Finite Group Databasebeta

← #7713215

Subgroups — #7713215

Order 512.

4594 conjugacy classes of subgroups.

The subgroup lattice has 1198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#48853C214yesmaximal, complemented
2#48852C214yesmaximal, complemented
3#47978C214yesmaximal, complemented
4#47977C214yesmaximal, complemented
5#47020C214yesmaximal, complemented
6#46844C214yesmaximal, complemented
7#46445C214yesmaximal, complemented
8#46435C214yesmaximal, complemented
9#39175C214yesmaximal, complemented
10#38962C214yesmaximal, complemented
11#38096C214yesmaximal, complemented
12#38096C214yesmaximal, complemented
13#37478C212yesmaximal, complemented
14#36750C212yesmaximal, complemented
15#36749C212yesmaximal, complemented
16#35033C211yesmaximal, characteristic, complemented
17#35020C211yesmaximal, characteristic, complemented
18#35012C212yesmaximal, complemented
19#34994C212yesmaximal, complemented
20#34379C212yesmaximal
21C2×#2333C211yesmaximal, characteristic
22C22×#121C2211yescharacteristic
23#2857C2212yes—
24#2851C2214yes—
25#2851C2211yescharacteristic
26#2851C2211yescharacteristic
27#2851C2211yescharacteristic
28#2851C2212yes—
29#2851C2211yescharacteristic
30#2848C2214yes—
31#2841C2214yescomplemented
32#2841C2214yescomplemented
33#2807C2214yescomplemented
34#2805C2214yescomplemented
35#2804C2214yescomplemented
36#2804C2214yescomplemented
37#2802C2214yescomplemented
38#2791C2214yescomplemented
39#2790C2214yescomplemented
40#2790C2214yescomplemented
41#2788C2214yescomplemented
42#2788C2214yescomplemented
43#2784C2214yescomplemented
44#2784C2214yescomplemented
45#2784C2214yescomplemented
46#2784C2214yescomplemented
47#2780C2214yescomplemented
48#2780C2214yescomplemented
49#2780C2214yescomplemented
50#2780C2214yescomplemented
51#2780C2214yescomplemented
52#2780C2214yescomplemented
53#2780C2214yescomplemented
54#2780C2214yescomplemented
55#2774C2214yescomplemented
56#2768C2214yescomplemented
57#2768C2214yescomplemented
58#2763C2214yescomplemented
59#2755C2214yescomplemented
60#2755C2214yescomplemented
61#2748C2214yescomplemented
62#2748C2214yescomplemented
63#2748C2214yescomplemented
64#2748C2214yescomplemented
65#2742C2214yescomplemented
66#2732C2214yescomplemented
67#2732C2214yescomplemented
68#2729C2214yescomplemented
69#2729C2214yescomplemented
70#2726C2214yescomplemented
71#2720C2214yescomplemented
72#2720C2214yescomplemented
73#2713C2214yescomplemented
74#2704C2214yescomplemented
75#2704C2214yescomplemented
76#2692C2214yescomplemented
77#2692C2214yescomplemented
78#2692C2214yescomplemented
79#2692C2214yescomplemented
80#2677C2214yescomplemented
81#2667C2214yescomplemented
82#2665C2214yescomplemented
83#2659C2212yes—
84#2659C2212yes—
85#2646C2214yes—
86#2646C2214yes—
87#2646C2212yes—
88#2646C2212yes—
89#2627C2214yescomplemented
90#2627C2214yescomplemented
