Finite Group Databasebeta

← #7647159

Subgroups — #7647159

Order 512.

4085 conjugacy classes of subgroups.

The subgroup lattice has 1524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42864C212yesmaximal, complemented
2#42832C212yesmaximal
3#42770C212yesmaximal
4#42744C212yesmaximal, complemented
5#41903C214yesmaximal, complemented
6#41845C214yesmaximal
7#39802C212yesmaximal, complemented
8#39762C211yesmaximal, characteristic, complemented
9#39724C211yesmaximal, characteristic
10#39626C211yesmaximal, characteristic, complemented
11#39599C211yesmaximal, characteristic
12#39299C212yesmaximal
13#39170C211yesmaximal, characteristic, complemented
14#39159C211yesmaximal, characteristic
15#38984C211yesmaximal, characteristic, complemented
16#38943C211yesmaximal, characteristic
17#38287C212yesmaximal
18#38239C212yesmaximal, complemented
19#37630C212yesmaximal, complemented
20#37598C212yesmaximal
21#37180C214yesmaximal
22#37163C214yesmaximal, complemented
23#35650C212yesmaximal
24#35643C212yesmaximal, complemented
25#35291C211yesmaximal, characteristic
26#35221C212yesmaximal, complemented
27#35217C212yesmaximal
28#35217C212yesmaximal
29#35199C211yesmaximal, characteristic, complemented
30#35187C212yesmaximal, complemented
31#34951C211yesmaximal, characteristic, complemented
32#34916C211yesmaximal, characteristic
33#34328C211yesmaximal, characteristic, complemented
34C4×#557C211yesmaximal, characteristic, complemented
35#34085C211yesmaximal, characteristic
36C2×#557C2211yescharacteristic
37C2×#557C2211yescharacteristic
38C2×#533C2211yescharacteristic
39#2866C2214yes—
40#2864C2214yes—
41#2863C2214yes—
42#2863C2214yes—
43#2863C2212yes—
44#2862C2211yescharacteristic
45#2862C2212yes—
46#2859C2211yescharacteristic
47#2857C2211yescharacteristic
48#2857C2211yescharacteristic
49#2839C2214yes—
50#2839C2214yes—
51#2839C2214yes—
52#2838C2214yes—
53#2809C2214yes—
54#2806C2214yes—
55#2805C2214yes—
56#2793C2214yes—
57#2792C2214yes—
58#2789C2214yes—
59#2789C2214yes—
60#2783C2214yes—
61#2783C2214yes—
62#2776C2214yes—
63#2776C2214yes—
64#2776C2214yes—
65#2776C2214yes—
66#2775C2214yes—
67#2769C2214yes—
68#2769C2214yes—
69#2767C2214yes—
70#2767C2214yes—
71#2767C2214yes—
72#2762C2214yes—
73#2762C2214yes—
74#2762C2214yes—
75#2758C2214yes—
76#2758C2214yes—
77#2745C2214yes—
78#2744C2214yes—
79#2726C2214yes—
80#2719C2214yes—
81#2719C2214yes—
82#2719C2214yes—
83#2704C2214yes—
84#2690C2214yes—
85#2666C2214yes—
86#2666C2214yes—
87#2666C2214yes—
88#2666C2214yes—
89#2660C2212yes—
90#2655C2214yes—
91#2655C2214yes—
92#2655C2214yes—
93#2655C2214yes—
94#2654C2214yes—
95#2650C2214yes—
96#2650C2214yes—
97#2647C2214yes—
98#2645C2212yes—
99#2645C2212yes—
100#2645C2212yes—
101#2645C2214yes—
102#2642C2212yes—
103#2642C2212yes—
104#2642C2212yes—
105#2629C2212yes—
106#2625C2212yes—
107#2621C2212yes—
108#2612C2214yes—
109#2605C2214yes—
110#2605C2214yes—
111#2594C2214yes—
112#2594C2214yes—
113#2590C2214yes—
114#2590C2212yes—
115#2589C2212yes—
116#2588C2212yes—
117#2588C2214yes—
118#2588C2214yes—
119#2588C2214yes—
120#2587C2212yes—
121#2586C2214yes—
122#2585C2214yes—
123#2585C2214yes—
124#2584C2212yes—
125#2582C2211yescharacteristic
126#2582C2212yes—
127#2582C2211yescharacteristic
128#2582C2212yes—
129#2581C2212yes—
130#2581C2212yes—
131#2571C2212yes—
132#2570C2214yes—
133#2568C2211yescharacteristic
134#2568C2212yes—
135#2568C2211yescharacteristic
136#2568C2212yes—
137#2568C2212yes—
138#2567C2212yes—
139#2565C2212yes—
140#2552C2211yescharacteristic
141#2552C2212yes—
142#2551C2211yescharacteristic
143#2550C2212yes—
144#2550C2212yes—
145#2546C2211yescharacteristic
146#2546C2212yes—
147#2546C2211yescharacteristic
148#2546C2212yes—
149#2533C2214yes—
150#2533C2214yes—
151#2532C2214yes—
152#2532C2214yes—
153#2529C2214yes—
