Finite Group Databasebeta

← #7660821

Subgroups — #7660821

Order 512.

4698 conjugacy classes of subgroups.

The subgroup lattice has 1475 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52290C211yesmaximal, characteristic, complemented
2#52281C212yesmaximal, complemented
3#42702C212yesmaximal, complemented
4#42526C212yesmaximal, complemented
5#42519C212yesmaximal, complemented
6#42378C214yesmaximal, complemented
7#41901C214yesmaximal, complemented
8#41780C214yesmaximal, complemented
9#40464C214yesmaximal, complemented
10#40026C212yesmaximal, complemented
11#39768C211yesmaximal, characteristic, complemented
12#39708C212yesmaximal, complemented
13#39640C211yesmaximal, characteristic, complemented
14#39200C212yesmaximal, complemented
15#38860C214yesmaximal, complemented
16#38763C212yesmaximal, complemented
17#37391C212yesmaximal, complemented
18#37299C211yesmaximal, characteristic, complemented
19#37167C212yesmaximal, complemented
20#37078C214yesmaximal, complemented
21#36556C212yesmaximal, complemented
22#36493C211yesmaximal, characteristic
23#36405C211yesmaximal, characteristic, complemented
24#36271C212yesmaximal, complemented
25#35959C212yesmaximal, complemented
26#35860C212yesmaximal, complemented
27#35817C212yesmaximal, complemented
28#34285C212yesmaximal, complemented
29#34268C211yesmaximal, characteristic, complemented
30C2×#559C2211yescharacteristic
31C2×#556C2211yescharacteristic
32C2×#556C2212yes—
33C2×#542C2212yes—
34C2×#536C2211yescharacteristic
35C2×#519C2211yescharacteristic
36C2×C4×#41C2211yescharacteristic
37#2864C2214yes—
38#2862C2212yes—
39#2860C2214yes—
40#2858C2212yes—
41#2857C2211yescharacteristic
42#2856C2211yescharacteristic
43#2855C2212yes—
44#2850C2212yes—
45#2836C2214yes—
46#2831C2214yes—
47#2824C2214yes—
48#2808C2212yes—
49#2806C2211yescharacteristic
50#2806C2212yes—
51#2805C2212yes—
52#2805C2211yescharacteristic
53#2804C2212yes—
54#2803C2214yes—
55#2791C2212yes—
56#2788C2212yes—
57#2786C2214yes—
58#2784C2214yes—
59#2779C2214yes—
60#2777C2214yes—
61#2775C2214yes—
62#2774C2212yes—
63#2774C2214yes—
64#2773C2214yes—
65#2773C2214yes—
66#2773C2214yes—
67#2772C2214yes—
68#2770C2214yes—
69#2768C2214yes—
70#2768C2212yes—
71#2754C2214yes—
72#2754C2214yes—
73#2753C2214yes—
74#2751C2214yes—
75#2738C2214yes—
76#2734C2211yescharacteristic
77#2729C2212yes—
78#2727C2212yes—
79#2727C2212yes—
80#2726C2211yescharacteristic
81#2723C2214yes—
82#2723C2214yes—
83#2720C2212yes—
84#2711C2214yes—
85#2710C2214yes—
86#2710C2214yes—
87#2706C2214yes—
88#2706C2214yes—
89#2701C2214yes—
90#2698C2214yes—
91#2695C2214yes—
92#2692C2214yes—
93#2692C2214yes—
94#2683C2212yes—
95#2683C2212yes—
96#2672C2214yes—
97#2672C2214yes—
98#2667C2214yes—
99#2665C2214yes—
100#2663C2214yes—
101#2658C2212yes—
102#2654C2214yes—
103#2649C2214yes—
104#2648C2214yes—
105#2648C2214yes—
106#2646C2212yes—
107#2640C2212yes—
108#2639C2212yes—
109#2637C2214yes—
110#2637C2214yes—
