Finite Group Databasebeta

← #7689027

Subgroups — #7689027

Order 512.

5137 conjugacy classes of subgroups.

The subgroup lattice has 1519 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59865C211yesmaximal, characteristic, complemented
2#59797C214yesmaximal, complemented
3#59773C214yesmaximal, complemented
4#59744C212yesmaximal, complemented
5#59309C212yesmaximal, complemented
6#59306C212yesmaximal, complemented
7#45251C211yesmaximal, characteristic, complemented
8#44914C211yesmaximal, characteristic, complemented
9#44898C212yesmaximal, complemented
10#44863C212yesmaximal, complemented
11#44428C214yesmaximal, complemented
12#43790C212yesmaximal, complemented
13#40138C214yesmaximal, complemented
14#40137C214yesmaximal, complemented
15#39463C212yesmaximal, complemented
16#39463C212yesmaximal, complemented
17#36534C211yesmaximal, characteristic, complemented
18#36501C214yesmaximal, complemented
19#36417C212yesmaximal, complemented
20#36254C212yesmaximal, complemented
21#36191C212yesmaximal, complemented
22#36089C211yesmaximal, characteristic, complemented
23#35759C211yesmaximal, characteristic, complemented
24#35688C212yesmaximal, complemented
25#34925C211yesmaximal, characteristic
26#34874C212yesmaximal, complemented
27#34208C212yesmaximal, complemented
28#34206C212yesmaximal, complemented
29C4×#552C212yesmaximal, complemented
30C2×#556C2211yescharacteristic
31C2×#554C2211yescharacteristic
32C2×#552C2212yes—
33C2×#532C2212yes—
34C2×#532C2212yes—
35C2×#520C2212yes—
36C2×#520C2211yescharacteristic
37C2×#520C2211yescharacteristic
38#2865C2214yes—
39#2862C2211yescharacteristic
40#2861C2212yes—
41#2852C2214yes—
42#2851C2212yes—
43#2851C2212yes—
44#2794C2212yes—
45#2789C2212yes—
46#2782C2212yes—
47#2766C2214yes—
48#2763C2212yes—
49#2761C2214yes—
50#2761C2214yes—
51#2760C2212yes—
52#2754C2214yes—
53#2751C2214yes—
54#2749C2214yes—
55#2747C2214yes—
56#2730C2214yes—
57#2723C2214yes—
58#2713C2214yes—
59#2713C2214yes—
60#2711C2214yes—
61#2711C2214yes—
62#2709C2214yes—
63#2709C2214yes—
64#2709C2212yes—
65#2708C2214yes—
66#2708C2214yes—
67#2691C2214yes—
68#2638C2214yes—
69#2637C2212yes—
70#2636C2212yes—
71#2616C2212yes—
72#2616C2211yescharacteristic
73#2616C2211yescharacteristic
74#2612C2212yes—
75#2610C2214yes—
76#2609C2212yes—
77#2607C2212yes—
78#2605C2214yes—
79#2604C2212yes—
80#2603C2214yes—
81#2603C2212yes—
82#2600C2214yes—
83#2597C2214yes—
84#2597C2214yes—
85#2596C2214yes—
86#2595C2214yes—
87#2595C2214yes—
88#2593C2212yes—
89#2585C2214yes—
90#2581C2212yes—
91#2578C2214yes—
92#2576C2214yes—
93#2575C2214yes—
94#2574C2214yes—
95#2574C2214yes—
96#2570C2212yes—
97#2570C2212yes—
98#2569C2214yes—
99#2565C2212yes—
100#2563C2211yescharacteristic
101#2562C2212yes—
102#2562C2212yes—
103#2560C2214yes—
104#2560C2214yes—
105#2559C2214yes—
106#2559C2214yes—
107#2555C2211yescharacteristic
108#2555C2211yescharacteristic
109#2555C2212yes—
110#2551C2211yescharacteristic
111#2547C2211yescharacteristic
112#2544C2212yes—
113#2541C2212yes—
114#2537C2211yescharacteristic
115#2536C2212yes—
116#2536C2212yes—
