Finite Group Databasebeta

← #7718354

Subgroups — #7718354

Order 512.

4596 conjugacy classes of subgroups.

The subgroup lattice has 1445 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51772C214yesmaximal, complemented
2#51572C214yesmaximal, complemented
3#49621C214yesmaximal, complemented
4#47915C214yesmaximal, complemented
5#45434C211yesmaximal, characteristic, complemented
6#45429C211yesmaximal, characteristic, complemented
7#45395C212yesmaximal, complemented
8#45349C211yesmaximal, characteristic, complemented
9#45344C211yesmaximal, characteristic, complemented
10#45276C211yesmaximal, characteristic, complemented
11#45231C211yesmaximal, characteristic, complemented
12#45156C212yesmaximal, complemented
13#45153C212yesmaximal, complemented
14#45137C211yesmaximal, characteristic, complemented
15#45056C211yesmaximal, characteristic, complemented
16#44964C212yesmaximal, complemented
17#40231C214yesmaximal, complemented
18#40035C212yesmaximal, complemented
19#40028C212yesmaximal, complemented
20#38631C214yesmaximal, complemented
21#37237C214yesmaximal, complemented
22#36437C212yesmaximal
23#36405C212yesmaximal, complemented
24#35241C211yesmaximal, characteristic, complemented
25#35211C211yesmaximal, characteristic
26#35200C211yesmaximal, characteristic, complemented
27#35059C214yesmaximal, complemented
28#34595C211yesmaximal, characteristic, complemented
29#34392C211yesmaximal, characteristic, complemented
30#34373C211yesmaximal, characteristic, complemented
31C4⋊C4×#41C211yesmaximal, characteristic, complemented
32C2×#559C2212yes—
33C2×#556C2212yes—
34C2×#533C2211yescharacteristic
35C2×#529C2211yescharacteristic
36C2×C4×#41C2211yescharacteristic
37C2×C4×#41C2212yes—
38#2857C2212yes—
39#2855C2214yes—
40#2853C2214yes—
41#2852C2214yes—
42#2851C2214yes—
43#2850C2212yes—
44#2793C2214yes—
45#2792C2214yes—
46#2792C2214yes—
47#2791C2214yes—
48#2791C2214yes—
49#2790C2214yes—
50#2787C2214yes—
51#2787C2214yes—
52#2786C2214yes—
53#2783C2214yes—
54#2776C2214yes—
55#2774C2214yes—
56#2772C2214yes—
57#2770C2214yes—
58#2770C2214yes—
59#2768C2214yes—
60#2766C2214yes—
61#2765C2214yes—
62#2765C2214yes—
63#2764C2214yes—
64#2757C2214yes—
65#2755C2214yes—
66#2747C2214yes—
67#2747C2214yes—
68#2746C2214yes—
69#2744C2214yes—
70#2741C2214yes—
71#2739C2214yes—
72#2728C2214yes—
73#2722C2214yes—
74#2718C2214yes—
75#2717C2214yes—
76#2717C2214yes—
77#2715C2214yes—
78#2704C2214yes—
79#2698C2214yes—
80#2695C2214yes—
81#2690C2214yes—
82#2687C2214yes—
83#2680C2214yes—
84#2666C2212yes—
85#2666C2212yes—
86#2666C2212yes—
87#2666C2212yes—
88#2664C2212yes—
89#2664C2212yes—
90#2659C2212yes—
91#2655C2214yes—
92#2654C2214yes—
93#2646C2212yes—
94#2638C2212yes—
95#2638C2212yes—
96#2630C2214yes—
97#2627C2212yes—
98#2627C2212yes—
99#2609C2214yes—
100#2606C2214yes—
101#2602C2214yes—
102#2600C2214yes—
103#2600C2214yes—
104#2599C2212yes—
105#2599C2212yes—
106#2596C2214yes—
