Finite Group Databasebeta

← #7712498

Subgroups — #7712498

Order 512.

4698 conjugacy classes of subgroups.

The subgroup lattice has 1476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60011C214yesmaximal, complemented
2#59109C214yesmaximal, complemented
3#46098C212yesmaximal, complemented
4#46091C212yesmaximal, complemented
5#45964C212yesmaximal, complemented
6#45948C212yesmaximal, complemented
7#39803C212yesmaximal, complemented
8#39756C211yesmaximal, characteristic, complemented
9#39749C211yesmaximal, characteristic, complemented
10#39683C212yesmaximal, complemented
11#39637C211yesmaximal, characteristic, complemented
12#39611C211yesmaximal, characteristic, complemented
13#38828C212yesmaximal, complemented
14#38771C212yesmaximal, complemented
15#38484C212yesmaximal, complemented
16#38427C212yesmaximal, complemented
17#38335C214yesmaximal, complemented
18#38175C214yesmaximal, complemented
19#37571C212yesmaximal, complemented
20#37353C212yesmaximal, complemented
21#37337C212yesmaximal, complemented
22#36640C211yesmaximal, characteristic, complemented
23#36631C211yesmaximal, characteristic
24#36544C212yesmaximal, complemented
25#36200C212yesmaximal, complemented
26#36200C212yesmaximal, complemented
27#36186C212yesmaximal, complemented
28#35304C212yesmaximal, complemented
29#35271C212yesmaximal
30#34489C212yesmaximal, complemented
31C2×#2295C211yesmaximal, characteristic, complemented
32C2×#554C2212yes—
33C2×#552C2214yes—
34C2×#529C2212yes—
35C22×C4×Q8C2211yescharacteristic
36#2864C2212yes—
37#2864C2212yes—
38#2861C2212yes—
39#2860C2212yes—
40#2860C2212yes—
41#2859C2211yescharacteristic
42#2859C2211yescharacteristic
43#2859C2211yescharacteristic
44#2859C2211yescharacteristic
45#2859C2211yescharacteristic
46#2858C2211yescharacteristic
47#2857C2211yescharacteristic
48#2857C2212yes—
49#2856C2211yescharacteristic
50#2854C2212yes—
51#2854C2212yes—
52#2854C2212yes—
53#2854C2212yes—
54#2851C2212yes—
55#2851C2212yes—
56#2851C2212yes—
57#2851C2212yes—
58#2851C2212yes—
59#2850C2212yes—
60#2836C2214yes—
61#2831C2214yes—
62#2809C2212yes—
63#2809C2212yes—
64#2808C2212yes—
65#2808C2212yes—
66#2806C2212yes—
67#2806C2212yes—
68#2805C2214yes—
69#2805C2212yes—
70#2805C2212yes—
71#2798C2214yes—
72#2791C2214yes—
73#2786C2214yes—
74#2783C2214yes—
75#2774C2214yes—
76#2755C2214yes—
77#2754C2214yes—
78#2744C2214yes—
79#2740C2214yes—
80#2732C2212yes—
81#2732C2212yes—
82#2727C2212yes—
83#2727C2212yes—
84#2726C2212yes—
85#2726C2212yes—
86#2725C2214yes—
87#2725C2214yes—
88#2725C2214yes—
89#2722C2214yes—
90#2721C2214yes—
91#2721C2214yes—
92#2715C2214yes—
93#2704C2214yes—
94#2704C2214yes—
95#2700C2214yes—
96#2698C2214yes—
97#2690C2214yes—
98#2689C2214yes—
99#2689C2214yes—
100#2683C2212yes—
101#2683C2212yes—
102#2664C2214yes—
103#2660C2212yes—
104#2660C2212yes—
105#2652C2214yes—
106#2652C2214yes—
107#2650C2214yes—
108#2647C2212yes—
