Finite Group Databasebeta

← #7693152

Subgroups — #7693152

Order 512.

5685 conjugacy classes of subgroups.

The subgroup lattice has 1384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59754C213yesmaximal, complemented
2#59478C213yesmaximal, complemented
3#59377C213yesmaximal, complemented
4#59276C213yesmaximal, complemented
5#59200C213yesmaximal, complemented
6#45401C213yesmaximal, complemented
7#45026C213yesmaximal, complemented
8#44959C213yesmaximal, complemented
9#44901C213yesmaximal, complemented
10#39066C213yesmaximal, complemented
11#39042C213yesmaximal, complemented
12#38061C213yesmaximal, complemented
13#37858C213yesmaximal, complemented
14#36458C211yesmaximal, characteristic, complemented
15#36433C211yesmaximal, characteristic, complemented
16#36433C211yesmaximal, characteristic, complemented
17#36431C211yesmaximal, characteristic, complemented
18#36429C211yesmaximal, characteristic
19#36401C213yesmaximal, complemented
20#36208C213yesmaximal, complemented
21#36049C211yesmaximal, characteristic, complemented
22#35898C211yesmaximal, characteristic, complemented
23#35845C211yesmaximal, characteristic, complemented
24#35801C211yesmaximal, characteristic, complemented
25#34849C213yesmaximal, complemented
26#34293C211yesmaximal, characteristic, complemented
27#34262C211yesmaximal, characteristic, complemented
28#34193C211yesmaximal, characteristic, complemented
29#34174C211yesmaximal, characteristic, complemented
30C4×#550C211yesmaximal, characteristic, complemented
31C22⋊C4×#41C211yesmaximal, characteristic, complemented
32C23×#41C2211yescharacteristic
33C2×#557C2211yescharacteristic, complemented
34C2×#550C2211yescharacteristic
35C2×#550C2211yescharacteristic
36C2×#548C2211yescharacteristic
37C2×#519C2211yescharacteristic
38C2×#519C2211yescharacteristic
39C2×C4×#41C2211yescharacteristic
40C2×C4×#41C2211yescharacteristic
41C2×C4×#41C2211yescharacteristic, complemented
42#2860C2213yescomplemented
43#2854C2213yescomplemented
44#2854C2213yescomplemented
45#2851C2213yescomplemented
46#2847C2213yes—
47#2797C2216yescomplemented
48#2753C2216yescomplemented
49#2752C2216yescomplemented
50#2749C2216yescomplemented
51#2743C2216yescomplemented
52#2737C2216yescomplemented
53#2737C2216yescomplemented
54#2735C2216yes—
55#2706C2216yescomplemented
56#2705C2216yescomplemented
57#2705C2216yescomplemented
58#2685C2216yes—
59#2685C2216yes—
60#2684C2216yes—
61#2644C2213yescomplemented
62#2641C2213yescomplemented
63#2628C2213yes—
64#2624C2213yes—
65#2610C2216yescomplemented
66#2603C2216yescomplemented
67#2602C2216yescomplemented
68#2601C2216yescomplemented
69#2597C2216yescomplemented
70#2595C2216yescomplemented
71#2581C2213yescomplemented
72#2580C2213yescomplemented
73#2578C2213yescomplemented
74#2578C2216yescomplemented
75#2577C2213yescomplemented
76#2576C2213yes—
77#2575C2211yescharacteristic
78#2575C2216yescomplemented
79#2574C2213yescomplemented
80#2573C2213yes—
81#2572C2213yes—
82#2569C2213yescomplemented
83#2567C2213yescomplemented
84#2566C2213yescomplemented
85#2564C2213yescomplemented
86#2562C2213yescomplemented
87#2561C2213yes—
88#2553C2213yescomplemented
89#2548C2213yescomplemented
90#2534C2213yes—
91#2526C2216yescomplemented
92#2521C2216yescomplemented
93#2518C2216yescomplemented
94#2518C2216yescomplemented
95#2516C2216yes—
96#2513C2213yescomplemented
97#2513C2213yescomplemented
98#2512C2213yescomplemented
99#2512C2213yescomplemented
100#2512C2213yescomplemented
101#2512C2213yescomplemented
102#2510C2216yescomplemented
103#2500C2213yes—
104#2500C2213yescomplemented
105#2500C2213yescomplemented
106#2497C2213yescomplemented
107#2497C2213yescomplemented
