Finite Group Databasebeta

← #7726862

Subgroups — #7726862

Order 512.

4938 conjugacy classes of subgroups.

The subgroup lattice has 1488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51620C214yesmaximal, complemented
2#51617C214yesmaximal, complemented
3#47710C214yesmaximal, complemented
4#47709C214yesmaximal, complemented
5#45434C211yesmaximal, characteristic, complemented
6#45430C211yesmaximal, characteristic, complemented
7#45350C211yesmaximal, characteristic, complemented
8#45211C211yesmaximal, characteristic, complemented
9#45083C211yesmaximal, characteristic, complemented
10#45056C211yesmaximal, characteristic, complemented
11#44979C211yesmaximal, characteristic, complemented
12#44947C211yesmaximal, characteristic, complemented
13#39810C212yesmaximal, complemented
14#39803C212yesmaximal, complemented
15#39761C212yesmaximal, complemented
16#39753C212yesmaximal, complemented
17#39431C214yesmaximal, complemented
18#39384C212yesmaximal, complemented
19#39199C212yesmaximal, complemented
20#37779C214yesmaximal, complemented
21#37632C211yesmaximal, characteristic, complemented
22#37000C214yesmaximal, complemented
23#36487C212yesmaximal, complemented
24#36117C212yesmaximal, complemented
25#35464C214yesmaximal, complemented
26#35317C211yesmaximal, characteristic, complemented
27#35303C211yesmaximal, characteristic
28#34878C211yesmaximal, characteristic, complemented
29#34398C211yesmaximal, characteristic, complemented
30#34229C211yesmaximal, characteristic, complemented
31C2×#2331C211yesmaximal, characteristic, complemented
32C2×#539C2214yes—
33C2×#536C2214yes—
34C2×#532C2211yescharacteristic
35C22×C4⋊Q8C2211yescharacteristic
36C2×#529C2211yescharacteristic
37C2×#529C2214yes—
38#2868C2212yes—
39#2858C2212yes—
40#2856C2211yescharacteristic
41#2856C2211yescharacteristic
42#2854C2214yes—
43#2853C2214yes—
44#2850C2211yescharacteristic
45#2850C2211yescharacteristic
46#2821C2212yes—
47#2821C2212yes—
48#2807C2214yes—
49#2798C2214yes—
50#2797C2214yes—
51#2793C2214yes—
52#2793C2214yes—
53#2791C2214yes—
54#2791C2214yes—
55#2786C2214yes—
56#2777C2214yes—
57#2773C2214yes—
58#2773C2214yes—
59#2771C2214yes—
60#2768C2214yes—
61#2752C2214yes—
62#2748C2214yes—
63#2743C2214yes—
64#2741C2214yes—
65#2740C2214yes—
66#2740C2214yes—
67#2738C2214yes—
68#2732C2214yes—
69#2727C2214yes—
70#2716C2214yes—
71#2716C2214yes—
72#2715C2214yes—
73#2713C2214yes—
74#2713C2214yes—
75#2712C2214yes—
76#2710C2214yes—
77#2704C2214yes—
78#2702C2214yes—
79#2700C2214yes—
80#2700C2214yes—
81#2698C2214yes—
82#2694C2214yes—
83#2694C2214yes—
84#2692C2214yes—
85#2690C2214yes—
86#2689C2214yes—
87#2687C2214yes—
88#2660C2212yes—
89#2660C2211yescharacteristic
90#2658C2212yes—
91#2658C2212yes—
92#2657C2211yescharacteristic
93#2641C2211yescharacteristic
94#2640C2212yes—
95#2640C2211yescharacteristic
96#2628C2214yes—
97#2623C2214yes—
98#2618C2214yes—
99#2614C2212yes—
100#2614C2212yes—
101#2612C2212yes—
102#2612C2212yes—
103#2611C2214yes—
104#2610C2214yes—
105#2606C2212yes—
106#2605C2212yes—
107#2604C2214yes—
108#2603C2214yes—
109#2602C2214yes—
110#2601C2214yes—
111#2596C2214yes—
112#2596C2214yes—
113#2592C2212yes—
114#2589C2214yes—
115#2582C2212yes—
