Finite Group Databasebeta

← #7645039

Subgroups — #7645039

Order 512.

4402 conjugacy classes of subgroups.

The subgroup lattice has 1192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40629C214yesmaximal, complemented
2#40628C214yesmaximal, complemented
3#40625C214yesmaximal, complemented
4#40624C214yesmaximal, complemented
5#39748C214yesmaximal, complemented
6#39620C214yesmaximal, complemented
7#39175C214yesmaximal, complemented
8#39175C214yesmaximal, complemented
9#37478C212yesmaximal
10#37477C212yesmaximal
11#37135C214yesmaximal, complemented
12#36752C212yesmaximal, complemented
13#36751C212yesmaximal, complemented
14#35403C214yesmaximal, complemented
15#35079C212yesmaximal
16#35079C212yesmaximal
17#35065C212yesmaximal
18#35015C212yesmaximal, complemented
19#35013C212yesmaximal, complemented
20#34958C212yesmaximal
21#34178C211yesmaximal, characteristic
22C2×#2345C211yesmaximal, characteristic
23C2×#2313C211yesmaximal, characteristic
24C23×C4⋊C4C2211yescharacteristic
25#2857C2214yes—
26#2857C2212yes—
27#2857C2212yes—
28#2855C2214yes—
29#2855C2214yes—
30#2851C2214yes—
31#2851C2212yes—
32#2851C2212yes—
33#2841C2214yes—
34#2841C2214yes—
35#2841C2214yes—
36#2841C2214yes—
37#2806C2214yescomplemented
38#2806C2214yescomplemented
39#2805C2214yescomplemented
40#2805C2214yescomplemented
41#2802C2214yescomplemented
42#2802C2214yescomplemented
43#2802C2214yescomplemented
44#2802C2214yescomplemented
45#2792C2214yescomplemented
46#2792C2214yescomplemented
47#2792C2214yescomplemented
48#2792C2214yescomplemented
49#2791C2214yescomplemented
50#2791C2214yescomplemented
51#2791C2214yescomplemented
52#2791C2214yescomplemented
53#2774C2214yescomplemented
54#2774C2214yescomplemented
55#2774C2214yescomplemented
56#2774C2214yescomplemented
57#2755C2214yescomplemented
58#2755C2214yescomplemented
59#2755C2214yescomplemented
60#2755C2214yescomplemented
61#2734C2214yescomplemented
62#2734C2214yescomplemented
63#2726C2214yescomplemented
64#2726C2214yescomplemented
65#2713C2214yescomplemented
66#2713C2214yescomplemented
67#2713C2214yescomplemented
68#2713C2214yescomplemented
69#2667C2212yes—
70#2667C2214yes—
71#2667C2212yes—
72#2667C2212yes—
73#2667C2212yes—
74#2667C2214yes—
75#2665C2214yes—
76#2665C2212yes—
77#2665C2212yes—
78#2665C2212yes—
79#2665C2212yes—
80#2665C2214yes—
81#2659C2214yes—
82#2659C2214yes—
83#2659C2212yes—
84#2659C2212yes—
85#2646C2214yes—
86#2646C2214yes—
87#2646C2212yes—
88#2646C2212yes—
89#2629C2214yes—
90#2628C2214yes—
91#2627C2214yes—
92#2627C2214yes—
93#2608C2214yes—
94#2608C2214yes—
95#2607C2214yes—
96#2607C2214yes—
97#2590C2214yescomplemented
98#2590C2214yescomplemented
99#2590C2214yescomplemented
100#2590C2214yescomplemented
101#2588C2214yescomplemented
102#2588C2214yescomplemented
103#2588C2214yescomplemented
104#2588C2214yescomplemented
105#2586C2214yescomplemented
106#2586C2214yescomplemented
107#2586C2214yescomplemented
108#2586C2214yescomplemented
109#2585C2214yescomplemented
110#2585C2214yescomplemented
