Finite Group Databasebeta

← #8345861

Subgroups — #8345861

Order 512.

4736 conjugacy classes of subgroups.

The subgroup lattice has 1500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59811C212yesmaximal, complemented
2#59753C212yesmaximal, complemented
3#59125C212yesmaximal, complemented
4#58208C214yesmaximal, complemented
5#57573C212yesmaximal, complemented
6#56508C212yesmaximal, complemented
7#54964C214yesmaximal, complemented
8#53478C214yesmaximal, complemented
9#53130C212yesmaximal, complemented
10#52716C212yesmaximal, complemented
11#52168C211yesmaximal, characteristic, complemented
12#50789C214yesmaximal, complemented
13#48459C214yesmaximal, complemented
14#45616C212yesmaximal, complemented
15#45391C212yesmaximal, complemented
16#43414C212yesmaximal, complemented
17#42958C211yesmaximal, characteristic, complemented
18#42927C212yesmaximal, complemented
19#42883C211yesmaximal, characteristic, complemented
20#42726C212yesmaximal, complemented
21#40972C214yesmaximal, complemented
22#40032C212yesmaximal, complemented
23#39223C212yesmaximal, complemented
24#38903C212yesmaximal, complemented
25#38035C212yesmaximal, complemented
26#37523C211yesmaximal, characteristic, complemented
27#36030C211yesmaximal, characteristic, complemented
28#36018C211yesmaximal, characteristic, complemented
29#35674C211yesmaximal, characteristic, complemented
30C2×#556C2211yescharacteristic
31C2×#550C2211yescharacteristic
32C2×#548C2212yes—
33C2×#548C2212yes—
34C2×#547C2212yes—
35C22×C4⋊Q8C2211yescharacteristic
36C2×#529C2212yes—
37C2×#519C2211yescharacteristic
38#2855C2212yes—
39#2850C2212yes—
40#2836C2214yes—
41#2836C2214yes—
42#2833C2212yes—
43#2832C2214yes—
44#2831C2214yes—
45#2826C2214yes—
46#2826C2212yes—
47#2824C2212yes—
48#2815C2212yes—
49#2814C2214yes—
50#2813C2214yes—
51#2802C2214yes—
52#2800C2214yes—
53#2800C2214yes—
54#2797C2214yes—
55#2797C2214yes—
56#2795C2214yes—
57#2791C2214yes—
58#2790C2214yes—
59#2789C2214yes—
60#2788C2214yes—
61#2778C2214yes—
62#2778C2214yes—
63#2771C2214yes—
64#2765C2214yes—
65#2764C2212yes—
66#2760C2212yes—
67#2756C2214yes—
68#2752C2214yes—
69#2747C2214yes—
70#2746C2214yes—
71#2746C2214yes—
72#2743C2214yes—
73#2742C2214yes—
74#2741C2214yes—
75#2741C2214yes—
76#2740C2214yes—
77#2737C2214yes—
78#2733C2212yes—
79#2730C2214yes—
80#2728C2212yes—
81#2725C2212yes—
82#2722C2211yescharacteristic
83#2712C2211yescharacteristic
84#2710C2214yes—
85#2709C2214yes—
86#2708C2214yes—
87#2705C2212yes—
88#2704C2214yes—
89#2704C2212yes—
90#2701C2214yes—
91#2700C2214yes—
92#2699C2214yes—
93#2699C2214yes—
94#2696C2214yes—
95#2695C2214yes—
96#2694C2214yes—
97#2693C2211yescharacteristic
98#2692C2214yes—
99#2691C2212yes—
100#2690C2214yes—
101#2688C2214yes—
102#2686C2214yes—
103#2681C2212yes—
104#2676C2214yes—
105#2675C2211yescharacteristic
106#2674C2214yes—
107#2674C2214yes—
108#2673C2214yes—
109#2672C2212yes—
110#2671C2214yes—
111#2665C2214yes—
112#2663C2214yes—
113#2655C2214yes—
114#2654C2214yes—
115#2653C2214yes—
116#2649C2214yes—
117#2648C2214yes—
118#2635C2214yes—
119#2632C2212yes—
120#2630C2214yes—
121#2628C2211yescharacteristic
