Finite Group Databasebeta

← #7676328

Subgroups — #7676328

Order 512.

4752 conjugacy classes of subgroups.

The subgroup lattice has 1232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59867C214yesmaximal, complemented
2#59866C214yesmaximal, complemented
3#59662C214yesmaximal, complemented
4#59661C214yesmaximal, complemented
5#43557C214yesmaximal, complemented
6#43552C214yesmaximal, complemented
7#43130C214yesmaximal, complemented
8#43125C214yesmaximal, complemented
9#39179C214yesmaximal, complemented
10#39175C214yesmaximal, complemented
11#39175C214yesmaximal, complemented
12#36519C214yesmaximal, complemented
13#35391C212yesmaximal
14#35368C212yesmaximal
15#35020C211yesmaximal, characteristic
16#34994C212yesmaximal
17C2×#2569C211yesmaximal, characteristic
18C2×#2549C211yesmaximal, characteristic
19#34212C211yesmaximal, characteristic
20#34212C212yesmaximal
21#34212C211yesmaximal, characteristic
22C2×#2368C211yesmaximal, characteristic
23C4×#543C211yesmaximal, characteristic
24C2×#543C2211yescharacteristic
25C22×C22⋊Q8C2212yes—
26C22×C22⋊Q8C2211yescharacteristic
27#2851C2214yes—
28#2851C2214yes—
29#2851C2214yes—
30#2809C2214yescomplemented
31#2809C2214yescomplemented
32#2806C2214yescomplemented
33#2806C2214yescomplemented
34#2805C2214yescomplemented
35#2805C2214yescomplemented
36#2802C2214yescomplemented
37#2802C2214yescomplemented
38#2799C2214yescomplemented
39#2799C2214yescomplemented
40#2799C2214yescomplemented
41#2799C2214yescomplemented
42#2791C2214yescomplemented
43#2791C2214yescomplemented
44#2774C2214yescomplemented
45#2774C2214yescomplemented
46#2755C2214yescomplemented
47#2755C2214yescomplemented
48#2755C2214yescomplemented
49#2755C2214yescomplemented
50#2726C2214yescomplemented
51#2726C2214yescomplemented
52#2713C2214yescomplemented
53#2713C2214yescomplemented
54#2646C2214yes—
55#2646C2214yes—
56#2646C2214yes—
57#2590C2214yescomplemented
58#2590C2214yescomplemented
59#2590C2214yescomplemented
60#2590C2214yescomplemented
61#2588C2214yescomplemented
62#2588C2214yescomplemented
63#2588C2214yescomplemented
64#2588C2214yescomplemented
65#2585C2214yescomplemented
66#2585C2214yescomplemented
67#2585C2214yescomplemented
68#2585C2214yescomplemented
69#2584C2214yescomplemented
70#2583C2214yes—
71#2583C2214yes—
72#2582C2214yescomplemented
73#2581C2214yescomplemented
74#2569C2212yes—
75#2569C2214yes—
76#2569C2214yes—
77#2569C2214yes—
78#2569C2212yes—
79#2569C2212yes—
80#2569C2212yes—
81#2569C2212yes—
82#2569C2212yes—
83#2569C2214yes—
84#2569C2212yes—
85#2569C2212yes—
86#2568C2214yescomplemented
87#2565C2214yescomplemented
88#2550C2214yescomplemented
89#2549C2212yes—
90#2549C2214yes—
91#2549C2214yes—
92#2549C2212yes—
93#2549C2212yes—
94#2549C2212yes—
95#2549C2214yes—
96#2549C2214yes—
97#2549C2214yes—
98#2549C2214yes—
99#2520C2214yescomplemented
100#2520C2214yescomplemented
