Finite Group Databasebeta

← #7646661

Subgroups — #7646661

Order 512.

4085 conjugacy classes of subgroups.

The subgroup lattice has 1523 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42856C212yesmaximal
2#42850C212yesmaximal, complemented
3#42765C212yesmaximal, complemented
4#42713C212yesmaximal
5#41890C214yesmaximal
6#41786C214yesmaximal, complemented
7#39754C211yesmaximal, characteristic, complemented
8#39724C211yesmaximal, characteristic
9#39673C212yesmaximal, complemented
10#39635C211yesmaximal, characteristic, complemented
11#39599C211yesmaximal, characteristic
12#39283C212yesmaximal
13#39170C211yesmaximal, characteristic, complemented
14#39149C211yesmaximal, characteristic
15#38984C211yesmaximal, characteristic, complemented
16#38933C211yesmaximal, characteristic
17#38279C212yesmaximal
18#38243C212yesmaximal, complemented
19#37598C212yesmaximal
20#37580C212yesmaximal, complemented
21#37115C214yesmaximal
22#37062C214yesmaximal, complemented
23#35656C212yesmaximal, complemented
24#35650C212yesmaximal
25#35291C211yesmaximal, characteristic
26#35221C212yesmaximal, complemented
27#35204C212yesmaximal
28#35204C212yesmaximal
29#35187C212yesmaximal, complemented
30#35187C211yesmaximal, characteristic, complemented
31#34951C211yesmaximal, characteristic, complemented
32#34916C211yesmaximal, characteristic
33#34337C211yesmaximal, characteristic, complemented
34C4×#557C211yesmaximal, characteristic, complemented
35#34085C211yesmaximal, characteristic
36C2×#557C2211yescharacteristic
37C2×#557C2211yescharacteristic
38C2×#533C2211yescharacteristic
39#2865C2214yes—
40#2864C2214yes—
41#2864C2212yes—
42#2864C2214yes—
43#2863C2212yes—
44#2863C2214yes—
45#2862C2211yescharacteristic
46#2859C2211yescharacteristic
47#2857C2211yescharacteristic
48#2857C2211yescharacteristic
49#2839C2214yes—
50#2839C2214yes—
51#2838C2214yes—
52#2833C2214yes—
53#2810C2214yes—
54#2802C2214yes—
55#2802C2214yes—
56#2802C2214yes—
57#2802C2214yes—
58#2794C2214yes—
59#2793C2214yes—
60#2792C2214yes—
61#2791C2214yes—
62#2777C2214yes—
63#2776C2214yes—
64#2776C2214yes—
65#2774C2214yes—
66#2774C2214yes—
67#2772C2214yes—
68#2772C2214yes—
69#2767C2214yes—
70#2767C2214yes—
71#2766C2214yes—
72#2766C2214yes—
73#2766C2214yes—
74#2762C2214yes—
75#2758C2214yes—
76#2755C2214yes—
77#2739C2214yes—
78#2738C2214yes—
79#2726C2214yes—
80#2719C2214yes—
81#2719C2214yes—
82#2719C2214yes—
83#2704C2214yes—
84#2690C2214yes—
85#2666C2214yes—
86#2666C2214yes—
87#2660C2212yes—
88#2655C2214yes—
89#2655C2214yes—
90#2655C2214yes—
91#2655C2214yes—
92#2655C2214yes—
93#2655C2214yes—
94#2655C2214yes—
95#2655C2214yes—
96#2654C2214yes—
97#2654C2214yes—
98#2650C2214yes—
99#2647C2212yes—
100#2647C2212yes—
101#2645C2212yes—
102#2645C2212yes—
103#2645C2212yes—
104#2642C2212yes—
105#2629C2212yes—
106#2625C2212yes—
107#2621C2212yes—
108#2596C2214yes—
109#2596C2214yes—
110#2594C2214yes—
111#2590C2212yes—
112#2590C2214yes—
113#2590C2214yes—
114#2590C2214yes—
115#2590C2214yes—
116#2589C2212yes—
117#2588C2214yes—
118#2588C2214yes—
119#2588C2212yes—
120#2587C2212yes—
121#2586C2214yes—
122#2585C2214yes—
123#2585C2214yes—
124#2585C2214yes—
125#2584C2212yes—
126#2584C2212yes—
127#2582C2211yescharacteristic
128#2582C2212yes—
129#2582C2211yescharacteristic
130#2581C2212yes—
131#2581C2212yes—
132#2581C2212yes—
133#2571C2212yes—
