Finite Group Databasebeta

← #8091810

Subgroups — #8091810

Order 512.

4557 conjugacy classes of subgroups.

The subgroup lattice has 1450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#46342C211yesmaximal, characteristic, complemented
2#46302C212yesmaximal, complemented
3#46053C214yesmaximal, complemented
4#46051C212yesmaximal, complemented
5#45931C214yesmaximal, complemented
6#45901C214yesmaximal, complemented
7#45880C214yesmaximal, complemented
8#45717C212yesmaximal, complemented
9#45692C212yesmaximal, complemented
10#45677C212yesmaximal, complemented
11#45667C211yesmaximal, characteristic, complemented
12#45666C214yesmaximal, complemented
13#45626C212yesmaximal, complemented
14#45624C212yesmaximal, complemented
15#45521C214yesmaximal, complemented
16#45519C212yesmaximal, complemented
17#45490C212yesmaximal
18#45488C211yesmaximal, characteristic, complemented
19#36579C212yesmaximal, complemented
20#36547C211yesmaximal, characteristic, complemented
21#36534C211yesmaximal, characteristic, complemented
22#36516C211yesmaximal, characteristic, complemented
23#36514C212yesmaximal, complemented
24#36491C212yesmaximal, complemented
25#36473C212yesmaximal, complemented
26#36451C212yesmaximal, complemented
27#36439C212yesmaximal, complemented
28C4×#563C212yesmaximal, complemented
29C4×#560C211yesmaximal, characteristic
30C2×#563C2212yes—
31C2×#560C2211yescharacteristic
32C2×#556C2212yes—
33C2×#556C2211yescharacteristic, complemented
34C2×#554C2211yescharacteristic
35C22×C4×Q8C2211yescharacteristic, complemented
36C22×#117C2211yescharacteristic
37#2866C2214yes—
38#2866C2214yes—
39#2864C2214yescomplemented
40#2863C2212yescomplemented
41#2862C2211yescharacteristic, complemented
42#2861C2212yescomplemented
43#2860C2214yes—
44#2857C2212yescomplemented
45#2857C2212yescomplemented
46#2855C2212yes—
47#2855C2212yescomplemented
48#2855C2211yescharacteristic, complemented
49#2855C2212yescomplemented
50#2852C2214yes—
51#2851C2212yescomplemented
52#2850C2214yes—
53#2848C2211yescharacteristic
54#2848C2212yes—
55#2839C2214yescomplemented
56#2838C2214yes—
57#2835C2212yes—
58#2831C2214yes—
59#2830C2214yes—
60#2830C2212yescomplemented
61#2827C2214yes—
62#2817C2212yescomplemented
63#2816C2214yes—
64#2807C2214yes—
65#2802C2214yescomplemented
66#2800C2214yes—
67#2799C2214yescomplemented
68#2798C2214yescomplemented
69#2798C2214yescomplemented
70#2796C2214yes—
71#2796C2214yes—
72#2792C2212yescomplemented
73#2792C2214yescomplemented
74#2790C2214yes—
75#2788C2214yescomplemented
76#2788C2214yescomplemented
77#2783C2214yes—
78#2782C2214yes—
79#2781C2214yescomplemented
80#2779C2214yes—
81#2775C2214yes—
82#2763C2214yes—
83#2762C2214yescomplemented
84#2761C2214yescomplemented
85#2759C2214yes—
86#2758C2214yescomplemented
87#2757C2214yes—
88#2757C2214yescomplemented
89#2755C2214yescomplemented
90#2754C2214yes—
91#2751C2214yes—
92#2750C2214yes—
93#2746C2214yescomplemented
94#2744C2214yescomplemented
95#2742C2214yescomplemented
96#2739C2214yes—
97#2737C2214yes—
98#2737C2214yes—
99#2736C2212yes—
100#2735C2214yes—
101#2722C2212yescomplemented
102#2717C2212yes—
103#2716C2214yes—
104#2713C2214yescomplemented
105#2711C2214yes—
106#2709C2212yes—
107#2691C2214yes—
108#2689C2214yes—