107#2594C2214yes—
108#2594C2214yes—
109#2590C2214yes—
110#2590C2214yes—
111#2588C2214yes—
112#2588C2214yes—
113#2588C2214yes—
114#2587C2214yes—
115#2586C2214yes—
116#2585C2214yes—
117#2585C2214yes—
118#2585C2214yes—
119#2582C2212yes—
120#2582C2212yes—
121#2582C2212yes—
122#2581C2212yes—
123#2581C2212yes—
124#2577C2214yes—
125#2573C2214yes—
126#2573C2214yes—
127#2570C2212yes—
128#2570C2212yes—
129#2570C2212yes—
130#2568C2211yescharacteristic
131#2567C2211yescharacteristic
132#2566C2211yescharacteristic
133#2565C2211yescharacteristic
134#2565C2212yes—
135#2563C2211yescharacteristic
136#2556C2214yes—
137#2552C2212yes—
138#2549C2214yes—
139#2547C2211yescharacteristic
140#2547C2211yescharacteristic
141#2546C2211yescharacteristic
142#2546C2212yes—
143#2546C2211yescharacteristic
144#2545C2212yes—
145#2545C2211yescharacteristic
146#2545C2212yes—
147#2544C2211yescharacteristic
148#2542C2211yescharacteristic
149#2538C2212yes—
150#2527C2214yes—
151#2525C2214yes—
152#2522C2214yes—
153#2514C2212yes—
154#2514C2212yes—
155#2513C2212yes—
156#2511C2212yes—
157#2500C2211yescharacteristic
158#2499C2211yescharacteristic
159#2499C2212yes—
160#2498C2214yes—
161#2498C2212yes—
162#2498C2212yes—
163#2493C2214yes—
164#2485C2214yes—
165#2485C2214yes—
166#2484C2214yes—
167#2478C2214yes—
168#2478C2214yes—
169#2478C2214yes—
170#2477C2214yes—
171#2475C2214yes—
172#2474C2214yes—
173#2474C2214yes—
174#2473C2214yes—
175#2470C2214yes—
176#2468C2214yes—
177#2468C2214yes—
178#2468C2214yes—
179#2461C2214yes—
180#2457C2214yes—
181#2449C2214yes—
182#2448C2212yes—
183#2447C2212yes—
184#2447C2212yes—
185#2447C2212yes—
186#2447C2212yes—
187#2446C2212yes—
188#2446C2212yes—
189#2445C2212yes—
190#2438C2214yes—
191#2432C2211yescharacteristic
192#2432C2212yes—
193#2431C2211yescharacteristic
194#2419C2214yes—
195#2419C2214yes—
196#2417C2214yes—
197#2415C2214yes—
198#2413C2214yes—
199#2402C2211yescharacteristic
200#2402C2211yescharacteristic
201#2402C2212yes—
202#2399C2211yescharacteristic
203#2399C2212yes—
204#2399C2211yescharacteristic
205#2378C2214yes—
206#2376C2214yes—
207#2367C2212yes—
208#2365C2212yes—
209#2365C2212yes—
210#2365C2212yes—
211#2363C2212yes—
212#2362C2212yes—
213#2362C2212yes—
214#2362C2212yes—
215#2357C2211yescharacteristic
216#2357C2212yes—
217#2356C2211yescharacteristic
218#2355C2214yes—
219#2355C2212yes—
220#2354C2212yes—
221#2351C2211yescharacteristic
222#2351C2211yescharacteristic
223#2351C2211yescharacteristic
224Q8×C4⋊C4C2212yes—
225Q8×C4⋊C4C2212yes—
226#2349C2211yescharacteristic
227#2349C2212yes—
228#2349C2211yescharacteristic
229#2349C2212yes—
230#2349C2211yescharacteristic
231D4×C4⋊C4C2214yes—
232D4×C4⋊C4C2212yes—
233#2347C2212yes—
234#2343C2212yes—
235#2336C2214yes—
236#2336C2214yes—
237#2334C2214yes—
238#2332C2214yes—
239#2331C2211yescharacteristic
240#2331C2211yescharacteristic
241#2330C2212yes—
242#2328C2211yescharacteristic
