Finite Group Databasebeta

← #7693167

Subgroups — #7693167

Order 512.

5554 conjugacy classes of subgroups.

The subgroup lattice has 1369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59769C213yesmaximal, complemented
2#59482C213yesmaximal, complemented
3#59380C213yesmaximal, complemented
4#59277C213yesmaximal, complemented
5#59201C213yesmaximal, complemented
6#45365C213yesmaximal, complemented
7#45182C213yesmaximal, complemented
8#45022C213yesmaximal, complemented
9#45019C213yesmaximal, complemented
10#39070C213yesmaximal, complemented
11#39046C213yesmaximal, complemented
12#38063C213yesmaximal, complemented
13#37856C213yesmaximal, complemented
14#36483C211yesmaximal, characteristic, complemented
15#36458C211yesmaximal, characteristic, complemented
16#36432C211yesmaximal, characteristic, complemented
17#36431C211yesmaximal, characteristic, complemented
18#36428C211yesmaximal, characteristic
19#36401C213yesmaximal, complemented
20#36207C213yesmaximal, complemented
21#36059C211yesmaximal, characteristic, complemented
22#35854C211yesmaximal, characteristic, complemented
23#35786C211yesmaximal, characteristic, complemented
24#35723C211yesmaximal, characteristic, complemented
25#34849C213yesmaximal, complemented
26#34291C211yesmaximal, characteristic, complemented
27#34262C211yesmaximal, characteristic, complemented
28#34193C211yesmaximal, characteristic, complemented
29#34174C211yesmaximal, characteristic, complemented
30C4×#548C211yesmaximal, characteristic, complemented
31C22⋊C4×#41C211yesmaximal, characteristic, complemented
32C23×#41C2211yescharacteristic
33C2×#557C2211yescharacteristic, complemented
34C2×D4×Q8C2211yescharacteristic
35C2×#548C2211yescharacteristic
36C2×#548C2211yescharacteristic
37C2×#519C2211yescharacteristic
38C2×#519C2211yescharacteristic
39C2×C4×#41C2211yescharacteristic
40C2×C4×#41C2211yescharacteristic
41C22×C4×Q8C2211yescharacteristic, complemented
42#2860C2213yescomplemented
43#2855C2213yescomplemented
44#2854C2213yescomplemented
45#2851C2213yescomplemented
46#2848C2213yes—
47#2796C2216yescomplemented
48#2761C2216yescomplemented
49#2757C2216yescomplemented
50#2751C2216yescomplemented
51#2744C2216yescomplemented
52#2740C2216yescomplemented
53#2740C2216yescomplemented
54#2738C2216yescomplemented
55#2737C2216yescomplemented
56#2736C2216yes—
57#2735C2216yes—
58#2735C2216yes—
59#2706C2216yescomplemented
60#2697C2216yes—
61#2644C2213yescomplemented
62#2640C2213yescomplemented
63#2629C2213yes—
64#2625C2213yes—
65#2603C2216yescomplemented
66#2602C2216yescomplemented
67#2597C2216yescomplemented
68#2595C2216yescomplemented
69#2592C2213yescomplemented
70#2582C2213yescomplemented
71#2580C2213yescomplemented
72#2578C2213yescomplemented
73#2577C2213yescomplemented
74#2577C2216yescomplemented
75#2576C2211yescharacteristic
76#2575C2213yes—
77#2574C2213yescomplemented
78#2573C2213yes—
79#2572C2213yes—
80#2572C2216yescomplemented
81#2569C2213yescomplemented
82#2566C2213yescomplemented
83#2565C2213yescomplemented
84#2564C2213yescomplemented
85#2563C2213yescomplemented
86#2561C2213yes—
87#2560C2216yescomplemented
88#2553C2213yescomplemented
89#2534C2213yes—
90#2531C2216yescomplemented
91#2523C2216yescomplemented
92#2522C2216yescomplemented
93#2517C2216yescomplemented
94#2515C2216yes—
95#2515C2216yescomplemented
96#2513C2213yescomplemented
