Finite Group Databasebeta

← #8932547

Subgroups — #8932547

Order 512.

4478 conjugacy classes of subgroups.

The subgroup lattice has 1251 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58247C214yesmaximal, complemented
2#57613C214yesmaximal, complemented
3#56118C214yesmaximal, complemented
4#55549C214yesmaximal, complemented
5#55003C214yesmaximal, complemented
6#53626C214yesmaximal, complemented
7#52079C212yesmaximal, complemented
8#52072C211yesmaximal, characteristic, complemented
9#51873C212yesmaximal, complemented
10#51542C211yesmaximal, characteristic, complemented
11#51412C214yesmaximal, complemented
12#50165C212yesmaximal
13#47180C212yesmaximal, complemented
14#47077C214yesmaximal, complemented
15#46329C212yesmaximal, complemented
16#46269C212yesmaximal, complemented
17#46136C212yesmaximal, complemented
18#46126C214yesmaximal, complemented
19#45759C212yesmaximal, complemented
20#37253C214yesmaximal, complemented
21#36819C212yesmaximal, complemented
22#35677C211yesmaximal, characteristic
23#35670C212yesmaximal, complemented
24C2×#563C2212yes—
25C2×#563C2211yescharacteristic, complemented
26C2×Q82C2211yescharacteristic, complemented
27C2×#551C2212yes—
28C2×#541C2212yes—
29C2×#536C2211yescharacteristic
30C2×#535C2211yescharacteristic
31C22×#124C2211yescharacteristic
32C2×#519C2211yescharacteristic
33#2865C2214yescomplemented
34#2860C2214yescomplemented
35#2851C2214yes—
36#2838C2214yescomplemented
37#2836C2214yescomplemented
38#2835C2212yes—
39#2834C2212yes—
40#2831C2214yescomplemented
41#2830C2212yes—
42#2830C2214yescomplemented
43#2830C2214yescomplemented
44#2823C2214yescomplemented
45#2820C2214yes—
46#2802C2214yescomplemented
47#2802C2214yescomplemented
48#2800C2214yes—
49#2800C2214yescomplemented
50#2796C2214yescomplemented
51#2795C2214yescomplemented
52#2793C2214yescomplemented
53#2793C2214yescomplemented
54#2792C2214yescomplemented
55#2790C2214yescomplemented
56#2790C2214yescomplemented
57#2790C2214yescomplemented
58#2787C2214yescomplemented
59#2786C2214yes—
60#2786C2214yescomplemented
61#2786C2214yescomplemented
62#2784C2212yes—
63#2784C2214yescomplemented
64#2783C2214yescomplemented
65#2783C2214yescomplemented
66#2781C2214yescomplemented
67#2780C2214yescomplemented
68#2776C2214yescomplemented
69#2772C2214yescomplemented
70#2772C2214yescomplemented
71#2761C2214yescomplemented
72#2757C2214yes—
73#2755C2214yescomplemented
74#2750C2214yes—
75#2747C2214yes—
76#2747C2214yescomplemented
77#2742C2212yes—
78#2740C2214yescomplemented
79#2737C2214yescomplemented
80#2736C2214yes—
81#2735C2214yes—
82#2734C2212yescomplemented
83#2734C2212yescomplemented
84#2731C2212yes—
85#2731C2212yes—
86#2731C2212yescomplemented
87#2729C2214yescomplemented
88#2728C2214yescomplemented
89#2724C2212yes—
90#2722C2212yes—
91#2720C2214yescomplemented
92#2717C2214yes—
93#2717C2212yescomplemented
94#2716C2214yescomplemented
95#2715C2214yes—
96#2715C2214yes—
