Finite Group Databasebeta

← #8678579

Subgroups — #8678579

Order 512.

5291 conjugacy classes of subgroups.

The subgroup lattice has 1559 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59771C212yesmaximal, complemented
2#59115C212yesmaximal, complemented
3#59066C212yesmaximal, complemented
4#57184C214yesmaximal, complemented
5#55093C214yesmaximal, complemented
6#53518C214yesmaximal, complemented
7#53180C212yesmaximal, complemented
8#52304C211yesmaximal, characteristic, complemented
9#51974C214yesmaximal, complemented
10#50285C214yesmaximal, complemented
11#47954C214yesmaximal, complemented
12#46015C211yesmaximal, characteristic, complemented
13#45998C211yesmaximal, characteristic, complemented
14#45997C211yesmaximal, characteristic, complemented
15#45033C212yesmaximal, complemented
16#45033C212yesmaximal, complemented
17#44931C212yesmaximal, complemented
18#42739C212yesmaximal, complemented
19#42590C212yesmaximal, complemented
20#42496C212yesmaximal, complemented
21#40126C212yesmaximal, complemented
22#40029C212yesmaximal, complemented
23#39359C212yesmaximal, complemented
24#39341C212yesmaximal, complemented
25#38802C212yesmaximal, complemented
26#38487C212yesmaximal, complemented
27#36463C211yesmaximal, characteristic, complemented
28#36412C211yesmaximal, characteristic, complemented
29#36290C211yesmaximal, characteristic, complemented
30C2×#563C2212yes—
31C2×#562C2212yes—
32C2×#555C2211yescharacteristic
33C2×#550C2211yescharacteristic
34C2×#550C2212yes—
35C2×#547C2214yes—
36C2×#537C2214yes—
37C2×#532C2212yes—
38#2859C2211yescharacteristic
39#2858C2211yescharacteristic
40#2858C2211yescharacteristic
41#2856C2212yes—
42#2856C2212yes—
43#2854C2212yes—
44#2851C2212yes—
45#2841C2214yes—
46#2826C2214yes—
47#2824C2214yes—
48#2820C2212yes—
49#2819C2212yes—
50#2819C2212yes—
51#2808C2212yes—
52#2805C2211yescharacteristic
53#2805C2211yescharacteristic
54#2804C2214yes—
55#2803C2214yes—
56#2790C2214yes—
57#2789C2212yes—
58#2788C2214yes—
59#2780C2214yes—
60#2778C2214yes—
61#2778C2214yes—
62#2765C2212yes—
63#2765C2212yes—
64#2750C2214yes—
65#2746C2214yes—
66#2729C2214yes—
67#2728C2214yes—
68#2727C2212yes—
69#2724C2211yescharacteristic
70#2723C2214yes—
71#2717C2212yes—
72#2714C2214yes—
73#2714C2214yes—
74#2711C2214yes—
75#2711C2214yes—
76#2710C2214yes—
77#2708C2214yes—
78#2706C2214yes—
79#2703C2214yes—
80#2703C2214yes—
81#2699C2214yes—
82#2699C2214yes—
83#2696C2214yes—
84#2691C2214yes—
85#2691C2214yes—
86#2690C2212yes—
87#2690C2212yes—
88#2688C2214yes—
89#2688C2214yes—
90#2687C2214yes—
91#2686C2214yes—
92#2683C2211yescharacteristic
93#2683C2212yes—
94#2682C2212yes—
95#2682C2214yes—
96#2682C2212yes—
97#2682C2212yes—
98#2681C2214yes—
99#2681C2214yes—
100#2677C2214yes—
101#2676C2214yes—
102#2676C2214yes—
103#2676C2214yes—
104#2676C2214yes—
105#2675C2214yes—
106#2675C2214yes—
107#2674C2214yes—
108#2673C2214yes—
109#2671C2214yes—
110#2671C2214yes—
111#2671C2214yes—
112#2671C2214yes—
113#2671C2214yes—
114#2671C2214yes—
115#2665C2214yes—
116#2661C2214yes—
117#2653C2214yes—
118#2651C2214yes—
119#2649C2214yes—
120#2647C2212yes—
121#2639C2214yes—
122#2627C2214yes—
123#2618C2214yes—
124#2615C2214yes—
125#2591C2214yes—
126#2591C2214yes—
127#2589C2214yes—
128#2587C2214yes—
129#2580C2212yes—
130#2580C2212yes—
131#2571C2211yescharacteristic
132#2570C2212yes—
133#2567C2211yescharacteristic
134#2563C2211yescharacteristic
