Finite Group Databasebeta

← #7678062

Subgroups — #7678062

Order 512.

4442 conjugacy classes of subgroups.

The subgroup lattice has 1377 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59925C212yesmaximal, complemented
2#59872C212yesmaximal, complemented
3#59681C212yesmaximal, complemented
4#59671C212yesmaximal, complemented
5#59671C212yesmaximal, complemented
6#59670C212yesmaximal, complemented
7#59669C212yesmaximal, complemented
8#59668C212yesmaximal, complemented
9#44737C214yesmaximal, complemented
10#44667C214yesmaximal, complemented
11#44419C214yesmaximal, complemented
12#44255C214yesmaximal, complemented
13#39496C212yesmaximal
14#39496C211yesmaximal, characteristic
15#39368C211yesmaximal, characteristic
16#39368C212yesmaximal
17#39178C212yesmaximal
18#38103C214yesmaximal
19#36599C211yesmaximal, characteristic
20#36564C211yesmaximal, characteristic
21#36425C212yesmaximal
22#35403C214yesmaximal
23#35104C211yesmaximal, characteristic
24#35015C212yesmaximal
25#34966C212yesmaximal
26#34271C212yesmaximal
27#34239C212yesmaximal
28C2×#2370C211yesmaximal, characteristic
29C4×#544C211yesmaximal, characteristic
30C2×#544C2211yescharacteristic
31C2×#544C2212yes—
32C22×#125C2211yescharacteristic
33#2857C2211yescharacteristic
34#2857C2211yescharacteristic
35#2857C2212yes—
36#2857C2212yes—
37#2855C2214yes—
38#2851C2212yes—
39#2806C2214yes—
40#2806C2214yes—
41#2806C2212yes—
42#2805C2214yes—
43#2805C2214yes—
44#2805C2212yes—
45#2802C2214yes—
46#2802C2214yes—
47#2802C2214yes—
48#2802C2214yes—
49#2802C2214yes—
50#2802C2214yes—
51#2792C2214yes—
52#2791C2214yes—
53#2791C2214yes—
54#2774C2214yes—
55#2774C2214yes—
56#2755C2214yes—
57#2734C2214yes—
58#2734C2212yes—
59#2726C2214yes—
60#2726C2212yes—
61#2713C2214yes—
62#2713C2214yes—
63#2713C2214yes—
64#2713C2214yes—
65#2646C2214yes—
66#2627C2212yes—
67#2627C2212yes—
68#2627C2212yes—
69#2627C2212yes—
70#2606C2214yes—
71#2606C2214yes—
72#2605C2214yes—
73#2605C2214yes—
74#2590C2214yes—
75#2590C2214yes—
76#2590C2214yes—
77#2590C2214yes—
78#2590C2214yes—
79#2590C2214yes—
80#2588C2214yes—
81#2588C2214yes—
82#2588C2214yes—
83#2588C2214yes—
84#2588C2214yes—
85#2588C2214yes—
86#2586C2214yes—
87#2586C2214yes—
88#2586C2214yes—
89#2586C2214yes—
90#2586C2214yes—
91#2585C2214yes—
92#2585C2214yes—
93#2585C2214yes—
94#2585C2214yes—
95#2585C2214yes—
96#2584C2212yes—
97#2584C2212yes—
98#2584C2212yes—
99#2584C2214yes—
100#2570C2212yes—
101#2570C2212yes—
102#2570C2212yes—
103#2570C2212yes—
104#2569C2214yes—
105#2567C2211yescharacteristic
106#2552C2212yes—
107#2552C2211yescharacteristic
108#2551C2212yes—
109#2551C2214yes—
110#2551C2211yescharacteristic
111#2550C2212yes—
112#2550C2212yes—
113#2550C2212yes—
114#2550C2212yes—
115#2550C2212yes—
116#2550C2214yes—
117#2550C2212yes—
118#2550C2212yes—
119#2549C2214yes—
120#2546C2212yes—
121#2546C2211yescharacteristic
122#2546C2212yes—
123#2546C2214yes—
124#2520C2214yes—
