Finite Group Databasebeta

← #7658072

Subgroups — #7658072

Order 512.

4699 conjugacy classes of subgroups.

The subgroup lattice has 1444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41565C214yesmaximal, complemented
2#41541C214yesmaximal, complemented
3#41509C214yesmaximal, complemented
4#41502C214yesmaximal, complemented
5#41495C214yesmaximal, complemented
6#41492C214yesmaximal, complemented
7#39766C211yesmaximal, characteristic, complemented
8#39757C211yesmaximal, characteristic, complemented
9#38937C212yesmaximal, complemented
10#38060C212yesmaximal, complemented
11#38055C212yesmaximal, complemented
12#37709C211yesmaximal, characteristic, complemented
13#37706C211yesmaximal, characteristic, complemented
14#37700C211yesmaximal, characteristic, complemented
15#37695C211yesmaximal, characteristic, complemented
16#37581C212yesmaximal, complemented
17#37500C212yesmaximal, complemented
18#37494C212yesmaximal, complemented
19#36374C212yesmaximal, complemented
20#36131C211yesmaximal, characteristic, complemented
21#36122C211yesmaximal, characteristic, complemented
22#35965C214yesmaximal, complemented
23#35892C214yesmaximal, complemented
24#35332C211yesmaximal, characteristic, complemented
25#35315C211yesmaximal, characteristic, complemented
26#35271C211yesmaximal, characteristic, complemented
27#34637C211yesmaximal, characteristic, complemented
28#34629C211yesmaximal, characteristic, complemented
29C2×#2642C211yesmaximal, characteristic, complemented
30#34327C212yesmaximal, complemented
31#34123C211yesmaximal, characteristic, complemented
32C2×#548C2212yes—
33C2×#541C2211yescharacteristic
34C2×#540C2211yescharacteristic
35C2×#533C2211yescharacteristic
36C2×#532C2211yescharacteristic
37C22×C4⋊Q8C2211yescharacteristic
38C22×#125C2211yescharacteristic
39C2×C4×#41C2211yescharacteristic
40#2859C2211yescharacteristic
41#2858C2211yescharacteristic
42#2857C2211yescharacteristic
43#2856C2211yescharacteristic
44#2855C2212yes—
45#2854C2212yes—
46#2851C2211yescharacteristic
47#2851C2211yescharacteristic
48#2850C2212yes—
49#2838C2214yes—
50#2832C2214yes—
51#2831C2214yes—
52#2831C2214yes—
53#2827C2214yes—
54#2826C2214yes—
55#2810C2214yes—
56#2805C2214yes—
57#2796C2214yes—
58#2784C2214yes—
59#2781C2214yes—
60#2775C2214yes—
61#2764C2214yes—
62#2763C2214yes—
63#2759C2214yes—
64#2754C2214yes—
65#2751C2214yes—
66#2750C2214yes—
67#2746C2214yes—
68#2744C2214yes—
69#2743C2214yes—
70#2743C2214yes—
71#2716C2214yes—
72#2713C2214yes—
73#2711C2214yes—
74#2708C2214yes—
75#2707C2214yes—
76#2702C2214yes—
77#2690C2214yes—
78#2688C2214yes—
79#2665C2214yes—
80#2665C2214yes—
81#2655C2214yes—
82#2654C2214yes—
83#2653C2214yes—
84#2652C2214yes—
85#2652C2214yes—
86#2652C2214yes—
87#2650C2214yes—
88#2649C2214yes—
89#2649C2214yes—
90#2648C2214yes—
91#2647C2211yescharacteristic
92#2645C2212yes—
93#2645C2212yes—
94#2644C2212yes—
95#2643C2214yes—
96#2642C2211yescharacteristic
97#2642C2212yes—
98#2642C2214yes—
99#2642C2214yes—
