Finite Group Databasebeta

← #7711622

Subgroups — #7711622

Order 512.

4758 conjugacy classes of subgroups.

The subgroup lattice has 1492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59948C212yesmaximal, complemented
2#59941C212yesmaximal, complemented
3#59925C211yesmaximal, characteristic, complemented
4#59909C212yesmaximal, complemented
5#59908C211yesmaximal, characteristic, complemented
6#46332C212yesmaximal, complemented
7#46331C211yesmaximal, characteristic, complemented
8#46329C211yesmaximal, characteristic, complemented
9#46327C212yesmaximal, complemented
10#46325C212yesmaximal, complemented
11#40022C212yesmaximal, complemented
12#40020C212yesmaximal, complemented
13#39974C212yesmaximal, complemented
14#39972C212yesmaximal, complemented
15#38851C214yesmaximal, complemented
16#38850C214yesmaximal, complemented
17#38607C214yesmaximal, complemented
18#38605C214yesmaximal, complemented
19#37602C212yesmaximal, complemented
20#37262C212yesmaximal, complemented
21#37261C212yesmaximal, complemented
22#36638C212yesmaximal, complemented
23#36200C212yesmaximal, complemented
24#36199C212yesmaximal, complemented
25#36140C212yesmaximal, complemented
26#36139C212yesmaximal
27#35249C211yesmaximal, characteristic
28#35248C211yesmaximal, characteristic, complemented
29#35247C212yesmaximal, complemented
30#34521C212yesmaximal, complemented
31C2×C4×C4⋊Q8C211yesmaximal, characteristic, complemented
32C2×#563C2212yes—
33C2×#533C2211yescharacteristic
34C2×#532C2211yescharacteristic
35C22×C4⋊Q8C2211yescharacteristic
36C2×#529C2212yes—
37C22×C4×Q8C2211yescharacteristic
38C22×C4×Q8C2211yescharacteristic
39#2866C2214yes—
40#2865C2214yes—
41#2864C2212yes—
42#2863C2212yes—
43#2861C2212yes—
44#2860C2212yes—
45#2855C2212yes—
46#2855C2212yes—
47#2855C2212yes—
48#2854C2212yes—
49#2854C2212yes—
50#2854C2212yes—
51#2853C2214yes—
52#2852C2214yes—
53#2851C2212yes—
54#2850C2212yes—
55#2843C2212yes—
56#2823C2212yes—
57#2821C2214yes—
58#2809C2212yes—
59#2805C2214yes—
60#2800C2214yes—
61#2799C2212yes—
62#2795C2212yes—
63#2795C2214yes—
64#2792C2212yes—
65#2792C2214yes—
66#2791C2214yes—
67#2791C2214yes—
68#2790C2214yes—
69#2790C2214yes—
70#2790C2214yes—
71#2788C2214yes—
72#2787C2214yes—
73#2779C2214yes—
74#2777C2214yes—
75#2777C2214yes—
76#2775C2214yes—
77#2774C2214yes—
78#2773C2214yes—
79#2771C2214yes—
80#2768C2214yes—
81#2765C2214yes—
82#2745C2214yes—
83#2734C2212yes—
84#2731C2212yes—
85#2731C2212yes—
86#2729C2214yes—
87#2728C2212yes—
88#2716C2214yes—
89#2713C2214yes—
90#2707C2214yes—
91#2702C2214yes—
92#2677C2214yes—
93#2674C2214yes—
94#2667C2214yes—
95#2666C2214yes—
96#2654C2214yes—
97#2649C2214yes—
98#2637C2214yes—
99#2637C2214yes—
100#2634C2212yes—
101#2634C2212yes—
102#2632C2212yes—
103#2632C2212yes—
104#2612C2214yes—
105#2605C2214yes—
106#2592C2212yes—
107#2592C2212yes—
108#2587C2214yes—
109#2586C2212yes—
110#2586C2214yes—
111#2584C2212yes—
112#2584C2212yes—
113#2582C2212yes—
114#2582C2212yes—
115#2581C2212yes—
116#2581C2212yes—
117#2580C2212yes—
118#2580C2212yes—
119#2574C2214yes—
120#2572C2212yes—
121#2570C2212yes—
122#2570C2212yes—
123#2568C2211yescharacteristic
124#2568C2211yescharacteristic
