Finite Group Databasebeta

← #8108051

Subgroups — #8108051

Order 512.

5467 conjugacy classes of subgroups.

The subgroup lattice has 1253 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53103C212yesmaximal, complemented
2#53073C214yesmaximal, complemented
3#52989C212yesmaximal, complemented
4#52967C212yesmaximal, complemented
5#52966C212yesmaximal, complemented
6#45408C212yesmaximal, complemented
7#45380C212yesmaximal, complemented
8#45315C212yesmaximal, complemented
9#45214C212yesmaximal, complemented
10#45093C214yesmaximal, complemented
11#42983C212yesmaximal, complemented
12#42961C212yesmaximal, complemented
13#42883C212yesmaximal, complemented
14#42751C214yesmaximal, complemented
15#42673C212yesmaximal, complemented
16#42619C214yesmaximal, complemented
17#42593C214yesmaximal, complemented
18#42539C214yesmaximal, complemented
19#36211C212yesmaximal, complemented
20#36210C212yesmaximal, complemented
21#36122C212yesmaximal, complemented
22#36121C212yesmaximal, complemented
23#35316C211yesmaximal, characteristic, complemented
24#35292C212yesmaximal, complemented
25#35288C212yesmaximal, complemented
26#35272C211yesmaximal, characteristic, complemented
27#34547C211yesmaximal, characteristic, complemented
28C2×#548C2214yescomplemented
29C2×#546C2214yes—
30C2×#536C2212yes—
31C2×#535C2212yes—
32C2×#532C2212yes—
33C22×C4⋊Q8C2211yescharacteristic, complemented
34C22×#127C2211yescharacteristic
35C2×C4×#41C2211yescharacteristic
36C2×C4×#41C2211yescharacteristic, complemented
37#2859C2212yescomplemented
38#2858C2212yes—
39#2857C2212yes—
40#2857C2212yescomplemented
41#2857C2212yescomplemented
42#2856C2212yes—
43#2856C2212yes—
44#2856C2212yes—
45#2832C2214yescomplemented
46#2830C2214yescomplemented
47#2829C2218yescomplemented
48#2828C2218yescomplemented
49#2827C2218yescomplemented
50#2825C2218yescomplemented
51#2815C2214yescomplemented
52#2812C2214yes—
53#2797C2218yescomplemented
54#2760C2214yescomplemented
55#2756C2218yescomplemented
56#2752C2214yescomplemented
57#2749C2218yescomplemented
58#2749C2218yescomplemented
59#2746C2218yescomplemented
60#2736C2214yes—
61#2735C2218yes—
62#2735C2214yes—
63#2733C2214yescomplemented
64#2730C2218yescomplemented
65#2728C2214yescomplemented
66#2724C2214yescomplemented
67#2701C2218yescomplemented
68#2699C2214yescomplemented
69#2678C2218yes—
70#2674C2218yescomplemented
71#2673C2218yescomplemented
72#2670C2218yes—
73#2653C2218yescomplemented
74#2651C2218yescomplemented
75#2644C2214yescomplemented
76#2635C2218yescomplemented
77#2624C2214yescomplemented
78#2624C2214yescomplemented
79#2622C2218yes—
80#2621C2212yes—
81#2621C2212yescomplemented
82#2619C2212yes—
83#2619C2212yes—
84#2615C2214yescomplemented
85#2600C2214yescomplemented
86#2593C2214yescomplemented
87#2592C2214yescomplemented
88#2580C2214yescomplemented
89#2572C2214yescomplemented
90#2562C2214yes—
91#2548C2212yes—
92#2548C2212yes—
93#2547C2212yes—
94#2547C2212yes—
95#2546C2212yescomplemented
96#2546C2212yescomplemented
97#2545C2214yescomplemented
98#2544C2214yes—
99#2541C2212yes—
100#2541C2212yes—
101#2540C2214yescomplemented
102#2535C2214yescomplemented
103#2535C2214yescomplemented
104#2514C2214yescomplemented
105#2513C2214yescomplemented
106#2513C2214yescomplemented
107#2513C2214yescomplemented
108#2509C2214yescomplemented
109#2495C2214yes—
110#2494C2214yes—
111#2494C2214yescomplemented
112#2491C2214yescomplemented
113#2491C2214yescomplemented
114#2491C2218yescomplemented
115#2490C2214yescomplemented
