Finite Group Databasebeta

← #8746533

Subgroups — #8746533

Order 512.

4993 conjugacy classes of subgroups.

The subgroup lattice has 1548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59895C212yesmaximal, complemented
2#59841C211yesmaximal, characteristic, complemented
3#55735C214yesmaximal, complemented
4#55222C214yesmaximal, complemented
5#54026C214yesmaximal, complemented
6#53794C212yesmaximal, complemented
7#53511C214yesmaximal, complemented
8#53090C212yesmaximal, complemented
9#52989C211yesmaximal, characteristic, complemented
10#52966C212yesmaximal, complemented
11#52388C214yesmaximal, complemented
12#47800C212yesmaximal, complemented
13#45437C211yesmaximal, characteristic, complemented
14#45368C212yesmaximal, complemented
15#45038C212yesmaximal, complemented
16#45034C212yesmaximal, complemented
17#44889C212yesmaximal, complemented
18#42678C211yesmaximal, characteristic, complemented
19#42617C212yesmaximal, complemented
20#42595C212yesmaximal, complemented
21#42518C212yesmaximal, complemented
22#42425C212yesmaximal, complemented
23#42050C212yesmaximal, complemented
24#41945C214yesmaximal, complemented
25#39745C211yesmaximal, characteristic, complemented
26#39386C212yesmaximal, complemented
27#36698C211yesmaximal, characteristic, complemented
28#35930C211yesmaximal, characteristic, complemented
29#35882C212yesmaximal, complemented
30C2×#559C2211yescharacteristic
31C2×#555C2212yes—
32C2×#554C2211yescharacteristic
33C2×#550C2211yescharacteristic
34C2×#550C2211yescharacteristic
35C2×#540C2212yes—
36C2×#540C2214yes—
37#2867C2211yescharacteristic
38#2844C2211yescharacteristic
39#2838C2212yes—
40#2838C2212yes—
41#2836C2212yes—
42#2836C2212yes—
43#2833C2212yes—
44#2832C2212yes—
45#2830C2211yescharacteristic
46#2830C2212yes—
47#2830C2211yescharacteristic
48#2828C2214yes—
49#2827C2214yes—
50#2825C2214yes—
51#2825C2214yes—
52#2825C2214yes—
53#2822C2211yescharacteristic
54#2820C2212yes—
55#2815C2214yes—
56#2815C2214yes—
57#2815C2214yes—
58#2814C2212yes—
59#2813C2214yes—
60#2787C2214yes—
61#2778C2214yes—
62#2778C2214yes—
63#2771C2214yes—
64#2760C2214yes—
65#2760C2214yes—
66#2756C2214yes—
67#2753C2214yes—
68#2749C2214yes—
69#2749C2214yes—
70#2746C2214yes—
71#2737C2214yes—
72#2731C2212yes—
73#2728C2212yes—
74#2724C2212yes—
75#2708C2214yes—
76#2708C2214yes—
77#2703C2214yes—
78#2701C2214yes—
79#2699C2212yes—
80#2699C2212yes—
81#2699C2214yes—
82#2699C2212yes—
83#2696C2214yes—
84#2688C2214yes—
85#2688C2214yes—
86#2688C2214yes—
87#2688C2214yes—
88#2688C2214yes—
89#2688C2214yes—
90#2688C2214yes—
91#2688C2214yes—
92#2687C2214yes—
93#2686C2214yes—
94#2681C2214yes—
95#2676C2214yes—
96#2676C2214yes—
97#2676C2214yes—
98#2675C2214yes—
99#2675C2214yes—
100#2675C2214yes—
101#2674C2214yes—
102#2674C2214yes—
103#2673C2214yes—
104#2673C2214yes—
105#2673C2214yes—
106#2673C2214yes—
107#2673C2214yes—
108#2673C2214yes—
109#2673C2214yes—
110#2673C2214yes—
111#2671C2214yes—
112#2671C2214yes—
113#2671C2214yes—
114#2661C2212yes—
115#2657C2212yes—
116#2657C2211yescharacteristic
117#2656C2214yes—
118#2649C2214yes—
119#2648C2214yes—
120#2644C2212yes—
121#2640C2211yescharacteristic
122#2639C2214yes—
123#2638C2212yes—
124#2635C2214yes—
125#2635C2214yes—
126#2631C2214yes—
127#2631C2214yes—
128#2623C2212yes—
129#2619C2212yes—
130#2619C2214yes—
131#2615C2214yes—
132#2611C2214yes—