134#2571C2211yescharacteristic
135#2570C2212yes—
136#2570C2212yes—
137#2568C2211yescharacteristic
138#2568C2211yescharacteristic
139#2568C2212yes—
140#2568C2212yes—
141#2565C2212yes—
142#2565C2212yes—
143#2552C2211yescharacteristic
144#2550C2212yes—
145#2546C2212yes—
146#2546C2211yescharacteristic
147#2546C2212yes—
148#2546C2211yescharacteristic
149#2533C2214yes—
150#2533C2214yes—
151#2529C2214yes—
152#2529C2214yes—
153#2528C2214yes—
154#2528C2214yes—
155#2528C2214yes—
156#2528C2214yes—
157#2525C2214yes—
158#2525C2214yes—
159#2524C2214yes—
160#2524C2214yes—
161#2524C2214yes—
162#2520C2214yes—
163#2514C2212yes—
164#2514C2212yes—
165#2514C2212yes—
166#2514C2214yes—
167#2514C2212yes—
168#2514C2212yes—
169#2511C2212yes—
170#2511C2212yes—
171#2511C2212yes—
172#2511C2211yescharacteristic
173#2511C2212yes—
174#2509C2212yes—
175#2509C2212yes—
176#2509C2214yes—
177#2509C2212yes—
178#2508C2212yes—
179#2508C2214yes—
180#2508C2212yes—
181#2508C2212yes—
182#2507C2212yes—
183#2507C2211yescharacteristic
184#2507C2212yes—
185#2497C2212yes—
186#2497C2211yescharacteristic
187#2495C2212yes—
188#2494C2212yes—
189#2494C2212yes—
190#2494C2212yes—
191#2492C2211yescharacteristic
192#2489C2212yes—
193#2489C2212yes—
194#2489C2212yes—
195#2453C2212yes—
196#2453C2212yes—
197#2453C2212yes—
198#2453C2212yes—
199#2453C2212yes—
200#2453C2212yes—
201#2453C2212yes—
202#2451C2212yes—
203#2451C2212yes—
204#2451C2211yescharacteristic
205#2446C2212yes—
206#2446C2212yes—
207#2446C2212yes—
208#2446C2212yes—
209#2446C2212yes—
210#2446C2211yescharacteristic
211#2446C2212yes—
212#2429C2212yes—
213#2429C2211yescharacteristic
214#2429C2212yes—
215#2429C2212yes—
216#2423C2212yes—
217#2423C2212yes—
218#2423C2211yescharacteristic
219#2421C2212yes—
220#2421C2212yes—
221#2421C2212yes—
222#2402C2212yes—
223#2402C2214yes—
224#2396C2212yes—
225#2370C2212yes—
226#2370C2214yes—
227#2370C2214yes—
228#2370C2212yes—
229#2365C2211yescharacteristic
230#2365C2211yescharacteristic
231#2365C2212yes—
232#2365C2212yes—
233#2355C2212yes—
234#2355C2211yescharacteristic
235#2351C2212yes—
236Q8×C4⋊C4C2211yescharacteristic
237Q8×C4⋊C4C2211yescharacteristic
238Q8×C4⋊C4C2212yes—
239Q8×C4⋊C4C2212yes—
240Q8×C4⋊C4C2211yescharacteristic
241#2336C2212yes—
242#2336C2212yes—
243#2332C2212yes—
244#2332C2212yes—
245#2331C2211yescharacteristic
246#2331C2211yescharacteristic
247#2330C2212yes—
248#2330C2214yes—
249#2330C2212yes—
250#2327C2212yes—
251#2327C2211yescharacteristic
252#2327C2211yescharacteristic
253#2327C2212yes—
254#2327C2212yes—
255#2327C2212yes—
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⋊Q8C2212yes—
269C4×C4⋊Q8C2211yescharacteristic
270C4×C4⋊Q8C2212yes—
271C4×C4⋊Q8C2211yescharacteristic
272C4×C4⋊Q8C2211yescharacteristic
273C4×C4⋊Q8C2212yes—
274C4×#125C2212yes—
275C4×#125C2214yes—
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⋊Q8C2312yes—
307C2×C4⋊Q8C2312yes—
308C2×C4⋊Q8C2311yescharacteristic
309C2×C4⋊Q8C2311yescharacteristic
310C2×C4⋊Q8C2311yescharacteristic
311C2×C4⋊Q8C2312yes—
312C2×#125C2312yes—
313C2×#125C2314yes—
314C2×#125C2314yes—
315C2×#125C2312yes—
316C2×#125C2312yes—
317C2×#125C2312yes—
318C2×#125C2312yes—
319C2×C22⋊Q8C2311yescharacteristic
320C2×C22⋊Q8C2311yescharacteristic
321C2×C22⋊Q8C2311yescharacteristic
322C2×C22⋊Q8C2312yes—
323C2×C22⋊Q8C2312yes—
324C2×C22⋊Q8C2312yes—
325C2×C22⋊Q8C2311yescharacteristic
