Finite Group Databasebeta

← #7726981

Subgroups — #7726981

Order 512.

4464 conjugacy classes of subgroups.

The subgroup lattice has 1455 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#48002C214yesmaximal, complemented
2#48001C214yesmaximal, complemented
3#47229C214yesmaximal, complemented
4#47015C214yesmaximal, complemented
5#45434C211yesmaximal, characteristic, complemented
6#45430C211yesmaximal, characteristic, complemented
7#45318C211yesmaximal, characteristic, complemented
8#45163C211yesmaximal, characteristic, complemented
9#45083C211yesmaximal, characteristic, complemented
10#45056C211yesmaximal, characteristic, complemented
11#45056C211yesmaximal, characteristic, complemented
12#44947C211yesmaximal, characteristic, complemented
13#40035C212yesmaximal, complemented
14#40029C212yesmaximal, complemented
15#39808C212yesmaximal, complemented
16#39801C212yesmaximal, complemented
17#39763C212yesmaximal, complemented
18#39749C212yesmaximal, complemented
19#38743C214yesmaximal, complemented
20#38730C214yesmaximal, complemented
21#37634C211yesmaximal, characteristic, complemented
22#37005C214yesmaximal, complemented
23#36420C212yesmaximal, complemented
24#36302C212yesmaximal, complemented
25#35503C214yesmaximal, complemented
26#35303C211yesmaximal, characteristic
27#35201C211yesmaximal, characteristic, complemented
28#34878C211yesmaximal, characteristic, complemented
29#34392C211yesmaximal, characteristic, complemented
30#34226C211yesmaximal, characteristic, complemented
31#34074C211yesmaximal, characteristic, complemented
32C2×#533C2211yescharacteristic
33C2×#532C2211yescharacteristic
34C2×#529C2211yescharacteristic
35#2865C2214yes—
36#2861C2214yes—
37#2861C2212yes—
38#2859C2212yes—
39#2856C2211yescharacteristic
40#2856C2211yescharacteristic
41#2850C2211yescharacteristic
42#2850C2211yescharacteristic
43#2816C2212yes—
44#2816C2212yes—
45#2809C2214yes—
46#2806C2214yes—
47#2805C2214yes—
48#2803C2214yes—
49#2803C2214yes—
50#2800C2214yes—
51#2800C2214yes—
52#2800C2214yes—
53#2800C2214yes—
54#2797C2214yes—
55#2788C2214yes—
56#2787C2214yes—
57#2786C2214yes—
58#2777C2214yes—
59#2768C2214yes—
60#2759C2214yes—
61#2759C2214yes—
62#2757C2214yes—
63#2754C2214yes—
64#2748C2214yes—
65#2746C2214yes—
66#2745C2214yes—
67#2741C2214yes—
68#2741C2214yes—
69#2740C2214yes—
70#2738C2214yes—
71#2738C2214yes—
72#2728C2214yes—
73#2726C2214yes—
74#2711C2214yes—
75#2710C2214yes—
76#2708C2214yes—
77#2704C2214yes—
78#2700C2214yes—
79#2692C2214yes—
80#2691C2214yes—
81#2690C2214yes—
82#2687C2214yes—
83#2687C2214yes—
84#2681C2214yes—
85#2663C2212yes—
86#2663C2212yes—
87#2660C2212yes—
88#2660C2211yescharacteristic
89#2657C2211yescharacteristic
90#2654C2214yes—
91#2651C2214yes—
92#2641C2212yes—
93#2641C2211yescharacteristic
94#2640C2211yescharacteristic
95#2632C2212yes—
96#2632C2212yes—
97#2616C2214yes—
98#2612C2212yes—
99#2612C2212yes—
100#2611C2214yes—
101#2610C2214yes—
102#2606C2212yes—
103#2605C2212yes—
104#2604C2214yes—
105#2604C2212yes—
106#2604C2212yes—
107#2603C2214yes—
108#2602C2214yes—
109#2600C2214yes—
110#2599C2214yes—
111#2595C2214yes—
112#2594C2214yes—
113#2592C2212yes—
114#2590C2214yes—
115#2590C2214yes—
116#2582C2212yes—
117#2580C2212yes—
118#2578C2214yes—
119#2577C2214yes—