109#2687C2214yes—
110#2685C2214yes—
111#2684C2212yes—
112#2604C2214yes—
113#2604C2214yescomplemented
114#2601C2214yes—
115#2599C2214yes—
116#2596C2214yes—
117#2595C2214yes—
118#2592C2214yes—
119#2590C2214yescomplemented
120#2583C2212yescomplemented
121#2581C2214yescomplemented
122#2579C2212yes—
123#2578C2214yescomplemented
124#2577C2214yescomplemented
125#2576C2214yes—
126#2575C2214yescomplemented
127#2573C2214yescomplemented
128#2570C2212yescomplemented
129#2568C2212yescomplemented
130#2565C2212yescomplemented
131#2563C2211yescharacteristic, complemented
132#2562C2212yes—
133#2561C2212yes—
134#2560C2214yes—
135#2560C2214yescomplemented
136#2559C2214yes—
137#2553C2214yes—
138#2551C2212yescomplemented
139#2547C2211yescharacteristic
140#2544C2212yes—
141#2542C2212yes—
142#2538C2212yes—
143#2536C2212yes—
144#2536C2212yescomplemented
145#2534C2212yes—
146#2533C2214yescomplemented
147#2531C2214yes—
148#2530C2214yes—
149#2528C2214yescomplemented
150#2525C2214yes—
151#2524C2214yescomplemented
152#2524C2214yescomplemented
153#2521C2214yes—
154#2521C2214yescomplemented
155#2519C2214yes—
156#2514C2212yescomplemented
157#2508C2212yescomplemented
158#2506C2212yescomplemented
159#2503C2211yescharacteristic
160#2499C2212yes—
161#2496C2212yes—
162#2496C2214yescomplemented
163#2496C2212yescomplemented
164#2495C2212yes—
165#2492C2212yes—
166#2492C2212yescomplemented
167#2491C2214yes—
168#2489C2212yes—
169#2489C2212yes—
170#2486C2211yescharacteristic
171#2485C2212yes—
172#2485C2212yes—
173#2485C2212yescomplemented
174#2481C2214yes—
175#2481C2214yescomplemented
176#2480C2214yes—
177#2478C2214yes—
178#2477C2214yes—
179#2475C2214yes—
180#2474C2214yes—
181#2472C2214yes—
182#2469C2214yes—
183#2469C2214yescomplemented
184#2465C2214yes—
185#2462C2214yescomplemented
186#2453C2212yescomplemented
187#2451C2212yescomplemented
188#2446C2212yescomplemented
189#2441C2212yescomplemented
190#2440C2212yes—
191#2439C2212yes—
192#2439C2212yes—
193#2434C2211yescharacteristic, complemented
194#2429C2212yes—
195#2429C2212yes—
196#2423C2212yes—
197#2421C2212yes—
198#2421C2212yescomplemented
199#2417C2212yes—
200#2415C2212yes—
201#2415C2212yes—
202#2415C2212yes—
203#2415C2212yes—
204#2415C2212yescomplemented
205#2409C2211yescharacteristic
206#2409C2212yes—
207#2409C2212yescomplemented
208#2383C2212yes—
209#2383C2214yes—
210#2383C2214yescomplemented
211#2382C2214yescomplemented
212#2381C2214yescomplemented
213#2380C2211yescharacteristic
214#2379C2212yes—
215#2378C2214yes—
216#2378C2214yescomplemented
217#2377C2212yes—
218#2377C2212yes—
219#2377C2212yes—
220#2376C2212yes—
221#2376C2211yescharacteristic
222#2376C2212yes—
223#2375C2212yes—
224#2375C2211yescharacteristic
225#2370C2212yescomplemented
226#2365C2212yescomplemented
227#2362C2212yes—
228#2362C2212yes—
229#2362C2212yescomplemented
230#2360C2212yes—
231#2355C2212yescomplemented
232#2354C2212yes—
233#2352C2212yes—
234#2352C2212yes—
235#2352C2212yescomplemented
236#2347C2212yes—
237#2345C2211yescharacteristic
238#2345C2211yescharacteristic, complemented
239C4×C4⋊Q8C2214yescomplemented
240C4×#127C2211yescharacteristic
241C4×#125C2214yescomplemented
242C4×#126C2212yes—
243C4×#126C2214yes—
244C4×#126C2214yescomplemented
245C4×#124C2212yes—