100#2642C2211yescharacteristic
101#2642C2211yescharacteristic
102#2642C2211yescharacteristic
103#2642C2211yescharacteristic
104#2642C2212yes—
105#2641C2211yescharacteristic
106#2641C2211yescharacteristic
107#2640C2212yes—
108#2640C2212yes—
109#2639C2214yes—
110#2639C2214yes—
111#2639C2214yes—
112#2629C2211yescharacteristic
113#2625C2212yes—
114#2621C2211yescharacteristic
115#2620C2212yes—
116#2597C2214yes—
117#2595C2214yes—
118#2592C2212yes—
119#2587C2214yes—
120#2581C2212yes—
121#2575C2214yes—
122#2573C2214yes—
123#2572C2214yes—
124#2564C2214yes—
125#2559C2214yes—
126#2559C2214yes—
127#2558C2214yes—
128#2558C2214yes—
129#2556C2214yes—
130#2550C2212yes—
131#2545C2212yes—
132#2533C2214yes—
133#2533C2214yes—
134#2533C2214yes—
135#2532C2214yes—
136#2531C2214yes—
137#2530C2214yes—
138#2528C2214yes—
139#2527C2214yes—
140#2526C2214yes—
141#2526C2214yes—
142#2516C2214yes—
143#2511C2212yes—
144#2511C2212yes—
145#2510C2214yes—
146#2505C2214yes—
147#2505C2214yes—
148#2495C2214yes—
149#2493C2214yes—
150#2493C2214yes—
151#2492C2212yes—
152#2491C2214yes—
153#2490C2212yes—
154#2488C2214yes—
155#2481C2214yes—
156#2477C2214yes—
157#2474C2214yes—
158#2473C2214yes—
159#2469C2214yes—
160#2465C2214yes—
161#2462C2214yes—
162#2459C2214yes—
163#2454C2212yes—
164#2453C2214yes—
165#2452C2214yes—
166#2451C2212yes—
167#2450C2214yes—
168#2449C2214yes—
169#2448C2212yes—
170#2447C2212yes—
171#2447C2212yes—
172#2446C2212yes—
173#2444C2214yes—
174#2444C2214yes—
175#2444C2214yes—
176#2444C2214yes—
177#2443C2214yes—
178#2441C2212yes—
179#2440C2212yes—
180#2436C2212yes—
181#2432C2212yes—
182#2430C2214yes—
183#2429C2212yes—
184#2427C2212yes—
185#2425C2214yes—
186#2419C2214yes—
187#2419C2214yes—
188#2416C2214yes—
189#2416C2212yes—
190#2416C2214yes—
191#2415C2212yes—
192#2409C2212yes—
193#2407C2212yes—
194#2402C2214yes—
195#2401C2214yes—
196#2398C2214yes—
197#2398C2214yes—
198C2×#400C2214yes—
199C2×#400C2214yes—
200#2372C2214yes—
201#2368C2214yes—
202#2367C2212yes—
203#2364C2214yes—
204#2364C2214yes—
205#2362C2212yes—
206#2361C2212yes—
207#2361C2214yes—
208#2360C2214yes—
209#2359C2214yes—
210#2356C2212yes—
211#2356C2212yes—
212#2353C2214yes—
213#2353C2212yes—
214#2353C2212yes—
215#2352C2212yes—
216#2349C2212yes—
217#2346C2212yes—
218#2343C2212yes—
219#2343C2212yes—
220Q8×C22⋊C4C2212yes—
221#2339C2212yes—
222#2339C2212yes—
223#2337C2214yes—
224#2332C2214yes—
225#2330C2211yescharacteristic
226#2330C2211yescharacteristic
227#2328C2211yescharacteristic
228#2327C2211yescharacteristic
229#2326C2212yes—
230#2325C2214yes—
231#2320C2212yes—
232#2319C2212yes—
233C4×C4⋊Q8C2211yescharacteristic
234C4×#125C2211yescharacteristic
235C4×#124C2212yes—
236C4×C22⋊Q8C2212yes—
237C4×C22⋊Q8C2212yes—
238C4×#121C2212yes—
239#2297C2212yes—
240#2297C2212yes—
241#2295C2212yes—
242#2295C2211yescharacteristic
243#2295C2211yescharacteristic
244C2×#391C2212yes—
245C2×#391C2212yes—
246#2290C2211yescharacteristic
247#2290C2211yescharacteristic
248#2290C2211yescharacteristic