125#2520C2214yes—
126#2520C2214yes—
127#2520C2214yes—
128#2511C2214yes—
129#2511C2214yes—
130#2511C2214yes—
131#2511C2212yes—
132#2509C2212yes—
133#2509C2212yes—
134#2509C2212yes—
135#2509C2212yes—
136#2509C2212yes—
137#2509C2214yes—
138#2508C2212yes—
139#2507C2214yes—
140#2507C2214yes—
141#2507C2212yes—
142#2507C2214yes—
143#2507C2214yes—
144#2507C2212yes—
145#2507C2212yes—
146#2507C2212yes—
147#2506C2212yes—
148#2506C2212yes—
149#2506C2214yes—
150#2506C2214yes—
151#2506C2212yes—
152#2462C2214yes—
153#2462C2214yes—
154#2451C2214yes—
155#2451C2214yes—
156#2451C2212yes—
157#2446C2214yes—
158#2446C2214yes—
159#2446C2212yes—
160#2442C2214yes—
161#2442C2212yes—
162#2442C2212yes—
163#2440C2214yes—
164#2440C2212yes—
165#2440C2212yes—
166#2438C2214yes—
167#2438C2214yes—
168#2438C2214yes—
169#2438C2214yes—
170#2438C2214yes—
171#2438C2214yes—
172#2402C2214yes—
173#2399C2214yes—
174#2371C2214yes—
175#2371C2214yes—
176#2370C2212yes—
177#2370C2212yes—
178#2370C2212yes—
179#2370C2212yes—
180#2370C2212yes—
181#2370C2214yes—
182#2370C2212yes—
183#2370C2212yes—
184#2370C2212yes—
185#2370C2212yes—
186#2370C2212yes—
187#2370C2212yes—
188#2370C2214yes—
189#2370C2214yes—
190#2370C2214yes—
191#2370C2214yes—
192#2370C2214yes—
193#2369C2212yes—
194#2369C2212yes—
195#2369C2214yes—
196#2369C2214yes—
197#2369C2211yescharacteristic
198#2365C2211yescharacteristic
199#2365C2214yes—
200#2365C2214yes—
201#2355C2212yes—
202#2355C2211yescharacteristic
203Q8×C4⋊C4C2211yescharacteristic
204#2345C2212yes—
205#2345C2212yes—
206#2344C2212yes—
207#2344C2214yes—
208#2344C2212yes—
209#2344C2214yes—
210#2336C2214yes—
211#2336C2214yes—
212#2331C2212yes—
213#2331C2212yes—
214#2330C2212yes—
215#2330C2212yes—
216#2329C2214yes—
217#2329C2212yes—
218#2329C2212yes—
219#2329C2212yes—
220#2329C2211yescharacteristic
221#2329C2211yescharacteristic
222#2317C2212yes—
223#2316C2211yescharacteristic
224#2316C2212yes—
225#2313C2214yes—
226C4×C4⋊Q8C2212yes—
227C4×C4⋊Q8C2212yes—
228C4×C4⋊Q8C2212yes—
229C4×C4⋊Q8C2212yes—
230C4×#125C2212yes—
231C4×#125C2212yes—
232C4×#125C2212yes—
233C4×#125C2212yes—
234C4×#125C2212yes—
235C4×#125C2212yes—
236C4×#125C2212yes—
237C4×#125C2212yes—
238C4×C22⋊Q8C2212yes—
239C4×C22⋊Q8C2211yescharacteristic
240C4×C22⋊Q8C2211yescharacteristic
241C4×C22⋊Q8C2212yes—
242C4×C22⋊Q8C2214yes—
243C4×C22⋊Q8C2214yes—
244C4×C22⋊Q8C2212yes—
245#2296C2214yes—
246C2×#389C2211yescharacteristic
247C2×#389C2211yescharacteristic
248C2×#389C2212yes—
249C2×#387C2212yes—
250C2×#387C2212yes—
251#2283C2212yes—
252#2274C2214yes—
253C4×#117C2212yes—
254C2×C4×C4⋊C4C2211yescharacteristic
255C2×C4×C4⋊C4C2211yescharacteristic
256C2×C4×C4⋊C4C2211yescharacteristic
257C2×C4×C4⋊C4C2212yes—
258C2×C4×C4⋊C4C2211yescharacteristic
259#544—28no—
260#544—216no—
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2314yes—
265C2×C4⋊Q8C2314yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2314yes—
272C2×#125Q8116yescomplemented
