Finite Group Databasebeta

← #8402646

Subgroups — #8402646

Order 512.

4525 conjugacy classes of subgroups.

The subgroup lattice has 1495 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59701C212yesmaximal, complemented
2#59581C212yesmaximal, complemented
3#54916C214yesmaximal, complemented
4#54393C214yesmaximal, complemented
5#50477C214yesmaximal, complemented
6#48888C214yesmaximal, complemented
7#48306C214yesmaximal, complemented
8#47886C214yesmaximal, complemented
9#46048C212yesmaximal, complemented
10#46048C212yesmaximal, complemented
11#45394C211yesmaximal, characteristic, complemented
12#45354C211yesmaximal, characteristic, complemented
13#45221C211yesmaximal, characteristic, complemented
14#45070C211yesmaximal, characteristic, complemented
15#44230C214yesmaximal, complemented
16#43664C214yesmaximal, complemented
17#42645C211yesmaximal, characteristic, complemented
18#42425C211yesmaximal, characteristic
19#40105C212yesmaximal, complemented
20#40026C212yesmaximal, complemented
21#39202C212yesmaximal, complemented
22#39025C212yesmaximal, complemented
23#37432C211yesmaximal, characteristic, complemented
24#36597C211yesmaximal, characteristic, complemented
25#36583C211yesmaximal, characteristic, complemented
26#36394C211yesmaximal, characteristic, complemented
27#36394C211yesmaximal, characteristic, complemented
28#36041C211yesmaximal, characteristic, complemented
29#35749C211yesmaximal, characteristic, complemented
30#35678C211yesmaximal, characteristic, complemented
31#34973C211yesmaximal, characteristic, complemented
32C2×#559C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#556C2211yescharacteristic
35C2×#550C2211yescharacteristic
36C2×#540C2211yescharacteristic
37C2×#519C2211yescharacteristic
38#2864C2211yescharacteristic
39#2863C2212yes—
40#2863C2212yes—
41#2858C2212yes—
42#2858C2211yescharacteristic
43#2858C2212yes—
44#2830C2214yes—
45#2830C2214yes—
46#2814C2212yes—
47#2813C2212yes—
48#2803C2214yes—
49#2803C2214yes—
50#2797C2214yes—
51#2797C2214yes—
52#2797C2214yes—
53#2797C2214yes—
54#2797C2214yes—
55#2795C2214yes—
56#2793C2214yes—
57#2786C2214yes—
58#2784C2214yes—
59#2784C2214yes—
60#2783C2214yes—
61#2773C2214yes—
62#2770C2214yes—
63#2770C2214yes—
64#2753C2214yes—
65#2753C2214yes—
66#2752C2214yes—
67#2752C2214yes—
68#2752C2214yes—
69#2749C2214yes—
70#2749C2214yes—
71#2749C2214yes—
72#2747C2214yes—
73#2747C2214yes—
74#2744C2214yes—
75#2741C2214yes—
76#2740C2214yes—
77#2738C2214yes—
78#2737C2214yes—
79#2737C2214yes—
80#2737C2214yes—
81#2737C2214yes—
82#2721C2214yes—
83#2721C2214yes—
84#2720C2214yes—
85#2711C2214yes—
86#2708C2214yes—
87#2701C2214yes—
88#2695C2214yes—
89#2691C2214yes—
90#2691C2214yes—
91#2691C2214yes—
92#2691C2214yes—
93#2686C2214yes—
94#2675C2214yes—
95#2671C2214yes—
96#2667C2214yes—
97#2656C2212yes—
98#2652C2214yes—
99#2648C2214yes—
100#2639C2212yes—
101#2634C2212yes—
102#2632C2212yes—
103#2624C2214yes—
104#2624C2212yes—
105#2621C2211yescharacteristic
106#2619C2211yescharacteristic
107#2615C2212yes—
108#2611C2212yes—
109#2610C2212yes—
110#2603C2214yes—
111#2601C2214yes—
112#2599C2212yes—
113#2599C2214yes—
114#2599C2214yes—
115#2598C2212yes—
116#2597C2214yes—
117#2591C2214yes—
