Finite Group Databasebeta

← #7657709

Subgroups — #7657709

Order 512.

4814 conjugacy classes of subgroups.

The subgroup lattice has 1524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42229C214yesmaximal, complemented
2#42060C214yesmaximal, complemented
3#41972C214yesmaximal, complemented
4#41026C214yesmaximal, complemented
5#41012C214yesmaximal, complemented
6#40554C214yesmaximal, complemented
7#39630C211yesmaximal, characteristic, complemented
8#39628C211yesmaximal, characteristic, complemented
9#39426C212yesmaximal, complemented
10#39424C212yesmaximal, complemented
11#39374C211yesmaximal, characteristic, complemented
12#39372C211yesmaximal, characteristic, complemented
13#37946C212yesmaximal, complemented
14#37944C212yesmaximal, complemented
15#37593C212yesmaximal, complemented
16#37591C212yesmaximal, complemented
17#37554C211yesmaximal, characteristic, complemented
18#37553C211yesmaximal, characteristic, complemented
19#36609C211yesmaximal, characteristic, complemented
20#36601C211yesmaximal, characteristic, complemented
21#36211C211yesmaximal, characteristic, complemented
22#36195C211yesmaximal, characteristic, complemented
23#36003C214yesmaximal, complemented
24#35744C214yesmaximal, complemented
25#35330C211yesmaximal, characteristic, complemented
26#35276C212yesmaximal, complemented
27#34625C212yesmaximal, complemented
28#34624C211yesmaximal, characteristic, complemented
29#34229C211yesmaximal, characteristic, complemented
30#34226C211yesmaximal, characteristic, complemented
31#34151C211yesmaximal, characteristic, complemented
32C2×#544C2212yes—
33C2×#542C2212yes—
34C2×#540C2212yes—
35C2×#532C2211yescharacteristic
36C2×#529C2211yescharacteristic
37C2×#529C2211yescharacteristic
38#2862C2211yescharacteristic
39#2862C2211yescharacteristic
40#2861C2212yes—
41#2859C2211yescharacteristic
42#2859C2211yescharacteristic
43#2858C2212yes—
44#2856C2212yes—
45#2850C2212yes—
46#2832C2214yes—
47#2831C2214yes—
48#2830C2214yes—
49#2829C2214yes—
50#2820C2212yes—
51#2819C2212yes—
52#2814C2212yes—
53#2813C2212yes—
54#2807C2214yes—
55#2804C2214yes—
56#2788C2214yes—
57#2783C2214yes—
58#2782C2214yes—
59#2779C2214yes—
60#2757C2214yes—
61#2749C2214yes—
62#2732C2214yes—
63#2731C2214yes—
64#2728C2214yes—
65#2725C2214yes—
66#2724C2214yes—
67#2711C2214yes—
68#2710C2214yes—
69#2708C2214yes—
70#2701C2214yes—
71#2696C2214yes—
72#2689C2214yes—
73#2688C2214yes—
74#2682C2214yes—
75#2681C2214yes—
76#2676C2214yes—
77#2674C2214yes—
78#2667C2214yes—
79#2666C2214yes—
80#2666C2214yes—
81#2665C2214yes—
82#2664C2212yes—
83#2663C2214yes—
84#2662C2212yes—
85#2662C2214yes—
86#2662C2214yes—
87#2661C2214yes—
88#2660C2212yes—
89#2660C2212yes—
90#2660C2211yescharacteristic
91#2657C2211yescharacteristic
92#2656C2212yes—
93#2652C2214yes—
94#2651C2214yes—
95#2651C2214yes—
96#2650C2214yes—
97#2647C2212yes—
98#2647C2212yes—
99#2641C2211yescharacteristic
100#2640C2211yescharacteristic
101#2639C2212yes—
102#2638C2214yes—
103#2636C2214yes—
104#2630C2214yes—
105#2630C2214yes—
106#2629C2212yes—
107#2629C2212yes—
108#2628C2212yes—
109#2628C2212yes—
110#2620C2211yescharacteristic
111#2620C2211yescharacteristic
112#2620C2212yes—
113#2619C2211yescharacteristic
114#2619C2211yescharacteristic
115#2619C2212yes—