120#2577C2214yes—
121#2570C2212yes—
122#2570C2212yes—
123#2570C2212yes—
124#2570C2212yes—
125#2569C2212yes—
126#2568C2211yescharacteristic
127#2567C2211yescharacteristic
128#2564C2214yes—
129#2563C2211yescharacteristic
130#2563C2211yescharacteristic
131#2563C2211yescharacteristic
132#2560C2214yes—
133#2560C2214yes—
134#2558C2214yes—
135#2556C2214yes—
136#2552C2212yes—
137#2552C2212yes—
138#2549C2212yes—
139#2549C2214yes—
140#2548C2212yes—
141#2543C2214yes—
142#2542C2211yescharacteristic
143#2542C2211yescharacteristic
144#2542C2211yescharacteristic
145#2538C2212yes—
146#2538C2212yes—
147#2536C2214yes—
148#2532C2214yes—
149#2532C2214yes—
150#2532C2214yes—
151#2532C2214yes—
152#2531C2214yes—
153#2531C2214yes—
154#2531C2214yes—
155#2530C2214yes—
156#2530C2214yes—
157#2521C2214yes—
158#2514C2212yes—
159#2513C2212yes—
160#2513C2212yes—
161#2513C2212yes—
162#2513C2212yes—
163#2513C2212yes—
164#2512C2212yes—
165#2511C2212yes—
166#2500C2212yes—
167#2500C2212yes—
168#2500C2212yes—
169#2499C2212yes—
170#2498C2214yes—
171#2498C2214yes—
172#2490C2214yes—
173#2485C2214yes—
174#2485C2214yes—
175#2478C2214yes—
176#2477C2214yes—
177#2477C2214yes—
178#2477C2214yes—
179#2476C2214yes—
180#2476C2214yes—
181#2462C2214yes—
182#2462C2214yes—
183#2459C2214yes—
184#2455C2214yes—
185#2450C2214yes—
186#2448C2212yes—
187#2447C2212yes—
188#2445C2212yes—
189#2445C2212yes—
190#2438C2214yes—
191#2438C2212yes—
192#2438C2212yes—
193#2430C2214yes—
194#2427C2214yes—
195#2415C2214yes—
196#2415C2214yes—
197#2415C2214yes—
198#2402C2211yescharacteristic
199#2402C2211yescharacteristic
200#2399C2211yescharacteristic
201#2399C2211yescharacteristic
202#2376C2214yes—
203#2367C2212yes—
204#2367C2214yes—
205#2366C2212yes—
206#2363C2212yes—
207#2363C2212yes—
208#2363C2212yes—
209#2362C2212yes—
210#2357C2211yescharacteristic
211#2357C2211yescharacteristic
212#2357C2211yescharacteristic
213#2356C2212yes—
214#2356C2211yescharacteristic
215#2355C2212yes—
216#2355C2212yes—
217#2354C2212yes—
218#2354C2212yes—
219#2354C2212yes—
220#2351C2211yescharacteristic
221#2349C2211yescharacteristic
222#2349C2211yescharacteristic
223#2349C2211yescharacteristic
224#2347C2212yes—
225#2343C2212yes—
226#2341C2212yes—
227#2339C2212yes—
228#2335C2214yes—
229#2334C2214yes—
230#2332C2214yes—
231#2331C2211yescharacteristic
232#2331C2211yescharacteristic
233#2331C2211yescharacteristic
234#2331C2211yescharacteristic
235#2330C2212yes—
236#2330C2212yes—
237#2330C2212yes—
238#2329C2214yes—
239#2329C2214yes—
240#2328C2211yescharacteristic
241#2328C2211yescharacteristic
242#2326C2211yescharacteristic
243#2326C2212yes—
244#2326C2211yescharacteristic
245#2324C2214yes—
246#2323C2214yes—
247#2319C2212yes—
248#2319C2212yes—
249#2318C2212yes—
250C4×C4⋊Q8C2212yes—
251C4×#127C2212yes—
252C4×C22⋊Q8C2212yes—
253C4×C22⋊Q8C2212yes—
254#2298C2214yes—
255#2296C2212yes—
256#2295C2214yes—
257#2295C2214yes—
258#2295C2212yes—
259#2295C2212yes—
260#2293C2214yes—
261#2285C2211yescharacteristic
262#2283C2211yescharacteristic
263#2275C2212yes—
264C4×#117C2212yes—
265C4×#117C2211yescharacteristic
266C2×#376C2211yescharacteristic
267C22×#41C2312yes—
268#533—28no—
269#532—28no—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2311yescharacteristic
273C2×#127C2311yescharacteristic