246C4×C22⋊Q8C2214yes—
247C4×C22⋊Q8C2214yescomplemented
248C4×#123C2212yes—
249C4×#123C2211yescharacteristic
250C4×#123C2212yes—
251C4×#123C2212yes—
252C4×#121C2212yes—
253C4×#121C2212yes—
254C4×#121C2212yes—
255C4×#120C2212yes—
256C4×#120C2211yescharacteristic
257C42×Q8C2211yescharacteristic, complemented
258C4×#117C2212yescomplemented
259C23×Q8C2311yescharacteristic
260C24×C4C2311yescharacteristic
261#563—216no—
262#560—28no—
263#556—48no—
264#556—44no—
265#554—44no—
266C2×C4⋊Q8C2314yes—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2311yescharacteristic
271C2×#127C2311yescharacteristic
272C2×#126C2314yes—
273C2×#126C2312yes—
274C2×#126C2314yes—
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#125C2314yes—
279C2×#125C2312yes—
280C2×#125C2312yes—
281C2×#124C2312yes—
282C2×#124C2314yes—
283C2×#124C2312yes—
284C2×#123C2312yes—
285C2×#123C2312yes—
286C2×#123C2311yescharacteristic
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2311yescharacteristic
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2311yescharacteristic
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2312yes—
300C2×#121C2312yes—
301C2×#121C2312yes—
302C2×#121C2312yes—
303C2×#120C2311yescharacteristic
304C2×#120C2312yes—
305C2×C4×Q8—44no—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2314yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2314yes—
312C2×C4×Q8C2312yes—
313C2×C4×D4C2311yescharacteristic
314C2×C4×D4C2312yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2311yescharacteristic
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×#117—44no—
322C2×#117C2312yes—
323C2×#117C2312yes—
324C2×#117C2314yes—
325C2×#117C2312yes—
326C2×#117C2312yes—
327C22×C4⋊C4C2311yescharacteristic
328C22×C4⋊C4C2311yescharacteristic
329C22×C4⋊C4C2312yes—
330C22×C4⋊C4C2311yescharacteristic
331C22×C22⋊C4C2312yes—
332C22×C42C2312yes—
333C22×C42C2312yes—
334C22×C42C2312yes—
335C22×C42C2311yescharacteristic
336#401C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#399C2314yes—
357#399C2314yes—
358#399C2314yes—
359#399C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2312yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#397C2312yes—
375#397C2312yes—
376#397C2314yes—
377#397C2314yes—
378#397C2312yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#395C2312yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#393C2314yes—
422#393C2314yes—
423#393C2314yes—
424#393C2314yes—
425#393C2314yes—
426#393C2314yes—
427#393C2312yes—
428#393C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2312yes—
433#391C2312yes—
434#391C2314yes—
435#391C2314yes—
436#391C2312yes—
437#391C2312yes—
438#391C2312yes—
439#391C2314yes—
440#391C2314yes—
441#391C2312yes—
442#391C2312yes—
443#391C2312yes—
444#391C2314yes—
445#391C2312yes—
446#391C2312yes—
447#391C2312yes—
448#391C2314yes—
449#390C2312yes—
450#390C2312yes—
451#390C2311yescharacteristic
452#390C2311yescharacteristic
453#390C2312yes—
454#390C2312yes—
455#390C2312yes—
456#390C2314yes—
457#390C2314yes—
458#390C2314yes—
459#390C2312yes—
460#389C2314yes—
461#389C2314yes—
462#389C2312yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2312yes—
467#389C2312yes—
468#389C2314yes—
469#389C2312yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2312yes—