122#2625C2212yes—
123#2624C2212yes—
124#2620C2212yes—
125#2619C2211yescharacteristic
126#2619C2212yes—
127#2618C2214yes—
128#2610C2212yes—
129#2600C2212yes—
130#2599C2212yes—
131#2597C2214yes—
132#2595C2214yes—
133#2594C2214yes—
134#2592C2212yes—
135#2592C2212yes—
136#2582C2212yes—
137#2581C2212yes—
138#2579C2214yes—
139#2578C2214yes—
140#2577C2214yes—
141#2577C2214yes—
142#2572C2212yes—
143#2567C2211yescharacteristic
144#2560C2214yes—
145#2559C2214yes—
146#2557C2214yes—
147#2557C2214yes—
148#2556C2214yes—
149#2556C2214yes—
150#2554C2214yes—
151#2548C2211yescharacteristic
152#2548C2212yes—
153#2547C2212yes—
154#2542C2212yes—
155#2536C2211yescharacteristic
156#2536C2211yescharacteristic
157#2536C2212yes—
158#2530C2214yes—
159#2526C2214yes—
160#2521C2214yes—
161#2516C2214yes—
162#2514C2212yes—
163#2513C2212yes—
164#2513C2212yes—
165#2509C2212yes—
166#2506C2212yes—
167#2503C2212yes—
168#2497C2214yes—
169#2494C2212yes—
170#2492C2212yes—
171#2491C2214yes—
172#2490C2214yes—
173#2485C2212yes—
174#2484C2212yes—
175#2484C2212yes—
176#2484C2212yes—
177#2484C2212yes—
178#2481C2214yes—
179#2479C2214yes—
180#2469C2214yes—
181#2468C2214yes—
182#2466C2214yes—
183#2464C2214yes—
184#2463C2212yes—
185#2460C2214yes—
186#2459C2214yes—
187#2458C2214yes—
188#2457C2214yes—
189#2455C2212yes—
190#2452C2212yes—
191#2448C2212yes—
192#2446C2214yes—
193#2446C2212yes—
194#2446C2212yes—
195#2446C2212yes—
196#2446C2212yes—
197#2446C2214yes—
198#2445C2212yes—
199#2443C2214yes—
200#2443C2214yes—
201#2440C2214yes—
202#2432C2212yes—
203#2432C2212yes—
204#2431C2212yes—
205#2429C2212yes—
206#2429C2212yes—
207#2426C2214yes—
208#2426C2212yes—
209#2423C2212yes—
210#2422C2212yes—
211#2421C2212yes—
212#2417C2212yes—
213#2417C2212yes—
214#2416C2212yes—
215#2416C2214yes—
216#2415C2212yes—
217#2414C2214yes—
218#2414C2212yes—
219#2414C2212yes—
220#2409C2212yes—
221#2409C2212yes—
222#2407C2212yes—
223#2407C2212yes—
224#2407C2212yes—
225#2399C2212yes—
226#2396C2212yes—
227#2392C2211yescharacteristic
228#2392C2212yes—
229#2392C2212yes—
230#2392C2211yescharacteristic
231#2377C2214yes—
232#2374C2214yes—
233#2365C2212yes—
234#2363C2212yes—
235#2362C2212yes—
236#2360C2214yes—
237#2356C2211yescharacteristic
238#2354C2212yes—
239#2352C2212yes—
240#2351C2211yescharacteristic
241D4×C4⋊C4C2214yes—
242#2345C2212yes—
243#2341C2212yes—
244#2336C2214yes—
245#2335C2214yes—
246#2323C2212yes—
247#2311C2212yes—
248#2310C2211yescharacteristic
249#2310C2211yescharacteristic
250#2310C2211yescharacteristic
251C4×C22⋊Q8C2212yes—
252C4×C22⋊Q8C2212yes—
253C4×#121C2212yes—
254C4×#121C2212yes—
255C4×#121C2212yes—
256#2297C2212yes—
257#2296C2211yescharacteristic
258#2296C2211yescharacteristic
259C22×#41C2312yes—
260C22×#41C2312yes—
261C23×Q8C2311yescharacteristic
262C23×Q8C2311yescharacteristic
263#556—44no—
264#550—44no—
265#548—48no—
266#548—48no—
267#547—48no—
268C2×C4⋊Q8—44no—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2314yes—
272C2×C4⋊Q8C2312yes—
273C2×#127C2312yes—
274C2×#127C2311yescharacteristic
275#529—48no—
276C2×#126C2312yes—
277C2×#126C2312yes—
278C2×#126C2314yes—
