Finite Group Databasebeta

← #7732462

Subgroups — #7732462

Order 512.

4414 conjugacy classes of subgroups.

The subgroup lattice has 1402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#50934C214yesmaximal, complemented
2#50734C214yesmaximal, complemented
3#46470C214yesmaximal, complemented
4#46401C214yesmaximal, complemented
5#45392C212yesmaximal, complemented
6#45367C212yesmaximal
7#45149C212yesmaximal, complemented
8#44961C212yesmaximal, complemented
9#40352C214yesmaximal, complemented
10#40337C214yesmaximal, complemented
11#40023C212yesmaximal, complemented
12#40020C212yesmaximal, complemented
13#39800C212yesmaximal, complemented
14#39800C212yesmaximal, complemented
15#39771C212yesmaximal, complemented
16#39765C212yesmaximal, complemented
17#37545C211yesmaximal, characteristic, complemented
18#37026C212yesmaximal, complemented
19#36832C212yesmaximal, complemented
20#36527C212yesmaximal, complemented
21#36485C212yesmaximal, complemented
22#35500C212yesmaximal, complemented
23#35428C212yesmaximal, complemented
24#35338C211yesmaximal, characteristic, complemented
25#35131C211yesmaximal, characteristic
26#34912C211yesmaximal, characteristic, complemented
27#34377C211yesmaximal, characteristic, complemented
28#34225C211yesmaximal, characteristic, complemented
29#34084C211yesmaximal, characteristic, complemented
30C2×#533C2211yescharacteristic
31C2×#529C2211yescharacteristic
32C22×#124C2211yescharacteristic
33#2865C2214yescomplemented
34#2861C2212yes—
35#2861C2212yes—
36#2861C2212yes—
37#2858C2212yes—
38#2852C2214yescomplemented
39#2814C2212yes—
40#2814C2212yes—
41#2808C2214yescomplemented
42#2808C2214yescomplemented
43#2804C2214yescomplemented
44#2800C2214yescomplemented
45#2796C2214yescomplemented
46#2796C2214yescomplemented
47#2795C2214yescomplemented
48#2793C2214yescomplemented
49#2783C2214yescomplemented
50#2783C2214yescomplemented
51#2779C2214yescomplemented
52#2775C2214yescomplemented
53#2775C2214yescomplemented
54#2772C2214yescomplemented
55#2763C2214yescomplemented
56#2762C2214yescomplemented
57#2761C2214yes—
58#2758C2214yescomplemented
59#2756C2214yes—
60#2754C2214yescomplemented
61#2751C2214yescomplemented
62#2751C2214yescomplemented
63#2749C2214yes—
64#2745C2214yes—
65#2745C2214yescomplemented
66#2745C2214yescomplemented
67#2743C2214yes—
68#2739C2214yes—
69#2739C2214yescomplemented
70#2737C2214yes—
71#2735C2214yes—
72#2735C2214yes—
73#2729C2214yescomplemented
74#2724C2214yescomplemented
75#2723C2214yes—
76#2697C2214yes—
77#2689C2214yescomplemented
78#2689C2214yescomplemented
79#2685C2214yes—
80#2674C2214yescomplemented
81#2662C2212yes—
82#2662C2212yes—
83#2660C2211yescharacteristic, complemented
84#2660C2211yescharacteristic, complemented
85#2650C2214yescomplemented
86#2649C2214yescomplemented
87#2640C2212yes—
88#2640C2212yes—
89#2640C2211yescharacteristic, complemented
90#2640C2211yescharacteristic, complemented
91#2638C2214yes—
92#2637C2214yescomplemented
93#2610C2212yes—
94#2610C2212yes—
95#2608C2212yes—
96#2607C2212yes—
97#2606C2211yescharacteristic, complemented
98#2606C2211yescharacteristic, complemented
99#2605C2211yescharacteristic, complemented