125#2567C2211yescharacteristic
126#2567C2211yescharacteristic
127#2566C2212yes—
128#2565C2212yes—
129#2550C2212yes—
130#2550C2212yes—
131#2548C2211yescharacteristic
132#2548C2211yescharacteristic
133#2546C2211yescharacteristic
134#2546C2211yescharacteristic
135#2545C2212yes—
136#2544C2212yes—
137#2538C2212yes—
138#2538C2212yes—
139#2532C2214yes—
140#2529C2214yes—
141#2528C2214yes—
142#2527C2214yes—
143#2526C2214yes—
144#2525C2214yes—
145#2524C2214yes—
146#2524C2214yes—
147#2522C2214yes—
148#2522C2214yes—
149#2521C2214yes—
150#2519C2214yes—
151#2518C2214yes—
152#2515C2214yes—
153#2514C2212yes—
154#2513C2212yes—
155#2512C2212yes—
156#2511C2212yes—
157#2509C2212yes—
158#2508C2212yes—
159#2507C2214yes—
160#2507C2212yes—
161#2506C2212yes—
162#2505C2214yes—
163#2503C2212yes—
164#2501C2212yes—
165#2493C2214yes—
166#2488C2214yes—
167#2486C2214yes—
168#2484C2212yes—
169#2484C2214yes—
170#2484C2212yes—
171#2481C2214yes—
172#2477C2214yes—
173#2475C2214yes—
174#2474C2214yes—
175#2474C2214yes—
176#2473C2214yes—
177#2469C2214yes—
178#2468C2214yes—
179#2454C2212yes—
180#2453C2212yes—
181#2452C2212yes—
182#2451C2212yes—
183#2449C2214yes—
184#2448C2212yes—
185#2447C2212yes—
186#2446C2212yes—
187#2445C2212yes—
188#2443C2214yes—
189#2439C2214yes—
190#2438C2214yes—
191#2436C2212yes—
192#2434C2212yes—
193#2425C2214yes—
194#2419C2214yes—
195#2413C2214yes—
196#2413C2214yes—
197#2413C2214yes—
198#2413C2214yes—
199#2409C2214yes—
200#2406C2212yes—
201#2406C2214yes—
202#2406C2212yes—
203#2383C2214yes—
204#2381C2212yes—
205#2373C2214yes—
206#2372C2212yes—
207#2371C2214yes—
208#2370C2212yes—
209#2370C2212yes—
210#2369C2212yes—
211#2368C2214yes—
212#2367C2212yes—
213#2367C2212yes—
214#2362C2214yes—
215#2359C2214yes—
216#2359C2214yes—
217#2359C2214yes—
218#2357C2212yes—
219#2356C2212yes—
220#2351C2212yes—
221#2349C2212yes—
222#2343C2214yes—
223#2339C2214yes—
224#2335C2214yes—
225#2334C2214yes—
226#2330C2214yes—
227#2329C2214yes—
228#2327C2212yes—
229#2327C2212yes—
230#2326C2212yes—
231#2326C2212yes—
232#2323C2214yes—
233#2323C2214yes—
234C4×C4⋊Q8C2211yescharacteristic
235C4×C4⋊Q8C2211yescharacteristic
236C4×C4⋊Q8C2212yes—
237C4×C4⋊Q8C2212yes—
238C4×C4⋊Q8C2211yescharacteristic
239C4×C4⋊Q8C2211yescharacteristic
240C4×C4⋊Q8C2212yes—
241C4×C4⋊Q8C2212yes—
242C4×C4⋊Q8C2211yescharacteristic
243C4×C4⋊Q8C2211yescharacteristic
244C4×C4⋊Q8C2211yescharacteristic
245C4×C4⋊Q8C2211yescharacteristic
246C4×#125C2212yes—
247C4×#126C2214yes—
248C4×#124C2212yes—
249C4×C22⋊Q8C2212yes—
250C4×#123C2214yes—
251C4×#121C2212yes—
252#2298C2214yes—
253#2295C2212yes—
254C2×#391C2211yescharacteristic
255C2×#391C2211yescharacteristic
256#2293C2212yes—
257C2×#389C2212yes—
258C2×#389C2212yes—
259#2290C2214yes—
260#2285C2212yes—
261C2×#384C2211yescharacteristic
262#2283C2211yescharacteristic
263#2283C2211yescharacteristic
264C2×C4×C4⋊C4C2212yes—
265C2×C4×C4⋊C4C2212yes—
266C2×C43C2211yescharacteristic
267C22×#41C2312yes—
268C23×Q8C2311yescharacteristic
269C23×Q8C2311yescharacteristic
270#563—216no—
271#533—44no—
272#532—44no—
273C2×C4⋊Q8—28no—
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2312yes—
277C2×C4⋊Q8C2311yescharacteristic