117#2536C2212yes—
118#2533C2214yes—
119#2531C2214yes—
120#2530C2214yes—
121#2529C2214yes—
122#2528C2214yes—
123#2526C2214yes—
124#2525C2214yes—
125#2521C2214yes—
126#2521C2214yes—
127#2520C2214yes—
128#2520C2214yes—
129#2516C2214yes—
130#2515C2214yes—
131#2510C2214yes—
132#2505C2214yes—
133#2503C2211yescharacteristic
134#2502C2211yescharacteristic
135#2499C2212yes—
136#2497C2212yes—
137#2496C2212yes—
138#2495C2212yes—
139#2494C2212yes—
140#2491C2212yes—
141#2491C2212yes—
142#2487C2212yes—
143#2487C2212yes—
144#2487C2211yescharacteristic
145#2486C2211yescharacteristic
146#2485C2212yes—
147#2485C2212yes—
148#2485C2212yes—
149#2479C2214yes—
150#2477C2214yes—
151#2476C2214yes—
152#2476C2214yes—
153#2476C2214yes—
154#2474C2214yes—
155#2474C2214yes—
156#2471C2214yes—
157#2468C2214yes—
158#2466C2214yes—
159#2465C2214yes—
160#2463C2214yes—
161#2463C2212yes—
162#2462C2214yes—
163#2461C2214yes—
164#2460C2214yes—
165#2459C2214yes—
166#2450C2214yes—
167#2450C2214yes—
168#2444C2214yes—
169#2444C2214yes—
170#2440C2212yes—
171#2440C2212yes—
172#2439C2212yes—
173#2439C2212yes—
174#2428C2212yes—
175#2428C2212yes—
176#2417C2212yes—
177#2417C2212yes—
178#2415C2212yes—
179#2415C2212yes—
180#2415C2214yes—
181#2399C2212yes—
182#2398C2212yes—
183#2392C2214yes—
184#2388C2212yes—
185#2388C2211yescharacteristic
186#2388C2211yescharacteristic
187#2374C2212yes—
188#2373C2214yes—
189#2373C2214yes—
190#2371C2214yes—
191#2370C2212yes—
192#2368C2214yes—
193#2368C2214yes—
194#2367C2214yes—
195#2367C2214yes—
196#2366C2214yes—
197#2365C2214yes—
198#2364C2214yes—
199#2364C2214yes—
200#2364C2214yes—
201#2364C2214yes—
202#2362C2212yes—
203#2360C2212yes—
204#2359C2214yes—
205#2356C2212yes—
206#2354C2212yes—
207#2354C2212yes—
208#2353C2214yes—
209#2352C2212yes—
210#2352C2212yes—
211#2352C2212yes—
212#2352C2212yes—
213#2352C2212yes—
214#2352C2212yes—
215#2352C2212yes—
216#2352C2212yes—
217#2352C2212yes—
218#2352C2212yes—
219#2352C2212yes—
220D4×C4⋊C4C2212yes—
221D4×C4⋊C4C2212yes—
222#2346C2211yescharacteristic
223#2346C2212yes—
224#2346C2211yescharacteristic
225#2344C2212yes—
226#2344C2212yes—
227#2343C2214yes—
228#2328C2214yes—
229#2327C2214yes—
230#2325C2214yes—
231#2325C2214yes—
232#2311C2212yes—
233#2311C2212yes—
234#2311C2212yes—
235#2311C2212yes—
236C4×#127C2211yescharacteristic
237C4×#125C2212yes—
238C4×#125C2214yes—
239C4×#126C2214yes—
240C4×#124C2212yes—
241C4×#124C2214yes—
242C4×#124C2214yes—
243C4×C22⋊Q8C2212yes—
244C4×C22⋊Q8C2212yes—
245C4×#123C2214yes—
246C4×#121C2214yes—
247C4×#121C2212yes—
248C4×#121C2212yes—
249C4×#121C2214yes—
250#2298C2214yes—
251#2290C2214yes—
252#2285C2212yes—
253C2×#382C2212yes—
254C42×Q8C2211yescharacteristic
255C42×D4C2212yes—
256C4×#117C2214yes—
257C4×#117C2212yes—
258C2×C4×C4⋊C4C2212yes—
259C22×#41C2312yes—
260C22×#41C2311yescharacteristic
261C22×#41C2311yescharacteristic
262#556—44no—
263#554—44no—
264#552—216no—
265#532—216no—
266#532—216no—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2311yescharacteristic
271C2×#127C2312yes—
272C2×#127C2312yes—
273C2×#127C2311yescharacteristic