100#2605C2211yescharacteristic, complemented
101#2599C2212yescomplemented
102#2599C2212yescomplemented
103#2597C2214yescomplemented
104#2597C2214yescomplemented
105#2595C2214yescomplemented
106#2594C2214yescomplemented
107#2594C2214yescomplemented
108#2594C2214yescomplemented
109#2594C2214yescomplemented
110#2592C2214yes—
111#2592C2212yes—
112#2592C2212yes—
113#2592C2212yes—
114#2592C2214yescomplemented
115#2592C2212yescomplemented
116#2587C2214yescomplemented
117#2586C2214yescomplemented
118#2581C2212yescomplemented
119#2581C2212yescomplemented
120#2580C2214yescomplemented
121#2577C2214yescomplemented
122#2577C2214yescomplemented
123#2576C2214yes—
124#2576C2214yescomplemented
125#2576C2214yescomplemented
126#2575C2214yes—
127#2575C2214yescomplemented
128#2570C2212yescomplemented
129#2568C2212yescomplemented
130#2566C2212yescomplemented
131#2565C2212yescomplemented
132#2561C2214yes—
133#2561C2212yes—
134#2561C2212yes—
135#2561C2214yes—
136#2558C2214yescomplemented
137#2554C2214yes—
138#2550C2212yescomplemented
139#2548C2212yes—
140#2545C2212yes—
141#2544C2212yes—
142#2538C2212yes—
143#2538C2212yes—
144#2534C2214yes—
145#2532C2214yescomplemented
146#2531C2214yes—
147#2530C2214yescomplemented
148#2529C2214yescomplemented
149#2527C2214yescomplemented
150#2526C2214yes—
151#2520C2214yescomplemented
152#2519C2214yescomplemented
153#2518C2214yescomplemented
154#2516C2214yes—
155#2515C2214yes—
156#2515C2214yescomplemented
157#2514C2212yescomplemented
158#2514C2212yescomplemented
159#2513C2212yes—
160#2513C2212yes—
161#2513C2214yescomplemented
162#2512C2212yes—
163#2512C2212yes—
164#2511C2212yescomplemented
165#2511C2212yescomplemented
166#2500C2212yes—
167#2499C2212yes—
168#2480C2214yes—
169#2477C2214yescomplemented
170#2474C2214yescomplemented
171#2472C2214yes—
172#2469C2214yescomplemented
173#2469C2214yescomplemented
174#2466C2214yescomplemented
175#2465C2214yescomplemented
176#2465C2214yescomplemented
177#2461C2214yes—
178#2458C2214yescomplemented
179#2458C2214yescomplemented
180#2448C2212yes—
181#2448C2212yescomplemented
182#2447C2212yes—
183#2447C2214yescomplemented
184#2447C2212yescomplemented
185#2446C2212yescomplemented
186#2446C2212yescomplemented
187#2445C2212yes—
188#2445C2212yes—
189#2441C2212yes—
190#2439C2212yes—
191#2436C2211yescharacteristic
192#2435C2211yescharacteristic
193#2434C2211yescharacteristic
194#2433C2211yescharacteristic
195#2411C2214yes—
196#2396C2212yes—
197#2396C2212yes—
198#2379C2214yes—
199#2370C2212yescomplemented
200#2370C2212yescomplemented
201#2367C2212yes—
202#2367C2212yes—
203#2367C2212yes—
204#2367C2212yescomplemented
205#2366C2212yes—
206#2365C2212yescomplemented
207#2362C2214yes—
208#2357C2212yes—
209#2357C2212yes—
210#2356C2212yescomplemented
211#2355C2212yescomplemented
212#2355C2212yescomplemented
213#2351C2212yescomplemented
214#2347C2212yes—
215#2346C2212yes—
216#2342C2214yes—
217Q8×C22⋊C4C2212yes—
218D4×C22⋊C4C2212yes—
219#2337C2212yes—
220#2337C2212yes—
221#2335C2214yes—
222#2335C2214yescomplemented
223#2334C2214yescomplemented
224#2332C2214yescomplemented
225#2330C2212yescomplemented
226#2326C2212yes—
227#2326C2212yes—
228#2326C2212yescomplemented
