Finite Group Databasebeta

← #7657472

Subgroups — #7657472

Order 512.

4092 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#42850C212yesmaximal, complemented
2#42848C212yesmaximal
3#42782C212yesmaximal, complemented
4#42772C212yesmaximal
5#42291C214yesmaximal
6#42289C214yesmaximal, complemented
7#41802C214yesmaximal
8#41786C214yesmaximal, complemented
9#39819C212yesmaximal
10#39724C211yesmaximal, characteristic
11#39693C212yesmaximal
12#39599C211yesmaximal, characteristic
13#39183C211yesmaximal, characteristic, complemented
14#39170C211yesmaximal, characteristic, complemented
15#38243C212yesmaximal, complemented
16#38227C212yesmaximal, complemented
17#37630C211yesmaximal, characteristic, complemented
18#37630C212yesmaximal, complemented
19#37630C211yesmaximal, characteristic, complemented
20#37580C212yesmaximal, complemented
21#36599C211yesmaximal, characteristic
22#36552C211yesmaximal, characteristic
23#36313C211yesmaximal, characteristic, complemented
24#36285C211yesmaximal, characteristic, complemented
25#35972C212yesmaximal, complemented
26#35886C212yesmaximal
27#35886C212yesmaximal
28#35870C212yesmaximal, complemented
29#35323C212yesmaximal
30#35291C211yesmaximal, characteristic
31#34629C211yesmaximal, characteristic
32#34629C212yesmaximal
33#34337C211yesmaximal, characteristic, complemented
34#34328C211yesmaximal, characteristic, complemented
35#34145C211yesmaximal, characteristic
36C2×#557C2211yescharacteristic
37C2×#557C2211yescharacteristic
38C2×#533C2211yescharacteristic
39#2863C2212yes—
40#2863C2212yes—
41#2862C2211yescharacteristic
42#2859C2211yescharacteristic
43#2857C2211yescharacteristic
44#2857C2212yes—
45#2857C2211yescharacteristic
46#2851C2212yes—
47#2839C2214yes—
48#2839C2214yes—
49#2839C2214yes—
50#2839C2214yes—
51#2839C2214yes—
52#2833C2214yes—
53#2810C2214yes—
54#2802C2214yes—
55#2802C2214yes—
56#2802C2214yes—
57#2794C2214yes—
58#2791C2214yes—
59#2791C2214yes—
60#2791C2214yes—
61#2790C2214yes—
62#2790C2214yes—
63#2787C2214yes—
64#2776C2214yes—
65#2776C2214yes—
66#2770C2214yes—
67#2767C2214yes—
68#2766C2214yes—
69#2758C2214yes—
70#2758C2214yes—
71#2726C2214yes—
72#2719C2214yes—
73#2719C2214yes—
74#2719C2214yes—
75#2704C2214yes—
76#2690C2214yes—
77#2666C2214yes—
78#2655C2214yes—
79#2655C2214yes—
80#2655C2214yes—
81#2655C2214yes—
82#2655C2212yes—
83#2655C2214yes—
84#2655C2212yes—
85#2655C2214yes—
86#2655C2214yes—
87#2655C2214yes—
88#2655C2214yes—
89#2652C2214yes—
90#2652C2212yes—
91#2652C2212yes—
92#2652C2214yes—
93#2647C2212yes—
94#2647C2214yes—
95#2647C2211yescharacteristic
96#2647C2212yes—
97#2647C2212yes—
98#2645C2212yes—
99#2645C2214yes—
100#2645C2212yes—
101#2645C2211yescharacteristic
102#2645C2211yescharacteristic
103#2645C2212yes—
104#2645C2212yes—
105#2645C2212yes—
106#2642C2212yes—
107#2642C2212yes—
108#2642C2211yescharacteristic
109#2642C2212yes—
110#2629C2211yescharacteristic
111#2629C2212yes—
112#2625C2211yescharacteristic
113#2625C2212yes—
114#2625C2211yescharacteristic
115#2621C2212yes—
116#2621C2211yescharacteristic
117#2612C2214yes—
118#2606C2214yes—
119#2606C2214yes—
120#2590C2214yes—
121#2590C2214yes—
122#2590C2214yes—
123#2590C2214yes—
124#2590C2214yes—
125#2588C2214yes—
126#2587C2214yes—
127#2587C2214yes—
128#2585C2214yes—
129#2585C2214yes—
130#2584C2212yes—
131#2582C2211yescharacteristic
132#2582C2212yes—
133#2582C2211yescharacteristic
134#2581C2212yes—
135#2577C2214yes—