101#2520C2214yescomplemented
102#2520C2214yescomplemented
103#2511C2214yescomplemented
104#2511C2214yescomplemented
105#2508C2214yescomplemented
106#2506C2214yescomplemented
107#2505C2214yes—
108#2505C2214yes—
109#2505C2214yes—
110#2505C2214yes—
111#2505C2214yes—
112#2505C2214yes—
113#2505C2214yes—
114#2505C2214yes—
115#2502C2214yes—
116#2473C2214yes—
117#2473C2214yes—
118#2473C2214yes—
119#2473C2214yes—
120#2473C2214yes—
121#2473C2214yes—
122#2473C2214yes—
123#2473C2214yes—
124#2462C2214yescomplemented
125#2462C2214yescomplemented
126#2462C2214yescomplemented
127#2462C2214yescomplemented
128#2453C2214yescomplemented
129#2453C2214yescomplemented
130#2453C2214yescomplemented
131#2451C2214yescomplemented
132#2446C2214yescomplemented
133#2446C2214yescomplemented
134#2442C2214yes—
135#2442C2214yes—
136#2442C2214yes—
137#2442C2214yes—
138#2440C2214yes—
139#2440C2214yes—
140#2440C2214yes—
141#2440C2214yes—
142#2434C2214yes—
143C2×#400C2212yes—
144C2×#398C2212yes—
145C2×#398C2212yes—
146C2×#395C2212yes—
147#2370C2214yescomplemented
148#2370C2214yescomplemented
149#2368C2212yes—
150#2368C2214yes—
151#2368C2214yes—
152#2368C2212yes—
153#2368C2214yes—
154#2368C2212yes—
155#2368C2212yes—
156#2368C2212yes—
157#2368C2212yes—
158#2368C2214yes—
159#2368C2212yes—
160#2368C2212yes—
161#2365C2214yescomplemented
162#2360C2214yes—
163#2360C2214yes—
164#2360C2214yes—
165#2360C2214yes—
166#2355C2214yescomplemented
167#2345C2212yes—
168#2345C2212yes—
169#2345C2214yes—
170#2345C2214yes—
171#2345C2214yes—
172#2345C2214yes—
173#2345C2214yes—
174Q8×C22⋊C4C2212yes—
175Q8×C22⋊C4C2212yes—
176Q8×C22⋊C4C2214yes—
177#2329C2214yes—
178#2329C2214yes—
179#2329C2214yes—
180#2329C2214yes—
181#2329C2214yes—
182#2329C2214yes—
183#2329C2214yes—
184#2315C2211yescharacteristic
185#2315C2212yes—
186#2315C2212yes—
187#2315C2211yescharacteristic
188#2315C2211yescharacteristic
189#2315C2212yes—
190#2315C2212yes—
191C4×C22⋊Q8C2214yes—
192C4×C22⋊Q8C2214yes—
193C4×C22⋊Q8C2214yes—
194C4×C22⋊Q8C2214yes—
195C4×C22⋊Q8C2214yes—
196C4×C22⋊Q8C2214yes—
197C4×C22⋊Q8C2214yes—
198C2×#391C2212yes—
199C2×#391C2212yes—
200C2×#389C2212yes—
201C2×#387C2212yes—
202C2×#387C2212yes—
203C2×#387C2212yes—
204C2×#387C2212yes—
205C2×#385C2212yes—
206C2×#385C2212yes—
207C2×#385C2212yes—
208C2×#380C2211yescharacteristic
209C2×#380C2212yes—
210C2×#380C2211yescharacteristic
211#2273C2212yes—
212#2273C2212yes—
213C2×C4×C4⋊C4C2212yes—
214C2×C4×C22⋊C4C2211yescharacteristic
215C2×C4×C22⋊C4C2211yescharacteristic
216C2×C4×C22⋊C4C2211yescharacteristic
217C2×C4×C22⋊C4C2212yes—
218C22×#95C2211yescharacteristic
219C23×Q8C2312yes—
220C23×Q8C2311yescharacteristic
221C24×C4C2312yes—
222C24×C4C2311yescharacteristic
223#543—28no—
224C2×C4⋊Q8C2314yes—
225C2×C4⋊Q8C2314yes—
226C2×#125C2314yes—
227C2×#125C2314yes—
228C2×#125C2314yes—
229C2×#125C2314yes—
230C2×#125C2314yes—