116#2490C2214yescomplemented
117#2490C2214yescomplemented
118#2486C2212yes—
119#2486C2212yes—
120#2486C2212yescomplemented
121#2486C2212yescomplemented
122#2485C2214yes—
123#2483C2214yes—
124#2472C2218yes—
125#2454C2214yescomplemented
126#2452C2214yescomplemented
127#2452C2214yescomplemented
128#2448C2214yescomplemented
129#2447C2214yescomplemented
130#2445C2214yes—
131#2445C2214yes—
132#2445C2218yescomplemented
133#2436C2214yescomplemented
134#2435C2214yes—
135#2432C2214yescomplemented
136#2431C2214yes—
137#2428C2214yes—
138#2428C2214yes—
139#2427C2214yescomplemented
140#2426C2214yescomplemented
141#2421C2214yescomplemented
142#2420C2214yescomplemented
143#2420C2214yescomplemented
144#2420C2214yescomplemented
145#2418C2218yes—
146#2416C2214yescomplemented
147#2416C2214yescomplemented
148#2415C2214yes—
149#2414C2214yescomplemented
150#2414C2214yescomplemented
151#2414C2214yescomplemented
152#2414C2214yescomplemented
153#2408C2214yes—
154#2408C2214yes—
155#2408C2212yes—
156#2408C2212yes—
157#2408C2212yes—
158#2408C2212yes—
159#2407C2214yescomplemented
160#2407C2214yescomplemented
161#2399C2211yescharacteristic, complemented
162#2398C2211yescharacteristic
163#2398C2211yescharacteristic, complemented
164#2397C2211yescharacteristic
165#2396C2211yescharacteristic
166#2396C2211yescharacteristic, complemented
167#2396C2212yescomplemented
168#2395C2211yescharacteristic
169#2395C2211yescharacteristic, complemented
170#2395C2212yescomplemented
171#2392C2212yes—
172#2392C2212yes—
173#2392C2211yescharacteristic
174#2392C2212yescomplemented
175#2392C2211yescharacteristic, complemented
176#2388C2212yes—
177#2388C2211yescharacteristic
178#2388C2211yescharacteristic, complemented
179#2370C2214yescomplemented
180#2363C2214yescomplemented
181#2363C2214yescomplemented
182#2362C2214yes—
183#2361C2214yescomplemented
184#2361C2214yescomplemented
185#2357C2214yescomplemented
186#2347C2214yescomplemented
187D4×C22⋊C4C2214yes—
188D4×C22⋊C4C2214yes—
189#2324C2214yescomplemented
190#2324C2214yescomplemented
191#2324C2214yescomplemented
192#2319C2214yescomplemented
193#2310C2212yescomplemented
194#2309C2212yes—
195C4×C4⋊Q8C2212yescomplemented
196C4×#127C2212yes—
197#2285C2211yescharacteristic
198#2285C2212yescomplemented
199#2285C2211yescharacteristic, complemented
200C42×D4C2212yes—
201C42×D4C2212yescomplemented
202C4×#117C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C22×#41C2314yes—
206C23×Q8C2312yes—
207C23×D4C2312yes—
208C23×D4C2312yes—
209C23×D4C2312yes—
210#548—416no—
211#546—416no—
212#536—48no—
213#535—48no—
214#532—48no—
215C2×C4⋊Q8—44no—
216C2×C4⋊Q8C2312yes—
217C2×C4⋊Q8C2312yes—
218C2×C4⋊Q8C2312yes—
219C2×C4⋊Q8C2312yes—
220C2×C4⋊Q8C2314yes—
221C2×#127—44no—
222C2×#127C2312yes—
223C2×#127C2312yes—
224C2×#127C2312yes—
225C2×#127C2312yes—
226C2×#127C2314yes—
227C2×#125C2314yes—
228C2×#124C2314yes—
229C2×#124C2314yes—
230C2×#124C2314yes—
231C2×#124C2314yes—
232C2×#124C2318yes—
233C2×#124C2314yes—
234C2×#123C2314yes—
235C2×#123C2314yes—
236C2×#123C2318yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2318yes—
241C2×#121C2314yes—
242C2×#121C2314yes—
243C2×#121C2314yes—
244C2×#121C2314yes—
245C2×#121C2314yes—
246C2×#121C2314yes—
247C2×#121C2314yes—
248C2×#121C2314yes—
249C2×#121C2314yes—
250C2×#121C2314yes—
251C2×#121C2318yes—
252C2×#121C2314yes—
253C2×#121C2318yes—
254C2×#120C2318yes—
255C2×#120C2314yes—
256C2×#120C2314yes—
257C4×#41—44no—
258C4×#41—44no—
259C2×C4×Q8C2314yes—
260C2×C4×Q8C2311yescharacteristic