97#2715C2214yes—
98#2713C2214yescomplemented
99#2709C2214yes—
100#2707C2214yes—
101#2707C2214yescomplemented
102#2707C2214yescomplemented
103#2707C2214yescomplemented
104#2704C2214yescomplemented
105#2702C2214yescomplemented
106#2702C2214yescomplemented
107#2701C2214yes—
108#2698C2214yescomplemented
109#2697C2212yes—
110#2695C2214yes—
111#2694C2214yescomplemented
112#2685C2214yes—
113#2684C2212yes—
114#2681C2214yes—
115#2680C2214yes—
116#2677C2214yescomplemented
117#2677C2214yescomplemented
118#2674C2214yes—
119#2674C2214yes—
120#2674C2214yes—
121#2674C2214yes—
122#2660C2212yescomplemented
123#2654C2214yescomplemented
124#2653C2214yescomplemented
125#2652C2214yescomplemented
126#2651C2214yescomplemented
127#2637C2214yescomplemented
128#2633C2214yescomplemented
129#2632C2212yescomplemented
130#2629C2214yescomplemented
131#2622C2214yes—
132#2611C2212yes—
133#2608C2212yescomplemented
134#2604C2214yescomplemented
135#2599C2212yes—
136#2599C2214yescomplemented
137#2597C2214yescomplemented
138#2595C2214yescomplemented
139#2593C2212yes—
140#2587C2214yescomplemented
141#2583C2212yescomplemented
142#2576C2214yescomplemented
143#2574C2214yescomplemented
144#2565C2212yescomplemented
145#2565C2212yescomplemented
146#2553C2214yes—
147#2548C2212yes—
148#2548C2212yes—
149#2546C2212yescomplemented
150#2546C2212yescomplemented
151#2545C2212yes—
152#2545C2212yes—
153#2538C2214yescomplemented
154#2531C2214yes—
155#2528C2214yescomplemented
156#2526C2214yescomplemented
157#2525C2214yescomplemented
158#2524C2214yescomplemented
159#2512C2214yescomplemented
160#2506C2214yescomplemented
161#2499C2212yes—
162#2499C2212yes—
163#2480C2214yes—
164#2480C2214yes—
165#2480C2214yes—
166#2480C2214yes—
167#2478C2214yes—
168#2478C2214yes—
169#2478C2214yes—
170#2478C2214yes—
171#2476C2214yes—
172#2475C2214yescomplemented
173#2474C2214yes—
174#2469C2214yescomplemented
175#2465C2214yescomplemented
176#2465C2214yescomplemented
177#2462C2214yescomplemented
178#2462C2214yescomplemented
179#2462C2214yescomplemented
180#2462C2214yescomplemented
181#2462C2214yescomplemented
182#2460C2214yescomplemented
183#2458C2214yes—
184#2458C2214yes—
185#2458C2214yescomplemented
186#2452C2214yescomplemented
187#2445C2214yes—
188#2443C2214yes—
189#2441C2214yescomplemented
190#2440C2214yescomplemented
191#2437C2214yes—
192#2437C2214yes—
193#2434C2212yes—
194#2434C2212yes—
195#2432C2212yes—
196#2429C2214yescomplemented
197#2426C2214yes—
198#2426C2214yes—
199#2411C2214yes—
200#2411C2214yes—
201#2406C2212yes—
202#2405C2214yes—
203#2383C2214yes—
204#2381C2211yescharacteristic, complemented
205#2379C2212yes—
206#2375C2212yes—
207#2372C2211yescharacteristic, complemented
208#2335C2214yes—
209#2332C2212yescomplemented
210#2327C2212yescomplemented
211#2327C2212yescomplemented
212#2313C2212yescomplemented
213#2309C2211yescharacteristic
214C4×C4⋊Q8C2212yescomplemented
215C4×C4⋊Q8C2212yescomplemented
216#2298C2212yes—