133#2609C2212yes—
134#2598C2214yes—
135#2597C2214yes—
136#2592C2211yescharacteristic
137#2592C2211yescharacteristic
138#2580C2212yes—
139#2576C2214yes—
140#2573C2214yes—
141#2555C2214yes—
142#2555C2214yes—
143#2555C2212yes—
144#2555C2212yes—
145#2548C2212yes—
146#2548C2211yescharacteristic
147#2548C2211yescharacteristic
148#2546C2211yescharacteristic
149#2544C2212yes—
150#2544C2212yes—
151#2543C2212yes—
152#2543C2214yes—
153#2543C2214yes—
154#2541C2212yes—
155#2541C2212yes—
156#2541C2211yescharacteristic
157#2541C2212yes—
158#2541C2212yes—
159#2541C2212yes—
160#2541C2212yes—
161#2541C2212yes—
162#2541C2212yes—
163#2540C2214yes—
164#2535C2214yes—
165#2515C2214yes—
166#2514C2212yes—
167#2514C2212yes—
168#2513C2212yes—
169#2510C2214yes—
170#2509C2212yes—
171#2508C2212yes—
172#2504C2212yes—
173#2494C2214yes—
174#2493C2214yes—
175#2491C2212yes—
176#2490C2212yes—
177#2486C2212yes—
178#2476C2214yes—
179#2471C2214yes—
180#2471C2214yes—
181#2464C2214yes—
182#2461C2214yes—
183#2459C2214yes—
184#2457C2214yes—
185#2456C2214yes—
186#2456C2214yes—
187#2454C2212yes—
188#2454C2212yes—
189#2453C2212yes—
190#2452C2212yes—
191#2447C2212yes—
192#2447C2212yes—
193#2447C2212yes—
194#2445C2212yes—
195#2445C2212yes—
196#2445C2212yes—
197#2445C2212yes—
198#2444C2214yes—
199#2444C2214yes—
200#2444C2214yes—
201#2443C2214yes—
202#2431C2212yes—
203#2431C2212yes—
204#2431C2212yes—
205#2431C2212yes—
206#2430C2214yes—
207#2430C2212yes—
208#2428C2214yes—
209#2428C2214yes—
210#2428C2212yes—
211#2428C2212yes—
212#2428C2212yes—
213#2428C2214yes—
214#2428C2212yes—
215#2428C2212yes—
216#2428C2212yes—
217#2428C2212yes—
218#2428C2214yes—
219#2425C2214yes—
220#2420C2212yes—
221#2420C2214yes—
222#2419C2214yes—
223#2419C2214yes—
224#2416C2214yes—
225#2416C2212yes—
226#2401C2212yes—
227#2401C2212yes—
228#2399C2211yescharacteristic
229#2399C2211yescharacteristic
230#2396C2212yes—
231#2396C2212yes—
232#2395C2212yes—
233#2392C2214yes—
234#2388C2212yes—
235#2370C2212yes—
236#2367C2212yes—
237#2366C2212yes—
238#2366C2212yes—
239#2366C2212yes—
240#2361C2212yes—
241#2361C2212yes—
242#2361C2212yes—
243#2357C2212yes—
244#2357C2212yes—
245#2349C2212yes—
246#2344C2212yes—
247#2343C2214yes—
248#2339C2212yes—
249#2328C2212yes—
250#2328C2212yes—
251#2324C2212yes—
252#2319C2211yescharacteristic
253#2311C2212yes—
254C4×#125C2212yes—
255C4×#124C2211yescharacteristic
256#2295C2211yescharacteristic
257#2293C2212yes—
258#2275C2211yescharacteristic
259C22×#41C2312yes—
260C22×#41C2312yes—
261#559—44no—
262#555—48no—
263#554—44no—
264#550—44no—
265#550—44no—
266#540—416no—
267#540—48no—
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2312yes—
270C2×#127C2312yes—
271C2×#127C2312yes—
272C2×#127C2312yes—
273C2×#127C2312yes—
274C2×#127C2311yescharacteristic
275C2×#127C2311yescharacteristic
276C2×#127C2312yes—
277C2×#127C2312yes—
278C2×#127C2312yes—
279C2×#127C2311yescharacteristic
280C2×#127C2312yes—
281C2×#127C2314yes—
282C2×#127C2312yes—
283C2×#127C2312yes—
284C2×#125C2312yes—
285C2×#125C2312yes—
286C2×#124C2311yescharacteristic
287C2×#124C2311yescharacteristic
288C2×#124C2311yescharacteristic
289C2×#124C2312yes—
290C2×#124C2314yes—
291C2×#124C2312yes—
292C2×#124C2312yes—
293C2×#124C2314yes—
294C2×#124C2312yes—
295C2×#123C2312yes—
296C2×#123C2312yes—
297C2×#123C2314yes—
298C2×#123C2314yes—