136#2577C2214yes—
137#2577C2214yes—
138#2570C2212yes—
139#2570C2212yes—
140#2569C2214yes—
141#2568C2211yescharacteristic
142#2568C2212yes—
143#2568C2211yescharacteristic
144#2565C2212yes—
145#2565C2212yes—
146#2565C2212yes—
147#2552C2212yes—
148#2552C2212yes—
149#2552C2211yescharacteristic
150#2552C2211yescharacteristic
151#2550C2212yes—
152#2546C2212yes—
153#2546C2211yescharacteristic
154#2546C2212yes—
155#2546C2211yescharacteristic
156#2533C2214yes—
157#2533C2214yes—
158#2533C2214yes—
159#2533C2214yes—
160#2533C2214yes—
161#2530C2214yes—
162#2530C2214yes—
163#2530C2214yes—
164#2528C2214yes—
165#2528C2214yes—
166#2528C2214yes—
167#2528C2214yes—
168#2524C2214yes—
169#2524C2214yes—
170#2514C2212yes—
171#2514C2212yes—
172#2514C2212yes—
173#2511C2212yes—
174#2511C2212yes—
175#2511C2214yes—
176#2511C2212yes—
177#2511C2212yes—
178#2509C2212yes—
179#2509C2212yes—
180#2509C2212yes—
181#2509C2212yes—
182#2509C2214yes—
183#2509C2214yes—
184#2509C2212yes—
185#2508C2212yes—
186#2508C2212yes—
187#2507C2214yes—
188#2507C2212yes—
189#2505C2214yes—
190#2502C2212yes—
191#2495C2212yes—
192#2494C2212yes—
193#2489C2212yes—
194#2489C2212yes—
195#2453C2212yes—
196#2453C2212yes—
197#2453C2212yes—
198#2453C2212yes—
199#2453C2212yes—
200#2453C2212yes—
201#2453C2212yes—
202#2453C2212yes—
203#2451C2212yes—
204#2446C2212yes—
205#2446C2212yes—
206#2446C2212yes—
207#2446C2212yes—
208#2446C2212yes—
209#2446C2212yes—
210#2446C2212yes—
211#2446C2212yes—
212#2442C2212yes—
213#2429C2212yes—
214#2429C2212yes—
215#2421C2212yes—
216#2421C2212yes—
217#2402C2212yes—
218#2402C2214yes—
219#2402C2214yes—
220#2402C2212yes—
221#2401C2212yes—
222#2401C2214yes—
223#2401C2214yes—
224#2401C2212yes—
225#2371C2214yes—
226#2370C2212yes—
227#2370C2212yes—
228#2370C2212yes—
229#2370C2214yes—
230#2370C2212yes—
231#2370C2212yes—
232#2370C2212yes—
233#2369C2211yescharacteristic
234#2369C2211yescharacteristic
235#2368C2212yes—
236#2368C2212yes—
237#2365C2212yes—
238#2365C2211yescharacteristic
239#2365C2211yescharacteristic
240#2365C2212yes—
241#2365C2212yes—
242#2365C2211yescharacteristic
243#2365C2211yescharacteristic
244#2360C2211yescharacteristic
245#2360C2211yescharacteristic
246#2360C2211yescharacteristic
247#2360C2212yes—
248#2360C2211yescharacteristic
249#2356C2212yes—
250#2356C2212yes—
251#2356C2212yes—
252#2356C2212yes—
253#2355C2211yescharacteristic
254#2355C2211yescharacteristic
255#2355C2212yes—
256Q8×C4⋊C4C2212yes—
257Q8×C4⋊C4C2211yescharacteristic
258Q8×C4⋊C4C2212yes—
259Q8×C4⋊C4C2211yescharacteristic
260#2345C2212yes—
261#2336C2214yes—
262#2330C2212yes—
263#2330C2212yes—
264#2330C2214yes—
265#2327C2212yes—
266#2327C2212yes—
267#2323C2212yes—
268#2323C2212yes—
269#2323C2212yes—
270#2320C2212yes—
271C4×C4⋊Q8C2211yescharacteristic
272C4×C4⋊Q8C2211yescharacteristic
273C4×C4⋊Q8C2212yes—
274C4×C4⋊Q8C2211yescharacteristic
275C4×#125C2211yescharacteristic
276C4×#125C2212yes—
277C4×C22⋊Q8C2212yes—
278C4×C22⋊Q8C2211yescharacteristic
279C4×C22⋊Q8C2212yes—
280C4×C22⋊Q8C2211yescharacteristic
281#2296C2212yes—
282#2295C2211yescharacteristic
283#2295C2211yescharacteristic
284#2295C2212yes—
285#2295C2211yescharacteristic
286#2295C2212yes—
287#2295C2212yes—
288#2295C2212yes—
289#2295C2212yes—
290#2295C2212yes—
291#2295C2211yescharacteristic
292#2276C2212yes—
293#2276C2212yes—
294C42×Q8C2211yescharacteristic
295C42×Q8C2211yescharacteristic
296C4×#117C2211yescharacteristic
