Finite Group Databasebeta

← #8107683

Subgroups — #8107683

Order 512.

4734 conjugacy classes of subgroups.

The subgroup lattice has 1491 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53100C211yesmaximal, characteristic, complemented
2#53099C211yesmaximal, characteristic, complemented
3#52994C212yesmaximal, complemented
4#52952C212yesmaximal, complemented
5#52951C212yesmaximal, complemented
6#52550C214yesmaximal, complemented
7#45434C212yesmaximal, complemented
8#45369C211yesmaximal, characteristic, complemented
9#45364C211yesmaximal, characteristic, complemented
10#44862C212yesmaximal, complemented
11#44861C212yesmaximal, complemented
12#44761C214yesmaximal, complemented
13#42822C212yesmaximal, complemented
14#42699C212yesmaximal, complemented
15#42526C212yesmaximal, complemented
16#42494C212yesmaximal, complemented
17#42363C214yesmaximal, complemented
18#42339C214yesmaximal, complemented
19#42191C212yesmaximal, complemented
20#42167C212yesmaximal, complemented
21#42021C212yesmaximal, complemented
22#41997C212yesmaximal, complemented
23#36193C212yesmaximal, complemented
24#36186C212yesmaximal, complemented
25#36140C212yesmaximal, complemented
26#36139C212yesmaximal
27#35270C212yesmaximal, complemented
28#35247C212yesmaximal, complemented
29#35179C211yesmaximal, characteristic, complemented
30#35178C211yesmaximal, characteristic
31C2×#2399C211yesmaximal, characteristic, complemented
32C2×#552C2214yes—
33C2×#536C2212yes—
34C2×#533C2211yescharacteristic
35C2×#532C2211yescharacteristic
36C2×#529C2212yes—
37C22×C4×Q8C2211yescharacteristic
38C22×C4×Q8C2211yescharacteristic
39#2857C2212yes—
40#2855C2212yes—
41#2855C2212yes—
42#2855C2212yes—
43#2854C2212yes—
44#2854C2212yes—
45#2854C2212yes—
46#2850C2212yes—
47#2845C2214yes—
48#2841C2214yes—
49#2841C2214yes—
50#2839C2214yes—
51#2838C2214yes—
52#2837C2214yes—
53#2836C2214yes—
54#2836C2214yes—
55#2833C2212yes—
56#2831C2214yes—
57#2830C2212yes—
58#2823C2212yes—
59#2822C2212yes—
60#2814C2214yes—
61#2811C2212yes—
62#2806C2214yes—
63#2806C2214yes—
64#2802C2214yes—
65#2799C2212yes—
66#2792C2212yes—
67#2789C2212yes—
68#2788C2214yes—
69#2787C2214yes—
70#2785C2212yes—
71#2784C2212yes—
72#2781C2214yes—
73#2775C2214yes—
74#2772C2214yes—
75#2770C2214yes—
76#2768C2214yes—
77#2768C2214yes—
78#2726C2214yes—
79#2725C2214yes—
80#2720C2214yes—
81#2715C2214yes—
82#2713C2214yes—
83#2713C2214yes—
84#2704C2214yes—
85#2704C2214yes—
86#2704C2214yes—
87#2704C2214yes—
88#2702C2214yes—
89#2700C2214yes—
90#2698C2214yes—
91#2692C2214yes—
92#2690C2214yes—
93#2689C2214yes—
94#2687C2214yes—
95#2683C2212yes—
96#2680C2212yes—
97#2666C2214yes—
98#2666C2214yes—
99#2665C2214yes—
100#2663C2214yes—
101#2659C2214yes—
102#2651C2214yes—
103#2647C2212yes—
104#2645C2212yes—
105#2644C2212yes—
106#2640C2212yes—
107#2637C2214yes—
108#2637C2214yes—
109#2637C2214yes—
110#2629C2214yes—
111#2627C2212yes—
112#2627C2212yes—
113#2618C2212yes—
114#2618C2212yes—
115#2609C2212yes—
116#2593C2212yes—
117#2592C2212yes—
118#2592C2212yes—
119#2586C2212yes—
120#2584C2212yes—
121#2584C2212yes—
122#2582C2212yes—
123#2582C2212yes—
124#2582C2212yes—
125#2582C2212yes—
126#2582C2212yes—
127#2581C2212yes—
128#2581C2212yes—
129#2568C2211yescharacteristic
130#2568C2211yescharacteristic
131#2567C2212yes—
132#2567C2211yescharacteristic
133#2567C2211yescharacteristic
134#2565C2212yes—
135#2565C2212yes—