278C2×C4⋊Q8C2311yescharacteristic
279C2×C4⋊Q8C2312yes—
280C2×C4⋊Q8C2311yescharacteristic
281C2×C4⋊Q8C2311yescharacteristic
282C2×C4⋊Q8C2312yes—
283C2×C4⋊Q8C2311yescharacteristic
284C2×C4⋊Q8C2311yescharacteristic
285C2×#127C2311yescharacteristic
286#529—48no—
287C2×#126C2314yes—
288C2×#126C2314yes—
289C2×#126C2314yes—
290C2×#125C2312yes—
291C2×#125C2314yes—
292C2×#125C2312yes—
293C2×#125C2312yes—
294C2×#124C2312yes—
295C2×#124C2312yes—
296C2×#124C2312yes—
297C2×#124C2312yes—
298C2×#124C2312yes—
299C2×#123C2314yes—
300C2×#123C2314yes—
301C2×#123C2314yes—
302C2×#123C2314yes—
303C2×#123C2314yes—
304C2×C22⋊Q8C2314yes—
305C2×C22⋊Q8C2314yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2314yes—
308C2×C22⋊Q8C2312yes—
309C2×#121C2312yes—
310C2×#121C2312yes—
311C2×C4×Q8—44no—
312C2×C4×Q8—44no—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2311yescharacteristic
315C2×C4×Q8C2311yescharacteristic
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2311yescharacteristic
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2311yescharacteristic
320C2×C4×Q8C2311yescharacteristic
321C2×C4×Q8C2311yescharacteristic
322C2×C4×Q8C2311yescharacteristic
323C2×C4×Q8C2312yes—
324C2×C4×Q8C2311yescharacteristic
325C2×C4×Q8C2311yescharacteristic
326C2×C4×Q8C2311yescharacteristic
327C2×C4×Q8C2311yescharacteristic
328C2×C4×Q8C2312yes—
329C2×C4×Q8C2312yes—
330C2×C4×Q8C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2312yes—
334C2×C4×D4C2314yes—
335C2×C4×D4C2314yes—
336C2×C4×D4C2312yes—
337C2×#117C2314yes—
338C2×#117C2314yes—
339C2×#117C2312yes—
340C2×#117C2314yes—
341C22×C4⋊C4C2312yes—
342C22×C4⋊C4C2312yes—
343C22×C4⋊C4C2311yescharacteristic
344C22×C4⋊C4C2311yescharacteristic
345C22×C4⋊C4C2311yescharacteristic
346C22×C4⋊C4C2312yes—
347C22×C4⋊C4C2311yescharacteristic
348C22×C4⋊C4C2312yes—
349C22×C4⋊C4C2312yes—
350C22×C42C2312yes—
351C22×C42C2311yescharacteristic
352C22×C42C2311yescharacteristic
353C22×C42C2311yescharacteristic
354C22×C42C2312yes—
355C22×C42C2311yescharacteristic
356C22×C42C2312yes—
357C22×C42C2311yescharacteristic
358#401C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2312yes—
362#400C2312yes—
363#400C2312yes—
364#400C2312yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#400C2314yes—
372#400C2314yes—
373#400C2314yes—
374#400C2314yes—
375#400C2314yes—
376#399C2314yes—
377#399C2314yes—
378#399C2314yes—
379#399C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2312yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2312yes—
398#398C2312yes—
399#398C2312yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#397C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#395C2314yes—
423#395C2314yes—
424#395C2312yes—
425#395C2312yes—
426#395C2312yes—
427#395C2312yes—
428#395C2314yes—
429#395C2314yes—
430#395C2314yes—
431#395C2314yes—
432#395C2314yes—
433#394C2312yes—
434#394C2314yes—
435#394C2312yes—
436#394C2312yes—
437#394C2312yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#393C2314yes—
442#393C2314yes—
443#393C2314yes—
444#393C2314yes—
445#393C2314yes—
446#391C2311yescharacteristic
447#391C2311yescharacteristic
448#391C2312yes—
449#391C2312yes—
450#391C2311yescharacteristic
