Finite Group Databasebeta

← #8107651

Subgroups — #8107651

Order 512.

4462 conjugacy classes of subgroups.

The subgroup lattice has 1465 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53153C212yesmaximal, complemented
2#53033C211yesmaximal, characteristic, complemented
3#52989C211yesmaximal, characteristic, complemented
4#52955C214yesmaximal, complemented
5#52914C212yesmaximal, complemented
6#52913C212yesmaximal, complemented
7#45425C212yesmaximal, complemented
8#45369C211yesmaximal, characteristic, complemented
9#45364C211yesmaximal, characteristic, complemented
10#44858C214yesmaximal, complemented
11#43342C212yesmaximal, complemented
12#43289C212yesmaximal, complemented
13#42821C212yesmaximal, complemented
14#42700C212yesmaximal, complemented
15#42523C212yesmaximal, complemented
16#42493C212yesmaximal, complemented
17#42382C212yesmaximal, complemented
18#42369C212yesmaximal, complemented
19#42344C212yesmaximal, complemented
20#42337C212yesmaximal, complemented
21#41532C214yesmaximal, complemented
22#40838C214yesmaximal, complemented
23#36177C212yesmaximal, complemented
24#36176C212yesmaximal, complemented
25#36140C212yesmaximal, complemented
26#36139C212yesmaximal
27#35270C212yesmaximal, complemented
28#35249C211yesmaximal, characteristic
29#35248C211yesmaximal, characteristic, complemented
30#35111C212yesmaximal, complemented
31C2×#2399C211yesmaximal, characteristic, complemented
32C2×#533C2211yescharacteristic
33C2×#532C2211yescharacteristic
34C2×#529C2212yes—
35C22×C4×Q8C2211yescharacteristic
36C22×C4×Q8C2211yescharacteristic
37#2857C2212yes—
38#2855C2212yes—
39#2855C2212yes—
40#2855C2212yes—
41#2854C2212yes—
42#2854C2212yes—
43#2854C2212yes—
44#2850C2212yes—
45#2844C2212yes—
46#2844C2214yes—
47#2843C2212yes—
48#2841C2214yes—
49#2838C2214yes—
50#2838C2214yes—
51#2838C2214yes—
52#2838C2214yes—
53#2835C2214yes—
54#2833C2214yes—
55#2832C2214yes—
56#2832C2212yes—
57#2830C2212yes—
58#2827C2214yes—
59#2811C2212yes—
60#2807C2214yes—
61#2806C2214yes—
62#2794C2212yes—
63#2792C2212yes—
64#2792C2214yes—
65#2789C2212yes—
66#2785C2212yes—
67#2784C2212yes—
68#2781C2214yes—
69#2774C2214yes—
70#2774C2214yes—
71#2773C2214yes—
72#2770C2214yes—
73#2768C2214yes—
74#2765C2214yes—
75#2764C2214yes—
76#2763C2214yes—
77#2763C2214yes—
78#2763C2214yes—
79#2763C2214yes—
80#2762C2214yes—
81#2759C2214yes—
82#2755C2214yes—
83#2754C2214yes—
84#2746C2214yes—
85#2742C2214yes—
86#2742C2214yes—
87#2741C2214yes—
88#2738C2214yes—
89#2737C2214yes—
90#2729C2214yes—
91#2728C2212yes—
92#2724C2212yes—
93#2717C2214yes—
94#2674C2214yes—
95#2666C2214yes—
96#2666C2214yes—
97#2653C2214yes—
98#2652C2214yes—
99#2650C2214yes—
100#2647C2212yes—
101#2646C2214yes—
102#2645C2212yes—
103#2644C2212yes—
104#2640C2212yes—
105#2634C2212yes—
106#2634C2212yes—
107#2632C2214yes—
108#2632C2212yes—
109#2632C2212yes—
110#2628C2214yes—
111#2623C2214yes—
112#2614C2214yes—
113#2609C2212yes—
114#2604C2214yes—
115#2604C2214yes—
116#2599C2214yes—
117#2599C2214yes—
118#2593C2212yes—
119#2592C2212yes—
120#2592C2212yes—
121#2589C2214yes—