109#2647C2212yes—
110#2647C2212yes—
111#2644C2212yes—
112#2644C2212yes—
113#2641C2212yes—
114#2612C2214yes—
115#2612C2214yes—
116#2606C2214yes—
117#2605C2214yes—
118#2601C2214yes—
119#2590C2214yes—
120#2588C2214yes—
121#2585C2214yes—
122#2584C2214yes—
123#2584C2212yes—
124#2584C2212yes—
125#2580C2212yes—
126#2580C2212yes—
127#2570C2212yes—
128#2570C2212yes—
129#2569C2214yes—
130#2567C2212yes—
131#2566C2212yes—
132#2566C2212yes—
133#2560C2214yes—
134#2552C2212yes—
135#2549C2214yes—
136#2542C2212yes—
137#2538C2212yes—
138#2531C2214yes—
139#2531C2214yes—
140#2529C2214yes—
141#2529C2214yes—
142#2526C2214yes—
143#2526C2214yes—
144#2525C2214yes—
145#2525C2214yes—
146#2521C2214yes—
147#2519C2214yes—
148#2519C2214yes—
149#2515C2214yes—
150#2515C2214yes—
151#2513C2212yes—
152#2513C2212yes—
153#2512C2212yes—
154#2512C2212yes—
155#2512C2212yes—
156#2512C2212yes—
157#2509C2212yes—
158#2509C2212yes—
159#2507C2212yes—
160#2507C2212yes—
161#2506C2212yes—
162#2506C2214yes—
163#2506C2212yes—
164#2498C2214yes—
165#2498C2214yes—
166#2489C2214yes—
167#2481C2214yes—
168#2481C2214yes—
169#2478C2214yes—
170#2475C2214yes—
171#2474C2214yes—
172#2466C2214yes—
173#2466C2214yes—
174#2465C2214yes—
175#2465C2214yes—
176#2462C2214yes—
177#2462C2214yes—
178#2453C2214yes—
179#2449C2214yes—
180#2449C2214yes—
181#2449C2214yes—
182#2449C2214yes—
183#2444C2214yes—
184#2444C2214yes—
185#2438C2214yes—
186#2438C2214yes—
187#2425C2214yes—
188#2425C2214yes—
189#2423C2214yes—
190#2419C2214yes—
191#2419C2214yes—
192#2417C2214yes—
193#2413C2214yes—
194#2413C2214yes—
195#2409C2214yes—
196#2378C2214yes—
197#2378C2214yes—
198#2373C2214yes—
199#2373C2214yes—
200#2370C2212yes—
201#2370C2212yes—
202#2365C2212yes—
203#2362C2214yes—
204#2362C2214yes—
205#2360C2214yes—
206#2359C2214yes—
207#2359C2214yes—
208#2357C2212yes—
209#2357C2212yes—
210#2355C2212yes—
211#2354C2212yes—
212D4×C4⋊C4C2214yes—
213#2344C2214yes—
214#2332C2214yes—
215#2332C2214yes—
216#2331C2212yes—
217#2331C2212yes—
218#2330C2212yes—
219#2330C2212yes—
220#2330C2212yes—
221#2328C2212yes—
222#2323C2214yes—
223#2319C2212yes—
224#2319C2212yes—
225#2313C2214yes—
226C4×C4⋊Q8C2211yescharacteristic
227C4×#127C2211yescharacteristic
228C4×#125C2212yes—
229C4×#125C2212yes—
230C4×#125C2212yes—
231C4×#125C2212yes—
232C4×#124C2212yes—
233C4×#121C2212yes—
234C4×#121C2212yes—
235C4×#121C2212yes—
236C4×#121C2212yes—
237#2296C2212yes—
238#2296C2212yes—
239#2295C2212yes—
240#2295C2211yescharacteristic
241#2295C2211yescharacteristic
242#2295C2212yes—
243#2295C2211yescharacteristic
244#2295C2211yescharacteristic
245#2295C2211yescharacteristic
246#2295C2211yescharacteristic
247#2295C2211yescharacteristic
248#2295C2212yes—
249#2295C2211yescharacteristic
250#2295C2212yes—
251C2×#391C2211yescharacteristic
252C2×#391C2211yescharacteristic
253#2293C2212yes—
254#2293C2212yes—
255C2×#389C2211yescharacteristic
