Finite Group Databasebeta

← #8374796

Subgroups — #8374796

Order 512.

5005 conjugacy classes of subgroups.

The subgroup lattice has 1532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59458C212yesmaximal, complemented
2#57628C214yesmaximal, complemented
3#57628C214yesmaximal, complemented
4#57488C214yesmaximal, complemented
5#56908C214yesmaximal, complemented
6#53118C212yesmaximal, complemented
7#51322C214yesmaximal, complemented
8#51058C214yesmaximal, complemented
9#46013C212yesmaximal, complemented
10#45354C211yesmaximal, characteristic, complemented
11#45083C211yesmaximal, characteristic, complemented
12#45070C211yesmaximal, characteristic, complemented
13#44970C212yesmaximal, complemented
14#44934C211yesmaximal, characteristic, complemented
15#42789C211yesmaximal, characteristic, complemented
16#42595C212yesmaximal, complemented
17#42559C212yesmaximal, complemented
18#42429C211yesmaximal, characteristic, complemented
19#41957C214yesmaximal, complemented
20#40589C214yesmaximal, complemented
21#39628C211yesmaximal, characteristic, complemented
22#39532C212yesmaximal, complemented
23#39406C212yesmaximal, complemented
24#39168C211yesmaximal, characteristic, complemented
25#37322C211yesmaximal, characteristic, complemented
26#36608C211yesmaximal, characteristic, complemented
27#36465C211yesmaximal, characteristic, complemented
28#35844C211yesmaximal, characteristic, complemented
29#35739C211yesmaximal, characteristic, complemented
30#35535C211yesmaximal, characteristic, complemented
31#34604C211yesmaximal, characteristic, complemented
32C2×#559C2211yescharacteristic
33C2×Q82C2211yescharacteristic
34C2×#554C2214yes—
35C2×#550C2211yescharacteristic
36C2×D4×Q8C2211yescharacteristic
37C2×#548C2214yes—
38C2×#542C2211yescharacteristic
39C2×#542C2214yes—
40C2×#520C2211yescharacteristic
41#2862C2212yes—
42#2862C2211yescharacteristic
43#2858C2211yescharacteristic
44#2858C2212yes—
45#2838C2214yes—
46#2838C2214yes—
47#2834C2214yes—
48#2825C2214yes—
49#2821C2212yes—
50#2821C2214yes—
51#2820C2214yes—
52#2817C2214yes—
53#2813C2212yes—
54#2808C2214yes—
55#2804C2214yes—
56#2778C2214yes—
57#2778C2214yes—
58#2777C2214yes—
59#2761C2214yes—
60#2761C2214yes—
61#2761C2214yes—
62#2760C2214yes—
63#2756C2214yes—
64#2753C2214yes—
65#2751C2214yes—
66#2751C2214yes—
67#2749C2214yes—
68#2749C2214yes—
69#2746C2214yes—
70#2738C2214yes—
71#2738C2214yes—
72#2732C2214yes—
73#2732C2214yes—
74#2730C2214yes—
75#2730C2214yes—
76#2729C2214yes—
77#2729C2214yes—
78#2728C2214yes—
79#2712C2214yes—
80#2710C2214yes—
81#2708C2214yes—
82#2708C2214yes—
83#2700C2214yes—
84#2700C2214yes—
85#2700C2214yes—
86#2692C2214yes—
87#2692C2214yes—
88#2692C2214yes—
89#2691C2214yes—
90#2691C2214yes—
91#2690C2214yes—
92#2690C2214yes—
93#2689C2214yes—
94#2688C2214yes—
95#2686C2214yes—
96#2677C2214yes—
97#2677C2214yes—
98#2677C2214yes—
99#2676C2214yes—
100#2676C2214yes—
101#2674C2214yes—
102#2674C2214yes—
103#2674C2214yes—
104#2674C2214yes—
105#2672C2214yes—
106#2666C2212yes—
107#2664C2212yes—
108#2658C2212yes—
109#2655C2212yes—
110#2655C2212yes—
111#2654C2212yes—
112#2650C2212yes—
113#2647C2212yes—
114#2640C2212yes—
115#2639C2212yes—
116#2639C2214yes—
117#2637C2212yes—
118#2636C2214yes—
119#2634C2212yes—
120#2633C2214yes—
121#2632C2212yes—
122#2632C2214yes—
123#2631C2212yes—
124#2631C2214yes—
125#2628C2211yescharacteristic
126#2627C2212yes—
127#2627C2214yes—
128#2619C2211yescharacteristic
129#2616C2212yes—
130#2611C2214yes—
131#2610C2212yes—
132#2604C2212yes—
133#2603C2214yes—
134#2598C2212yes—
135#2598C2214yes—
136#2591C2214yes—
137#2581C2211yescharacteristic
138#2581C2214yes—
139#2581C2211yescharacteristic
140#2580C2211yescharacteristic
141#2580C2211yescharacteristic
142#2580C2214yes—