451#391C2311yescharacteristic
452#391C2312yes—
453#391C2312yes—
454#391C2311yescharacteristic
455#391C2311yescharacteristic
456#391C2311yescharacteristic
457#391C2311yescharacteristic
458#391C2312yes—
459#391C2312yes—
460#391C2312yes—
461#391C2312yes—
462#391C2312yes—
463#391C2312yes—
464#391C2312yes—
465#391C2312yes—
466#391C2312yes—
467#391C2314yes—
468#391C2314yes—
469#391C2312yes—
470#391C2312yes—
471#391C2312yes—
472#391C2314yes—
473#391C2314yes—
474#391C2312yes—
475#391C2314yes—
476#391C2312yes—
477#390C2312yes—
478#390C2312yes—
479#390C2312yes—
480#390C2312yes—
481#390C2312yes—
482#390C2312yes—
483#390C2312yes—
484#390C2312yes—
485#390C2312yes—
486#390C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2312yes—
494#389C2312yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2312yes—
509#389C2312yes—
510#389C2312yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2314yes—
515#389C2314yes—
516#389C2314yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2314yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#389C2314yes—
526#389C2312yes—
527#389C2312yes—
528#389C2312yes—
529#389C2314yes—
530#389C2312yes—
531#389C2314yes—
532#389C2314yes—
533#389C2314yes—
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#388C2314yes—
550#388C2314yes—
551#388C2314yes—
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#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#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
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#384C2311yescharacteristic
647#384C2311yescharacteristic
648#384C2311yescharacteristic
649#384C2312yes—
650#384C2312yes—
651#384C2311yescharacteristic
652#384C2312yes—
653#384C2312yes—
654#384C2312yes—
655#384C2312yes—
656#383C2314yes—
657#383C2314yes—
658#383C2314yes—
659#383C2312yes—
660#383C2312yes—
661#382C2312yes—
662#382C2312yes—
663#382C2312yes—
664#382C2312yes—
665#382C2312yes—
666#382C2312yes—
667#382C2314yes—
668#382C2314yes—
669#382C2314yes—
670#381C2314yes—
671#381C2314yes—
672#381C2314yes—
673#381C2314yes—
674#381C2314yes—
675#381C2312yes—
676#381C2312yes—
677#380C2314yes—
678#380C2314yes—
679#380C2314yes—
680#380C2314yes—
681#380C2312yes—
682#380C2312yes—
683#380C2314yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2312yes—
704C4×C4⋊C4C2312yes—
705C4×C4⋊C4C2312yes—
706C4×C4⋊C4C2311yescharacteristic
707C4×C4⋊C4C2311yescharacteristic
708C4×C4⋊C4C2311yescharacteristic
709C4×C4⋊C4C2311yescharacteristic
710C4×C4⋊C4C2314yes—
711C4×C4⋊C4C2312yes—
712C4×C4⋊C4C2312yes—
713C4×C4⋊C4C2314yes—
714C4×C4⋊C4C2314yes—
715C4×C4⋊C4C2314yes—
716C4×C22⋊C4C2314yes—
717C4×C22⋊C4C2314yes—
718C4×C22⋊C4C2314yes—
719C4×C22⋊C4C2314yes—
720C4×C22⋊C4C2314yes—
721C4×C22⋊C4C2314yes—
722C4×C22⋊C4C2312yes—
723C4×C22⋊C4C2314yes—
724C4×C22⋊C4C2312yes—
725C4×C22⋊C4C2314yes—
726#376C2312yes—
727#376C2312yes—
728#376C2314yes—
729#376C2314yes—
730C2×#95C2314yes—
731C2×#95C2312yes—
732C2×#95C2312yes—
733C2×#95C2312yes—
734C2×#95C2312yes—
735C43C2311yescharacteristic
736C43C2311yescharacteristic
737C43C2311yescharacteristic
738C43C2312yes—
739C43C2312yes—
740C43C2311yescharacteristic
741C2×#41—44no—
742C2×#41—48no—
743C22×Q8—24no—