116#2580C2212yes—
117#2575C2214yes—
118#2571C2212yes—
119#2570C2212yes—
120#2570C2212yes—
121#2569C2212yes—
122#2567C2211yescharacteristic
123#2567C2211yescharacteristic
124#2565C2214yes—
125#2564C2214yes—
126#2563C2211yescharacteristic
127#2563C2211yescharacteristic
128#2560C2214yes—
129#2560C2214yes—
130#2557C2214yes—
131#2557C2214yes—
132#2556C2214yes—
133#2556C2214yes—
134#2553C2214yes—
135#2552C2212yes—
136#2552C2212yes—
137#2552C2212yes—
138#2550C2214yes—
139#2549C2214yes—
140#2549C2212yes—
141#2548C2212yes—
142#2543C2214yes—
143#2542C2211yescharacteristic
144#2542C2211yescharacteristic
145#2542C2211yescharacteristic
146#2542C2214yes—
147#2542C2211yescharacteristic
148#2538C2212yes—
149#2538C2212yes—
150#2521C2214yes—
151#2521C2214yes—
152#2519C2214yes—
153#2513C2212yes—
154#2513C2212yes—
155#2512C2212yes—
156#2512C2212yes—
157#2512C2212yes—
158#2512C2212yes—
159#2511C2212yes—
160#2511C2212yes—
161#2506C2214yes—
162#2503C2212yes—
163#2501C2212yes—
164#2501C2212yes—
165#2501C2212yes—
166#2501C2212yes—
167#2501C2212yes—
168#2499C2214yes—
169#2498C2214yes—
170#2496C2214yes—
171#2492C2214yes—
172#2488C2214yes—
173#2488C2214yes—
174#2488C2214yes—
175#2486C2214yes—
176#2479C2214yes—
177#2479C2214yes—
178#2477C2214yes—
179#2474C2214yes—
180#2465C2214yes—
181#2459C2214yes—
182#2454C2214yes—
183#2451C2214yes—
184#2450C2214yes—
185#2448C2214yes—
186#2448C2212yes—
187#2447C2212yes—
188#2445C2212yes—
189#2445C2212yes—
190#2439C2214yes—
191#2438C2212yes—
192#2438C2214yes—
193#2438C2212yes—
194#2430C2214yes—
195#2425C2214yes—
196#2425C2214yes—
197#2425C2214yes—
198#2425C2214yes—
199#2419C2214yes—
200#2419C2214yes—
201#2402C2211yescharacteristic
202#2402C2211yescharacteristic
203#2399C2211yescharacteristic
204#2399C2211yescharacteristic
205#2379C2214yes—
206#2367C2212yes—
207#2366C2212yes—
208#2361C2212yes—
209#2361C2212yes—
210#2361C2212yes—
211#2360C2212yes—
212#2359C2214yes—
213#2357C2211yescharacteristic
214#2357C2211yescharacteristic
215#2357C2211yescharacteristic
216#2357C2212yes—
217#2356C2211yescharacteristic
218#2355C2212yes—
219#2355C2212yes—
220#2354C2212yes—
221#2354C2212yes—
222#2351C2211yescharacteristic
223Q8×C4⋊C4C2212yes—
224#2349C2211yescharacteristic
225#2349C2211yescharacteristic
226#2349C2211yescharacteristic
227#2346C2212yes—
228#2343C2212yes—
229#2339C2212yes—
230#2339C2212yes—
231#2334C2214yes—
232#2331C2211yescharacteristic
233#2331C2211yescharacteristic
234#2331C2212yes—
235#2331C2212yes—
236#2331C2214yes—
237#2331C2211yescharacteristic
238#2331C2211yescharacteristic
239#2331C2214yes—
240#2331C2212yes—
241#2328C2211yescharacteristic
242#2328C2212yes—
243#2328C2211yescharacteristic
244#2326C2211yescharacteristic
245#2326C2211yescharacteristic
246#2325C2214yes—
247#2322C2214yes—
248#2318C2212yes—
249#2318C2212yes—
250#2318C2212yes—
251C4×#125C2212yes—
252C4×#124C2212yes—
253C4×C22⋊Q8C2212yes—
254C4×C22⋊Q8C2212yes—
255C4×#123C2214yes—
256#2295C2212yes—
257#2295C2212yes—
258C2×#391C2214yes—
259C2×#389C2212yes—
260C2×#387C2214yes—
261#2283C2211yescharacteristic
262C2×#382C2211yescharacteristic
263#2275C2212yes—
264C4×#117C2211yescharacteristic
265C2×C4×C4⋊C4C2212yes—
