Finite Group Databasebeta

← #8726328

Subgroups — #8726328

Order 512.

5019 conjugacy classes of subgroups.

The subgroup lattice has 1501 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59817C211yesmaximal, characteristic, complemented
2#59695C212yesmaximal, complemented
3#59402C212yesmaximal, complemented
4#59127C212yesmaximal, complemented
5#59127C212yesmaximal, complemented
6#58957C214yesmaximal, complemented
7#58591C212yesmaximal, complemented
8#56706C214yesmaximal, complemented
9#55121C214yesmaximal, complemented
10#53136C212yesmaximal, complemented
11#53008C211yesmaximal, characteristic, complemented
12#52297C211yesmaximal, characteristic
13#47726C212yesmaximal, complemented
14#46584C214yesmaximal, complemented
15#45435C212yesmaximal, complemented
16#45321C211yesmaximal, characteristic, complemented
17#45321C212yesmaximal, complemented
18#43399C214yesmaximal, complemented
19#42911C211yesmaximal, characteristic, complemented
20#42786C212yesmaximal, complemented
21#42361C212yesmaximal, complemented
22#41191C214yesmaximal, complemented
23#40196C212yesmaximal, complemented
24#40070C212yesmaximal, complemented
25#39663C212yesmaximal, complemented
26#39593C212yesmaximal, complemented
27#39167C211yesmaximal, characteristic, complemented
28#36007C211yesmaximal, characteristic, complemented
29#35700C212yesmaximal, complemented
30C2×#556C2211yescharacteristic
31C2×D4×Q8C2212yes—
32C2×D4×Q8C2212yes—
33C2×D4×Q8C2212yes—
34C2×D4×Q8C2212yes—
35C2×D4×Q8C2212yes—
36C2×D4×Q8C2211yescharacteristic
37C2×#536C2212yes—
38C2×#536C2211yescharacteristic
39C22×C4⋊Q8C2212yes—
40C2×#519C2211yescharacteristic
41#2862C2211yescharacteristic
42#2855C2212yes—
43#2843C2212yes—
44#2838C2214yes—
45#2838C2214yes—
46#2838C2214yes—
47#2834C2212yes—
48#2830C2214yes—
49#2827C2214yes—
50#2821C2212yes—
51#2814C2214yes—
52#2807C2212yes—
53#2806C2214yes—
54#2803C2212yes—
55#2797C2214yes—
56#2796C2214yes—
57#2795C2211yescharacteristic
58#2793C2214yes—
59#2792C2212yes—
60#2792C2211yescharacteristic
61#2792C2214yes—
62#2790C2214yes—
63#2788C2214yes—
64#2787C2214yes—
65#2784C2211yescharacteristic
66#2776C2214yes—
67#2774C2214yes—
68#2773C2214yes—
69#2772C2214yes—
70#2768C2214yes—
71#2768C2214yes—
72#2766C2214yes—
73#2759C2214yes—
74#2757C2214yes—
75#2756C2212yes—
76#2745C2214yes—
77#2737C2212yes—
78#2734C2214yes—
79#2734C2214yes—
80#2734C2214yes—
81#2731C2214yes—
82#2730C2214yes—
83#2729C2214yes—
84#2729C2214yes—
85#2729C2214yes—
86#2725C2214yes—
87#2723C2214yes—
88#2723C2214yes—
89#2718C2214yes—
90#2714C2212yes—
91#2711C2214yes—
92#2710C2214yes—
93#2705C2212yes—
94#2699C2211yescharacteristic
95#2686C2214yes—
96#2683C2212yes—
97#2683C2212yes—
98#2680C2214yes—
99#2680C2212yes—
100#2677C2212yes—
101#2677C2214yes—
102#2677C2214yes—
103#2677C2214yes—
104#2677C2214yes—
105#2677C2214yes—
106#2674C2214yes—
107#2674C2214yes—
108#2674C2214yes—
109#2673C2212yes—
110#2666C2214yes—
111#2663C2214yes—
112#2662C2212yes—
113#2653C2214yes—
114#2651C2214yes—
115#2640C2212yes—
116#2637C2212yes—
117#2632C2212yes—
118#2630C2214yes—
119#2627C2214yes—
120#2625C2211yescharacteristic
121#2621C2212yes—
122#2621C2214yes—
123#2616C2211yescharacteristic
124#2606C2214yes—
125#2604C2212yes—
126#2602C2214yes—
127#2595C2214yes—
128#2595C2214yes—
129#2594C2214yes—
130#2594C2214yes—
131#2590C2214yes—
132#2589C2214yes—
133#2587C2214yes—
