Finite Group Databasebeta

← #8700420

Subgroups — #8700420

Order 512.

4573 conjugacy classes of subgroups.

The subgroup lattice has 1423 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59841C211yesmaximal, characteristic
2#59832C211yesmaximal, characteristic, complemented
3#59749C212yesmaximal, complemented
4#59659C212yesmaximal, complemented
5#59502C212yesmaximal, complemented
6#58921C214yesmaximal, complemented
7#58316C214yesmaximal, complemented
8#57133C214yesmaximal, complemented
9#52306C211yesmaximal, characteristic, complemented
10#52079C212yesmaximal, complemented
11#51586C212yesmaximal, complemented
12#48528C214yesmaximal, complemented
13#48219C214yesmaximal, complemented
14#46329C211yesmaximal, characteristic, complemented
15#46062C212yesmaximal, complemented
16#45360C212yesmaximal, complemented
17#45287C212yesmaximal, complemented
18#45207C212yesmaximal, complemented
19#42804C212yesmaximal, complemented
20#42618C212yesmaximal, complemented
21#42492C212yesmaximal, complemented
22#39977C212yesmaximal, complemented
23#39789C212yesmaximal, complemented
24#39172C211yesmaximal, characteristic, complemented
25#39168C211yesmaximal, characteristic, complemented
26#37262C212yesmaximal, complemented
27#37050C214yesmaximal, complemented
28#36490C212yesmaximal, complemented
29#36474C211yesmaximal, characteristic, complemented
30C2×#563C2212yes—
31C2×#559C2211yescharacteristic
32C2×Q82C2211yescharacteristic
33C2×Q82C2212yes—
34C2×#557C2211yescharacteristic
35C2×#556C2211yescharacteristic
36C2×#555C2212yes—
37C2×#542C2212yes—
38#2866C2214yes—
39#2862C2211yescharacteristic
40#2862C2212yes—
41#2862C2211yescharacteristic
42#2860C2212yes—
43#2858C2211yescharacteristic
44#2841C2214yes—
45#2832C2214yes—
46#2830C2214yes—
47#2823C2212yes—
48#2820C2214yes—
49#2809C2211yescharacteristic
50#2806C2214yes—
51#2800C2214yes—
52#2791C2214yes—
53#2790C2214yes—
54#2788C2214yes—
55#2788C2214yes—
56#2784C2214yes—
57#2775C2212yes—
58#2775C2212yes—
59#2772C2214yes—
60#2769C2212yes—
61#2765C2214yes—
62#2763C2214yes—
63#2762C2214yes—
64#2759C2214yes—
65#2755C2214yes—
66#2754C2214yes—
67#2745C2214yes—
68#2734C2212yes—
69#2734C2211yescharacteristic
70#2734C2212yes—
71#2731C2211yescharacteristic
72#2731C2212yes—
73#2731C2214yes—
74#2731C2211yescharacteristic
75#2731C2212yes—
76#2729C2214yes—
77#2728C2212yes—
78#2727C2212yes—
79#2727C2214yes—
80#2723C2214yes—
81#2721C2212yes—
82#2721C2212yes—
83#2716C2214yes—
84#2716C2214yes—
85#2716C2214yes—
86#2715C2214yes—
87#2715C2214yes—
88#2713C2214yes—
89#2712C2214yes—
90#2710C2214yes—
91#2707C2214yes—
92#2706C2214yes—
93#2704C2214yes—
94#2702C2214yes—
95#2702C2214yes—
96#2701C2214yes—
97#2700C2214yes—
98#2700C2214yes—
99#2699C2212yes—
100#2698C2214yes—
101#2695C2214yes—
102#2694C2214yes—