326C2×C4×Q8C2312yes—
327C2×C4×Q8C2311yescharacteristic
328C2×C4×Q8C2311yescharacteristic
329C2×C4×Q8C2311yescharacteristic
330C2×C4×Q8C2312yes—
331C2×C4×Q8C2312yes—
332C2×C4×Q8C2311yescharacteristic
333C2×C4×Q8C2312yes—
334C2×C4×Q8C2311yescharacteristic
335C2×C4×Q8C2312yes—
336C2×C4×Q8C2312yes—
337C2×C4×Q8C2311yescharacteristic
338C2×C4×Q8C2312yes—
339C2×C4×Q8C2311yescharacteristic
340C2×C4×Q8C2312yes—
341C2×C4×Q8C2312yes—
342C2×C4×Q8C2312yes—
343C2×C4×Q8C2312yes—
344C2×C4×Q8C2311yescharacteristic
345C2×C4×Q8C2311yescharacteristic
346C2×C4×Q8C2312yes—
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#400C2314yes—
372#400C2314yes—
373#400C2314yes—
374#400C2314yes—
375#400C2312yes—
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#400C2312yes—
393#400C2314yes—
394#400C2314yes—
395#400C2314yes—
396#400C2314yes—
397#400C2314yes—
398#400C2314yes—
399#400C2314yes—
400#399C2314yes—
401#399C2312yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2314yes—
406#398C2314yes—
407#398C2314yes—
408#398C2312yes—
409#398C2314yes—
410#398C2314yes—
411#398C2314yes—
412#398C2314yes—
413#398C2314yes—
414#398C2314yes—
415#398C2312yes—
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#398C2312yes—
429#398C2314yes—
430#398C2314yes—
431#398C2314yes—
432#398C2312yes—
433#398C2314yes—
434#398C2314yes—
435#398C2314yes—
436#398C2314yes—
437#398C2314yes—
438#398C2314yes—
439#397C2314yes—
440#397C2314yes—
441#397C2314yes—
442#397C2314yes—
443#397C2314yes—
444#397C2314yes—
445#396C2314yes—
446#396C2312yes—
447#396C2312yes—
448#396C2314yes—
449#396C2314yes—
450#395C2314yes—
451#395C2314yes—
452#395C2314yes—
453#395C2314yes—
454#395C2314yes—
455#395C2312yes—
456#393C2312yes—
457#391C2312yes—
458#391C2311yescharacteristic
459#391C2312yes—
460#391C2312yes—
461#391C2312yes—
462#391C2312yes—
463#391C2311yescharacteristic
464#391C2312yes—
465#391C2312yes—
466#391C2311yescharacteristic
467#391C2312yes—
468#391C2312yes—
469#391C2312yes—
470#391C2312yes—
471#391C2311yescharacteristic
472#391C2312yes—
473#391C2311yescharacteristic
474#391C2312yes—
475#391C2312yes—
476#391C2312yes—
477#391C2312yes—
478#391C2312yes—
479#391C2312yes—
480#391C2314yes—
481#391C2314yes—
482#391C2312yes—
483#391C2312yes—
484#391C2311yescharacteristic
485#391C2311yescharacteristic
486#391C2311yescharacteristic
487#391C2312yes—
488#391C2311yescharacteristic
489#391C2312yes—
490#391C2314yes—
491#391C2312yes—
492#391C2312yes—
493#391C2312yes—
494#391C2312yes—
495#391C2312yes—
496#391C2312yes—
497#391C2312yes—
498#391C2311yescharacteristic
499#391C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2314yes—
503#389C2312yes—
504#389C2314yes—
505#389C2312yes—
506#389C2311yescharacteristic
507#389C2311yescharacteristic
508#389C2314yes—
509#389C2312yes—
510#389C2314yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2314yes—
521#389C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2312yes—
525#389C2312yes—
526#389C2314yes—
527#389C2312yes—
528#389C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2311yescharacteristic
532#389C2312yes—
533#389C2312yes—
534#389C2311yescharacteristic
535#389C2312yes—
536#389C2312yes—
537#389C2314yes—
538#389C2311yescharacteristic
539#389C2311yescharacteristic
540#389C2314yes—
541#389C2314yes—
542#389C2312yes—
543#389C2312yes—
544#389C2312yes—
