Finite Group Databasebeta

← #7891984

Subgroups — #7891984

Order 512.

5269 conjugacy classes of subgroups.

The subgroup lattice has 1545 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59815C211yesmaximal, characteristic, complemented
2#59693C212yesmaximal, complemented
3#52272C211yesmaximal, characteristic, complemented
4#50740C214yesmaximal, complemented
5#49797C214yesmaximal, complemented
6#47997C214yesmaximal, complemented
7#47446C214yesmaximal, complemented
8#45801C212yesmaximal, complemented
9#45131C212yesmaximal, complemented
10#45042C212yesmaximal, complemented
11#45033C212yesmaximal, complemented
12#43108C214yesmaximal, complemented
13#42545C212yesmaximal, complemented
14#42425C212yesmaximal, complemented
15#42041C214yesmaximal, complemented
16#40121C212yesmaximal, complemented
17#39756C211yesmaximal, characteristic, complemented
18#39742C212yesmaximal, complemented
19#39483C211yesmaximal, characteristic, complemented
20#39169C212yesmaximal, complemented
21#38487C212yesmaximal, complemented
22#38286C212yesmaximal, complemented
23#37316C212yesmaximal, complemented
24#36261C211yesmaximal, characteristic, complemented
25#35941C212yesmaximal, complemented
26#35612C212yesmaximal, complemented
27#35171C211yesmaximal, characteristic, complemented
28#34431C212yesmaximal, complemented
29#34330C211yesmaximal, characteristic, complemented
30C2×#554C2212yes—
31C2×#553C2214yes—
32C2×#553C2212yes—
33C2×#550C2211yescharacteristic
34C2×#550C2212yes—
35C2×#547C2212yes—
36C2×#540C2212yes—
37#2859C2211yescharacteristic
38#2858C2212yes—
39#2857C2212yes—
40#2856C2212yes—
41#2854C2212yes—
42#2837C2214yes—
43#2813C2214yes—
44#2810C2211yescharacteristic
45#2808C2211yescharacteristic
46#2808C2212yes—
47#2808C2212yes—
48#2805C2211yescharacteristic
49#2804C2214yes—
50#2803C2214yes—
51#2800C2212yes—
52#2798C2212yes—
53#2793C2212yes—
54#2788C2214yes—
55#2788C2214yes—
56#2784C2214yes—
57#2778C2214yes—
58#2776C2212yes—
59#2759C2212yes—
60#2746C2214yes—
61#2737C2214yes—
62#2733C2214yes—
63#2731C2214yes—
64#2727C2211yescharacteristic
65#2727C2212yes—
66#2727C2212yes—
67#2727C2212yes—
68#2727C2212yes—
69#2718C2214yes—
70#2716C2212yes—
71#2714C2214yes—
72#2711C2214yes—
73#2705C2214yes—
74#2705C2214yes—
75#2703C2214yes—
76#2703C2214yes—
77#2702C2214yes—
78#2701C2214yes—
79#2699C2214yes—
80#2696C2214yes—
81#2688C2214yes—
82#2686C2214yes—
83#2686C2214yes—
84#2682C2212yes—
85#2682C2212yes—
86#2682C2212yes—
87#2682C2212yes—
88#2681C2214yes—
89#2676C2214yes—
90#2676C2214yes—
91#2676C2214yes—
92#2676C2214yes—
93#2676C2214yes—
94#2675C2214yes—
95#2675C2214yes—
96#2671C2214yes—
97#2671C2214yes—
98#2662C2214yes—
99#2661C2214yes—
100#2661C2214yes—
101#2656C2214yes—
102#2649C2214yes—
103#2641C2212yes—
104#2641C2212yes—
105#2630C2214yes—
106#2619C2212yes—
107#2615C2214yes—
108#2608C2214yes—
109#2598C2214yes—
110#2591C2214yes—
111#2589C2214yes—
112#2587C2214yes—
113#2584C2212yes—
114#2583C2214yes—
115#2580C2212yes—
116#2579C2214yes—
117#2569C2214yes—
118#2566C2212yes—
119#2566C2212yes—
120#2563C2212yes—
121#2559C2214yes—
122#2559C2214yes—
123#2559C2214yes—
124#2556C2214yes—
125#2555C2214yes—
126#2552C2211yescharacteristic
127#2552C2211yescharacteristic
128#2551C2211yescharacteristic
