Finite Group Databasebeta

← #7893281

Subgroups — #7893281

Order 512.

4801 conjugacy classes of subgroups.

The subgroup lattice has 1501 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59815C211yesmaximal, characteristic, complemented
2#59279C212yesmaximal, complemented
3#52273C211yesmaximal, characteristic, complemented
4#50774C214yesmaximal, complemented
5#50354C214yesmaximal, complemented
6#50080C214yesmaximal, complemented
7#47248C214yesmaximal, complemented
8#46289C212yesmaximal, complemented
9#45313C212yesmaximal, complemented
10#45269C212yesmaximal, complemented
11#44920C212yesmaximal, complemented
12#43673C214yesmaximal, complemented
13#42892C212yesmaximal, complemented
14#42515C212yesmaximal, complemented
15#41505C214yesmaximal, complemented
16#40125C212yesmaximal, complemented
17#39836C212yesmaximal, complemented
18#39756C211yesmaximal, characteristic, complemented
19#39612C211yesmaximal, characteristic, complemented
20#38823C212yesmaximal, complemented
21#38089C212yesmaximal, complemented
22#37954C212yesmaximal, complemented
23#37156C212yesmaximal, complemented
24#36468C211yesmaximal, characteristic, complemented
25#36049C212yesmaximal, complemented
26#35657C212yesmaximal, complemented
27#35197C211yesmaximal, characteristic, complemented
28#34473C212yesmaximal, complemented
29#34324C211yesmaximal, characteristic, complemented
30C2×#557C2212yes—
31C2×#556C2211yescharacteristic
32C2×#553C2212yes—
33C2×#550C2212yes—
34C2×#547C2212yes—
35#2859C2211yescharacteristic
36#2856C2212yes—
37#2854C2212yes—
38#2854C2212yes—
39#2850C2212yes—
40#2837C2214yes—
41#2829C2214yes—
42#2808C2212yes—
43#2808C2211yescharacteristic
44#2808C2211yescharacteristic
45#2808C2212yes—
46#2804C2211yescharacteristic
47#2803C2214yes—
48#2803C2214yes—
49#2796C2212yes—
50#2796C2212yes—
51#2796C2214yes—
52#2794C2212yes—
53#2784C2214yes—
54#2761C2214yes—
55#2756C2214yes—
56#2756C2214yes—
57#2752C2214yes—
58#2751C2212yes—
59#2751C2212yes—
60#2742C2214yes—
61#2742C2214yes—
62#2738C2214yes—
63#2737C2214yes—
64#2734C2212yes—
65#2734C2212yes—
66#2727C2212yes—
67#2727C2212yes—
68#2726C2212yes—
69#2726C2212yes—
70#2725C2214yes—
71#2724C2211yescharacteristic
72#2723C2214yes—
73#2717C2214yes—
74#2714C2214yes—
75#2714C2214yes—
76#2714C2214yes—
77#2711C2214yes—
78#2709C2212yes—
79#2707C2214yes—
80#2701C2214yes—
81#2699C2214yes—
82#2696C2214yes—
83#2696C2214yes—
84#2695C2214yes—
85#2686C2214yes—
86#2686C2214yes—
87#2682C2212yes—
88#2682C2212yes—
89#2682C2214yes—
90#2674C2214yes—
91#2673C2214yes—
92#2673C2214yes—
93#2672C2214yes—
94#2671C2214yes—
95#2671C2214yes—
96#2663C2214yes—
97#2662C2214yes—
98#2661C2214yes—
99#2660C2212yes—
100#2648C2214yes—
101#2648C2214yes—
102#2641C2214yes—
103#2641C2212yes—
104#2632C2214yes—
105#2619C2212yes—
106#2610C2214yes—
107#2602C2214yes—
108#2602C2214yes—
109#2597C2214yes—
110#2587C2214yes—
111#2580C2212yes—
112#2578C2214yes—
113#2577C2214yes—
114#2571C2211yescharacteristic
115#2567C2212yes—
116#2565C2212yes—