744C22×Q8—24no—
745C22×Q8—42no—
746C22×Q8—42no—
747C22×Q8—42no—
748C22×Q8—42no—
749C22×Q8C2412yes—
750C22×Q8C2412yes—
751C22×Q8C2411yescharacteristic
752C22×Q8C2411yescharacteristic
753C22×Q8C2411yescharacteristic
754C22×Q8C2411yescharacteristic
755C22×Q8C2412yes—
756C22×Q8C2412yes—
757C22×Q8C2411yescharacteristic
758C22×Q8C2411yescharacteristic
759C22×D4C2412yes—
760C22×D4C2414yes—
761C22×D4C2412yes—
762C22×D4C2412yes—
763C23×C4C2411yescharacteristic
764C23×C4C2412yes—
765C23×C4C2411yescharacteristic
766C23×C4C2411yescharacteristic
767C23×C4C2412yes—
768C23×C4C2411yescharacteristic
769C23×C4C2412yes—
770C23×C4C2411yescharacteristic
771C23×C4C2411yescharacteristic
772C23×C4C2412yes—
773C23×C4C2411yescharacteristic
774C23×C4C2414yes—
775C23×C4C2414yes—
776C23×C4C2414yes—
777C4⋊Q8—24no—
778C4⋊Q8—24no—
779C4⋊Q8—28no—
780C4⋊Q8—28no—
781C4⋊Q8—28no—
782C4⋊Q8—24no—
783C4⋊Q8—42no—
784C4⋊Q8—42no—
785C4⋊Q8—42no—
786C4⋊Q8—44no—
787C4⋊Q8#4118yescomplemented
788#127—42no—
789#126—216no—
790#126—216no—
791#126—48no—
792#125—216no—
793#125—28no—
794#125—44no—
795#125—44no—
796#124—28no—
797#124—28no—
798#124—44no—
799#124—44no—
800#124—44no—
801#123—216no—
802#123—48no—
803#123—48no—
804#123—48no—
805#123—48no—
806C22⋊Q8—216no—
807C22⋊Q8—28no—
808C22⋊Q8—216no—
809C22⋊Q8—44no—
810C22⋊Q8—48no—
811#121—28no—
812#121—44no—
813C4×Q8—28no—
814C4×Q8—42no—
815C4×Q8—44no—
816C4×Q8—42no—
817C4×Q8—42no—
818C4×Q8—42no—
819C4×Q8—42no—
820C4×Q8—42no—
821C4×Q8—44no—
822C4×Q8—42no—
823C4×Q8—42no—
824C4×Q8—42no—
825C4×Q8—42no—
826C4×Q8—42no—
827C4×Q8—42no—
828C4×Q8—44no—
829C4×Q8—44no—
830C4×Q8—44no—
831C4×D4—28no—
832C4×D4—44no—
833C4×D4—44no—
834C4×D4—44no—
835C4×D4—48no—
836C4×D4—48no—
837#117—48no—
838#117—48no—
839#117—48no—
840#117—44no—
841C2×C4⋊C4—28no—
842C2×C4⋊C4—28no—
843C2×C4⋊C4—44no—
844C2×C4⋊C4—44no—
845C2×C4⋊C4—42no—
846C2×C4⋊C4—42no—
847C2×C4⋊C4—42no—
848C2×C4⋊C4—44no—
849C2×C4⋊C4—42no—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2411yescharacteristic
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2411yescharacteristic
884C2×C4⋊C4C2411yescharacteristic
885C2×C4⋊C4C2411yescharacteristic
886C2×C4⋊C4C2411yescharacteristic
887C2×C4⋊C4C2411yescharacteristic
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2411yescharacteristic
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2411yescharacteristic
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2414yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2414yes—
912C2×C4⋊C4C2414yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2414yes—
915C2×C4⋊C4C2414yes—
916C2×C4⋊C4C2414yes—
917C2×C4⋊C4C2414yes—
918C2×C4⋊C4C2414yes—
919C2×C4⋊C4C2414yes—
920C2×C4⋊C4C2414yes—
921C2×C4⋊C4C2412yes—
922C2×C4⋊C4C2412yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
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×C42—24no—
951C2×C42—28no—
952C2×C42—24no—
953C2×C42—24no—
954C2×C42—24no—
955C2×C42—28no—
956C2×C42—42no—
957C2×C42—44no—
958C2×C42C2412yes—
959C2×C42C2412yes—
960C2×C42C2411yescharacteristic
961C2×C42C2411yescharacteristic
962C2×C42C2412yes—
963C2×C42C2411yescharacteristic
964C2×C42C2411yescharacteristic
965C2×C42C2411yescharacteristic