279C2×#125C2314yes—
280C2×#125C2312yes—
281C2×#124C2312yes—
282C2×#124C2312yes—
283C2×#124C2312yes—
284C2×#124C2312yes—
285C2×#124C2314yes—
286C2×#124C2314yes—
287C2×#123C2314yes—
288C2×#123C2314yes—
289C2×#123C2314yes—
290C2×#123C2312yes—
291C2×#123C2312yes—
292C2×#123C2314yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2312yes—
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2312yes—
303C2×C22⋊Q8C2314yes—
304C2×#121C2312yes—
305C2×#121C2312yes—
306C2×#121C2314yes—
307C2×#121C2314yes—
308C2×#121C2312yes—
309C2×#121C2314yes—
310C2×#121C2314yes—
311C2×#121C2314yes—
312C2×#121C2312yes—
313C2×#121C2312yes—
314C2×#121C2312yes—
315#519—44no—
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2311yescharacteristic
318C2×C4×Q8C2311yescharacteristic
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2311yescharacteristic
324C2×C4×Q8C2312yes—
325C2×C4×Q8C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2314yes—
330C2×C4×D4C2314yes—
331C2×C4×D4C2314yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2311yescharacteristic
334C2×C4×D4C2312yes—
335C2×C4×D4C2311yescharacteristic
336C2×C4×D4C2312yes—
337C2×#117C2311yescharacteristic
338C2×#117C2311yescharacteristic
339C2×#117C2311yescharacteristic
340C2×#117C2311yescharacteristic
341C2×#117C2312yes—
342C2×#117C2312yes—
343C2×#117C2312yes—
344C2×#117C2312yes—
345C22×C4⋊C4C2312yes—
346C22×C4⋊C4C2314yes—
347C22×C4⋊C4C2312yes—
348C22×C4⋊C4C2312yes—
349C22×C42C2312yes—
350C22×C42C2311yescharacteristic
351#401C2314yes—
352#401C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2312yes—
358#400C2312yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#399C2314yes—
370#399C2312yes—
371#399C2314yes—
372#399C2314yes—
373#399C2314yes—
374#399C2312yes—
375#399C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2312yes—
379#398C2311yescharacteristic
380#398C2314yes—
381#398C2312yes—
382#398C2312yes—
383#398C2312yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2312yes—
389#398C2314yes—
390#398C2314yes—
391#398C2311yescharacteristic
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#397C2314yes—
411#397C2314yes—
412#397C2311yescharacteristic
413#397C2314yes—
414#397C2311yescharacteristic
415#397C2312yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#396C2312yes—
423#396C2312yes—
424#396C2314yes—
425#396C2312yes—
426#396C2312yes—
427#396C2314yes—
428#396C2312yes—
429#396C2312yes—
430#396C2314yes—
431#395C2312yes—
432#395C2312yes—
433#395C2314yes—
434#395C2314yes—
435#395C2312yes—
436#395C2312yes—
437#395C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#394C2312yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2311yescharacteristic
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#394C2312yes—
452#394C2314yes—
453#394C2314yes—
454#394C2314yes—
455#394C2312yes—
456#394C2312yes—
457#394C2312yes—
458#394C2312yes—
459#394C2311yescharacteristic
460#394C2312yes—
461#394C2314yes—
462#394C2312yes—
463#394C2314yes—
464#394C2312yes—
465#394C2312yes—
466#394C2312yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#393C2314yes—
472#393C2314yes—
473#393C2312yes—