274C2×#126C2314yes—
275C2×#126C2312yes—
276C2×#126C2312yes—
277C2×#126C2314yes—
278C2×#125C2312yes—
279C2×#125C2314yes—
280C2×#125C2312yes—
281C2×#124C2312yes—
282C2×#124C2312yes—
283C2×#124C2312yes—
284C2×#124C2312yes—
285C2×#124C2312yes—
286C2×#124C2312yes—
287C2×#123C2314yes—
288C2×#123C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2311yescharacteristic
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2311yescharacteristic
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2314yes—
297C2×#121C2312yes—
298C2×#121C2312yes—
299C2×#121C2312yes—
300C2×#121C2312yes—
301C2×#121C2312yes—
302C2×#121C2312yes—
303C2×#121C2312yes—
304C2×#121C2312yes—
305C2×#121C2312yes—
306C2×#121C2312yes—
307#520—44no—
308#520—48no—
309#520—44no—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2314yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2311yescharacteristic
323C2×C4×D4C2311yescharacteristic
324C2×C4×D4C2312yes—
325C2×C4×D4C2314yes—
326C2×C4×D4C2314yes—
327C2×C4×D4C2314yes—
328C2×C4×D4C2314yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2314yes—
331C2×C4×D4C2314yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2314yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2312yes—
337C2×#117C2312yes—
338C2×#117C2314yes—
339C2×#117C2311yescharacteristic
340C2×#117C2311yescharacteristic
341C2×#117C2312yes—
342C2×#117C2312yes—
343C2×#117C2312yes—
344C2×#117C2314yes—
345C2×#117C2314yes—
346C2×#117C2312yes—
347C22×C4⋊C4C2312yes—
348C22×C4⋊C4C2312yes—
349C22×C4⋊C4C2312yes—
350C22×C4⋊C4C2312yes—
351C22×C4⋊C4C2312yes—
352C22×C4⋊C4C2311yescharacteristic
353C22×C4⋊C4C2311yescharacteristic
354C22×C42C2312yes—
355C22×C42C2312yes—
356C22×C42C2314yes—
357#401C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2312yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2312yes—
368#400C2312yes—
369#400C2314yes—
370#399C2314yes—
371#399C2314yes—
372#399C2312yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2312yes—
380#398C2312yes—
381#398C2312yes—
382#398C2314yes—
383#398C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2312yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2311yescharacteristic
404#395C2312yes—
405#395C2312yes—
406#395C2311yescharacteristic
407#395C2312yes—
408#395C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2312yes—
417#394C2314yes—
418#394C2314yes—
419#394C2312yes—
420#394C2311yescharacteristic
421#394C2312yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2312yes—
427#394C2312yes—
428#394C2312yes—
429#394C2312yes—
430#394C2311yescharacteristic
431#394C2314yes—
432#393C2312yes—
433#393C2312yes—
434#393C2314yes—
435#393C2314yes—
436#393C2311yescharacteristic
437#393C2311yescharacteristic
438#393C2312yes—
439#392C2312yes—
440#392C2311yescharacteristic
441#392C2312yes—
442#392C2312yes—
443#392C2311yescharacteristic
444#392C2312yes—
445#392C2312yes—
446#391C2314yes—
447#391C2312yes—
448#391C2312yes—
449#391C2314yes—
450#391C2314yes—
451#391C2314yes—
452#391C2314yes—
453#391C2312yes—
454#391C2314yes—
455#391C2314yes—
456#391C2312yes—