274C2×#127C2311yescharacteristic
275C2×#127C2311yescharacteristic
276#529—28no—
277C2×#126C2312yes—
278C2×#126C2314yes—
279C2×#125C2311yescharacteristic
280C2×#125C2312yes—
281C2×#125C2314yes—
282C2×#125C2314yes—
283C2×#124C2311yescharacteristic
284C2×#124C2311yescharacteristic
285C2×#124C2312yes—
286C2×#124C2311yescharacteristic
287C2×#124C2314yes—
288C2×#123C2312yes—
289C2×#123C2314yes—
290C2×#123C2314yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2311yescharacteristic
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2314yes—
301C2×#121C2312yes—
302C2×#121C2311yescharacteristic
303C2×#121C2311yescharacteristic
304C2×#121C2311yescharacteristic
305C2×#121C2314yes—
306C2×#121C2314yes—
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2314yes—
314C2×C4×D4C2311yescharacteristic
315C2×C4×D4C2311yescharacteristic
316C2×C4×D4C2311yescharacteristic
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2314yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2314yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2314yes—
325C2×#117C2312yes—
326C2×#117C2312yes—
327C2×#117C2312yes—
328C2×#117C2314yes—
329C2×#117C2312yes—
330C2×#117C2314yes—
331C2×#117C2314yes—
332C22×C42C2311yescharacteristic
333C22×C42C2311yescharacteristic
334C22×C42C2311yescharacteristic
335#401C2314yes—
336#400C2314yes—
337#400C2312yes—
338#400C2312yes—
339#400C2312yes—
340#400C2312yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2312yes—
347#400C2312yes—
348#400C2314yes—
349#399C2312yes—
350#399C2312yes—
351#399C2312yes—
352#399C2312yes—
353#399C2312yes—
354#399C2314yes—
355#399C2312yes—
356#399C2314yes—
357#398C2312yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2312yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2312yes—
371#398C2312yes—
372#398C2312yes—
373#398C2312yes—
374#398C2312yes—
375#398C2312yes—
376#398C2314yes—
377#398C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#395C2312yes—
402#395C2312yes—
403#395C2312yes—
404#395C2314yes—
405#395C2314yes—
406#395C2312yes—
407#395C2312yes—
408#395C2314yes—
409#395C2312yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#393C2312yes—
429#393C2314yes—
430#393C2312yes—
431#393C2312yes—
432#393C2312yes—
433#393C2312yes—
434#393C2312yes—
435#393C2314yes—
436#393C2314yes—
437#392C2314yes—
438#392C2314yes—
439#391C2312yes—
440#391C2314yes—
441#391C2314yes—
442#391C2312yes—
443#391C2314yes—
444#391C2312yes—
445#391C2311yescharacteristic
446#391C2312yes—
447#391C2311yescharacteristic
448#391C2314yes—
449#391C2314yes—
450#391C2314yes—
451#391C2314yes—
452#391C2312yes—
453#391C2312yes—
454#391C2312yes—
455#391C2314yes—
456#391C2314yes—
457#391C2312yes—
458#391C2312yes—
459#390C2314yes—
460#390C2314yes—
461#390C2314yes—
462#390C2312yes—
463#390C2314yes—
464#390C2312yes—
465#390C2312yes—
466#390C2312yes—
467#390C2312yes—
468#390C2314yes—
469#390C2314yes—
470#390C2314yes—
471#390C2311yescharacteristic
472#390C2312yes—
473#390C2311yescharacteristic
474#390C2311yescharacteristic
475#390C2312yes—
476#390C2311yescharacteristic
477#390C2311yescharacteristic
478#390C2311yescharacteristic
479#390C2314yes—
480#390C2314yes—
481#390C2312yes—
482#390C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2314yes—