299C2×#123C2314yes—
300C2×#123C2314yes—
301C2×#123C2314yes—
302C2×#123C2314yes—
303C2×C22⋊Q8C2312yes—
304C2×C22⋊Q8C2314yes—
305C2×C22⋊Q8C2314yes—
306C2×#121C2312yes—
307C2×#121C2312yes—
308C2×#121C2314yes—
309C2×#121C2312yes—
310C2×#121C2312yes—
311C2×#121C2314yes—
312C2×#121C2314yes—
313C2×#121C2314yes—
314C2×#121C2312yes—
315C2×#121C2314yes—
316C2×#121C2314yes—
317C2×#121C2314yes—
318C2×#121C2312yes—
319C2×#121C2314yes—
320C2×#121C2314yes—
321C2×#121C2314yes—
322C2×#121C2314yes—
323C2×#121C2314yes—
324C2×#121C2314yes—
325C2×#121C2314yes—
326C2×#121C2314yes—
327C2×#121C2314yes—
328C2×#121C2314yes—
329C2×#121C2314yes—
330C2×#121C2314yes—
331C2×#121C2314yes—
332C2×#121C2314yes—
333C2×#121C2314yes—
334C2×#121C2314yes—
335C2×#121C2314yes—
336C2×#121C2314yes—
337C2×#121C2314yes—
338C2×C4×Q8C2311yescharacteristic
339C2×C4×Q8C2311yescharacteristic
340C2×C4×Q8C2311yescharacteristic
341C2×C4×Q8C2311yescharacteristic
342C2×C4×D4C2311yescharacteristic
343C2×C4×D4C2312yes—
344C2×C4×D4C2311yescharacteristic
345C2×C4×D4C2312yes—
346C2×C4×D4C2312yes—
347C2×C4×D4C2312yes—
348C2×C4×D4C2312yes—
349C2×C4×D4C2312yes—
350C2×C4×D4C2312yes—
351C2×C4×D4C2314yes—
352C2×C4×D4C2312yes—
353C2×C4×D4C2312yes—
354C2×C4×D4C2314yes—
355C2×C4×D4C2314yes—
356C2×C4×D4C2311yescharacteristic
357C2×C4×D4C2314yes—
358C2×C4×D4C2314yes—
359C2×C4×D4C2314yes—
360C2×#117C2314yes—
361C2×#117C2312yes—
362C2×#117C2314yes—
363C22×C4⋊C4C2312yes—
364C22×C4⋊C4C2312yes—
365#401C2312yes—
366#401C2314yes—
367#401C2314yes—
368#401C2312yes—
369#400C2312yes—
370#400C2312yes—
371#400C2314yes—
372#400C2314yes—
373#400C2314yes—
374#400C2314yes—
375#400C2312yes—
376#400C2312yes—
377#400C2312yes—
378#400C2312yes—
379#400C2312yes—
380#400C2312yes—
381#400C2312yes—
382#400C2314yes—
383#400C2314yes—
384#399C2312yes—
385#399C2312yes—
386#399C2314yes—
387#399C2312yes—
388#399C2314yes—
389#399C2314yes—
390#398C2311yescharacteristic
391#398C2311yescharacteristic
392#398C2312yes—
393#398C2312yes—
394#398C2312yes—
395#398C2312yes—
396#398C2312yes—
397#398C2312yes—
398#398C2312yes—
399#398C2312yes—
400#398C2311yescharacteristic
401#398C2311yescharacteristic
402#398C2312yes—
403#398C2314yes—
404#398C2314yes—
405#397C2312yes—
406#397C2312yes—
407#397C2312yes—
408#397C2312yes—
409#397C2314yes—
410#397C2312yes—
411#397C2314yes—
412#397C2314yes—
413#397C2314yes—
414#397C2314yes—
415#397C2314yes—
416#397C2314yes—
417#397C2312yes—
418#397C2314yes—
419#397C2312yes—
420#397C2312yes—
421#397C2312yes—
422#397C2314yes—
423#397C2314yes—
424#397C2312yes—
425#397C2312yes—
426#397C2312yes—
427#397C2314yes—
428#397C2314yes—
429#397C2312yes—
430#397C2314yes—
431#397C2314yes—
432#397C2314yes—
433#396C2312yes—
434#396C2312yes—
435#396C2312yes—
436#396C2312yes—
437#396C2312yes—
438#396C2314yes—
439#396C2314yes—
440#396C2314yes—
441#396C2312yes—
442#396C2314yes—
443#396C2314yes—
444#395C2312yes—
445#395C2312yes—
446#395C2311yescharacteristic
447#395C2311yescharacteristic
448#395C2311yescharacteristic
449#395C2311yescharacteristic
450#395C2312yes—
451#395C2312yes—
452#394C2312yes—
453#394C2312yes—
454#394C2314yes—
455#394C2314yes—
456#394C2314yes—
457#394C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2314yes—
461#394C2314yes—
462#394C2312yes—
463#394C2314yes—
464#394C2314yes—
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#394C2312yes—