474#389C2314yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2314yes—
479#389C2314yes—
480#389C2312yes—
481#389C2312yes—
482#389C2314yes—
483#389C2314yes—
484#389C2312yes—
485#389C2312yes—
486#389C2314yes—
487#389C2314yes—
488#389C2312yes—
489#389C2314yes—
490#388C2312yes—
491#388C2312yes—
492#388C2314yes—
493#388C2312yes—
494#388C2312yes—
495#388C2314yes—
496#388C2312yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2312yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2312yes—
523#388C2314yes—
524#388C2314yes—
525#388C2312yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2312yes—
534#388C2312yes—
535#388C2312yes—
536#388C2312yes—
537#388C2314yes—
538#388C2314yes—
539#387C2312yes—
540#387C2314yes—
541#387C2314yes—
542#387C2312yes—
543#387C2312yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
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#387C2312yes—
585#387C2312yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2312yes—
593#386C2312yes—
594#386C2312yes—
595#386C2311yescharacteristic
596#386C2312yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2312yes—
601#386C2314yes—
602#386C2312yes—
603#386C2312yes—
604#386C2312yes—
605#386C2311yescharacteristic
606#386C2312yes—
607#386C2312yes—
608#386C2312yes—
609#386C2312yes—
610#385C2312yes—
611#385C2314yes—
612#385C2314yes—
613#385C2312yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2312yes—
618#385C2312yes—
619#385C2311yescharacteristic
620#385C2311yescharacteristic
621#385C2312yes—
622#385C2312yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2312yes—
628#385C2312yes—
629#385C2314yes—
630#385C2312yes—
631#385C2312yes—
632#385C2314yes—
633#384C2311yescharacteristic
634#384C2314yes—
635#384C2312yes—
636#384C2312yes—
637#383C2314yes—
638#383C2312yes—
639#383C2314yes—
640#383C2314yes—
641#383C2314yes—
642#382C2314yes—
643#382C2312yes—
644#382C2312yes—
645#382C2312yes—
646#382C2314yes—
647#382C2314yes—
648#382C2314yes—
649#382C2312yes—
650#381C2312yes—
651#381C2312yes—
652#381C2312yes—
653#381C2311yescharacteristic
654#381C2312yes—
655#381C2314yes—
656#381C2312yes—
657#380C2311yescharacteristic
658#380C2312yes—
659#380C2312yes—
660#380C2312yes—
661#380C2312yes—
662#380C2312yes—
663#380C2312yes—
664#380C2312yes—
665#380C2311yescharacteristic
666#380C2312yes—
667#380C2312yes—
668#380C2312yes—
669#380C2312yes—
670#380C2312yes—
671#380C2314yes—
672#380C2314yes—
673#380C2314yes—
674#380C2312yes—
675#380C2312yes—
676#380C2314yes—
677#379C2311yescharacteristic
678#379C2312yes—
679#379C2314yes—
680#379C2312yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2311yescharacteristic
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2311yescharacteristic
712C4×C22⋊C4C2311yescharacteristic
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2312yes—
715#376C2314yes—
716C43C2311yescharacteristic
717C43C2314yes—
718C43C2312yes—
719C25C2411yescharacteristic
720C22×Q8—42no—
721C22×Q8—44no—
722C22×Q8C2411yescharacteristic
723C22×Q8C2412yes—
724C22×Q8C2414yes—
725C22×Q8C2412yes—
726C22×Q8C2412yes—
727C22×Q8C2412yes—
728C22×D4C2412yes—
729C22×D4C2412yes—
730C22×D4C2412yes—
731C22×D4C2412yes—
732C22×D4C2411yescharacteristic
733C22×D4C2412yes—
734C22×D4C2411yescharacteristic
