Finite Group Databasebeta

← #7692912

Subgroups — #7692912

Order 512.

5711 conjugacy classes of subgroups.

The subgroup lattice has 1386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59637C213yesmaximal, complemented
2#59487C213yesmaximal, complemented
3#59374C213yesmaximal, complemented
4#59224C213yesmaximal, complemented
5#59197C213yesmaximal, complemented
6#45401C213yesmaximal, complemented
7#45260C213yesmaximal, complemented
8#45053C213yesmaximal, complemented
9#44960C213yesmaximal, complemented
10#39069C213yesmaximal, complemented
11#39045C213yesmaximal, complemented
12#38056C213yesmaximal, complemented
13#37852C213yesmaximal, complemented
14#36585C211yesmaximal, characteristic, complemented
15#36578C211yesmaximal, characteristic, complemented
16#36435C211yesmaximal, characteristic, complemented
17#36433C211yesmaximal, characteristic, complemented
18#36429C211yesmaximal, characteristic
19#36291C213yesmaximal, complemented
20#36168C213yesmaximal, complemented
21#36076C211yesmaximal, characteristic, complemented
22#36059C211yesmaximal, characteristic, complemented
23#36049C211yesmaximal, characteristic, complemented
24#36040C211yesmaximal, characteristic, complemented
25#34849C213yesmaximal, complemented
26#34295C211yesmaximal, characteristic, complemented
27#34263C211yesmaximal, characteristic, complemented
28#34192C211yesmaximal, characteristic, complemented
29#34175C211yesmaximal, characteristic, complemented
30C4×#548C211yesmaximal, characteristic, complemented
31C2×#2341C211yesmaximal, characteristic, complemented
32C23×#41C2211yescharacteristic
33C2×#557C2211yescharacteristic, complemented
34C2×#550C2211yescharacteristic
35C2×#550C2211yescharacteristic
36C2×#548C2211yescharacteristic
37C2×#520C2211yescharacteristic
38C2×#520C2211yescharacteristic
39C2×C4×#41C2211yescharacteristic, complemented
40C22×C4×Q8C2211yescharacteristic
41C22×C4×Q8C2211yescharacteristic
42#2860C2213yescomplemented
43#2854C2213yes—
44#2854C2213yescomplemented
45#2851C2213yes—
46#2847C2213yes—
47#2797C2216yescomplemented
48#2756C2216yescomplemented
49#2756C2216yescomplemented
50#2753C2216yescomplemented
51#2752C2216yescomplemented
52#2749C2216yescomplemented
53#2747C2216yescomplemented
54#2746C2216yescomplemented
55#2741C2216yescomplemented
56#2741C2216yescomplemented
57#2737C2216yescomplemented
58#2737C2216yescomplemented
59#2717C2216yescomplemented
60#2706C2216yescomplemented
61#2644C2213yescomplemented
62#2641C2213yescomplemented
63#2628C2213yescomplemented
64#2624C2213yescomplemented
65#2610C2216yescomplemented
66#2602C2216yescomplemented
67#2595C2216yescomplemented
68#2581C2213yescomplemented
69#2580C2213yescomplemented
70#2578C2213yescomplemented
71#2578C2216yescomplemented
72#2577C2213yescomplemented
73#2576C2213yescomplemented
74#2575C2213yescomplemented
75#2574C2213yescomplemented
76#2573C2213yescomplemented
77#2572C2213yescomplemented
78#2569C2213yes—
79#2565C2213yescomplemented
80#2564C2213yes—
81#2563C2213yescomplemented
82#2562C2213yescomplemented
83#2561C2213yes—
84#2557C2216yescomplemented
85#2553C2213yescomplemented
86#2548C2213yescomplemented
87#2534C2213yes—
88#2531C2216yescomplemented
89#2531C2216yescomplemented
90#2516C2216yescomplemented
91#2513C2213yescomplemented
92#2513C2213yescomplemented
93#2513C2213yescomplemented
94#2513C2213yescomplemented
95#2513C2213yescomplemented
96#2513C2213yescomplemented
97#2510C2216yes—
98#2510C2216yescomplemented
99#2504C2213yes—
100#2504C2213yescomplemented
101#2500C2213yescomplemented
102#2498C2216yescomplemented
103#2495C2213yescomplemented
104#2495C2213yescomplemented
105#2495C2213yescomplemented
106#2494C2213yescomplemented
107#2494C2213yescomplemented
108#2494C2213yescomplemented
109#2493C2211yescharacteristic
110#2493C2216yescomplemented
111#2491C2213yescomplemented
112#2491C2213yescomplemented
113#2490C2213yescomplemented