243#2327C2211yescharacteristic
244#2327C2211yescharacteristic
245#2327C2211yescharacteristic
246#2327C2212yes—
247#2326C2211yescharacteristic
248#2326C2212yes—
249#2326C2212yes—
250#2326C2211yescharacteristic
251#2323C2214yes—
252#2319C2212yes—
253#2318C2212yes—
254#2314C2214yes—
255C4×C22⋊Q8C2212yes—
256C4×C22⋊Q8C2212yes—
257C4×#123C2214yes—
258#2296C2214yes—
259#2296C2214yes—
260#2296C2212yes—
261#2285C2211yescharacteristic
262#2285C2212yes—
263#2283C2211yescharacteristic
264#2283C2211yescharacteristic
265C2×C4×C4⋊C4C2211yescharacteristic
266C2×C4×C4⋊C4C2212yes—
267C22×#41C2311yescharacteristic
268#559—48no—
269#556—48no—
270#533—28no—
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2312yes—
276C2×#127C2311yescharacteristic
277#529—28no—
278C2×#126C2312yes—
279C2×#126C2314yes—
280C2×#126C2314yes—
281C2×#125C2311yescharacteristic
282C2×#125C2312yes—
283C2×#125C2314yes—
284C2×#124C2311yescharacteristic
285C2×#124C2311yescharacteristic
286C2×#124C2311yescharacteristic
287C2×#124C2312yes—
288C2×#124C2312yes—
289C2×#124C2314yes—
290C2×#123C2312yes—
291C2×#123C2314yes—
292C2×#123C2314yes—
293C2×#123C2314yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2311yescharacteristic
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2312yes—
301C2×C22⋊Q8C2312yes—
302C2×#121C2311yescharacteristic
303C4×#41—28no—
304C4×#41—48no—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×D4C2311yescharacteristic
318C2×C4×D4C2311yescharacteristic
319C2×C4×D4C2312yes—
320C2×C4×D4C2311yescharacteristic
321C2×C4×D4C2312yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2314yes—
327C2×C4×D4C2314yes—
328C2×C4×D4C2314yes—
329C2×#117C2312yes—
330C2×#117C2312yes—
331C2×#117C2312yes—
332C2×#117C2311yescharacteristic
333C2×#117C2314yes—
334C2×#117C2312yes—
335C2×#117C2314yes—
336C2×#117C2314yes—
337C22×C4⋊C4C2312yes—
338C22×C4⋊C4C2314yes—
339C22×C42C2312yes—
340C22×C42C2312yes—
341C22×C42C2314yes—
342C22×C42C2311yescharacteristic
343#401C2314yes—
344#401C2314yes—
345#400C2312yes—
346#400C2312yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2312yes—
351#400C2312yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2312yes—
361#400C2312yes—
362#400C2312yes—
363#400C2312yes—
364#400C2312yes—
365#400C2312yes—
366#399C2314yes—
367#399C2312yes—
368#399C2312yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2312yes—
382#398C2312yes—
383#398C2312yes—
384#398C2312yes—
385#398C2314yes—
386#398C2312yes—
387#398C2314yes—
388#398C2312yes—
389#398C2314yes—
390#398C2312yes—
391#398C2312yes—
392#398C2312yes—
393#398C2312yes—
394#398C2314yes—
395#398C2312yes—
396#398C2312yes—
397#398C2312yes—
398#398C2312yes—
399#398C2312yes—
400#398C2312yes—
401#398C2312yes—
402#398C2314yes—
403#398C2312yes—
404#398C2312yes—
405#398C2312yes—
406#398C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#397C2314yes—
411#397C2314yes—
412#397C2314yes—
413#397C2312yes—