118#2581C2211yescharacteristic
119#2581C2211yescharacteristic
120#2580C2211yescharacteristic
121#2580C2211yescharacteristic
122#2578C2214yes—
123#2577C2214yes—
124#2577C2214yes—
125#2577C2214yes—
126#2575C2214yes—
127#2575C2214yes—
128#2573C2214yes—
129#2569C2214yes—
130#2565C2211yescharacteristic
131#2565C2211yescharacteristic
132#2559C2214yes—
133#2554C2214yes—
134#2554C2214yes—
135#2554C2214yes—
136#2548C2211yescharacteristic
137#2548C2211yescharacteristic
138#2548C2212yes—
139#2548C2211yescharacteristic
140#2547C2212yes—
141#2547C2212yes—
142#2547C2211yescharacteristic
143#2546C2211yescharacteristic
144#2545C2212yes—
145#2545C2212yes—
146#2544C2212yes—
147#2544C2212yes—
148#2544C2212yes—
149#2544C2212yes—
150#2541C2211yescharacteristic
151#2541C2212yes—
152#2530C2214yes—
153#2524C2212yes—
154#2524C2212yes—
155#2519C2212yes—
156#2519C2212yes—
157#2518C2214yes—
158#2517C2214yes—
159#2512C2212yes—
160#2511C2212yes—
161#2508C2212yes—
162#2508C2212yes—
163#2500C2214yes—
164#2500C2211yescharacteristic
165#2500C2211yescharacteristic
166#2498C2212yes—
167#2490C2214yes—
168#2490C2214yes—
169#2490C2214yes—
170#2490C2214yes—
171#2476C2214yes—
172#2476C2214yes—
173#2476C2214yes—
174#2476C2214yes—
175#2475C2214yes—
176#2475C2214yes—
177#2473C2214yes—
178#2471C2214yes—
179#2471C2214yes—
180#2469C2212yes—
181#2469C2214yes—
182#2469C2212yes—
183#2467C2214yes—
184#2462C2212yes—
185#2462C2214yes—
186#2462C2212yes—
187#2458C2214yes—
188#2458C2214yes—
189#2458C2214yes—
190#2454C2212yes—
191#2453C2212yes—
192#2448C2212yes—
193#2448C2212yes—
194#2448C2212yes—
195#2447C2212yes—
196#2447C2212yes—
197#2447C2212yes—
198#2447C2212yes—
199#2447C2212yes—
200#2446C2212yes—
201#2446C2212yes—
202#2446C2212yes—
203#2445C2212yes—
204#2444C2214yes—
205#2443C2214yes—
206#2436C2211yescharacteristic
207#2436C2211yescharacteristic
208#2436C2212yes—
209#2434C2212yes—
210#2430C2212yes—
211#2428C2212yes—
212#2428C2212yes—
213#2427C2212yes—
214#2427C2212yes—
215#2426C2214yes—
216#2426C2212yes—
217#2426C2212yes—
218#2420C2214yes—
219#2406C2214yes—
220#2402C2211yescharacteristic
221#2399C2211yescharacteristic
222#2399C2212yes—
223#2398C2212yes—
224#2396C2211yescharacteristic
225#2396C2211yescharacteristic
226#2377C2214yes—
227#2377C2214yes—
228#2374C2214yes—
229#2367C2212yes—
230#2367C2212yes—
231#2366C2212yes—
232#2365C2212yes—
233#2363C2212yes—
234#2363C2214yes—
235#2362C2212yes—
236#2356C2211yescharacteristic
237#2356C2211yescharacteristic
238#2352C2214yes—
239Q8×C4⋊C4C2212yes—
240#2349C2211yescharacteristic
241#2349C2211yescharacteristic
242D4×C4⋊C4C2212yes—
243#2343C2214yes—
244#2343C2214yes—
245#2341C2214yes—
246#2334C2214yes—
247#2333C2214yes—
248#2328C2211yescharacteristic
249#2327C2211yescharacteristic
250#2326C2211yescharacteristic
251#2326C2211yescharacteristic
252#2324C2214yes—
253#2313C2214yes—
254C4×#125C2212yes—
255C4×#125C2212yes—
256C4×#126C2212yes—
257C4×#126C2212yes—
258C4×#124C2211yescharacteristic
259C4×#124C2211yescharacteristic
260C4×#124C2212yes—
261C4×#124C2212yes—
262#2298C2211yescharacteristic
263#2293C2212yes—
264#2293C2212yes—
265C42×Q8C2211yescharacteristic
266C42×Q8C2211yescharacteristic
267C22×#41C2312yes—