545#389C2311yescharacteristic
546#389C2312yes—
547#389C2312yes—
548#389C2312yes—
549#389C2314yes—
550#389C2311yescharacteristic
551#389C2314yes—
552#389C2312yes—
553#389C2314yes—
554#389C2314yes—
555#389C2312yes—
556#389C2314yes—
557#389C2314yes—
558#389C2314yes—
559#389C2314yes—
560#389C2314yes—
561#389C2314yes—
562#389C2314yes—
563#389C2314yes—
564#389C2314yes—
565#389C2312yes—
566#389C2314yes—
567#389C2312yes—
568#389C2312yes—
569#389C2312yes—
570#389C2312yes—
571#389C2311yescharacteristic
572#389C2312yes—
573#389C2314yes—
574#389C2311yescharacteristic
575#388C2312yes—
576#388C2312yes—
577#388C2312yes—
578#388C2312yes—
579#388C2312yes—
580#388C2312yes—
581#388C2312yes—
582#388C2312yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2312yes—
590#388C2312yes—
591#388C2312yes—
592#388C2312yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#387C2314yes—
598#387C2314yes—
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#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2312yes—
623#387C2314yes—
624#387C2312yes—
625#387C2312yes—
626#387C2312yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2312yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2312yes—
639#387C2312yes—
640#387C2312yes—
641#387C2312yes—
642#387C2314yes—
643#387C2314yes—
644#387C2312yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2312yes—
650#387C2312yes—
651#387C2314yes—
652#387C2314yes—
653#387C2314yes—
654#387C2314yes—
655#387C2312yes—
656#387C2312yes—
657#387C2314yes—
658#387C2314yes—
659#387C2314yes—
660#387C2314yes—
661#387C2314yes—
662#387C2314yes—
663#387C2312yes—
664#387C2314yes—
665#387C2314yes—
666#387C2314yes—
667#387C2314yes—
668#387C2312yes—
669#387C2312yes—
670#387C2312yes—
671#387C2312yes—
672#387C2312yes—
673#387C2312yes—
674#387C2312yes—
675#387C2312yes—
676#387C2312yes—
677#387C2312yes—
678#387C2312yes—
679#387C2312yes—
680#387C2312yes—
681#387C2312yes—
682#387C2312yes—
683#387C2312yes—
684#387C2314yes—
685#387C2314yes—
686#387C2314yes—
687#387C2312yes—
688#387C2314yes—
689#387C2314yes—
690#387C2314yes—
691#387C2314yes—
692#385C2312yes—
693#385C2312yes—
694#384C2311yescharacteristic
695#384C2312yes—
696#384C2312yes—
697#384C2311yescharacteristic
698#384C2312yes—
699#384C2311yescharacteristic
700#384C2311yescharacteristic
701#384C2312yes—
702#384C2314yes—
703#383C2314yes—
704#383C2314yes—
705#383C2314yes—
706#383C2314yes—
707#383C2312yes—
708#383C2314yes—
709#382C2312yes—
710#382C2312yes—
711#382C2314yes—
712#382C2311yescharacteristic
713#382C2312yes—
714#382C2314yes—
715#382C2314yes—
716#382C2311yescharacteristic
717#382C2312yes—
718#382C2312yes—
719#382C2312yes—
720#382C2314yes—
721#382C2314yes—
722#382C2314yes—
723#382C2314yes—
724#382C2312yes—
725#382C2312yes—
726#381C2312yes—
727#380C2311yescharacteristic
728#380C2311yescharacteristic
729#380C2311yescharacteristic
730#380C2312yes—
731#380C2312yes—
732#380C2312yes—
733#380C2312yes—
734#380C2311yescharacteristic
735C4×C4⋊C4C2312yes—
736C4×C4⋊C4C2314yes—
737C4×C4⋊C4C2311yescharacteristic
738C4×C4⋊C4C2312yes—
739C4×C4⋊C4C2312yes—
740C4×C4⋊C4C2314yes—
741C4×C4⋊C4C2311yescharacteristic
742C4×C4⋊C4C2312yes—
743C4×C4⋊C4C2314yes—
744C4×C4⋊C4C2312yes—
745C4×C4⋊C4C2314yes—
746C4×C4⋊C4C2314yes—
747C4×C4⋊C4C2311yescharacteristic
748C4×C4⋊C4C2311yescharacteristic
749C4×C4⋊C4C2314yes—
750C4×C4⋊C4C2314yes—
751C4×C4⋊C4C2314yes—