256C2×#389C2211yescharacteristic
257C2×#387C2212yes—
258C2×#387C2212yes—
259#2285C2211yescharacteristic
260#2285C2211yescharacteristic
261#2285C2212yes—
262#2283C2212yes—
263C2×C4×C4⋊C4C2212yes—
264C2×C4×C4⋊C4C2211yescharacteristic
265C2×#376C2212yes—
266C2×C43C2211yescharacteristic
267C23×Q8C2311yescharacteristic
268#554—216no—
269#552—416no—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2312yes—
272C2×#127C2311yescharacteristic
273#529—48no—
274C2×#126C2314yes—
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#126C2314yes—
279C2×#125C2312yes—
280C2×#125C2312yes—
281C2×#125C2312yes—
282C2×#125C2312yes—
283C2×#125C2312yes—
284C2×#125C2314yes—
285C2×#125C2312yes—
286C2×#125C2314yes—
287C2×#125C2314yes—
288C2×#124C2312yes—
289C2×#124C2312yes—
290C2×#123C2314yes—
291C2×#123C2314yes—
292C2×#123C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2314yes—
301C2×#121C2312yes—
302C2×#121C2312yes—
303C2×#121C2312yes—
304C2×C4×Q8—28no—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2311yescharacteristic
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2314yes—
312C2×C4×Q8C2311yescharacteristic
313C2×C4×D4C2312yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2314yes—
319C2×C4×D4C2314yes—
320C2×C4×D4C2314yes—
321C2×#117C2312yes—
322C2×#117C2314yes—
323C2×#117C2314yes—
324C2×#117C2312yes—
325C2×#117C2314yes—
326C22×C4⋊C4C2314yes—
327C22×C4⋊C4C2312yes—
328C22×C4⋊C4C2311yescharacteristic
329C22×C4⋊C4C2312yes—
330C22×C4⋊C4C2311yescharacteristic
331C22×C4⋊C4C2312yes—
332C22×C4⋊C4C2311yescharacteristic
333C22×C42C2311yescharacteristic
334C22×C42C2311yescharacteristic
335C22×C42C2312yes—
336C22×C42C2311yescharacteristic
337C22×C42C2312yes—
338C22×C42C2311yescharacteristic
339C22×C42C2311yescharacteristic
340C22×C42C2311yescharacteristic
341C22×C42C2311yescharacteristic
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#399C2314yes—
357#399C2314yes—
358#399C2314yes—
359#399C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2314yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#393C2314yes—
421#393C2314yes—
422#391C2312yes—
423#391C2312yes—
424#391C2314yes—
425#391C2311yescharacteristic
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2311yescharacteristic
431#391C2314yes—
432#391C2314yes—
433#391C2312yes—
434#391C2314yes—
435#391C2311yescharacteristic
436#391C2311yescharacteristic
437#391C2312yes—
438#391C2312yes—
439#391C2312yes—
440#391C2311yescharacteristic
441#391C2311yescharacteristic
442#391C2311yescharacteristic
443#391C2311yescharacteristic
444#390C2312yes—
445#390C2312yes—
446#390C2312yes—
447#390C2312yes—
448#390C2312yes—
449#390C2312yes—
450#390C2312yes—
451#390C2312yes—
452#390C2312yes—
453#390C2312yes—
454#390C2312yes—
455#390C2312yes—
456#390C2312yes—
457#390C2312yes—
458#390C2312yes—
459#390C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2311yescharacteristic
