Finite Group Databasebeta

← #8096721

Subgroups — #8096721

Order 512.

4510 conjugacy classes of subgroups.

The subgroup lattice has 1464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53137C211yesmaximal, characteristic, complemented
2#53134C212yesmaximal, complemented
3#53042C212yesmaximal, complemented
4#52961C211yesmaximal, characteristic, complemented
5#52942C212yesmaximal, complemented
6#52926C214yesmaximal, complemented
7#52749C212yesmaximal, complemented
8#52537C214yesmaximal, complemented
9#52292C211yesmaximal, characteristic, complemented
10#52178C212yesmaximal, complemented
11#46296C214yesmaximal, complemented
12#46046C214yesmaximal, complemented
13#45852C214yesmaximal, complemented
14#45695C212yesmaximal, complemented
15#45687C212yesmaximal, complemented
16#45680C212yesmaximal, complemented
17#45667C211yesmaximal, characteristic, complemented
18#45646C212yesmaximal, complemented
19#45617C212yesmaximal, complemented
20#45468C214yesmaximal, complemented
21#36581C211yesmaximal, characteristic, complemented
22#36451C212yesmaximal, complemented
23#36417C212yesmaximal, complemented
24#36269C212yesmaximal, complemented
25#36163C212yesmaximal, complemented
26#36062C211yesmaximal, characteristic, complemented
27#35985C211yesmaximal, characteristic, complemented
28#35875C212yesmaximal, complemented
29#35832C212yesmaximal, complemented
30C2×#555C2211yescharacteristic, complemented
31C2×#553C2211yescharacteristic
32C2×#552C2212yes—
33C2×#519C2211yescharacteristic, complemented
34C23×C4⋊C4C2211yescharacteristic
35#2865C2214yescomplemented
36#2864C2214yescomplemented
37#2861C2214yescomplemented
38#2855C2212yescomplemented
39#2851C2212yescomplemented
40#2850C2212yescomplemented
41#2849C2214yes—
42#2848C2212yes—
43#2847C2211yescharacteristic
44#2847C2212yes—
45#2841C2214yes—
46#2839C2214yescomplemented
47#2839C2214yescomplemented
48#2838C2214yescomplemented
49#2838C2214yescomplemented
50#2836C2214yescomplemented
51#2836C2214yescomplemented
52#2835C2212yes—
53#2834C2212yes—
54#2833C2214yescomplemented
55#2833C2212yescomplemented
56#2829C2214yescomplemented
57#2827C2214yescomplemented
58#2827C2214yescomplemented
59#2827C2214yescomplemented
60#2826C2214yes—
61#2826C2212yescomplemented
62#2824C2212yes—
63#2813C2214yes—
64#2809C2212yescomplemented
65#2807C2211yescharacteristic
66#2807C2212yescomplemented
67#2802C2214yescomplemented
68#2797C2214yes—
69#2796C2214yes—
70#2796C2212yes—
71#2786C2214yes—
72#2784C2214yescomplemented
73#2782C2214yes—
74#2781C2214yescomplemented
75#2780C2212yes—
76#2780C2214yes—
77#2778C2212yes—
78#2778C2214yes—
79#2772C2214yescomplemented
80#2765C2214yes—
81#2763C2214yes—
82#2762C2214yescomplemented
83#2761C2214yescomplemented
84#2760C2214yes—
85#2749C2214yescomplemented
86#2747C2214yescomplemented
87#2746C2212yes—
88#2746C2214yescomplemented
89#2745C2214yes—
90#2744C2214yescomplemented
91#2744C2214yescomplemented
92#2742C2212yes—
93#2741C2214yes—
94#2740C2214yes—
95#2740C2214yes—
96#2739C2214yes—
97#2738C2214yes—
98#2737C2214yes—
99#2736C2212yes—
100#2735C2211yescharacteristic
101#2722C2212yes—
102#2715C2214yes—
103#2708C2214yes—
104#2706C2214yes—
105#2701C2214yes—
106#2701C2214yes—
107#2693C2211yescharacteristic
108#2691C2214yes—
109#2688C2212yes—
110#2688C2214yes—
111#2685C2214yes—
112#2684C2212yes—
