Finite Group Databasebeta

← #8726637

Subgroups — #8726637

Order 512.

4476 conjugacy classes of subgroups.

The subgroup lattice has 1466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59645C212yesmaximal, complemented
2#59431C212yesmaximal, complemented
3#59421C212yesmaximal, complemented
4#59201C211yesmaximal, characteristic, complemented
5#59025C212yesmaximal, complemented
6#56840C214yesmaximal, complemented
7#55502C214yesmaximal, complemented
8#54948C214yesmaximal, complemented
9#53903C212yesmaximal, complemented
10#53044C212yesmaximal, complemented
11#53005C211yesmaximal, characteristic, complemented
12#52294C211yesmaximal, characteristic, complemented
13#47489C214yesmaximal, complemented
14#47182C212yesmaximal, complemented
15#45420C212yesmaximal, complemented
16#45419C211yesmaximal, characteristic, complemented
17#45402C212yesmaximal, complemented
18#44405C214yesmaximal, complemented
19#42691C212yesmaximal, complemented
20#42485C211yesmaximal, characteristic, complemented
21#41896C212yesmaximal, complemented
22#41059C214yesmaximal, complemented
23#40104C212yesmaximal, complemented
24#39910C212yesmaximal, complemented
25#39722C211yesmaximal, characteristic, complemented
26#39527C212yesmaximal, complemented
27#39216C212yesmaximal, complemented
28#36083C211yesmaximal, characteristic, complemented
29#35759C212yesmaximal, complemented
30C2×#556C2212yes—
31C2×#553C2211yescharacteristic
32C2×D4×Q8C2211yescharacteristic, complemented
33C22×C22⋊Q8C2211yescharacteristic
34C2×#520C2211yescharacteristic, complemented
35#2863C2212yescomplemented
36#2847C2211yescharacteristic
37#2844C2212yescomplemented
38#2832C2214yescomplemented
39#2831C2214yes—
40#2830C2214yes—
41#2829C2214yescomplemented
42#2828C2214yes—
43#2824C2212yes—
44#2814C2212yescomplemented
45#2813C2214yes—
46#2803C2214yes—
47#2803C2214yescomplemented
48#2800C2214yes—
49#2798C2214yescomplemented
50#2798C2214yescomplemented
51#2797C2214yes—
52#2785C2214yes—
53#2785C2212yescomplemented
54#2779C2214yes—
55#2775C2214yescomplemented
56#2774C2214yescomplemented
57#2773C2214yes—
58#2770C2214yescomplemented
59#2767C2214yescomplemented
60#2767C2214yescomplemented
61#2764C2212yescomplemented
62#2763C2212yes—
63#2763C2212yes—
64#2763C2211yescharacteristic
65#2761C2214yes—
66#2758C2214yescomplemented
67#2758C2214yescomplemented
68#2757C2214yes—
69#2756C2214yes—
70#2755C2214yescomplemented
71#2754C2214yes—
72#2753C2214yes—
73#2753C2212yes—
74#2753C2212yes—
75#2753C2212yes—
76#2751C2214yescomplemented
77#2749C2214yes—
78#2743C2214yes—
79#2742C2214yescomplemented
80#2737C2214yes—
81#2737C2214yescomplemented
82#2736C2212yes—
83#2736C2211yescharacteristic
84#2723C2214yes—
85#2722C2212yes—
86#2715C2214yes—
87#2714C2214yes—
88#2712C2212yes—
89#2712C2211yescharacteristic
90#2705C2214yescomplemented
91#2702C2214yes—
92#2702C2214yescomplemented
93#2700C2214yes—
94#2698C2214yescomplemented
95#2697C2212yes—
96#2696C2214yes—
97#2689C2214yes—
98#2686C2214yes—
99#2685C2214yes—
100#2681C2214yes—
101#2670C2211yescharacteristic
102#2670C2212yes—
103#2668C2214yes—
104#2665C2214yescomplemented
105#2665C2214yescomplemented
106#2660C2211yescharacteristic, complemented
107#2654C2214yes—
108#2650C2214yes—
109#2649C2214yes—
110#2638C2212yes—
111#2637C2212yescomplemented
112#2636C2214yes—
113#2632C2214yes—