470#394C2314yes—
471#394C2314yes—
472#394C2312yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2314yes—
478#394C2314yes—
479#394C2312yes—
480#394C2314yes—
481#394C2314yes—
482#394C2314yes—
483#393C2314yes—
484#393C2312yes—
485#393C2312yes—
486#393C2314yes—
487#393C2312yes—
488#393C2312yes—
489#393C2314yes—
490#393C2314yes—
491#392C2314yes—
492#392C2314yes—
493#392C2314yes—
494#392C2314yes—
495#392C2314yes—
496#392C2314yes—
497#392C2314yes—
498#392C2314yes—
499#392C2314yes—
500#392C2314yes—
501#392C2314yes—
502#392C2314yes—
503#392C2314yes—
504#392C2314yes—
505#392C2314yes—
506#392C2314yes—
507#392C2314yes—
508#392C2314yes—
509#392C2314yes—
510#392C2314yes—
511#392C2314yes—
512#392C2314yes—
513#392C2314yes—
514#392C2314yes—
515#392C2314yes—
516#392C2314yes—
517#392C2314yes—
518#392C2312yes—
519#392C2314yes—
520#392C2314yes—
521#392C2314yes—
522#392C2312yes—
523#392C2314yes—
524#392C2314yes—
525#392C2314yes—
526#391C2312yes—
527#391C2312yes—
528#391C2312yes—
529#391C2311yescharacteristic
530#391C2312yes—
531#391C2312yes—
532#390C2312yes—
533#390C2312yes—
534#390C2314yes—
535#390C2311yescharacteristic
536#390C2312yes—
537#390C2312yes—
538#390C2312yes—
539#390C2312yes—
540#390C2312yes—
541#390C2312yes—
542#390C2312yes—
543#390C2312yes—
544#390C2314yes—
545#390C2312yes—
546#390C2312yes—
547#390C2312yes—
548#390C2314yes—
549#390C2312yes—
550#390C2312yes—
551#390C2314yes—
552#390C2314yes—
553#390C2312yes—
554#390C2314yes—
555#390C2312yes—
556#389C2312yes—
557#389C2312yes—
558#389C2314yes—
559#389C2312yes—
560#389C2312yes—
561#389C2312yes—
562#389C2312yes—
563#389C2312yes—
564#389C2314yes—
565#389C2312yes—
566#389C2312yes—
567#389C2314yes—
568#389C2312yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2312yes—
578#388C2312yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#387C2312yes—
591#387C2312yes—
592#387C2312yes—
593#387C2312yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
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#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2314yes—
630#386C2314yes—
631#386C2314yes—
632#386C2314yes—
633#386C2314yes—
634#386C2314yes—
635#386C2314yes—
636#386C2314yes—
637#386C2314yes—
638#386C2314yes—
639#386C2314yes—
640#386C2314yes—
641#386C2314yes—
642#386C2314yes—
643#386C2314yes—
644#386C2314yes—
645#386C2314yes—
646#386C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2314yes—
661#385C2314yes—
662#383C2314yes—
663#383C2314yes—
664#382C2312yes—
665#382C2311yescharacteristic
666#382C2314yes—
667#382C2312yes—
668#382C2312yes—
669#381C2314yes—
670#381C2312yes—
671#381C2314yes—
672#381C2314yes—
673#381C2314yes—
674#381C2314yes—
675#381C2314yes—
676#381C2314yes—
677#381C2314yes—
678#380C2314yes—
679#380C2314yes—
680#380C2312yes—
681#380C2312yes—
682#380C2314yes—
683#380C2314yes—
684#380C2314yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2311yescharacteristic
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2311yescharacteristic
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2314yes—
712#376C2311yescharacteristic
713#376C2312yes—
714#376C2311yescharacteristic
715C2×#95C2314yes—
716C2×#95C2314yes—
717C2×#95C2312yes—
718C43C2311yescharacteristic
719C2×#41—44no—
720C2×#41—44no—
721C2×#41—44no—
722C2×#41—44no—
723C2×#41—84no—
724C22×Q8C2411yescharacteristic