97#2513C2213yescomplemented
98#2513C2213yescomplemented
99#2513C2213yescomplemented
100#2512C2213yescomplemented
101#2512C2213yescomplemented
102#2505C2216yescomplemented
103#2501C2213yescomplemented
104#2499C2213yes—
105#2499C2213yescomplemented
106#2497C2213yescomplemented
107#2496C2213yescomplemented
108#2495C2213yescomplemented
109#2495C2213yescomplemented
110#2495C2213yescomplemented
111#2495C2213yescomplemented
112#2493C2213yescomplemented
113#2490C2213yescomplemented
114#2490C2213yescomplemented
115#2489C2213yescomplemented
116#2489C2213yescomplemented
117#2486C2213yescomplemented
118#2485C2213yes—
119#2485C2213yescomplemented
120#2482C2216yes—
121#2480C2213yes—
122#2480C2216yes—
123#2479C2216yescomplemented
124#2471C2216yescomplemented
125#2454C2213yescomplemented
126#2453C2213yescomplemented
127#2452C2213yescomplemented
128#2451C2213yescomplemented
129#2448C2213yescomplemented
130#2448C2213yescomplemented
131#2447C2213yescomplemented
132#2447C2213yescomplemented
133#2446C2213yescomplemented
134#2446C2213yescomplemented
135#2441C2213yes—
136#2441C2213yescomplemented
137#2439C2213yes—
138#2439C2213yescomplemented
139#2435C2213yes—
140#2432C2213yes—
141#2432C2213yes—
142#2423C2213yescomplemented
143#2423C2213yescomplemented
144#2423C2213yescomplemented
145#2422C2213yescomplemented
146#2421C2213yescomplemented
147#2420C2213yescomplemented
148#2419C2213yescomplemented
149#2418C2213yes—
150#2408C2213yes—
151#2407C2213yes—
152#2407C2213yes—
153#2401C2213yescomplemented
154#2398C2213yescomplemented
155#2396C2213yes—
156#2395C2213yes—
157#2374C2216yescomplemented
158#2373C2216yescomplemented
159#2367C2213yescomplemented
160#2365C2213yescomplemented
161#2362C2213yes—
162#2362C2213yescomplemented
163#2361C2213yescomplemented
164#2360C2213yescomplemented
165#2356C2213yescomplemented
166#2355C2213yescomplemented
167#2354C2213yescomplemented
168#2354C2213yescomplemented
169#2352C2213yes—
170#2352C2213yescomplemented
171#2351C2211yescharacteristic, complemented
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
179#2347C2213yes—
180#2347C2213yescomplemented
181#2347C2213yescomplemented
182#2346C2213yes—
183#2343C2216yescomplemented
184#2341C2211yescharacteristic
185#2341C2211yescharacteristic
186#2341C2213yes—
187#2341C2211yescharacteristic
188#2341C2211yescharacteristic
189#2341C2211yescharacteristic
190#2341C2211yescharacteristic
191#2341C2213yes—
192#2341C2211yescharacteristic
193#2341C2213yes—
194#2341C2213yes—
195#2341C2211yescharacteristic
196Q8×C22⋊C4C2211yescharacteristic
197Q8×C22⋊C4C2211yescharacteristic
198Q8×C22⋊C4C2211yescharacteristic
199Q8×C22⋊C4C2211yescharacteristic, complemented
200Q8×C22⋊C4C2211yescharacteristic, complemented
201Q8×C22⋊C4C2211yescharacteristic, complemented
202#2339C2213yes—
203#2339C2213yes—
204D4×C22⋊C4C2213yes—
205D4×C22⋊C4C2213yes—
206#2327C2213yescomplemented
207#2323C2213yes—
208#2320C2213yescomplemented
209#2319C2213yescomplemented
210#2319C2213yescomplemented
211#2314C2213yes—
212#2309C2213yes—
213#2309C2213yes—
214C4×#126C2213yescomplemented
215C4×#124C2213yescomplemented
216C4×C22⋊Q8C2213yescomplemented
217C4×C22⋊Q8C2213yescomplemented
218C4×C22⋊Q8C2213yescomplemented
219C4×#123C2213yescomplemented
220C4×#123C2213yescomplemented
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×#41C2313yes—
