Finite Group Databasebeta

← #8107592

Subgroups — #8107592

Order 512.

4403 conjugacy classes of subgroups.

The subgroup lattice has 1470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53138C212yesmaximal, complemented
2#53105C212yesmaximal, complemented
3#52876C214yesmaximal, complemented
4#52699C214yesmaximal, complemented
5#45266C211yesmaximal, characteristic, complemented
6#45151C211yesmaximal, characteristic, complemented
7#45139C211yesmaximal, characteristic, complemented
8#44947C211yesmaximal, characteristic, complemented
9#44515C214yesmaximal, complemented
10#43994C214yesmaximal, complemented
11#42875C211yesmaximal, characteristic, complemented
12#42826C212yesmaximal, complemented
13#42651C211yesmaximal, characteristic, complemented
14#42649C211yesmaximal, characteristic, complemented
15#42645C211yesmaximal, characteristic, complemented
16#42528C212yesmaximal, complemented
17#42383C214yesmaximal, complemented
18#42349C214yesmaximal, complemented
19#41540C214yesmaximal, complemented
20#40857C214yesmaximal, complemented
21#36534C211yesmaximal, characteristic, complemented
22#36513C212yesmaximal, complemented
23#36508C211yesmaximal, characteristic, complemented
24#36394C211yesmaximal, characteristic, complemented
25#36370C211yesmaximal, characteristic, complemented
26#36302C212yesmaximal, complemented
27#35314C211yesmaximal, characteristic, complemented
28#35276C211yesmaximal, characteristic
29#35184C212yesmaximal, complemented
30#35114C212yesmaximal, complemented
31#34552C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#556C2211yescharacteristic
34C2×#556C2211yescharacteristic
35C2×#554C2211yescharacteristic
36C2×#542C2211yescharacteristic
37C2×#540C2211yescharacteristic
38#2864C2211yescharacteristic
39#2863C2212yes—
40#2863C2212yes—
41#2862C2211yescharacteristic
42#2861C2212yes—
43#2861C2211yescharacteristic
44#2861C2212yes—
45#2860C2212yes—
46#2858C2211yescharacteristic
47#2856C2211yescharacteristic
48#2850C2211yescharacteristic
49#2845C2214yes—
50#2837C2214yes—
51#2836C2214yes—
52#2831C2214yes—
53#2829C2214yes—
54#2829C2214yes—
55#2829C2214yes—
56#2827C2214yes—
57#2827C2214yes—
58#2821C2212yes—
59#2816C2212yes—
60#2814C2214yes—
61#2814C2212yes—
62#2814C2212yes—
63#2808C2214yes—
64#2792C2214yes—
65#2791C2214yes—
66#2791C2214yes—
67#2781C2214yes—
68#2775C2214yes—
69#2768C2214yes—
70#2761C2214yes—
71#2756C2214yes—
72#2755C2214yes—
73#2753C2214yes—
74#2749C2214yes—
75#2748C2214yes—
76#2744C2214yes—
77#2741C2214yes—
78#2739C2214yes—
79#2729C2214yes—
80#2723C2214yes—
81#2723C2214yes—
82#2722C2214yes—
83#2720C2214yes—
84#2715C2214yes—
85#2706C2214yes—
86#2706C2214yes—
87#2696C2214yes—
88#2695C2214yes—
89#2694C2214yes—
90#2692C2214yes—
91#2691C2214yes—
92#2690C2214yes—
93#2681C2214yes—
94#2680C2214yes—
95#2666C2214yes—
96#2666C2214yes—
97#2663C2212yes—
98#2660C2211yescharacteristic
99#2659C2212yes—
100#2657C2211yescharacteristic
101#2654C2214yes—
102#2654C2214yes—
103#2651C2214yes—
104#2648C2214yes—
105#2640C2212yes—