249#2290C2211yescharacteristic
250#2283C2211yescharacteristic
251#2283C2211yescharacteristic
252#2283C2211yescharacteristic
253#2275C2214yes—
254C42×D4C2211yescharacteristic
255C42×D4C2211yescharacteristic
256C4×#117C2211yescharacteristic
257C2×#376C2211yescharacteristic
258C2×#376C2211yescharacteristic
259C22×#41C2311yescharacteristic
260C22×#41C2312yes—
261C23×Q8C2312yes—
262#548—216no—
263#541—44no—
264#540—44no—
265#533—44no—
266#532—44no—
267C2×C4⋊Q8—44no—
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2314yes—
273C2×#127C2311yescharacteristic
274C2×#126C2314yes—
275C2×#125—44no—
276C2×#125C2311yescharacteristic
277C2×#125C2311yescharacteristic
278C2×#125C2311yescharacteristic
279C2×#125C2312yes—
280C2×#125C2314yes—
281C2×#125C2314yes—
282C2×#124C2312yes—
283C2×#124C2314yes—
284C2×#124C2312yes—
285C2×#124C2312yes—
286C2×#123C2314yes—
287C2×#123C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2314yes—
294C2×#121C2314yes—
295C2×#121C2312yes—
296C2×#121C2312yes—
297C2×#121C2314yes—
298C2×#121C2314yes—
299C2×#121C2314yes—
300C2×#121C2314yes—
301C4×#41—28no—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2314yes—
308C2×C4×D4C2311yescharacteristic
309C2×C4×D4C2311yescharacteristic
310C2×C4×D4C2311yescharacteristic
311C2×C4×D4C2314yes—
312C2×C4×D4C2311yescharacteristic
313C2×C4×D4C2311yescharacteristic
314C2×C4×D4C2314yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2314yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2314yes—
321C2×C4×D4C2311yescharacteristic
322C2×#117C2311yescharacteristic
323C2×#117C2311yescharacteristic
324C2×#117C2311yescharacteristic
325C2×#117C2311yescharacteristic
326C2×#117C2312yes—
327C2×#117C2311yescharacteristic
328C22×C4⋊C4C2312yes—
329C22×C4⋊C4C2314yes—
330C22×C4⋊C4C2314yes—
331C22×C42C2311yescharacteristic
332C22×C42C2311yescharacteristic
333C22×C42C2311yescharacteristic
334C22×C42C2311yescharacteristic
335C22×C42C2311yescharacteristic
336C22×C42C2311yescharacteristic
337C22×C42C2311yescharacteristic
338#401C2314yes—
339#401C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#400C2314yes—
372#400C2314yes—
373#399C2314yes—
374#399C2314yes—
375#399C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#395C2314yes—
415#395C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#393C2314yes—
433#393C2314yes—
434#393C2314yes—
435#393C2314yes—
436#393C2314yes—
437#393C2314yes—
438#393C2314yes—
439#393C2314yes—
440#393C2314yes—
441#392C2314yes—
442#391C2312yes—
443#391C2314yes—
444#391C2312yes—
445#391C2314yes—
446#391C2312yes—
447#391C2312yes—
448#391C2312yes—
449#391C2312yes—
450#391C2312yes—
451#391C2314yes—
452#391C2314yes—
453#391C2312yes—
454#391C2314yes—
455#391C2312yes—
456#391C2312yes—
457#391C2312yes—
458#391C2312yes—
459#391C2312yes—
460#391C2312yes—
461#391C2312yes—
462#391C2312yes—
463#391C2314yes—
464#391C2314yes—
465#391C2314yes—
466#391C2314yes—
467#390C2312yes—
468#390C2312yes—
469#390C2312yes—
470#390C2312yes—
471#390C2314yes—