457#391C2312yes—
458#390C2312yes—
459#390C2312yes—
460#390C2311yescharacteristic
461#390C2311yescharacteristic
462#390C2312yes—
463#390C2314yes—
464#390C2314yes—
465#390C2314yes—
466#390C2314yes—
467#390C2312yes—
468#390C2314yes—
469#390C2314yes—
470#390C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2314yes—
474#389C2314yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2314yes—
480#389C2312yes—
481#389C2314yes—
482#389C2314yes—
483#389C2312yes—
484#389C2312yes—
485#389C2314yes—
486#389C2312yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2312yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2312yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2312yes—
526#388C2314yes—
527#388C2312yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
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#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2312yes—
582#386C2314yes—
583#386C2312yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#386C2312yes—
594#386C2314yes—
595#386C2312yes—
596#386C2314yes—
597#386C2314yes—
598#386C2312yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2312yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#384C2311yescharacteristic
617#384C2312yes—
618#384C2312yes—
619#383C2314yes—
620#383C2314yes—
621#382C2314yes—
622#382C2312yes—
623#382C2312yes—
624#382C2312yes—
625#382C2312yes—
626#382C2312yes—
627#382C2312yes—
628#382C2314yes—
629#382C2314yes—
630#382C2312yes—
631#382C2312yes—
632#381C2314yes—
633#381C2314yes—
634#381C2312yes—
635#381C2314yes—
636#380C2312yes—
637#380C2311yescharacteristic
638#380C2311yescharacteristic
639#380C2312yes—
640#380C2312yes—
641#380C2312yes—
642#380C2312yes—
643#380C2312yes—
644#380C2312yes—
645#380C2312yes—
646#380C2312yes—
647#380C2312yes—
648#380C2312yes—
649#380C2312yes—
650#380C2312yes—
651#380C2312yes—
652#380C2312yes—
653#380C2312yes—
654#380C2314yes—
655#380C2314yes—
656#380C2314yes—
657#380C2314yes—
658#380C2312yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2311yescharacteristic
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C22⋊C4C2312yes—
685C4×C22⋊C4C2314yes—
686C4×C22⋊C4C2314yes—
687C4×C22⋊C4C2314yes—
688C4×C22⋊C4C2314yes—
689C4×C22⋊C4C2314yes—
690C4×C22⋊C4C2312yes—
691C4×C22⋊C4C2312yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2311yescharacteristic
701C4×C22⋊C4C2311yescharacteristic
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709#376C2314yes—
710#376C2314yes—
711#376C2312yes—
712#376C2312yes—
713#376C2314yes—
714C2×#95C2314yes—
715C2×#95C2314yes—
716C2×#95C2314yes—
717C43C2312yes—
718C43C2311yescharacteristic
719C43C2314yes—
720C2×#41—28no—
721C2×#41—28no—
722C2×#41—28no—
723C2×#41—28no—
724C2×#41—42no—
725C2×#41—44no—
726C2×#41—42no—
727C22×Q8C2411yescharacteristic
728C22×Q8C2411yescharacteristic
729C22×Q8C2411yescharacteristic
730C22×Q8C2412yes—
731C22×Q8C2412yes—
732C22×Q8C2412yes—
733C22×D4C2412yes—
734C22×D4C2412yes—
735C22×D4C2411yescharacteristic
736C22×D4C2412yes—
737C22×D4C2411yescharacteristic
738C22×D4C2412yes—
739C22×D4C2412yes—
740C22×D4C2412yes—