474#393C2312yes—
475#393C2314yes—
476#393C2314yes—
477#393C2314yes—
478#393C2314yes—
479#392C2312yes—
480#392C2312yes—
481#392C2314yes—
482#392C2311yescharacteristic
483#392C2311yescharacteristic
484#392C2314yes—
485#392C2314yes—
486#392C2314yes—
487#392C2314yes—
488#392C2312yes—
489#392C2314yes—
490#392C2314yes—
491#391C2314yes—
492#391C2312yes—
493#391C2312yes—
494#391C2312yes—
495#391C2312yes—
496#391C2312yes—
497#391C2312yes—
498#391C2312yes—
499#391C2312yes—
500#391C2314yes—
501#391C2312yes—
502#391C2312yes—
503#391C2314yes—
504#391C2314yes—
505#391C2312yes—
506#391C2312yes—
507#391C2312yes—
508#390C2314yes—
509#390C2312yes—
510#390C2312yes—
511#390C2314yes—
512#390C2312yes—
513#390C2312yes—
514#390C2312yes—
515#390C2314yes—
516#390C2314yes—
517#390C2314yes—
518#390C2314yes—
519#390C2314yes—
520#390C2314yes—
521#390C2314yes—
522#390C2312yes—
523#390C2312yes—
524#390C2312yes—
525#389C2314yes—
526#389C2314yes—
527#389C2312yes—
528#389C2312yes—
529#389C2314yes—
530#389C2312yes—
531#389C2312yes—
532#389C2312yes—
533#389C2314yes—
534#389C2312yes—
535#389C2312yes—
536#389C2314yes—
537#389C2314yes—
538#389C2312yes—
539#389C2314yes—
540#389C2312yes—
541#389C2314yes—
542#389C2312yes—
543#389C2312yes—
544#389C2314yes—
545#389C2312yes—
546#389C2312yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2312yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2312yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2312yes—
584#388C2312yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2312yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2312yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2312yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2314yes—
630#386C2314yes—
631#386C2312yes—
632#386C2314yes—
633#386C2314yes—
634#386C2314yes—
635#386C2314yes—
636#386C2312yes—
637#386C2312yes—
638#386C2314yes—
639#385C2311yescharacteristic
640#385C2311yescharacteristic
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#385C2311yescharacteristic
654#385C2312yes—
655#385C2311yescharacteristic
656#385C2314yes—
657#385C2312yes—
658#385C2312yes—
659#385C2312yes—
660#384C2312yes—
661#384C2314yes—
662#383C2314yes—
663#383C2312yes—
664#382C2312yes—
665#382C2311yescharacteristic
666#382C2312yes—
667#382C2311yescharacteristic
668#381C2312yes—
669#381C2312yes—
670#381C2312yes—
671#381C2312yes—
672#381C2312yes—
673#381C2312yes—
674#381C2314yes—
675#381C2314yes—
676#381C2314yes—
677#380C2314yes—
678#380C2314yes—
679#380C2312yes—
680#380C2314yes—
681#380C2312yes—
682#380C2314yes—
683#380C2314yes—
684#380C2312yes—
685#380C2314yes—
686#380C2312yes—
687#380C2312yes—
688#380C2312yes—
689#380C2314yes—
690#380C2312yes—
691#380C2314yes—
692#380C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2311yescharacteristic
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2314yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2314yes—
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2311yescharacteristic
704C4×C4⋊C4C2312yes—
705C4×C4⋊C4C2312yes—
706C4×C4⋊C4C2312yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2314yes—
715C4×C22⋊C4C2314yes—