231C2×C22⋊Q8—216no—
232C2×C22⋊Q8Q8116yescomplemented
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2312yes—
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2312yes—
243C2×C22⋊Q8C2312yes—
244C2×C4×Q8C2314yes—
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2314yes—
249C22×C4⋊C4C2312yes—
250C22×C4⋊C4C2312yes—
251C22×C4⋊C4C2312yes—
252C22×C4⋊C4C2312yes—
253C22×C4⋊C4C2312yes—
254C22×C4⋊C4C2312yes—
255C22×C4⋊C4C2312yes—
256C22×C4⋊C4C2312yes—
257C22×C4⋊C4C2312yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2312yes—
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2312yes—
263C22×C4⋊C4C2311yescharacteristic
264C22×C22⋊C4C2311yescharacteristic
265C22×C22⋊C4C2311yescharacteristic
266C22×C22⋊C4C2312yes—
267C22×C22⋊C4C2311yescharacteristic
268C22×C22⋊C4C2311yescharacteristic
269C22×C22⋊C4C2312yes—
270C22×C22⋊C4C2311yescharacteristic
271C22×C22⋊C4C2312yes—
272C22×C22⋊C4C2311yescharacteristic
273C22×C42C2312yes—
274C22×C42C2312yes—
275C22×C42C2312yes—
276C22×C42C2312yes—
277C22×C42C2312yes—
278#400C2314yes—
279#400C2314yes—
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#398C2314yes—
303#398C2314yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
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#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#391C2314yes—
367#391C2314yes—
368#391C2314yes—
369#391C2314yes—
370#391C2314yes—
371#391C2314yes—
372#391C2314yes—
373#391C2314yes—
374#391C2314yes—
375#391C2314yes—
376#391C2314yes—
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#389C2314yes—
390#389C2314yes—
391#389C2314yes—
392#389C2314yes—
393#389C2314yes—
394#389C2314yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2314yes—
405#389C2314yes—
406#389C2314yes—
407#389C2314yes—
408#389C2314yes—
409#389C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2314yes—
413#389C2314yes—
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#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#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#384C2314yes—
516#382C2314yes—
517#382C2314yes—
518#382C2314yes—
519#382C2314yes—
520#382C2314yes—
521#380C2312yes—
522#380C2314yes—
523#380C2314yes—
524#380C2314yes—
525#380C2312yes—
526#380C2312yes—
527#380C2312yes—
528#380C2314yes—
529#380C2314yes—
530#380C2312yes—
531#380C2314yes—
532#380C2314yes—
533#380C2314yes—
534#380C2314yes—
535#380C2314yes—
536#380C2314yes—
537#380C2314yes—
538#380C2314yes—
539#380C2314yes—
540#380C2314yes—
541#380C2312yes—
542#380C2312yes—
543#380C2312yes—
544C4×C4⋊C4C2314yes—
545C4×C4⋊C4C2314yes—
546C4×C4⋊C4C2314yes—
547C4×C4⋊C4C2314yes—
548C4×C4⋊C4C2314yes—
549C4×C4⋊C4C2314yes—
550C4×C4⋊C4C2314yes—
551C4×C4⋊C4C2314yes—
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×C22⋊C4C2312yes—
564C4×C22⋊C4C2312yes—
565C4×C22⋊C4C2312yes—
566C4×C22⋊C4C2312yes—
567C4×C22⋊C4C2312yes—
568C4×C22⋊C4C2312yes—