116#2603C2214yes—
117#2601C2214yes—
118#2596C2214yes—
119#2595C2214yes—
120#2592C2214yes—
121#2587C2214yes—
122#2581C2211yescharacteristic
123#2580C2211yescharacteristic
124#2580C2211yescharacteristic
125#2580C2211yescharacteristic
126#2573C2214yes—
127#2572C2214yes—
128#2560C2214yes—
129#2559C2214yes—
130#2558C2214yes—
131#2558C2214yes—
132#2555C2214yes—
133#2555C2214yes—
134#2554C2214yes—
135#2554C2214yes—
136#2550C2214yes—
137#2550C2214yes—
138#2549C2214yes—
139#2549C2214yes—
140#2540C2214yes—
141#2536C2211yescharacteristic
142#2535C2211yescharacteristic
143#2535C2211yescharacteristic
144#2535C2211yescharacteristic
145#2532C2214yes—
146#2526C2214yes—
147#2522C2214yes—
148#2521C2214yes—
149#2513C2212yes—
150#2513C2212yes—
151#2513C2214yes—
152#2512C2212yes—
153#2511C2212yes—
154#2505C2214yes—
155#2492C2212yes—
156#2491C2214yes—
157#2491C2212yes—
158#2490C2212yes—
159#2490C2212yes—
160#2488C2214yes—
161#2476C2214yes—
162#2470C2214yes—
163#2469C2214yes—
164#2468C2214yes—
165#2465C2214yes—
166#2464C2214yes—
167#2464C2214yes—
168#2464C2214yes—
169#2461C2214yes—
170#2461C2214yes—
171#2461C2214yes—
172#2461C2214yes—
173#2459C2214yes—
174#2458C2214yes—
175#2454C2212yes—
176#2453C2212yes—
177#2452C2212yes—
178#2452C2212yes—
179#2450C2214yes—
180#2450C2214yes—
181#2448C2214yes—
182#2447C2214yes—
183#2430C2214yes—
184#2429C2214yes—
185#2426C2214yes—
186#2425C2214yes—
187#2425C2214yes—
188#2422C2212yes—
189#2422C2212yes—
190#2421C2212yes—
191#2420C2212yes—
192#2420C2214yes—
193#2416C2212yes—
194#2416C2212yes—
195#2415C2212yes—
196#2414C2212yes—
197#2414C2214yes—
198#2402C2214yes—
199#2399C2214yes—
200#2396C2214yes—
201#2396C2214yes—
202#2392C2214yes—
203#2388C2214yes—
204#2374C2212yes—
205#2374C2212yes—
206#2373C2212yes—
207#2373C2212yes—
208#2373C2214yes—
209#2372C2214yes—
210#2370C2212yes—
211#2367C2214yes—
212#2367C2212yes—
213#2367C2214yes—
214#2363C2212yes—
215#2363C2212yes—
216#2363C2212yes—
217#2363C2214yes—
218#2362C2212yes—
219#2361C2212yes—
220#2360C2212yes—
221#2359C2214yes—
222#2357C2211yescharacteristic
223#2357C2211yescharacteristic
224#2357C2211yescharacteristic
225#2356C2211yescharacteristic
226#2351C2211yescharacteristic
227#2349C2211yescharacteristic
228#2349C2211yescharacteristic
229#2349C2211yescharacteristic
230#2346C2212yes—
231#2343C2212yes—
232#2341C2212yes—
233#2339C2212yes—
234#2334C2214yes—
235#2328C2212yes—
236#2326C2212yes—
237#2324C2214yes—
238#2319C2212yes—
239#2318C2212yes—
240#2317C2212yes—
241C4×C4⋊Q8C2212yes—
242C4×C4⋊Q8C2212yes—
243C4×#127C2211yescharacteristic
244C4×#127C2211yescharacteristic
245C4×#127C2212yes—
246C4×#125C2212yes—
247C4×#125C2212yes—
248C4×#124C2211yescharacteristic
249C4×#124C2211yescharacteristic
250C4×#124C2212yes—
251#2298C2212yes—
252#2295C2211yescharacteristic
253#2293C2212yes—
254#2293C2211yescharacteristic
255#2290C2212yes—
256#2285C2211yescharacteristic
257#2285C2212yes—
258#2283C2212yes—
259C2×#382C2211yescharacteristic
260#2275C2212yes—
261#2275C2212yes—
262C42×Q8C2211yescharacteristic
263C42×D4C2211yescharacteristic
264C4×#117C2211yescharacteristic
265C4×#117C2212yes—
266C4×#117C2211yescharacteristic
267C22×#41C2312yes—
268#544—48no—
269#542—48no—
270#540—48no—
271#532—28no—