111#2630C2214yes—
112#2625C2214yes—
113#2620C2212yes—
114#2609C2214yes—
115#2601C2214yes—
116#2601C2214yes—
117#2601C2214yes—
118#2592C2212yes—
119#2592C2212yes—
120#2592C2212yes—
121#2588C2214yes—
122#2588C2214yes—
123#2582C2212yes—
124#2582C2211yescharacteristic
125#2568C2212yes—
126#2567C2212yes—
127#2564C2214yes—
128#2560C2214yes—
129#2560C2214yes—
130#2560C2214yes—
131#2553C2214yes—
132#2553C2214yes—
133#2553C2214yes—
134#2548C2212yes—
135#2547C2212yes—
136#2547C2212yes—
137#2546C2212yes—
138#2546C2211yescharacteristic
139#2546C2212yes—
140#2545C2212yes—
141#2545C2212yes—
142#2545C2212yes—
143#2544C2212yes—
144#2544C2212yes—
145#2544C2212yes—
146#2542C2212yes—
147#2541C2211yescharacteristic
148#2540C2212yes—
149#2538C2211yescharacteristic
150#2535C2212yes—
151#2522C2214yes—
152#2521C2214yes—
153#2521C2214yes—
154#2520C2214yes—
155#2520C2214yes—
156#2516C2214yes—
157#2512C2214yes—
158#2512C2212yes—
159#2511C2212yes—
160#2511C2212yes—
161#2511C2212yes—
162#2509C2214yes—
163#2508C2214yes—
164#2505C2214yes—
165#2498C2214yes—
166#2492C2214yes—
167#2488C2214yes—
168#2485C2212yes—
169#2479C2214yes—
170#2478C2214yes—
171#2477C2214yes—
172#2477C2214yes—
173#2476C2214yes—
174#2471C2214yes—
175#2471C2214yes—
176#2469C2214yes—
177#2468C2214yes—
178#2467C2214yes—
179#2465C2214yes—
180#2465C2214yes—
181#2456C2214yes—
182#2452C2214yes—
183#2450C2214yes—
184#2448C2212yes—
185#2448C2212yes—
186#2447C2212yes—
187#2447C2212yes—
188#2446C2212yes—
189#2446C2212yes—
190#2446C2212yes—
191#2445C2212yes—
192#2444C2214yes—
193#2436C2212yes—
194#2434C2212yes—
195#2432C2212yes—
196#2431C2212yes—
197#2423C2214yes—
198#2415C2212yes—
199#2402C2212yes—
200#2399C2212yes—
201#2396C2212yes—
202#2396C2214yes—
203#2395C2214yes—
204#2395C2214yes—
205#2374C2214yes—
206#2369C2212yes—
207#2368C2214yes—
208#2367C2212yes—
209#2367C2212yes—
210#2367C2212yes—
211#2367C2212yes—
212#2367C2212yes—
213#2366C2212yes—
214#2365C2212yes—
215#2365C2212yes—
216#2365C2212yes—
217#2365C2212yes—
218#2365C2212yes—
219#2363C2212yes—
220#2362C2212yes—
221#2362C2214yes—
222#2361C2212yes—
223#2360C2212yes—
224#2359C2214yes—
225#2359C2214yes—
226#2359C2214yes—
227#2355C2212yes—
228#2355C2211yescharacteristic
229#2354C2211yescharacteristic
230#2337C2214yes—
231#2334C2214yes—
232#2333C2214yes—
233#2329C2212yes—
234#2325C2212yes—
235#2323C2214yes—
236#2323C2212yes—
237#2323C2212yes—
238#2320C2212yes—
239#2311C2211yescharacteristic
240C4×C4⋊Q8C2212yes—
241C4×#125C2214yes—
242C4×#125C2212yes—
243C4×#126C2214yes—
244C4×#124C2214yes—
245C4×C22⋊Q8C2212yes—
246C4×C22⋊Q8C2212yes—
247C4×C22⋊Q8C2211yescharacteristic
248C4×C22⋊Q8C2211yescharacteristic
249C4×#121C2212yes—
250#2298C2212yes—
251#2296C2212yes—
252#2296C2211yescharacteristic
253C2×#391C2211yescharacteristic
254#2293C2212yes—
255#2293C2214yes—
256#2275C2212yes—
257#2274C2211yescharacteristic
258C42×Q8C2212yes—
259C22×#41C2311yescharacteristic