229#2324C2212yes—
230#2323C2212yes—
231#2323C2214yes—
232#2321C2214yes—
233#2320C2212yescomplemented
234#2315C2212yes—
235#2312C2212yes—
236#2310C2212yes—
237#2309C2212yes—
238C4×C4⋊Q8C2212yescomplemented
239C4×C4⋊Q8C2212yescomplemented
240C4×C4⋊Q8C2212yescomplemented
241C4×#125C2212yescomplemented
242C4×#126C2214yescomplemented
243C4×#123C2214yescomplemented
244#2298C2212yescomplemented
245#2296C2212yescomplemented
246#2295C2211yescharacteristic, complemented
247#2295C2212yescomplemented
248#2295C2212yescomplemented
249#2293C2212yes—
250#2293C2211yescharacteristic, complemented
251#2290C2212yes—
252#2285C2211yescharacteristic
253#2283C2211yescharacteristic
254#2276C2212yescomplemented
255C42×Q8C2211yescharacteristic, complemented
256C42×D4C2211yescharacteristic, complemented
257C4×#117C2211yescharacteristic
258C4×#117C2211yescharacteristic
259C23×Q8C2311yescharacteristic
260C23×D4C2311yescharacteristic
261#533—28no—
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2312yes—
266C2×#127C2312yes—
267#529—28no—
268C2×#126C2312yes—
269C2×#126C2314yes—
270C2×#126C2314yes—
271C2×#125C2312yes—
272C2×#125C2311yescharacteristic
273C2×#125C2312yes—
274C2×#124—28no—
275C2×#124C2312yes—
276C2×#124C2311yescharacteristic
277C2×#124C2312yes—
278C2×#124C2312yes—
279C2×#124C2312yes—
280C2×#124C2312yes—
281C2×#124C2312yes—
282C2×#124C2314yes—
283C2×#123C2312yes—
284C2×#123C2314yes—
285C2×#123C2314yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2311yescharacteristic
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×#121C2311yescharacteristic
292C2×#120C2314yes—
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2314yes—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2314yes—
303C2×C4×D4C2311yescharacteristic
304C2×C4×D4C2312yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2314yes—
309C2×#117C2312yes—
310C2×#117C2312yes—
311C2×#117C2312yes—
312C2×#117C2312yes—
313C2×#117C2312yes—
314C2×#117C2312yes—
315C22×C22⋊C4C2312yes—
316C22×C22⋊C4C2312yes—
317C22×C22⋊C4C2314yes—
318C22×C42C2312yes—
319C22×C42C2311yescharacteristic
320#401C2314yes—
321#401C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2312yes—
325#400C2312yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#399C2312yes—
337#399C2314yes—
338#399C2314yes—
339#399C2312yes—
340#398C2314yes—
341#398C2314yes—
342#398C2312yes—
343#398C2312yes—
344#398C2312yes—
345#398C2314yes—
346#398C2314yes—
347#398C2312yes—
348#398C2312yes—
349#398C2312yes—
350#398C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2312yes—
367#397C2312yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2312yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2312yes—
384#396C2312yes—
385#396C2312yes—
386#396C2314yes—
387#396C2314yes—
388#395C2314yes—
389#395C2314yes—
390#395C2312yes—
391#395C2312yes—
392#395C2312yes—
393#395C2312yes—
394#395C2312yes—
395#395C2312yes—
396#395C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2312yes—
403#394C2312yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#393C2312yes—
410#393C2314yes—
411#393C2314yes—
412#393C2314yes—
413#393C2314yes—
414#393C2314yes—
415#393C2314yes—
416#393C2314yes—