114#2490C2213yescomplemented
115#2487C2213yes—
116#2486C2213yescomplemented
117#2485C2213yescomplemented
118#2480C2213yes—
119#2472C2216yes—
120#2471C2216yescomplemented
121#2467C2216yescomplemented
122#2454C2213yescomplemented
123#2454C2213yescomplemented
124#2453C2213yescomplemented
125#2451C2213yescomplemented
126#2448C2213yescomplemented
127#2448C2213yescomplemented
128#2445C2213yescomplemented
129#2445C2213yescomplemented
130#2445C2213yescomplemented
131#2445C2213yescomplemented
132#2442C2213yes—
133#2442C2213yescomplemented
134#2442C2213yescomplemented
135#2440C2213yes—
136#2433C2213yes—
137#2431C2213yes—
138#2431C2213yes—
139#2422C2213yescomplemented
140#2421C2213yescomplemented
141#2421C2213yescomplemented
142#2420C2213yescomplemented
143#2420C2213yescomplemented
144#2420C2213yescomplemented
145#2419C2213yes—
146#2418C2213yes—
147#2418C2216yes—
148#2412C2216yes—
149#2412C2216yes—
150#2408C2213yes—
151#2407C2213yes—
152#2407C2213yes—
153#2401C2213yescomplemented
154#2398C2213yescomplemented
155#2396C2213yescomplemented
156#2395C2213yescomplemented
157#2367C2213yescomplemented
158#2366C2213yescomplemented
159#2363C2213yescomplemented
160#2362C2213yescomplemented
161#2361C2213yes—
162#2361C2213yescomplemented
163#2358C2216yes—
164#2357C2213yescomplemented
165#2356C2213yescomplemented
166#2356C2213yescomplemented
167#2354C2213yescomplemented
168#2353C2216yescomplemented
169#2352C2213yes—
170#2352C2213yescomplemented
171#2351C2211yescharacteristic, complemented
172#2351C2211yescharacteristic, complemented
173#2351C2211yescharacteristic, complemented
174#2351C2211yescharacteristic, complemented
175#2351C2211yescharacteristic, complemented
176#2351C2211yescharacteristic, complemented
177#2351C2211yescharacteristic, complemented
178Q8×C4⋊C4C2211yescharacteristic, complemented
179#2345C2213yes—
180#2345C2213yes—
181#2345C2213yescomplemented
182#2344C2213yescomplemented
183#2342C2216yes—
184#2341C2211yescharacteristic
185#2341C2213yes—
186#2341C2213yes—
187#2341C2213yes—
188#2341C2213yes—
189#2341C2211yescharacteristic
190#2341C2211yescharacteristic
191#2341C2211yescharacteristic
192#2341C2211yescharacteristic
193#2341C2211yescharacteristic
194#2341C2211yescharacteristic
195#2341C2211yescharacteristic
196#2341C2211yescharacteristic, complemented
197#2341C2211yescharacteristic, complemented
198#2341C2211yescharacteristic, complemented
199Q8×C22⋊C4C2211yescharacteristic
200Q8×C22⋊C4C2211yescharacteristic
201Q8×C22⋊C4C2211yescharacteristic
202#2339C2213yes—
203#2339C2213yes—
204D4×C22⋊C4C2213yes—
205D4×C22⋊C4C2213yes—
206#2328C2213yescomplemented
207#2324C2213yescomplemented
208#2320C2213yescomplemented
209#2320C2213yescomplemented
210#2319C2213yescomplemented
211#2314C2213yescomplemented
212#2311C2213yes—
213#2311C2213yes—
214C4×#126C2213yescomplemented
215C4×#124C2213yescomplemented
216C4×C22⋊Q8C2213yes—
217C4×C22⋊Q8C2213yescomplemented
218C4×#123C2213yes—
219C4×#123C2213yescomplemented
220C4×#121C2213yes—
221C4×#121C2213yescomplemented
222C4×#120C2213yes—
223#2298C2213yescomplemented
224#2293C2213yescomplemented
225C2×#390C2213yes—
226C2×#390C2213yes—
227#2290C2213yescomplemented
228#2283C2213yes—
229#2283C2213yes—
230#2280C2213yes—
231C2×#380C2213yes—
232C2×#380C2213yes—
233#2276C2211yescharacteristic, complemented
234#2276C2211yescharacteristic, complemented
235C42×Q8C2211yescharacteristic, complemented
236C42×D4C2213yes—
237C2×C4×C22⋊C4C2213yes—
238C22×#41—28no—
239C22×#41—28no—
240C22×#41—44no—
241C22×#41C2311yescharacteristic
242C22×#41C2311yescharacteristic
243C22×#41C2313yes—
244C22×#41C2313yes—
245C22×#41C2311yescharacteristic
246C23×Q8C2311yescharacteristic
247C23×D4C2313yes—
248C24×C4C2313yes—
249#557—44no—
250#550—28no—
251#550—44no—
252#548—28no—
253C2×C4⋊Q8C2313yes—
254C2×#127C2313yes—
255C2×#127C2313yes—
256C2×#126C2313yes—
257C2×#125C2313yes—
258C2×#125C2313yes—
