Finite Group Databasebeta

← #7713256

Subgroups — #7713256

Order 512.

4206 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#48855C214yesmaximal, complemented
2#48854C214yesmaximal, complemented
3#47980C214yesmaximal, complemented
4#47979C214yesmaximal, complemented
5#47021C214yesmaximal, complemented
6#46845C214yesmaximal, complemented
7#46446C214yesmaximal, complemented
8#46438C214yesmaximal, complemented
9#39179C214yesmaximal, complemented
10#38959C214yesmaximal
11#38103C214yesmaximal, complemented
12#38102C214yesmaximal
13#37478C212yesmaximal
14#36752C212yesmaximal, complemented
15#36751C212yesmaximal, complemented
16#35159C212yesmaximal, complemented
17#35033C211yesmaximal, characteristic
18#35020C211yesmaximal, characteristic
19#35013C212yesmaximal, complemented
20#34380C212yesmaximal
21C2×#2332C211yesmaximal, characteristic
22C22×C22⋊Q8C2211yescharacteristic
23#2857C2212yes—
24#2855C2214yes—
25#2851C2214yes—
26#2851C2211yescharacteristic
27#2851C2212yes—
28#2851C2211yescharacteristic
29#2851C2211yescharacteristic
30#2851C2211yescharacteristic
31#2841C2214yes—
32#2841C2214yes—
33#2809C2214yescomplemented
34#2809C2214yescomplemented
35#2807C2214yes—
36#2806C2214yescomplemented
37#2806C2214yescomplemented
38#2806C2214yescomplemented
39#2806C2214yescomplemented
40#2805C2214yescomplemented
41#2805C2214yescomplemented
42#2802C2214yescomplemented
43#2802C2214yescomplemented
44#2802C2214yescomplemented
45#2802C2214yescomplemented
46#2799C2214yescomplemented
47#2799C2214yescomplemented
48#2799C2214yescomplemented
49#2799C2214yescomplemented
50#2792C2214yescomplemented
51#2792C2214yescomplemented
52#2792C2214yescomplemented
53#2791C2214yescomplemented
54#2791C2214yescomplemented
55#2791C2214yescomplemented
56#2790C2214yes—
57#2790C2214yes—
58#2788C2214yes—
59#2788C2214yes—
60#2788C2214yes—
61#2774C2214yescomplemented
62#2774C2214yescomplemented
63#2774C2214yescomplemented
64#2768C2214yes—
65#2768C2214yes—
66#2768C2214yes—
67#2763C2214yes—
68#2755C2214yescomplemented
69#2755C2214yescomplemented
70#2755C2214yescomplemented
71#2742C2214yes—
72#2742C2214yes—
73#2734C2214yescomplemented
74#2729C2214yes—
75#2726C2214yescomplemented
76#2720C2214yes—
77#2713C2214yescomplemented
78#2713C2214yescomplemented
79#2704C2214yes—
80#2704C2214yes—
81#2667C2214yes—
82#2665C2214yes—
83#2659C2212yes—
84#2659C2212yes—
85#2646C2214yes—
86#2646C2214yes—
87#2646C2212yes—
88#2646C2212yes—
89#2627C2214yes—
90#2627C2214yes—
91#2627C2214yes—
92#2626C2214yes—
93#2608C2214yes—
94#2607C2214yes—
95#2590C2214yescomplemented
96#2589C2214yes—
97#2589C2214yes—
98#2588C2214yescomplemented
99#2587C2214yes—
100#2587C2214yes—
101#2586C2214yescomplemented
102#2586C2214yescomplemented
103#2586C2214yescomplemented
104#2585C2214yescomplemented
105#2585C2214yescomplemented
106#2585C2214yescomplemented
107#2582C2214yescomplemented
108#2581C2214yescomplemented
109#2574C2214yes—
110#2574C2214yes—
111#2574C2214yes—
112#2569C2214yes—
113#2569C2214yes—
114#2569C2214yes—