114#2617C2212yes—
115#2616C2212yescomplemented
116#2615C2211yescharacteristic, complemented
117#2614C2212yescomplemented
118#2607C2212yescomplemented
119#2605C2214yescomplemented
120#2604C2214yes—
121#2603C2212yescomplemented
122#2597C2214yescomplemented
123#2595C2214yes—
124#2592C2212yescomplemented
125#2584C2212yescomplemented
126#2584C2211yescharacteristic, complemented
127#2582C2212yescomplemented
128#2581C2214yescomplemented
129#2581C2212yescomplemented
130#2578C2214yes—
131#2578C2214yes—
132#2572C2214yes—
133#2572C2214yescomplemented
134#2563C2211yescharacteristic
135#2562C2212yes—
136#2560C2214yes—
137#2560C2214yes—
138#2560C2214yes—
139#2560C2214yescomplemented
140#2559C2214yes—
141#2557C2214yes—
142#2553C2214yes—
143#2540C2212yes—
144#2538C2212yes—
145#2537C2212yes—
146#2535C2212yes—
147#2529C2214yes—
148#2529C2214yescomplemented
149#2526C2214yes—
150#2525C2214yescomplemented
151#2525C2214yescomplemented
152#2523C2212yes—
153#2523C2212yes—
154#2521C2214yes—
155#2517C2214yescomplemented
156#2515C2214yes—
157#2515C2214yescomplemented
158#2513C2214yes—
159#2513C2214yescomplemented
160#2508C2214yescomplemented
161#2504C2212yes—
162#2504C2211yescharacteristic, complemented
163#2503C2212yescomplemented
164#2499C2212yes—
165#2497C2212yescomplemented
166#2496C2212yes—
167#2496C2212yescomplemented
168#2495C2212yes—
169#2495C2212yes—
170#2495C2214yescomplemented
171#2492C2212yes—
172#2492C2212yescomplemented
173#2490C2212yes—
174#2489C2212yes—
175#2489C2212yescomplemented
176#2489C2212yescomplemented
177#2487C2212yes—
178#2487C2212yes—
179#2486C2211yescharacteristic
180#2485C2212yes—
181#2481C2214yes—
182#2480C2214yes—
183#2472C2214yes—
184#2469C2214yescomplemented
185#2466C2214yescomplemented
186#2466C2214yescomplemented
187#2465C2214yes—
188#2464C2214yes—
189#2459C2214yes—
190#2459C2214yes—
191#2457C2214yescomplemented
192#2442C2212yescomplemented
193#2441C2212yes—
194#2440C2212yes—
195#2439C2212yes—
196#2439C2212yescomplemented
197#2439C2212yescomplemented
198#2436C2214yes—
199#2436C2211yescharacteristic
200#2427C2212yes—
201#2427C2212yescomplemented
202#2426C2214yes—
203#2426C2212yescomplemented
204#2423C2212yescomplemented
205#2422C2212yescomplemented
206#2421C2214yes—
207#2421C2212yes—
208#2421C2214yescomplemented
209#2420C2212yes—
210#2416C2212yes—
211#2415C2212yes—
212#2415C2212yes—
213#2415C2212yes—
214#2414C2212yes—
215#2409C2211yescharacteristic
216#2409C2212yes—
217#2409C2212yes—
218#2398C2212yes—
219#2398C2211yescharacteristic
220#2398C2212yes—
221#2398C2214yescomplemented
222#2388C2211yescharacteristic
223#2388C2212yes—
224#2374C2212yes—
225#2374C2214yescomplemented
226#2373C2214yes—
227#2363C2212yes—
228#2363C2212yescomplemented
229#2362C2212yes—
230#2360C2214yes—
231#2360C2212yescomplemented
232#2360C2212yescomplemented
233#2355C2212yescomplemented
234#2352C2212yes—
235#2352C2212yes—
236#2352C2212yes—
237#2347C2212yes—
238#2346C2212yescomplemented
239#2346C2211yescharacteristic, complemented
240#2345C2211yescharacteristic
241Q8×C22⋊C4C2212yes—
242Q8×C22⋊C4C2214yescomplemented
243#2334C2214yescomplemented
244#2333C2214yes—
245#2333C2214yes—
246#2321C2212yes—
247#2320C2212yescomplemented
248#2320C2214yescomplemented
249#2319C2211yescharacteristic, complemented
250C4×C4⋊Q8C2212yescomplemented
251C4×#125C2212yescomplemented