297C4×#117C2212yes—
298C2×C4×C4⋊C4C2211yescharacteristic
299#557—28no—
300#557—28no—
301#533—28no—
302C2×C4⋊Q8C2311yescharacteristic
303C2×C4⋊Q8C2311yescharacteristic
304C2×C4⋊Q8C2312yes—
305C2×C4⋊Q8C2312yes—
306C2×C4⋊Q8C2311yescharacteristic
307C2×C4⋊Q8C2311yescharacteristic
308C2×C4⋊Q8C2311yescharacteristic
309C2×C4⋊Q8C2312yes—
310C2×C4⋊Q8C2312yes—
311C2×#125C2312yes—
312C2×#125C2314yes—
313C2×#125C2312yes—
314C2×#125C2314yes—
315C2×#125C2312yes—
316C2×#125C2311yescharacteristic
317C2×#125C2312yes—
318C2×#125C2312yes—
319C2×#125C2312yes—
320C2×C22⋊Q8C2312yes—
321C2×C22⋊Q8C2311yescharacteristic
322C2×C22⋊Q8C2311yescharacteristic
323C2×C22⋊Q8C2311yescharacteristic
324C2×C22⋊Q8C2311yescharacteristic
325C2×C22⋊Q8C2312yes—
326C2×C22⋊Q8C2312yes—
327C2×C4×Q8C2311yescharacteristic
328C2×C4×Q8C2311yescharacteristic
329C2×C4×Q8C2312yes—
330C2×C4×Q8C2312yes—
331C2×C4×Q8C2311yescharacteristic
332C2×C4×Q8C2312yes—
333C2×C4×Q8C2312yes—
334C2×C4×Q8C2312yes—
335C2×C4×Q8C2311yescharacteristic
336C2×C4×Q8C2312yes—
337C2×C4×Q8C2311yescharacteristic
338C2×C4×Q8C2312yes—
339C2×C4×Q8C2312yes—
340C2×C4×Q8C2312yes—
341C2×C4×Q8C2312yes—
342C2×C4×Q8C2311yescharacteristic
343C2×C4×Q8C2312yes—
344C2×C4×Q8C2311yescharacteristic
345C2×C4×Q8C2311yescharacteristic
346C2×#117C2312yes—
347C2×#117C2311yescharacteristic
348C2×#117C2311yescharacteristic
349C22×C4⋊C4C2311yescharacteristic
350C22×C4⋊C4C2311yescharacteristic
351C22×C42C2311yescharacteristic
352C22×C42C2312yes—
353#401C2314yes—
354#401C2314yes—
355#401C2314yes—
356#401C2314yes—
357#401C2312yes—
358#401C2312yes—
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#400C2312yes—
375#400C2312yes—
376#400C2314yes—
377#400C2314yes—
378#400C2314yes—
379#400C2312yes—
380#400C2314yes—
381#400C2314yes—
382#400C2314yes—
383#400C2314yes—
384#400C2314yes—
385#400C2314yes—
386#400C2314yes—
387#400C2314yes—
388#400C2314yes—
389#400C2314yes—
390#400C2314yes—
391#400C2314yes—
392#400C2314yes—
393#400C2314yes—
394#400C2314yes—
395#400C2312yes—
396#400C2314yes—
397#400C2312yes—
398#400C2312yes—
399#400C2314yes—
400#400C2312yes—
401#400C2312yes—
402#400C2314yes—
403#400C2312yes—
404#400C2314yes—
405#400C2314yes—
406#400C2314yes—
407#400C2314yes—
408#400C2312yes—
409#400C2312yes—
410#400C2312yes—
411#400C2312yes—
412#400C2312yes—
413#400C2314yes—
414#400C2314yes—
415#398C2314yes—
416#398C2314yes—
417#398C2314yes—
418#398C2314yes—
419#398C2314yes—
420#398C2314yes—
421#398C2314yes—
422#398C2314yes—
423#398C2314yes—
424#398C2314yes—
425#398C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2312yes—
429#398C2314yes—
430#398C2314yes—
431#398C2314yes—
432#398C2314yes—
433#398C2314yes—
434#398C2314yes—
435#398C2314yes—
436#398C2314yes—
437#398C2314yes—
438#398C2314yes—
439#398C2314yes—
440#398C2314yes—
441#398C2314yes—
442#398C2314yes—
443#398C2314yes—
444#398C2312yes—
445#398C2314yes—
446#398C2312yes—
447#398C2312yes—
448#398C2314yes—
449#398C2314yes—
450#398C2312yes—
451#398C2314yes—
452#398C2314yes—
453#398C2312yes—
454#398C2314yes—
455#398C2312yes—
456#398C2312yes—
457#397C2312yes—
458#397C2312yes—
459#397C2314yes—
460#397C2314yes—
461#397C2314yes—
462#397C2312yes—
463#397C2312yes—
464#397C2312yes—
465#397C2314yes—
466#397C2312yes—
467#396C2312yes—
468#396C2312yes—
469#396C2314yes—
470#396C2314yes—
471#395C2314yes—
472#395C2314yes—
473#391C2311yescharacteristic
474#391C2312yes—
475#391C2311yescharacteristic
476#391C2312yes—