106#2639C2212yes—
107#2632C2214yes—
108#2632C2212yes—
109#2630C2214yes—
110#2628C2211yescharacteristic
111#2625C2212yes—
112#2625C2212yes—
113#2624C2212yes—
114#2623C2212yes—
115#2621C2211yescharacteristic
116#2620C2211yescharacteristic
117#2619C2211yescharacteristic
118#2604C2212yes—
119#2601C2214yes—
120#2599C2214yes—
121#2592C2212yes—
122#2587C2214yes—
123#2581C2211yescharacteristic
124#2580C2211yescharacteristic
125#2580C2211yescharacteristic
126#2580C2212yes—
127#2580C2211yescharacteristic
128#2577C2214yes—
129#2575C2214yes—
130#2574C2214yes—
131#2570C2212yes—
132#2570C2214yes—
133#2568C2212yes—
134#2565C2212yes—
135#2565C2212yes—
136#2564C2214yes—
137#2563C2211yescharacteristic
138#2560C2214yes—
139#2560C2214yes—
140#2555C2214yes—
141#2554C2214yes—
142#2552C2212yes—
143#2552C2212yes—
144#2550C2212yes—
145#2548C2212yes—
146#2547C2212yes—
147#2547C2211yescharacteristic
148#2546C2211yescharacteristic
149#2545C2212yes—
150#2545C2212yes—
151#2544C2212yes—
152#2544C2212yes—
153#2542C2211yescharacteristic
154#2538C2212yes—
155#2536C2214yes—
156#2531C2214yes—
157#2531C2214yes—
158#2529C2214yes—
159#2529C2214yes—
160#2525C2214yes—
161#2525C2214yes—
162#2525C2214yes—
163#2524C2214yes—
164#2523C2214yes—
165#2521C2214yes—
166#2520C2214yes—
167#2519C2214yes—
168#2519C2214yes—
169#2518C2214yes—
170#2517C2214yes—
171#2513C2214yes—
172#2508C2212yes—
173#2507C2212yes—
174#2501C2212yes—
175#2500C2214yes—
176#2498C2212yes—
177#2498C2212yes—
178#2495C2214yes—
179#2490C2212yes—
180#2490C2212yes—
181#2479C2214yes—
182#2479C2214yes—
183#2479C2214yes—
184#2479C2214yes—
185#2476C2214yes—
186#2476C2214yes—
187#2474C2214yes—
188#2473C2214yes—
189#2470C2214yes—
190#2468C2214yes—
191#2464C2214yes—
192#2461C2214yes—
193#2458C2214yes—
194#2458C2214yes—
195#2457C2214yes—
196#2454C2212yes—
197#2453C2212yes—
198#2453C2212yes—
199#2451C2212yes—
200#2450C2214yes—
201#2448C2212yes—
202#2448C2212yes—
203#2448C2212yes—
204#2447C2212yes—
205#2445C2212yes—
206#2445C2212yes—
207#2429C2212yes—
208#2429C2214yes—
209#2427C2212yes—
210#2427C2212yes—
211#2426C2212yes—
212#2423C2214yes—
213#2423C2214yes—
214#2422C2212yes—
215#2421C2212yes—
216#2402C2212yes—
217#2402C2212yes—
218#2402C2212yes—
219#2399C2211yescharacteristic
220#2399C2211yescharacteristic
221#2399C2212yes—
222#2399C2212yes—
223#2396C2212yes—
224#2396C2211yescharacteristic
225#2396C2212yes—
226#2396C2212yes—
227#2396C2212yes—
228#2396C2211yescharacteristic
229#2396C2212yes—
230#2374C2214yes—
231#2373C2214yes—
232#2367C2212yes—
233#2366C2212yes—
234#2363C2214yes—
235#2362C2214yes—
236#2359C2214yes—
237#2357C2211yescharacteristic
238#2356C2211yescharacteristic
239#2355C2212yes—
240#2354C2214yes—
241#2352C2214yes—
242#2351C2212yes—
243#2349C2211yescharacteristic
244#2349C2211yescharacteristic
245#2343C2214yes—
246#2337C2214yes—
247#2335C2214yes—
248#2331C2211yescharacteristic
249#2328C2211yescharacteristic
250#2327C2211yescharacteristic
251#2326C2211yescharacteristic
252#2323C2214yes—
253#2320C2212yes—
254#2314C2214yes—