478#389C2314yes—
479#389C2314yes—
480#389C2312yes—
481#389C2312yes—
482#389C2311yescharacteristic
483#389C2312yes—
484#389C2312yes—
485#389C2314yes—
486#389C2312yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2312yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2312yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2312yes—
502#389C2312yes—
503#389C2314yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2312yes—
509#389C2312yes—
510#389C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2314yes—
514#389C2314yes—
515#389C2311yescharacteristic
516#389C2311yescharacteristic
517#389C2311yescharacteristic
518#389C2311yescharacteristic
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2311yescharacteristic
523#389C2311yescharacteristic
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2312yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2312yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2312yes—
594#387C2314yes—
595#387C2314yes—
596#387C2312yes—
597#387C2314yes—
598#387C2312yes—
599#387C2312yes—
600#387C2312yes—
601#387C2312yes—
602#387C2312yes—
603#387C2312yes—
604#387C2312yes—
605#387C2312yes—
606#387C2312yes—
607#387C2312yes—
608#387C2312yes—
609#387C2312yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#384C2311yescharacteristic
635#384C2311yescharacteristic
636#384C2311yescharacteristic
637#384C2312yes—
638#384C2314yes—
639#384C2311yescharacteristic
640#384C2312yes—
641#384C2312yes—
642#384C2311yescharacteristic
643#384C2311yescharacteristic
644#383C2314yes—
645#382C2312yes—
646#382C2312yes—
647#382C2312yes—
648#382C2312yes—
649#382C2312yes—
650#382C2312yes—
651#382C2312yes—
652#382C2312yes—
653#382C2312yes—
654#382C2312yes—
655#382C2314yes—
656#381C2314yes—
657#381C2314yes—
658#381C2314yes—
659#381C2314yes—
660#381C2314yes—
661#380C2314yes—
662#380C2314yes—
663#380C2312yes—
664#380C2314yes—
665#380C2314yes—
666#380C2314yes—
667#380C2312yes—
668#380C2312yes—
669#380C2312yes—
670#380C2312yes—
671#380C2312yes—
672#380C2314yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2311yescharacteristic
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2312yes—
704C4×C4⋊C4C2312yes—
705C4×C4⋊C4C2311yescharacteristic
706C4×C4⋊C4C2311yescharacteristic
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2314yes—
714#376C2312yes—
715#376C2312yes—
716#376C2312yes—
717#376C2312yes—
718#376C2312yes—
719#376C2314yes—
720#376C2312yes—
721#376C2312yes—
722#376C2312yes—
723C2×#95C2312yes—
724C2×#95C2312yes—
725C2×#95C2312yes—
726C2×#95C2312yes—
727C2×#95C2312yes—
728C2×#95C2312yes—
729C2×#95C2312yes—
730C43C2311yescharacteristic
731C43C2311yescharacteristic
732C43C2311yescharacteristic
733C43C2311yescharacteristic
734C43C2311yescharacteristic
735C43C2311yescharacteristic
736C43C2311yescharacteristic
737C43C2311yescharacteristic
738C22×Q8—24no—
739C22×Q8—42no—
740C22×Q8—42no—
741C22×Q8C2412yes—