122#2589C2214yes—
123#2586C2212yes—
124#2584C2212yes—
125#2584C2212yes—
126#2582C2212yes—
127#2581C2212yes—
128#2581C2212yes—
129#2581C2212yes—
130#2581C2212yes—
131#2580C2212yes—
132#2580C2212yes—
133#2580C2212yes—
134#2580C2212yes—
135#2571C2212yes—
136#2571C2212yes—
137#2570C2214yes—
138#2568C2211yescharacteristic
139#2568C2212yes—
140#2568C2211yescharacteristic
141#2567C2211yescharacteristic
142#2567C2211yescharacteristic
143#2563C2212yes—
144#2550C2212yes—
145#2550C2212yes—
146#2548C2211yescharacteristic
147#2548C2211yescharacteristic
148#2546C2211yescharacteristic
149#2546C2211yescharacteristic
150#2545C2212yes—
151#2544C2212yes—
152#2533C2214yes—
153#2533C2214yes—
154#2532C2214yes—
155#2532C2214yes—
156#2532C2214yes—
157#2530C2214yes—
158#2529C2214yes—
159#2527C2214yes—
160#2521C2214yes—
161#2519C2214yes—
162#2515C2214yes—
163#2514C2212yes—
164#2514C2214yes—
165#2514C2212yes—
166#2513C2212yes—
167#2513C2212yes—
168#2510C2214yes—
169#2509C2212yes—
170#2509C2212yes—
171#2508C2212yes—
172#2508C2212yes—
173#2505C2214yes—
174#2505C2214yes—
175#2503C2214yes—
176#2503C2212yes—
177#2501C2212yes—
178#2495C2214yes—
179#2493C2214yes—
180#2493C2214yes—
181#2488C2214yes—
182#2488C2214yes—
183#2488C2214yes—
184#2488C2214yes—
185#2486C2214yes—
186#2484C2212yes—
187#2484C2212yes—
188#2475C2214yes—
189#2474C2214yes—
190#2474C2214yes—
191#2469C2214yes—
192#2468C2214yes—
193#2458C2214yes—
194#2454C2212yes—
195#2453C2212yes—
196#2452C2212yes—
197#2451C2212yes—
198#2451C2214yes—
199#2450C2214yes—
200#2449C2214yes—
201#2448C2212yes—
202#2447C2212yes—
203#2446C2212yes—
204#2445C2212yes—
205#2443C2214yes—
206#2438C2214yes—
207#2436C2212yes—
208#2434C2212yes—
209#2425C2214yes—
210#2419C2214yes—
211#2413C2214yes—
212#2406C2214yes—
213#2406C2212yes—
214#2406C2212yes—
215#2399C2212yes—
216#2399C2211yescharacteristic
217#2399C2211yescharacteristic
218#2399C2212yes—
219#2399C2211yescharacteristic
220#2399C2211yescharacteristic
221#2399C2211yescharacteristic
222#2399C2211yescharacteristic
223#2399C2211yescharacteristic
224#2399C2211yescharacteristic
225#2399C2212yes—
226#2399C2212yes—
227C2×#398C2211yescharacteristic
228C2×#398C2212yes—
229C2×#398C2211yescharacteristic
230C2×#395C2212yes—
231C2×#395C2211yescharacteristic
232C2×#395C2211yescharacteristic
233#2369C2212yes—
234#2367C2212yes—
235#2367C2212yes—
236#2365C2212yes—
237#2362C2214yes—
238#2360C2214yes—
239#2359C2214yes—
240#2359C2214yes—
241#2356C2214yes—
242#2355C2212yes—
243#2354C2212yes—
244#2352C2214yes—
245#2351C2212yes—
246#2349C2212yes—
247#2346C2214yes—
248#2339C2214yes—
249#2331C2212yes—
250#2327C2212yes—
251#2327C2212yes—
252#2326C2212yes—
253#2326C2212yes—
254#2326C2212yes—
255#2322C2214yes—
256#2322C2214yes—
257#2320C2212yes—
258#2319C2212yes—
259C4×C22⋊Q8C2212yes—
260C4×#121C2212yes—
261#2283C2212yes—
262#2283C2211yescharacteristic
263#2283C2211yescharacteristic
264C2×C4×C4⋊C4C2212yes—
265C2×C4×C4⋊C4C2212yes—
266C2×#376C2211yescharacteristic
267C22×#41C2312yes—
268C23×Q8C2311yescharacteristic
269C23×Q8C2311yescharacteristic
270#533—44no—