716C4×C22⋊C4C2312yes—
717C4×C22⋊C4C2312yes—
718C4×C22⋊C4C2312yes—
719#376C2312yes—
720C2×#41—28no—
721C2×#41—44no—
722C2×#41—44no—
723C2×#41—44no—
724C2×#41—44no—
725C2×#41—44no—
726C22×Q8—24no—
727C22×Q8—24no—
728C22×Q8—24no—
729C22×Q8—42no—
730C22×Q8—42no—
731C22×Q8—42no—
732C22×Q8C2411yescharacteristic
733C22×Q8C2412yes—
734C22×Q8C2412yes—
735C22×Q8C2411yescharacteristic
736C22×Q8C2412yes—
737C22×Q8C2412yes—
738C22×Q8C2412yes—
739C22×D4C2412yes—
740C22×D4C2414yes—
741C22×D4C2412yes—
742C22×D4C2412yes—
743C22×D4C2412yes—
744C22×D4C2414yes—
745C22×D4C2412yes—
746C22×D4C2411yescharacteristic
747C22×D4C2412yes—
748C22×D4C2411yescharacteristic
749C22×D4C2414yes—
750C22×D4C2412yes—
751C22×D4C2414yes—
752C22×D4C2414yes—
753C23×C4C2412yes—
754C23×C4C2412yes—
755C23×C4C2412yes—
756C23×C4C2411yescharacteristic
757C23×C4C2411yescharacteristic
758C23×C4C2412yes—
759C23×C4C2414yes—
760C23×C4C2414yes—
761C23×C4C2411yescharacteristic
762C23×C4C2414yes—
763C23×C4C2414yes—
764C23×C4C2412yes—
765C23×C4C2412yes—
766C4⋊Q8—28no—
767C4⋊Q8—42no—
768C4⋊Q8—44no—
769C4⋊Q8—48no—
770#127—42no—
771#127—44no—
772#126—44no—
773#126—44no—
774#126—48no—
775#125—48no—
776#125—44no—
777#124—44no—
778#124—44no—
779#124—44no—
780#124—44no—
781#124—48no—
782#124—48no—
783#123—44no—
784#123—44no—
785#123—48no—
786#123—48no—
787#123—48no—
788#123—48no—
789C22⋊Q8—28no—
790C22⋊Q8—44no—
791C22⋊Q8—44no—
792C22⋊Q8—48no—
793C22⋊Q8—48no—
794C22⋊Q8—48no—
795C22⋊Q8—44no—
796C22⋊Q8—44no—
797C22⋊Q8—44no—
798C22⋊Q8—44no—
799C22⋊Q8—44no—
800#121—28no—
801#121—44no—
802#121—48no—
803#121—44no—
804#121—48no—
805#121—44no—
806#121—44no—
807#121—44no—
808#121—48no—
809#121—48no—
810#121—48no—
811C4×Q8—24no—
812C4×Q8—24no—
813C4×Q8—44no—
814C4×Q8—44no—
815C4×Q8—42no—
816C4×Q8—44no—
817C4×Q8—42no—
818C4×Q8—44no—
819C4×Q8—44no—
820C4×Q8—44no—
821C4×D4—28no—
822C4×D4—28no—
823C4×D4—44no—
824C4×D4—44no—
825C4×D4—44no—
826C4×D4—42no—
827C4×D4—44no—
828C4×D4—42no—
829C4×D4—48no—
830C4×D4—48no—
831C4×D4—48no—
832#117—24no—
833#117—42no—
834#117—44no—
835#117—44no—
836#117—42no—
837#117—42no—
838#117—44no—
839#117—44no—
840C2×C4⋊C4—44no—
841C2×C4⋊C4—44no—
842C2×C4⋊C4—44no—
843C2×C4⋊C4—48no—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2414yes—
900C2×C22⋊C4C2411yescharacteristic
901C2×C22⋊C4C2411yescharacteristic
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2411yescharacteristic
913C2×C22⋊C4C2411yescharacteristic
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2412yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2412yes—
950C2×C22⋊C4C2414yes—
951C2×C22⋊C4C2412yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2412yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2414yes—
956C2×C22⋊C4C2414yes—
957C2×C22⋊C4C2414yes—
958C2×C42—44no—
959C2×C42—42no—
960C2×C42C2412yes—
961C2×C42C2412yes—
962C2×C42C2411yescharacteristic
963C2×C42C2412yes—
964C2×C42C2411yescharacteristic
965C2×C42C2412yes—
966C2×C42C2412yes—
967C2×C42C2412yes—
968C2×C42C2412yes—
969C2×C42C2412yes—
970C2×C42C2412yes—
971C2×C42C2414yes—
972C2×C42C2412yes—
973C2×C42C2414yes—
974C2×C42C2414yes—