414#397C2312yes—
415#397C2312yes—
416#397C2314yes—
417#397C2314yes—
418#397C2314yes—
419#397C2314yes—
420#397C2312yes—
421#397C2314yes—
422#397C2314yes—
423#397C2314yes—
424#397C2314yes—
425#396C2314yes—
426#396C2314yes—
427#396C2314yes—
428#396C2314yes—
429#396C2314yes—
430#396C2314yes—
431#396C2314yes—
432#396C2314yes—
433#395C2312yes—
434#395C2312yes—
435#395C2314yes—
436#395C2314yes—
437#395C2312yes—
438#395C2312yes—
439#395C2312yes—
440#395C2312yes—
441#395C2312yes—
442#395C2312yes—
443#395C2312yes—
444#395C2312yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#393C2312yes—
453#393C2312yes—
454#392C2314yes—
455#391C2311yescharacteristic
456#391C2312yes—
457#391C2311yescharacteristic
458#391C2312yes—
459#391C2312yes—
460#391C2314yes—
461#391C2312yes—
462#391C2312yes—
463#391C2312yes—
464#391C2311yescharacteristic
465#391C2312yes—
466#391C2311yescharacteristic
467#391C2314yes—
468#391C2314yes—
469#391C2314yes—
470#391C2312yes—
471#391C2312yes—
472#391C2314yes—
473#391C2314yes—
474#391C2312yes—
475#391C2312yes—
476#390C2312yes—
477#390C2311yescharacteristic
478#390C2311yescharacteristic
479#390C2314yes—
480#390C2312yes—
481#390C2311yescharacteristic
482#390C2311yescharacteristic
483#390C2312yes—
484#389C2314yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2312yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#389C2314yes—
511#389C2312yes—
512#389C2314yes—
513#389C2314yes—
514#389C2312yes—
515#389C2314yes—
516#389C2312yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2312yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2312yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2312yes—
602#387C2312yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2312yes—
626#385C2314yes—
627#385C2312yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2312yes—
634#385C2312yes—
635#385C2314yes—
636#385C2314yes—
637#384C2311yescharacteristic
638#384C2312yes—
639#384C2311yescharacteristic
640#384C2312yes—
641#384C2314yes—
642#384C2312yes—
643#384C2314yes—
644#383C2314yes—
645#383C2314yes—
646#383C2312yes—
647#383C2312yes—
648#383C2311yescharacteristic
649#383C2311yescharacteristic
650#382C2312yes—
651#382C2312yes—
652#382C2311yescharacteristic
653#382C2311yescharacteristic
654#382C2314yes—
655#382C2312yes—
656#382C2311yescharacteristic
657#382C2311yescharacteristic
658#382C2312yes—
659#382C2312yes—
660#382C2312yes—
661#382C2312yes—
662#381C2314yes—
663#381C2314yes—
664#381C2311yescharacteristic
665#381C2311yescharacteristic
666#381C2312yes—
667#381C2314yes—
668#381C2314yes—
669#381C2312yes—
670#381C2314yes—
671#380C2314yes—
672#380C2312yes—
673#380C2312yes—
674#380C2312yes—
675#380C2312yes—
676#380C2314yes—
677#380C2314yes—
678#380C2314yes—
679#380C2314yes—
680#380C2314yes—
681#380C2314yes—
682#380C2314yes—
683#380C2312yes—
684#380C2312yes—
685#380C2312yes—
686#380C2312yes—
687#380C2312yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2311yescharacteristic