260C23×Q8C2311yescharacteristic
261#559—44no—
262#556—44no—
263#556—48no—
264#542—216no—
265#536—28no—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2312yes—
273C2×#127C2311yescharacteristic
274C2×#127C2312yes—
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#126C2314yes—
279C2×#126C2314yes—
280C2×#125C2312yes—
281C2×#124C2314yes—
282C2×#124C2312yes—
283C2×#124C2312yes—
284C2×#124C2312yes—
285C2×#124C2312yes—
286C2×#124C2312yes—
287C2×#124C2312yes—
288C2×#124C2312yes—
289C2×#124C2312yes—
290C2×#123C2314yes—
291C2×#123C2314yes—
292C2×#123C2314yes—
293C2×#123C2314yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2311yescharacteristic
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2314yes—
302C2×C22⋊Q8C2311yescharacteristic
303C2×C22⋊Q8C2314yes—
304C2×C22⋊Q8C2312yes—
305C2×#121C2312yes—
306C2×#121C2312yes—
307C2×#121C2312yes—
308C2×#121C2312yes—
309C2×#121C2312yes—
310#519—44no—
311C4×#41—44no—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2311yescharacteristic
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2311yescharacteristic
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2311yescharacteristic
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2312yes—
324C2×C4×Q8C2314yes—
325C2×C4×D4C2311yescharacteristic
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2314yes—
333C2×C4×D4C2311yescharacteristic
334C2×C4×D4C2314yes—
335C2×#117C2311yescharacteristic
336C2×#117C2311yescharacteristic
337C2×#117C2312yes—
338C2×#117C2312yes—
339C2×#117C2314yes—
340C2×#117C2314yes—
341C2×#117C2312yes—
342C2×#117C2314yes—
343C2×#117C2311yescharacteristic
344C22×C4⋊C4C2311yescharacteristic
345C22×C42C2312yes—
346C22×C42C2311yescharacteristic
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2312yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2312yes—
359#400C2314yes—
360#400C2312yes—
361#400C2312yes—
362#400C2312yes—
363#399C2314yes—
364#399C2314yes—
365#399C2314yes—
366#399C2314yes—
367#399C2314yes—
368#399C2312yes—
369#399C2314yes—
370#399C2314yes—
371#399C2314yes—
372#398C2312yes—
373#398C2314yes—
374#398C2314yes—
375#398C2312yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2312yes—
384#398C2312yes—
385#398C2314yes—
386#398C2314yes—
387#398C2312yes—
388#398C2312yes—
389#398C2312yes—
390#398C2312yes—
391#398C2312yes—
392#398C2312yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2312yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2312yes—
418#396C2314yes—
419#396C2314yes—
420#396C2314yes—
421#395C2312yes—
422#395C2314yes—
423#395C2314yes—
424#395C2314yes—
425#395C2314yes—
426#395C2312yes—
427#395C2312yes—
428#395C2312yes—
429#395C2312yes—
430#394C2314yes—
431#394C2314yes—
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#393C2314yes—
445#393C2314yes—
446#393C2314yes—
447#393C2314yes—
448#393C2312yes—
449#393C2314yes—
450#393C2314yes—
451#393C2314yes—
452#392C2314yes—
453#392C2314yes—
454#392C2314yes—
455#391C2312yes—