271#532—44no—
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2312yes—
277C2×C4⋊Q8C2311yescharacteristic
278C2×#127C2311yescharacteristic
279#529—48no—
280C2×#126C2314yes—
281C2×#125C2312yes—
282C2×#125C2312yes—
283C2×#124C2312yes—
284C2×#124C2312yes—
285C2×#124C2312yes—
286C2×#124C2312yes—
287C2×#124C2312yes—
288C2×#123C2314yes—
289C2×#123C2314yes—
290C2×#123C2314yes—
291C2×#123C2314yes—
292C2×#123C2314yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2312yes—
297C2×#121C2312yes—
298C2×#121C2312yes—
299C2×C4×Q8—44no—
300C2×C4×Q8—44no—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2311yescharacteristic
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2314yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2311yescharacteristic
315C2×C4×Q8C2311yescharacteristic
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2311yescharacteristic
319C2×C4×Q8C2311yescharacteristic
320C2×C4×D4C2312yes—
321C2×C4×D4C2314yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2314yes—
326C2×#117C2314yes—
327C2×#117C2314yes—
328C2×#117C2312yes—
329C22×C4⋊C4C2311yescharacteristic
330C22×C4⋊C4C2312yes—
331C22×C4⋊C4C2312yes—
332C22×C4⋊C4C2312yes—
333C22×C4⋊C4C2311yescharacteristic
334C22×C4⋊C4C2311yescharacteristic
335C22×C4⋊C4C2312yes—
336C22×C4⋊C4C2312yes—
337C22×C4⋊C4C2311yescharacteristic
338C22×C42C2312yes—
339C22×C42C2311yescharacteristic
340C22×C42C2311yescharacteristic
341C22×C42C2312yes—
342C22×C42C2311yescharacteristic
343#401C2314yes—
344#401C2314yes—
345#401C2314yes—
346#400C2312yes—
347#400C2312yes—
348#400C2314yes—
349#400C2312yes—
350#400C2312yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#400C2314yes—
372#400C2314yes—
373#400C2314yes—
374#400C2314yes—
375#399C2314yes—
376#399C2314yes—
377#399C2314yes—
378#399C2314yes—
379#399C2314yes—
380#399C2314yes—
381#398C2312yes—
382#398C2314yes—
383#398C2312yes—
384#398C2312yes—
385#398C2312yes—
386#398C2314yes—
387#398C2314yes—
388#398C2311yescharacteristic
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2312yes—
394#398C2314yes—
395#398C2314yes—
396#398C2311yescharacteristic
397#398C2314yes—
398#398C2311yescharacteristic
399#398C2312yes—
400#398C2312yes—
401#398C2312yes—
402#398C2312yes—
403#398C2312yes—
404#398C2311yescharacteristic
405#398C2311yescharacteristic
406#398C2311yescharacteristic
407#398C2312yes—
408#398C2312yes—
409#398C2312yes—
410#398C2311yescharacteristic
411#398C2312yes—
412#398C2312yes—
413#398C2311yescharacteristic
414#398C2312yes—
415#398C2314yes—
416#397C2314yes—
417#397C2314yes—
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#397C2314yes—
422#397C2314yes—
423#397C2314yes—
424#397C2314yes—
425#397C2314yes—
426#397C2314yes—
427#397C2314yes—
428#397C2314yes—
429#397C2314yes—
430#396C2314yes—
431#396C2314yes—
432#396C2314yes—
433#396C2314yes—
434#396C2314yes—
435#395C2312yes—
436#395C2312yes—
437#395C2312yes—
438#395C2312yes—
439#395C2311yescharacteristic
440#395C2312yes—
441#395C2311yescharacteristic
442#395C2314yes—
443#395C2311yescharacteristic
444#395C2314yes—
445#395C2314yes—
446#395C2314yes—