966C2×C42C2411yescharacteristic
967C2×C42C2411yescharacteristic
968C2×C42C2411yescharacteristic
969C2×C42C2411yescharacteristic
970C2×C42C2412yes—
971C2×C42C2411yescharacteristic
972C2×C42C2412yes—
973C2×C42C2411yescharacteristic
974C2×C42C2411yescharacteristic
975C2×C42C2414yes—
976C2×C42C2412yes—
977C2×C42C2412yes—
978C2×C42C2412yes—
979C2×C42C2411yescharacteristic
980C2×C42C2412yes—
981C2×C42C2412yes—
982C2×C42C2412yes—
983C2×C42C2414yes—
984C2×C42C2414yes—
985C2×C42C2414yes—
986C2×C42C2414yes—
987C2×C42C2414yes—
988C2×C42C2414yes—
989C2×C42C2412yes—
990C2×C42C2412yes—
991C2×C42C2411yescharacteristic
992C2×C42C2412yes—
993C2×C42C2412yes—
994C2×C42C2412yes—
995C2×C42C2412yes—
996C2×C42C2411yescharacteristic
997C2×C42C2411yescharacteristic
998C2×C42C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
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#95C2412yes—
1046#95C2414yes—
1047#95C2412yes—
1048#95C2412yes—
1049#95C2412yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2414yes—
1053#95C2414yes—
1054#95C2414yes—
1055#95C2414yes—
1056#95C2414yes—
1057#95C2414yes—
1058#95C2414yes—
1059#95C2414yes—
1060#95C2414yes—
1061#95C2414yes—
1062#95C2414yes—
1063#95C2414yes—
1064#95C2414yes—
1065C24C2514yes—
1066C24C2511yescharacteristic
1067#41—816no—
1068C2×Q8—22no—
1069C2×Q8—22no—
1070C2×Q8—24no—
1071C2×Q8—22no—
1072C2×Q8—22no—
1073C2×Q8—24no—
1074C2×Q8—24no—
1075C2×Q8—24no—
1076C2×Q8—24no—
1077C2×Q8—24no—
1078C2×Q8—22no—
1079C2×Q8—22no—
1080C2×Q8—41no—
1081C2×Q8—42no—
1082C2×Q8—41no—
1083C2×Q8—41no—
1084C2×Q8—41no—
1085C2×Q8—41no—
1086C2×Q8—41no—
1087C2×Q8—41no—
1088C2×Q8—41no—
1089C2×Q8—41no—
1090C2×Q8—41no—
1091C2×Q8—42no—
1092C2×Q8—42no—
1093C2×Q8—42no—
1094C2×Q8—44no—
1095C2×Q8—416no—
1096C2×Q8—416no—
1097C2×Q8C2×#4114yes—
1098C2×Q8C2×#4114yes—
1099C2×D4—28no—
1100C2×D4—28no—
1101C2×D4—28no—
1102C2×D4—24no—
1103C2×D4—24no—
1104C2×D4—24no—
1105C2×D4—24no—
1106C2×D4—42no—
1107C2×D4—42no—
1108C2×D4—42no—
1109C2×D4—44no—
1110C22×C4—22no—
1111C22×C4—24no—
1112C22×C4—24no—
1113C22×C4—22no—
1114C22×C4—24no—
1115C22×C4—24no—
1116C22×C4—22no—
1117C22×C4—22no—
1118C22×C4—22no—
1119C22×C4—24no—
1120C22×C4—22no—
1121C22×C4—24no—
1122C22×C4—22no—
1123C22×C4—22no—
1124C22×C4—24no—
1125C22×C4—24no—
1126C22×C4—24no—
1127C22×C4—24no—
1128C22×C4—24no—
1129C22×C4—24no—
1130C22×C4—22no—
1131C22×C4—22no—
1132C22×C4—24no—
1133C22×C4—24no—
1134C22×C4—28no—
1135C22×C4—28no—
1136C22×C4—42no—
1137C22×C4—41no—
1138C22×C4—41no—
1139C22×C4—42no—
1140C22×C4—44no—
1141C22×C4—44no—
1142C22×C4—44no—
1143C22×C4—44no—
1144C22×C4—44no—
1145C22×C4—44no—
1146C22×C4—44no—
1147C22×C4H(5,𝔽2)14yes—
1148C22×C4C2512yes—
1149C22×C4C2514yes—
1150C22×C4C2514yes—
1151C22×C4C2511yescharacteristic
1152C22×C4C2511yescharacteristic
1153C22×C4C2514yes—
1154C22×C4C2514yes—
1155C22×C4C2514yes—
1156C22×C4C2511yescharacteristic
1157C22×C4C2512yes—
1158C22×C4C2511yescharacteristic
1159C22×C4C2514yes—
1160C22×C4C2514yes—
1161C22×C4C2511yescharacteristic
1162C22×C4C2512yes—
1163C22×C4C2511yescharacteristic
1164C22×C4C2511yescharacteristic
1165C22×C4C2512yes—
1166C22×C4C2511yescharacteristic
1167C22×C4C2512yes—