143#2567C2211yescharacteristic
144#2567C2211yescharacteristic
145#2564C2212yes—
146#2552C2212yes—
147#2551C2212yes—
148#2551C2212yes—
149#2548C2211yescharacteristic
150#2545C2212yes—
151#2545C2211yescharacteristic
152#2544C2212yes—
153#2544C2212yes—
154#2544C2211yescharacteristic
155#2544C2212yes—
156#2542C2212yes—
157#2542C2211yescharacteristic
158#2542C2212yes—
159#2542C2211yescharacteristic
160#2541C2211yescharacteristic
161#2541C2212yes—
162#2540C2214yes—
163#2540C2214yes—
164#2540C2214yes—
165#2514C2214yes—
166#2514C2214yes—
167#2514C2212yes—
168#2514C2212yes—
169#2513C2212yes—
170#2512C2212yes—
171#2511C2212yes—
172#2502C2211yescharacteristic
173#2501C2211yescharacteristic
174#2491C2212yes—
175#2491C2212yes—
176#2479C2214yes—
177#2479C2214yes—
178#2476C2214yes—
179#2465C2214yes—
180#2461C2214yes—
181#2461C2214yes—
182#2459C2214yes—
183#2456C2214yes—
184#2455C2214yes—
185#2454C2214yes—
186#2452C2214yes—
187#2452C2214yes—
188#2452C2212yes—
189#2452C2212yes—
190#2452C2212yes—
191#2452C2212yes—
192#2452C2212yes—
193#2451C2212yes—
194#2451C2212yes—
195#2450C2214yes—
196#2450C2214yes—
197#2450C2214yes—
198#2449C2214yes—
199#2449C2214yes—
200#2449C2214yes—
201#2449C2214yes—
202#2449C2214yes—
203#2448C2214yes—
204#2448C2212yes—
205#2448C2212yes—
206#2447C2212yes—
207#2447C2212yes—
208#2447C2212yes—
209#2445C2212yes—
210#2444C2214yes—
211#2444C2214yes—
212#2443C2214yes—
213#2443C2214yes—
214#2443C2214yes—
215#2440C2212yes—
216#2438C2214yes—
217#2438C2214yes—
218#2434C2214yes—
219#2432C2211yescharacteristic
220#2431C2212yes—
221#2431C2211yescharacteristic
222#2430C2212yes—
223#2428C2212yes—
224#2427C2212yes—
225#2423C2212yes—
226#2420C2212yes—
227#2409C2212yes—
228#2406C2214yes—
229#2402C2211yescharacteristic
230#2402C2212yes—
231#2401C2212yes—
232#2399C2211yescharacteristic
233#2397C2212yes—
234#2396C2211yescharacteristic
235#2396C2211yescharacteristic
236C2×#395C2212yes—
237#2379C2214yes—
238#2367C2212yes—
239#2366C2212yes—
240#2366C2212yes—
241#2361C2212yes—
242#2356C2211yescharacteristic
243#2356C2211yescharacteristic
244#2356C2214yes—
245#2354C2212yes—
246#2349C2211yescharacteristic
247#2349C2211yescharacteristic
248D4×C4⋊C4C2212yes—
249D4×C4⋊C4C2212yes—
250#2339C2212yes—
251#2331C2211yescharacteristic
252#2328C2211yescharacteristic
253#2328C2212yes—
254#2326C2212yes—
255#2326C2211yescharacteristic
256#2326C2211yescharacteristic
257#2318C2214yes—
258C4×C4⋊Q8C2211yescharacteristic
259C4×C4⋊Q8C2212yes—
260C4×#127C2212yes—
261C4×#127C2211yescharacteristic
262C4×#125C2212yes—
263C4×#126C2212yes—
264#2298C2211yescharacteristic
265#2295C2211yescharacteristic
266C42×Q8C2211yescharacteristic
267C22×#41C2311yescharacteristic
268C22×#41C2312yes—
269C23×Q8C2312yes—
270#559—44no—
271Q82—44no—
272#554—416no—
273#550—44no—
274D4×Q8—44no—
275#548—416no—
276#542—44no—
277#542—416no—
278C2×C4⋊Q8C2311yescharacteristic
279C2×C4⋊Q8C2311yescharacteristic
280C2×C4⋊Q8C2312yes—
281C2×C4⋊Q8C2314yes—
282C2×C4⋊Q8C2312yes—
283C2×C4⋊Q8C2311yescharacteristic
284C2×C4⋊Q8C2312yes—
285C2×C4⋊Q8C2312yes—
286C2×C4⋊Q8C2314yes—
287C2×C4⋊Q8C2314yes—
288C2×#127C2311yescharacteristic
289C2×#127C2312yes—
290C2×#127C2311yescharacteristic
291C2×#127C2312yes—
292C2×#126C2312yes—
293C2×#126C2314yes—
294C2×#126C2312yes—
295C2×#125C2312yes—
296C2×#125C2314yes—
297C2×#124C2314yes—
298C2×#124C2311yescharacteristic
299C2×#124C2312yes—
300C2×#124C2311yescharacteristic
301C2×#124C2314yes—
302C2×#124C2314yes—
303C2×#124C2312yes—
304C2×#124C2314yes—
305C2×#124C2312yes—
306C2×#124C2312yes—
307C2×#124C2311yescharacteristic
308C2×#124C2314yes—
309C2×#123C2314yes—
310C2×#123C2314yes—
311C2×#123C2314yes—
312C2×#123C2312yes—
313C2×C22⋊Q8C2314yes—
314C2×C22⋊Q8C2314yes—