735C23×C4—42no—
736C23×C4—44no—
737C23×C4C2411yescharacteristic
738C23×C4C2411yescharacteristic
739C23×C4C2412yes—
740C23×C4C2412yes—
741C23×C4C2412yes—
742C23×C4C2412yes—
743C23×C4C2412yes—
744C23×C4C2412yes—
745C23×C4C2411yescharacteristic
746C23×C4C2412yes—
747C23×C4C2412yes—
748C23×C4C2411yescharacteristic
749C23×C4C2412yes—
750C23×C4C2411yescharacteristic
751C4⋊Q8—216no—
752C4⋊Q8—42no—
753C4⋊Q8—44no—
754C4⋊Q8—42no—
755C4⋊Q8—44no—
756#127—24no—
757#126—28no—
758#126—216no—
759#126—216no—
760#126—48no—
761#126—48no—
762#126—48no—
763#125—216no—
764#125—44no—
765#125—44no—
766#124—28no—
767#124—48no—
768#124—44no—
769#123—28no—
770#123—28no—
771#123#4118yes—
772C22⋊Q8—216no—
773C22⋊Q8—216no—
774C22⋊Q8—44no—
775C22⋊Q8—44no—
776C22⋊Q8—44no—
777C22⋊Q8—44no—
778C22⋊Q8—44no—
779C22⋊Q8—44no—
780C22⋊Q8—42no—
781C22⋊Q8—42no—
782C22⋊Q8—44no—
783C22⋊Q8—44no—
784C22⋊Q8—44no—
785#121—28no—
786#121—28no—
787#121—28no—
788#120—24no—
789#120—28no—
790C4×Q8—28no—
791C4×Q8—24no—
792C4×Q8—48no—
793C4×Q8—44no—
794C4×Q8—48no—
795C4×Q8—44no—
796C4×Q8—44no—
797C4×D4—44no—
798C4×D4—44no—
799C4×D4—44no—
800C4×D4—44no—
801C4×D4—42no—
802C4×D4—44no—
803C4×D4—44no—
804C4×D4—42no—
805#117—28no—
806#117—28no—
807#117—48no—
808#117—44no—
809#117—44no—
810C2×C4⋊C4—24no—
811C2×C4⋊C4—24no—
812C2×C4⋊C4—42no—
813C2×C4⋊C4—44no—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2411yescharacteristic
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2411yescharacteristic
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2411yescharacteristic
872C2×C22⋊C4—44no—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2411yescharacteristic
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2411yescharacteristic
888C2×C22⋊C4C2411yescharacteristic
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2411yescharacteristic
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2411yescharacteristic
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2411yescharacteristic
924C2×C42—44no—
925C2×C42—42no—
926C2×C42—44no—
927C2×C42—44no—
928C2×C42C2414yes—
929C2×C42C2414yes—
930C2×C42C2411yescharacteristic
931C2×C42C2412yes—
932C2×C42C2412yes—
933C2×C42C2412yes—
934C2×C42C2412yes—
935C2×C42C2412yes—
936C2×C42C2414yes—
937C2×C42C2412yes—
938C2×C42C2411yescharacteristic
939C2×C42C2414yes—
940C2×C42C2414yes—
941C2×C42C2414yes—
942C2×C42C2412yes—
943C2×C42C2414yes—
944C2×C42C2414yes—
945C2×C42C2411yescharacteristic
946C2×C42C2412yes—
947C2×C42C2414yes—
948C2×C42C2414yes—
949C2×C42C2414yes—
950C2×C42C2414yes—
951C2×C42C2412yes—
952C2×C42C2412yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2414yes—
969#95C2414yes—
970#95C2412yes—
971#95C2412yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2412yes—
976#95C2414yes—
977#95C2412yes—
978#95C2414yes—
979#95C2412yes—
980#95C2414yes—
981#95C2412yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2412yes—
990#95C2412yes—
991#95C2414yes—
992#95C2412yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2412yes—
997#95C2412yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2412yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020C24—22no—
1021C24—41no—
1022C24—42no—
1023C24—41no—
1024C24—42no—
1025C24C2512yes—
1026C24C2512yes—