135#2560C2214yes—
136#2559C2214yes—
137#2559C2214yes—
138#2558C2214yes—
139#2557C2214yes—
140#2555C2214yes—
141#2555C2214yes—
142#2552C2211yescharacteristic
143#2551C2212yes—
144#2546C2212yes—
145#2542C2212yes—
146#2541C2211yescharacteristic
147#2541C2211yescharacteristic
148#2541C2212yes—
149#2541C2212yes—
150#2541C2212yes—
151#2538C2212yes—
152#2513C2212yes—
153#2512C2212yes—
154#2512C2212yes—
155#2509C2212yes—
156#2509C2212yes—
157#2507C2212yes—
158#2505C2214yes—
159#2500C2212yes—
160#2500C2212yes—
161#2500C2212yes—
162#2500C2212yes—
163#2492C2214yes—
164#2491C2214yes—
165#2490C2212yes—
166#2488C2214yes—
167#2481C2214yes—
168#2474C2214yes—
169#2473C2214yes—
170#2464C2214yes—
171#2461C2214yes—
172#2459C2214yes—
173#2457C2214yes—
174#2457C2214yes—
175#2452C2212yes—
176#2452C2212yes—
177#2452C2214yes—
178#2452C2212yes—
179#2452C2212yes—
180#2450C2214yes—
181#2445C2212yes—
182#2445C2212yes—
183#2445C2212yes—
184#2445C2212yes—
185#2445C2212yes—
186#2445C2212yes—
187#2443C2214yes—
188#2443C2214yes—
189#2442C2212yes—
190#2442C2212yes—
191#2440C2214yes—
192#2439C2212yes—
193#2439C2212yes—
194#2432C2214yes—
195#2432C2214yes—
196#2431C2212yes—
197#2430C2214yes—
198#2430C2214yes—
199#2430C2214yes—
200#2430C2214yes—
201#2430C2214yes—
202#2428C2212yes—
203#2428C2212yes—
204#2428C2214yes—
205#2428C2212yes—
206#2428C2212yes—
207#2428C2212yes—
208#2428C2212yes—
209#2428C2212yes—
210#2427C2214yes—
211#2422C2212yes—
212#2422C2212yes—
213#2420C2212yes—
214#2420C2212yes—
215#2416C2214yes—
216#2416C2214yes—
217#2416C2214yes—
218#2414C2212yes—
219#2407C2214yes—
220#2407C2214yes—
221#2401C2212yes—
222#2401C2212yes—
223#2399C2212yes—
224#2379C2212yes—
225#2369C2211yescharacteristic
226#2368C2214yes—
227#2366C2212yes—
228#2366C2211yescharacteristic
229#2363C2212yes—
230#2363C2212yes—
231#2363C2212yes—
232#2363C2212yes—
233#2363C2212yes—
234#2359C2214yes—
235#2357C2212yes—
236#2349C2212yes—
237#2349C2212yes—
238D4×C4⋊C4C2212yes—
239D4×C4⋊C4C2212yes—
240D4×C4⋊C4C2211yescharacteristic
241D4×C4⋊C4C2211yescharacteristic
242#2335C2214yes—
243#2333C2214yes—
244#2328C2212yes—
245#2328C2212yes—
246#2319C2212yes—
247C4×#125C2211yescharacteristic
248C4×#125C2211yescharacteristic
249C4×#124C2211yescharacteristic
250C4×C22⋊Q8C2212yes—
251C4×C22⋊Q8C2212yes—
252C4×#123C2212yes—
253C4×#121C2212yes—
254C4×#121C2212yes—
255#2297C2212yes—
256#2296C2212yes—
257C2×#389C2212yes—
258C42×D4C2211yescharacteristic
259C22×#41C2314yes—
260C22×#41C2314yes—
261C22×#41C2312yes—
262#563—48no—
263#562—48no—
264#555—44no—
265#550—48no—
266#550—44no—
267#547—416no—
268#537—416no—
269#532—48no—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2314yes—
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2314yes—
275C2×#127C2312yes—
276C2×#127C2312yes—
277C2×#127C2312yes—
278C2×#127C2312yes—
279C2×#127C2311yescharacteristic
280C2×#127C2311yescharacteristic
281C2×#127C2312yes—
282C2×#126C2314yes—
283C2×#126C2314yes—
284C2×#125C2311yescharacteristic
285C2×#125C2311yescharacteristic
286C2×#125C2312yes—
287C2×#125C2312yes—
288C2×#124C2311yescharacteristic
289C2×#124C2312yes—
290C2×#124C2312yes—
291C2×#124C2312yes—
292C2×#124C2312yes—
293C2×#124C2314yes—
294C2×#124C2314yes—
295C2×#123C2314yes—
296C2×#123C2314yes—
297C2×#123C2314yes—
298C2×#123C2314yes—
299C2×#123C2314yes—
300C2×#123C2314yes—
301C2×#123C2312yes—
302C2×#123C2314yes—
303C2×#123C2314yes—
304C2×C22⋊Q8C2314yes—