243C22×#41C2313yes—
244C22×#41C2311yescharacteristic
245C23×Q8C2311yescharacteristic
246C23×Q8C2311yescharacteristic
247C23×D4C2313yes—
248C24×C4C2313yes—
249#557—44no—
250D4×Q8—28no—
251#548—28no—
252#548—44no—
253C2×C4⋊Q8C2313yes—
254C2×C4⋊Q8C2313yes—
255C2×#126C2313yes—
256C2×#126C2316yes—
257C2×#125C2313yes—
258C2×#125C2313yes—
259C2×#124C2313yes—
260C2×#124C2313yes—
261C2×#123C2316yes—
262C2×#123C2313yes—
263C2×#123C2313yes—
264C2×C22⋊Q8C2313yes—
265C2×C22⋊Q8C2313yes—
266C2×C22⋊Q8C2313yes—
267C2×C22⋊Q8C2313yes—
268C2×C22⋊Q8C2313yes—
269C2×#121C2313yes—
270C2×#121C2313yes—
271C2×#120C2313yes—
272#519—28no—
273#519—44no—
274C4×#41—28no—
275C4×#41—44no—
276C2×C4×Q8—44no—
277C2×C4×Q8C2313yes—
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
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×Q8C2313yes—
290C2×C4×Q8C2313yes—
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×#117C2313yes—
305C2×#117C2313yes—
306C2×#117C2313yes—
307C2×#117C2313yes—
308C2×#117C2313yes—
309C2×#117C2316yes—
310C2×#117C2313yes—
311C22×C4⋊C4C2313yes—
312C22×C22⋊C4C2313yes—
313C22×C22⋊C4C2313yes—
314C22×C42C2313yes—
315C22×C42C2313yes—
316C22×C42C2313yes—
317#401C2311yescharacteristic
318#400C2313yes—
319#400C2313yes—
320#400C2313yes—
321#400C2316yes—
322#400C2313yes—
323#400C2313yes—
324#400C2316yes—
325#400C2313yes—
326#400C2313yes—
327#399C2313yes—
328#399C2313yes—
329#399C2316yes—
330#399C2316yes—
331#399C2316yes—
332#398C2316yes—
333#398C2313yes—
334#398C2316yes—
335#398C2313yes—
336#398C2313yes—
337#398C2316yes—
338#398C2316yes—
339#397C2316yes—
340#397C2313yes—
341#397C2313yes—
342#397C2313yes—
343#397C2311yescharacteristic
344#397C2313yes—
345#397C2316yes—
346#397C2316yes—
347#397C2313yes—
348#397C2313yes—
349#397C2313yes—
350#397C2316yes—
351#397C2316yes—
352#397C2316yes—
353#397C2316yes—
354#397C2316yes—
355#397C2316yes—
356#397C2316yes—
357#397C2316yes—
358#397C2316yes—
359#396C2316yes—
360#396C2316yes—
361#396C2313yes—
362#396C2313yes—
363#396C2311yescharacteristic
364#396C2316yes—
365#396C2316yes—
366#395C2313yes—
367#394C2316yes—
368#394C2313yes—
369#394C2316yes—
370#394C2311yescharacteristic
371#394C2313yes—
372#394C2316yes—
373#394C2313yes—
374#394C2316yes—
375#393C2316yes—
376#393C2313yes—
377#393C2313yes—
378#393C2313yes—
379#393C2316yes—
380#392C2316yes—
381#391C2316yes—
382#391C2313yes—
383#391C2313yes—
384#391C2313yes—
385#391C2313yes—
386#391C2313yes—
387#391C2313yes—
388#391C2313yes—
389#391C2313yes—
390#391C2313yes—
391#391C2313yes—
392#391C2313yes—
393#391C2313yes—
394#391C2313yes—
395#390C2316yes—
396#390C2316yes—
397#390C2313yes—
398#390C2313yes—
399#390C2313yes—
400#390C2313yes—
401#390C2313yes—
402#390C2316yes—
403#390C2316yes—
404#390C2313yes—
405#390C2313yes—
406#390C2313yes—
407#390C2316yes—
408#390C2313yes—
409#390C2313yes—
410#390C2313yes—
411#390C2313yes—
412#390C2313yes—
413#390C2313yes—
414#390C2313yes—
415#390C2313yes—
416#389C2313yes—
417#389C2313yes—
418#389C2313yes—
419#389C2313yes—
420#389C2313yes—
421#389C2313yes—
422#389C2313yes—
423#389C2313yes—
424#389C2316yes—
425#389C2316yes—
426#389C2313yes—
427#389C2313yes—
428#389C2313yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#388C2313yes—
436#388C2313yes—
437#388C2313yes—
438#388C2313yes—
439#388C2316yes—
440#388C2316yes—
441#388C2311yescharacteristic