252C4×#124C2212yes—
253C4×#124C2212yes—
254C4×#124C2212yes—
255C4×#124C2212yescomplemented
256C4×#120C2211yescharacteristic
257C4×#120C2212yes—
258#2280C2212yes—
259C22×#41C2311yescharacteristic
260C23×Q8C2311yescharacteristic
261C23×Q8C2312yes—
262C24×C4C2311yescharacteristic
263#556—48no—
264#553—44no—
265D4×Q8—44no—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2311yescharacteristic
268C2×#126C2314yes—
269C2×#126C2314yes—
270C2×#126C2314yes—
271C2×#126C2312yes—
272C2×#126C2314yes—
273C2×#125C2312yes—
274C2×#125C2311yescharacteristic
275C2×#124C2312yes—
276C2×#124C2312yes—
277C2×#124C2312yes—
278C2×#124C2312yes—
279C2×#124C2314yes—
280C2×#123C2314yes—
281C2×#123C2312yes—
282C2×#123C2312yes—
283C2×C22⋊Q8—44no—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×#121C2314yes—
294C2×#121C2314yes—
295C2×#121C2312yes—
296C2×#121C2311yescharacteristic
297C2×#121C2312yes—
298C2×#121C2311yescharacteristic
299C2×#121C2312yes—
300C2×#120C2312yes—
301C2×#120C2311yescharacteristic
302C2×#120C2312yes—
303#520—44no—
304C2×C4×Q8C2314yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2314yes—
309C2×C4×Q8C2311yescharacteristic
310C2×C4×Q8C2312yes—
311C2×C4×D4C2311yescharacteristic
312C2×C4×D4C2312yes—
313C2×C4×D4C2311yescharacteristic
314C2×C4×D4C2312yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2314yes—
320C2×C4×D4C2312yes—
321C2×#117C2312yes—
322C2×#117C2311yescharacteristic
323C2×#117C2312yes—
324C2×#117C2312yes—
325C22×C4⋊C4C2311yescharacteristic
326C22×C4⋊C4C2311yescharacteristic
327C22×C4⋊C4C2312yes—
328C22×C4⋊C4C2312yes—
329C22×C22⋊C4C2312yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2312yes—
345#400C2312yes—
346#400C2312yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#399C2314yes—
351#399C2314yes—
352#399C2314yes—
353#399C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2312yes—
362#398C2312yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2312yes—
380#397C2312yes—
381#397C2311yescharacteristic
382#397C2314yes—
383#397C2312yes—
384#397C2314yes—
385#397C2312yes—
386#397C2311yescharacteristic
387#397C2312yes—
388#397C2314yes—
389#397C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2312yes—
403#395C2314yes—
404#395C2312yes—
405#395C2311yescharacteristic
406#395C2312yes—
407#395C2314yes—
408#395C2312yes—
409#395C2312yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2312yes—
421#394C2314yes—
422#394C2312yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2311yescharacteristic
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2312yes—
431#394C2312yes—
432#394C2312yes—
433#394C2312yes—
434#394C2312yes—
435#394C2314yes—
436#393C2314yes—
437#393C2314yes—
438#393C2314yes—
439#393C2312yes—
440#393C2312yes—
441#393C2314yes—
442#393C2314yes—
443#393C2312yes—
444#393C2312yes—
445#393C2312yes—
446#393C2312yes—
447#393C2314yes—
448#393C2311yescharacteristic
449#393C2314yes—
450#393C2314yes—
451#393C2311yescharacteristic
452#393C2311yescharacteristic
453#393C2312yes—
454#392C2311yescharacteristic
455#392C2312yes—
456#392C2314yes—
457#392C2314yes—
458#392C2314yes—
459#392C2312yes—
460#392C2312yes—
461#392C2312yes—
462#392C2312yes—
463#391C2314yes—
464#391C2314yes—
465#391C2314yes—
466#391C2314yes—
467#391C2314yes—
468#391C2314yes—
469#391C2314yes—
470#391C2314yes—
471#391C2312yes—
472#391C2312yes—