113#2678C2212yes—
114#2678C2214yes—
115#2668C2211yescharacteristic
116#2661C2212yescomplemented
117#2660C2211yescharacteristic, complemented
118#2652C2214yescomplemented
119#2645C2212yescomplemented
120#2637C2212yescomplemented
121#2637C2214yescomplemented
122#2629C2212yescomplemented
123#2624C2211yescharacteristic, complemented
124#2611C2214yescomplemented
125#2610C2214yes—
126#2609C2214yes—
127#2604C2212yescomplemented
128#2601C2214yescomplemented
129#2597C2214yescomplemented
130#2591C2212yes—
131#2580C2212yes—
132#2579C2212yes—
133#2576C2214yes—
134#2576C2214yes—
135#2576C2214yes—
136#2575C2214yescomplemented
137#2575C2214yescomplemented
138#2573C2214yescomplemented
139#2570C2212yescomplemented
140#2565C2212yescomplemented
141#2562C2212yes—
142#2562C2211yescharacteristic, complemented
143#2559C2214yescomplemented
144#2557C2214yes—
145#2555C2214yes—
146#2553C2214yes—
147#2550C2212yescomplemented
148#2547C2211yescharacteristic
149#2543C2212yes—
150#2540C2212yes—
151#2538C2212yes—
152#2537C2212yes—
153#2535C2212yescomplemented
154#2530C2214yes—
155#2530C2214yescomplemented
156#2528C2214yescomplemented
157#2528C2214yescomplemented
158#2526C2214yes—
159#2521C2214yescomplemented
160#2521C2214yescomplemented
161#2514C2212yescomplemented
162#2508C2212yescomplemented
163#2507C2212yescomplemented
164#2505C2214yescomplemented
165#2504C2211yescharacteristic
166#2503C2212yes—
167#2498C2212yescomplemented
168#2497C2212yes—
169#2496C2212yes—
170#2494C2214yescomplemented
171#2494C2212yescomplemented
172#2492C2212yes—
173#2490C2212yescomplemented
174#2489C2212yes—
175#2489C2212yes—
176#2487C2211yescharacteristic
177#2486C2212yes—
178#2485C2212yes—
179#2485C2212yescomplemented
180#2484C2214yes—
181#2481C2214yes—
182#2481C2214yes—
183#2481C2214yes—
184#2476C2214yes—
185#2476C2214yes—
186#2475C2214yescomplemented
187#2473C2214yes—
188#2473C2214yes—
189#2471C2214yes—
190#2470C2214yes—
191#2470C2214yescomplemented
192#2464C2214yes—
193#2462C2214yescomplemented
194#2458C2214yes—
195#2454C2212yescomplemented
196#2453C2212yescomplemented
197#2447C2212yescomplemented
198#2443C2214yes—
199#2442C2212yes—
200#2442C2212yes—
201#2442C2212yes—
202#2441C2212yescomplemented
203#2436C2211yescharacteristic, complemented
204#2427C2212yes—
205#2426C2212yes—
206#2423C2212yes—
207#2422C2212yes—
208#2421C2212yescomplemented
209#2419C2214yes—
210#2417C2212yes—
211#2417C2212yes—
212#2416C2212yes—
213#2415C2212yes—
214#2415C2212yescomplemented
215#2414C2212yes—
216#2413C2214yes—
217#2409C2212yes—
218#2409C2211yescharacteristic
219#2409C2212yescomplemented
220#2401C2212yes—
221#2398C2212yes—
222#2397C2211yescharacteristic
223#2396C2214yes—
224#2395C2212yes—
225#2395C2214yes—
226#2395C2211yescharacteristic
227#2392C2212yes—
228#2379C2212yes—
229#2377C2214yes—
230#2377C2214yes—
231#2376C2214yes—
232#2376C2214yes—
233#2370C2212yescomplemented
234#2367C2212yescomplemented
235#2362C2212yescomplemented
236#2361C2212yes—
237#2360C2212yes—
238#2360C2212yes—
239#2355C2212yescomplemented
240#2354C2212yescomplemented
241#2352C2212yes—
242#2352C2212yes—
243#2352C2212yes—
244#2346C2211yescharacteristic, complemented
245#2345C2211yescharacteristic
246#2344C2212yes—
247C4×#126C2214yes—
248C4×#123C2212yes—
249C4×#121C2212yes—
250C4×#121C2212yes—
251C4×#120C2212yes—