725C22×Q8C2411yescharacteristic
726C22×Q8C2411yescharacteristic
727C22×Q8C2411yescharacteristic
728C22×Q8C2412yes—
729C22×D4C2411yescharacteristic
730C22×D4C2412yes—
731C22×D4C2411yescharacteristic
732C22×D4C2412yes—
733C22×D4C2414yes—
734C22×D4C2411yescharacteristic
735C22×D4C2414yes—
736C22×D4C2414yes—
737C22×D4C2412yes—
738C22×D4C2412yes—
739C22×D4C2414yes—
740C22×D4C2414yes—
741C22×D4C2414yes—
742C22×D4C2414yes—
743C22×D4C2414yes—
744C22×D4C2414yes—
745C22×D4C2412yes—
746C22×D4C2414yes—
747C22×D4C2414yes—
748C22×D4C2414yes—
749C22×D4C2412yes—
750C22×D4C2414yes—
751C22×D4C2414yes—
752C22×D4C2414yes—
753C22×D4C2412yes—
754C22×D4C2412yes—
755C22×D4C2414yes—
756C22×D4C2414yes—
757C22×D4C2414yes—
758C23×C4C2412yes—
759C23×C4C2412yes—
760C23×C4C2414yes—
761C23×C4C2412yes—
762C23×C4C2414yes—
763C23×C4C2414yes—
764C23×C4C2414yes—
765C23×C4C2414yes—
766C23×C4C2414yes—
767C23×C4C2414yes—
768C23×C4C2414yes—
769C23×C4C2414yes—
770C4⋊Q8—42no—
771C4⋊Q8—44no—
772#127—28no—
773#127—44no—
774#127—44no—
775#127—44no—
776#127—44no—
777#127—44no—
778#127—44no—
779#127—42no—
780#127—44no—
781#127—42no—
782#127—42no—
783#127—82no—
784#127—84no—
785#127—82no—
786#125—28no—
787#125—28no—
788#124—24no—
789#124—48no—
790#124—44no—
791#124—44no—
792#124—42no—
793#124—42no—
794#124—44no—
795#124—84no—
796#124—82no—
797#123—48no—
798#123—48no—
799#123—44no—
800#123—44no—
801#123—48no—
802#123—48no—
803#123—48no—
804#123—48no—
805C22⋊Q8—48no—
806C22⋊Q8—44no—
807C22⋊Q8—84no—
808#121—28no—
809#121—44no—
810#121—48no—
811#121—48no—
812#121—48no—
813#121—48no—
814#121—48no—
815#121—48no—
816#121—48no—
817#121—48no—
818#121—48no—
819#121—44no—
820#121—44no—
821#121—44no—
822#121—48no—
823#121—48no—
824#121—48no—
825#121—44no—
826#121—84no—
827#121—84no—
828#121—84no—
829#121—84no—
830#121—84no—
831#121—84no—
832#121—84no—
833#121—84no—
834#121—84no—
835#121—84no—
836#121—84no—
837#121—84no—
838#121—84no—
839#121—84no—
840C4×Q8—24no—
841C4×Q8—42no—
842C4×Q8—42no—
843C4×Q8—42no—
844C4×D4—28no—
845C4×D4—24no—
846C4×D4—24no—
847C4×D4—44no—
848C4×D4—44no—
849C4×D4—44no—
850C4×D4—44no—
851C4×D4—44no—
852C4×D4—48no—
853C4×D4—48no—
854C4×D4—44no—
855C4×D4—44no—
856C4×D4—42no—
857C4×D4—44no—
858C4×D4—48no—
859C4×D4—84no—
860C4×D4—84no—
861C4×D4—84no—
862#117—216no—
863#117—44no—
864#117—48no—
865C2×C4⋊C4—44no—
866C2×C4⋊C4—44no—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2411yescharacteristic
889C2×C4⋊C4C2411yescharacteristic
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2411yescharacteristic
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2411yescharacteristic
897C2×C4⋊C4C2411yescharacteristic
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2411yescharacteristic
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2412yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2412yes—
947C2×C22⋊C4C2412yes—
948C2×C22⋊C4C2412yes—
949C2×C22⋊C4C2412yes—
950C2×C22⋊C4C2414yes—
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2414yes—
956C2×C22⋊C4C2414yes—
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⋊C4C2412yes—
970C2×C22⋊C4C2412yes—
971C2×C22⋊C4C2414yes—
972C2×C22⋊C4C2414yes—
973C2×C42C2414yes—
974C2×C42C2412yes—
975C2×C42C2412yes—
976C2×C42C2412yes—
977C2×C42C2412yes—
978C2×C42C2411yescharacteristic
979C2×C42C2411yescharacteristic
980C2×C42C2411yescharacteristic