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2314yes—
276C2×#127C2311yescharacteristic
277C2×#127C2311yescharacteristic
278C2×#127C2311yescharacteristic
279#529—28no—
280#529—28no—
281C2×#126C2312yes—
282C2×#126C2312yes—
283C2×#126C2314yes—
284C2×#126C2314yes—
285C2×#125C2311yescharacteristic
286C2×#125C2312yes—
287C2×#125C2311yescharacteristic
288C2×#125C2312yes—
289C2×#125C2314yes—
290C2×#124C2311yescharacteristic
291C2×#124C2312yes—
292C2×#124C2311yescharacteristic
293C2×#124C2311yescharacteristic
294C2×#124C2311yescharacteristic
295C2×#124C2314yes—
296C2×#124C2314yes—
297C2×#124C2314yes—
298C2×#124C2314yes—
299C2×#123C2312yes—
300C2×#123C2312yes—
301C2×#123C2314yes—
302C2×#123C2314yes—
303C2×#123C2314yes—
304C2×#123C2314yes—
305C2×#123C2314yes—
306C2×C22⋊Q8C2311yescharacteristic
307C2×C22⋊Q8C2311yescharacteristic
308C2×C22⋊Q8C2314yes—
309C2×C22⋊Q8C2312yes—
310C2×C22⋊Q8C2314yes—
311C2×C22⋊Q8C2314yes—
312C2×C22⋊Q8C2314yes—
313C2×C22⋊Q8C2314yes—
314C2×#121C2312yes—
315C2×#121C2311yescharacteristic
316C2×#121C2311yescharacteristic
317C2×#121C2311yescharacteristic
318C2×#121C2311yescharacteristic
319C2×#121C2312yes—
320C2×#121C2314yes—
321C2×#121C2312yes—
322C2×#121C2312yes—
323C2×#121C2314yes—
324C2×#121C2314yes—
325C2×#121C2314yes—
326C2×#121C2314yes—
327C2×#121C2314yes—
328C2×C4×Q8C2311yescharacteristic
329C2×C4×Q8C2311yescharacteristic
330C2×C4×Q8C2312yes—
331C2×C4×Q8C2312yes—
332C2×C4×Q8C2314yes—
333C2×C4×Q8C2314yes—
334C2×C4×D4C2311yescharacteristic
335C2×C4×D4C2311yescharacteristic
336C2×C4×D4C2311yescharacteristic
337C2×C4×D4C2312yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2312yes—
340C2×C4×D4C2311yescharacteristic
341C2×C4×D4C2314yes—
342C2×C4×D4C2312yes—
343C2×C4×D4C2312yes—
344C2×C4×D4C2312yes—
345C2×C4×D4C2314yes—
346C2×C4×D4C2312yes—
347C2×C4×D4C2314yes—
348C2×C4×D4C2314yes—
349C2×C4×D4C2314yes—
350C2×#117C2311yescharacteristic
351C2×#117C2312yes—
352C2×#117C2312yes—
353C2×#117C2311yescharacteristic
354C2×#117C2312yes—
355C2×#117C2312yes—
356C2×#117C2312yes—
357C2×#117C2314yes—
358C22×C4⋊C4C2312yes—
359C22×C42C2312yes—
360C22×C42C2311yescharacteristic
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2312yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#400C2314yes—
372#400C2314yes—
373#399C2312yes—
374#399C2312yes—
375#399C2314yes—
376#399C2312yes—
377#399C2314yes—
378#399C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2312yes—
394#397C2314yes—
395#397C2312yes—
396#397C2312yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2312yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#396C2314yes—
423#396C2314yes—
424#395C2314yes—
425#395C2314yes—
426#395C2314yes—
427#395C2312yes—
428#395C2314yes—
429#395C2314yes—
430#395C2314yes—
431#395C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#394C2314yes—
437#394C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#394C2312yes—
453#393C2314yes—
454#393C2314yes—
455#393C2312yes—
456#393C2312yes—
457#393C2314yes—
458#393C2314yes—
459#393C2314yes—
460#393C2314yes—
461#393C2312yes—
462#393C2314yes—
463#392C2314yes—
464#392C2312yes—
465#392C2312yes—
466#392C2314yes—
467#392C2314yes—
468#392C2314yes—
469#392C2314yes—
470#392C2314yes—
471#392C2314yes—
472#392C2312yes—
473#391C2314yes—
474#391C2314yes—