259C2×#124C2313yes—
260C2×#124C2316yes—
261C2×#123C2313yes—
262C2×#123C2313yes—
263C2×#123C2316yes—
264C2×#123C2316yes—
265C2×C22⋊Q8C2313yes—
266C2×C22⋊Q8C2313yes—
267C2×#121C2313yes—
268C2×#121C2313yes—
269C2×#121C2313yes—
270C2×#121C2313yes—
271C2×#121C2313yes—
272C2×#120C2316yes—
273C2×#120C2313yes—
274#520—28no—
275#520—44no—
276C4×#41—44no—
277C2×C4×Q8—28no—
278C2×C4×Q8—44no—
279C2×C4×Q8C2313yes—
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2313yes—
292C2×C4×Q8C2313yes—
293C2×C4×Q8C2313yes—
294C2×C4×Q8C2313yes—
295C2×C4×D4C2313yes—
296C2×C4×D4C2313yes—
297C2×C4×D4C2313yes—
298C2×C4×D4C2313yes—
299C2×C4×D4C2313yes—
300C2×C4×D4C2313yes—
301C2×C4×D4C2313yes—
302C2×C4×D4C2313yes—
303C2×C4×D4C2313yes—
304C2×C4×D4C2316yes—
305C2×C4×D4C2313yes—
306C2×C4×D4C2313yes—
307C2×#117C2313yes—
308C2×#117C2313yes—
309C2×#117C2313yes—
310C2×#117C2316yes—
311C22×C4⋊C4C2313yes—
312C22×C4⋊C4C2313yes—
313C22×C4⋊C4C2313yes—
314C22×C4⋊C4C2313yes—
315C22×C22⋊C4C2313yes—
316C22×C22⋊C4C2316yes—
317C22×C22⋊C4C2313yes—
318C22×C22⋊C4C2316yes—
319C22×C42C2313yes—
320C22×C42C2313yes—
321C22×C42C2313yes—
322#401C2311yescharacteristic
323#401C2316yes—
324#400C2313yes—
325#400C2313yes—
326#400C2313yes—
327#400C2311yescharacteristic
328#400C2313yes—
329#400C2311yescharacteristic
330#400C2311yescharacteristic
331#400C2316yes—
332#400C2316yes—
333#400C2316yes—
334#399C2313yes—
335#399C2313yes—
336#399C2316yes—
337#399C2316yes—
338#398C2316yes—
339#398C2316yes—
340#398C2313yes—
341#398C2313yes—
342#398C2313yes—
343#397C2313yes—
344#397C2313yes—
345#397C2313yes—
346#397C2313yes—
347#397C2313yes—
348#397C2313yes—
349#397C2316yes—
350#397C2316yes—
351#397C2313yes—
352#397C2313yes—
353#397C2316yes—
354#397C2316yes—
355#397C2316yes—
356#397C2316yes—
357#397C2316yes—
358#397C2316yes—
359#397C2316yes—
360#397C2316yes—
361#396C2313yes—
362#396C2313yes—
363#396C2313yes—
364#395C2313yes—
365#395C2316yes—
366#394C2316yes—
367#394C2313yes—
368#394C2313yes—
369#394C2316yes—
370#394C2313yes—
371#394C2316yes—
372#394C2316yes—
373#394C2316yes—
374#394C2316yes—
375#394C2313yes—
376#394C2316yes—
377#394C2316yes—
378#394C2316yes—
379#393C2313yes—
380#393C2313yes—
381#393C2316yes—
382#393C2313yes—
383#392C2316yes—
384#392C2316yes—
385#392C2316yes—
386#391C2313yes—
387#391C2313yes—
388#391C2313yes—
389#391C2313yes—
390#391C2313yes—
391#391C2313yes—
392#391C2313yes—
393#390C2313yes—
394#390C2313yes—
395#390C2313yes—
396#390C2313yes—
397#390C2313yes—
398#390C2313yes—
399#390C2313yes—
400#390C2313yes—
401#390C2313yes—
402#390C2316yes—
403#390C2313yes—
404#390C2313yes—
405#390C2316yes—
406#390C2313yes—
407#390C2316yes—
408#390C2316yes—
409#390C2313yes—
410#390C2313yes—
411#390C2313yes—
412#390C2316yes—
413#390C2313yes—
414#390C2313yes—
415#390C2313yes—
416#390C2313yes—
417#390C2313yes—
418#390C2313yes—
419#390C2313yes—
420#390C2316yes—
421#389C2313yes—
422#389C2313yes—
423#389C2313yes—
424#389C2313yes—
425#389C2313yes—
426#389C2313yes—
427#389C2313yes—
428#389C2313yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2313yes—
438#388C2313yes—
439#388C2313yes—
440#388C2313yes—
441#388C2313yes—
442#388C2313yes—
443#388C2313yes—
444#388C2316yes—
445#388C2316yes—
446#388C2316yes—
447#388C2316yes—
448#388C2313yes—
449#388C2313yes—
450#388C2313yes—
451#388C2313yes—
452#388C2313yes—
453#388C2313yes—
454#388C2313yes—
455#388C2316yes—
456#388C2316yes—
457#388C2316yes—
458#388C2316yes—
459#388C2316yes—
460#388C2316yes—
461#388C2316yes—
462#388C2316yes—
463#388C2316yes—
464#388C2316yes—
465#388C2316yes—
466#388C2316yes—
467#388C2316yes—
468#387C2313yes—
469#387C2313yes—
470#387C2313yes—
471#387C2313yes—
472#387C2313yes—
473#387C2316yes—
474#387C2313yes—
475#387C2313yes—
476#387C2313yes—
477#387C2316yes—
478#387C2311yescharacteristic
479#387C2313yes—
480#387C2311yescharacteristic
481#387C2313yes—
482#387C2313yes—
483#387C2313yes—
484#387C2316yes—