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2314yes—
308C2×C22⋊Q8C2314yes—
309C2×C22⋊Q8C2314yes—
310C2×C22⋊Q8C2314yes—
311C2×C22⋊Q8C2314yes—
312C2×C22⋊Q8C2314yes—
313C2×#121C2312yes—
314C2×#121C2312yes—
315C2×#121C2312yes—
316C2×#121C2314yes—
317C2×#121C2314yes—
318C2×#121C2314yes—
319C2×#121C2314yes—
320C2×#121C2312yes—
321C2×#121C2312yes—
322C2×#121C2312yes—
323C2×#121C2314yes—
324C2×#121C2312yes—
325C2×#121C2314yes—
326C2×#121C2314yes—
327C2×#121C2314yes—
328C2×#121C2312yes—
329C2×#121C2314yes—
330C2×#121C2314yes—
331C2×#121C2314yes—
332C2×#121C2314yes—
333C2×#121C2314yes—
334C2×#121C2314yes—
335C2×#121C2314yes—
336C2×#121C2314yes—
337C2×#121C2314yes—
338C2×#121C2314yes—
339C2×#121C2312yes—
340C2×#121C2314yes—
341C2×#121C2314yes—
342C2×C4×Q8C2311yescharacteristic
343C2×C4×Q8C2312yes—
344C2×C4×D4C2312yes—
345C2×C4×D4C2312yes—
346C2×C4×D4C2311yescharacteristic
347C2×C4×D4C2311yescharacteristic
348C2×C4×D4C2311yescharacteristic
349C2×C4×D4C2312yes—
350C2×C4×D4C2312yes—
351C2×C4×D4C2312yes—
352C2×C4×D4C2312yes—
353C2×C4×D4C2312yes—
354C2×C4×D4C2312yes—
355C2×C4×D4C2314yes—
356C2×C4×D4C2314yes—
357C2×C4×D4C2314yes—
358C2×C4×D4C2311yescharacteristic
359C2×C4×D4C2312yes—
360C2×#117C2312yes—
361C2×#117C2312yes—
362C2×#117C2312yes—
363C22×C4⋊C4C2312yes—
364C22×C4⋊C4C2314yes—
365C22×C4⋊C4C2314yes—
366C22×C4⋊C4C2312yes—
367C22×C42C2312yes—
368C22×C42C2312yes—
369#401C2312yes—
370#401C2312yes—
371#400C2314yes—
372#400C2314yes—
373#400C2314yes—
374#400C2314yes—
375#400C2314yes—
376#400C2314yes—
377#400C2312yes—
378#400C2312yes—
379#400C2314yes—
380#400C2314yes—
381#400C2312yes—
382#400C2312yes—
383#400C2312yes—
384#400C2312yes—
385#399C2314yes—
386#399C2314yes—
387#399C2314yes—
388#399C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2312yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2312yes—
397#398C2314yes—
398#398C2314yes—
399#398C2312yes—
400#398C2312yes—
401#397C2314yes—
402#397C2314yes—
403#397C2312yes—
404#397C2314yes—
405#397C2312yes—
406#397C2314yes—
407#397C2312yes—
408#397C2314yes—
409#397C2314yes—
410#397C2314yes—
411#397C2312yes—
412#397C2312yes—
413#397C2312yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#396C2312yes—
421#396C2314yes—
422#396C2312yes—
423#396C2314yes—
424#396C2314yes—
425#396C2314yes—
426#395C2314yes—
427#395C2314yes—
428#395C2312yes—
429#395C2312yes—
430#395C2312yes—
431#395C2312yes—
432#395C2314yes—
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#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#394C2314yes—
453#394C2314yes—
454#394C2314yes—
455#394C2314yes—
456#394C2314yes—
457#394C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2314yes—
461#394C2314yes—
462#393C2314yes—
463#393C2314yes—
464#393C2314yes—
465#393C2314yes—
466#393C2314yes—
467#393C2314yes—
468#393C2314yes—
469#393C2314yes—
470#393C2314yes—
471#392C2314yes—
472#392C2314yes—
473#392C2314yes—
474#392C2314yes—
475#392C2314yes—
476#392C2314yes—
477#392C2314yes—
478#392C2314yes—
479#392C2314yes—
480#392C2314yes—
481#392C2314yes—
482#392C2314yes—
483#392C2314yes—
484#392C2314yes—
485#392C2314yes—
486#392C2314yes—
487#391C2312yes—
488#391C2312yes—
489#391C2314yes—
490#391C2314yes—
491#391C2314yes—
492#391C2314yes—
493#391C2312yes—
494#391C2311yescharacteristic
495#390C2314yes—
496#390C2312yes—
497#390C2312yes—
498#390C2312yes—
499#390C2312yes—
500#390C2312yes—
501#390C2312yes—