569C4×C22⋊C4C2314yes—
570C4×C22⋊C4C2314yes—
571C4×C22⋊C4C2314yes—
572C4×C22⋊C4C2314yes—
573C4×C22⋊C4C2312yes—
574C4×C22⋊C4C2312yes—
575C4×C22⋊C4C2312yes—
576C4×C22⋊C4C2312yes—
577C4×C22⋊C4C2314yes—
578C4×C22⋊C4C2314yes—
579C4×C22⋊C4C2314yes—
580C4×C22⋊C4C2314yes—
581C4×C22⋊C4C2314yes—
582C4×C22⋊C4C2314yes—
583C4×C22⋊C4C2314yes—
584C4×C22⋊C4C2314yes—
585C4×C22⋊C4C2312yes—
586C4×C22⋊C4C2314yes—
587C4×C22⋊C4C2314yes—
588C4×C22⋊C4C2314yes—
589C4×C22⋊C4C2314yes—
590C4×C22⋊C4C2312yes—
591C2×#95C2311yescharacteristic
592C2×#95C2311yescharacteristic
593C2×#95C2312yes—
594C2×#95C2311yescharacteristic
595C2×#95C2311yescharacteristic
596C2×#95C2311yescharacteristic
597C2×#95C2311yescharacteristic
598C2×#95C2311yescharacteristic
599C2×#95C2311yescharacteristic
600C2×#95C2312yes—
601C2×#95C2312yes—
602C2×#95C2312yes—
603C2×#95C2312yes—
604C2×#95C2312yes—
605C2×#95C2312yes—
606C2×#95C2312yes—
607C2×#95C2312yes—
608C2×#95C2311yescharacteristic
609C2×#95C2311yescharacteristic
610C2×#95C2312yes—
611C2×#95C2312yes—
612C2×#95C2312yes—
613C2×#95C2312yes—
614C2×#95C2312yes—
615C2×#95C2312yes—
616C2×#95C2312yes—
617C25C2411yescharacteristic
618C22×Q8—28no—
619C22×Q8—44no—
620C22×Q8—82no—
621C22×Q8—82no—
622C22×Q8C2×Q818yescomplemented
623C22×Q8C2414yes—
624C22×Q8C2414yes—
625C22×Q8C2414yes—
626C22×Q8C2412yes—
627C22×Q8C2412yes—
628C23×C4—28no—
629C23×C4—44no—
630C23×C4—82no—
631C23×C4—82no—
632C23×C4C2×Q818yes—
633C23×C4C2412yes—
634C23×C4C2412yes—
635C23×C4C2412yes—
636C23×C4C2412yes—
637C23×C4C2412yes—
638C23×C4C2412yes—
639C23×C4C2412yes—
640C23×C4C2412yes—
641C23×C4C2412yes—
642C23×C4C2412yes—
643C23×C4C2412yes—
644C23×C4C2412yes—
645C23×C4C2412yes—
646C23×C4C2412yes—
647C23×C4C2412yes—
648C23×C4C2412yes—
649C23×C4C2412yes—
650C23×C4C2411yescharacteristic
651C23×C4C2411yescharacteristic
652C23×C4C2411yescharacteristic
653C23×C4C2411yescharacteristic
654C23×C4C2411yescharacteristic
655C23×C4C2411yescharacteristic
656C23×C4C2412yes—
657C4⋊Q8—48no—
658C4⋊Q8—84no—
659#125—48no—
660#125—48no—
661#125—84no—
662#125—84no—
663#125—84no—
664C22⋊Q8—216no—
665C22⋊Q8—216no—
666C22⋊Q8—216no—
667C22⋊Q8—216no—
668C22⋊Q8—216no—
669C22⋊Q8—216no—
670C22⋊Q8—216no—
671C22⋊Q8C2×Q8116yes—
672C22⋊Q8C2×Q8116yes—
673C22⋊Q8C2×Q8116yescomplemented
674C22⋊Q8C2×Q8116yescomplemented
675C4×Q8—48no—
676C4×Q8—84no—
677C4×Q8—84no—
678C4×Q8—84no—
679C4×Q8—84no—
680C2×C4⋊C4—28no—
681C2×C4⋊C4—28no—
682C2×C4⋊C4—28no—
683C2×C4⋊C4—44no—
684C2×C4⋊C4—44no—
685C2×C4⋊C4—44no—
686C2×C4⋊C4—44no—
687C2×C4⋊C4—82no—
688C2×C4⋊C4—82no—
689C2×C4⋊C4—82no—
690C2×C4⋊C4—82no—
691C2×C4⋊C4—82no—
692C2×C4⋊C4—82no—
693C2×C4⋊C4C2×Q818yescomplemented
694C2×C4⋊C4C2×Q8116yescomplemented
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×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×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2414yes—