477#391C2311yescharacteristic
478#391C2311yescharacteristic
479#391C2312yes—
480#391C2312yes—
481#391C2312yes—
482#391C2312yes—
483#391C2312yes—
484#391C2312yes—
485#391C2311yescharacteristic
486#391C2312yes—
487#391C2312yes—
488#391C2312yes—
489#391C2314yes—
490#391C2312yes—
491#391C2312yes—
492#391C2312yes—
493#391C2312yes—
494#391C2312yes—
495#391C2312yes—
496#391C2312yes—
497#391C2311yescharacteristic
498#391C2314yes—
499#391C2312yes—
500#391C2312yes—
501#391C2312yes—
502#391C2312yes—
503#391C2312yes—
504#391C2312yes—
505#391C2312yes—
506#391C2311yescharacteristic
507#391C2312yes—
508#391C2311yescharacteristic
509#391C2311yescharacteristic
510#391C2311yescharacteristic
511#391C2311yescharacteristic
512#391C2312yes—
513#391C2312yes—
514#391C2311yescharacteristic
515#389C2311yescharacteristic
516#389C2312yes—
517#389C2311yescharacteristic
518#389C2311yescharacteristic
519#389C2312yes—
520#389C2312yes—
521#389C2314yes—
522#389C2314yes—
523#389C2312yes—
524#389C2312yes—
525#389C2312yes—
526#389C2312yes—
527#389C2312yes—
528#389C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2312yes—
533#389C2312yes—
534#389C2314yes—
535#389C2314yes—
536#389C2314yes—
537#389C2311yescharacteristic
538#389C2312yes—
539#389C2312yes—
540#389C2314yes—
541#389C2312yes—
542#389C2311yescharacteristic
543#389C2314yes—
544#389C2314yes—
545#389C2312yes—
546#389C2312yes—
547#389C2314yes—
548#389C2314yes—
549#389C2314yes—
550#389C2314yes—
551#389C2314yes—
552#389C2314yes—
553#389C2314yes—
554#389C2314yes—
555#389C2312yes—
556#389C2314yes—
557#389C2312yes—
558#389C2314yes—
559#389C2314yes—
560#389C2314yes—
561#389C2314yes—
562#389C2314yes—
563#389C2312yes—
564#389C2312yes—
565#389C2314yes—
566#389C2312yes—
567#389C2312yes—
568#389C2312yes—
569#389C2312yes—
570#389C2312yes—
571#389C2312yes—
572#389C2311yescharacteristic
573#389C2312yes—
574#389C2314yes—
575#389C2314yes—
576#389C2311yescharacteristic
577#389C2311yescharacteristic
578#389C2311yescharacteristic
579#389C2311yescharacteristic
580#389C2312yes—
581#389C2312yes—
582#389C2312yes—
583#389C2312yes—
584#389C2312yes—
585#389C2312yes—
586#389C2311yescharacteristic
587#389C2311yescharacteristic
588#389C2312yes—
589#389C2312yes—
590#389C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2312yes—
600#387C2312yes—
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#387C2314yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2312yes—
636#387C2312yes—
637#387C2312yes—
638#387C2312yes—
639#387C2312yes—
640#387C2312yes—
641#387C2312yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#387C2312yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#387C2314yes—
653#387C2314yes—
654#387C2314yes—
655#387C2314yes—
656#387C2314yes—
657#387C2314yes—
658#387C2314yes—
659#387C2312yes—
660#387C2314yes—
661#387C2314yes—
662#387C2314yes—
663#387C2314yes—
664#387C2314yes—
665#387C2314yes—
666#387C2312yes—
667#387C2314yes—
668#387C2314yes—
669#387C2312yes—
670#387C2312yes—
671#387C2312yes—
672#387C2312yes—
673#387C2312yes—
674#387C2312yes—
675#387C2314yes—
676#387C2312yes—
677#387C2312yes—
678#387C2314yes—
679#387C2314yes—
680#387C2314yes—
681#385C2312yes—
682#385C2314yes—
683#385C2312yes—
684#385C2314yes—
685#385C2314yes—
686#385C2312yes—
687#385C2312yes—
688#385C2312yes—
689#385C2312yes—
690#385C2314yes—
691#384C2311yescharacteristic
692#384C2311yescharacteristic
693#384C2311yescharacteristic