268C23×Q8C2311yescharacteristic
269#559—44no—
270#557—44no—
271#556—44no—
272#550—44no—
273#540—44no—
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2312yes—
277C2×#127C2311yescharacteristic
278C2×#127C2312yes—
279C2×#127C2312yes—
280C2×#127C2311yescharacteristic
281C2×#126C2312yes—
282C2×#126C2312yes—
283C2×#126C2314yes—
284C2×#126C2314yes—
285C2×#125C2312yes—
286C2×#125C2312yes—
287C2×#125C2311yescharacteristic
288C2×#125C2312yes—
289C2×#125C2314yes—
290C2×#124C2311yescharacteristic
291C2×#124C2311yescharacteristic
292C2×#124C2312yes—
293C2×#124C2312yes—
294C2×#124C2311yescharacteristic
295C2×#124C2311yescharacteristic
296C2×#124C2312yes—
297C2×#124C2312yes—
298C2×#124C2312yes—
299C2×#124C2312yes—
300C2×#124C2312yes—
301C2×#123C2314yes—
302C2×#123C2314yes—
303C2×#123C2312yes—
304C2×#123C2312yes—
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2312yes—
307C2×#121C2314yes—
308C2×#121C2314yes—
309C2×#121C2314yes—
310C2×#121C2312yes—
311C2×#121C2312yes—
312C2×#121C2314yes—
313C2×#121C2312yes—
314C2×#121C2314yes—
315C2×#121C2312yes—
316C2×#121C2314yes—
317C2×#121C2311yescharacteristic
318C2×#121C2311yescharacteristic
319#519—44no—
320C2×C4×Q8C2311yescharacteristic
321C2×C4×Q8C2311yescharacteristic
322C2×C4×Q8C2311yescharacteristic
323C2×C4×Q8C2311yescharacteristic
324C2×C4×Q8C2311yescharacteristic
325C2×C4×Q8C2311yescharacteristic
326C2×C4×Q8C2312yes—
327C2×C4×Q8C2312yes—
328C2×C4×Q8C2312yes—
329C2×C4×Q8C2312yes—
330C2×C4×Q8C2312yes—
331C2×C4×Q8C2312yes—
332C2×C4×Q8C2312yes—
333C2×C4×Q8C2312yes—
334C2×C4×D4C2311yescharacteristic
335C2×C4×D4C2311yescharacteristic
336C2×C4×D4C2314yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2312yes—
340C2×C4×D4C2312yes—
341C2×C4×D4C2312yes—
342C2×C4×D4C2312yes—
343C2×#117C2311yescharacteristic
344C2×#117C2314yes—
345C2×#117C2312yes—
346C2×#117C2314yes—
347C2×#117C2312yes—
348C2×#117C2311yescharacteristic
349C2×#117C2312yes—
350C22×C4⋊C4C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2312yes—
355#400C2312yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2311yescharacteristic
360#400C2314yes—
361#400C2311yescharacteristic
362#400C2312yes—
363#400C2312yes—
364#400C2314yes—
365#399C2312yes—
366#399C2312yes—
367#399C2311yescharacteristic
368#399C2311yescharacteristic
369#399C2314yes—
370#399C2314yes—
371#399C2314yes—
372#399C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2312yes—
376#398C2312yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2312yes—
382#398C2312yes—
383#398C2312yes—
384#398C2312yes—
385#398C2312yes—
386#398C2312yes—
387#398C2314yes—
388#398C2312yes—
389#398C2312yes—
390#398C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2312yes—
406#397C2314yes—
407#397C2312yes—
408#397C2314yes—
409#397C2312yes—
410#397C2312yes—
411#397C2314yes—
412#397C2314yes—
413#397C2314yes—
414#397C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#396C2312yes—
421#396C2312yes—
422#396C2314yes—
423#396C2314yes—
424#396C2314yes—
425#395C2314yes—
426#395C2312yes—
427#395C2312yes—
428#395C2311yescharacteristic
429#395C2311yescharacteristic
430#395C2312yes—
431#395C2312yes—
432#395C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#394C2314yes—