115#2569C2214yes—
116#2568C2214yescomplemented
117#2565C2214yescomplemented
118#2556C2214yes—
119#2549C2214yes—
120#2549C2214yes—
121#2522C2214yes—
122#2522C2214yes—
123#2522C2214yes—
124#2520C2214yescomplemented
125#2520C2214yescomplemented
126#2520C2214yescomplemented
127#2520C2214yescomplemented
128#2511C2214yescomplemented
129#2509C2214yescomplemented
130#2509C2214yescomplemented
131#2508C2214yescomplemented
132#2508C2214yescomplemented
133#2507C2214yescomplemented
134#2507C2214yescomplemented
135#2507C2214yescomplemented
136#2506C2214yescomplemented
137#2506C2214yescomplemented
138#2497C2214yes—
139#2497C2214yes—
140#2492C2214yes—
141#2465C2214yes—
142#2462C2214yescomplemented
143#2462C2214yescomplemented
144#2453C2214yescomplemented
145#2453C2214yescomplemented
146#2453C2214yescomplemented
147#2451C2214yescomplemented
148#2442C2214yes—
149#2442C2212yes—
150#2442C2212yes—
151#2442C2212yes—
152#2442C2212yes—
153#2441C2212yes—
154#2441C2212yes—
155#2440C2214yes—
156#2439C2212yes—
157#2439C2212yes—
158#2438C2214yes—
159#2438C2214yes—
160#2438C2214yes—
161#2438C2214yes—
162#2438C2214yes—
163#2438C2214yes—
164#2437C2214yes—
165#2437C2214yes—
166#2423C2214yes—
167#2378C2214yes—
168#2378C2214yes—
169#2360C2214yes—
170#2360C2214yes—
171#2344C2214yes—
172#2342C2214yes—
173#2342C2214yes—
174Q8×C22⋊C4C2214yes—
175#2332C2214yes—
176#2332C2214yes—
177#2332C2214yes—
178#2332C2214yes—
179#2329C2214yes—
180#2329C2214yes—
181#2329C2214yes—
182#2329C2214yes—
183#2323C2214yes—
184#2323C2214yes—
185#2317C2214yes—
186#2316C2212yes—
187#2316C2212yes—
188#2315C2214yes—
189#2313C2212yes—
190#2313C2212yes—
191C4×C22⋊Q8C2214yes—
192#2296C2214yes—
193C2×#391C2212yes—
194C2×#388C2212yes—
195C2×#388C2212yes—
196C2×#387C2212yes—
197C2×#387C2212yes—
198#2280C2212yes—
199C2×#381C2211yescharacteristic
200C2×#380C2212yes—
201C2×C4×C4⋊C4C2212yes—
202C2×C4×C22⋊C4C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C24×C4C2311yescharacteristic
205C2×C4⋊Q8C2314yes—
206C2×C4⋊Q8C2312yes—
207C2×#125C2314yes—
208C2×#125C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×#125C2311yescharacteristic
211C2×#125C2312yes—
212C2×#125C2311yescharacteristic
213C2×#125C2314yes—
214C2×C22⋊Q8Q8116yescomplemented
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2314yes—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2314yes—
222C2×C4×Q8C2314yes—
223C2×C4×Q8C2314yes—
224C2×C4×Q8C2314yes—
225C2×#117C2314yes—
226C2×#117C2314yes—
227C2×#117C2312yes—
228C2×#117C2312yes—
229C22×C4⋊C4C2312yes—
230C22×C4⋊C4C2312yes—
231C22×C4⋊C4C2312yes—
232C22×C4⋊C4C2312yes—
233C22×C4⋊C4C2312yes—
234C22×C4⋊C4C2311yescharacteristic
235C22×C22⋊C4C2314yes—
236C22×C22⋊C4C2312yes—
237C22×C22⋊C4C2311yescharacteristic
238C22×C22⋊C4C2311yescharacteristic
239C22×C22⋊C4C2312yes—
240C22×C42C2312yes—
241C22×C42C2311yescharacteristic
242C22×C42C2311yescharacteristic
243C22×C42C2312yes—
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#400C2314yes—
260#400C2314yes—
261#400C2314yes—
262#400C2314yes—