472#390C2314yes—
473#390C2314yes—
474#390C2314yes—
475#390C2312yes—
476#390C2312yes—
477#389C2312yes—
478#389C2314yes—
479#389C2314yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2312yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2312yes—
496#389C2312yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2312yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2312yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2312yes—
524#388C2312yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2312yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2312yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2312yes—
555#387C2314yes—
556#387C2314yes—
557#387C2312yes—
558#387C2312yes—
559#387C2312yes—
560#387C2312yes—
561#387C2312yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2312yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2312yes—
580#386C2312yes—
581#386C2312yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2312yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2312yes—
603#385C2312yes—
604#385C2312yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#384C2311yescharacteristic
611#384C2312yes—
612#383C2314yes—
613#383C2314yes—
614#383C2312yes—
615#383C2312yes—
616#383C2312yes—
617#382C2311yescharacteristic
618#382C2312yes—
619#382C2314yes—
620#382C2312yes—
621#382C2312yes—
622#382C2312yes—
623#381C2312yes—
624#381C2314yes—
625#381C2314yes—
626#381C2312yes—
627#381C2312yes—
628#381C2314yes—
629#381C2314yes—
630#381C2314yes—
631#380C2312yes—
632#380C2314yes—
633#380C2314yes—
634#380C2312yes—
635#380C2312yes—
636#380C2312yes—
637#380C2314yes—
638#380C2312yes—
639#380C2312yes—
640#380C2314yes—
641#380C2314yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2314yes—
645C4×C4⋊C4C2314yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2311yescharacteristic
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2311yescharacteristic
657C4×C4⋊C4C2311yescharacteristic
658C4×C4⋊C4C2311yescharacteristic
659C4×C4⋊C4C2311yescharacteristic
660C4×C4⋊C4C2311yescharacteristic
661C4×C22⋊C4C2314yes—
662C4×C22⋊C4C2314yes—
663C4×C22⋊C4C2314yes—
664C4×C22⋊C4C2314yes—
665C4×C22⋊C4C2314yes—
666C4×C22⋊C4C2314yes—
667C4×C22⋊C4C2312yes—
668C4×C22⋊C4C2314yes—
669C4×C22⋊C4C2311yescharacteristic
670C4×C22⋊C4C2312yes—
671C4×C22⋊C4C2311yescharacteristic
672C4×C22⋊C4C2314yes—
673C4×C22⋊C4C2312yes—
674C4×C22⋊C4C2312yes—
675C4×C22⋊C4C2312yes—
676C4×C22⋊C4C2314yes—
677C4×C22⋊C4C2312yes—
678C4×C22⋊C4C2314yes—
679C4×C22⋊C4C2314yes—
680C4×C22⋊C4C2314yes—
681C4×C22⋊C4C2311yescharacteristic
682C4×C22⋊C4C2311yescharacteristic
683C4×C22⋊C4C2311yescharacteristic
684C4×C22⋊C4C2311yescharacteristic
685#376C2311yescharacteristic
686#376C2311yescharacteristic
687#376C2311yescharacteristic
688#376C2311yescharacteristic
689#376C2311yescharacteristic
690#376C2312yes—
691#376C2312yes—
692#376C2312yes—
693#376C2312yes—
694#376C2314yes—
695#376C2314yes—
696#376C2311yescharacteristic
697#376C2311yescharacteristic