473#391C2314yes—
474#391C2312yes—
475#391C2312yes—
476#391C2312yes—
477#391C2314yes—
478#391C2312yes—
479#391C2312yes—
480#391C2312yes—
481#391C2312yes—
482#390C2312yes—
483#390C2314yes—
484#390C2314yes—
485#390C2314yes—
486#390C2312yes—
487#390C2314yes—
488#390C2314yes—
489#390C2312yes—
490#390C2314yes—
491#390C2314yes—
492#390C2312yes—
493#390C2314yes—
494#390C2312yes—
495#390C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2314yes—
501#389C2312yes—
502#389C2314yes—
503#389C2312yes—
504#389C2312yes—
505#389C2314yes—
506#389C2312yes—
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#389C2312yes—
511#389C2312yes—
512#389C2314yes—
513#389C2314yes—
514#389C2314yes—
515#389C2314yes—
516#389C2314yes—
517#389C2314yes—
518#388C2312yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2312yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2312yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2312yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2312yes—
547#388C2314yes—
548#388C2314yes—
549#388C2312yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2312yes—
559#388C2312yes—
560#388C2314yes—
561#388C2312yes—
562#388C2314yes—
563#388C2312yes—
564#388C2312yes—
565#388C2312yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#386C2312yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2312yes—
602#386C2314yes—
603#386C2314yes—
604#386C2312yes—
605#386C2314yes—
606#386C2312yes—
607#386C2312yes—
608#386C2312yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2312yes—
615#386C2314yes—
616#386C2311yescharacteristic
617#386C2312yes—
618#385C2312yes—
619#385C2312yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2312yes—
628#385C2312yes—
629#385C2311yescharacteristic
630#385C2312yes—
631#384C2312yes—
632#384C2312yes—
633#383C2314yes—
634#383C2314yes—
635#383C2314yes—
636#383C2314yes—
637#383C2314yes—
638#382C2312yes—
639#382C2312yes—
640#382C2312yes—
641#382C2314yes—
642#382C2314yes—
643#382C2314yes—
644#382C2312yes—
645#382C2314yes—
646#382C2314yes—
647#382C2312yes—
648#382C2312yes—
649#382C2312yes—
650#382C2312yes—
651#381C2312yes—
652#381C2314yes—
653#381C2314yes—
654#381C2314yes—
655#381C2312yes—
656#381C2314yes—
657#380C2311yescharacteristic
658#380C2312yes—
659#380C2312yes—
660#380C2312yes—
661#380C2312yes—
662#380C2312yes—
663#380C2314yes—
664#380C2314yes—
665#380C2312yes—
666#380C2312yes—
667#380C2314yes—
668#380C2314yes—
669#380C2312yes—
670#380C2311yescharacteristic
671#380C2312yes—
672#380C2312yes—
673#380C2314yes—
674#380C2312yes—
675#379C2311yescharacteristic
676#379C2314yes—
677#379C2312yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2314yes—
690C4×C22⋊C4C2312yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2311yescharacteristic
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2311yescharacteristic
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713#376C2311yescharacteristic
714#376C2312yes—
715#376C2314yes—
716C43C2312yes—
717C25C2411yescharacteristic
718C2×#41—42no—
719C2×#41—44no—
720C22×Q8—42no—
721C22×Q8—44no—
722C22×Q8—44no—
723C22×Q8—48no—
724C22×Q8C2412yes—
725C22×Q8C2414yes—
726C22×Q8C2411yescharacteristic
727C22×Q8C2411yescharacteristic
728C22×Q8C2412yes—
729C22×Q8C2412yes—
730C22×Q8C2412yes—
731C22×D4C2411yescharacteristic
732C22×D4C2412yes—
733C22×D4C2411yescharacteristic