117#2565C2212yes—
118#2562C2212yes—
119#2562C2214yes—
120#2559C2214yes—
121#2559C2214yes—
122#2555C2214yes—
123#2555C2214yes—
124#2554C2214yes—
125#2553C2214yes—
126#2548C2211yescharacteristic
127#2548C2214yes—
128#2541C2211yescharacteristic
129#2541C2212yes—
130#2538C2211yescharacteristic
131#2538C2212yes—
132#2537C2212yes—
133#2537C2211yescharacteristic
134#2537C2211yescharacteristic
135#2535C2212yes—
136#2533C2214yes—
137#2533C2214yes—
138#2531C2214yes—
139#2531C2214yes—
140#2529C2214yes—
141#2526C2214yes—
142#2525C2214yes—
143#2522C2214yes—
144#2518C2214yes—
145#2516C2214yes—
146#2515C2214yes—
147#2513C2212yes—
148#2512C2212yes—
149#2512C2212yes—
150#2501C2212yes—
151#2500C2212yes—
152#2497C2212yes—
153#2496C2212yes—
154#2495C2212yes—
155#2491C2212yes—
156#2491C2212yes—
157#2491C2214yes—
158#2491C2212yes—
159#2491C2214yes—
160#2490C2212yes—
161#2490C2212yes—
162#2490C2212yes—
163#2490C2214yes—
164#2490C2214yes—
165#2481C2214yes—
166#2481C2214yes—
167#2476C2214yes—
168#2471C2214yes—
169#2471C2214yes—
170#2469C2214yes—
171#2467C2214yes—
172#2467C2214yes—
173#2466C2214yes—
174#2466C2214yes—
175#2464C2214yes—
176#2464C2214yes—
177#2462C2214yes—
178#2462C2214yes—
179#2461C2214yes—
180#2460C2214yes—
181#2458C2214yes—
182#2457C2214yes—
183#2452C2214yes—
184#2445C2214yes—
185#2445C2212yes—
186#2441C2212yes—
187#2440C2212yes—
188#2431C2212yes—
189#2431C2212yes—
190#2428C2212yes—
191#2427C2212yes—
192#2426C2214yes—
193#2426C2212yes—
194#2426C2212yes—
195#2421C2212yes—
196#2421C2212yes—
197#2420C2212yes—
198#2416C2214yes—
199#2407C2212yes—
200#2407C2212yes—
201#2398C2212yes—
202#2398C2212yes—
203#2398C2214yes—
204#2395C2212yes—
205#2377C2214yes—
206#2376C2214yes—
207#2374C2214yes—
208#2373C2214yes—
209#2373C2214yes—
210#2367C2212yes—
211#2365C2211yescharacteristic
212#2362C2212yes—
213#2362C2212yes—
214#2360C2212yes—
215#2357C2212yes—
216#2355C2212yes—
217#2354C2211yescharacteristic
218#2354C2211yescharacteristic
219#2352C2212yes—
220Q8×C4⋊C4C2211yescharacteristic
221D4×C4⋊C4C2211yescharacteristic
222D4×C4⋊C4C2212yes—
223#2346C2212yes—
224#2345C2214yes—
225#2341C2212yes—
226#2341C2212yes—
227#2341C2212yes—
228#2341C2212yes—
229#2335C2214yes—
230#2335C2214yes—
231#2335C2214yes—
232#2334C2214yes—
233#2333C2214yes—
234#2330C2212yes—
235#2328C2212yes—
236#2327C2212yes—
237#2326C2212yes—
238#2323C2212yes—
239#2319C2212yes—
240#2314C2212yes—
241#2313C2214yes—
242#2311C2212yes—
243C4×C4⋊Q8C2211yescharacteristic
244C4×#127C2211yescharacteristic
245C4×#127C2211yescharacteristic
246C4×C22⋊Q8C2212yes—
247C4×C22⋊Q8C2212yes—
248C4×#123C2212yes—
249C4×#121C2212yes—
250#2297C2212yes—
251#2296C2212yes—
252#2295C2211yescharacteristic
253#2295C2211yescharacteristic
254#2290C2212yes—
255#2290C2212yes—
256#2283C2212yes—
257#2276C2212yes—
258C42×D4C2211yescharacteristic
259C22×#41C2312yes—
260C22×#41C2312yes—
261#557—48no—
262#556—28no—
263#553—48no—
264#550—48no—
265#547—216no—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2314yes—
