Finite Group Databasebeta

← #7646505

Subgroups — #7646505

Order 512.

4574 conjugacy classes of subgroups.

The subgroup lattice has 1485 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42670C212yesmaximal, complemented
2#42666C212yesmaximal, complemented
3#42471C212yesmaximal, complemented
4#42467C212yesmaximal, complemented
5#40685C214yesmaximal, complemented
6#40681C214yesmaximal, complemented
7#39937C212yesmaximal, complemented
8#39933C212yesmaximal, complemented
9#39912C212yesmaximal, complemented
10#39909C212yesmaximal, complemented
11#38499C214yesmaximal, complemented
12#38497C214yesmaximal, complemented
13#37568C214yesmaximal, complemented
14#36821C212yesmaximal, complemented
15#36819C212yesmaximal, complemented
16#36816C212yesmaximal, complemented
17#36812C212yesmaximal, complemented
18#35614C212yesmaximal, complemented
19#35597C212yesmaximal, complemented
20#35301C211yesmaximal, characteristic, complemented
21#35218C212yesmaximal, complemented
22#35207C212yesmaximal, complemented
23#35191C211yesmaximal, characteristic, complemented
24#35105C214yesmaximal, complemented
25#34912C211yesmaximal, characteristic, complemented
26#34877C211yesmaximal, characteristic, complemented
27#34244C211yesmaximal, characteristic, complemented
28#34155C211yesmaximal, characteristic, complemented
29#34048C211yesmaximal, characteristic, complemented
30C2×#532C2211yescharacteristic
31C2×#529C2211yescharacteristic
32C22×#117C2211yescharacteristic
33#2861C2212yescomplemented
34#2858C2212yescomplemented
35#2854C2211yescharacteristic
36#2854C2214yes—
37#2854C2211yescharacteristic
38#2853C2214yescomplemented
39#2852C2214yes—
40#2851C2214yescomplemented
41#2847C2211yescharacteristic
42#2847C2211yescharacteristic
43#2838C2214yescomplemented
44#2836C2214yes—
45#2830C2214yescomplemented
46#2828C2214yes—
47#2798C2214yes—
48#2797C2214yes—
49#2789C2214yescomplemented
50#2786C2214yescomplemented
51#2761C2214yes—
52#2760C2214yes—
53#2759C2214yes—
54#2755C2214yescomplemented
55#2752C2214yes—
56#2751C2214yescomplemented
57#2750C2214yes—
58#2746C2214yes—
59#2737C2214yes—
60#2716C2214yes—
61#2715C2214yescomplemented
62#2713C2214yescomplemented
63#2712C2214yes—
64#2710C2214yes—
65#2709C2214yescomplemented
66#2707C2214yes—
67#2706C2214yes—
68#2705C2214yes—
69#2705C2214yes—
70#2700C2214yescomplemented
71#2696C2214yes—
72#2695C2214yes—
73#2693C2214yes—
74#2685C2214yes—
75#2684C2214yes—
76#2678C2214yes—
77#2678C2214yes—
78#2673C2214yes—
79#2663C2214yes—
80#2662C2214yes—
81#2661C2214yes—
82#2655C2214yescomplemented
83#2655C2214yescomplemented
84#2653C2214yes—
85#2653C2214yes—
86#2653C2214yescomplemented
87#2652C2214yescomplemented
88#2651C2214yes—
89#2651C2214yescomplemented
90#2650C2214yescomplemented
91#2648C2214yes—
92#2648C2214yes—
93#2648C2214yescomplemented
94#2630C2214yes—
95#2630C2214yescomplemented
96#2628C2212yes—
97#2619C2212yes—
98#2611C2212yes—
99#2610C2212yes—
100#2610C2214yes—
101#2608C2212yes—
102#2607C2212yes—
103#2606C2212yescomplemented
104#2605C2212yescomplemented
105#2603C2214yescomplemented
106#2601C2212yes—
107#2601C2212yes—
108#2598C2214yes—
109#2597C2214yes—
110#2597C2214yes—
111#2597C2214yescomplemented
112#2595C2214yes—
113#2595C2214yescomplemented
114#2594C2214yescomplemented
115#2594C2214yescomplemented
