C4×C4⋊C4C2312yes—
587C4×C4⋊C4C2312yes—
588C4×C4⋊C4C2312yes—
589C4×C22⋊C4C2314yes—
590C4×C22⋊C4C2314yes—
591C4×C22⋊C4C2314yes—
592C4×C22⋊C4C2314yes—
593C4×C22⋊C4C2314yes—
594C4×C22⋊C4C2314yes—
595C4×C22⋊C4C2314yes—
596C4×C22⋊C4C2312yes—
597C4×C22⋊C4C2314yes—
598C4×C22⋊C4C2312yes—
599C4×C22⋊C4C2312yes—
600C4×C22⋊C4C2312yes—
601C4×C22⋊C4C2314yes—
602#376C2314yes—
603#376C2314yes—
604#376C2314yes—
605#376C2314yes—
606#376C2314yes—
607C2×#95C2314yes—
608C2×#95C2314yes—
609C2×#95C2314yes—
610C2×#95C2314yes—
611C2×#95C2314yes—
612C2×#95C2314yes—
613C2×#95C2312yes—
614C2×#95C2312yes—
615C2×#41—42no—
616C2×#41—42no—
617C2×#41C2×Q818yes—
618C22×Q8—44no—
619C22×Q8—84no—
620C22×Q8C2412yes—
621C22×Q8C2414yes—
622C22×Q8C2412yes—
623C22×Q8C2414yes—
624C22×Q8C2412yes—
625C22×Q8C2414yes—
626C22×Q8C2412yes—
627C22×Q8C2411yescharacteristic
628C22×D4C2412yes—
629C22×D4C2411yescharacteristic
630C23×C4C2411yescharacteristic
631C23×C4C2414yes—
632C23×C4C2412yes—
633C23×C4C2414yes—
634C23×C4C2412yes—
635C23×C4C2414yes—
636C23×C4C2414yes—
637C23×C4C2412yes—
638C23×C4C2412yes—
639C23×C4C2412yes—
640C23×C4C2412yes—
641C4⋊Q8—84no—
642C4⋊Q8—84no—
643#125—84no—
644#125—84no—
645C22⋊Q8—48no—
646C22⋊Q8—48no—
647C22⋊Q8—44no—
648C22⋊Q8—44no—
649C22⋊Q8—84no—
650C22⋊Q8—84no—
651C22⋊Q8—84no—
652C22⋊Q8—84no—
653C4×Q8—84no—
654C4×Q8—84no—
655C4×Q8C2×Q8116yescomplemented
656C4×D4—48no—
657C4×D4—48no—
658C4×D4C2×Q8116yes—
659C4×D4C2×Q8116yes—
660C4×D4C2×Q8116yescomplemented
661#117—42no—
662#117—42no—
663#117—82no—
664#117—82no—
665#117C2×Q818yes—
666#117C2×Q8116yescomplemented
667C2×C4⋊C4—42no—
668C2×C4⋊C4—42no—
669C2×C4⋊C4—44no—
670C2×C4⋊C4—82no—
671C2×C4⋊C4—82no—
672C2×C4⋊C4—82no—
673C2×C4⋊C4—82no—
674C2×C4⋊C4—84no—
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2412yes—
680C2×C4⋊C4C2412yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
693C2×C4⋊C4C2412yes—
694C2×C4⋊C4C2412yes—
695C2×C4⋊C4C2412yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2412yes—
698C2×C4⋊C4C2412yes—
699C2×C4⋊C4C2412yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2412yes—
739C2×C22⋊C4C2412yes—
740C2×C22⋊C4C2412yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2414yes—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2414yes—
747C2×C22⋊C4C2414yes—
748C2×C22⋊C4C2414yes—
749C2×C22⋊C4C2414yes—
750C2×C22⋊C4C2414yes—
751C2×C22⋊C4C2414yes—
752C2×C22⋊C4C2414yes—
753C2×C22⋊C4C2411yescharacteristic
754C2×C22⋊C4C2411yescharacteristic
755C2×C22⋊C4C2412yes—
756C2×C22⋊C4C2412yes—
757C2×C42C2×Q818yes—
758C2×C42C2×Q8116yescomplemented
759C2×C42C2414yes—
760C2×C42C2414yes—
761C2×C42C2412yes—
762C2×C42C2412yes—
763C2×C42C2414yes—
764C2×C42C2414yes—
765C2×C42C2414yes—
766C2×C42C2414yes—
767C2×C42C2414yes—
768C2×C42C2414yes—
769C2×C42C2414yes—
770C2×C42C2414yes—
771C2×C42C2414yes—
772C2×C42C2414yes—
773C2×C42C2411yescharacteristic
774C2×C42C2412yes—
775C2×C42C2412yes—
776C2×C42C2412yes—
777C2×C42C2412yes—
778C2×C42C2411yescharacteristic
779#95C2414yes—
780#95C2414yes—
781#95C2414yes—