268C2×C4⋊Q8C2311yescharacteristic
269C2×#127C2311yescharacteristic
270C2×#127C2311yescharacteristic
271C2×#127C2312yes—
272C2×#127C2314yes—
273C2×#126C2314yes—
274C2×#126C2314yes—
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#125C2312yes—
278C2×#125C2314yes—
279C2×#125C2312yes—
280C2×#125C2314yes—
281C2×#124C2312yes—
282C2×#124C2312yes—
283C2×#124C2314yes—
284C2×#124C2314yes—
285C2×#124C2314yes—
286C2×#123C2314yes—
287C2×#123C2314yes—
288C2×#123C2314yes—
289C2×#123C2314yes—
290C2×#123C2312yes—
291C2×#123C2314yes—
292C2×#123C2314yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2314yes—
298C2×#121C2314yes—
299C2×#121C2312yes—
300C2×#121C2312yes—
301C2×#121C2312yes—
302C2×#121C2312yes—
303C2×#121C2312yes—
304C2×#121C2314yes—
305C2×#121C2314yes—
306C2×#121C2314yes—
307C2×#121C2312yes—
308C2×#121C2312yes—
309C2×#121C2312yes—
310C2×#121C2314yes—
311C2×#121C2314yes—
312C2×#121C2314yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2311yescharacteristic
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2314yes—
321C2×C4×Q8C2312yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2311yescharacteristic
326C2×C4×D4C2311yescharacteristic
327C2×C4×D4C2311yescharacteristic
328C2×C4×D4C2312yes—
329C2×C4×D4C2311yescharacteristic
330C2×C4×D4C2314yes—
331C2×C4×D4C2314yes—
332C2×C4×D4C2311yescharacteristic
333C2×C4×D4C2312yes—
334C2×C4×D4C2312yes—
335C2×#117C2312yes—
336C2×#117C2312yes—
337C2×#117C2312yes—
338C2×#117C2312yes—
339C22×C4⋊C4C2314yes—
340C22×C4⋊C4C2312yes—
341C22×C42C2312yes—
342C22×C42C2312yes—
343#400C2312yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2312yes—
348#400C2314yes—
349#400C2312yes—
350#400C2312yes—
351#400C2312yes—
352#400C2314yes—
353#400C2314yes—
354#399C2312yes—
355#399C2314yes—
356#399C2314yes—
357#399C2314yes—
358#399C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2312yes—
366#398C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2312yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2312yes—
377#397C2314yes—
378#397C2314yes—
379#397C2312yes—
380#397C2312yes—
381#397C2312yes—
382#397C2312yes—
383#397C2312yes—
384#397C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2312yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2312yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2312yes—
424#394C2312yes—
425#394C2312yes—
426#394C2312yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#393C2314yes—
432#393C2314yes—
433#393C2312yes—
434#393C2314yes—
435#393C2312yes—
436#393C2314yes—
437#393C2312yes—
438#393C2312yes—
439#392C2314yes—
440#392C2314yes—
441#392C2314yes—
442#392C2314yes—
443#392C2314yes—
444#392C2314yes—
445#392C2314yes—
446#392C2314yes—
447#392C2314yes—
448#392C2314yes—
449#391C2312yes—
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2311yescharacteristic
454#391C2311yescharacteristic
455#391C2311yescharacteristic
456#391C2311yescharacteristic
457#390C2312yes—
458#390C2311yescharacteristic
459#390C2312yes—
460#390C2312yes—
461#390C2312yes—
462#390C2311yescharacteristic