502#390C2312yes—
503#390C2312yes—
504#390C2312yes—
505#390C2312yes—
506#390C2314yes—
507#390C2312yes—
508#390C2312yes—
509#390C2311yescharacteristic
510#390C2312yes—
511#390C2312yes—
512#390C2314yes—
513#390C2314yes—
514#390C2312yes—
515#390C2312yes—
516#390C2312yes—
517#390C2312yes—
518#390C2312yes—
519#390C2314yes—
520#390C2314yes—
521#390C2314yes—
522#390C2314yes—
523#390C2314yes—
524#389C2311yescharacteristic
525#389C2311yescharacteristic
526#389C2311yescharacteristic
527#389C2311yescharacteristic
528#389C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2312yes—
533#389C2312yes—
534#389C2312yes—
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2312yes—
539#389C2312yes—
540#389C2314yes—
541#389C2314yes—
542#389C2312yes—
543#389C2312yes—
544#389C2312yes—
545#389C2312yes—
546#389C2312yes—
547#389C2314yes—
548#389C2312yes—
549#389C2312yes—
550#389C2314yes—
551#389C2312yes—
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#388C2312yes—
573#388C2314yes—
574#388C2312yes—
575#388C2312yes—
576#388C2312yes—
577#387C2314yes—
578#387C2312yes—
579#387C2312yes—
580#387C2312yes—
581#387C2312yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2312yes—
586#387C2314yes—
587#387C2312yes—
588#387C2312yes—
589#387C2314yes—
590#387C2312yes—
591#387C2312yes—
592#387C2314yes—
593#387C2312yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2312yes—
625#386C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
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#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2312yes—
647#385C2312yes—
648#385C2312yes—
649#385C2312yes—
650#385C2314yes—
651#385C2314yes—
652#385C2312yes—
653#384C2312yes—
654#384C2312yes—
655#384C2311yescharacteristic
656#384C2311yescharacteristic
657#384C2312yes—
658#382C2311yescharacteristic
659#382C2311yescharacteristic
660#382C2312yes—
661#382C2312yes—
662#382C2312yes—
663#382C2312yes—
664#382C2312yes—
665#382C2311yescharacteristic
666#381C2314yes—
667#381C2314yes—
668#381C2314yes—
669#381C2312yes—
670#380C2312yes—
671#380C2312yes—
672#380C2314yes—
673#380C2314yes—
674#380C2314yes—
675#380C2312yes—
676#380C2312yes—
677#380C2314yes—
678#380C2314yes—
679#380C2314yes—
680#380C2312yes—
681#380C2312yes—
682#380C2312yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2311yescharacteristic
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2311yescharacteristic
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2311yescharacteristic
700C4×C4⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2312yes—
715C4×C22⋊C4C2312yes—
716#376C2312yes—
717C2×#95C2314yes—
718C2×#95C2314yes—
719C43C2311yescharacteristic
720C2×#41—48no—
721C2×#41—48no—
722C2×#41—44no—
723C2×#41—48no—
724C2×#41—48no—
725C2×#41—48no—
726C2×#41—48no—
727C2×#41—44no—
728C2×#41—82no—
729C22×Q8C2412yes—
730C22×Q8C2411yescharacteristic
731C22×Q8C2414yes—
732C22×Q8C2412yes—
733C22×Q8C2412yes—
734C22×D4C2412yes—
735C22×D4C2412yes—
736C22×D4C2414yes—
737C22×D4C2411yescharacteristic
738C22×D4C2412yes—
739C22×D4C2414yes—
740C22×D4C2414yes—
741C22×D4C2411yescharacteristic
742C22×D4C2414yes—
743C22×D4C2414yes—
744C22×D4C2414yes—
745C22×D4C2414yes—
746C22×D4C2412yes—
747C22×D4C2414yes—
748C22×D4C2414yes—
749C22×D4C2414yes—
750C22×D4C2414yes—
751C22×D4C2412yes—
752C22×D4C2414yes—
753C22×D4C2414yes—
754C22×D4C2412yes—
755C23×C4C2412yes—
756C23×C4C2412yes—
757C23×C4C2414yes—
758C23×C4C2412yes—