111#2585C2214yescomplemented
112#2585C2214yescomplemented
113#2569C2214yes—
114#2569C2214yes—
115#2569C2212yes—
116#2569C2212yes—
117#2569C2214yes—
118#2569C2214yes—
119#2569C2212yes—
120#2569C2212yes—
121#2549C2214yes—
122#2549C2214yes—
123#2549C2212yes—
124#2549C2212yes—
125#2549C2214yes—
126#2549C2214yes—
127#2549C2212yes—
128#2549C2212yes—
129#2520C2214yescomplemented
130#2520C2214yescomplemented
131#2520C2214yescomplemented
132#2520C2214yescomplemented
133#2511C2214yescomplemented
134#2511C2214yescomplemented
135#2507C2214yescomplemented
136#2507C2214yescomplemented
137#2462C2214yescomplemented
138#2462C2214yescomplemented
139#2462C2214yescomplemented
140#2462C2214yescomplemented
141#2451C2214yescomplemented
142#2451C2214yescomplemented
143#2446C2214yescomplemented
144#2446C2214yescomplemented
145#2442C2212yes—
146#2442C2214yes—
147#2442C2212yes—
148#2442C2214yes—
149#2442C2214yes—
150#2441C2212yes—
151#2441C2214yes—
152#2441C2212yes—
153#2440C2212yes—
154#2440C2214yes—
155#2440C2212yes—
156#2440C2214yes—
157#2440C2214yes—
158#2439C2214yes—
159#2439C2212yes—
160#2439C2212yes—
161#2438C2214yes—
162#2438C2214yes—
163#2438C2214yes—
164#2438C2214yes—
165#2437C2214yes—
166#2437C2214yes—
167#2437C2214yes—
168#2437C2214yes—
169#2396C2214yes—
170#2396C2214yes—
171#2345C2214yes—
172#2345C2214yes—
173#2345C2214yes—
174#2345C2214yes—
175#2345C2214yes—
176#2345C2214yes—
177#2344C2214yes—
178#2344C2214yes—
179#2329C2214yes—
180#2329C2214yes—
181#2329C2214yes—
182#2329C2214yes—
183#2329C2214yes—
184#2329C2214yes—
185#2316C2212yes—
186#2313C2212yes—
187#2313C2212yes—
188#2313C2212yes—
189#2313C2211yescharacteristic
190#2313C2211yescharacteristic
191#2313C2211yescharacteristic
192#2313C2211yescharacteristic
193#2313C2214yes—
194#2313C2214yes—
195#2313C2212yes—
196C4×C22⋊Q8C2214yes—
197C4×C22⋊Q8C2214yes—
198C4×C22⋊Q8C2214yes—
199C4×C22⋊Q8C2214yes—
200C2×#389C2212yes—
201C2×#387C2214yes—
202C2×#387C2214yes—
203C2×#387C2212yes—
204C2×#387C2212yes—
205#2280C2212yes—
206#2280C2212yes—
207#2280C2212yes—
208C2×#381C2212yes—
209C2×#380C2211yescharacteristic
210C2×#380C2212yes—
211C2×#380C2211yescharacteristic
212C2×#380C2211yescharacteristic
213#2274C2212yes—
214C2×C4×C4⋊C4C2212yes—
215C2×C4×C22⋊C4C2211yescharacteristic
216C2×C4×C22⋊C4C2212yes—
217C2×C4×C22⋊C4C2211yescharacteristic
218C2×C4×C22⋊C4C2211yescharacteristic
219C24×C4C2311yescharacteristic
220C24×C4C2311yescharacteristic
221C24×C4C2311yescharacteristic
222C2×C4⋊Q8C2312yes—
223C2×C4⋊Q8C2312yes—
224C2×C4⋊Q8C2314yes—
225C2×C4⋊Q8C2314yes—
226C2×#125C2312yes—
227C2×#125C2314yes—
228C2×#125C2312yes—
229C2×#125C2314yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2314yes—
238C2×C4×Q8C2314yes—
239C2×C4×Q8C2314yes—
240C2×#117C2314yes—
241C2×#117C2312yes—
242C2×#117C2312yes—
243C2×#117C2314yes—
244C22×C4⋊C4Q8116yescomplemented
245C22×C4⋊C4C2312yes—
246C22×C4⋊C4C2312yes—
247C22×C4⋊C4C2312yes—
248C22×C4⋊C4C2312yes—
249C22×C4⋊C4C2312yes—