694#384C2312yes—
695#384C2312yes—
696#384C2312yes—
697#384C2312yes—
698#384C2314yes—
699#384C2314yes—
700#383C2314yes—
701#383C2314yes—
702#383C2314yes—
703#383C2314yes—
704#383C2314yes—
705#382C2311yescharacteristic
706#382C2312yes—
707#382C2312yes—
708#382C2312yes—
709#382C2312yes—
710#382C2312yes—
711#382C2314yes—
712#382C2314yes—
713#382C2312yes—
714#382C2312yes—
715#382C2314yes—
716#380C2312yes—
717#380C2314yes—
718#380C2314yes—
719#380C2311yescharacteristic
720#380C2312yes—
721#380C2312yes—
722#380C2312yes—
723#380C2311yescharacteristic
724C4×C4⋊C4C2312yes—
725C4×C4⋊C4C2311yescharacteristic
726C4×C4⋊C4C2314yes—
727C4×C4⋊C4C2311yescharacteristic
728C4×C4⋊C4C2312yes—
729C4×C4⋊C4C2312yes—
730C4×C4⋊C4C2312yes—
731C4×C4⋊C4C2314yes—
732C4×C4⋊C4C2312yes—
733C4×C4⋊C4C2312yes—
734C4×C4⋊C4C2312yes—
735C4×C4⋊C4C2314yes—
736C4×C4⋊C4C2312yes—
737C4×C4⋊C4C2312yes—
738C4×C4⋊C4C2314yes—
739C4×C4⋊C4C2312yes—
740C4×C4⋊C4C2312yes—
741C4×C4⋊C4C2312yes—
742C4×C4⋊C4C2311yescharacteristic
743C4×C4⋊C4C2311yescharacteristic
744C4×C4⋊C4C2312yes—
745C4×C4⋊C4C2314yes—
746C4×C4⋊C4C2314yes—
747C4×C4⋊C4C2314yes—
748C4×C4⋊C4C2312yes—
749C4×C4⋊C4C2314yes—
750C4×C4⋊C4C2314yes—
751C4×C4⋊C4C2311yescharacteristic
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2314yes—
754C4×C4⋊C4C2314yes—
755C4×C4⋊C4C2314yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2311yescharacteristic
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2311yescharacteristic
775C4×C4⋊C4C2311yescharacteristic
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2314yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2311yescharacteristic
780C4×C4⋊C4C2311yescharacteristic
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C22⋊C4C2314yes—
786C4×C22⋊C4C2312yes—
787C4×C22⋊C4C2312yes—
788C4×C22⋊C4C2314yes—
789C4×C22⋊C4C2312yes—
790C4×C22⋊C4C2311yescharacteristic
791C4×C22⋊C4C2311yescharacteristic
792C4×C22⋊C4C2312yes—
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2311yescharacteristic
796C4×C22⋊C4C2311yescharacteristic
797#376C2311yescharacteristic
798#376C2312yes—
799#376C2312yes—
800#376C2312yes—
801#376C2314yes—
802#376C2314yes—
803#376C2314yes—
804#376C2314yes—
805#376C2314yes—
806#376C2311yescharacteristic
807#376C2312yes—
808C2×#95C2312yes—
809C43C2311yescharacteristic
810C43C2312yes—
811C43C2311yescharacteristic
812C43C2312yes—
813C22×Q8C2411yescharacteristic
814C22×Q8C2411yescharacteristic
815C22×Q8C2412yes—
816C22×Q8C2411yescharacteristic
817C22×Q8C2412yes—
818C22×Q8C2411yescharacteristic
819C22×Q8C2412yes—
820C23×C4C2411yescharacteristic
821C23×C4C2411yescharacteristic
822C23×C4C2412yes—
823C23×C4C2411yescharacteristic
824C23×C4C2412yes—
825C4⋊Q8—24no—
826C4⋊Q8—28no—
827C4⋊Q8—24no—
828C4⋊Q8—24no—
829C4⋊Q8—24no—
830C4⋊Q8—28no—
831C4⋊Q8—44no—
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—42no—
841#125—44no—
842#125—44no—
843C22⋊Q8—24no—
844C22⋊Q8—28no—
845C22⋊Q8—24no—
846C22⋊Q8—24no—
847C22⋊Q8—24no—
848C22⋊Q8—28no—
849C22⋊Q8—44no—
850C4×Q8—28no—
851C4×Q8—28no—
852C4×Q8—24no—
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—44no—
862C4×Q8—44no—
863C4×Q8—44no—
864C4×Q8—42no—
865C4×Q8—44no—
866C4×Q8—42no—
867C4×Q8—44no—
868C4×Q8#4118yes—
869#117—24no—
870#117—28no—
871#117—42no—
872C2×C4⋊C4—24no—
873C2×C4⋊C4—42no—
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2411yescharacteristic
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2411yescharacteristic