261C2×C4×Q8C2311yescharacteristic
262C2×C4×Q8C2311yescharacteristic
263C2×C4×Q8C2311yescharacteristic
264C2×C4×D4C2312yes—
265C2×C4×D4C2312yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2312yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2318yes—
273C2×C4×D4C2311yescharacteristic
274C2×C4×D4C2312yes—
275C2×C4×D4C2312yes—
276C2×C4×D4C2311yescharacteristic
277C2×C4×D4C2311yescharacteristic
278C2×C4×D4C2311yescharacteristic
279C2×C4×D4C2311yescharacteristic
280C2×C4×D4C2312yes—
281C2×C4×D4C2312yes—
282C2×C4×D4C2311yescharacteristic
283C2×C4×D4C2312yes—
284C2×C4×D4C2311yescharacteristic
285C2×C4×D4C2311yescharacteristic
286C2×#117C2311yescharacteristic
287C2×#117C2312yes—
288C2×#117C2311yescharacteristic
289C2×#117C2312yes—
290C2×#117C2311yescharacteristic
291C2×#117C2312yes—
292C2×#117C2312yes—
293C2×#117C2314yes—
294C2×#117C2311yescharacteristic
295C22×C4⋊C4C2312yes—
296C22×C4⋊C4C2312yes—
297C22×C22⋊C4C2318yes—
298C22×C42C2311yescharacteristic
299C22×C42C2311yescharacteristic
300C22×C42C2312yes—
301C22×C42C2311yescharacteristic
302#401C2318yes—
303#400C2318yes—
304#400C2318yes—
305#400C2311yescharacteristic
306#400C2311yescharacteristic
307#400C2312yes—
308#399C2318yes—
309#399C2312yes—
310#399C2318yes—
311#399C2311yescharacteristic
312#399C2311yescharacteristic
313#398C2312yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2311yescharacteristic
319#398C2312yes—
320#398C2311yescharacteristic
321#398C2312yes—
322#397C2314yes—
323#397C2318yes—
324#397C2318yes—
325#397C2318yes—
326#397C2318yes—
327#397C2314yes—
328#397C2318yes—
329#397C2318yes—
330#397C2318yes—
331#397C2318yes—
332#397C2311yescharacteristic
333#397C2314yes—
334#397C2314yes—
335#397C2318yes—
336#397C2318yes—
337#397C2311yescharacteristic
338#397C2312yes—
339#397C2312yes—
340#397C2312yes—
341#396C2318yes—
342#396C2318yes—
343#396C2318yes—
344#396C2312yes—
345#396C2312yes—
346#396C2312yes—
347#396C2312yes—
348#395C2311yescharacteristic
349#395C2311yescharacteristic
350#395C2312yes—
351#394C2318yes—
352#394C2312yes—
353#394C2318yes—
354#394C2318yes—
355#394C2314yes—
356#394C2318yes—
357#394C2314yes—
358#394C2312yes—
359#394C2318yes—
360#394C2318yes—
361#394C2318yes—
362#394C2314yes—
363#394C2318yes—
364#394C2318yes—
365#394C2318yes—
366#394C2318yes—
367#394C2318yes—
368#394C2314yes—
369#394C2312yes—
370#394C2318yes—
371#394C2312yes—
372#394C2312yes—
373#394C2312yes—
374#394C2312yes—
375#394C2311yescharacteristic
376#394C2311yescharacteristic
377#393C2318yes—
378#393C2318yes—
379#393C2318yes—
380#393C2311yescharacteristic
381#393C2312yes—
382#393C2311yescharacteristic
383#392C2314yes—
384#392C2318yes—
385#392C2318yes—
386#392C2318yes—
387#392C2314yes—
388#392C2318yes—
389#392C2314yes—
390#392C2318yes—
391#392C2314yes—
392#392C2318yes—
393#392C2312yes—
394#392C2312yes—
395#392C2312yes—
396#392C2311yescharacteristic
397#392C2311yescharacteristic
398#391C2314yes—
399#391C2314yes—
400#391C2314yes—
401#391C2314yes—
402#391C2314yes—
403#391C2314yes—
404#390C2314yes—
405#390C2314yes—
406#390C2314yes—
407#390C2314yes—
408#390C2314yes—
409#390C2314yes—
410#390C2314yes—
411#390C2318yes—
412#390C2318yes—
413#390C2314yes—
414#390C2314yes—
415#390C2314yes—
416#390C2314yes—
417#390C2314yes—
418#390C2318yes—
419#390C2314yes—
420#390C2314yes—
421#390C2314yes—
422#390C2314yes—
423#390C2314yes—
424#390C2314yes—
425#390C2318yes—
426#390C2318yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2314yes—
437#389C2314yes—
438#389C2314yes—