437#394C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2312yes—
441#394C2314yes—
442#394C2314yes—
443#394C2312yes—
444#394C2312yes—
445#394C2312yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#394C2314yes—
453#394C2314yes—
454#394C2314yes—
455#394C2314yes—
456#394C2314yes—
457#394C2314yes—
458#394C2314yes—
459#393C2314yes—
460#393C2314yes—
461#393C2314yes—
462#393C2312yes—
463#393C2312yes—
464#393C2311yescharacteristic
465#393C2311yescharacteristic
466#393C2314yes—
467#392C2312yes—
468#392C2312yes—
469#392C2312yes—
470#392C2314yes—
471#392C2314yes—
472#392C2312yes—
473#392C2314yes—
474#392C2314yes—
475#391C2311yescharacteristic
476#391C2311yescharacteristic
477#391C2311yescharacteristic
478#391C2311yescharacteristic
479#391C2312yes—
480#391C2312yes—
481#391C2312yes—
482#391C2312yes—
483#391C2312yes—
484#391C2312yes—
485#391C2312yes—
486#391C2312yes—
487#390C2314yes—
488#390C2314yes—
489#390C2314yes—
490#390C2314yes—
491#390C2314yes—
492#390C2312yes—
493#390C2312yes—
494#390C2311yescharacteristic
495#390C2311yescharacteristic
496#390C2312yes—
497#390C2314yes—
498#390C2314yes—
499#390C2314yes—
500#390C2314yes—
501#390C2314yes—
502#390C2314yes—
503#390C2314yes—
504#390C2314yes—
505#390C2314yes—
506#390C2314yes—
507#390C2314yes—
508#390C2314yes—
509#390C2312yes—
510#390C2312yes—
511#390C2314yes—
512#390C2314yes—
513#390C2312yes—
514#390C2311yescharacteristic
515#390C2311yescharacteristic
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2314yes—
521#389C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2312yes—
525#389C2314yes—
526#389C2312yes—
527#389C2312yes—
528#389C2314yes—
529#389C2312yes—
530#389C2312yes—
531#389C2314yes—
532#389C2314yes—
533#388C2312yes—
534#388C2312yes—
535#388C2312yes—
536#388C2312yes—
537#388C2312yes—
538#388C2312yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
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#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2312yes—
574#388C2312yes—
575#387C2312yes—
576#387C2312yes—
577#387C2312yes—
578#387C2312yes—
579#387C2312yes—
580#387C2312yes—
581#387C2312yes—
582#387C2312yes—
583#387C2312yes—
584#387C2312yes—
585#387C2312yes—
586#387C2312yes—
587#387C2312yes—
588#387C2312yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2312yes—
620#387C2312yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
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#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2314yes—
661#384C2311yescharacteristic
662#384C2311yescharacteristic
663#384C2314yes—
664#383C2312yes—
665#383C2312yes—
666#383C2314yes—
667#383C2312yes—
668#383C2312yes—
669#383C2314yes—
670#382C2312yes—
671#382C2312yes—
672#382C2311yescharacteristic
673#382C2311yescharacteristic
674#382C2314yes—
675#382C2314yes—
676#382C2311yescharacteristic
677#382C2311yescharacteristic
678#381C2314yes—
679#381C2314yes—
680#381C2314yes—
681#381C2314yes—
682#381C2314yes—
683#380C2314yes—
684#380C2314yes—
685#380C2314yes—
686#380C2314yes—
687#380C2314yes—
688#380C2312yes—
689#380C2312yes—
690#380C2314yes—
691#380C2314yes—
692#380C2314yes—
693#380C2314yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2311yescharacteristic