252C4×#120C2211yescharacteristic
253C4×#120C2212yes—
254#2298C2214yes—
255#2293C2214yes—
256#2280C2214yes—
257#2275C2211yescharacteristic, complemented
258C4×#117C2212yescomplemented
259C23×Q8C2311yescharacteristic
260C24×C4C2311yescharacteristic
261C24×C4C2312yes—
262#555—44no—
263#553—44no—
264#552—48no—
265C2×C4⋊Q8C2311yescharacteristic
266C2×#126C2314yes—
267C2×#126C2314yes—
268C2×#126C2312yes—
269C2×#125C2312yes—
270C2×#125C2311yescharacteristic
271C2×#125C2312yes—
272C2×#125C2314yes—
273C2×#124C2312yes—
274C2×#124C2314yes—
275C2×#124C2312yes—
276C2×#123C2314yes—
277C2×#123C2314yes—
278C2×#123C2314yes—
279C2×#123C2312yes—
280C2×#123C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×#121C2312yes—
287C2×#121C2312yes—
288C2×#121C2314yes—
289C2×#121C2311yescharacteristic
290C2×#121C2312yes—
291C2×#121C2311yescharacteristic
292C2×#121C2314yes—
293C2×#121C2312yes—
294C2×#121C2312yes—
295C2×#121C2312yes—
296C2×#120C2311yescharacteristic
297C2×#120C2312yes—
298C2×#120C2312yes—
299#519—44no—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×D4C2311yescharacteristic
305C2×C4×D4C2312yes—
306C2×C4×D4C2311yescharacteristic
307C2×C4×D4C2312yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2314yes—
312C2×C4×D4C2312yes—
313C2×C4×D4C2311yescharacteristic
314C2×C4×D4C2312yes—
315C2×#117C2311yescharacteristic
316C2×#117C2312yes—
317C2×#117C2314yes—
318C2×#117C2314yes—
319C2×#117C2314yes—
320C2×#117C2312yes—
321C2×#117C2311yescharacteristic
322C2×#117C2312yes—
323C22×C4⋊C4—44no—
324C22×C4⋊C4C2312yes—
325C22×C4⋊C4C2311yescharacteristic
326C22×C4⋊C4C2312yes—
327C22×C4⋊C4C2314yes—
328C22×C4⋊C4C2312yes—
329C22×C4⋊C4C2311yescharacteristic
330C22×C42C2312yes—
331#401C2314yes—
332#401C2314yes—
333#401C2314yes—
334#401C2312yes—
335#400C2314yes—
336#400C2312yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2312yes—
349#400C2314yes—
350#400C2314yes—
351#400C2312yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2312yes—
356#400C2312yes—
357#400C2314yes—
358#400C2311yescharacteristic
359#400C2314yes—
360#399C2314yes—
361#399C2312yes—
362#399C2314yes—
363#399C2314yes—
364#399C2311yescharacteristic
365#399C2312yes—
366#399C2312yes—
367#399C2314yes—
368#399C2311yescharacteristic
369#399C2311yescharacteristic
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2311yescharacteristic
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2312yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2312yes—
390#398C2312yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2312yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2312yes—
403#397C2314yes—
404#397C2312yes—
405#397C2312yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#397C2312yes—
411#397C2312yes—
412#397C2311yescharacteristic
413#397C2314yes—
414#397C2314yes—
415#397C2312yes—
416#397C2312yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#396C2312yes—
421#396C2314yes—
422#396C2314yes—
423#396C2314yes—
424#396C2314yes—
425#396C2312yes—
426#396C2314yes—
427#396C2314yes—
428#396C2314yes—
429#396C2314yes—
430#396C2312yes—
431#395C2314yes—
432#395C2314yes—
433#395C2314yes—
434#395C2312yes—
435#395C2314yes—
436#394C2314yes—
437#394C2312yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2312yes—
447#394C2314yes—
448#394C2314yes—
449#394C2312yes—
450#394C2312yes—
451#394C2312yes—