981C2×C42C2412yes—
982C2×C42C2412yes—
983C2×C42C2412yes—
984C2×C42C2412yes—
985C2×C42C2414yes—
986C2×C42C2414yes—
987C2×C42C2412yes—
988C2×C42C2412yes—
989C2×C42C2411yescharacteristic
990C2×C42C2411yescharacteristic
991#95C2411yescharacteristic
992#95C2412yes—
993#95C2412yes—
994#95C2414yes—
995#95C2412yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2412yes—
1003#95C2411yescharacteristic
1004#95C2411yescharacteristic
1005#95C2411yescharacteristic
1006#95C2414yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2412yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2414yes—
1022#95C2412yes—
1023#95C2412yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2412yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2412yes—
1030#95C2414yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2412yes—
1037#95C2412yes—
1038#95C2412yes—
1039#95C2412yes—
1040#95C2412yes—
1041#95C2412yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2414yes—
1050C24C2512yes—
1051C24C2514yes—
1052C24C2512yes—
1053C24C2512yes—
1054C24C2514yes—
1055#41—816no—
1056#41—816no—
1057C2×Q8—22no—
1058C2×Q8—22no—
1059C2×Q8—24no—
1060C2×Q8—41no—
1061C2×Q8—42no—
1062C2×Q8—41no—
1063C2×Q8—41no—
1064C2×Q8—41no—
1065C2×Q8—42no—
1066C2×Q8—42no—
1067C2×Q8—42no—
1068C2×Q8—42no—
1069C2×D4—22no—
1070C2×D4—24no—
1071C2×D4—22no—
1072C2×D4—24no—
1073C2×D4—28no—
1074C2×D4—28no—
1075C2×D4—28no—
1076C2×D4—22no—
1077C2×D4—24no—
1078C2×D4—24no—
1079C2×D4—24no—
1080C2×D4—24no—
1081C2×D4—24no—
1082C2×D4—24no—
1083C2×D4—24no—
1084C2×D4—24no—
1085C2×D4—44no—
1086C2×D4—42no—
1087C2×D4—42no—
1088C2×D4—41no—
1089C2×D4—44no—
1090C2×D4—44no—
1091C2×D4—44no—
1092C2×D4—44no—
1093C2×D4—44no—
1094C2×D4—42no—
1095C2×D4—44no—
1096C2×D4—44no—
1097C2×D4—44no—
1098C2×D4—44no—
1099C2×D4—44no—
1100C2×D4—44no—
1101C2×D4—44no—
1102C2×D4—44no—
1103C2×D4—44no—
1104C2×D4—44no—
1105C2×D4—44no—
1106C2×D4—42no—
1107C2×D4—44no—
1108C2×D4—44no—
1109C2×D4—44no—
1110C2×D4—41no—
1111C2×D4—42no—
1112C2×D4—44no—
1113C2×D4—44no—
1114C2×D4—44no—
1115C2×D4—44no—
1116C2×D4—44no—
1117C2×D4—44no—
1118C2×D4—44no—
1119C2×D4—44no—
1120C2×D4—42no—
1121C2×D4—42no—
1122C2×D4—44no—
1123C2×D4—42no—
1124C2×D4—44no—
1125C2×D4—44no—
1126C2×D4—44no—
1127C2×D4—44no—
1128C2×D4—42no—
1129C2×D4—44no—
1130C2×D4—44no—
1131C2×D4—44no—
1132C2×D4—44no—
1133C2×D4—44no—
1134C2×D4—44no—
1135C2×D4—44no—
1136C2×D4—44no—
1137C2×D4—44no—
1138C2×D4—44no—
1139C2×D4—44no—
1140C2×D4—44no—
1141C2×D4—44no—
1142C2×D4—44no—
1143C2×D4—44no—
1144C2×D4—44no—
1145C2×D4—42no—
1146C2×D4—44no—
1147C2×D4—44no—
1148C2×D4—44no—
1149C2×D4—44no—
1150C2×D4—44no—
1151C22×C4—24no—
1152C22×C4—24no—
1153C22×C4—24no—
1154C22×C4—24no—
1155C22×C4—28no—
1156C22×C4—24no—
1157C22×C4—28no—
1158C22×C4—44no—
1159C22×C4—44no—
1160C22×C4—44no—
1161C22×C4—44no—
1162C22×C4—44no—
1163C22×C4—44no—
1164C22×C4—44no—
1165C22×C4—44no—
1166C22×C4—44no—
1167C22×C4—44no—
1168C22×C4—44no—
1169C22×C4—44no—
1170C22×C4—44no—
1171C22×C4—44no—
1172C22×C4—44no—
1173C22×C4—44no—
1174C22×C4—44no—
1175C22×C4—44no—
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×C4—44no—
1185C22×C4C2512yes—
1186C22×C4C2512yes—
1187C22×C4C2512yes—
1188C22×C4C2514yes—
1189C22×C4C2512yes—
1190C22×C4C2512yes—
1191C22×C4C2512yes—
1192C22×C4C2511yescharacteristic
1193C22×C4C2512yes—
1194C22×C4C2514yes—
1195C22×C4C2512yes—