485#387C2316yes—
486#387C2316yes—
487#387C2316yes—
488#387C2316yes—
489#387C2316yes—
490#387C2311yescharacteristic
491#386C2313yes—
492#386C2313yes—
493#386C2316yes—
494#386C2316yes—
495#386C2316yes—
496#386C2316yes—
497#386C2313yes—
498#386C2313yes—
499#386C2313yes—
500#386C2316yes—
501#386C2316yes—
502#386C2313yes—
503#386C2313yes—
504#386C2316yes—
505#386C2316yes—
506#386C2316yes—
507#386C2316yes—
508#386C2316yes—
509#386C2316yes—
510#386C2316yes—
511#386C2316yes—
512#385C2313yes—
513#385C2313yes—
514#385C2311yescharacteristic
515#385C2313yes—
516#385C2313yes—
517#385C2313yes—
518#385C2313yes—
519#385C2316yes—
520#385C2316yes—
521#385C2313yes—
522#385C2316yes—
523#385C2316yes—
524#385C2311yescharacteristic
525#384C2313yes—
526#383C2311yescharacteristic
527#383C2313yes—
528#383C2313yes—
529#383C2316yes—
530#383C2316yes—
531#382C2313yes—
532#382C2313yes—
533#382C2313yes—
534#382C2313yes—
535#382C2313yes—
536#382C2313yes—
537#382C2313yes—
538#382C2313yes—
539#382C2313yes—
540#381C2311yescharacteristic
541#381C2313yes—
542#381C2313yes—
543#381C2313yes—
544#381C2313yes—
545#381C2316yes—
546#381C2316yes—
547#381C2311yescharacteristic
548#380C2313yes—
549#380C2313yes—
550#380C2313yes—
551#380C2313yes—
552#380C2316yes—
553#380C2316yes—
554#380C2311yescharacteristic
555#380C2313yes—
556#380C2313yes—
557#380C2313yes—
558#380C2316yes—
559#380C2313yes—
560#380C2313yes—
561#380C2313yes—
562#380C2313yes—
563#380C2313yes—
564#380C2316yes—
565#380C2313yes—
566#380C2313yes—
567#380C2313yes—
568#380C2313yes—
569#380C2313yes—
570#380C2313yes—
571#380C2313yes—
572#380C2316yes—
573#380C2316yes—
574#380C2313yes—
575#379C2313yes—
576#379C2313yes—
577#379C2313yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C22⋊C4C2313yes—
598C4×C22⋊C4C2313yes—
599C4×C22⋊C4C2313yes—
600C4×C22⋊C4C2313yes—
601C4×C22⋊C4C2313yes—
602C4×C22⋊C4C2313yes—
603C4×C22⋊C4C2313yes—
604C4×C22⋊C4C2313yes—
605C4×C22⋊C4C2313yes—
606C4×C22⋊C4C2313yes—
607C4×C22⋊C4C2316yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2316yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2316yes—
621C4×C22⋊C4C2316yes—
622C4×C22⋊C4C2311yescharacteristic
623#376C2313yes—
624#376C2313yes—
625#376C2316yes—
626C2×#95C2313yes—
627C2×#95C2316yes—
628C2×#95C2311yescharacteristic
629C43C2313yes—
630C25C2413yes—
631C2×#41—24no—
632C2×#41—24no—
633C2×#41—24no—
634C2×#41—212no—
635C2×#41—212no—
636C2×#41—24no—
637C2×#41—24no—
638C2×#41—24no—
639C2×#41—24no—
640C2×#41—24no—
641C2×#41—212no—
642C2×#41—212no—
643C2×#41—46no—
644C2×#41—46no—
645C2×#41—464no—
646C2×#41#4118yes—
647C22×Q8—24no—
648C22×Q8—24no—
649C22×Q8#4118yes—
650C22×Q8C2413yes—
651C22×Q8C2413yes—
652C22×Q8C2411yescharacteristic
653C22×D4—212no—
654C22×D4—212no—
655C22×D4—46no—
656C22×D4C2413yes—
657C22×D4C2413yes—
658C22×D4C2413yes—
659C22×D4C2416yes—
660C22×D4C2413yes—
661C22×D4C2416yes—
662C22×D4C2413yes—
663C22×D4C2413yes—
664C22×D4C2416yes—
665C23×C4—212no—
666C23×C4—212no—
667C23×C4—46no—
668C23×C4C2411yescharacteristic
669C23×C4C2413yes—
670C23×C4C2413yes—
671C23×C4C2411yescharacteristic
672C23×C4C2411yescharacteristic
673C23×C4C2413yes—
674C23×C4C2413yes—
675C23×C4C2413yes—
676C23×C4C2413yes—
677C23×C4C2413yes—
678C23×C4C2413yes—
679C23×C4C2416yes—
680C23×C4C2413yes—
681C23×C4C2416yes—
682C23×C4C2413yes—
683C4⋊Q8—46no—
684#127—212no—
685#127—46no—
686#126—46no—
687#125—46no—
688#125—46no—
689#124—212no—
690#124—86no—
691#123—46no—
692#123—46no—
693#123—86no—
694#123—86no—
695C22⋊Q8—212no—
696C22⋊Q8—46no—
697#121—212no—
698#121—212no—
699#121—212no—
700#121—46no—
701#121—46no—
702#120—46no—
703#120—412no—
704C4×Q8—212no—
705C4×Q8—212no—
706C4×Q8—24no—
707C4×Q8—24no—
708C4×Q8—24no—
709C4×Q8—24no—
710C4×Q8—24no—
711C4×Q8—24no—
712C4×Q8—24no—
713C4×Q8—24no—
714C4×Q8—24no—
715C4×Q8—24no—
716C4×Q8—24no—
717C4×Q8—46no—
718C4×Q8—46no—
719C4×Q8—46no—
720C4×D4—212no—
721C4×D4—212no—