742C22×Q8C2411yescharacteristic
743C22×Q8C2414yes—
744C22×Q8C2412yes—
745C22×Q8C2411yescharacteristic
746C22×D4C2414yes—
747C22×D4C2412yes—
748C22×D4C2412yes—
749C22×D4C2412yes—
750C23×C4C2411yescharacteristic
751C23×C4C2412yes—
752C23×C4C2412yes—
753C23×C4C2411yescharacteristic
754C23×C4C2411yescharacteristic
755C23×C4C2412yes—
756C23×C4C2411yescharacteristic
757C23×C4C2411yescharacteristic
758C23×C4C2411yescharacteristic
759C23×C4C2411yescharacteristic
760C23×C4C2412yes—
761C23×C4C2414yes—
762C23×C4C2414yes—
763C23×C4C2414yes—
764C4⋊Q8—28no—
765C4⋊Q8—24no—
766#127—24no—
767#126—48no—
768#126—48no—
769#126—48no—
770#126—48no—
771#126—48no—
772#125—28no—
773#125—28no—
774#125—28no—
775#125—44no—
776#125—44no—
777#125—44no—
778#125—48no—
779#125—48no—
780#125—48no—
781#124—44no—
782#124—44no—
783#123—216no—
784#123—48no—
785#123—48no—
786C22⋊Q8—216no—
787C22⋊Q8—216no—
788C22⋊Q8—216no—
789C22⋊Q8—44no—
790C22⋊Q8—48no—
791C22⋊Q8—48no—
792C22⋊Q8—48no—
793C22⋊Q8—48no—
794#121—28no—
795#121—44no—
796#121—44no—
797C4×Q8—24no—
798C4×Q8—28no—
799C4×Q8—24no—
800C4×Q8—24no—
801C4×Q8—28no—
802C4×Q8—44no—
803C4×Q8—48no—
804C4×Q8#4118yes—
805C4×D4—28no—
806C4×D4—28no—
807C4×D4—28no—
808C4×D4—44no—
809C4×D4—44no—
810C4×D4—48no—
811C4×D4—48no—
812C4×D4—48no—
813#117—28no—
814#117—48no—
815#117—48no—
816#117—44no—
817#117—48no—
818C2×C4⋊C4—28no—
819C2×C4⋊C4—28no—
820C2×C4⋊C4—24no—
821C2×C4⋊C4—216no—
822C2×C4⋊C4—44no—
823C2×C4⋊C4—42no—
824C2×C4⋊C4—42no—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2411yescharacteristic
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2411yescharacteristic
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2411yescharacteristic
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2411yescharacteristic
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C42—24no—
925C2×C42—24no—
926C2×C42—28no—
927C2×C42—24no—
928C2×C42—28no—
929C2×C42—24no—
930C2×C42—42no—
931C2×C42—42no—
932C2×C42—42no—
933C2×C42C2411yescharacteristic
934C2×C42C2414yes—
935C2×C42C2411yescharacteristic
936C2×C42C2411yescharacteristic
937C2×C42C2411yescharacteristic
938C2×C42C2411yescharacteristic
939C2×C42C2411yescharacteristic
940C2×C42C2412yes—
941C2×C42C2412yes—
942C2×C42C2412yes—
943C2×C42C2411yescharacteristic
944C2×C42C2411yescharacteristic
945C2×C42C2411yescharacteristic
946C2×C42C2411yescharacteristic
947C2×C42C2411yescharacteristic
948C2×C42C2411yescharacteristic
949C2×C42C2411yescharacteristic
950C2×C42C2411yescharacteristic
951C2×C42C2411yescharacteristic
952C2×C42C2411yescharacteristic
953C2×C42C2411yescharacteristic
954C2×C42C2411yescharacteristic
955C2×C42C2412yes—
956C2×C42C2412yes—
957C2×C42C2412yes—
958C2×C42C2412yes—
959C2×C42C2414yes—
960C2×C42C2414yes—
961C2×C42C2414yes—
962C2×C42C2414yes—
963C2×C42C2414yes—
964C2×C42C2414yes—
965C2×C42C2414yes—
966C2×C42C2414yes—
967C2×C42C2411yescharacteristic
