Finite Group Databasebeta

← #8345842

Subgroups — #8345842

Order 512.

4482 conjugacy classes of subgroups.

The subgroup lattice has 1424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59833C212yesmaximal, complemented
2#59754C212yesmaximal, complemented
3#59136C212yesmaximal, complemented
4#58264C214yesmaximal, complemented
5#57382C212yesmaximal, complemented
6#56347C212yesmaximal, complemented
7#55477C214yesmaximal, complemented
8#54965C214yesmaximal, complemented
9#53125C212yesmaximal, complemented
10#53005C212yesmaximal, complemented
11#52289C211yesmaximal, characteristic, complemented
12#50817C214yesmaximal, complemented
13#48472C214yesmaximal, complemented
14#46345C212yesmaximal, complemented
15#45407C212yesmaximal, complemented
16#44306C212yesmaximal, complemented
17#42955C211yesmaximal, characteristic, complemented
18#42821C212yesmaximal, complemented
19#42517C211yesmaximal, characteristic, complemented
20#42479C212yesmaximal, complemented
21#40958C214yesmaximal, complemented
22#40128C212yesmaximal, complemented
23#39217C212yesmaximal, complemented
24#39083C212yesmaximal, complemented
25#39069C212yesmaximal, complemented
26#37523C211yesmaximal, characteristic, complemented
27#36040C211yesmaximal, characteristic, complemented
28#35704C211yesmaximal, characteristic
29#35574C211yesmaximal, characteristic, complemented
30C2×#557C2211yescharacteristic
31C2×#554C2212yes—
32C2×#550C2211yescharacteristic
33C22×C4⋊Q8C2211yescharacteristic
34C2×#520C2211yescharacteristic
35#2860C2212yes—
36#2860C2212yes—
37#2844C2214yes—
38#2843C2212yes—
39#2832C2214yes—
40#2832C2214yes—
41#2832C2214yes—
42#2826C2212yes—
43#2824C2212yes—
44#2824C2212yes—
45#2816C2214yes—
46#2814C2214yes—
47#2814C2214yes—
48#2808C2214yes—
49#2807C2211yescharacteristic
50#2802C2212yes—
51#2797C2214yes—
52#2792C2214yes—
53#2792C2212yes—
54#2790C2212yes—
55#2785C2214yes—
56#2785C2212yes—
57#2782C2212yes—
58#2781C2214yes—
59#2781C2214yes—
60#2775C2214yes—
61#2774C2214yes—
62#2774C2214yes—
63#2770C2214yes—
64#2768C2214yes—
65#2768C2214yes—
66#2763C2211yescharacteristic
67#2763C2212yes—
68#2756C2214yes—
69#2755C2212yes—
70#2755C2214yes—
71#2754C2214yes—
72#2754C2214yes—
73#2753C2214yes—
74#2753C2214yes—
75#2742C2211yescharacteristic
76#2742C2212yes—
77#2741C2214yes—
78#2741C2214yes—
79#2741C2214yes—
80#2739C2214yes—
81#2738C2214yes—
82#2731C2214yes—
83#2729C2214yes—
84#2729C2214yes—
85#2725C2214yes—
86#2723C2214yes—
87#2723C2214yes—
88#2720C2214yes—
89#2718C2214yes—
90#2718C2214yes—
91#2718C2214yes—
92#2713C2212yes—
93#2704C2212yes—
94#2702C2214yes—
95#2702C2214yes—
96#2698C2214yes—
97#2695C2214yes—
98#2695C2214yes—
99#2694C2214yes—
100#2689C2214yes—
101#2681C2214yes—
102#2681C2214yes—
103#2680C2214yes—
104#2677C2211yescharacteristic
105#2677C2214yes—
106#2672C2214yes—
107#2672C2214yes—
108#2666C2214yes—
109#2666C2214yes—
110#2666C2214yes—
111#2663C2214yes—
112#2663C2214yes—
113#2650C2214yes—
114#2649C2214yes—
115#2647C2212yes—
116#2641C2212yes—
117#2636C2214yes—
118#2635C2212yes—
119#2628C2211yescharacteristic
120#2628C2212yes—
121#2624C2212yes—
122#2619C2211yescharacteristic
123#2618C2214yes—
124#2616C2214yes—
125#2602C2214yes—
126#2596C2214yes—
127#2591C2212yes—
128#2584C2212yes—