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2311yescharacteristic
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2311yescharacteristic
765C4×C4⋊C4C2311yescharacteristic
766C4×C4⋊C4C2311yescharacteristic
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2314yes—
770C4×C4⋊C4C2314yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2314yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2314yes—
778C4×C4⋊C4C2314yes—
779C4×C4⋊C4C2314yes—
780C4×C4⋊C4C2311yescharacteristic
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2314yes—
787C4×C4⋊C4C2311yescharacteristic
788C4×C4⋊C4C2311yescharacteristic
789C4×C4⋊C4C2312yes—
790C4×C4⋊C4C2311yescharacteristic
791C4×C4⋊C4C2312yes—
792C4×C22⋊C4C2311yescharacteristic
793C4×C22⋊C4C2311yescharacteristic
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2311yescharacteristic
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2311yescharacteristic
799#376C2311yescharacteristic
800#376C2312yes—
801#376C2312yes—
802#376C2312yes—
803#376C2312yes—
804#376C2311yescharacteristic
805#376C2314yes—
806#376C2314yes—
807C43C2312yes—
808C43C2312yes—
809C43C2314yes—
810C43C2311yescharacteristic
811C43C2311yescharacteristic
812C43C2312yes—
813C22×Q8C2411yescharacteristic
814C22×Q8C2412yes—
815C22×Q8C2411yescharacteristic
816C22×Q8C2412yes—
817C22×Q8C2411yescharacteristic
818C22×Q8C2411yescharacteristic
819C22×Q8C2412yes—
820C22×Q8C2412yes—
821C23×C4C2411yescharacteristic
822C23×C4C2411yescharacteristic
823C23×C4C2411yescharacteristic
824C4⋊Q8—24no—
825C4⋊Q8—28no—
826C4⋊Q8—24no—
827C4⋊Q8—28no—
828C4⋊Q8—24no—
829C4⋊Q8—24no—
830C4⋊Q8—24no—
831C4⋊Q8—28no—
832C4⋊Q8—42no—
833C4⋊Q8—44no—
834#125—28no—
835#125—28no—
836#125—216no—
837#125—216no—
838#125—28no—
839#125—44no—
840#125—44no—
841C22⋊Q8—24no—
842C22⋊Q8—24no—
843C22⋊Q8—24no—
844C22⋊Q8—28no—
845C22⋊Q8—44no—
846C22⋊Q8—44no—
847C22⋊Q8—42no—
848C4×Q8—28no—
849C4×Q8—24no—
850C4×Q8—28no—
851C4×Q8—28no—
852C4×Q8—24no—
853C4×Q8—24no—
854C4×Q8—28no—
855C4×Q8—28no—
856C4×Q8—24no—
857C4×Q8—24no—
858C4×Q8—28no—
859C4×Q8—24no—
860C4×Q8—44no—
861C4×Q8—42no—
862C4×Q8—42no—
863C4×Q8—44no—
864C4×Q8—44no—
865C4×Q8—44no—
866C4×Q8—44no—
867C4×Q8—42no—
868C4×Q8—44no—
869C4×Q8—44no—
870C4×Q8#4118yes—
871#117—28no—
872#117—24no—
873#117—42no—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2411yescharacteristic
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2411yescharacteristic
888C2×C4⋊C4C2411yescharacteristic
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2411yescharacteristic
891C2×C4⋊C4C2411yescharacteristic
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2411yescharacteristic
901C2×C4⋊C4C2411yescharacteristic
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2411yescharacteristic
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2411yescharacteristic
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2414yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2414yes—
915C2×C4⋊C4C2412yes—
916C2×C4⋊C4C2414yes—
917C2×C4⋊C4C2412yes—
918C2×C4⋊C4C2411yescharacteristic
919C2×C4⋊C4C2411yescharacteristic
920C2×C4⋊C4C2412yes—
921C2×C4⋊C4C2414yes—
922C2×C4⋊C4C2412yes—
923C2×C4⋊C4C2414yes—
924C2×C4⋊C4C2412yes—
925C2×C4⋊C4C2414yes—
926C2×C4⋊C4C2412yes—
927C2×C4⋊C4C2412yes—
928C2×C4⋊C4C2414yes—
929C2×C4⋊C4C2414yes—
930C2×C4⋊C4C2414yes—
931C2×C4⋊C4C2412yes—