442#388C2313yes—
443#388C2313yes—
444#388C2316yes—
445#388C2313yes—
446#388C2313yes—
447#388C2316yes—
448#388C2313yes—
449#388C2313yes—
450#388C2316yes—
451#388C2316yes—
452#388C2316yes—
453#388C2313yes—
454#388C2311yescharacteristic
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#387C2311yescharacteristic
468#387C2313yes—
469#387C2313yes—
470#387C2313yes—
471#387C2316yes—
472#387C2316yes—
473#387C2313yes—
474#387C2313yes—
475#387C2313yes—
476#387C2316yes—
477#387C2316yes—
478#387C2313yes—
479#387C2313yes—
480#387C2313yes—
481#387C2313yes—
482#387C2313yes—
483#387C2313yes—
484#387C2311yescharacteristic
485#387C2316yes—
486#387C2316yes—
487#387C2316yes—
488#387C2316yes—
489#387C2316yes—
490#387C2316yes—
491#387C2316yes—
492#387C2316yes—
493#387C2313yes—
494#387C2316yes—
495#386C2316yes—
496#386C2313yes—
497#386C2313yes—
498#386C2311yescharacteristic
499#386C2313yes—
500#386C2316yes—
501#386C2311yescharacteristic
502#386C2313yes—
503#386C2313yes—
504#386C2316yes—
505#386C2316yes—
506#386C2316yes—
507#385C2311yescharacteristic
508#385C2313yes—
509#385C2313yes—
510#385C2316yes—
511#385C2313yes—
512#385C2313yes—
513#385C2313yes—
514#385C2313yes—
515#385C2316yes—
516#385C2313yes—
517#385C2316yes—
518#385C2316yes—
519#385C2316yes—
520#385C2313yes—
521#385C2316yes—
522#384C2313yes—
523#384C2313yes—
524#384C2313yes—
525#384C2313yes—
526#383C2313yes—
527#383C2313yes—
528#383C2316yes—
529#383C2316yes—
530#383C2313yes—
531#382C2316yes—
532#382C2313yes—
533#382C2313yes—
534#382C2313yes—
535#382C2311yescharacteristic
536#382C2313yes—
537#382C2316yes—
538#382C2313yes—
539#381C2313yes—
540#381C2313yes—
541#381C2313yes—
542#381C2313yes—
543#381C2316yes—
544#381C2311yescharacteristic
545#381C2313yes—
546#381C2316yes—
547#380C2313yes—
548#380C2313yes—
549#380C2313yes—
550#380C2313yes—
551#380C2313yes—
552#380C2313yes—
553#380C2313yes—
554#380C2313yes—
555#380C2313yes—
556#380C2313yes—
557#380C2313yes—
558#380C2313yes—
559#380C2316yes—
560#380C2313yes—
561#380C2313yes—
562#380C2313yes—
563#380C2313yes—
564#380C2313yes—
565#380C2313yes—
566#380C2313yes—
567#380C2313yes—
568#380C2313yes—
569#379C2313yes—
570#379C2313yes—
571#379C2316yes—
572#379C2313yes—
573#379C2316yes—
574#379C2316yes—
575C4×C4⋊C4C2313yes—
576C4×C4⋊C4C2313yes—
577C4×C4⋊C4C2313yes—
578C4×C4⋊C4C2316yes—
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⋊C4C2316yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2316yes—
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⋊C4C2316yes—
601C4×C22⋊C4C2313yes—
602C4×C22⋊C4C2313yes—
603C4×C22⋊C4C2313yes—
604C4×C22⋊C4C2316yes—
605C4×C22⋊C4C2316yes—
606C4×C22⋊C4C2313yes—
607C4×C22⋊C4C2311yescharacteristic
608C4×C22⋊C4C2311yescharacteristic
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2316yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2316yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623C4×C22⋊C4C2313yes—
624#376C2313yes—
625#376C2313yes—
626#376C2316yes—
627C2×#95C2313yes—
628C2×#95C2313yes—
629C43C2313yes—
630C25C2413yes—
631C2×#41—24no—
632C2×#41—212no—
633C2×#41—212no—
634C2×#41—24no—
635C2×#41—24no—
636C2×#41—24no—
637C2×#41—24no—
638C2×#41—212no—
639C2×#41—212no—
640C2×#41—46no—
641C2×#41—46no—
642C2×#41—464no—
643C2×#41#4118yes—
644C22×Q8—24no—
645C22×Q8—24no—
646C22×Q8—24no—
647C22×Q8—24no—
648C22×Q8—24no—