417#393C2312yes—
418#393C2312yes—
419#393C2312yes—
420#393C2312yes—
421#393C2312yes—
422#392C2312yes—
423#392C2312yes—
424#391C2314yes—
425#391C2312yes—
426#391C2312yes—
427#391C2314yes—
428#391C2312yes—
429#391C2312yes—
430#391C2312yes—
431#391C2312yes—
432#391C2314yes—
433#391C2314yes—
434#391C2312yes—
435#391C2312yes—
436#391C2312yes—
437#391C2312yes—
438#391C2314yes—
439#391C2312yes—
440#391C2312yes—
441#391C2312yes—
442#391C2314yes—
443#391C2312yes—
444#391C2314yes—
445#391C2312yes—
446#391C2312yes—
447#391C2312yes—
448#390C2314yes—
449#390C2314yes—
450#390C2312yes—
451#390C2312yes—
452#390C2312yes—
453#390C2312yes—
454#390C2312yes—
455#390C2312yes—
456#390C2314yes—
457#390C2314yes—
458#390C2312yes—
459#390C2314yes—
460#390C2314yes—
461#390C2312yes—
462#390C2312yes—
463#390C2314yes—
464#390C2314yes—
465#390C2314yes—
466#390C2312yes—
467#390C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2314yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2314yes—
479#389C2312yes—
480#389C2312yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2312yes—
485#389C2312yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
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#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#387C2312yes—
549#387C2314yes—
550#387C2314yes—
551#387C2312yes—
552#387C2312yes—
553#387C2312yes—
554#387C2314yes—
555#387C2312yes—
556#387C2312yes—
557#387C2312yes—
558#387C2312yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2312yes—
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#387C2314yes—
585#387C2312yes—
586#387C2314yes—
587#387C2314yes—
588#387C2312yes—
589#387C2312yes—
590#387C2314yes—
591#387C2314yes—
592#386C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#384C2312yes—
619#384C2312yes—
620#384C2312yes—
621#384C2312yes—
622#383C2314yes—
623#383C2314yes—
624#383C2314yes—
625#383C2311yescharacteristic
626#383C2311yescharacteristic
627#382C2312yes—
628#382C2312yes—
629#382C2312yes—
630#382C2314yes—
631#382C2312yes—
632#382C2314yes—
633#382C2314yes—
634#382C2314yes—
635#382C2312yes—
636#381C2314yes—
637#381C2314yes—
638#381C2314yes—
639#381C2314yes—
640#381C2314yes—
641#381C2314yes—
642#381C2312yes—
643#380C2311yescharacteristic
644#380C2312yes—
645#380C2311yescharacteristic
646#380C2314yes—
647#380C2314yes—
648#380C2314yes—
649#380C2312yes—
650#379C2314yes—
651#379C2314yes—
652#379C2314yes—
653#379C2314yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2311yescharacteristic
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2311yescharacteristic
687C4×C22⋊C4C2314yes—
688C4×C22⋊C4C2314yes—
689C4×C22⋊C4C2314yes—
690C4×C22⋊C4C2312yes—
691C4×C22⋊C4C2311yescharacteristic
692C4×C22⋊C4C2311yescharacteristic
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2312yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2311yescharacteristic
703C4×C22⋊C4C2311yescharacteristic
704#376C2311yescharacteristic
705#376C2311yescharacteristic
706#376C2311yescharacteristic
707#376C2312yes—
708#376C2314yes—
709#376C2311yescharacteristic
710#376C2312yes—
711C43C2312yes—
712C43C2311yescharacteristic
713C43C2312yes—
714C43C2311yescharacteristic
715C25C2412yes—