217#2297C2211yescharacteristic
218#2296C2211yescharacteristic
219C22×#41C2311yescharacteristic
220C23×Q8C2311yescharacteristic
221C23×D4C2311yescharacteristic
222#563—48no—
223#563—44no—
224Q82—44no—
225#551—48no—
226#541—48no—
227#536—44no—
228#535—44no—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2311yescharacteristic
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2311yescharacteristic
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2314yes—
237C2×C4⋊Q8C2312yes—
238C2×#127C2312yes—
239C2×#126C2314yes—
240C2×#126C2314yes—
241C2×#126C2314yes—
242C2×#126C2314yes—
243C2×#126C2314yes—
244C2×#125C2314yes—
245C2×#125C2312yes—
246C2×#125C2312yes—
247C2×#125C2314yes—
248C2×#125C2314yes—
249C2×#124—44no—
250C2×#124C2311yescharacteristic
251C2×#124C2312yes—
252C2×#124C2312yes—
253C2×#124C2311yescharacteristic
254C2×#124C2314yes—
255C2×#124C2312yes—
256C2×#124C2312yes—
257C2×#123C2314yes—
258C2×#123C2314yes—
259C2×#123C2312yes—
260C2×#123C2312yes—
261C2×#123C2314yes—
262C2×#123C2314yes—
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2312yes—
270C2×C22⋊Q8C2314yes—
271C2×#121C2314yes—
272C2×#120C2312yes—
273C2×#120C2312yes—
274#519—44no—
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2312yes—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2314yes—
282C2×C4×Q8C2312yes—
283C2×C4×D4C2314yes—
284C2×#117C2312yes—
285C2×#117C2311yescharacteristic
286C2×#117C2311yescharacteristic
287C2×#117C2311yescharacteristic
288C2×#117C2314yes—
289C2×#117C2312yes—
290C22×C4⋊C4C2312yes—
291C22×C22⋊C4C2314yes—
292C22×C22⋊C4C2314yes—
293C22×C42C2311yescharacteristic
294#401C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2312yes—
306#399C2314yes—
307#399C2314yes—
308#399C2312yes—
309#399C2314yes—
310#399C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2312yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2312yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2312yes—
349#397C2314yes—
350#397C2312yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2312yes—
386#395C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#393C2314yes—
411#393C2314yes—
412#393C2314yes—
413#393C2314yes—
414#393C2314yes—
415#393C2312yes—
416#393C2314yes—
417#393C2314yes—
418#391C2312yes—
419#391C2312yes—
420#391C2312yes—
421#391C2312yes—
422#391C2312yes—
423#391C2312yes—
424#391C2314yes—
425#391C2312yes—
426#391C2312yes—
427#391C2312yes—
428#391C2312yes—
429#390C2312yes—
430#390C2312yes—
431#390C2312yes—
432#390C2312yes—
433#390C2314yes—
434#390C2314yes—
435#390C2314yes—
436#390C2314yes—
437#390C2314yes—
438#390C2314yes—
439#390C2312yes—
440#390C2314yes—
441#390C2312yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2312yes—
553#386C2312yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2312yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2312yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#384C2312yes—
581#384C2312yes—
582#384C2314yes—