447#395C2314yes—
448#395C2314yes—
449#395C2312yes—
450#395C2311yescharacteristic
451#395C2312yes—
452#395C2314yes—
453#395C2314yes—
454#395C2314yes—
455#395C2312yes—
456#395C2312yes—
457#395C2312yes—
458#395C2312yes—
459#395C2312yes—
460#395C2312yes—
461#395C2312yes—
462#395C2311yescharacteristic
463#395C2312yes—
464#395C2312yes—
465#395C2311yescharacteristic
466#395C2311yescharacteristic
467#395C2311yescharacteristic
468#394C2312yes—
469#394C2314yes—
470#394C2314yes—
471#394C2312yes—
472#394C2312yes—
473#394C2314yes—
474#394C2314yes—
475#394C2312yes—
476#393C2314yes—
477#393C2314yes—
478#393C2314yes—
479#393C2314yes—
480#393C2314yes—
481#393C2314yes—
482#393C2314yes—
483#393C2314yes—
484#393C2314yes—
485#393C2314yes—
486#393C2314yes—
487#391C2312yes—
488#391C2312yes—
489#391C2312yes—
490#391C2312yes—
491#391C2312yes—
492#391C2312yes—
493#391C2312yes—
494#391C2312yes—
495#391C2312yes—
496#391C2314yes—
497#391C2314yes—
498#391C2312yes—
499#391C2312yes—
500#391C2314yes—
501#391C2314yes—
502#391C2312yes—
503#391C2314yes—
504#391C2314yes—
505#391C2312yes—
506#391C2314yes—
507#391C2314yes—
508#391C2314yes—
509#391C2314yes—
510#391C2314yes—
511#391C2312yes—
512#390C2312yes—
513#390C2312yes—
514#390C2312yes—
515#390C2312yes—
516#390C2312yes—
517#390C2312yes—
518#390C2312yes—
519#390C2312yes—
520#390C2312yes—
521#390C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2312yes—
525#389C2312yes—
526#389C2314yes—
527#389C2314yes—
528#389C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2314yes—
532#389C2314yes—
533#389C2312yes—
534#389C2312yes—
535#389C2312yes—
536#389C2314yes—
537#389C2314yes—
538#389C2314yes—
539#389C2312yes—
540#389C2312yes—
541#389C2312yes—
542#389C2312yes—
543#389C2314yes—
544#389C2314yes—
545#389C2314yes—
546#389C2314yes—
547#389C2314yes—
548#389C2314yes—
549#389C2314yes—
550#389C2314yes—
551#389C2312yes—
552#389C2312yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
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#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#384C2312yes—
648#384C2312yes—
649#384C2312yes—
650#383C2314yes—
651#383C2314yes—
652#383C2314yes—
653#383C2314yes—
654#383C2312yes—
655#383C2312yes—
656#382C2312yes—
657#382C2312yes—
658#382C2312yes—
659#382C2312yes—
660#382C2312yes—
661#382C2312yes—
662#382C2314yes—
663#382C2314yes—
664#382C2314yes—
665#382C2314yes—
666#382C2312yes—
667#382C2314yes—
668#382C2314yes—
669#382C2314yes—
670#381C2314yes—
671#381C2314yes—
672#381C2314yes—
673#381C2314yes—
674#381C2314yes—
675#381C2314yes—
676#381C2312yes—
677#381C2312yes—
678#380C2314yes—
679#380C2314yes—
680#380C2314yes—
681#380C2314yes—
682#380C2314yes—
683#380C2314yes—
684#380C2312yes—
685#380C2312yes—
686#380C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2314yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2312yes—
704C4×C4⋊C4C2314yes—
705C4×C4⋊C4C2312yes—
706C4×C4⋊C4C2312yes—
707C4×C4⋊C4C2312yes—
708C4×C4⋊C4C2312yes—
709C4×C4⋊C4C2312yes—
710C4×C4⋊C4C2312yes—
711C4×C4⋊C4C2312yes—
712C4×C4⋊C4C2312yes—
713C4×C4⋊C4C2312yes—