759C23×C4C2412yes—
760C23×C4C2412yes—
761C23×C4C2414yes—
762C23×C4C2414yes—
763C23×C4C2414yes—
764C23×C4C2414yes—
765C23×C4C2414yes—
766C23×C4C2414yes—
767C23×C4C2414yes—
768C23×C4C2412yes—
769C4⋊Q8—42no—
770C4⋊Q8—44no—
771C4⋊Q8—42no—
772C4⋊Q8—48no—
773C4⋊Q8—48no—
774#127—28no—
775#127—28no—
776#127—44no—
777#127—42no—
778#127—44no—
779#127—42no—
780#127—82no—
781#126—48no—
782#126—48no—
783#125—24no—
784#125—24no—
785#125—44no—
786#125—82no—
787#124—44no—
788#124—44no—
789#124—44no—
790#124—44no—
791#124—42no—
792#124—48no—
793#124—48no—
794#123—216no—
795#123—48no—
796#123—48no—
797#123—48no—
798#123—48no—
799#123—48no—
800#123—48no—
801#123—44no—
802#123—84no—
803C22⋊Q8—28no—
804C22⋊Q8—216no—
805C22⋊Q8—28no—
806C22⋊Q8—48no—
807C22⋊Q8—48no—
808C22⋊Q8—48no—
809C22⋊Q8—48no—
810C22⋊Q8—48no—
811C22⋊Q8—48no—
812#121—28no—
813#121—28no—
814#121—28no—
815#121—48no—
816#121—48no—
817#121—48no—
818#121—48no—
819#121—48no—
820#121—48no—
821#121—48no—
822#121—48no—
823#121—48no—
824#121—48no—
825#121—48no—
826#121—48no—
827#121—48no—
828#121—48no—
829#121—48no—
830#121—44no—
831#121—44no—
832#121—44no—
833#121—48no—
834#121—44no—
835#121—48no—
836#121—44no—
837#121—82no—
838#121—84no—
839#121—84no—
840#121—84no—
841C4×Q8—44no—
842C4×Q8—42no—
843C4×D4—28no—
844C4×D4—24no—
845C4×D4—24no—
846C4×D4—28no—
847C4×D4—44no—
848C4×D4—44no—
849C4×D4—42no—
850C4×D4—44no—
851C4×D4—44no—
852C4×D4—44no—
853C4×D4—44no—
854C4×D4—42no—
855C4×D4—48no—
856C4×D4—48no—
857C4×D4—48no—
858C4×D4—82no—
859#117—44no—
860#117—44no—
861#117—44no—
862C2×C4⋊C4—28no—
863C2×C4⋊C4—48no—
864C2×C4⋊C4—48no—
865C2×C4⋊C4—82no—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2411yescharacteristic
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2411yescharacteristic
889C2×C4⋊C4C2411yescharacteristic
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2411yescharacteristic
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2411yescharacteristic
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2411yescharacteristic
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2411yescharacteristic
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2414yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2414yes—
912C2×C4⋊C4C2414yes—
913C2×C4⋊C4C2412yes—
914C2×C4⋊C4C2414yes—
915C2×C4⋊C4C2414yes—
916C2×C4⋊C4C2414yes—
917C2×C4⋊C4C2411yescharacteristic
918C2×C4⋊C4C2412yes—
919C2×C4⋊C4C2412yes—
920C2×C4⋊C4C2411yescharacteristic
921C2×C4⋊C4C2411yescharacteristic
922C2×C4⋊C4C2411yescharacteristic
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2412yes—
951C2×C22⋊C4C2412yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2414yes—
956C2×C22⋊C4C2412yes—
957C2×C22⋊C4C2414yes—
958C2×C22⋊C4C2414yes—
959C2×C22⋊C4C2414yes—
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2414yes—
963C2×C22⋊C4C2414yes—
964C2×C22⋊C4C2414yes—
965C2×C22⋊C4C2414yes—
966C2×C22⋊C4C2414yes—
967C2×C22⋊C4C2414yes—
968C2×C22⋊C4C2414yes—
969C2×C22⋊C4C2414yes—
970C2×C22⋊C4C2414yes—
971C2×C22⋊C4C2414yes—
972C2×C22⋊C4C2412yes—
973C2×C22⋊C4C2412yes—
974C2×C22⋊C4C2412yes—
975C2×C22⋊C4C2414yes—
976C2×C22⋊C4C2412yes—
977C2×C22⋊C4C2412yes—
978C2×C22⋊C4C2414yes—
979C2×C42—44no—
980C2×C42—82no—
981C2×C42C2412yes—
982C2×C42C2411yescharacteristic
983C2×C42C2412yes—
984C2×C42C2412yes—
985C2×C42C2412yes—
986C2×C42C2411yescharacteristic
987C2×C42C2411yescharacteristic
988C2×C42C2412yes—