932C2×C4⋊C4C2412yes—
933C2×C4⋊C4C2414yes—
934C2×C4⋊C4C2414yes—
935C2×C4⋊C4C2414yes—
936C2×C4⋊C4C2414yes—
937C2×C4⋊C4C2414yes—
938C2×C4⋊C4C2414yes—
939C2×C4⋊C4C2412yes—
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⋊C4C2414yes—
951C2×C4⋊C4C2412yes—
952C2×C4⋊C4C2414yes—
953C2×C4⋊C4C2412yes—
954C2×C4⋊C4C2412yes—
955C2×C4⋊C4C2412yes—
956C2×C4⋊C4C2412yes—
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2412yes—
959C2×C4⋊C4C2414yes—
960C2×C4⋊C4C2414yes—
961C2×C4⋊C4C2414yes—
962C2×C4⋊C4C2411yescharacteristic
963C2×C4⋊C4C2412yes—
964C2×C22⋊C4C2412yes—
965C2×C22⋊C4C2412yes—
966C2×C22⋊C4C2411yescharacteristic
967C2×C22⋊C4C2411yescharacteristic
968C2×C22⋊C4C2412yes—
969C2×C22⋊C4C2411yescharacteristic
970C2×C22⋊C4C2411yescharacteristic
971C2×C22⋊C4C2412yes—
972C2×C22⋊C4C2414yes—
973C2×C22⋊C4C2414yes—
974C2×C22⋊C4C2412yes—
975C2×C22⋊C4C2412yes—
976C2×C22⋊C4C2412yes—
977C2×C22⋊C4C2412yes—
978C2×C42—24no—
979C2×C42C2411yescharacteristic
980C2×C42C2412yes—
981C2×C42C2411yescharacteristic
982C2×C42C2411yescharacteristic
983C2×C42C2411yescharacteristic
984C2×C42C2412yes—
985C2×C42C2412yes—
986C2×C42C2414yes—
987C2×C42C2412yes—
988C2×C42C2414yes—
989C2×C42C2412yes—
990C2×C42C2412yes—
991C2×C42C2411yescharacteristic
992C2×C42C2411yescharacteristic
993C2×C42C2412yes—
994C2×C42C2412yes—
995C2×C42C2412yes—
996C2×C42C2414yes—
997C2×C42C2411yescharacteristic
998C2×C42C2411yescharacteristic
999C2×C42C2411yescharacteristic
1000C2×C42C2411yescharacteristic
1001C2×C42C2412yes—
1002C2×C42C2412yes—
1003C2×C42C2412yes—
1004C2×C42C2414yes—
1005C2×C42C2414yes—
1006C2×C42C2412yes—
1007C2×C42C2414yes—
1008C2×C42C2414yes—
1009C2×C42C2414yes—
1010C2×C42C2414yes—
1011C2×C42C2412yes—
1012C2×C42C2412yes—
1013C2×C42C2411yescharacteristic
1014C2×C42C2411yescharacteristic
1015C2×C42C2411yescharacteristic
1016C2×C42C2411yescharacteristic
1017C2×C42C2412yes—
1018C2×C42C2412yes—
1019C2×C42C2412yes—
1020C2×C42C2414yes—
1021C2×C42C2412yes—
1022C2×C42C2412yes—
1023C2×C42C2411yescharacteristic
1024C2×C42C2411yescharacteristic
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#95C2414yes—
1047#95C2412yes—
1048#95C2412yes—
1049#95C2412yes—
1050#95C2412yes—
1051#95C2412yes—
1052#95C2412yes—
1053#95C2412yes—
1054#95C2414yes—
1055#95C2414yes—
1056#95C2412yes—
1057#95C2412yes—
1058#95C2412yes—
1059#95C2412yes—
1060#95C2412yes—
1061#95C2412yes—
1062#95C2412yes—
1063#95C2412yes—
1064#95C2412yes—
1065#95C2412yes—
1066#95C2414yes—
1067#95C2412yes—
1068#95C2414yes—
1069#95C2412yes—
1070#95C2412yes—
1071#95C2414yes—
1072#95C2412yes—
1073#95C2412yes—
1074#95C2414yes—
1075#95C2414yes—
1076#95C2412yes—
1077#95C2414yes—
1078#95C2412yes—
1079#95C2412yes—
1080#95C2412yes—
1081#95C2414yes—
1082#95C2414yes—
1083#95C2414yes—
1084#95C2414yes—
1085#95C2414yes—
1086#95C2412yes—
1087#95C2412yes—
1088#95C2412yes—
1089#95C2412yes—
1090#95C2412yes—
1091#95C2412yes—
1092#95C2412yes—
1093#95C2412yes—
1094#95C2414yes—
1095#95C2412yes—
1096#95C2414yes—
1097#95C2412yes—
1098#95C2414yes—
1099#95C2414yes—
1100#95C2414yes—
1101#95C2412yes—
1102#95C2412yes—
1103#95C2414yes—
1104#95C2412yes—
1105#95C2414yes—
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—22no—
1138C2×Q8—24no—
1139C2×Q8—22no—
1140C2×Q8—22no—
1141C2×Q8—24no—
1142C2×Q8—22no—
1143C2×Q8—24no—
1144C2×Q8—22no—
1145C2×Q8—42no—
1146C2×Q8—42no—