266C2×#376C2211yescharacteristic
267C22×#41C2312yes—
268C23×Q8C2312yes—
269#539—416no—
270#536—416no—
271#532—28no—
272C2×C4⋊Q8—28no—
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2312yes—
277C2×C4⋊Q8C2311yescharacteristic
278C2×C4⋊Q8C2312yes—
279C2×C4⋊Q8C2314yes—
280C2×C4⋊Q8C2314yes—
281C2×#127C2311yescharacteristic
282C2×#127C2311yescharacteristic
283C2×#127C2311yescharacteristic
284#529—28no—
285#529—416no—
286C2×#126C2312yes—
287C2×#126C2314yes—
288C2×#126C2314yes—
289C2×#126C2314yes—
290C2×#126C2314yes—
291C2×#125C2311yescharacteristic
292C2×#125C2314yes—
293C2×#125C2314yes—
294C2×#125C2314yes—
295C2×#124C2311yescharacteristic
296C2×#124C2312yes—
297C2×#124C2311yescharacteristic
298C2×#124C2311yescharacteristic
299C2×#124C2314yes—
300C2×#124C2314yes—
301C2×#124C2314yes—
302C2×#123C2314yes—
303C2×#123C2312yes—
304C2×#123C2314yes—
305C2×#123C2314yes—
306C2×#123C2314yes—
307C2×#123C2314yes—
308C2×#123C2314yes—
309C2×#123C2314yes—
310C2×#123C2314yes—
311C2×C22⋊Q8C2311yescharacteristic
312C2×C22⋊Q8C2312yes—
313C2×C22⋊Q8C2312yes—
314C2×C22⋊Q8C2314yes—
315C2×C22⋊Q8C2314yes—
316C2×C22⋊Q8C2314yes—
317C2×C22⋊Q8C2314yes—
318C2×C22⋊Q8C2314yes—
319C2×C22⋊Q8C2314yes—
320C2×#121C2312yes—
321C2×#121C2311yescharacteristic
322C2×#121C2311yescharacteristic
323C2×#121C2311yescharacteristic
324C2×#121C2314yes—
325C2×#121C2314yes—
326C2×C4×Q8C2311yescharacteristic
327C2×C4×Q8C2312yes—
328C2×C4×Q8C2314yes—
329C2×C4×Q8C2312yes—
330C2×C4×Q8C2312yes—
331C2×C4×D4C2311yescharacteristic
332C2×C4×D4C2312yes—
333C2×C4×D4C2312yes—
334C2×C4×D4C2311yescharacteristic
335C2×C4×D4C2311yescharacteristic
336C2×C4×D4C2314yes—
337C2×C4×D4C2314yes—
338C2×C4×D4C2314yes—
339C2×C4×D4C2312yes—
340C2×C4×D4C2314yes—
341C2×C4×D4C2312yes—
342C2×C4×D4C2312yes—
343C2×#117C2312yes—
344C2×#117C2312yes—
345C2×#117C2314yes—
346C2×#117C2314yes—
347C22×C4⋊C4C2312yes—
348C22×C4⋊C4C2312yes—
349C22×C4⋊C4C2314yes—
350C22×C4⋊C4C2312yes—
351C22×C42C2311yescharacteristic
352C22×C42C2311yescharacteristic
353C22×C42C2314yes—
354C22×C42C2311yescharacteristic
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2312yes—
359#400C2312yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2312yes—
367#400C2312yes—
368#400C2314yes—
369#399C2312yes—
370#399C2314yes—
371#399C2314yes—
372#399C2314yes—
373#399C2314yes—
374#399C2314yes—
375#399C2312yes—
376#399C2312yes—
377#399C2314yes—
378#399C2314yes—
379#399C2314yes—
380#399C2312yes—
381#399C2312yes—
382#399C2312yes—
383#399C2312yes—
384#399C2312yes—
385#398C2312yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2312yes—
392#398C2312yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2312yes—
398#398C2312yes—
399#398C2312yes—
400#398C2312yes—
401#398C2312yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#397C2314yes—
411#397C2314yes—
412#397C2314yes—
413#397C2314yes—
414#397C2314yes—
415#397C2314yes—
416#397C2314yes—
417#397C2314yes—
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#396C2314yes—
422#396C2314yes—
423#396C2314yes—
424#396C2314yes—
425#396C2314yes—
426#396C2314yes—
427#396C2314yes—
428#396C2314yes—
429#395C2312yes—
430#395C2312yes—
431#395C2312yes—
432#395C2312yes—
433#395C2312yes—
434#395C2312yes—