734C22×D4C2412yes—
735C22×D4C2412yes—
736C22×D4C2411yescharacteristic
737C22×D4C2412yes—
738C22×D4C2412yes—
739C22×D4C2412yes—
740C22×D4C2414yes—
741C22×D4C2414yes—
742C22×D4C2412yes—
743C23×C4—42no—
744C23×C4—44no—
745C23×C4C2411yescharacteristic
746C23×C4C2412yes—
747C23×C4C2411yescharacteristic
748C23×C4C2412yes—
749C23×C4C2412yes—
750C23×C4C2412yes—
751C23×C4C2414yes—
752C23×C4C2412yes—
753C23×C4C2411yescharacteristic
754C23×C4C2414yes—
755C23×C4C2412yes—
756C23×C4C2412yes—
757C4⋊Q8—28no—
758C4⋊Q8—42no—
759#126—44no—
760#126—48no—
761#126—48no—
762#126—48no—
763#126—48no—
764#125—44no—
765#125—42no—
766#124—44no—
767#124—44no—
768#124—44no—
769#124—44no—
770#124—48no—
771#123—44no—
772#123—48no—
773#123—44no—
774C22⋊Q8—28no—
775C22⋊Q8—48no—
776C22⋊Q8—48no—
777C22⋊Q8—48no—
778C22⋊Q8—44no—
779C22⋊Q8—44no—
780C22⋊Q8—44no—
781C22⋊Q8—44no—
782C22⋊Q8—44no—
783#121—44no—
784#121—48no—
785#121—44no—
786#121—48no—
787#121—44no—
788#121—42no—
789#121—42no—
790#120—44no—
791#120—42no—
792#120—44no—
793C4×Q8—44no—
794C4×Q8—44no—
795C4×Q8—42no—
796C4×Q8—44no—
797C4×Q8—48no—
798C4×Q8—48no—
799C4×Q8—44no—
800C4×D4—24no—
801C4×D4—44no—
802C4×D4—48no—
803C4×D4—44no—
804C4×D4—44no—
805C4×D4—44no—
806C4×D4—44no—
807C4×D4—44no—
808C4×D4—42no—
809C4×D4—44no—
810#117—24no—
811#117—28no—
812#117—44no—
813#117—44no—
814C2×C4⋊C4—24no—
815C2×C4⋊C4—42no—
816C2×C4⋊C4—44no—
817C2×C4⋊C4—44no—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2411yescharacteristic
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2411yescharacteristic
866C2×C22⋊C4—44no—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2411yescharacteristic
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2411yescharacteristic
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2411yescharacteristic
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2411yescharacteristic
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2414yes—
928C2×C42C2412yes—
929C2×C42C2414yes—
930C2×C42C2412yes—
931C2×C42C2411yescharacteristic
932C2×C42C2412yes—
933C2×C42C2412yes—
934C2×C42C2412yes—
935C2×C42C2412yes—
936C2×C42C2414yes—
937C2×C42C2414yes—
938C2×C42C2414yes—
939C2×C42C2414yes—
940C2×C42C2414yes—
941C2×C42C2414yes—
942C2×C42C2412yes—
943C2×C42C2412yes—
944C2×C42C2414yes—
945C2×C42C2414yes—
946C2×C42C2412yes—
947C2×C42C2414yes—
948C2×C42C2412yes—
949#95C2411yescharacteristic
950#95C2412yes—
951#95C2414yes—
952#95C2411yescharacteristic
953#95C2414yes—
954#95C2412yes—
955#95C2411yescharacteristic
956#95C2414yes—
957#95C2412yes—
958#95C2414yes—
959#95C2412yes—
960#95C2412yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2412yes—
965#95C2412yes—
966#95C2414yes—
967#95C2414yes—
968#95C2412yes—
969#95C2412yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2412yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2411yescharacteristic
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2414yes—
992#95C2412yes—
993#95C2414yes—
994#95C2412yes—
995#95C2412yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2412yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016C24—22no—
1017C24—41no—
1018C24—41no—
1019C24—42no—
1020C24—42no—
1021C24C2512yes—
1022C24C2512yes—
1023C24C2511yescharacteristic
1024C24C2512yes—
1025C24C2511yescharacteristic
1026#41—416no—
1027C2×Q8—24no—
1028C2×Q8—28no—
1029C2×Q8—28no—