975C2×C42C2414yes—
976C2×C42C2412yes—
977C2×C42C2414yes—
978C2×C42C2412yes—
979C2×C42C2412yes—
980C2×C42C2414yes—
981#95C2411yescharacteristic
982#95C2414yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2414yes—
987#95C2414yes—
988#95C2412yes—
989#95C2412yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2412yes—
994#95C2412yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2411yescharacteristic
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2411yescharacteristic
1015#95C2412yes—
1016#95C2411yescharacteristic
1017#95C2412yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2412yes—
1023#95C2412yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2412yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2412yes—
1040#95C2414yes—
1041C24C2512yes—
1042C24C2512yes—
1043C24C2514yes—
1044C24C2511yescharacteristic
1045#41—816no—
1046#41—816no—
1047C2×Q8—22no—
1048C2×Q8—24no—
1049C2×Q8—22no—
1050C2×Q8—24no—
1051C2×Q8—24no—
1052C2×Q8—22no—
1053C2×Q8—24no—
1054C2×Q8—24no—
1055C2×Q8—22no—
1056C2×Q8—22no—
1057C2×Q8—24no—
1058C2×Q8—42no—
1059C2×Q8—42no—
1060C2×Q8—42no—
1061C2×Q8—44no—
1062C2×Q8—42no—
1063C2×Q8—42no—
1064C2×Q8—42no—
1065C2×Q8—42no—
1066C2×Q8—416no—
1067C2×Q8—88no—
1068C2×Q8H(5,𝔽2)14yes—
1069C2×D4—28no—
1070C2×D4—24no—
1071C2×D4—24no—
1072C2×D4—24no—
1073C2×D4—24no—
1074C2×D4—28no—
1075C2×D4—24no—
1076C2×D4—24no—
1077C2×D4—44no—
1078C2×D4—44no—
1079C2×D4—42no—
1080C2×D4—42no—
1081C2×D4—41no—
1082C2×D4—41no—
1083C2×D4—42no—
1084C2×D4—44no—
1085C2×D4—44no—
1086C2×D4—44no—
1087C2×D4—42no—
1088C2×D4—42no—
1089C2×D4—42no—
1090C2×D4—42no—
1091C2×D4—42no—
1092C2×D4—42no—
1093C2×D4—42no—
1094C2×D4—42no—
1095C2×D4—44no—
1096C2×D4—42no—
1097C2×D4—44no—
1098C2×D4—44no—
1099C2×D4—44no—
1100C2×D4—42no—
1101C2×D4—44no—
1102C2×D4—44no—
1103C2×D4—44no—
1104C2×D4—44no—
1105C2×D4—44no—
1106C2×D4—44no—
1107C22×C4—22no—
1108C22×C4—22no—
1109C22×C4—24no—
1110C22×C4—24no—
1111C22×C4—24no—
1112C22×C4—24no—
1113C22×C4—24no—
1114C22×C4—24no—
1115C22×C4—24no—
1116C22×C4—24no—
1117C22×C4—24no—
1118C22×C4—24no—
1119C22×C4—28no—
1120C22×C4—28no—
1121C22×C4—41no—
1122C22×C4—41no—
1123C22×C4—42no—
1124C22×C4—42no—
1125C22×C4—42no—
1126C22×C4—42no—
1127C22×C4—42no—
1128C22×C4—44no—
1129C22×C4—44no—
1130C22×C4—44no—
1131C22×C4—44no—
1132C22×C4—44no—
1133C22×C4—42no—
1134C22×C4—42no—
1135C22×C4—42no—
1136C22×C4—42no—
1137C22×C4—42no—
1138C22×C4—44no—
1139C22×C4—44no—
1140C22×C4—44no—
1141C22×C4—44no—
1142C22×C4—44no—
1143C22×C4H(5,𝔽2)14yes—
1144C22×C4C2511yescharacteristic
1145C22×C4C2514yes—
1146C22×C4C2514yes—
1147C22×C4C2512yes—
1148C22×C4C2511yescharacteristic
1149C22×C4C2512yes—
1150C22×C4C2512yes—
1151C22×C4C2512yes—
1152C22×C4C2514yes—
1153C22×C4C2512yes—
1154C22×C4C2512yes—
1155C22×C4C2511yescharacteristic
1156C22×C4C2512yes—
1157C22×C4C2512yes—
1158C22×C4C2514yes—
1159C22×C4C2511yescharacteristic
1160C22×C4C2512yes—
1161C22×C4C2514yes—
1162C22×C4C2512yes—
1163C22×C4C2512yes—
1164C22×C4C2512yes—
1165C22×C4C2512yes—
1166C22×C4C2511yescharacteristic
1167C22×C4C2512yes—
1168C22×C4C2511yescharacteristic
1169C4⋊C4—28no—
1170C4⋊C4—28no—