989C2×C42C2411yescharacteristic
990C2×C42C2411yescharacteristic
991C2×C42C2411yescharacteristic
992C2×C42C2414yes—
993C2×C42C2414yes—
994C2×C42C2414yes—
995C2×C42C2412yes—
996C2×C42C2412yes—
997C2×C42C2412yes—
998C2×C42C2412yes—
999C2×C42C2414yes—
1000C2×C42C2412yes—
1001C2×C42C2411yescharacteristic
1002#95C2412yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2412yes—
1030#95C2412yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2414yes—
1035#95C2412yes—
1036#95C2412yes—
1037#95C2414yes—
1038#95C2412yes—
1039#95C2412yes—
1040#95C2412yes—
1041#95C2414yes—
1042#95C2412yes—
1043#95C2414yes—
1044#95C2412yes—
1045#95C2412yes—
1046#95C2412yes—
1047#95C2412yes—
1048#95C2412yes—
1049#95C2414yes—
1050#95C2412yes—
1051#95C2412yes—
1052#95C2414yes—
1053#95C2414yes—
1054#95C2414yes—
1055#95C2414yes—
1056#95C2414yes—
1057C24C2514yes—
1058C24C2512yes—
1059C24C2514yes—
1060C24C2512yes—
1061#41—832no—
1062#41—832no—
1063#41—816no—
1064C2×Q8—24no—
1065C2×Q8—24no—
1066C2×Q8—28no—
1067C2×Q8—22no—
1068C2×Q8—42no—
1069C2×Q8—41no—
1070C2×Q8—41no—
1071C2×Q8—44no—
1072C2×Q8—44no—
1073C2×Q8—42no—
1074C2×Q8—42no—
1075C2×Q8—42no—
1076C2×Q8—42no—
1077C2×Q8—42no—
1078C2×Q8—42no—
1079C2×D4—28no—
1080C2×D4—28no—
1081C2×D4—28no—
1082C2×D4—28no—
1083C2×D4—28no—
1084C2×D4—24no—
1085C2×D4—24no—
1086C2×D4—28no—
1087C2×D4—24no—
1088C2×D4—28no—
1089C2×D4—22no—
1090C2×D4—24no—
1091C2×D4—24no—
1092C2×D4—28no—
1093C2×D4—22no—
1094C2×D4—24no—
1095C2×D4—24no—
1096C2×D4—24no—
1097C2×D4—22no—
1098C2×D4—44no—
1099C2×D4—41no—
1100C2×D4—44no—
1101C2×D4—42no—
1102C2×D4—44no—
1103C2×D4—44no—
1104C2×D4—44no—
1105C2×D4—44no—
1106C2×D4—44no—
1107C2×D4—44no—
1108C2×D4—44no—
1109C2×D4—44no—
1110C2×D4—44no—
1111C2×D4—42no—
1112C2×D4—44no—
1113C2×D4—44no—
1114C2×D4—44no—
1115C2×D4—44no—
1116C2×D4—42no—
1117C2×D4—41no—
1118C2×D4—42no—
1119C2×D4—44no—
1120C2×D4—44no—
1121C2×D4—44no—
1122C2×D4—44no—
1123C2×D4—44no—
1124C2×D4—42no—
1125C2×D4—42no—
1126C2×D4—44no—
1127C2×D4—42no—
1128C2×D4—44no—
1129C2×D4—44no—
1130C2×D4—44no—
1131C2×D4—44no—
1132C2×D4—44no—
1133C2×D4—44no—
1134C2×D4—44no—
1135C2×D4—44no—
1136C2×D4—42no—
1137C2×D4—42no—
1138C2×D4—44no—
1139C2×D4—44no—
1140C2×D4—42no—
1141C2×D4H(5,𝔽2)14yes—
1142C22×C4—24no—
1143C22×C4—28no—
1144C22×C4—24no—
1145C22×C4—24no—
1146C22×C4—28no—
1147C22×C4—24no—
1148C22×C4—24no—
1149C22×C4—24no—
1150C22×C4—24no—
1151C22×C4—24no—
1152C22×C4—24no—
1153C22×C4—24no—
1154C22×C4—28no—
1155C22×C4—28no—
1156C22×C4—28no—
1157C22×C4—42no—
1158C22×C4—42no—
1159C22×C4—42no—
1160C22×C4—44no—
1161C22×C4—42no—
1162C22×C4—42no—
1163C22×C4—44no—
1164C22×C4—44no—
1165C22×C4—44no—
1166C22×C4—44no—
1167C22×C4—44no—
1168C22×C4—44no—
1169C22×C4—44no—
1170C22×C4—42no—
1171C22×C4—44no—
1172C22×C4—44no—
1173C22×C4—44no—
1174C22×C4—42no—
1175C22×C4—42no—
1176C22×C4—44no—
1177C22×C4—44no—
1178C22×C4—44no—
1179C22×C4—44no—
1180C22×C4—44no—
1181C22×C4—44no—
1182C22×C4—44no—
1183C22×C4—44no—
1184C22×C4C2511yescharacteristic
1185C22×C4C2512yes—
1186C22×C4C2512yes—
1187C22×C4C2512yes—
1188C22×C4C2512yes—
1189C22×C4C2512yes—
1190C22×C4C2512yes—
1191C22×C4C2511yescharacteristic
1192C22×C4C2512yes—
1193C22×C4C2514yes—
1194C22×C4C2512yes—
1195C22×C4C2512yes—
1196C22×C4C2512yes—
1197C22×C4C2514yes—
1198C22×C4C2512yes—
1199C22×C4C2514yes—
1200C22×C4C2511yescharacteristic
1201C22×C4C2514yes—
1202C22×C4C2512yes—
1203C22×C4C2512yes—
1204C22×C4C2511yescharacteristic