108#2496C2213yescomplemented
109#2496C2213yescomplemented
110#2495C2213yescomplemented
111#2494C2213yescomplemented
112#2493C2213yescomplemented
113#2491C2213yescomplemented
114#2491C2213yescomplemented
115#2490C2213yescomplemented
116#2490C2213yescomplemented
117#2485C2213yes—
118#2485C2213yescomplemented
119#2485C2213yescomplemented
120#2480C2213yes—
121#2467C2216yescomplemented
122#2461C2216yescomplemented
123#2454C2213yescomplemented
124#2453C2213yescomplemented
125#2453C2213yescomplemented
126#2452C2213yescomplemented
127#2448C2213yescomplemented
128#2448C2213yescomplemented
129#2445C2213yescomplemented
130#2445C2213yescomplemented
131#2445C2213yescomplemented
132#2445C2213yescomplemented
133#2441C2213yes—
134#2441C2213yes—
135#2441C2213yescomplemented
136#2439C2213yescomplemented
137#2433C2213yes—
138#2431C2213yes—
139#2431C2213yes—
140#2423C2213yescomplemented
141#2422C2213yescomplemented
142#2422C2213yescomplemented
143#2421C2213yescomplemented
144#2420C2213yescomplemented
145#2420C2213yescomplemented
146#2419C2213yescomplemented
147#2418C2213yes—
148#2418C2216yes—
149#2411C2216yes—
150#2408C2213yes—
151#2407C2213yes—
152#2407C2213yes—
153#2401C2213yescomplemented
154#2398C2213yescomplemented
155#2396C2213yes—
156#2395C2213yes—
157#2374C2216yescomplemented
158#2373C2216yescomplemented
159#2367C2213yescomplemented
160#2366C2213yescomplemented
161#2363C2213yes—
162#2363C2213yescomplemented
163#2363C2213yescomplemented
164#2362C2213yescomplemented
165#2359C2216yescomplemented
166#2356C2213yescomplemented
167#2355C2213yescomplemented
168#2354C2213yes—
169#2354C2213yescomplemented
170#2354C2213yescomplemented
171#2354C2213yescomplemented
172#2351C2211yescharacteristic, complemented
173#2351C2211yescharacteristic, complemented
174#2351C2211yescharacteristic, complemented
175Q8×C4⋊C4C2211yescharacteristic, complemented
176Q8×C4⋊C4C2211yescharacteristic, complemented
177Q8×C4⋊C4C2211yescharacteristic, complemented
178Q8×C4⋊C4C2211yescharacteristic, complemented
179Q8×C4⋊C4C2211yescharacteristic, complemented
180#2347C2213yes—
181#2347C2213yescomplemented
182#2347C2213yescomplemented
183#2346C2213yes—
184#2341C2213yes—
185#2341C2211yescharacteristic
186#2341C2211yescharacteristic
187#2341C2211yescharacteristic
188#2341C2211yescharacteristic
189#2341C2211yescharacteristic
190#2341C2211yescharacteristic
191#2341C2213yes—
192#2341C2211yescharacteristic
193#2341C2213yes—
194#2341C2211yescharacteristic
195#2341C2213yes—
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#2326C2213yescomplemented
207#2324C2213yes—
208#2320C2213yescomplemented
209#2319C2213yescomplemented
210#2319C2213yescomplemented
211#2314C2213yes—
212#2309C2213yes—
213#2309C2213yes—
214C4×#127C2213yescomplemented
215C4×#126C2213yescomplemented
216C4×C22⋊Q8C2213yescomplemented
217C4×C22⋊Q8C2213yescomplemented
218C4×#123C2213yescomplemented
219C4×#123C2213yescomplemented
220C4×#121C2213yescomplemented
221C4×#121C2213yescomplemented
222C4×#120C2213yes—
223#2298C2213yes—
224#2297C2213yes—
225#2297C2213yes—
226#2295C2213yescomplemented
227#2290C2213yes—
228#2285C2213yescomplemented
229#2283C2213yescomplemented
230#2280C2213yes—
231#2280C2213yes—
232#2280C2213yes—
233#2276C2211yescharacteristic, complemented
234#2276C2211yescharacteristic, complemented
235C42×Q8C2211yescharacteristic, complemented
236C42×D4C2213yescomplemented
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×#126C2316yes—
258C2×#126C2316yes—
259C2×#125C2313yes—
260C2×#125C2313yes—
261C2×#124C2313yes—
262C2×#124C2316yes—
263C2×#123C2316yes—
264C2×#123C2316yes—
265C2×#123C2313yes—
266C2×#123C2313yes—
267C2×C22⋊Q8C2313yes—