649C22×Q8#4118yes—
650C22×Q8C2413yes—
651C22×Q8C2413yes—
652C22×Q8C2413yes—
653C22×Q8C2411yescharacteristic
654C22×D4—212no—
655C22×D4—212no—
656C22×D4—46no—
657C22×D4C2413yes—
658C22×D4C2411yescharacteristic
659C22×D4C2413yes—
660C22×D4C2416yes—
661C22×D4C2413yes—
662C22×D4C2413yes—
663C23×C4—212no—
664C23×C4—212no—
665C23×C4—46no—
666C23×C4C2413yes—
667C23×C4C2413yes—
668C23×C4C2413yes—
669C23×C4C2411yescharacteristic
670C23×C4C2413yes—
671C23×C4C2413yes—
672C23×C4C2413yes—
673C23×C4C2413yes—
674C23×C4C2413yes—
675C23×C4C2413yes—
676C23×C4C2413yes—
677C23×C4C2411yescharacteristic
678C23×C4C2413yes—
679C4⋊Q8—212no—
680C4⋊Q8—46no—
681#126—412no—
682#126—46no—
683#125—46no—
684#125—46no—
685#124—212no—
686#124—46no—
687#123—46no—
688#123—46no—
689#123—412no—
690C22⋊Q8—212no—
691C22⋊Q8—212no—
692C22⋊Q8—212no—
693C22⋊Q8—46no—
694C22⋊Q8—46no—
695#121—212no—
696#121—46no—
697#120—46no—
698C4×Q8—24no—
699C4×Q8—24no—
700C4×Q8—212no—
701C4×Q8—212no—
702C4×Q8—24no—
703C4×Q8—24no—
704C4×Q8—24no—
705C4×Q8—24no—
706C4×Q8—24no—
707C4×Q8—24no—
708C4×Q8—24no—
709C4×Q8—24no—
710C4×Q8—24no—
711C4×Q8—46no—
712C4×Q8—46no—
713C4×Q8—46no—
714C4×Q8—46no—
715C4×Q8—46no—
716C4×D4—212no—
717C4×D4—212no—
718C4×D4—212no—
719C4×D4—212no—
720C4×D4—46no—
721C4×D4—46no—
722C4×D4—46no—
723C4×D4—46no—
724C4×D4—46no—
725#117—212no—
726#117—212no—
727#117—212no—
728#117—46no—
729#117—412no—
730#117—46no—
731#117—46no—
732C2×C4⋊C4—46no—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
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⋊C4C2416yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2411yescharacteristic
754C2×C4⋊C4C2416yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2411yescharacteristic
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2416yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2416yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2416yes—
770C2×C4⋊C4C2416yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2416yes—
773C2×C4⋊C4C2411yescharacteristic
774C2×C4⋊C4C2411yescharacteristic
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C22⋊C4—46no—
778C2×C22⋊C4—46no—
779C2×C22⋊C4C2411yescharacteristic
780C2×C22⋊C4C2411yescharacteristic
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2413yes—
783C2×C22⋊C4C2411yescharacteristic
784C2×C22⋊C4C2413yes—
785C2×C22⋊C4C2416yes—
786C2×C22⋊C4C2411yescharacteristic
787C2×C22⋊C4C2411yescharacteristic
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2416yes—
792C2×C22⋊C4C2411yescharacteristic
793C2×C22⋊C4C2411yescharacteristic
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2413yes—
798C2×C22⋊C4C2413yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2411yescharacteristic
801C2×C22⋊C4C2416yes—
802C2×C22⋊C4C2416yes—
803C2×C22⋊C4C2416yes—
804C2×C22⋊C4C2411yescharacteristic
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2416yes—
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2416yes—
817C2×C22⋊C4C2416yes—
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2416yes—
821C2×C22⋊C4C2413yes—
822C2×C22⋊C4C2416yes—
823C2×C22⋊C4C2411yescharacteristic
824C2×C22⋊C4C2413yes—
825C2×C22⋊C4C2416yes—
826C2×C22⋊C4C2416yes—
827C2×C22⋊C4C2413yes—
828C2×C22⋊C4C2413yes—
829C2×C42—212no—
830C2×C42—46no—
831C2×C42—46no—
832C2×C42C2413yes—
833C2×C42C2413yes—
834C2×C42C2413yes—
835C2×C42C2413yes—