273C2×#125C2312yes—
274C2×#125C2312yes—
275C2×#125C2312yes—
276C2×#125C2314yes—
277C2×#125C2314yes—
278C2×#125C2312yes—
279C2×#125C2312yes—
280C2×#125C2314yes—
281C2×#125C2312yes—
282C2×#125C2312yes—
283C2×#125C2314yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2311yescharacteristic
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2311yescharacteristic
291C2×C4×Q8C2311yescharacteristic
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2314yes—
295C2×C4×Q8C2314yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×#117C2312yes—
299C2×#117C2314yes—
300C2×#117C2312yes—
301C2×#117C2314yes—
302C22×C4⋊C4C2311yescharacteristic
303C22×C4⋊C4C2312yes—
304C22×C4⋊C4C2311yescharacteristic
305C22×C4⋊C4C2311yescharacteristic
306C22×C4⋊C4C2311yescharacteristic
307C22×C4⋊C4C2312yes—
308C22×C4⋊C4C2312yes—
309C22×C4⋊C4C2311yescharacteristic
310C22×C4⋊C4C2312yes—
311C22×C4⋊C4C2311yescharacteristic
312C22×C42C2311yescharacteristic
313C22×C42C2312yes—
314C22×C42C2311yescharacteristic
315C22×C42C2312yes—
316C22×C42C2312yes—
317C22×C42C2311yescharacteristic
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#395C2314yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#391C2312yes—
391#391C2312yes—
392#391C2312yes—
393#391C2312yes—
394#391C2314yes—
395#391C2314yes—
396#391C2312yes—
397#391C2314yes—
398#391C2314yes—
399#391C2314yes—
400#391C2314yes—
401#391C2312yes—
402#391C2312yes—
403#391C2314yes—
404#391C2314yes—
405#391C2314yes—
406#391C2314yes—
407#391C2314yes—
408#391C2314yes—
409#391C2314yes—
410#391C2311yescharacteristic
411#391C2311yescharacteristic
412#391C2314yes—
413#391C2312yes—
414#391C2312yes—
415#391C2314yes—
416#391C2314yes—
417#391C2314yes—
418#391C2312yes—
419#391C2312yes—
420#389C2312yes—
421#389C2312yes—
422#389C2312yes—
423#389C2312yes—
424#389C2312yes—
425#389C2312yes—
426#389C2312yes—
427#389C2312yes—
428#389C2312yes—
429#389C2312yes—
430#389C2312yes—
431#389C2312yes—
432#389C2312yes—
433#389C2312yes—
434#389C2312yes—
435#389C2312yes—
436#389C2312yes—
437#389C2312yes—
438#389C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2314yes—
443#389C2312yes—
444#389C2312yes—
445#389C2312yes—
446#389C2312yes—
447#389C2312yes—
448#389C2314yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2312yes—
469#389C2312yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2312yes—
474#389C2312yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2311yescharacteristic
481#389C2311yescharacteristic
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2312yes—
488#389C2312yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2314yes—
500#389C2312yes—
501#389C2314yes—
502#389C2312yes—
503#389C2312yes—
504#389C2314yes—
505#389C2314yes—
506#389C2312yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2312yes—
512#387C2312yes—
513#387C2312yes—
514#387C2312yes—
515#387C2312yes—
516#387C2312yes—
517#387C2312yes—