435#395C2312yes—
436#395C2312yes—
437#395C2314yes—
438#395C2314yes—
439#395C2314yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#393C2312yes—
449#393C2314yes—
450#393C2312yes—
451#393C2312yes—
452#393C2312yes—
453#393C2314yes—
454#393C2314yes—
455#393C2314yes—
456#393C2314yes—
457#392C2314yes—
458#392C2314yes—
459#391C2312yes—
460#391C2314yes—
461#391C2312yes—
462#391C2314yes—
463#391C2312yes—
464#391C2312yes—
465#391C2311yescharacteristic
466#391C2311yescharacteristic
467#391C2314yes—
468#391C2314yes—
469#391C2314yes—
470#391C2314yes—
471#391C2314yes—
472#391C2314yes—
473#391C2314yes—
474#391C2314yes—
475#391C2314yes—
476#391C2314yes—
477#391C2312yes—
478#391C2312yes—
479#391C2312yes—
480#391C2312yes—
481#391C2312yes—
482#390C2314yes—
483#390C2314yes—
484#390C2312yes—
485#390C2312yes—
486#390C2311yescharacteristic
487#390C2312yes—
488#390C2311yescharacteristic
489#390C2311yescharacteristic
490#390C2312yes—
491#390C2311yescharacteristic
492#390C2311yescharacteristic
493#390C2311yescharacteristic
494#390C2312yes—
495#390C2312yes—
496#390C2314yes—
497#390C2314yes—
498#390C2314yes—
499#390C2312yes—
500#390C2312yes—
501#390C2314yes—
502#390C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2314yes—
506#389C2314yes—
507#389C2312yes—
508#389C2312yes—
509#389C2314yes—
510#389C2312yes—
511#389C2312yes—
512#389C2314yes—
513#389C2312yes—
514#389C2312yes—
515#389C2314yes—
516#389C2314yes—
517#389C2314yes—
518#389C2314yes—
519#389C2312yes—
520#389C2314yes—
521#389C2314yes—
522#389C2312yes—
523#389C2312yes—
524#389C2314yes—
525#389C2314yes—
526#389C2312yes—
527#389C2314yes—
528#389C2312yes—
529#389C2312yes—
530#389C2314yes—
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#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2312yes—
573#387C2312yes—
574#387C2312yes—
575#387C2312yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2312yes—
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#387C2314yes—
593#387C2314yes—
594#387C2312yes—
595#387C2312yes—
596#387C2312yes—
597#387C2312yes—
598#387C2312yes—
599#387C2312yes—
600#387C2314yes—
601#386C2314yes—
602#386C2314yes—
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#386C2314yes—
617#386C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2312yes—
621#385C2312yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2312yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2312yes—
635#384C2314yes—
636#384C2312yes—
637#384C2312yes—
638#384C2312yes—
639#384C2312yes—
640#384C2312yes—
641#384C2311yescharacteristic
642#384C2311yescharacteristic
643#384C2312yes—
644#384C2314yes—
645#383C2311yescharacteristic
646#383C2311yescharacteristic
647#383C2312yes—
648#382C2312yes—
649#382C2312yes—
650#382C2312yes—
651#382C2314yes—
652#382C2311yescharacteristic
653#382C2311yescharacteristic
654#382C2312yes—
655#382C2312yes—
656#382C2314yes—
657#382C2312yes—
658#382C2311yescharacteristic
659#382C2311yescharacteristic
660#382C2312yes—
661#381C2312yes—
662#381C2312yes—
663#381C2312yes—
664#381C2314yes—
665#381C2314yes—
666#381C2311yescharacteristic
667#381C2311yescharacteristic
668#381C2314yes—
669#381C2314yes—
670#380C2314yes—
671#380C2314yes—
672#380C2314yes—