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2314yes—
703C4×C4⋊C4C2312yes—
704C4×C4⋊C4C2314yes—
705C4×C4⋊C4C2312yes—
706C4×C4⋊C4C2314yes—
707C4×C4⋊C4C2312yes—
708C4×C4⋊C4C2314yes—
709C4×C4⋊C4C2314yes—
710C4×C4⋊C4C2312yes—
711C4×C4⋊C4C2314yes—
712C4×C4⋊C4C2314yes—
713C4×C4⋊C4C2314yes—
714C4×C4⋊C4C2312yes—
715C4×C4⋊C4C2312yes—
716C4×C4⋊C4C2314yes—
717C4×C4⋊C4C2312yes—
718C4×C4⋊C4C2311yescharacteristic
719C4×C4⋊C4C2312yes—
720C4×C4⋊C4C2312yes—
721C4×C4⋊C4C2312yes—
722C4×C4⋊C4C2311yescharacteristic
723C4×C4⋊C4C2311yescharacteristic
724C4×C22⋊C4C2314yes—
725C4×C22⋊C4C2314yes—
726C4×C22⋊C4C2312yes—
727C4×C22⋊C4C2314yes—
728C4×C22⋊C4C2311yescharacteristic
729C4×C22⋊C4C2311yescharacteristic
730C4×C22⋊C4C2312yes—
731#376C2312yes—
732#376C2312yes—
733#376C2311yescharacteristic
734#376C2311yescharacteristic
735C2×#95C2312yes—
736C2×#95C2311yescharacteristic
737C2×#95C2311yescharacteristic
738C2×#95C2312yes—
739C2×#95C2312yes—
740C2×#41—24no—
741C2×#41—24no—
742C2×#41—24no—
743C22×Q8C2411yescharacteristic
744C22×Q8C2412yes—
745C22×Q8C2411yescharacteristic
746C22×Q8C2412yes—
747C22×Q8C2412yes—
748C22×Q8C2412yes—
749C22×D4C2412yes—
750C22×D4C2411yescharacteristic
751C22×D4C2411yescharacteristic
752C22×D4C2412yes—
753C22×D4C2414yes—
754C23×C4C2412yes—
755C23×C4C2414yes—
756C23×C4C2411yescharacteristic
757C23×C4C2412yes—
758C23×C4C2414yes—
759C23×C4C2412yes—
760C23×C4C2412yes—
761C23×C4C2412yes—
762C23×C4C2412yes—
763C23×C4C2414yes—
764C23×C4C2411yescharacteristic
765C23×C4C2411yescharacteristic
766C4⋊Q8—24no—
767C4⋊Q8—28no—
768C4⋊Q8—24no—
769C4⋊Q8—24no—
770C4⋊Q8—44no—
771#127—24no—
772#126—28no—
773#126—48no—
774#126—48no—
775#125—24no—
776#125—28no—
777#125—48no—
778#124—24no—
779#124—24no—
780#124—28no—
781#124—24no—
782#124—44no—
783#124—48no—
784#123—28no—
785#123—48no—
786#123—48no—
787#123—48no—
788C22⋊Q8—24no—
789C22⋊Q8—28no—
790C22⋊Q8—28no—
791C22⋊Q8—48no—
792C22⋊Q8—48no—
793C22⋊Q8—48no—
794C22⋊Q8—44no—
795C22⋊Q8—44no—
796#121—24no—
797C4×Q8—24no—
798C4×Q8—24no—
799C4×Q8—24no—
800C4×Q8—28no—
801C4×Q8—28no—
802C4×Q8—44no—
803C4×Q8—44no—
804C4×Q8—44no—
805C4×Q8—44no—
806C4×Q8—44no—
807C4×Q8—44no—
808C4×Q8—44no—
809C4×D4—28no—
810C4×D4—28no—
811C4×D4—28no—
812C4×D4—28no—
813C4×D4—28no—
814C4×D4—24no—
815C4×D4—24no—
816C4×D4—24no—
817C4×D4—44no—
818C4×D4—48no—
819C4×D4—48no—
820C4×D4—48no—
821#117—24no—
822#117—28no—
823#117—28no—
824#117—28no—
825#117—48no—
826#117—48no—
827#117—48no—
828#117—44no—
829C2×C4⋊C4—44no—
830C2×C4⋊C4—48no—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2411yescharacteristic
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2411yescharacteristic
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2412yes—
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×C42—28no—
935C2×C42—44no—
936C2×C42—48no—
937C2×C42#4118yes—
938C2×C42C2412yes—
939C2×C42C2412yes—