452#394C2314yes—
453#394C2314yes—
454#394C2314yes—
455#393C2312yes—
456#393C2314yes—
457#393C2312yes—
458#393C2314yes—
459#393C2312yes—
460#393C2314yes—
461#392C2311yescharacteristic
462#392C2314yes—
463#392C2311yescharacteristic
464#392C2314yes—
465#392C2312yes—
466#392C2312yes—
467#392C2314yes—
468#391C2312yes—
469#391C2312yes—
470#391C2314yes—
471#391C2312yes—
472#391C2312yes—
473#391C2312yes—
474#391C2314yes—
475#391C2312yes—
476#391C2312yes—
477#390C2314yes—
478#390C2314yes—
479#390C2312yes—
480#390C2314yes—
481#390C2314yes—
482#390C2312yes—
483#390C2314yes—
484#390C2312yes—
485#390C2314yes—
486#390C2314yes—
487#390C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2312yes—
495#389C2314yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2314yes—
500#389C2314yes—
501#389C2312yes—
502#389C2314yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2314yes—
509#389C2314yes—
510#388C2312yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2312yes—
535#388C2314yes—
536#388C2314yes—
537#388C2312yes—
538#388C2314yes—
539#388C2314yes—
540#388C2312yes—
541#388C2314yes—
542#388C2314yes—
543#388C2312yes—
544#388C2312yes—
545#388C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2312yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2312yes—
581#386C2314yes—
582#386C2312yes—
583#386C2314yes—
584#386C2314yes—
585#386C2312yes—
586#386C2314yes—
587#386C2314yes—
588#386C2312yes—
589#386C2312yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#386C2312yes—
595#386C2312yes—
596#386C2311yescharacteristic
597#386C2312yes—
598#386C2312yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2312yes—
603#386C2314yes—
604#386C2312yes—
605#386C2314yes—
606#386C2314yes—
607#386C2312yes—
608#386C2312yes—
609#386C2314yes—
610#386C2312yes—
611#386C2312yes—
612#385C2312yes—
613#385C2314yes—
614#385C2312yes—
615#385C2312yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2311yescharacteristic
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2312yes—
633#385C2314yes—
634#385C2314yes—
635#385C2312yes—
636#385C2312yes—
637#385C2312yes—
638#384C2312yes—
639#384C2312yes—
640#383C2314yes—
641#382C2312yes—
642#382C2312yes—
643#382C2314yes—
644#382C2314yes—
645#382C2312yes—
646#382C2314yes—
647#382C2314yes—
648#382C2312yes—
649#381C2312yes—
650#381C2314yes—
651#381C2314yes—
652#381C2314yes—
653#381C2314yes—
654#381C2314yes—
655#381C2314yes—
656#380C2311yescharacteristic
657#380C2312yes—
658#380C2312yes—
659#380C2312yes—
660#380C2312yes—
661#380C2312yes—
662#380C2312yes—
663#380C2314yes—
664#380C2314yes—
665#380C2311yescharacteristic
666#380C2312yes—
667#380C2312yes—
668#380C2312yes—
669#380C2312yes—
670#380C2314yes—
671#380C2314yes—
672#380C2314yes—
673#380C2314yes—
674#380C2314yes—
675#380C2312yes—
676#380C2314yes—
677#380C2312yes—
678#379C2314yes—
679#379C2311yescharacteristic
680#379C2312yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C22⋊C4C2312yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2311yescharacteristic
704C4×C22⋊C4C2311yescharacteristic
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2312yes—
712#376C2312yes—
713#376C2314yes—
714#376C2311yescharacteristic
715C2×#95C2312yes—
716C43C2314yes—
717C25C2411yescharacteristic
718C22×Q8—42no—
719C22×Q8—44no—
720C22×Q8C2412yes—
721C22×Q8C2412yes—
722C22×Q8C2412yes—