714C4×C4⋊C4C2312yes—
715C4×C22⋊C4C2314yes—
716C4×C22⋊C4C2314yes—
717C4×C22⋊C4C2314yes—
718C4×C22⋊C4C2314yes—
719C4×C22⋊C4C2312yes—
720C4×C22⋊C4C2314yes—
721C4×C22⋊C4C2312yes—
722#376C2312yes—
723#376C2311yescharacteristic
724#376C2312yes—
725#376C2312yes—
726#376C2314yes—
727#376C2311yescharacteristic
728#376C2312yes—
729#376C2311yescharacteristic
730#376C2311yescharacteristic
731C2×#95C2312yes—
732C2×#95C2314yes—
733C2×#95C2312yes—
734C2×#95C2312yes—
735C2×#95C2312yes—
736C2×#95C2311yescharacteristic
737C2×#95C2312yes—
738C2×#95C2311yescharacteristic
739C2×#41—44no—
740C2×#41—48no—
741C22×Q8—42no—
742C22×Q8—42no—
743C22×Q8—44no—
744C22×Q8—42no—
745C22×Q8—42no—
746C22×Q8C2412yes—
747C22×Q8C2411yescharacteristic
748C22×Q8C2411yescharacteristic
749C22×Q8C2411yescharacteristic
750C22×Q8C2412yes—
751C22×Q8C2414yes—
752C22×Q8C2411yescharacteristic
753C22×Q8C2411yescharacteristic
754C22×Q8C2412yes—
755C22×Q8C2411yescharacteristic
756C22×Q8C2412yes—
757C22×D4C2412yes—
758C22×D4C2414yes—
759C22×D4C2412yes—
760C22×D4C2412yes—
761C23×C4C2411yescharacteristic
762C23×C4C2411yescharacteristic
763C23×C4C2411yescharacteristic
764C23×C4C2412yes—
765C23×C4C2411yescharacteristic
766C23×C4C2411yescharacteristic
767C23×C4C2412yes—
768C23×C4C2412yes—
769C23×C4C2411yescharacteristic
770C23×C4C2412yes—
771C23×C4C2411yescharacteristic
772C23×C4C2414yes—
773C23×C4C2414yes—
774C23×C4C2414yes—
775C4⋊Q8—28no—
776C4⋊Q8—42no—
777C4⋊Q8—42no—
778C4⋊Q8—44no—
779C4⋊Q8—42no—
780C4⋊Q8—44no—
781#127—42no—
782#126—48no—
783#125—44no—
784#125—44no—
785#124—28no—
786#124—44no—
787#124—44no—
788#124—44no—
789#124—44no—
790#123—48no—
791#123—48no—
792#123—48no—
793#123—48no—
794#123—48no—
795C22⋊Q8—28no—
796C22⋊Q8—48no—
797C22⋊Q8—44no—
798C22⋊Q8—48no—
799#121—28no—
800#121—44no—
801C4×Q8—28no—
802C4×Q8—42no—
803C4×Q8—44no—
804C4×Q8—42no—
805C4×Q8—42no—
806C4×Q8—42no—
807C4×Q8—42no—
808C4×Q8—42no—
809C4×Q8—44no—
810C4×Q8—42no—
811C4×Q8—42no—
812C4×Q8—42no—
813C4×Q8—42no—
814C4×Q8—42no—
815C4×Q8—42no—
816C4×Q8—48no—
817C4×Q8—44no—
818C4×Q8—44no—
819C4×Q8—44no—
820C4×D4—28no—
821C4×D4—44no—
822C4×D4—44no—
823C4×D4—44no—
824C4×D4—48no—
825C4×D4—48no—
826#117—48no—
827#117—48no—
828#117—44no—
829C2×C4⋊C4—44no—
830C2×C4⋊C4—44no—
831C2×C4⋊C4—44no—
832C2×C4⋊C4—44no—
833C2×C4⋊C4—42no—
834C2×C4⋊C4—42no—
835C2×C4⋊C4—42no—
836C2×C4⋊C4—44no—
837C2×C4⋊C4—42no—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2411yescharacteristic
856C2×C4⋊C4C2411yescharacteristic
857C2×C4⋊C4C2411yescharacteristic
858C2×C4⋊C4C2411yescharacteristic
859C2×C4⋊C4C2411yescharacteristic
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2411yescharacteristic
864C2×C4⋊C4C2411yescharacteristic
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2411yescharacteristic
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2412yes—
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⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
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×C42—24no—
936C2×C42—28no—
937C2×C42—24no—
938C2×C42—24no—
939C2×C42—28no—