134#2586C2214yes—
135#2586C2214yes—
136#2583C2214yes—
137#2581C2212yes—
138#2579C2214yes—
139#2567C2212yes—
140#2567C2212yes—
141#2558C2214yes—
142#2551C2214yes—
143#2551C2212yes—
144#2551C2214yes—
145#2551C2212yes—
146#2551C2214yes—
147#2547C2211yescharacteristic
148#2546C2212yes—
149#2546C2212yes—
150#2546C2214yes—
151#2546C2212yes—
152#2544C2212yes—
153#2542C2211yescharacteristic
154#2542C2212yes—
155#2542C2212yes—
156#2538C2212yes—
157#2538C2212yes—
158#2536C2212yes—
159#2536C2214yes—
160#2529C2214yes—
161#2526C2214yes—
162#2525C2214yes—
163#2516C2214yes—
164#2515C2214yes—
165#2514C2212yes—
166#2511C2212yes—
167#2506C2212yes—
168#2499C2212yes—
169#2494C2212yes—
170#2492C2212yes—
171#2485C2212yes—
172#2478C2214yes—
173#2474C2214yes—
174#2461C2214yes—
175#2461C2214yes—
176#2461C2214yes—
177#2455C2214yes—
178#2455C2212yes—
179#2452C2214yes—
180#2452C2214yes—
181#2452C2214yes—
182#2452C2214yes—
183#2451C2212yes—
184#2449C2214yes—
185#2449C2214yes—
186#2449C2214yes—
187#2449C2214yes—
188#2446C2212yes—
189#2446C2212yes—
190#2440C2214yes—
191#2440C2214yes—
192#2434C2212yes—
193#2434C2212yes—
194#2434C2212yes—
195#2434C2212yes—
196#2434C2211yescharacteristic
197#2434C2211yescharacteristic
198#2429C2212yes—
199#2429C2212yes—
200#2429C2212yes—
201#2429C2212yes—
202#2429C2212yes—
203#2429C2212yes—
204#2429C2212yes—
205#2429C2212yes—
206#2429C2214yes—
207#2429C2214yes—
208#2423C2212yes—
209#2421C2212yes—
210#2415C2212yes—
211#2415C2212yes—
212#2415C2212yes—
213#2415C2214yes—
214#2415C2214yes—
215#2415C2212yes—
216#2415C2212yes—
217#2409C2212yes—
218#2409C2212yes—
219#2409C2211yescharacteristic
220#2409C2211yescharacteristic
221#2409C2212yes—
222#2409C2212yes—
223#2409C2212yes—
224#2399C2212yes—
225#2395C2211yescharacteristic
226#2392C2212yes—
227#2392C2214yes—
228#2388C2212yes—
229#2388C2211yescharacteristic
230#2370C2214yes—
231#2370C2214yes—
232#2366C2212yes—
233#2365C2212yes—
234#2365C2212yes—
235#2362C2212yes—
236#2362C2212yes—
237#2362C2212yes—
238#2361C2214yes—
239#2361C2214yes—
240#2351C2212yes—
241#2347C2211yescharacteristic
242#2346C2211yescharacteristic
243Q8×C22⋊C4C2212yes—
244Q8×C22⋊C4C2212yes—
245#2337C2214yes—
246#2334C2214yes—
247#2330C2214yes—
248#2326C2212yes—
249#2322C2214yes—
250C4×C4⋊Q8C2212yes—
251C4×#127C2211yescharacteristic
252C4×#126C2212yes—
253C4×C22⋊Q8C2212yes—
254C4×C22⋊Q8C2212yes—
255C4×#123C2212yes—
256C4×#121C2212yes—
257C4×#121C2212yes—
258#2295C2211yescharacteristic
259C22×#41C2311yescharacteristic
260C23×Q8C2311yescharacteristic
261C23×Q8C2312yes—
262C23×Q8C2312yes—
263C23×Q8C2312yes—
264C23×Q8C2311yescharacteristic
265#556—44no—
266D4×Q8—48no—
267D4×Q8—44no—
268D4×Q8—48no—
269D4×Q8—48no—
270D4×Q8—48no—
271D4×Q8—48no—
272#536—44no—
273#536—48no—
274C2×C4⋊Q8—48no—
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2312yes—
277C2×C4⋊Q8C2312yes—
278C2×C4⋊Q8C2312yes—
279C2×C4⋊Q8C2312yes—
280C2×C4⋊Q8C2311yescharacteristic
281C2×C4⋊Q8C2311yescharacteristic
282C2×C4⋊Q8C2314yes—
283C2×C4⋊Q8C2312yes—
284C2×C4⋊Q8C2314yes—
285C2×C4⋊Q8C2312yes—
286C2×C4⋊Q8C2312yes—
287C2×C4⋊Q8C2314yes—
288C2×C4⋊Q8C2314yes—
289C2×C4⋊Q8C2314yes—
290C2×C4⋊Q8C2314yes—
291C2×C4⋊Q8C2314yes—
292C2×C4⋊Q8C2314yes—
293C2×#127C2311yescharacteristic
294C2×#126C2312yes—
295C2×#126C2312yes—
296C2×#126C2312yes—
297C2×#125C2314yes—
298C2×#124C2312yes—
299C2×#124C2312yes—