91#2626C2214yes—
92#2626C2214yes—
93#2608C2214yescomplemented
94#2607C2214yescomplemented
95#2590C2214yescomplemented
96#2588C2214yescomplemented
97#2585C2214yescomplemented
98#2585C2214yescomplemented
99#2580C2214yescomplemented
100#2579C2214yescomplemented
101#2579C2214yescomplemented
102#2574C2214yescomplemented
103#2574C2214yescomplemented
104#2569C2214yes—
105#2569C2214yes—
106#2569C2214yescomplemented
107#2569C2214yescomplemented
108#2566C2214yescomplemented
109#2564C2214yescomplemented
110#2564C2214yescomplemented
111#2563C2214yescomplemented
112#2556C2214yescomplemented
113#2556C2214yescomplemented
114#2549C2214yes—
115#2549C2214yes—
116#2538C2214yescomplemented
117#2522C2214yescomplemented
118#2522C2214yescomplemented
119#2520C2214yescomplemented
120#2511C2214yescomplemented
121#2505C2214yescomplemented
122#2505C2214yescomplemented
123#2505C2214yescomplemented
124#2505C2214yescomplemented
125#2487C2214yescomplemented
126#2487C2214yescomplemented
127#2473C2214yescomplemented
128#2473C2214yescomplemented
129#2473C2214yescomplemented
130#2473C2214yescomplemented
131#2465C2214yescomplemented
132#2465C2214yescomplemented
133#2462C2214yescomplemented
134#2454C2214yescomplemented
135#2454C2214yescomplemented
136#2454C2214yescomplemented
137#2452C2214yescomplemented
138#2450C2214yescomplemented
139#2450C2214yescomplemented
140#2450C2214yescomplemented
141#2450C2214yescomplemented
142#2450C2214yescomplemented
143#2450C2214yescomplemented
144#2449C2214yescomplemented
145#2449C2214yescomplemented
146#2446C2214yescomplemented
147#2442C2214yes—
148#2442C2212yescomplemented
149#2442C2212yescomplemented
150#2442C2212yescomplemented
151#2442C2212yescomplemented
152#2441C2212yescomplemented
153#2441C2212yescomplemented
154#2440C2214yes—
155#2439C2212yescomplemented
156#2439C2212yescomplemented
157#2438C2214yescomplemented
158#2438C2214yescomplemented
159#2437C2214yes—
160#2437C2214yes—
161#2437C2214yes—
162#2437C2214yes—
163#2437C2214yes—
164#2437C2214yes—
165#2417C2214yescomplemented
166#2417C2214yescomplemented
167#2377C2214yes—
168#2377C2214yes—
169#2361C2214yes—
170#2361C2214yes—
171#2345C2214yes—
172D4×C22⋊C4C2214yes—
173D4×C22⋊C4C2214yes—
174D4×C22⋊C4C2214yes—
175#2333C2214yes—
176#2333C2214yes—
177#2333C2214yes—
178#2333C2214yes—
179#2329C2214yes—
180#2329C2214yes—
181#2325C2214yes—
182#2325C2214yes—
183#2324C2214yes—
184#2324C2214yes—
185#2315C2214yes—
186#2315C2214yes—
187#2315C2212yes—
188#2315C2212yes—
189#2312C2212yes—
190#2312C2212yes—
191C4×C22⋊Q8C2214yes—
192C2×#390C2212yes—
193C2×#388C2212yes—
194C2×#387C2212yes—
195C2×#386C2212yes—
196C2×#386C2212yes—
197C2×#385C2214yes—
198#2280C2212yes—
199C2×#381C2211yescharacteristic
200C2×#380C2212yes—
201C2×C4×C22⋊C4C2212yes—
202C2×C4×C22⋊C4C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C23×D4C2312yes—
205C24×C4C2312yes—