129#2581C2211yescharacteristic
130#2581C2212yes—
131#2580C2211yescharacteristic
132#2580C2212yes—
133#2580C2212yes—
134#2579C2212yes—
135#2579C2212yes—
136#2578C2214yes—
137#2578C2214yes—
138#2575C2214yes—
139#2571C2212yes—
140#2571C2212yes—
141#2570C2214yes—
142#2567C2212yes—
143#2563C2212yes—
144#2563C2212yes—
145#2563C2211yescharacteristic
146#2562C2214yes—
147#2560C2214yes—
148#2556C2214yes—
149#2556C2214yes—
150#2553C2214yes—
151#2553C2214yes—
152#2550C2212yes—
153#2550C2212yes—
154#2550C2212yes—
155#2548C2212yes—
156#2548C2211yescharacteristic
157#2525C2214yes—
158#2521C2214yes—
159#2519C2214yes—
160#2519C2214yes—
161#2519C2214yes—
162#2518C2214yes—
163#2513C2212yes—
164#2513C2212yes—
165#2513C2212yes—
166#2513C2212yes—
167#2512C2212yes—
168#2512C2212yes—
169#2509C2212yes—
170#2508C2212yes—
171#2508C2212yes—
172#2508C2212yes—
173#2506C2212yes—
174#2500C2212yes—
175#2492C2214yes—
176#2492C2214yes—
177#2489C2214yes—
178#2489C2214yes—
179#2476C2214yes—
180#2473C2214yes—
181#2468C2214yes—
182#2467C2214yes—
183#2467C2214yes—
184#2465C2214yes—
185#2463C2212yes—
186#2461C2214yes—
187#2456C2214yes—
188#2455C2212yes—
189#2455C2212yes—
190#2454C2212yes—
191#2454C2214yes—
192#2454C2212yes—
193#2453C2212yes—
194#2452C2212yes—
195#2452C2212yes—
196#2452C2212yes—
197#2452C2212yes—
198#2452C2212yes—
199#2451C2212yes—
200#2451C2212yes—
201#2448C2212yes—
202#2448C2212yes—
203#2445C2212yes—
204#2445C2212yes—
205#2445C2212yes—
206#2445C2212yes—
207#2445C2212yes—
208#2442C2212yes—
209#2442C2212yes—
210#2442C2214yes—
211#2440C2214yes—
212#2440C2214yes—
213#2439C2214yes—
214#2431C2212yes—
215#2417C2214yes—
216#2409C2214yes—
217#2409C2214yes—
218#2409C2212yes—
219#2409C2212yes—
220#2406C2214yes—
221#2406C2212yes—
222#2402C2212yes—
223#2399C2212yes—
224#2396C2211yescharacteristic
225#2396C2211yescharacteristic
226#2396C2212yes—
227#2388C2212yes—
228#2379C2214yes—
229#2374C2214yes—
230#2369C2212yes—
231#2367C2212yes—
232#2367C2212yes—
233#2361C2212yes—
234#2361C2212yes—
235#2360C2214yes—
236#2357C2211yescharacteristic
237#2355C2212yes—
238#2351C2212yes—
239#2351C2211yescharacteristic
240D4×C4⋊C4C2214yes—
241#2347C2212yes—
242#2341C2212yes—
243#2335C2214yes—
244#2334C2214yes—
245#2320C2212yes—
246#2319C2212yes—
247#2317C2211yescharacteristic
248#2316C2211yescharacteristic
249#2311C2211yescharacteristic
250C4×C4⋊Q8C2212yes—
251C4×#125C2212yes—
252C4×#125C2212yes—
253C4×#124C2212yes—
254C4×C22⋊Q8C2212yes—
255C4×#121C2212yes—
256#2298C2212yes—
257#2297C2211yescharacteristic
258#2296C2211yescharacteristic
259C22×#41C2311yescharacteristic
260C22×#41C2312yes—
261C23×Q8C2312yes—
262#557—44no—
263#554—48no—
264#550—44no—
265C2×C4⋊Q8—44no—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2314yes—
272C2×#127C2311yescharacteristic
273C2×#127C2312yes—
274C2×#126C2314yes—
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#125C2312yes—
279C2×#125C2312yes—
280C2×#125C2312yes—
281C2×#125C2314yes—
282C2×#125C2314yes—
283C2×#124C2312yes—
284C2×#124C2314yes—
285C2×#123C2314yes—
286C2×#123C2314yes—
287C2×#123C2314yes—
288C2×#123C2314yes—
289C2×#123C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2314yes—
299C2×#121C2312yes—
300C2×#121C2314yes—
301C2×#121C2312yes—