300C2×#124C2312yes—
301C2×#124C2314yes—
302C2×#123C2312yes—
303C2×#123C2314yes—
304C2×#123C2314yes—
305C2×#123C2314yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2312yes—
308C2×C22⋊Q8C2312yes—
309C2×C22⋊Q8C2312yes—
310C2×C22⋊Q8C2312yes—
311C2×C22⋊Q8C2314yes—
312C2×C22⋊Q8C2312yes—
313C2×C22⋊Q8C2311yescharacteristic
314C2×C22⋊Q8C2312yes—
315C2×C22⋊Q8C2312yes—
316C2×C22⋊Q8C2312yes—
317C2×C22⋊Q8C2314yes—
318C2×C22⋊Q8C2314yes—
319C2×C22⋊Q8C2311yescharacteristic
320C2×C22⋊Q8C2314yes—
321C2×C22⋊Q8C2312yes—
322C2×C22⋊Q8C2312yes—
323C2×C22⋊Q8C2312yes—
324C2×C22⋊Q8C2314yes—
325C2×C22⋊Q8C2314yes—
326C2×C22⋊Q8C2314yes—
327C2×C22⋊Q8C2314yes—
328C2×C22⋊Q8C2314yes—
329C2×C22⋊Q8C2314yes—
330C2×C22⋊Q8C2314yes—
331C2×#121C2312yes—
332C2×#121C2312yes—
333#519—44no—
334C2×C4×Q8C2312yes—
335C2×C4×Q8C2311yescharacteristic
336C2×C4×Q8C2312yes—
337C2×C4×Q8C2312yes—
338C2×C4×Q8C2312yes—
339C2×C4×Q8C2312yes—
340C2×C4×Q8C2312yes—
341C2×C4×Q8C2312yes—
342C2×C4×Q8C2312yes—
343C2×C4×Q8C2312yes—
344C2×C4×D4C2311yescharacteristic
345C2×C4×D4C2312yes—
346C2×C4×D4C2312yes—
347C2×C4×D4C2311yescharacteristic
348C2×C4×D4C2314yes—
349C2×C4×D4C2312yes—
350C2×C4×D4C2314yes—
351C2×C4×D4C2314yes—
352C2×C4×D4C2314yes—
353C2×C4×D4C2314yes—
354C2×C4×D4C2312yes—
355C2×C4×D4C2312yes—
356C2×C4×D4C2312yes—
357C2×#117C2311yescharacteristic
358C2×#117C2311yescharacteristic
359C2×#117C2312yes—
360C2×#117C2311yescharacteristic
361C2×#117C2314yes—
362C22×C4⋊C4C2314yes—
363C22×C4⋊C4C2314yes—
364C22×C42C2312yes—
365#401C2314yes—
366#401C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2311yescharacteristic
371#400C2312yes—
372#400C2314yes—
373#400C2314yes—
374#400C2314yes—
375#400C2314yes—
376#400C2314yes—
377#399C2314yes—
378#399C2314yes—
379#399C2312yes—
380#399C2312yes—
381#399C2314yes—
382#399C2311yescharacteristic
383#399C2314yes—
384#399C2314yes—
385#398C2314yes—
386#398C2312yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2314yes—
406#398C2314yes—
407#398C2312yes—
408#398C2311yescharacteristic
409#398C2314yes—
410#397C2314yes—
411#397C2314yes—
412#397C2314yes—
413#397C2314yes—
414#397C2314yes—
415#397C2314yes—
416#397C2314yes—
417#397C2311yescharacteristic
418#397C2314yes—
419#397C2312yes—
420#397C2314yes—
421#397C2312yes—
422#397C2314yes—
423#397C2314yes—
424#397C2314yes—
425#397C2314yes—
426#397C2314yes—
427#396C2314yes—
428#396C2314yes—
429#396C2314yes—
430#396C2314yes—
431#396C2314yes—
432#396C2312yes—
433#396C2314yes—
434#396C2314yes—
435#396C2314yes—
436#396C2314yes—
437#396C2314yes—
438#396C2314yes—
439#396C2314yes—
440#396C2312yes—
441#395C2312yes—
442#395C2312yes—
443#395C2311yescharacteristic
444#395C2314yes—
445#395C2312yes—
446#395C2312yes—
447#395C2314yes—
448#395C2314yes—
449#395C2312yes—
450#395C2312yes—
451#395C2314yes—
452#395C2314yes—
453#395C2314yes—
454#395C2314yes—
455#395C2314yes—
456#395C2314yes—
457#395C2314yes—
458#395C2314yes—
459#395C2314yes—
460#395C2312yes—
461#395C2312yes—
462#395C2314yes—
463#395C2314yes—
464#394C2312yes—
465#394C2314yes—
466#394C2312yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2312yes—
472#394C2314yes—
473#394C2311yescharacteristic
474#394C2312yes—
475#394C2312yes—
476#394C2312yes—
477#394C2312yes—
478#394C2314yes—
479#394C2312yes—
480#394C2314yes—
481#394C2312yes—
482#393C2311yescharacteristic
483#393C2312yes—
484#393C2314yes—
485#393C2314yes—