475#391C2314yes—
476#391C2314yes—
477#391C2312yes—
478#391C2314yes—
479#391C2312yes—
480#391C2314yes—
481#391C2314yes—
482#391C2312yes—
483#391C2311yescharacteristic
484#391C2311yescharacteristic
485#390C2314yes—
486#390C2314yes—
487#390C2314yes—
488#390C2312yes—
489#390C2314yes—
490#390C2312yes—
491#390C2311yescharacteristic
492#390C2311yescharacteristic
493#390C2311yescharacteristic
494#390C2311yescharacteristic
495#390C2314yes—
496#390C2314yes—
497#390C2312yes—
498#390C2312yes—
499#390C2312yes—
500#390C2314yes—
501#390C2312yes—
502#390C2314yes—
503#390C2314yes—
504#390C2314yes—
505#390C2314yes—
506#390C2312yes—
507#390C2312yes—
508#390C2312yes—
509#390C2314yes—
510#390C2314yes—
511#390C2311yescharacteristic
512#390C2311yescharacteristic
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2314yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
527#389C2314yes—
528#389C2314yes—
529#389C2314yes—
530#389C2314yes—
531#389C2314yes—
532#389C2312yes—
533#389C2312yes—
534#389C2312yes—
535#389C2312yes—
536#389C2314yes—
537#388C2312yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2312yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2312yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2312yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2312yes—
567#388C2312yes—
568#388C2312yes—
569#388C2314yes—
570#388C2312yes—
571#388C2312yes—
572#388C2312yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2312yes—
577#388C2312yes—
578#388C2314yes—
579#388C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2312yes—
587#387C2312yes—
588#387C2312yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2312yes—
595#387C2312yes—
596#387C2312yes—
597#387C2312yes—
598#387C2312yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2312yes—
613#386C2312yes—
614#386C2314yes—
615#386C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2312yes—
631#385C2312yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#384C2311yescharacteristic
636#384C2312yes—
637#384C2311yescharacteristic
638#384C2312yes—
639#384C2312yes—
640#383C2312yes—
641#383C2314yes—
642#382C2311yescharacteristic
643#382C2312yes—
644#382C2312yes—
645#382C2312yes—
646#382C2312yes—
647#382C2312yes—
648#382C2311yescharacteristic
649#382C2311yescharacteristic
650#382C2311yescharacteristic
651#382C2311yescharacteristic
652#382C2312yes—
653#382C2311yescharacteristic
654#382C2314yes—
655#381C2312yes—
656#381C2314yes—
657#381C2312yes—
658#381C2312yes—
659#381C2314yes—
660#380C2312yes—
661#380C2312yes—
662#380C2312yes—
663#380C2312yes—
664#380C2312yes—
665#380C2312yes—
666#380C2312yes—
667#380C2312yes—
668#380C2312yes—
669#380C2314yes—
670#380C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2311yescharacteristic
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2311yescharacteristic
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2311yescharacteristic
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2312yes—
715C4×C22⋊C4C2314yes—
716C4×C22⋊C4C2312yes—
717C4×C22⋊C4C2312yes—
718C4×C22⋊C4C2312yes—
719C4×C22⋊C4C2312yes—
720C4×C22⋊C4C2314yes—
721C4×C22⋊C4C2312yes—
722C4×C22⋊C4C2312yes—
723C4×C22⋊C4C2312yes—
724#376C2311yescharacteristic
725#376C2312yes—
726#376C2311yescharacteristic
727#376C2312yes—
728#376C2314yes—