268C2×C22⋊Q8C2313yes—
269C2×#121C2313yes—
270C2×#121C2313yes—
271C2×#121C2313yes—
272C2×#121C2313yes—
273C2×#121C2313yes—
274C2×#120C2313yes—
275C2×#120C2316yes—
276#519—28no—
277#519—44no—
278C4×#41—28no—
279C4×#41—44no—
280C4×#41—44no—
281C2×C4×Q8C2313yes—
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×Q8C2311yescharacteristic
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2313yes—
294C2×C4×Q8C2313yes—
295C2×C4×Q8C2313yes—
296C2×C4×Q8C2313yes—
297C2×C4×D4C2313yes—
298C2×C4×D4C2313yes—
299C2×C4×D4C2313yes—
300C2×C4×D4C2313yes—
301C2×C4×D4C2313yes—
302C2×C4×D4C2313yes—
303C2×C4×D4C2313yes—
304C2×C4×D4C2313yes—
305C2×C4×D4C2313yes—
306C2×C4×D4C2313yes—
307C2×C4×D4C2313yes—
308C2×C4×D4C2316yes—
309C2×#117C2313yes—
310C2×#117C2313yes—
311C2×#117C2313yes—
312C2×#117C2313yes—
313C2×#117C2313yes—
314C2×#117C2313yes—
315C2×#117C2313yes—
316C2×#117C2316yes—
317C22×C22⋊C4C2313yes—
318C22×C22⋊C4C2313yes—
319C22×C42C2313yes—
320C22×C42C2313yes—
321C22×C42C2313yes—
322#401C2313yes—
323#400C2313yes—
324#400C2313yes—
325#400C2313yes—
326#400C2311yescharacteristic
327#400C2311yescharacteristic
328#400C2316yes—
329#400C2313yes—
330#400C2313yes—
331#400C2316yes—
332#399C2313yes—
333#399C2311yescharacteristic
334#399C2316yes—
335#399C2316yes—
336#399C2316yes—
337#398C2313yes—
338#398C2313yes—
339#398C2313yes—
340#397C2313yes—
341#397C2313yes—
342#397C2311yescharacteristic
343#397C2316yes—
344#397C2313yes—
345#397C2313yes—
346#397C2313yes—
347#397C2316yes—
348#397C2316yes—
349#397C2313yes—
350#397C2313yes—
351#397C2316yes—
352#397C2316yes—
353#397C2316yes—
354#397C2316yes—
355#396C2316yes—
356#396C2316yes—
357#396C2313yes—
358#396C2313yes—
359#396C2313yes—
360#396C2316yes—
361#396C2316yes—
362#395C2313yes—
363#395C2316yes—
364#394C2316yes—
365#394C2313yes—
366#394C2313yes—
367#394C2316yes—
368#394C2313yes—
369#394C2316yes—
370#394C2316yes—
371#394C2316yes—
372#394C2316yes—
373#394C2313yes—
374#394C2316yes—
375#394C2316yes—
376#394C2316yes—
377#394C2316yes—
378#394C2316yes—
379#393C2313yes—
380#393C2313yes—
381#393C2313yes—
382#393C2316yes—
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#390C2316yes—
396#390C2316yes—
397#390C2313yes—
398#390C2313yes—
399#390C2313yes—
400#390C2316yes—
401#390C2316yes—
402#390C2313yes—
403#390C2316yes—
404#390C2313yes—
405#390C2316yes—
406#390C2313yes—
407#390C2313yes—
408#390C2313yes—
409#390C2313yes—
410#390C2313yes—
411#390C2316yes—
412#390C2313yes—
413#390C2313yes—
414#390C2313yes—
415#390C2313yes—
416#390C2313yes—
417#390C2313yes—
418#390C2313yes—
419#390C2313yes—
420#390C2313yes—
421#390C2313yes—
422#390C2316yes—
423#389C2316yes—
424#389C2316yes—
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#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#388C2313yes—
443#388C2313yes—
444#388C2313yes—
445#388C2311yescharacteristic
446#388C2313yes—
447#388C2313yes—
448#388C2316yes—
449#388C2316yes—
450#388C2313yes—
451#388C2316yes—
452#388C2313yes—
453#388C2313yes—
454#388C2313yes—
455#388C2313yes—
456#388C2316yes—
457#388C2316yes—
458#388C2316yes—
459#388C2316yes—
460#388C2311yescharacteristic
461#388C2316yes—
462#388C2313yes—
463#388C2316yes—
464#388C2316yes—
465#388C2316yes—
466#388C2316yes—
467#388C2316yes—
468#388C2316yes—
469#388C2316yes—
470#388C2316yes—
471#388C2316yes—
472#388C2316yes—
473#388C2316yes—
474#388C2316yes—
475#388C2316yes—
476#387C2311yescharacteristic
477#387C2313yes—
478#387C2313yes—
479#387C2313yes—
480#387C2311yescharacteristic
481#387C2313yes—
482#387C2313yes—
483#387C2316yes—
484#387C2316yes—
485#387C2313yes—
486#387C2313yes—
487#387C2311yescharacteristic
488#387C2313yes—
489#387C2313yes—