486#393C2314yes—
487#393C2312yes—
488#393C2314yes—
489#393C2312yes—
490#393C2314yes—
491#393C2314yes—
492#392C2312yes—
493#392C2312yes—
494#392C2311yescharacteristic
495#392C2312yes—
496#392C2312yes—
497#392C2312yes—
498#391C2312yes—
499#391C2312yes—
500#391C2312yes—
501#391C2314yes—
502#391C2312yes—
503#391C2314yes—
504#391C2312yes—
505#391C2314yes—
506#391C2314yes—
507#391C2312yes—
508#391C2312yes—
509#391C2312yes—
510#391C2312yes—
511#391C2314yes—
512#391C2314yes—
513#391C2312yes—
514#391C2312yes—
515#391C2312yes—
516#391C2312yes—
517#391C2312yes—
518#391C2312yes—
519#390C2311yescharacteristic
520#390C2311yescharacteristic
521#390C2312yes—
522#390C2312yes—
523#390C2314yes—
524#390C2312yes—
525#390C2314yes—
526#390C2314yes—
527#390C2314yes—
528#390C2312yes—
529#390C2312yes—
530#389C2314yes—
531#389C2314yes—
532#389C2314yes—
533#389C2314yes—
534#389C2314yes—
535#389C2314yes—
536#389C2314yes—
537#389C2314yes—
538#389C2314yes—
539#389C2314yes—
540#389C2314yes—
541#389C2314yes—
542#389C2314yes—
543#389C2314yes—
544#389C2314yes—
545#389C2312yes—
546#389C2314yes—
547#389C2314yes—
548#389C2312yes—
549#389C2314yes—
550#389C2314yes—
551#389C2314yes—
552#389C2314yes—
553#389C2314yes—
554#389C2314yes—
555#389C2314yes—
556#389C2312yes—
557#389C2312yes—
558#389C2312yes—
559#389C2312yes—
560#389C2312yes—
561#389C2314yes—
562#389C2314yes—
563#389C2314yes—
564#389C2312yes—
565#388C2312yes—
566#388C2312yes—
567#388C2312yes—
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#388C2312yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2312yes—
598#388C2312yes—
599#388C2312yes—
600#388C2312yes—
601#388C2312yes—
602#387C2312yes—
603#387C2312yes—
604#387C2312yes—
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#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2312yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2312yes—
634#386C2314yes—
635#386C2314yes—
636#386C2312yes—
637#386C2312yes—
638#386C2314yes—
639#386C2314yes—
640#386C2314yes—
641#386C2312yes—
642#386C2312yes—
643#386C2312yes—
644#386C2312yes—
645#386C2312yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2312yes—
653#385C2314yes—
654#385C2314yes—
655#385C2312yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2314yes—
661#385C2314yes—
662#385C2314yes—
663#385C2314yes—
664#385C2314yes—
665#385C2312yes—
666#385C2314yes—
667#384C2311yescharacteristic
668#384C2312yes—
669#384C2312yes—
670#384C2314yes—
671#384C2314yes—
672#383C2312yes—
673#383C2312yes—
674#383C2314yes—
675#382C2312yes—
676#382C2314yes—
677#382C2312yes—
678#382C2314yes—
679#381C2314yes—
680#381C2312yes—
681#380C2314yes—
682#380C2312yes—
683#380C2312yes—
684#380C2314yes—
685#380C2311yescharacteristic
686#380C2311yescharacteristic
687#380C2312yes—
688#380C2312yes—
689#380C2312yes—
690#380C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2314yes—
700C4×C4⋊C4C2314yes—
701C4×C4⋊C4C2314yes—
702C4×C4⋊C4C2314yes—
703C4×C4⋊C4C2314yes—
704C4×C4⋊C4C2312yes—
705C4×C4⋊C4C2312yes—
706C4×C4⋊C4C2314yes—
707C4×C4⋊C4C2311yescharacteristic
708C4×C4⋊C4C2314yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2314yes—
714C4×C22⋊C4C2314yes—
715C4×C22⋊C4C2312yes—
716C4×C22⋊C4C2311yescharacteristic
717C4×C22⋊C4C2311yescharacteristic
718C4×C22⋊C4C2314yes—
719C4×C22⋊C4C2312yes—
720#376C2312yes—
721#376C2312yes—
722C43C2311yescharacteristic
723C2×#41—42no—