129#2550C2212yes—
130#2549C2214yes—
131#2543C2214yes—
132#2541C2211yescharacteristic
133#2541C2212yes—
134#2541C2212yes—
135#2541C2211yescharacteristic
136#2541C2212yes—
137#2538C2212yes—
138#2537C2212yes—
139#2537C2211yescharacteristic
140#2522C2214yes—
141#2521C2214yes—
142#2512C2212yes—
143#2512C2212yes—
144#2509C2212yes—
145#2506C2212yes—
146#2501C2212yes—
147#2500C2212yes—
148#2497C2214yes—
149#2491C2214yes—
150#2491C2212yes—
151#2490C2212yes—
152#2490C2212yes—
153#2481C2214yes—
154#2476C2214yes—
155#2473C2214yes—
156#2467C2214yes—
157#2466C2214yes—
158#2466C2214yes—
159#2464C2214yes—
160#2464C2214yes—
161#2463C2214yes—
162#2459C2214yes—
163#2457C2214yes—
164#2456C2214yes—
165#2455C2214yes—
166#2455C2214yes—
167#2454C2212yes—
168#2454C2212yes—
169#2454C2214yes—
170#2445C2212yes—
171#2445C2212yes—
172#2443C2214yes—
173#2442C2212yes—
174#2441C2214yes—
175#2440C2212yes—
176#2440C2212yes—
177#2439C2212yes—
178#2438C2214yes—
179#2430C2214yes—
180#2430C2214yes—
181#2428C2212yes—
182#2428C2212yes—
183#2428C2212yes—
184#2428C2212yes—
185#2428C2214yes—
186#2428C2212yes—
187#2428C2214yes—
188#2428C2212yes—
189#2428C2212yes—
190#2428C2212yes—
191#2427C2214yes—
192#2422C2214yes—
193#2422C2212yes—
194#2416C2214yes—
195#2416C2214yes—
196#2416C2214yes—
197#2416C2214yes—
198#2416C2214yes—
199#2414C2214yes—
200#2407C2214yes—
201#2407C2214yes—
202#2407C2214yes—
203#2401C2212yes—
204#2398C2212yes—
205#2396C2212yes—
206#2388C2214yes—
207#2377C2214yes—
208#2376C2214yes—
209#2366C2212yes—
210#2366C2211yescharacteristic
211#2364C2214yes—
212#2363C2212yes—
213#2363C2212yes—
214#2363C2212yes—
215#2363C2212yes—
216#2361C2212yes—
217#2361C2212yes—
218#2361C2212yes—
219#2361C2214yes—
220#2359C2214yes—
221#2357C2212yes—
222#2357C2212yes—
223#2355C2211yescharacteristic
224#2354C2211yescharacteristic
225#2349C2212yes—
226D4×C4⋊C4C2211yescharacteristic
227D4×C4⋊C4C2212yes—
228D4×C4⋊C4C2211yescharacteristic
229#2339C2212yes—
230#2335C2214yes—
231#2335C2214yes—
232#2333C2214yes—
233#2330C2212yes—
234#2330C2212yes—
235#2328C2212yes—
236#2328C2212yes—
237#2325C2214yes—
238#2324C2214yes—
239#2324C2212yes—
240#2322C2214yes—
241#2319C2212yes—
242#2317C2212yes—
243C4×C4⋊Q8C2211yescharacteristic
244C4×#127C2212yes—
245C4×#127C2211yescharacteristic
246C4×#127C2211yescharacteristic
247C4×#125C2212yes—
248C4×#126C2212yes—
249C4×#121C2212yes—
250#2298C2212yes—
251#2297C2212yes—
252#2295C2212yes—
253#2295C2211yescharacteristic
254#2293C2212yes—
255#2293C2211yescharacteristic
256C2×#389C2212yes—
257#2275C2212yes—
258C42×D4C2211yescharacteristic
259C22×#41C2312yes—
260C22×#41C2314yes—
261#554—48no—
262#553—416no—
263#553—48no—
264#550—28no—
265#550—48no—
266#547—48no—
267#540—216no—
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2312yes—
271C2×#127C2312yes—
272C2×#127C2311yescharacteristic
273C2×#127C2311yescharacteristic
274C2×#127C2312yes—
275C2×#127C2312yes—
276C2×#127C2312yes—
277C2×#127C2312yes—
278C2×#126C2312yes—
279C2×#126C2314yes—
280C2×#126C2314yes—
281C2×#126C2314yes—
282C2×#125C2312yes—
283C2×#125C2312yes—
284C2×#125C2312yes—
285C2×#125C2314yes—
286C2×#124C2314yes—
287C2×#124C2314yes—
288C2×#124C2314yes—
289C2×#123C2314yes—
290C2×#123C2314yes—
291C2×#123C2314yes—
292C2×#123C2314yes—
293C2×#123C2314yes—