750C2×C22⋊C4—28no—
751C2×C22⋊C4—24no—
752C2×C22⋊C4—24no—
753C2×C22⋊C4—24no—
754C2×C22⋊C4—24no—
755C2×C22⋊C4—28no—
756C2×C22⋊C4—24no—
757C2×C22⋊C4C2×Q8116yes—
758C2×C22⋊C4#4118yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2414yes—
761C2×C22⋊C4C2412yes—
762C2×C22⋊C4C2412yes—
763C2×C22⋊C4C2412yes—
764C2×C22⋊C4C2412yes—
765C2×C22⋊C4C2412yes—
766C2×C22⋊C4C2412yes—
767C2×C22⋊C4C2412yes—
768C2×C22⋊C4C2412yes—
769C2×C22⋊C4C2412yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2412yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2412yes—
776C2×C22⋊C4C2412yes—
777C2×C42—44no—
778C2×C42—82no—
779C2×C42—82no—
780C2×C42—82no—
781C2×C42—82no—
782C2×C42C2414yes—
783C2×C42C2414yes—
784C2×C42C2414yes—
785C2×C42C2414yes—
786C2×C42C2414yes—
787C2×C42C2414yes—
788C2×C42C2414yes—
789C2×C42C2414yes—
790C2×C42C2414yes—
791C2×C42C2414yes—
792C2×C42C2414yes—
793C2×C42C2414yes—
794C2×C42C2414yes—
795C2×C42C2414yes—
796C2×C42C2414yes—
797C2×C42C2414yes—
798C2×C42C2414yes—
799C2×C42C2414yes—
800#95C2412yes—
801#95C2411yescharacteristic
802#95C2411yescharacteristic
803#95C2412yes—
804#95C2412yes—
805#95C2412yes—
806#95C2411yescharacteristic
807#95C2411yescharacteristic
808#95C2412yes—
809#95C2412yes—
810#95C2414yes—
811#95C2414yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2412yes—
822#95C2412yes—
823#95C2412yes—
824#95C2412yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2412yes—
830#95C2412yes—
831#95C2414yes—
832#95C2412yes—
833#95C2412yes—
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—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874C24—42no—
875C24—42no—
876C24C22×Q814yes—
877C24C2×#4114yes—
878C242−1+414yes—
879C24C2511yescharacteristic
880C24C2511yescharacteristic
881C24C2511yescharacteristic
882C2×Q8—28no—
883C2×Q8—28no—
884C2×Q8—28no—
885C2×Q8—28no—
886C2×Q8—44no—
887C2×Q8—44no—
888C2×Q8—44no—
889C2×Q8—44no—
890C2×Q8—44no—
891C2×Q8—44no—
892C2×Q8—44no—
893C2×Q8—88no—
894C2×Q8—816no—
895C2×Q8C22×Q818yes—
896C2×Q8C22×Q818yes—
897C22×C4—24no—
898C22×C4—24no—
899C22×C4—24no—
900C22×C4—24no—
901C22×C4—24no—
902C22×C4—24no—
903C22×C4—24no—
904C22×C4—24no—
905C22×C4—24no—
906C22×C4—24no—
907C22×C4—24no—
908C22×C4—24no—
909C22×C4—24no—
910C22×C4—24no—
911C22×C4—24no—
912C22×C4—24no—
913C22×C4—24no—
914C22×C4—24no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—42no—
954C22×C4—88no—
955C22×C4—816no—
956C22×C4C22×Q818yes—
957C22×C4C22×Q818yes—
958C22×C4C22×Q814yes—
959C22×C4C22×Q814yes—
960C22×C4C22×Q814yes—
961C22×C4C22×Q814yes—
962C22×C4C22×Q814yes—
963C22×C4C22×Q814yes—
964C22×C4C2×#4118yes—
965C22×C4C2512yes—
966C22×C4C2514yes—
967C22×C4C2514yes—
968C22×C4C2512yes—
969C22×C4C2514yes—
970C22×C4C2514yes—
971C22×C4C2514yes—
972C22×C4C2514yes—
973C22×C4C2512yes—
974C22×C4C2514yes—
975C22×C4C2514yes—
976C22×C4C2514yes—
977C22×C4C2511yescharacteristic
978C22×C4C2511yescharacteristic