103#2692C2214yes—
104#2692C2214yes—
105#2691C2214yes—
106#2690C2214yes—
107#2677C2214yes—
108#2674C2214yes—
109#2674C2214yes—
110#2674C2214yes—
111#2674C2214yes—
112#2672C2214yes—
113#2665C2214yes—
114#2665C2214yes—
115#2664C2214yes—
116#2662C2214yes—
117#2653C2214yes—
118#2640C2212yes—
119#2640C2212yes—
120#2637C2214yes—
121#2637C2214yes—
122#2629C2212yes—
123#2629C2214yes—
124#2611C2214yes—
125#2609C2212yes—
126#2604C2214yes—
127#2597C2214yes—
128#2590C2214yes—
129#2589C2214yes—
130#2582C2212yes—
131#2575C2214yes—
132#2570C2212yes—
133#2568C2212yes—
134#2567C2211yescharacteristic
135#2567C2211yescharacteristic
136#2567C2212yes—
137#2566C2212yes—
138#2563C2211yescharacteristic
139#2563C2212yes—
140#2556C2214yes—
141#2553C2214yes—
142#2551C2212yes—
143#2551C2212yes—
144#2550C2212yes—
145#2550C2212yes—
146#2550C2214yes—
147#2550C2214yes—
148#2550C2212yes—
149#2549C2214yes—
150#2548C2211yescharacteristic
151#2546C2211yescharacteristic
152#2546C2212yes—
153#2546C2211yescharacteristic
154#2546C2212yes—
155#2545C2212yes—
156#2545C2212yes—
157#2545C2214yes—
158#2542C2212yes—
159#2538C2214yes—
160#2538C2212yes—
161#2529C2214yes—
162#2528C2214yes—
163#2521C2214yes—
164#2517C2214yes—
165#2515C2214yes—
166#2513C2212yes—
167#2512C2212yes—
168#2509C2212yes—
169#2509C2212yes—
170#2508C2212yes—
171#2507C2212yes—
172#2506C2212yes—
173#2500C2212yes—
174#2494C2212yes—
175#2491C2214yes—
176#2491C2214yes—
177#2491C2212yes—
178#2491C2212yes—
179#2490C2212yes—
180#2488C2214yes—
181#2478C2214yes—
182#2476C2214yes—
183#2469C2214yes—
184#2469C2214yes—
185#2468C2214yes—
186#2468C2214yes—
187#2465C2214yes—
188#2462C2214yes—
189#2459C2214yes—
190#2458C2214yes—
191#2452C2212yes—
192#2452C2212yes—
193#2452C2212yes—
194#2452C2212yes—
195#2451C2214yes—
196#2451C2212yes—
197#2451C2214yes—
198#2450C2214yes—
199#2448C2212yes—
200#2448C2212yes—
201#2448C2212yes—
202#2445C2212yes—
203#2440C2212yes—
204#2439C2212yes—
205#2439C2212yes—
206#2439C2214yes—
207#2439C2214yes—
208#2439C2212yes—
209#2438C2214yes—
210#2429C2214yes—
211#2428C2212yes—
212#2426C2214yes—
213#2426C2214yes—
214#2426C2212yes—
215#2425C2214yes—
216#2423C2212yes—
217#2421C2212yes—
218#2421C2212yes—
219#2420C2212yes—
220#2416C2212yes—
221#2396C2212yes—
222#2396C2212yes—
223#2395C2212yes—
224#2378C2214yes—
225#2367C2212yes—
226#2365C2212yes—
227#2365C2212yes—
228#2363C2212yes—
229#2362C2214yes—
230#2362C2214yes—
231#2361C2212yes—
232#2360C2212yes—
233#2357C2212yes—
234#2355C2212yes—
235#2351C2212yes—
236#2351C2212yes—
237#2349C2212yes—
238#2345C2212yes—
239#2344C2212yes—
240#2337C2214yes—
241#2329C2214yes—
242#2327C2212yes—
243#2326C2212yes—
244#2324C2212yes—
245#2316C2212yes—
246C4×C4⋊Q8C2211yescharacteristic
247C4×C4⋊Q8C2212yes—
248C4×C4⋊Q8C2211yescharacteristic
249C4×C4⋊Q8C2212yes—