723C22×D4C2411yescharacteristic
724C22×D4C2412yes—
725C22×D4C2412yes—
726C22×D4C2412yes—
727C22×D4C2414yes—
728C22×D4C2411yescharacteristic
729C22×D4C2412yes—
730C22×D4C2412yes—
731C22×D4C2411yescharacteristic
732C22×D4C2412yes—
733C22×D4C2412yes—
734C22×D4C2414yes—
735C23×C4—42no—
736C23×C4—44no—
737C23×C4—44no—
738C23×C4—48no—
739C23×C4C2411yescharacteristic
740C23×C4C2412yes—
741C23×C4C2412yes—
742C23×C4C2411yescharacteristic
743C23×C4C2414yes—
744C23×C4C2412yes—
745C23×C4C2414yes—
746C23×C4C2412yes—
747C23×C4C2412yes—
748C23×C4C2411yescharacteristic
749C23×C4C2412yes—
750C23×C4C2412yes—
751C23×C4C2414yes—
752C23×C4C2412yes—
753C23×C4C2412yes—
754C4⋊Q8—42no—
755#126—48no—
756#126—44no—
757#126—48no—
758#125—44no—
759#125—48no—
760#125—44no—
761#125—42no—
762#124—48no—
763#124—44no—
764#124—44no—
765#123—48no—
766#123—44no—
767#123—48no—
768#123—44no—
769#123—48no—
770C22⋊Q8—44no—
771C22⋊Q8—44no—
772C22⋊Q8—44no—
773C22⋊Q8—44no—
774C22⋊Q8—44no—
775#121—44no—
776#121—44no—
777#121—44no—
778#121—44no—
779#121—48no—
780#121—44no—
781#121—42no—
782#121—42no—
783#121—44no—
784#121—48no—
785#120—44no—
786#120—42no—
787#120—44no—
788C4×Q8—28no—
789C4×Q8—44no—
790C4×Q8—44no—
791C4×Q8—44no—
792C4×D4—24no—
793C4×D4—44no—
794C4×D4—44no—
795C4×D4—44no—
796C4×D4—44no—
797C4×D4—44no—
798C4×D4—44no—
799C4×D4—44no—
800C4×D4—42no—
801C4×D4—42no—
802C4×D4—48no—
803#117—24no—
804#117—28no—
805#117—42no—
806#117—48no—
807#117—44no—
808#117—48no—
809#117—48no—
810#117—44no—
811C2×C4⋊C4—28no—
812C2×C4⋊C4—24no—
813C2×C4⋊C4—44no—
814C2×C4⋊C4—42no—
815C2×C4⋊C4—48no—
816C2×C4⋊C4—44no—
817C2×C4⋊C4C2411yescharacteristic
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2411yescharacteristic
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2411yescharacteristic
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2411yescharacteristic
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2411yescharacteristic
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2411yescharacteristic
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2411yescharacteristic
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2412yes—
930C2×C42—44no—
931C2×C42C2414yes—
932C2×C42C2414yes—
933C2×C42C2412yes—
934C2×C42C2412yes—
935C2×C42C2411yescharacteristic
936C2×C42C2412yes—
937C2×C42C2412yes—
938C2×C42C2412yes—
939C2×C42C2414yes—
940C2×C42C2414yes—
941C2×C42C2414yes—
942C2×C42C2414yes—
943C2×C42C2414yes—
944C2×C42C2412yes—
945C2×C42C2414yes—
946C2×C42C2412yes—
947C2×C42C2414yes—
948C2×C42C2412yes—
949#95C2411yescharacteristic
950#95C2414yes—
951#95C2412yes—
952#95C2411yescharacteristic
953#95C2412yes—
954#95C2411yescharacteristic
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2412yes—
960#95C2414yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2412yes—
973#95C2414yes—
974#95C2412yes—
975#95C2414yes—
976#95C2412yes—
977#95C2411yescharacteristic
978#95C2414yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2414yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2412yes—
992#95C2412yes—
993#95C2414yes—
994#95C2414yes—
995#95C2412yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016C24—22no—
1017C24—24no—
1018C24—41no—
1019C24—42no—
1020C24—41no—
1021C24C2512yes—
1022C24C2511yescharacteristic
1023C24C2512yes—
1024C24C2512yes—