583#384C2314yes—
584#383C2312yes—
585#383C2314yes—
586#382C2314yes—
587#382C2312yes—
588#382C2312yes—
589#382C2314yes—
590#381C2314yes—
591#381C2312yes—
592#380C2314yes—
593#380C2314yes—
594#380C2314yes—
595#380C2314yes—
596#380C2314yes—
597#380C2314yes—
598#380C2314yes—
599#380C2314yes—
600#379C2314yes—
601#379C2314yes—
602#379C2314yes—
603#379C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2314yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2312yes—
609C4×C4⋊C4C2312yes—
610C4×C4⋊C4C2312yes—
611C4×C4⋊C4C2312yes—
612C4×C22⋊C4C2312yes—
613C4×C22⋊C4C2312yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2312yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2312yes—
619C4×C22⋊C4C2312yes—
620#376C2312yes—
621#376C2312yes—
622C43C2312yes—
623C25C2412yes—
624C2×#41—42no—
625C2×#41—42no—
626C2×#41—42no—
627C22×Q8—24no—
628C22×Q8—42no—
629C22×Q8—42no—
630C22×Q8C2412yes—
631C22×Q8C2411yescharacteristic
632C22×Q8C2412yes—
633C22×Q8C2412yes—
634C22×Q8C2411yescharacteristic
635C22×Q8C2412yes—
636C22×Q8C2412yes—
637C22×Q8C2411yescharacteristic
638C22×D4—42no—
639C22×D4—42no—
640C22×D4—42no—
641C22×D4C2414yes—
642C22×D4C2412yes—
643C22×D4C2412yes—
644C22×D4C2412yes—
645C22×D4C2411yescharacteristic
646C22×D4C2414yes—
647C23×C4C2411yescharacteristic
648C23×C4C2412yes—
649C23×C4C2412yes—
650C23×C4C2412yes—
651C23×C4C2414yes—
652C23×C4C2414yes—
653C23×C4C2412yes—
654C23×C4C2412yes—
655C4⋊Q8—24no—
656C4⋊Q8—28no—
657C4⋊Q8—28no—
658C4⋊Q8—44no—
659C4⋊Q8—42no—
660C4⋊Q8—44no—
661C4⋊Q8—44no—
662C4⋊Q8—48no—
663C4⋊Q8—44no—
664#127—44no—
665#126—216no—
666#126—48no—
667#126—48no—
668#126—48no—
669#126—48no—
670#125—44no—
671#125—48no—
672#125—48no—
673#125—44no—
674#125—48no—
675#124—28no—
676#124—24no—
677#124—44no—
678#124—44no—
679#124—42no—
680#124—44no—
681#124—48no—
682#123—44no—
683#123—48no—
684#123—48no—
685#123—48no—
686#123—48no—
687#123—44no—
688C22⋊Q8—44no—
689C22⋊Q8—44no—
690C22⋊Q8—48no—
691C22⋊Q8—48no—
692C22⋊Q8—48no—
693C22⋊Q8—48no—
694C22⋊Q8—48no—
695C22⋊Q8—44no—
696#121—48no—
697#120—28no—
698#120—44no—
699C4×Q8—44no—
700C4×Q8—44no—
701C4×Q8—44no—
702C4×Q8—44no—
703C4×Q8—44no—
704C4×Q8—44no—
705C4×Q8—44no—
706C4×Q8—48no—
707C4×D4—48no—
708#117—24no—
709#117—28no—
710#117—42no—
711#117—48no—
712#117—44no—
713#117—42no—
714C2×C4⋊C4—44no—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2412yes—
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⋊C4C2412yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C22⋊C4—48no—
769C2×C22⋊C4—48no—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2411yescharacteristic
775C2×C22⋊C4C2412yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2412yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2411yescharacteristic
814C2×C42—42no—
815C2×C42C2414yes—
816C2×C42C2412yes—
817C2×C42C2412yes—
818C2×C42C2411yescharacteristic
819C2×C42C2412yes—
820C2×C42C2411yescharacteristic
821C2×C42C2412yes—