116#2593C2214yes—
117#2591C2211yescharacteristic
118#2591C2212yes—
119#2587C2214yescomplemented
120#2583C2211yescharacteristic
121#2577C2214yescomplemented
122#2576C2214yes—
123#2576C2214yescomplemented
124#2573C2214yescomplemented
125#2570C2212yescomplemented
126#2570C2212yescomplemented
127#2566C2212yescomplemented
128#2563C2212yes—
129#2563C2212yescomplemented
130#2562C2212yes—
131#2561C2211yescharacteristic
132#2560C2214yescomplemented
133#2559C2214yes—
134#2559C2214yes—
135#2558C2214yescomplemented
136#2557C2214yes—
137#2554C2214yes—
138#2554C2214yes—
139#2552C2212yescomplemented
140#2550C2212yescomplemented
141#2548C2211yescharacteristic, complemented
142#2547C2211yescharacteristic, complemented
143#2546C2211yescharacteristic, complemented
144#2541C2211yescharacteristic, complemented
145#2539C2211yescharacteristic
146#2539C2212yes—
147#2537C2212yes—
148#2535C2212yes—
149#2519C2214yes—
150#2516C2214yescomplemented
151#2515C2214yescomplemented
152#2513C2214yes—
153#2512C2212yescomplemented
154#2512C2212yescomplemented
155#2509C2212yescomplemented
156#2508C2212yescomplemented
157#2504C2212yescomplemented
158#2500C2212yescomplemented
159#2497C2212yes—
160#2496C2212yes—
161#2495C2212yescomplemented
162#2494C2212yes—
163#2494C2212yes—
164#2494C2212yescomplemented
165#2494C2214yescomplemented
166#2491C2212yes—
167#2490C2212yes—
168#2490C2214yes—
169#2486C2212yes—
170#2485C2212yes—
171#2478C2214yescomplemented
172#2477C2214yescomplemented
173#2474C2214yes—
174#2471C2214yes—
175#2469C2214yescomplemented
176#2468C2214yescomplemented
177#2464C2214yes—
178#2458C2214yes—
179#2458C2214yescomplemented
180#2441C2212yes—
181#2441C2212yescomplemented
182#2440C2212yescomplemented
183#2439C2212yes—
184#2432C2212yes—
185#2431C2212yes—
186#2426C2214yes—
187#2422C2212yes—
188#2422C2212yescomplemented
189#2422C2212yescomplemented
190#2420C2212yes—
191#2416C2212yes—
192#2414C2212yes—
193#2414C2212yes—
194#2414C2212yes—
195#2413C2212yes—
196#2411C2212yes—
197#2406C2212yes—
198#2404C2212yes—
199#2396C2212yes—
200#2396C2214yes—
201#2392C2212yes—
202#2374C2214yes—
203#2372C2212yescomplemented
204#2372C2214yescomplemented
205#2371C2212yescomplemented
206#2369C2212yescomplemented
207#2366C2212yescomplemented
208#2363C2212yes—
209#2363C2212yes—
210#2363C2214yes—
211#2355C2212yescomplemented
212#2354C2212yes—
213#2352C2212yes—
214#2352C2212yescomplemented
215#2335C2214yes—
216#2335C2214yescomplemented
217#2334C2214yescomplemented
218#2333C2214yes—
219#2333C2212yes—
220#2332C2212yes—
221#2324C2212yes—
222#2324C2212yes—
223#2324C2212yescomplemented
224#2324C2212yescomplemented
225#2314C2212yes—
226#2314C2212yes—
227#2314C2212yes—
228#2314C2212yes—
229#2314C2212yescomplemented
230#2313C2212yes—
231#2313C2212yes—
232#2312C2212yes—
233#2312C2212yes—
234C4×C4⋊Q8C2212yescomplemented
235C4×#125C2212yescomplemented
236C4×#126C2214yescomplemented
237C4×#123C2212yes—
238C4×#120C2212yes—
239#2298C2214yes—
240#2298C2214yes—
241#2297C2212yes—
242#2297C2212yes—
243#2295C2214yescomplemented
244#2293C2212yes—
245#2293C2212yes—
246#2293C2211yescharacteristic, complemented
247#2293C2211yescharacteristic, complemented
248#2293C2212yescomplemented
249#2285C2212yes—
250#2283C2211yescharacteristic
251#2280C2212yes—
252#2274C2212yescomplemented