716C22×Q8—24no—
717C22×Q8—44no—
718C22×Q8C2411yescharacteristic
719C22×Q8C2412yes—
720C22×Q8C2412yes—
721C22×Q8C2412yes—
722C22×Q8C2412yes—
723C22×Q8C2412yes—
724C22×Q8C2412yes—
725C22×D4—24no—
726C22×D4—44no—
727C22×D4C2411yescharacteristic
728C22×D4C2412yes—
729C22×D4C2412yes—
730C22×D4C2414yes—
731C22×D4C2412yes—
732C22×D4C2414yes—
733C23×C4C2411yescharacteristic
734C23×C4C2412yes—
735C23×C4C2412yes—
736C23×C4C2414yes—
737C23×C4C2414yes—
738C23×C4C2414yes—
739C23×C4C2411yescharacteristic
740C23×C4C2411yescharacteristic
741C4⋊Q8—24no—
742C4⋊Q8—24no—
743C4⋊Q8—44no—
744C4⋊Q8—44no—
745#127—44no—
746#126—28no—
747#126—48no—
748#126—84no—
749#125—24no—
750#125—28no—
751#125—44no—
752#124—28no—
753#124—28no—
754#124—28no—
755#124—28no—
756#124—24no—
757#124—44no—
758#124—44no—
759#124—84no—
760#123—28no—
761#123—48no—
762#123—48no—
763C22⋊Q8—24no—
764C22⋊Q8—28no—
765C22⋊Q8—28no—
766C22⋊Q8—48no—
767C22⋊Q8—84no—
768#121—24no—
769#120—48no—
770C4×Q8—24no—
771C4×Q8—28no—
772C4×Q8—28no—
773C4×Q8—44no—
774C4×Q8—44no—
775C4×Q8—48no—
776C4×Q8—44no—
777C4×Q8—44no—
778C4×Q8—44no—
779C4×Q8—84no—
780C4×D4—28no—
781C4×D4—24no—
782C4×D4—44no—
783C4×D4—44no—
784C4×D4—44no—
785C4×D4—84no—
786#117—28no—
787#117—28no—
788#117—44no—
789#117—44no—
790#117—82no—
791#117—82no—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2411yescharacteristic
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2411yescharacteristic
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C22⋊C4—28no—
848C2×C22⋊C4—28no—
849C2×C22⋊C4—84no—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C42—82no—
897C2×C42#4118yes—
898C2×C42C2412yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2414yes—
903C2×C42C2412yes—
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2411yescharacteristic
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2414yes—
912C2×C42C2412yes—
913C2×C42C2414yes—
914C2×C42C2414yes—
915C2×C42C2414yes—
916C2×C42C2414yes—
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2412yes—
920C2×C42C2414yes—
921C2×C42C2414yes—
922C2×C42C2412yes—
923C2×C42C2411yescharacteristic
924C2×C42C2411yescharacteristic
925C2×C42C2411yescharacteristic
926C2×C42C2412yes—
927C2×C42C2411yescharacteristic
928C2×C42C2411yescharacteristic
929C2×C42C2411yescharacteristic
930C2×C42C2411yescharacteristic
931#95C2411yescharacteristic
932#95C2412yes—
933#95C2411yescharacteristic
934#95C2411yescharacteristic
935#95C2411yescharacteristic
936#95C2412yes—
937#95C2412yes—
938#95C2412yes—
939#95C2412yes—
940#95C2412yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2411yescharacteristic
945#95C2411yescharacteristic
946#95C2411yescharacteristic
947#95C2411yescharacteristic
948#95C2414yes—
949#95C2412yes—
950#95C2412yes—
951#95C2414yes—
952#95C2412yes—
953#95C2412yes—
954#95C2414yes—
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2412yes—
968#95C2412yes—
969#95C2414yes—
970#95C2414yes—
971#95C2412yes—
972#95C2414yes—
973#95C2414yes—
974#95C2412yes—
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2412yes—
986#95C2414yes—
987#95C2412yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004C24—24no—
1005C24—42no—