206C24×C4C2311yescharacteristic
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2312yes—
209C2×#125C2314yes—
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#125C2312yes—
215C2×#125C2314yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2314yes—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2314yes—
227C2×#121Q8116yescomplemented
228C2×#121C2314yes—
229C2×#121C2314yes—
230C2×C4×Q8C2314yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2314yes—
237C2×#117C2312yes—
238C2×#117C2312yes—
239C22×C4⋊C4C2314yes—
240C22×C4⋊C4C2314yes—
241C22×C4⋊C4C2312yes—
242C22×C4⋊C4C2312yes—
243C22×C4⋊C4C2312yes—
244C22×C4⋊C4C2311yescharacteristic
245C22×C22⋊C4C2314yes—
246C22×C22⋊C4C2314yes—
247C22×C22⋊C4C2314yes—
248C22×C22⋊C4C2312yes—
249C22×C22⋊C4C2312yes—
250C22×C22⋊C4C2311yescharacteristic
251C22×C22⋊C4C2311yescharacteristic
252C22×C22⋊C4C2312yes—
253C22×C22⋊C4C2312yes—
254C22×C22⋊C4C2312yes—
255C22×C42C2311yescharacteristic
256C22×C42C2311yescharacteristic
257C22×C42C2312yes—
258#400C2314yes—
259#400C2314yes—
260#400C2314yes—
261#400C2314yes—
262#400C2314yes—
263#400C2314yes—
264#400C2314yes—
265#400C2314yes—
266#400C2314yes—
267#400C2314yes—
268#400C2314yes—
269#400C2314yes—
270#400C2314yes—
271#400C2314yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#400C2314yes—
276#399C2314yes—
277#399C2314yes—
278#399C2314yes—
279#399C2314yes—
280#399C2314yes—
281#399C2314yes—
282#399C2314yes—
283#399C2314yes—
284#399C2314yes—
285#399C2314yes—
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#398C2314yes—
313#398C2314yes—
314#396C2314yes—
315#396C2314yes—
316#396C2314yes—
317#396C2314yes—
318#396C2314yes—
319#396C2314yes—
320#396C2314yes—
321#396C2314yes—
322#396C2314yes—
323#396C2314yes—
324#396C2314yes—
325#396C2314yes—
326#396C2314yes—
327#396C2314yes—
328#396C2314yes—
329#396C2314yes—
330#396C2314yes—
331#396C2314yes—
332#396C2314yes—
333#396C2314yes—
334#395C2314yes—
335#395C2314yes—
336#395C2314yes—
337#395C2314yes—
338#395C2314yes—
339#395C2314yes—
340#395C2314yes—
341#395C2314yes—
342#395C2314yes—
343#395C2314yes—
344#393C2314yes—
345#393C2314yes—
346#393C2314yes—
347#393C2314yes—
348#393C2314yes—
349#393C2314yes—
350#393C2314yes—
351#393C2314yes—
352#393C2314yes—
353#393C2314yes—
354#391C2314yes—
355#391C2314yes—
356#391C2314yes—
357#391C2314yes—
358#391C2314yes—
359#391C2314yes—
360#391C2314yes—
361#391C2314yes—
362#391C2314yes—
363#391C2314yes—
364#390C2314yes—
365#390C2314yes—
366#390C2314yes—
367#390C2314yes—
368#390C2314yes—
369#390C2314yes—
370#390C2314yes—
371#390C2314yes—
372#390C2314yes—
373#390C2314yes—
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#389C2314yes—
389#389C2312yes—
390#389C2312yes—
391#389C2312yes—
392#389C2312yes—
393#389C2312yes—
394#389C2312yes—
395#389C2314yes—
396#389C2314yes—
397#389C2312yes—
398#389C2312yes—