456#391C2312yes—
457#391C2314yes—
458#391C2312yes—
459#391C2312yes—
460#391C2312yes—
461#391C2312yes—
462#391C2312yes—
463#391C2314yes—
464#391C2312yes—
465#391C2314yes—
466#391C2312yes—
467#391C2312yes—
468#391C2314yes—
469#391C2312yes—
470#391C2312yes—
471#391C2312yes—
472#391C2314yes—
473#391C2314yes—
474#391C2314yes—
475#391C2312yes—
476#391C2311yescharacteristic
477#391C2311yescharacteristic
478#391C2312yes—
479#391C2312yes—
480#391C2312yes—
481#391C2312yes—
482#390C2314yes—
483#390C2314yes—
484#390C2312yes—
485#390C2314yes—
486#390C2314yes—
487#390C2312yes—
488#390C2312yes—
489#390C2312yes—
490#390C2312yes—
491#390C2312yes—
492#390C2312yes—
493#390C2314yes—
494#390C2314yes—
495#390C2314yes—
496#390C2312yes—
497#390C2312yes—
498#390C2314yes—
499#389C2314yes—
500#389C2312yes—
501#389C2314yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2314yes—
508#389C2312yes—
509#389C2312yes—
510#389C2312yes—
511#389C2311yescharacteristic
512#389C2311yescharacteristic
513#389C2314yes—
514#389C2314yes—
515#389C2314yes—
516#389C2312yes—
517#389C2314yes—
518#389C2314yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#389C2312yes—
523#389C2312yes—
524#389C2312yes—
525#389C2314yes—
526#389C2312yes—
527#389C2312yes—
528#389C2311yescharacteristic
529#389C2314yes—
530#389C2311yescharacteristic
531#389C2311yescharacteristic
532#389C2311yescharacteristic
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2312yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2312yes—
566#388C2312yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2312yes—
571#387C2312yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2312yes—
579#387C2312yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2312yes—
584#387C2312yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2312yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2312yes—
607#387C2312yes—
608#387C2312yes—
609#387C2312yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2312yes—
637#385C2312yes—
638#385C2314yes—
639#385C2314yes—
640#385C2312yes—
641#385C2314yes—
642#385C2312yes—
643#384C2312yes—
644#384C2311yescharacteristic
645#384C2312yes—
646#384C2311yescharacteristic
647#383C2314yes—
648#382C2314yes—
649#382C2312yes—
650#382C2314yes—
651#382C2314yes—
652#382C2312yes—
653#382C2314yes—
654#382C2314yes—
655#381C2314yes—
656#381C2314yes—
657#380C2314yes—
658#380C2314yes—
659#380C2312yes—
660#380C2312yes—
661#380C2314yes—
662#380C2311yescharacteristic
663#380C2312yes—
664#380C2312yes—
665#380C2312yes—
666#380C2311yescharacteristic
667#380C2312yes—
668#380C2314yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2311yescharacteristic
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2311yescharacteristic
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2314yes—
713#376C2312yes—
714C2×#95C2314yes—
715C2×#95C2312yes—
716C2×#95C2312yes—
717C43C2314yes—
718C43C2312yes—
719C2×#41—24no—
720C2×#41—42no—