302#520—44no—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2311yescharacteristic
311C2×C4×D4C2312yes—
312C2×C4×D4C2311yescharacteristic
313C2×C4×D4C2312yes—
314C2×C4×D4C2311yescharacteristic
315C2×C4×D4C2312yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2314yes—
319C2×C4×D4C2314yes—
320C2×C4×D4C2314yes—
321C2×#117C2311yescharacteristic
322C2×#117C2311yescharacteristic
323C2×#117C2311yescharacteristic
324C2×#117C2312yes—
325C22×C4⋊C4C2311yescharacteristic
326C22×C4⋊C4C2311yescharacteristic
327C22×C4⋊C4C2312yes—
328C22×C4⋊C4C2312yes—
329C22×C4⋊C4C2314yes—
330C22×C42C2311yescharacteristic
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2311yescharacteristic
338#400C2314yes—
339#400C2312yes—
340#400C2312yes—
341#400C2314yes—
342#400C2312yes—
343#400C2312yes—
344#400C2314yes—
345#400C2314yes—
346#400C2312yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2311yescharacteristic
352#400C2312yes—
353#399C2314yes—
354#399C2314yes—
355#399C2312yes—
356#399C2314yes—
357#399C2311yescharacteristic
358#399C2312yes—
359#399C2314yes—
360#399C2314yes—
361#399C2311yescharacteristic
362#399C2314yes—
363#398C2314yes—
364#398C2312yes—
365#398C2314yes—
366#398C2312yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2312yes—
376#398C2314yes—
377#398C2312yes—
378#398C2312yes—
379#398C2312yes—
380#398C2312yes—
381#398C2312yes—
382#398C2312yes—
383#398C2312yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
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#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2312yes—
408#396C2314yes—
409#396C2312yes—
410#396C2314yes—
411#396C2314yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2314yes—
416#395C2312yes—
417#395C2314yes—
418#395C2314yes—
419#395C2311yescharacteristic
420#395C2312yes—
421#395C2314yes—
422#395C2312yes—
423#395C2311yescharacteristic
424#395C2314yes—
425#395C2312yes—
426#395C2312yes—
427#395C2312yes—
428#395C2314yes—
429#394C2314yes—
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#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2312yes—
448#394C2312yes—
449#394C2314yes—
450#394C2312yes—
451#394C2312yes—
452#394C2314yes—
453#393C2314yes—
454#393C2314yes—
455#393C2314yes—
456#393C2311yescharacteristic
457#393C2312yes—
458#393C2312yes—
459#393C2312yes—
460#393C2312yes—
461#393C2314yes—
462#393C2314yes—
463#393C2314yes—
464#393C2314yes—
465#393C2314yes—
466#393C2311yescharacteristic
467#392C2312yes—
468#392C2312yes—
469#392C2314yes—
470#392C2314yes—
471#391C2314yes—
472#391C2312yes—
473#391C2312yes—
474#391C2312yes—
475#391C2314yes—
476#391C2312yes—
477#391C2314yes—
478#391C2314yes—
479#391C2312yes—
480#391C2314yes—
481#391C2314yes—
482#391C2314yes—
483#391C2314yes—
484#391C2312yes—
485#390C2314yes—
486#390C2312yes—
487#390C2314yes—
488#390C2312yes—
489#390C2312yes—
490#390C2312yes—
491#390C2312yes—
492#390C2312yes—
493#390C2314yes—
494#390C2312yes—
495#390C2312yes—
496#390C2312yes—
497#390C2312yes—
498#390C2312yes—
499#390C2314yes—
500#390C2312yes—
501#390C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2312yes—
509#389C2312yes—
510#389C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2314yes—
515#389C2314yes—
516#389C2312yes—
517#389C2314yes—
518#389C2314yes—
519#389C2314yes—