399#389C2314yes—
400#388C2314yes—
401#388C2314yes—
402#388C2314yes—
403#388C2314yes—
404#388C2314yes—
405#388C2314yes—
406#388C2314yes—
407#388C2314yes—
408#388C2314yes—
409#388C2314yes—
410#388C2314yes—
411#388C2314yes—
412#387C2314yes—
413#387C2314yes—
414#387C2314yes—
415#387C2314yes—
416#387C2314yes—
417#387C2314yes—
418#387C2314yes—
419#387C2314yes—
420#387C2314yes—
421#387C2314yes—
422#387C2314yes—
423#387C2314yes—
424#387C2314yes—
425#387C2314yes—
426#387C2314yes—
427#387C2314yes—
428#387C2314yes—
429#387C2314yes—
430#387C2314yes—
431#387C2314yes—
432#387C2314yes—
433#387C2314yes—
434#387C2314yes—
435#387C2314yes—
436#387C2314yes—
437#387C2314yes—
438#387C2314yes—
439#387C2314yes—
440#387C2314yes—
441#387C2314yes—
442#387C2314yes—
443#387C2314yes—
444#387C2314yes—
445#387C2314yes—
446#387C2314yes—
447#387C2314yes—
448#386C2314yes—
449#386C2314yes—
450#386C2314yes—
451#386C2314yes—
452#386C2314yes—
453#386C2314yes—
454#386C2314yes—
455#386C2314yes—
456#386C2314yes—
457#386C2314yes—
458#386C2314yes—
459#386C2314yes—
460#386C2314yes—
461#386C2314yes—
462#386C2314yes—
463#386C2314yes—
464#386C2314yes—
465#386C2314yes—
466#386C2314yes—
467#386C2314yes—
468#385C2314yes—
469#385C2314yes—
470#385C2314yes—
471#385C2314yes—
472#385C2314yes—
473#385C2314yes—
474#385C2314yes—
475#385C2314yes—
476#385C2314yes—
477#385C2314yes—
478#385C2314yes—
479#385C2314yes—
480#385C2314yes—
481#385C2314yes—
482#385C2314yes—
483#385C2314yes—
484#385C2314yes—
485#385C2314yes—
486#385C2314yes—
487#385C2314yes—
488#385C2314yes—
489#385C2314yes—
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#385C2314yes—
513#385C2314yes—
514#384C2314yes—
515#384C2312yes—
516#382C2314yes—
517#382C2314yes—
518#382C2311yescharacteristic
519#382C2312yes—
520#382C2311yescharacteristic
521#382C2311yescharacteristic
522#382C2311yescharacteristic
523#381C2314yes—
524#381C2314yes—
525#381C2314yes—
526#380C2314yes—
527#380C2314yes—
528#380C2314yes—
529#380C2314yes—
530#380C2314yes—
531#380C2314yes—
532#380C2314yes—
533#380C2314yes—
534#380C2312yes—
535#380C2312yes—
536#380C2312yes—
537#380C2314yes—
538#380C2314yes—
539#380C2314yes—
540#380C2314yes—
541#380C2314yes—
542#380C2314yes—
543#380C2314yes—
544#380C2314yes—
545#380C2314yes—
546#380C2312yes—
547#380C2314yes—
548#380C2314yes—
549#380C2314yes—
550#380C2314yes—
551#380C2314yes—
552#380C2312yes—
553#380C2312yes—
554#380C2314yes—
555#380C2312yes—
556#380C2312yes—
557#379C2314yes—
558#379C2314yes—
559#379C2314yes—
560C4×C4⋊C4C2314yes—
561C4×C4⋊C4C2314yes—
562C4×C4⋊C4C2314yes—
563C4×C4⋊C4C2314yes—
564C4×C4⋊C4C2314yes—
565C4×C22⋊C4C2314yes—
566C4×C22⋊C4C2314yes—
567C4×C22⋊C4C2314yes—
568C4×C22⋊C4C2312yes—
569C4×C22⋊C4C2312yes—
570C4×C22⋊C4C2314yes—
571C4×C22⋊C4C2314yes—
572C4×C22⋊C4C2312yes—
573C4×C22⋊C4C2312yes—
574C4×C22⋊C4C2314yes—
575C4×C22⋊C4C2314yes—