250C4×#125C2212yes—
251C4×#126C2212yes—
252C4×#126C2212yes—
253C4×#124C2211yescharacteristic
254C4×#124C2214yes—
255#2295C2211yescharacteristic
256#2295C2211yescharacteristic
257#2293C2212yes—
258C42×Q8C2211yescharacteristic
259#563—48no—
260#559—44no—
261Q82—44no—
262Q82—48no—
263#557—44no—
264#556—44no—
265#555—48no—
266#542—48no—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2311yescharacteristic
277C2×C4⋊Q8C2312yes—
278C2×C4⋊Q8C2312yes—
279C2×C4⋊Q8C2311yescharacteristic
280C2×C4⋊Q8C2311yescharacteristic
281C2×C4⋊Q8C2312yes—
282C2×C4⋊Q8C2314yes—
283C2×C4⋊Q8C2314yes—
284C2×C4⋊Q8C2314yes—
285C2×#127C2311yescharacteristic
286C2×#126C2312yes—
287C2×#126C2312yes—
288C2×#126C2314yes—
289C2×#126C2314yes—
290C2×#126C2314yes—
291C2×#126C2314yes—
292C2×#125C2312yes—
293C2×#125C2314yes—
294C2×#125C2312yes—
295C2×#125C2314yes—
296C2×#124C2312yes—
297C2×#124C2312yes—
298C2×#124C2311yescharacteristic
299C2×#124C2314yes—
300C2×#124C2314yes—
301C2×#124C2312yes—
302C2×#124C2312yes—
303C2×#124C2314yes—
304C2×#124C2314yes—
305C2×#123C2314yes—
306C2×#123C2314yes—
307C2×#123C2314yes—
308C2×C22⋊Q8C2312yes—
309C2×C22⋊Q8C2314yes—
310C2×C22⋊Q8C2314yes—
311C2×C22⋊Q8C2314yes—
312C2×C22⋊Q8C2314yes—
313C2×C22⋊Q8C2314yes—
314C2×C22⋊Q8C2314yes—
315C2×C22⋊Q8C2314yes—
316C2×#121C2312yes—
317C2×#121C2314yes—
318C2×#121C2312yes—
319C2×#121C2314yes—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2311yescharacteristic
323C2×C4×Q8C2311yescharacteristic
324C2×C4×Q8C2311yescharacteristic
325C2×C4×Q8C2311yescharacteristic
326C2×C4×Q8C2312yes—
327C2×C4×Q8C2311yescharacteristic
328C2×C4×Q8C2311yescharacteristic
329C2×C4×Q8C2312yes—
330C2×C4×Q8C2314yes—
331C2×C4×Q8C2312yes—
332C2×C4×Q8C2314yes—
333C2×C4×Q8C2314yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2311yescharacteristic
337C2×C4×D4C2312yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2314yes—
340C2×#117C2312yes—
341C2×#117C2312yes—
342C2×#117C2314yes—
343C2×#117C2314yes—
344C22×C4⋊C4C2312yes—
345#401C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2312yes—
354#400C2312yes—
355#400C2312yes—
356#400C2314yes—
357#400C2314yes—
358#399C2314yes—
359#399C2314yes—
360#399C2312yes—
361#399C2314yes—
362#399C2312yes—
363#399C2312yes—
364#399C2314yes—
365#398C2314yes—
366#398C2312yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2312yes—
371#398C2312yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2312yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2312yes—
383#398C2312yes—
384#398C2314yes—
385#398C2312yes—
386#398C2312yes—
387#398C2312yes—
388#398C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2312yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2312yes—
399#397C2312yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#396C2312yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2312yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2312yes—