294C2×#123C2314yes—
295C2×#123C2314yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2314yes—
300C2×#121C2314yes—
301C2×#121C2312yes—
302C2×#121C2314yes—
303C2×#121C2312yes—
304C2×#121C2312yes—
305C2×#121C2314yes—
306C2×#121C2312yes—
307C2×#121C2314yes—
308C2×#121C2312yes—
309C2×#121C2312yes—
310C2×#121C2314yes—
311C2×#121C2314yes—
312C2×#121C2314yes—
313C2×#121C2314yes—
314C2×#121C2314yes—
315C2×#121C2314yes—
316C2×#121C2314yes—
317C2×#121C2314yes—
318C2×#121C2314yes—
319C2×#121C2312yes—
320C2×#121C2312yes—
321C2×#121C2312yes—
322C2×#121C2314yes—
323C2×#121C2314yes—
324C2×#121C2314yes—
325C2×#121C2314yes—
326C2×#121C2314yes—
327C2×#121C2314yes—
328C2×#121C2314yes—
329C2×C4×Q8C2312yes—
330C2×C4×Q8C2311yescharacteristic
331C2×C4×D4C2312yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2312yes—
334C2×C4×D4C2311yescharacteristic
335C2×C4×D4C2311yescharacteristic
336C2×C4×D4C2312yes—
337C2×C4×D4C2311yescharacteristic
338C2×C4×D4C2312yes—
339C2×C4×D4C2314yes—
340C2×C4×D4C2312yes—
341C2×C4×D4C2312yes—
342C2×C4×D4C2312yes—
343C2×C4×D4C2312yes—
344C2×C4×D4C2314yes—
345C2×C4×D4C2314yes—
346C2×C4×D4C2312yes—
347C2×C4×D4C2314yes—
348C2×C4×D4C2314yes—
349C2×C4×D4C2312yes—
350C2×C4×D4C2314yes—
351C2×C4×D4C2312yes—
352C2×C4×D4C2314yes—
353C2×C4×D4C2312yes—
354C2×C4×D4C2311yescharacteristic
355C2×#117C2312yes—
356C2×#117C2312yes—
357C2×#117C2314yes—
358C2×#117C2312yes—
359C22×C4⋊C4C2312yes—
360C22×C4⋊C4C2312yes—
361C22×C4⋊C4C2314yes—
362C22×C4⋊C4C2314yes—
363C22×C4⋊C4C2312yes—
364C22×C42C2312yes—
365#401C2312yes—
366#400C2314yes—
367#400C2314yes—
368#400C2312yes—
369#400C2312yes—
370#400C2312yes—
371#400C2314yes—
372#400C2312yes—
373#400C2312yes—
374#400C2312yes—
375#400C2314yes—
376#399C2314yes—
377#399C2314yes—
378#399C2314yes—
379#399C2314yes—
380#399C2312yes—
381#399C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2312yes—
389#398C2312yes—
390#397C2314yes—
391#397C2314yes—
392#397C2312yes—
393#397C2314yes—
394#397C2312yes—
395#397C2312yes—
396#397C2312yes—
397#397C2312yes—
398#397C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2312yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2312yes—
411#396C2312yes—
412#396C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2314yes—
416#395C2312yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2312yes—
436#394C2312yes—
437#394C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#393C2314yes—
447#393C2314yes—
448#393C2314yes—
449#393C2312yes—
450#393C2312yes—
451#393C2312yes—
452#393C2314yes—
453#393C2314yes—
454#392C2314yes—
455#392C2314yes—
456#392C2314yes—
457#392C2314yes—
458#392C2314yes—
459#392C2314yes—
460#392C2314yes—
461#392C2314yes—
462#392C2314yes—
463#392C2314yes—
464#392C2314yes—
465#392C2314yes—
466#392C2314yes—
467#392C2314yes—
468#392C2314yes—
469#392C2314yes—
470#392C2314yes—
471#391C2312yes—
472#391C2314yes—
473#391C2314yes—
474#391C2311yescharacteristic
475#391C2312yes—
476#391C2312yes—
477#391C2312yes—
478#391C2311yescharacteristic
479#390C2314yes—
480#390C2312yes—
481#390C2312yes—
482#390C2312yes—
483#390C2312yes—
484#390C2312yes—
485#390C2314yes—
486#390C2312yes—
487#390C2312yes—
488#390C2312yes—
489#390C2312yes—
490#390C2312yes—
491#390C2312yes—
492#390C2312yes—
493#390C2312yes—