1168C22×C4C2511yescharacteristic
1169C22×C4C2511yescharacteristic
1170C22×C4C2511yescharacteristic
1171C22×C4C2512yes—
1172C22×C4C2511yescharacteristic
1173C22×C4C2512yes—
1174C22×C4C2512yes—
1175C22×C4C2511yescharacteristic
1176C22×C4C2511yescharacteristic
1177C4⋊C4—24no—
1178C4⋊C4—24no—
1179C4⋊C4—24no—
1180C4⋊C4—24no—
1181C4⋊C4—24no—
1182C4⋊C4—24no—
1183C4⋊C4—28no—
1184C4⋊C4—28no—
1185C4⋊C4—28no—
1186C4⋊C4—28no—
1187C4⋊C4—28no—
1188C4⋊C4—28no—
1189C4⋊C4—28no—
1190C4⋊C4—24no—
1191C4⋊C4—24no—
1192C4⋊C4—24no—
1193C4⋊C4—24no—
1194C4⋊C4—28no—
1195C4⋊C4—28no—
1196C4⋊C4—28no—
1197C4⋊C4—24no—
1198C4⋊C4—24no—
1199C4⋊C4—28no—
1200C4⋊C4—42no—
1201C4⋊C4—42no—
1202C4⋊C4—42no—
1203C4⋊C4—42no—
1204C4⋊C4—42no—
1205C4⋊C4—42no—
1206C4⋊C4—42no—
1207C4⋊C4—42no—
1208C4⋊C4—42no—
1209C4⋊C4—42no—
1210C4⋊C4—41no—
1211C4⋊C4—41no—
1212C4⋊C4—41no—
1213C4⋊C4—41no—
1214C4⋊C4—41no—
1215C4⋊C4—42no—
1216C4⋊C4—41no—
1217C4⋊C4—41no—
1218C4⋊C4—41no—
1219C4⋊C4—41no—
1220C4⋊C4—41no—
1221C4⋊C4—41no—
1222C4⋊C4—41no—
1223C4⋊C4—42no—
1224C4⋊C4—42no—
1225C4⋊C4—41no—
1226C4⋊C4—41no—
1227C4⋊C4—44no—
1228C4⋊C4—44no—
1229C4⋊C4—44no—
1230C4⋊C4—44no—
1231C4⋊C4—42no—
1232C4⋊C4—42no—
1233C4⋊C4—44no—
1234C4⋊C4—42no—
1235C4⋊C4—44no—
1236C4⋊C4—44no—
1237C4⋊C4—42no—
1238C4⋊C4—44no—
1239C4⋊C4—44no—
1240C4⋊C4—44no—
1241C4⋊C4—44no—
1242C4⋊C4—44no—
1243C4⋊C4—44no—
1244C4⋊C4—44no—
1245C4⋊C4—44no—
1246C4⋊C4—44no—
1247C4⋊C4—44no—
1248C4⋊C4C2×#4118yes—
1249C4⋊C4C2×#4118yes—
1250C22⋊C4—28no—
1251C22⋊C4—28no—
1252C22⋊C4—28no—
1253C22⋊C4—28no—
1254C22⋊C4—28no—
1255C22⋊C4—28no—
1256C22⋊C4—28no—
1257C22⋊C4—28no—
1258C22⋊C4—28no—
1259C22⋊C4—28no—
1260C22⋊C4—28no—
1261C22⋊C4—28no—
1262C22⋊C4—28no—
1263C22⋊C4—44no—
1264C22⋊C4—44no—
1265C22⋊C4—44no—
1266C22⋊C4—44no—
1267C22⋊C4—44no—
1268C22⋊C4—44no—
1269C22⋊C4—44no—
1270C22⋊C4—44no—
1271C22⋊C4—44no—
1272C22⋊C4—44no—
1273C22⋊C4—44no—
1274C22⋊C4—44no—
1275C22⋊C4—44no—
1276C22⋊C4—44no—
1277C42—22no—
1278C42—24no—
1279C42—24no—
1280C42—24no—
1281C42—24no—
1282C42—22no—
1283C42—22no—
1284C42—24no—
1285C42—22no—
1286C42—22no—
1287C42—22no—
1288C42—22no—
1289C42—22no—
1290C42—22no—
1291C42—22no—
1292C42—24no—
1293C42—22no—
1294C42—24no—
1295C42—22no—
1296C42—22no—
1297C42—24no—
1298C42—24no—
1299C42—24no—
1300C42—28no—
1301C42—24no—
1302C42—41no—
1303C42—42no—
1304C42—42no—
1305C42—42no—
1306C42—42no—
1307C42—41no—
1308C42—44no—
1309C42—44no—
1310C42—44no—
1311C42—44no—
1312C42—44no—
1313C42—44no—
1314C42—42no—
1315C42—42no—
1316C42C2×#4114yes—
1317C422−1+418yes—
1318C23—21no—
1319C23—22no—
1320C23—21no—
1321C23—24no—
1322C23—24no—
1323C23—24no—
1324C23—24no—
1325C23—24no—
1326C23—24no—
1327C23—24no—
1328C23C2×H(5,𝔽2)12yes—
1329C23#58514yes—
1330C23C2611yescharacteristic
1331Q8—44no—
1332Q8—44no—
1333Q8—48no—
1334Q8—44no—
1335Q8—44no—
1336Q8—44no—
1337Q8—44no—
1338Q8—48no—
1339Q8—84no—
1340Q8—84no—
1341D4—416no—
1342D4—48no—
1343D4—84no—
1344D4—84no—
1345C2×C4—216no—
1346C2×C4—28no—
1347C2×C4—22no—
1348C2×C4—21no—
1349C2×C4—22no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—21no—
1353C2×C4—21no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—21no—
1361C2×C4—21no—
1362C2×C4—21no—
1363C2×C4—22no—
1364C2×C4—28no—