1171C4⋊C4—28no—
1172C4⋊C4—24no—
1173C4⋊C4—22no—
1174C4⋊C4—24no—
1175C4⋊C4—24no—
1176C4⋊C4—22no—
1177C4⋊C4—24no—
1178C4⋊C4—24no—
1179C4⋊C4—24no—
1180C4⋊C4—24no—
1181C4⋊C4—24no—
1182C4⋊C4—24no—
1183C4⋊C4—28no—
1184C4⋊C4—24no—
1185C4⋊C4—28no—
1186C4⋊C4—24no—
1187C4⋊C4—24no—
1188C4⋊C4—42no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—44no—
1193C4⋊C4—42no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—42no—
1197C4⋊C4—42no—
1198C4⋊C4—41no—
1199C4⋊C4—41no—
1200C4⋊C4—42no—
1201C4⋊C4—42no—
1202C4⋊C4—42no—
1203C4⋊C4—42no—
1204C4⋊C4—41no—
1205C4⋊C4—41no—
1206C4⋊C4—44no—
1207C4⋊C4—44no—
1208C4⋊C4—42no—
1209C4⋊C4—44no—
1210C4⋊C4—44no—
1211C4⋊C4—42no—
1212C4⋊C4—42no—
1213C4⋊C4—42no—
1214C4⋊C4—42no—
1215C4⋊C4—42no—
1216C4⋊C4—44no—
1217C4⋊C4—44no—
1218C4⋊C4—44no—
1219C4⋊C4—44no—
1220C4⋊C4—44no—
1221C4⋊C4—44no—
1222C4⋊C4—44no—
1223C4⋊C4—44no—
1224C4⋊C4—42no—
1225C22⋊C4—22no—
1226C22⋊C4—22no—
1227C22⋊C4—24no—
1228C22⋊C4—24no—
1229C22⋊C4—24no—
1230C22⋊C4—24no—
1231C22⋊C4—28no—
1232C22⋊C4—28no—
1233C22⋊C4—28no—
1234C22⋊C4—24no—
1235C22⋊C4—24no—
1236C22⋊C4—42no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—42no—
1243C22⋊C4—42no—
1244C22⋊C4—42no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4—44no—
1248C22⋊C4—42no—
1249C22⋊C4—41no—
1250C22⋊C4—42no—
1251C22⋊C4—41no—
1252C22⋊C4—42no—
1253C22⋊C4—42no—
1254C22⋊C4—44no—
1255C22⋊C4—44no—
1256C22⋊C4—42no—
1257C22⋊C4—44no—
1258C22⋊C4—42no—
1259C22⋊C4—42no—
1260C22⋊C4—44no—
1261C22⋊C4—42no—
1262C22⋊C4—44no—
1263C22⋊C4—44no—
1264C22⋊C4—42no—
1265C22⋊C4—42no—
1266C22⋊C4—44no—
1267C22⋊C4—44no—
1268C22⋊C4—42no—
1269C22⋊C4—44no—
1270C22⋊C4—44no—
1271C22⋊C4—44no—
1272C22⋊C4—44no—
1273C22⋊C4—44no—
1274C22⋊C4—44no—
1275C22⋊C4—44no—
1276C22⋊C4—44no—
1277C22⋊C4—44no—
1278C22⋊C4—42no—
1279C22⋊C4—44no—
1280C22⋊C4—44no—
1281C22⋊C4—44no—
1282C22⋊C4—44no—
1283C42—24no—
1284C42—24no—
1285C42—24no—
1286C42—24no—
1287C42—24no—
1288C42—22no—
1289C42—22no—
1290C42—24no—
1291C42—42no—
1292C42—42no—
1293C42—42no—
1294C42—44no—
1295C42—42no—
1296C42—42no—
1297C42—42no—
1298C42—42no—
1299C42—44no—
1300C42—44no—
1301C42—44no—
1302C42—44no—
1303C42—44no—
1304C23—21no—
1305C23—21no—
1306C23—22no—
1307C23—22no—
1308C23—22no—
1309C23—22no—
1310C23—24no—
1311C23—22no—
1312C23—22no—
1313C23—24no—
1314C23—22no—
1315C23—24no—
1316C23—22no—
1317C23—24no—
1318C23—22no—
1319C23—22no—
1320C23—22no—
1321C23—24no—
1322C23—22no—
1323C23—22no—
1324C23—24no—
1325C23—22no—
1326C23—24no—
1327C23—22no—
1328C23—22no—
1329C23C2×H(5,𝔽2)12yes—
1330C23C2611yescharacteristic
1331Q8—28no—
1332Q8—48no—
1333Q8—44no—
1334Q8—48no—
1335Q8—84no—
1336Q8—84no—
1337Q8—84no—
1338D4—416no—
1339D4—48no—
1340D4—84no—
1341D4—88no—
1342D4—84no—
1343D4—84no—
1344D4—82no—
1345D4—82no—
1346D4—84no—
1347D4—84no—
1348D4—88no—
1349D4—162no—
1350D4—164no—
1351D4—164no—
1352C2×C4—22no—
1353C2×C4—21no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—21no—
1357C2×C4—22no—
1358C2×C4—28no—
1359C2×C4—21no—
1360C2×C4—21no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—21no—
1365C2×C4—22no—