722C4×D4—212no—
723C4×D4—212no—
724C4×D4—46no—
725C4×D4—46no—
726C4×D4—46no—
727C4×D4—46no—
728C4×D4—46no—
729C4×D4—412no—
730C4×D4—46no—
731C4×D4—46no—
732#117—212no—
733#117—46no—
734#117—46no—
735#117—86no—
736C2×C4⋊C4—212no—
737C2×C4⋊C4—212no—
738C2×C4⋊C4—46no—
739C2×C4⋊C4—46no—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2416yes—
750C2×C4⋊C4C2411yescharacteristic
751C2×C4⋊C4C2411yescharacteristic
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2411yescharacteristic
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2416yes—
760C2×C4⋊C4C2411yescharacteristic
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2416yes—
763C2×C4⋊C4C2411yescharacteristic
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2411yescharacteristic
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2416yes—
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2413yes—
781C2×C22⋊C4—46no—
782C2×C22⋊C4—412no—
783C2×C22⋊C4—46no—
784C2×C22⋊C4—86no—
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2411yescharacteristic
792C2×C22⋊C4C2411yescharacteristic
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2411yescharacteristic
797C2×C22⋊C4C2413yes—
798C2×C22⋊C4C2416yes—
799C2×C22⋊C4C2411yescharacteristic
800C2×C22⋊C4C2416yes—
801C2×C22⋊C4C2416yes—
802C2×C22⋊C4C2416yes—
803C2×C22⋊C4C2416yes—
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2416yes—
811C2×C22⋊C4C2416yes—
812C2×C22⋊C4C2413yes—
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2416yes—
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2413yes—
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2416yes—
821C2×C22⋊C4C2416yes—
822C2×C22⋊C4C2413yes—
823C2×C22⋊C4C2413yes—
824C2×C22⋊C4C2416yes—
825C2×C22⋊C4C2413yes—
826C2×C22⋊C4C2416yes—
827C2×C22⋊C4C2416yes—
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2413yes—
830C2×C22⋊C4C2413yes—
831C2×C22⋊C4C2413yes—
832C2×C22⋊C4C2413yes—
833C2×C22⋊C4C2413yes—
834C2×C22⋊C4C2413yes—
835C2×C22⋊C4C2413yes—
836C2×C42—212no—
837C2×C42—46no—
838C2×C42—46no—
839C2×C42C2413yes—
840C2×C42C2413yes—
841C2×C42C2413yes—
842C2×C42C2413yes—
843C2×C42C2413yes—
844C2×C42C2413yes—
845C2×C42C2413yes—
846C2×C42C2413yes—
847C2×C42C2413yes—
848C2×C42C2413yes—
849C2×C42C2413yes—
850C2×C42C2413yes—
851C2×C42C2413yes—
852C2×C42C2411yescharacteristic
853C2×C42C2413yes—
854C2×C42C2413yes—
855C2×C42C2416yes—
856C2×C42C2413yes—
857C2×C42C2413yes—
858C2×C42C2416yes—
859C2×C42C2413yes—
860C2×C42C2413yes—
861C2×C42C2411yescharacteristic
862#95C2413yes—
863#95C2413yes—
864#95C2416yes—
865#95C2411yescharacteristic
866#95C2411yescharacteristic
867#95C2411yescharacteristic
868#95C2411yescharacteristic
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2416yes—
874#95C2411yescharacteristic
875#95C2411yescharacteristic
876#95C2413yes—
877#95C2413yes—
878#95C2413yes—
879#95C2413yes—
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2416yes—
885#95C2411yescharacteristic
886#95C2411yescharacteristic
887#95C2413yes—
888#95C2411yescharacteristic
889#95C2411yescharacteristic
890#95C2411yescharacteristic
891#95C2411yescharacteristic
892#95C2411yescharacteristic
893#95C2411yescharacteristic
894#95C2413yes—
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2413yes—
902#95C2413yes—
903#95C2413yes—
904#95C2416yes—
905#95C2416yes—
906#95C2416yes—
907#95C2416yes—
908#95C2413yes—
909#95C2413yes—
910#95C2416yes—
911#95C2416yes—
912#95C2411yescharacteristic
913#95C2411yescharacteristic
914#95C2411yescharacteristic
915#95C2411yescharacteristic
916#95C2411yescharacteristic
917#95C2411yescharacteristic
918#95C2413yes—
919#95C2413yes—
920#95C2413yes—
921#95C2413yes—
922#95C2413yes—
923#95C2416yes—
924#95C2416yes—
925C24—26no—
926C24—26no—
927C24—26no—
928C24—26no—
929C24—43no—
930C24—43no—
931C24—43no—
932C24C2513yes—
933C24C2513yes—
934C24C2513yes—
935C24C2511yescharacteristic
936#41—232no—
937#41—448no—
938#41—448no—