1030C2×Q8—24no—
1031C2×Q8—24no—
1032C2×Q8—24no—
1033C2×Q8—41no—
1034C2×Q8—41no—
1035C2×Q8—44no—
1036C2×Q8—42no—
1037C2×Q8—42no—
1038C2×Q8—42no—
1039C2×Q8—42no—
1040C2×Q8—42no—
1041C2×Q8—42no—
1042C2×Q8—44no—
1043C2×Q8—44no—
1044C2×Q8—88no—
1045C2×Q8—816no—
1046C2×D4—24no—
1047C2×D4—22no—
1048C2×D4—24no—
1049C2×D4—22no—
1050C2×D4—24no—
1051C2×D4—24no—
1052C2×D4—41no—
1053C2×D4—42no—
1054C2×D4—42no—
1055C2×D4—42no—
1056C2×D4—42no—
1057C2×D4—41no—
1058C2×D4—42no—
1059C2×D4—42no—
1060C2×D4—42no—
1061C2×D4—42no—
1062C2×D4—42no—
1063C2×D4—42no—
1064C2×D4—42no—
1065C2×D4—42no—
1066C2×D4—42no—
1067C2×D4—42no—
1068C2×D4—41no—
1069C2×D4—42no—
1070C2×D4—42no—
1071C2×D4—44no—
1072C2×D4—42no—
1073C2×D4—44no—
1074C2×D4—44no—
1075C2×D4—44no—
1076C2×D4—44no—
1077C2×D4—44no—
1078C2×D4—44no—
1079C22×C4—22no—
1080C22×C4—22no—
1081C22×C4—24no—
1082C22×C4—24no—
1083C22×C4—24no—
1084C22×C4—24no—
1085C22×C4—24no—
1086C22×C4—24no—
1087C22×C4—24no—
1088C22×C4—24no—
1089C22×C4—24no—
1090C22×C4—24no—
1091C22×C4—28no—
1092C22×C4—42no—
1093C22×C4—41no—
1094C22×C4—44no—
1095C22×C4—42no—
1096C22×C4—44no—
1097C22×C4—42no—
1098C22×C4—42no—
1099C22×C4—42no—
1100C22×C4—44no—
1101C22×C4—44no—
1102C22×C4—44no—
1103C22×C4—42no—
1104C22×C4—44no—
1105C22×C4—44no—
1106C22×C4—42no—
1107C22×C4—42no—
1108C22×C4—44no—
1109C22×C4—88no—
1110C22×C4C2511yescharacteristic
1111C22×C4C2511yescharacteristic
1112C22×C4C2512yes—
1113C22×C4C2512yes—
1114C22×C4C2512yes—
1115C22×C4C2512yes—
1116C22×C4C2512yes—
1117C22×C4C2512yes—
1118C22×C4C2514yes—
1119C22×C4C2512yes—
1120C22×C4C2514yes—
1121C22×C4C2512yes—
1122C22×C4C2514yes—
1123C22×C4C2514yes—
1124C22×C4C2514yes—
1125C22×C4C2514yes—
1126C22×C4C2511yescharacteristic
1127C22×C4C2512yes—
1128C22×C4C2511yescharacteristic
1129C22×C4C2512yes—
1130C22×C4C2512yes—
1131C22×C4C2512yes—
1132C22×C4C2512yes—
1133C22×C4C2511yescharacteristic
1134C4⋊C4—22no—
1135C4⋊C4—24no—
1136C4⋊C4—24no—
1137C4⋊C4—22no—
1138C4⋊C4—28no—
1139C4⋊C4—24no—
1140C4⋊C4—28no—
1141C4⋊C4—24no—
1142C4⋊C4—24no—
1143C4⋊C4—28no—
1144C4⋊C4—24no—
1145C4⋊C4—28no—
1146C4⋊C4—42no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—42no—
1153C4⋊C4—42no—
1154C4⋊C4—42no—
1155C4⋊C4—41no—
1156C4⋊C4—44no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—42no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—42no—
1163C4⋊C4—41no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—42no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—42no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4H(5,𝔽2)14yes—
1182C22⋊C4—22no—
1183C22⋊C4—24no—
1184C22⋊C4—28no—
1185C22⋊C4—24no—
1186C22⋊C4—28no—
1187C22⋊C4—24no—
1188C22⋊C4—28no—
1189C22⋊C4—24no—
1190C22⋊C4—24no—
1191C22⋊C4—24no—
1192C22⋊C4—24no—
1193C22⋊C4—24no—
1194C22⋊C4—44no—
1195C22⋊C4—41no—
1196C22⋊C4—42no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—42no—
1200C22⋊C4—42no—
1201C22⋊C4—44no—
1202C22⋊C4—42no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—42no—
1206C22⋊C4—42no—
1207C22⋊C4—42no—
1208C22⋊C4—42no—
1209C22⋊C4—42no—
1210C22⋊C4—42no—
1211C22⋊C4—41no—
1212C22⋊C4—42no—
1213C22⋊C4—44no—
1214C22⋊C4—41no—
1215C22⋊C4—42no—
1216C22⋊C4—42no—
1217C22⋊C4—42no—
1218C22⋊C4—42no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—42no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—42no—
1232C22⋊C4—44no—
1233C22⋊C4—42no—