253C42×D4C2212yescomplemented
254C42×D4C2211yescharacteristic, complemented
255C42×D4C2211yescharacteristic, complemented
256C4×#117C2211yescharacteristic
257C4×#117C2211yescharacteristic
258C4×#117C2211yescharacteristic
259C22×#41C2312yes—
260C24×C4C2311yescharacteristic
261#532—28no—
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2312yes—
265C2×#127C2311yescharacteristic
266C2×#127C2312yes—
267#529—28no—
268C2×#126C2312yes—
269C2×#126C2314yes—
270C2×#126C2314yes—
271C2×#126C2314yes—
272C2×#125C2311yescharacteristic
273C2×#125C2312yes—
274C2×#125C2314yes—
275C2×#124C2311yescharacteristic
276C2×#124C2312yes—
277C2×#124C2312yes—
278C2×#124C2312yes—
279C2×#124C2314yes—
280C2×#123C2312yes—
281C2×#123C2314yes—
282C2×#123C2314yes—
283C2×#123C2312yes—
284C2×#123C2314yes—
285C2×#123C2312yes—
286C2×#123C2312yes—
287C2×#123C2314yes—
288C2×C22⋊Q8C2311yescharacteristic
289C2×C22⋊Q8C2314yes—
290C2×#121C2311yescharacteristic
291C2×#121C2312yes—
292C2×#121C2311yescharacteristic
293C2×#121C2311yescharacteristic
294C2×#121C2312yes—
295C2×#121C2312yes—
296C2×#121C2312yes—
297C2×#121C2312yes—
298C2×#121C2314yes—
299C2×#121C2314yes—
300C2×#120C2312yes—
301C2×#120C2312yes—
302C2×#120C2312yes—
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2314yes—
305C2×C4×D4C2311yescharacteristic
306C2×C4×D4C2311yescharacteristic
307C2×C4×D4C2312yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2311yescharacteristic
310C2×C4×D4C2312yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2312yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2314yes—
315C2×#117—28no—
316C2×#117C2312yes—
317C2×#117C2312yes—
318C2×#117C2312yes—
319C2×#117C2312yes—
320C2×#117C2312yes—
321C2×#117C2312yes—
322C2×#117C2312yes—
323C2×#117C2312yes—
324C2×#117C2312yes—
325C2×#117C2312yes—
326C2×#117C2312yes—
327C22×C4⋊C4C2311yescharacteristic
328C22×C4⋊C4C2311yescharacteristic
329C22×C4⋊C4C2312yes—
330C22×C22⋊C4C2311yescharacteristic
331C22×C22⋊C4C2311yescharacteristic
332C22×C42C2311yescharacteristic
333C22×C42C2312yes—
334C22×C42C2312yes—
335C22×C42C2311yescharacteristic
336#401C2314yes—
337#401C2314yes—
338#401C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2312yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#399C2314yes—
351#399C2314yes—
352#399C2314yes—
353#399C2312yes—
354#398C2314yes—
355#398C2314yes—
356#398C2312yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2312yes—
363#398C2312yes—
364#398C2314yes—
365#398C2314yes—
366#397C2314yes—
367#397C2312yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2312yes—
391#396C2314yes—
392#396C2312yes—
393#396C2314yes—
394#396C2312yes—
395#396C2312yes—
396#396C2314yes—
397#396C2314yes—
398#395C2314yes—
399#395C2314yes—
400#395C2312yes—
401#395C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2312yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2312yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2312yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#393C2314yes—
425#393C2312yes—
426#393C2314yes—
427#393C2314yes—
428#393C2314yes—
429#393C2314yes—
430#393C2314yes—
431#393C2314yes—
432#392C2314yes—
433#392C2314yes—
434#392C2314yes—
435#392C2314yes—
436#392C2314yes—
437#392C2312yes—
438#392C2314yes—
439#392C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2312yes—
444#391C2312yes—