939#41—416no—
940#41—416no—
941C2×Q8—232no—
942C2×Q8—26no—
943C2×Q8—26no—
944C2×Q8—43no—
945C2×Q8—43no—
946C2×Q8—43no—
947C2×Q8C2×#41112yes—
948C2×Q8C2×#4114yes—
949C2×Q8C2×#4114yes—
950C2×Q8H(5,𝔽2)14yes—
951C2×D4—26no—
952C2×D4—212no—
953C2×D4—26no—
954C2×D4—26no—
955C2×D4—26no—
956C2×D4—212no—
957C2×D4—26no—
958C2×D4—26no—
959C2×D4—26no—
960C2×D4—212no—
961C2×D4—26no—
962C2×D4—26no—
963C2×D4—26no—
964C2×D4—26no—
965C2×D4—26no—
966C2×D4—448no—
967C2×D4—46no—
968C2×D4—43no—
969C2×D4—46no—
970C2×D4—43no—
971C2×D4—43no—
972C2×D4—46no—
973C2×D4—43no—
974C2×D4—43no—
975C2×D4—46no—
976C2×D4—46no—
977C2×D4—46no—
978C2×D4C2×#41112yes—
979C22×C4—26no—
980C22×C4—26no—
981C22×C4—26no—
982C22×C4—26no—
983C22×C4—22no—
984C22×C4—22no—
985C22×C4—26no—
986C22×C4—22no—
987C22×C4—22no—
988C22×C4—22no—
989C22×C4—26no—
990C22×C4—212no—
991C22×C4—26no—
992C22×C4—26no—
993C22×C4—26no—
994C22×C4—22no—
995C22×C4—26no—
996C22×C4—26no—
997C22×C4—26no—
998C22×C4—26no—
999C22×C4—26no—
1000C22×C4—26no—
1001C22×C4—26no—
1002C22×C4—22no—
1003C22×C4—26no—
1004C22×C4—41no—
1005C22×C4—41no—
1006C22×C4—43no—
1007C22×C4—43no—
1008C22×C4—448no—
1009C22×C4—43no—
1010C22×C4—43no—
1011C22×C4—43no—
1012C22×C4—43no—
1013C22×C4—46no—
1014C22×C4—43no—
1015C22×C4—43no—
1016C22×C4—46no—
1017C22×C4—43no—
1018C22×C4—43no—
1019C22×C4—43no—
1020C22×C4—46no—
1021C22×C4—46no—
1022C22×C4—46no—
1023C22×C4C2×#41112yes—
1024C22×C4C2×#41112yes—
1025C22×C4C2511yescharacteristic
1026C22×C4C2513yes—
1027C22×C4C2511yescharacteristic
1028C22×C4C2511yescharacteristic
1029C22×C4C2511yescharacteristic
1030C22×C4C2513yes—
1031C22×C4C2511yescharacteristic
1032C22×C4C2513yes—
1033C22×C4C2513yes—
1034C22×C4C2511yescharacteristic
1035C22×C4C2513yes—
1036C22×C4C2511yescharacteristic
1037C22×C4C2513yes—
1038C22×C4C2511yescharacteristic
1039C22×C4C2511yescharacteristic
1040C22×C4C2511yescharacteristic
1041C22×C4C2513yes—
1042C22×C4C2513yes—
1043C22×C4C2513yes—
1044C22×C4C2511yescharacteristic
1045C22×C4C2511yescharacteristic
1046C22×C4C2513yes—
1047C22×C4C2513yes—
1048C22×C4C2513yes—
1049C22×C4C2511yescharacteristic
1050C22×C4C2511yescharacteristic
1051C22×C4C2513yes—
1052C4⋊C4—26no—
1053C4⋊C4—26no—
1054C4⋊C4—26no—
1055C4⋊C4—212no—
1056C4⋊C4—26no—
1057C4⋊C4—26no—
1058C4⋊C4—22no—
1059C4⋊C4—22no—
1060C4⋊C4—26no—
1061C4⋊C4—26no—
1062C4⋊C4—26no—
1063C4⋊C4—26no—
1064C4⋊C4—26no—
1065C4⋊C4—26no—
1066C4⋊C4—26no—
1067C4⋊C4—26no—
1068C4⋊C4—26no—
1069C4⋊C4—22no—
1070C4⋊C4—43no—
1071C4⋊C4—46no—
1072C4⋊C4—41no—
1073C4⋊C4—43no—
1074C4⋊C4—46no—
1075C4⋊C4—43no—
1076C4⋊C4—43no—
1077C4⋊C4—41no—
1078C4⋊C4—41no—
1079C4⋊C4—43no—
1080C4⋊C4—43no—
1081C4⋊C4—43no—
1082C4⋊C4—43no—
1083C4⋊C4—43no—
1084C4⋊C4—43no—
1085C4⋊C4—43no—
1086C4⋊C4—43no—
1087C4⋊C4—43no—
1088C4⋊C4—43no—
1089C4⋊C4—43no—
1090C4⋊C4—46no—
1091C4⋊C4—43no—
1092C4⋊C4—43no—
1093C22⋊C4—26no—
1094C22⋊C4—26no—
1095C22⋊C4—22no—
1096C22⋊C4—26no—
1097C22⋊C4—26no—
1098C22⋊C4—26no—
1099C22⋊C4—22no—
1100C22⋊C4—22no—
1101C22⋊C4—26no—
1102C22⋊C4—22no—
1103C22⋊C4—26no—
1104C22⋊C4—26no—
1105C22⋊C4—212no—
1106C22⋊C4—26no—
1107C22⋊C4—26no—
1108C22⋊C4—43no—
1109C22⋊C4—46no—
1110C22⋊C4—43no—
1111C22⋊C4—43no—
1112C22⋊C4—46no—
1113C22⋊C4—43no—
1114C22⋊C4—43no—
1115C22⋊C4—43no—
1116C22⋊C4—46no—
1117C22⋊C4—46no—
1118C22⋊C4—46no—
1119C22⋊C4—46no—
1120C22⋊C4—43no—
1121C22⋊C4—43no—
1122C22⋊C4—46no—
1123C22⋊C4—43no—
1124C22⋊C4—43no—
1125C22⋊C4—46no—
1126C22⋊C4—43no—
1127C22⋊C4—43no—
1128C22⋊C4—43no—
1129C22⋊C4—46no—
1130C22⋊C4—46no—
1131C22⋊C4—43no—
1132C22⋊C4—43no—
1133C22⋊C4—43no—
1134C22⋊C4—43no—
1135C22⋊C4—43no—
1136C22⋊C4—43no—
1137C22⋊C4—46no—
1138C22⋊C4—43no—
1139C22⋊C4—46no—
1140C22⋊C4—43no—
1141C22⋊C4—43no—
1142C22⋊C4—43no—
1143C22⋊C4—43no—
1144C42—26no—
1145C42—26no—
1146C42—26no—
1147C42—26no—
1148C42—26no—
1149C42—26no—
1150C42—26no—
1151C42—26no—
1152C42—26no—
1153C42—26no—
1154C42—26no—
1155C42—26no—
1156C42—26no—
1157C42—22no—