418#396C2312yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#396C2314yes—
423#395C2314yes—
424#395C2314yes—
425#395C2314yes—
426#395C2314yes—
427#395C2314yes—
428#395C2314yes—
429#395C2314yes—
430#395C2314yes—
431#395C2314yes—
432#395C2312yes—
433#395C2312yes—
434#395C2314yes—
435#395C2314yes—
436#394C2314yes—
437#394C2314yes—
438#394C2314yes—
439#394C2312yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2312yes—
445#394C2312yes—
446#394C2312yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#393C2314yes—
452#393C2314yes—
453#393C2314yes—
454#393C2314yes—
455#393C2314yes—
456#393C2314yes—
457#393C2314yes—
458#393C2314yes—
459#393C2314yes—
460#393C2314yes—
461#393C2314yes—
462#393C2312yes—
463#393C2312yes—
464#393C2314yes—
465#392C2314yes—
466#391C2311yescharacteristic
467#391C2311yescharacteristic
468#391C2311yescharacteristic
469#391C2312yes—
470#391C2311yescharacteristic
471#391C2314yes—
472#391C2312yes—
473#391C2312yes—
474#391C2312yes—
475#391C2312yes—
476#391C2314yes—
477#391C2312yes—
478#391C2314yes—
479#391C2312yes—
480#391C2314yes—
481#391C2314yes—
482#391C2314yes—
483#391C2311yescharacteristic
484#391C2312yes—
485#391C2314yes—
486#391C2314yes—
487#391C2314yes—
488#391C2314yes—
489#391C2312yes—
490#391C2312yes—
491#391C2314yes—
492#391C2314yes—
493#391C2314yes—
494#390C2312yes—
495#390C2312yes—
496#390C2312yes—
497#390C2312yes—
498#390C2314yes—
499#390C2312yes—
500#390C2312yes—
501#390C2314yes—
502#390C2312yes—
503#390C2312yes—
504#390C2312yes—
505#390C2312yes—
506#390C2314yes—
507#390C2311yescharacteristic
508#390C2312yes—
509#390C2314yes—
510#390C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2314yes—
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2314yes—
519#389C2314yes—
520#389C2312yes—
521#389C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2312yes—
525#389C2314yes—
526#389C2312yes—
527#389C2314yes—
528#389C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2314yes—
533#389C2314yes—
534#389C2314yes—
535#389C2314yes—
536#389C2314yes—
537#389C2314yes—
538#389C2314yes—
539#389C2312yes—
540#389C2312yes—
541#389C2314yes—
542#389C2312yes—
543#389C2314yes—
544#389C2312yes—
545#389C2314yes—
546#389C2312yes—
547#389C2314yes—
548#389C2312yes—
549#388C2312yes—
550#388C2312yes—
551#388C2312yes—
552#388C2312yes—
553#388C2312yes—
554#388C2312yes—
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#388C2312yes—
587#388C2312yes—
588#387C2312yes—
589#387C2312yes—
590#387C2312yes—
591#387C2312yes—
592#387C2312yes—
593#387C2312yes—
594#387C2312yes—
595#387C2312yes—
596#387C2312yes—
597#387C2312yes—
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#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2314yes—