445#391C2314yes—
446#391C2314yes—
447#391C2314yes—
448#390C2314yes—
449#390C2314yes—
450#390C2312yes—
451#390C2312yes—
452#390C2312yes—
453#390C2312yes—
454#390C2314yes—
455#390C2314yes—
456#390C2314yes—
457#390C2314yes—
458#390C2314yes—
459#390C2314yes—
460#390C2314yes—
461#390C2314yes—
462#390C2314yes—
463#390C2312yes—
464#390C2312yes—
465#390C2312yes—
466#390C2312yes—
467#390C2312yes—
468#390C2312yes—
469#390C2314yes—
470#390C2314yes—
471#390C2312yes—
472#390C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2314yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2314yes—
484#389C2312yes—
485#389C2312yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2312yes—
492#389C2312yes—
493#389C2312yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2312yes—
498#388C2314yes—
499#388C2314yes—
500#388C2312yes—
501#388C2312yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2312yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2312yes—
530#388C2314yes—
531#388C2314yes—
532#388C2312yes—
533#388C2312yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2312yes—
542#388C2312yes—
543#388C2312yes—
544#388C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2312yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2312yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2312yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2312yes—
593#386C2312yes—
594#386C2312yes—
595#386C2312yes—
596#386C2312yes—
597#386C2312yes—
598#386C2314yes—
599#386C2312yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2312yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2312yes—
614#385C2312yes—
615#385C2314yes—
616#385C2314yes—
617#385C2312yes—
618#384C2312yes—
619#384C2312yes—
620#384C2312yes—
621#384C2312yes—
622#383C2312yes—
623#383C2314yes—
624#382C2312yes—
625#382C2314yes—
626#382C2312yes—
627#382C2312yes—
628#382C2312yes—
629#382C2312yes—
630#382C2314yes—
631#381C2312yes—
632#381C2314yes—
633#381C2314yes—
634#381C2314yes—
635#381C2312yes—
636#380C2312yes—
637#380C2312yes—
638#380C2312yes—
639#380C2312yes—
640#380C2312yes—
641#380C2312yes—
642#380C2312yes—
643#380C2314yes—
644#380C2314yes—
645#380C2314yes—
646#380C2314yes—
647#380C2312yes—
648#380C2312yes—
649#380C2312yes—
650#380C2314yes—
651#380C2311yescharacteristic
652#380C2311yescharacteristic
653#379C2312yes—
654#379C2314yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2311yescharacteristic
669C4×C4⋊C4C2311yescharacteristic
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2311yescharacteristic
672C4×C4⋊C4C2311yescharacteristic
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2311yescharacteristic
677C4×C4⋊C4C2311yescharacteristic
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C22⋊C4C2314yes—
682C4×C22⋊C4C2314yes—
683C4×C22⋊C4C2314yes—
684C4×C22⋊C4C2311yescharacteristic
685C4×C22⋊C4C2312yes—
686C4×C22⋊C4C2312yes—
687C4×C22⋊C4C2312yes—
688C4×C22⋊C4C2312yes—
689C4×C22⋊C4C2314yes—
690C4×C22⋊C4C2314yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2312yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2311yescharacteristic
695C4×C22⋊C4C2312yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707#376C2312yes—
708#376C2312yes—
709#376C2312yes—
710#376C2312yes—
711C43C2312yes—
712C43C2311yescharacteristic
713C43C2311yescharacteristic