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2411yescharacteristic
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2411yescharacteristic
905C2×C4⋊C4C2411yescharacteristic
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2411yescharacteristic
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2412yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
924C2×C4⋊C4C2414yes—
925C2×C4⋊C4C2414yes—
926C2×C4⋊C4C2414yes—
927C2×C4⋊C4C2412yes—
928C2×C4⋊C4C2414yes—
929C2×C4⋊C4C2412yes—
930C2×C4⋊C4C2414yes—
931C2×C4⋊C4C2414yes—
932C2×C4⋊C4C2414yes—
933C2×C4⋊C4C2414yes—
934C2×C4⋊C4C2414yes—
935C2×C4⋊C4C2412yes—
936C2×C4⋊C4C2412yes—
937C2×C4⋊C4C2414yes—
938C2×C4⋊C4C2414yes—
939C2×C4⋊C4C2414yes—
940C2×C4⋊C4C2412yes—
941C2×C4⋊C4C2412yes—
942C2×C4⋊C4C2412yes—
943C2×C4⋊C4C2412yes—
944C2×C4⋊C4C2412yes—
945C2×C4⋊C4C2412yes—
946C2×C4⋊C4C2414yes—
947C2×C4⋊C4C2414yes—
948C2×C4⋊C4C2412yes—
949C2×C4⋊C4C2412yes—
950C2×C4⋊C4C2414yes—
951C2×C4⋊C4C2412yes—
952C2×C4⋊C4C2412yes—
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×C4⋊C4C2411yescharacteristic
965C2×C22⋊C4C2412yes—
966C2×C22⋊C4C2412yes—
967C2×C22⋊C4C2411yescharacteristic
968C2×C22⋊C4C2411yescharacteristic
969C2×C22⋊C4C2412yes—
970C2×C22⋊C4C2414yes—
971C2×C22⋊C4C2412yes—
972C2×C22⋊C4C2411yescharacteristic
973C2×C22⋊C4C2411yescharacteristic
974C2×C22⋊C4C2414yes—
975C2×C22⋊C4C2412yes—
976C2×C22⋊C4C2412yes—
977C2×C42—24no—
978C2×C42—44no—
979C2×C42C2411yescharacteristic
980C2×C42C2412yes—
981C2×C42C2411yescharacteristic
982C2×C42C2411yescharacteristic
983C2×C42C2411yescharacteristic
984C2×C42C2411yescharacteristic
985C2×C42C2414yes—
986C2×C42C2412yes—
987C2×C42C2414yes—
988C2×C42C2412yes—
989C2×C42C2412yes—
990C2×C42C2411yescharacteristic
991C2×C42C2411yescharacteristic
992C2×C42C2412yes—
993C2×C42C2412yes—
994C2×C42C2411yescharacteristic
995C2×C42C2412yes—
996C2×C42C2411yescharacteristic
997C2×C42C2414yes—
998C2×C42C2412yes—
999C2×C42C2411yescharacteristic
1000C2×C42C2412yes—
1001C2×C42C2411yescharacteristic
1002C2×C42C2412yes—
1003C2×C42C2412yes—
1004C2×C42C2414yes—
1005C2×C42C2414yes—
1006C2×C42C2414yes—
1007C2×C42C2414yes—
1008C2×C42C2414yes—
1009C2×C42C2412yes—
1010C2×C42C2412yes—
1011C2×C42C2412yes—
1012C2×C42C2411yescharacteristic
1013C2×C42C2411yescharacteristic
1014C2×C42C2411yescharacteristic
1015C2×C42C2411yescharacteristic
1016C2×C42C2412yes—
1017C2×C42C2414yes—
1018C2×C42C2414yes—
1019C2×C42C2412yes—
1020C2×C42C2412yes—
1021C2×C42C2412yes—
1022C2×C42C2411yescharacteristic
1023#95C2412yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2412yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2412yes—
1030#95C2412yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2411yescharacteristic
1034#95C2411yescharacteristic
1035#95C2411yescharacteristic
1036#95C2412yes—
1037#95C2412yes—
1038#95C2411yescharacteristic
1039#95C2412yes—
1040#95C2412yes—
1041#95C2411yescharacteristic
1042#95C2411yescharacteristic
1043#95C2412yes—
1044#95C2412yes—
1045#95C2412yes—
1046#95C2412yes—
1047#95C2411yescharacteristic
1048#95C2411yescharacteristic
1049#95C2414yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2414yes—
1053#95C2412yes—
1054#95C2412yes—
1055#95C2412yes—
1056#95C2412yes—
1057#95C2414yes—
1058#95C2412yes—
1059#95C2412yes—
1060#95C2414yes—
1061#95C2414yes—
1062#95C2414yes—
1063#95C2414yes—
1064#95C2414yes—
1065#95C2414yes—
1066#95C2414yes—
1067#95C2414yes—