439#389C2318yes—
440#388C2318yes—
441#388C2318yes—
442#388C2318yes—
443#388C2318yes—
444#388C2318yes—
445#388C2318yes—
446#388C2318yes—
447#388C2318yes—
448#388C2318yes—
449#388C2318yes—
450#388C2318yes—
451#388C2318yes—
452#388C2318yes—
453#388C2318yes—
454#388C2318yes—
455#387C2318yes—
456#387C2318yes—
457#387C2318yes—
458#386C2318yes—
459#386C2318yes—
460#386C2318yes—
461#386C2318yes—
462#386C2318yes—
463#386C2318yes—
464#386C2318yes—
465#386C2318yes—
466#386C2318yes—
467#386C2318yes—
468#386C2318yes—
469#385C2318yes—
470#385C2318yes—
471#385C2318yes—
472#385C2318yes—
473#385C2318yes—
474#384C2312yes—
475#384C2312yes—
476#383C2318yes—
477#382C2314yes—
478#382C2314yes—
479#382C2312yes—
480#382C2312yes—
481#381C2314yes—
482#381C2314yes—
483#381C2318yes—
484#381C2318yes—
485#380C2312yes—
486#380C2314yes—
487#380C2314yes—
488#380C2314yes—
489#380C2318yes—
490#380C2314yes—
491#380C2314yes—
492#380C2314yes—
493#380C2314yes—
494#380C2314yes—
495#380C2312yes—
496#380C2312yes—
497#380C2312yes—
498#379C2314yes—
499#379C2314yes—
500#379C2318yes—
501#379C2318yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2314yes—
506C4×C4⋊C4C2318yes—
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2311yescharacteristic
514C4×C4⋊C4C2312yes—
515C4×C4⋊C4C2312yes—
516C4×C4⋊C4C2311yescharacteristic
517C4×C4⋊C4C2312yes—
518C4×C4⋊C4C2312yes—
519C4×C4⋊C4C2312yes—
520C4×C22⋊C4C2318yes—
521C4×C22⋊C4C2312yes—
522C4×C22⋊C4C2312yes—
523C4×C22⋊C4C2312yes—
524C4×C22⋊C4C2312yes—
525C4×C22⋊C4C2312yes—
526C4×C22⋊C4C2312yes—
527C4×C22⋊C4C2312yes—
528C4×C22⋊C4C2312yes—
529C4×C22⋊C4C2312yes—
530C4×C22⋊C4C2311yescharacteristic
531C4×C22⋊C4C2312yes—
532C4×C22⋊C4C2311yescharacteristic
533C4×C22⋊C4C2312yes—
534C4×C22⋊C4C2312yes—
535C4×C22⋊C4C2312yes—
536#376C2311yescharacteristic
537#376C2311yescharacteristic
538C43C2312yes—
539C25C2414yes—
540C2×#41—24no—
541C2×#41—24no—
542C2×#41—42no—
543C2×#41—42no—
544C2×#41—44no—
545C2×#41—48no—
546C2×#41—48no—
547C2×#41—48no—
548C22×Q8—28no—
549C22×Q8—44no—
550C22×Q8—44no—
551C22×Q8C2414yes—
552C22×Q8C2411yescharacteristic
553C22×Q8C2414yes—
554C22×Q8C2411yescharacteristic
555C22×D4—28no—
556C22×D4—44no—
557C22×D4—44no—
558C22×D4—44no—
559C22×D4—44no—
560C22×D4—48no—
561C22×D4—48no—
562C22×D4C2414yes—
563C22×D4C2414yes—
564C22×D4C2414yes—
565C22×D4C2411yescharacteristic
566C22×D4C2411yescharacteristic
567C22×D4C2411yescharacteristic
568C22×D4C2412yes—
569C22×D4C2412yes—
570C22×D4C2418yes—
571C22×D4C2414yes—
572C22×D4C2412yes—
573C22×D4C2411yescharacteristic
574C22×D4C2418yes—
575C22×D4C2418yes—
576C22×D4C2418yes—
577C22×D4C2414yes—
578C22×D4C2414yes—
579C23×C4C2411yescharacteristic
580C23×C4C2411yescharacteristic
581C23×C4C2412yes—
582C23×C4C2411yescharacteristic
583C23×C4C2411yescharacteristic
584C23×C4C2411yescharacteristic
585C23×C4C2412yes—
586C23×C4C2412yes—
587C23×C4C2411yescharacteristic
588C23×C4C2411yescharacteristic
589C23×C4C2411yescharacteristic
590C23×C4C2411yescharacteristic
591C23×C4C2414yes—
592C23×C4C2418yes—
593C23×C4C2418yes—
594C4⋊Q8—28no—
595C4⋊Q8—44no—
596C4⋊Q8—44no—
597C4⋊Q8—44no—
598C4⋊Q8—48no—
599#127—28no—
600#127—44no—
601#127—44no—
602#127—44no—
603#127—48no—
604#125—48no—
605#124—48no—
606#124—48no—
607#124—48no—
608#124—48no—
609#124—48no—
610#124—416no—
611#123—48no—
612#123—48no—
613#123—416no—
614C22⋊Q8—216no—
615C22⋊Q8—416no—
616C22⋊Q8—48no—
617C22⋊Q8—48no—
618#121—216no—
619#121—416no—
620#121—48no—
621#121—48no—
622#121—48no—
623#121—48no—
624#121—48no—