673#380C2312yes—
674#380C2312yes—
675#380C2312yes—
676#380C2312yes—
677#380C2312yes—
678#380C2312yes—
679#380C2314yes—
680#380C2314yes—
681#380C2314yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2314yes—
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⋊C4C2314yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2314yes—
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2311yescharacteristic
704C4×C4⋊C4C2312yes—
705C4×C4⋊C4C2312yes—
706C4×C4⋊C4C2311yescharacteristic
707C4×C4⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2311yescharacteristic
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2314yes—
714C4×C22⋊C4C2314yes—
715C4×C22⋊C4C2314yes—
716C4×C22⋊C4C2312yes—
717C4×C22⋊C4C2312yes—
718C4×C22⋊C4C2312yes—
719C4×C22⋊C4C2311yescharacteristic
720#376C2311yescharacteristic
721#376C2311yescharacteristic
722#376C2312yes—
723#376C2312yes—
724#376C2312yes—
725#376C2311yescharacteristic
726#376C2311yescharacteristic
727#376C2311yescharacteristic
728#376C2311yescharacteristic
729#376C2312yes—
730C2×#95C2312yes—
731C2×#95C2312yes—
732C2×#95C2312yes—
733C2×#95C2312yes—
734C2×#95C2312yes—
735C2×#95C2312yes—
736C2×#95C2314yes—
737C2×#95C2314yes—
738C2×#95C2312yes—
739C43C2312yes—
740C2×#41—28no—
741C2×#41—48no—
742C22×Q8—28no—
743C22×Q8—48no—
744C22×Q8C2411yescharacteristic
745C22×Q8C2412yes—
746C22×Q8C2412yes—
747C22×Q8C2412yes—
748C22×Q8C2412yes—
749C22×Q8C2414yes—
750C22×Q8C2412yes—
751C22×D4C2412yes—
752C22×D4C2411yescharacteristic
753C22×D4C2411yescharacteristic
754C22×D4C2411yescharacteristic
755C22×D4C2412yes—
756C22×D4C2412yes—
757C22×D4C2414yes—
758C22×D4C2412yes—
759C22×D4C2412yes—
760C22×D4C2414yes—
761C23×C4C2414yes—
762C23×C4C2412yes—
763C23×C4C2411yescharacteristic
764C23×C4C2411yescharacteristic
765C23×C4C2414yes—
766C23×C4C2412yes—
767C23×C4C2414yes—
768C23×C4C2412yes—
769C23×C4C2412yes—
770C23×C4C2412yes—
771C23×C4C2414yes—
772C23×C4C2414yes—
773C23×C4C2411yescharacteristic
774C4⋊Q8—28no—
775C4⋊Q8—24no—
776C4⋊Q8—24no—
777C4⋊Q8—28no—
778C4⋊Q8—28no—
779C4⋊Q8—24no—
780C4⋊Q8—48no—
781C4⋊Q8—48no—
782#127—24no—
783#127—24no—
784#127—42no—
785#126—28no—
786#126—48no—
787#126—48no—
788#126—48no—
789#126—48no—
790#125—24no—
791#125—48no—
792#125—48no—
793#125—48no—
794#124—24no—
795#124—28no—
796#124—24no—
797#124—48no—
798#124—48no—
799#124—42no—
800#124—48no—
801#123—28no—
802#123—216no—
803#123—216no—
804#123—48no—
805#123—48no—
806#123—48no—
807#123—48no—
808#123—48no—
809#123—48no—
810C22⋊Q8—24no—
811C22⋊Q8—28no—
812C22⋊Q8—28no—
813C22⋊Q8—48no—
814C22⋊Q8—48no—
815C22⋊Q8—48no—
816C22⋊Q8—48no—
817C22⋊Q8—48no—
818C22⋊Q8—48no—
819#121—24no—
820#121—24no—
821#121—24no—
822#121—28no—
823#121—48no—
824#121—48no—
825C4×Q8—24no—
826C4×Q8—28no—
827C4×Q8—44no—
828C4×Q8—44no—
829C4×Q8—48no—
830C4×D4—28no—
831C4×D4—216no—
832C4×D4—24no—
833C4×D4—24no—
834C4×D4—24no—
835C4×D4—28no—
836C4×D4—44no—
837C4×D4—44no—
838C4×D4—44no—
839C4×D4—48no—
840C4×D4—48no—
841C4×D4—48no—
842#117—28no—
843#117—28no—
844#117—48no—
845#117—48no—
846C2×C4⋊C4—28no—
847C2×C4⋊C4—28no—
848C2×C4⋊C4—44no—
849C2×C4⋊C4—48no—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2411yescharacteristic