1196C22×C4C2511yescharacteristic
1197C22×C4C2514yes—
1198C22×C4C2512yes—
1199C22×C4C2511yescharacteristic
1200C22×C4C2514yes—
1201C22×C4C2512yes—
1202C22×C4C2512yes—
1203C22×C4C2511yescharacteristic
1204C22×C4C2511yescharacteristic
1205C22×C4C2512yes—
1206C22×C4C2512yes—
1207C22×C4C2511yescharacteristic
1208C22×C4C2511yescharacteristic
1209C4⋊C4—28no—
1210C4⋊C4—28no—
1211C4⋊C4—28no—
1212C4⋊C4—24no—
1213C4⋊C4—24no—
1214C4⋊C4—24no—
1215C4⋊C4—24no—
1216C4⋊C4—24no—
1217C4⋊C4—24no—
1218C4⋊C4—24no—
1219C4⋊C4—24no—
1220C4⋊C4—28no—
1221C4⋊C4—24no—
1222C4⋊C4—24no—
1223C4⋊C4—24no—
1224C4⋊C4—41no—
1225C4⋊C4—44no—
1226C4⋊C4—42no—
1227C4⋊C4—44no—
1228C4⋊C4—42no—
1229C4⋊C4—42no—
1230C4⋊C4—41no—
1231C4⋊C4—41no—
1232C4⋊C4—42no—
1233C4⋊C4—44no—
1234C4⋊C4—44no—
1235C4⋊C4—42no—
1236C4⋊C4—41no—
1237C4⋊C4—42no—
1238C4⋊C4—41no—
1239C4⋊C4—41no—
1240C4⋊C4—44no—
1241C4⋊C4—42no—
1242C4⋊C4—42no—
1243C4⋊C4—42no—
1244C4⋊C4—42no—
1245C4⋊C4—42no—
1246C4⋊C4—42no—
1247C4⋊C4—42no—
1248C4⋊C4—42no—
1249C4⋊C4—44no—
1250C4⋊C4—44no—
1251C4⋊C4—42no—
1252C4⋊C4H(5,𝔽2)14yes—
1253C22⋊C4—28no—
1254C22⋊C4—28no—
1255C22⋊C4—24no—
1256C22⋊C4—28no—
1257C22⋊C4—24no—
1258C22⋊C4—24no—
1259C22⋊C4—24no—
1260C22⋊C4—28no—
1261C22⋊C4—42no—
1262C22⋊C4—42no—
1263C22⋊C4—44no—
1264C22⋊C4—44no—
1265C22⋊C4—44no—
1266C22⋊C4—44no—
1267C22⋊C4—44no—
1268C22⋊C4—42no—
1269C22⋊C4—44no—
1270C22⋊C4—44no—
1271C22⋊C4—44no—
1272C22⋊C4—44no—
1273C22⋊C4—44no—
1274C22⋊C4—44no—
1275C22⋊C4—42no—
1276C22⋊C4—42no—
1277C22⋊C4—44no—
1278C22⋊C4—42no—
1279C22⋊C4—42no—
1280C22⋊C4—44no—
1281C22⋊C4—44no—
1282C22⋊C4—44no—
1283C22⋊C4—44no—
1284C22⋊C4—44no—
1285C22⋊C4—44no—
1286C22⋊C4—44no—
1287C22⋊C4—44no—
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—42no—
1298C22⋊C4—44no—
1299C22⋊C4—44no—
1300C22⋊C4—42no—
1301C22⋊C4—44no—
1302C22⋊C4—42no—
1303C22⋊C4—42no—
1304C22⋊C4—42no—
1305C22⋊C4—44no—
1306C22⋊C4—44no—
1307C22⋊C4—44no—
1308C22⋊C4—44no—
1309C22⋊C4—44no—
1310C22⋊C4—44no—
1311C22⋊C4—42no—
1312C22⋊C4—42no—
1313C22⋊C4—44no—
1314C22⋊C4—44no—
1315C42—28no—
1316C42—24no—
1317C42—24no—
1318C42—22no—
1319C42—22no—
1320C42—24no—
1321C42—22no—
1322C42—24no—
1323C42—24no—
1324C42—24no—
1325C42—42no—
1326C42—42no—
1327C42—44no—
1328C42—44no—
1329C42—42no—
1330C42—41no—
1331C42—42no—
1332C42H(5,𝔽2)14yes—
1333C23—22no—
1334C23—24no—
1335C23—22no—
1336C23—22no—
1337C23—24no—
1338C23—24no—
1339C23—22no—
1340C23—24no—
1341C23—22no—
1342C23—22no—
1343C23—24no—
1344C23—24no—
1345C23—24no—
1346C23—24no—
1347C23—24no—
1348C23—22no—
1349C23—22no—
1350C23—24no—
1351C23—22no—
1352C23—24no—
1353C23—22no—
1354C23—24no—
1355C23—24no—
1356C23—24no—
1357C23—24no—
1358C23—24no—
1359C23—22no—
1360C23—22no—
1361C23—24no—
1362C23—24no—
1363C23—22no—
1364C23C2611yescharacteristic
1365Q8—44no—
1366Q8—44no—
1367Q8—82no—
1368Q8—82no—
1369Q8—162no—
1370D4—44no—
1371D4—48no—
1372D4—44no—
1373D4—48no—
1374D4—88no—
1375D4—84no—
1376D4—84no—
1377D4—82no—
1378D4—88no—
1379D4—88no—
1380D4—88no—
1381D4—88no—
1382D4—88no—
1383D4—88no—
1384D4—88no—
1385D4—84no—
1386D4—162no—
1387D4—162no—
1388D4—164no—
1389D4—164no—
1390D4—164no—
1391D4—164no—
1392D4—164no—
1393D4—164no—
1394D4—164no—
1395D4—164no—
1396D4—162no—
1397D4—164no—
1398D4—164no—
1399C2×C4—21no—
1400C2×C4—22no—
1401C2×C4—21no—
1402C2×C4—24no—
1403C2×C4—22no—
1404C2×C4—24no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—22no—