729#376C2311yescharacteristic
730#376C2311yescharacteristic
731C2×#95C2312yes—
732C2×#95C2312yes—
733C2×#95C2312yes—
734C2×#95C2312yes—
735C2×#95C2312yes—
736C43C2312yes—
737C43C2312yes—
738C43C2311yescharacteristic
739C43C2311yescharacteristic
740C2×#41—28no—
741C2×#41—84no—
742C22×Q8C2411yescharacteristic
743C22×Q8C2411yescharacteristic
744C22×Q8C2412yes—
745C22×Q8C2414yes—
746C22×Q8C2414yes—
747C22×D4C2411yescharacteristic
748C22×D4C2411yescharacteristic
749C22×D4C2411yescharacteristic
750C22×D4C2412yes—
751C22×D4C2411yescharacteristic
752C22×D4C2412yes—
753C22×D4C2412yes—
754C22×D4C2412yes—
755C22×D4C2414yes—
756C22×D4C2414yes—
757C22×D4C2412yes—
758C22×D4C2412yes—
759C22×D4C2414yes—
760C22×D4C2414yes—
761C22×D4C2414yes—
762C23×C4C2412yes—
763C23×C4C2412yes—
764C23×C4C2411yescharacteristic
765C23×C4C2412yes—
766C23×C4C2412yes—
767C23×C4C2412yes—
768C23×C4C2412yes—
769C23×C4C2414yes—
770C23×C4C2414yes—
771C23×C4C2414yes—
772C23×C4C2414yes—
773C23×C4C2411yescharacteristic
774C23×C4C2411yescharacteristic
775C4⋊Q8—24no—
776C4⋊Q8—28no—
777C4⋊Q8—44no—
778C4⋊Q8—48no—
779#127—24no—
780#127—24no—
781#127—24no—
782#126—28no—
783#126—28no—
784#126—48no—
785#126—48no—
786#125—24no—
787#125—24no—
788#125—28no—
789#125—44no—
790#125—48no—
791#124—24no—
792#124—24no—
793#124—28no—
794#124—24no—
795#124—24no—
796#124—48no—
797#124—48no—
798#124—48no—
799#124—84no—
800#123—28no—
801#123—28no—
802#123—48no—
803#123—48no—
804#123—48no—
805#123—84no—
806#123—84no—
807C22⋊Q8—24no—
808C22⋊Q8—24no—
809C22⋊Q8—48no—
810C22⋊Q8—48no—
811C22⋊Q8—48no—
812C22⋊Q8—44no—
813C22⋊Q8—84no—
814C22⋊Q8—84no—
815#121—24no—
816#121—24no—
817#121—24no—
818#121—24no—
819#121—28no—
820#121—48no—
821#121—48no—
822#121—48no—
823#121—44no—
824#121—44no—
825#121—44no—
826#121—84no—
827#121—84no—
828#121—84no—
829C4×Q8—24no—
830C4×Q8—24no—
831C4×Q8—44no—
832C4×Q8—44no—
833C4×Q8—84no—
834C4×Q8—84no—
835C4×D4—28no—
836C4×D4—28no—
837C4×D4—24no—
838C4×D4—24no—
839C4×D4—28no—
840C4×D4—24no—
841C4×D4—24no—
842C4×D4—48no—
843C4×D4—48no—
844C4×D4—44no—
845C4×D4—44no—
846C4×D4—44no—
847C4×D4—44no—
848C4×D4—84no—
849C4×D4—84no—
850C4×D4—84no—
851#117—28no—
852#117—28no—
853#117—28no—
854#117—24no—
855#117—24no—
856#117—44no—
857#117—44no—
858#117—84no—
859C2×C4⋊C4—44no—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2414yes—
910C2×C4⋊C4C2414yes—
911C2×C4⋊C4C2414yes—
912C2×C4⋊C4C2414yes—
913C2×C4⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2412yes—
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⋊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⋊C4C2412yes—
963C2×C22⋊C4C2412yes—
964C2×C22⋊C4C2414yes—
965C2×C22⋊C4C2414yes—
966C2×C22⋊C4C2414yes—
967C2×C22⋊C4C2414yes—
968C2×C22⋊C4C2414yes—
969C2×C22⋊C4C2414yes—
970C2×C42—28no—
971C2×C42#4118yes—
972C2×C42C2412yes—
973C2×C42C2412yes—
974C2×C42C2412yes—
975C2×C42C2412yes—
976C2×C42C2411yescharacteristic
977C2×C42C2411yescharacteristic
978C2×C42C2414yes—
979C2×C42C2412yes—
980C2×C42C2412yes—
981C2×C42C2412yes—
982C2×C42C2412yes—
983C2×C42C2414yes—
984C2×C42C2414yes—
985C2×C42C2414yes—
986C2×C42C2412yes—
987C2×C42C2412yes—
988C2×C42C2412yes—
989C2×C42C2412yes—
990C2×C42C2412yes—
991C2×C42C2412yes—
992C2×C42C2412yes—
993C2×C42C2414yes—