625#121—48no—
626#121—48no—
627#121—48no—
628#121—48no—
629#121—48no—
630#121—416no—
631#120—48no—
632#120—416no—
633#120—48no—
634C4×Q8—42no—
635C4×Q8—42no—
636C4×Q8—42no—
637C4×Q8—42no—
638C4×Q8—48no—
639C4×D4—28no—
640C4×D4—28no—
641C4×D4—48no—
642C4×D4—48no—
643C4×D4—48no—
644C4×D4—48no—
645C4×D4—48no—
646C4×D4—44no—
647C4×D4—44no—
648C4×D4—44no—
649C4×D4—44no—
650C4×D4—42no—
651C4×D4—42no—
652C4×D4—44no—
653C4×D4—42no—
654C4×D4—42no—
655C4×D4—44no—
656C4×D4—42no—
657C4×D4—42no—
658C4×D4—42no—
659C4×D4—42no—
660C4×D4—416no—
661#117—44no—
662#117—42no—
663#117—44no—
664#117—42no—
665#117—42no—
666#117—42no—
667#117—48no—
668#117—44no—
669#117—44no—
670C2×C4⋊C4—44no—
671C2×C4⋊C4—44no—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2412yes—
680C2×C4⋊C4C2412yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2418yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2412yes—
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2412yes—
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
693C2×C4⋊C4C2411yescharacteristic
694C2×C4⋊C4C2411yescharacteristic
695C2×C4⋊C4C2412yes—
696C2×C4⋊C4C2412yes—
697C2×C4⋊C4C2418yes—
698C2×C4⋊C4C2412yes—
699C2×C4⋊C4C2412yes—
700C2×C4⋊C4C2412yes—
701C2×C4⋊C4C2412yes—
702C2×C4⋊C4C2418yes—
703C2×C4⋊C4C2418yes—
704C2×C4⋊C4C2418yes—
705C2×C4⋊C4C2418yes—
706C2×C22⋊C4—416no—
707C2×C22⋊C4C2412yes—
708C2×C22⋊C4C2418yes—
709C2×C22⋊C4C2412yes—
710C2×C22⋊C4C2412yes—
711C2×C22⋊C4C2412yes—
712C2×C22⋊C4C2418yes—
713C2×C22⋊C4C2418yes—
714C2×C22⋊C4C2418yes—
715C2×C22⋊C4C2411yescharacteristic
716C2×C22⋊C4C2411yescharacteristic
717C2×C22⋊C4C2411yescharacteristic
718C2×C22⋊C4C2411yescharacteristic
719C2×C22⋊C4C2412yes—
720C2×C22⋊C4C2412yes—
721C2×C22⋊C4C2412yes—
722C2×C22⋊C4C2411yescharacteristic
723C2×C22⋊C4C2411yescharacteristic
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2412yes—
727C2×C22⋊C4C2412yes—
728C2×C22⋊C4C2418yes—
729C2×C22⋊C4C2418yes—
730C2×C22⋊C4C2418yes—
731C2×C22⋊C4C2418yes—
732C2×C22⋊C4C2418yes—
733C2×C22⋊C4C2412yes—
734C2×C22⋊C4C2412yes—
735C2×C22⋊C4C2412yes—
736C2×C22⋊C4C2412yes—
737C2×C22⋊C4C2412yes—
738C2×C22⋊C4C2412yes—
739C2×C22⋊C4C2412yes—
740C2×C22⋊C4C2412yes—
741C2×C22⋊C4C2418yes—
742C2×C22⋊C4C2418yes—
743C2×C22⋊C4C2418yes—
744C2×C22⋊C4C2418yes—
745C2×C22⋊C4C2418yes—
746C2×C22⋊C4C2418yes—
747C2×C22⋊C4C2418yes—
748C2×C22⋊C4C2418yes—
749C2×C22⋊C4C2418yes—
750C2×C22⋊C4C2418yes—
751C2×C22⋊C4C2418yes—
752C2×C22⋊C4C2418yes—
753C2×C22⋊C4C2418yes—
754C2×C42—24no—
755C2×C42—24no—
756C2×C42—24no—
757C2×C42—28no—
758C2×C42C2412yes—
759C2×C42C2411yescharacteristic
760C2×C42C2411yescharacteristic
761C2×C42C2411yescharacteristic
762C2×C42C2411yescharacteristic
763C2×C42C2412yes—
764C2×C42C2412yes—
765C2×C42C2412yes—
766C2×C42C2412yes—
767C2×C42C2412yes—
768C2×C42C2411yescharacteristic
769C2×C42C2412yes—
770C2×C42C2412yes—
771C2×C42C2411yescharacteristic
772C2×C42C2411yescharacteristic
773C2×C42C2411yescharacteristic
774C2×C42C2411yescharacteristic
775C2×C42C2412yes—
776C2×C42C2414yes—
777C2×C42C2414yes—
778C2×C42C2418yes—
779C2×C42C2418yes—
780C2×C42C2411yescharacteristic
781#95C2412yes—
782#95C2411yescharacteristic
783#95C2411yescharacteristic
784#95C2412yes—
785#95C2411yescharacteristic
786#95C2411yescharacteristic
787#95C2412yes—
788#95C2412yes—
789#95C2412yes—
790#95C2412yes—
791#95C2412yes—
792#95C2412yes—
793#95C2412yes—
794#95C2412yes—
795#95C2412yes—
796#95C2412yes—
797#95C2412yes—
798#95C2412yes—
799#95C2418yes—
800#95C2414yes—
801#95C2418yes—