263#400C2314yes—
264#400C2314yes—
265#400C2314yes—
266#400C2314yes—
267#400C2314yes—
268#399C2314yes—
269#399C2314yes—
270#399C2314yes—
271#399C2314yes—
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#398C2314yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#396C2314yes—
313#396C2314yes—
314#396C2314yes—
315#396C2314yes—
316#396C2314yes—
317#396C2314yes—
318#396C2314yes—
319#396C2314yes—
320#395C2314yes—
321#395C2314yes—
322#395C2314yes—
323#395C2314yes—
324#395C2314yes—
325#395C2314yes—
326#395C2314yes—
327#395C2314yes—
328#395C2314yes—
329#395C2314yes—
330#395C2314yes—
331#395C2314yes—
332#395C2314yes—
333#395C2314yes—
334#395C2314yes—
335#395C2314yes—
336#393C2314yes—
337#393C2314yes—
338#393C2314yes—
339#393C2314yes—
340#391C2314yes—
341#391C2314yes—
342#391C2314yes—
343#391C2314yes—
344#391C2314yes—
345#391C2314yes—
346#391C2314yes—
347#391C2314yes—
348#391C2314yes—
349#391C2314yes—
350#391C2314yes—
351#391C2314yes—
352#391C2314yes—
353#391C2314yes—
354#391C2314yes—
355#391C2314yes—
356#391C2314yes—
357#391C2314yes—
358#391C2314yes—
359#391C2314yes—
360#391C2314yes—
361#391C2314yes—
362#391C2314yes—
363#391C2314yes—
364#391C2314yes—
365#391C2314yes—
366#389C2314yes—
367#389C2314yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2314yes—
385#389C2314yes—
386#389C2314yes—
387#389C2314yes—
388#389C2312yes—
389#389C2314yes—
390#389C2312yes—
391#389C2314yes—
392#389C2314yes—
393#389C2312yes—
394#389C2314yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2312yes—
400#389C2312yes—
401#389C2312yes—
402#389C2314yes—
403#389C2312yes—
404#389C2312yes—
405#389C2314yes—
406#389C2314yes—
407#389C2314yes—
408#389C2314yes—
409#389C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2314yes—
413#389C2314yes—
414#388C2314yes—
415#388C2314yes—
416#388C2314yes—
417#388C2314yes—
418#388C2314yes—
419#388C2314yes—
420#388C2314yes—
421#388C2314yes—
422#388C2314yes—
423#388C2314yes—
424#388C2314yes—
425#388C2314yes—
426#388C2314yes—
427#388C2314yes—
428#388C2314yes—
429#388C2314yes—
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#385C2314yes—
491#385C2314yes—
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#385C2314yes—
511#385C2314yes—
512#384C2314yes—
513#384C2314yes—
514#384C2314yes—
515#384C2312yes—
516#382C2314yes—
517#382C2314yes—
518#382C2314yes—
519#382C2314yes—
520#382C2311yescharacteristic
521#382C2311yescharacteristic
522#382C2311yescharacteristic
523#382C2312yes—
524#382C2311yescharacteristic
525#381C2314yes—
526#381C2314yes—
527#381C2314yes—
528#381C2314yes—
529#381C2314yes—
530#380C2312yes—
531#380C2312yes—
532#380C2312yes—
533#380C2314yes—
534#380C2314yes—
535#380C2314yes—
536#380C2314yes—
537#380C2314yes—
538#380C2314yes—
539#380C2314yes—
540#380C2314yes—
541#380C2314yes—
542#380C2314yes—
543#380C2312yes—
544#380C2314yes—
545#380C2314yes—
546#380C2312yes—
547#380C2312yes—
548#380C2314yes—
549#380C2312yes—
550#380C2312yes—
551#379C2314yes—
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×C4⋊C4C2314yes—