494#390C2312yes—
495#390C2314yes—
496#390C2314yes—
497#390C2314yes—
498#390C2312yes—
499#390C2312yes—
500#390C2314yes—
501#390C2314yes—
502#390C2312yes—
503#390C2311yescharacteristic
504#390C2314yes—
505#390C2314yes—
506#390C2312yes—
507#390C2314yes—
508#390C2314yes—
509#390C2311yescharacteristic
510#390C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2311yescharacteristic
515#389C2311yescharacteristic
516#389C2314yes—
517#389C2314yes—
518#389C2312yes—
519#389C2312yes—
520#389C2314yes—
521#389C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2314yes—
525#389C2314yes—
526#389C2312yes—
527#389C2312yes—
528#389C2312yes—
529#389C2314yes—
530#389C2314yes—
531#389C2314yes—
532#389C2312yes—
533#389C2312yes—
534#389C2312yes—
535#389C2311yescharacteristic
536#389C2312yes—
537#389C2312yes—
538#389C2312yes—
539#389C2311yescharacteristic
540#389C2312yes—
541#389C2314yes—
542#389C2312yes—
543#389C2314yes—
544#389C2311yescharacteristic
545#389C2311yescharacteristic
546#388C2312yes—
547#388C2312yes—
548#388C2312yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2312yes—
554#388C2314yes—
555#388C2314yes—
556#388C2312yes—
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#388C2312yes—
572#388C2312yes—
573#388C2312yes—
574#388C2314yes—
575#388C2314yes—
576#388C2312yes—
577#388C2314yes—
578#387C2312yes—
579#387C2312yes—
580#387C2312yes—
581#387C2314yes—
582#387C2314yes—
583#387C2312yes—
584#387C2314yes—
585#387C2314yes—
586#387C2312yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2312yes—
592#387C2314yes—
593#387C2312yes—
594#387C2314yes—
595#387C2312yes—
596#387C2312yes—
597#387C2312yes—
598#387C2312yes—
599#387C2312yes—
600#387C2312yes—
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#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
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#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#384C2312yes—
650#384C2311yescharacteristic
651#384C2311yescharacteristic
652#384C2311yescharacteristic
653#384C2312yes—
654#384C2312yes—
655#384C2311yescharacteristic
656#384C2311yescharacteristic
657#383C2312yes—
658#382C2312yes—
659#382C2312yes—
660#382C2312yes—
661#381C2314yes—
662#381C2314yes—
663#381C2314yes—
664#380C2314yes—
665#380C2314yes—
666#380C2314yes—
667#380C2314yes—
668#380C2314yes—
669#380C2314yes—
670#380C2312yes—
671#380C2312yes—
672#380C2314yes—
673#380C2312yes—
674#380C2312yes—
675#380C2312yes—
676#380C2314yes—
677#380C2314yes—
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2311yescharacteristic
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2311yescharacteristic
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2311yescharacteristic
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2312yes—
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⋊C4C2314yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713#376C2312yes—
714#376C2312yes—
715C2×#95C2314yes—
716C2×#95C2314yes—
717C43C2312yes—
718C43C2311yescharacteristic
719C2×#41—28no—
720C2×#41—48no—
721C2×#41—48no—
722C2×#41—82no—
723C2×#41—82no—
724C2×#41—84no—
725C22×Q8C2412yes—
726C22×Q8C2411yescharacteristic
727C22×Q8C2414yes—
728C22×D4C2412yes—
729C22×D4C2412yes—
730C22×D4C2411yescharacteristic
731C22×D4C2412yes—