940C2×C42C2414yes—
941C2×C42C2412yes—
942C2×C42C2412yes—
943C2×C42C2412yes—
944C2×C42C2412yes—
945C2×C42C2412yes—
946C2×C42C2411yescharacteristic
947C2×C42C2411yescharacteristic
948C2×C42C2411yescharacteristic
949C2×C42C2412yes—
950C2×C42C2411yescharacteristic
951C2×C42C2414yes—
952C2×C42C2412yes—
953C2×C42C2414yes—
954C2×C42C2414yes—
955C2×C42C2414yes—
956C2×C42C2414yes—
957C2×C42C2414yes—
958C2×C42C2414yes—
959C2×C42C2414yes—
960C2×C42C2414yes—
961C2×C42C2414yes—
962C2×C42C2412yes—
963C2×C42C2411yescharacteristic
964C2×C42C2411yescharacteristic
965C2×C42C2411yescharacteristic
966C2×C42C2411yescharacteristic
967#95C2411yescharacteristic
968#95C2411yescharacteristic
969#95C2411yescharacteristic
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2411yescharacteristic
974#95C2411yescharacteristic
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2414yes—
979#95C2414yes—
980#95C2411yescharacteristic
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2414yes—
990#95C2412yes—
991#95C2412yes—
992#95C2411yescharacteristic
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2411yescharacteristic
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2412yes—
1019#95C2414yes—
1020#95C2412yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2412yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2412yes—
1029#95C2412yes—
1030#95C2412yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047C24C2512yes—
1048C24C2511yescharacteristic
1049C24C2512yes—
1050#41—232no—
1051C2×Q8—22no—
1052C2×Q8—22no—
1053C2×Q8—24no—
1054C2×Q8—24no—
1055C2×Q8—22no—
1056C2×Q8—24no—
1057C2×Q8—22no—
1058C2×Q8—22no—
1059C2×Q8—24no—
1060C2×Q8—24no—
1061C2×Q8—42no—
1062C2×Q8—42no—
1063C2×Q8—44no—
1064C2×Q8—42no—
1065C2×Q8—42no—
1066C2×Q8—42no—
1067C2×Q82−1+414yes—
1068C2×D4—24no—
1069C2×D4—24no—
1070C2×D4—24no—
1071C2×D4—28no—
1072C2×D4—22no—
1073C2×D4—22no—
1074C2×D4—22no—
1075C2×D4—24no—
1076C2×D4—22no—
1077C2×D4—22no—
1078C2×D4—44no—
1079C2×D4—44no—
1080C2×D4—44no—
1081C2×D4H(5,𝔽2)14yes—
1082C22×C4—24no—
1083C22×C4—24no—
1084C22×C4—22no—
1085C22×C4—24no—
1086C22×C4—22no—
1087C22×C4—28no—
1088C22×C4—28no—
1089C22×C4—24no—
1090C22×C4—28no—
1091C22×C4—24no—
1092C22×C4—24no—
1093C22×C4—24no—
1094C22×C4—42no—
1095C22×C4—44no—
1096C22×C4—42no—
1097C22×C4—44no—
1098C22×C4—42no—
1099C22×C4—42no—
1100C22×C4—44no—
1101C22×C4—42no—
1102C22×C4—44no—
1103C22×C4—44no—
1104C22×C4—42no—
1105C22×C4—44no—
1106C22×C4—42no—
1107C22×C4—44no—
1108C22×C4—44no—
1109C22×C4—44no—
1110C22×C4C2×#4114yes—
1111C22×C4C2×#4114yes—
1112C22×C4C2×#4114yes—
1113C22×C4C2512yes—
1114C22×C4C2512yes—
1115C22×C4C2512yes—
1116C22×C4C2512yes—
1117C22×C4C2512yes—
1118C22×C4C2512yes—
1119C22×C4C2512yes—
1120C22×C4C2512yes—
1121C22×C4C2512yes—
1122C22×C4C2514yes—
1123C22×C4C2512yes—
1124C22×C4C2514yes—
1125C22×C4C2514yes—
1126C22×C4C2512yes—
1127C22×C4C2512yes—
1128C22×C4C2512yes—