576C4×C22⋊C4C2314yes—
577C2×#95C2314yes—
578C2×#95C2314yes—
579C2×#95C2312yes—
580C2×#95C2312yes—
581C2×#95C2314yes—
582C2×#95C2312yes—
583C2×#95C2312yes—
584C2×#95C2312yes—
585C25C2411yescharacteristic
586C25C2412yes—
587C22×Q8C2414yes—
588C22×Q8C2414yes—
589C22×Q8C2414yes—
590C22×D4—82no—
591C22×D4—82no—
592C22×D4—81no—
593C22×D4—81no—
594C22×D4C2×Q8116yes—
595C22×D4C2×Q818yes—
596C22×D4C2414yes—
597C22×D4C2414yes—
598C22×D4C2414yes—
599C23×C4—44no—
600C23×C4—81no—
601C23×C4—81no—
602C23×C4—82no—
603C23×C4—82no—
604C23×C4C2×Q818yes—
605C23×C4C2412yes—
606C23×C4C2412yes—
607C23×C4C2412yes—
608C23×C4C2412yes—
609C23×C4C2414yes—
610C23×C4C2414yes—
611C23×C4C2414yes—
612C23×C4C2414yes—
613C23×C4C2414yes—
614C23×C4C2414yes—
615C23×C4C2414yes—
616C23×C4C2414yes—
617C23×C4C2411yescharacteristic
618C23×C4C2412yes—
619C23×C4C2412yes—
620C23×C4C2411yescharacteristic
621C23×C4C2412yes—
622C4⋊Q8—82no—
623C4⋊Q8—84no—
624#125—81no—
625#125—82no—
626#125—84no—
627#125—81no—
628#125—81no—
629#125—81no—
630#125—84no—
631C22⋊Q8—48no—
632C22⋊Q8—48no—
633C22⋊Q8—48no—
634C22⋊Q8—84no—
635C22⋊Q8—84no—
636C22⋊Q8—84no—
637C22⋊Q8—84no—
638C22⋊Q8—84no—
639C22⋊Q8—84no—
640C22⋊Q8—84no—
641C22⋊Q8—84no—
642#121C2×Q8132yes—
643#121C2×Q8132yes—
644C4×Q8—84no—
645C4×D4—84no—
646C4×D4—84no—
647C4×D4—84no—
648C4×D4—84no—
649C4×D4—84no—
650C4×D4—84no—
651#117—82no—
652#117—82no—
653C2×C4⋊C4—82no—
654C2×C4⋊C4—82no—
655C2×C4⋊C4—84no—
656C2×C4⋊C4—84no—
657C2×C4⋊C4—82no—
658C2×C4⋊C4C2×Q818yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2412yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2412yes—
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×C4⋊C4C2414yes—
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×C22⋊C4—48no—
712C2×C22⋊C4—48no—
713C2×C22⋊C4—48no—
714C2×C22⋊C4—44no—
715C2×C22⋊C4—44no—
716C2×C22⋊C4—82no—
717C2×C22⋊C4—81no—
718C2×C22⋊C4—82no—
719C2×C22⋊C4—81no—
720C2×C22⋊C4C2×Q8116yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2414yes—
727C2×C22⋊C4C2414yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2414yes—
731C2×C22⋊C4C2412yes—
732C2×C22⋊C4C2412yes—
733C2×C22⋊C4C2414yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2412yes—
736C2×C22⋊C4C2412yes—
737C2×C22⋊C4C2414yes—
738C2×C22⋊C4C2414yes—
739C2×C22⋊C4C2414yes—
740C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
754C2×C22⋊C4C2414yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2414yes—
757C2×C42—82no—
758C2×C42—81no—
759C2×C42—81no—
760C2×C42C2414yes—
761C2×C42C2414yes—
762C2×C42C2414yes—
763C2×C42C2414yes—
764C2×C42C2414yes—
765C2×C42C2414yes—
766C2×C42C2414yes—
767C2×C42C2411yescharacteristic
768C2×C42C2411yescharacteristic
769C2×C42C2412yes—
770C2×C42C2414yes—
771C2×C42C2411yescharacteristic
772C2×C42C2411yescharacteristic
773C2×C42C2412yes—
774#95C2414yes—
775#95C2414yes—
776#95C2412yes—
777#95C2412yes—