994C2×C42C2414yes—
995C2×C42C2412yes—
996C2×C42C2412yes—
997C2×C42C2412yes—
998C2×C42C2411yescharacteristic
999C2×C42C2411yescharacteristic
1000C2×C42C2411yescharacteristic
1001C2×C42C2411yescharacteristic
1002C2×C42C2411yescharacteristic
1003C2×C42C2411yescharacteristic
1004#95C2411yescharacteristic
1005#95C2411yescharacteristic
1006#95C2412yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2411yescharacteristic
1018#95C2412yes—
1019#95C2411yescharacteristic
1020#95C2412yes—
1021#95C2412yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2412yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2412yes—
1030#95C2412yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2412yes—
1035#95C2412yes—
1036#95C2414yes—
1037#95C2412yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2412yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2412yes—
1044#95C2412yes—
1045#95C2412yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2412yes—
1050#95C2412yes—
1051#95C2414yes—
1052#95C2414yes—
1053#95C2414yes—
1054#95C2414yes—
1055#95C2414yes—
1056#95C2412yes—
1057#95C2414yes—
1058#95C2414yes—
1059#95C2414yes—
1060#95C2414yes—
1061#95C2414yes—
1062#95C2414yes—
1063#95C2414yes—
1064C24C2512yes—
1065C24C2512yes—
1066C24C2512yes—
1067C24C2512yes—
1068C24C2511yescharacteristic
1069#41—816no—
1070C2×Q8—22no—
1071C2×Q8—22no—
1072C2×Q8—24no—
1073C2×Q8—22no—
1074C2×Q8—28no—
1075C2×Q8—22no—
1076C2×Q8—42no—
1077C2×Q8—44no—
1078C2×Q8—44no—
1079C2×Q8—44no—
1080C2×Q8—44no—
1081C2×Q8—44no—
1082C2×Q8—44no—
1083C2×D4—24no—
1084C2×D4—24no—
1085C2×D4—24no—
1086C2×D4—24no—
1087C2×D4—22no—
1088C2×D4—22no—
1089C2×D4—24no—
1090C2×D4—22no—
1091C2×D4—22no—
1092C2×D4—24no—
1093C2×D4—22no—
1094C2×D4—22no—
1095C2×D4—22no—
1096C2×D4—28no—
1097C2×D4—22no—
1098C2×D4—22no—
1099C2×D4—22no—
1100C2×D4—28no—
1101C2×D4—44no—
1102C2×D4—42no—
1103C2×D4—44no—
1104C2×D4—44no—
1105C2×D4—44no—
1106C2×D4—44no—
1107C2×D4—44no—
1108C2×D4—42no—
1109C2×D4—42no—
1110C2×D4—44no—
1111C2×D4—44no—
1112C2×D4—44no—
1113C2×D4—44no—
1114C2×D4—44no—
1115C2×D4—44no—
1116C2×D4—44no—
1117C2×D4—44no—
1118C2×D4—44no—
1119C2×D4—44no—
1120C2×D4—44no—
1121C2×D4—44no—
1122C22×C4—22no—
1123C22×C4—22no—
1124C22×C4—24no—
1125C22×C4—24no—
1126C22×C4—24no—
1127C22×C4—24no—
1128C22×C4—24no—
1129C22×C4—24no—
1130C22×C4—24no—
1131C22×C4—24no—
1132C22×C4—24no—
1133C22×C4—42no—
1134C22×C4—42no—
1135C22×C4—42no—
1136C22×C4—42no—
1137C22×C4—44no—
1138C22×C4—44no—
1139C22×C4—44no—
1140C22×C4—42no—
1141C22×C4—44no—
1142C22×C4—44no—
1143C22×C4—44no—
1144C22×C4—44no—
1145C22×C4—44no—
1146C22×C4—44no—
1147C22×C4—44no—
1148C22×C4—44no—
1149C22×C4—44no—
1150C22×C4—44no—
1151C22×C4—44no—
1152C22×C4—44no—
1153C22×C4C2×#4114yes—
1154C22×C4C2×#4114yes—
1155C22×C4C2×#4114yes—
1156C22×C4C2512yes—
1157C22×C4C2512yes—
1158C22×C4C2512yes—
1159C22×C4C2512yes—
1160C22×C4C2512yes—
1161C22×C4C2512yes—
1162C22×C4C2512yes—
1163C22×C4C2512yes—
1164C22×C4C2512yes—
1165C22×C4C2514yes—
1166C22×C4C2514yes—
1167C22×C4C2514yes—
1168C22×C4C2512yes—
1169C22×C4C2512yes—
1170C22×C4C2512yes—
1171C22×C4C2512yes—
1172C22×C4C2514yes—
1173C22×C4C2511yescharacteristic
1174C22×C4C2511yescharacteristic
1175C22×C4C2511yescharacteristic
1176C22×C4C2511yescharacteristic
1177C22×C4C2511yescharacteristic