968C2×C42C2411yescharacteristic
969C2×C42C2411yescharacteristic
970C2×C42C2411yescharacteristic
971C2×C42C2411yescharacteristic
972C2×C42C2411yescharacteristic
973C2×C42C2411yescharacteristic
974C2×C42C2411yescharacteristic
975C2×C42C2411yescharacteristic
976C2×C42C2412yes—
977C2×C42C2411yescharacteristic
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046C24C2514yes—
1047C24C2511yescharacteristic
1048C2×Q8—24no—
1049C2×Q8—22no—
1050C2×Q8—28no—
1051C2×Q8—24no—
1052C2×Q8—24no—
1053C2×Q8—41no—
1054C2×Q8—42no—
1055C2×Q8—41no—
1056C2×Q8—41no—
1057C2×Q8—41no—
1058C2×Q8—44no—
1059C2×Q8—42no—
1060C2×Q8—44no—
1061C2×Q8—42no—
1062C2×Q8—416no—
1063C2×Q8C2×#4114yes—
1064C2×D4—28no—
1065C2×D4—28no—
1066C2×D4—28no—
1067C2×D4—24no—
1068C2×D4—24no—
1069C2×D4—24no—
1070C2×D4—24no—
1071C2×D4—24no—
1072C2×D4—42no—
1073C2×D4—42no—
1074C2×D4—42no—
1075C2×D4—42no—
1076C22×C4—22no—
1077C22×C4—22no—
1078C22×C4—22no—
1079C22×C4—22no—
1080C22×C4—22no—
1081C22×C4—22no—
1082C22×C4—22no—
1083C22×C4—22no—
1084C22×C4—22no—
1085C22×C4—24no—
1086C22×C4—24no—
1087C22×C4—22no—
1088C22×C4—24no—
1089C22×C4—22no—
1090C22×C4—24no—
1091C22×C4—24no—
1092C22×C4—24no—
1093C22×C4—24no—
1094C22×C4—22no—
1095C22×C4—24no—
1096C22×C4—22no—
1097C22×C4—22no—
1098C22×C4—22no—
1099C22×C4—28no—
1100C22×C4—28no—
1101C22×C4—28no—
1102C22×C4—41no—
1103C22×C4—41no—
1104C22×C4—41no—
1105C22×C4—41no—
1106C22×C4—42no—
1107C22×C4—42no—
1108C22×C4—42no—
1109C22×C4—42no—
1110C22×C4—44no—
1111C22×C4—44no—
1112C22×C4—44no—
1113C22×C4—44no—
1114C22×C4—44no—
1115C22×C4—44no—
1116C22×C4H(5,𝔽2)14yes—
1117C22×C42−1+414yes—
1118C22×C4C2511yescharacteristic
1119C22×C4C2511yescharacteristic
1120C22×C4C2512yes—
1121C22×C4C2512yes—
1122C22×C4C2512yes—
1123C22×C4C2514yes—
1124C22×C4C2511yescharacteristic
1125C22×C4C2512yes—
1126C22×C4C2514yes—
1127C22×C4C2514yes—
1128C22×C4C2514yes—
1129C22×C4C2512yes—
1130C22×C4C2514yes—
1131C22×C4C2514yes—
1132C22×C4C2514yes—
1133C22×C4C2511yescharacteristic
1134C22×C4C2512yes—
1135C22×C4C2512yes—
1136C22×C4C2511yescharacteristic
1137C22×C4C2511yescharacteristic
1138C22×C4C2512yes—
1139C22×C4C2511yescharacteristic
1140C22×C4C2511yescharacteristic
1141C22×C4C2511yescharacteristic
1142C22×C4C2511yescharacteristic
1143C22×C4C2511yescharacteristic
1144C22×C4C2511yescharacteristic
1145C22×C4C2511yescharacteristic
1146C22×C4C2511yescharacteristic
1147C4⋊C4—24no—
1148C4⋊C4—22no—
1149C4⋊C4—24no—
1150C4⋊C4—24no—
1151C4⋊C4—24no—
1152C4⋊C4—28no—
1153C4⋊C4—28no—
1154C4⋊C4—28no—
1155C4⋊C4—24no—
1156C4⋊C4—24no—
1157C4⋊C4—24no—
1158C4⋊C4—28no—
1159C4⋊C4—28no—
1160C4⋊C4—24no—
1161C4⋊C4—24no—
1162C4⋊C4—24no—
1163C4⋊C4—24no—
1164C4⋊C4—24no—
1165C4⋊C4—24no—
1166C4⋊C4—28no—
1167C4⋊C4—28no—
1168C4⋊C4—24no—
1169C4⋊C4—28no—
1170C4⋊C4—28no—
1171C4⋊C4—24no—
1172C4⋊C4—24no—
1173C4⋊C4—24no—
1174C4⋊C4—24no—
1175C4⋊C4—24no—
1176C4⋊C4—24no—
1177C4⋊C4—24no—