315C2×C22⋊Q8C2312yes—
316C2×C22⋊Q8C2312yes—
317C2×C22⋊Q8C2314yes—
318C2×C22⋊Q8C2314yes—
319C2×C22⋊Q8C2314yes—
320C2×C22⋊Q8C2314yes—
321C2×C22⋊Q8C2314yes—
322C2×C22⋊Q8C2314yes—
323C2×C22⋊Q8C2314yes—
324C2×C22⋊Q8C2311yescharacteristic
325C2×C22⋊Q8C2314yes—
326C2×C22⋊Q8C2314yes—
327C2×C22⋊Q8C2314yes—
328C2×C22⋊Q8C2314yes—
329C2×#121C2314yes—
330C2×#121C2312yes—
331C2×#121C2312yes—
332C2×#121C2314yes—
333C2×#121C2314yes—
334C2×#121C2314yes—
335C2×#121C2311yescharacteristic
336C2×#121C2314yes—
337#520—44no—
338C2×C4×Q8C2311yescharacteristic
339C2×C4×Q8C2314yes—
340C2×C4×Q8C2311yescharacteristic
341C2×C4×Q8C2311yescharacteristic
342C2×C4×Q8C2312yes—
343C2×C4×Q8C2311yescharacteristic
344C2×C4×Q8C2311yescharacteristic
345C2×C4×Q8C2312yes—
346C2×C4×Q8C2312yes—
347C2×C4×D4C2314yes—
348C2×C4×D4C2311yescharacteristic
349C2×C4×D4C2311yescharacteristic
350C2×C4×D4C2312yes—
351C2×C4×D4C2312yes—
352C2×C4×D4C2314yes—
353C2×C4×D4C2314yes—
354C2×C4×D4C2312yes—
355C2×C4×D4C2312yes—
356C2×C4×D4C2312yes—
357C2×C4×D4C2312yes—
358C2×C4×D4C2312yes—
359C2×C4×D4C2314yes—
360C2×C4×D4C2312yes—
361C2×C4×D4C2314yes—
362C2×C4×D4C2311yescharacteristic
363C2×C4×D4C2314yes—
364C2×C4×D4C2312yes—
365C2×#117C2311yescharacteristic
366C2×#117C2314yes—
367C2×#117C2312yes—
368C22×C4⋊C4C2314yes—
369C22×C4⋊C4C2314yes—
370C22×C4⋊C4C2311yescharacteristic
371C22×C4⋊C4C2312yes—
372#401C2314yes—
373#401C2312yes—
374#401C2314yes—
375#400C2312yes—
376#400C2314yes—
377#400C2314yes—
378#400C2314yes—
379#400C2312yes—
380#400C2311yescharacteristic
381#400C2312yes—
382#400C2312yes—
383#400C2314yes—
384#400C2314yes—
385#400C2312yes—
386#400C2312yes—
387#400C2312yes—
388#400C2314yes—
389#400C2312yes—
390#400C2311yescharacteristic
391#400C2312yes—
392#400C2312yes—
393#400C2312yes—
394#400C2312yes—
395#399C2311yescharacteristic
396#399C2314yes—
397#399C2314yes—
398#399C2312yes—
399#399C2312yes—
400#399C2314yes—
401#399C2314yes—
402#399C2312yes—
403#399C2314yes—
404#399C2314yes—
405#399C2312yes—
406#399C2312yes—
407#399C2314yes—
408#399C2314yes—
409#399C2314yes—
410#399C2311yescharacteristic
411#398C2314yes—
412#398C2314yes—
413#398C2314yes—
414#398C2314yes—
415#398C2314yes—
416#398C2314yes—
417#398C2314yes—
418#398C2314yes—
419#398C2312yes—
420#398C2314yes—
421#398C2312yes—
422#398C2312yes—
423#398C2312yes—
424#398C2312yes—
425#398C2312yes—
426#398C2312yes—
427#398C2312yes—
428#398C2312yes—
429#398C2312yes—
430#397C2314yes—
431#397C2314yes—
432#397C2314yes—
433#397C2314yes—
434#397C2314yes—
435#397C2314yes—
436#397C2314yes—
437#397C2314yes—
438#397C2312yes—
439#397C2314yes—
440#397C2314yes—
441#397C2314yes—
442#397C2314yes—
443#397C2314yes—
444#397C2314yes—
445#397C2314yes—
446#397C2312yes—
447#397C2312yes—
448#396C2314yes—
449#396C2314yes—
450#396C2314yes—
451#396C2314yes—
452#396C2314yes—
453#396C2314yes—
454#396C2314yes—
455#396C2314yes—
456#396C2314yes—
457#396C2312yes—
458#396C2312yes—
459#396C2312yes—
460#395C2314yes—
461#395C2314yes—
462#395C2314yes—
463#395C2314yes—
464#395C2312yes—
465#395C2314yes—
466#395C2314yes—
467#395C2314yes—
468#395C2312yes—
469#395C2312yes—
470#395C2312yes—
471#395C2311yescharacteristic
472#395C2311yescharacteristic
473#395C2312yes—
474#395C2314yes—
475#395C2312yes—
476#395C2312yes—
477#394C2314yes—
478#394C2314yes—
479#394C2314yes—
480#394C2314yes—
481#394C2314yes—
482#394C2314yes—
483#394C2314yes—
484#394C2312yes—
485#394C2312yes—
486#394C2314yes—
487#394C2312yes—
488#394C2314yes—
489#394C2314yes—
490#394C2314yes—
491#394C2312yes—
492#394C2314yes—
493#394C2314yes—
494#394C2314yes—
495#394C2314yes—
496#393C2312yes—
497#393C2314yes—
498#393C2314yes—
499#393C2314yes—
500#393C2312yes—
501#393C2312yes—
502#393C2314yes—
503#393C2314yes—
504#393C2314yes—