836C2×C42C2416yes—
837C2×C42C2413yes—
838C2×C42C2413yes—
839C2×C42C2413yes—
840C2×C42C2413yes—
841C2×C42C2413yes—
842C2×C42C2413yes—
843C2×C42C2413yes—
844C2×C42C2413yes—
845C2×C42C2413yes—
846C2×C42C2411yescharacteristic
847C2×C42C2413yes—
848C2×C42C2416yes—
849C2×C42C2416yes—
850C2×C42C2416yes—
851C2×C42C2413yes—
852C2×C42C2413yes—
853C2×C42C2413yes—
854C2×C42C2413yes—
855C2×C42C2411yescharacteristic
856C2×C42C2411yescharacteristic
857#95C2411yescharacteristic
858#95C2411yescharacteristic
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2413yes—
864#95C2413yes—
865#95C2411yescharacteristic
866#95C2411yescharacteristic
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2416yes—
875#95C2416yes—
876#95C2411yescharacteristic
877#95C2413yes—
878#95C2411yescharacteristic
879#95C2413yes—
880#95C2413yes—
881#95C2411yescharacteristic
882#95C2413yes—
883#95C2411yescharacteristic
884#95C2411yescharacteristic
885#95C2411yescharacteristic
886#95C2411yescharacteristic
887#95C2416yes—
888#95C2413yes—
889#95C2413yes—
890#95C2413yes—
891#95C2413yes—
892#95C2413yes—
893#95C2413yes—
894#95C2416yes—
895#95C2416yes—
896#95C2413yes—
897#95C2413yes—
898#95C2413yes—
899#95C2416yes—
900#95C2416yes—
901#95C2413yes—
902#95C2413yes—
903#95C2411yescharacteristic
904#95C2411yescharacteristic
905#95C2416yes—
906#95C2411yescharacteristic
907#95C2416yes—
908#95C2413yes—
909#95C2413yes—
910#95C2413yes—
911#95C2413yes—
912#95C2413yes—
913#95C2413yes—
914#95C2413yes—
915#95C2413yes—
916#95C2413yes—
917#95C2413yes—
918#95C2416yes—
919#95C2416yes—
920C24—26no—
921C24—26no—
922C24—43no—
923C24—43no—
924C24—43no—
925C24—43no—
926C24—43no—
927C24C2513yes—
928C24C2511yescharacteristic
929C24C2513yes—
930C24C2511yescharacteristic
931#41—232no—
932#41—448no—
933#41—448no—
934#41—416no—
935C2×Q8—232no—
936C2×Q8—26no—
937C2×Q8—26no—
938C2×Q8—26no—
939C2×Q8—26no—
940C2×Q8—26no—
941C2×Q8—43no—
942C2×Q8—43no—
943C2×Q8—43no—
944C2×Q8—416no—
945C2×Q8C2×#41112yes—
946C2×Q8C2×#4114yes—
947C2×Q8C2×#4114yes—
948C2×Q8H(5,𝔽2)14yes—
949C2×D4—22no—
950C2×D4—26no—
951C2×D4—212no—
952C2×D4—26no—
953C2×D4—22no—
954C2×D4—26no—
955C2×D4—26no—
956C2×D4—212no—
957C2×D4—26no—
958C2×D4—26no—
959C2×D4—26no—
960C2×D4—26no—
961C2×D4—448no—
962C2×D4—43no—
963C2×D4—46no—
964C2×D4—41no—
965C2×D4—43no—
966C2×D4—43no—
967C2×D4C2×#41112yes—
968C22×C4—26no—
969C22×C4—26no—
970C22×C4—26no—
971C22×C4—26no—
972C22×C4—26no—
973C22×C4—22no—
974C22×C4—26no—
975C22×C4—26no—
976C22×C4—26no—
977C22×C4—26no—
978C22×C4—26no—
979C22×C4—22no—
980C22×C4—26no—
981C22×C4—26no—
982C22×C4—26no—
983C22×C4—26no—
984C22×C4—26no—
985C22×C4—26no—
986C22×C4—26no—
987C22×C4—26no—
988C22×C4—22no—
989C22×C4—26no—
990C22×C4—41no—
991C22×C4—41no—
992C22×C4—43no—
993C22×C4—43no—
994C22×C4—41no—
995C22×C4—43no—
996C22×C4—448no—
997C22×C4—43no—
998C22×C4—43no—
999C22×C4—43no—
1000C22×C4—43no—
1001C22×C4—43no—
1002C22×C4—43no—
1003C22×C4—43no—
1004C22×C4—43no—
1005C22×C4—43no—
1006C22×C4C2×#41112yes—
1007C22×C4C2×#41112yes—
1008C22×C4C2511yescharacteristic
1009C22×C4C2511yescharacteristic
1010C22×C4C2513yes—
1011C22×C4C2511yescharacteristic
1012C22×C4C2511yescharacteristic
1013C22×C4C2511yescharacteristic
1014C22×C4C2511yescharacteristic
1015C22×C4C2511yescharacteristic
1016C22×C4C2513yes—
1017C22×C4C2513yes—
1018C22×C4C2513yes—
1019C22×C4C2513yes—