698#376C2311yescharacteristic
699C2×#95C2314yes—
700C2×#95C2314yes—
701C2×#95C2312yes—
702C2×#95C2312yes—
703C2×#95C2314yes—
704C2×#95C2312yes—
705C2×#95C2312yes—
706C2×#95C2314yes—
707C2×#95C2314yes—
708C43C2311yescharacteristic
709C43C2311yescharacteristic
710C2×#41—24no—
711C2×#41—28no—
712C2×#41—44no—
713C2×#41—44no—
714C2×#41—44no—
715C22×Q8—28no—
716C22×Q8—44no—
717C22×Q8—44no—
718C22×Q8C2412yes—
719C22×Q8C2412yes—
720C22×Q8C2411yescharacteristic
721C22×Q8C2414yes—
722C22×Q8C2414yes—
723C22×D4C2414yes—
724C22×D4C2411yescharacteristic
725C22×D4C2412yes—
726C22×D4C2411yescharacteristic
727C22×D4C2411yescharacteristic
728C22×D4C2414yes—
729C22×D4C2414yes—
730C22×D4C2414yes—
731C23×C4C2411yescharacteristic
732C23×C4C2411yescharacteristic
733C23×C4C2412yes—
734C23×C4C2411yescharacteristic
735C23×C4C2411yescharacteristic
736C23×C4C2414yes—
737C23×C4C2414yes—
738C23×C4C2411yescharacteristic
739C23×C4C2411yescharacteristic
740C23×C4C2414yes—
741C23×C4C2412yes—
742C23×C4C2411yescharacteristic
743C23×C4C2411yescharacteristic
744C23×C4C2411yescharacteristic
745C23×C4C2412yes—
746C23×C4C2414yes—
747C23×C4C2414yes—
748C23×C4C2412yes—
749C4⋊Q8—24no—
750C4⋊Q8—24no—
751C4⋊Q8—48no—
752C4⋊Q8—44no—
753C4⋊Q8—44no—
754#127—24no—
755#126—48no—
756#125—24no—
757#125—24no—
758#125—24no—
759#125—44no—
760#125—48no—
761#125—48no—
762#124—216no—
763#124—28no—
764#124—44no—
765#124—44no—
766#123—48no—
767#123—48no—
768C22⋊Q8—28no—
769C22⋊Q8—216no—
770C22⋊Q8—48no—
771C22⋊Q8—48no—
772C22⋊Q8—44no—
773C22⋊Q8—44no—
774#121—216no—
775#121—28no—
776#121—48no—
777#121—48no—
778#121—44no—
779#121—48no—
780#121—48no—
781C4×Q8—24no—
782C4×Q8—24no—
783C4×Q8—28no—
784C4×Q8—48no—
785C4×Q8—44no—
786C4×Q8—44no—
787C4×D4—24no—
788C4×D4—24no—
789C4×D4—24no—
790C4×D4—24no—
791C4×D4—24no—
792C4×D4—216no—
793C4×D4—44no—
794C4×D4—48no—
795C4×D4—44no—
796C4×D4—44no—
797C4×D4—48no—
798C4×D4—44no—
799C4×D4—48no—
800C4×D4#4118yes—
801#117—24no—
802#117—24no—
803#117—24no—
804#117—24no—
805#117—42no—
806#117—44no—
807C2×C4⋊C4—44no—
808C2×C4⋊C4—48no—
809C2×C4⋊C4—48no—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2411yescharacteristic
817C2×C4⋊C4C2411yescharacteristic
818C2×C4⋊C4C2411yescharacteristic
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2411yescharacteristic
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2411yescharacteristic
857C2×C22⋊C4C2411yescharacteristic
858C2×C22⋊C4C2411yescharacteristic
859C2×C22⋊C4C2411yescharacteristic
860C2×C22⋊C4C2411yescharacteristic
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2411yescharacteristic
899C2×C22⋊C4C2411yescharacteristic
900C2×C42—24no—
901C2×C42—24no—
902C2×C42—24no—
903C2×C42—24no—
904C2×C42—24no—
905C2×C42—42no—
906C2×C42—42no—
907C2×C42C2411yescharacteristic
908C2×C42C2411yescharacteristic
909C2×C42C2411yescharacteristic
910C2×C42C2411yescharacteristic
911C2×C42C2411yescharacteristic
912C2×C42C2411yescharacteristic
913C2×C42C2412yes—
914C2×C42C2411yescharacteristic