778#95C2414yes—
779#95C2414yes—
780#95C2412yes—
781#95C2412yes—
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—
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—
828C24—24no—
829C24—24no—
830C24—24no—
831C24—41no—
832C24—41no—
833C24—42no—
834C24—42no—
835C24—42no—
836C24—42no—
837C24—42no—
838C24C22×Q818yes—
839C24C22×Q814yes—
840C24C2512yes—
841C24C2514yes—
842C24C2511yescharacteristic
843C2×Q8—44no—
844C2×Q8—44no—
845C2×Q8—44no—
846C2×Q8—44no—
847C2×Q8—44no—
848C2×Q8—44no—
849C2×Q8—44no—
850C2×Q8—44no—
851C2×Q8—44no—
852C2×D4—44no—
853C2×D4—44no—
854C2×D4—44no—
855C2×D4—44no—
856C2×D4—44no—
857C2×D4—44no—
858C2×D4—88no—
859C2×D4—816no—
860C2×D4C22×Q8116yes—
861C2×D4C22×Q8116yes—
862C2×D4C22×Q8116yes—
863C22×C4—24no—
864C22×C4—24no—
865C22×C4—24no—
866C22×C4—24no—
867C22×C4—41no—
868C22×C4—41no—
869C22×C4—42no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—41no—
878C22×C4—41no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4—44no—
891C22×C4—44no—
892C22×C4—44no—
893C22×C4—44no—
894C22×C4—44no—
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×C4—44no—
908C22×C4—44no—
909C22×C4—88no—
910C22×C4—816no—
911C22×C4C22×Q814yes—
912C22×C4C22×Q818yes—
913C22×C4C22×Q814yes—
914C22×C4C22×Q818yes—
915C22×C4C22×Q818yes—
916C22×C4C2514yes—
917C22×C4C2512yes—
918C22×C4C2512yes—
919C22×C4C2512yes—
920C22×C4C2514yes—
921C22×C4C2514yes—
922C22×C4C2514yes—
923C22×C4C2514yes—
924C22×C4C2514yes—
925C22×C4C2514yes—
926C22×C4C2514yes—
927C22×C4C2514yes—
928C22×C4C2514yes—
929C22×C4C2512yes—
930C22×C4C2512yes—
931C22×C4C2514yes—
932C22×C4C2511yescharacteristic
933C22×C4C2511yescharacteristic
934C4⋊C4—44no—
935C4⋊C4—44no—
936C4⋊C4—44no—
937C4⋊C4—44no—
938C4⋊C4—44no—
939C4⋊C4—44no—
940C4⋊C4—42no—
941C4⋊C4—42no—
942C4⋊C4—42no—
943C4⋊C4—42no—
944C4⋊C4—44no—
945C4⋊C4—44no—
946C4⋊C4—44no—
947C4⋊C4—44no—
948C4⋊C4—44no—
949C4⋊C4—44no—
950C4⋊C4—42no—
951C4⋊C4—42no—
952C4⋊C4—42no—
953C4⋊C4—42no—
954C4⋊C4—44no—
955C4⋊C4—44no—
956C4⋊C4—44no—
957C4⋊C4—44no—
958C4⋊C4—44no—
959C4⋊C4—44no—
960C4⋊C4—44no—
961C4⋊C4—44no—
962C4⋊C4—44no—
963C4⋊C4—44no—
964C4⋊C4—44no—
965C4⋊C4—44no—
966C4⋊C4—44no—
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⋊C4C22×Q8116yes—
986C22⋊C4—28no—
987C22⋊C4—28no—
988C22⋊C4—28no—
989C22⋊C4—28no—
990C22⋊C4—44no—
991C22⋊C4—44no—
992C22⋊C4—44no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C22⋊C4—44no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—42no—
1001C22⋊C4—42no—
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⋊C4—44no—
1012C22⋊C4—44no—
1013C22⋊C4—44no—
1014C22⋊C4—44no—
1015C22⋊C4—44no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—44no—
1020C22⋊C4C22×Q8116yes—
1021C22⋊C4C22×Q8116yes—
1022C42—44no—
1023C42—44no—
1024C42—41no—
1025C42—41no—
1026C42—42no—
1027C42—41no—
1028C42—41no—
1029C42—42no—
1030C42—44no—
1031C42—44no—