1006C24—42no—
1007C24—44no—
1008C24—44no—
1009C24C2514yes—
1010C24C2512yes—
1011C24C2511yescharacteristic
1012C2×Q8—22no—
1013C2×Q8—24no—
1014C2×Q8—24no—
1015C2×Q8—24no—
1016C2×Q8—24no—
1017C2×Q8—24no—
1018C2×Q8—24no—
1019C2×Q8—24no—
1020C2×Q8—24no—
1021C2×Q8—44no—
1022C2×Q8—42no—
1023C2×Q8—42no—
1024C2×Q8—42no—
1025C2×Q8—42no—
1026C2×Q8—42no—
1027C2×Q8—42no—
1028C2×Q8—42no—
1029C2×Q8—44no—
1030C2×Q8—88no—
1031C2×D4—24no—
1032C2×D4—22no—
1033C2×D4—24no—
1034C2×D4—24no—
1035C2×D4—24no—
1036C2×D4—24no—
1037C2×D4—24no—
1038C2×D4—28no—
1039C2×D4—44no—
1040C2×D4—44no—
1041C2×D4—44no—
1042C2×D4—44no—
1043C2×D4—44no—
1044C2×D4—44no—
1045C2×D4—44no—
1046C2×D4—88no—
1047C22×C4—24no—
1048C22×C4—24no—
1049C22×C4—24no—
1050C22×C4—42no—
1051C22×C4—42no—
1052C22×C4—41no—
1053C22×C4—41no—
1054C22×C4—42no—
1055C22×C4—44no—
1056C22×C4—44no—
1057C22×C4—44no—
1058C22×C4—44no—
1059C22×C4—44no—
1060C22×C4—44no—
1061C22×C4—44no—
1062C22×C4—44no—
1063C22×C4—44no—
1064C22×C4—44no—
1065C22×C4C2×#4114yes—
1066C22×C4C2×#4114yes—
1067C22×C4C2×#4114yes—
1068C22×C4C2512yes—
1069C22×C4C2514yes—
1070C22×C4C2512yes—
1071C22×C4C2512yes—
1072C22×C4C2512yes—
1073C22×C4C2512yes—
1074C22×C4C2512yes—
1075C22×C4C2514yes—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C22×C4C2512yes—
1080C22×C4C2514yes—
1081C22×C4C2514yes—
1082C22×C4C2512yes—
1083C22×C4C2512yes—
1084C22×C4C2512yes—
1085C22×C4C2514yes—
1086C22×C4C2512yes—
1087C22×C4C2511yescharacteristic
1088C22×C4C2511yescharacteristic
1089C22×C4C2511yescharacteristic
1090C22×C4C2511yescharacteristic
1091C22×C4C2511yescharacteristic
1092C22×C4C2512yes—
1093C22×C4C2511yescharacteristic
1094C4⋊C4—24no—
1095C4⋊C4—24no—
1096C4⋊C4—24no—
1097C4⋊C4—24no—
1098C4⋊C4—22no—
1099C4⋊C4—24no—
1100C4⋊C4—22no—
1101C4⋊C4—28no—
1102C4⋊C4—28no—
1103C4⋊C4—24no—
1104C4⋊C4—24no—
1105C4⋊C4—24no—
1106C4⋊C4—24no—
1107C4⋊C4—24no—
1108C4⋊C4—24no—
1109C4⋊C4—28no—
1110C4⋊C4—28no—
1111C4⋊C4—24no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—42no—
1115C4⋊C4—42no—
1116C4⋊C4—42no—
1117C4⋊C4—42no—
1118C4⋊C4—44no—
1119C4⋊C4—42no—
1120C4⋊C4—42no—
1121C4⋊C4—42no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—42no—
1125C4⋊C4—44no—
1126C4⋊C4—42no—
1127C4⋊C4—42no—
1128C4⋊C4—42no—
1129C4⋊C4—42no—
1130C4⋊C4—42no—
1131C4⋊C4—42no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—42no—
1141C4⋊C4—42no—
1142C4⋊C4—42no—
1143C4⋊C4—44no—
1144C4⋊C4—42no—
1145C4⋊C4—44no—
1146C4⋊C4—42no—
1147C4⋊C4—44no—
1148C4⋊C4—42no—
1149C22⋊C4—28no—
1150C22⋊C4—24no—
1151C22⋊C4—28no—
1152C22⋊C4—28no—
1153C22⋊C4—28no—
1154C22⋊C4—28no—
1155C22⋊C4—24no—
1156C22⋊C4—24no—
1157C22⋊C4—24no—
1158C22⋊C4—24no—
1159C22⋊C4—24no—
1160C22⋊C4—28no—
1161C22⋊C4—42no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—42no—
1170C22⋊C4—42no—
1171C22⋊C4—42no—
1172C22⋊C4—42no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C42—24no—
1196C42—28no—
1197C42—24no—
1198C42—24no—
1199C42—24no—
1200C42—24no—
1201C42—24no—
1202C42—24no—
1203C42—24no—
1204C42—41no—
1205C42—42no—
1206C42—44no—
1207C42—41no—
1208C42—41no—
1209C42—42no—
1210C42—42no—
1211C42—42no—
1212C42—41no—
1213C42—44no—
1214C42—44no—
1215C42—44no—
1216C42—44no—
1217C42—44no—