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2314yes—
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2314yes—
256C22×C22⋊C4C2311yescharacteristic
257C22×C22⋊C4C2311yescharacteristic
258C22×C22⋊C4C2311yescharacteristic
259C22×C22⋊C4C2311yescharacteristic
260C22×C22⋊C4C2314yes—
261C22×C42C2312yes—
262C22×C42C2312yes—
263C22×C42C2314yes—
264C22×C42C2312yes—
265#400C2314yes—
266#400C2314yes—
267#400C2314yes—
268#400C2314yes—
269#400C2314yes—
270#400C2314yes—
271#400C2314yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#400C2314yes—
276#400C2314yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
283#400C2314yes—
284#400C2314yes—
285#399C2314yes—
286#399C2314yes—
287#399C2314yes—
288#399C2314yes—
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#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#396C2314yes—
330#396C2314yes—
331#396C2314yes—
332#396C2314yes—
333#396C2314yes—
334#396C2314yes—
335#396C2314yes—
336#396C2314yes—
337#395C2314yes—
338#395C2314yes—
339#395C2314yes—
340#395C2314yes—
341#395C2314yes—
342#395C2314yes—
343#395C2314yes—
344#395C2314yes—
345#395C2314yes—
346#395C2314yes—
347#395C2314yes—
348#395C2314yes—
349#395C2314yes—
350#395C2314yes—
351#395C2314yes—
352#395C2314yes—
353#395C2314yes—
354#395C2314yes—
355#395C2314yes—
356#395C2314yes—
357#393C2314yes—
358#393C2314yes—
359#393C2314yes—
360#393C2314yes—
361#391C2314yes—
362#391C2314yes—
363#391C2314yes—
364#391C2314yes—
365#391C2314yes—
366#391C2314yes—
367#391C2314yes—
368#391C2314yes—
369#391C2314yes—
370#391C2314yes—
371#391C2314yes—
372#391C2314yes—
373#391C2314yes—
374#391C2314yes—
375#391C2314yes—
376#391C2314yes—
377#391C2314yes—
378#391C2314yes—
379#391C2314yes—
380#391C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2314yes—
385#389C2314yes—
386#389C2314yes—
387#389C2314yes—
388#389C2314yes—
389#389C2314yes—
390#389C2314yes—
391#389C2314yes—
392#389C2314yes—
393#389C2314yes—
394#389C2314yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2312yes—
399#389C2312yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2314yes—
405#389C2312yes—
406#389C2312yes—
407#389C2314yes—
408#389C2312yes—
409#389C2312yes—
410#389C2314yes—
411#389C2314yes—
412#389C2312yes—
413#389C2312yes—
414#389C2314yes—
415#389C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
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#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
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#385C2314yes—
511#385C2314yes—
512#385C2314yes—
513#384C2312yes—
514#384C2312yes—
515#384C2314yes—
516#384C2314yes—
517#382C2314yes—
518#382C2312yes—
519#382C2312yes—
520#382C2314yes—
521#381C2314yes—
522#381C2314yes—
523#381C2312yes—
524#381C2312yes—
525#381C2312yes—
526#381C2312yes—
527#381C2312yes—
528#381C2312yes—
529#381C2314yes—
530#381C2312yes—
531#381C2312yes—
532#380C2314yes—
533#380C2312yes—
534#380C2312yes—
535#380C2312yes—
536#380C2312yes—
537#380C2314yes—
538#380C2314yes—
539#380C2312yes—
540#380C2312yes—
541#380C2314yes—