505#393C2311yescharacteristic
506#393C2314yes—
507#393C2314yes—
508#393C2314yes—
509#393C2311yescharacteristic
510#392C2314yes—
511#392C2314yes—
512#392C2314yes—
513#392C2314yes—
514#392C2312yes—
515#392C2314yes—
516#392C2312yes—
517#392C2312yes—
518#392C2312yes—
519#392C2314yes—
520#391C2311yescharacteristic
521#391C2311yescharacteristic
522#391C2314yes—
523#391C2311yescharacteristic
524#391C2312yes—
525#391C2312yes—
526#391C2312yes—
527#391C2314yes—
528#391C2314yes—
529#391C2311yescharacteristic
530#391C2314yes—
531#391C2312yes—
532#391C2312yes—
533#391C2314yes—
534#391C2314yes—
535#391C2314yes—
536#391C2314yes—
537#391C2312yes—
538#390C2311yescharacteristic
539#390C2311yescharacteristic
540#390C2312yes—
541#390C2314yes—
542#390C2314yes—
543#390C2314yes—
544#390C2312yes—
545#390C2312yes—
546#390C2314yes—
547#390C2314yes—
548#390C2312yes—
549#390C2311yescharacteristic
550#390C2311yescharacteristic
551#390C2312yes—
552#390C2312yes—
553#390C2312yes—
554#390C2314yes—
555#390C2314yes—
556#390C2314yes—
557#390C2314yes—
558#390C2312yes—
559#390C2312yes—
560#389C2312yes—
561#389C2312yes—
562#389C2312yes—
563#389C2314yes—
564#389C2314yes—
565#389C2312yes—
566#389C2314yes—
567#389C2314yes—
568#389C2312yes—
569#389C2314yes—
570#389C2314yes—
571#389C2312yes—
572#389C2314yes—
573#389C2312yes—
574#389C2312yes—
575#389C2312yes—
576#389C2312yes—
577#389C2312yes—
578#388C2312yes—
579#388C2312yes—
580#388C2312yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2312yes—
603#388C2312yes—
604#388C2314yes—
605#387C2312yes—
606#387C2312yes—
607#387C2312yes—
608#387C2312yes—
609#387C2312yes—
610#387C2312yes—
611#387C2312yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2312yes—
624#387C2312yes—
625#387C2312yes—
626#387C2312yes—
627#387C2314yes—
628#386C2314yes—
629#386C2314yes—
630#386C2314yes—
631#386C2314yes—
632#386C2314yes—
633#386C2314yes—
634#386C2314yes—
635#386C2314yes—
636#386C2314yes—
637#386C2314yes—
638#386C2314yes—
639#386C2314yes—
640#386C2314yes—
641#386C2314yes—
642#386C2314yes—
643#386C2314yes—
644#386C2314yes—
645#386C2314yes—
646#386C2314yes—
647#386C2314yes—
648#386C2314yes—
649#386C2314yes—
650#386C2314yes—
651#386C2314yes—
652#386C2314yes—
653#386C2314yes—
654#386C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2314yes—
661#385C2314yes—
662#385C2314yes—
663#385C2314yes—
664#385C2314yes—
665#385C2314yes—
666#385C2314yes—
667#385C2314yes—
668#385C2314yes—
669#385C2314yes—
670#385C2314yes—
671#385C2314yes—
672#385C2314yes—
673#385C2314yes—
674#385C2314yes—
675#385C2314yes—
676#385C2314yes—
677#385C2314yes—
678#385C2314yes—
679#385C2314yes—
680#384C2311yescharacteristic
681#384C2312yes—
682#384C2311yescharacteristic
683#384C2312yes—
684#384C2311yescharacteristic
685#384C2311yescharacteristic
686#383C2312yes—
687#383C2314yes—
688#383C2312yes—
689#383C2312yes—
690#383C2314yes—
691#382C2312yes—
692#382C2314yes—
693#382C2311yescharacteristic
694#382C2311yescharacteristic
695#382C2312yes—
696#382C2314yes—
697#381C2314yes—
698#381C2314yes—
699#381C2314yes—
700#381C2314yes—
701#381C2314yes—
702#380C2314yes—
703#380C2314yes—
704#380C2312yes—
705#380C2314yes—
706#380C2312yes—
707#380C2312yes—
708#380C2314yes—
709C4×C4⋊C4C2312yes—
710C4×C4⋊C4C2312yes—
711C4×C4⋊C4C2312yes—
712C4×C4⋊C4C2311yescharacteristic
713C4×C4⋊C4C2312yes—
714C4×C4⋊C4C2312yes—
715C4×C4⋊C4C2312yes—
716C4×C4⋊C4C2312yes—
717C4×C4⋊C4C2312yes—
718C4×C4⋊C4C2312yes—
719C4×C4⋊C4C2314yes—
720C4×C4⋊C4C2314yes—
721C4×C4⋊C4C2311yescharacteristic
722C4×C4⋊C4C2311yescharacteristic
723C4×C4⋊C4C2312yes—
724C4×C4⋊C4C2311yescharacteristic
725C4×C4⋊C4C2312yes—
726C4×C4⋊C4C2312yes—
727C4×C4⋊C4C2312yes—
728C4×C4⋊C4C2312yes—
729C4×C22⋊C4C2311yescharacteristic
730C4×C22⋊C4C2312yes—