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2412yes—
955C2×C42—24no—
956C2×C42—42no—
957C2×C42—48no—
958C2×C42#4118yes—
959C2×C42C2414yes—
960C2×C42C2412yes—
961C2×C42C2412yes—
962C2×C42C2412yes—
963C2×C42C2412yes—
964C2×C42C2412yes—
965C2×C42C2411yescharacteristic
966C2×C42C2412yes—
967C2×C42C2412yes—
968C2×C42C2411yescharacteristic
969C2×C42C2411yescharacteristic
970C2×C42C2412yes—
971C2×C42C2414yes—
972C2×C42C2414yes—
973C2×C42C2414yes—
974C2×C42C2414yes—
975C2×C42C2414yes—
976C2×C42C2414yes—
977C2×C42C2414yes—
978C2×C42C2412yes—
979C2×C42C2412yes—
980C2×C42C2412yes—
981C2×C42C2414yes—
982C2×C42C2411yescharacteristic
983C2×C42C2411yescharacteristic
984C2×C42C2411yescharacteristic
985C2×C42C2411yescharacteristic
986C2×C42C2411yescharacteristic
987#95C2411yescharacteristic
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2411yescharacteristic
992#95C2411yescharacteristic
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2411yescharacteristic
1016#95C2414yes—
1017#95C2411yescharacteristic
1018#95C2411yescharacteristic
1019#95C2412yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2412yes—
1024#95C2412yes—
1025#95C2411yescharacteristic
1026#95C2411yescharacteristic
1027#95C2412yes—
1028#95C2412yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2412yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2412yes—
1041#95C2412yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2412yes—
1048#95C2412yes—
1049#95C2412yes—
1050#95C2412yes—
1051#95C2412yes—
1052#95C2412yes—
1053#95C2414yes—
1054#95C2414yes—
1055#95C2414yes—
1056#95C2414yes—
1057#95C2414yes—
1058#95C2414yes—
1059C24C2512yes—
1060C24C2512yes—
1061C24C2512yes—
1062C24C2511yescharacteristic
1063#41—816no—
1064C2×Q8—22no—
1065C2×Q8—24no—
1066C2×Q8—24no—
1067C2×Q8—24no—
1068C2×Q8—28no—
1069C2×Q8—24no—
1070C2×Q8—24no—
1071C2×Q8—24no—
1072C2×Q8—22no—
1073C2×Q8—22no—
1074C2×Q8—42no—
1075C2×Q8—42no—
1076C2×Q8—44no—
1077C2×Q8—44no—
1078C2×Q8—44no—
1079C2×Q8—44no—
1080C2×Q8—44no—
1081C2×Q8—42no—
1082C2×Q8—816no—
1083C2×D4—24no—
1084C2×D4—24no—
1085C2×D4—24no—
1086C2×D4—28no—
1087C2×D4—28no—
1088C2×D4—28no—
1089C2×D4—22no—
1090C2×D4—22no—
1091C2×D4—22no—
1092C2×D4—24no—
1093C2×D4—24no—
1094C2×D4—22no—
1095C2×D4—22no—
1096C2×D4—22no—
1097C2×D4—28no—
1098C2×D4—22no—
1099C2×D4—22no—
1100C2×D4—22no—
1101C2×D4—44no—
1102C2×D4—44no—
1103C2×D4—44no—
1104C2×D4—44no—
1105C2×D4—44no—
1106C2×D4—44no—
1107C2×D4—44no—
1108C22×C4—24no—
1109C22×C4—22no—
1110C22×C4—22no—
1111C22×C4—28no—
1112C22×C4—24no—
1113C22×C4—28no—
1114C22×C4—28no—
1115C22×C4—28no—
1116C22×C4—24no—
1117C22×C4—24no—
1118C22×C4—24no—
1119C22×C4—24no—
1120C22×C4—24no—
1121C22×C4—28no—
1122C22×C4—42no—
1123C22×C4—42no—
1124C22×C4—42no—
1125C22×C4—44no—
1126C22×C4—44no—
1127C22×C4—44no—
1128C22×C4—44no—
1129C22×C4—44no—
1130C22×C4—44no—
1131C22×C4—44no—
1132C22×C4—44no—
1133C22×C4—44no—
1134C22×C4—42no—
1135C22×C4—44no—
1136C22×C4—44no—
1137C22×C4—44no—
1138C22×C4—44no—
1139C22×C4C2×#4114yes—
1140C22×C4C2×#4114yes—
1141C22×C4C2×#4114yes—
1142C22×C4C2512yes—
1143C22×C4C2512yes—
1144C22×C4C2512yes—
1145C22×C4C2514yes—
1146C22×C4C2512yes—
1147C22×C4C2512yes—
1148C22×C4C2512yes—
1149C22×C4C2514yes—