520#389C2314yes—
521#389C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2312yes—
525#389C2314yes—
526#389C2312yes—
527#389C2312yes—
528#389C2312yes—
529#389C2314yes—
530#389C2314yes—
531#389C2312yes—
532#389C2314yes—
533#389C2312yes—
534#389C2314yes—
535#389C2314yes—
536#389C2314yes—
537#389C2312yes—
538#389C2312yes—
539#389C2312yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2312yes—
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#388C2314yes—
564#388C2314yes—
565#388C2312yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2312yes—
578#388C2314yes—
579#388C2312yes—
580#387C2312yes—
581#387C2312yes—
582#387C2314yes—
583#387C2312yes—
584#387C2314yes—
585#387C2312yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2312yes—
596#387C2312yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2312yes—
601#387C2314yes—
602#387C2314yes—
603#387C2312yes—
604#387C2314yes—
605#387C2312yes—
606#387C2312yes—
607#386C2314yes—
608#386C2312yes—
609#386C2312yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2312yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2312yes—
621#385C2311yescharacteristic
622#385C2312yes—
623#385C2311yescharacteristic
624#385C2312yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2311yescharacteristic
629#385C2311yescharacteristic
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2312yes—
644#385C2312yes—
645#384C2312yes—
646#384C2314yes—
647#384C2312yes—
648#384C2312yes—
649#383C2314yes—
650#383C2314yes—
651#382C2312yes—
652#382C2312yes—
653#382C2312yes—
654#382C2314yes—
655#382C2312yes—
656#382C2314yes—
657#382C2314yes—
658#382C2311yescharacteristic
659#382C2314yes—
660#382C2314yes—
661#382C2314yes—
662#382C2312yes—
663#382C2312yes—
664#382C2311yescharacteristic
665#382C2314yes—
666#381C2314yes—
667#381C2312yes—
668#380C2312yes—
669#380C2314yes—
670#380C2314yes—
671#380C2314yes—
672#380C2314yes—
673#380C2314yes—
674#380C2314yes—
675#380C2314yes—
676#380C2314yes—
677#380C2312yes—
678#380C2314yes—
679#380C2312yes—
680#380C2312yes—
681#380C2314yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2311yescharacteristic
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2314yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2314yes—
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2314yes—
704C4×C4⋊C4C2312yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2312yes—
715#376C2312yes—
716C43C2312yes—
717C2×#41—24no—
718C2×#41—24no—
719C2×#41—44no—
720C2×#41—42no—
721C2×#41—84no—
722C22×Q8—44no—
723C22×Q8—84no—
724C22×Q8C2411yescharacteristic
725C22×Q8C2412yes—
726C22×Q8C2414yes—
727C22×Q8C2412yes—
728C22×Q8C2411yescharacteristic
729C22×Q8C2411yescharacteristic
730C22×Q8C2414yes—
731C22×D4C2412yes—
732C22×D4C2411yescharacteristic
733C22×D4C2412yes—
734C22×D4C2414yes—
735C22×D4C2412yes—
736C22×D4C2414yes—
737C22×D4C2414yes—
738C22×D4C2412yes—
739C23×C4C2411yescharacteristic
740C23×C4C2412yes—
741C23×C4C2411yescharacteristic
742C23×C4C2412yes—
743C23×C4C2412yes—
744C23×C4C2414yes—
745C23×C4C2414yes—
746C23×C4C2412yes—
747C23×C4C2414yes—
748C23×C4C2412yes—
749C23×C4C2411yescharacteristic
750C4⋊Q8—28no—
751C4⋊Q8—44no—
752C4⋊Q8—42no—
753C4⋊Q8—44no—
754C4⋊Q8—48no—
755C4⋊Q8—44no—
756#127—42no—
757#127—44no—
758#126—48no—