1234C22⋊C4—42no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—42no—
1238C22⋊C4—42no—
1239C22⋊C4—42no—
1240C22⋊C4—42no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C42—24no—
1244C42—28no—
1245C42—22no—
1246C42—24no—
1247C42—24no—
1248C42—24no—
1249C42—24no—
1250C42—24no—
1251C42—44no—
1252C42—42no—
1253C42—42no—
1254C42—44no—
1255C42—44no—
1256C42—44no—
1257C42—44no—
1258C42—44no—
1259C42—44no—
1260C42—42no—
1261C42—42no—
1262C42—44no—
1263C42—44no—
1264C23—21no—
1265C23—22no—
1266C23—22no—
1267C23—21no—
1268C23—22no—
1269C23—22no—
1270C23—21no—
1271C23—22no—
1272C23—22no—
1273C23—22no—
1274C23—22no—
1275C23—24no—
1276C23—22no—
1277C23—22no—
1278C23—22no—
1279C23—22no—
1280C23—22no—
1281C23—22no—
1282C23—21no—
1283C23—22no—
1284C23—22no—
1285C23—24no—
1286C23—22no—
1287C23—22no—
1288C23—22no—
1289C23—22no—
1290C23—21no—
1291C23—22no—
1292C23—44no—
1293C23—84no—
1294C23—82no—
1295C23—82no—
1296C23—84no—
1297C23#58512yes—
1298C23C2611yescharacteristic
1299Q8—416no—
1300Q8—44no—
1301Q8—44no—
1302Q8—48no—
1303Q8—84no—
1304Q8—84no—
1305Q8—84no—
1306D4—44no—
1307D4—48no—
1308D4—44no—
1309D4—84no—
1310D4—84no—
1311D4—84no—
1312D4—82no—
1313D4—84no—
1314D4—84no—
1315D4—162no—
1316D4—164no—
1317D4—164no—
1318C2×C4—22no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—21no—
1322C2×C4—22no—
1323C2×C4—24no—
1324C2×C4—21no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—21no—
1328C2×C4—22no—
1329C2×C4—24no—
1330C2×C4—24no—
1331C2×C4—22no—
1332C2×C4—21no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—24no—
1344C2×C4—24no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—24no—
1350C2×C4—24no—
1351C2×C4—24no—
1352C2×C4—24no—
1353C2×C4—22no—
1354C2×C4—24no—
1355C2×C4—24no—
1356C2×C4—24no—
1357C2×C4—22no—
1358C2×C4—24no—
1359C2×C4—22no—
1360C2×C4—24no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—24no—
1364C2×C4—24no—
1365C2×C4—24no—
1366C2×C4—21no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—24no—
1374C2×C4—21no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—24no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—48no—
1381C2×C4—44no—
1382C2×C4—44no—
1383C2×C4—48no—
1384C2×C4—84no—
1385C2×C4—84no—
1386C2×C4—88no—
1387C2×C4—82no—
1388C2×C4—84no—
1389C2×C4—84no—
1390C2×C4—162no—
1391C2×C4—164no—
1392C2×C4C2×H(5,𝔽2)14yes—
1393C2×C4C2×H(5,𝔽2)12yes—
1394C2×C4#58514yes—
1395C2×C4#58514yes—
1396C22—24no—
1397C22—22no—
1398C22—41no—
1399C22—41no—
1400C22—42no—
1401C22—42no—
1402C22—42no—
1403C22—41no—
1404C22—42no—
1405C22—42no—
1406C22—42no—
1407C22—42no—
1408C22—41no—
1409C22—42no—
1410C22—42no—
1411C22—42no—
1412C22—44no—
1413C22—42no—
1414C22—42no—
1415C22—41no—
1416C22—42no—
1417C22—42no—
1418C22—42no—
1419C22—42no—
1420C22—42no—
1421C22—42no—
1422C22—42no—
1423C22—44no—
1424C22—42no—
1425C22—88no—
1426C22C22×H(5,𝔽2)11yescharacteristic
1427C22C2×#58512yes—
1428C22C2×#58512yes—
1429C22C2×#58511yescharacteristic
1430C222−1+611yescharacteristic
1431C4—24no—
1432C4—24no—
1433C4—42no—
1434C4—41no—
1435C4—41no—
1436C4—42no—
1437C4—44no—
1438C4—41no—
1439C4—42no—
1440C4—44no—
1441C4—42no—
1442C4—42no—
1443C4—44no—
1444C4—44no—
1445C4—42no—
1446C4—42no—
1447C4—44no—
1448C4—42no—
1449C4—41no—
1450C4—42no—
1451C4—42no—
1452C4—44no—
1453C4—42no—
1454C4#354014yes—
1455C2—42no—
1456C2—82no—
1457C2—81no—