1025C24C2511yescharacteristic
1026C2×Q8—24no—
1027C2×Q8—24no—
1028C2×Q8—24no—
1029C2×Q8—42no—
1030C2×Q8—44no—
1031C2×Q8—42no—
1032C2×Q8—42no—
1033C2×Q8—42no—
1034C2×Q8—416no—
1035C2×D4—28no—
1036C2×D4—24no—
1037C2×D4—24no—
1038C2×D4—22no—
1039C2×D4—24no—
1040C2×D4—24no—
1041C2×D4—24no—
1042C2×D4—22no—
1043C2×D4—24no—
1044C2×D4—42no—
1045C2×D4—41no—
1046C2×D4—41no—
1047C2×D4—42no—
1048C2×D4—42no—
1049C2×D4—42no—
1050C2×D4—42no—
1051C2×D4—42no—
1052C2×D4—44no—
1053C2×D4—42no—
1054C2×D4—42no—
1055C2×D4—42no—
1056C2×D4—42no—
1057C2×D4—44no—
1058C2×D4—42no—
1059C2×D4—42no—
1060C2×D4—42no—
1061C2×D4—42no—
1062C2×D4—41no—
1063C2×D4—42no—
1064C2×D4—44no—
1065C2×D4—44no—
1066C2×D4—44no—
1067C2×D4—44no—
1068C22×C4—28no—
1069C22×C4—28no—
1070C22×C4—28no—
1071C22×C4—22no—
1072C22×C4—24no—
1073C22×C4—22no—
1074C22×C4—24no—
1075C22×C4—24no—
1076C22×C4—24no—
1077C22×C4—24no—
1078C22×C4—24no—
1079C22×C4—24no—
1080C22×C4—24no—
1081C22×C4—24no—
1082C22×C4—24no—
1083C22×C4—42no—
1084C22×C4—41no—
1085C22×C4—42no—
1086C22×C4—44no—
1087C22×C4—42no—
1088C22×C4—42no—
1089C22×C4—42no—
1090C22×C4—44no—
1091C22×C4—42no—
1092C22×C4—42no—
1093C22×C4—42no—
1094C22×C4—44no—
1095C22×C4—44no—
1096C22×C4—42no—
1097C22×C4—42no—
1098C22×C4—42no—
1099C22×C4—44no—
1100C22×C4—44no—
1101C22×C4—44no—
1102C22×C4—42no—
1103C22×C4—44no—
1104C22×C4—44no—
1105C22×C4—44no—
1106C22×C4—416no—
1107C22×C4—816no—
1108C22×C4C2512yes—
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2512yes—
1112C22×C4C2511yescharacteristic
1113C22×C4C2512yes—
1114C22×C4C2512yes—
1115C22×C4C2512yes—
1116C22×C4C2514yes—
1117C22×C4C2514yes—
1118C22×C4C2514yes—
1119C22×C4C2514yes—
1120C22×C4C2511yescharacteristic
1121C22×C4C2514yes—
1122C22×C4C2511yescharacteristic
1123C22×C4C2511yescharacteristic
1124C22×C4C2512yes—
1125C22×C4C2514yes—
1126C22×C4C2512yes—
1127C22×C4C2512yes—
1128C22×C4C2512yes—
1129C22×C4C2512yes—
1130C22×C4C2512yes—
1131C22×C4C2511yescharacteristic
1132C4⋊C4—22no—
1133C4⋊C4—24no—
1134C4⋊C4—24no—
1135C4⋊C4—28no—
1136C4⋊C4—22no—
1137C4⋊C4—24no—
1138C4⋊C4—28no—
1139C4⋊C4—24no—
1140C4⋊C4—24no—
1141C4⋊C4—24no—
1142C4⋊C4—42no—
1143C4⋊C4—44no—
1144C4⋊C4—42no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—42no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—41no—
1151C4⋊C4—41no—
1152C4⋊C4—44no—
1153C4⋊C4—41no—
1154C4⋊C4—42no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—42no—
1160C4⋊C4—42no—
1161C4⋊C4—44no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4—41no—
1165C4⋊C4—42no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—42no—
1169C4⋊C4—42no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—42no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—42no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4H(5,𝔽2)14yes—
1187C22⋊C4—24no—
1188C22⋊C4—28no—
1189C22⋊C4—24no—
1190C22⋊C4—24no—
1191C22⋊C4—22no—
1192C22⋊C4—24no—
1193C22⋊C4—28no—
1194C22⋊C4—24no—
1195C22⋊C4—24no—
1196C22⋊C4—28no—
1197C22⋊C4—24no—
1198C22⋊C4—41no—
1199C22⋊C4—42no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—42no—
1203C22⋊C4—44no—
1204C22⋊C4—42no—
1205C22⋊C4—42no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—42no—
1209C22⋊C4—42no—
1210C22⋊C4—42no—
1211C22⋊C4—42no—
1212C22⋊C4—42no—
1213C22⋊C4—44no—
1214C22⋊C4—42no—
1215C22⋊C4—42no—
1216C22⋊C4—42no—
1217C22⋊C4—44no—