562C4×C4⋊C4C2314yes—
563C4×C4⋊C4C2314yes—
564C4×C4⋊C4C2314yes—
565C4×C22⋊C4C2314yes—
566C4×C22⋊C4C2314yes—
567C4×C22⋊C4C2312yes—
568C4×C22⋊C4C2312yes—
569C4×C22⋊C4C2314yes—
570C4×C22⋊C4C2314yes—
571C4×C22⋊C4C2314yes—
572C4×C22⋊C4C2314yes—
573C4×C22⋊C4C2314yes—
574C4×C22⋊C4C2312yes—
575C4×C22⋊C4C2312yes—
576C4×C22⋊C4C2314yes—
577C2×#95C2314yes—
578C2×#95C2312yes—
579C2×#95C2312yes—
580C2×#95C2312yes—
581C2×#95C2312yes—
582C2×#95C2312yes—
583C2×#95C2312yes—
584C2×#95C2312yes—
585C25C2411yescharacteristic
586C22×Q8—81no—
587C22×Q8—81no—
588C22×Q8C2×Q818yes—
589C22×Q8C2414yes—
590C22×Q8C2414yes—
591C22×Q8C2414yes—
592C22×Q8C2414yes—
593C23×C4—81no—
594C23×C4—81no—
595C23×C4C2×Q818yes—
596C23×C4C2412yes—
597C23×C4C2412yes—
598C23×C4C2412yes—
599C23×C4C2412yes—
600C23×C4C2412yes—
601C23×C4C2414yes—
602C23×C4C2414yes—
603C23×C4C2412yes—
604C23×C4C2412yes—
605C23×C4C2411yescharacteristic
606C23×C4C2411yescharacteristic
607C23×C4C2412yes—
608C4⋊Q8—82no—
609C4⋊Q8—84no—
610#125—82no—
611#125—81no—
612#125—81no—
613#125—81no—
614#125—81no—
615#125—84no—
616#125—84no—
617C22⋊Q8—48no—
618C22⋊Q8—48no—
619C22⋊Q8—48no—
620C22⋊Q8—84no—
621C22⋊Q8—84no—
622C22⋊Q8C2×Q8132yes—
623C22⋊Q8C2×Q8132yes—
624C4×Q8—84no—
625C4×Q8—84no—
626C4×Q8—84no—
627#117—48no—
628#117—48no—
629#117—82no—
630#117—82no—
631C2×C4⋊C4—44no—
632C2×C4⋊C4—82no—
633C2×C4⋊C4—82no—
634C2×C4⋊C4—82no—
635C2×C4⋊C4C2×Q818yes—
636C2×C4⋊C4C2×Q8116yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
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×C4⋊C4C2414yes—
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⋊C4C2414yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C22⋊C4—48no—
698C2×C22⋊C4—44no—
699C2×C22⋊C4—81no—
700C2×C22⋊C4—81no—
701C2×C22⋊C4C2×Q8116yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2412yes—
709C2×C22⋊C4C2412yes—
710C2×C22⋊C4C2412yes—
711C2×C22⋊C4C2412yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2414yes—
720C2×C42—44no—
721C2×C42—82no—
722C2×C42—81no—
723C2×C42—81no—
724C2×C42C2414yes—
725C2×C42C2414yes—
726C2×C42C2414yes—
727C2×C42C2414yes—
728C2×C42C2414yes—
729C2×C42C2414yes—
730C2×C42C2414yes—
731C2×C42C2414yes—
732C2×C42C2414yes—
733C2×C42C2414yes—
734C2×C42C2414yes—
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2412yes—
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740C2×C42C2414yes—
741C2×C42C2412yes—
742C2×C42C2414yes—
743C2×C42C2414yes—
744#95C2412yes—
745#95C2412yes—
746#95C2412yes—
747#95C2412yes—
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—
789#95C2414yes—
790#95C2414yes—
791#95C2414yes—
792#95C2414yes—
793#95C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2414yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2414yes—
809#95C2414yes—
810C24—24no—
811C24—41no—
812C24—41no—
813C24—42no—
814C24C22×Q814yes—
815C24C2512yes—
816C24C2511yescharacteristic
817C2×Q8—44no—
818C2×Q8—44no—
819C2×Q8—44no—
820C2×Q8—44no—
821C2×Q8—44no—
822C2×Q8—44no—
823C2×Q8—44no—
824C2×Q8—44no—
825C2×Q8—44no—
826C2×Q8—44no—