721C2×#41—42no—
722C22×Q8—24no—
723C22×Q8—42no—
724C22×Q8—42no—
725C22×Q8C2412yes—
726C22×Q8C2412yes—
727C22×Q8C2411yescharacteristic
728C22×Q8C2412yes—
729C22×Q8C2411yescharacteristic
730C22×Q8C2414yes—
731C22×Q8C2411yescharacteristic
732C22×Q8C2412yes—
733C22×D4C2412yes—
734C22×D4C2411yescharacteristic
735C22×D4C2412yes—
736C22×D4C2414yes—
737C22×D4C2412yes—
738C22×D4C2414yes—
739C22×D4C2412yes—
740C22×D4C2414yes—
741C23×C4C2412yes—
742C23×C4C2411yescharacteristic
743C23×C4C2412yes—
744C23×C4C2414yes—
745C23×C4C2414yes—
746C23×C4C2412yes—
747C23×C4C2411yescharacteristic
748C23×C4C2411yescharacteristic
749C23×C4C2412yes—
750C23×C4C2412yes—
751C23×C4C2414yes—
752C4⋊Q8—28no—
753C4⋊Q8—28no—
754C4⋊Q8—44no—
755C4⋊Q8—44no—
756C4⋊Q8—42no—
757C4⋊Q8—44no—
758C4⋊Q8—44no—
759#127—44no—
760#127—42no—
761#126—216no—
762#126—48no—
763#126—48no—
764#126—48no—
765#126—84no—
766#125—28no—
767#124—216no—
768#124—28no—
769#124—28no—
770#124—44no—
771#124—44no—
772#124—44no—
773#124—44no—
774#124—44no—
775#124—44no—
776#123—216no—
777#123—216no—
778#123—48no—
779#123—84no—
780C22⋊Q8—28no—
781C22⋊Q8—28no—
782C22⋊Q8—28no—
783C22⋊Q8—216no—
784C22⋊Q8—24no—
785C22⋊Q8—48no—
786C22⋊Q8—48no—
787C22⋊Q8—44no—
788C22⋊Q8—42no—
789C22⋊Q8—84no—
790C22⋊Q8—82no—
791#121—28no—
792#121—28no—
793#121—44no—
794#121—82no—
795#121—82no—
796C4×Q8—24no—
797C4×Q8—28no—
798C4×Q8—28no—
799C4×Q8—28no—
800C4×Q8—44no—
801C4×Q8—42no—
802C4×Q8—44no—
803C4×Q8—42no—
804C4×Q8—44no—
805C4×Q8—44no—
806C4×Q8—42no—
807C4×Q8—44no—
808C4×Q8—84no—
809C4×D4—24no—
810C4×D4—28no—
811C4×D4—28no—
812C4×D4—44no—
813C4×D4—44no—
814C4×D4—42no—
815C4×D4—44no—
816C4×D4—48no—
817C4×D4—44no—
818C4×D4—84no—
819#117—24no—
820#117—42no—
821#117—48no—
822#117—44no—
823#117—44no—
824#117—48no—
825#117—44no—
826#117—84no—
827#117#4118yes—
828C2×C4⋊C4—42no—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2411yescharacteristic
856C2×C4⋊C4C2411yescharacteristic
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2411yescharacteristic
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2411yescharacteristic
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2411yescharacteristic
894C2×C4⋊C4C2411yescharacteristic
895C2×C4⋊C4C2411yescharacteristic
896C2×C4⋊C4C2411yescharacteristic
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2412yes—
939C2×C42—44no—
940C2×C42—42no—
941C2×C42C2414yes—
942C2×C42C2412yes—
943C2×C42C2414yes—
944C2×C42C2412yes—
945C2×C42C2412yes—
946C2×C42C2412yes—
947C2×C42C2411yescharacteristic
948C2×C42C2411yescharacteristic
949C2×C42C2412yes—
950C2×C42C2412yes—
951C2×C42C2414yes—
952C2×C42C2412yes—
953C2×C42C2412yes—
954C2×C42C2412yes—
955C2×C42C2411yescharacteristic
956C2×C42C2414yes—
957C2×C42C2414yes—
958C2×C42C2414yes—
959C2×C42C2414yes—
960C2×C42C2412yes—
961C2×C42C2414yes—
962C2×C42C2414yes—
963C2×C42C2414yes—
964C2×C42C2412yes—
965C2×C42C2414yes—
966C2×C42C2412yes—
967C2×C42C2411yescharacteristic