1158C42—41no—
1159C42—43no—
1160C42—43no—
1161C42—43no—
1162C42—43no—
1163C42—46no—
1164C42—43no—
1165C42—43no—
1166C42—46no—
1167C23—21no—
1168C23—21no—
1169C23—21no—
1170C23—21no—
1171C23—23no—
1172C23—23no—
1173C23—23no—
1174C23—23no—
1175C23—23no—
1176C23—23no—
1177C23—23no—
1178C23—23no—
1179C23—23no—
1180C23—23no—
1181C23—23no—
1182C23—23no—
1183C23—23no—
1184C23—23no—
1185C23—23no—
1186C23—23no—
1187C23—23no—
1188C23—23no—
1189C23—23no—
1190C23—23no—
1191C23—412no—
1192C23—412no—
1193C23—412no—
1194C23—412no—
1195C23—86no—
1196C23—86no—
1197C23—86no—
1198C23C22×#4116yes—
1199C23C22×#4112yes—
1200C23#58512yes—
1201C23#58512yes—
1202C23C2611yescharacteristic
1203Q8—224no—
1204Q8—86no—
1205Q8#551116yes—
1206D4—224no—
1207D4—424no—
1208D4—412no—
1209D4—412no—
1210D4—412no—
1211D4—86no—
1212D4—812no—
1213D4—86no—
1214D4—166no—
1215C2×C4—21no—
1216C2×C4—23no—
1217C2×C4—21no—
1218C2×C4—23no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—224no—
1222C2×C4—224no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—23no—
1230C2×C4—23no—
1231C2×C4—23no—
1232C2×C4—23no—
1233C2×C4—23no—
1234C2×C4—23no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—23no—
1244C2×C4—23no—
1245C2×C4—23no—
1246C2×C4—23no—
1247C2×C4—23no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—23no—
1254C2×C4—23no—
1255C2×C4—23no—
1256C2×C4—23no—
1257C2×C4—23no—
1258C2×C4—23no—
1259C2×C4—23no—
1260C2×C4—23no—
1261C2×C4—23no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—23no—
1265C2×C4—23no—
1266C2×C4—23no—
1267C2×C4—23no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—23no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—23no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—23no—
1283C2×C4—23no—
1284C2×C4—23no—
1285C2×C4—23no—
1286C2×C4—23no—
1287C2×C4—23no—
1288C2×C4—21no—
1289C2×C4—23no—
1290C2×C4—21no—
1291C2×C4—21no—
1292C2×C4—412no—
1293C2×C4—44no—
1294C2×C4—44no—
1295C2×C4—412no—
1296C2×C4—44no—
1297C2×C4—412no—
1298C2×C4—412no—
1299C2×C4—86no—
1300C2×C4—86no—
1301C2×C4—812no—
1302C2×C4—86no—
1303C2×C4—86no—
1304C2×C4—166no—
1305C2×C4C22×#4116yes—
1306C2×C4C22×#4112yes—
1307C2×C4C22×#4116yes—
1308C2×C4C22×#4116yes—
1309C2×C4C2×H(5,𝔽2)16yes—
1310C2×C4#58512yes—
1311C22—22no—
1312C22—22no—
1313C22—22no—
1314C22—22no—
1315C22—22no—
1316C22—22no—
1317C22—26no—
1318C22—26no—
1319C22—26no—
1320C22—43no—
1321C22—43no—
1322C22—43no—
1323C22—43no—
1324C22—43no—
1325C22—43no—
1326C22—43no—
1327C22—43no—
1328C22—43no—
1329C22—43no—
1330C22—43no—
1331C22—43no—
1332C22—43no—
1333C22—43no—
1334C22—43no—
1335C22—43no—
1336C22—43no—
1337C22—43no—
1338C22—824no—
1339C22#352414yes—
1340C22C23×#4111yescharacteristic
1341C22C23×#4111yescharacteristic
1342C22C22×H(5,𝔽2)11yescharacteristic
1343C22C2×#58511yescharacteristic
1344C22C2×#58511yescharacteristic
1345C22C2×#58511yescharacteristic
1346C22H(7,𝔽2)11yescharacteristic
1347C4—22no—
1348C4—22no—
1349C4—26no—
1350C4—41no—
1351C4—43no—
1352C4—43no—
1353C4—43no—
1354C4—43no—
1355C4—41no—
1356C4—41no—
1357C4—43no—
1358C4—43no—
1359C4—41no—
1360C4—41no—
1361C4—41no—
1362C4—43no—
1363C4—41no—
1364C4—41no—
1365C4—43no—
1366C4—43no—
1367C4—41no—
1368C4—43no—
1369C4—43no—
1370C4—41no—
1371C4—41no—
1372C4—41no—
1373C4C2×#551112yes—
1374C2—24no—
1375C2—46no—
1376C2—83no—
1377C2—83no—
1378C2C22×#55111yescharacteristic
1379C2C2×#352411yescharacteristic
1380C2#6281011yescharacteristic
1381C2#6289911yescharacteristic
1382C2#6300611yescharacteristic
1383C2#6300811yescharacteristic
1384C2#6302011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36429C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59637C2semidirect
2. #59487C2semidirect
3. #59374C2semidirect
4. #59224C2semidirect
5. #59197C2semidirect
6. #45401C2semidirect
7. #45260C2semidirect
8. #45053C2semidirect
9. #44960C2semidirect
10. #39069C2semidirect
11. #39045C2semidirect
12. #38056C2semidirect