154#2528C2214yes—
155#2525C2214yes—
156#2525C2214yes—
157#2524C2214yes—
158#2524C2214yes—
159#2524C2214yes—
160#2520C2214yes—
161#2520C2214yes—
162#2514C2212yes—
163#2514C2212yes—
164#2514C2212yes—
165#2514C2212yes—
166#2514C2212yes—
167#2514C2214yes—
168#2514C2212yes—
169#2514C2212yes—
170#2511C2214yes—
171#2511C2212yes—
172#2511C2212yes—
173#2511C2211yescharacteristic
174#2509C2212yes—
175#2509C2214yes—
176#2509C2212yes—
177#2509C2212yes—
178#2509C2212yes—
179#2508C2212yes—
180#2508C2212yes—
181#2508C2214yes—
182#2508C2212yes—
183#2507C2212yes—
184#2507C2211yescharacteristic
185#2497C2212yes—
186#2497C2211yescharacteristic
187#2495C2212yes—
188#2495C2212yes—
189#2495C2212yes—
190#2494C2212yes—
191#2492C2212yes—
192#2492C2211yescharacteristic
193#2492C2212yes—
194#2489C2212yes—
195#2489C2212yes—
196#2489C2212yes—
197#2453C2212yes—
198#2453C2212yes—
199#2453C2212yes—
200#2453C2212yes—
201#2451C2212yes—
202#2451C2212yes—
203#2451C2212yes—
204#2451C2211yescharacteristic
205#2451C2212yes—
206#2451C2212yes—
207#2446C2212yes—
208#2446C2212yes—
209#2446C2212yes—
210#2446C2212yes—
211#2446C2212yes—
212#2446C2211yescharacteristic
213#2446C2212yes—
214#2429C2212yes—
215#2429C2212yes—
216#2429C2212yes—
217#2429C2211yescharacteristic
218#2423C2211yescharacteristic
219#2421C2212yes—
220#2421C2212yes—
221#2421C2212yes—
222#2402C2212yes—
223#2402C2214yes—
224#2396C2212yes—
225#2371C2214yes—
226#2370C2212yes—
227#2370C2212yes—
228#2370C2214yes—
229#2365C2211yescharacteristic
230#2365C2212yes—
231#2365C2211yescharacteristic
232#2365C2212yes—
233#2356C2212yes—
234#2356C2212yes—
235#2355C2211yescharacteristic
236#2355C2211yescharacteristic
237#2355C2211yescharacteristic
238#2355C2212yes—
239#2351C2212yes—
240Q8×C4⋊C4C2211yescharacteristic
241#2336C2214yes—
242#2336C2212yes—
243#2336C2212yes—
244#2332C2212yes—
245#2332C2212yes—
246#2331C2211yescharacteristic
247#2331C2211yescharacteristic
248#2331C2212yes—
249#2331C2212yes—
250#2331C2212yes—
251#2330C2212yes—
252#2327C2212yes—
253#2327C2212yes—
254#2327C2211yescharacteristic
255#2327C2211yescharacteristic
256#2323C2211yescharacteristic
257#2323C2211yescharacteristic
258#2323C2211yescharacteristic
259#2323C2211yescharacteristic
260#2323C2212yes—
261#2323C2212yes—
262#2323C2212yes—
263#2320C2212yes—
264#2320C2212yes—
265#2320C2212yes—
266#2320C2212yes—
267C4×C4⋊Q8C2211yescharacteristic
268C4×C4⋊Q8C2211yescharacteristic
269C4×C4⋊Q8C2212yes—
270C4×C4⋊Q8C2211yescharacteristic
271C4×C4⋊Q8C2211yescharacteristic
272C4×C4⋊Q8C2212yes—
273C4×#125C2212yes—
274C4×#125C2214yes—
275C4×#125C2212yes—
276C4×#125C2212yes—
277C4×C22⋊Q8C2211yescharacteristic
278C4×C22⋊Q8C2211yescharacteristic
279#2298C2212yes—
280#2298C2212yes—
281#2298C2212yes—
282#2295C2211yescharacteristic
283#2295C2211yescharacteristic
284#2295C2212yes—
285#2295C2211yescharacteristic
286#2295C2212yes—
287#2295C2212yes—
288#2295C2212yes—
289#2295C2212yes—
290#2295C2212yes—
291#2283C2211yescharacteristic
292#2276C2212yes—
293C42×Q8C2211yescharacteristic
294C42×Q8C2211yescharacteristic
295C42×Q8C2211yescharacteristic
296C42×Q8C2212yes—
297C42×Q8C2212yes—
298C4×#117C2211yescharacteristic
299#557—28no—
300#557—28no—
301#533—28no—
302C2×C4⋊Q8C2311yescharacteristic
303C2×C4⋊Q8C2311yescharacteristic
304C2×C4⋊Q8C2312yes—
305C2×C4⋊Q8C2311yescharacteristic
306C2×C4⋊Q8C2311yescharacteristic
307C2×C4⋊Q8C2312yes—
308C2×C4⋊Q8C2311yescharacteristic
309C2×C4⋊Q8C2312yes—
310C2×C4⋊Q8C2311yescharacteristic
311C2×C4⋊Q8C2312yes—
312C2×C4⋊Q8C2312yes—
313C2×C4⋊Q8C2312yes—
314C2×#125C2312yes—
315C2×#125C2314yes—
316C2×#125C2312yes—
317C2×#125C2312yes—
318C2×#125C2314yes—
319C2×#125C2312yes—
320C2×#125C2312yes—
321C2×C22⋊Q8C2311yescharacteristic
322C2×C22⋊Q8C2311yescharacteristic
323C2×C22⋊Q8C2311yescharacteristic