915C2×C42C2414yes—
916C2×C42C2411yescharacteristic
917C2×C42C2411yescharacteristic
918C2×C42C2411yescharacteristic
919C2×C42C2411yescharacteristic
920C2×C42C2411yescharacteristic
921C2×C42C2411yescharacteristic
922C2×C42C2411yescharacteristic
923C2×C42C2411yescharacteristic
924C2×C42C2412yes—
925C2×C42C2411yescharacteristic
926C2×C42C2414yes—
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2414yes—
930C2×C42C2414yes—
931C2×C42C2414yes—
932C2×C42C2414yes—
933C2×C42C2412yes—
934C2×C42C2412yes—
935C2×C42C2412yes—
936C2×C42C2412yes—
937C2×C42C2414yes—
938C2×C42C2411yescharacteristic
939C2×C42C2411yescharacteristic
940#95C2412yes—
941#95C2412yes—
942#95C2414yes—
943#95C2412yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2412yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2412yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2412yes—
978#95C2412yes—
979#95C2414yes—
980#95C2414yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2412yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2412yes—
994#95C2414yes—
995#95C2414yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013C24C2514yes—
1014C24C2511yescharacteristic
1015C24C2511yescharacteristic
1016C24C2511yescharacteristic
1017#41—416no—
1018#41—816no—
1019C2×Q8—22no—
1020C2×Q8—24no—
1021C2×Q8—24no—
1022C2×Q8—28no—
1023C2×Q8—24no—
1024C2×Q8—24no—
1025C2×Q8—24no—
1026C2×Q8—24no—
1027C2×Q8—42no—
1028C2×Q8—44no—
1029C2×Q8—44no—
1030C2×Q8—44no—
1031C2×Q8—44no—
1032C2×Q8—44no—
1033C2×Q8—816no—
1034C2×D4—24no—
1035C2×D4—22no—
1036C2×D4—22no—
1037C2×D4—28no—
1038C2×D4—28no—
1039C2×D4—28no—
1040C2×D4—24no—
1041C2×D4—28no—
1042C2×D4—24no—
1043C2×D4—24no—
1044C2×D4—28no—
1045C2×D4—24no—
1046C2×D4—42no—
1047C2×D4—44no—
1048C2×D4—44no—
1049C2×D4—44no—
1050C2×D4—44no—
1051C2×D4—44no—
1052C2×D4—44no—
1053C2×D4—44no—
1054C2×D4C2×#4114yes—
1055C22×C4—22no—
1056C22×C4—22no—
1057C22×C4—22no—
1058C22×C4—22no—
1059C22×C4—22no—
1060C22×C4—22no—
1061C22×C4—24no—
1062C22×C4—24no—
1063C22×C4—22no—
1064C22×C4—22no—
1065C22×C4—28no—
1066C22×C4—24no—
1067C22×C4—28no—
1068C22×C4—22no—
1069C22×C4—22no—
1070C22×C4—24no—
1071C22×C4—22no—
1072C22×C4—22no—
1073C22×C4—22no—
1074C22×C4—28no—
1075C22×C4—24no—
1076C22×C4—42no—
1077C22×C4—42no—
1078C22×C4—42no—
1079C22×C4—42no—
1080C22×C4—42no—
1081C22×C4—44no—
1082C22×C4—44no—
1083C22×C4—44no—
1084C22×C4—42no—
1085C22×C4—42no—
1086C22×C4—42no—
1087C22×C4—42no—
1088C22×C4—42no—
1089C22×C4—42no—
1090C22×C4—44no—
1091C22×C4—42no—
1092C22×C4—42no—
1093C22×C4—44no—
1094C22×C4—44no—
1095C22×C4—44no—
1096C22×C4—44no—
1097C22×C4—44no—
1098C22×C4—44no—
1099C22×C4—44no—
1100C22×C4—44no—
1101C22×C4C2×#4114yes—
1102C22×C4C2×#4114yes—
1103C22×C4C2511yescharacteristic
1104C22×C4C2512yes—
1105C22×C4C2512yes—
1106C22×C4C2511yescharacteristic
1107C22×C4C2511yescharacteristic
1108C22×C4C2511yescharacteristic
1109C22×C4C2511yescharacteristic
1110C22×C4C2511yescharacteristic
1111C22×C4C2514yes—
1112C22×C4C2512yes—
1113C22×C4C2514yes—