731C4×C22⋊C4C2312yes—
732C4×C22⋊C4C2314yes—
733C4×C22⋊C4C2311yescharacteristic
734#376C2311yescharacteristic
735#376C2312yes—
736#376C2312yes—
737#376C2312yes—
738C2×#95C2312yes—
739C2×#95C2314yes—
740C2×#95C2312yes—
741C43C2312yes—
742C43C2311yescharacteristic
743C2×#41—24no—
744C2×#41—42no—
745C2×#41—42no—
746C2×#41—48no—
747C2×#41—44no—
748C22×Q8—48no—
749C22×Q8—44no—
750C22×Q8C2411yescharacteristic
751C22×Q8C2411yescharacteristic
752C22×Q8C2411yescharacteristic
753C22×Q8C2411yescharacteristic
754C22×Q8C2414yes—
755C22×Q8C2414yes—
756C22×Q8C2412yes—
757C22×Q8C2412yes—
758C22×Q8C2414yes—
759C22×D4C2411yescharacteristic
760C22×D4C2412yes—
761C22×D4C2414yes—
762C22×D4C2411yescharacteristic
763C22×D4C2412yes—
764C22×D4C2412yes—
765C22×D4C2414yes—
766C22×D4C2414yes—
767C22×D4C2414yes—
768C22×D4C2412yes—
769C22×D4C2414yes—
770C22×D4C2412yes—
771C22×D4C2414yes—
772C23×C4C2411yescharacteristic
773C23×C4C2412yes—
774C23×C4C2412yes—
775C23×C4C2414yes—
776C23×C4C2414yes—
777C23×C4C2412yes—
778C23×C4C2412yes—
779C23×C4C2412yes—
780C23×C4C2414yes—
781C23×C4C2414yes—
782C23×C4C2414yes—
783C23×C4C2414yes—
784C4⋊Q8—24no—
785C4⋊Q8—44no—
786C4⋊Q8—42no—
787C4⋊Q8—44no—
788C4⋊Q8—48no—
789C4⋊Q8—44no—
790C4⋊Q8—44no—
791C4⋊Q8—42no—
792C4⋊Q8—48no—
793C4⋊Q8—48no—
794#127—28no—
795#127—24no—
796#127—24no—
797#127—44no—
798#126—28no—
799#126—48no—
800#126—44no—
801#125—28no—
802#125—48no—
803#124—24no—
804#124—216no—
805#124—48no—
806#124—44no—
807#124—48no—
808#124—48no—
809#124—42no—
810#124—44no—
811#124—42no—
812#124—44no—
813#124—44no—
814#124—48no—
815#123—48no—
816#123—44no—
817#123—48no—
818#123—48no—
819C22⋊Q8—48no—
820C22⋊Q8—48no—
821C22⋊Q8—48no—
822C22⋊Q8—48no—
823C22⋊Q8—48no—
824C22⋊Q8—48no—
825C22⋊Q8—48no—
826C22⋊Q8—48no—
827C22⋊Q8—48no—
828C22⋊Q8—48no—
829C22⋊Q8—44no—
830C22⋊Q8—48no—
831C22⋊Q8—48no—
832C22⋊Q8—42no—
833C22⋊Q8—48no—
834C22⋊Q8—44no—
835#121—48no—
836#121—48no—
837#121—48no—
838#121—48no—
839#121—44no—
840#121—42no—
841#121—48no—
842#121—44no—
843C4×Q8—24no—
844C4×Q8—216no—
845C4×Q8—24no—
846C4×Q8—28no—
847C4×Q8—24no—
848C4×Q8—24no—
849C4×Q8—42no—
850C4×Q8—44no—
851C4×Q8—44no—
852C4×D4—24no—
853C4×D4—24no—
854C4×D4—216no—
855C4×D4—44no—
856C4×D4—48no—
857C4×D4—48no—
858C4×D4—48no—
859C4×D4—44no—
860C4×D4—44no—
861C4×D4—44no—
862C4×D4—42no—
863C4×D4—44no—
864C4×D4—44no—
865C4×D4—48no—
866C4×D4—48no—
867C4×D4—44no—
868C4×D4—44no—
869C4×D4—44no—
870#117—24no—
871#117—44no—
872#117—48no—
873C2×C4⋊C4—44no—
874C2×C4⋊C4—42no—
875C2×C4⋊C4—48no—
876C2×C4⋊C4—48no—
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2411yescharacteristic
884C2×C4⋊C4C2411yescharacteristic
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2411yescharacteristic
887C2×C4⋊C4C2411yescharacteristic
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2411yescharacteristic
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2411yescharacteristic
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2412yes—
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2414yes—
912C2×C4⋊C4C2414yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2414yes—
915C2×C4⋊C4C2414yes—
916C2×C4⋊C4C2414yes—
917C2×C4⋊C4C2414yes—
918C2×C4⋊C4C2414yes—
919C2×C4⋊C4C2414yes—
920C2×C4⋊C4C2414yes—
921C2×C4⋊C4C2414yes—
922C2×C4⋊C4C2414yes—
923C2×C4⋊C4C2412yes—
924C2×C4⋊C4C2414yes—
925C2×C4⋊C4C2414yes—
926C2×C4⋊C4C2414yes—
927C2×C4⋊C4C2412yes—
928C2×C4⋊C4C2414yes—
929C2×C4⋊C4C2414yes—
930C2×C4⋊C4C2412yes—
931C2×C4⋊C4C2412yes—
932C2×C4⋊C4C2412yes—
933C2×C4⋊C4C2412yes—
934C2×C4⋊C4C2412yes—
935C2×C4⋊C4C2412yes—
936C2×C4⋊C4C2412yes—
937C2×C4⋊C4C2412yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2411yescharacteristic
940C2×C22⋊C4C2411yescharacteristic
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2412yes—