1129C22×C4C2514yes—
1130C22×C4C2512yes—
1131C22×C4C2512yes—
1132C22×C4C2512yes—
1133C22×C4C2511yescharacteristic
1134C22×C4C2511yescharacteristic
1135C22×C4C2511yescharacteristic
1136C22×C4C2511yescharacteristic
1137C22×C4C2511yescharacteristic
1138C22×C4C2512yes—
1139C22×C4C2512yes—
1140C22×C4C2511yescharacteristic
1141C4⋊C4—24no—
1142C4⋊C4—24no—
1143C4⋊C4—22no—
1144C4⋊C4—22no—
1145C4⋊C4—24no—
1146C4⋊C4—24no—
1147C4⋊C4—24no—
1148C4⋊C4—24no—
1149C4⋊C4—22no—
1150C4⋊C4—24no—
1151C4⋊C4—22no—
1152C4⋊C4—28no—
1153C4⋊C4—28no—
1154C4⋊C4—24no—
1155C4⋊C4—24no—
1156C4⋊C4—24no—
1157C4⋊C4—24no—
1158C4⋊C4—24no—
1159C4⋊C4—28no—
1160C4⋊C4—28no—
1161C4⋊C4—28no—
1162C4⋊C4—24no—
1163C4⋊C4—24no—
1164C4⋊C4—28no—
1165C4⋊C4—24no—
1166C4⋊C4—28no—
1167C4⋊C4—24no—
1168C4⋊C4—24no—
1169C4⋊C4—44no—
1170C4⋊C4—42no—
1171C4⋊C4—42no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—42no—
1175C4⋊C4—42no—
1176C4⋊C4—42no—
1177C4⋊C4—42no—
1178C4⋊C4—42no—
1179C4⋊C4—42no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—42no—
1184C4⋊C4—42no—
1185C4⋊C4—42no—
1186C4⋊C4—42no—
1187C4⋊C4—44no—
1188C4⋊C4—42no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—42no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—42no—
1196C4⋊C4—42no—
1197C4⋊C4—44no—
1198C4⋊C4—42no—
1199C4⋊C4—42no—
1200C4⋊C4—42no—
1201C4⋊C4—42no—
1202C4⋊C4—42no—
1203C4⋊C4—44no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4—44no—
1207C4⋊C4—44no—
1208C4⋊C4—44no—
1209C4⋊C4—44no—
1210C4⋊C4—44no—
1211C22⋊C4—24no—
1212C22⋊C4—28no—
1213C22⋊C4—24no—
1214C22⋊C4—28no—
1215C22⋊C4—28no—
1216C22⋊C4—28no—
1217C22⋊C4—28no—
1218C22⋊C4—28no—
1219C22⋊C4—24no—
1220C22⋊C4—24no—
1221C22⋊C4—24no—
1222C22⋊C4—24no—
1223C22⋊C4—24no—
1224C22⋊C4—24no—
1225C22⋊C4—28no—
1226C22⋊C4—28no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—42no—
1236C22⋊C4—42no—
1237C22⋊C4—44no—
1238C22⋊C4—42no—
1239C22⋊C4—42no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C42—24no—
1245C42—24no—
1246C42—24no—
1247C42—24no—
1248C42—28no—
1249C42—24no—
1250C42—24no—
1251C42—24no—
1252C42—22no—
1253C42—22no—
1254C42—22no—
1255C42—24no—
1256C42—22no—
1257C42—42no—
1258C42—42no—
1259C42—44no—
1260C42—44no—
1261C42—44no—
1262C42—44no—
1263C42—44no—
1264C42—44no—
1265C42—44no—
1266C42—44no—
1267C42—44no—
1268C42—44no—
1269C42C2×#4114yes—
1270C42C2×#4114yes—
1271C42C2×#4114yes—
1272C42C2×#4114yes—
1273C23—22no—
1274C23—21no—
1275C23—21no—
1276C23—22no—
1277C23—22no—
1278C23—24no—
1279C23—24no—
1280C23—22no—
1281C23—22no—
1282C23—22no—
1283C23—22no—
1284C23—24no—
1285C23—24no—
1286C23C22×#4112yes—
1287C23C2×H(5,𝔽2)14yes—
1288C23C2611yescharacteristic
1289Q8—28no—
1290Q8—44no—
1291Q8—48no—
1292Q8—84no—
1293Q8—84no—
1294Q8—84no—
1295D4—216no—
1296D4—28no—
1297D4—44no—
1298D4—84no—
1299D4—88no—
1300C2×C4—216no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—21no—
1304C2×C4—22no—