714C43C2312yes—
715C25C2411yescharacteristic
716C2×#41—28no—
717C2×#41—82no—
718C2×#41—82no—
719C22×Q8C2411yescharacteristic
720C22×Q8C2412yes—
721C22×Q8C2414yes—
722C22×D4C2411yescharacteristic
723C22×D4C2411yescharacteristic
724C22×D4C2412yes—
725C22×D4C2412yes—
726C22×D4C2412yes—
727C22×D4C2411yescharacteristic
728C22×D4C2412yes—
729C22×D4C2412yes—
730C22×D4C2412yes—
731C22×D4C2412yes—
732C22×D4C2414yes—
733C22×D4C2414yes—
734C22×D4C2414yes—
735C22×D4C2414yes—
736C23×C4—24no—
737C23×C4—44no—
738C23×C4C2412yes—
739C23×C4C2412yes—
740C23×C4C2411yescharacteristic
741C23×C4C2411yescharacteristic
742C23×C4C2411yescharacteristic
743C23×C4C2411yescharacteristic
744C23×C4C2412yes—
745C23×C4C2412yes—
746C23×C4C2412yes—
747C23×C4C2414yes—
748C23×C4C2414yes—
749C23×C4C2414yes—
750C23×C4C2411yescharacteristic
751C23×C4C2411yescharacteristic
752C4⋊Q8—24no—
753C4⋊Q8—44no—
754C4⋊Q8—82no—
755#127—24no—
756#127—82no—
757#126—28no—
758#126—48no—
759#126—84no—
760#126—84no—
761#125—24no—
762#125—44no—
763#125—84no—
764#124—24no—
765#124—28no—
766#124—82no—
767#124—82no—
768#124—84no—
769#123—28no—
770#123—44no—
771#123—48no—
772#123—48no—
773#123—82no—
774#123—84no—
775#123—82no—
776#123—84no—
777C22⋊Q8—24no—
778C22⋊Q8—84no—
779#121—24no—
780#121—24no—
781#121—24no—
782#121—28no—
783#121—48no—
784#121—44no—
785#121—44no—
786#121—44no—
787#121—44no—
788#121—84no—
789#120—44no—
790#120—82no—
791#120—82no—
792C4×Q8—24no—
793C4×Q8—48no—
794C4×D4—28no—
795C4×D4—24no—
796C4×D4—24no—
797C4×D4—24no—
798C4×D4—28no—
799C4×D4—44no—
800C4×D4—44no—
801C4×D4—44no—
802C4×D4—44no—
803C4×D4—48no—
804#117—28no—
805#117—28no—
806#117—28no—
807#117—28no—
808#117—28no—
809#117—44no—
810#117—44no—
811#117—44no—
812#117—44no—
813#117—82no—
814#117—82no—
815C2×C4⋊C4—24no—
816C2×C4⋊C4—24no—
817C2×C4⋊C4—44no—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C22⋊C4—24no—
868C2×C22⋊C4—24no—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C42—24no—
930C2×C42—82no—
931C2×C42—82no—
932C2×C42#4118yes—
933C2×C42C2412yes—
934C2×C42C2412yes—
935C2×C42C2412yes—
936C2×C42C2412yes—
937C2×C42C2412yes—
938C2×C42C2412yes—
939C2×C42C2412yes—
940C2×C42C2411yescharacteristic
941C2×C42C2411yescharacteristic
942C2×C42C2414yes—
943C2×C42C2412yes—
944C2×C42C2414yes—
945C2×C42C2414yes—
946C2×C42C2414yes—
947C2×C42C2414yes—
948C2×C42C2414yes—
949C2×C42C2412yes—
950C2×C42C2414yes—
951C2×C42C2414yes—
952C2×C42C2414yes—
953C2×C42C2414yes—
954C2×C42C2412yes—
955C2×C42C2412yes—
956C2×C42C2411yescharacteristic
957C2×C42C2411yescharacteristic
958C2×C42C2411yescharacteristic
959C2×C42C2411yescharacteristic
960C2×C42C2411yescharacteristic
961C2×C42C2411yescharacteristic
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2414yes—
967#95C2412yes—
968#95C2414yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2412yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021C24—22no—
1022C24—42no—
1023C24—42no—
1024C24—41no—
1025C24—41no—
1026C24C2512yes—
1027C24C2512yes—
1028C24C2512yes—
1029C24C2512yes—
1030C24C2511yescharacteristic
1031#41—816no—
1032C2×Q8—22no—
1033C2×Q8—24no—
1034C2×Q8—44no—
1035C2×Q8—44no—
1036C2×Q8—41no—
1037C2×Q8—42no—
1038C2×Q8—44no—
1039C2×Q8—41no—
1040C2×Q8—42no—
1041C2×D4—24no—
1042C2×D4—24no—
1043C2×D4—24no—
1044C2×D4—24no—
1045C2×D4—22no—