1205C22×C4C2511yescharacteristic
1206C22×C4C2512yes—
1207C22×C4C2511yescharacteristic
1208C22×C4C2511yescharacteristic
1209C4⋊C4—28no—
1210C4⋊C4—24no—
1211C4⋊C4—24no—
1212C4⋊C4—24no—
1213C4⋊C4—28no—
1214C4⋊C4—22no—
1215C4⋊C4—24no—
1216C4⋊C4—24no—
1217C4⋊C4—24no—
1218C4⋊C4—24no—
1219C4⋊C4—24no—
1220C4⋊C4—24no—
1221C4⋊C4—28no—
1222C4⋊C4—28no—
1223C4⋊C4—24no—
1224C4⋊C4—22no—
1225C4⋊C4—24no—
1226C4⋊C4—22no—
1227C4⋊C4—24no—
1228C4⋊C4—24no—
1229C4⋊C4—22no—
1230C4⋊C4—24no—
1231C4⋊C4—24no—
1232C4⋊C4—44no—
1233C4⋊C4—44no—
1234C4⋊C4—44no—
1235C4⋊C4—44no—
1236C4⋊C4—41no—
1237C4⋊C4—44no—
1238C4⋊C4—42no—
1239C4⋊C4—41no—
1240C4⋊C4—42no—
1241C4⋊C4—44no—
1242C4⋊C4—41no—
1243C4⋊C4—42no—
1244C4⋊C4—42no—
1245C4⋊C4—41no—
1246C4⋊C4—42no—
1247C4⋊C4—42no—
1248C4⋊C4—44no—
1249C4⋊C4—41no—
1250C4⋊C4—42no—
1251C4⋊C4—44no—
1252C4⋊C4—44no—
1253C4⋊C4—42no—
1254C4⋊C4—44no—
1255C4⋊C4—44no—
1256C4⋊C4—44no—
1257C4⋊C4—44no—
1258C4⋊C4—42no—
1259C4⋊C4—44no—
1260C4⋊C4—42no—
1261C4⋊C4—41no—
1262C4⋊C4—42no—
1263C4⋊C4H(5,𝔽2)14yes—
1264C4⋊C4H(5,𝔽2)14yes—
1265C4⋊C42−1+414yes—
1266C22⋊C4—28no—
1267C22⋊C4—28no—
1268C22⋊C4—24no—
1269C22⋊C4—28no—
1270C22⋊C4—28no—
1271C22⋊C4—28no—
1272C22⋊C4—24no—
1273C22⋊C4—24no—
1274C22⋊C4—24no—
1275C22⋊C4—24no—
1276C22⋊C4—28no—
1277C22⋊C4—28no—
1278C22⋊C4—28no—
1279C22⋊C4—24no—
1280C22⋊C4—28no—
1281C22⋊C4—28no—
1282C22⋊C4—28no—
1283C22⋊C4—44no—
1284C22⋊C4—44no—
1285C22⋊C4—44no—
1286C22⋊C4—44no—
1287C22⋊C4—42no—
1288C22⋊C4—44no—
1289C22⋊C4—44no—
1290C22⋊C4—44no—
1291C22⋊C4—44no—
1292C22⋊C4—44no—
1293C22⋊C4—44no—
1294C22⋊C4—44no—
1295C22⋊C4—42no—
1296C22⋊C4—44no—
1297C22⋊C4—44no—
1298C22⋊C4—44no—
1299C22⋊C4—44no—
1300C22⋊C4—44no—
1301C22⋊C4—44no—
1302C22⋊C4—44no—
1303C22⋊C4—44no—
1304C22⋊C4—44no—
1305C22⋊C4—44no—
1306C22⋊C4—44no—
1307C22⋊C4—42no—
1308C22⋊C4—44no—
1309C22⋊C4—44no—
1310C22⋊C4—44no—
1311C22⋊C4—44no—
1312C22⋊C4—44no—
1313C22⋊C4—44no—
1314C22⋊C4—42no—
1315C22⋊C4—42no—
1316C22⋊C4—44no—
1317C22⋊C4—42no—
1318C22⋊C4—44no—
1319C22⋊C4—44no—
1320C22⋊C4—42no—
1321C22⋊C4—42no—
1322C42—24no—
1323C42—24no—
1324C42—22no—
1325C42—24no—
1326C42—22no—
1327C42—22no—
1328C42—22no—
1329C42—24no—
1330C42—24no—
1331C42—22no—
1332C42—22no—
1333C42—42no—
1334C42—42no—
1335C42—41no—
1336C42—42no—
1337C42—42no—
1338C42—42no—
1339C42—44no—
1340C42—44no—
1341C42—44no—
1342C42—44no—
1343C23—22no—
1344C23—22no—
1345C23—22no—
1346C23—22no—
1347C23—22no—
1348C23—22no—
1349C23—24no—
1350C23—22no—
1351C23—24no—
1352C23—22no—
1353C23—24no—
1354C23—24no—
1355C23—22no—
1356C23—24no—
1357C23—24no—
1358C23—24no—
1359C23—24no—
1360C23—22no—
1361C23—24no—
1362C23—22no—
1363C23—22no—
1364C23—24no—
1365C23—24no—
1366C23—24no—
1367C23—24no—
1368C23—24no—
1369C23—22no—
1370C23C2×H(5,𝔽2)14yes—
1371C23C2611yescharacteristic
1372Q8—48no—
1373Q8—44no—
1374Q8—88no—
1375Q8—162no—
1376Q8—162no—
1377D4—28no—
1378D4—416no—
1379D4—48no—
1380D4—48no—
1381D4—82no—
1382D4—88no—
1383D4—84no—
1384D4—88no—
1385D4—84no—
1386D4—88no—
1387D4—88no—
1388D4—88no—
1389D4—88no—
1390D4—88no—
1391D4—162no—
1392D4—164no—
1393D4—162no—
1394D4—164no—
1395D4—164no—
1396D4—164no—
1397D4—164no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—21no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—22no—
1410C2×C4—22no—
1411C2×C4—22no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—22no—
1417C2×C4—22no—
1418C2×C4—21no—
1419C2×C4—22no—
1420C2×C4—22no—
1421C2×C4—22no—