630#386C2314yes—
631#386C2314yes—
632#386C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#384C2312yes—
647#384C2311yescharacteristic
648#384C2312yes—
649#384C2311yescharacteristic
650#384C2312yes—
651#384C2312yes—
652#383C2312yes—
653#383C2312yes—
654#382C2312yes—
655#382C2312yes—
656#382C2312yes—
657#382C2312yes—
658#382C2314yes—
659#382C2312yes—
660#382C2311yescharacteristic
661#382C2314yes—
662#382C2312yes—
663#382C2314yes—
664#382C2314yes—
665#381C2314yes—
666#381C2314yes—
667#381C2314yes—
668#380C2312yes—
669#380C2314yes—
670#380C2312yes—
671#380C2314yes—
672#380C2314yes—
673#380C2314yes—
674#380C2314yes—
675#380C2312yes—
676#380C2314yes—
677#380C2314yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2314yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2314yes—
713#376C2312yes—
714#376C2312yes—
715C2×#95C2314yes—
716C43C2311yescharacteristic
717C43C2311yescharacteristic
718C43C2311yescharacteristic
719C43C2312yes—
720C22×Q8C2414yes—
721C22×Q8C2411yescharacteristic
722C22×Q8C2411yescharacteristic
723C22×Q8C2412yes—
724C22×Q8C2411yescharacteristic
725C22×Q8C2412yes—
726C22×Q8C2412yes—
727C22×Q8C2412yes—
728C22×Q8C2414yes—
729C22×Q8C2412yes—
730C22×Q8C2411yescharacteristic
731C22×D4C2412yes—
732C22×D4C2411yescharacteristic
733C22×D4C2414yes—
734C22×D4C2412yes—
735C22×D4C2414yes—
736C22×D4C2412yes—
737C23×C4C2412yes—
738C23×C4C2414yes—
739C23×C4C2414yes—
740C23×C4C2414yes—
741C23×C4C2414yes—
742C4⋊Q8—28no—
743C4⋊Q8—24no—
744C4⋊Q8—28no—
745C4⋊Q8—24no—
746C4⋊Q8—28no—
747C4⋊Q8—44no—
748C4⋊Q8—42no—
749C4⋊Q8—42no—
750C4⋊Q8—44no—
751C4⋊Q8—44no—
752C4⋊Q8—42no—
753C4⋊Q8—44no—
754C4⋊Q8—42no—
755C4⋊Q8—42no—
756C4⋊Q8—44no—
757C4⋊Q8—48no—
758C4⋊Q8—48no—
759C4⋊Q8—48no—
760#127—42no—
761#126—44no—
762#126—48no—
763#126—48no—
764#126—48no—
765#126—44no—
766#126—48no—
767#125—44no—
768#125—48no—
769#125—48no—
770#125—44no—
771#124—28no—
772#124—24no—
773#124—28no—
774#124—48no—
775#124—48no—
776#124—44no—
777#124—44no—
778#124—48no—
779#124—48no—
780#123—48no—
781#123—48no—
782#123—48no—
783C22⋊Q8—28no—
784C22⋊Q8—48no—
785C22⋊Q8—48no—
786C22⋊Q8—48no—
787C22⋊Q8—48no—
788C22⋊Q8—48no—
789C22⋊Q8—48no—
790C22⋊Q8—48no—
791#121—28no—
792#121—48no—
793#121—48no—
794#121—44no—
795C4×Q8—28no—
796C4×Q8—24no—
797C4×Q8—24no—
798C4×Q8—24no—
799C4×Q8—28no—
800C4×Q8—42no—
801C4×Q8—44no—
802C4×Q8—44no—
803C4×Q8—42no—
804C4×Q8—42no—
805C4×Q8—44no—
806C4×Q8—48no—
807C4×Q8—48no—
808C4×Q8—48no—
809C4×D4—28no—
810C4×D4—48no—
811C4×D4—44no—
812C4×D4—44no—
813C4×D4—44no—
814C4×D4—42no—
815#117—44no—
816#117—48no—
817#117—48no—
818#117—44no—
819C2×C4⋊C4—28no—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2411yescharacteristic
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2411yescharacteristic