490#387C2311yescharacteristic
491#387C2316yes—
492#387C2316yes—
493#387C2316yes—
494#387C2313yes—
495#387C2313yes—
496#387C2316yes—
497#387C2316yes—
498#386C2313yes—
499#386C2313yes—
500#386C2313yes—
501#386C2313yes—
502#386C2313yes—
503#386C2316yes—
504#386C2316yes—
505#386C2313yes—
506#386C2313yes—
507#386C2316yes—
508#386C2316yes—
509#386C2316yes—
510#386C2316yes—
511#386C2316yes—
512#386C2316yes—
513#386C2316yes—
514#386C2316yes—
515#385C2313yes—
516#385C2313yes—
517#385C2313yes—
518#385C2316yes—
519#385C2313yes—
520#385C2313yes—
521#385C2311yescharacteristic
522#385C2313yes—
523#385C2316yes—
524#385C2313yes—
525#385C2313yes—
526#385C2316yes—
527#384C2313yes—
528#384C2313yes—
529#384C2313yes—
530#384C2313yes—
531#384C2313yes—
532#383C2313yes—
533#383C2313yes—
534#383C2313yes—
535#383C2316yes—
536#382C2313yes—
537#382C2313yes—
538#382C2311yescharacteristic
539#382C2316yes—
540#382C2313yes—
541#382C2313yes—
542#381C2313yes—
543#381C2313yes—
544#381C2311yescharacteristic
545#381C2313yes—
546#381C2313yes—
547#381C2313yes—
548#381C2316yes—
549#380C2313yes—
550#380C2313yes—
551#380C2313yes—
552#380C2313yes—
553#380C2313yes—
554#380C2313yes—
555#380C2313yes—
556#380C2313yes—
557#380C2313yes—
558#380C2313yes—
559#380C2313yes—
560#380C2313yes—
561#380C2316yes—
562#380C2313yes—
563#380C2313yes—
564#380C2313yes—
565#380C2313yes—
566#380C2313yes—
567#380C2313yes—
568#380C2313yes—
569#380C2313yes—
570#380C2313yes—
571#379C2313yes—
572#379C2313yes—
573#379C2316yes—
574#379C2313yes—
575#379C2316yes—
576C4×C4⋊C4C2313yes—
577C4×C4⋊C4C2313yes—
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⋊C4C2311yescharacteristic
587C4×C4⋊C4C2316yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2316yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2316yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C22⋊C4C2313yes—
599C4×C22⋊C4C2313yes—
600C4×C22⋊C4C2313yes—
601C4×C22⋊C4C2313yes—
602C4×C22⋊C4C2313yes—
603C4×C22⋊C4C2313yes—
604C4×C22⋊C4C2313yes—
605C4×C22⋊C4C2311yescharacteristic
606C4×C22⋊C4C2316yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2316yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2316yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623C4×C22⋊C4C2316yes—
624#376C2313yes—
625#376C2313yes—
626#376C2316yes—
627C2×#95C2313yes—
628C2×#95C2313yes—
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×D4C2413yes—
662C22×D4C2416yes—
663C22×D4C2413yes—
664C22×D4C2416yes—
665C23×C4—212no—
666C23×C4—212no—
667C23×C4—46no—
668C23×C4C2413yes—
669C23×C4C2413yes—
670C23×C4C2413yes—
671C23×C4C2411yescharacteristic
672C23×C4C2413yes—
673C23×C4C2413yes—
674C23×C4C2413yes—
675C23×C4C2413yes—
676C23×C4C2413yes—
677C23×C4C2413yes—
678C23×C4C2413yes—
679C23×C4C2413yes—
680C23×C4C2413yes—
681C4⋊Q8—46no—
682#127—212no—
683#127—46no—
684#126—412no—
685#126—46no—
686#126—86no—
687#125—46no—
688#125—46no—
689#124—212no—
690#124—86no—
691#123—46no—
692#123—412no—
693#123—412no—
694#123—46no—
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—86no—
704C4×Q8—24no—
705C4×Q8—24no—
706C4×Q8—212no—
707C4×Q8—212no—
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—46no—
730C4×D4—46no—
731C4×D4—86no—
732#117—212no—
733#117—212no—
734#117—212no—
735#117—46no—
736#117—46no—
737#117—46no—
738#117—46no—
739#117—86no—
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⋊C4C2413yes—
750C2×C4⋊C4C2411yescharacteristic
751C2×C4⋊C4C2411yescharacteristic
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2411yescharacteristic
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2411yescharacteristic
759C2×C4⋊C4C2411yescharacteristic