324C2×C22⋊Q8C2312yes—
325C2×C22⋊Q8C2312yes—
326C2×C22⋊Q8C2312yes—
327C2×C22⋊Q8C2311yescharacteristic
328C2×C4×Q8C2311yescharacteristic
329C2×C4×Q8C2312yes—
330C2×C4×Q8C2311yescharacteristic
331C2×C4×Q8C2311yescharacteristic
332C2×C4×Q8C2312yes—
333C2×C4×Q8C2312yes—
334C2×C4×Q8C2311yescharacteristic
335C2×C4×Q8C2312yes—
336C2×C4×Q8C2312yes—
337C2×C4×Q8C2311yescharacteristic
338C2×C4×Q8C2312yes—
339C2×C4×Q8C2312yes—
340C2×C4×Q8C2311yescharacteristic
341C2×C4×Q8C2312yes—
342C2×C4×Q8C2311yescharacteristic
343C2×C4×Q8C2312yes—
344C2×C4×Q8C2312yes—
345C2×C4×Q8C2311yescharacteristic
346C2×C4×Q8C2311yescharacteristic
347C2×C4×Q8C2312yes—
348C2×C4×Q8C2311yescharacteristic
349C2×#117C2311yescharacteristic
350C2×#117C2312yes—
351C2×#117C2311yescharacteristic
352C22×C42C2311yescharacteristic
353#401C2314yes—
354#401C2314yes—
355#401C2314yes—
356#401C2314yes—
357#401C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#400C2312yes—
372#400C2314yes—
373#400C2314yes—
374#400C2314yes—
375#400C2314yes—
376#400C2314yes—
377#400C2314yes—
378#400C2314yes—
379#400C2314yes—
380#400C2314yes—
381#400C2314yes—
382#400C2314yes—
383#400C2314yes—
384#400C2314yes—
385#400C2314yes—
386#400C2312yes—
387#400C2314yes—
388#400C2314yes—
389#400C2312yes—
390#400C2314yes—
391#400C2312yes—
392#400C2314yes—
393#400C2312yes—
394#400C2314yes—
395#400C2314yes—
396#400C2314yes—
397#400C2314yes—
398#400C2314yes—
399#400C2314yes—
400#400C2314yes—
401#399C2312yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2314yes—
406#398C2314yes—
407#398C2314yes—
408#398C2314yes—
409#398C2314yes—
410#398C2314yes—
411#398C2314yes—
412#398C2312yes—
413#398C2312yes—
414#398C2314yes—
415#398C2314yes—
416#398C2314yes—
417#398C2314yes—
418#398C2314yes—
419#398C2314yes—
420#398C2314yes—
421#398C2314yes—
422#398C2314yes—
423#398C2314yes—
424#398C2314yes—
425#398C2314yes—
426#398C2312yes—
427#398C2312yes—
428#398C2314yes—
429#398C2312yes—
430#398C2312yes—
431#398C2314yes—
432#398C2314yes—
433#398C2314yes—
434#398C2314yes—
435#397C2314yes—
436#397C2314yes—
437#397C2314yes—
438#397C2314yes—
439#397C2314yes—
440#397C2314yes—
441#396C2314yes—
442#396C2312yes—
443#396C2312yes—
444#396C2314yes—
445#396C2314yes—
446#395C2314yes—
447#395C2314yes—
448#395C2314yes—
449#395C2314yes—
450#395C2314yes—
451#395C2314yes—
452#395C2314yes—
453#395C2312yes—
454#395C2314yes—
455#393C2314yes—
456#393C2312yes—
457#391C2312yes—
458#391C2312yes—
459#391C2311yescharacteristic
460#391C2312yes—
461#391C2312yes—
462#391C2312yes—
463#391C2312yes—
464#391C2312yes—
465#391C2311yescharacteristic
466#391C2312yes—
467#391C2312yes—
468#391C2314yes—
469#391C2312yes—
470#391C2311yescharacteristic
471#391C2312yes—
472#391C2311yescharacteristic
473#391C2312yes—
474#391C2312yes—
475#391C2312yes—
476#391C2312yes—
477#391C2312yes—
478#391C2312yes—
479#391C2312yes—
480#391C2314yes—
481#391C2314yes—
482#391C2314yes—
483#391C2314yes—
484#391C2312yes—
485#391C2312yes—
486#391C2311yescharacteristic
487#391C2312yes—
488#391C2311yescharacteristic
489#391C2311yescharacteristic
490#391C2312yes—
491#391C2312yes—
492#391C2311yescharacteristic
493#391C2312yes—
494#391C2314yes—
495#391C2314yes—
496#391C2312yes—
497#391C2312yes—
498#391C2314yes—
499#391C2312yes—
500#391C2312yes—
501#391C2312yes—
502#391C2314yes—
503#391C2314yes—
504#391C2312yes—
505#391C2314yes—
506#391C2312yes—
507#391C2311yescharacteristic
508#391C2314yes—
509#391C2312yes—
510#391C2311yescharacteristic
511#389C2311yescharacteristic
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2314yes—
518#389C2314yes—
519#389C2311yescharacteristic
520#389C2314yes—
521#389C2314yes—
522#389C2312yes—
523#389C2314yes—
524#389C2314yes—
525#389C2312yes—
526#389C2312yes—
527#389C2312yes—
528#389C2312yes—
529#389C2312yes—