968C2×C42C2412yes—
969#95C2412yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2414yes—
985#95C2412yes—
986#95C2412yes—
987#95C2414yes—
988#95C2412yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2412yes—
996#95C2412yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2412yes—
1014#95C2414yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2412yes—
1019#95C2414yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2412yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033C24C2514yes—
1034C24C2512yes—
1035C24C2511yescharacteristic
1036#41—416no—
1037C2×Q8—24no—
1038C2×Q8—24no—
1039C2×Q8—24no—
1040C2×Q8—22no—
1041C2×Q8—28no—
1042C2×Q8—22no—
1043C2×Q8—24no—
1044C2×Q8—24no—
1045C2×Q8—22no—
1046C2×Q8—24no—
1047C2×Q8—24no—
1048C2×Q8—22no—
1049C2×Q8—22no—
1050C2×Q8—42no—
1051C2×Q8—42no—
1052C2×Q8—41no—
1053C2×Q8—42no—
1054C2×Q8—41no—
1055C2×Q8—44no—
1056C2×Q8—44no—
1057C2×Q8—41no—
1058C2×Q8—42no—
1059C2×Q8—41no—
1060C2×Q8—42no—
1061C2×Q8—416no—
1062C2×D4—24no—
1063C2×D4—28no—
1064C2×D4—24no—
1065C2×D4—22no—
1066C2×D4—22no—
1067C2×D4—24no—
1068C2×D4—28no—
1069C2×D4—24no—
1070C2×D4—24no—
1071C2×D4—22no—
1072C2×D4—42no—
1073C2×D4—42no—
1074C2×D4—42no—
1075C2×D4—44no—
1076C2×D4—44no—
1077C2×D4—44no—
1078C2×D4—42no—
1079C2×D4—44no—
1080C2×D4—42no—
1081C2×D4—44no—
1082C2×D4—42no—
1083C2×D4—44no—
1084C2×D4—44no—
1085C2×D4—42no—
1086C22×C4—22no—
1087C22×C4—22no—
1088C22×C4—24no—
1089C22×C4—24no—
1090C22×C4—24no—
1091C22×C4—24no—
1092C22×C4—28no—
1093C22×C4—28no—
1094C22×C4—24no—
1095C22×C4—22no—
1096C22×C4—22no—
1097C22×C4—42no—
1098C22×C4—42no—
1099C22×C4—42no—
1100C22×C4—42no—
1101C22×C4—42no—
1102C22×C4—42no—
1103C22×C4—41no—
1104C22×C4—41no—
1105C22×C4—44no—
1106C22×C4—44no—
1107C22×C4—41no—
1108C22×C4—42no—
1109C22×C4—44no—
1110C22×C4—44no—
1111C22×C4—41no—
1112C22×C4—42no—
1113C22×C4—44no—
1114C22×C4—42no—
1115C22×C4—44no—
1116C22×C4—42no—
1117C22×C4—44no—
1118C22×C4C2×#4114yes—
1119C22×C4C2514yes—
1120C22×C4C2512yes—
1121C22×C4C2512yes—
1122C22×C4C2511yescharacteristic
1123C22×C4C2512yes—
1124C22×C4C2512yes—
1125C22×C4C2512yes—
1126C22×C4C2514yes—
1127C22×C4C2514yes—
1128C22×C4C2514yes—
1129C22×C4C2512yes—
1130C22×C4C2512yes—
1131C22×C4C2512yes—
1132C22×C4C2512yes—
1133C22×C4C2511yescharacteristic
1134C22×C4C2512yes—
1135C22×C4C2512yes—
1136C22×C4C2514yes—
1137C22×C4C2512yes—
1138C22×C4C2512yes—
1139C22×C4C2511yescharacteristic
1140C22×C4C2512yes—
1141C22×C4C2511yescharacteristic
1142C22×C4C2512yes—
1143C22×C4C2511yescharacteristic
1144C22×C4C2511yescharacteristic
1145C4⋊C4—24no—
1146C4⋊C4—24no—
1147C4⋊C4—28no—
1148C4⋊C4—28no—
1149C4⋊C4—28no—
1150C4⋊C4—28no—
1151C4⋊C4—28no—
1152C4⋊C4—22no—
1153C4⋊C4—24no—
1154C4⋊C4—28no—
1155C4⋊C4—28no—
1156C4⋊C4—24no—
1157C4⋊C4—24no—
1158C4⋊C4—24no—
1159C4⋊C4—24no—
1160C4⋊C4—24no—
1161C4⋊C4—24no—
1162C4⋊C4—24no—
1163C4⋊C4—22no—
1164C4⋊C4—24no—
1165C4⋊C4—24no—
1166C4⋊C4—24no—
1167C4⋊C4—42no—
1168C4⋊C4—42no—