486#389C2314yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2312yes—
495#389C2312yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2312yes—
508#389C2312yes—
509#389C2312yes—
510#389C2312yes—
511#389C2312yes—
512#389C2312yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#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#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2312yes—
565#387C2312yes—
566#387C2312yes—
567#387C2312yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2312yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2312yes—
592#387C2312yes—
593#387C2312yes—
594#387C2314yes—
595#387C2314yes—
596#387C2312yes—
597#387C2312yes—
598#387C2314yes—
599#387C2314yes—
600#387C2312yes—
601#387C2312yes—
602#387C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2312yes—
619#385C2312yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2312yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2312yes—
633#384C2312yes—
634#384C2312yes—
635#384C2311yescharacteristic
636#384C2312yes—
637#384C2312yes—
638#384C2311yescharacteristic
639#384C2312yes—
640#383C2312yes—
641#383C2314yes—
642#383C2314yes—
643#383C2311yescharacteristic
644#383C2311yescharacteristic
645#382C2312yes—
646#382C2312yes—
647#382C2312yes—
648#382C2312yes—
649#382C2311yescharacteristic
650#382C2311yescharacteristic
651#382C2312yes—
652#382C2311yescharacteristic
653#382C2311yescharacteristic
654#382C2312yes—
655#381C2311yescharacteristic
656#381C2311yescharacteristic
657#381C2312yes—
658#381C2312yes—
659#381C2312yes—
660#381C2314yes—
661#380C2314yes—
662#380C2314yes—
663#380C2314yes—
664#380C2314yes—
665#380C2312yes—
666#380C2312yes—
667#380C2312yes—
668#380C2312yes—
669#380C2312yes—
670#380C2312yes—
671#380C2312yes—
672#380C2314yes—
673#380C2312yes—
674#380C2314yes—
675#380C2314yes—
676#380C2314yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2314yes—
700C4×C4⋊C4C2314yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2312yes—
704C4×C4⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2311yescharacteristic
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2314yes—
714C4×C22⋊C4C2314yes—
715C4×C22⋊C4C2311yescharacteristic
716C4×C22⋊C4C2312yes—
717C4×C22⋊C4C2312yes—
718#376C2311yescharacteristic
719#376C2312yes—
720#376C2311yescharacteristic
721#376C2311yescharacteristic
722#376C2312yes—
723#376C2311yescharacteristic
724#376C2311yescharacteristic
725#376C2312yes—
726#376C2311yescharacteristic
727#376C2314yes—
728#376C2312yes—
729#376C2314yes—
730C2×#95C2312yes—
731C2×#95C2312yes—
732C2×#95C2312yes—
733C2×#95C2312yes—
734C2×#95C2312yes—
735C43C2312yes—
736C43C2314yes—
737C2×#41—28no—
738C2×#41—84no—
739C22×Q8C2411yescharacteristic
740C22×Q8C2412yes—
741C22×Q8C2412yes—
742C22×Q8C2412yes—
743C22×Q8C2412yes—
744C22×Q8C2412yes—
745C22×D4C2411yescharacteristic
746C22×D4C2411yescharacteristic
747C22×D4C2411yescharacteristic
748C22×D4C2412yes—
749C22×D4C2412yes—
750C22×D4C2412yes—
751C22×D4C2414yes—
752C22×D4C2412yes—
753C22×D4C2412yes—
754C22×D4C2414yes—
755C23×C4C2411yescharacteristic
756C23×C4C2414yes—
757C23×C4C2414yes—
758C23×C4C2412yes—
759C23×C4C2412yes—
760C23×C4C2412yes—
761C23×C4C2412yes—
762C23×C4C2414yes—
763C23×C4C2412yes—
764C23×C4C2411yescharacteristic
765C23×C4C2411yescharacteristic
766C4⋊Q8—24no—