827C2×Q8—44no—
828C2×Q8—88no—
829C2×Q8C22×Q8116yes—
830C22×C4—24no—
831C22×C4—24no—
832C22×C4—24no—
833C22×C4—24no—
834C22×C4—24no—
835C22×C4—24no—
836C22×C4—42no—
837C22×C4—41no—
838C22×C4—41no—
839C22×C4—42no—
840C22×C4—42no—
841C22×C4—42no—
842C22×C4—42no—
843C22×C4—42no—
844C22×C4—42no—
845C22×C4—41no—
846C22×C4—41no—
847C22×C4—42no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—88no—
861C22×C4C22×Q818yes—
862C22×C4C22×Q818yes—
863C22×C4C22×Q814yes—
864C22×C4C22×Q814yes—
865C22×C4C22×Q818yes—
866C22×C4C22×Q818yes—
867C22×C4C2512yes—
868C22×C4C2514yes—
869C22×C4C2514yes—
870C22×C4C2514yes—
871C22×C4C2514yes—
872C22×C4C2514yes—
873C22×C4C2512yes—
874C22×C4C2512yes—
875C22×C4C2514yes—
876C22×C4C2514yes—
877C22×C4C2514yes—
878C22×C4C2514yes—
879C22×C4C2512yes—
880C22×C4C2514yes—
881C22×C4C2512yes—
882C22×C4C2514yes—
883C22×C4C2514yes—
884C22×C4C2511yescharacteristic
885C22×C4C2511yescharacteristic
886C4⋊C4—44no—
887C4⋊C4—44no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—42no—
891C4⋊C4—42no—
892C4⋊C4—42no—
893C4⋊C4—42no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—42no—
914C4⋊C4—42no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—44no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C4—44no—
922C4⋊C4—44no—
923C4⋊C4—44no—
924C4⋊C4—44no—
925C4⋊C4—44no—
926C4⋊C4—44no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4—44no—
930C4⋊C4—44no—
931C4⋊C4—44no—
932C4⋊C4—44no—
933C4⋊C4—44no—
934C4⋊C4—44no—
935C4⋊C4—44no—
936C4⋊C4—44no—
937C4⋊C4—44no—
938C4⋊C4—44no—
939C4⋊C4—44no—
940C4⋊C4—44no—
941C4⋊C4—44no—
942C4⋊C4—44no—
943C4⋊C4C22×Q8116yes—
944C4⋊C4C22×Q8116yes—
945C4⋊C4C22×Q8116yes—
946C22⋊C4—28no—
947C22⋊C4—28no—
948C22⋊C4—28no—
949C22⋊C4—28no—
950C22⋊C4—42no—
951C22⋊C4—42no—
952C22⋊C4—42no—
953C22⋊C4—42no—
954C22⋊C4—44no—
955C22⋊C4—44no—
956C22⋊C4—44no—
957C22⋊C4—44no—
958C22⋊C4—44no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—44no—
962C22⋊C4C22×Q8116yes—
963C22⋊C4C22×Q8116yes—
964C42—44no—
965C42—44no—
966C42—44no—
967C42—44no—
968C42—42no—
969C42—41no—
970C42—41no—
971C42—41no—
972C42—41no—
973C42—42no—
974C42—44no—
975C42—44no—
976C42—44no—
977C42—44no—
978C42—44no—
979C42—44no—
980C42—44no—
981C42—44no—
982C42—44no—
983C42—44no—
984C23—21no—
985C23—21no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—28no—
994C23—44no—
995C23—44no—
996C23—84no—
997C23—84no—
998C23C23×Q814yes—
999C23C23×Q812yes—
1000C23#58514yes—
1001C23C2611yescharacteristic
1002Q8—416no—
1003Q8—88no—
1004Q8—164no—
1005Q8—164no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—24no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—216no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—24no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—24no—
1052C2×C4—22no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—22no—
1059C2×C4—44no—
1060C2×C4—48no—
1061C2×C4—48no—
1062C2×C4—44no—
1063C2×C4—48no—
1064C2×C4—48no—
1065C2×C4—84no—
1066C2×C4—84no—
1067C2×C4—84no—
1068C2×C4—164no—
1069C2×C4—164no—