701C4×C4⋊C4C2311yescharacteristic
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2312yes—
704C4×C4⋊C4C2314yes—
705C4×C4⋊C4C2312yes—
706C4×C4⋊C4C2312yes—
707C4×C4⋊C4C2312yes—
708C4×C4⋊C4C2312yes—
709C4×C4⋊C4C2314yes—
710C4×C4⋊C4C2314yes—
711C4×C4⋊C4C2312yes—
712C4×C4⋊C4C2312yes—
713C4×C4⋊C4C2311yescharacteristic
714C4×C4⋊C4C2311yescharacteristic
715C4×C4⋊C4C2312yes—
716C4×C4⋊C4C2312yes—
717C4×C22⋊C4C2312yes—
718C4×C22⋊C4C2312yes—
719C4×C22⋊C4C2311yescharacteristic
720C4×C22⋊C4C2311yescharacteristic
721C4×C22⋊C4C2314yes—
722C4×C22⋊C4C2314yes—
723C4×C22⋊C4C2314yes—
724C4×C22⋊C4C2314yes—
725C4×C22⋊C4C2314yes—
726C4×C22⋊C4C2314yes—
727C4×C22⋊C4C2314yes—
728C4×C22⋊C4C2314yes—
729C4×C22⋊C4C2314yes—
730C4×C22⋊C4C2314yes—
731C4×C22⋊C4C2314yes—
732#376C2311yescharacteristic
733#376C2312yes—
734#376C2312yes—
735C2×#95C2312yes—
736C2×#95C2312yes—
737C43C2312yes—
738C43C2312yes—
739C43C2311yescharacteristic
740C2×#41—44no—
741C2×#41—48no—
742C22×Q8—42no—
743C22×Q8—42no—
744C22×Q8—42no—
745C22×Q8C2411yescharacteristic
746C22×Q8C2412yes—
747C22×Q8C2411yescharacteristic
748C22×Q8C2411yescharacteristic
749C22×Q8C2411yescharacteristic
750C22×Q8C2412yes—
751C22×D4C2411yescharacteristic
752C22×D4C2411yescharacteristic
753C22×D4C2412yes—
754C22×D4C2412yes—
755C22×D4C2414yes—
756C22×D4C2414yes—
757C22×D4C2412yes—
758C22×D4C2412yes—
759C22×D4C2412yes—
760C22×D4C2414yes—
761C22×D4C2412yes—
762C22×D4C2412yes—
763C22×D4C2414yes—
764C22×D4C2414yes—
765C23×C4C2411yescharacteristic
766C23×C4C2414yes—
767C23×C4C2412yes—
768C23×C4C2414yes—
769C23×C4C2412yes—
770C23×C4C2414yes—
771C23×C4C2414yes—
772C23×C4C2412yes—
773C23×C4C2414yes—
774C4⋊Q8—24no—
775C4⋊Q8—44no—
776C4⋊Q8—44no—
777#127—24no—
778#127—44no—
779#127—42no—
780#127—44no—
781#126—48no—
782#126—44no—
783#126—44no—
784#126—48no—
785#125—42no—
786#125—44no—
787#125—44no—
788#125—44no—
789#125—48no—
790#124—42no—
791#124—44no—
792#124—44no—
793#124—42no—
794#124—42no—
795#124—42no—
796#124—44no—
797#124—44no—
798#124—44no—
799#124—44no—
800#124—44no—
801#123—44no—
802#123—44no—
803#123—48no—
804#123—48no—
805C22⋊Q8—44no—
806C22⋊Q8—44no—
807#121—48no—
808#121—48no—
809#121—44no—
810#121—44no—
811#121—48no—
812#121—48no—
813#121—48no—
814#121—44no—
815#121—48no—
816#121—42no—
817#121—42no—
818#121—44no—
819C4×Q8—24no—
820C4×Q8—24no—
821C4×Q8—24no—
822C4×Q8—24no—
823C4×Q8—44no—
824C4×Q8—44no—
825C4×Q8—44no—
826C4×Q8—44no—
827C4×Q8—44no—
828C4×Q8—42no—
829C4×Q8—42no—
830C4×Q8—44no—
831C4×Q8—44no—
832C4×Q8—44no—
833C4×D4—24no—
834C4×D4—24no—
835C4×D4—48no—
836C4×D4—44no—
837C4×D4—44no—
838C4×D4—44no—
839C4×D4—44no—
840C4×D4—44no—
841C4×D4—44no—
842#117—24no—
843#117—48no—
844#117—48no—
845#117—44no—
846#117—44no—
847#117—42no—
848#117—44no—
849C2×C4⋊C4—48no—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2411yescharacteristic
857C2×C4⋊C4C2411yescharacteristic
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2411yescharacteristic
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2411yescharacteristic
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2414yes—
908C2×C22⋊C4C2411yescharacteristic
909C2×C22⋊C4C2411yescharacteristic
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2414yes—