767C4⋊Q8—24no—
768C4⋊Q8—24no—
769#127—24no—
770#127—24no—
771#127—42no—
772#126—28no—
773#126—84no—
774#125—24no—
775#125—28no—
776#125—84no—
777#125—84no—
778#124—24no—
779#124—28no—
780#124—24no—
781#124—42no—
782#124—84no—
783#123—28no—
784#123—48no—
785#123—84no—
786C22⋊Q8—24no—
787C22⋊Q8—28no—
788C22⋊Q8—28no—
789C22⋊Q8—44no—
790C22⋊Q8—48no—
791C22⋊Q8—44no—
792C22⋊Q8—48no—
793C22⋊Q8—84no—
794C22⋊Q8—84no—
795C22⋊Q8—84no—
796#121—24no—
797#121—24no—
798#121—24no—
799#121—28no—
800#121—84no—
801#121—84no—
802C4×Q8—24no—
803C4×Q8—28no—
804C4×Q8—28no—
805C4×Q8—28no—
806C4×Q8—44no—
807C4×Q8—44no—
808C4×Q8—84no—
809C4×D4—28no—
810C4×D4—24no—
811C4×D4—24no—
812C4×D4—24no—
813C4×D4—28no—
814C4×D4—44no—
815C4×D4—44no—
816C4×D4—44no—
817C4×D4—48no—
818C4×D4—48no—
819C4×D4—84no—
820#117—28no—
821#117—28no—
822#117—44no—
823#117—48no—
824#117—44no—
825#117—84no—
826#117—84no—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C42—24no—
932C2×C42—42no—
933C2×C42#4118yes—
934C2×C42C2412yes—
935C2×C42C2412yes—
936C2×C42C2414yes—
937C2×C42C2412yes—
938C2×C42C2412yes—
939C2×C42C2411yescharacteristic
940C2×C42C2412yes—
941C2×C42C2412yes—
942C2×C42C2411yescharacteristic
943C2×C42C2412yes—
944C2×C42C2411yescharacteristic
945C2×C42C2414yes—
946C2×C42C2414yes—
947C2×C42C2414yes—
948C2×C42C2414yes—
949C2×C42C2414yes—
950C2×C42C2412yes—
951C2×C42C2414yes—
952C2×C42C2412yes—
953C2×C42C2414yes—
954C2×C42C2412yes—
955C2×C42C2414yes—
956C2×C42C2414yes—
957C2×C42C2414yes—
958C2×C42C2412yes—
959C2×C42C2411yescharacteristic
960C2×C42C2411yescharacteristic
961C2×C42C2411yescharacteristic
962C2×C42C2411yescharacteristic
963C2×C42C2411yescharacteristic
964#95C2411yescharacteristic
965#95C2411yescharacteristic
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2412yes—
981#95C2411yescharacteristic
982#95C2412yes—
983#95C2411yescharacteristic
984#95C2411yescharacteristic
985#95C2414yes—
986#95C2414yes—
987#95C2411yescharacteristic
988#95C2414yes—
989#95C2414yes—
990#95C2412yes—
991#95C2414yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2411yescharacteristic
1001#95C2412yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2411yescharacteristic
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2412yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2414yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2412yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038C24C2512yes—
1039C24C2512yes—
1040C24C2512yes—
1041C24C2511yescharacteristic
1042#41—816no—
1043C2×Q8—22no—
1044C2×Q8—24no—
1045C2×Q8—24no—
1046C2×Q8—24no—
1047C2×Q8—22no—
1048C2×Q8—24no—
1049C2×Q8—22no—
1050C2×Q8—24no—
1051C2×Q8—44no—
1052C2×Q8—42no—
1053C2×Q8—42no—
1054C2×Q8—44no—
1055C2×Q8—42no—
1056C2×Q8—44no—
1057C2×Q8—42no—
1058C2×D4—24no—
1059C2×D4—24no—
1060C2×D4—24no—
1061C2×D4—22no—
1062C2×D4—24no—
1063C2×D4—22no—
1064C2×D4—22no—
1065C2×D4—24no—
1066C2×D4—22no—
1067C2×D4—22no—
1068C2×D4—22no—
1069C2×D4—28no—
1070C2×D4—22no—
1071C2×D4—22no—
1072C2×D4—22no—
1073C2×D4—44no—
1074C2×D4—44no—
1075C2×D4—44no—
1076C2×D4—44no—
1077C2×D4—44no—
1078C2×D4—44no—
1079C2×D4—44no—
1080C2×D4—44no—
1081C2×D4—44no—
1082C2×D4—44no—
1083C22×C4—22no—
1084C22×C4—22no—
1085C22×C4—24no—
1086C22×C4—24no—
1087C22×C4—24no—
1088C22×C4—24no—