1422C2×C4—24no—
1423C2×C4—24no—
1424C2×C4—24no—
1425C2×C4—24no—
1426C2×C4—22no—
1427C2×C4—22no—
1428C2×C4—24no—
1429C2×C4—22no—
1430C2×C4—24no—
1431C2×C4—22no—
1432C2×C4—22no—
1433C2×C4—22no—
1434C2×C4—24no—
1435C2×C4—24no—
1436C2×C4—21no—
1437C2×C4—22no—
1438C2×C4—22no—
1439C2×C4—22no—
1440C2×C4—21no—
1441C2×C4—22no—
1442C2×C4—22no—
1443C2×C4—21no—
1444C2×C4—21no—
1445C2×C4—22no—
1446C2×C4—24no—
1447C2×C4—24no—
1448C2×C4—24no—
1449C2×C4—22no—
1450C2×C4—22no—
1451C2×C4—22no—
1452C2×C4—22no—
1453C2×C4—22no—
1454C2×C4—22no—
1455C2×C4—22no—
1456C2×C4—22no—
1457C2×C4—22no—
1458C2×C4—22no—
1459C2×C4—22no—
1460C2×C4—24no—
1461C2×C4—22no—
1462C2×C4—22no—
1463C2×C4—22no—
1464C2×C4—48no—
1465C2×C4—48no—
1466C2×C4—48no—
1467C2×C4—416no—
1468C2×C4—48no—
1469C2×C4—88no—
1470C2×C4—84no—
1471C2×C4—88no—
1472C2×C4—88no—
1473C2×C4—84no—
1474C2×C4—88no—
1475C2×C4—88no—
1476C2×C4—164no—
1477C2×C4—164no—
1478C2×C4C2×H(5,𝔽2)12yes—
1479C2×C4C2×H(5,𝔽2)12yes—
1480C2×C4C2×H(5,𝔽2)14yes—
1481C2×C4C2×H(5,𝔽2)14yes—
1482C2×C4C2×H(5,𝔽2)12yes—
1483C2×C4C2×2−1+414yes—
1484C2×C4C2×2−1+412yes—
1485C2×C4#58512yes—
1486C2×C4#58512yes—
1487C22—24no—
1488C22—24no—
1489C22—24no—
1490C22—42no—
1491C22—42no—
1492C22—42no—
1493C22—42no—
1494C22—42no—
1495C22—44no—
1496C22—44no—
1497C22—42no—
1498C22—44no—
1499C22—44no—
1500C22—44no—
1501C22—44no—
1502C22—42no—
1503C22—44no—
1504C22—42no—
1505C22—44no—
1506C22—44no—
1507C22—42no—
1508C22—44no—
1509C22—44no—
1510C22—42no—
1511C22—44no—
1512C22—44no—
1513C22—42no—
1514C22—44no—
1515C22C22×H(5,𝔽2)11yescharacteristic
1516C22C22×H(5,𝔽2)11yescharacteristic
1517C22C22×H(5,𝔽2)11yescharacteristic
1518C22C22×2−1+411yescharacteristic
1519C22C2×#58511yescharacteristic
1520C22C2×#58511yescharacteristic
1521C22H(7,𝔽2)11yescharacteristic
1522C4—24no—
1523C4—24no—
1524C4—22no—
1525C4—22no—
1526C4—24no—
1527C4—22no—
1528C4—42no—
1529C4—44no—
1530C4—42no—
1531C4—44no—
1532C4—41no—
1533C4—42no—
1534C4—44no—
1535C4—41no—
1536C4—41no—
1537C4—42no—
1538C4—42no—
1539C4—42no—
1540C4—42no—
1541C4—42no—
1542C4—42no—
1543C4—42no—
1544C4—42no—
1545C4—44no—
1546C4#355914yes—
1547C2—44no—
1548C2—82no—
1549C2—84no—
1550C2—84no—
1551C2C2×#355911yescharacteristic
1552C2#6289611yescharacteristic
1553C2#6294411yescharacteristic
1554C2#6296111yescharacteristic
1555C2#6301111yescharacteristic
1556C2#6303511yescharacteristic
1557C2#6303911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59771C2semidirect
2. #59115C2semidirect
3. #59066C2semidirect
4. #57184C2semidirect
5. #55093C2semidirect
6. #53518C2semidirect
7. #53180C2semidirect
8. #52304C2semidirect
9. #51974C2semidirect
10. #50285C2semidirect
11. #47954C2semidirect
12. #46015C2semidirect
13. #45998C2semidirect
14. #45997C2semidirect
15. #45033C2semidirect
16. #45033C2semidirect
17. #44931C2semidirect
18. #42739C2semidirect
19. #42590C2semidirect
20. #42496C2semidirect
21. #40126C2semidirect
22. #40029C2semidirect
23. #39359C2semidirect
24. #39341C2semidirect
25. #38802C2semidirect
26. #38487C2semidirect
27. #36463C2semidirect
28. #36412C2semidirect
29. #36290C2semidirect

Maximal subgroups

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

subgroupindex
#597712
#591152
#590662
#571842
#550932
#535182
#531802
#523042
#519742
#502852
#479542
#460152
#459982
#459972
#450332
#449312
#427392
#425902
#424962
#401262
#400292
#393592
#393412
#388022
#384872
#364632
#364122
#362902