759#126—84no—
760#126—84no—
761#126—84no—
762#125—28no—
763#125—44no—
764#125—44no—
765#125—48no—
766#125—84no—
767#124—28no—
768#124—48no—
769#123—48no—
770#123—48no—
771#123—84no—
772#123—84no—
773#123—84no—
774C22⋊Q8—48no—
775C22⋊Q8—48no—
776C22⋊Q8—48no—
777C22⋊Q8—44no—
778C22⋊Q8—48no—
779C22⋊Q8—84no—
780C22⋊Q8—84no—
781C22⋊Q8—84no—
782C22⋊Q8—84no—
783#121—28no—
784#121—48no—
785#121—44no—
786C4×Q8—28no—
787C4×Q8—24no—
788C4×Q8—42no—
789C4×Q8—44no—
790C4×Q8—42no—
791C4×Q8—44no—
792C4×Q8—42no—
793C4×Q8—44no—
794C4×D4—24no—
795C4×D4—28no—
796C4×D4—42no—
797C4×D4—44no—
798C4×D4—44no—
799C4×D4—44no—
800C4×D4—48no—
801C4×D4—44no—
802C4×D4—84no—
803C4×D4—84no—
804#117—24no—
805#117—24no—
806#117—42no—
807#117—44no—
808C2×C4⋊C4—24no—
809C2×C4⋊C4—44no—
810C2×C4⋊C4—44no—
811C2×C4⋊C4—42no—
812C2×C4⋊C4—48no—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2411yescharacteristic
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2411yescharacteristic
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2411yescharacteristic
883C2×C22⋊C4C2411yescharacteristic
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2411yescharacteristic
892C2×C22⋊C4C2411yescharacteristic
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
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⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C42—42no—
926C2×C42C2411yescharacteristic
927C2×C42C2412yes—
928C2×C42C2411yescharacteristic
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2412yes—
932C2×C42C2412yes—
933C2×C42C2412yes—
934C2×C42C2412yes—
935C2×C42C2414yes—
936C2×C42C2412yes—
937C2×C42C2412yes—
938C2×C42C2414yes—
939C2×C42C2414yes—
940C2×C42C2414yes—
941C2×C42C2414yes—
942C2×C42C2414yes—
943C2×C42C2412yes—
944C2×C42C2412yes—
945C2×C42C2412yes—
946C2×C42C2414yes—
947C2×C42C2412yes—
948C2×C42C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2414yes—
955#95C2412yes—
956#95C2411yescharacteristic
957#95C2414yes—
958#95C2412yes—
959#95C2412yes—
960#95C2414yes—
961#95C2412yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2412yes—
966#95C2414yes—
967#95C2414yes—
968#95C2412yes—
969#95C2414yes—
970#95C2412yes—
971#95C2411yescharacteristic
972#95C2414yes—
973#95C2412yes—
974#95C2412yes—
975#95C2414yes—
976#95C2414yes—
977#95C2412yes—
978#95C2411yescharacteristic
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2414yes—
987#95C2411yescharacteristic
988#95C2414yes—
989#95C2412yes—
990#95C2412yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2412yes—
995#95C2412yes—
996#95C2414yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017C24C2514yes—
1018C24C2512yes—
1019C24C2511yescharacteristic
1020#41—416no—
1021#41—816no—
1022C2×Q8—22no—
1023C2×Q8—28no—
1024C2×Q8—22no—
1025C2×Q8—24no—
1026C2×Q8—41no—
1027C2×Q8—42no—
1028C2×Q8—42no—
1029C2×Q8—41no—
1030C2×Q8—42no—
1031C2×Q8—42no—
1032C2×Q8—44no—
1033C2×Q8—44no—
1034C2×Q8—44no—
1035C2×Q8—44no—
1036C2×Q8—44no—
1037C2×Q8—44no—
1038C2×Q8—42no—
1039C2×Q8—816no—
1040C2×Q82−1+414yes—
1041C2×D4—28no—
1042C2×D4—24no—
1043C2×D4—24no—
1044C2×D4—22no—
1045C2×D4—24no—
1046C2×D4—24no—
1047C2×D4—24no—
1048C2×D4—22no—
1049C2×D4—22no—
1050C2×D4—42no—
1051C2×D4—44no—
1052C2×D4—44no—
1053C2×D4—42no—
1054C2×D4—44no—
1055C2×D4—44no—