822C2×C42C2412yes—
823C2×C42C2412yes—
824C2×C42C2412yes—
825C2×C42C2411yescharacteristic
826C2×C42C2411yescharacteristic
827C2×C42C2412yes—
828C2×C42C2412yes—
829C2×C42C2412yes—
830C2×C42C2414yes—
831C2×C42C2414yes—
832C2×C42C2412yes—
833C2×C42C2412yes—
834C2×C42C2412yes—
835C2×C42C2414yes—
836C2×C42C2414yes—
837C2×C42C2414yes—
838#95C2412yes—
839#95C2412yes—
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—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2412yes—
881#95C2412yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890C24—24no—
891C24—42no—
892C24—44no—
893C24—44no—
894C24—42no—
895C24C2514yes—
896C24C2512yes—
897C24C2511yescharacteristic
898#41—88no—
899C2×Q8—24no—
900C2×Q8—22no—
901C2×Q8—24no—
902C2×Q8—24no—
903C2×Q8—22no—
904C2×Q8—24no—
905C2×Q8—42no—
906C2×Q8—41no—
907C2×Q8—42no—
908C2×Q8—41no—
909C2×Q8—41no—
910C2×Q8—41no—
911C2×Q8—44no—
912C2×Q8—42no—
913C2×Q8—42no—
914C2×Q8—41no—
915C2×Q8—42no—
916C2×Q8—42no—
917C2×Q8—41no—
918C2×Q8—42no—
919C2×Q8—42no—
920C2×Q8—42no—
921C2×Q8—416no—
922C2×Q8H(5,𝔽2)14yes—
923C2×D4—24no—
924C2×D4—28no—
925C2×D4—24no—
926C2×D4—22no—
927C2×D4—24no—
928C2×D4—42no—
929C2×D4—42no—
930C2×D4—42no—
931C2×D4—42no—
932C2×D4—41no—
933C2×D4—42no—
934C2×D4—44no—
935C2×D4—44no—
936C2×D4—41no—
937C2×D4—42no—
938C2×D4—44no—
939C2×D4—44no—
940C2×D4—44no—
941C2×D4—88no—
942C22×C4—22no—
943C22×C4—22no—
944C22×C4—22no—
945C22×C4—24no—
946C22×C4—24no—
947C22×C4—24no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—44no—
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—42no—
960C22×C4—42no—
961C22×C4—44no—
962C22×C4—42no—
963C22×C4—44no—
964C22×C4C2514yes—
965C22×C4C2514yes—
966C22×C4C2512yes—
967C22×C4C2512yes—
968C22×C4C2514yes—
969C22×C4C2514yes—
970C22×C4C2514yes—
971C22×C4C2514yes—
972C22×C4C2512yes—
973C22×C4C2512yes—
974C22×C4C2512yes—
975C22×C4C2514yes—
976C22×C4C2512yes—
977C22×C4C2512yes—
978C22×C4C2514yes—
979C22×C4C2514yes—
980C22×C4C2511yescharacteristic
981C22×C4C2512yes—
982C22×C4C2512yes—
983C22×C4C2511yescharacteristic
984C4⋊C4—24no—
985C4⋊C4—24no—
986C4⋊C4—24no—
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—44no—
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—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—44no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—44no—
1020C4⋊C4—42no—
1021C4⋊C4—44no—
1022C4⋊C4—42no—
1023C4⋊C4—44no—
1024C4⋊C4—42no—
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—42no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C22⋊C4—28no—
1038C22⋊C4—28no—
1039C22⋊C4—22no—
1040C22⋊C4—24no—
1041C22⋊C4—28no—
1042C22⋊C4—28no—
1043C22⋊C4—28no—
1044C22⋊C4—28no—
1045C22⋊C4—44no—
1046C22⋊C4—44no—
1047C22⋊C4—44no—
1048C22⋊C4—44no—
1049C22⋊C4—44no—
1050C22⋊C4—44no—
1051C22⋊C4—44no—
1052C22⋊C4—44no—
1053C22⋊C4—44no—
1054C22⋊C4—44no—
1055C22⋊C4—44no—
1056C22⋊C4—44no—
1057C22⋊C4—44no—
1058C22⋊C4—44no—
1059C22⋊C4—44no—
1060C22⋊C4—44no—