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2412yes—
955C2×C22⋊C4C2412yes—
956C2×C22⋊C4C2412yes—
957C2×C22⋊C4C2412yes—
958C2×C22⋊C4C2414yes—
959C2×C22⋊C4C2414yes—
960C2×C42C2412yes—
961C2×C42C2412yes—
962C2×C42C2412yes—
963C2×C42C2414yes—
964C2×C42C2412yes—
965C2×C42C2411yescharacteristic
966C2×C42C2411yescharacteristic
967C2×C42C2412yes—
968C2×C42C2412yes—
969C2×C42C2412yes—
970C2×C42C2412yes—
971C2×C42C2411yescharacteristic
972C2×C42C2411yescharacteristic
973C2×C42C2411yescharacteristic
974C2×C42C2412yes—
975C2×C42C2412yes—
976C2×C42C2412yes—
977C2×C42C2414yes—
978C2×C42C2414yes—
979C2×C42C2414yes—
980C2×C42C2412yes—
981C2×C42C2412yes—
982C2×C42C2412yes—
983C2×C42C2412yes—
984C2×C42C2414yes—
985C2×C42C2412yes—
986C2×C42C2412yes—
987C2×C42C2412yes—
988C2×C42C2412yes—
989C2×C42C2411yescharacteristic
990#95C2411yescharacteristic
991#95C2411yescharacteristic
992#95C2412yes—
993#95C2412yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2412yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2412yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2412yes—
1019#95C2414yes—
1020#95C2412yes—
1021#95C2414yes—
1022#95C2412yes—
1023#95C2411yescharacteristic
1024#95C2411yescharacteristic
1025#95C2412yes—
1026#95C2412yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2412yes—
1030#95C2414yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2414yes—
1035#95C2412yes—
1036#95C2412yes—
1037#95C2412yes—
1038#95C2412yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2412yes—
1042#95C2412yes—
1043#95C2414yes—
1044#95C2412yes—
1045#95C2412yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2414yes—
1053#95C2414yes—
1054#95C2414yes—
1055#95C2414yes—
1056C24C2511yescharacteristic
1057C24C2512yes—
1058C24C2512yes—
1059C24C2514yes—
1060#41—816no—
1061C2×Q8—22no—
1062C2×Q8—22no—
1063C2×Q8—22no—
1064C2×Q8—22no—
1065C2×Q8—24no—
1066C2×Q8—24no—
1067C2×Q8—24no—
1068C2×Q8—24no—
1069C2×Q8—22no—
1070C2×Q8—22no—
1071C2×Q8—22no—
1072C2×Q8—22no—
1073C2×Q8—42no—
1074C2×Q8—42no—
1075C2×Q8—42no—
1076C2×Q8—42no—
1077C2×Q8—416no—
1078C2×D4—22no—
1079C2×D4—22no—
1080C2×D4—24no—
1081C2×D4—24no—
1082C2×D4—24no—
1083C2×D4—22no—
1084C2×D4—22no—
1085C2×D4—24no—
1086C2×D4—24no—
1087C2×D4—22no—
1088C2×D4—22no—
1089C2×D4—28no—
1090C2×D4—28no—
1091C2×D4—44no—
1092C2×D4—44no—
1093C2×D4—44no—
1094C2×D4—44no—
1095C2×D4—44no—
1096C2×D4—44no—
1097C2×D4—42no—
1098C2×D4—42no—
1099C2×D4—44no—
1100C2×D4—42no—
1101C2×D4—42no—
1102C2×D4—44no—
1103C2×D4—44no—
1104C2×D4—44no—
1105C2×D4—44no—
1106C2×D4—44no—
1107C2×D4—44no—
1108C2×D4—44no—
1109C2×D4—44no—
1110C2×D4—44no—
1111C2×D4—44no—
1112C2×D4—44no—
1113C2×D4—44no—
1114C22×C4—22no—
1115C22×C4—22no—
1116C22×C4—22no—
1117C22×C4—24no—
1118C22×C4—24no—
1119C22×C4—28no—
1120C22×C4—28no—
1121C22×C4—42no—
1122C22×C4—42no—
1123C22×C4—42no—
1124C22×C4—44no—
1125C22×C4—44no—
1126C22×C4—44no—
1127C22×C4—44no—
1128C22×C4—44no—
1129C22×C4—44no—
1130C22×C4—44no—
1131C22×C4—44no—
1132C22×C4—44no—
1133C22×C4—44no—
1134C22×C4—44no—
1135C22×C4—44no—
1136C22×C4—44no—
1137C22×C4—44no—
1138C22×C4—44no—
1139C22×C4C2512yes—
1140C22×C4C2512yes—
1141C22×C4C2514yes—
1142C22×C4C2512yes—
1143C22×C4C2514yes—