518#387C2312yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2312yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2312yes—
563#387C2312yes—
564#387C2312yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#385C2312yes—
588#385C2314yes—
589#385C2312yes—
590#385C2312yes—
591#385C2312yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#384C2312yes—
598#384C2312yes—
599#384C2312yes—
600#384C2312yes—
601#384C2312yes—
602#384C2311yescharacteristic
603#384C2311yescharacteristic
604#384C2312yes—
605#384C2314yes—
606#383C2314yes—
607#382C2312yes—
608#382C2312yes—
609#382C2312yes—
610#382C2312yes—
611#382C2312yes—
612#382C2312yes—
613#382C2312yes—
614#382C2314yes—
615#381C2314yes—
616#381C2314yes—
617#381C2314yes—
618#380C2314yes—
619#380C2314yes—
620#380C2312yes—
621#380C2314yes—
622#380C2311yescharacteristic
623#380C2312yes—
624#380C2311yescharacteristic
625#380C2312yes—
626#380C2314yes—
627#380C2312yes—
628#380C2312yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2312yes—
631C4×C4⋊C4C2311yescharacteristic
632C4×C4⋊C4C2311yescharacteristic
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2314yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2314yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2311yescharacteristic
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2312yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703#376C2312yes—
704#376C2312yes—
705#376C2314yes—
706C2×#95C2312yes—
707C2×#95C2311yescharacteristic
708C2×#95C2311yescharacteristic
709C2×#95C2312yes—
710C2×#95C2312yes—
711C2×#95C2312yes—
712C2×#95C2312yes—
713C43C2312yes—
714C43C2312yes—
715C22×Q8C2411yescharacteristic
716C22×Q8C2412yes—
717C22×Q8C2412yes—
718C22×Q8C2414yes—
719C22×Q8C2414yes—
720C22×Q8C2412yes—
721C22×Q8C2411yescharacteristic
722C23×C4C2412yes—
723C23×C4C2412yes—
724C23×C4C2411yescharacteristic
725C23×C4C2411yescharacteristic
726C23×C4C2411yescharacteristic
727C23×C4C2412yes—
728C23×C4C2411yescharacteristic
729C23×C4C2411yescharacteristic
730C23×C4C2412yes—
731C23×C4C2411yescharacteristic
732C23×C4C2411yescharacteristic
733C4⋊Q8—28no—
734C4⋊Q8—216no—
735C4⋊Q8—28no—
736C4⋊Q8—216no—
737C4⋊Q8—28no—
738C4⋊Q8—42no—
739C4⋊Q8—42no—
740C4⋊Q8—44no—
741C4⋊Q8—82no—
742C4⋊Q8—82no—
743C4⋊Q8—84no—
744#125—28no—
745#125—216no—
746#125—28no—
747#125—216no—
748#125—28no—
749#125—44no—
750#125—44no—
751#125—84no—
752#125C2×Q8116yes—
753#125C2×Q8116yes—
754#125C2×Q8132yes—
755C22⋊Q8—28no—
756C22⋊Q8—24no—
757C22⋊Q8—216no—
758C22⋊Q8—28no—
759C22⋊Q8—48no—
760C22⋊Q8—44no—
761C22⋊Q8#4118yes—
762C4×Q8—44no—
763C4×Q8—42no—
764C4×Q8—42no—
765C4×Q8—84no—
766C4×Q8—84no—
767C4×Q8—82no—
768C4×Q8—82no—
769#117—28no—
770#117—216no—
771#117—48no—
772#117—44no—
773C2×C4⋊C4—24no—
774C2×C4⋊C4—28no—
775C2×C4⋊C4—24no—
776C2×C4⋊C4—42no—
777C2×C4⋊C4—42no—
778C2×C4⋊C4—82no—
779C2×C4⋊C4C2×Q818yes—
780C2×C4⋊C4C2×Q8116yes—
781C2×C4⋊C4C2×Q818yes—