463#390C2312yes—
464#390C2312yes—
465#390C2312yes—
466#390C2314yes—
467#390C2312yes—
468#390C2312yes—
469#390C2312yes—
470#390C2312yes—
471#390C2312yes—
472#390C2312yes—
473#390C2314yes—
474#390C2314yes—
475#390C2314yes—
476#390C2314yes—
477#390C2314yes—
478#390C2312yes—
479#390C2314yes—
480#390C2314yes—
481#390C2314yes—
482#390C2314yes—
483#390C2312yes—
484#390C2312yes—
485#390C2314yes—
486#390C2314yes—
487#390C2314yes—
488#390C2314yes—
489#390C2314yes—
490#390C2314yes—
491#389C2312yes—
492#389C2312yes—
493#389C2314yes—
494#389C2314yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2314yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2312yes—
506#389C2314yes—
507#389C2311yescharacteristic
508#389C2312yes—
509#389C2312yes—
510#389C2311yescharacteristic
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2314yes—
515#389C2314yes—
516#389C2311yescharacteristic
517#389C2311yescharacteristic
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2312yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2312yes—
554#388C2312yes—
555#388C2314yes—
556#388C2314yes—
557#388C2312yes—
558#388C2312yes—
559#388C2314yes—
560#388C2312yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2312yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2312yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2312yes—
585#387C2314yes—
586#387C2314yes—
587#387C2312yes—
588#387C2312yes—
589#387C2312yes—
590#387C2314yes—
591#387C2312yes—
592#387C2312yes—
593#387C2312yes—
594#387C2312yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2312yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2312yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2312yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2312yes—
616#386C2314yes—
617#386C2312yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2312yes—
625#385C2314yes—
626#385C2312yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2312yes—
632#385C2312yes—
633#385C2312yes—
634#384C2311yescharacteristic
635#384C2311yescharacteristic
636#384C2311yescharacteristic
637#384C2311yescharacteristic
638#384C2312yes—
639#384C2311yescharacteristic
640#384C2312yes—
641#383C2314yes—
642#383C2314yes—
643#382C2312yes—
644#382C2312yes—
645#382C2312yes—
646#382C2312yes—
647#382C2314yes—
648#381C2314yes—
649#381C2314yes—
650#381C2312yes—
651#381C2314yes—
652#380C2314yes—
653#380C2312yes—
654#380C2314yes—
655#380C2312yes—
656#380C2314yes—
657#380C2312yes—
658#380C2312yes—
659#380C2314yes—
660#380C2314yes—
661#380C2314yes—
662#380C2312yes—
663#380C2314yes—
664#380C2312yes—
665#380C2312yes—
666#380C2312yes—
667#380C2312yes—
668#380C2314yes—
669#380C2312yes—
670C4×C4⋊C4C2311yescharacteristic
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2311yescharacteristic
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2314yes—
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⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712#376C2312yes—
713#376C2312yes—
714#376C2314yes—
715#376C2314yes—