530#389C2311yescharacteristic
531#389C2311yescharacteristic
532#389C2312yes—
533#389C2312yes—
534#389C2314yes—
535#389C2314yes—
536#389C2312yes—
537#389C2312yes—
538#389C2314yes—
539#389C2311yescharacteristic
540#389C2312yes—
541#389C2312yes—
542#389C2312yes—
543#389C2311yescharacteristic
544#389C2312yes—
545#389C2314yes—
546#389C2311yescharacteristic
547#389C2311yescharacteristic
548#389C2312yes—
549#389C2312yes—
550#389C2312yes—
551#389C2312yes—
552#389C2314yes—
553#389C2311yescharacteristic
554#389C2312yes—
555#389C2312yes—
556#389C2312yes—
557#389C2314yes—
558#389C2314yes—
559#389C2312yes—
560#389C2314yes—
561#389C2314yes—
562#389C2314yes—
563#389C2312yes—
564#389C2312yes—
565#389C2312yes—
566#389C2312yes—
567#389C2314yes—
568#389C2312yes—
569#389C2312yes—
570#389C2312yes—
571#389C2312yes—
572#389C2311yescharacteristic
573#389C2314yes—
574#389C2312yes—
575#389C2314yes—
576#389C2314yes—
577#388C2312yes—
578#388C2312yes—
579#388C2312yes—
580#388C2312yes—
581#388C2312yes—
582#388C2312yes—
583#388C2312yes—
584#388C2312yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2312yes—
592#388C2312yes—
593#388C2312yes—
594#388C2312yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2312yes—
612#387C2312yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2312yes—
623#387C2314yes—
624#387C2314yes—
625#387C2312yes—
626#387C2312yes—
627#387C2312yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2312yes—
633#387C2312yes—
634#387C2312yes—
635#387C2312yes—
636#387C2314yes—
637#387C2314yes—
638#387C2314yes—
639#387C2312yes—
640#387C2314yes—
641#387C2312yes—
642#387C2312yes—
643#387C2312yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2312yes—
648#387C2314yes—
649#387C2312yes—
650#387C2314yes—
651#387C2314yes—
652#387C2314yes—
653#387C2314yes—
654#387C2314yes—
655#387C2314yes—
656#387C2314yes—
657#387C2312yes—
658#387C2314yes—
659#387C2312yes—
660#387C2314yes—
661#387C2314yes—
662#387C2314yes—
663#387C2312yes—
664#387C2312yes—
665#387C2312yes—
666#387C2312yes—
667#387C2312yes—
668#387C2312yes—
669#387C2312yes—
670#387C2312yes—
671#387C2312yes—
672#387C2314yes—
673#387C2312yes—
674#387C2312yes—
675#387C2312yes—
676#387C2312yes—
677#387C2312yes—
678#387C2314yes—
679#387C2314yes—
680#387C2314yes—
681#387C2314yes—
682#387C2314yes—
683#387C2314yes—
684#387C2314yes—
685#387C2314yes—
686#387C2314yes—
687#387C2314yes—
688#385C2312yes—
689#385C2312yes—
690#384C2311yescharacteristic
691#384C2312yes—
692#384C2311yescharacteristic
693#384C2311yescharacteristic
694#384C2312yes—
695#384C2311yescharacteristic
696#384C2314yes—
697#383C2314yes—
698#383C2314yes—
699#383C2314yes—
700#383C2314yes—
701#383C2312yes—
702#383C2314yes—
703#383C2314yes—
704#383C2314yes—
705#383C2314yes—
706#382C2312yes—
707#382C2312yes—
708#382C2312yes—
709#382C2314yes—
710#382C2311yescharacteristic
711#382C2314yes—
712#382C2312yes—
713#382C2314yes—
714#382C2314yes—
715#382C2314yes—
716#382C2311yescharacteristic
717#382C2314yes—
718#382C2312yes—
719#382C2314yes—
720#382C2312yes—
721#382C2312yes—
722#382C2312yes—
723#382C2314yes—
724#381C2312yes—
725#380C2311yescharacteristic
726#380C2311yescharacteristic
727#380C2311yescharacteristic
728#380C2312yes—
729#380C2312yes—
730#380C2312yes—
731#380C2312yes—
732#380C2311yescharacteristic
733C4×C4⋊C4C2312yes—
734C4×C4⋊C4C2314yes—
735C4×C4⋊C4C2311yescharacteristic
736C4×C4⋊C4C2312yes—
737C4×C4⋊C4C2314yes—
738C4×C4⋊C4C2312yes—
739C4×C4⋊C4C2311yescharacteristic
740C4×C4⋊C4C2312yes—
741C4×C4⋊C4C2312yes—
742C4×C4⋊C4C2314yes—
743C4×C4⋊C4C2314yes—
744C4×C4⋊C4C2314yes—
745C4×C4⋊C4C2312yes—
746C4×C4⋊C4C2312yes—
747C4×C4⋊C4C2314yes—
748C4×C4⋊C4C2314yes—
749C4×C4⋊C4C2311yescharacteristic
750C4×C4⋊C4C2311yescharacteristic