136#2556C2214yes—
137#2556C2214yes—
138#2552C2212yes—
139#2552C2212yes—
140#2550C2212yes—
141#2550C2212yes—
142#2550C2214yes—
143#2549C2214yes—
144#2549C2214yes—
145#2548C2211yescharacteristic
146#2548C2211yescharacteristic
147#2546C2211yescharacteristic
148#2546C2211yescharacteristic
149#2545C2212yes—
150#2545C2212yes—
151#2545C2212yes—
152#2544C2212yes—
153#2542C2212yes—
154#2538C2212yes—
155#2538C2212yes—
156#2538C2212yes—
157#2538C2212yes—
158#2536C2212yes—
159#2536C2212yes—
160#2532C2214yes—
161#2530C2214yes—
162#2529C2214yes—
163#2527C2214yes—
164#2521C2214yes—
165#2521C2214yes—
166#2520C2214yes—
167#2520C2214yes—
168#2519C2214yes—
169#2519C2214yes—
170#2519C2214yes—
171#2512C2212yes—
172#2512C2212yes—
173#2511C2212yes—
174#2511C2212yes—
175#2510C2214yes—
176#2508C2214yes—
177#2507C2212yes—
178#2507C2212yes—
179#2506C2212yes—
180#2506C2212yes—
181#2498C2214yes—
182#2498C2214yes—
183#2489C2214yes—
184#2488C2214yes—
185#2488C2214yes—
186#2486C2214yes—
187#2475C2214yes—
188#2474C2214yes—
189#2474C2214yes—
190#2469C2214yes—
191#2468C2214yes—
192#2465C2214yes—
193#2454C2212yes—
194#2453C2212yes—
195#2452C2212yes—
196#2451C2212yes—
197#2451C2214yes—
198#2450C2214yes—
199#2449C2214yes—
200#2448C2212yes—
201#2447C2212yes—
202#2446C2212yes—
203#2445C2212yes—
204#2443C2214yes—
205#2442C2214yes—
206#2438C2214yes—
207#2438C2214yes—
208#2438C2214yes—
209#2425C2214yes—
210#2419C2214yes—
211#2417C2214yes—
212#2413C2214yes—
213#2413C2214yes—
214#2413C2214yes—
215#2409C2214yes—
216#2406C2214yes—
217#2399C2211yescharacteristic
218#2399C2212yes—
219#2399C2211yescharacteristic
220#2399C2211yescharacteristic
221#2399C2211yescharacteristic
222#2399C2212yes—
223#2399C2212yes—
224#2399C2211yescharacteristic
225#2399C2211yescharacteristic
226#2399C2212yes—
227#2399C2211yescharacteristic
228#2399C2211yescharacteristic
229C2×#398C2212yes—
230C2×#398C2211yescharacteristic
231C2×#398C2211yescharacteristic
232C2×#395C2211yescharacteristic
233C2×#395C2211yescharacteristic
234C2×#395C2212yes—
235#2370C2214yes—
236#2369C2212yes—
237#2367C2212yes—
238#2367C2212yes—
239#2365C2212yes—
240#2362C2214yes—
241#2362C2214yes—
242#2359C2214yes—
243#2359C2214yes—
244#2355C2212yes—
245#2354C2212yes—
246#2351C2212yes—
247#2349C2212yes—
248#2344C2214yes—
249#2339C2214yes—
250#2331C2212yes—
251#2326C2212yes—
252#2323C2214yes—
253#2323C2214yes—
254#2320C2212yes—
255#2319C2212yes—
256#2317C2212yes—
257#2311C2212yes—
258#2310C2212yes—
259C4×C22⋊Q8C2212yes—
260C4×#121C2212yes—
261#2285C2211yescharacteristic
262#2285C2212yes—
263#2285C2211yescharacteristic
264C2×C4×C4⋊C4C2212yes—
265C2×C4×C4⋊C4C2212yes—
266C2×#376C2211yescharacteristic
267C22×#41C2312yes—
268C23×Q8C2311yescharacteristic
269C23×Q8C2311yescharacteristic
270#552—416no—
271#536—48no—
272#533—44no—
273#532—44no—
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2311yescharacteristic
276C2×C4⋊Q8C2311yescharacteristic
277C2×C4⋊Q8C2311yescharacteristic
278C2×C4⋊Q8C2312yes—
279C2×C4⋊Q8C2312yes—
280C2×#127C2311yescharacteristic
281#529—48no—
282C2×#126C2314yes—
283C2×#126C2314yes—
284C2×#126C2314yes—
285C2×#125C2312yes—
286C2×#125C2314yes—
287C2×#125C2312yes—
288C2×#125C2314yes—
289C2×#125C2314yes—
290C2×#125C2314yes—
291C2×#124C2312yes—
292C2×#124C2312yes—
293C2×#124C2312yes—
294C2×#124C2312yes—
295C2×#124C2312yes—
296C2×#123C2314yes—
297C2×#123C2314yes—