1147C2×Q8—42no—
1148C2×Q8—42no—
1149C2×Q8—42no—
1150C2×Q8C2×#4114yes—
1151C2×Q82−1+414yes—
1152C22×C4—22no—
1153C22×C4—22no—
1154C22×C4—22no—
1155C22×C4—22no—
1156C22×C4—22no—
1157C22×C4—22no—
1158C22×C4—22no—
1159C22×C4—41no—
1160C22×C4—41no—
1161C22×C4C2511yescharacteristic
1162C22×C4C2512yes—
1163C22×C4C2511yescharacteristic
1164C22×C4C2512yes—
1165C22×C4C2511yescharacteristic
1166C22×C4C2512yes—
1167C22×C4C2511yescharacteristic
1168C22×C4C2511yescharacteristic
1169C22×C4C2514yes—
1170C22×C4C2512yes—
1171C22×C4C2512yes—
1172C22×C4C2512yes—
1173C22×C4C2512yes—
1174C22×C4C2514yes—
1175C22×C4C2514yes—
1176C22×C4C2512yes—
1177C22×C4C2511yescharacteristic
1178C22×C4C2511yescharacteristic
1179C22×C4C2511yescharacteristic
1180C22×C4C2512yes—
1181C22×C4C2512yes—
1182C22×C4C2512yes—
1183C22×C4C2512yes—
1184C22×C4C2511yescharacteristic
1185C22×C4C2512yes—
1186C22×C4C2514yes—
1187C22×C4C2512yes—
1188C22×C4C2512yes—
1189C22×C4C2511yescharacteristic
1190C22×C4C2511yescharacteristic
1191C22×C4C2511yescharacteristic
1192C22×C4C2512yes—
1193C22×C4C2511yescharacteristic
1194C22×C4C2511yescharacteristic
1195C4⋊C4—24no—
1196C4⋊C4—24no—
1197C4⋊C4—22no—
1198C4⋊C4—24no—
1199C4⋊C4—24no—
1200C4⋊C4—24no—
1201C4⋊C4—24no—
1202C4⋊C4—22no—
1203C4⋊C4—24no—
1204C4⋊C4—28no—
1205C4⋊C4—24no—
1206C4⋊C4—22no—
1207C4⋊C4—28no—
1208C4⋊C4—28no—
1209C4⋊C4—28no—
1210C4⋊C4—24no—
1211C4⋊C4—24no—
1212C4⋊C4—28no—
1213C4⋊C4—28no—
1214C4⋊C4—24no—
1215C4⋊C4—24no—
1216C4⋊C4—22no—
1217C4⋊C4—22no—
1218C4⋊C4—24no—
1219C4⋊C4—24no—
1220C4⋊C4—22no—
1221C4⋊C4—22no—
1222C4⋊C4—24no—
1223C4⋊C4—22no—
1224C4⋊C4—24no—
1225C4⋊C4—28no—
1226C4⋊C4—22no—
1227C4⋊C4—24no—
1228C4⋊C4—28no—
1229C4⋊C4—24no—
1230C4⋊C4—28no—
1231C4⋊C4—24no—
1232C4⋊C4—22no—
1233C4⋊C4—24no—
1234C4⋊C4—22no—
1235C4⋊C4—24no—
1236C4⋊C4—24no—
1237C4⋊C4—22no—
1238C4⋊C4—22no—
1239C4⋊C4—42no—
1240C4⋊C4—42no—
1241C4⋊C4—42no—
1242C4⋊C4—42no—
1243C4⋊C4—44no—
1244C4⋊C4—42no—
1245C4⋊C4—42no—
1246C4⋊C4—42no—
1247C4⋊C4—44no—
1248C4⋊C4—42no—
1249C4⋊C4—42no—
1250C4⋊C4—44no—
1251C4⋊C4—42no—
1252C4⋊C4—44no—
1253C4⋊C4—44no—
1254C4⋊C4—44no—
1255C4⋊C4—42no—
1256C4⋊C4—44no—
1257C4⋊C4—42no—
1258C4⋊C4—42no—
1259C4⋊C4—41no—
1260C4⋊C4—41no—
1261C4⋊C4—44no—
1262C4⋊C4—42no—
1263C4⋊C4—42no—
1264C4⋊C4—44no—
1265C4⋊C4—42no—
1266C4⋊C4—42no—
1267C4⋊C4—42no—
1268C4⋊C4—42no—
1269C4⋊C4—44no—
1270C4⋊C4—44no—
1271C4⋊C4—44no—
1272C4⋊C4—44no—
1273C4⋊C4—44no—
1274C4⋊C4—42no—
1275C4⋊C4—44no—
1276C4⋊C4—44no—
1277C4⋊C4—44no—
1278C4⋊C4—44no—
1279C4⋊C4—44no—
1280C4⋊C4—44no—
1281C4⋊C4—42no—
1282C4⋊C4—44no—
1283C4⋊C4C2×#4114yes—
1284C4⋊C4C2×#4118yes—
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—42no—
1298C22⋊C4—44no—
1299C42—22no—
1300C42—22no—
1301C42—22no—
1302C42—24no—
1303C42—28no—
1304C42—28no—
1305C42—24no—
1306C42—24no—
1307C42—22no—
1308C42—24no—
1309C42—22no—
1310C42—24no—
1311C42—28no—
1312C42—24no—
1313C42—22no—
1314C42—24no—
1315C42—22no—
1316C42—22no—
1317C42—22no—
1318C42—24no—
1319C42—24no—
1320C42—24no—
1321C42—22no—
1322C42—41no—
1323C42—41no—
1324C42—42no—
1325C42—42no—
1326C42—42no—
1327C42—42no—
1328C42—44no—
1329C42—42no—
1330C42—41no—
1331C42—41no—
1332C42—42no—
1333C42—42no—
1334C42—44no—
1335C42—42no—
1336C42—44no—
1337C42—44no—
1338C42—44no—
1339C42—44no—
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—28no—
1355Q8—44no—
1356Q8—48no—
1357Q8—44no—
1358Q8—48no—