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2314yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2311yescharacteristic
762C4×C4⋊C4C2314yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2311yescharacteristic
766C4×C4⋊C4C2311yescharacteristic
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2314yes—
774C4×C4⋊C4C2314yes—
775C4×C4⋊C4C2314yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2311yescharacteristic
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2311yescharacteristic
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2314yes—
785C4×C4⋊C4C2314yes—
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2311yescharacteristic
788C4×C4⋊C4C2311yescharacteristic
789C4×C4⋊C4C2312yes—
790C4×C4⋊C4C2311yescharacteristic
791C4×C22⋊C4C2311yescharacteristic
792C4×C22⋊C4C2311yescharacteristic
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2311yescharacteristic
796C4×C22⋊C4C2311yescharacteristic
797C4×C22⋊C4C2312yes—
798#376C2311yescharacteristic
799#376C2312yes—
800#376C2312yes—
801#376C2312yes—
802#376C2312yes—
803#376C2311yescharacteristic
804#376C2314yes—
805#376C2314yes—
806#376C2314yes—
807C43C2312yes—
808C43C2312yes—
809C43C2312yes—
810C43C2314yes—
811C43C2311yescharacteristic
812C43C2311yescharacteristic
813C22×Q8C2411yescharacteristic
814C22×Q8C2411yescharacteristic
815C22×Q8C2412yes—
816C22×Q8C2411yescharacteristic
817C22×Q8C2412yes—
818C22×Q8C2411yescharacteristic
819C22×Q8C2412yes—
820C22×Q8C2412yes—
821C22×Q8C2414yes—
822C23×C4C2411yescharacteristic
823C23×C4C2411yescharacteristic
824C23×C4C2411yescharacteristic
825C4⋊Q8—24no—
826C4⋊Q8—28no—
827C4⋊Q8—24no—
828C4⋊Q8—24no—
829C4⋊Q8—24no—
830C4⋊Q8—24no—
831C4⋊Q8—28no—
832C4⋊Q8—44no—
833C4⋊Q8—44no—
834C4⋊Q8—44no—
835C4⋊Q8—42no—
836C4⋊Q8—44no—
837#125—28no—
838#125—28no—
839#125—216no—
840#125—216no—
841#125—28no—
842#125—44no—
843#125—44no—
844C22⋊Q8—24no—
845C22⋊Q8—24no—
846C22⋊Q8—28no—
847C22⋊Q8—24no—
848C22⋊Q8—44no—
849C22⋊Q8—44no—
850C22⋊Q8—42no—
851C4×Q8—28no—
852C4×Q8—28no—
853C4×Q8—28no—
854C4×Q8—24no—
855C4×Q8—28no—
856C4×Q8—24no—
857C4×Q8—24no—
858C4×Q8—28no—
859C4×Q8—28no—
860C4×Q8—24no—
861C4×Q8—24no—
862C4×Q8—24no—
863C4×Q8—28no—
864C4×Q8—44no—
865C4×Q8—42no—
866C4×Q8—42no—
867C4×Q8—42no—
868C4×Q8—44no—
869C4×Q8—44no—
870C4×Q8—44no—
871C4×Q8#4118yes—
872#117—28no—
873#117—24no—
874#117—42no—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2411yescharacteristic
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2411yescharacteristic
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2411yescharacteristic
888C2×C4⋊C4C2411yescharacteristic
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2411yescharacteristic
899C2×C4⋊C4C2411yescharacteristic
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2411yescharacteristic
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2411yescharacteristic
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2414yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2411yescharacteristic
915C2×C4⋊C4C2412yes—
916C2×C4⋊C4C2411yescharacteristic
917C2×C4⋊C4C2411yescharacteristic
918C2×C4⋊C4C2412yes—
919C2×C4⋊C4C2414yes—
920C2×C4⋊C4C2412yes—
921C2×C4⋊C4C2414yes—
922C2×C4⋊C4C2414yes—
923C2×C4⋊C4C2412yes—
924C2×C4⋊C4C2412yes—
925C2×C4⋊C4C2412yes—
926C2×C4⋊C4C2412yes—
927C2×C4⋊C4C2412yes—
928C2×C4⋊C4C2414yes—
929C2×C4⋊C4C2414yes—
930C2×C4⋊C4C2414yes—
931C2×C4⋊C4C2414yes—
932C2×C4⋊C4C2414yes—
933C2×C4⋊C4C2414yes—
934C2×C4⋊C4C2414yes—
935C2×C4⋊C4C2414yes—
936C2×C4⋊C4C2412yes—
937C2×C4⋊C4C2412yes—
938C2×C4⋊C4C2414yes—
939C2×C4⋊C4C2414yes—
940C2×C4⋊C4C2414yes—
941C2×C4⋊C4C2414yes—
942C2×C4⋊C4C2412yes—
943C2×C4⋊C4C2412yes—
944C2×C4⋊C4C2412yes—
945C2×C4⋊C4C2412yes—
946C2×C4⋊C4C2414yes—
947C2×C4⋊C4C2412yes—
948C2×C4⋊C4C2414yes—
949C2×C4⋊C4C2412yes—
950C2×C4⋊C4C2412yes—
951C2×C4⋊C4C2412yes—