255C4×C4⋊Q8C2212yes—
256C4×#127C2211yescharacteristic
257C4×#124C2212yes—
258C4×#124C2211yescharacteristic
259C4×C22⋊Q8C2212yes—
260#2293C2212yes—
261#2293C2212yes—
262C42×Q8C2211yescharacteristic
263C42×Q8C2212yes—
264C42×Q8C2211yescharacteristic
265C4×#117C2212yes—
266C4×#117C2211yescharacteristic
267#557—44no—
268#556—44no—
269#556—44no—
270#554—44no—
271#542—44no—
272#540—44no—
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2312yes—
277C2×C4⋊Q8C2311yescharacteristic
278C2×#127C2311yescharacteristic
279C2×#127C2311yescharacteristic
280C2×#127C2311yescharacteristic
281C2×#126C2314yes—
282C2×#126C2312yes—
283C2×#126C2314yes—
284C2×#126C2314yes—
285C2×#125C2312yes—
286C2×#125C2312yes—
287C2×#125C2311yescharacteristic
288C2×#125C2314yes—
289C2×#124C2311yescharacteristic
290C2×#124C2312yes—
291C2×#124C2314yes—
292C2×#124C2311yescharacteristic
293C2×#124C2312yes—
294C2×#124C2312yes—
295C2×#124C2311yescharacteristic
296C2×#124C2312yes—
297C2×#123C2314yes—
298C2×#123C2314yes—
299C2×#123C2312yes—
300C2×#123C2314yes—
301C2×#123C2312yes—
302C2×#123C2312yes—
303C2×C22⋊Q8C2314yes—
304C2×C22⋊Q8C2312yes—
305C2×C22⋊Q8C2314yes—
306C2×C22⋊Q8C2311yescharacteristic
307C2×C22⋊Q8C2314yes—
308C2×C22⋊Q8C2312yes—
309C2×C22⋊Q8C2312yes—
310C2×C22⋊Q8C2312yes—
311C2×C22⋊Q8C2312yes—
312C2×#121C2312yes—
313C2×#121C2311yescharacteristic
314C2×#121C2314yes—
315C2×#121C2311yescharacteristic
316C2×#121C2311yescharacteristic
317C2×#121C2312yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2311yescharacteristic
320C2×C4×Q8C2311yescharacteristic
321C2×C4×Q8C2311yescharacteristic
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2312yes—
324C2×C4×Q8C2312yes—
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2312yes—
327C2×C4×Q8C2312yes—
328C2×C4×Q8C2312yes—
329C2×C4×Q8C2312yes—
330C2×C4×Q8C2312yes—
331C2×C4×D4C2311yescharacteristic
332C2×C4×D4C2311yescharacteristic
333C2×C4×D4C2311yescharacteristic
334C2×C4×D4C2314yes—
335C2×C4×D4C2314yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2312yes—
339C2×#117C2311yescharacteristic
340C2×#117C2314yes—
341C2×#117C2314yes—
342C2×#117C2312yes—
343C2×#117C2312yes—
344C2×#117C2312yes—
345C2×#117C2312yes—
346C2×#117C2311yescharacteristic
347C22×C4⋊C4C2312yes—
348C22×C42C2311yescharacteristic
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2312yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2312yes—
358#400C2311yescharacteristic
359#400C2311yescharacteristic
360#400C2312yes—
361#400C2314yes—
362#400C2312yes—
363#400C2312yes—
364#400C2312yes—
365#400C2312yes—
366#399C2312yes—
367#399C2312yes—
368#399C2312yes—
369#399C2314yes—
370#399C2312yes—
371#399C2314yes—
372#399C2314yes—
373#399C2312yes—
374#399C2314yes—
375#399C2312yes—
376#399C2312yes—
377#399C2314yes—
378#399C2311yescharacteristic
379#399C2311yescharacteristic
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2312yes—
390#398C2314yes—
391#398C2312yes—
392#398C2314yes—
393#398C2312yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2312yes—