1218C22⋊C4—41no—
1219C22⋊C4—42no—
1220C22⋊C4—41no—
1221C22⋊C4—42no—
1222C22⋊C4—42no—
1223C22⋊C4—42no—
1224C22⋊C4—44no—
1225C22⋊C4—42no—
1226C22⋊C4—42no—
1227C22⋊C4—42no—
1228C22⋊C4—42no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—42no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—42no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C42—28no—
1246C42—24no—
1247C42—28no—
1248C42—24no—
1249C42—22no—
1250C42—24no—
1251C42—24no—
1252C42—24no—
1253C42—42no—
1254C42—42no—
1255C42—44no—
1256C42—44no—
1257C42—44no—
1258C42—44no—
1259C42—44no—
1260C42—44no—
1261C42—42no—
1262C42—44no—
1263C23—22no—
1264C23—21no—
1265C23—22no—
1266C23—22no—
1267C23—22no—
1268C23—22no—
1269C23—22no—
1270C23—22no—
1271C23—22no—
1272C23—21no—
1273C23—22no—
1274C23—21no—
1275C23—22no—
1276C23—22no—
1277C23—22no—
1278C23—24no—
1279C23—21no—
1280C23—22no—
1281C23—24no—
1282C23—22no—
1283C23—22no—
1284C23—22no—
1285C23—22no—
1286C23—22no—
1287C23—21no—
1288C23—22no—
1289C23—22no—
1290C23—44no—
1291C23—48no—
1292C23—48no—
1293C23—44no—
1294C23—44no—
1295C23#58512yes—
1296C23#58514yes—
1297C23C2611yescharacteristic
1298Q8—48no—
1299Q8—48no—
1300Q8—162no—
1301D4—44no—
1302D4—84no—
1303D4—84no—
1304D4—84no—
1305D4—88no—
1306D4—84no—
1307D4—84no—
1308D4—82no—
1309D4—82no—
1310D4—84no—
1311D4—162no—
1312D4—164no—
1313C2×C4—24no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—21no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—24no—
1320C2×C4—21no—
1321C2×C4—24no—
1322C2×C4—21no—
1323C2×C4—21no—
1324C2×C4—24no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—21no—
1339C2×C4—22no—
1340C2×C4—24no—
1341C2×C4—24no—
1342C2×C4—24no—
1343C2×C4—24no—
1344C2×C4—24no—
1345C2×C4—24no—
1346C2×C4—24no—
1347C2×C4—24no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—24no—
1356C2×C4—22no—
1357C2×C4—24no—
1358C2×C4—24no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—24no—
1362C2×C4—22no—
1363C2×C4—24no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—24no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—24no—
1370C2×C4—24no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—21no—
1376C2×C4—416no—
1377C2×C4—48no—
1378C2×C4—44no—
1379C2×C4—48no—
1380C2×C4—48no—
1381C2×C4—44no—
1382C2×C4—48no—
1383C2×C4—44no—
1384C2×C4—84no—
1385C2×C4—84no—
1386C2×C4—88no—
1387C2×C4—84no—
1388C2×C4—84no—
1389C2×C4—84no—
1390C2×C4—164no—
1391C2×C4C2×H(5,𝔽2)14yes—
1392C2×C4C2×H(5,𝔽2)12yes—
1393C2×C4#58514yes—
1394C22—24no—
1395C22—24no—
1396C22—24no—
1397C22—24no—
1398C22—22no—
1399C22—416no—
1400C22—41no—
1401C22—42no—
1402C22—42no—
1403C22—42no—
1404C22—42no—
1405C22—42no—
1406C22—41no—
1407C22—42no—
1408C22—42no—
1409C22—41no—
1410C22—42no—
1411C22—44no—
1412C22—42no—
1413C22—42no—
1414C22—42no—
1415C22—42no—
1416C22—42no—
1417C22—44no—
1418C22—42no—
1419C22—41no—
1420C22—42no—
1421C22—41no—
1422C22—42no—
1423C22—42no—
1424C22C22×H(5,𝔽2)11yescharacteristic
1425C22C2×#58512yes—
1426C22C2×#58511yescharacteristic
1427C22C2×#58512yes—
1428C222−1+611yescharacteristic
1429C4—24no—
1430C4—44no—
1431C4—42no—
1432C4—41no—
1433C4—42no—
1434C4—42no—
1435C4—42no—
1436C4—44no—
1437C4—42no—
1438C4—44no—
1439C4—44no—
1440C4—42no—
1441C4—42no—
1442C4—42no—
1443C4—42no—
1444C4—42no—
1445C4—41no—
1446C4—44no—
1447C4—42no—
1448C4—41no—
1449C4—42no—
1450C4—41no—