1089C22×C4—28no—
1090C22×C4—28no—
1091C22×C4—42no—
1092C22×C4—42no—
1093C22×C4—42no—
1094C22×C4—44no—
1095C22×C4—44no—
1096C22×C4—44no—
1097C22×C4—44no—
1098C22×C4—44no—
1099C22×C4—44no—
1100C22×C4—44no—
1101C22×C4—42no—
1102C22×C4—42no—
1103C22×C4—42no—
1104C22×C4—44no—
1105C22×C4—42no—
1106C22×C4—44no—
1107C22×C4—44no—
1108C22×C4C2×#4114yes—
1109C22×C4C2×#4114yes—
1110C22×C4C2×#4114yes—
1111C22×C4C2512yes—
1112C22×C4C2512yes—
1113C22×C4C2512yes—
1114C22×C4C2512yes—
1115C22×C4C2512yes—
1116C22×C4C2512yes—
1117C22×C4C2514yes—
1118C22×C4C2512yes—
1119C22×C4C2514yes—
1120C22×C4C2512yes—
1121C22×C4C2512yes—
1122C22×C4C2512yes—
1123C22×C4C2512yes—
1124C22×C4C2512yes—
1125C22×C4C2514yes—
1126C22×C4C2512yes—
1127C22×C4C2512yes—
1128C22×C4C2514yes—
1129C22×C4C2512yes—
1130C22×C4C2511yescharacteristic
1131C22×C4C2511yescharacteristic
1132C22×C4C2511yescharacteristic
1133C22×C4C2511yescharacteristic
1134C22×C4C2511yescharacteristic
1135C22×C4C2512yes—
1136C22×C4C2512yes—
1137C22×C4C2511yescharacteristic
1138C4⋊C4—24no—
1139C4⋊C4—24no—
1140C4⋊C4—24no—
1141C4⋊C4—24no—
1142C4⋊C4—24no—
1143C4⋊C4—22no—
1144C4⋊C4—22no—
1145C4⋊C4—22no—
1146C4⋊C4—24no—
1147C4⋊C4—22no—
1148C4⋊C4—28no—
1149C4⋊C4—28no—
1150C4⋊C4—24no—
1151C4⋊C4—24no—
1152C4⋊C4—24no—
1153C4⋊C4—24no—
1154C4⋊C4—24no—
1155C4⋊C4—24no—
1156C4⋊C4—24no—
1157C4⋊C4—24no—
1158C4⋊C4—24no—
1159C4⋊C4—24no—
1160C4⋊C4—28no—
1161C4⋊C4—24no—
1162C4⋊C4—24no—
1163C4⋊C4—42no—
1164C4⋊C4—42no—
1165C4⋊C4—42no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—42no—
1171C4⋊C4—42no—
1172C4⋊C4—42no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—42no—
1179C4⋊C4—44no—
1180C4⋊C4—42no—
1181C4⋊C4—42no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4—42no—
1185C4⋊C4—42no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—42no—
1193C4⋊C4—44no—
1194C4⋊C4—42no—
1195C4⋊C4—42no—
1196C4⋊C4—44no—
1197C4⋊C4—42no—
1198C22⋊C4—28no—
1199C22⋊C4—24no—
1200C22⋊C4—24no—
1201C22⋊C4—24no—
1202C22⋊C4—24no—
1203C22⋊C4—24no—
1204C22⋊C4—24no—
1205C22⋊C4—24no—
1206C22⋊C4—24no—
1207C22⋊C4—24no—
1208C22⋊C4—28no—
1209C22⋊C4—24no—
1210C22⋊C4—28no—
1211C22⋊C4—42no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4—44no—
1218C22⋊C4—44no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—42no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—42no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C42—24no—
1243C42—28no—
1244C42—24no—
1245C42—22no—
1246C42—24no—
1247C42—24no—
1248C42—22no—
1249C42—22no—
1250C42—24no—
1251C42—24no—
1252C42—24no—
1253C42—42no—
1254C42—42no—
1255C42—44no—
1256C42—44no—
1257C42—44no—
1258C42—44no—
1259C42—44no—
1260C42—44no—
1261C42—44no—
1262C42—42no—
1263C42—44no—
1264C42—42no—
1265C42—44no—
1266C42—44no—
1267C42C2×#4114yes—
1268C42C2×#4114yes—
1269C42C2×#4114yes—
1270C42C2×#4114yes—
1271C422−1+414yes—
1272C23—21no—
1273C23—22no—
1274C23—21no—
1275C23—22no—
1276C23—22no—
1277C23—22no—
1278C23—22no—
1279C23—22no—
1280C23—22no—
1281C23—22no—
1282C23—24no—
1283C23—24no—
1284C23—24no—
1285C23—22no—
1286C23—22no—
1287C23—22no—
1288C23—24no—
1289C23—24no—
1290C23—24no—
1291C23C22×#4112yes—
1292C23C2611yescharacteristic
1293Q8—48no—
1294Q8—44no—
1295Q8—84no—
1296Q8—84no—
1297Q8—84no—
1298Q8—84no—
1299D4—48no—
1300D4—48no—
1301D4—44no—