1020C22×C4C2513yes—
1021C22×C4C2513yes—
1022C22×C4C2511yescharacteristic
1023C22×C4C2513yes—
1024C22×C4C2511yescharacteristic
1025C22×C4C2513yes—
1026C22×C4C2513yes—
1027C22×C4C2513yes—
1028C22×C4C2513yes—
1029C22×C4C2511yescharacteristic
1030C22×C4C2511yescharacteristic
1031C22×C4C2513yes—
1032C22×C4C2511yescharacteristic
1033C22×C4C2511yescharacteristic
1034C22×C4C2513yes—
1035C4⋊C4—26no—
1036C4⋊C4—26no—
1037C4⋊C4—26no—
1038C4⋊C4—26no—
1039C4⋊C4—26no—
1040C4⋊C4—26no—
1041C4⋊C4—26no—
1042C4⋊C4—26no—
1043C4⋊C4—26no—
1044C4⋊C4—26no—
1045C4⋊C4—212no—
1046C4⋊C4—26no—
1047C4⋊C4—26no—
1048C4⋊C4—26no—
1049C4⋊C4—26no—
1050C4⋊C4—26no—
1051C4⋊C4—26no—
1052C4⋊C4—26no—
1053C4⋊C4—22no—
1054C4⋊C4—26no—
1055C4⋊C4—22no—
1056C4⋊C4—46no—
1057C4⋊C4—41no—
1058C4⋊C4—41no—
1059C4⋊C4—43no—
1060C4⋊C4—43no—
1061C4⋊C4—43no—
1062C4⋊C4—43no—
1063C4⋊C4—43no—
1064C4⋊C4—43no—
1065C4⋊C4—43no—
1066C4⋊C4—41no—
1067C4⋊C4—43no—
1068C4⋊C4—43no—
1069C4⋊C4—43no—
1070C4⋊C4—43no—
1071C4⋊C4—43no—
1072C4⋊C4—43no—
1073C4⋊C4—46no—
1074C4⋊C4—46no—
1075C4⋊C4—46no—
1076C4⋊C4—46no—
1077C4⋊C4—46no—
1078C4⋊C4—43no—
1079C22⋊C4—22no—
1080C22⋊C4—26no—
1081C22⋊C4—212no—
1082C22⋊C4—26no—
1083C22⋊C4—26no—
1084C22⋊C4—212no—
1085C22⋊C4—22no—
1086C22⋊C4—26no—
1087C22⋊C4—22no—
1088C22⋊C4—22no—
1089C22⋊C4—26no—
1090C22⋊C4—22no—
1091C22⋊C4—22no—
1092C22⋊C4—26no—
1093C22⋊C4—26no—
1094C22⋊C4—22no—
1095C22⋊C4—43no—
1096C22⋊C4—43no—
1097C22⋊C4—43no—
1098C22⋊C4—43no—
1099C22⋊C4—43no—
1100C22⋊C4—41no—
1101C22⋊C4—46no—
1102C22⋊C4—43no—
1103C22⋊C4—43no—
1104C22⋊C4—46no—
1105C22⋊C4—46no—
1106C22⋊C4—46no—
1107C22⋊C4—41no—
1108C22⋊C4—43no—
1109C22⋊C4—46no—
1110C22⋊C4—43no—
1111C22⋊C4—43no—
1112C22⋊C4—43no—
1113C22⋊C4—41no—
1114C22⋊C4—43no—
1115C22⋊C4—43no—
1116C22⋊C4—43no—
1117C22⋊C4—43no—
1118C22⋊C4—46no—
1119C22⋊C4—43no—
1120C22⋊C4—43no—
1121C22⋊C4—43no—
1122C22⋊C4—46no—
1123C22⋊C4—43no—
1124C22⋊C4—46no—
1125C22⋊C4—46no—
1126C22⋊C4—46no—
1127C22⋊C4—43no—
1128C22⋊C4—43no—
1129C42—22no—
1130C42—26no—
1131C42—26no—
1132C42—26no—
1133C42—212no—
1134C42—26no—
1135C42—26no—
1136C42—26no—
1137C42—26no—
1138C42—26no—
1139C42—26no—
1140C42—26no—
1141C42—26no—
1142C42—26no—
1143C42—26no—
1144C42—41no—
1145C42—43no—
1146C42—43no—
1147C42—43no—
1148C42—41no—
1149C42—46no—
1150C42—46no—
1151C42—46no—
1152C42—43no—
1153C42—43no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—23no—
1158C23—21no—
1159C23—23no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—23no—
1165C23—23no—
1166C23—21no—
1167C23—23no—
1168C23—21no—
1169C23—21no—
1170C23—23no—
1171C23—21no—
1172C23—23no—
1173C23—23no—
1174C23—23no—
1175C23—23no—
1176C23—23no—
1177C23—23no—
1178C23—23no—
1179C23—412no—
1180C23—412no—
1181C23—86no—
1182C23—86no—
1183C23—86no—
1184C23—86no—
1185C23—86no—
1186C23C22×#4112yes—
1187C23C22×#4116yes—
1188C23#58512yes—
1189C23C2611yescharacteristic
1190Q8—224no—
1191Q8—412no—
1192Q8—86no—
1193Q8#551116yes—
1194D4—224no—
1195D4—424no—
1196D4—44no—
1197D4—412no—
1198D4—412no—
1199D4—86no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—23no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—23no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—224no—
1209C2×C4—224no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—23no—
1214C2×C4—23no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—23no—
1218C2×C4—23no—