979C22×C4C2511yescharacteristic
980C22×C4C2514yes—
981C22×C4C2514yes—
982C22×C4C2511yescharacteristic
983C22×C4C2514yes—
984C22×C4C2512yes—
985C4⋊C4—28no—
986C4⋊C4—28no—
987C4⋊C4—28no—
988C4⋊C4—28no—
989C4⋊C4—28no—
990C4⋊C4—28no—
991C4⋊C4—28no—
992C4⋊C4—28no—
993C4⋊C4—28no—
994C4⋊C4—28no—
995C4⋊C4—28no—
996C4⋊C4—28no—
997C4⋊C4—28no—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C4⋊C4—44no—
1001C4⋊C4—44no—
1002C4⋊C4—44no—
1003C4⋊C4—44no—
1004C4⋊C4—44no—
1005C4⋊C4—44no—
1006C4⋊C4—44no—
1007C4⋊C4—44no—
1008C4⋊C4—44no—
1009C4⋊C4—44no—
1010C4⋊C4—44no—
1011C4⋊C4—44no—
1012C4⋊C4—44no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—44no—
1022C4⋊C4—44no—
1023C4⋊C4—44no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4C22×Q818yes—
1037C4⋊C4C22×Q818yes—
1038C4⋊C4C22×Q8116yes—
1039C4⋊C4C22×Q8116yes—
1040C22⋊C4—28no—
1041C22⋊C4—28no—
1042C22⋊C4—24no—
1043C22⋊C4—24no—
1044C22⋊C4—24no—
1045C22⋊C4—24no—
1046C22⋊C4—24no—
1047C22⋊C4—24no—
1048C22⋊C4—24no—
1049C22⋊C4—24no—
1050C22⋊C4—28no—
1051C22⋊C4—28no—
1052C22⋊C4—24no—
1053C22⋊C4—24no—
1054C22⋊C4C22×Q8116yes—
1055C22⋊C4C22×Q8116yes—
1056C22⋊C4C2×#4118yes—
1057C22⋊C4C2×#4118yes—
1058C42—28no—
1059C42—44no—
1060C42—44no—
1061C42—44no—
1062C42—44no—
1063C42—44no—
1064C42—44no—
1065C42—44no—
1066C42—44no—
1067C42—44no—
1068C42—44no—
1069C42—44no—
1070C42—44no—
1071C42—44no—
1072C42—44no—
1073C42—44no—
1074C42—44no—
1075C42—44no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—44no—
1083C23—48no—
1084C23—44no—
1085C23—48no—
1086C23#557116yes—
1087C23C23×Q812yes—
1088C23C23×Q812yes—
1089C23C23×Q812yes—
1090C23C22×#4112yes—
1091C23C22×#4112yes—
1092C23C22×#4112yes—
1093C23C2×2−1+412yes—
1094C23C2×2−1+412yes—
1095C23C2×2−1+412yes—
1096C23C2611yescharacteristic
1097Q8—48no—
1098Q8—48no—
1099Q8—416no—
1100Q8—88no—
1101Q8—88no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—22no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—22no—
1110C2×C4—24no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—24no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—22no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—44no—
1151C2×C4—44no—
1152C2×C4—44no—
1153C2×C4—44no—
1154C2×C4—44no—
1155C2×C4—44no—
1156C2×C4—48no—
1157C2×C4—48no—
1158C2×C4—48no—
1159C2×C4—48no—
1160C2×C4—48no—
1161C2×C4—48no—
1162C2×C4—48no—
1163C2×C4—48no—
1164C2×C4—84no—
1165C2×C4—84no—
1166C2×C4—84no—
1167C2×C4—84no—
1168C2×C4—84no—
1169C2×C4—84no—
1170C2×C4—84no—
1171C2×C4—84no—
1172C2×C4—84no—
1173C2×C4—84no—
1174C2×C4C23×Q818yes—
1175C2×C4C23×Q818yes—
1176C2×C4C23×Q812yes—
1177C2×C4C23×Q812yes—
1178C2×C4C23×Q812yes—
1179C2×C4C23×Q812yes—
1180C2×C4C22×#4118yes—
1181C2×C4#58514yes—
1182C22—24no—
1183C22—24no—
1184C22—24no—
1185C22—22no—
1186C22—22no—
1187C22—22no—
1188C22—22no—
1189C22—22no—
1190C22—22no—
1191C22—24no—
1192C22—24no—
1193C22—24no—