1150C22×C4C2512yes—
1151C22×C4C2512yes—
1152C22×C4C2512yes—
1153C22×C4C2512yes—
1154C22×C4C2512yes—
1155C22×C4C2514yes—
1156C22×C4C2514yes—
1157C22×C4C2512yes—
1158C22×C4C2512yes—
1159C22×C4C2512yes—
1160C22×C4C2511yescharacteristic
1161C22×C4C2511yescharacteristic
1162C22×C4C2511yescharacteristic
1163C22×C4C2511yescharacteristic
1164C22×C4C2511yescharacteristic
1165C22×C4C2512yes—
1166C22×C4C2512yes—
1167C22×C4C2512yes—
1168C22×C4C2511yescharacteristic
1169C4⋊C4—24no—
1170C4⋊C4—24no—
1171C4⋊C4—28no—
1172C4⋊C4—28no—
1173C4⋊C4—24no—
1174C4⋊C4—24no—
1175C4⋊C4—24no—
1176C4⋊C4—24no—
1177C4⋊C4—24no—
1178C4⋊C4—22no—
1179C4⋊C4—22no—
1180C4⋊C4—22no—
1181C4⋊C4—24no—
1182C4⋊C4—22no—
1183C4⋊C4—24no—
1184C4⋊C4—24no—
1185C4⋊C4—24no—
1186C4⋊C4—24no—
1187C4⋊C4—24no—
1188C4⋊C4—28no—
1189C4⋊C4—28no—
1190C4⋊C4—24no—
1191C4⋊C4—28no—
1192C4⋊C4—24no—
1193C4⋊C4—24no—
1194C4⋊C4—24no—
1195C4⋊C4—28no—
1196C4⋊C4—28no—
1197C4⋊C4—24no—
1198C4⋊C4—24no—
1199C4⋊C4—24no—
1200C4⋊C4—24no—
1201C4⋊C4—24no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4—44no—
1207C4⋊C4—42no—
1208C4⋊C4—42no—
1209C4⋊C4—42no—
1210C4⋊C4—42no—
1211C4⋊C4—42no—
1212C4⋊C4—42no—
1213C4⋊C4—42no—
1214C4⋊C4—44no—
1215C4⋊C4—42no—
1216C4⋊C4—44no—
1217C4⋊C4—44no—
1218C4⋊C4—44no—
1219C4⋊C4—42no—
1220C4⋊C4—42no—
1221C4⋊C4—42no—
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—44no—
1231C4⋊C4—44no—
1232C22⋊C4—24no—
1233C22⋊C4—24no—
1234C22⋊C4—24no—
1235C22⋊C4—24no—
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—28no—
1245C22⋊C4—28no—
1246C22⋊C4—28no—
1247C22⋊C4—28no—
1248C22⋊C4—28no—
1249C22⋊C4—28no—
1250C22⋊C4—44no—
1251C22⋊C4—44no—
1252C22⋊C4—44no—
1253C22⋊C4—44no—
1254C22⋊C4—44no—
1255C22⋊C4—44no—
1256C22⋊C4—44no—
1257C22⋊C4—44no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—44no—
1261C22⋊C4—44no—
1262C22⋊C4—44no—
1263C22⋊C4—44no—
1264C22⋊C4—44no—
1265C22⋊C4—44no—
1266C22⋊C4—44no—
1267C22⋊C4—44no—
1268C22⋊C4—44no—
1269C22⋊C4—44no—
1270C22⋊C4—44no—
1271C22⋊C4—44no—
1272C22⋊C4—44no—
1273C22⋊C4H(5,𝔽2)18yes—
1274C42—24no—
1275C42—24no—
1276C42—24no—
1277C42—28no—
1278C42—24no—
1279C42—22no—
1280C42—24no—
1281C42—24no—
1282C42—22no—
1283C42—22no—
1284C42—24no—
1285C42—24no—
1286C42—42no—
1287C42—44no—
1288C42—44no—
1289C42—44no—
1290C42—44no—
1291C42—42no—
1292C42—44no—
1293C42—42no—
1294C42—44no—
1295C42—44no—
1296C42—44no—
1297C42C2×#4114yes—
1298C42C2×#4114yes—
1299C42C2×#4114yes—
1300C42C2×#4114yes—
1301C422−1+414yes—
1302C23—21no—
1303C23—21no—
1304C23—22no—
1305C23—22no—
1306C23—22no—
1307C23—22no—
1308C23—24no—
1309C23—24no—
1310C23—24no—
1311C23—22no—
1312C23—22no—
1313C23—22no—
1314C23—22no—
1315C23—22no—
1316C23—22no—
1317C23—24no—
1318C23—24no—
1319C23—24no—
1320C23C22×#4112yes—
1321C23C2×H(5,𝔽2)14yes—
1322C23C2611yescharacteristic
1323Q8—48no—
1324Q8—44no—
1325Q8—84no—
1326Q8—84no—
1327Q8—84no—
1328Q8—88no—
1329Q8—84no—
1330D4—48no—
1331D4—48no—
1332D4—48no—
1333D4—44no—
1334D4—44no—
1335D4—44no—
1336D4—84no—
1337D4—88no—
1338D4—84no—
1339D4—164no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—21no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—21no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—28no—