542#380C2314yes—
543#380C2314yes—
544#380C2314yes—
545#380C2314yes—
546#380C2314yes—
547#380C2312yes—
548#380C2314yes—
549#380C2312yes—
550#380C2312yes—
551#380C2314yes—
552#380C2312yes—
553#380C2314yes—
554#380C2314yes—
555#380C2314yes—
556#380C2314yes—
557#380C2312yes—
558#380C2312yes—
559#380C2312yes—
560#380C2314yes—
561#380C2312yes—
562#380C2312yes—
563#380C2312yes—
564#379C2314yes—
565C4×C4⋊C4C2314yes—
566C4×C4⋊C4C2314yes—
567C4×C4⋊C4C2314yes—
568C4×C4⋊C4C2314yes—
569C4×C4⋊C4C2314yes—
570C4×C4⋊C4C2314yes—
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×C22⋊C4C2312yes—
580C4×C22⋊C4C2314yes—
581C4×C22⋊C4C2314yes—
582C4×C22⋊C4C2312yes—
583C4×C22⋊C4C2312yes—
584C4×C22⋊C4C2312yes—
585C4×C22⋊C4C2314yes—
586C4×C22⋊C4C2312yes—
587C4×C22⋊C4C2312yes—
588C4×C22⋊C4C2312yes—
589C4×C22⋊C4C2312yes—
590C4×C22⋊C4C2314yes—
591C4×C22⋊C4C2314yes—
592C4×C22⋊C4C2312yes—
593C4×C22⋊C4C2314yes—
594C4×C22⋊C4C2312yes—
595C4×C22⋊C4C2312yes—
596C4×C22⋊C4C2312yes—
597C4×C22⋊C4C2312yes—
598C4×C22⋊C4C2314yes—
599C4×C22⋊C4C2314yes—
600C4×C22⋊C4C2312yes—
601C4×C22⋊C4C2312yes—
602C4×C22⋊C4C2312yes—
603C2×#95C2312yes—
604C2×#95C2312yes—
605C2×#95C2312yes—
606C2×#95C2312yes—
607C2×#95C2312yes—
608C2×#95C2312yes—
609C2×#95C2312yes—
610C2×#95C2314yes—
611C2×#95C2314yes—
612C2×#95C2312yes—
613C2×#95C2312yes—
614C2×#95C2312yes—
615C25C2411yescharacteristic
616C22×Q8C2414yes—
617C22×Q8C2414yes—
618C22×Q8C2414yes—
619C22×Q8C2414yes—
620C23×C4—44no—
621C23×C4—82no—
622C23×C4—82no—
623C23×C4C2×Q818yes—
624C23×C4C2×Q818yes—
625C23×C4C2×Q818yes—
626C23×C4C2412yes—
627C23×C4C2411yescharacteristic
628C23×C4C2411yescharacteristic
629C23×C4C2412yes—
630C23×C4C2412yes—
631C23×C4C2412yes—
632C23×C4C2414yes—
633C23×C4C2414yes—
634C23×C4C2412yes—
635C23×C4C2411yescharacteristic
636C23×C4C2411yescharacteristic
637C23×C4C2412yes—
638C23×C4C2412yes—
639C23×C4C2412yes—
640C23×C4C2411yescharacteristic
641C23×C4C2412yes—
642C23×C4C2411yescharacteristic
643C23×C4C2412yes—
644C4⋊Q8—82no—
645C4⋊Q8—82no—
646C4⋊Q8—84no—
647C4⋊Q8—84no—
648#125—82no—
649#125—82no—
650#125—84no—
651#125—84no—
652C22⋊Q8—216no—
653C22⋊Q8—48no—
654C22⋊Q8—48no—
655C22⋊Q8—48no—
656C22⋊Q8—48no—
657C22⋊Q8—48no—
658C22⋊Q8—48no—
659C22⋊Q8—48no—
660C4×Q8—84no—
661C4×Q8—84no—
662#117—48no—
663#117—84no—
664#117—82no—
665#117—82no—
666C2×C4⋊C4—44no—
667C2×C4⋊C4—82no—
668C2×C4⋊C4—82no—
669C2×C4⋊C4—82no—
670C2×C4⋊C4—82no—
671C2×C4⋊C4C2×Q818yes—
672C2×C4⋊C4C2×Q818yes—
673C2×C4⋊C4C2×Q818yes—
674C2×C4⋊C4C2×Q818yes—
675C2×C4⋊C4C2×Q8132yes—
676C2×C4⋊C4C2×Q8132yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2412yes—
683C2×C4⋊C4C2412yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2412yes—
686C2×C4⋊C4C2412yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2412yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2412yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2412yes—
697C2×C4⋊C4C2412yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C22⋊C4—24no—
738C2×C22⋊C4—42no—