1056C2×D4—44no—
1057C2×D4—44no—
1058C2×D4—42no—
1059C2×D4—44no—
1060C2×D4—44no—
1061C2×D4—44no—
1062C2×D4—44no—
1063C22×C4—22no—
1064C22×C4—22no—
1065C22×C4—24no—
1066C22×C4—24no—
1067C22×C4—24no—
1068C22×C4—24no—
1069C22×C4—24no—
1070C22×C4—28no—
1071C22×C4—28no—
1072C22×C4—41no—
1073C22×C4—41no—
1074C22×C4—42no—
1075C22×C4—42no—
1076C22×C4—42no—
1077C22×C4—44no—
1078C22×C4—44no—
1079C22×C4—44no—
1080C22×C4—44no—
1081C22×C4—44no—
1082C22×C4—44no—
1083C22×C4—44no—
1084C22×C4—42no—
1085C22×C4—44no—
1086C22×C4—44no—
1087C22×C4—44no—
1088C22×C4—44no—
1089C22×C42−1+414yes—
1090C22×C4C2514yes—
1091C22×C4C2512yes—
1092C22×C4C2512yes—
1093C22×C4C2512yes—
1094C22×C4C2514yes—
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2514yes—
1098C22×C4C2512yes—
1099C22×C4C2511yescharacteristic
1100C22×C4C2512yes—
1101C22×C4C2512yes—
1102C22×C4C2511yescharacteristic
1103C22×C4C2512yes—
1104C22×C4C2512yes—
1105C22×C4C2511yescharacteristic
1106C22×C4C2514yes—
1107C22×C4C2512yes—
1108C22×C4C2514yes—
1109C22×C4C2512yes—
1110C22×C4C2511yescharacteristic
1111C22×C4C2512yes—
1112C22×C4C2512yes—
1113C22×C4C2511yescharacteristic
1114C22×C4C2512yes—
1115C22×C4C2511yescharacteristic
1116C4⋊C4—24no—
1117C4⋊C4—22no—
1118C4⋊C4—28no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—28no—
1122C4⋊C4—24no—
1123C4⋊C4—28no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—28no—
1127C4⋊C4—24no—
1128C4⋊C4—24no—
1129C4⋊C4—28no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—24no—
1133C4⋊C4—24no—
1134C4⋊C4—24no—
1135C4⋊C4—41no—
1136C4⋊C4—42no—
1137C4⋊C4—42no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—42no—
1141C4⋊C4—41no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—41no—
1145C4⋊C4—42no—
1146C4⋊C4—41no—
1147C4⋊C4—42no—
1148C4⋊C4—42no—
1149C4⋊C4—42no—
1150C4⋊C4—44no—
1151C4⋊C4—42no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—42no—
1155C4⋊C4—42no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—42no—
1169C4⋊C4—42no—
1170C4⋊C4—42no—
1171C4⋊C4—42no—
1172C4⋊C4—42no—
1173C4⋊C4—42no—
1174C4⋊C4—42no—
1175C4⋊C4—42no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—42no—
1181C4⋊C4—42no—
1182C4⋊C4—42no—
1183C4⋊C4H(5,𝔽2)14yes—
1184C22⋊C4—22no—
1185C22⋊C4—22no—
1186C22⋊C4—24no—
1187C22⋊C4—24no—
1188C22⋊C4—28no—
1189C22⋊C4—28no—
1190C22⋊C4—28no—
1191C22⋊C4—28no—
1192C22⋊C4—28no—
1193C22⋊C4—28no—
1194C22⋊C4—41no—
1195C22⋊C4—42no—
1196C22⋊C4—41no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—42no—
1201C22⋊C4—42no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—42no—
1207C22⋊C4—42no—
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⋊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—
1228C42—24no—
1229C42—22no—
1230C42—24no—
1231C42—22no—
1232C42—24no—
1233C42—24no—
1234C42—24no—
1235C42—24no—
1236C42—28no—
1237C42—24no—
1238C42—24no—
1239C42—42no—
1240C42—42no—
1241C42—44no—
1242C42—44no—
1243C42—44no—
1244C42—44no—
1245C42—44no—
1246C42—42no—
1247C42—44no—
1248C42—42no—
1249C42—42no—
1250C42—42no—
1251C23—21no—
1252C23—21no—
1253C23—22no—
1254C23—22no—
1255C23—24no—
1256C23—22no—
1257C23—24no—
1258C23—24no—
1259C23—22no—
1260C23—22no—
1261C23—24no—
1262C23—24no—
1263C23—24no—
1264C23—24no—
1265C23—24no—
1266C23—24no—
1267C23C2×2−1+412yes—