782C2×C4⋊C4C2×Q8116yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2411yescharacteristic
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2411yescharacteristic
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2411yescharacteristic
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2411yescharacteristic
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2411yescharacteristic
864C2×C4⋊C4C2411yescharacteristic
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2411yescharacteristic
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2412yes—
878C2×C42—42no—
879C2×C42—42no—
880C2×C42—44no—
881C2×C42—82no—
882C2×C42—82no—
883C2×C42C2×Q818yes—
884C2×C42C2412yes—
885C2×C42C2412yes—
886C2×C42C2414yes—
887C2×C42C2414yes—
888C2×C42C2412yes—
889C2×C42C2412yes—
890C2×C42C2412yes—
891C2×C42C2411yescharacteristic
892C2×C42C2411yescharacteristic
893C2×C42C2412yes—
894C2×C42C2412yes—
895C2×C42C2412yes—
896C2×C42C2412yes—
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2414yes—
902C2×C42C2414yes—
903C2×C42C2414yes—
904C2×C42C2414yes—
905C2×C42C2414yes—
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2412yes—
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2414yes—
913C2×C42C2414yes—
914C2×C42C2414yes—
915C2×C42C2414yes—
916C2×C42C2414yes—
917C2×C42C2412yes—
918C2×C42C2411yescharacteristic
919C2×C42C2411yescharacteristic
920C2×C42C2412yes—
921C2×C42C2412yes—
922#95C2412yes—
923#95C2412yes—
924#95C2412yes—
925#95C2412yes—
926#95C2412yes—
927#95C2412yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2412yes—
935#95C2412yes—
936#95C2414yes—
937#95C2414yes—
938#95C2412yes—
939#95C2412yes—
940#95C2412yes—
941#95C2412yes—
942#95C2412yes—
943#95C2412yes—
944#95C2412yes—
945#95C2412yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2412yes—
957#95C2412yes—
958#95C2414yes—
959#95C2412yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2412yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2412yes—
973#95C2412yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2412yes—
986#95C2414yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000C24C2511yescharacteristic
1001C2×Q8—22no—
1002C2×Q8—24no—
1003C2×Q8—24no—
1004C2×Q8—28no—
1005C2×Q8—28no—
1006C2×Q8—41no—
1007C2×Q8—41no—
1008C2×Q8—41no—
1009C2×Q8—42no—
1010C2×Q8—44no—
1011C2×Q8—42no—
1012C2×Q8—44no—
1013C2×Q8—44no—
1014C2×Q8—42no—
1015C2×Q8—44no—
1016C2×Q8—41no—
1017C2×Q8—42no—
1018C2×Q8—42no—
1019C2×Q8—42no—
1020C2×Q8—42no—
1021C2×Q8C2×#4114yes—
1022C22×C4—24no—
1023C22×C4—22no—
1024C22×C4—24no—
1025C22×C4—22no—
1026C22×C4—22no—
1027C22×C4—22no—
1028C22×C4—22no—
1029C22×C4—24no—
1030C22×C4—22no—
1031C22×C4—24no—
1032C22×C4—22no—
1033C22×C4—24no—
1034C22×C4—41no—
1035C22×C4—41no—
1036C22×C4—41no—
1037C22×C4—41no—
1038C22×C4—42no—
1039C22×C4—42no—
1040C22×C4—41no—
1041C22×C4—42no—
1042C22×C4—41no—
1043C22×C4—41no—
1044C22×C4—41no—
1045C22×C4—42no—
1046C22×C4—42no—
1047C22×C4—41no—
1048C22×C4—41no—
1049C22×C4C22×Q814yes—