1032C42—44no—
1033C42—44no—
1034C42—44no—
1035C42—44no—
1036C23—21no—
1037C23—22no—
1038C23—21no—
1039C23—22no—
1040C23—24no—
1041C23—24no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—24no—
1046C23—24no—
1047C23—24no—
1048C23—24no—
1049C23—22no—
1050C23—22no—
1051C23—28no—
1052C23—216no—
1053C23—44no—
1054C23—44no—
1055C23—48no—
1056C23—48no—
1057C23—84no—
1058C23—84no—
1059C23—84no—
1060C23—84no—
1061C23—84no—
1062C23—84no—
1063C23C23×Q818yes—
1064C23C23×Q814yes—
1065C23C23×Q812yes—
1066C23#58514yes—
1067C23C2611yescharacteristic
1068Q8—88no—
1069Q8—164no—
1070Q8—164no—
1071D4—416no—
1072D4—416no—
1073D4—416no—
1074C2×C4—24no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—24no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—24no—
1094C2×C4—22no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—24no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—24no—
1124C2×C4—44no—
1125C2×C4—48no—
1126C2×C4—48no—
1127C2×C4—44no—
1128C2×C4—48no—
1129C2×C4—48no—
1130C2×C4—84no—
1131C2×C4—84no—
1132C2×C4—84no—
1133C2×C4—88no—
1134C2×C4—88no—
1135C2×C4—88no—
1136C2×C4—88no—
1137C2×C4—164no—
1138C2×C4—164no—
1139C2×C4—164no—
1140C2×C4—164no—
1141C2×C4C23×Q812yes—
1142C2×C4C23×Q812yes—
1143C2×C4C23×Q818yes—
1144C2×C4C23×Q814yes—
1145C22—22no—
1146C22—22no—
1147C22—24no—
1148C22—24no—
1149C22—24no—
1150C22—28no—
1151C22—24no—
1152C22—24no—
1153C22—28no—
1154C22—28no—
1155C22—44no—
1156C22—44no—
1157C22—42no—
1158C22—42no—
1159C22—44no—
1160C22—42no—
1161C22—44no—
1162C22—42no—
1163C22—88no—
1164C22—816no—
1165C22#350414yes—
1166C22C24×Q811yescharacteristic
1167C22C2×#58512yes—
1168C22H(7,𝔽2)11yescharacteristic
1169C22H(7,𝔽2)12yes—
1170C22H(7,𝔽2)11yescharacteristic
1171C4—22no—
1172C4—22no—
1173C4—24no—
1174C4—28no—
1175C4—42no—
1176C4—42no—
1177C4—44no—
1178C4—44no—
1179C4—44no—
1180C4—44no—
1181C4—44no—
1182C4—42no—
1183C4—44no—
1184C4—44no—
1185C4—44no—
1186C4—42no—
1187C4—44no—
1188C4—44no—
1189C2—24no—
1190C2—44no—
1191C2—48no—
1192C2C2×#350411yescharacteristic
1193C2#6284311yescharacteristic
1194C2#6284311yescharacteristic
1195C2#6286712yes—
1196C2#6287012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#121C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #48853C2semidirect
2. #48852C2semidirect
3. #47978C2semidirect
4. #47977C2semidirect
5. #47020C2semidirect
6. #46844C2semidirect
7. #46445C2semidirect
8. #46435C2semidirect
9. #39175C2semidirect
10. #38962C2semidirect
11. #38096C2semidirect
12. #38096C2semidirect
13. #37478C2semidirect
14. #36750C2semidirect
15. #36749C2semidirect
16. #35033C2semidirect
17. #35020C2semidirect
18. #35012C2semidirect
19. #34994C2semidirect
31. #2841C22semidirect
32. #2841C22semidirect
33. #2807C22semidirect
34. #2805C22semidirect
35. #2804C22semidirect
36. #2804C22semidirect
37. #2802C22semidirect
38. #2791C22semidirect