741C22×D4C2412yes—
742C22×D4C2411yescharacteristic
743C22×D4C2412yes—
744C22×D4C2412yes—
745C22×D4C2412yes—
746C22×D4C2412yes—
747C22×D4C2411yescharacteristic
748C22×D4C2412yes—
749C23×C4C2412yes—
750C23×C4C2411yescharacteristic
751C23×C4C2411yescharacteristic
752C23×C4C2412yes—
753C23×C4C2412yes—
754C23×C4C2412yes—
755C23×C4C2414yes—
756C23×C4C2414yes—
757C23×C4C2414yes—
758C23×C4C2412yes—
759C23×C4C2412yes—
760C23×C4C2412yes—
761C23×C4C2412yes—
762C23×C4C2414yes—
763C23×C4C2414yes—
764C23×C4C2412yes—
765C4⋊Q8—28no—
766C4⋊Q8—28no—
767C4⋊Q8—42no—
768C4⋊Q8—42no—
769#127—28no—
770#127—28no—
771#127—42no—
772#126—216no—
773#126—48no—
774#126—44no—
775#126—44no—
776#125—216no—
777#125—28no—
778#125—44no—
779#124—28no—
780#124—28no—
781#124—28no—
782#124—28no—
783#124—44no—
784#124—44no—
785#123—216no—
786#123—44no—
787C22⋊Q8—28no—
788C22⋊Q8—28no—
789C22⋊Q8—48no—
790C22⋊Q8—48no—
791C22⋊Q8—48no—
792C22⋊Q8—44no—
793C22⋊Q8—42no—
794C22⋊Q8—42no—
795#121—28no—
796#121—28no—
797#121—28no—
798#121—28no—
799#121—28no—
800#121—28no—
801#121—28no—
802#121—28no—
803#121—44no—
804#121—44no—
805C4×Q8—24no—
806C4×Q8—28no—
807C4×Q8—44no—
808C4×Q8—44no—
809C4×Q8—48no—
810C4×Q8—44no—
811C4×D4—28no—
812C4×D4—28no—
813C4×D4—28no—
814C4×D4—28no—
815C4×D4—28no—
816C4×D4—28no—
817C4×D4—44no—
818C4×D4—48no—
819C4×D4—44no—
820C4×D4—48no—
821C4×D4—48no—
822C4×D4—48no—
823C4×D4—44no—
824C4×D4—42no—
825C4×D4—44no—
826C4×D4—42no—
827C4×D4—44no—
828C4×D4—48no—
829C4×D4—48no—
830C4×D4—48no—
831C4×D4#41116yes—
832#117—28no—
833#117—28no—
834#117—24no—
835#117—24no—
836#117—216no—
837#117—48no—
838#117—48no—
839#117—44no—
840#117—44no—
841#117—44no—
842C2×C4⋊C4—28no—
843C2×C4⋊C4—28no—
844C2×C4⋊C4—28no—
845C2×C4⋊C4—42no—
846C2×C4⋊C4—44no—
847C2×C4⋊C4—42no—
848C2×C4⋊C4—44no—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2411yescharacteristic
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2411yescharacteristic
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2411yescharacteristic
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2411yescharacteristic
930C2×C22⋊C4C2411yescharacteristic
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2412yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2412yes—
951C2×C22⋊C4C2412yes—
952C2×C22⋊C4C2412yes—
953C2×C42—28no—
954C2×C42—28no—
955C2×C42—48no—
956C2×C42C2412yes—
957C2×C42C2414yes—
958C2×C42C2414yes—
959C2×C42C2412yes—
960C2×C42C2412yes—
961C2×C42C2414yes—
962C2×C42C2414yes—
963C2×C42C2411yescharacteristic
964C2×C42C2411yescharacteristic
965C2×C42C2412yes—
966C2×C42C2412yes—
967C2×C42C2412yes—
968C2×C42C2414yes—
969C2×C42C2412yes—
970C2×C42C2412yes—
971C2×C42C2412yes—
972C2×C42C2412yes—
973C2×C42C2414yes—
974C2×C42C2414yes—
975C2×C42C2414yes—
976C2×C42C2414yes—
977C2×C42C2414yes—
978C2×C42C2412yes—
979C2×C42C2411yescharacteristic
980C2×C42C2414yes—
981C2×C42C2414yes—
982C2×C42C2414yes—
983C2×C42C2412yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2412yes—
997#95C2412yes—
998#95C2411yescharacteristic
999#95C2411yescharacteristic