802#95C2418yes—
803#95C2414yes—
804#95C2414yes—
805#95C2418yes—
806#95C2414yes—
807#95C2418yes—
808#95C2418yes—
809#95C2418yes—
810#95C2418yes—
811#95C2418yes—
812#95C2418yes—
813#95C2418yes—
814#95C2418yes—
815C24—28no—
816C24—44no—
817C24—48no—
818C24—48no—
819C24—44no—
820C24C2518yes—
821C24C2512yes—
822C24C2511yescharacteristic
823C24C2511yescharacteristic
824C24C2511yescharacteristic
825#41—416no—
826#41—416no—
827#41—832no—
828C2×Q8—28no—
829C2×Q8—28no—
830C2×Q8—22no—
831C2×Q8—28no—
832C2×Q8—22no—
833C2×Q8—28no—
834C2×Q8—41no—
835C2×Q8—41no—
836C2×Q8—42no—
837C2×Q8—44no—
838C2×Q8—44no—
839C2×Q8—816no—
840C2×D4—24no—
841C2×D4—24no—
842C2×D4—22no—
843C2×D4—22no—
844C2×D4—22no—
845C2×D4—22no—
846C2×D4—216no—
847C2×D4—28no—
848C2×D4—28no—
849C2×D4—28no—
850C2×D4—22no—
851C2×D4—28no—
852C2×D4—22no—
853C2×D4—28no—
854C2×D4—28no—
855C2×D4—28no—
856C2×D4—28no—
857C2×D4—28no—
858C2×D4—28no—
859C2×D4—41no—
860C2×D4—41no—
861C2×D4—42no—
862C2×D4—41no—
863C2×D4—41no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—48no—
872C2×D4—48no—
873C2×D4—48no—
874C2×D4—48no—
875C2×D4—48no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—48no—
881C2×D4—48no—
882C2×D4—48no—
883C2×D4—48no—
884C2×D4—48no—
885C2×D4—48no—
886C2×D4—48no—
887C2×D4—48no—
888C2×D4—816no—
889C2×D4—816no—
890C2×D4—816no—
891C22×C4—22no—
892C22×C4—22no—
893C22×C4—22no—
894C22×C4—22no—
895C22×C4—28no—
896C22×C4—22no—
897C22×C4—22no—
898C22×C4—22no—
899C22×C4—22no—
900C22×C4—24no—
901C22×C4—22no—
902C22×C4—24no—
903C22×C4—22no—
904C22×C4—22no—
905C22×C4—24no—
906C22×C4—24no—
907C22×C4—24no—
908C22×C4—22no—
909C22×C4—22no—
910C22×C4—24no—
911C22×C4—24no—
912C22×C4—24no—
913C22×C4—24no—
914C22×C4—24no—
915C22×C4—24no—
916C22×C4—24no—
917C22×C4—24no—
918C22×C4—24no—
919C22×C4—24no—
920C22×C4—48no—
921C22×C4—44no—
922C22×C4—48no—
923C22×C4—48no—
924C22×C4—44no—
925C22×C4—48no—
926C22×C4—48no—
927C22×C4—48no—
928C22×C4H(5,𝔽2)14yes—
929C22×C4H(5,𝔽2)14yes—
930C22×C4C2511yescharacteristic
931C22×C4C2511yescharacteristic
932C22×C4C2512yes—
933C22×C4C2512yes—
934C22×C4C2511yescharacteristic
935C22×C4C2518yes—
936C22×C4C2518yes—
937C22×C4C2512yes—
938C22×C4C2512yes—
939C22×C4C2512yes—
940C22×C4C2511yescharacteristic
941C22×C4C2511yescharacteristic
942C22×C4C2511yescharacteristic
943C22×C4C2512yes—
944C22×C4C2518yes—
945C22×C4C2512yes—
946C22×C4C2511yescharacteristic
947C22×C4C2511yescharacteristic
948C22×C4C2511yescharacteristic
949C22×C4C2511yescharacteristic
950C22×C4C2511yescharacteristic
951C22×C4C2511yescharacteristic
952C4⋊C4—28no—
953C4⋊C4—28no—
954C4⋊C4—28no—
955C4⋊C4—28no—
956C4⋊C4—24no—
957C4⋊C4—24no—
958C4⋊C4—216no—
959C4⋊C4—28no—
960C4⋊C4—28no—
961C4⋊C4—28no—
962C4⋊C4—28no—
963C4⋊C4—44no—
964C4⋊C4—44no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—41no—
968C4⋊C4—41no—
969C4⋊C4—41no—
970C4⋊C4—41no—
971C4⋊C4—41no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—41no—
975C4⋊C4—41no—
976C4⋊C4—41no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—48no—
982C4⋊C4—48no—
983C4⋊C4—48no—
984C4⋊C4—48no—
985C4⋊C4—48no—
986C22⋊C4—24no—
987C22⋊C4—216no—
988C22⋊C4—24no—
989C22⋊C4—24no—
990C22⋊C4—24no—
991C22⋊C4—216no—
992C22⋊C4—48no—
993C22⋊C4—48no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—48no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—41no—
1000C22⋊C4—42no—
1001C22⋊C4—41no—
1002C22⋊C4—41no—
1003C22⋊C4—41no—
1004C22⋊C4—41no—
1005C22⋊C4—41no—
1006C22⋊C4—44no—
1007C22⋊C4—44no—
1008C22⋊C4—48no—