739C2×C22⋊C4—42no—
740C2×C22⋊C4—42no—
741C2×C22⋊C4—48no—
742C2×C22⋊C4C2412yes—
743C2×C22⋊C4C2412yes—
744C2×C22⋊C4C2412yes—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2414yes—
747C2×C22⋊C4C2411yescharacteristic
748C2×C22⋊C4C2412yes—
749C2×C22⋊C4C2414yes—
750C2×C22⋊C4C2414yes—
751C2×C22⋊C4C2414yes—
752C2×C22⋊C4C2414yes—
753C2×C22⋊C4C2411yescharacteristic
754C2×C22⋊C4C2412yes—
755C2×C22⋊C4C2412yes—
756C2×C22⋊C4C2411yescharacteristic
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2414yes—
761C2×C22⋊C4C2411yescharacteristic
762C2×C42—44no—
763C2×C42—82no—
764C2×C42—84no—
765C2×C42—82no—
766C2×C42C2414yes—
767C2×C42C2414yes—
768C2×C42C2414yes—
769C2×C42C2414yes—
770C2×C42C2414yes—
771C2×C42C2414yes—
772C2×C42C2414yes—
773C2×C42C2414yes—
774C2×C42C2414yes—
775C2×C42C2414yes—
776C2×C42C2412yes—
777C2×C42C2412yes—
778C2×C42C2414yes—
779C2×C42C2412yes—
780C2×C42C2412yes—
781C2×C42C2414yes—
782C2×C42C2414yes—
783C2×C42C2414yes—
784#95C2414yes—
785#95C2414yes—
786#95C2412yes—
787#95C2412yes—
788#95C2414yes—
789#95C2414yes—
790#95C2414yes—
791#95C2414yes—
792#95C2412yes—
793#95C2412yes—
794#95C2412yes—
795#95C2412yes—
796#95C2412yes—
797#95C2412yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2414yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2412yes—
809#95C2412yes—
810#95C2414yes—
811#95C2414yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2412yes—
817#95C2412yes—
818#95C2412yes—
819#95C2412yes—
820#95C2412yes—
821#95C2412yes—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2412yes—
826#95C2412yes—
827#95C2414yes—
828#95C2414yes—
829#95C2412yes—
830#95C2412yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858C24—22no—
859C24—22no—
860C24—24no—
861C24—42no—
862C24C22×Q814yes—
863C24C2511yescharacteristic
864C24C2511yescharacteristic
865C24C2511yescharacteristic
866C2×Q8—28no—
867C2×Q8—44no—
868C2×Q8—44no—
869C2×Q8—44no—
870C2×Q8—44no—
871C2×Q8—44no—
872C2×Q8—44no—
873C2×Q8—44no—
874C2×Q8—44no—
875C2×Q8—44no—
876C2×Q8—44no—
877C2×Q8—44no—
878C22×C4—24no—
879C22×C4—24no—
880C22×C4—24no—
881C22×C4—28no—
882C22×C4—24no—
883C22×C4—24no—
884C22×C4—24no—
885C22×C4—28no—
886C22×C4—24no—
887C22×C4—42no—
888C22×C4—42no—
889C22×C4—44no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—42no—
894C22×C4—42no—
895C22×C4—44no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—416no—
899C22×C4—44no—
900C22×C4—44no—
901C22×C4—44no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—44no—
905C22×C4—44no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—44no—
910C22×C4—42no—
911C22×C4—88no—
912C22×C4—88no—
913C22×C4C22×Q814yes—
914C22×C4C22×Q814yes—
915C22×C4C22×Q818yes—
916C22×C4C22×Q818yes—
917C22×C4C22×Q818yes—
918C22×C4C22×Q818yes—
919C22×C4C22×Q814yes—
920C22×C4C22×Q814yes—
921C22×C4C22×Q814yes—
922C22×C4C22×Q814yes—
923C22×C4C22×Q818yes—
924C22×C4C22×Q818yes—
925C22×C4C2514yes—
926C22×C4C2512yes—
927C22×C4C2514yes—
928C22×C4C2514yes—
929C22×C4C2514yes—
930C22×C4C2512yes—
931C22×C4C2514yes—