1050C22×C4C22×Q814yes—
1051C22×C4C22×Q818yes—
1052C22×C4C22×Q814yes—
1053C22×C4C22×Q818yes—
1054C22×C4C2×#4114yes—
1055C22×C4C2511yescharacteristic
1056C22×C4C2512yes—
1057C22×C4C2514yes—
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2512yes—
1061C22×C4C2514yes—
1062C22×C4C2514yes—
1063C22×C4C2511yescharacteristic
1064C22×C4C2512yes—
1065C22×C4C2512yes—
1066C22×C4C2512yes—
1067C22×C4C2512yes—
1068C22×C4C2514yes—
1069C22×C4C2512yes—
1070C22×C4C2514yes—
1071C22×C4C2511yescharacteristic
1072C22×C4C2512yes—
1073C22×C4C2514yes—
1074C22×C4C2512yes—
1075C22×C4C2512yes—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C22×C4C2511yescharacteristic
1080C22×C4C2511yescharacteristic
1081C22×C4C2512yes—
1082C22×C4C2511yescharacteristic
1083C4⋊C4—24no—
1084C4⋊C4—28no—
1085C4⋊C4—24no—
1086C4⋊C4—28no—
1087C4⋊C4—24no—
1088C4⋊C4—28no—
1089C4⋊C4—24no—
1090C4⋊C4—28no—
1091C4⋊C4—22no—
1092C4⋊C4—24no—
1093C4⋊C4—24no—
1094C4⋊C4—28no—
1095C4⋊C4—24no—
1096C4⋊C4—28no—
1097C4⋊C4—24no—
1098C4⋊C4—28no—
1099C4⋊C4—24no—
1100C4⋊C4—28no—
1101C4⋊C4—24no—
1102C4⋊C4—22no—
1103C4⋊C4—28no—
1104C4⋊C4—28no—
1105C4⋊C4—24no—
1106C4⋊C4—28no—
1107C4⋊C4—24no—
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—42no—
1112C4⋊C4—42no—
1113C4⋊C4—42no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—42no—
1117C4⋊C4—42no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—42no—
1121C4⋊C4—42no—
1122C4⋊C4—44no—
1123C4⋊C4—42no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—42no—
1127C4⋊C4—42no—
1128C4⋊C4—41no—
1129C4⋊C4—41no—
1130C4⋊C4—42no—
1131C4⋊C4—42no—
1132C4⋊C4—42no—
1133C4⋊C4—42no—
1134C4⋊C4—42no—
1135C4⋊C4—41no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—42no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—42no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—42no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—42no—
1156C4⋊C4—42no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—41no—
1160C4⋊C4C22×Q8116yes—
1161C4⋊C4C22×Q8116yes—
1162C4⋊C4C22×Q818yes—
1163C4⋊C4C22×Q818yes—
1164C4⋊C4C22×Q8116yes—
1165C4⋊C4C22×Q8116yes—
1166C4⋊C4C22×Q814yes—
1167C4⋊C4C22×Q814yes—
1168C4⋊C4C22×Q818yes—
1169C4⋊C4C2×#4114yes—
1170C4⋊C4C2×#4118yes—
1171C4⋊C42−1+414yes—
1172C22⋊C4—24no—
1173C22⋊C4—28no—
1174C22⋊C4—24no—
1175C22⋊C4—24no—
1176C22⋊C4—28no—
1177C22⋊C4C2×#4118yes—
1178C42—24no—
1179C42—28no—
1180C42—24no—
1181C42—28no—
1182C42—24no—
1183C42—24no—
1184C42—24no—
1185C42—22no—
1186C42—22no—
1187C42—24no—
1188C42—24no—
1189C42—41no—
1190C42—41no—
1191C42—44no—
1192C42—42no—
1193C42—44no—
1194C42—44no—
1195C42—44no—
1196C42—42no—
1197C42—42no—
1198C42—42no—
1199C42—42no—
1200C42—42no—
1201C42—44no—
1202C42—42no—
1203C42—44no—
1204C42—44no—
1205C42—44no—
1206C42—44no—
1207C42—42no—
1208C42—42no—
1209C42—42no—
1210C42—44no—
1211C42—42no—
1212C42—44no—
1213C42—44no—
1214C42C22×Q818yes—
1215C42C22×Q818yes—
1216C23—21no—
1217C23—21no—
1218C23—21no—