944C2×C22⋊C4C2412yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2412yes—
950C2×C22⋊C4C2412yes—
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2412yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2414yes—
956C2×C22⋊C4C2414yes—
957C2×C22⋊C4C2414yes—
958C2×C22⋊C4C2414yes—
959C2×C22⋊C4C2414yes—
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2414yes—
963C2×C22⋊C4C2414yes—
964C2×C22⋊C4C2414yes—
965C2×C22⋊C4C2414yes—
966C2×C22⋊C4C2414yes—
967C2×C22⋊C4C2414yes—
968C2×C22⋊C4C2414yes—
969C2×C22⋊C4C2414yes—
970C2×C22⋊C4C2412yes—
971C2×C22⋊C4C2414yes—
972C2×C22⋊C4C2412yes—
973C2×C22⋊C4C2414yes—
974C2×C22⋊C4C2414yes—
975C2×C22⋊C4C2412yes—
976C2×C22⋊C4C2414yes—
977C2×C22⋊C4C2414yes—
978C2×C22⋊C4C2412yes—
979C2×C22⋊C4C2414yes—
980C2×C22⋊C4C2414yes—
981C2×C22⋊C4C2414yes—
982C2×C22⋊C4C2414yes—
983C2×C22⋊C4C2412yes—
984C2×C22⋊C4C2412yes—
985C2×C22⋊C4C2412yes—
986C2×C22⋊C4C2414yes—
987C2×C22⋊C4C2414yes—
988C2×C22⋊C4C2414yes—
989C2×C42C2412yes—
990C2×C42C2414yes—
991C2×C42C2411yescharacteristic
992C2×C42C2412yes—
993C2×C42C2412yes—
994C2×C42C2412yes—
995C2×C42C2412yes—
996C2×C42C2411yescharacteristic
997C2×C42C2412yes—
998C2×C42C2414yes—
999C2×C42C2412yes—
1000C2×C42C2411yescharacteristic
1001C2×C42C2411yescharacteristic
1002C2×C42C2412yes—
1003C2×C42C2411yescharacteristic
1004C2×C42C2412yes—
1005C2×C42C2414yes—
1006C2×C42C2414yes—
1007C2×C42C2412yes—
1008C2×C42C2412yes—
1009C2×C42C2412yes—
1010C2×C42C2411yescharacteristic
1011C2×C42C2412yes—
1012#95C2412yes—
1013#95C2411yescharacteristic
1014#95C2411yescharacteristic
1015#95C2414yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2411yescharacteristic
1023#95C2412yes—
1024#95C2412yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2412yes—
1030#95C2412yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2414yes—
1035#95C2412yes—
1036#95C2412yes—
1037#95C2412yes—
1038#95C2412yes—
1039#95C2412yes—
1040#95C2411yescharacteristic
1041#95C2412yes—
1042#95C2412yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2412yes—
1047#95C2412yes—
1048#95C2412yes—
1049#95C2412yes—
1050#95C2412yes—
1051#95C2412yes—
1052#95C2414yes—
1053#95C2412yes—
1054#95C2412yes—
1055#95C2414yes—
1056#95C2414yes—
1057#95C2414yes—
1058#95C2412yes—
1059#95C2412yes—
1060#95C2412yes—
1061#95C2412yes—
1062#95C2412yes—
1063#95C2412yes—
1064#95C2412yes—
1065#95C2414yes—
1066#95C2414yes—
1067#95C2414yes—
1068#95C2414yes—
1069#95C2414yes—
1070#95C2414yes—
1071#95C2414yes—
1072#95C2414yes—
1073#95C2414yes—
1074#95C2414yes—
1075#95C2414yes—
1076#95C2414yes—
1077#95C2414yes—
1078C24C2511yescharacteristic
1079C24C2512yes—
1080C24C2514yes—
1081C24C2512yes—
1082#41—416no—
1083#41—816no—
1084C2×Q8—24no—
1085C2×Q8—22no—
1086C2×Q8—22no—
1087C2×Q8—22no—
1088C2×Q8—22no—
1089C2×Q8—28no—
1090C2×Q8—28no—
1091C2×Q8—24no—
1092C2×Q8—22no—
1093C2×Q8—22no—
1094C2×Q8—22no—
1095C2×Q8—22no—
1096C2×Q8—42no—
1097C2×Q8—44no—
1098C2×Q8—44no—
1099C2×Q8—44no—
1100C2×Q8—44no—
1101C2×Q8—44no—
1102C2×Q8—44no—
1103C2×Q8—44no—
1104C2×Q8—42no—
1105C2×Q8—44no—
1106C2×Q8—44no—
1107C2×Q8—816no—
1108C2×D4—28no—
1109C2×D4—24no—
1110C2×D4—28no—
1111C2×D4—28no—
1112C2×D4—22no—
1113C2×D4—28no—
1114C2×D4—22no—
1115C2×D4—24no—
1116C2×D4—24no—
1117C2×D4—28no—
1118C2×D4—24no—
1119C2×D4—22no—
1120C2×D4—24no—
1121C2×D4—22no—
1122C2×D4—22no—
1123C2×D4—24no—
1124C2×D4—42no—
1125C2×D4—44no—
1126C2×D4—42no—
1127C2×D4—44no—
1128C2×D4—44no—
1129C2×D4—44no—
1130C2×D4—44no—
1131C2×D4—44no—
1132C2×D4—44no—
1133C2×D4—44no—
1134C2×D4—44no—
1135C2×D4—44no—
1136C2×D4—44no—
1137C2×D4—44no—
1138C2×D4—44no—
1139C2×D4—44no—
1140C2×D4—42no—
1141C2×D4—44no—
1142C2×D4—44no—
1143C2×D42−1+414yes—
1144C22×C4—24no—
1145C22×C4—22no—
1146C22×C4—22no—