402#398C2312yes—
403#398C2314yes—
404#398C2312yes—
405#398C2312yes—
406#398C2312yes—
407#398C2312yes—
408#398C2312yes—
409#398C2312yes—
410#398C2312yes—
411#398C2312yes—
412#398C2312yes—
413#398C2312yes—
414#398C2312yes—
415#397C2312yes—
416#397C2312yes—
417#397C2314yes—
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#397C2314yes—
422#397C2314yes—
423#397C2314yes—
424#397C2314yes—
425#397C2314yes—
426#397C2314yes—
427#397C2314yes—
428#397C2314yes—
429#397C2314yes—
430#397C2312yes—
431#397C2312yes—
432#397C2314yes—
433#397C2314yes—
434#397C2314yes—
435#396C2314yes—
436#396C2314yes—
437#396C2314yes—
438#396C2314yes—
439#396C2312yes—
440#396C2314yes—
441#396C2314yes—
442#396C2314yes—
443#396C2314yes—
444#396C2314yes—
445#396C2314yes—
446#396C2312yes—
447#396C2312yes—
448#396C2312yes—
449#395C2312yes—
450#395C2311yescharacteristic
451#395C2312yes—
452#395C2312yes—
453#395C2312yes—
454#395C2314yes—
455#395C2314yes—
456#395C2311yescharacteristic
457#395C2312yes—
458#395C2312yes—
459#395C2312yes—
460#395C2314yes—
461#394C2314yes—
462#394C2314yes—
463#394C2314yes—
464#394C2314yes—
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2314yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2314yes—
478#394C2314yes—
479#393C2312yes—
480#393C2312yes—
481#393C2311yescharacteristic
482#393C2312yes—
483#393C2314yes—
484#393C2312yes—
485#393C2314yes—
486#393C2312yes—
487#393C2312yes—
488#393C2311yescharacteristic
489#393C2312yes—
490#392C2314yes—
491#392C2314yes—
492#392C2314yes—
493#391C2314yes—
494#391C2311yescharacteristic
495#391C2312yes—
496#391C2312yes—
497#391C2312yes—
498#391C2312yes—
499#391C2311yescharacteristic
500#391C2314yes—
501#391C2312yes—
502#391C2312yes—
503#391C2312yes—
504#391C2312yes—
505#391C2314yes—
506#391C2314yes—
507#391C2314yes—
508#390C2314yes—
509#390C2311yescharacteristic
510#390C2311yescharacteristic
511#390C2312yes—
512#390C2314yes—
513#390C2314yes—
514#390C2314yes—
515#390C2311yescharacteristic
516#390C2312yes—
517#390C2312yes—
518#390C2312yes—
519#390C2312yes—
520#390C2311yescharacteristic
521#390C2311yescharacteristic
522#390C2314yes—
523#390C2312yes—
524#390C2311yescharacteristic
525#390C2314yes—
526#390C2314yes—
527#390C2314yes—
528#390C2314yes—
529#389C2314yes—
530#389C2314yes—
531#389C2312yes—
532#389C2314yes—
533#389C2312yes—
534#389C2314yes—
535#389C2312yes—
536#389C2312yes—
537#389C2314yes—
538#389C2314yes—
539#389C2314yes—
540#389C2312yes—
541#389C2312yes—
542#389C2312yes—
543#389C2312yes—
544#389C2314yes—
545#389C2312yes—
546#389C2314yes—
547#389C2314yes—
548#389C2312yes—
549#389C2314yes—
550#389C2314yes—
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#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2314yes—
630#386C2314yes—
631#386C2314yes—
632#386C2314yes—
633#386C2314yes—
634#386C2314yes—
635#386C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#384C2311yescharacteristic
650#384C2312yes—
651#384C2314yes—
652#384C2311yescharacteristic
653#384C2314yes—
654#383C2312yes—
655#383C2314yes—