1218C42—44no—
1219C42—42no—
1220C42—44no—
1221C42—42no—
1222C42—44no—
1223C42—42no—
1224C42C2×#4114yes—
1225C42C2×#4114yes—
1226C42C2×#4114yes—
1227C42C2×#4114yes—
1228C23—22no—
1229C23—22no—
1230C23—21no—
1231C23—21no—
1232C23—22no—
1233C23—24no—
1234C23—24no—
1235C23—24no—
1236C23—24no—
1237C23—24no—
1238C23—24no—
1239C23—24no—
1240C23—24no—
1241C23—22no—
1242C23—24no—
1243C23—22no—
1244C23—48no—
1245C23—84no—
1246C23—84no—
1247C23—164no—
1248C23—164no—
1249C23C22×#4112yes—
1250C23C2611yescharacteristic
1251Q8—48no—
1252Q8—48no—
1253Q8—44no—
1254Q8—48no—
1255Q8—84no—
1256Q8—84no—
1257Q8—84no—
1258D4—44no—
1259D4—48no—
1260D4—88no—
1261D4—84no—
1262D4—84no—
1263D4—164no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—21no—
1269C2×C4—22no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—28no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—24no—
1294C2×C4—24no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—22no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—22no—
1304C2×C4—24no—
1305C2×C4—22no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—24no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—44no—
1330C2×C4—44no—
1331C2×C4—48no—
1332C2×C4—84no—
1333C2×C4—88no—
1334C2×C4—164no—
1335C2×C4—164no—
1336C2×C4C22×#4112yes—
1337C2×C4C22×#4112yes—
1338C2×C4C22×#4112yes—
1339C2×C4C22×#4112yes—
1340C2×C4C22×#4112yes—
1341C2×C4C22×#4112yes—
1342C2×C4#58514yes—
1343C2×C4#58514yes—
1344C22—22no—
1345C22—22no—
1346C22—22no—
1347C22—42no—
1348C22—42no—
1349C22—44no—
1350C22—42no—
1351C22—42no—
1352C22—44no—
1353C22—42no—
1354C22—44no—
1355C22—44no—
1356C22—44no—
1357C22—44no—
1358C22—44no—
1359C22—44no—
1360C22—44no—
1361C22—168no—
1362C22C23×#4111yescharacteristic
1363C22C2×#58512yes—
1364C22C2×#58512yes—
1365C22H(7,𝔽2)11yescharacteristic
1366C222−1+611yescharacteristic
1367C4—22no—
1368C4—22no—
1369C4—22no—
1370C4—22no—
1371C4—22no—
1372C4—24no—
1373C4—44no—
1374C4—42no—
1375C4—42no—
1376C4—44no—
1377C4—42no—
1378C4—44no—
1379C4—42no—
1380C4—42no—
1381C4—42no—
1382C4—42no—
1383C4—42no—
1384C4—42no—
1385C4—42no—
1386C4—44no—
1387C4—44no—
1388C4—42no—
1389C4—42no—
1390C4—42no—
1391C4—42no—
1392C4#351014yes—
1393C2—42no—
1394C2—82no—
1395C2—84no—
1396C2C2×#351011yescharacteristic
1397C2#6281511yescharacteristic
1398C2#6284511yescharacteristic
1399C2#6296812yes—
1400C2#6297012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2433C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #50934C2semidirect
2. #50734C2semidirect
3. #46470C2semidirect
4. #46401C2semidirect
5. #45392C2semidirect
7. #45149C2semidirect
8. #44961C2semidirect
9. #40352C2semidirect
10. #40337C2semidirect
11. #40023C2semidirect
12. #40020C2semidirect
13. #39800C2semidirect
14. #39800C2semidirect
15. #39771C2semidirect
16. #39765C2semidirect
17. #37545C2semidirect
18. #37026C2semidirect
19. #36832C2semidirect
20. #36527C2semidirect
21. #36485C2semidirect
22. #35500C2semidirect
23. #35428C2semidirect
24. #35338C2semidirect
26. #34912C2semidirect
27. #34377C2semidirect
28. #34225C2semidirect
29. #34084C2semidirect
33. #2865C22semidirect
38. #2852C22semidirect
41. #2808C22semidirect