1169C4⋊C4—42no—
1170C4⋊C4—41no—
1171C4⋊C4—42no—
1172C4⋊C4—41no—
1173C4⋊C4—42no—
1174C4⋊C4—42no—
1175C4⋊C4—41no—
1176C4⋊C4—41no—
1177C4⋊C4—44no—
1178C4⋊C4—42no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—41no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—42no—
1186C4⋊C4—42no—
1187C4⋊C4—42no—
1188C4⋊C4—42no—
1189C4⋊C4—42no—
1190C4⋊C4—44no—
1191C4⋊C4—42no—
1192C4⋊C4—41no—
1193C4⋊C4—42no—
1194C4⋊C4—42no—
1195C4⋊C4—44no—
1196C4⋊C4—42no—
1197C4⋊C4—42no—
1198C4⋊C4—44no—
1199C4⋊C4—42no—
1200C4⋊C4—42no—
1201C4⋊C4—44no—
1202C4⋊C4—42no—
1203C4⋊C4—44no—
1204C4⋊C4—42no—
1205C4⋊C4—42no—
1206C4⋊C4—44no—
1207C4⋊C4—44no—
1208C4⋊C4—44no—
1209C4⋊C4C2×#4114yes—
1210C4⋊C4C2×#4114yes—
1211C4⋊C4H(5,𝔽2)14yes—
1212C4⋊C42−1+414yes—
1213C22⋊C4—28no—
1214C22⋊C4—28no—
1215C22⋊C4—28no—
1216C22⋊C4—28no—
1217C22⋊C4—28no—
1218C22⋊C4—28no—
1219C22⋊C4—28no—
1220C22⋊C4—24no—
1221C22⋊C4—24no—
1222C22⋊C4—28no—
1223C22⋊C4—28no—
1224C22⋊C4—24no—
1225C22⋊C4—28no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—42no—
1229C22⋊C4—44no—
1230C22⋊C4—42no—
1231C22⋊C4—42no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—42no—
1241C22⋊C4—44no—
1242C22⋊C4—42no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4—44no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—44no—
1251C22⋊C4—44no—
1252C22⋊C4—44no—
1253C22⋊C4—44no—
1254C22⋊C4C2×#4118yes—
1255C42—28no—
1256C42—24no—
1257C42—22no—
1258C42—24no—
1259C42—22no—
1260C42—28no—
1261C42—28no—
1262C42—24no—
1263C42—24no—
1264C42—24no—
1265C42—24no—
1266C42—24no—
1267C42—24no—
1268C42—41no—
1269C42—41no—
1270C42—42no—
1271C42—44no—
1272C42—42no—
1273C42—44no—
1274C42—44no—
1275C42—42no—
1276C42—44no—
1277C42—44no—
1278C42—44no—
1279C42—44no—
1280C42—44no—
1281C42—42no—
1282C42C2×#4118yes—
1283C23—21no—
1284C23—21no—
1285C23—21no—
1286C23—21no—
1287C23—21no—
1288C23—21no—
1289C23—24no—
1290C23—22no—
1291C23—24no—
1292C23—22no—
1293C23—24no—
1294C23—22no—
1295C23—24no—
1296C23—22no—
1297C23—24no—
1298C23—22no—
1299C23—22no—
1300C23—24no—
1301C23—22no—
1302C23—24no—
1303C23C22×#4112yes—
1304C23C2611yescharacteristic
1305Q8—48no—
1306Q8—48no—
1307Q8—48no—
1308Q8—44no—
1309Q8—88no—
1310Q8—82no—
1311Q8—82no—
1312Q8—84no—
1313D4—48no—
1314D4—48no—
1315D4—44no—
1316D4—88no—
1317D4—84no—
1318D4—88no—
1319D4—164no—
1320D4—162no—
1321C2×C4—21no—
1322C2×C4—21no—
1323C2×C4—21no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—21no—
1330C2×C4—22no—
1331C2×C4—21no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—21no—
1335C2×C4—28no—
1336C2×C4—24no—
1337C2×C4—24no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—21no—
1346C2×C4—22no—
1347C2×C4—21no—
1348C2×C4—24no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—24no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—21no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—24no—
1364C2×C4—24no—
1365C2×C4—24no—
1366C2×C4—22no—
1367C2×C4—24no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—24no—