724C2×#41—44no—
725C22×Q8—28no—
726C22×Q8—28no—
727C22×Q8—28no—
728C22×Q8—42no—
729C22×Q8—44no—
730C22×Q8—42no—
731C22×Q8—44no—
732C22×Q8—44no—
733C22×Q8—44no—
734C22×Q8—44no—
735C22×Q8—44no—
736C22×Q8—44no—
737C22×Q8—44no—
738C22×Q8C2411yescharacteristic
739C22×Q8C2412yes—
740C22×Q8C2412yes—
741C22×Q8C2412yes—
742C22×Q8C2412yes—
743C22×Q8C2412yes—
744C22×Q8C2414yes—
745C22×Q8C2414yes—
746C22×Q8C2412yes—
747C22×Q8C2414yes—
748C22×Q8C2411yescharacteristic
749C22×D4C2412yes—
750C22×D4C2412yes—
751C22×D4C2412yes—
752C22×D4C2412yes—
753C22×D4C2412yes—
754C22×D4C2411yescharacteristic
755C22×D4C2412yes—
756C22×D4C2411yescharacteristic
757C22×D4C2411yescharacteristic
758C23×C4C2411yescharacteristic
759C23×C4C2411yescharacteristic
760C23×C4C2412yes—
761C23×C4C2412yes—
762C23×C4C2412yes—
763C23×C4C2412yes—
764C23×C4C2414yes—
765C23×C4C2412yes—
766C23×C4C2414yes—
767C23×C4C2414yes—
768C23×C4C2412yes—
769C4⋊Q8—28no—
770C4⋊Q8—28no—
771C4⋊Q8—28no—
772C4⋊Q8—44no—
773C4⋊Q8—48no—
774C4⋊Q8—44no—
775C4⋊Q8—42no—
776C4⋊Q8—44no—
777C4⋊Q8—44no—
778C4⋊Q8—44no—
779C4⋊Q8—42no—
780C4⋊Q8—48no—
781C4⋊Q8—48no—
782C4⋊Q8—48no—
783C4⋊Q8—48no—
784C4⋊Q8—48no—
785C4⋊Q8—48no—
786C4⋊Q8—48no—
787#127—24no—
788#126—28no—
789#126—44no—
790#126—44no—
791#125—216no—
792#124—28no—
793#124—44no—
794#124—44no—
795#124—48no—
796#123—28no—
797#123—48no—
798#123—48no—
799#123—48no—
800C22⋊Q8—28no—
801C22⋊Q8—28no—
802C22⋊Q8—28no—
803C22⋊Q8—28no—
804C22⋊Q8—28no—
805C22⋊Q8—48no—
806C22⋊Q8—48no—
807C22⋊Q8—48no—
808C22⋊Q8—48no—
809C22⋊Q8—48no—
810C22⋊Q8—48no—
811C22⋊Q8—48no—
812C22⋊Q8—48no—
813C22⋊Q8—48no—
814C22⋊Q8—48no—
815C22⋊Q8—48no—
816C22⋊Q8—44no—
817C22⋊Q8—44no—
818C22⋊Q8—44no—
819C22⋊Q8—44no—
820C22⋊Q8—44no—
821C22⋊Q8—44no—
822C22⋊Q8—44no—
823C22⋊Q8—42no—
824C22⋊Q8—42no—
825#121—28no—
826#121—28no—
827C4×Q8—28no—
828C4×Q8—24no—
829C4×Q8—44no—
830C4×Q8—44no—
831C4×Q8—44no—
832C4×Q8—44no—
833C4×Q8—44no—
834C4×Q8—44no—
835C4×Q8—44no—
836C4×Q8—44no—
837C4×D4—48no—
838C4×D4—44no—
839C4×D4—44no—
840C4×D4—44no—
841C4×D4—44no—
842C4×D4—42no—
843C4×D4—44no—
844C4×D4—44no—
845C4×D4—42no—
846C4×D4—48no—
847C4×D4—48no—
848C4×D4—48no—
849C4×D4—48no—
850#117—24no—
851#117—24no—
852#117—42no—
853#117—48no—
854#117—44no—
855C2×C4⋊C4—48no—
856C2×C4⋊C4—48no—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2411yescharacteristic
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2411yescharacteristic
890C2×C4⋊C4C2411yescharacteristic
891C2×C4⋊C4C2411yescharacteristic
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2411yescharacteristic
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2414yes—
910C2×C4⋊C4C2414yes—
911C2×C4⋊C4C2414yes—
912C2×C4⋊C4C2414yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2414yes—
915C2×C4⋊C4C2412yes—
916C2×C4⋊C4C2412yes—
917C2×C4⋊C4C2414yes—
918C2×C4⋊C4C2414yes—
919C2×C4⋊C4C2414yes—
920C2×C4⋊C4C2411yescharacteristic
921C2×C4⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2412yes—
941C2×C22⋊C4C2412yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2412yes—
944C2×C22⋊C4C2412yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2412yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2412yes—
949C2×C22⋊C4C2412yes—
950C2×C22⋊C4C2412yes—
951C2×C22⋊C4C2412yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2412yes—
956C2×C22⋊C4C2412yes—
957C2×C22⋊C4C2412yes—