1027C24C2511yescharacteristic
1028C24C2511yescharacteristic
1029C2×Q8—28no—
1030C2×Q8—24no—
1031C2×Q8—24no—
1032C2×Q8—22no—
1033C2×Q8—24no—
1034C2×Q8—24no—
1035C2×Q8—24no—
1036C2×Q8—42no—
1037C2×Q8—44no—
1038C2×Q8—44no—
1039C2×Q8—42no—
1040C2×Q8—42no—
1041C2×Q8—44no—
1042C2×Q8—42no—
1043C2×Q8—44no—
1044C2×Q8—416no—
1045C2×D4—24no—
1046C2×D4—24no—
1047C2×D4—24no—
1048C2×D4—24no—
1049C2×D4—24no—
1050C2×D4—22no—
1051C2×D4—41no—
1052C2×D4—41no—
1053C2×D4—42no—
1054C2×D4—41no—
1055C2×D4—42no—
1056C2×D4—42no—
1057C2×D4—42no—
1058C2×D4—42no—
1059C2×D4—42no—
1060C2×D4—41no—
1061C2×D4—42no—
1062C2×D4—42no—
1063C2×D4—42no—
1064C2×D4—42no—
1065C2×D4C2×#4114yes—
1066C22×C4—24no—
1067C22×C4—22no—
1068C22×C4—22no—
1069C22×C4—24no—
1070C22×C4—24no—
1071C22×C4—24no—
1072C22×C4—24no—
1073C22×C4—24no—
1074C22×C4—24no—
1075C22×C4—24no—
1076C22×C4—24no—
1077C22×C4—24no—
1078C22×C4—24no—
1079C22×C4—24no—
1080C22×C4—41no—
1081C22×C4—41no—
1082C22×C4—42no—
1083C22×C4—42no—
1084C22×C4—42no—
1085C22×C4—42no—
1086C22×C4—42no—
1087C22×C4—41no—
1088C22×C4—44no—
1089C22×C4—42no—
1090C22×C4—41no—
1091C22×C4—42no—
1092C22×C4—42no—
1093C22×C4—44no—
1094C22×C4—44no—
1095C22×C4—42no—
1096C22×C4—42no—
1097C22×C4—42no—
1098C22×C4—42no—
1099C22×C4—42no—
1100C22×C4—416no—
1101C22×C4C2×#4114yes—
1102C22×C4C2512yes—
1103C22×C4C2512yes—
1104C22×C4C2512yes—
1105C22×C4C2512yes—
1106C22×C4C2512yes—
1107C22×C4C2514yes—
1108C22×C4C2511yescharacteristic
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2512yes—
1112C22×C4C2514yes—
1113C22×C4C2514yes—
1114C22×C4C2514yes—
1115C22×C4C2512yes—
1116C22×C4C2514yes—
1117C22×C4C2514yes—
1118C22×C4C2511yescharacteristic
1119C22×C4C2511yescharacteristic
1120C22×C4C2512yes—
1121C22×C4C2512yes—
1122C22×C4C2511yescharacteristic
1123C22×C4C2512yes—
1124C22×C4C2512yes—
1125C22×C4C2512yes—
1126C22×C4C2511yescharacteristic
1127C4⋊C4—24no—
1128C4⋊C4—24no—
1129C4⋊C4—28no—
1130C4⋊C4—28no—
1131C4⋊C4—28no—
1132C4⋊C4—28no—
1133C4⋊C4—28no—
1134C4⋊C4—28no—
1135C4⋊C4—28no—
1136C4⋊C4—24no—
1137C4⋊C4—22no—
1138C4⋊C4—24no—
1139C4⋊C4—22no—
1140C4⋊C4—24no—
1141C4⋊C4—28no—
1142C4⋊C4—24no—
1143C4⋊C4—24no—
1144C4⋊C4—24no—
1145C4⋊C4—24no—
1146C4⋊C4—24no—
1147C4⋊C4—42no—
1148C4⋊C4—44no—
1149C4⋊C4—42no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—42no—
1160C4⋊C4—42no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4—41no—
1165C4⋊C4—41no—
1166C4⋊C4—42no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—42no—
1176C4⋊C4—42no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—42no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4C2×#4118yes—
1184C4⋊C4H(5,𝔽2)14yes—
1185C22⋊C4—22no—
1186C22⋊C4—28no—
1187C22⋊C4—28no—
1188C22⋊C4—28no—
1189C22⋊C4—24no—
1190C22⋊C4—24no—
1191C22⋊C4—24no—
1192C22⋊C4—24no—
1193C22⋊C4—24no—
1194C22⋊C4—28no—
1195C22⋊C4—28no—
1196C22⋊C4—44no—
1197C22⋊C4—42no—
1198C22⋊C4—42no—
1199C22⋊C4—42no—
1200C22⋊C4—41no—
1201C22⋊C4—42no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—42no—
1208C22⋊C4—44no—
1209C22⋊C4—41no—
1210C22⋊C4—42no—
1211C22⋊C4—44no—
1212C22⋊C4—42no—
1213C22⋊C4—42no—
1214C22⋊C4—42no—
1215C22⋊C4—42no—
1216C22⋊C4—42no—
1217C22⋊C4—42no—
1218C22⋊C4—42no—
1219C22⋊C4—42no—
1220C22⋊C4—41no—
1221C22⋊C4—41no—
1222C22⋊C4—42no—