1371C2×C4—21no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—24no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—24no—
1378C2×C4—22no—
1379C2×C4—24no—
1380C2×C4—22no—
1381C2×C4—21no—
1382C2×C4—22no—
1383C2×C4—24no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—21no—
1390C2×C4—48no—
1391C2×C4—48no—
1392C2×C4—48no—
1393C2×C4—88no—
1394C2×C4—82no—
1395C2×C4—88no—
1396C2×C4—82no—
1397C2×C4—84no—
1398C2×C4—162no—
1399C2×C4—164no—
1400C2×C4C22×#4114yes—
1401C2×C4C22×#4114yes—
1402C2×C4C22×#4112yes—
1403C2×C4C22×#4112yes—
1404C2×C4C2×H(5,𝔽2)14yes—
1405C2×C4C2×H(5,𝔽2)12yes—
1406C2×C4C2×2−1+414yes—
1407C2×C4C2×2−1+412yes—
1408C2×C4#58512yes—
1409C2×C4#58512yes—
1410C22—22no—
1411C22—22no—
1412C22—22no—
1413C22—41no—
1414C22—41no—
1415C22—41no—
1416C22—41no—
1417C22—44no—
1418C22—42no—
1419C22—44no—
1420C22—42no—
1421C22—42no—
1422C22—44no—
1423C22—44no—
1424C22—42no—
1425C22—42no—
1426C22—44no—
1427C22—42no—
1428C22—44no—
1429C22—42no—
1430C22—44no—
1431C22C23×#4111yescharacteristic
1432C22C22×H(5,𝔽2)11yescharacteristic
1433C22C22×2−1+411yescharacteristic
1434C22C2×#58511yescharacteristic
1435C22C2×#58511yescharacteristic
1436C22H(7,𝔽2)11yescharacteristic
1437C222−1+611yescharacteristic
1438C4—24no—
1439C4—24no—
1440C4—24no—
1441C4—22no—
1442C4—24no—
1443C4—22no—
1444C4—22no—
1445C4—44no—
1446C4—44no—
1447C4—42no—
1448C4—42no—
1449C4—44no—
1450C4—42no—
1451C4—42no—
1452C4—41no—
1453C4—42no—
1454C4—42no—
1455C4—42no—
1456C4—42no—
1457C4—42no—
1458C4—41no—
1459C4—42no—
1460C4—42no—
1461C4—44no—
1462C4—44no—
1463C4#346014yes—
1464C2—42no—
1465C2—84no—
1466C2—82no—
1467C2C2×#346011yescharacteristic
1468C2#6289811yescharacteristic
1469C2#6291711yescharacteristic
1470C2#6300111yescharacteristic
1471C2#6301011yescharacteristic
1472C2#6302511yescharacteristic
1473C2#6306911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36493C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52290C2semidirect
2. #52281C2semidirect
3. #42702C2semidirect
4. #42526C2semidirect
5. #42519C2semidirect
6. #42378C2semidirect
7. #41901C2semidirect
8. #41780C2semidirect
9. #40464C2semidirect
10. #40026C2semidirect
11. #39768C2semidirect
12. #39708C2semidirect
13. #39640C2semidirect
14. #39200C2semidirect
15. #38860C2semidirect
16. #38763C2semidirect
17. #37391C2semidirect
18. #37299C2semidirect
19. #37167C2semidirect
20. #37078C2semidirect
21. #36556C2semidirect
23. #36405C2semidirect
24. #36271C2semidirect
25. #35959C2semidirect
26. #35860C2semidirect
27. #35817C2semidirect
28. #34285C2semidirect
29. #34268C2semidirect

Maximal subgroups

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

subgroupindex
#522902
#522812
#427022
#425262
#425192
#423782
#419012
#417802
#404642
#400262
#397682
#397082
#396402
#392002
#388602
#387632
#373912
#372992
#371672
#370782
#365562
#364932
#364052
#362712
#359592
#358602
#358172
#342852
#342682