1147C22×C4—22no—
1148C22×C4—24no—
1149C22×C4—28no—
1150C22×C4—28no—
1151C22×C4—24no—
1152C22×C4—42no—
1153C22×C4—42no—
1154C22×C4—44no—
1155C22×C4—44no—
1156C22×C4—44no—
1157C22×C4—44no—
1158C22×C4—44no—
1159C22×C4—44no—
1160C22×C4—44no—
1161C22×C4—44no—
1162C22×C4—44no—
1163C22×C4—44no—
1164C22×C4—44no—
1165C22×C4—44no—
1166C22×C4—44no—
1167C22×C4—44no—
1168C22×C4—44no—
1169C22×C4—42no—
1170C22×C4—42no—
1171C22×C4—44no—
1172C22×C4—44no—
1173C22×C4—44no—
1174C22×C4—44no—
1175C22×C4—44no—
1176C22×C4C2512yes—
1177C22×C4C2512yes—
1178C22×C4C2512yes—
1179C22×C4C2511yescharacteristic
1180C22×C4C2512yes—
1181C22×C4C2514yes—
1182C22×C4C2514yes—
1183C22×C4C2512yes—
1184C22×C4C2512yes—
1185C22×C4C2512yes—
1186C22×C4C2512yes—
1187C22×C4C2512yes—
1188C22×C4C2512yes—
1189C22×C4C2511yescharacteristic
1190C22×C4C2512yes—
1191C22×C4C2512yes—
1192C22×C4C2514yes—
1193C22×C4C2511yescharacteristic
1194C22×C4C2512yes—
1195C22×C4C2512yes—
1196C22×C4C2512yes—
1197C22×C4C2512yes—
1198C22×C4C2511yescharacteristic
1199C22×C4C2512yes—
1200C22×C4C2511yescharacteristic
1201C22×C4C2512yes—
1202C22×C4C2511yescharacteristic
1203C4⋊C4—22no—
1204C4⋊C4—28no—
1205C4⋊C4—24no—
1206C4⋊C4—24no—
1207C4⋊C4—22no—
1208C4⋊C4—22no—
1209C4⋊C4—24no—
1210C4⋊C4—22no—
1211C4⋊C4—24no—
1212C4⋊C4—22no—
1213C4⋊C4—28no—
1214C4⋊C4—22no—
1215C4⋊C4—24no—
1216C4⋊C4—24no—
1217C4⋊C4—24no—
1218C4⋊C4—24no—
1219C4⋊C4—24no—
1220C4⋊C4—24no—
1221C4⋊C4—24no—
1222C4⋊C4—22no—
1223C4⋊C4—28no—
1224C4⋊C4—22no—
1225C4⋊C4—28no—
1226C4⋊C4—24no—
1227C4⋊C4—24no—
1228C4⋊C4—24no—
1229C4⋊C4—24no—
1230C4⋊C4—24no—
1231C4⋊C4—24no—
1232C4⋊C4—24no—
1233C4⋊C4—24no—
1234C4⋊C4—24no—
1235C4⋊C4—42no—
1236C4⋊C4—42no—
1237C4⋊C4—44no—
1238C4⋊C4—44no—
1239C4⋊C4—44no—
1240C4⋊C4—44no—
1241C4⋊C4—42no—
1242C4⋊C4—42no—
1243C4⋊C4—42no—
1244C4⋊C4—42no—
1245C4⋊C4—42no—
1246C4⋊C4—42no—
1247C4⋊C4—42no—
1248C4⋊C4—42no—
1249C4⋊C4—44no—
1250C4⋊C4—44no—
1251C4⋊C4—44no—
1252C4⋊C4—44no—
1253C4⋊C4—44no—
1254C4⋊C4—44no—
1255C4⋊C4—44no—
1256C4⋊C4—44no—
1257C4⋊C4—42no—
1258C4⋊C4—44no—
1259C4⋊C4—44no—
1260C4⋊C4—42no—
1261C4⋊C4—44no—
1262C4⋊C4—44no—
1263C4⋊C4—44no—
1264C22⋊C4—28no—
1265C22⋊C4—22no—
1266C22⋊C4—22no—
1267C22⋊C4—24no—
1268C22⋊C4—28no—
1269C22⋊C4—28no—
1270C22⋊C4—24no—
1271C22⋊C4—28no—
1272C22⋊C4—24no—
1273C22⋊C4—28no—
1274C22⋊C4—28no—
1275C22⋊C4—28no—
1276C22⋊C4—24no—
1277C22⋊C4—24no—
1278C22⋊C4—42no—
1279C22⋊C4—42no—
1280C22⋊C4—42no—
1281C22⋊C4—44no—
1282C22⋊C4—44no—
1283C22⋊C4—44no—
1284C22⋊C4—44no—
1285C22⋊C4—42no—
1286C22⋊C4—44no—
1287C22⋊C4—44no—
1288C22⋊C4—44no—
1289C22⋊C4—44no—
1290C22⋊C4—44no—
1291C22⋊C4—44no—
1292C22⋊C4—44no—
1293C22⋊C4—44no—
1294C22⋊C4—44no—
1295C22⋊C4—44no—
1296C22⋊C4—44no—
1297C22⋊C4—44no—
1298C22⋊C4—44no—
1299C22⋊C4—44no—
1300C22⋊C4—44no—
1301C22⋊C4—44no—
1302C22⋊C4—44no—
1303C22⋊C4—44no—
1304C22⋊C4—42no—
1305C22⋊C4—42no—
1306C22⋊C4—44no—
1307C22⋊C4—42no—
1308C22⋊C4—44no—
1309C22⋊C4—44no—
1310C22⋊C4—42no—
1311C22⋊C4—44no—
1312C22⋊C4—44no—
1313C22⋊C4—44no—
1314C22⋊C4—44no—
1315C42—22no—
1316C42—24no—
1317C42—28no—
1318C42—24no—
1319C42—24no—
1320C42—24no—
1321C42—24no—
1322C42—28no—
1323C42—24no—
1324C42—22no—
1325C42—24no—
1326C42—22no—
1327C42—24no—
1328C42—22no—
1329C42—22no—
1330C42—42no—
1331C42—42no—
1332C42—42no—
1333C42—42no—
1334C42—44no—
1335C42—44no—
1336C42H(5,𝔽2)14yes—
1337C42H(5,𝔽2)18yes—
1338C23—22no—
1339C23—24no—
1340C23—22no—
1341C23—24no—
1342C23—22no—
1343C23—24no—
1344C23—24no—
1345C23—21no—
1346C23—24no—
1347C23—22no—
1348C23—24no—
1349C23—21no—
1350C23—24no—
1351C23—22no—
1352C23—22no—
1353C23—24no—
1354C23—21no—
1355C23—22no—
1356C23—24no—
1357C23—24no—
1358C23—24no—
1359C23C2×2−1+414yes—
1360C23C2611yescharacteristic
1361Q8—28no—
1362Q8—44no—
1363Q8—44no—
1364Q8—44no—
1365Q8—88no—