1223C22⋊C4—42no—
1224C22⋊C4—42no—
1225C22⋊C4—42no—
1226C22⋊C4—42no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4C2×#4118yes—
1235C22⋊C4C2×#4114yes—
1236C42—24no—
1237C42—22no—
1238C42—28no—
1239C42—28no—
1240C42—24no—
1241C42—28no—
1242C42—28no—
1243C42—22no—
1244C42—24no—
1245C42—24no—
1246C42—24no—
1247C42—24no—
1248C42—42no—
1249C42—42no—
1250C42—44no—
1251C42—42no—
1252C42—44no—
1253C42—44no—
1254C42—44no—
1255C42—44no—
1256C42—41no—
1257C42—42no—
1258C42—44no—
1259C42—44no—
1260C42—44no—
1261C23—21no—
1262C23—21no—
1263C23—22no—
1264C23—22no—
1265C23—21no—
1266C23—21no—
1267C23—22no—
1268C23—22no—
1269C23—22no—
1270C23—22no—
1271C23—22no—
1272C23—22no—
1273C23—22no—
1274C23—22no—
1275C23—22no—
1276C23—22no—
1277C23—22no—
1278C23—22no—
1279C23—22no—
1280C23—22no—
1281C23—22no—
1282C23—22no—
1283C23—44no—
1284C23—82no—
1285C23—84no—
1286C23—84no—
1287C23—82no—
1288C23C22×#4112yes—
1289C23C22×#4112yes—
1290C23C2611yescharacteristic
1291Q8—48no—
1292Q8—44no—
1293Q8—48no—
1294Q8—88no—
1295Q8—84no—
1296Q8—162no—
1297D4—44no—
1298D4—84no—
1299D4—82no—
1300D4—84no—
1301D4—84no—
1302D4—84no—
1303D4—84no—
1304C2×C4—22no—
1305C2×C4—21no—
1306C2×C4—22no—
1307C2×C4—24no—
1308C2×C4—22no—
1309C2×C4—21no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—22no—
1314C2×C4—24no—
1315C2×C4—22no—
1316C2×C4—24no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—24no—
1323C2×C4—21no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—21no—
1328C2×C4—21no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—24no—
1337C2×C4—24no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—22no—
1341C2×C4—24no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—24no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—24no—
1350C2×C4—24no—
1351C2×C4—24no—
1352C2×C4—22no—
1353C2×C4—24no—
1354C2×C4—24no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—24no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—24no—
1363C2×C4—24no—
1364C2×C4—22no—
1365C2×C4—44no—
1366C2×C4—44no—
1367C2×C4—48no—
1368C2×C4—48no—
1369C2×C4—48no—
1370C2×C4—44no—
1371C2×C4—48no—
1372C2×C4—44no—
1373C2×C4—84no—
1374C2×C4—84no—
1375C2×C4—84no—
1376C2×C4—84no—
1377C2×C4—84no—
1378C2×C4—82no—
1379C2×C4C22×#4112yes—
1380C2×C4C22×#4114yes—
1381C2×C4C22×#4114yes—
1382C2×C4C2×H(5,𝔽2)14yes—
1383C2×C4C2×H(5,𝔽2)12yes—
1384C2×C4#58514yes—
1385C22—22no—
1386C22—22no—
1387C22—24no—
1388C22—24no—
1389C22—42no—
1390C22—42no—
1391C22—41no—
1392C22—41no—
1393C22—41no—
1394C22—41no—
1395C22—42no—
1396C22—42no—
1397C22—42no—
1398C22—42no—
1399C22—42no—
1400C22—42no—
1401C22—42no—
1402C22—42no—
1403C22—42no—
1404C22—42no—
1405C22—42no—
1406C22—42no—
1407C22—42no—
1408C22—42no—
1409C22—88no—
1410C22C23×#4111yescharacteristic
1411C22C22×H(5,𝔽2)11yescharacteristic
1412C22C2×#58512yes—
1413C222−1+611yescharacteristic
1414C222−1+612yes—
1415C4—24no—
1416C4—22no—
1417C4—24no—
1418C4—24no—
1419C4—44no—
1420C4—44no—
1421C4—44no—
1422C4—44no—
1423C4—42no—
1424C4—42no—
1425C4—42no—
1426C4—44no—
1427C4—42no—
1428C4—42no—
1429C4—42no—
1430C4—42no—
1431C4—42no—
1432C4—41no—
1433C4—42no—
1434C4—42no—
1435C4—41no—
1436C4—44no—
1437C4—41no—
1438C4—42no—
1439C4#352914yes—
1440C2—42no—
1441C2—42no—
1442C2—82no—
1443C2—82no—