958C2×C22⋊C4C2411yescharacteristic
959C2×C22⋊C4C2411yescharacteristic
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2414yes—
963C2×C22⋊C4C2412yes—
964C2×C22⋊C4C2412yes—
965C2×C22⋊C4C2412yes—
966C2×C22⋊C4C2414yes—
967C2×C22⋊C4C2414yes—
968C2×C22⋊C4C2412yes—
969C2×C22⋊C4C2412yes—
970C2×C22⋊C4C2412yes—
971C2×C42—44no—
972C2×C42C2412yes—
973C2×C42C2414yes—
974C2×C42C2412yes—
975C2×C42C2412yes—
976C2×C42C2412yes—
977C2×C42C2411yescharacteristic
978C2×C42C2412yes—
979C2×C42C2412yes—
980C2×C42C2412yes—
981C2×C42C2412yes—
982C2×C42C2414yes—
983C2×C42C2412yes—
984C2×C42C2411yescharacteristic
985C2×C42C2414yes—
986C2×C42C2414yes—
987C2×C42C2414yes—
988C2×C42C2414yes—
989C2×C42C2414yes—
990C2×C42C2414yes—
991C2×C42C2412yes—
992C2×C42C2412yes—
993C2×C42C2411yescharacteristic
994C2×C42C2414yes—
995#95C2411yescharacteristic
996#95C2412yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2412yes—
1001#95C2411yescharacteristic
1002#95C2412yes—
1003#95C2412yes—
1004#95C2411yescharacteristic
1005#95C2412yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2411yescharacteristic
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2412yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2412yes—
1018#95C2414yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2412yes—
1024#95C2412yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2412yes—
1028#95C2414yes—
1029#95C2412yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2412yes—
1034#95C2414yes—
1035#95C2412yes—
1036#95C2414yes—
1037#95C2412yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2412yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2414yes—
1053#95C2414yes—
1054#95C2414yes—
1055#95C2414yes—
1056C24C2511yescharacteristic
1057C24C2511yescharacteristic
1058C24C2512yes—
1059C24C2512yes—
1060#41—88no—
1061C2×Q8—24no—
1062C2×Q8—24no—
1063C2×Q8—22no—
1064C2×Q8—24no—
1065C2×Q8—24no—
1066C2×Q8—24no—
1067C2×Q8—24no—
1068C2×Q8—24no—
1069C2×Q8—28no—
1070C2×Q8—24no—
1071C2×Q8—24no—
1072C2×Q8—28no—
1073C2×Q8—28no—
1074C2×Q8—24no—
1075C2×Q8—42no—
1076C2×Q8—42no—
1077C2×Q8—44no—
1078C2×Q8—44no—
1079C2×Q8—44no—
1080C2×Q8—44no—
1081C2×Q8—44no—
1082C2×Q8—44no—
1083C2×Q8—44no—
1084C2×Q8—42no—
1085C2×Q8—44no—
1086C2×Q8—41no—
1087C2×Q8—42no—
1088C2×Q8—42no—
1089C2×Q8—416no—
1090C2×Q8—816no—
1091C2×Q8—816no—
1092C2×Q8—816no—
1093C2×Q8—88no—
1094C2×Q8H(5,𝔽2)18yes—
1095C2×D4—24no—
1096C2×D4—24no—
1097C2×D4—24no—
1098C2×D4—24no—
1099C2×D4—24no—
1100C2×D4—24no—
1101C2×D4—24no—
1102C2×D4—24no—
1103C2×D4—22no—
1104C2×D4—41no—
1105C2×D4—42no—
1106C2×D4—42no—
1107C2×D4—42no—
1108C2×D4—42no—
1109C2×D4—42no—
1110C2×D4—42no—
1111C2×D4—41no—
1112C2×D4—42no—
1113C2×D4—41no—
1114C2×D4—42no—
1115C2×D4—42no—
1116C2×D4—42no—
1117C2×D4—41no—
1118C2×D4—42no—
1119C2×D4—41no—
1120C2×D42−1+414yes—
1121C22×C4—24no—
1122C22×C4—24no—
1123C22×C4—22no—
1124C22×C4—22no—
1125C22×C4—24no—
1126C22×C4—24no—
1127C22×C4—24no—
1128C22×C4—28no—
1129C22×C4—24no—
1130C22×C4—24no—
1131C22×C4—24no—
1132C22×C4—24no—
1133C22×C4—24no—
1134C22×C4—24no—
1135C22×C4—28no—
1136C22×C4—28no—
1137C22×C4—42no—
1138C22×C4—42no—
1139C22×C4—42no—
1140C22×C4—42no—
1141C22×C4—44no—
1142C22×C4—44no—
1143C22×C4—44no—
1144C22×C4—44no—
1145C22×C4—44no—
1146C22×C4—44no—
1147C22×C4—44no—
1148C22×C4—44no—
1149C22×C4—42no—
1150C22×C4C2512yes—
1151C22×C4C2512yes—
1152C22×C4C2511yescharacteristic