932C22×C4C2514yes—
933C22×C4C2514yes—
934C22×C4C2514yes—
935C22×C4C2514yes—
936C22×C4C2514yes—
937C22×C4C2512yes—
938C22×C4C2512yes—
939C22×C4C2512yes—
940C22×C4C2512yes—
941C22×C4C2512yes—
942C22×C4C2512yes—
943C22×C4C2512yes—
944C22×C4C2512yes—
945C4⋊C4—28no—
946C4⋊C4—28no—
947C4⋊C4—28no—
948C4⋊C4—44no—
949C4⋊C4—44no—
950C4⋊C4—42no—
951C4⋊C4—44no—
952C4⋊C4—44no—
953C4⋊C4—42no—
954C4⋊C4—44no—
955C4⋊C4—42no—
956C4⋊C4—44no—
957C4⋊C4—44no—
958C4⋊C4—42no—
959C4⋊C4—44no—
960C4⋊C4—44no—
961C4⋊C4—44no—
962C4⋊C4—42no—
963C4⋊C4—44no—
964C4⋊C4—42no—
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—44no—
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—44no—
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⋊C4—44no—
995C4⋊C4—44no—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C4⋊C4—44no—
1001C4⋊C4C22×Q8116yes—
1002C4⋊C4C22×Q8116yes—
1003C4⋊C4C22×Q8116yes—
1004C4⋊C4C22×Q8116yes—
1005C22⋊C4—22no—
1006C22⋊C4—28no—
1007C22⋊C4—28no—
1008C22⋊C4—24no—
1009C22⋊C4—28no—
1010C22⋊C4—24no—
1011C22⋊C4—24no—
1012C22⋊C4—28no—
1013C22⋊C4—28no—
1014C22⋊C4—28no—
1015C22⋊C4—24no—
1016C22⋊C4—41no—
1017C22⋊C4—44no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—44no—
1021C22⋊C4—41no—
1022C22⋊C4—44no—
1023C22⋊C4—44no—
1024C22⋊C42−1+414yes—
1025C42—44no—
1026C42—44no—
1027C42—44no—
1028C42—44no—
1029C42—44no—
1030C42—44no—
1031C42—42no—
1032C42—42no—
1033C42—44no—
1034C42—42no—
1035C42—42no—
1036C42—44no—
1037C42—44no—
1038C42—44no—
1039C42—44no—
1040C42—44no—
1041C42—44no—
1042C42—44no—
1043C23—21no—
1044C23—21no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—21no—
1049C23—21no—
1050C23—22no—
1051C23—22no—
1052C23—28no—
1053C23—28no—
1054C23—44no—
1055C23—48no—
1056C23—48no—
1057C23C23×Q812yes—
1058C23C23×Q812yes—
1059C23C23×Q812yes—
1060C23C2×2−1+412yes—
1061C23#58514yes—
1062C23#58512yes—
1063C23C2611yescharacteristic
1064Q8—88no—
1065Q8—88no—
1066Q8—164no—
1067Q8—164no—
1068C2×C4—24no—
1069C2×C4—24no—
1070C2×C4—22no—
1071C2×C4—24no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—24no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—28no—
1079C2×C4—28no—
1080C2×C4—22no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—22no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—24no—
1092C2×C4—22no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—22no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—22no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—22no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—22no—
1118C2×C4—24no—
1119C2×C4—48no—
1120C2×C4—48no—
1121C2×C4—44no—
1122C2×C4—48no—
1123C2×C4—44no—
1124C2×C4—44no—
1125C2×C4—44no—
1126C2×C4—48no—
1127C2×C4—48no—
1128C2×C4—48no—
1129C2×C4—48no—
1130C2×C4—88no—
1131C2×C4—84no—
1132C2×C4—84no—
1133C2×C4—88no—
1134C2×C4—84no—
1135C2×C4C23×Q814yes—
1136C2×C4C23×Q814yes—
1137C2×C4C23×Q814yes—
1138C2×C4C23×Q814yes—
1139C2×C4C23×Q814yes—
1140C2×C4C23×Q814yes—
1141C2×C4C2×2−1+414yes—
1142C22—22no—
1143C22—22no—
1144C22—22no—
1145C22—22no—