1458C2—82no—
1459C2—82no—
1460C2C2×#354011yescharacteristic
1461C2#6291911yescharacteristic
1462C2#6293912yes—
1463C2#6301711yescharacteristic
1464C2#6302912yes—
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. #59645C2semidirect
2. #59431C2semidirect
3. #59421C2semidirect
4. #59201C2semidirect
5. #59025C2semidirect
6. #56840C2semidirect
7. #55502C2semidirect
8. #54948C2semidirect
9. #53903C2semidirect
10. #53044C2semidirect
11. #53005C2semidirect
12. #52294C2semidirect
13. #47489C2semidirect
14. #47182C2semidirect
15. #45420C2semidirect
16. #45419C2semidirect
17. #45402C2semidirect
18. #44405C2semidirect
19. #42691C2semidirect
20. #42485C2semidirect
21. #41896C2semidirect
22. #41059C2semidirect
23. #40104C2semidirect
24. #39910C2semidirect
25. #39722C2semidirect
26. #39527C2semidirect
27. #39216C2semidirect
28. #36083C2semidirect
29. #35759C2semidirect
32. C2×D4×Q8C22semidirect
34. C2×#520C22semidirect
35. #2863C22semidirect
37. #2844C22semidirect
38. #2832C22semidirect
41. #2829C22semidirect
44. #2814C22semidirect
47. #2803C22semidirect
49. #2798C22semidirect
50. #2798C22semidirect
53. #2785C22semidirect
55. #2775C22semidirect
56. #2774C22semidirect
58. #2770C22semidirect
59. #2767C22semidirect
60. #2767C22semidirect
61. #2764C22semidirect
66. #2758C22semidirect
67. #2758C22semidirect
70. #2755C22semidirect
76. #2751C22semidirect
79. #2742C22semidirect
81. #2737C22semidirect
90. #2705C22semidirect
92. #2702C22semidirect
94. #2698C22semidirect
104. #2665C22semidirect
105. #2665C22semidirect
106. #2660C22semidirect
111. #2637C22semidirect
115. #2616C22semidirect
116. #2615C22semidirect
117. #2614C22semidirect
118. #2607C22semidirect
119. #2605C22semidirect
121. #2603C22semidirect
122. #2597C22semidirect
124. #2592C22semidirect
125. #2584C22semidirect
126. #2584C22semidirect
127. #2582C22semidirect
128. #2581C22semidirect
129. #2581C22semidirect
133. #2572C22semidirect
139. #2560C22semidirect
148. #2529C22semidirect
150. #2525C22semidirect
151. #2525C22semidirect
155. #2517C22semidirect
157. #2515C22semidirect
159. #2513C22semidirect
160. #2508C22semidirect
162. #2504C22semidirect
163. #2503C22semidirect
165. #2497C22semidirect
167. #2496C22semidirect
170. #2495C22semidirect
172. #2492C22semidirect
175. #2489C22semidirect
176. #2489C22semidirect
184. #2469C22semidirect
185. #2466C22semidirect
186. #2466C22semidirect
191. #2457C22semidirect
192. #2442C22semidirect
196. #2439C22semidirect
197. #2439C22semidirect
201. #2427C22semidirect
203. #2426C22semidirect
204. #2423C22semidirect
205. #2422C22semidirect
208. #2421C22semidirect
221. #2398C22semidirect
225. #2374C22semidirect
228. #2363C22semidirect
231. #2360C22semidirect
232. #2360C22semidirect
233. #2355C22semidirect
238. #2346C22semidirect
239. #2346C22semidirect
242. Q8×C22⋊C4C22semidirect
243. #2334C22semidirect
247. #2320C22semidirect
248. #2320C22semidirect
249. #2319C22semidirect
250. C4×C4⋊Q8C22semidirect
251. C4×#125C22semidirect
255. C4×#124C22semidirect

Maximal subgroups

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

subgroupindex
#596452
#594312
#594212
#592012
#590252
#568402
#555022
#549482
#539032
#530442
#530052
#522942
#474892
#471822
#454202
#454192
#454022
#444052
#426912
#424852
#418962
#410592
#401042
#399102
#397222
#395272
#392162
#360832
#357592