716C43C2311yescharacteristic
717C2×#41—28no—
718C2×#41—28no—
719C2×#41—44no—
720C2×#41—44no—
721C2×#41—44no—
722C2×#41—44no—
723C22×Q8C2412yes—
724C22×Q8C2411yescharacteristic
725C22×Q8C2411yescharacteristic
726C22×Q8C2414yes—
727C22×D4C2411yescharacteristic
728C22×D4C2412yes—
729C22×D4C2411yescharacteristic
730C22×D4C2412yes—
731C22×D4C2412yes—
732C22×D4C2412yes—
733C22×D4C2411yescharacteristic
734C22×D4C2412yes—
735C22×D4C2414yes—
736C22×D4C2414yes—
737C22×D4C2414yes—
738C22×D4C2414yes—
739C22×D4C2414yes—
740C22×D4C2414yes—
741C22×D4C2414yes—
742C22×D4C2414yes—
743C23×C4C2412yes—
744C23×C4C2412yes—
745C23×C4C2414yes—
746C23×C4C2414yes—
747C23×C4C2414yes—
748C23×C4C2412yes—
749C23×C4C2412yes—
750C23×C4C2412yes—
751C23×C4C2414yes—
752C23×C4C2412yes—
753C23×C4C2412yes—
754C4⋊Q8—44no—
755C4⋊Q8—48no—
756C4⋊Q8#4118yes—
757#127—24no—
758#127—44no—
759#127—42no—
760#127—48no—
761#126—216no—
762#126—48no—
763#126—48no—
764#126—84no—
765#125—28no—
766#125—48no—
767#125—44no—
768#125—48no—
769#124—28no—
770#124—82no—
771#124—84no—
772#124—84no—
773#124—84no—
774#123—216no—
775#123—216no—
776#123—48no—
777#123—48no—
778#123—44no—
779#123—84no—
780#123—84no—
781C22⋊Q8—28no—
782C22⋊Q8—28no—
783C22⋊Q8—28no—
784C22⋊Q8—84no—
785C22⋊Q8—82no—
786#121—216no—
787#121—48no—
788#121—48no—
789#121—48no—
790#121—44no—
791#121—44no—
792#121—44no—
793#121—44no—
794#121—44no—
795#121—84no—
796#121—84no—
797#121—82no—
798#121—82no—
799#121—82no—
800#121—84no—
801C4×Q8—28no—
802C4×Q8—24no—
803C4×Q8—28no—
804C4×Q8—24no—
805C4×Q8—48no—
806C4×Q8—44no—
807C4×Q8—44no—
808C4×Q8—44no—
809C4×Q8—82no—
810C4×D4—28no—
811C4×D4—28no—
812C4×D4—24no—
813C4×D4—28no—
814C4×D4—24no—
815C4×D4—44no—
816C4×D4—42no—
817C4×D4—48no—
818C4×D4—42no—
819C4×D4—42no—
820C4×D4—48no—
821C4×D4—82no—
822C4×D4—82no—
823#117—28no—
824#117—44no—
825#117—44no—
826#117—82no—
827C2×C4⋊C4—216no—
828C2×C4⋊C4—44no—
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2411yescharacteristic
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2411yescharacteristic
859C2×C4⋊C4C2411yescharacteristic
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2411yescharacteristic
868C2×C4⋊C4C2411yescharacteristic
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2412yes—
942C2×C22⋊C4C2412yes—
943C2×C22⋊C4C2414yes—
944C2×C42—44no—
945C2×C42—82no—
946C2×C42C2414yes—
947C2×C42C2412yes—
948C2×C42C2412yes—
949C2×C42C2411yescharacteristic
950C2×C42C2411yescharacteristic
951C2×C42C2414yes—
952C2×C42C2412yes—
953C2×C42C2412yes—
954C2×C42C2414yes—
955C2×C42C2414yes—
956C2×C42C2411yescharacteristic
957C2×C42C2412yes—
958C2×C42C2414yes—
959C2×C42C2414yes—
960C2×C42C2414yes—
961C2×C42C2414yes—
962C2×C42C2412yes—
963C2×C42C2414yes—
964C2×C42C2412yes—
965C2×C42C2414yes—
966C2×C42C2411yescharacteristic
967C2×C42C2411yescharacteristic
968C2×C42C2412yes—
969C2×C42C2412yes—
970C2×C42C2411yescharacteristic
971C2×C42C2411yescharacteristic
972#95C2412yes—
973#95C2412yes—
974#95C2414yes—