1268C23C2611yescharacteristic
1269Q8—28no—
1270Q8—44no—
1271Q8—84no—
1272Q8—88no—
1273Q8—84no—
1274Q8—82no—
1275Q8—88no—
1276D4—48no—
1277D4—416no—
1278D4—48no—
1279D4—44no—
1280D4—84no—
1281D4—88no—
1282D4—162no—
1283D4—164no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—24no—
1291C2×C4—28no—
1292C2×C4—21no—
1293C2×C4—21no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—21no—
1299C2×C4—21no—
1300C2×C4—22no—
1301C2×C4—24no—
1302C2×C4—22no—
1303C2×C4—24no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—24no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—24no—
1311C2×C4—22no—
1312C2×C4—24no—
1313C2×C4—22no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—24no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—24no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—24no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—24no—
1344C2×C4—24no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—44no—
1351C2×C4—48no—
1352C2×C4—44no—
1353C2×C4—88no—
1354C2×C4—84no—
1355C2×C4—84no—
1356C2×C4—88no—
1357C2×C4—84no—
1358C2×C4—162no—
1359C2×C4—164no—
1360C2×C4C2×H(5,𝔽2)14yes—
1361C2×C4C2×H(5,𝔽2)12yes—
1362C2×C4C2×2−1+412yes—
1363C2×C4C2×2−1+414yes—
1364C2×C4C2×2−1+412yes—
1365C2×C4C2×2−1+412yes—
1366C2×C4#58514yes—
1367C22—22no—
1368C22—24no—
1369C22—41no—
1370C22—41no—
1371C22—42no—
1372C22—42no—
1373C22—44no—
1374C22—44no—
1375C22—42no—
1376C22—44no—
1377C22—42no—
1378C22—44no—
1379C22—44no—
1380C22—44no—
1381C22—44no—
1382C22—44no—
1383C22—44no—
1384C22C22×H(5,𝔽2)11yescharacteristic
1385C22C22×2−1+411yescharacteristic
1386C22C22×2−1+411yescharacteristic
1387C22C2×#58512yes—
1388C22H(7,𝔽2)12yes—
1389C4—22no—
1390C4—24no—
1391C4—24no—
1392C4—24no—
1393C4—44no—
1394C4—41no—
1395C4—42no—
1396C4—42no—
1397C4—41no—
1398C4—42no—
1399C4—41no—
1400C4—42no—
1401C4—42no—
1402C4—44no—
1403C4—42no—
1404C4—41no—
1405C4—44no—
1406C4—42no—
1407C4—42no—
1408C4—44no—
1409C4—42no—
1410C4—42no—
1411C4—42no—
1412C4—44no—
1413C4—42no—
1414C4#353814yes—
1415C2—42no—
1416C2—82no—
1417C2—84no—
1418C2C2×#353811yescharacteristic
1419C2#6292612yes—
1420C2#6295212yes—
1421C2#6302011yescharacteristic
1422C2#6304511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35704C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59833C2semidirect
2. #59754C2semidirect
3. #59136C2semidirect
4. #58264C2semidirect
5. #57382C2semidirect
6. #56347C2semidirect
7. #55477C2semidirect
8. #54965C2semidirect
9. #53125C2semidirect
10. #53005C2semidirect
11. #52289C2semidirect
12. #50817C2semidirect
13. #48472C2semidirect
14. #46345C2semidirect
15. #45407C2semidirect
16. #44306C2semidirect
17. #42955C2semidirect
18. #42821C2semidirect
19. #42517C2semidirect
20. #42479C2semidirect
21. #40958C2semidirect
22. #40128C2semidirect
23. #39217C2semidirect
24. #39083C2semidirect
25. #39069C2semidirect
26. #37523C2semidirect
27. #36040C2semidirect
29. #35574C2semidirect

Maximal subgroups

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

subgroupindex
#598332
#597542
#591362
#582642
#573822
#563472
#554772
#549652
#531252
#530052
#522892
#508172
#484722
#463452
#454072
#443062
#429552
#428212
#425172
#424792
#409582
#401282
#392172
#390832
#390692
#375232
#360402
#357042
#355742