1009C22⋊C4—48no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—48no—
1019C22⋊C4—48no—
1020C22⋊C4—48no—
1021C22⋊C4—48no—
1022C22⋊C4—48no—
1023C22⋊C4—48no—
1024C22⋊C4—48no—
1025C22⋊C4—48no—
1026C22⋊C4—48no—
1027C22⋊C4—48no—
1028C22⋊C4—48no—
1029C22⋊C4—48no—
1030C22⋊C4—48no—
1031C22⋊C4—48no—
1032C22⋊C4—48no—
1033C42—24no—
1034C42—22no—
1035C42—22no—
1036C42—22no—
1037C42—22no—
1038C42—24no—
1039C42—22no—
1040C42—24no—
1041C42—22no—
1042C42—22no—
1043C42—22no—
1044C42—22no—
1045C42—24no—
1046C42—24no—
1047C42—24no—
1048C42—24no—
1049C42—24no—
1050C42—24no—
1051C42—48no—
1052C42—44no—
1053C42—44no—
1054C42—48no—
1055C42H(5,𝔽2)14yes—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—28no—
1066C23—22no—
1067C23—21no—
1068C23—21no—
1069C23—28no—
1070C23—22no—
1071C23—28no—
1072C23—21no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—28no—
1077C23—28no—
1078C23—28no—
1079C23—28no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—88no—
1084C23—816no—
1085C23—88no—
1086C23—88no—
1087C23—168no—
1088C23C2×H(5,𝔽2)12yes—
1089C23C2×H(5,𝔽2)12yes—
1090C23C2611yescharacteristic
1091Q8—44no—
1092Q8—44no—
1093Q8—416no—
1094Q8—88no—
1095D4—44no—
1096D4—44no—
1097D4—44no—
1098D4—48no—
1099D4—48no—
1100D4—48no—
1101D4—44no—
1102D4—416no—
1103D4—416no—
1104D4—416no—
1105D4—88no—
1106D4—816no—
1107D4—88no—
1108D4—88no—
1109D4—816no—
1110D4—168no—
1111D4—168no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—28no—
1117C2×C4—28no—
1118C2×C4—22no—
1119C2×C4—21no—
1120C2×C4—22no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—22no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—28no—
1133C2×C4—28no—
1134C2×C4—28no—
1135C2×C4—22no—
1136C2×C4—28no—
1137C2×C4—22no—
1138C2×C4—21no—
1139C2×C4—28no—
1140C2×C4—21no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—28no—
1151C2×C4—28no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—28no—
1159C2×C4—28no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—44no—
1164C2×C4—48no—
1165C2×C4—44no—
1166C2×C4—44no—
1167C2×C4—44no—
1168C2×C4—48no—
1169C2×C4—44no—
1170C2×C4—44no—
1171C2×C4—48no—
1172C2×C4—44no—
1173C2×C4—88no—
1174C2×C4—816no—
1175C2×C4—168no—
1176C2×C4C2×H(5,𝔽2)12yes—
1177C2×C4C2×H(5,𝔽2)12yes—
1178C2×C4C2×H(5,𝔽2)12yes—
1179C2×C4C2×H(5,𝔽2)12yes—
1180C2×C4C2×H(5,𝔽2)12yes—
1181C2×C4C2×H(5,𝔽2)12yes—
1182C2×C4C2×H(5,𝔽2)12yes—
1183C2×C4#58514yes—
1184C2×C4#58514yes—
1185C22—22no—
1186C22—22no—
1187C22—24no—
1188C22—24no—
1189C22—41no—
1190C22—41no—
1191C22—41no—
1192C22—41no—
1193C22—42no—
1194C22—42no—
1195C22—41no—
1196C22—42no—
1197C22—48no—
1198C22—41no—
1199C22—42no—
1200C22—48no—
1201C22—41no—
1202C22—42no—
1203C22—48no—
1204C22—48no—
1205C22—42no—
1206C22—42no—
1207C22—48no—
1208C22—42no—
1209C22—42no—
1210C22—48no—
1211C22—48no—
1212C22—42no—
1213C22—42no—
1214C22—1616no—
1215C22C22×H(5,𝔽2)11yescharacteristic
1216C22C22×H(5,𝔽2)11yescharacteristic
1217C22C22×H(5,𝔽2)11yescharacteristic
1218C22C2×#58512yes—
1219C22C2×#58512yes—
1220C4—22no—
1221C4—22no—
1222C4—42no—
1223C4—41no—
1224C4—48no—
1225C4—41no—
1226C4—42no—
1227C4—41no—
1228C4—41no—
1229C4—42no—
1230C4—41no—
1231C4—41no—
1232C4—41no—
1233C4—42no—
1234C4—42no—
1235C4—48no—
1236C4—42no—
1237C4—42no—
1238C4—48no—
1239C4#353714yes—
1240C4#354014yes—
1241C4#355114yes—
1242C2—42no—
1243C2—42no—
1244C2—81no—
1245C2—82no—
1246C2—88no—
1247C2C2×#353711yescharacteristic
1248C2C2×#354011yescharacteristic
1249C2C2×#355111yescharacteristic
1250C2#6283612yes—
1251C2#6283612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53103C2semidirect