39. #2790C22semidirect
40. #2790C22semidirect
41. #2788C22semidirect
42. #2788C22semidirect
43. #2784C22semidirect
44. #2784C22semidirect
45. #2784C22semidirect
46. #2784C22semidirect
47. #2780C22semidirect
48. #2780C22semidirect
49. #2780C22semidirect
50. #2780C22semidirect
51. #2780C22semidirect
52. #2780C22semidirect
53. #2780C22semidirect
54. #2780C22semidirect
55. #2774C22semidirect
56. #2768C22semidirect
57. #2768C22semidirect
58. #2763C22semidirect
59. #2755C22semidirect
60. #2755C22semidirect
61. #2748C22semidirect
62. #2748C22semidirect
63. #2748C22semidirect
64. #2748C22semidirect
65. #2742C22semidirect
66. #2732C22semidirect
67. #2732C22semidirect
68. #2729C22semidirect
69. #2729C22semidirect
70. #2726C22semidirect
71. #2720C22semidirect
72. #2720C22semidirect
73. #2713C22semidirect
74. #2704C22semidirect
75. #2704C22semidirect
76. #2692C22semidirect
77. #2692C22semidirect
78. #2692C22semidirect
79. #2692C22semidirect
80. #2677C22semidirect
81. #2667C22semidirect
82. #2665C22semidirect
89. #2627C22semidirect
90. #2627C22semidirect
93. #2608C22semidirect
94. #2607C22semidirect
95. #2590C22semidirect
96. #2588C22semidirect
97. #2585C22semidirect
98. #2585C22semidirect
99. #2580C22semidirect
100. #2579C22semidirect
101. #2579C22semidirect
102. #2574C22semidirect
103. #2574C22semidirect
106. #2569C22semidirect
107. #2569C22semidirect
108. #2566C22semidirect
109. #2564C22semidirect
110. #2564C22semidirect
111. #2563C22semidirect
112. #2556C22semidirect
113. #2556C22semidirect
116. #2538C22semidirect
117. #2522C22semidirect
118. #2522C22semidirect
119. #2520C22semidirect
120. #2511C22semidirect
121. #2505C22semidirect
122. #2505C22semidirect
123. #2505C22semidirect
124. #2505C22semidirect
125. #2487C22semidirect
126. #2487C22semidirect
127. #2473C22semidirect
128. #2473C22semidirect
129. #2473C22semidirect
130. #2473C22semidirect
131. #2465C22semidirect
132. #2465C22semidirect
133. #2462C22semidirect
134. #2454C22semidirect
135. #2454C22semidirect
136. #2454C22semidirect
137. #2452C22semidirect
138. #2450C22semidirect
139. #2450C22semidirect
140. #2450C22semidirect
141. #2450C22semidirect
142. #2450C22semidirect
143. #2450C22semidirect
144. #2449C22semidirect
145. #2449C22semidirect
146. #2446C22semidirect
148. #2442C22semidirect
149. #2442C22semidirect
150. #2442C22semidirect
151. #2442C22semidirect
152. #2441C22semidirect
153. #2441C22semidirect
155. #2439C22semidirect
156. #2439C22semidirect
157. #2438C22semidirect
158. #2438C22semidirect
165. #2417C22semidirect
166. #2417C22semidirect
227. C2×#121Q8semidirect

Maximal subgroups

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

subgroupindex
#488532
#488522
#479782
#479772
#470202
#468442
#464452
#464352
#391752
#389622
#380962
#374782
#367502
#367492
#350332
#350202
#350122
#349942
#343792
C2×#23332