732C22×D4C2414yes—
733C22×D4C2411yescharacteristic
734C22×D4C2412yes—
735C22×D4C2414yes—
736C22×D4C2412yes—
737C22×D4C2414yes—
738C22×D4C2414yes—
739C22×D4C2414yes—
740C22×D4C2414yes—
741C22×D4C2412yes—
742C22×D4C2414yes—
743C22×D4C2414yes—
744C22×D4C2414yes—
745C22×D4C2414yes—
746C22×D4C2414yes—
747C22×D4C2414yes—
748C22×D4C2414yes—
749C23×C4C2412yes—
750C23×C4C2412yes—
751C23×C4C2414yes—
752C23×C4C2412yes—
753C23×C4C2414yes—
754C23×C4C2414yes—
755C23×C4C2414yes—
756C23×C4C2414yes—
757C23×C4C2414yes—
758C23×C4C2414yes—
759C23×C4C2414yes—
760C23×C4C2414yes—
761C23×C4C2412yes—
762C4⋊Q8—24no—
763C4⋊Q8—44no—
764C4⋊Q8—82no—
765#127—28no—
766#127—28no—
767#127—24no—
768#127—24no—
769#127—44no—
770#127—44no—
771#127—82no—
772#126—28no—
773#126—48no—
774#126—48no—
775#126—84no—
776#125—28no—
777#125—28no—
778#125—44no—
779#125—48no—
780#124—84no—
781#124—84no—
782#124—84no—
783#123—216no—
784#123—216no—
785#123—216no—
786#123—48no—
787#123—48no—
788#123—48no—
789#123—84no—
790C22⋊Q8—48no—
791C22⋊Q8—48no—
792C22⋊Q8—48no—
793C22⋊Q8—48no—
794#121—28no—
795#121—216no—
796#121—28no—
797#121—28no—
798#121—28no—
799#121—216no—
800#121—216no—
801#121—48no—
802#121—48no—
803#121—48no—
804#121—48no—
805#121—48no—
806#121—48no—
807#121—48no—
808#121—48no—
809#121—48no—
810#121—44no—
811#121—44no—
812#121—84no—
813#121—84no—
814#121—84no—
815#121—84no—
816#121—84no—
817#121—84no—
818#121—84no—
819#121—82no—
820#121—82no—
821#121—82no—
822#121—84no—
823C4×Q8—24no—
824C4×Q8—28no—
825C4×D4—28no—
826C4×D4—24no—
827C4×D4—28no—
828C4×D4—28no—
829C4×D4—28no—
830C4×D4—24no—
831C4×D4—24no—
832C4×D4—44no—
833C4×D4—44no—
834C4×D4—44no—
835C4×D4—44no—
836C4×D4—44no—
837C4×D4—44no—
838C4×D4—48no—
839C4×D4—48no—
840C4×D4—48no—
841C4×D4—48no—
842C4×D4—48no—
843C4×D4—82no—
844C4×D4—84no—
845C4×D4—84no—
846C4×D4—82no—
847C4×D4—82no—
848C4×D4#4118yescomplemented
849#117—28no—
850#117—48no—
851#117—44no—
852#117—82no—
853C2×C4⋊C4—28no—
854C2×C4⋊C4—48no—
855C2×C4⋊C4—44no—
856C2×C4⋊C4—48no—
857C2×C4⋊C4—82no—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2411yescharacteristic
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2411yescharacteristic
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2411yescharacteristic
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2411yescharacteristic
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2411yescharacteristic
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2411yescharacteristic
913C2×C4⋊C4C2411yescharacteristic
914C2×C4⋊C4C2411yescharacteristic
915C2×C4⋊C4C2411yescharacteristic
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
953C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
969C2×C22⋊C4C2414yes—
970C2×C22⋊C4C2412yes—
971C2×C22⋊C4C2414yes—
972C2×C22⋊C4C2412yes—
973C2×C42—82no—
974C2×C42C2412yes—
975C2×C42C2412yes—
976C2×C42C2411yescharacteristic
977C2×C42C2412yes—
978C2×C42C2412yes—
979C2×C42C2412yes—
980C2×C42C2412yes—
981C2×C42C2411yescharacteristic
982C2×C42C2414yes—
983C2×C42C2414yes—
984C2×C42C2414yes—
985C2×C42C2414yes—
986C2×C42C2411yescharacteristic
987C2×C42C2411yescharacteristic
988C2×C42C2412yes—
989C2×C42C2412yes—
990C2×C42C2412yes—
991C2×C42C2412yes—
992C2×C42C2414yes—
993C2×C42C2412yes—
994C2×C42C2412yes—