298C2×#123C2314yes—
299C2×#123C2314yes—
300C2×#123C2314yes—
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2314yes—
303C2×C22⋊Q8C2314yes—
304C2×C22⋊Q8C2314yes—
305C2×C22⋊Q8C2314yes—
306C2×C22⋊Q8C2314yes—
307C2×C22⋊Q8C2312yes—
308C2×C22⋊Q8C2314yes—
309C2×C22⋊Q8C2314yes—
310C2×C22⋊Q8C2314yes—
311C2×#121C2312yes—
312C2×#121C2312yes—
313C2×C4×Q8—44no—
314C2×C4×Q8—44no—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2311yescharacteristic
318C2×C4×Q8C2311yescharacteristic
319C2×C4×Q8C2311yescharacteristic
320C2×C4×Q8C2311yescharacteristic
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2311yescharacteristic
324C2×C4×Q8C2311yescharacteristic
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2312yes—
327C2×C4×Q8C2311yescharacteristic
328C2×C4×Q8C2311yescharacteristic
329C2×C4×Q8C2311yescharacteristic
330C2×C4×Q8C2312yes—
331C2×C4×Q8C2314yes—
332C2×C4×Q8C2311yescharacteristic
333C2×C4×Q8C2311yescharacteristic
334C2×C4×D4C2312yes—
335C2×C4×D4C2314yes—
336C2×C4×D4C2314yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2312yes—
340C2×#117C2312yes—
341C2×#117C2312yes—
342C2×#117C2312yes—
343C2×#117C2314yes—
344C2×#117C2314yes—
345C2×#117C2314yes—
346C22×C4⋊C4C2312yes—
347C22×C4⋊C4C2312yes—
348C22×C4⋊C4C2311yescharacteristic
349C22×C4⋊C4C2311yescharacteristic
350C22×C4⋊C4C2311yescharacteristic
351C22×C4⋊C4C2312yes—
352C22×C4⋊C4C2312yes—
353C22×C4⋊C4C2312yes—
354C22×C4⋊C4C2311yescharacteristic
355C22×C42C2312yes—
356C22×C42C2311yescharacteristic
357C22×C42C2311yescharacteristic
358C22×C42C2312yes—
359C22×C42C2311yescharacteristic
360#401C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2312yes—
364#400C2312yes—
365#400C2312yes—
366#400C2312yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#400C2314yes—
372#400C2314yes—
373#400C2314yes—
374#400C2314yes—
375#400C2314yes—
376#400C2314yes—
377#400C2314yes—
378#399C2314yes—
379#399C2314yes—
380#399C2314yes—
381#399C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2311yescharacteristic
387#398C2314yes—
388#398C2312yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2311yescharacteristic
393#398C2312yes—
394#398C2314yes—
395#398C2312yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2312yes—
401#398C2311yescharacteristic
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2312yes—
406#398C2312yes—
407#398C2314yes—
408#398C2314yes—
409#398C2314yes—
410#398C2314yes—
411#398C2311yescharacteristic
412#398C2312yes—
413#398C2314yes—
414#398C2314yes—
415#398C2314yes—
416#398C2312yes—
417#398C2312yes—
418#398C2314yes—
419#398C2312yes—
420#398C2312yes—
421#398C2312yes—
422#398C2311yescharacteristic
423#398C2312yes—
424#398C2312yes—
425#398C2311yescharacteristic
426#398C2311yescharacteristic
427#398C2312yes—
428#398C2312yes—
429#398C2311yescharacteristic
430#398C2314yes—
431#398C2314yes—
432#398C2314yes—
433#397C2314yes—
434#397C2314yes—
435#397C2314yes—
436#397C2314yes—
437#397C2314yes—
438#397C2314yes—
439#397C2314yes—
440#397C2314yes—
441#397C2314yes—
442#397C2314yes—
443#397C2314yes—
444#397C2314yes—
445#396C2314yes—
446#396C2314yes—
447#396C2314yes—
448#396C2314yes—
449#396C2314yes—
450#396C2314yes—
451#396C2314yes—
452#396C2314yes—
453#396C2314yes—
454#396C2314yes—
455#396C2314yes—
456#396C2314yes—
457#396C2314yes—
458#396C2314yes—
459#396C2314yes—
460#395C2312yes—
461#395C2314yes—
462#395C2312yes—
463#395C2312yes—
464#395C2312yes—