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2414yes—
1018#95C2411yescharacteristic
1019#95C2414yes—
1020#95C2412yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2411yescharacteristic
1032#95C2412yes—
1033#95C2412yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043C24C2511yescharacteristic
1044C24C2511yescharacteristic
1045C24C2512yes—
1046C24C2512yes—
1047C24C2512yes—
1048#41—416no—
1049#41—432no—
1050#41—416no—
1051C2×Q8—24no—
1052C2×Q8—24no—
1053C2×Q8—24no—
1054C2×Q8—24no—
1055C2×Q8—24no—
1056C2×Q8—22no—
1057C2×Q8—24no—
1058C2×Q8—41no—
1059C2×Q8—42no—
1060C2×Q8—41no—
1061C2×Q8—42no—
1062C2×Q8—42no—
1063C2×Q8—42no—
1064C2×Q8—44no—
1065C2×D4—24no—
1066C2×D4—24no—
1067C2×D4—24no—
1068C2×D4—24no—
1069C2×D4—24no—
1070C2×D4—24no—
1071C2×D4—24no—
1072C2×D4—24no—
1073C2×D4—24no—
1074C2×D4—24no—
1075C2×D4—24no—
1076C2×D4—24no—
1077C2×D4—24no—
1078C2×D4—24no—
1079C2×D4—24no—
1080C2×D4—24no—
1081C2×D4—24no—
1082C2×D4—24no—
1083C2×D4—24no—
1084C2×D4—24no—
1085C2×D4—22no—
1086C2×D4—22no—
1087C2×D4—41no—
1088C2×D4—42no—
1089C2×D4—42no—
1090C2×D4—42no—
1091C2×D4—42no—
1092C2×D4—41no—
1093C2×D4—41no—
1094C2×D4—42no—
1095C2×D4—42no—
1096C2×D4—42no—
1097C2×D4—41no—
1098C2×D4—42no—
1099C2×D4—42no—
1100C2×D4—41no—
1101C2×D4—42no—
1102C2×D4—42no—
1103C2×D4—42no—
1104C2×D4—42no—
1105C2×D4—42no—
1106C2×D4—42no—
1107C2×D4—41no—
1108C2×D4—42no—
1109C2×D4—42no—
1110C2×D4C2×#4118yes—
1111C22×C4—24no—
1112C22×C4—24no—
1113C22×C4—24no—
1114C22×C4—24no—
1115C22×C4—28no—
1116C22×C4—24no—
1117C22×C4—24no—
1118C22×C4—24no—
1119C22×C4—24no—
1120C22×C4—24no—
1121C22×C4—24no—
1122C22×C4—22no—
1123C22×C4—22no—
1124C22×C4—24no—
1125C22×C4—24no—
1126C22×C4—24no—
1127C22×C4—24no—
1128C22×C4—28no—
1129C22×C4—28no—
1130C22×C4—44no—
1131C22×C4—44no—
1132C22×C4—42no—
1133C22×C4—44no—
1134C22×C4—44no—
1135C22×C4—44no—
1136C22×C4—44no—
1137C22×C4—42no—
1138C22×C4—42no—
1139C22×C4—42no—
1140C22×C4—42no—
1141C22×C4—42no—
1142C22×C4—42no—
1143C22×C4—42no—
1144C22×C4—44no—
1145C22×C4—42no—
1146C22×C4—44no—
1147C22×C4—44no—
1148C22×C4—44no—
1149C22×C4—44no—
1150C22×C4—44no—
1151C22×C4—42no—
1152C22×C4—42no—
1153C22×C4—44no—
1154C22×C4C2×#4118yes—
1155C22×C4C2×#4118yes—
1156C22×C4C2512yes—
1157C22×C4C2512yes—
1158C22×C4C2512yes—
1159C22×C4C2514yes—
1160C22×C4C2514yes—
1161C22×C4C2514yes—
1162C22×C4C2514yes—
1163C22×C4C2512yes—
1164C22×C4C2514yes—
1165C22×C4C2511yescharacteristic
1166C22×C4C2511yescharacteristic
1167C22×C4C2512yes—
1168C22×C4C2514yes—
1169C22×C4C2512yes—
1170C22×C4C2511yescharacteristic
1171C22×C4C2512yes—
1172C22×C4C2512yes—
1173C22×C4C2512yes—
1174C22×C4C2512yes—
1175C22×C4C2512yes—
1176C22×C4C2512yes—
1177C22×C4C2512yes—
1178C22×C4C2511yescharacteristic
1179C22×C4C2511yescharacteristic
1180C4⋊C4—24no—
1181C4⋊C4—24no—
1182C4⋊C4—28no—
1183C4⋊C4—24no—
1184C4⋊C4—28no—
1185C4⋊C4—28no—
1186C4⋊C4—24no—
1187C4⋊C4—24no—
1188C4⋊C4—24no—
1189C4⋊C4—24no—
1190C4⋊C4—24no—
1191C4⋊C4—24no—
1192C4⋊C4—28no—
1193C4⋊C4—28no—
1194C4⋊C4—28no—
1195C4⋊C4—24no—
1196C4⋊C4—24no—
1197C4⋊C4—28no—
1198C4⋊C4—28no—
1199C4⋊C4—24no—