1219C23—21no—
1220C23C23×Q812yes—
1221C23C22×#4112yes—
1222C23#58512yes—
1223C23C2611yescharacteristic
1224Q8—44no—
1225Q8—82no—
1226Q8—84no—
1227Q8—84no—
1228Q8—88no—
1229Q8—88no—
1230Q8—162no—
1231C2×C4—24no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—22no—
1238C2×C4—21no—
1239C2×C4—24no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—21no—
1246C2×C4—22no—
1247C2×C4—21no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—216no—
1254C2×C4—28no—
1255C2×C4—28no—
1256C2×C4—22no—
1257C2×C4—24no—
1258C2×C4—22no—
1259C2×C4—24no—
1260C2×C4—22no—
1261C2×C4—24no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—22no—
1267C2×C4—24no—
1268C2×C4—22no—
1269C2×C4—21no—
1270C2×C4—22no—
1271C2×C4—21no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—22no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—21no—
1303C2×C4—21no—
1304C2×C4—44no—
1305C2×C4—48no—
1306C2×C4—44no—
1307C2×C4—48no—
1308C2×C4—44no—
1309C2×C4—82no—
1310C2×C4—84no—
1311C2×C4—82no—
1312C2×C4C23×Q812yes—
1313C2×C4C23×Q814yes—
1314C2×C4C23×Q814yes—
1315C2×C4C23×Q814yes—
1316C2×C4C23×Q814yes—
1317C2×C4C23×Q818yes—
1318C2×C4C23×Q812yes—
1319C2×C4C22×#4114yes—
1320C2×C4C22×#4114yes—
1321C2×C4C22×#4112yes—
1322C2×C4C22×#4112yes—
1323C2×C4C2×2−1+414yes—
1324C2×C4C2×2−1+412yes—
1325C2×C4#58512yes—
1326C22—22no—
1327C22—22no—
1328C22—22no—
1329C22—22no—
1330C22—22no—
1331C22—22no—
1332C22Q8×#4114yes—
1333C22C24×Q811yescharacteristic
1334C22C23×#4111yescharacteristic
1335C22C22×2−1+411yescharacteristic
1336C22C2×#58511yescharacteristic
1337C22C2×#58511yescharacteristic
1338C22H(7,𝔽2)11yescharacteristic
1339C222−1+611yescharacteristic
1340C4—22no—
1341C4—22no—
1342C4—24no—
1343C4—24no—
1344C4—22no—
1345C4—24no—
1346C4—24no—
1347C4—24no—
1348C4—24no—
1349C4—28no—
1350C4—24no—
1351C4—42no—
1352C4—44no—
1353C4—42no—
1354C4—44no—
1355C4—42no—
1356C4—44no—
1357C4—42no—
1358C4—42no—
1359C4—42no—
1360C4—41no—
1361C4—41no—
1362C4—44no—
1363C4—42no—
1364C4—42no—
1365C4—44no—
1366C4—42no—
1367C4#350214yes—
1368C2—24no—
1369C2C2×Q8×#4111yescharacteristic
1370C2C2×#350211yescharacteristic
1371C2#6285411yescharacteristic
1372C2#6293411yescharacteristic
1373C2#6294811yescharacteristic
1374C2#6299211yescharacteristic
1375C2#6300111yescharacteristic
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. #59925C2semidirect
2. #59872C2semidirect
3. #59681C2semidirect
4. #59671C2semidirect
5. #59671C2semidirect
6. #59670C2semidirect
7. #59669C2semidirect
8. #59668C2semidirect
9. #44737C2semidirect
10. #44667C2semidirect
11. #44419C2semidirect
12. #44255C2semidirect
272. C2×#125Q8semidirect

Maximal subgroups

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

subgroupindex
#599252
#598722
#596812
#596712
#596702
#596692
#596682
#447372
#446672
#444192
#442552
#394962
#393682
#391782
#381032
#365992
#365642
#364252
#354032
#351042
#350152
#349662
#342712
#342392
C2×#23702
C4×#5442