1178C4⋊C4—24no—
1179C4⋊C4—28no—
1180C4⋊C4—24no—
1181C4⋊C4—41no—
1182C4⋊C4—41no—
1183C4⋊C4—41no—
1184C4⋊C4—42no—
1185C4⋊C4—41no—
1186C4⋊C4—42no—
1187C4⋊C4—42no—
1188C4⋊C4—42no—
1189C4⋊C4—42no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C4⋊C4—42no—
1195C4⋊C4—44no—
1196C4⋊C4—42no—
1197C4⋊C4—44no—
1198C4⋊C4—44no—
1199C4⋊C4—42no—
1200C4⋊C4—44no—
1201C4⋊C4—42no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4—44no—
1207C4⋊C4—44no—
1208C4⋊C4—44no—
1209C4⋊C4—44no—
1210C4⋊C4—42no—
1211C4⋊C4—42no—
1212C4⋊C4—44no—
1213C4⋊C4—44no—
1214C4⋊C4—44no—
1215C4⋊C4—44no—
1216C4⋊C4—44no—
1217C4⋊C4C2×#4118yes—
1218C4⋊C4C2×#4114yes—
1219C22⋊C4—28no—
1220C22⋊C4—28no—
1221C22⋊C4—28no—
1222C22⋊C4—28no—
1223C22⋊C4—28no—
1224C22⋊C4—28no—
1225C22⋊C4—28no—
1226C22⋊C4—28no—
1227C22⋊C4—28no—
1228C22⋊C4—28no—
1229C22⋊C4—28no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C42—22no—
1247C42—22no—
1248C42—24no—
1249C42—24no—
1250C42—22no—
1251C42—24no—
1252C42—22no—
1253C42—22no—
1254C42—22no—
1255C42—22no—
1256C42—28no—
1257C42—22no—
1258C42—22no—
1259C42—22no—
1260C42—22no—
1261C42—22no—
1262C42—22no—
1263C42—24no—
1264C42—24no—
1265C42—24no—
1266C42—24no—
1267C42—22no—
1268C42—22no—
1269C42—22no—
1270C42—22no—
1271C42—22no—
1272C42—41no—
1273C42—41no—
1274C42—41no—
1275C42—41no—
1276C42—41no—
1277C42—41no—
1278C42—41no—
1279C42—41no—
1280C42—44no—
1281C42—44no—
1282C42—44no—
1283C42—44no—
1284C42—44no—
1285C42—44no—
1286C42—44no—
1287C42—44no—
1288C42C2×#4114yes—
1289C42C2×#4118yes—
1290C422−1+414yes—
1291C23—21no—
1292C23—21no—
1293C23—21no—
1294C23—21no—
1295C23—24no—
1296C23—24no—
1297C23—24no—
1298C23—24no—
1299C23—24no—
1300C23—24no—
1301C23—24no—
1302C23C2×H(5,𝔽2)12yes—
1303C23C2×2−1+412yes—
1304C23#58512yes—
1305C23C2611yescharacteristic
1306Q8—44no—
1307Q8—48no—
1308Q8—44no—
1309Q8—88no—
1310Q8—84no—
1311D4—416no—
1312D4—48no—
1313D4—84no—
1314D4—84no—
1315C2×C4—28no—
1316C2×C4—21no—
1317C2×C4—21no—
1318C2×C4—21no—
1319C2×C4—21no—
1320C2×C4—22no—
1321C2×C4—21no—
1322C2×C4—21no—
1323C2×C4—21no—
1324C2×C4—21no—
1325C2×C4—21no—
1326C2×C4—21no—
1327C2×C4—21no—
1328C2×C4—21no—
1329C2×C4—21no—
1330C2×C4—21no—
1331C2×C4—21no—
1332C2×C4—21no—
1333C2×C4—21no—
1334C2×C4—21no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—28no—
1339C2×C4—28no—
1340C2×C4—21no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—24no—
1344C2×C4—24no—
1345C2×C4—24no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—24no—
1349C2×C4—24no—
1350C2×C4—22no—
1351C2×C4—24no—
1352C2×C4—24no—
1353C2×C4—24no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—21no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—21no—
1362C2×C4—21no—
1363C2×C4—24no—
1364C2×C4—24no—
1365C2×C4—24no—
1366C2×C4—24no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—21no—
1370C2×C4—21no—
1371C2×C4—24no—
1372C2×C4—21no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—21no—