1144C22×C4C2512yes—
1145C22×C4C2512yes—
1146C22×C4C2512yes—
1147C22×C4C2511yescharacteristic
1148C22×C4C2512yes—
1149C22×C4C2512yes—
1150C22×C4C2512yes—
1151C22×C4C2512yes—
1152C22×C4C2512yes—
1153C22×C4C2512yes—
1154C22×C4C2511yescharacteristic
1155C22×C4C2511yescharacteristic
1156C22×C4C2512yes—
1157C22×C4C2512yes—
1158C22×C4C2512yes—
1159C22×C4C2514yes—
1160C22×C4C2512yes—
1161C22×C4C2511yescharacteristic
1162C22×C4C2511yescharacteristic
1163C22×C4C2512yes—
1164C22×C4C2512yes—
1165C22×C4C2511yescharacteristic
1166C4⋊C4—22no—
1167C4⋊C4—22no—
1168C4⋊C4—22no—
1169C4⋊C4—22no—
1170C4⋊C4—22no—
1171C4⋊C4—24no—
1172C4⋊C4—24no—
1173C4⋊C4—24no—
1174C4⋊C4—22no—
1175C4⋊C4—22no—
1176C4⋊C4—24no—
1177C4⋊C4—22no—
1178C4⋊C4—24no—
1179C4⋊C4—24no—
1180C4⋊C4—24no—
1181C4⋊C4—28no—
1182C4⋊C4—24no—
1183C4⋊C4—24no—
1184C4⋊C4—24no—
1185C4⋊C4—24no—
1186C4⋊C4—24no—
1187C4⋊C4—24no—
1188C4⋊C4—24no—
1189C4⋊C4—24no—
1190C4⋊C4—24no—
1191C4⋊C4—24no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—42no—
1198C4⋊C4—42no—
1199C4⋊C4—42no—
1200C4⋊C4—42no—
1201C4⋊C4—44no—
1202C4⋊C4—42no—
1203C4⋊C4—44no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4—44no—
1207C4⋊C4—44no—
1208C4⋊C4—42no—
1209C4⋊C4—42no—
1210C4⋊C4—44no—
1211C4⋊C4—42no—
1212C4⋊C4—42no—
1213C4⋊C4—42no—
1214C4⋊C4—42no—
1215C4⋊C4—42no—
1216C4⋊C4—42no—
1217C4⋊C4—44no—
1218C4⋊C4—44no—
1219C4⋊C4—44no—
1220C4⋊C4—42no—
1221C4⋊C4—42no—
1222C4⋊C4—44no—
1223C4⋊C4—44no—
1224C22⋊C4—22no—
1225C22⋊C4—22no—
1226C22⋊C4—24no—
1227C22⋊C4—24no—
1228C22⋊C4—28no—
1229C22⋊C4—24no—
1230C22⋊C4—24no—
1231C22⋊C4—28no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—42no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4—44no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—42no—
1251C22⋊C4—42no—
1252C22⋊C4—44no—
1253C22⋊C4—44no—
1254C22⋊C4—44no—
1255C22⋊C4—44no—
1256C22⋊C4—44no—
1257C22⋊C4—44no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—44no—
1261C22⋊C4—44no—
1262C22⋊C4—44no—
1263C22⋊C4—44no—
1264C22⋊C4—44no—
1265C22⋊C4—44no—
1266C22⋊C4—44no—
1267C22⋊C4—44no—
1268C22⋊C4—44no—
1269C22⋊C4—44no—
1270C22⋊C4—44no—
1271C22⋊C4—44no—
1272C22⋊C4—42no—
1273C22⋊C4—42no—
1274C22⋊C4—42no—
1275C22⋊C4—42no—
1276C42—22no—
1277C42—24no—
1278C42—24no—
1279C42—24no—
1280C42—24no—
1281C42—24no—
1282C42—24no—
1283C42—28no—
1284C42—22no—
1285C42—24no—
1286C42—24no—
1287C42—22no—
1288C42—22no—
1289C42—22no—
1290C42—44no—
1291C42—42no—
1292C42—42no—
1293C42—42no—
1294C42—44no—
1295C42—42no—
1296C42—42no—
1297C42—42no—
1298C42—44no—
1299C42—42no—
1300C42—44no—
1301C42—42no—
1302C42—42no—
1303C42—42no—
1304C42—42no—
1305C42H(5,𝔽2)14yes—
1306C23—21no—
1307C23—22no—
1308C23—22no—
1309C23—24no—
1310C23—22no—
1311C23—24no—
1312C23—22no—
1313C23—24no—
1314C23—22no—
1315C23—24no—
1316C23—21no—
1317C23—22no—
1318C23—22no—
1319C23—24no—
1320C23—24no—
1321C23—24no—
1322C23—24no—
1323C23—24no—
1324C23—24no—
1325C23—22no—
1326C23—21no—
1327C23—24no—
1328C23C2611yescharacteristic
1329Q8—28no—
1330Q8—44no—
1331Q8—48no—
1332Q8—48no—
1333Q8—44no—
1334Q8—44no—
1335D4—44no—
1336D4—44no—
1337D4—48no—
1338D4—88no—
1339D4—84no—
1340D4—84no—
1341D4—88no—
1342D4—164no—
1343D4—164no—
1344D4—162no—
1345D4—162no—
1346D4—162no—
1347D4—162no—