2. #53073C2semidirect
3. #52989C2semidirect
4. #52967C2semidirect
5. #52966C2semidirect
6. #45408C2semidirect
7. #45380C2semidirect
8. #45315C2semidirect
9. #45214C2semidirect
10. #45093C2semidirect
11. #42983C2semidirect
12. #42961C2semidirect
13. #42883C2semidirect
14. #42751C2semidirect
15. #42673C2semidirect
16. #42619C2semidirect
17. #42593C2semidirect
18. #42539C2semidirect
19. #36211C2semidirect
20. #36210C2semidirect
21. #36122C2semidirect
22. #36121C2semidirect
23. #35316C2semidirect
24. #35292C2semidirect
25. #35288C2semidirect
26. #35272C2semidirect
27. #34547C2semidirect
28. C2×#548C22semidirect
33. C22×C4⋊Q8C22semidirect
36. C2×C4×#41C22semidirect
37. #2859C22semidirect
40. #2857C22semidirect
41. #2857C22semidirect
45. #2832C22semidirect
46. #2830C22semidirect
47. #2829C22semidirect
48. #2828C22semidirect
49. #2827C22semidirect
50. #2825C22semidirect
51. #2815C22semidirect
53. #2797C22semidirect
54. #2760C22semidirect
55. #2756C22semidirect
56. #2752C22semidirect
57. #2749C22semidirect
58. #2749C22semidirect
59. #2746C22semidirect
63. #2733C22semidirect
64. #2730C22semidirect
65. #2728C22semidirect
66. #2724C22semidirect
67. #2701C22semidirect
68. #2699C22semidirect
70. #2674C22semidirect
71. #2673C22semidirect
73. #2653C22semidirect
74. #2651C22semidirect
75. #2644C22semidirect
76. #2635C22semidirect
77. #2624C22semidirect
78. #2624C22semidirect
81. #2621C22semidirect
84. #2615C22semidirect
85. #2600C22semidirect
86. #2593C22semidirect
87. #2592C22semidirect
88. #2580C22semidirect
89. #2572C22semidirect
95. #2546C22semidirect
96. #2546C22semidirect
97. #2545C22semidirect
101. #2540C22semidirect
102. #2535C22semidirect
103. #2535C22semidirect
104. #2514C22semidirect
105. #2513C22semidirect
106. #2513C22semidirect
107. #2513C22semidirect
108. #2509C22semidirect
111. #2494C22semidirect
112. #2491C22semidirect
113. #2491C22semidirect
114. #2491C22semidirect
115. #2490C22semidirect
116. #2490C22semidirect
117. #2490C22semidirect
120. #2486C22semidirect
121. #2486C22semidirect
125. #2454C22semidirect
126. #2452C22semidirect
127. #2452C22semidirect
128. #2448C22semidirect
129. #2447C22semidirect
132. #2445C22semidirect
133. #2436C22semidirect
135. #2432C22semidirect
139. #2427C22semidirect
140. #2426C22semidirect
141. #2421C22semidirect
142. #2420C22semidirect
143. #2420C22semidirect
144. #2420C22semidirect
146. #2416C22semidirect
147. #2416C22semidirect
149. #2414C22semidirect
150. #2414C22semidirect
151. #2414C22semidirect
152. #2414C22semidirect
159. #2407C22semidirect
160. #2407C22semidirect
161. #2399C22semidirect
163. #2398C22semidirect
166. #2396C22semidirect
167. #2396C22semidirect
169. #2395C22semidirect
170. #2395C22semidirect
174. #2392C22semidirect
175. #2392C22semidirect
178. #2388C22semidirect
179. #2370C22semidirect
180. #2363C22semidirect
181. #2363C22semidirect
183. #2361C22semidirect
184. #2361C22semidirect
185. #2357C22semidirect
186. #2347C22semidirect
189. #2324C22semidirect
190. #2324C22semidirect
191. #2324C22semidirect
192. #2319C22semidirect
193. #2310C22semidirect
195. C4×C4⋊Q8C22semidirect
198. #2285C22semidirect
199. #2285C22semidirect
201. C42×D4C22semidirect
202. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#531032
#530732
#529892
#529672
#529662
#454082
#453802
#453152
#452142
#450932
#429832
#429612
#428832
#427512
#426732
#426192
#425932
#425392
#362112
#362102
#361222
#361212
#353162
#352922
#352882
#352722
#345472