13. #37852C2semidirect
14. #36585C2semidirect
15. #36578C2semidirect
16. #36435C2semidirect
17. #36433C2semidirect
19. #36291C2semidirect
20. #36168C2semidirect
21. #36076C2semidirect
22. #36059C2semidirect
23. #36049C2semidirect
24. #36040C2semidirect
25. #34849C2semidirect
26. #34295C2semidirect
27. #34263C2semidirect
28. #34192C2semidirect
29. #34175C2semidirect
30. C4×#548C2semidirect
31. C2×#2341C2semidirect
33. C2×#557C22semidirect
39. C2×C4×#41C22semidirect
42. #2860C22semidirect
44. #2854C22semidirect
47. #2797C22semidirect
48. #2756C22semidirect
49. #2756C22semidirect
50. #2753C22semidirect
51. #2752C22semidirect
52. #2749C22semidirect
53. #2747C22semidirect
54. #2746C22semidirect
55. #2741C22semidirect
56. #2741C22semidirect
57. #2737C22semidirect
58. #2737C22semidirect
59. #2717C22semidirect
60. #2706C22semidirect
61. #2644C22semidirect
62. #2641C22semidirect
63. #2628C22semidirect
64. #2624C22semidirect
65. #2610C22semidirect
66. #2602C22semidirect
67. #2595C22semidirect
68. #2581C22semidirect
69. #2580C22semidirect
70. #2578C22semidirect
71. #2578C22semidirect
72. #2577C22semidirect
73. #2576C22semidirect
74. #2575C22semidirect
75. #2574C22semidirect
76. #2573C22semidirect
77. #2572C22semidirect
79. #2565C22semidirect
81. #2563C22semidirect
82. #2562C22semidirect
84. #2557C22semidirect
85. #2553C22semidirect
86. #2548C22semidirect
88. #2531C22semidirect
89. #2531C22semidirect
90. #2516C22semidirect
91. #2513C22semidirect
92. #2513C22semidirect
93. #2513C22semidirect
94. #2513C22semidirect
95. #2513C22semidirect
96. #2513C22semidirect
98. #2510C22semidirect
100. #2504C22semidirect
101. #2500C22semidirect
102. #2498C22semidirect
103. #2495C22semidirect
104. #2495C22semidirect
105. #2495C22semidirect
106. #2494C22semidirect
107. #2494C22semidirect
108. #2494C22semidirect
110. #2493C22semidirect
111. #2491C22semidirect
112. #2491C22semidirect
113. #2490C22semidirect
114. #2490C22semidirect
116. #2486C22semidirect
117. #2485C22semidirect
120. #2471C22semidirect
121. #2467C22semidirect
122. #2454C22semidirect
123. #2454C22semidirect
124. #2453C22semidirect
125. #2451C22semidirect
126. #2448C22semidirect
127. #2448C22semidirect
128. #2445C22semidirect
129. #2445C22semidirect
130. #2445C22semidirect
131. #2445C22semidirect
133. #2442C22semidirect
134. #2442C22semidirect
139. #2422C22semidirect
140. #2421C22semidirect
141. #2421C22semidirect
142. #2420C22semidirect
143. #2420C22semidirect
144. #2420C22semidirect
153. #2401C22semidirect
154. #2398C22semidirect
155. #2396C22semidirect
156. #2395C22semidirect
157. #2367C22semidirect
158. #2366C22semidirect
159. #2363C22semidirect
160. #2362C22semidirect
162. #2361C22semidirect
164. #2357C22semidirect
165. #2356C22semidirect
166. #2356C22semidirect
167. #2354C22semidirect
168. #2353C22semidirect
170. #2352C22semidirect
171. #2351C22semidirect
172. #2351C22semidirect
173. #2351C22semidirect
174. #2351C22semidirect
175. #2351C22semidirect
176. #2351C22semidirect
177. #2351C22semidirect
178. Q8×C4⋊C4C22semidirect
181. #2345C22semidirect
182. #2344C22semidirect
196. #2341C22semidirect
197. #2341C22semidirect
198. #2341C22semidirect
206. #2328C22semidirect
207. #2324C22semidirect
208. #2320C22semidirect
209. #2320C22semidirect
210. #2319C22semidirect
211. #2314C22semidirect
214. C4×#126C22semidirect
215. C4×#124C22semidirect
217. C4×C22⋊Q8C22semidirect
219. C4×#123C22semidirect
221. C4×#121C22semidirect
223. #2298C22semidirect
224. #2293C22semidirect
227. #2290C22semidirect
233. #2276C22semidirect
234. #2276C22semidirect
235. C42×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#596372
#594872
#593742
#592242
#591972
#454012
#452602
#450532
#449602
#390692
#390452
#380562
#378522
#365852
#365782
#364352
#364332
#364292
#362912
#361682
#360762
#360592
#360492
#360402
#348492
#342952
#342632
#341922
#341752
C4×#5482
C2×#23412