1200C4⋊C4—22no—
1201C4⋊C4—22no—
1202C4⋊C4—24no—
1203C4⋊C4—28no—
1204C4⋊C4—28no—
1205C4⋊C4—28no—
1206C4⋊C4—24no—
1207C4⋊C4—44no—
1208C4⋊C4—44no—
1209C4⋊C4—42no—
1210C4⋊C4—42no—
1211C4⋊C4—44no—
1212C4⋊C4—44no—
1213C4⋊C4—44no—
1214C4⋊C4—44no—
1215C4⋊C4—42no—
1216C4⋊C4—41no—
1217C4⋊C4—41no—
1218C4⋊C4—42no—
1219C4⋊C4—42no—
1220C4⋊C4—42no—
1221C4⋊C4—44no—
1222C4⋊C4—44no—
1223C4⋊C4—44no—
1224C4⋊C4—44no—
1225C4⋊C4—44no—
1226C4⋊C4—44no—
1227C4⋊C4—42no—
1228C4⋊C4C2×#4118yes—
1229C4⋊C4H(5,𝔽2)14yes—
1230C22⋊C4—28no—
1231C22⋊C4—28no—
1232C22⋊C4—24no—
1233C22⋊C4—24no—
1234C22⋊C4—24no—
1235C22⋊C4—24no—
1236C22⋊C4—28no—
1237C22⋊C4—24no—
1238C22⋊C4—24no—
1239C22⋊C4—24no—
1240C22⋊C4—24no—
1241C22⋊C4—24no—
1242C22⋊C4—24no—
1243C22⋊C4—24no—
1244C22⋊C4—24no—
1245C22⋊C4—28no—
1246C22⋊C4—24no—
1247C22⋊C4—24no—
1248C22⋊C4—24no—
1249C22⋊C4—24no—
1250C22⋊C4—24no—
1251C22⋊C4—24no—
1252C22⋊C4—24no—
1253C22⋊C4—42no—
1254C22⋊C4—44no—
1255C22⋊C4—44no—
1256C22⋊C4—44no—
1257C22⋊C4—44no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—44no—
1261C22⋊C4—44no—
1262C22⋊C4—44no—
1263C22⋊C4—44no—
1264C22⋊C4—44no—
1265C22⋊C4—42no—
1266C22⋊C4—42no—
1267C22⋊C4—44no—
1268C22⋊C4—41no—
1269C22⋊C4—41no—
1270C22⋊C4—42no—
1271C22⋊C4—42no—
1272C22⋊C4—44no—
1273C22⋊C4—44no—
1274C22⋊C4—42no—
1275C22⋊C4—42no—
1276C22⋊C4—44no—
1277C22⋊C4—42no—
1278C22⋊C4—44no—
1279C22⋊C4—44no—
1280C22⋊C4—44no—
1281C22⋊C4—44no—
1282C22⋊C4C2×#4118yes—
1283C22⋊C4C2×#4118yes—
1284C42—24no—
1285C42—24no—
1286C42—24no—
1287C42—24no—
1288C42—24no—
1289C42—24no—
1290C42—28no—
1291C42—28no—
1292C42—28no—
1293C42—24no—
1294C42—24no—
1295C42—22no—
1296C42—24no—
1297C42—28no—
1298C42—28no—
1299C42—24no—
1300C42—22no—
1301C42—44no—
1302C42—44no—
1303C42—41no—
1304C42—44no—
1305C42—44no—
1306C42—44no—
1307C42—44no—
1308C42—44no—
1309C42—44no—
1310C42—42no—
1311C42C2×#4118yes—
1312C23—22no—
1313C23—22no—
1314C23—22no—
1315C23—22no—
1316C23—22no—
1317C23—22no—
1318C23—22no—
1319C23—22no—
1320C23—22no—
1321C23—22no—
1322C23—22no—
1323C23—22no—
1324C23—22no—
1325C23—22no—
1326C23—22no—
1327C23—22no—
1328C23—21no—
1329C23—21no—
1330C23—22no—
1331C23—22no—
1332C23—22no—
1333C23—22no—
1334C23—21no—
1335C23—22no—
1336C23—22no—
1337C23—21no—
1338C23—21no—
1339C23—22no—
1340C23—21no—
1341C23C22×#4114yes—
1342C23C22×#4114yes—
1343C23C2611yescharacteristic
1344Q8—44no—
1345Q8—48no—
1346Q8—44no—
1347Q8—44no—
1348Q8—84no—
1349Q8—162no—
1350D4—48no—
1351D4—48no—
1352D4—48no—
1353D4—48no—
1354D4—48no—
1355D4—48no—
1356D4—48no—
1357D4—44no—
1358D4—44no—
1359D4—44no—
1360D4—48no—
1361D4—84no—
1362D4—84no—
1363D4—82no—
1364D4—84no—
1365D4—84no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—21no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—24no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—21no—
1378C2×C4—22no—
1379C2×C4—216no—
1380C2×C4—216no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—24no—
1384C2×C4—22no—
1385C2×C4—24no—
1386C2×C4—24no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—24no—
1392C2×C4—21no—
1393C2×C4—21no—
1394C2×C4—22no—
1395C2×C4—24no—