1408C2×C4—24no—
1409C2×C4—22no—
1410C2×C4—22no—
1411C2×C4—22no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—22no—
1416C2×C4—21no—
1417C2×C4—21no—
1418C2×C4—24no—
1419C2×C4—22no—
1420C2×C4—22no—
1421C2×C4—22no—
1422C2×C4—22no—
1423C2×C4—22no—
1424C2×C4—24no—
1425C2×C4—22no—
1426C2×C4—22no—
1427C2×C4—22no—
1428C2×C4—22no—
1429C2×C4—22no—
1430C2×C4—22no—
1431C2×C4—24no—
1432C2×C4—24no—
1433C2×C4—24no—
1434C2×C4—22no—
1435C2×C4—24no—
1436C2×C4—24no—
1437C2×C4—22no—
1438C2×C4—22no—
1439C2×C4—24no—
1440C2×C4—24no—
1441C2×C4—22no—
1442C2×C4—22no—
1443C2×C4—22no—
1444C2×C4—22no—
1445C2×C4—24no—
1446C2×C4—22no—
1447C2×C4—21no—
1448C2×C4—21no—
1449C2×C4—22no—
1450C2×C4—22no—
1451C2×C4—22no—
1452C2×C4—22no—
1453C2×C4—24no—
1454C2×C4—22no—
1455C2×C4—22no—
1456C2×C4—22no—
1457C2×C4—22no—
1458C2×C4—22no—
1459C2×C4—22no—
1460C2×C4—48no—
1461C2×C4—84no—
1462C2×C4—88no—
1463C2×C4—84no—
1464C2×C4—88no—
1465C2×C4—88no—
1466C2×C4—88no—
1467C2×C4—164no—
1468C2×C4—164no—
1469C2×C4—164no—
1470C2×C4—164no—
1471C2×C4—164no—
1472C2×C4C2×H(5,𝔽2)14yes—
1473C2×C4C2×H(5,𝔽2)14yes—
1474C2×C4C2×H(5,𝔽2)12yes—
1475C2×C4C2×H(5,𝔽2)12yes—
1476C2×C4#58514yes—
1477C22—42no—
1478C22—44no—
1479C22—42no—
1480C22—42no—
1481C22—44no—
1482C22—42no—
1483C22—44no—
1484C22—42no—
1485C22—42no—
1486C22—44no—
1487C22—44no—
1488C22—42no—
1489C22—44no—
1490C22—44no—
1491C22—44no—
1492C22—42no—
1493C22—44no—
1494C22—44no—
1495C22—42no—
1496C22—44no—
1497C22—42no—
1498C22—42no—
1499C22—44no—
1500C22—42no—
1501C22—44no—
1502C22—44no—
1503C22—44no—
1504C22—42no—
1505C22—44no—
1506C22—44no—
1507C22—44no—
1508C22C22×H(5,𝔽2)11yescharacteristic
1509C22C22×H(5,𝔽2)11yescharacteristic
1510C22C2×#58512yes—
1511C22H(7,𝔽2)12yes—
1512C22H(7,𝔽2)11yescharacteristic
1513C4—24no—
1514C4—22no—
1515C4—24no—
1516C4—42no—
1517C4—42no—
1518C4—42no—
1519C4—41no—
1520C4—41no—
1521C4—41no—
1522C4—42no—
1523C4—42no—
1524C4—44no—
1525C4—42no—
1526C4—42no—
1527C4—42no—
1528C4—42no—
1529C4—44no—
1530C4—41no—
1531C4—41no—
1532C4—44no—
1533C4—44no—
1534C4—42no—
1535C4—42no—
1536C4#355114yes—
1537C2—82no—
1538C2—84no—
1539C2—84no—
1540C2—82no—
1541C2—82no—
1542C2C2×#355111yescharacteristic
1543C2#6291611yescharacteristic
1544C2#6295512yes—
1545C2#6304111yescharacteristic
1546C2#6306012yes—
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. #59895C2semidirect
2. #59841C2semidirect
3. #55735C2semidirect
4. #55222C2semidirect
5. #54026C2semidirect
6. #53794C2semidirect
7. #53511C2semidirect
8. #53090C2semidirect
9. #52989C2semidirect
10. #52966C2semidirect
11. #52388C2semidirect
12. #47800C2semidirect
13. #45437C2semidirect
14. #45368C2semidirect
15. #45038C2semidirect
16. #45034C2semidirect
17. #44889C2semidirect
18. #42678C2semidirect
19. #42617C2semidirect
20. #42595C2semidirect
21. #42518C2semidirect
22. #42425C2semidirect
23. #42050C2semidirect
24. #41945C2semidirect
25. #39745C2semidirect
26. #39386C2semidirect
27. #36698C2semidirect
28. #35930C2semidirect
29. #35882C2semidirect

Maximal subgroups

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

subgroupindex
#598952
#598412
#557352
#552222
#540262
#537942
#535112
#530902
#529892
#529662
#523882
#478002
#454372
#453682
#450382
#450342
#448892
#426782
#426172
#425952
#425182
#424252
#420502
#419452
#397452
#393862
#366982
#359302
#358822