1366Q8—88no—
1367Q8—84no—
1368Q8—162no—
1369Q8—164no—
1370D4—28no—
1371D4—416no—
1372D4—48no—
1373D4—44no—
1374D4—48no—
1375D4—84no—
1376D4—84no—
1377D4—88no—
1378D4—88no—
1379D4—88no—
1380D4—88no—
1381D4—162no—
1382D4—164no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—21no—
1392C2×C4—22no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—24no—
1396C2×C4—21no—
1397C2×C4—22no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—22no—
1401C2×C4—24no—
1402C2×C4—24no—
1403C2×C4—22no—
1404C2×C4—24no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—24no—
1408C2×C4—22no—
1409C2×C4—24no—
1410C2×C4—24no—
1411C2×C4—22no—
1412C2×C4—22no—
1413C2×C4—22no—
1414C2×C4—24no—
1415C2×C4—24no—
1416C2×C4—22no—
1417C2×C4—22no—
1418C2×C4—22no—
1419C2×C4—22no—
1420C2×C4—21no—
1421C2×C4—22no—
1422C2×C4—22no—
1423C2×C4—22no—
1424C2×C4—22no—
1425C2×C4—21no—
1426C2×C4—22no—
1427C2×C4—22no—
1428C2×C4—22no—
1429C2×C4—22no—
1430C2×C4—22no—
1431C2×C4—21no—
1432C2×C4—24no—
1433C2×C4—24no—
1434C2×C4—22no—
1435C2×C4—22no—
1436C2×C4—22no—
1437C2×C4—22no—
1438C2×C4—22no—
1439C2×C4—22no—
1440C2×C4—22no—
1441C2×C4—22no—
1442C2×C4—22no—
1443C2×C4—24no—
1444C2×C4—24no—
1445C2×C4—22no—
1446C2×C4—22no—
1447C2×C4—22no—
1448C2×C4—48no—
1449C2×C4—44no—
1450C2×C4—84no—
1451C2×C4—88no—
1452C2×C4—88no—
1453C2×C4—84no—
1454C2×C4—88no—
1455C2×C4—88no—
1456C2×C4—88no—
1457C2×C4—162no—
1458C2×C4—162no—
1459C2×C4—164no—
1460C2×C4C2×H(5,𝔽2)14yes—
1461C2×C4C2×H(5,𝔽2)12yes—
1462C2×C4C2×H(5,𝔽2)14yes—
1463C2×C4C2×H(5,𝔽2)12yes—
1464C2×C4C2×H(5,𝔽2)14yes—
1465C2×C4C2×H(5,𝔽2)12yes—
1466C2×C4C2×2−1+412yes—
1467C2×C4#58512yes—
1468C22—24no—
1469C22—28no—
1470C22—42no—
1471C22—42no—
1472C22—44no—
1473C22—41no—
1474C22—42no—
1475C22—44no—
1476C22—44no—
1477C22—42no—
1478C22—41no—
1479C22—44no—
1480C22—42no—
1481C22—41no—
1482C22—44no—
1483C22—44no—
1484C22—44no—
1485C22—42no—
1486C22—44no—
1487C22—44no—
1488C22—42no—
1489C22—44no—
1490C22C22×H(5,𝔽2)11yescharacteristic
1491C22C22×H(5,𝔽2)12yes—
1492C22C22×2−1+411yescharacteristic
1493C22C2×#58511yescharacteristic
1494C222−1+612yes—
1495C4—24no—
1496C4—22no—
1497C4—22no—
1498C4—24no—
1499C4—24no—
1500C4—41no—
1501C4—42no—
1502C4—42no—
1503C4—42no—
1504C4—42no—
1505C4—44no—
1506C4—42no—
1507C4—41no—
1508C4—42no—
1509C4—42no—
1510C4—41no—
1511C4—42no—
1512C4—42no—
1513C4—42no—
1514C4—42no—
1515C4—42no—
1516C4—42no—
1517C4—42no—
1518C4—42no—
1519C4—44no—
1520C4—44no—
1521C4#354114yes—
1522C2—44no—
1523C2—81no—
1524C2—84no—
1525C2—82no—
1526C2C2×#354111yescharacteristic
1527C2#6283211yescharacteristic
1528C2#6288711yescharacteristic
1529C2#6294212yes—
1530C2#6296012yes—
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. #59458C2semidirect
2. #57628C2semidirect
3. #57628C2semidirect
4. #57488C2semidirect
5. #56908C2semidirect
6. #53118C2semidirect
7. #51322C2semidirect
8. #51058C2semidirect
9. #46013C2semidirect
10. #45354C2semidirect
11. #45083C2semidirect
12. #45070C2semidirect
13. #44970C2semidirect
14. #44934C2semidirect
15. #42789C2semidirect
16. #42595C2semidirect
17. #42559C2semidirect
18. #42429C2semidirect
19. #41957C2semidirect
20. #40589C2semidirect
21. #39628C2semidirect
22. #39532C2semidirect
23. #39406C2semidirect
24. #39168C2semidirect
25. #37322C2semidirect
26. #36608C2semidirect
27. #36465C2semidirect
28. #35844C2semidirect
29. #35739C2semidirect
30. #35535C2semidirect
31. #34604C2semidirect

Maximal subgroups

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

subgroupindex
#594582
#576282
#574882
#569082
#531182
#513222
#510582
#460132
#453542
#450832
#450702
#449702
#449342
#427892
#425952
#425592
#424292
#419572
#405892
#396282
#395322
#394062
#391682
#373222
#366082
#364652
#358442
#357392
#355352
#346042