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2411yescharacteristic
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2416yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2411yescharacteristic
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2416yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2416yes—
777C2×C4⋊C4C2416yes—
778C2×C4⋊C4C2413yes—
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2416yes—
781C2×C4⋊C4C2413yes—
782C2×C4⋊C4C2416yes—
783C2×C22⋊C4—46no—
784C2×C22⋊C4—46no—
785C2×C22⋊C4C2411yescharacteristic
786C2×C22⋊C4C2411yescharacteristic
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2411yescharacteristic
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2416yes—
792C2×C22⋊C4C2411yescharacteristic
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2411yescharacteristic
797C2×C22⋊C4C2413yes—
798C2×C22⋊C4C2416yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2411yescharacteristic
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2416yes—
807C2×C22⋊C4C2416yes—
808C2×C22⋊C4C2416yes—
809C2×C22⋊C4C2416yes—
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2416yes—
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2413yes—
818C2×C22⋊C4C2416yes—
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2413yes—
821C2×C22⋊C4C2413yes—
822C2×C22⋊C4C2413yes—
823C2×C22⋊C4C2416yes—
824C2×C22⋊C4C2413yes—
825C2×C22⋊C4C2416yes—
826C2×C22⋊C4C2416yes—
827C2×C22⋊C4C2413yes—
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2416yes—
830C2×C22⋊C4C2413yes—
831C2×C22⋊C4C2413yes—
832C2×C22⋊C4C2416yes—
833C2×C22⋊C4C2413yes—
834C2×C22⋊C4C2416yes—
835C2×C22⋊C4C2413yes—
836C2×C22⋊C4C2416yes—
837C2×C22⋊C4C2413yes—
838C2×C42—212no—
839C2×C42—46no—
840C2×C42—46no—
841C2×C42C2413yes—
842C2×C42C2413yes—
843C2×C42C2413yes—
844C2×C42C2413yes—
845C2×C42C2416yes—
846C2×C42C2413yes—
847C2×C42C2411yescharacteristic
848C2×C42C2413yes—
849C2×C42C2413yes—
850C2×C42C2413yes—
851C2×C42C2413yes—
852C2×C42C2413yes—
853C2×C42C2413yes—
854C2×C42C2413yes—
855C2×C42C2413yes—
856C2×C42C2411yescharacteristic
857C2×C42C2413yes—
858C2×C42C2413yes—
859C2×C42C2416yes—
860C2×C42C2416yes—
861C2×C42C2416yes—
862C2×C42C2413yes—
863C2×C42C2413yes—
864C2×C42C2411yescharacteristic
865C2×C42C2411yescharacteristic
866#95C2411yescharacteristic
867#95C2411yescharacteristic
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2411yescharacteristic
875#95C2411yescharacteristic
876#95C2413yes—
877#95C2413yes—
878#95C2416yes—
879#95C2413yes—
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2416yes—
886#95C2411yescharacteristic
887#95C2411yescharacteristic
888#95C2413yes—
889#95C2411yescharacteristic
890#95C2411yescharacteristic
891#95C2413yes—
892#95C2413yes—
893#95C2411yescharacteristic
894#95C2413yes—
895#95C2411yescharacteristic
896#95C2411yescharacteristic
897#95C2411yescharacteristic
898#95C2411yescharacteristic
899#95C2413yes—
900#95C2413yes—
901#95C2413yes—
902#95C2413yes—
903#95C2413yes—
904#95C2413yes—
905#95C2413yes—
906#95C2413yes—
907#95C2416yes—
908#95C2413yes—
909#95C2411yescharacteristic
910#95C2416yes—
911#95C2411yescharacteristic
912#95C2411yescharacteristic
913#95C2416yes—
914#95C2413yes—
915#95C2413yes—
916#95C2413yes—
917#95C2413yes—
918#95C2413yes—
919#95C2413yes—
920#95C2413yes—
921#95C2413yes—
922#95C2413yes—
923#95C2416yes—
924#95C2416yes—
925C24—26no—
926C24—26no—
927C24—43no—
928C24—43no—
929C24—43no—
930C24—43no—
931C24—43no—
932C24C2513yes—
933C24C2513yes—
934C24C2511yescharacteristic
935C24C2513yes—
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—212no—
955C2×D4—26no—
956C2×D4—26no—
957C2×D4—26no—
958C2×D4—212no—
959C2×D4—26no—
960C2×D4—26no—
961C2×D4—26no—