782#95C2414yes—
783#95C2414yes—
784#95C2414yes—
785#95C2414yes—
786#95C2414yes—
787#95C2414yes—
788#95C2414yes—
789#95C2414yes—
790#95C2414yes—
791#95C2412yes—
792#95C2412yes—
793#95C2414yes—
794#95C2412yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2412yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2414yes—
809#95C2414yes—
810#95C2414yes—
811#95C2414yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2412yes—
840#95C2414yes—
841#95C2414yes—
842#95C2412yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2412yes—
847#95C2412yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851C24C2512yes—
852C24C2511yescharacteristic
853#41—416no—
854C2×Q8—44no—
855C2×Q8—42no—
856C2×Q8—41no—
857C2×Q8—41no—
858C2×Q8—44no—
859C2×Q8—44no—
860C2×Q8—44no—
861C2×Q8—44no—
862C2×Q8—44no—
863C2×Q8—42no—
864C2×Q8—44no—
865C2×Q8—44no—
866C2×Q8—42no—
867C2×Q8—44no—
868C2×Q8—42no—
869C2×Q8—44no—
870C2×Q8—44no—
871C2×Q8—44no—
872C2×Q8—44no—
873C2×Q8—816no—
874C2×Q8C22×Q814yes—
875C2×D4—24no—
876C2×D4—24no—
877C2×D4—41no—
878C2×D4—41no—
879C2×D4C22×Q818yes—
880C2×D4C22×Q814yes—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—24no—
884C22×C4—28no—
885C22×C4—24no—
886C22×C4—28no—
887C22×C4—42no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—42no—
894C22×C4—42no—
895C22×C4—44no—
896C22×C4—44no—
897C22×C4—44no—
898C22×C4—44no—
899C22×C4—44no—
900C22×C4—44no—
901C22×C4—44no—
902C22×C4—44no—
903C22×C4—44no—
904C22×C4—44no—
905C22×C4—44no—
906C22×C4—44no—
907C22×C4C22×Q814yes—
908C22×C4C22×Q818yes—
909C22×C4C22×Q818yes—
910C22×C4C22×Q818yes—
911C22×C4C22×Q818yes—
912C22×C4C2512yes—
913C22×C4C2514yes—
914C22×C4C2512yes—
915C22×C4C2514yes—
916C22×C4C2514yes—
917C22×C4C2514yes—
918C22×C4C2512yes—
919C22×C4C2514yes—
920C22×C4C2514yes—
921C22×C4C2514yes—
922C22×C4C2514yes—
923C22×C4C2514yes—
924C22×C4C2512yes—
925C22×C4C2514yes—
926C22×C4C2511yescharacteristic
927C22×C4C2512yes—
928C22×C4C2511yescharacteristic
929C22×C4C2512yes—
930C22×C4C2512yes—
931C22×C4C2512yes—
932C22×C4C2512yes—
933C4⋊C4—41no—
934C4⋊C4—41no—
935C4⋊C4—41no—
936C4⋊C4—41no—
937C4⋊C4—42no—
938C4⋊C4—42no—
939C4⋊C4—42no—
940C4⋊C4—44no—
941C4⋊C4—42no—
942C4⋊C4—42no—
943C4⋊C4—42no—
944C4⋊C4—42no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—42no—
948C4⋊C4—44no—
949C4⋊C4—44no—
950C4⋊C4—44no—
951C4⋊C4—44no—
952C4⋊C4—44no—
953C4⋊C4—44no—
954C4⋊C4—44no—
955C4⋊C4—44no—
956C4⋊C4—44no—
957C4⋊C4—44no—
958C4⋊C4—42no—
959C4⋊C4—42no—
960C4⋊C4—44no—
961C4⋊C4—44no—
962C4⋊C4—44no—
963C4⋊C4—44no—
964C4⋊C4—44no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—44no—
968C4⋊C4—44no—
969C4⋊C4—44no—
970C4⋊C4—44no—
971C4⋊C4—44no—
972C4⋊C4—44no—
973C4⋊C4—44no—
974C4⋊C4—42no—
975C4⋊C4—44no—
976C4⋊C4—44no—
977C4⋊C4—44no—
978C4⋊C4—44no—
979C4⋊C4—44no—
980C4⋊C4—44no—
981C4⋊C4—44no—
982C4⋊C4—44no—
983C4⋊C4—42no—
984C4⋊C4—44no—
985C4⋊C4—44no—
986C4⋊C4—44no—
987C4⋊C4—44no—
988C4⋊C4—44no—
989C4⋊C4—44no—
990C4⋊C4—44no—
991C4⋊C4—44no—
992C4⋊C4—44no—
993C4⋊C4—44no—
994C4⋊C4C22×Q818yes—