1302D4—44no—
1303D4—44no—
1304D4—88no—
1305D4—84no—
1306D4—84no—
1307D4—84no—
1308D4—164no—
1309C2×C4—21no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—21no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—28no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—24no—
1323C2×C4—24no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—24no—
1342C2×C4—24no—
1343C2×C4—22no—
1344C2×C4—24no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—24no—
1348C2×C4—24no—
1349C2×C4—24no—
1350C2×C4—24no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—24no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—24no—
1361C2×C4—22no—
1362C2×C4—24no—
1363C2×C4—24no—
1364C2×C4—24no—
1365C2×C4—24no—
1366C2×C4—24no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—44no—
1374C2×C4—44no—
1375C2×C4—84no—
1376C2×C4—84no—
1377C2×C4—88no—
1378C2×C4—88no—
1379C2×C4—84no—
1380C2×C4—84no—
1381C2×C4—88no—
1382C2×C4—84no—
1383C2×C4C22×#4112yes—
1384C2×C4C22×#4112yes—
1385C2×C4C22×#4112yes—
1386C2×C4C22×#4112yes—
1387C2×C4C22×#4112yes—
1388C2×C4C22×#4112yes—
1389C2×C4C2×2−1+414yes—
1390C2×C4C2×2−1+412yes—
1391C2×C4#58514yes—
1392C2×C4#58512yes—
1393C22—22no—
1394C22—22no—
1395C22—22no—
1396C22—42no—
1397C22—42no—
1398C22—42no—
1399C22—42no—
1400C22—42no—
1401C22—42no—
1402C22—42no—
1403C22—42no—
1404C22—42no—
1405C22—42no—
1406C22—42no—
1407C22—44no—
1408C22—44no—
1409C22—44no—
1410C22—44no—
1411C22—44no—
1412C22—44no—
1413C22C23×#4111yescharacteristic
1414C22C22×2−1+411yescharacteristic
1415C22C2×#58511yescharacteristic
1416C22C2×#58512yes—
1417C22H(7,𝔽2)12yes—
1418C4—22no—
1419C4—22no—
1420C4—22no—
1421C4—22no—
1422C4—22no—
1423C4—24no—
1424C4—24no—
1425C4—42no—
1426C4—42no—
1427C4—44no—
1428C4—42no—
1429C4—42no—
1430C4—42no—
1431C4—44no—
1432C4—42no—
1433C4—42no—
1434C4—42no—
1435C4—42no—
1436C4—42no—
1437C4—42no—
1438C4—44no—
1439C4—42no—
1440C4—44no—
1441C4—42no—
1442C4—42no—
1443C4—42no—
1444C4#350714yes—
1445C2—42no—
1446C2—82no—
1447C2—82no—
1448C2—82no—
1449C2C2×#350711yescharacteristic
1450C2#6281511yescharacteristic
1451C2#6285511yescharacteristic
1452C2#6292912yes—
1453C2#6294112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35303C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #48002C2semidirect
2. #48001C2semidirect
3. #47229C2semidirect
4. #47015C2semidirect
5. #45434C2semidirect
6. #45430C2semidirect
7. #45318C2semidirect
8. #45163C2semidirect
9. #45083C2semidirect
10. #45056C2semidirect
11. #45056C2semidirect
12. #44947C2semidirect
13. #40035C2semidirect
14. #40029C2semidirect
15. #39808C2semidirect
16. #39801C2semidirect
17. #39763C2semidirect
18. #39749C2semidirect
19. #38743C2semidirect
20. #38730C2semidirect
21. #37634C2semidirect
22. #37005C2semidirect
23. #36420C2semidirect
24. #36302C2semidirect
25. #35503C2semidirect
27. #35201C2semidirect
28. #34878C2semidirect
29. #34392C2semidirect
30. #34226C2semidirect
31. #34074C2semidirect

Maximal subgroups

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

subgroupindex
#480022
#480012
#472292
#470152
#454342
#454302
#453182
#451632
#450832
#450562
#449472
#400352
#400292
#398082
#398012
#397632
#397492
#387432
#387302
#376342
#370052
#364202
#363022
#355032
#353032
#352012
#348782
#343922
#342262
#340742