940C2×C42C2412yes—
941C2×C42C2412yes—
942C2×C42C2411yescharacteristic
943C2×C42C2411yescharacteristic
944C2×C42C2412yes—
945C2×C42C2411yescharacteristic
946C2×C42C2411yescharacteristic
947C2×C42C2411yescharacteristic
948C2×C42C2411yescharacteristic
949C2×C42C2411yescharacteristic
950C2×C42C2411yescharacteristic
951C2×C42C2411yescharacteristic
952C2×C42C2412yes—
953C2×C42C2412yes—
954C2×C42C2411yescharacteristic
955C2×C42C2412yes—
956C2×C42C2411yescharacteristic
957C2×C42C2411yescharacteristic
958C2×C42C2414yes—
959C2×C42C2412yes—
960C2×C42C2412yes—
961C2×C42C2412yes—
962C2×C42C2414yes—
963C2×C42C2414yes—
964C2×C42C2414yes—
965C2×C42C2414yes—
966C2×C42C2414yes—
967C2×C42C2414yes—
968C2×C42C2412yes—
969C2×C42C2412yes—
970C2×C42C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2411yescharacteristic
977#95C2412yes—
978#95C2411yescharacteristic
979#95C2412yes—
980#95C2411yescharacteristic
981#95C2411yescharacteristic
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2412yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2412yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2412yes—
1019#95C2414yes—
1020#95C2412yes—
1021#95C2414yes—
1022#95C2412yes—
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#95C2414yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049C24C2514yes—
1050C24C2511yescharacteristic
1051#41—816no—
1052C2×Q8—24no—
1053C2×Q8—24no—
1054C2×Q8—24no—
1055C2×Q8—28no—
1056C2×Q8—22no—
1057C2×Q8—22no—
1058C2×Q8—22no—
1059C2×Q8—22no—
1060C2×Q8—24no—
1061C2×Q8—41no—
1062C2×Q8—41no—
1063C2×Q8—41no—
1064C2×Q8—41no—
1065C2×Q8—41no—
1066C2×Q8—42no—
1067C2×Q8—41no—
1068C2×Q8—41no—
1069C2×Q8—41no—
1070C2×Q8—41no—
1071C2×Q8—41no—
1072C2×Q8—42no—
1073C2×Q8—42no—
1074C2×Q8—42no—
1075C2×Q8—42no—
1076C2×Q8—42no—
1077C2×Q8—44no—
1078C2×Q8—44no—
1079C2×Q8—42no—
1080C2×Q8—42no—
1081C2×Q8—44no—
1082C2×Q8—416no—
1083C2×Q8—416no—
1084C2×D4—28no—
1085C2×D4—28no—
1086C2×D4—28no—
1087C2×D4—24no—
1088C2×D4—24no—
1089C2×D4—24no—
1090C2×D4—24no—
1091C2×D4—42no—
1092C2×D4—42no—
1093C2×D4—42no—
1094C2×D4—44no—
1095C22×C4—24no—
1096C22×C4—22no—
1097C22×C4—22no—
1098C22×C4—22no—
1099C22×C4—22no—
1100C22×C4—22no—
1101C22×C4—22no—
1102C22×C4—24no—
1103C22×C4—24no—
1104C22×C4—24no—
1105C22×C4—24no—
1106C22×C4—24no—
1107C22×C4—24no—
1108C22×C4—24no—
1109C22×C4—24no—
1110C22×C4—24no—
1111C22×C4—24no—
1112C22×C4—24no—
1113C22×C4—22no—
1114C22×C4—22no—
1115C22×C4—28no—
1116C22×C4—42no—
1117C22×C4—42no—
1118C22×C4—41no—
1119C22×C4—41no—
1120C22×C4—41no—
1121C22×C4—41no—
1122C22×C4—42no—
1123C22×C4—42no—
1124C22×C4—44no—
1125C22×C4—44no—
1126C22×C4—44no—
1127C22×C4—44no—
1128C22×C4—44no—
1129C22×C4—44no—
1130C22×C4—44no—
1131C22×C4—44no—
1132C22×C4H(5,𝔽2)14yes—
1133C22×C4C2514yes—
1134C22×C4C2514yes—
1135C22×C4C2514yes—
1136C22×C4C2512yes—
1137C22×C4C2512yes—
1138C22×C4C2514yes—
1139C22×C4C2511yescharacteristic
1140C22×C4C2511yescharacteristic
1141C22×C4C2514yes—
1142C22×C4C2512yes—
1143C22×C4C2511yescharacteristic
1144C22×C4C2512yes—
1145C22×C4C2512yes—
1146C22×C4C2511yescharacteristic