1046C2×D4—22no—
1047C2×D4—22no—
1048C2×D4—24no—
1049C2×D4—24no—
1050C2×D4—24no—
1051C2×D4—24no—
1052C2×D4—44no—
1053C2×D4—42no—
1054C2×D4—42no—
1055C2×D4—42no—
1056C2×D4—42no—
1057C2×D4—42no—
1058C2×D4—42no—
1059C2×D4—42no—
1060C2×D4—42no—
1061C2×D4—42no—
1062C2×D4—42no—
1063C2×D4—42no—
1064C2×D4—41no—
1065C2×D4—42no—
1066C2×D4—41no—
1067C2×D4—42no—
1068C2×D4—44no—
1069C2×D4—44no—
1070C2×D4—44no—
1071C2×D4—44no—
1072C2×D4—44no—
1073C2×D4—44no—
1074C2×D4—44no—
1075C2×D4—44no—
1076C2×D4—44no—
1077C2×D4—44no—
1078C2×D4—44no—
1079C2×D4—44no—
1080C22×C4—24no—
1081C22×C4—22no—
1082C22×C4—22no—
1083C22×C4—22no—
1084C22×C4—24no—
1085C22×C4—24no—
1086C22×C4—24no—
1087C22×C4—24no—
1088C22×C4—24no—
1089C22×C4—24no—
1090C22×C4—24no—
1091C22×C4—24no—
1092C22×C4—24no—
1093C22×C4—28no—
1094C22×C4—42no—
1095C22×C4—42no—
1096C22×C4—42no—
1097C22×C4—42no—
1098C22×C4—42no—
1099C22×C4—42no—
1100C22×C4—42no—
1101C22×C4—42no—
1102C22×C4—41no—
1103C22×C4—41no—
1104C22×C4—44no—
1105C22×C4—44no—
1106C22×C4—44no—
1107C22×C4—44no—
1108C22×C4—44no—
1109C22×C4—42no—
1110C22×C4—41no—
1111C22×C4—41no—
1112C22×C4—44no—
1113C22×C4—44no—
1114C22×C4—44no—
1115C22×C4—416no—
1116C22×C4C2×#4114yes—
1117C22×C4C2×#4114yes—
1118C22×C4C2×#4114yes—
1119C22×C4C2512yes—
1120C22×C4C2514yes—
1121C22×C4C2512yes—
1122C22×C4C2514yes—
1123C22×C4C2512yes—
1124C22×C4C2512yes—
1125C22×C4C2514yes—
1126C22×C4C2512yes—
1127C22×C4C2512yes—
1128C22×C4C2512yes—
1129C22×C4C2512yes—
1130C22×C4C2514yes—
1131C22×C4C2514yes—
1132C22×C4C2512yes—
1133C22×C4C2514yes—
1134C22×C4C2512yes—
1135C22×C4C2512yes—
1136C22×C4C2511yescharacteristic
1137C22×C4C2511yescharacteristic
1138C22×C4C2511yescharacteristic
1139C22×C4C2511yescharacteristic
1140C22×C4C2511yescharacteristic
1141C22×C4C2512yes—
1142C22×C4C2511yescharacteristic
1143C4⋊C4—24no—
1144C4⋊C4—24no—
1145C4⋊C4—24no—
1146C4⋊C4—24no—
1147C4⋊C4—24no—
1148C4⋊C4—24no—
1149C4⋊C4—24no—
1150C4⋊C4—22no—
1151C4⋊C4—22no—
1152C4⋊C4—22no—
1153C4⋊C4—24no—
1154C4⋊C4—22no—
1155C4⋊C4—24no—
1156C4⋊C4—24no—
1157C4⋊C4—24no—
1158C4⋊C4—24no—
1159C4⋊C4—24no—
1160C4⋊C4—24no—
1161C4⋊C4—24no—
1162C4⋊C4—24no—
1163C4⋊C4—28no—
1164C4⋊C4—28no—
1165C4⋊C4—24no—
1166C4⋊C4—44no—
1167C4⋊C4—42no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—42no—
1171C4⋊C4—42no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—42no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—42no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—42no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C22⋊C4—24no—
1193C22⋊C4—24no—
1194C22⋊C4—24no—
1195C22⋊C4—24no—
1196C22⋊C4—24no—
1197C22⋊C4—24no—
1198C22⋊C4—24no—
1199C22⋊C4—24no—
1200C22⋊C4—24no—
1201C22⋊C4—24no—
1202C22⋊C4—24no—
1203C22⋊C4—24no—
1204C22⋊C4—24no—
1205C22⋊C4—24no—
1206C22⋊C4—28no—
1207C22⋊C4—24no—
1208C22⋊C4—24no—
1209C22⋊C4—42no—
1210C22⋊C4—44no—
1211C22⋊C4—44no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—42no—
1216C22⋊C4—44no—
1217C22⋊C4—42no—
1218C22⋊C4—44no—
1219C22⋊C4—42no—
1220C22⋊C4—42no—
1221C22⋊C4—44no—
1222C22⋊C4—42no—
1223C22⋊C4—42no—
1224C22⋊C4—44no—
1225C22⋊C4—42no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—42no—
1235C22⋊C4—44no—
1236C22⋊C4—42no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—42no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4—42no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—44no—