656#383C2314yes—
657#383C2314yes—
658#382C2312yes—
659#382C2311yescharacteristic
660#382C2314yes—
661#382C2311yescharacteristic
662#382C2314yes—
663#382C2314yes—
664#382C2311yescharacteristic
665#382C2311yescharacteristic
666#382C2314yes—
667#382C2314yes—
668#382C2314yes—
669#381C2312yes—
670#381C2314yes—
671#380C2314yes—
672#380C2314yes—
673#380C2314yes—
674#380C2314yes—
675#380C2312yes—
676#380C2314yes—
677#380C2314yes—
678#380C2312yes—
679#380C2314yes—
680#380C2314yes—
681#380C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2311yescharacteristic
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2314yes—
703C4×C4⋊C4C2312yes—
704C4×C4⋊C4C2312yes—
705C4×C4⋊C4C2312yes—
706C4×C4⋊C4C2312yes—
707C4×C4⋊C4C2312yes—
708C4×C4⋊C4C2312yes—
709C4×C4⋊C4C2312yes—
710C4×C4⋊C4C2312yes—
711C4×C4⋊C4C2312yes—
712C4×C4⋊C4C2312yes—
713C4×C4⋊C4C2312yes—
714C4×C4⋊C4C2312yes—
715C4×C22⋊C4C2314yes—
716C4×C22⋊C4C2314yes—
717C4×C22⋊C4C2312yes—
718C4×C22⋊C4C2314yes—
719C4×C22⋊C4C2314yes—
720C4×C22⋊C4C2314yes—
721C4×C22⋊C4C2314yes—
722C4×C22⋊C4C2314yes—
723C4×C22⋊C4C2312yes—
724C4×C22⋊C4C2312yes—
725C4×C22⋊C4C2312yes—
726C4×C22⋊C4C2312yes—
727C4×C22⋊C4C2312yes—
728C4×C22⋊C4C2312yes—
729#376C2311yescharacteristic
730#376C2311yescharacteristic
731#376C2312yes—
732#376C2312yes—
733#376C2312yes—
734C2×#95C2312yes—
735C2×#95C2312yes—
736C43C2311yescharacteristic
737C43C2312yes—
738C43C2311yescharacteristic
739C43C2312yes—
740C22×Q8C2411yescharacteristic
741C22×Q8C2412yes—
742C22×Q8C2411yescharacteristic
743C22×Q8C2411yescharacteristic
744C22×Q8C2412yes—
745C22×Q8C2412yes—
746C22×Q8C2412yes—
747C22×D4C2411yescharacteristic
748C22×D4C2411yescharacteristic
749C22×D4C2411yescharacteristic
750C22×D4C2414yes—
751C22×D4C2414yes—
752C22×D4C2412yes—
753C22×D4C2412yes—
754C22×D4C2412yes—
755C22×D4C2412yes—
756C22×D4C2412yes—
757C23×C4C2411yescharacteristic
758C23×C4C2412yes—
759C23×C4C2412yes—
760C23×C4C2412yes—
761C23×C4C2414yes—
762C23×C4C2412yes—
763C23×C4C2414yes—
764C23×C4C2414yes—
765C4⋊Q8—24no—
766C4⋊Q8—24no—
767C4⋊Q8—42no—
768C4⋊Q8—44no—
769C4⋊Q8—44no—
770#127—24no—
771#127—42no—
772#127—42no—
773#126—48no—
774#126—44no—
775#126—48no—
776#126—48no—
777#125—42no—
778#125—44no—
779#125—44no—
780#125—48no—
781#124—24no—
782#124—48no—
783#124—44no—
784#124—42no—
785#124—44no—
786#124—42no—
787#124—44no—
788#124—44no—
789#123—48no—
790#123—48no—
791#123—48no—
792#123—44no—
793#123—44no—
794#123—44no—
795C22⋊Q8—48no—
796C22⋊Q8—48no—
797C22⋊Q8—44no—
798C22⋊Q8—44no—
799C22⋊Q8—48no—
800C22⋊Q8—42no—
801C22⋊Q8—44no—
802C22⋊Q8—44no—
803C22⋊Q8—44no—
804#121—48no—
805#121—44no—
806#121—44no—
807#121—42no—
808#121—42no—
809#121—42no—
810C4×Q8—24no—
811C4×Q8—24no—
812C4×Q8—24no—
813C4×Q8—28no—
814C4×Q8—44no—
815C4×Q8—44no—
816C4×Q8—44no—
817C4×Q8—44no—
818C4×Q8—44no—
819C4×Q8—44no—
820C4×Q8—44no—
821C4×Q8—44no—
822C4×Q8—44no—
823C4×D4—24no—
824C4×D4—24no—
825C4×D4—24no—
826C4×D4—48no—
827C4×D4—44no—
828C4×D4—44no—
829C4×D4—44no—
830C4×D4—48no—
831#117—24no—
832#117—42no—
833#117—44no—