1178C22×C4C2512yes—
1179C22×C4C2512yes—
1180C22×C4C2512yes—
1181C22×C4C2511yescharacteristic
1182C4⋊C4—24no—
1183C4⋊C4—24no—
1184C4⋊C4—24no—
1185C4⋊C4—24no—
1186C4⋊C4—24no—
1187C4⋊C4—22no—
1188C4⋊C4—22no—
1189C4⋊C4—22no—
1190C4⋊C4—22no—
1191C4⋊C4—24no—
1192C4⋊C4—24no—
1193C4⋊C4—22no—
1194C4⋊C4—22no—
1195C4⋊C4—24no—
1196C4⋊C4—24no—
1197C4⋊C4—24no—
1198C4⋊C4—24no—
1199C4⋊C4—24no—
1200C4⋊C4—24no—
1201C4⋊C4—24no—
1202C4⋊C4—24no—
1203C4⋊C4—24no—
1204C4⋊C4—28no—
1205C4⋊C4—28no—
1206C4⋊C4—28no—
1207C4⋊C4—24no—
1208C4⋊C4—24no—
1209C4⋊C4—24no—
1210C4⋊C4—44no—
1211C4⋊C4—42no—
1212C4⋊C4—44no—
1213C4⋊C4—44no—
1214C4⋊C4—44no—
1215C4⋊C4—44no—
1216C4⋊C4—44no—
1217C4⋊C4—44no—
1218C4⋊C4—42no—
1219C4⋊C4—44no—
1220C4⋊C4—44no—
1221C4⋊C4—44no—
1222C4⋊C4—44no—
1223C4⋊C4—44no—
1224C4⋊C4—44no—
1225C4⋊C4—44no—
1226C4⋊C4—44no—
1227C4⋊C4—44no—
1228C4⋊C4—44no—
1229C4⋊C4—44no—
1230C4⋊C4—42no—
1231C4⋊C4—42no—
1232C4⋊C4—44no—
1233C4⋊C4—44no—
1234C4⋊C4—44no—
1235C4⋊C4—44no—
1236C22⋊C4—24no—
1237C22⋊C4—24no—
1238C22⋊C4—24no—
1239C22⋊C4—24no—
1240C22⋊C4—24no—
1241C22⋊C4—24no—
1242C22⋊C4—24no—
1243C22⋊C4—24no—
1244C22⋊C4—24no—
1245C22⋊C4—24no—
1246C22⋊C4—24no—
1247C22⋊C4—24no—
1248C22⋊C4—24no—
1249C22⋊C4—24no—
1250C22⋊C4—24no—
1251C22⋊C4—24no—
1252C22⋊C4—24no—
1253C22⋊C4—28no—
1254C22⋊C4—24no—
1255C22⋊C4—28no—
1256C22⋊C4—24no—
1257C22⋊C4—28no—
1258C22⋊C4—28no—
1259C22⋊C4—24no—
1260C22⋊C4—28no—
1261C22⋊C4—42no—
1262C22⋊C4—44no—
1263C22⋊C4—44no—
1264C22⋊C4—44no—
1265C22⋊C4—42no—
1266C22⋊C4—44no—
1267C22⋊C4—44no—
1268C22⋊C4—44no—
1269C22⋊C4—44no—
1270C22⋊C4—44no—
1271C22⋊C4—44no—
1272C22⋊C4—44no—
1273C22⋊C4—44no—
1274C22⋊C4—44no—
1275C22⋊C4—44no—
1276C22⋊C4—44no—
1277C22⋊C4—44no—
1278C22⋊C4—44no—
1279C22⋊C4—44no—
1280C22⋊C4—44no—
1281C22⋊C4—44no—
1282C22⋊C4—44no—
1283C22⋊C4—44no—
1284C22⋊C4—42no—
1285C22⋊C4—42no—
1286C22⋊C4—44no—
1287C22⋊C4—44no—
1288C22⋊C4—44no—
1289C22⋊C4—44no—
1290C22⋊C4—44no—
1291C22⋊C4—44no—
1292C42—24no—
1293C42—24no—
1294C42—24no—
1295C42—22no—
1296C42—24no—
1297C42—24no—
1298C42—24no—
1299C42—22no—
1300C42—24no—
1301C42—28no—
1302C42—24no—
1303C42—42no—
1304C42—44no—
1305C42—44no—
1306C42—44no—
1307C42—42no—
1308C42—42no—
1309C42—42no—
1310C42—42no—
1311C42—42no—
1312C42—42no—
1313C42—44no—
1314C42—42no—
1315C42—42no—
1316C42—44no—
1317C42—42no—
1318C42C2×#4114yes—
1319C42C2×#4114yes—
1320C42C2×#4114yes—
1321C42C2×#4114yes—
1322C42H(5,𝔽2)14yes—
1323C422−1+414yes—
1324C23—21no—
1325C23—21no—
1326C23—22no—
1327C23—22no—
1328C23—22no—
1329C23—22no—
1330C23—22no—
1331C23—22no—
1332C23—22no—
1333C23—22no—
1334C23—22no—
1335C23—22no—
1336C23—22no—
1337C23—22no—
1338C23—22no—
1339C23—22no—
1340C23—22no—
1341C23—24no—
1342C23—24no—
1343C23—24no—
1344C23—22no—
1345C23—22no—
1346C23—24no—
1347C23—24no—
1348C23—24no—
1349C23—22no—
1350C23C22×#4112yes—
1351C23C2611yescharacteristic
1352Q8—44no—
1353Q8—48no—
1354Q8—44no—
1355Q8—88no—
1356Q8—164no—
1357D4—48no—
1358D4—44no—
1359D4—48no—
1360D4—48no—
1361D4—44no—
1362D4—44no—
1363D4—44no—
1364D4—88no—
1365D4—88no—
1366D4—84no—
1367D4—84no—
1368D4—84no—
1369D4—164no—
1370D4—164no—
1371D4—164no—
1372C2×C4—21no—
1373C2×C4—22no—
1374C2×C4—21no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—28no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—22no—