952C2×C4⋊C4C2412yes—
953C2×C4⋊C4C2412yes—
954C2×C4⋊C4C2412yes—
955C2×C4⋊C4C2412yes—
956C2×C4⋊C4C2414yes—
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2414yes—
959C2×C4⋊C4C2411yescharacteristic
960C2×C4⋊C4C2412yes—
961C2×C4⋊C4C2411yescharacteristic
962C2×C22⋊C4C2412yes—
963C2×C22⋊C4C2412yes—
964C2×C22⋊C4C2411yescharacteristic
965C2×C22⋊C4C2411yescharacteristic
966C2×C22⋊C4C2412yes—
967C2×C22⋊C4C2411yescharacteristic
968C2×C22⋊C4C2411yescharacteristic
969C2×C22⋊C4C2412yes—
970C2×C22⋊C4C2414yes—
971C2×C22⋊C4C2414yes—
972C2×C22⋊C4C2412yes—
973C2×C22⋊C4C2412yes—
974C2×C22⋊C4C2412yes—
975C2×C22⋊C4C2412yes—
976C2×C42—24no—
977C2×C42C2411yescharacteristic
978C2×C42C2412yes—
979C2×C42C2411yescharacteristic
980C2×C42C2411yescharacteristic
981C2×C42C2411yescharacteristic
982C2×C42C2412yes—
983C2×C42C2414yes—
984C2×C42C2414yes—
985C2×C42C2412yes—
986C2×C42C2412yes—
987C2×C42C2412yes—
988C2×C42C2411yescharacteristic
989C2×C42C2411yescharacteristic
990C2×C42C2412yes—
991C2×C42C2412yes—
992C2×C42C2412yes—
993C2×C42C2412yes—
994C2×C42C2414yes—
995C2×C42C2414yes—
996C2×C42C2411yescharacteristic
997C2×C42C2411yescharacteristic
998C2×C42C2412yes—
999C2×C42C2411yescharacteristic
1000C2×C42C2411yescharacteristic
1001C2×C42C2412yes—
1002C2×C42C2412yes—
1003C2×C42C2414yes—
1004C2×C42C2414yes—
1005C2×C42C2412yes—
1006C2×C42C2414yes—
1007C2×C42C2412yes—
1008C2×C42C2412yes—
1009C2×C42C2412yes—
1010C2×C42C2411yescharacteristic
1011C2×C42C2411yescharacteristic
1012C2×C42C2411yescharacteristic
1013C2×C42C2411yescharacteristic
1014C2×C42C2412yes—
1015C2×C42C2412yes—
1016C2×C42C2414yes—
1017C2×C42C2412yes—
1018C2×C42C2414yes—
1019C2×C42C2414yes—
1020C2×C42C2412yes—
1021C2×C42C2411yescharacteristic
1022C2×C42C2411yescharacteristic
1023#95C2412yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2411yescharacteristic
1027#95C2411yescharacteristic
1028#95C2411yescharacteristic
1029#95C2411yescharacteristic
1030#95C2411yescharacteristic
1031#95C2411yescharacteristic
1032#95C2411yescharacteristic
1033#95C2411yescharacteristic
1034#95C2414yes—
1035#95C2412yes—
1036#95C2412yes—
1037#95C2412yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2412yes—
1041#95C2412yes—
1042#95C2412yes—
1043#95C2412yes—
1044#95C2412yes—
1045#95C2414yes—
1046#95C2412yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2412yes—
1051#95C2412yes—
1052#95C2412yes—
1053#95C2412yes—
1054#95C2412yes—
1055#95C2412yes—
1056#95C2414yes—
1057#95C2414yes—
1058#95C2412yes—
1059#95C2412yes—
1060#95C2412yes—
1061#95C2412yes—
1062#95C2412yes—
1063#95C2412yes—
1064#95C2412yes—
1065#95C2412yes—
1066#95C2412yes—
1067#95C2414yes—
1068#95C2412yes—
1069#95C2414yes—
1070#95C2412yes—
1071#95C2412yes—
1072#95C2412yes—
1073#95C2414yes—
1074#95C2412yes—
1075#95C2414yes—
1076#95C2414yes—
1077#95C2412yes—
1078#95C2412yes—
1079#95C2412yes—
1080#95C2414yes—
1081#95C2414yes—
1082#95C2414yes—
1083#95C2414yes—
1084#95C2414yes—
1085#95C2414yes—
1086#95C2414yes—
1087#95C2414yes—
1088#95C2414yes—
1089#95C2412yes—
1090#95C2412yes—
1091#95C2412yes—
1092#95C2412yes—
1093#95C2412yes—
1094#95C2414yes—
1095#95C2414yes—
1096#95C2412yes—
1097#95C2412yes—
1098#95C2412yes—
1099#95C2412yes—
1100#95C2412yes—
1101#95C2414yes—
1102#95C2412yes—
1103#95C2412yes—
1104#95C2414yes—
1105#95C2412yes—
1106#95C2414yes—
1107#95C2414yes—
1108#95C2414yes—
1109#95C2414yes—
1110#95C2414yes—
1111#95C2414yes—
1112#95C2414yes—
1113#95C2414yes—
1114#95C2414yes—
1115#95C2414yes—
1116#95C2414yes—
1117#95C2414yes—
1118#95C2414yes—
1119#95C2414yes—
1120#95C2414yes—
1121#95C2414yes—
1122#95C2414yes—
1123#95C2414yes—
1124#95C2414yes—
1125#95C2414yes—
1126#95C2414yes—
1127C24C2511yescharacteristic
1128C2×Q8—22no—
1129C2×Q8—22no—
1130C2×Q8—24no—
1131C2×Q8—22no—
1132C2×Q8—24no—
1133C2×Q8—24no—