1359Q8—84no—
1360Q8—84no—
1361C2×C4—22no—
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—21no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—24no—
1381C2×C4—22no—
1382C2×C4—24no—
1383C2×C4—21no—
1384C2×C4—21no—
1385C2×C4—21no—
1386C2×C4—22no—
1387C2×C4—22no—
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—21no—
1398C2×C4—21no—
1399C2×C4—24no—
1400C2×C4—22no—
1401C2×C4—22no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—22no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—22no—
1412C2×C4—22no—
1413C2×C4—21no—
1414C2×C4—22no—
1415C2×C4—24no—
1416C2×C4—22no—
1417C2×C4—24no—
1418C2×C4—22no—
1419C2×C4—24no—
1420C2×C4—24no—
1421C2×C4—22no—
1422C2×C4—24no—
1423C2×C4—22no—
1424C2×C4—22no—
1425C2×C4—21no—
1426C2×C4—21no—
1427C2×C4—22no—
1428C2×C4—21no—
1429C2×C4—21no—
1430C2×C4—22no—
1431C2×C4—22no—
1432C2×C4—22no—
1433C2×C4—22no—
1434C2×C4—22no—
1435C2×C4—22no—
1436C2×C4—21no—
1437C2×C4—21no—
1438C2×C4—21no—
1439C2×C4—24no—
1440C2×C4—22no—
1441C2×C4—22no—
1442C2×C4—22no—
1443C2×C4—21no—
1444C2×C4—22no—
1445C2×C4—22no—
1446C2×C4—22no—
1447C2×C4—22no—
1448C2×C4—24no—
1449C2×C4—21no—
1450C2×C4—21no—
1451C2×C4—44no—
1452C2×C4—44no—
1453C2×C4—82no—
1454C2×C4C22×#4114yes—
1455C2×C4C22×#4114yes—
1456C2×C4C22×#4112yes—
1457C2×C4C22×#4112yes—
1458C2×C4C22×#4112yes—
1459C2×C4C2×2−1+412yes—
1460C2×C4C2×2−1+412yes—
1461C2×C4C2×2−1+414yes—
1462C2×C4C2×2−1+412yes—
1463C2×C4C2×2−1+412yes—
1464C2×C4#58512yes—
1465C2×C4#58512yes—
1466C22—41no—
1467C22—41no—
1468C22—41no—
1469C22—41no—
1470C22—41no—
1471C22—41no—
1472C22—41no—
1473C22C23×#4111yescharacteristic
1474C22C22×2−1+411yescharacteristic
1475C22C22×2−1+411yescharacteristic
1476C22C2×#58511yescharacteristic
1477C22C2×#58511yescharacteristic
1478C222−1+611yescharacteristic
1479C222−1+611yescharacteristic
1480C4—24no—
1481C4—22no—
1482C4—24no—
1483C4—24no—
1484C4—22no—
1485C4—22no—
1486C4—41no—
1487C4—44no—
1488C4—42no—
1489C4—42no—
1490C4—42no—
1491C4—41no—
1492C4—42no—
1493C4—41no—
1494C4—42no—
1495C4—44no—
1496C4—41no—
1497C4—42no—
1498C4—41no—
1499C4—42no—
1500C4—41no—
1501C4—42no—
1502C4—42no—
1503C4—41no—
1504C4—42no—
1505C4—44no—
1506C4—41no—
1507C4—42no—
1508C4—44no—
1509C4—42no—
1510C4—42no—
1511C4—41no—
1512C4#346114yes—
1513C4#351614yes—
1514C2—81no—
1515C2C2×#346111yescharacteristic
1516C2C2×#351611yescharacteristic
1517C2#6286111yescharacteristic
1518C2#6294711yescharacteristic
1519C2#6295311yescharacteristic
1520C2#6295611yescharacteristic
1521C2#6296711yescharacteristic
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
2. #42850C2semidirect
3. #42765C2semidirect
6. #41786C2semidirect
7. #39754C2semidirect
9. #39673C2semidirect
10. #39635C2semidirect
13. #39170C2semidirect
15. #38984C2semidirect
18. #38243C2semidirect
20. #37580C2semidirect
22. #37062C2semidirect
23. #35656C2semidirect
26. #35221C2semidirect
29. #35187C2semidirect
30. #35187C2semidirect
31. #34951C2semidirect
33. #34337C2semidirect
34. C4×#557C2semidirect

Maximal subgroups

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

subgroupindex
#428562
#428502
#427652
#427132
#418902
#417862
#397542
#397242
#396732
#396352
#395992
#392832
#391702
#391492
#389842
#389332
#382792
#382432
#375982
#375802
#371152
#370622
#356562
#356502
#352912
#352212
#352042
#351872
#349512
#349162
#343372
C4×#5572
#340852