1194C22—416no—
1195C22C2×#55714yes—
1196C22C2×#55714yes—
1197C22C2×#55714yes—
1198C22C24×Q811yescharacteristic
1199C22C23×#4111yescharacteristic
1200C22C22×2−1+411yescharacteristic
1201C22C2×#58512yes—
1202C22H(7,𝔽2)12yes—
1203C4—24no—
1204C4—28no—
1205C4—28no—
1206C4—22no—
1207C4—22no—
1208C4—22no—
1209C4—22no—
1210C4—28no—
1211C4—42no—
1212C4—42no—
1213C4—42no—
1214C4—44no—
1215C4—44no—
1216C4—44no—
1217C4—44no—
1218C4—44no—
1219C4—44no—
1220C4—44no—
1221C4—44no—
1222C4—44no—
1223C2—24no—
1224C2—24no—
1225C2—24no—
1226C2C22×#55711yescharacteristic
1227C2#6281311yescharacteristic
1228C2#6284311yescharacteristic
1229C2#6290212yes—
1230C2#6299012yes—
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. #59867C2semidirect
2. #59866C2semidirect
3. #59662C2semidirect
4. #59661C2semidirect
5. #43557C2semidirect
6. #43552C2semidirect
7. #43130C2semidirect
8. #43125C2semidirect
9. #39179C2semidirect
10. #39175C2semidirect
11. #39175C2semidirect
12. #36519C2semidirect
30. #2809C22semidirect
31. #2809C22semidirect
32. #2806C22semidirect
33. #2806C22semidirect
34. #2805C22semidirect
35. #2805C22semidirect
36. #2802C22semidirect
37. #2802C22semidirect
38. #2799C22semidirect
39. #2799C22semidirect
40. #2799C22semidirect
41. #2799C22semidirect
42. #2791C22semidirect
43. #2791C22semidirect
44. #2774C22semidirect
45. #2774C22semidirect
46. #2755C22semidirect
47. #2755C22semidirect
48. #2755C22semidirect
49. #2755C22semidirect
50. #2726C22semidirect
51. #2726C22semidirect
52. #2713C22semidirect
53. #2713C22semidirect
57. #2590C22semidirect
58. #2590C22semidirect
59. #2590C22semidirect
60. #2590C22semidirect
61. #2588C22semidirect
62. #2588C22semidirect
63. #2588C22semidirect
64. #2588C22semidirect
65. #2585C22semidirect
66. #2585C22semidirect
67. #2585C22semidirect
68. #2585C22semidirect
69. #2584C22semidirect
72. #2582C22semidirect
73. #2581C22semidirect
86. #2568C22semidirect
87. #2565C22semidirect
88. #2550C22semidirect
99. #2520C22semidirect
100. #2520C22semidirect
101. #2520C22semidirect
102. #2520C22semidirect
103. #2511C22semidirect
104. #2511C22semidirect
105. #2508C22semidirect
106. #2506C22semidirect
124. #2462C22semidirect
125. #2462C22semidirect
126. #2462C22semidirect
127. #2462C22semidirect
128. #2453C22semidirect
129. #2453C22semidirect
130. #2453C22semidirect
131. #2451C22semidirect
132. #2446C22semidirect
133. #2446C22semidirect
147. #2370C22semidirect
148. #2370C22semidirect
161. #2365C22semidirect
166. #2355C22semidirect
232. C2×C22⋊Q8Q8semidirect
622. C22×Q8C2×Q8semidirect
673. C22⋊Q8C2×Q8semidirect
674. C22⋊Q8C2×Q8semidirect
693. C2×C4⋊C4C2×Q8semidirect
694. C2×C4⋊C4C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#598672
#598662
#596622
#596612
#435572
#435522
#431302
#431252
#391792
#391752
#365192
#353912
#353682
#350202
#349942
C2×#25692
C2×#25492
#342122
C2×#23682
C4×#5432