1114C22×C4C2512yes—
1115C22×C4C2514yes—
1116C22×C4C2512yes—
1117C22×C4C2512yes—
1118C22×C4C2514yes—
1119C22×C4C2514yes—
1120C22×C4C2514yes—
1121C22×C4C2514yes—
1122C22×C4C2512yes—
1123C22×C4C2511yescharacteristic
1124C22×C4C2511yescharacteristic
1125C22×C4C2511yescharacteristic
1126C22×C4C2511yescharacteristic
1127C22×C4C2511yescharacteristic
1128C22×C4C2512yes—
1129C22×C4C2511yescharacteristic
1130C4⋊C4—22no—
1131C4⋊C4—22no—
1132C4⋊C4—22no—
1133C4⋊C4—22no—
1134C4⋊C4—22no—
1135C4⋊C4—28no—
1136C4⋊C4—24no—
1137C4⋊C4—28no—
1138C4⋊C4—24no—
1139C4⋊C4—24no—
1140C4⋊C4—28no—
1141C4⋊C4—28no—
1142C4⋊C4—28no—
1143C4⋊C4—28no—
1144C4⋊C4—24no—
1145C4⋊C4—24no—
1146C4⋊C4—28no—
1147C4⋊C4—24no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—42no—
1155C4⋊C4—42no—
1156C4⋊C4—44no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—42no—
1160C4⋊C4—42no—
1161C4⋊C4—42no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4C2×#4114yes—
1177C22⋊C4—22no—
1178C22⋊C4—22no—
1179C22⋊C4—28no—
1180C22⋊C4—24no—
1181C22⋊C4—24no—
1182C22⋊C4—28no—
1183C22⋊C4—22no—
1184C22⋊C4—22no—
1185C22⋊C4—28no—
1186C22⋊C4—28no—
1187C22⋊C4—28no—
1188C22⋊C4—24no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—42no—
1195C22⋊C4—44no—
1196C22⋊C4—42no—
1197C22⋊C4—42no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—42no—
1202C22⋊C4—44no—
1203C22⋊C4—42no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—44no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4—44no—
1218C22⋊C4C2×#4114yes—
1219C22⋊C4C2×#4114yes—
1220C42—22no—
1221C42—22no—
1222C42—22no—
1223C42—22no—
1224C42—22no—
1225C42—22no—
1226C42—22no—
1227C42—22no—
1228C42—22no—
1229C42—28no—
1230C42—24no—
1231C42—22no—
1232C42—24no—
1233C42—22no—
1234C42—22no—
1235C42—22no—
1236C42—22no—
1237C42—22no—
1238C42—22no—
1239C42—42no—
1240C42—42no—
1241C42—42no—
1242C42—44no—
1243C42—42no—
1244C42—44no—
1245C42—42no—
1246C42—42no—
1247C42—44no—
1248C42—44no—
1249C42—44no—
1250C42—44no—
1251C42C2×#4114yes—
1252C42H(5,𝔽2)14yes—
1253C23—21no—
1254C23—21no—
1255C23—22no—
1256C23—21no—
1257C23—22no—
1258C23—21no—
1259C23—22no—
1260C23—24no—
1261C23—21no—
1262C23—21no—
1263C23—24no—
1264C23—21no—
1265C23—24no—
1266C23—24no—
1267C23—24no—
1268C23—22no—
1269C23—24no—
1270C23—24no—
1271C23—22no—
1272C23C22×#4112yes—
1273C23C22×#4112yes—
1274C23#58514yes—
1275C23C2611yescharacteristic
1276Q8—44no—
1277Q8—48no—
1278Q8—48no—
1279Q8—88no—
1280Q8—88no—
1281D4—28no—
1282D4—44no—
1283D4—416no—
1284D4—44no—
1285D4—48no—
1286D4—88no—
1287D4—88no—
1288D4—164no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—22no—
1292C2×C4—21no—
1293C2×C4—21no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—28no—
1298C2×C4—28no—
1299C2×C4—21no—
1300C2×C4—21no—
1301C2×C4—21no—
1302C2×C4—21no—
1303C2×C4—21no—
1304C2×C4—21no—
1305C2×C4—21no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—21no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—24no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—24no—