1251C22⋊C4—42no—
1252C42—24no—
1253C42—24no—
1254C42—24no—
1255C42—24no—
1256C42—24no—
1257C42—24no—
1258C42—41no—
1259C42—42no—
1260C42—41no—
1261C42—44no—
1262C42—44no—
1263C42—42no—
1264C42—44no—
1265C42—44no—
1266C42—44no—
1267C42—42no—
1268C42—41no—
1269C42—41no—
1270C42—44no—
1271C42—44no—
1272C42—44no—
1273C42—42no—
1274C42—44no—
1275C42—44no—
1276C42—42no—
1277C42C2×#4114yes—
1278C42C2×#4114yes—
1279C42C2×#4114yes—
1280C42C2×#4114yes—
1281C23—22no—
1282C23—22no—
1283C23—21no—
1284C23—21no—
1285C23—22no—
1286C23—22no—
1287C23—22no—
1288C23—22no—
1289C23—22no—
1290C23—24no—
1291C23—22no—
1292C23—24no—
1293C23—22no—
1294C23—24no—
1295C23—24no—
1296C23—22no—
1297C23—22no—
1298C23—22no—
1299C23—22no—
1300C23—22no—
1301C23—22no—
1302C23—22no—
1303C23—22no—
1304C23—22no—
1305C23—22no—
1306C23—22no—
1307C23—22no—
1308C23—22no—
1309C23—44no—
1310C23—82no—
1311C23—82no—
1312C23—84no—
1313C23—84no—
1314C23C22×#4112yes—
1315C23C2611yescharacteristic
1316Q8—82no—
1317Q8—84no—
1318Q8—88no—
1319D4—48no—
1320D4—44no—
1321D4—44no—
1322D4—82no—
1323D4—84no—
1324D4—84no—
1325D4—84no—
1326D4—84no—
1327D4—84no—
1328D4—84no—
1329D4—164no—
1330D4—164no—
1331D4—164no—
1332D4—164no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—21no—
1338C2×C4—21no—
1339C2×C4—22no—
1340C2×C4—21no—
1341C2×C4—21no—
1342C2×C4—28no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—24no—
1356C2×C4—22no—
1357C2×C4—24no—
1358C2×C4—22no—
1359C2×C4—24no—
1360C2×C4—22no—
1361C2×C4—24no—
1362C2×C4—22no—
1363C2×C4—24no—
1364C2×C4—24no—
1365C2×C4—24no—
1366C2×C4—24no—
1367C2×C4—24no—
1368C2×C4—24no—
1369C2×C4—24no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—24no—
1377C2×C4—24no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—24no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—24no—
1384C2×C4—22no—
1385C2×C4—24no—
1386C2×C4—22no—
1387C2×C4—24no—
1388C2×C4—24no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—22no—
1394C2×C4—44no—
1395C2×C4—44no—
1396C2×C4—48no—
1397C2×C4—48no—
1398C2×C4—48no—
1399C2×C4—44no—
1400C2×C4—48no—
1401C2×C4—48no—
1402C2×C4—88no—
1403C2×C4—82no—
1404C2×C4—82no—
1405C2×C4—88no—
1406C2×C4—164no—
1407C2×C4C22×#4112yes—
1408C2×C4C22×#4112yes—
1409C2×C4C22×#4112yes—
1410C2×C4C22×#4112yes—
1411C2×C4C22×#4112yes—
1412C2×C4C22×#4112yes—
1413C2×C4#58514yes—
1414C2×C4#58514yes—
1415C22—22no—
1416C22—22no—
1417C22—22no—
1418C22—42no—
1419C22—42no—
1420C22—42no—
1421C22—42no—
1422C22—42no—
1423C22—42no—
1424C22—42no—
1425C22—42no—
1426C22—42no—
1427C22—42no—
1428C22—42no—
1429C22—42no—
1430C22—42no—
1431C22—44no—
1432C22—42no—
1433C22—44no—
1434C22—42no—
1435C22—42no—
1436C22—42no—
1437C22—42no—
1438C22—44no—
1439C22—44no—
1440C22—42no—
1441C22—42no—
1442C22—42no—
1443C22—42no—
1444C22—88no—
1445C22C23×#4111yescharacteristic
1446C22C2×#58512yes—
1447C22C2×#58512yes—
1448C22H(7,𝔽2)11yescharacteristic
1449C22H(7,𝔽2)11yescharacteristic
1450C4—22no—
1451C4—22no—
1452C4—22no—
1453C4—22no—
1454C4—22no—
1455C4—24no—
1456C4—42no—
1457C4—42no—
1458C4—42no—
1459C4—42no—
1460C4—42no—
1461C4—42no—
1462C4—44no—
1463C4—44no—
1464C4—42no—
1465C4—44no—
1466C4—42no—
1467C4—42no—
1468C4—42no—
1469C4—42no—
1470C4—44no—
1471C4—44no—
1472C4—44no—
1473C4#345514yes—
1474C2—42no—