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2414yes—
979#95C2412yes—
980#95C2414yes—
981#95C2412yes—
982#95C2412yes—
983#95C2414yes—
984#95C2414yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2414yes—
992#95C2412yes—
993#95C2414yes—
994#95C2412yes—
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2412yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2414yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029C24C2512yes—
1030C24C2512yes—
1031C24C2512yes—
1032C24C2514yes—
1033#41—816no—
1034#41—816no—
1035C2×Q8—22no—
1036C2×Q8—24no—
1037C2×Q8—22no—
1038C2×Q8—24no—
1039C2×Q8—41no—
1040C2×Q8—41no—
1041C2×Q8—44no—
1042C2×Q8—41no—
1043C2×Q8—44no—
1044C2×Q8—41no—
1045C2×Q8—44no—
1046C2×Q8C2×#4118yes—
1047C2×D4—22no—
1048C2×D4—24no—
1049C2×D4—24no—
1050C2×D4—28no—
1051C2×D4—28no—
1052C2×D4—22no—
1053C2×D4—24no—
1054C2×D4—24no—
1055C2×D4—24no—
1056C2×D4—24no—
1057C2×D4—22no—
1058C2×D4—22no—
1059C2×D4—24no—
1060C2×D4—22no—
1061C2×D4—41no—
1062C2×D4—42no—
1063C2×D4—41no—
1064C2×D4—42no—
1065C2×D4—44no—
1066C2×D4—41no—
1067C2×D4—42no—
1068C2×D4—44no—
1069C2×D4—44no—
1070C2×D4—44no—
1071C2×D4—41no—
1072C2×D4—42no—
1073C2×D4—42no—
1074C2×D4—42no—
1075C2×D4—42no—
1076C2×D4—42no—
1077C2×D4—44no—
1078C2×D4—44no—
1079C2×D4—44no—
1080C2×D4—44no—
1081C2×D4—44no—
1082C2×D4—44no—
1083C2×D4—44no—
1084C2×D4—44no—
1085C2×D4—44no—
1086C2×D4—44no—
1087C2×D4—44no—
1088C2×D4—44no—
1089C2×D4—44no—
1090C2×D4—44no—
1091C2×D4—44no—
1092C2×D4—44no—
1093C2×D4—44no—
1094C2×D4—44no—
1095C22×C4—24no—
1096C22×C4—24no—
1097C22×C4—24no—
1098C22×C4—24no—
1099C22×C4—24no—
1100C22×C4—24no—
1101C22×C4—24no—
1102C22×C4—28no—
1103C22×C4—28no—
1104C22×C4—28no—
1105C22×C4—24no—
1106C22×C4—24no—
1107C22×C4—42no—
1108C22×C4—42no—
1109C22×C4—42no—
1110C22×C4—42no—
1111C22×C4—42no—
1112C22×C4—42no—
1113C22×C4—44no—
1114C22×C4—44no—
1115C22×C4—42no—
1116C22×C4—44no—
1117C22×C4—44no—
1118C22×C4—42no—
1119C22×C4—42no—
1120C22×C4—42no—
1121C22×C4—42no—
1122C22×C4—42no—
1123C22×C4—44no—
1124C22×C4—44no—
1125C22×C4—44no—
1126C22×C4—44no—
1127C22×C4—44no—
1128C22×C4C2512yes—
1129C22×C4C2512yes—
1130C22×C4C2512yes—
1131C22×C4C2512yes—
1132C22×C4C2512yes—
1133C22×C4C2512yes—
1134C22×C4C2512yes—
1135C22×C4C2512yes—
1136C22×C4C2512yes—
1137C22×C4C2511yescharacteristic
1138C22×C4C2514yes—
1139C22×C4C2514yes—
1140C22×C4C2512yes—
1141C22×C4C2512yes—
1142C22×C4C2512yes—
1143C22×C4C2512yes—
1144C22×C4C2514yes—
1145C22×C4C2514yes—
1146C22×C4C2511yescharacteristic
1147C22×C4C2511yescharacteristic
1148C22×C4C2514yes—
1149C22×C4C2511yescharacteristic
1150C22×C4C2511yescharacteristic
1151C22×C4C2511yescharacteristic
1152C22×C4C2511yescharacteristic
1153C4⋊C4—24no—
1154C4⋊C4—28no—
1155C4⋊C4—28no—
1156C4⋊C4—22no—
1157C4⋊C4—22no—
1158C4⋊C4—24no—
1159C4⋊C4—28no—
1160C4⋊C4—24no—
1161C4⋊C4—22no—
1162C4⋊C4—24no—
1163C4⋊C4—24no—
1164C4⋊C4—24no—
1165C4⋊C4—28no—
1166C4⋊C4—24no—
1167C4⋊C4—28no—
1168C4⋊C4—24no—
1169C4⋊C4—22no—
1170C4⋊C4—28no—
1171C4⋊C4—22no—
1172C4⋊C4—24no—
1173C4⋊C4—24no—
1174C4⋊C4—24no—