1376C2×C4—24no—
1377C2×C4—24no—
1378C2×C4—24no—
1379C2×C4—24no—
1380C2×C4—24no—
1381C2×C4—24no—
1382C2×C4—24no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—24no—
1391C2×C4—44no—
1392C2×C4—44no—
1393C2×C4—48no—
1394C2×C4—44no—
1395C2×C4—44no—
1396C2×C4—48no—
1397C2×C4—48no—
1398C2×C4—88no—
1399C2×C4—88no—
1400C2×C4—88no—
1401C2×C4—84no—
1402C2×C4C22×#4112yes—
1403C2×C4C22×#4114yes—
1404C2×C4C22×#4114yes—
1405C2×C4C22×#4112yes—
1406C2×C4C22×#4112yes—
1407C2×C4C2×H(5,𝔽2)12yes—
1408C2×C4C2×H(5,𝔽2)12yes—
1409C2×C4C2×2−1+412yes—
1410C2×C4C2×2−1+412yes—
1411C2×C4C2×2−1+412yes—
1412C2×C4C2×2−1+412yes—
1413C2×C4C2×2−1+412yes—
1414C2×C4#58512yes—
1415C2×C4#58512yes—
1416C22—22no—
1417C22—22no—
1418C22—22no—
1419C22—22no—
1420C22—22no—
1421C22—22no—
1422C22—44no—
1423C22—44no—
1424C22—44no—
1425C22—44no—
1426C22—44no—
1427C22—44no—
1428C22—44no—
1429C22#355914yes—
1430C22C23×#4111yescharacteristic
1431C22C22×H(5,𝔽2)11yescharacteristic
1432C22C22×2−1+411yescharacteristic
1433C22C22×2−1+411yescharacteristic
1434C22C2×#58511yescharacteristic
1435C22C2×#58511yescharacteristic
1436C22C2×#58511yescharacteristic
1437C4—22no—
1438C4—22no—
1439C4—22no—
1440C4—22no—
1441C4—22no—
1442C4—24no—
1443C4—22no—
1444C4—22no—
1445C4—24no—
1446C4—22no—
1447C4—22no—
1448C4—42no—
1449C4—42no—
1450C4—44no—
1451C4—41no—
1452C4—42no—
1453C4—42no—
1454C4—41no—
1455C4—42no—
1456C4—44no—
1457C4—44no—
1458C4—42no—
1459C4—44no—
1460C4—44no—
1461C4—41no—
1462C4—44no—
1463C4—41no—
1464C4—44no—
1465C4#352314yes—
1466C2—24no—
1467C2—84no—
1468C2C2×#355911yescharacteristic
1469C2#6275211yescharacteristic
1470C2C2×#352311yescharacteristic
1471C2#6280011yescharacteristic
1472C2#6281411yescharacteristic
1473C2#6283111yescharacteristic
1474C2#6283511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2856C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #60011C2semidirect
2. #59109C2semidirect
3. #46098C2semidirect
4. #46091C2semidirect
5. #45964C2semidirect
6. #45948C2semidirect
7. #39803C2semidirect
8. #39756C2semidirect
9. #39749C2semidirect
10. #39683C2semidirect
11. #39637C2semidirect
12. #39611C2semidirect
13. #38828C2semidirect
14. #38771C2semidirect
15. #38484C2semidirect
16. #38427C2semidirect
17. #38335C2semidirect
18. #38175C2semidirect
19. #37571C2semidirect
20. #37353C2semidirect
21. #37337C2semidirect
22. #36640C2semidirect
24. #36544C2semidirect
25. #36200C2semidirect
26. #36200C2semidirect
27. #36186C2semidirect
28. #35304C2semidirect
30. #34489C2semidirect
31. C2×#2295C2semidirect

Maximal subgroups

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

subgroupindex
#600112
#591092
#460982
#460912
#459642
#459482
#398032
#397562
#397492
#396832
#396372
#396112
#388282
#387712
#384842
#384272
#383352
#381752
#375712
#373532
#373372
#366402
#366312
#365442
#362002
#361862
#353042
#352712
#344892
C2×#22952