1147C22×C4C2511yescharacteristic
1148C22×C4C2511yescharacteristic
1149C22×C4C2511yescharacteristic
1150C22×C4C2511yescharacteristic
1151C22×C4C2514yes—
1152C22×C4C2514yes—
1153C22×C4C2511yescharacteristic
1154C22×C4C2512yes—
1155C22×C4C2511yescharacteristic
1156C22×C4C2511yescharacteristic
1157C22×C4C2512yes—
1158C22×C4C2512yes—
1159C22×C4C2511yescharacteristic
1160C22×C4C2511yescharacteristic
1161C22×C4C2511yescharacteristic
1162C4⋊C4—28no—
1163C4⋊C4—24no—
1164C4⋊C4—24no—
1165C4⋊C4—24no—
1166C4⋊C4—24no—
1167C4⋊C4—28no—
1168C4⋊C4—28no—
1169C4⋊C4—24no—
1170C4⋊C4—24no—
1171C4⋊C4—24no—
1172C4⋊C4—24no—
1173C4⋊C4—24no—
1174C4⋊C4—24no—
1175C4⋊C4—28no—
1176C4⋊C4—42no—
1177C4⋊C4—42no—
1178C4⋊C4—42no—
1179C4⋊C4—42no—
1180C4⋊C4—42no—
1181C4⋊C4—42no—
1182C4⋊C4—42no—
1183C4⋊C4—42no—
1184C4⋊C4—42no—
1185C4⋊C4—42no—
1186C4⋊C4—42no—
1187C4⋊C4—42no—
1188C4⋊C4—41no—
1189C4⋊C4—41no—
1190C4⋊C4—41no—
1191C4⋊C4—41no—
1192C4⋊C4—41no—
1193C4⋊C4—41no—
1194C4⋊C4—41no—
1195C4⋊C4—41no—
1196C4⋊C4—42no—
1197C4⋊C4—42no—
1198C4⋊C4—42no—
1199C4⋊C4—41no—
1200C4⋊C4—41no—
1201C4⋊C4—42no—
1202C4⋊C4—42no—
1203C4⋊C4—41no—
1204C4⋊C4—41no—
1205C4⋊C4—41no—
1206C4⋊C4—41no—
1207C4⋊C4—44no—
1208C4⋊C4—44no—
1209C4⋊C4—42no—
1210C4⋊C4—42no—
1211C4⋊C4—44no—
1212C4⋊C4—42no—
1213C4⋊C4—44no—
1214C4⋊C4—44no—
1215C4⋊C4—44no—
1216C4⋊C4—42no—
1217C4⋊C4—44no—
1218C4⋊C4—44no—
1219C4⋊C4—44no—
1220C4⋊C4—44no—
1221C4⋊C4—44no—
1222C4⋊C4—44no—
1223C4⋊C4—44no—
1224C4⋊C4—44no—
1225C4⋊C4—44no—
1226C4⋊C4—44no—
1227C4⋊C4—44no—
1228C4⋊C4—44no—
1229C4⋊C4—44no—
1230C4⋊C4—44no—
1231C4⋊C4—44no—
1232C22⋊C4—28no—
1233C22⋊C4—28no—
1234C22⋊C4—28no—
1235C22⋊C4—28no—
1236C22⋊C4—28no—
1237C22⋊C4—28no—
1238C22⋊C4—28no—
1239C22⋊C4—28no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4—44no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—44no—
1251C22⋊C4—44no—
1252C22⋊C4—44no—
1253C22⋊C4—44no—
1254C22⋊C4—44no—
1255C22⋊C4—44no—
1256C22⋊C4—44no—
1257C22⋊C4—44no—
1258C22⋊C4—44no—
1259C42—24no—
1260C42—22no—
1261C42—22no—
1262C42—24no—
1263C42—22no—
1264C42—22no—
1265C42—22no—
1266C42—22no—
1267C42—22no—
1268C42—22no—
1269C42—22no—
1270C42—24no—
1271C42—22no—
1272C42—24no—
1273C42—22no—
1274C42—22no—
1275C42—24no—
1276C42—24no—
1277C42—24no—
1278C42—28no—
1279C42—24no—
1280C42—24no—
1281C42—44no—
1282C42—44no—
1283C42—44no—
1284C42—44no—
1285C42—44no—
1286C42—44no—
1287C42—42no—
1288C42—42no—
1289C422−1+418yes—
1290C23—22no—
1291C23—21no—
1292C23—21no—
1293C23—24no—
1294C23—24no—
1295C23—24no—
1296C23—24no—
1297C23—24no—
1298C23—24no—
1299C23—24no—
1300C23C2×H(5,𝔽2)12yes—
1301C23#58514yes—
1302C23C2611yescharacteristic
1303Q8—44no—
1304Q8—44no—
1305Q8—44no—
1306Q8—44no—
1307Q8—48no—
1308Q8—44no—
1309Q8—44no—
1310Q8—48no—
1311Q8—84no—
1312Q8—88no—
1313Q8—84no—
1314D4—416no—
1315D4—48no—
1316D4—84no—
1317D4—84no—
1318C2×C4—21no—
1319C2×C4—21no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—21no—
1324C2×C4—21no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—28no—
1328C2×C4—21no—
1329C2×C4—22no—
1330C2×C4—21no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—21no—