834#117—48no—
835#117—48no—
836#117—44no—
837#117—44no—
838#117—44no—
839C2×C4⋊C4—44no—
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2411yescharacteristic
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2411yescharacteristic
908C2×C22⋊C4C2411yescharacteristic
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2412yes—
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×C42—24no—
954C2×C42C2412yes—
955C2×C42C2412yes—
956C2×C42C2412yes—
957C2×C42C2412yes—
958C2×C42C2411yescharacteristic
959C2×C42C2411yescharacteristic
960C2×C42C2411yescharacteristic
961C2×C42C2412yes—
962C2×C42C2412yes—
963C2×C42C2412yes—
964C2×C42C2412yes—
965C2×C42C2412yes—
966C2×C42C2412yes—
967C2×C42C2412yes—
968C2×C42C2412yes—
969C2×C42C2414yes—
970C2×C42C2411yescharacteristic
971C2×C42C2412yes—
972C2×C42C2414yes—
973C2×C42C2414yes—
974C2×C42C2412yes—
975C2×C42C2414yes—
976C2×C42C2414yes—
977C2×C42C2414yes—
978C2×C42C2414yes—
979C2×C42C2412yes—
980C2×C42C2412yes—
981C2×C42C2412yes—
982C2×C42C2412yes—
983C2×C42C2411yescharacteristic
984C2×C42C2411yescharacteristic
985#95C2411yescharacteristic
986#95C2411yescharacteristic
987#95C2414yes—
988#95C2412yes—
989#95C2412yes—
990#95C2414yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2412yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2411yescharacteristic
1017#95C2411yescharacteristic
1018#95C2412yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2412yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2412yes—
1027#95C2412yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2414yes—
1051C24C2511yescharacteristic
1052C24C2512yes—
1053C24C2512yes—
1054C24C2512yes—
1055C2×Q8—22no—
1056C2×Q8—22no—
1057C2×Q8—22no—
1058C2×Q8—24no—
1059C2×Q8—24no—
1060C2×Q8—24no—
1061C2×Q8—22no—
1062C2×Q8—24no—
1063C2×Q8—24no—
1064C2×Q8—22no—
1065C2×Q8—42no—
1066C2×Q8—42no—
1067C2×Q8—42no—
1068C2×Q8—42no—
1069C2×Q8—44no—
1070C2×Q8—42no—
1071C2×Q8—44no—
1072C2×D4—22no—
1073C2×D4—22no—
1074C2×D4—22no—
1075C2×D4—22no—
1076C2×D4—22no—
1077C2×D4—22no—
1078C2×D4—28no—
1079C2×D4—22no—
1080C2×D4—22no—
1081C2×D4—22no—
1082C2×D4—44no—
1083C2×D4—44no—
1084C2×D4—44no—
1085C2×D4—44no—
1086C2×D4—44no—
1087C2×D4—42no—
1088C2×D4—42no—
1089C2×D4—42no—
1090C2×D4—42no—
1091C2×D4—42no—
1092C2×D4—44no—
1093C2×D4—44no—
1094C2×D4—44no—
1095C2×D4—44no—
1096C2×D4—44no—
1097C22×C4—22no—
1098C22×C4—24no—
1099C22×C4—22no—
1100C22×C4—24no—
1101C22×C4—22no—
1102C22×C4—24no—
1103C22×C4—24no—
1104C22×C4—24no—
1105C22×C4—28no—
1106C22×C4—42no—
1107C22×C4—44no—
1108C22×C4—44no—
1109C22×C4—44no—
1110C22×C4—44no—
1111C22×C4—44no—
1112C22×C4—44no—
1113C22×C4—44no—
1114C22×C4—44no—
1115C22×C4—44no—
1116C22×C4—44no—
1117C22×C4—44no—
1118C22×C4C2512yes—
1119C22×C4C2514yes—
1120C22×C4C2512yes—
1121C22×C4C2511yescharacteristic
1122C22×C4C2514yes—
1123C22×C4C2512yes—
1124C22×C4C2514yes—
1125C22×C4C2512yes—
1126C22×C4C2512yes—
1127C22×C4C2511yescharacteristic
1128C22×C4C2512yes—
1129C22×C4C2512yes—
1130C22×C4C2512yes—
1131C22×C4C2511yescharacteristic