995C2×C42C2411yescharacteristic
996C2×C42C2411yescharacteristic
997C2×C42C2411yescharacteristic
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2412yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2412yes—
1030#95C2412yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2414yes—
1034#95C2412yes—
1035#95C2412yes—
1036#95C2412yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2412yes—
1042#95C2414yes—
1043#95C2412yes—
1044#95C2412yes—
1045#95C2412yes—
1046#95C2412yes—
1047#95C2412yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2414yes—
1051C24C2512yes—
1052C24C2514yes—
1053C24C2514yes—
1054C24C2512yes—
1055#41—816no—
1056#41—832no—
1057C2×Q8—22no—
1058C2×Q8—24no—
1059C2×Q8—24no—
1060C2×Q8—41no—
1061C2×Q8—41no—
1062C2×Q8—42no—
1063C2×Q8—44no—
1064C2×Q8—44no—
1065C2×Q8—44no—
1066C2×D4—28no—
1067C2×D4—28no—
1068C2×D4—28no—
1069C2×D4—28no—
1070C2×D4—28no—
1071C2×D4—24no—
1072C2×D4—24no—
1073C2×D4—24no—
1074C2×D4—28no—
1075C2×D4—24no—
1076C2×D4—22no—
1077C2×D4—24no—
1078C2×D4—24no—
1079C2×D4—24no—
1080C2×D4—22no—
1081C2×D4—24no—
1082C2×D4—28no—
1083C2×D4—22no—
1084C2×D4—24no—
1085C2×D4—24no—
1086C2×D4—28no—
1087C2×D4—42no—
1088C2×D4—42no—
1089C2×D4—42no—
1090C2×D4—42no—
1091C2×D4—42no—
1092C2×D4—44no—
1093C2×D4—44no—
1094C2×D4—44no—
1095C2×D4—44no—
1096C2×D4—44no—
1097C2×D4—44no—
1098C2×D4—42no—
1099C2×D4—44no—
1100C2×D4—44no—
1101C2×D4—44no—
1102C2×D4—44no—
1103C2×D4—41no—
1104C2×D4—42no—
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—44no—
1117C2×D4—44no—
1118C2×D4—41no—
1119C2×D4—44no—
1120C2×D4—44no—
1121C2×D4—44no—
1122C2×D4—44no—
1123C2×D4—44no—
1124C2×D4—44no—
1125C2×D4—44no—
1126C2×D4—44no—
1127C2×D4—44no—
1128C2×D4C2×#4114yes—
1129C22×C4—24no—
1130C22×C4—24no—
1131C22×C4—24no—
1132C22×C4—24no—
1133C22×C4—24no—
1134C22×C4—28no—
1135C22×C4—28no—
1136C22×C4—28no—
1137C22×C4—24no—
1138C22×C4—28no—
1139C22×C4—28no—
1140C22×C4—28no—
1141C22×C4—42no—
1142C22×C4—42no—
1143C22×C4—42no—
1144C22×C4—42no—
1145C22×C4—44no—
1146C22×C4—44no—
1147C22×C4—44no—
1148C22×C4—44no—
1149C22×C4—44no—
1150C22×C4—44no—
1151C22×C4—44no—
1152C22×C4—44no—
1153C22×C4—44no—
1154C22×C4—44no—
1155C22×C4—44no—
1156C22×C4—44no—
1157C22×C4—44no—
1158C22×C4—42no—
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×C4C2×#4118yes—
1168C22×C4C2512yes—
1169C22×C4C2512yes—
1170C22×C4C2512yes—
1171C22×C4C2512yes—
1172C22×C4C2511yescharacteristic
1173C22×C4C2512yes—
1174C22×C4C2512yes—
1175C22×C4C2512yes—
1176C22×C4C2512yes—
1177C22×C4C2512yes—
1178C22×C4C2512yes—
1179C22×C4C2514yes—
1180C22×C4C2512yes—
1181C22×C4C2514yes—
1182C22×C4C2514yes—
1183C22×C4C2514yes—
1184C22×C4C2511yescharacteristic
1185C22×C4C2512yes—
1186C22×C4C2511yescharacteristic
1187C22×C4C2511yescharacteristic
1188C22×C4C2512yes—
1189C22×C4C2511yescharacteristic
1190C22×C4C2511yescharacteristic
1191C22×C4C2512yes—
1192C22×C4C2511yescharacteristic
1193C4⋊C4—24no—
1194C4⋊C4—24no—
1195C4⋊C4—24no—
1196C4⋊C4—22no—
1197C4⋊C4—24no—
1198C4⋊C4—28no—
1199C4⋊C4—28no—
1200C4⋊C4—28no—
1201C4⋊C4—24no—
1202C4⋊C4—24no—
1203C4⋊C4—24no—
1204C4⋊C4—24no—
1205C4⋊C4—24no—
1206C4⋊C4—28no—
1207C4⋊C4—28no—
1208C4⋊C4—24no—
1209C4⋊C4—22no—
1210C4⋊C4—22no—
1211C4⋊C4—24no—
1212C4⋊C4—28no—
1213C4⋊C4—24no—
1214C4⋊C4—24no—
1215C4⋊C4—24no—