962C2×D4—26no—
963C2×D4—26no—
964C2×D4—26no—
965C2×D4—448no—
966C2×D4—43no—
967C2×D4—46no—
968C2×D4—43no—
969C2×D4—46no—
970C2×D4—43no—
971C2×D4—43no—
972C2×D4—43no—
973C2×D4—46no—
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—26no—
984C22×C4—22no—
985C22×C4—26no—
986C22×C4—26no—
987C22×C4—26no—
988C22×C4—26no—
989C22×C4—22no—
990C22×C4—26no—
991C22×C4—26no—
992C22×C4—26no—
993C22×C4—26no—
994C22×C4—26no—
995C22×C4—26no—
996C22×C4—26no—
997C22×C4—26no—
998C22×C4—26no—
999C22×C4—26no—
1000C22×C4—43no—
1001C22×C4—41no—
1002C22×C4—43no—
1003C22×C4—43no—
1004C22×C4—448no—
1005C22×C4—43no—
1006C22×C4—43no—
1007C22×C4—43no—
1008C22×C4—43no—
1009C22×C4—43no—
1010C22×C4—43no—
1011C22×C4—43no—
1012C22×C4—43no—
1013C22×C4—43no—
1014C22×C4—43no—
1015C22×C4—43no—
1016C22×C4—43no—
1017C22×C4C2×#41112yes—
1018C22×C4C2×#41112yes—
1019C22×C4C2511yescharacteristic
1020C22×C4C2511yescharacteristic
1021C22×C4C2511yescharacteristic
1022C22×C4C2511yescharacteristic
1023C22×C4C2511yescharacteristic
1024C22×C4C2513yes—
1025C22×C4C2511yescharacteristic
1026C22×C4C2513yes—
1027C22×C4C2511yescharacteristic
1028C22×C4C2513yes—
1029C22×C4C2513yes—
1030C22×C4C2511yescharacteristic
1031C22×C4C2513yes—
1032C22×C4C2511yescharacteristic
1033C22×C4C2513yes—
1034C22×C4C2513yes—
1035C22×C4C2513yes—
1036C22×C4C2511yescharacteristic
1037C22×C4C2513yes—
1038C22×C4C2513yes—
1039C22×C4C2513yes—
1040C22×C4C2511yescharacteristic
1041C22×C4C2513yes—
1042C22×C4C2511yescharacteristic
1043C22×C4C2511yescharacteristic
1044C22×C4C2511yescharacteristic
1045C22×C4C2513yes—
1046C4⋊C4—26no—
1047C4⋊C4—26no—
1048C4⋊C4—26no—
1049C4⋊C4—26no—
1050C4⋊C4—26no—
1051C4⋊C4—26no—
1052C4⋊C4—22no—
1053C4⋊C4—26no—
1054C4⋊C4—26no—
1055C4⋊C4—26no—
1056C4⋊C4—26no—
1057C4⋊C4—26no—
1058C4⋊C4—26no—
1059C4⋊C4—26no—
1060C4⋊C4—26no—
1061C4⋊C4—22no—
1062C4⋊C4—22no—
1063C4⋊C4—26no—
1064C4⋊C4—22no—
1065C4⋊C4—22no—
1066C4⋊C4—26no—
1067C4⋊C4—26no—
1068C4⋊C4—22no—
1069C4⋊C4—43no—
1070C4⋊C4—43no—
1071C4⋊C4—43no—
1072C4⋊C4—43no—
1073C4⋊C4—43no—
1074C4⋊C4—41no—
1075C4⋊C4—46no—
1076C4⋊C4—41no—
1077C4⋊C4—43no—
1078C4⋊C4—43no—
1079C4⋊C4—43no—
1080C4⋊C4—43no—
1081C4⋊C4—46no—
1082C4⋊C4—46no—
1083C4⋊C4—46no—
1084C4⋊C4—46no—
1085C4⋊C4—46no—
1086C4⋊C4—43no—
1087C4⋊C4—43no—
1088C4⋊C4—43no—
1089C22⋊C4—26no—
1090C22⋊C4—22no—
1091C22⋊C4—212no—
1092C22⋊C4—22no—
1093C22⋊C4—26no—
1094C22⋊C4—26no—
1095C22⋊C4—26no—
1096C22⋊C4—212no—
1097C22⋊C4—22no—
1098C22⋊C4—22no—
1099C22⋊C4—26no—
1100C22⋊C4—26no—
1101C22⋊C4—22no—
1102C22⋊C4—26no—
1103C22⋊C4—26no—
1104C22⋊C4—43no—
1105C22⋊C4—43no—
1106C22⋊C4—43no—
1107C22⋊C4—43no—
1108C22⋊C4—41no—
1109C22⋊C4—43no—
1110C22⋊C4—46no—
1111C22⋊C4—46no—
1112C22⋊C4—46no—
1113C22⋊C4—46no—
1114C22⋊C4—43no—
1115C22⋊C4—43no—
1116C22⋊C4—43no—
1117C22⋊C4—43no—
1118C22⋊C4—43no—
1119C22⋊C4—43no—
1120C22⋊C4—46no—
1121C22⋊C4—43no—
1122C22⋊C4—43no—
1123C22⋊C4—46no—
1124C22⋊C4—43no—
1125C22⋊C4—43no—
1126C22⋊C4—46no—
1127C22⋊C4—43no—
1128C22⋊C4—46no—
1129C22⋊C4—43no—
1130C22⋊C4—43no—
1131C22⋊C4—46no—
1132C22⋊C4—46no—
1133C22⋊C4—43no—
1134C22⋊C4—43no—
1135C22⋊C4—43no—
1136C22⋊C4—46no—
1137C22⋊C4—46no—
1138C22⋊C4—46no—
1139C22⋊C4—43no—
1140C22⋊C4—43no—
1141C22⋊C4—43no—
1142C42—22no—
1143C42—26no—
1144C42—26no—
1145C42—26no—
1146C42—212no—
1147C42—26no—
1148C42—26no—
1149C42—26no—
1150C42—26no—
1151C42—26no—
1152C42—26no—
1153C42—26no—
1154C42—26no—
1155C42—26no—
1156C42—22no—
1157C42—26no—
1158C42—41no—
1159C42—41no—
1160C42—43no—
1161C42—43no—
1162C42—46no—
1163C42—46no—
1164C42—46no—
1165C42—43no—
1166C42—43no—
1167C23—21no—
1168C23—23no—
1169C23—21no—
1170C23—23no—
1171C23—21no—
1172C23—21no—
1173C23—21no—
1174C23—23no—