1175C4⋊C4—44no—
1176C4⋊C4—41no—
1177C4⋊C4—42no—
1178C4⋊C4—42no—
1179C4⋊C4—42no—
1180C4⋊C4—42no—
1181C4⋊C4—41no—
1182C4⋊C4—42no—
1183C4⋊C4—41no—
1184C4⋊C4—41no—
1185C4⋊C4—42no—
1186C4⋊C4—42no—
1187C4⋊C4—42no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—44no—
1193C4⋊C4—41no—
1194C4⋊C4—41no—
1195C4⋊C4—42no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—44no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—44no—
1205C4⋊C4—42no—
1206C4⋊C4—42no—
1207C4⋊C4C2×#4118yes—
1208C4⋊C4C2×#4118yes—
1209C22⋊C4—28no—
1210C22⋊C4—28no—
1211C22⋊C4—24no—
1212C22⋊C4—24no—
1213C22⋊C4—24no—
1214C22⋊C4—28no—
1215C22⋊C4—28no—
1216C22⋊C4—28no—
1217C22⋊C4—24no—
1218C22⋊C4—24no—
1219C22⋊C4—24no—
1220C22⋊C4—28no—
1221C22⋊C4—44no—
1222C22⋊C4—42no—
1223C22⋊C4—42no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C22⋊C4—42no—
1227C22⋊C4—44no—
1228C22⋊C4—42no—
1229C22⋊C4—42no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—42no—
1233C22⋊C4—42no—
1234C22⋊C4—42no—
1235C22⋊C4—44no—
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—44no—
1252C22⋊C4—42no—
1253C22⋊C4—44no—
1254C22⋊C4—42no—
1255C22⋊C4—44no—
1256C22⋊C4—42no—
1257C22⋊C4—42no—
1258C22⋊C4—42no—
1259C22⋊C4—44no—
1260C22⋊C4—44no—
1261C22⋊C4—44no—
1262C22⋊C4—44no—
1263C22⋊C4—42no—
1264C22⋊C4—42no—
1265C22⋊C4—42no—
1266C22⋊C4—44no—
1267C22⋊C4—44no—
1268C42—28no—
1269C42—24no—
1270C42—28no—
1271C42—24no—
1272C42—24no—
1273C42—24no—
1274C42—22no—
1275C42—22no—
1276C42—42no—
1277C42—42no—
1278C42—41no—
1279C42—42no—
1280C42—42no—
1281C42—42no—
1282C42—41no—
1283C42—44no—
1284C42—44no—
1285C42—41no—
1286C42—44no—
1287C42—44no—
1288C42—44no—
1289C42—44no—
1290C42—44no—
1291C42—44no—
1292C42C2×#4114yes—
1293C42H(5,𝔽2)14yes—
1294C23—22no—
1295C23—22no—
1296C23—22no—
1297C23—24no—
1298C23—22no—
1299C23—22no—
1300C23—22no—
1301C23—24no—
1302C23—24no—
1303C23—22no—
1304C23—22no—
1305C23—22no—
1306C23—22no—
1307C23—22no—
1308C23—22no—
1309C23—24no—
1310C23—24no—
1311C23—22no—
1312C23—22no—
1313C23—24no—
1314C23—22no—
1315C23—22no—
1316C23—22no—
1317C23—22no—
1318C23—22no—
1319C23—24no—
1320C23—22no—
1321C23—22no—
1322C23C2611yescharacteristic
1323Q8—216no—
1324Q8—44no—
1325Q8—82no—
1326Q8—88no—
1327D4—44no—
1328D4—48no—
1329D4—44no—
1330D4—48no—
1331D4—84no—
1332D4—84no—
1333D4—82no—
1334D4—84no—
1335D4—88no—
1336D4—88no—
1337D4—88no—
1338D4—164no—
1339D4—164no—
1340D4—164no—
1341D4—164no—
1342D4—164no—
1343C2×C4—24no—
1344C2×C4—21no—
1345C2×C4—21no—
1346C2×C4—21no—
1347C2×C4—24no—
1348C2×C4—21no—
1349C2×C4—21no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—21no—
1353C2×C4—21no—
1354C2×C4—21no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—24no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—24no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—24no—
1367C2×C4—24no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—21no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—24no—
1378C2×C4—24no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—24no—