1216C4⋊C4—22no—
1217C4⋊C4—42no—
1218C4⋊C4—44no—
1219C4⋊C4—44no—
1220C4⋊C4—44no—
1221C4⋊C4—44no—
1222C4⋊C4—41no—
1223C4⋊C4—44no—
1224C4⋊C4—42no—
1225C4⋊C4—44no—
1226C4⋊C4—41no—
1227C4⋊C4—42no—
1228C4⋊C4—42no—
1229C4⋊C4—44no—
1230C4⋊C4—41no—
1231C4⋊C4—44no—
1232C4⋊C4—42no—
1233C4⋊C4—44no—
1234C4⋊C4—44no—
1235C4⋊C4—41no—
1236C4⋊C4—41no—
1237C4⋊C4—42no—
1238C4⋊C4—42no—
1239C4⋊C4—42no—
1240C4⋊C4—42no—
1241C4⋊C4—44no—
1242C4⋊C4—44no—
1243C4⋊C4—44no—
1244C4⋊C4—42no—
1245C4⋊C4—42no—
1246C4⋊C4—42no—
1247C4⋊C4—41no—
1248C4⋊C4C2×#4114yes—
1249C4⋊C4H(5,𝔽2)14yes—
1250C4⋊C42−1+414yes—
1251C22⋊C4—28no—
1252C22⋊C4—24no—
1253C22⋊C4—24no—
1254C22⋊C4—28no—
1255C22⋊C4—28no—
1256C22⋊C4—28no—
1257C22⋊C4—28no—
1258C22⋊C4—24no—
1259C22⋊C4—28no—
1260C22⋊C4—24no—
1261C22⋊C4—24no—
1262C22⋊C4—24no—
1263C22⋊C4—28no—
1264C22⋊C4—28no—
1265C22⋊C4—24no—
1266C22⋊C4—24no—
1267C22⋊C4—28no—
1268C22⋊C4—28no—
1269C22⋊C4—44no—
1270C22⋊C4—44no—
1271C22⋊C4—44no—
1272C22⋊C4—44no—
1273C22⋊C4—44no—
1274C22⋊C4—44no—
1275C22⋊C4—44no—
1276C22⋊C4—44no—
1277C22⋊C4—44no—
1278C22⋊C4—44no—
1279C22⋊C4—44no—
1280C22⋊C4—44no—
1281C22⋊C4—42no—
1282C22⋊C4—44no—
1283C22⋊C4—44no—
1284C22⋊C4—44no—
1285C22⋊C4—44no—
1286C22⋊C4—44no—
1287C22⋊C4—42no—
1288C22⋊C4—44no—
1289C22⋊C4—42no—
1290C22⋊C4—42no—
1291C22⋊C4—44no—
1292C22⋊C4—44no—
1293C22⋊C4—42no—
1294C22⋊C4—44no—
1295C22⋊C4—44no—
1296C22⋊C4—44no—
1297C22⋊C4—44no—
1298C22⋊C4—44no—
1299C22⋊C4—44no—
1300C22⋊C4—44no—
1301C22⋊C4—44no—
1302C22⋊C4—44no—
1303C22⋊C4—42no—
1304C22⋊C4—42no—
1305C22⋊C4—44no—
1306C22⋊C4—44no—
1307C22⋊C4C2×#4118yes—
1308C42—24no—
1309C42—24no—
1310C42—24no—
1311C42—22no—
1312C42—24no—
1313C42—24no—
1314C42—22no—
1315C42—24no—
1316C42—41no—
1317C42—42no—
1318C42—42no—
1319C42—42no—
1320C42—44no—
1321C42—44no—
1322C42—44no—
1323C42—44no—
1324C42—41no—
1325C42—41no—
1326C42—42no—
1327C42—42no—
1328C42—42no—
1329C42—44no—
1330C42C2×#4114yes—
1331C42H(5,𝔽2)14yes—
1332C23—22no—
1333C23—22no—
1334C23—22no—
1335C23—22no—
1336C23—22no—
1337C23—22no—
1338C23—24no—
1339C23—22no—
1340C23—24no—
1341C23—22no—
1342C23—24no—
1343C23—24no—
1344C23—22no—
1345C23—24no—
1346C23—24no—
1347C23—24no—
1348C23—24no—
1349C23—22no—
1350C23—24no—
1351C23—22no—
1352C23—24no—
1353C23—22no—
1354C23—24no—
1355C23—24no—
1356C23—24no—
1357C23—24no—
1358C23—22no—
1359C23C22×#4114yes—
1360C23C2611yescharacteristic
1361Q8—48no—
1362Q8—44no—
1363Q8—164no—
1364D4—28no—
1365D4—48no—
1366D4—48no—
1367D4—48no—
1368D4—48no—
1369D4—84no—
1370D4—88no—
1371D4—82no—
1372D4—84no—
1373D4—88no—
1374D4—88no—
1375D4—88no—
1376D4—88no—
1377D4—88no—
1378D4—88no—
1379D4—88no—
1380D4—88no—
1381D4—88no—
1382D4—164no—
1383D4—164no—
1384D4—164no—
1385C2×C4—21no—
1386C2×C4—22no—
1387C2×C4—21no—
1388C2×C4—22no—
1389C2×C4—21no—
1390C2×C4—21no—
1391C2×C4—21no—
1392C2×C4—21no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—21no—
1397C2×C4—21no—
1398C2×C4—21no—
1399C2×C4—22no—
1400C2×C4—21no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—22no—
1405C2×C4—22no—
1406C2×C4—24no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—22no—
1411C2×C4—22no—
1412C2×C4—22no—
1413C2×C4—22no—
1414C2×C4—24no—
1415C2×C4—24no—
1416C2×C4—24no—
1417C2×C4—24no—
1418C2×C4—24no—
1419C2×C4—22no—
1420C2×C4—24no—
1421C2×C4—22no—