1134C2×Q8—22no—
1135C2×Q8—22no—
1136C2×Q8—24no—
1137C2×Q8—24no—
1138C2×Q8—22no—
1139C2×Q8—22no—
1140C2×Q8—24no—
1141C2×Q8—22no—
1142C2×Q8—24no—
1143C2×Q8—22no—
1144C2×Q8—24no—
1145C2×Q8—22no—
1146C2×Q8—22no—
1147C2×Q8—42no—
1148C2×Q8—42no—
1149C2×Q8—42no—
1150C2×Q8—42no—
1151C2×Q8—44no—
1152C2×Q8—44no—
1153C2×Q8—44no—
1154C2×Q8C2×#4114yes—
1155C22×C4—22no—
1156C22×C4—22no—
1157C22×C4—22no—
1158C22×C4—22no—
1159C22×C4—22no—
1160C22×C4—22no—
1161C22×C4—22no—
1162C22×C4—41no—
1163C22×C4—41no—
1164C22×C4C2512yes—
1165C22×C4C2511yescharacteristic
1166C22×C4C2511yescharacteristic
1167C22×C4C2511yescharacteristic
1168C22×C4C2512yes—
1169C22×C4C2511yescharacteristic
1170C22×C4C2512yes—
1171C22×C4C2511yescharacteristic
1172C22×C4C2512yes—
1173C22×C4C2514yes—
1174C22×C4C2512yes—
1175C22×C4C2512yes—
1176C22×C4C2512yes—
1177C22×C4C2514yes—
1178C22×C4C2512yes—
1179C22×C4C2514yes—
1180C22×C4C2512yes—
1181C22×C4C2512yes—
1182C22×C4C2511yescharacteristic
1183C22×C4C2511yescharacteristic
1184C22×C4C2512yes—
1185C22×C4C2512yes—
1186C22×C4C2514yes—
1187C22×C4C2511yescharacteristic
1188C22×C4C2511yescharacteristic
1189C22×C4C2512yes—
1190C22×C4C2512yes—
1191C22×C4C2512yes—
1192C22×C4C2511yescharacteristic
1193C22×C4C2511yescharacteristic
1194C22×C4C2512yes—
1195C22×C4C2511yescharacteristic
1196C22×C4C2511yescharacteristic
1197C22×C4C2511yescharacteristic
1198C4⋊C4—24no—
1199C4⋊C4—24no—
1200C4⋊C4—22no—
1201C4⋊C4—24no—
1202C4⋊C4—24no—
1203C4⋊C4—24no—
1204C4⋊C4—24no—
1205C4⋊C4—22no—
1206C4⋊C4—28no—
1207C4⋊C4—24no—
1208C4⋊C4—24no—
1209C4⋊C4—22no—
1210C4⋊C4—28no—
1211C4⋊C4—28no—
1212C4⋊C4—28no—
1213C4⋊C4—24no—
1214C4⋊C4—24no—
1215C4⋊C4—28no—
1216C4⋊C4—28no—
1217C4⋊C4—24no—
1218C4⋊C4—24no—
1219C4⋊C4—22no—
1220C4⋊C4—22no—
1221C4⋊C4—24no—
1222C4⋊C4—22no—
1223C4⋊C4—22no—
1224C4⋊C4—24no—
1225C4⋊C4—28no—
1226C4⋊C4—24no—
1227C4⋊C4—24no—
1228C4⋊C4—28no—
1229C4⋊C4—24no—
1230C4⋊C4—24no—
1231C4⋊C4—22no—
1232C4⋊C4—22no—
1233C4⋊C4—24no—
1234C4⋊C4—22no—
1235C4⋊C4—24no—
1236C4⋊C4—22no—
1237C4⋊C4—24no—
1238C4⋊C4—22no—
1239C4⋊C4—42no—
1240C4⋊C4—42no—
1241C4⋊C4—42no—
1242C4⋊C4—44no—
1243C4⋊C4—42no—
1244C4⋊C4—44no—
1245C4⋊C4—42no—
1246C4⋊C4—42no—
1247C4⋊C4—42no—
1248C4⋊C4—42no—
1249C4⋊C4—42no—
1250C4⋊C4—42no—
1251C4⋊C4—42no—
1252C4⋊C4—42no—
1253C4⋊C4—44no—
1254C4⋊C4—42no—
1255C4⋊C4—44no—
1256C4⋊C4—41no—
1257C4⋊C4—41no—
1258C4⋊C4—42no—
1259C4⋊C4—42no—
1260C4⋊C4—44no—
1261C4⋊C4—42no—
1262C4⋊C4—42no—
1263C4⋊C4—42no—
1264C4⋊C4—42no—
1265C4⋊C4—44no—
1266C4⋊C4—44no—
1267C4⋊C4—44no—
1268C4⋊C4—44no—
1269C4⋊C4—42no—
1270C4⋊C4—44no—
1271C4⋊C4—44no—
1272C4⋊C4—44no—
1273C4⋊C4—44no—
1274C4⋊C4—44no—
1275C4⋊C4—44no—
1276C4⋊C4—42no—
1277C4⋊C4—42no—
1278C4⋊C4—44no—
1279C4⋊C4—44no—
1280C4⋊C4—44no—
1281C4⋊C4—44no—
1282C4⋊C4C2×#4114yes—
1283C4⋊C4C2×#4118yes—
1284C4⋊C42−1+414yes—
1285C22⋊C4—24no—
1286C22⋊C4—24no—
1287C22⋊C4—22no—
1288C22⋊C4—22no—
1289C22⋊C4—24no—
1290C22⋊C4—42no—
1291C22⋊C4—42no—
1292C22⋊C4—42no—
1293C22⋊C4—42no—
1294C22⋊C4—41no—
1295C22⋊C4—41no—
1296C22⋊C4—44no—
1297C22⋊C4—44no—
1298C22⋊C4—42no—
1299C42—22no—
1300C42—22no—
1301C42—22no—
1302C42—24no—
1303C42—28no—
1304C42—24no—
1305C42—28no—
1306C42—24no—
1307C42—22no—
1308C42—22no—
1309C42—24no—
1310C42—24no—
1311C42—24no—
1312C42—28no—
1313C42—24no—
1314C42—28no—
1315C42—22no—
1316C42—22no—
1317C42—22no—
1318C42—22no—
1319C42—24no—
1320C42—24no—
1321C42—22no—
1322C42—24no—
1323C42—42no—
1324C42—41no—
1325C42—41no—
1326C42—42no—
1327C42—42no—
1328C42—42no—
1329C42—44no—
1330C42—41no—
1331C42—41no—
1332C42—42no—
1333C42—44no—
1334C42—44no—
1335C42—42no—
1336C42—42no—
1337C42—44no—
1338C42—44no—
1339C42—42no—
1340C42—42no—
1341C42—44no—
1342C42C2×#4114yes—
1343C42C2×#4118yes—
1344C422−1+414yes—
1345C23—21no—
1346C23—21no—
1347C23—21no—
1348C23—21no—
1349C23—21no—