465#395C2314yes—
466#395C2314yes—
467#395C2311yescharacteristic
468#395C2314yes—
469#395C2314yes—
470#395C2311yescharacteristic
471#395C2314yes—
472#395C2314yes—
473#395C2312yes—
474#395C2312yes—
475#395C2311yescharacteristic
476#395C2311yescharacteristic
477#395C2312yes—
478#395C2312yes—
479#395C2312yes—
480#395C2312yes—
481#395C2312yes—
482#395C2312yes—
483#395C2312yes—
484#395C2312yes—
485#395C2312yes—
486#395C2311yescharacteristic
487#395C2311yescharacteristic
488#395C2311yescharacteristic
489#395C2312yes—
490#395C2311yescharacteristic
491#394C2314yes—
492#394C2312yes—
493#394C2314yes—
494#394C2312yes—
495#394C2314yes—
496#394C2314yes—
497#394C2312yes—
498#394C2312yes—
499#393C2314yes—
500#393C2314yes—
501#393C2314yes—
502#393C2314yes—
503#393C2314yes—
504#391C2312yes—
505#391C2312yes—
506#391C2312yes—
507#391C2312yes—
508#391C2314yes—
509#391C2314yes—
510#391C2312yes—
511#391C2312yes—
512#391C2312yes—
513#391C2312yes—
514#391C2312yes—
515#391C2312yes—
516#391C2312yes—
517#391C2314yes—
518#391C2312yes—
519#391C2314yes—
520#391C2314yes—
521#391C2314yes—
522#391C2312yes—
523#391C2314yes—
524#391C2314yes—
525#391C2314yes—
526#391C2314yes—
527#391C2314yes—
528#391C2314yes—
529#391C2314yes—
530#391C2312yes—
531#390C2312yes—
532#390C2312yes—
533#390C2312yes—
534#390C2312yes—
535#390C2312yes—
536#390C2312yes—
537#390C2312yes—
538#390C2312yes—
539#390C2312yes—
540#390C2312yes—
541#389C2312yes—
542#389C2312yes—
543#389C2312yes—
544#389C2312yes—
545#389C2314yes—
546#389C2314yes—
547#389C2314yes—
548#389C2314yes—
549#389C2312yes—
550#389C2312yes—
551#389C2312yes—
552#389C2314yes—
553#389C2314yes—
554#389C2314yes—
555#389C2314yes—
556#389C2314yes—
557#389C2314yes—
558#389C2314yes—
559#389C2314yes—
560#389C2312yes—
561#389C2312yes—
562#389C2312yes—
563#389C2314yes—
564#389C2312yes—
565#389C2312yes—
566#389C2312yes—
567#389C2312yes—
568#389C2314yes—
569#389C2314yes—
570#389C2314yes—
571#389C2314yes—
572#389C2314yes—
573#389C2314yes—
574#389C2314yes—
575#389C2314yes—
576#389C2312yes—
577#389C2312yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#386C2314yes—
635#386C2314yes—
636#386C2314yes—
637#386C2314yes—
638#386C2314yes—
639#386C2314yes—
640#386C2314yes—
641#386C2314yes—
642#386C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#384C2312yes—
657#384C2312yes—
658#384C2312yes—
659#384C2312yes—
660#384C2312yes—
661#384C2312yes—
662#384C2312yes—
663#383C2314yes—
664#382C2312yes—
665#382C2312yes—
666#382C2314yes—
667#382C2312yes—
668#382C2312yes—
669#382C2314yes—
670#382C2314yes—
671#382C2314yes—
672#382C2312yes—
673#381C2314yes—
674#381C2314yes—
675#381C2314yes—
676#381C2314yes—
677#381C2314yes—
678#380C2314yes—
679#380C2314yes—
680#380C2314yes—
681#380C2314yes—
682#380C2314yes—
683#380C2314yes—
684#380C2314yes—
685#380C2314yes—
686#380C2312yes—
687#380C2312yes—
688#380C2314yes—
689#380C2312yes—
690#380C2312yes—
691#380C2314yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2311yescharacteristic
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2314yes—
702C4×C4⋊C4C2314yes—
703C4×C4⋊C4C2314yes—
704C4×C4⋊C4C2312yes—
705C4×C4⋊C4C2312yes—
706C4×C4⋊C4C2311yescharacteristic
707C4×C4⋊C4C2312yes—
708C4×C4⋊C4C2312yes—
709C4×C4⋊C4C2312yes—
710C4×C4⋊C4C2312yes—
711C4×C4⋊C4C2314yes—
712C4×C4⋊C4C2311yescharacteristic
713C4×C4⋊C4C2312yes—
714C4×C4⋊C4C2312yes—
715C4×C4⋊C4C2312yes—