1475C2—82no—
1476C2—82no—
1477C2—82no—
1478C2—82no—
1479C2C2×#345511yescharacteristic
1480C2#6281511yescharacteristic
1481C2#6285511yescharacteristic
1482C2#6293712yes—
1483C2#6297012yes—
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. #42670C2semidirect
2. #42666C2semidirect
3. #42471C2semidirect
4. #42467C2semidirect
5. #40685C2semidirect
6. #40681C2semidirect
7. #39937C2semidirect
8. #39933C2semidirect
9. #39912C2semidirect
10. #39909C2semidirect
11. #38499C2semidirect
12. #38497C2semidirect
13. #37568C2semidirect
14. #36821C2semidirect
15. #36819C2semidirect
16. #36816C2semidirect
17. #36812C2semidirect
18. #35614C2semidirect
19. #35597C2semidirect
20. #35301C2semidirect
21. #35218C2semidirect
22. #35207C2semidirect
23. #35191C2semidirect
24. #35105C2semidirect
25. #34912C2semidirect
26. #34877C2semidirect
27. #34244C2semidirect
28. #34155C2semidirect
29. #34048C2semidirect
33. #2861C22semidirect
34. #2858C22semidirect
38. #2853C22semidirect
40. #2851C22semidirect
43. #2838C22semidirect
45. #2830C22semidirect
49. #2789C22semidirect
50. #2786C22semidirect
54. #2755C22semidirect
56. #2751C22semidirect
61. #2715C22semidirect
62. #2713C22semidirect
65. #2709C22semidirect
70. #2700C22semidirect
82. #2655C22semidirect
83. #2655C22semidirect
86. #2653C22semidirect
87. #2652C22semidirect
89. #2651C22semidirect
90. #2650C22semidirect
93. #2648C22semidirect
95. #2630C22semidirect
103. #2606C22semidirect
104. #2605C22semidirect
105. #2603C22semidirect
111. #2597C22semidirect
113. #2595C22semidirect
114. #2594C22semidirect
115. #2594C22semidirect
119. #2587C22semidirect
121. #2577C22semidirect
123. #2576C22semidirect
124. #2573C22semidirect
125. #2570C22semidirect
126. #2570C22semidirect
127. #2566C22semidirect
129. #2563C22semidirect
132. #2560C22semidirect
135. #2558C22semidirect
139. #2552C22semidirect
140. #2550C22semidirect
141. #2548C22semidirect
142. #2547C22semidirect
143. #2546C22semidirect
144. #2541C22semidirect
150. #2516C22semidirect
151. #2515C22semidirect
153. #2512C22semidirect
154. #2512C22semidirect
155. #2509C22semidirect
156. #2508C22semidirect
157. #2504C22semidirect
158. #2500C22semidirect
161. #2495C22semidirect
164. #2494C22semidirect
165. #2494C22semidirect
171. #2478C22semidirect
172. #2477C22semidirect
175. #2469C22semidirect
176. #2468C22semidirect
179. #2458C22semidirect
181. #2441C22semidirect
182. #2440C22semidirect
188. #2422C22semidirect
189. #2422C22semidirect
203. #2372C22semidirect
204. #2372C22semidirect
205. #2371C22semidirect
206. #2369C22semidirect
207. #2366C22semidirect
211. #2355C22semidirect
214. #2352C22semidirect
216. #2335C22semidirect
217. #2334C22semidirect
223. #2324C22semidirect
224. #2324C22semidirect
229. #2314C22semidirect
234. C4×C4⋊Q8C22semidirect
235. C4×#125C22semidirect
236. C4×#126C22semidirect
243. #2295C22semidirect
246. #2293C22semidirect
247. #2293C22semidirect
248. #2293C22semidirect
252. #2274C22semidirect
253. C42×D4C22semidirect
254. C42×D4C22semidirect
255. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#426702
#426662
#424712
#424672
#406852
#406812
#399372
#399332
#399122
#399092
#384992
#384972
#375682
#368212
#368192
#368162
#368122
#356142
#355972
#353012
#352182
#352072
#351912
#351052
#349122
#348772
#342442
#341552
#340482