1132C22×C4C2512yes—
1133C22×C4C2514yes—
1134C22×C4C2512yes—
1135C22×C4C2512yes—
1136C22×C4C2512yes—
1137C22×C4C2512yes—
1138C22×C4C2512yes—
1139C22×C4C2511yescharacteristic
1140C22×C4C2511yescharacteristic
1141C22×C4C2512yes—
1142C22×C4C2512yes—
1143C22×C4C2512yes—
1144C22×C4C2511yescharacteristic
1145C4⋊C4—22no—
1146C4⋊C4—24no—
1147C4⋊C4—22no—
1148C4⋊C4—22no—
1149C4⋊C4—22no—
1150C4⋊C4—24no—
1151C4⋊C4—24no—
1152C4⋊C4—22no—
1153C4⋊C4—22no—
1154C4⋊C4—22no—
1155C4⋊C4—24no—
1156C4⋊C4—22no—
1157C4⋊C4—24no—
1158C4⋊C4—24no—
1159C4⋊C4—24no—
1160C4⋊C4—24no—
1161C4⋊C4—28no—
1162C4⋊C4—28no—
1163C4⋊C4—24no—
1164C4⋊C4—24no—
1165C4⋊C4—24no—
1166C4⋊C4—24no—
1167C4⋊C4—24no—
1168C4⋊C4—28no—
1169C4⋊C4—44no—
1170C4⋊C4—42no—
1171C4⋊C4—42no—
1172C4⋊C4—42no—
1173C4⋊C4—42no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—42no—
1178C4⋊C4—42no—
1179C4⋊C4—42no—
1180C4⋊C4—42no—
1181C4⋊C4—42no—
1182C4⋊C4—42no—
1183C4⋊C4—42no—
1184C4⋊C4—42no—
1185C4⋊C4—42no—
1186C4⋊C4—42no—
1187C4⋊C4—42no—
1188C4⋊C4—42no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C4⋊C4—42no—
1195C4⋊C4—42no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—42no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—44no—
1205C4⋊C4—42no—
1206C4⋊C4—44no—
1207C4⋊C4—44no—
1208C4⋊C4—44no—
1209C4⋊C4—44no—
1210C4⋊C4—44no—
1211C22⋊C4—22no—
1212C22⋊C4—22no—
1213C22⋊C4—24no—
1214C22⋊C4—24no—
1215C22⋊C4—24no—
1216C22⋊C4—28no—
1217C22⋊C4—28no—
1218C22⋊C4—28no—
1219C22⋊C4—24no—
1220C22⋊C4—28no—
1221C22⋊C4—28no—
1222C22⋊C4—28no—
1223C22⋊C4—42no—
1224C22⋊C4—42no—
1225C22⋊C4—42no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—42no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—42no—
1236C22⋊C4—42no—
1237C22⋊C4—42no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—42no—
1243C22⋊C4—42no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4—44no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—42no—
1251C22⋊C4—44no—
1252C22⋊C4—44no—
1253C22⋊C4—44no—
1254C22⋊C4—44no—
1255C22⋊C4—44no—
1256C22⋊C4—44no—
1257C22⋊C4—44no—
1258C42—22no—
1259C42—24no—
1260C42—24no—
1261C42—24no—
1262C42—22no—
1263C42—24no—
1264C42—28no—
1265C42—24no—
1266C42—24no—
1267C42—24no—
1268C42—24no—
1269C42—22no—
1270C42—22no—
1271C42—24no—
1272C42—24no—
1273C42—24no—
1274C42—24no—
1275C42—24no—
1276C42—42no—
1277C42—44no—
1278C42—44no—
1279C42—44no—
1280C42—44no—
1281C42—44no—
1282C42—42no—
1283C42—42no—
1284C42—42no—
1285C42—42no—
1286C42—44no—
1287C42H(5,𝔽2)14yes—
1288C422−1+414yes—
1289C23—21no—
1290C23—22no—
1291C23—22no—
1292C23—22no—
1293C23—22no—
1294C23—21no—
1295C23—22no—
1296C23—22no—
1297C23—24no—
1298C23—22no—
1299C23—24no—
1300C23—24no—
1301C23—24no—
1302C23—24no—
1303C23—21no—
1304C23—24no—
1305C23—22no—
1306C23—22no—
1307C23—22no—
1308C23—22no—
1309C23C2611yescharacteristic
1310Q8—48no—
1311Q8—44no—
1312Q8—44no—
1313Q8—44no—
1314Q8—48no—
1315Q8—84no—
1316Q8—162no—
1317D4—44no—
1318D4—44no—
1319D4—44no—
1320D4—88no—
1321D4—88no—
1322D4—162no—
1323D4—162no—
1324D4—162no—
1325D4—162no—
1326D4—162no—