1146C22—24no—
1147C22—24no—
1148C22—24no—
1149C22—24no—
1150C22—22no—
1151C22—22no—
1152C22—22no—
1153C22—416no—
1154C22—42no—
1155C22—42no—
1156C22#345814yes—
1157C22#350214yes—
1158C22C24×Q811yescharacteristic
1159C22C22×2−1+411yescharacteristic
1160C22C2×#58511yescharacteristic
1161C22C2×#58512yes—
1162C22H(7,𝔽2)12yes—
1163C4—24no—
1164C4—24no—
1165C4—24no—
1166C4—24no—
1167C4—24no—
1168C4—24no—
1169C4—24no—
1170C4—44no—
1171C4—42no—
1172C4—44no—
1173C4—44no—
1174C4—44no—
1175C4—42no—
1176C4—44no—
1177C4—44no—
1178C4—44no—
1179C4—42no—
1180C4—44no—
1181C4—44no—
1182C4—44no—
1183C2—24no—
1184C2—24no—
1185C2—42no—
1186C2C2×#345811yescharacteristic
1187C2C2×#350211yescharacteristic
1188C2#6284311yescharacteristic
1189C2#6294812yes—
1190C2#6296312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC25C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #40629C2semidirect
2. #40628C2semidirect
3. #40625C2semidirect
4. #40624C2semidirect
5. #39748C2semidirect
6. #39620C2semidirect
7. #39175C2semidirect
8. #39175C2semidirect
11. #37135C2semidirect
12. #36752C2semidirect
13. #36751C2semidirect
14. #35403C2semidirect
18. #35015C2semidirect
19. #35013C2semidirect
37. #2806C22semidirect
38. #2806C22semidirect
39. #2805C22semidirect
40. #2805C22semidirect
41. #2802C22semidirect
42. #2802C22semidirect
43. #2802C22semidirect
44. #2802C22semidirect
45. #2792C22semidirect
46. #2792C22semidirect
47. #2792C22semidirect
48. #2792C22semidirect
49. #2791C22semidirect
50. #2791C22semidirect
51. #2791C22semidirect
52. #2791C22semidirect
53. #2774C22semidirect
54. #2774C22semidirect
55. #2774C22semidirect
56. #2774C22semidirect
57. #2755C22semidirect
58. #2755C22semidirect
59. #2755C22semidirect
60. #2755C22semidirect
61. #2734C22semidirect
62. #2734C22semidirect
63. #2726C22semidirect
64. #2726C22semidirect
65. #2713C22semidirect
66. #2713C22semidirect
67. #2713C22semidirect
68. #2713C22semidirect
97. #2590C22semidirect
98. #2590C22semidirect
99. #2590C22semidirect
100. #2590C22semidirect
101. #2588C22semidirect
102. #2588C22semidirect
103. #2588C22semidirect
104. #2588C22semidirect
105. #2586C22semidirect
106. #2586C22semidirect
107. #2586C22semidirect
108. #2586C22semidirect
109. #2585C22semidirect
110. #2585C22semidirect
111. #2585C22semidirect
112. #2585C22semidirect
129. #2520C22semidirect
130. #2520C22semidirect
131. #2520C22semidirect
132. #2520C22semidirect
133. #2511C22semidirect
134. #2511C22semidirect
135. #2507C22semidirect
136. #2507C22semidirect
137. #2462C22semidirect
138. #2462C22semidirect
139. #2462C22semidirect
140. #2462C22semidirect
141. #2451C22semidirect
142. #2451C22semidirect
143. #2446C22semidirect
144. #2446C22semidirect
244. C22×C4⋊C4Q8semidirect

Maximal subgroups

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

subgroupindex
#406292
#406282
#406252
#406242
#397482
#396202
#391752
#374782
#374772
#371352
#367522
#367512
#354032
#350792
#350652
#350152
#350132
#349582
#341782
C2×#23452
C2×#23132