1153C22×C4C2514yes—
1154C22×C4C2512yes—
1155C22×C4C2512yes—
1156C22×C4C2512yes—
1157C22×C4C2512yes—
1158C22×C4C2512yes—
1159C22×C4C2514yes—
1160C22×C4C2514yes—
1161C22×C4C2512yes—
1162C22×C4C2511yescharacteristic
1163C22×C4C2512yes—
1164C22×C4C2512yes—
1165C22×C4C2514yes—
1166C22×C4C2514yes—
1167C22×C4C2511yescharacteristic
1168C22×C4C2512yes—
1169C22×C4C2514yes—
1170C22×C4C2511yescharacteristic
1171C22×C4C2512yes—
1172C22×C4C2512yes—
1173C22×C4C2512yes—
1174C22×C4C2511yescharacteristic
1175C4⋊C4—28no—
1176C4⋊C4—28no—
1177C4⋊C4—28no—
1178C4⋊C4—28no—
1179C4⋊C4—22no—
1180C4⋊C4—22no—
1181C4⋊C4—28no—
1182C4⋊C4—24no—
1183C4⋊C4—24no—
1184C4⋊C4—28no—
1185C4⋊C4—24no—
1186C4⋊C4—24no—
1187C4⋊C4—28no—
1188C4⋊C4—28no—
1189C4⋊C4—28no—
1190C4⋊C4—28no—
1191C4⋊C4—28no—
1192C4⋊C4—28no—
1193C4⋊C4—24no—
1194C4⋊C4—24no—
1195C4⋊C4—28no—
1196C4⋊C4—28no—
1197C4⋊C4—28no—
1198C4⋊C4—28no—
1199C4⋊C4—28no—
1200C4⋊C4—24no—
1201C4⋊C4—24no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4—42no—
1207C4⋊C4—44no—
1208C4⋊C4—44no—
1209C4⋊C4—44no—
1210C4⋊C4—44no—
1211C4⋊C4—41no—
1212C4⋊C4—41no—
1213C4⋊C4—41no—
1214C4⋊C4—42no—
1215C4⋊C4—41no—
1216C4⋊C4—42no—
1217C4⋊C4—42no—
1218C4⋊C4—42no—
1219C4⋊C4—42no—
1220C4⋊C4—44no—
1221C4⋊C4—42no—
1222C4⋊C4—44no—
1223C4⋊C4—44no—
1224C4⋊C4—44no—
1225C4⋊C4—44no—
1226C4⋊C4—42no—
1227C4⋊C4—42no—
1228C4⋊C4—44no—
1229C4⋊C4—42no—
1230C4⋊C4—44no—
1231C4⋊C4—44no—
1232C4⋊C4—44no—
1233C4⋊C4—44no—
1234C4⋊C4—44no—
1235C4⋊C4—44no—
1236C4⋊C4—44no—
1237C4⋊C4—42no—
1238C4⋊C4H(5,𝔽2)14yes—
1239C4⋊C42−1+418yes—
1240C22⋊C4—24no—
1241C22⋊C4—28no—
1242C22⋊C4—28no—
1243C22⋊C4—24no—
1244C22⋊C4—24no—
1245C22⋊C4—28no—
1246C22⋊C4—28no—
1247C22⋊C4—28no—
1248C22⋊C4—28no—
1249C22⋊C4—28no—
1250C22⋊C4—24no—
1251C22⋊C4—24no—
1252C22⋊C4—24no—
1253C22⋊C4—24no—
1254C22⋊C4—24no—
1255C22⋊C4—24no—
1256C22⋊C4—24no—
1257C22⋊C4—24no—
1258C22⋊C4—24no—
1259C22⋊C4—42no—
1260C22⋊C4—44no—
1261C22⋊C4—44no—
1262C22⋊C4—42no—
1263C22⋊C4—42no—
1264C22⋊C4—42no—
1265C22⋊C4—42no—
1266C22⋊C4—44no—
1267C22⋊C4—42no—
1268C22⋊C4—42no—
1269C22⋊C4—42no—
1270C22⋊C4—42no—
1271C22⋊C4—42no—
1272C22⋊C4—42no—
1273C22⋊C4—42no—
1274C22⋊C4—42no—
1275C22⋊C4—42no—
1276C22⋊C4—42no—
1277C22⋊C4—42no—
1278C22⋊C4—44no—
1279C22⋊C4—44no—
1280C22⋊C4—44no—
1281C22⋊C4—44no—
1282C22⋊C4—41no—
1283C22⋊C4—41no—
1284C22⋊C4—44no—
1285C22⋊C4—44no—
1286C22⋊C4—44no—
1287C22⋊C4—42no—
1288C22⋊C4—42no—
1289C42—24no—
1290C42—24no—
1291C42—24no—
1292C42—24no—
1293C42—28no—
1294C42—24no—
1295C42—22no—
1296C42—24no—
1297C42—24no—
1298C42—24no—
1299C42—28no—
1300C42—24no—
1301C42—22no—
1302C42—42no—
1303C42—42no—
1304C42—44no—
1305C42—41no—
1306C42—44no—
1307C42—44no—
1308C42—44no—
1309C42—44no—
1310C42—44no—
1311C42—44no—
1312C23—22no—
1313C23—22no—
1314C23—22no—
1315C23—22no—
1316C23—22no—
1317C23—22no—
1318C23—21no—
1319C23—22no—
1320C23—22no—
1321C23—22no—
1322C23—21no—
1323C23—22no—
1324C23—22no—
1325C23—22no—
1326C23—22no—
1327C23—22no—
1328C23—22no—
1329C23—22no—
1330C23—21no—
1331C23—21no—
1332C23—21no—
1333C23—22no—
1334C23—21no—
1335C23C2×2−1+414yes—
1336C23C2611yescharacteristic
1337Q8—216no—
1338Q8—48no—
1339Q8—44no—
1340Q8—48no—
1341Q8—48no—
1342Q8—84no—
1343Q8—88no—
1344Q8—88no—
1345Q8—84no—
1346Q8—88no—
1347Q8—82no—
1348D4—44no—
1349D4—48no—
1350D4—48no—
1351D4—48no—
1352D4—48no—
1353D4—48no—
1354D4—82no—
1355D4—82no—
1356D4—84no—