1070C2×C4C23×Q818yes—
1071C2×C4C23×Q818yes—
1072C2×C4C23×Q812yes—
1073C2×C4C23×Q812yes—
1074C2×C4C23×Q814yes—
1075C22—22no—
1076C22—22no—
1077C22—24no—
1078C22—24no—
1079C22—24no—
1080C22—24no—
1081C22—24no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—88no—
1087C22#350414yes—
1088C22C24×Q811yescharacteristic
1089C22C2×#58512yes—
1090C22H(7,𝔽2)11yescharacteristic
1091C22H(7,𝔽2)11yescharacteristic
1092C222−1+612yes—
1093C4—28no—
1094C4—22no—
1095C4—22no—
1096C4—24no—
1097C4—28no—
1098C4—44no—
1099C4—42no—
1100C4—42no—
1101C4—44no—
1102C4—44no—
1103C4—44no—
1104C4—44no—
1105C4—42no—
1106C4—44no—
1107C4—42no—
1108C4—44no—
1109C4—44no—
1110C4—44no—
1111C4—44no—
1112C2—24no—
1113C2—44no—
1114C2C2×#350411yescharacteristic
1115C2#6284311yescharacteristic
1116C2#6284911yescharacteristic
1117C2#6286812yes—
1118C2#6287212yes—
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. #48855C2semidirect
2. #48854C2semidirect
3. #47980C2semidirect
4. #47979C2semidirect
5. #47021C2semidirect
6. #46845C2semidirect
7. #46446C2semidirect
8. #46438C2semidirect
9. #39179C2semidirect
11. #38103C2semidirect
14. #36752C2semidirect
15. #36751C2semidirect
16. #35159C2semidirect
19. #35013C2semidirect
33. #2809C22semidirect
34. #2809C22semidirect
36. #2806C22semidirect
37. #2806C22semidirect
38. #2806C22semidirect
39. #2806C22semidirect
40. #2805C22semidirect
41. #2805C22semidirect
42. #2802C22semidirect
43. #2802C22semidirect
44. #2802C22semidirect
45. #2802C22semidirect
46. #2799C22semidirect
47. #2799C22semidirect
48. #2799C22semidirect
49. #2799C22semidirect
50. #2792C22semidirect
51. #2792C22semidirect
52. #2792C22semidirect
53. #2791C22semidirect
54. #2791C22semidirect
55. #2791C22semidirect
61. #2774C22semidirect
62. #2774C22semidirect
63. #2774C22semidirect
68. #2755C22semidirect
69. #2755C22semidirect
70. #2755C22semidirect
73. #2734C22semidirect
75. #2726C22semidirect
77. #2713C22semidirect
78. #2713C22semidirect
95. #2590C22semidirect
98. #2588C22semidirect
101. #2586C22semidirect
102. #2586C22semidirect
103. #2586C22semidirect
104. #2585C22semidirect
105. #2585C22semidirect
106. #2585C22semidirect
107. #2582C22semidirect
108. #2581C22semidirect
116. #2568C22semidirect
117. #2565C22semidirect
124. #2520C22semidirect
125. #2520C22semidirect
126. #2520C22semidirect
127. #2520C22semidirect
128. #2511C22semidirect
129. #2509C22semidirect
130. #2509C22semidirect
131. #2508C22semidirect
132. #2508C22semidirect
133. #2507C22semidirect
134. #2507C22semidirect
135. #2507C22semidirect
136. #2506C22semidirect
137. #2506C22semidirect
142. #2462C22semidirect
143. #2462C22semidirect
144. #2453C22semidirect
145. #2453C22semidirect
146. #2453C22semidirect
147. #2451C22semidirect
214. C2×C22⋊Q8Q8semidirect

Maximal subgroups

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

subgroupindex
#488552
#488542
#479802
#479792
#470212
#468452
#464462
#464382
#391792
#389592
#381032
#381022
#374782
#367522
#367512
#351592
#350332
#350202
#350132
#343802
C2×#23322