1328C2×C4—24no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—24no—
1333C2×C4—24no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—24no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—24no—
1341C2×C4—21no—
1342C2×C4—24no—
1343C2×C4—22no—
1344C2×C4—24no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—24no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—24no—
1355C2×C4—22no—
1356C2×C4—48no—
1357C2×C4—44no—
1358C2×C4—44no—
1359C2×C4—44no—
1360C2×C4—44no—
1361C2×C4—82no—
1362C2×C4—84no—
1363C2×C4—88no—
1364C2×C4—82no—
1365C2×C4—82no—
1366C2×C4—88no—
1367C2×C4—84no—
1368C2×C4—88no—
1369C2×C4—84no—
1370C2×C4—164no—
1371C2×C4—164no—
1372C2×C4C22×#4112yes—
1373C2×C4C22×#4112yes—
1374C2×C4C22×#4112yes—
1375C2×C4C22×#4112yes—
1376C2×C4C22×#4112yes—
1377C2×C4C2×H(5,𝔽2)14yes—
1378C2×C4C2×H(5,𝔽2)12yes—
1379C2×C4#58512yes—
1380C22—22no—
1381C22—22no—
1382C22—24no—
1383C22—24no—
1384C22—22no—
1385C22—22no—
1386C22—22no—
1387C22—42no—
1388C22—42no—
1389C22—41no—
1390C22—44no—
1391C22—41no—
1392C22—44no—
1393C22—41no—
1394C22—44no—
1395C22—44no—
1396C22—44no—
1397C22—42no—
1398C22—44no—
1399C22—42no—
1400C22—44no—
1401C22#345514yes—
1402C22C23×#4111yescharacteristic
1403C22C22×H(5,𝔽2)11yescharacteristic
1404C22C2×#58511yescharacteristic
1405C22C2×#58512yes—
1406C222−1+612yes—
1407C4—22no—
1408C4—22no—
1409C4—22no—
1410C4—22no—
1411C4—24no—
1412C4—41no—
1413C4—44no—
1414C4—44no—
1415C4—41no—
1416C4—41no—
1417C4—41no—
1418C4—41no—
1419C4—41no—
1420C4—41no—
1421C4—44no—
1422C4—42no—
1423C4—44no—
1424C4—44no—
1425C4—42no—
1426C4—42no—
1427C4—44no—
1428C4—42no—
1429C4—42no—
1430C4—42no—
1431C4—42no—
1432C4—44no—
1433C4#351414yes—
1434C2—24no—
1435C2—42no—
1436C2—81no—
1437C2—84no—
1438C2C2×#345511yescharacteristic
1439C2C2×#351411yescharacteristic
1440C2#6286111yescharacteristic
1441C2#6295412yes—
1442C2#6297112yes—
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. #41565C2semidirect
2. #41541C2semidirect
3. #41509C2semidirect
4. #41502C2semidirect
5. #41495C2semidirect
6. #41492C2semidirect
7. #39766C2semidirect
8. #39757C2semidirect
9. #38937C2semidirect
10. #38060C2semidirect
11. #38055C2semidirect
12. #37709C2semidirect
13. #37706C2semidirect
14. #37700C2semidirect
15. #37695C2semidirect
16. #37581C2semidirect
17. #37500C2semidirect
18. #37494C2semidirect
19. #36374C2semidirect
20. #36131C2semidirect
21. #36122C2semidirect
22. #35965C2semidirect
23. #35892C2semidirect
24. #35332C2semidirect
25. #35315C2semidirect
26. #35271C2semidirect
27. #34637C2semidirect
28. #34629C2semidirect
29. C2×#2642C2semidirect
30. #34327C2semidirect
31. #34123C2semidirect

Maximal subgroups

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

subgroupindex
#415652
#415412
#415092
#415022
#414952
#414922
#397662
#397572
#389372
#380602
#380552
#377092
#377062
#377002
#376952
#375812
#375002
#374942
#363742
#361312
#361222
#359652
#358922
#353322
#353152
#352712
#346372
#346292
C2×#26422
#343272
#341232