1397C2×C4—24no—
1398C2×C4—24no—
1399C2×C4—24no—
1400C2×C4—22no—
1401C2×C4—24no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—22no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—24no—
1408C2×C4—22no—
1409C2×C4—24no—
1410C2×C4—22no—
1411C2×C4—22no—
1412C2×C4—22no—
1413C2×C4—22no—
1414C2×C4—22no—
1415C2×C4—24no—
1416C2×C4—24no—
1417C2×C4—24no—
1418C2×C4—22no—
1419C2×C4—22no—
1420C2×C4—22no—
1421C2×C4—22no—
1422C2×C4—24no—
1423C2×C4—24no—
1424C2×C4—22no—
1425C2×C4—24no—
1426C2×C4—24no—
1427C2×C4—24no—
1428C2×C4—24no—
1429C2×C4—22no—
1430C2×C4—22no—
1431C2×C4—24no—
1432C2×C4—44no—
1433C2×C4—44no—
1434C2×C4—48no—
1435C2×C4—48no—
1436C2×C4—84no—
1437C2×C4—84no—
1438C2×C4—84no—
1439C2×C4—84no—
1440C2×C4—164no—
1441C2×C4—164no—
1442C2×C4—164no—
1443C2×C4—164no—
1444C2×C4C22×#4112yes—
1445C2×C4C22×#4112yes—
1446C2×C4C22×#4112yes—
1447C2×C4C22×#4112yes—
1448C2×C4C22×#4112yes—
1449C2×C4C22×#4112yes—
1450C2×C4C2×H(5,𝔽2)14yes—
1451C2×C4C2×H(5,𝔽2)12yes—
1452C2×C4C2×2−1+414yes—
1453C2×C4C2×2−1+412yes—
1454C2×C4#58514yes—
1455C22—22no—
1456C22—22no—
1457C22—22no—
1458C22—42no—
1459C22—42no—
1460C22—42no—
1461C22—42no—
1462C22—42no—
1463C22—42no—
1464C22—42no—
1465C22—42no—
1466C22—42no—
1467C22—42no—
1468C22—42no—
1469C22—42no—
1470C22—42no—
1471C22—42no—
1472C22—42no—
1473C22—42no—
1474C22—44no—
1475C22—44no—
1476C22—44no—
1477C22—44no—
1478C22—44no—
1479C22—44no—
1480C22—42no—
1481C22—42no—
1482C22C23×#4111yescharacteristic
1483C22C22×H(5,𝔽2)11yescharacteristic
1484C22C22×2−1+411yescharacteristic
1485C22C2×#58512yes—
1486C22H(7,𝔽2)12yes—
1487C4—22no—
1488C4—22no—
1489C4—22no—
1490C4—22no—
1491C4—22no—
1492C4—24no—
1493C4—24no—
1494C4—24no—
1495C4—42no—
1496C4—42no—
1497C4—42no—
1498C4—42no—
1499C4—42no—
1500C4—42no—
1501C4—42no—
1502C4—42no—
1503C4—42no—
1504C4—42no—
1505C4—42no—
1506C4—42no—
1507C4—44no—
1508C4—44no—
1509C4—44no—
1510C4—44no—
1511C4—42no—
1512C4#351114yes—
1513C2—42no—
1514C2—82no—
1515C2—82no—
1516C2—82no—
1517C2—82no—
1518C2#6268611yescharacteristic
1519C2C2×#351111yescharacteristic
1520C2#6285511yescharacteristic
1521C2#6295812yes—
1522C2#6296112yes—
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. #42229C2semidirect
2. #42060C2semidirect
3. #41972C2semidirect
4. #41026C2semidirect
5. #41012C2semidirect
6. #40554C2semidirect
7. #39630C2semidirect
8. #39628C2semidirect
9. #39426C2semidirect
10. #39424C2semidirect
11. #39374C2semidirect
12. #39372C2semidirect
13. #37946C2semidirect
14. #37944C2semidirect
15. #37593C2semidirect
16. #37591C2semidirect
17. #37554C2semidirect
18. #37553C2semidirect
19. #36609C2semidirect
20. #36601C2semidirect
21. #36211C2semidirect
22. #36195C2semidirect
23. #36003C2semidirect
24. #35744C2semidirect
25. #35330C2semidirect
26. #35276C2semidirect
27. #34625C2semidirect
28. #34624C2semidirect
29. #34229C2semidirect
30. #34226C2semidirect
31. #34151C2semidirect

Maximal subgroups

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

subgroupindex
#422292
#420602
#419722
#410262
#410122
#405542
#396302
#396282
#394262
#394242
#393742
#393722
#379462
#379442
#375932
#375912
#375542
#375532
#366092
#366012
#362112
#361952
#360032
#357442
#353302
#352762
#346252
#346242
#342292
#342262
#341512