1068#95C2414yes—
1069#95C2412yes—
1070#95C2412yes—
1071#95C2414yes—
1072#95C2414yes—
1073#95C2412yes—
1074#95C2412yes—
1075#95C2414yes—
1076#95C2414yes—
1077#95C2412yes—
1078#95C2412yes—
1079#95C2412yes—
1080#95C2412yes—
1081#95C2412yes—
1082#95C2414yes—
1083#95C2412yes—
1084#95C2414yes—
1085#95C2412yes—
1086#95C2414yes—
1087#95C2414yes—
1088#95C2414yes—
1089#95C2412yes—
1090#95C2414yes—
1091#95C2414yes—
1092#95C2412yes—
1093#95C2412yes—
1094#95C2412yes—
1095#95C2412yes—
1096#95C2414yes—
1097#95C2412yes—
1098#95C2412yes—
1099#95C2412yes—
1100#95C2412yes—
1101#95C2412yes—
1102#95C2412yes—
1103#95C2414yes—
1104#95C2414yes—
1105#95C2412yes—
1106#95C2412yes—
1107#95C2412yes—
1108#95C2412yes—
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—22no—
1142C2×Q8—24no—
1143C2×Q8—24no—
1144C2×Q8—22no—
1145C2×Q8—22no—
1146C2×Q8—42no—
1147C2×Q8—42no—
1148C2×Q8C2×#4114yes—
1149C22×C4—22no—
1150C22×C4—22no—
1151C22×C4—22no—
1152C22×C4—22no—
1153C22×C4—22no—
1154C22×C4—22no—
1155C22×C4—24no—
1156C22×C4—42no—
1157C22×C4—42no—
1158C22×C4—42no—
1159C22×C4—42no—
1160C22×C4—41no—
1161C22×C4—41no—
1162C22×C4—42no—
1163C22×C42−1+414yes—
1164C22×C4C2511yescharacteristic
1165C22×C4C2511yescharacteristic
1166C22×C4C2512yes—
1167C22×C4C2511yescharacteristic
1168C22×C4C2512yes—
1169C22×C4C2511yescharacteristic
1170C22×C4C2511yescharacteristic
1171C22×C4C2511yescharacteristic
1172C22×C4C2511yescharacteristic
1173C22×C4C2512yes—
1174C22×C4C2512yes—
1175C22×C4C2514yes—
1176C22×C4C2512yes—
1177C22×C4C2512yes—
1178C22×C4C2512yes—
1179C22×C4C2514yes—
1180C22×C4C2512yes—
1181C22×C4C2514yes—
1182C22×C4C2511yescharacteristic
1183C22×C4C2512yes—
1184C22×C4C2512yes—
1185C22×C4C2512yes—
1186C22×C4C2512yes—
1187C22×C4C2511yescharacteristic
1188C22×C4C2511yescharacteristic
1189C22×C4C2512yes—
1190C22×C4C2514yes—
1191C22×C4C2512yes—
1192C22×C4C2512yes—
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—24no—
1220C4⋊C4—22no—
1221C4⋊C4—22no—
1222C4⋊C4—22no—
1223C4⋊C4—24no—
1224C4⋊C4—28no—
1225C4⋊C4—24no—
1226C4⋊C4—22no—
1227C4⋊C4—22no—
1228C4⋊C4—24no—
1229C4⋊C4—24no—
1230C4⋊C4—28no—
1231C4⋊C4—24no—
1232C4⋊C4—22no—
1233C4⋊C4—22no—
1234C4⋊C4—24no—
1235C4⋊C4—22no—
1236C4⋊C4—24no—
1237C4⋊C4—24no—
1238C4⋊C4—22no—
1239C4⋊C4—42no—
1240C4⋊C4—42no—
1241C4⋊C4—42no—
1242C4⋊C4—42no—
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—44no—
1252C4⋊C4—44no—
1253C4⋊C4—42no—
1254C4⋊C4—44no—
1255C4⋊C4—42no—
1256C4⋊C4—42no—
1257C4⋊C4—42no—
1258C4⋊C4—42no—
1259C4⋊C4—44no—
1260C4⋊C4—44no—
1261C4⋊C4—42no—
1262C4⋊C4—41no—
1263C4⋊C4—41no—
1264C4⋊C4—42no—
1265C4⋊C4—44no—
1266C4⋊C4—44no—
1267C4⋊C4—44no—
1268C4⋊C4—44no—
1269C4⋊C4—44no—
1270C4⋊C4—42no—
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⋊C4—44no—
1283C4⋊C4—42no—
1284C4⋊C4—42no—
1285C4⋊C4—44no—
1286C4⋊C4C2×#4114yes—
1287C4⋊C4C2×#4118yes—
1288C4⋊C42−1+414yes—
1289C22⋊C4—22no—
1290C22⋊C4—22no—
1291C22⋊C4—24no—
1292C22⋊C4—28no—
1293C22⋊C4—24no—
1294C22⋊C4—24no—
1295C22⋊C4—24no—
1296C22⋊C4—42no—
1297C22⋊C4—42no—
1298C22⋊C4—41no—
1299C22⋊C4—41no—
1300C22⋊C4—44no—
1301C42—22no—
1302C42—22no—
1303C42—22no—
1304C42—24no—
1305C42—28no—
1306C42—24no—
1307C42—28no—
1308C42—24no—
1309C42—22no—
1310C42—22no—
1311C42—24no—
1312C42—22no—
1313C42—22no—
1314C42—24no—
1315C42—24no—
1316C42—28no—
1317C42—24no—
1318C42—24no—
1319C42—22no—
1320C42—22no—
1321C42—22no—
1322C42—22no—
1323C42—24no—
1324C42—42no—
1325C42—42no—
1326C42—42no—