716C4×C4⋊C4C2312yes—
717C4×C4⋊C4C2312yes—
718C4×C4⋊C4C2312yes—
719C4×C4⋊C4C2312yes—
720C4×C4⋊C4C2312yes—
721C4×C4⋊C4C2312yes—
722C4×C4⋊C4C2312yes—
723C4×C22⋊C4C2314yes—
724C4×C22⋊C4C2314yes—
725C4×C22⋊C4C2314yes—
726C4×C22⋊C4C2314yes—
727#376C2312yes—
728#376C2311yescharacteristic
729#376C2311yescharacteristic
730#376C2311yescharacteristic
731#376C2311yescharacteristic
732#376C2312yes—
733C2×#95C2312yes—
734C2×#95C2314yes—
735C2×#95C2312yes—
736C2×#95C2312yes—
737C2×#95C2311yescharacteristic
738C2×#95C2311yescharacteristic
739C2×#95C2312yes—
740C2×#95C2312yes—
741C2×#41—28no—
742C2×#41—44no—
743C2×#41—44no—
744C22×Q8—24no—
745C22×Q8—24no—
746C22×Q8—42no—
747C22×Q8—42no—
748C22×Q8—44no—
749C22×Q8C2412yes—
750C22×Q8C2411yescharacteristic
751C22×Q8C2411yescharacteristic
752C22×Q8C2411yescharacteristic
753C22×Q8C2411yescharacteristic
754C22×Q8C2411yescharacteristic
755C22×Q8C2412yes—
756C22×Q8C2414yes—
757C22×Q8C2412yes—
758C22×Q8C2411yescharacteristic
759C22×Q8C2412yes—
760C22×D4C2412yes—
761C22×D4C2414yes—
762C22×D4C2412yes—
763C22×D4C2412yes—
764C23×C4C2412yes—
765C23×C4C2411yescharacteristic
766C23×C4C2412yes—
767C23×C4C2412yes—
768C23×C4C2412yes—
769C23×C4C2411yescharacteristic
770C23×C4C2411yescharacteristic
771C23×C4C2411yescharacteristic
772C23×C4C2411yescharacteristic
773C23×C4C2411yescharacteristic
774C23×C4C2411yescharacteristic
775C23×C4C2414yes—
776C23×C4C2414yes—
777C23×C4C2414yes—
778C4⋊Q8—28no—
779C4⋊Q8—42no—
780C4⋊Q8—42no—
781C4⋊Q8—42no—
782C4⋊Q8—44no—
783C4⋊Q8—44no—
784#127—42no—
785#126—48no—
786#126—48no—
787#126—48no—
788#125—44no—
789#125—44no—
790#125—48no—
791#125—48no—
792#125—48no—
793#125—48no—
794#124—28no—
795#124—44no—
796#124—44no—
797#124—44no—
798#124—44no—
799#123—216no—
800#123—48no—
801#123—48no—
802#123—48no—
803#123—48no—
804C22⋊Q8—28no—
805C22⋊Q8—44no—
806C22⋊Q8—48no—
807C22⋊Q8—48no—
808C22⋊Q8—48no—
809C22⋊Q8—48no—
810C22⋊Q8—48no—
811C22⋊Q8—48no—
812C22⋊Q8—48no—
813C22⋊Q8—48no—
814#121—28no—
815#121—44no—
816C4×Q8—28no—
817C4×Q8—42no—
818C4×Q8—44no—
819C4×Q8—42no—
820C4×Q8—42no—
821C4×Q8—42no—
822C4×Q8—42no—
823C4×Q8—42no—
824C4×Q8—44no—
825C4×Q8—42no—
826C4×Q8—42no—
827C4×Q8—42no—
828C4×Q8—42no—
829C4×Q8—42no—
830C4×Q8—42no—
831C4×Q8—44no—
832C4×Q8—48no—
833C4×Q8—44no—
834C4×Q8—44no—
835C4×D4—28no—
836C4×D4—44no—
837C4×D4—44no—
838C4×D4—44no—
839C4×D4—48no—
840C4×D4—48no—
841#117—28no—
842#117—48no—
843#117—48no—
844#117—44no—
845#117—44no—
846#117—48no—
847C2×C4⋊C4—28no—
848C2×C4⋊C4—28no—
849C2×C4⋊C4—44no—
850C2×C4⋊C4—44no—
851C2×C4⋊C4—42no—
852C2×C4⋊C4—42no—
853C2×C4⋊C4—42no—
854C2×C4⋊C4—44no—
855C2×C4⋊C4—42no—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2411yescharacteristic
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2411yescharacteristic
887C2×C4⋊C4C2411yescharacteristic
888C2×C4⋊C4C2411yescharacteristic
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2411yescharacteristic
892C2×C4⋊C4C2411yescharacteristic
893C2×C4⋊C4C2411yescharacteristic
894C2×C4⋊C4C2411yescharacteristic
895C2×C4⋊C4C2411yescharacteristic
896C2×C4⋊C4C2411yescharacteristic
897C2×C4⋊C4C2411yescharacteristic
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2411yescharacteristic
900C2×C4⋊C4C2411yescharacteristic
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2414yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2412yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2414yes—