1451C4—44no—
1452C4#352914yes—
1453C2—44no—
1454C2—42no—
1455C2—82no—
1456C2—82no—
1457C2—81no—
1458C2C2×#352911yescharacteristic
1459C2#6290712yes—
1460C2#6291911yescharacteristic
1461C2#6301711yescharacteristic
1462C2#6302712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53137C2semidirect
2. #53134C2semidirect
3. #53042C2semidirect
4. #52961C2semidirect
5. #52942C2semidirect
6. #52926C2semidirect
7. #52749C2semidirect
8. #52537C2semidirect
9. #52292C2semidirect
10. #52178C2semidirect
11. #46296C2semidirect
12. #46046C2semidirect
13. #45852C2semidirect
14. #45695C2semidirect
15. #45687C2semidirect
16. #45680C2semidirect
17. #45667C2semidirect
18. #45646C2semidirect
19. #45617C2semidirect
20. #45468C2semidirect
21. #36581C2semidirect
22. #36451C2semidirect
23. #36417C2semidirect
24. #36269C2semidirect
25. #36163C2semidirect
26. #36062C2semidirect
27. #35985C2semidirect
28. #35875C2semidirect
29. #35832C2semidirect
30. C2×#555C22semidirect
33. C2×#519C22semidirect
35. #2865C22semidirect
36. #2864C22semidirect
37. #2861C22semidirect
38. #2855C22semidirect
39. #2851C22semidirect
40. #2850C22semidirect
46. #2839C22semidirect
47. #2839C22semidirect
48. #2838C22semidirect
49. #2838C22semidirect
50. #2836C22semidirect
51. #2836C22semidirect
54. #2833C22semidirect
55. #2833C22semidirect
56. #2829C22semidirect
57. #2827C22semidirect
58. #2827C22semidirect
59. #2827C22semidirect
61. #2826C22semidirect
64. #2809C22semidirect
66. #2807C22semidirect
67. #2802C22semidirect
72. #2784C22semidirect
74. #2781C22semidirect
79. #2772C22semidirect
82. #2762C22semidirect
83. #2761C22semidirect
85. #2749C22semidirect
86. #2747C22semidirect
88. #2746C22semidirect
90. #2744C22semidirect
91. #2744C22semidirect
116. #2661C22semidirect
117. #2660C22semidirect
118. #2652C22semidirect
119. #2645C22semidirect
120. #2637C22semidirect
121. #2637C22semidirect
122. #2629C22semidirect
123. #2624C22semidirect
124. #2611C22semidirect
127. #2604C22semidirect
128. #2601C22semidirect
129. #2597C22semidirect
136. #2575C22semidirect
137. #2575C22semidirect
138. #2573C22semidirect
139. #2570C22semidirect
140. #2565C22semidirect
142. #2562C22semidirect
143. #2559C22semidirect
147. #2550C22semidirect
153. #2535C22semidirect
155. #2530C22semidirect
156. #2528C22semidirect
157. #2528C22semidirect
159. #2521C22semidirect
160. #2521C22semidirect
161. #2514C22semidirect
162. #2508C22semidirect
163. #2507C22semidirect
164. #2505C22semidirect
167. #2498C22semidirect
170. #2494C22semidirect
171. #2494C22semidirect
173. #2490C22semidirect
179. #2485C22semidirect
186. #2475C22semidirect
191. #2470C22semidirect
193. #2462C22semidirect
195. #2454C22semidirect
196. #2453C22semidirect
197. #2447C22semidirect
202. #2441C22semidirect
203. #2436C22semidirect
208. #2421C22semidirect
214. #2415C22semidirect
219. #2409C22semidirect
233. #2370C22semidirect
234. #2367C22semidirect
235. #2362C22semidirect
239. #2355C22semidirect
240. #2354C22semidirect
244. #2346C22semidirect
257. #2275C22semidirect
258. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#531372
#531342
#530422
#529612
#529422
#529262
#527492
#525372
#522922
#521782
#462962
#460462
#458522
#456952
#456872
#456802
#456672
#456462
#456172
#454682
#365812
#364512
#364172
#362692
#361632
#360622
#359852
#358752
#358322