1396C2×C4—22no—
1397C2×C4—21no—
1398C2×C4—22no—
1399C2×C4—24no—
1400C2×C4—22no—
1401C2×C4—24no—
1402C2×C4—24no—
1403C2×C4—24no—
1404C2×C4—24no—
1405C2×C4—24no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—24no—
1410C2×C4—24no—
1411C2×C4—22no—
1412C2×C4—22no—
1413C2×C4—22no—
1414C2×C4—24no—
1415C2×C4—24no—
1416C2×C4—22no—
1417C2×C4—24no—
1418C2×C4—22no—
1419C2×C4—24no—
1420C2×C4—24no—
1421C2×C4—24no—
1422C2×C4—22no—
1423C2×C4—22no—
1424C2×C4—22no—
1425C2×C4—48no—
1426C2×C4—416no—
1427C2×C4—48no—
1428C2×C4—44no—
1429C2×C4—44no—
1430C2×C4—84no—
1431C2×C4—88no—
1432C2×C4—88no—
1433C2×C4—84no—
1434C2×C4—84no—
1435C2×C4—162no—
1436C2×C4—164no—
1437C2×C4—162no—
1438C2×C4—164no—
1439C2×C4C22×#4114yes—
1440C2×C4C22×#4114yes—
1441C2×C4C22×#4114yes—
1442C2×C4C22×#4114yes—
1443C2×C4C22×#4114yes—
1444C2×C4C2×H(5,𝔽2)14yes—
1445C2×C4C2×H(5,𝔽2)12yes—
1446C2×C4#58514yes—
1447C2×C4#58512yes—
1448C22—24no—
1449C22—24no—
1450C22—24no—
1451C22—24no—
1452C22—24no—
1453C22—24no—
1454C22—42no—
1455C22—42no—
1456C22—42no—
1457C22—42no—
1458C22—42no—
1459C22—42no—
1460C22—42no—
1461C22—42no—
1462C22—42no—
1463C22—42no—
1464C22—42no—
1465C22—42no—
1466C22—42no—
1467C22—41no—
1468C22—41no—
1469C22—42no—
1470C22—42no—
1471C22—42no—
1472C22—42no—
1473C22—41no—
1474C22—42no—
1475C22—41no—
1476C22—41no—
1477C22—41no—
1478C22—42no—
1479C22C23×#4112yes—
1480C22C22×H(5,𝔽2)11yescharacteristic
1481C22C2×#58512yes—
1482C22C2×#58511yescharacteristic
1483C222−1+611yescharacteristic
1484C4—24no—
1485C4—24no—
1486C4—24no—
1487C4—24no—
1488C4—22no—
1489C4—24no—
1490C4—24no—
1491C4—44no—
1492C4—42no—
1493C4—44no—
1494C4—44no—
1495C4—41no—
1496C4—44no—
1497C4—44no—
1498C4—42no—
1499C4—42no—
1500C4—44no—
1501C4—42no—
1502C4—42no—
1503C4—41no—
1504C4—41no—
1505C4—42no—
1506C4—42no—
1507C4#348114yes—
1508C2—44no—
1509C2—44no—
1510C2—81no—
1511C2—82no—
1512C2—81no—
1513C2C2×#348111yescharacteristic
1514C2#6281512yes—
1515C2#6291911yescharacteristic
1516C2#6299312yes—
1517C2#6302411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34925C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59865C2semidirect
2. #59797C2semidirect
3. #59773C2semidirect
4. #59744C2semidirect
5. #59309C2semidirect
6. #59306C2semidirect
7. #45251C2semidirect
8. #44914C2semidirect
9. #44898C2semidirect
10. #44863C2semidirect
11. #44428C2semidirect
12. #43790C2semidirect
13. #40138C2semidirect
14. #40137C2semidirect
15. #39463C2semidirect
16. #39463C2semidirect
17. #36534C2semidirect
18. #36501C2semidirect
19. #36417C2semidirect
20. #36254C2semidirect
21. #36191C2semidirect
22. #36089C2semidirect
23. #35759C2semidirect
24. #35688C2semidirect
26. #34874C2semidirect
27. #34208C2semidirect
28. #34206C2semidirect
29. C4×#552C2semidirect

Maximal subgroups

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

subgroupindex
#598652
#597972
#597732
#597442
#593092
#593062
#452512
#449142
#448982
#448632
#444282
#437902
#401382
#401372
#394632
#365342
#365012
#364172
#362542
#361912
#360892
#357592
#356882
#349252
#348742
#342082
#342062
C4×#5522