1365C2×C4—24no—
1366C2×C4—24no—
1367C2×C4—24no—
1368C2×C4—21no—
1369C2×C4—22no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—21no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—21no—
1380C2×C4—21no—
1381C2×C4—21no—
1382C2×C4—24no—
1383C2×C4—24no—
1384C2×C4—24no—
1385C2×C4—22no—
1386C2×C4—24no—
1387C2×C4—24no—
1388C2×C4—24no—
1389C2×C4—24no—
1390C2×C4—24no—
1391C2×C4—24no—
1392C2×C4—22no—
1393C2×C4—22no—
1394C2×C4—24no—
1395C2×C4—24no—
1396C2×C4—22no—
1397C2×C4—22no—
1398C2×C4—22no—
1399C2×C4—24no—
1400C2×C4—24no—
1401C2×C4—24no—
1402C2×C4—24no—
1403C2×C4—24no—
1404C2×C4—24no—
1405C2×C4—21no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—22no—
1411C2×C4—22no—
1412C2×C4—24no—
1413C2×C4—21no—
1414C2×C4—22no—
1415C2×C4—22no—
1416C2×C4—48no—
1417C2×C4—48no—
1418C2×C4—44no—
1419C2×C4—44no—
1420C2×C4—44no—
1421C2×C4—44no—
1422C2×C4—48no—
1423C2×C4—44no—
1424C2×C4—88no—
1425C2×C4—88no—
1426C2×C4—88no—
1427C2×C4C22×#4112yes—
1428C2×C4C22×#4112yes—
1429C2×C4C22×#4114yes—
1430C2×C4C22×#4112yes—
1431C2×C4C22×#4114yes—
1432C2×C4C2×H(5,𝔽2)12yes—
1433C2×C4C2×H(5,𝔽2)12yes—
1434C2×C4C2×2−1+414yes—
1435C2×C4C2×2−1+414yes—
1436C2×C4C2×2−1+414yes—
1437C2×C4#58512yes—
1438C22—22no—
1439C22—22no—
1440C22—24no—
1441C22—24no—
1442C22—44no—
1443C22—44no—
1444C22—44no—
1445C22—44no—
1446C22—44no—
1447C22—44no—
1448C22—44no—
1449C22#355114yes—
1450C22C23×#4111yescharacteristic
1451C22C22×H(5,𝔽2)11yescharacteristic
1452C22C22×2−1+412yes—
1453C22C2×#58512yes—
1454C22C2×#58511yescharacteristic
1455C4—22no—
1456C4—22no—
1457C4—22no—
1458C4—24no—
1459C4—22no—
1460C4—22no—
1461C4—24no—
1462C4—24no—
1463C4—24no—
1464C4—41no—
1465C4—42no—
1466C4—42no—
1467C4—41no—
1468C4—41no—
1469C4—41no—
1470C4—41no—
1471C4—41no—
1472C4—44no—
1473C4—44no—
1474C4—41no—
1475C4—42no—
1476C4—41no—
1477C4—44no—
1478C4—44no—
1479C4—44no—
1480C4—44no—
1481C4—42no—
1482C4—44no—
1483C4#354414yes—
1484C2—24no—
1485C2—84no—
1486C2C2×#355111yescharacteristic
1487C2C2×#354411yescharacteristic
1488C2#6277311yescharacteristic
1489C2#6278812yes—
1490C2#6283112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#532C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59948C2semidirect
2. #59941C2semidirect
3. #59925C2semidirect
4. #59909C2semidirect
5. #59908C2semidirect
6. #46332C2semidirect
7. #46331C2semidirect
8. #46329C2semidirect
9. #46327C2semidirect
10. #46325C2semidirect
11. #40022C2semidirect
12. #40020C2semidirect
13. #39974C2semidirect
14. #39972C2semidirect
15. #38851C2semidirect
16. #38850C2semidirect
17. #38607C2semidirect
18. #38605C2semidirect
19. #37602C2semidirect
20. #37262C2semidirect
21. #37261C2semidirect
22. #36638C2semidirect
23. #36200C2semidirect
24. #36199C2semidirect
25. #36140C2semidirect
28. #35248C2semidirect
29. #35247C2semidirect
30. #34521C2semidirect
31. C2×C4×C4⋊Q8C2semidirect
787. C4⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#599482
#599412
#599252
#599092
#599082
#463322
#463312
#463292
#463272
#463252
#400222
#400202
#399742
#399722
#388512
#388502
#386072
#386052
#376022
#372622
#372612
#366382
#362002
#361992
#361402
#361392
#352492
#352482
#352472
#345212
C2×C4×C4⋊Q82