1357C2×C4—21no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—24no—
1362C2×C4—24no—
1363C2×C4—24no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—21no—
1368C2×C4—22no—
1369C2×C4—21no—
1370C2×C4—21no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—21no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—24no—
1380C2×C4—24no—
1381C2×C4—24no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—24no—
1385C2×C4—24no—
1386C2×C4—24no—
1387C2×C4—24no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—24no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—24no—
1396C2×C4—24no—
1397C2×C4—24no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—24no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—22no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—24no—
1410C2×C4—24no—
1411C2×C4—22no—
1412C2×C4—24no—
1413C2×C4—22no—
1414C2×C4—24no—
1415C2×C4—22no—
1416C2×C4—22no—
1417C2×C4—22no—
1418C2×C4—48no—
1419C2×C4—48no—
1420C2×C4—48no—
1421C2×C4—44no—
1422C2×C4—48no—
1423C2×C4—44no—
1424C2×C4—48no—
1425C2×C4—88no—
1426C2×C4—88no—
1427C2×C4—88no—
1428C2×C4—84no—
1429C2×C4C2×H(5,𝔽2)14yes—
1430C2×C4C2×H(5,𝔽2)18yes—
1431C2×C4C2×H(5,𝔽2)14yes—
1432C2×C4C2×H(5,𝔽2)12yes—
1433C2×C4C2×2−1+412yes—
1434C2×C4C2×2−1+414yes—
1435C2×C4C2×2−1+414yes—
1436C2×C4C2×2−1+414yes—
1437C22—24no—
1438C22—24no—
1439C22—24no—
1440C22—42no—
1441C22—42no—
1442C22—42no—
1443C22—42no—
1444C22—41no—
1445C22—42no—
1446C22—41no—
1447C22—42no—
1448C22—42no—
1449C22—42no—
1450C22—42no—
1451C22—41no—
1452C22—42no—
1453C22—41no—
1454C22—42no—
1455C22—41no—
1456C22—41no—
1457C22—42no—
1458C22—42no—
1459C22—42no—
1460C22—42no—
1461C22C22×H(5,𝔽2)12yes—
1462C22C22×H(5,𝔽2)11yescharacteristic
1463C22C22×2−1+411yescharacteristic
1464C22C22×2−1+412yes—
1465C222−1+611yescharacteristic
1466C4—28no—
1467C4—24no—
1468C4—24no—
1469C4—24no—
1470C4—22no—
1471C4—24no—
1472C4—41no—
1473C4—42no—
1474C4—41no—
1475C4—42no—
1476C4—42no—
1477C4—44no—
1478C4—44no—
1479C4—44no—
1480C4—42no—
1481C4—42no—
1482C4—41no—
1483C4—42no—
1484C4—42no—
1485C4—42no—
1486C4—42no—
1487C4—44no—
1488C4—44no—
1489C4—42no—
1490C4#353714yes—
1491C2—44no—
1492C2—81no—
1493C2—81no—
1494C2—82no—
1495C2C2×#353711yescharacteristic
1496C2#6289311yescharacteristic
1497C2#6291312yes—
1498C2#6301612yes—
1499C2#6303711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#52297C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59817C2semidirect
2. #59695C2semidirect
3. #59402C2semidirect
4. #59127C2semidirect
5. #59127C2semidirect
6. #58957C2semidirect
7. #58591C2semidirect
8. #56706C2semidirect
9. #55121C2semidirect
10. #53136C2semidirect
11. #53008C2semidirect
13. #47726C2semidirect
14. #46584C2semidirect
15. #45435C2semidirect
16. #45321C2semidirect
17. #45321C2semidirect
18. #43399C2semidirect
19. #42911C2semidirect
20. #42786C2semidirect
21. #42361C2semidirect
22. #41191C2semidirect
23. #40196C2semidirect
24. #40070C2semidirect
25. #39663C2semidirect
26. #39593C2semidirect
27. #39167C2semidirect
28. #36007C2semidirect
29. #35700C2semidirect

Maximal subgroups

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

subgroupindex
#598172
#596952
#594022
#591272
#589572
#585912
#567062
#551212
#531362
#530082
#522972
#477262
#465842
#454352
#453212
#433992
#429112
#427862
#423612
#411912
#401962
#400702
#396632
#395932
#391672
#360072
#357002