1061C22⋊C4—44no—
1062C22⋊C4—44no—
1063C22⋊C4—44no—
1064C22⋊C4—44no—
1065C22⋊C4—44no—
1066C22⋊C4—42no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—44no—
1070C22⋊C4—44no—
1071C22⋊C4—44no—
1072C22⋊C4—44no—
1073C22⋊C4—44no—
1074C22⋊C4—44no—
1075C22⋊C4—44no—
1076C22⋊C4—44no—
1077C22⋊C4—42no—
1078C22⋊C4—44no—
1079C22⋊C4—42no—
1080C22⋊C4H(5,𝔽2)14yes—
1081C42—24no—
1082C42—24no—
1083C42—24no—
1084C42—24no—
1085C42—28no—
1086C42—22no—
1087C42—22no—
1088C42—24no—
1089C42—24no—
1090C42—42no—
1091C42—44no—
1092C42—44no—
1093C42—44no—
1094C42—42no—
1095C42—41no—
1096C42—41no—
1097C42—42no—
1098C42—42no—
1099C42—44no—
1100C42—42no—
1101C42—44no—
1102C42—42no—
1103C42—42no—
1104C23—21no—
1105C23—21no—
1106C23—24no—
1107C23—22no—
1108C23—24no—
1109C23—24no—
1110C23—22no—
1111C23—24no—
1112C23—22no—
1113C23—24no—
1114C23—24no—
1115C23—24no—
1116C23—24no—
1117C23—24no—
1118C23—24no—
1119C23—84no—
1120C23—88no—
1121C23—88no—
1122C23—162no—
1123C23—162no—
1124C23C2×H(5,𝔽2)12yes—
1125C23C2611yescharacteristic
1126Q8—44no—
1127Q8—48no—
1128Q8—44no—
1129Q8—48no—
1130Q8—84no—
1131Q8—84no—
1132Q8—82no—
1133Q8—162no—
1134D4—88no—
1135D4—84no—
1136D4—84no—
1137D4—82no—
1138D4—84no—
1139D4—164no—
1140C2×C4—28no—
1141C2×C4—22no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—22no—
1146C2×C4—21no—
1147C2×C4—24no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—22no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—48no—
1192C2×C4—84no—
1193C2×C4—84no—
1194C2×C4—88no—
1195C2×C4—84no—
1196C2×C4—162no—
1197C2×C4—164no—
1198C2×C4C2×H(5,𝔽2)14yes—
1199C2×C4C2×H(5,𝔽2)12yes—
1200C2×C4C2×H(5,𝔽2)14yes—
1201C2×C4#58512yes—
1202C22—24no—
1203C22—22no—
1204C22—42no—
1205C22—42no—
1206C22—44no—
1207C22—44no—
1208C22—44no—
1209C22—44no—
1210C22—44no—
1211C22—44no—
1212C22—42no—
1213C22—44no—
1214C22—42no—
1215C22—42no—
1216C22—44no—
1217C22—44no—
1218C22—168no—
1219C22C22×H(5,𝔽2)11yescharacteristic
1220C22C22×H(5,𝔽2)11yescharacteristic
1221C22C2×#58511yescharacteristic
1222C222−1+614yes—
1223C4—24no—
1224C4—22no—
1225C4—22no—
1226C4—24no—
1227C4—42no—
1228C4—44no—
1229C4—44no—
1230C4—42no—
1231C4—44no—
1232C4—42no—
1233C4—42no—
1234C4—44no—
1235C4—44no—
1236C4—42no—
1237C4—42no—
1238C4—42no—
1239C4—44no—
1240C4—44no—
1241C4—44no—
1242C4—44no—
1243C2—42no—
1244C2—82no—
1245C2—84no—
1246C2#6281811yescharacteristic
1247C2#6289112yes—
1248C2#6304412yes—
1249C2#6306312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#535C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58247C2semidirect
2. #57613C2semidirect
3. #56118C2semidirect
4. #55549C2semidirect
5. #55003C2semidirect
6. #53626C2semidirect
7. #52079C2semidirect
8. #52072C2semidirect
9. #51873C2semidirect
10. #51542C2semidirect
11. #51412C2semidirect
13. #47180C2semidirect
14. #47077C2semidirect
15. #46329C2semidirect
16. #46269C2semidirect
17. #46136C2semidirect
18. #46126C2semidirect
19. #45759C2semidirect