864C2×C4⋊C4C2411yescharacteristic
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
889C2×C4⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2412yes—
931C2×C42C2411yescharacteristic
932C2×C42C2412yes—
933C2×C42C2412yes—
934C2×C42C2412yes—
935C2×C42C2412yes—
936C2×C42C2412yes—
937C2×C42C2411yescharacteristic
938C2×C42C2412yes—
939C2×C42C2411yescharacteristic
940C2×C42C2412yes—
941C2×C42C2411yescharacteristic
942C2×C42C2411yescharacteristic
943C2×C42C2412yes—
944C2×C42C2414yes—
945C2×C42C2412yes—
946C2×C42C2412yes—
947C2×C42C2414yes—
948C2×C42C2412yes—
949C2×C42C2411yescharacteristic
950C2×C42C2412yes—
951C2×C42C2414yes—
952C2×C42C2414yes—
953C2×C42C2414yes—
954C2×C42C2414yes—
955C2×C42C2414yes—
956C2×C42C2414yes—
957C2×C42C2412yes—
958C2×C42C2412yes—
959C2×C42C2411yescharacteristic
960C2×C42C2411yescharacteristic
961C2×C42C2411yescharacteristic
962#95C2412yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2412yes—
980#95C2412yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2414yes—
990#95C2412yes—
991#95C2414yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2414yes—
997#95C2414yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2414yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2414yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027C24C2512yes—
1028C24C2514yes—
1029C2×Q8—22no—
1030C2×Q8—24no—
1031C2×Q8—24no—
1032C2×Q8—22no—
1033C2×Q8—24no—
1034C2×Q8—28no—
1035C2×Q8—28no—
1036C2×Q8—41no—
1037C2×Q8—44no—
1038C2×Q8—41no—
1039C2×Q8—41no—
1040C2×Q8—42no—
1041C2×Q8—41no—
1042C2×Q8—42no—
1043C2×Q8—41no—
1044C2×Q8—42no—
1045C2×Q8—41no—
1046C2×Q8—42no—
1047C2×Q8—44no—
1048C2×Q8—44no—
1049C2×Q8—44no—
1050C2×Q8—44no—
1051C2×Q8—42no—
1052C2×Q8—42no—
1053C2×Q8—42no—
1054C2×Q8—44no—
1055C2×Q8—44no—
1056C2×Q8H(5,𝔽2)14yes—
1057C2×Q8H(5,𝔽2)14yes—
1058C2×D4—24no—
1059C2×D4—22no—
1060C2×D4—24no—
1061C2×D4—24no—
1062C2×D4—24no—
1063C2×D4—28no—
1064C2×D4—44no—
1065C2×D4—41no—
1066C2×D4—42no—
1067C2×D4—44no—
1068C2×D4—42no—
1069C2×D4—41no—
1070C2×D4—44no—
1071C2×D4—44no—
1072C2×D4—42no—
1073C2×D4—44no—
1074C2×D4—44no—
1075C22×C4—24no—
1076C22×C4—24no—
1077C22×C4—24no—
1078C22×C4—28no—
1079C22×C4—28no—
1080C22×C4—44no—
1081C22×C4—44no—
1082C22×C4—44no—
1083C22×C4—44no—
1084C22×C4—44no—
1085C22×C4—44no—
1086C22×C4—44no—
1087C22×C4—44no—
1088C22×C4—44no—
1089C22×C4—44no—
1090C22×C4C2512yes—
1091C22×C4C2512yes—
1092C22×C4C2512yes—
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2511yescharacteristic
1096C22×C4C2512yes—
1097C22×C4C2514yes—
1098C22×C4C2514yes—
1099C22×C4C2512yes—
1100C22×C4C2512yes—
1101C22×C4C2511yescharacteristic
1102C22×C4C2512yes—
1103C22×C4C2511yescharacteristic
1104C22×C4C2512yes—
1105C22×C4C2514yes—
1106C22×C4C2514yes—
1107C22×C4C2512yes—
1108C22×C4C2512yes—