1391C2×C4—21no—
1392C2×C4—24no—
1393C2×C4—24no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—24no—
1397C2×C4—22no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—24no—
1401C2×C4—22no—
1402C2×C4—21no—
1403C2×C4—22no—
1404C2×C4—22no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—24no—
1408C2×C4—22no—
1409C2×C4—48no—
1410C2×C4—48no—
1411C2×C4—48no—
1412C2×C4—88no—
1413C2×C4—84no—
1414C2×C4—84no—
1415C2×C4—88no—
1416C2×C4—88no—
1417C2×C4—84no—
1418C2×C4—84no—
1419C2×C4—164no—
1420C2×C4C22×#4118yes—
1421C2×C4C22×#4112yes—
1422C2×C4C22×#4112yes—
1423C2×C4C22×#4112yes—
1424C2×C4C2×H(5,𝔽2)12yes—
1425C2×C4C2×H(5,𝔽2)12yes—
1426C2×C4C2×H(5,𝔽2)12yes—
1427C2×C4#58512yes—
1428C2×C4#58512yes—
1429C22—44no—
1430C22—42no—
1431C22—42no—
1432C22—42no—
1433C22—42no—
1434C22—42no—
1435C22—44no—
1436C22—42no—
1437C22—42no—
1438C22—42no—
1439C22—44no—
1440C22—42no—
1441C22—42no—
1442C22—42no—
1443C22—42no—
1444C22—44no—
1445C22—42no—
1446C22—42no—
1447C22—44no—
1448C22—42no—
1449C22—42no—
1450C22—42no—
1451C22—42no—
1452C22—44no—
1453C22—44no—
1454C22—42no—
1455C22—42no—
1456C22—42no—
1457C22C23×#4111yescharacteristic
1458C22C22×H(5,𝔽2)11yescharacteristic
1459C22C2×#58511yescharacteristic
1460C22C2×#58511yescharacteristic
1461C22H(7,𝔽2)11yescharacteristic
1462C22H(7,𝔽2)11yescharacteristic
1463C222−1+611yescharacteristic
1464C4—22no—
1465C4—28no—
1466C4—22no—
1467C4—22no—
1468C4—22no—
1469C4—22no—
1470C4—42no—
1471C4—44no—
1472C4—42no—
1473C4—42no—
1474C4—41no—
1475C4—42no—
1476C4—42no—
1477C4—42no—
1478C4—42no—
1479C4—42no—
1480C4—44no—
1481C4—44no—
1482C4—42no—
1483C4—42no—
1484C4—42no—
1485C4—42no—
1486C4—42no—
1487C4—44no—
1488C4#351414yes—
1489C2—84no—
1490C2—82no—
1491C2—82no—
1492C2—82no—
1493C2C2×#351411yescharacteristic
1494C2#6285111yescharacteristic
1495C2#6288011yescharacteristic
1496C2#6290811yescharacteristic
1497C2#6292511yescharacteristic
1498C2#6300611yescharacteristic
1499C2#6306511yescharacteristic
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. #59815C2semidirect
2. #59279C2semidirect
3. #52273C2semidirect
4. #50774C2semidirect
5. #50354C2semidirect
6. #50080C2semidirect
7. #47248C2semidirect
8. #46289C2semidirect
9. #45313C2semidirect
10. #45269C2semidirect
11. #44920C2semidirect
12. #43673C2semidirect
13. #42892C2semidirect
14. #42515C2semidirect
15. #41505C2semidirect
16. #40125C2semidirect
17. #39836C2semidirect
18. #39756C2semidirect
19. #39612C2semidirect
20. #38823C2semidirect
21. #38089C2semidirect
22. #37954C2semidirect
23. #37156C2semidirect
24. #36468C2semidirect
25. #36049C2semidirect
26. #35657C2semidirect
27. #35197C2semidirect
28. #34473C2semidirect
29. #34324C2semidirect

Maximal subgroups

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

subgroupindex
#598152
#592792
#522732
#507742
#503542
#500802
#472482
#462892
#453132
#452692
#449202
#436732
#428922
#425152
#415052
#401252
#398362
#397562
#396122
#388232
#380892
#379542
#371562
#364682
#360492
#356572
#351972
#344732
#343242