42. #2808C22semidirect
43. #2804C22semidirect
44. #2800C22semidirect
45. #2796C22semidirect
46. #2796C22semidirect
47. #2795C22semidirect
48. #2793C22semidirect
49. #2783C22semidirect
50. #2783C22semidirect
51. #2779C22semidirect
52. #2775C22semidirect
53. #2775C22semidirect
54. #2772C22semidirect
55. #2763C22semidirect
56. #2762C22semidirect
58. #2758C22semidirect
60. #2754C22semidirect
61. #2751C22semidirect
62. #2751C22semidirect
65. #2745C22semidirect
66. #2745C22semidirect
69. #2739C22semidirect
73. #2729C22semidirect
74. #2724C22semidirect
77. #2689C22semidirect
78. #2689C22semidirect
80. #2674C22semidirect
83. #2660C22semidirect
84. #2660C22semidirect
85. #2650C22semidirect
86. #2649C22semidirect
89. #2640C22semidirect
90. #2640C22semidirect
92. #2637C22semidirect
97. #2606C22semidirect
98. #2606C22semidirect
99. #2605C22semidirect
100. #2605C22semidirect
101. #2599C22semidirect
102. #2599C22semidirect
103. #2597C22semidirect
104. #2597C22semidirect
105. #2595C22semidirect
106. #2594C22semidirect
107. #2594C22semidirect
108. #2594C22semidirect
109. #2594C22semidirect
114. #2592C22semidirect
115. #2592C22semidirect
116. #2587C22semidirect
117. #2586C22semidirect
118. #2581C22semidirect
119. #2581C22semidirect
120. #2580C22semidirect
121. #2577C22semidirect
122. #2577C22semidirect
124. #2576C22semidirect
125. #2576C22semidirect
127. #2575C22semidirect
128. #2570C22semidirect
129. #2568C22semidirect
130. #2566C22semidirect
131. #2565C22semidirect
136. #2558C22semidirect
138. #2550C22semidirect
145. #2532C22semidirect
147. #2530C22semidirect
148. #2529C22semidirect
149. #2527C22semidirect
151. #2520C22semidirect
152. #2519C22semidirect
153. #2518C22semidirect
156. #2515C22semidirect
157. #2514C22semidirect
158. #2514C22semidirect
161. #2513C22semidirect
164. #2511C22semidirect
165. #2511C22semidirect
169. #2477C22semidirect
170. #2474C22semidirect
172. #2469C22semidirect
173. #2469C22semidirect
174. #2466C22semidirect
175. #2465C22semidirect
176. #2465C22semidirect
178. #2458C22semidirect
179. #2458C22semidirect
181. #2448C22semidirect
183. #2447C22semidirect
184. #2447C22semidirect
185. #2446C22semidirect
186. #2446C22semidirect
199. #2370C22semidirect
200. #2370C22semidirect
204. #2367C22semidirect
206. #2365C22semidirect
210. #2356C22semidirect
211. #2355C22semidirect
212. #2355C22semidirect
213. #2351C22semidirect
222. #2335C22semidirect
223. #2334C22semidirect
224. #2332C22semidirect
225. #2330C22semidirect
228. #2326C22semidirect
233. #2320C22semidirect
238. C4×C4⋊Q8C22semidirect
239. C4×C4⋊Q8C22semidirect
240. C4×C4⋊Q8C22semidirect
241. C4×#125C22semidirect
242. C4×#126C22semidirect
243. C4×#123C22semidirect
244. #2298C22semidirect
245. #2296C22semidirect
246. #2295C22semidirect
247. #2295C22semidirect
248. #2295C22semidirect
250. #2293C22semidirect
254. #2276C22semidirect
255. C42×Q8C22semidirect
256. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#509342
#507342
#464702
#464012
#453922
#453672
#451492
#449612
#403522
#403372
#400232
#400202
#398002
#397712
#397652
#375452
#370262
#368322
#365272
#364852
#355002
#354282
#353382
#351312
#349122
#343772
#342252
#340842