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—21no—
1339C2×C4—21no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—24no—
1346C2×C4—24no—
1347C2×C4—22no—
1348C2×C4—21no—
1349C2×C4—21no—
1350C2×C4—24no—
1351C2×C4—24no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—24no—
1370C2×C4—24no—
1371C2×C4—24no—
1372C2×C4—22no—
1373C2×C4—24no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—24no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—24no—
1384C2×C4—24no—
1385C2×C4—24no—
1386C2×C4—24no—
1387C2×C4—24no—
1388C2×C4—22no—
1389C2×C4—24no—
1390C2×C4—24no—
1391C2×C4—21no—
1392C2×C4—48no—
1393C2×C4—44no—
1394C2×C4—88no—
1395C2×C4—84no—
1396C2×C4—84no—
1397C2×C4—84no—
1398C2×C4—88no—
1399C2×C4—164no—
1400C2×C4C2×H(5,𝔽2)12yes—
1401C2×C4C2×H(5,𝔽2)12yes—
1402C2×C4C2×H(5,𝔽2)12yes—
1403C2×C4C2×2−1+414yes—
1404C2×C4C2×2−1+412yes—
1405C2×C4#58514yes—
1406C2×C4#58514yes—
1407C2×C4#58512yes—
1408C22—44no—
1409C22—44no—
1410C22—44no—
1411C22—42no—
1412C22—41no—
1413C22—42no—
1414C22—42no—
1415C22—42no—
1416C22—42no—
1417C22—44no—
1418C22—44no—
1419C22—44no—
1420C22—42no—
1421C22—42no—
1422C22—42no—
1423C22—42no—
1424C22—41no—
1425C22—41no—
1426C22—42no—
1427C22—42no—
1428C22C22×H(5,𝔽2)11yescharacteristic
1429C22C22×2−1+411yescharacteristic
1430C22C2×#58511yescharacteristic
1431C22C2×#58512yes—
1432C22C2×#58512yes—
1433C4—24no—
1434C4—24no—
1435C4—24no—
1436C4—22no—
1437C4—22no—
1438C4—42no—
1439C4—42no—
1440C4—44no—
1441C4—42no—
1442C4—42no—
1443C4—42no—
1444C4—41no—
1445C4—42no—
1446C4—44no—
1447C4—44no—
1448C4—42no—
1449C4—42no—
1450C4—42no—
1451C4—42no—
1452C4—42no—
1453C4—44no—
1454C4—41no—
1455C4—41no—
1456C4—42no—
1457C4—42no—
1458C4—42no—
1459C4#354714yes—
1460C2—82no—
1461C2—82no—
1462C2—82no—
1463C2—81no—
1464C2#6274312yes—
1465C2C2×#354711yescharacteristic
1466C2#6283112yes—
1467C2#6283611yescharacteristic
1468C2#6283611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35276C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53138C2semidirect
2. #53105C2semidirect
3. #52876C2semidirect
4. #52699C2semidirect
5. #45266C2semidirect
6. #45151C2semidirect
7. #45139C2semidirect
8. #44947C2semidirect
9. #44515C2semidirect
10. #43994C2semidirect
11. #42875C2semidirect
12. #42826C2semidirect
13. #42651C2semidirect
14. #42649C2semidirect
15. #42645C2semidirect
16. #42528C2semidirect
17. #42383C2semidirect
18. #42349C2semidirect
19. #41540C2semidirect
20. #40857C2semidirect
21. #36534C2semidirect
22. #36513C2semidirect
23. #36508C2semidirect
24. #36394C2semidirect
25. #36370C2semidirect
26. #36302C2semidirect
27. #35314C2semidirect
29. #35184C2semidirect
30. #35114C2semidirect
31. #34552C2semidirect

Maximal subgroups

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

subgroupindex
#531382
#531052
#528762
#526992
#452662
#451512
#451392
#449472
#445152
#439942
#428752
#428262
#426512
#426492
#426452
#425282
#423832
#423492
#415402
#408572
#365342
#365132
#365082
#363942
#363702
#363022
#353142
#352762
#351842
#351142
#345522