1366C2×C4—21no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—24no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—24no—
1377C2×C4—24no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—24no—
1382C2×C4—22no—
1383C2×C4—24no—
1384C2×C4—24no—
1385C2×C4—24no—
1386C2×C4—24no—
1387C2×C4—24no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—24no—
1393C2×C4—22no—
1394C2×C4—24no—
1395C2×C4—22no—
1396C2×C4—22no—
1397C2×C4—22no—
1398C2×C4—24no—
1399C2×C4—22no—
1400C2×C4—24no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—24no—
1404C2×C4—24no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—24no—
1409C2×C4—22no—
1410C2×C4—22no—
1411C2×C4—24no—
1412C2×C4—22no—
1413C2×C4—22no—
1414C2×C4—22no—
1415C2×C4—22no—
1416C2×C4—44no—
1417C2×C4—48no—
1418C2×C4—44no—
1419C2×C4—48no—
1420C2×C4—48no—
1421C2×C4—88no—
1422C2×C4—88no—
1423C2×C4—84no—
1424C2×C4—84no—
1425C2×C4—84no—
1426C2×C4—88no—
1427C2×C4—164no—
1428C2×C4C2×H(5,𝔽2)14yes—
1429C2×C4C2×H(5,𝔽2)12yes—
1430C2×C4C2×H(5,𝔽2)12yes—
1431C2×C4C2×H(5,𝔽2)12yes—
1432C2×C4#58514yes—
1433C2×C4#58512yes—
1434C22—22no—
1435C22—24no—
1436C22—41no—
1437C22—41no—
1438C22—42no—
1439C22—42no—
1440C22—42no—
1441C22—44no—
1442C22—44no—
1443C22—42no—
1444C22—42no—
1445C22—42no—
1446C22—44no—
1447C22—42no—
1448C22—42no—
1449C22—42no—
1450C22—44no—
1451C22—42no—
1452C22—42no—
1453C22—44no—
1454C22—42no—
1455C22—42no—
1456C22—44no—
1457C22—42no—
1458C22—42no—
1459C22—44no—
1460C22C22×H(5,𝔽2)11yescharacteristic
1461C22C22×H(5,𝔽2)11yescharacteristic
1462C22C2×#58511yescharacteristic
1463C22C2×#58512yes—
1464C222−1+612yes—
1465C4—22no—
1466C4—24no—
1467C4—24no—
1468C4—42no—
1469C4—42no—
1470C4—42no—
1471C4—44no—
1472C4—44no—
1473C4—41no—
1474C4—42no—
1475C4—41no—
1476C4—42no—
1477C4—41no—
1478C4—42no—
1479C4—41no—
1480C4—42no—
1481C4—42no—
1482C4—42no—
1483C4—42no—
1484C4—44no—
1485C4—42no—
1486C4—42no—
1487C4—44no—
1488C4—44no—
1489C4#353414yes—
1490C2—42no—
1491C2—82no—
1492C2—82no—
1493C2—84no—
1494C2C2×#353411yescharacteristic
1495C2#6292512yes—
1496C2#6296812yes—
1497C2#6302011yescharacteristic
1498C2#6304411yescharacteristic
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. #59811C2semidirect
2. #59753C2semidirect
3. #59125C2semidirect
4. #58208C2semidirect
5. #57573C2semidirect
6. #56508C2semidirect
7. #54964C2semidirect
8. #53478C2semidirect
9. #53130C2semidirect
10. #52716C2semidirect
11. #52168C2semidirect
12. #50789C2semidirect
13. #48459C2semidirect
14. #45616C2semidirect
15. #45391C2semidirect
16. #43414C2semidirect
17. #42958C2semidirect
18. #42927C2semidirect
19. #42883C2semidirect
20. #42726C2semidirect
21. #40972C2semidirect
22. #40032C2semidirect
23. #39223C2semidirect
24. #38903C2semidirect
25. #38035C2semidirect
26. #37523C2semidirect
27. #36030C2semidirect
28. #36018C2semidirect
29. #35674C2semidirect

Maximal subgroups

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

subgroupindex
#598112
#597532
#591252
#582082
#575732
#565082
#549642
#534782
#531302
#527162
#521682
#507892
#484592
#456162
#453912
#434142
#429582
#429272
#428832
#427262
#409722
#400322
#392232
#389032
#380352
#375232
#360302
#360182
#356742