20. #37253C2semidirect
21. #36819C2semidirect
23. #35670C2semidirect
25. C2×#563C22semidirect
26. C2×Q82C22semidirect
33. #2865C22semidirect
34. #2860C22semidirect
36. #2838C22semidirect
37. #2836C22semidirect
40. #2831C22semidirect
42. #2830C22semidirect
43. #2830C22semidirect
44. #2823C22semidirect
46. #2802C22semidirect
47. #2802C22semidirect
49. #2800C22semidirect
50. #2796C22semidirect
51. #2795C22semidirect
52. #2793C22semidirect
53. #2793C22semidirect
54. #2792C22semidirect
55. #2790C22semidirect
56. #2790C22semidirect
57. #2790C22semidirect
58. #2787C22semidirect
60. #2786C22semidirect
61. #2786C22semidirect
63. #2784C22semidirect
64. #2783C22semidirect
65. #2783C22semidirect
66. #2781C22semidirect
67. #2780C22semidirect
68. #2776C22semidirect
69. #2772C22semidirect
70. #2772C22semidirect
71. #2761C22semidirect
73. #2755C22semidirect
76. #2747C22semidirect
78. #2740C22semidirect
79. #2737C22semidirect
82. #2734C22semidirect
83. #2734C22semidirect
86. #2731C22semidirect
87. #2729C22semidirect
88. #2728C22semidirect
91. #2720C22semidirect
93. #2717C22semidirect
94. #2716C22semidirect
98. #2713C22semidirect
101. #2707C22semidirect
102. #2707C22semidirect
103. #2707C22semidirect
104. #2704C22semidirect
105. #2702C22semidirect
106. #2702C22semidirect
108. #2698C22semidirect
111. #2694C22semidirect
116. #2677C22semidirect
117. #2677C22semidirect
122. #2660C22semidirect
123. #2654C22semidirect
124. #2653C22semidirect
125. #2652C22semidirect
126. #2651C22semidirect
127. #2637C22semidirect
128. #2633C22semidirect
129. #2632C22semidirect
130. #2629C22semidirect
133. #2608C22semidirect
134. #2604C22semidirect
136. #2599C22semidirect
137. #2597C22semidirect
138. #2595C22semidirect
140. #2587C22semidirect
141. #2583C22semidirect
142. #2576C22semidirect
143. #2574C22semidirect
144. #2565C22semidirect
145. #2565C22semidirect
149. #2546C22semidirect
150. #2546C22semidirect
153. #2538C22semidirect
155. #2528C22semidirect
156. #2526C22semidirect
157. #2525C22semidirect
158. #2524C22semidirect
159. #2512C22semidirect
160. #2506C22semidirect
172. #2475C22semidirect
174. #2469C22semidirect
175. #2465C22semidirect
176. #2465C22semidirect
177. #2462C22semidirect
178. #2462C22semidirect
179. #2462C22semidirect
180. #2462C22semidirect
181. #2462C22semidirect
182. #2460C22semidirect
185. #2458C22semidirect
186. #2452C22semidirect
189. #2441C22semidirect
190. #2440C22semidirect
196. #2429C22semidirect
204. #2381C22semidirect
207. #2372C22semidirect
209. #2332C22semidirect
210. #2327C22semidirect
211. #2327C22semidirect
212. #2313C22semidirect
214. C4×C4⋊Q8C22semidirect
215. C4×C4⋊Q8C22semidirect

Maximal subgroups

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

subgroupindex
#582472
#576132
#561182
#555492
#550032
#536262
#520792
#520722
#518732
#515422
#514122
#501652
#471802
#470772
#463292
#462692
#461362
#461262
#457592
#372532
#368192
#356772
#356702