915C2×C4⋊C4C2414yes—
916C2×C4⋊C4C2412yes—
917C2×C4⋊C4C2414yes—
918C2×C4⋊C4C2414yes—
919C2×C4⋊C4C2414yes—
920C2×C4⋊C4C2414yes—
921C2×C4⋊C4C2414yes—
922C2×C4⋊C4C2414yes—
923C2×C4⋊C4C2414yes—
924C2×C4⋊C4C2414yes—
925C2×C4⋊C4C2414yes—
926C2×C4⋊C4C2414yes—
927C2×C4⋊C4C2414yes—
928C2×C4⋊C4C2414yes—
929C2×C4⋊C4C2414yes—
930C2×C4⋊C4C2414yes—
931C2×C4⋊C4C2414yes—
932C2×C4⋊C4C2414yes—
933C2×C4⋊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×C22⋊C4C2414yes—
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2414yes—
956C2×C22⋊C4C2414yes—
957C2×C22⋊C4C2414yes—
958C2×C22⋊C4C2414yes—
959C2×C22⋊C4C2414yes—
960C2×C22⋊C4C2414yes—
961C2×C42—24no—
962C2×C42—28no—
963C2×C42—24no—
964C2×C42—24no—
965C2×C42—28no—
966C2×C42C2412yes—
967C2×C42C2412yes—
968C2×C42C2412yes—
969C2×C42C2411yescharacteristic
970C2×C42C2411yescharacteristic
971C2×C42C2412yes—
972C2×C42C2411yescharacteristic
973C2×C42C2411yescharacteristic
974C2×C42C2411yescharacteristic
975C2×C42C2411yescharacteristic
976C2×C42C2411yescharacteristic
977C2×C42C2411yescharacteristic
978C2×C42C2411yescharacteristic
979C2×C42C2412yes—
980C2×C42C2411yescharacteristic
981C2×C42C2412yes—
982C2×C42C2411yescharacteristic
983C2×C42C2411yescharacteristic
984C2×C42C2414yes—
985C2×C42C2412yes—
986C2×C42C2412yes—
987C2×C42C2412yes—
988C2×C42C2414yes—
989C2×C42C2414yes—
990C2×C42C2414yes—
991C2×C42C2414yes—
992C2×C42C2412yes—
993C2×C42C2412yes—
994C2×C42C2414yes—
995C2×C42C2414yes—
996C2×C42C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2411yescharacteristic
1003#95C2412yes—
1004#95C2411yescharacteristic
1005#95C2411yescharacteristic
1006#95C2412yes—
1007#95C2411yescharacteristic
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#95C2412yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2412yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2412yes—
1038#95C2412yes—
1039#95C2414yes—
1040#95C2412yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2414yes—
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—
1065#95C2414yes—
1066#95C2414yes—
1067C24C2514yes—
1068C24C2511yescharacteristic
1069#41—816no—
1070C2×Q8—24no—
1071C2×Q8—22no—
1072C2×Q8—22no—
1073C2×Q8—22no—
1074C2×Q8—22no—
1075C2×Q8—24no—
1076C2×Q8—24no—
1077C2×Q8—22no—
1078C2×Q8—22no—
1079C2×Q8—22no—
1080C2×Q8—22no—
1081C2×Q8—28no—
1082C2×Q8—24no—
1083C2×Q8—24no—
1084C2×Q8—24no—
1085C2×Q8—41no—
1086C2×Q8—41no—
1087C2×Q8—41no—
1088C2×Q8—42no—
1089C2×Q8—41no—
1090C2×Q8—41no—
1091C2×Q8—41no—
1092C2×Q8—42no—
1093C2×Q8—42no—
1094C2×Q8—44no—
1095C2×Q8—42no—
1096C2×Q8—44no—
1097C2×Q8—44no—
1098C2×Q8—42no—
1099C2×Q8—42no—
1100C2×Q8—416no—
1101C2×Q8—416no—
1102C2×D4—28no—
1103C2×D4—28no—
1104C2×D4—28no—
1105C2×D4—24no—
1106C2×D4—24no—
1107C2×D4—24no—
1108C2×D4—24no—
1109C2×D4—42no—
1110C2×D4—44no—
1111C2×D4—42no—
1112C2×D4—42no—
1113C22×C4—22no—
1114C22×C4—22no—
1115C22×C4—22no—
1116C22×C4—22no—
1117C22×C4—24no—
1118C22×C4—22no—
1119C22×C4—22no—
1120C22×C4—24no—
1121C22×C4—24no—
1122C22×C4—24no—
1123C22×C4—24no—
1124C22×C4—22no—
1125C22×C4—24no—
1126C22×C4—24no—
1127C22×C4—22no—
1128C22×C4—22no—
1129C22×C4—22no—
1130C22×C4—24no—
1131C22×C4—24no—
1132C22×C4—24no—
1133C22×C4—28no—
1134C22×C4—28no—
1135C22×C4—28no—
1136C22×C4—42no—
1137C22×C4—42no—
1138C22×C4—42no—
1139C22×C4—42no—
1140C22×C4—42no—
1141C22×C4—42no—
1142C22×C4—44no—
1143C22×C4—44no—