1175C23—23no—
1176C23—23no—
1177C23—23no—
1178C23—21no—
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—23no—
1192C23—23no—
1193C23—412no—
1194C23—412no—
1195C23—86no—
1196C23—86no—
1197C23—86no—
1198C23—86no—
1199C23—86no—
1200C23C22×#4112yes—
1201C23C22×#4116yes—
1202C23C2611yescharacteristic
1203Q8—224no—
1204Q8—86no—
1205Q8#551116yes—
1206D4—224no—
1207D4—412no—
1208D4—424no—
1209D4—412no—
1210D4—412no—
1211D4—86no—
1212D4—812no—
1213D4—86no—
1214D4—166no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—23no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—23no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—224no—
1226C2×C4—224no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—23no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—23no—
1233C2×C4—23no—
1234C2×C4—23no—
1235C2×C4—23no—
1236C2×C4—23no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—23no—
1246C2×C4—23no—
1247C2×C4—23no—
1248C2×C4—23no—
1249C2×C4—23no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—23no—
1254C2×C4—23no—
1255C2×C4—21no—
1256C2×C4—23no—
1257C2×C4—23no—
1258C2×C4—23no—
1259C2×C4—23no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—23no—
1264C2×C4—21no—
1265C2×C4—23no—
1266C2×C4—23no—
1267C2×C4—23no—
1268C2×C4—23no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—23no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—23no—
1278C2×C4—23no—
1279C2×C4—23no—
1280C2×C4—21no—
1281C2×C4—23no—
1282C2×C4—23no—
1283C2×C4—23no—
1284C2×C4—23no—
1285C2×C4—23no—
1286C2×C4—23no—
1287C2×C4—21no—
1288C2×C4—23no—
1289C2×C4—21no—
1290C2×C4—412no—
1291C2×C4—412no—
1292C2×C4—44no—
1293C2×C4—412no—
1294C2×C4—412no—
1295C2×C4—412no—
1296C2×C4—86no—
1297C2×C4—86no—
1298C2×C4—86no—
1299C2×C4—86no—
1300C2×C4—86no—
1301C2×C4C22×#4112yes—
1302C2×C4C22×#4116yes—
1303C2×C4C22×#4116yes—
1304C2×C4C22×#4116yes—
1305C2×C4C2×H(5,𝔽2)16yes—
1306C2×C4#58512yes—
1307C2×C4#58512yes—
1308C2×C4#58512yes—
1309C22—22no—
1310C22—26no—
1311C22—22no—
1312C22—26no—
1313C22—22no—
1314C22—26no—
1315C22—43no—
1316C22—41no—
1317C22—43no—
1318C22—41no—
1319C22—43no—
1320C22—41no—
1321C22—43no—
1322C22—41no—
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—824no—
1338C22C23×#4111yescharacteristic
1339C22C23×#4111yescharacteristic
1340C22C22×H(5,𝔽2)11yescharacteristic
1341C22C2×#58511yescharacteristic
1342C22C2×#58511yescharacteristic
1343C22C2×#58511yescharacteristic
1344C22H(7,𝔽2)11yescharacteristic
1345C4—22no—
1346C4—22no—
1347C4—22no—
1348C4—22no—
1349C4—26no—
1350C4—43no—
1351C4—41no—
1352C4—43no—
1353C4—43no—
1354C4—43no—
1355C4—43no—
1356C4—43no—
1357C4—41no—
1358C4—41no—
1359C4—41no—
1360C4—41no—
1361C4—41no—
1362C4—43no—
1363C4—43no—
1364C4—41no—
1365C4—43no—
1366C4—43no—
1367C4—43no—
1368C4—41no—
1369C4—41no—
1370C4—41no—
1371C4C2×#551112yes—
1372C2—46no—
1373C2—42no—
1374C2—83no—
1375C2—83no—
1376C2C22×#55111yescharacteristic
1377C2#6279311yescharacteristic
1378C2#6281611yescharacteristic
1379C2#6289911yescharacteristic
1380C2#6300611yescharacteristic
1381C2#6300811yescharacteristic
1382C2#6302211yescharacteristic
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. #59754C2semidirect
2. #59478C2semidirect
3. #59377C2semidirect
4. #59276C2semidirect
5. #59200C2semidirect
6. #45401C2semidirect
7. #45026C2semidirect
8. #44959C2semidirect
9. #44901C2semidirect
10. #39066C2semidirect
11. #39042C2semidirect
12. #38061C2semidirect
13. #37858C2semidirect
14. #36458C2semidirect
15. #36433C2semidirect
16. #36433C2semidirect
17. #36431C2semidirect
19. #36401C2semidirect
20. #36208C2semidirect
21. #36049C2semidirect
22. #35898C2semidirect
23. #35845C2semidirect
24. #35801C2semidirect