1350C23—21no—
1351C23—21no—
1352C23C2611yescharacteristic
1353Q8—28no—
1354Q8—44no—
1355Q8—48no—
1356Q8—44no—
1357Q8—44no—
1358Q8—48no—
1359Q8—84no—
1360Q8—84no—
1361Q8—164no—
1362C2×C4—21no—
1363C2×C4—22no—
1364C2×C4—21no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—22no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—21no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—24no—
1383C2×C4—22no—
1384C2×C4—24no—
1385C2×C4—22no—
1386C2×C4—21no—
1387C2×C4—21no—
1388C2×C4—21no—
1389C2×C4—22no—
1390C2×C4—21no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—24no—
1394C2×C4—22no—
1395C2×C4—24no—
1396C2×C4—22no—
1397C2×C4—24no—
1398C2×C4—21no—
1399C2×C4—22no—
1400C2×C4—21no—
1401C2×C4—21no—
1402C2×C4—22no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—22no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—22no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—22no—
1413C2×C4—22no—
1414C2×C4—22no—
1415C2×C4—22no—
1416C2×C4—24no—
1417C2×C4—22no—
1418C2×C4—24no—
1419C2×C4—24no—
1420C2×C4—22no—
1421C2×C4—24no—
1422C2×C4—22no—
1423C2×C4—22no—
1424C2×C4—24no—
1425C2×C4—22no—
1426C2×C4—21no—
1427C2×C4—21no—
1428C2×C4—22no—
1429C2×C4—22no—
1430C2×C4—22no—
1431C2×C4—22no—
1432C2×C4—21no—
1433C2×C4—21no—
1434C2×C4—22no—
1435C2×C4—22no—
1436C2×C4—24no—
1437C2×C4—22no—
1438C2×C4—22no—
1439C2×C4—22no—
1440C2×C4—22no—
1441C2×C4—21no—
1442C2×C4—21no—
1443C2×C4—21no—
1444C2×C4—22no—
1445C2×C4—22no—
1446C2×C4—24no—
1447C2×C4—21no—
1448C2×C4—22no—
1449C2×C4—22no—
1450C2×C4—21no—
1451C2×C4—21no—
1452C2×C4—44no—
1453C2×C4—44no—
1454C2×C4—82no—
1455C2×C4C22×#4114yes—
1456C2×C4C22×#4114yes—
1457C2×C4C22×#4112yes—
1458C2×C4C22×#4112yes—
1459C2×C4C22×#4112yes—
1460C2×C4C2×2−1+412yes—
1461C2×C4C2×2−1+414yes—
1462C2×C4C2×2−1+412yes—
1463C2×C4C2×2−1+412yes—
1464C2×C4C2×2−1+412yes—
1465C2×C4#58512yes—
1466C2×C4#58512yes—
1467C22—41no—
1468C22—41no—
1469C22—41no—
1470C22—41no—
1471C22—41no—
1472C22—41no—
1473C22—41no—
1474C22C23×#4111yescharacteristic
1475C22C22×2−1+411yescharacteristic
1476C22C22×2−1+411yescharacteristic
1477C22C2×#58511yescharacteristic
1478C22C2×#58511yescharacteristic
1479C222−1+611yescharacteristic
1480C222−1+611yescharacteristic
1481C4—22no—
1482C4—24no—
1483C4—24no—
1484C4—22no—
1485C4—24no—
1486C4—22no—
1487C4—41no—
1488C4—42no—
1489C4—44no—
1490C4—42no—
1491C4—42no—
1492C4—42no—
1493C4—41no—
1494C4—42no—
1495C4—41no—
1496C4—42no—
1497C4—44no—
1498C4—42no—
1499C4—41no—
1500C4—41no—
1501C4—42no—
1502C4—42no—
1503C4—41no—
1504C4—41no—
1505C4—42no—
1506C4—44no—
1507C4—41no—
1508C4—41no—
1509C4—42no—
1510C4—44no—
1511C4—42no—
1512C4—42no—
1513C4#346114yes—
1514C4#351814yes—
1515C2—81no—
1516C2C2×#346111yescharacteristic
1517C2C2×#351811yescharacteristic
1518C2#6286111yescharacteristic
1519C2#6294711yescharacteristic
1520C2#6295011yescharacteristic
1521C2#6295611yescharacteristic
1522C2#6296811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC24C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42864C2semidirect
4. #42744C2semidirect
5. #41903C2semidirect
7. #39802C2semidirect
8. #39762C2semidirect
10. #39626C2semidirect
13. #39170C2semidirect
15. #38984C2semidirect
18. #38239C2semidirect
19. #37630C2semidirect
22. #37163C2semidirect
24. #35643C2semidirect
26. #35221C2semidirect
29. #35199C2semidirect
30. #35187C2semidirect
31. #34951C2semidirect
33. #34328C2semidirect
34. C4×#557C2semidirect

Maximal subgroups

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

subgroupindex
#428642
#428322
#427702
#427442
#419032
#418452
#398022
#397622
#397242
#396262
#395992
#392992
#391702
#391592
#389842
#389432
#382872
#382392
#376302
#375982
#371802
#371632
#356502
#356432
#352912
#352212
#352172
#351992
#351872
#349512
#349162
#343282
C4×#5572
#340852