1353C2×C4—28no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—24no—
1360C2×C4—24no—
1361C2×C4—24no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—24no—
1365C2×C4—22no—
1366C2×C4—24no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—24no—
1370C2×C4—24no—
1371C2×C4—24no—
1372C2×C4—24no—
1373C2×C4—22no—
1374C2×C4—24no—
1375C2×C4—24no—
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—22no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—24no—
1391C2×C4—24no—
1392C2×C4—22no—
1393C2×C4—24no—
1394C2×C4—24no—
1395C2×C4—22no—
1396C2×C4—22no—
1397C2×C4—22no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—24no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—44no—
1405C2×C4—48no—
1406C2×C4—416no—
1407C2×C4—84no—
1408C2×C4—88no—
1409C2×C4—84no—
1410C2×C4—84no—
1411C2×C4—88no—
1412C2×C4—84no—
1413C2×C4—88no—
1414C2×C4—164no—
1415C2×C4C22×#4112yes—
1416C2×C4C22×#4112yes—
1417C2×C4C22×#4112yes—
1418C2×C4C22×#4112yes—
1419C2×C4C22×#4112yes—
1420C2×C4C22×#4112yes—
1421C2×C4C2×H(5,𝔽2)14yes—
1422C2×C4C2×H(5,𝔽2)14yes—
1423C2×C4C2×2−1+414yes—
1424C2×C4C2×2−1+412yes—
1425C2×C4#58512yes—
1426C22—22no—
1427C22—22no—
1428C22—24no—
1429C22—24no—
1430C22—42no—
1431C22—42no—
1432C22—42no—
1433C22—42no—
1434C22—42no—
1435C22—42no—
1436C22—42no—
1437C22—42no—
1438C22—42no—
1439C22—44no—
1440C22—44no—
1441C22—44no—
1442C22—44no—
1443C22—44no—
1444C22—44no—
1445C22#350814yes—
1446C22C23×#4111yescharacteristic
1447C22C22×H(5,𝔽2)12yes—
1448C22C22×2−1+411yescharacteristic
1449C22C2×#58511yescharacteristic
1450C222−1+612yes—
1451C4—22no—
1452C4—22no—
1453C4—22no—
1454C4—22no—
1455C4—22no—
1456C4—24no—
1457C4—24no—
1458C4—24no—
1459C4—42no—
1460C4—44no—
1461C4—44no—
1462C4—42no—
1463C4—42no—
1464C4—42no—
1465C4—42no—
1466C4—42no—
1467C4—42no—
1468C4—42no—
1469C4—42no—
1470C4—42no—
1471C4—42no—
1472C4—44no—
1473C4—44no—
1474C4—42no—
1475C4—42no—
1476C4—42no—
1477C4#350714yes—
1478C2—24no—
1479C2—82no—
1480C2—82no—
1481C2—82no—
1482C2C2×#350711yescharacteristic
1483C2C2×#350811yescharacteristic
1484C2#6286011yescharacteristic
1485C2#6291512yes—
1486C2#6292112yes—
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. #51620C2semidirect
2. #51617C2semidirect
3. #47710C2semidirect
4. #47709C2semidirect
5. #45434C2semidirect
6. #45430C2semidirect
7. #45350C2semidirect
8. #45211C2semidirect
9. #45083C2semidirect
10. #45056C2semidirect
11. #44979C2semidirect
12. #44947C2semidirect
13. #39810C2semidirect
14. #39803C2semidirect
15. #39761C2semidirect
16. #39753C2semidirect
17. #39431C2semidirect
18. #39384C2semidirect
19. #39199C2semidirect
20. #37779C2semidirect
21. #37632C2semidirect
22. #37000C2semidirect
23. #36487C2semidirect
24. #36117C2semidirect
25. #35464C2semidirect
26. #35317C2semidirect
28. #34878C2semidirect
29. #34398C2semidirect
30. #34229C2semidirect
31. C2×#2331C2semidirect

Maximal subgroups

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

subgroupindex
#516202
#516172
#477102
#477092
#454342
#454302
#453502
#452112
#450832
#450562
#449792
#449472
#398102
#398032
#397612
#397532
#394312
#393842
#391992
#377792
#376322
#370002
#364872
#361172
#354642
#353172
#353032
#348782
#343982
#342292
C2×#23312