1335C2×C4—21no—
1336C2×C4—21no—
1337C2×C4—21no—
1338C2×C4—21no—
1339C2×C4—21no—
1340C2×C4—21no—
1341C2×C4—21no—
1342C2×C4—24no—
1343C2×C4—24no—
1344C2×C4—24no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—24no—
1348C2×C4—24no—
1349C2×C4—24no—
1350C2×C4—24no—
1351C2×C4—24no—
1352C2×C4—24no—
1353C2×C4—24no—
1354C2×C4—24no—
1355C2×C4—24no—
1356C2×C4—22no—
1357C2×C4—24no—
1358C2×C4—22no—
1359C2×C4—24no—
1360C2×C4—24no—
1361C2×C4—24no—
1362C2×C4—24no—
1363C2×C4—24no—
1364C2×C4—24no—
1365C2×C4—22no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—24no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—21no—
1384C2×C4—21no—
1385C2×C4—24no—
1386C2×C4—21no—
1387C2×C4—21no—
1388C2×C4—21no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—48no—
1392C2×C4—48no—
1393C2×C4—44no—
1394C2×C4—44no—
1395C2×C4—44no—
1396C2×C4—44no—
1397C2×C4—44no—
1398C2×C4—48no—
1399C2×C4—44no—
1400C2×C4—88no—
1401C2×C4—84no—
1402C2×C4—88no—
1403C2×C4—88no—
1404C2×C4C2×H(5,𝔽2)12yes—
1405C2×C4C2×H(5,𝔽2)12yes—
1406C2×C4C2×2−1+414yes—
1407C2×C4C2×2−1+414yes—
1408C2×C4C2×2−1+414yes—
1409C2×C4#58512yes—
1410C2×C4#58512yes—
1411C22—22no—
1412C22—22no—
1413C22—24no—
1414C22—24no—
1415C22—44no—
1416C22—44no—
1417C22—44no—
1418C22—44no—
1419C22—44no—
1420C22—44no—
1421C22—44no—
1422C22#354014yes—
1423C22C22×H(5,𝔽2)11yescharacteristic
1424C22C22×2−1+412yes—
1425C22C2×#58512yes—
1426C22C2×#58511yescharacteristic
1427C22C2×#58511yescharacteristic
1428C4—22no—
1429C4—22no—
1430C4—22no—
1431C4—24no—
1432C4—24no—
1433C4—41no—
1434C4—41no—
1435C4—41no—
1436C4—41no—
1437C4—42no—
1438C4—42no—
1439C4—41no—
1440C4—41no—
1441C4—44no—
1442C4—41no—
1443C4—41no—
1444C4—41no—
1445C4—41no—
1446C4—42no—
1447C4—42no—
1448C4—44no—
1449C4—44no—
1450C4—44no—
1451C4—42no—
1452C4—42no—
1453C4—44no—
1454C4—44no—
1455C4—44no—
1456C4#354414yes—
1457C2—24no—
1458C2—84no—
1459C2C2×#354011yescharacteristic
1460C2#6272911yescharacteristic
1461C2C2×#354411yescharacteristic
1462C2#6283112yes—
1463C2#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. #53153C2semidirect
2. #53033C2semidirect
3. #52989C2semidirect
4. #52955C2semidirect
5. #52914C2semidirect
6. #52913C2semidirect
7. #45425C2semidirect
8. #45369C2semidirect
9. #45364C2semidirect
10. #44858C2semidirect
11. #43342C2semidirect
12. #43289C2semidirect
13. #42821C2semidirect
14. #42700C2semidirect
15. #42523C2semidirect
16. #42493C2semidirect
17. #42382C2semidirect
18. #42369C2semidirect
19. #42344C2semidirect
20. #42337C2semidirect
21. #41532C2semidirect
22. #40838C2semidirect
23. #36177C2semidirect
24. #36176C2semidirect
25. #36140C2semidirect
27. #35270C2semidirect
29. #35248C2semidirect
30. #35111C2semidirect
31. C2×#2399C2semidirect

Maximal subgroups

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

subgroupindex
#531532
#530332
#529892
#529552
#529142
#529132
#454252
#453692
#453642
#448582
#433422
#432892
#428212
#427002
#425232
#424932
#423822
#423692
#423442
#423372
#415322
#408382
#361772
#361762
#361402
#361392
#352702
#352492
#352482
#351112
C2×#23992