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2511yescharacteristic
1112C22×C4C2511yescharacteristic
1113C22×C4C2511yescharacteristic
1114C22×C4C2514yes—
1115C22×C4C2512yes—
1116C22×C4C2511yescharacteristic
1117C4⋊C4—22no—
1118C4⋊C4—24no—
1119C4⋊C4—28no—
1120C4⋊C4—28no—
1121C4⋊C4—22no—
1122C4⋊C4—24no—
1123C4⋊C4—28no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—22no—
1127C4⋊C4—24no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—28no—
1131C4⋊C4—28no—
1132C4⋊C4—28no—
1133C4⋊C4—24no—
1134C4⋊C4—24no—
1135C4⋊C4—28no—
1136C4⋊C4—24no—
1137C4⋊C4—28no—
1138C4⋊C4—28no—
1139C4⋊C4—24no—
1140C4⋊C4—28no—
1141C4⋊C4—24no—
1142C4⋊C4—24no—
1143C4⋊C4—24no—
1144C4⋊C4—24no—
1145C4⋊C4—42no—
1146C4⋊C4—42no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—42no—
1150C4⋊C4—42no—
1151C4⋊C4—41no—
1152C4⋊C4—41no—
1153C4⋊C4—41no—
1154C4⋊C4—42no—
1155C4⋊C4—42no—
1156C4⋊C4—44no—
1157C4⋊C4—42no—
1158C4⋊C4—41no—
1159C4⋊C4—42no—
1160C4⋊C4—41no—
1161C4⋊C4—42no—
1162C4⋊C4—41no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—42no—
1177C4⋊C4—42no—
1178C4⋊C4—42no—
1179C4⋊C4—44no—
1180C4⋊C4—42no—
1181C4⋊C4—44no—
1182C4⋊C4—42no—
1183C4⋊C4—42no—
1184C4⋊C4—42no—
1185C4⋊C4—42no—
1186C4⋊C42−1+418yes—
1187C22⋊C4—24no—
1188C22⋊C4—28no—
1189C22⋊C4—24no—
1190C22⋊C4—28no—
1191C22⋊C4—28no—
1192C22⋊C4—28no—
1193C22⋊C4—28no—
1194C22⋊C4—28no—
1195C22⋊C4—28no—
1196C22⋊C4—28no—
1197C22⋊C4—24no—
1198C22⋊C4—28no—
1199C22⋊C4—24no—
1200C22⋊C4—44no—
1201C22⋊C4—42no—
1202C22⋊C4—44no—
1203C22⋊C4—42no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—42no—
1207C22⋊C4—42no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
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—42no—
1225C22⋊C4—42no—
1226C22⋊C4—42no—
1227C22⋊C4—42no—
1228C42—22no—
1229C42—24no—
1230C42—24no—
1231C42—24no—
1232C42—24no—
1233C42—24no—
1234C42—22no—
1235C42—24no—
1236C42—22no—
1237C42—24no—
1238C42—22no—
1239C42—28no—
1240C42—22no—
1241C42—24no—
1242C42—22no—
1243C42—24no—
1244C42—28no—
1245C42—24no—
1246C42—24no—
1247C42—24no—
1248C42—41no—
1249C42—41no—
1250C42—41no—
1251C42—44no—
1252C42—44no—
1253C42—44no—
1254C42—44no—
1255C42—44no—
1256C42—44no—
1257C42—42no—
1258C42—42no—
1259C23—22no—
1260C23—24no—
1261C23—24no—
1262C23—22no—
1263C23—24no—
1264C23—24no—
1265C23—22no—
1266C23—22no—
1267C23—22no—
1268C23—22no—
1269C23—24no—
1270C23—24no—
1271C23—24no—
1272C23—22no—
1273C23C2611yescharacteristic
1274Q8—28no—
1275Q8—44no—
1276Q8—416no—
1277Q8—82no—
1278Q8—84no—
1279Q8—82no—
1280Q8—84no—
1281Q8—162no—
1282Q8—162no—
1283Q8—162no—
1284Q8—164no—
1285D4—48no—
1286D4—88no—
1287D4—84no—
1288D4—82no—
1289D4—162no—
1290D4—164no—
1291C2×C4—21no—
1292C2×C4—21no—
1293C2×C4—21no—
1294C2×C4—22no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—21no—
1300C2×C4—21no—