25. #34849C2semidirect
26. #34293C2semidirect
27. #34262C2semidirect
28. #34193C2semidirect
29. #34174C2semidirect
30. C4×#550C2semidirect
31. C22⋊C4×#41C2semidirect
33. C2×#557C22semidirect
41. C2×C4×#41C22semidirect
42. #2860C22semidirect
43. #2854C22semidirect
44. #2854C22semidirect
45. #2851C22semidirect
47. #2797C22semidirect
48. #2753C22semidirect
49. #2752C22semidirect
50. #2749C22semidirect
51. #2743C22semidirect
52. #2737C22semidirect
53. #2737C22semidirect
55. #2706C22semidirect
56. #2705C22semidirect
57. #2705C22semidirect
61. #2644C22semidirect
62. #2641C22semidirect
65. #2610C22semidirect
66. #2603C22semidirect
67. #2602C22semidirect
68. #2601C22semidirect
69. #2597C22semidirect
70. #2595C22semidirect
71. #2581C22semidirect
72. #2580C22semidirect
73. #2578C22semidirect
74. #2578C22semidirect
75. #2577C22semidirect
78. #2575C22semidirect
79. #2574C22semidirect
82. #2569C22semidirect
83. #2567C22semidirect
84. #2566C22semidirect
85. #2564C22semidirect
86. #2562C22semidirect
88. #2553C22semidirect
89. #2548C22semidirect
91. #2526C22semidirect
92. #2521C22semidirect
93. #2518C22semidirect
94. #2518C22semidirect
96. #2513C22semidirect
97. #2513C22semidirect
98. #2512C22semidirect
99. #2512C22semidirect
100. #2512C22semidirect
101. #2512C22semidirect
102. #2510C22semidirect
104. #2500C22semidirect
105. #2500C22semidirect
106. #2497C22semidirect
107. #2497C22semidirect
108. #2496C22semidirect
109. #2496C22semidirect
110. #2495C22semidirect
111. #2494C22semidirect
112. #2493C22semidirect
113. #2491C22semidirect
114. #2491C22semidirect
115. #2490C22semidirect
116. #2490C22semidirect
118. #2485C22semidirect
119. #2485C22semidirect
121. #2467C22semidirect
122. #2461C22semidirect
123. #2454C22semidirect
124. #2453C22semidirect
125. #2453C22semidirect
126. #2452C22semidirect
127. #2448C22semidirect
128. #2448C22semidirect
129. #2445C22semidirect
130. #2445C22semidirect
131. #2445C22semidirect
132. #2445C22semidirect
135. #2441C22semidirect
136. #2439C22semidirect
140. #2423C22semidirect
141. #2422C22semidirect
142. #2422C22semidirect
143. #2421C22semidirect
144. #2420C22semidirect
145. #2420C22semidirect
146. #2419C22semidirect
153. #2401C22semidirect
154. #2398C22semidirect
157. #2374C22semidirect
158. #2373C22semidirect
159. #2367C22semidirect
160. #2366C22semidirect
162. #2363C22semidirect
163. #2363C22semidirect
164. #2362C22semidirect
165. #2359C22semidirect
166. #2356C22semidirect
167. #2355C22semidirect
169. #2354C22semidirect
170. #2354C22semidirect
171. #2354C22semidirect
172. #2351C22semidirect
173. #2351C22semidirect
174. #2351C22semidirect
175. Q8×C4⋊C4C22semidirect
176. Q8×C4⋊C4C22semidirect
177. Q8×C4⋊C4C22semidirect
178. Q8×C4⋊C4C22semidirect
179. Q8×C4⋊C4C22semidirect
181. #2347C22semidirect
182. #2347C22semidirect
196. #2341C22semidirect
197. #2341C22semidirect
198. #2341C22semidirect
206. #2326C22semidirect
208. #2320C22semidirect
209. #2319C22semidirect
210. #2319C22semidirect
214. C4×#127C22semidirect
215. C4×#126C22semidirect
216. C4×C22⋊Q8C22semidirect
217. C4×C22⋊Q8C22semidirect
218. C4×#123C22semidirect
219. C4×#123C22semidirect
220. C4×#121C22semidirect
221. C4×#121C22semidirect
226. #2295C22semidirect
228. #2285C22semidirect
229. #2283C22semidirect
233. #2276C22semidirect
234. #2276C22semidirect
235. C42×Q8C22semidirect
236. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#597542
#594782
#593772
#592762
#592002
#454012
#450262
#449592
#449012
#390662
#390422
#380612
#378582
#364582
#364332
#364312
#364292
#364012
#362082
#360492
#358982
#358452
#358012
#348492
#342932
#342622
#341932
#341742
C4×#5502
C22⋊C4×#412