1327C42—42no—
1328C42—44no—
1329C42—44no—
1330C42—41no—
1331C42—41no—
1332C42—41no—
1333C42—41no—
1334C42—42no—
1335C42—42no—
1336C42—44no—
1337C42—44no—
1338C42—42no—
1339C42—44no—
1340C42—44no—
1341C42—44no—
1342C42—42no—
1343C42C2×#4114yes—
1344C42C2×#4118yes—
1345C23—21no—
1346C23—21no—
1347C23—21no—
1348C23—21no—
1349C23—21no—
1350C23—21no—
1351C23C2×2−1+412yes—
1352C23C2611yescharacteristic
1353Q8—28no—
1354Q8—44no—
1355Q8—48no—
1356Q8—44no—
1357Q8—44no—
1358Q8—48no—
1359Q8—84no—
1360C2×C4—21no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—21no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—22no—
1370C2×C4—28no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—24no—
1379C2×C4—22no—
1380C2×C4—24no—
1381C2×C4—21no—
1382C2×C4—21no—
1383C2×C4—22no—
1384C2×C4—21no—
1385C2×C4—21no—
1386C2×C4—21no—
1387C2×C4—21no—
1388C2×C4—21no—
1389C2×C4—21no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—24no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—24no—
1396C2×C4—22no—
1397C2×C4—22no—
1398C2×C4—24no—
1399C2×C4—21no—
1400C2×C4—22no—
1401C2×C4—21no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—21no—
1413C2×C4—22no—
1414C2×C4—22no—
1415C2×C4—24no—
1416C2×C4—22no—
1417C2×C4—22no—
1418C2×C4—24no—
1419C2×C4—24no—
1420C2×C4—24no—
1421C2×C4—24no—
1422C2×C4—22no—
1423C2×C4—22no—
1424C2×C4—22no—
1425C2×C4—21no—
1426C2×C4—22no—
1427C2×C4—21no—
1428C2×C4—21no—
1429C2×C4—21no—
1430C2×C4—21no—
1431C2×C4—22no—
1432C2×C4—22no—
1433C2×C4—24no—
1434C2×C4—22no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—21no—
1438C2×C4—21no—
1439C2×C4—22no—
1440C2×C4—22no—
1441C2×C4—22no—
1442C2×C4—22no—
1443C2×C4—22no—
1444C2×C4—22no—
1445C2×C4—22no—
1446C2×C4—22no—
1447C2×C4—24no—
1448C2×C4—22no—
1449C2×C4—22no—
1450C2×C4—21no—
1451C2×C4—21no—
1452C2×C4—44no—
1453C2×C4—82no—
1454C2×C4—84no—
1455C2×C4—84no—
1456C2×C4C22×#4114yes—
1457C2×C4C22×#4114yes—
1458C2×C4C22×#4112yes—
1459C2×C4C22×#4112yes—
1460C2×C4C22×#4112yes—
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—22no—
1468C22—22no—
1469C22—22no—
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—22no—
1483C4—24no—
1484C4—24no—
1485C4—24no—
1486C4—42no—
1487C4—44no—
1488C4—42no—
1489C4—42no—
1490C4—42no—
1491C4—41no—
1492C4—42no—
1493C4—41no—
1494C4—42no—
1495C4—44no—
1496C4—41no—
1497C4—41no—
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#351614yes—
1515C2—42no—
1516C2C2×#346111yescharacteristic
1517C2C2×#351611yescharacteristic
1518C2#6286111yescharacteristic
1519C2#6294711yescharacteristic
1520C2#6295011yescharacteristic
1521C2#6295611yescharacteristic
1522C2#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
1. #42850C2semidirect
3. #42782C2semidirect
6. #42289C2semidirect
8. #41786C2semidirect
13. #39183C2semidirect
14. #39170C2semidirect
15. #38243C2semidirect
16. #38227C2semidirect
17. #37630C2semidirect
18. #37630C2semidirect
19. #37630C2semidirect
20. #37580C2semidirect
23. #36313C2semidirect
24. #36285C2semidirect
25. #35972C2semidirect
28. #35870C2semidirect
33. #34337C2semidirect
34. #34328C2semidirect

Maximal subgroups

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

subgroupindex
#428502
#428482
#427822
#427722
#422912
#422892
#418022
#417862
#398192
#397242
#396932
#395992
#391832
#391702
#382432
#382272
#376302
#375802
#365992
#365522
#363132
#362852
#359722
#358862
#358702
#353232
#352912
#346292
#343372
#343282
#341452