1144C22×C4—44no—
1145C22×C4—44no—
1146C22×C4—44no—
1147C22×C4—44no—
1148C22×C4H(5,𝔽2)14yes—
1149C22×C4H(5,𝔽2)14yes—
1150C22×C42−1+414yes—
1151C22×C4C2512yes—
1152C22×C4C2514yes—
1153C22×C4C2514yes—
1154C22×C4C2514yes—
1155C22×C4C2514yes—
1156C22×C4C2512yes—
1157C22×C4C2512yes—
1158C22×C4C2511yescharacteristic
1159C22×C4C2511yescharacteristic
1160C22×C4C2511yescharacteristic
1161C22×C4C2511yescharacteristic
1162C22×C4C2511yescharacteristic
1163C22×C4C2514yes—
1164C22×C4C2511yescharacteristic
1165C22×C4C2514yes—
1166C22×C4C2514yes—
1167C22×C4C2512yes—
1168C22×C4C2511yescharacteristic
1169C22×C4C2512yes—
1170C22×C4C2511yescharacteristic
1171C22×C4C2511yescharacteristic
1172C22×C4C2511yescharacteristic
1173C22×C4C2511yescharacteristic
1174C22×C4C2512yes—
1175C22×C4C2511yescharacteristic
1176C22×C4C2512yes—
1177C22×C4C2511yescharacteristic
1178C22×C4C2512yes—
1179C22×C4C2511yescharacteristic
1180C4⋊C4—24no—
1181C4⋊C4—24no—
1182C4⋊C4—24no—
1183C4⋊C4—24no—
1184C4⋊C4—28no—
1185C4⋊C4—28no—
1186C4⋊C4—24no—
1187C4⋊C4—24no—
1188C4⋊C4—28no—
1189C4⋊C4—28no—
1190C4⋊C4—24no—
1191C4⋊C4—24no—
1192C4⋊C4—24no—
1193C4⋊C4—24no—
1194C4⋊C4—24no—
1195C4⋊C4—24no—
1196C4⋊C4—28no—
1197C4⋊C4—28no—
1198C4⋊C4—24no—
1199C4⋊C4—24no—
1200C4⋊C4—24no—
1201C4⋊C4—24no—
1202C4⋊C4—24no—
1203C4⋊C4—24no—
1204C4⋊C4—28no—
1205C4⋊C4—28no—
1206C4⋊C4—42no—
1207C4⋊C4—42no—
1208C4⋊C4—42no—
1209C4⋊C4—42no—
1210C4⋊C4—41no—
1211C4⋊C4—41no—
1212C4⋊C4—42no—
1213C4⋊C4—42no—
1214C4⋊C4—41no—
1215C4⋊C4—41no—
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—41no—
1225C4⋊C4—42no—
1226C4⋊C4—42no—
1227C4⋊C4—41no—
1228C4⋊C4—41no—
1229C4⋊C4—44no—
1230C4⋊C4—44no—
1231C4⋊C4—44no—
1232C4⋊C4—44no—
1233C4⋊C4—44no—
1234C4⋊C4—42no—
1235C4⋊C4—42no—
1236C4⋊C4—42no—
1237C4⋊C4—44no—
1238C4⋊C4—44no—
1239C4⋊C4—44no—
1240C4⋊C4—42no—
1241C4⋊C4—44no—
1242C4⋊C4—44no—
1243C4⋊C4—44no—
1244C4⋊C4—44no—
1245C4⋊C4—44no—
1246C4⋊C4—44no—
1247C4⋊C4—44no—
1248C4⋊C4—44no—
1249C4⋊C4—44no—
1250C4⋊C4—44no—
1251C4⋊C4—44no—
1252C4⋊C4—44no—
1253C4⋊C4—44no—
1254C4⋊C4—44no—
1255C4⋊C4—44no—
1256C4⋊C4—44no—
1257C4⋊C4—44no—
1258C22⋊C4—28no—
1259C22⋊C4—28no—
1260C22⋊C4—28no—
1261C22⋊C4—28no—
1262C22⋊C4—28no—
1263C22⋊C4—28no—
1264C22⋊C4—28no—
1265C22⋊C4—28no—
1266C22⋊C4—28no—
1267C22⋊C4—28no—
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—
1277C22⋊C4—44no—
1278C22⋊C4—44no—
1279C22⋊C4—44no—
1280C22⋊C4—44no—
1281C22⋊C4—44no—
1282C22⋊C4—44no—
1283C22⋊C4—44no—
1284C22⋊C4—44no—
1285C42—24no—
1286C42—22no—
1287C42—22no—
1288C42—24no—
1289C42—22no—
1290C42—22no—
1291C42—22no—
1292C42—22no—
1293C42—22no—
1294C42—22no—
1295C42—22no—
1296C42—24no—
1297C42—22no—
1298C42—24no—
1299C42—22no—
1300C42—22no—
1301C42—24no—
1302C42—24no—
1303C42—24no—
1304C42—24no—
1305C42—24no—
1306C42—28no—
1307C42—44no—
1308C42—44no—
1309C42—44no—
1310C42—44no—
1311C42—42no—
1312C42—42no—
1313C42—44no—
1314C42—44no—
1315C422−1+418yes—
1316C23—22no—
1317C23—22no—
1318C23—24no—
1319C23—24no—
1320C23—24no—
1321C23—24no—
1322C23—24no—
1323C23—24no—
1324C23—24no—
1325C23C2×H(5,𝔽2)12yes—
1326C23C2×H(5,𝔽2)12yes—
1327C23C2×2−1+412yes—
1328C23C2611yescharacteristic
1329Q8—44no—
1330Q8—44no—
1331Q8—44no—
1332Q8—44no—
1333Q8—44no—
1334Q8—48no—
1335Q8—44no—
1336Q8—48no—
1337Q8—88no—
1338Q8—84no—
1339Q8—84no—
1340D4—416no—
1341D4—48no—
1342D4—84no—
1343D4—84no—
1344C2×C4—21no—
1345C2×C4—22no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—21no—