1348D4—164no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—21no—
1366C2×C4—24no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—24no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—24no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—24no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—24no—
1390C2×C4—24no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—24no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—22no—
1397C2×C4—24no—
1398C2×C4—22no—
1399C2×C4—24no—
1400C2×C4—21no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—24no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—24no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—24no—
1411C2×C4—22no—
1412C2×C4—21no—
1413C2×C4—22no—
1414C2×C4—24no—
1415C2×C4—48no—
1416C2×C4—44no—
1417C2×C4—88no—
1418C2×C4—84no—
1419C2×C4—84no—
1420C2×C4—88no—
1421C2×C4—88no—
1422C2×C4—88no—
1423C2×C4—164no—
1424C2×C4C2×H(5,𝔽2)12yes—
1425C2×C4C2×H(5,𝔽2)12yes—
1426C2×C4C2×H(5,𝔽2)12yes—
1427C2×C4#58514yes—
1428C2×C4#58514yes—
1429C2×C4#58512yes—
1430C2×C4#58512yes—
1431C22—41no—
1432C22—42no—
1433C22—42no—
1434C22—44no—
1435C22—44no—
1436C22—44no—
1437C22—44no—
1438C22—42no—
1439C22—44no—
1440C22—44no—
1441C22—44no—
1442C22—42no—
1443C22—44no—
1444C22—44no—
1445C22—44no—
1446C22—42no—
1447C22—41no—
1448C22—42no—
1449C22—42no—
1450C22—44no—
1451C22—42no—
1452C22—41no—
1453C22C22×H(5,𝔽2)11yescharacteristic
1454C22C2×#58511yescharacteristic
1455C22C2×#58511yescharacteristic
1456C22C2×#58512yes—
1457C22C2×#58512yes—
1458C4—24no—
1459C4—22no—
1460C4—24no—
1461C4—22no—
1462C4—42no—
1463C4—42no—
1464C4—41no—
1465C4—44no—
1466C4—42no—
1467C4—42no—
1468C4—44no—
1469C4—42no—
1470C4—42no—
1471C4—42no—
1472C4—42no—
1473C4—42no—
1474C4—44no—
1475C4—42no—
1476C4—42no—
1477C4—42no—
1478C4—41no—
1479C4—42no—
1480C4—42no—
1481C4—41no—
1482C4—42no—
1483C4—42no—
1484C4#353914yes—
1485C2—81no—
1486C2—82no—
1487C2—82no—
1488C2—84no—
1489C2C2×#353911yescharacteristic
1490C2#6282411yescharacteristic
1491C2#6283611yescharacteristic
1492C2#6303012yes—
1493C2#6303112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#42425C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59701C2semidirect
2. #59581C2semidirect
3. #54916C2semidirect
4. #54393C2semidirect
5. #50477C2semidirect
6. #48888C2semidirect
7. #48306C2semidirect
8. #47886C2semidirect
9. #46048C2semidirect
10. #46048C2semidirect
11. #45394C2semidirect
12. #45354C2semidirect
13. #45221C2semidirect
14. #45070C2semidirect
15. #44230C2semidirect
16. #43664C2semidirect
17. #42645C2semidirect
19. #40105C2semidirect
20. #40026C2semidirect
21. #39202C2semidirect
22. #39025C2semidirect
23. #37432C2semidirect
24. #36597C2semidirect
25. #36583C2semidirect
26. #36394C2semidirect
27. #36394C2semidirect
28. #36041C2semidirect
29. #35749C2semidirect
30. #35678C2semidirect
31. #34973C2semidirect

Maximal subgroups

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

subgroupindex
#597012
#595812
#549162
#543932
#504772
#488882
#483062
#478862
#460482
#453942
#453542
#452212
#450702
#442302
#436642
#426452
#424252
#401052
#400262
#392022
#390252
#374322
#365972
#365832
#363942
#360412
#357492
#356782
#349732