995C4⋊C4C22×Q818yes—
996C4⋊C4C22×Q818yes—
997C22⋊C4—24no—
998C22⋊C4—24no—
999C22⋊C4—28no—
1000C22⋊C4—28no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C22⋊C4—44no—
1005C22⋊C4—44no—
1006C22⋊C4—44no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4C22×Q814yes—
1012C22⋊C4C22×Q814yes—
1013C22⋊C4C22×Q818yes—
1014C22⋊C4C22×Q818yes—
1015C42—44no—
1016C42—44no—
1017C42—44no—
1018C42—44no—
1019C42—42no—
1020C42—42no—
1021C42—44no—
1022C42—44no—
1023C42—44no—
1024C42—44no—
1025C42—44no—
1026C42—44no—
1027C42—44no—
1028C42—44no—
1029C42C22×Q814yes—
1030C42C22×Q814yes—
1031C42C22×Q818yes—
1032C42C22×Q818yes—
1033C42C22×Q818yes—
1034C42C22×Q818yes—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23C23×Q814yes—
1044C23C23×Q812yes—
1045C23#58512yes—
1046C23#58512yes—
1047C23C2611yescharacteristic
1048Q8—44no—
1049Q8—48no—
1050Q8—88no—
1051Q8—84no—
1052Q8—88no—
1053Q8—162no—
1054Q8—164no—
1055Q8—162no—
1056D4—216no—
1057D4—44no—
1058C2×C4—21no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—28no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—24no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—48no—
1112C2×C4—48no—
1113C2×C4—48no—
1114C2×C4—48no—
1115C2×C4—88no—
1116C2×C4—84no—
1117C2×C4—88no—
1118C2×C4—84no—
1119C2×C4—164no—
1120C2×C4—164no—
1121C2×C4C23×Q814yes—
1122C2×C4C23×Q812yes—
1123C2×C4C23×Q814yes—
1124C2×C4C23×Q814yes—
1125C2×C4C23×Q814yes—
1126C2×C4C23×Q812yes—
1127C2×C4C23×Q814yes—
1128C22—22no—
1129C22—24no—
1130C22—22no—
1131C22—24no—
1132C22—24no—
1133C22—24no—
1134C22—24no—
1135C22—42no—
1136C22—42no—
1137C22—42no—
1138C22—42no—
1139C22#345814yes—
1140C22C24×Q811yescharacteristic
1141C22C2×#58511yescharacteristic
1142C22C2×#58511yescharacteristic
1143C22H(7,𝔽2)12yes—
1144C222−1+612yes—
1145C4—24no—
1146C4—24no—
1147C4—24no—
1148C4—24no—
1149C4—22no—
1150C4—22no—
1151C4—24no—
1152C4—44no—
1153C4—44no—
1154C4—42no—
1155C4—42no—
1156C4—44no—
1157C4—44no—
1158C4—44no—
1159C4—44no—
1160C4—44no—
1161C4—44no—
1162C4—44no—
1163C4—42no—
1164C4—42no—
1165C4—44no—
1166C2—24no—
1167C2—44no—
1168C2C2×#345811yescharacteristic
1169C2#6285412yes—
1170C2#6304611yescharacteristic
1171C2#6305912yes—
1172C2#6306411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42187C2semidirect
2. #42183C2semidirect
4. #42005C2semidirect
5. #42004C2semidirect
7. #40637C2semidirect
8. #40633C2semidirect
9. #40620C2semidirect
10. #40616C2semidirect
11. #37609C2semidirect
12. #37609C2semidirect
13. #37563C2semidirect
14. #37561C2semidirect
15. #37561C2semidirect
16. #36691C2semidirect
17. C2×#2844C2semidirect
18. #36035C2semidirect
19. #35962C2semidirect
20. #35931C2semidirect
21. #35743C2semidirect
233. C4×#41Q8semidirect
655. C4×Q8C2×Q8semidirect
660. C4×D4C2×Q8semidirect
666. #117C2×Q8semidirect
758. C2×C42C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#421872
#421832
#421802
#420052
#420042
#419972
#406372
#406332
#406202
#406162
#376092
#375632
#375612
#366912
C2×#28442
#360352
#359622
#359312
#357432
#341912
#341892