1301C2×C4—21no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—24no—
1305C2×C4—22no—
1306C2×C4—24no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—21no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—24no—
1314C2×C4—22no—
1315C2×C4—21no—
1316C2×C4—21no—
1317C2×C4—22no—
1318C2×C4—24no—
1319C2×C4—22no—
1320C2×C4—24no—
1321C2×C4—24no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—24no—
1342C2×C4—22no—
1343C2×C4—24no—
1344C2×C4—22no—
1345C2×C4—24no—
1346C2×C4—22no—
1347C2×C4—24no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—24no—
1354C2×C4—24no—
1355C2×C4—22no—
1356C2×C4—48no—
1357C2×C4—88no—
1358C2×C4—88no—
1359C2×C4—164no—
1360C2×C4—164no—
1361C2×C4C2×H(5,𝔽2)14yes—
1362C2×C4C2×H(5,𝔽2)12yes—
1363C2×C4C2×H(5,𝔽2)12yes—
1364C2×C4C2×H(5,𝔽2)12yes—
1365C2×C4C2×H(5,𝔽2)12yes—
1366C2×C4C2×2−1+418yes—
1367C2×C4C2×2−1+414yes—
1368C2×C4#58514yes—
1369C22—42no—
1370C22—44no—
1371C22—42no—
1372C22—44no—
1373C22—42no—
1374C22—44no—
1375C22—44no—
1376C22—42no—
1377C22—44no—
1378C22—42no—
1379C22—44no—
1380C22—44no—
1381C22—42no—
1382C22—42no—
1383C22C22×H(5,𝔽2)11yescharacteristic
1384C22C22×H(5,𝔽2)11yescharacteristic
1385C22C22×2−1+412yes—
1386C22C2×#58512yes—
1387C222−1+611yescharacteristic
1388C4—24no—
1389C4—28no—
1390C4—24no—
1391C4—22no—
1392C4—22no—
1393C4—22no—
1394C4—42no—
1395C4—42no—
1396C4—44no—
1397C4—42no—
1398C4—44no—
1399C4—42no—
1400C4—42no—
1401C4—42no—
1402C4—41no—
1403C4—42no—
1404C4—41no—
1405C4—42no—
1406C4—41no—
1407C4—42no—
1408C4—44no—
1409C4—44no—
1410C4—42no—
1411C4—42no—
1412C4—42no—
1413C4—42no—
1414C4#354414yes—
1415C2—82no—
1416C2—84no—
1417C2C2×#354411yescharacteristic
1418C2#6289511yescharacteristic
1419C2#6295312yes—
1420C2#6301512yes—
1421C2#6303511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#59841C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #59832C2semidirect
3. #59749C2semidirect
4. #59659C2semidirect
5. #59502C2semidirect
6. #58921C2semidirect
7. #58316C2semidirect
8. #57133C2semidirect
9. #52306C2semidirect
10. #52079C2semidirect
11. #51586C2semidirect
12. #48528C2semidirect
13. #48219C2semidirect
14. #46329C2semidirect
15. #46062C2semidirect
16. #45360C2semidirect
17. #45287C2semidirect
18. #45207C2semidirect
19. #42804C2semidirect
20. #42618C2semidirect
21. #42492C2semidirect
22. #39977C2semidirect
23. #39789C2semidirect
24. #39172C2semidirect
25. #39168C2semidirect
26. #37262C2semidirect
27. #37050C2semidirect
28. #36490C2semidirect
29. #36474C2semidirect

Maximal subgroups

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

subgroupindex
#598412
#598322
#597492
#596592
#595022
#589212
#583162
#571332
#523062
#520792
#515862
#485282
#482192
#463292
#460622
#453602
#452872
#452072
#428042
#426182
#424922
#399772
#397892
#391722
#391682
#372622
#370502
#364902
#364742