1444C2C2×#352911yescharacteristic
1445C2#6298411yescharacteristic
1446C2#6299512yes—
1447C2#6305312yes—
1448C2#6306311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#560C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #46342C2semidirect
2. #46302C2semidirect
3. #46053C2semidirect
4. #46051C2semidirect
5. #45931C2semidirect
6. #45901C2semidirect
7. #45880C2semidirect
8. #45717C2semidirect
9. #45692C2semidirect
10. #45677C2semidirect
11. #45667C2semidirect
12. #45666C2semidirect
13. #45626C2semidirect
14. #45624C2semidirect
15. #45521C2semidirect
16. #45519C2semidirect
18. #45488C2semidirect
19. #36579C2semidirect
20. #36547C2semidirect
21. #36534C2semidirect
22. #36516C2semidirect
23. #36514C2semidirect
24. #36491C2semidirect
25. #36473C2semidirect
26. #36451C2semidirect
27. #36439C2semidirect
28. C4×#563C2semidirect
33. C2×#556C22semidirect
35. C22×C4×Q8C22semidirect
39. #2864C22semidirect
40. #2863C22semidirect
41. #2862C22semidirect
42. #2861C22semidirect
44. #2857C22semidirect
45. #2857C22semidirect
47. #2855C22semidirect
48. #2855C22semidirect
49. #2855C22semidirect
51. #2851C22semidirect
55. #2839C22semidirect
60. #2830C22semidirect
62. #2817C22semidirect
65. #2802C22semidirect
67. #2799C22semidirect
68. #2798C22semidirect
69. #2798C22semidirect
72. #2792C22semidirect
73. #2792C22semidirect
75. #2788C22semidirect
76. #2788C22semidirect
79. #2781C22semidirect
83. #2762C22semidirect
84. #2761C22semidirect
86. #2758C22semidirect
88. #2757C22semidirect
89. #2755C22semidirect
93. #2746C22semidirect
94. #2744C22semidirect
95. #2742C22semidirect
101. #2722C22semidirect
104. #2713C22semidirect
113. #2604C22semidirect
119. #2590C22semidirect
120. #2583C22semidirect
121. #2581C22semidirect
123. #2578C22semidirect
124. #2577C22semidirect
126. #2575C22semidirect
127. #2573C22semidirect
128. #2570C22semidirect
129. #2568C22semidirect
130. #2565C22semidirect
131. #2563C22semidirect
135. #2560C22semidirect
138. #2551C22semidirect
144. #2536C22semidirect
146. #2533C22semidirect
149. #2528C22semidirect
151. #2524C22semidirect
152. #2524C22semidirect
154. #2521C22semidirect
156. #2514C22semidirect
157. #2508C22semidirect
158. #2506C22semidirect
162. #2496C22semidirect
163. #2496C22semidirect
166. #2492C22semidirect
173. #2485C22semidirect
175. #2481C22semidirect
183. #2469C22semidirect
185. #2462C22semidirect
186. #2453C22semidirect
187. #2451C22semidirect
188. #2446C22semidirect
189. #2441C22semidirect
193. #2434C22semidirect
198. #2421C22semidirect
204. #2415C22semidirect
207. #2409C22semidirect
210. #2383C22semidirect
211. #2382C22semidirect
212. #2381C22semidirect
216. #2378C22semidirect
225. #2370C22semidirect
226. #2365C22semidirect
229. #2362C22semidirect
231. #2355C22semidirect
235. #2352C22semidirect
238. #2345C22semidirect
239. C4×C4⋊Q8C22semidirect
241. C4×#125C22semidirect
244. C4×#126C22semidirect
247. C4×C22⋊Q8C22semidirect
257. C42×Q8C22semidirect
258. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#463422
#463022
#460532
#460512
#459312
#459012
#458802
#457172
#456922
#456772
#456672
#456662
#456262
#456242
#455212
#455192
#454902
#454882
#365792
#365472
#365342
#365162
#365142
#364912
#364732
#364512
#364392
C4×#5632
C4×#5602