1422C2×C4—22no—
1423C2×C4—21no—
1424C2×C4—22no—
1425C2×C4—22no—
1426C2×C4—22no—
1427C2×C4—22no—
1428C2×C4—22no—
1429C2×C4—21no—
1430C2×C4—22no—
1431C2×C4—21no—
1432C2×C4—24no—
1433C2×C4—22no—
1434C2×C4—22no—
1435C2×C4—22no—
1436C2×C4—24no—
1437C2×C4—22no—
1438C2×C4—24no—
1439C2×C4—22no—
1440C2×C4—22no—
1441C2×C4—22no—
1442C2×C4—24no—
1443C2×C4—24no—
1444C2×C4—22no—
1445C2×C4—22no—
1446C2×C4—22no—
1447C2×C4—22no—
1448C2×C4—22no—
1449C2×C4—48no—
1450C2×C4—48no—
1451C2×C4—48no—
1452C2×C4—88no—
1453C2×C4—84no—
1454C2×C4—88no—
1455C2×C4—88no—
1456C2×C4—88no—
1457C2×C4—88no—
1458C2×C4—88no—
1459C2×C4—88no—
1460C2×C4—164no—
1461C2×C4—164no—
1462C2×C4C22×#4112yes—
1463C2×C4C22×#4112yes—
1464C2×C4C22×#4114yes—
1465C2×C4C22×#4112yes—
1466C2×C4C2×H(5,𝔽2)12yes—
1467C2×C4C2×H(5,𝔽2)14yes—
1468C2×C4C2×H(5,𝔽2)12yes—
1469C2×C4C2×H(5,𝔽2)12yes—
1470C2×C4C2×H(5,𝔽2)12yes—
1471C2×C4C2×2−1+414yes—
1472C2×C4C2×2−1+412yes—
1473C22—24no—
1474C22—24no—
1475C22—24no—
1476C22—42no—
1477C22—42no—
1478C22—42no—
1479C22—42no—
1480C22—44no—
1481C22—44no—
1482C22—42no—
1483C22—42no—
1484C22—44no—
1485C22—44no—
1486C22—44no—
1487C22—44no—
1488C22—42no—
1489C22—44no—
1490C22—42no—
1491C22—44no—
1492C22—42no—
1493C22—44no—
1494C22—44no—
1495C22—44no—
1496C22—44no—
1497C22—42no—
1498C22—44no—
1499C22—42no—
1500C22—44no—
1501C22C23×#4111yescharacteristic
1502C22C22×H(5,𝔽2)11yescharacteristic
1503C22C22×H(5,𝔽2)11yescharacteristic
1504C22C22×2−1+411yescharacteristic
1505C22H(7,𝔽2)11yescharacteristic
1506C22H(7,𝔽2)11yescharacteristic
1507C22H(7,𝔽2)11yescharacteristic
1508C4—22no—
1509C4—22no—
1510C4—24no—
1511C4—22no—
1512C4—22no—
1513C4—24no—
1514C4—22no—
1515C4—24no—
1516C4—44no—
1517C4—42no—
1518C4—42no—
1519C4—42no—
1520C4—42no—
1521C4—41no—
1522C4—42no—
1523C4—42no—
1524C4—42no—
1525C4—42no—
1526C4—44no—
1527C4—42no—
1528C4—44no—
1529C4—42no—
1530C4—44no—
1531C4—42no—
1532C4#351114yes—
1533C2—44no—
1534C2—84no—
1535C2—82no—
1536C2—84no—
1537C2C2×#351111yescharacteristic
1538C2#6284611yescharacteristic
1539C2#6288011yescharacteristic
1540C2#6291211yescharacteristic
1541C2#6294411yescharacteristic
1542C2#6298611yescharacteristic
1543C2#6307011yescharacteristic
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. #59815C2semidirect
2. #59693C2semidirect
3. #52272C2semidirect
4. #50740C2semidirect
5. #49797C2semidirect
6. #47997C2semidirect
7. #47446C2semidirect
8. #45801C2semidirect
9. #45131C2semidirect
10. #45042C2semidirect
11. #45033C2semidirect
12. #43108C2semidirect
13. #42545C2semidirect
14. #42425C2semidirect
15. #42041C2semidirect
16. #40121C2semidirect
17. #39756C2semidirect
18. #39742C2semidirect
19. #39483C2semidirect
20. #39169C2semidirect
21. #38487C2semidirect
22. #38286C2semidirect
23. #37316C2semidirect
24. #36261C2semidirect
25. #35941C2semidirect
26. #35612C2semidirect
27. #35171C2semidirect
28. #34431C2semidirect
29. #34330C2semidirect
848. C4×D4#41semidirect

Maximal subgroups

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

subgroupindex
#598152
#596932
#522722
#507402
#497972
#479972
#474462
#458012
#451312
#450422
#450332
#431082
#425452
#424252
#420412
#401212
#397562
#397422
#394832
#391692
#384872
#382862
#373162
#362612
#359412
#356122
#351712
#344312
#343302