1305C2×C4—21no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—28no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—24no—
1327C2×C4—24no—
1328C2×C4—24no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—22no—
1340C2×C4—24no—
1341C2×C4—24no—
1342C2×C4—24no—
1343C2×C4—24no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—24no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—24no—
1355C2×C4—24no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—24no—
1360C2×C4—24no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—44no—
1369C2×C4—44no—
1370C2×C4—416no—
1371C2×C4—48no—
1372C2×C4—84no—
1373C2×C4—84no—
1374C2×C4—84no—
1375C2×C4—88no—
1376C2×C4—84no—
1377C2×C4—164no—
1378C2×C4C22×#4112yes—
1379C2×C4C22×#4112yes—
1380C2×C4C22×#4112yes—
1381C2×C4C22×#4112yes—
1382C2×C4C22×#4112yes—
1383C2×C4C22×#4112yes—
1384C2×C4C2×H(5,𝔽2)12yes—
1385C2×C4C2×2−1+414yes—
1386C2×C4C2×2−1+412yes—
1387C2×C4#58514yes—
1388C22—22no—
1389C22—24no—
1390C22—22no—
1391C22—22no—
1392C22—28no—
1393C22—42no—
1394C22—42no—
1395C22—42no—
1396C22—42no—
1397C22—44no—
1398C22—42no—
1399C22—42no—
1400C22—42no—
1401C22—44no—
1402C22—44no—
1403C22C23×#4111yescharacteristic
1404C22C22×H(5,𝔽2)11yescharacteristic
1405C22C22×2−1+411yescharacteristic
1406C22C2×#58512yes—
1407C222−1+612yes—
1408C4—22no—
1409C4—24no—
1410C4—22no—
1411C4—22no—
1412C4—22no—
1413C4—22no—
1414C4—24no—
1415C4—42no—
1416C4—44no—
1417C4—42no—
1418C4—42no—
1419C4—44no—
1420C4—42no—
1421C4—42no—
1422C4—44no—
1423C4—42no—
1424C4—42no—
1425C4—44no—
1426C4—42no—
1427C4—42no—
1428C4—42no—
1429C4—42no—
1430C4—42no—
1431C4—42no—
1432C4—42no—
1433C4—42no—
1434C4—42no—
1435C4#349214yes—
1436C2—42no—
1437C2—44no—
1438C2—82no—
1439C2C2×#349211yescharacteristic
1440C2#6281511yescharacteristic
1441C2#6286011yescharacteristic
1442C2#6289812yes—
1443C2#6295312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2431C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #51772C2semidirect
2. #51572C2semidirect
3. #49621C2semidirect
4. #47915C2semidirect
5. #45434C2semidirect
6. #45429C2semidirect
7. #45395C2semidirect
8. #45349C2semidirect
9. #45344C2semidirect
10. #45276C2semidirect
11. #45231C2semidirect
12. #45156C2semidirect
13. #45153C2semidirect
14. #45137C2semidirect
15. #45056C2semidirect
16. #44964C2semidirect
17. #40231C2semidirect
18. #40035C2semidirect
19. #40028C2semidirect
20. #38631C2semidirect
21. #37237C2semidirect
23. #36405C2semidirect
24. #35241C2semidirect
26. #35200C2semidirect
27. #35059C2semidirect
28. #34595C2semidirect
29. #34392C2semidirect
30. #34373C2semidirect
31. C4⋊C4×#41C2semidirect

Maximal subgroups

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

subgroupindex
#517722
#515722
#496212
#479152
#454342
#454292
#453952
#453492
#453442
#452762
#452312
#451562
#451532
#451372
#450562
#449642
#402312
#400352
#400282
#386312
#372372
#364372
#364052
#352412
#352112
#352002
#350592
#345952
#343922
#343732
C4⋊C4×#412