1349C2×C4—21no—
1350C2×C4—22no—
1351C2×C4—21no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—21no—
1355C2×C4—21no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—28no—
1360C2×C4—28no—
1361C2×C4—28no—
1362C2×C4—21no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—21no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—24no—
1374C2×C4—24no—
1375C2×C4—22no—
1376C2×C4—24no—
1377C2×C4—24no—
1378C2×C4—24no—
1379C2×C4—24no—
1380C2×C4—24no—
1381C2×C4—24no—
1382C2×C4—21no—
1383C2×C4—21no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—24no—
1389C2×C4—24no—
1390C2×C4—24no—
1391C2×C4—24no—
1392C2×C4—22no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—24no—
1396C2×C4—24no—
1397C2×C4—24no—
1398C2×C4—21no—
1399C2×C4—21no—
1400C2×C4—24no—
1401C2×C4—24no—
1402C2×C4—24no—
1403C2×C4—22no—
1404C2×C4—24no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—22no—
1411C2×C4—24no—
1412C2×C4—24no—
1413C2×C4—22no—
1414C2×C4—22no—
1415C2×C4—22no—
1416C2×C4—48no—
1417C2×C4—48no—
1418C2×C4—48no—
1419C2×C4—44no—
1420C2×C4—48no—
1421C2×C4—44no—
1422C2×C4—88no—
1423C2×C4—88no—
1424C2×C4—88no—
1425C2×C4—82no—
1426C2×C4—82no—
1427C2×C4C2×H(5,𝔽2)12yes—
1428C2×C4C2×H(5,𝔽2)12yes—
1429C2×C4C2×H(5,𝔽2)12yes—
1430C2×C4C2×H(5,𝔽2)12yes—
1431C2×C4C2×2−1+414yes—
1432C2×C4C2×2−1+414yes—
1433C2×C4C2×2−1+412yes—
1434C2×C4C2×2−1+412yes—
1435C2×C4C2×2−1+414yes—
1436C2×C4#58514yes—
1437C22—22no—
1438C22—22no—
1439C22—24no—
1440C22—24no—
1441C22—44no—
1442C22—44no—
1443C22—44no—
1444C22—44no—
1445C22—44no—
1446C22—44no—
1447C22—44no—
1448C22#353614yes—
1449C22C22×H(5,𝔽2)11yescharacteristic
1450C22C22×H(5,𝔽2)11yescharacteristic
1451C22C22×2−1+411yescharacteristic
1452C22C22×2−1+412yes—
1453C22C2×#58512yes—
1454C4—22no—
1455C4—22no—
1456C4—22no—
1457C4—22no—
1458C4—24no—
1459C4—22no—
1460C4—24no—
1461C4—24no—
1462C4—42no—
1463C4—42no—
1464C4—41no—
1465C4—41no—
1466C4—44no—
1467C4—42no—
1468C4—41no—
1469C4—41no—
1470C4—41no—
1471C4—41no—
1472C4—41no—
1473C4—44no—
1474C4—41no—
1475C4—44no—
1476C4—44no—
1477C4—42no—
1478C4—44no—
1479C4—44no—
1480C4—44no—
1481C4—42no—
1482C4#354414yes—
1483C2—24no—
1484C2—84no—
1485C2C2×#353611yescharacteristic
1486C2#6272911yescharacteristic
1487C2C2×#354411yescharacteristic
1488C2#6283512yes—
1489C2#6283712yes—
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. #53100C2semidirect
2. #53099C2semidirect
3. #52994C2semidirect
4. #52952C2semidirect
5. #52951C2semidirect
6. #52550C2semidirect
7. #45434C2semidirect
8. #45369C2semidirect
9. #45364C2semidirect
10. #44862C2semidirect
11. #44861C2semidirect
12. #44761C2semidirect
13. #42822C2semidirect
14. #42699C2semidirect
15. #42526C2semidirect
16. #42494C2semidirect
17. #42363C2semidirect
18. #42339C2semidirect
19. #42191C2semidirect
20. #42167C2semidirect
21. #42021C2semidirect
22. #41997C2semidirect
23. #36193C2semidirect
24. #36186C2semidirect
25. #36140C2semidirect
27. #35270C2semidirect
28. #35247C2semidirect
29. #35179C2semidirect
31. C2×#2399C2semidirect

Maximal subgroups

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

subgroupindex
#531002
#530992
#529942
#529522
#529512
#525502
#454342
#453692
#453642
#448622
#448612
#447612
#428222
#426992
#425262
#424942
#423632
#423392
#421912
#421672
#420212
#419972
#361932
#361862
#361402
#361392
#352702
#352472
#351792
#351782
C2×#23992