1219C2×C4—23no—
1220C2×C4—23no—
1221C2×C4—23no—
1222C2×C4—23no—
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—23no—
1237C2×C4—23no—
1238C2×C4—23no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—23no—
1242C2×C4—23no—
1243C2×C4—23no—
1244C2×C4—23no—
1245C2×C4—23no—
1246C2×C4—23no—
1247C2×C4—23no—
1248C2×C4—23no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—23no—
1254C2×C4—23no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—23no—
1261C2×C4—23no—
1262C2×C4—21no—
1263C2×C4—23no—
1264C2×C4—21no—
1265C2×C4—23no—
1266C2×C4—23no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—23no—
1270C2×C4—23no—
1271C2×C4—23no—
1272C2×C4—21no—
1273C2×C4—23no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—412no—
1277C2×C4—412no—
1278C2×C4—44no—
1279C2×C4—412no—
1280C2×C4—44no—
1281C2×C4—412no—
1282C2×C4—412no—
1283C2×C4—86no—
1284C2×C4—86no—
1285C2×C4—86no—
1286C2×C4—86no—
1287C2×C4C22×#4112yes—
1288C2×C4C22×#4116yes—
1289C2×C4C22×#4116yes—
1290C2×C4C22×#4116yes—
1291C2×C4C2×H(5,𝔽2)16yes—
1292C2×C4#58512yes—
1293C2×C4#58512yes—
1294C22—26no—
1295C22—22no—
1296C22—22no—
1297C22—22no—
1298C22—22no—
1299C22—26no—
1300C22—22no—
1301C22—22no—
1302C22—26no—
1303C22—41no—
1304C22—41no—
1305C22—43no—
1306C22—43no—
1307C22—41no—
1308C22—41no—
1309C22—43no—
1310C22—41no—
1311C22—41no—
1312C22—43no—
1313C22—41no—
1314C22—41no—
1315C22—43no—
1316C22—43no—
1317C22—43no—
1318C22—43no—
1319C22—43no—
1320C22—43no—
1321C22—43no—
1322C22—824no—
1323C22C23×#4111yescharacteristic
1324C22C23×#4111yescharacteristic
1325C22C22×H(5,𝔽2)11yescharacteristic
1326C22C2×#58511yescharacteristic
1327C22C2×#58511yescharacteristic
1328C22C2×#58511yescharacteristic
1329C222−1+611yescharacteristic
1330C4—22no—
1331C4—22no—
1332C4—22no—
1333C4—26no—
1334C4—41no—
1335C4—43no—
1336C4—41no—
1337C4—43no—
1338C4—41no—
1339C4—41no—
1340C4—43no—
1341C4—43no—
1342C4—41no—
1343C4—43no—
1344C4—43no—
1345C4—41no—
1346C4—43no—
1347C4—43no—
1348C4—41no—
1349C4—43no—
1350C4—41no—
1351C4—43no—
1352C4—43no—
1353C4—41no—
1354C4—41no—
1355C4—43no—
1356C4C2×#551112yes—
1357C2—42no—
1358C2—46no—
1359C2—42no—
1360C2—83no—
1361C2C22×#55111yescharacteristic
1362C2#6279311yescharacteristic
1363C2#6281611yescharacteristic
1364C2#6289711yescharacteristic
1365C2#6299311yescharacteristic
1366C2#6300511yescharacteristic
1367C2#6301911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36428C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59769C2semidirect
2. #59482C2semidirect
3. #59380C2semidirect
4. #59277C2semidirect
5. #59201C2semidirect
6. #45365C2semidirect
7. #45182C2semidirect
8. #45022C2semidirect
9. #45019C2semidirect
10. #39070C2semidirect
11. #39046C2semidirect
12. #38063C2semidirect
13. #37856C2semidirect
14. #36483C2semidirect
15. #36458C2semidirect
16. #36432C2semidirect
17. #36431C2semidirect
19. #36401C2semidirect
20. #36207C2semidirect
21. #36059C2semidirect
22. #35854C2semidirect
23. #35786C2semidirect
24. #35723C2semidirect
25. #34849C2semidirect
26. #34291C2semidirect
27. #34262C2semidirect
28. #34193C2semidirect
29. #34174C2semidirect
30. C4×#548C2semidirect
31. C22⋊C4×#41C2semidirect
33. C2×#557C22semidirect
41. C22×C4×Q8C22semidirect
42. #2860C22semidirect
43. #2855C22semidirect
44. #2854C22semidirect
45. #2851C22semidirect
47. #2796C22semidirect
48. #2761C22semidirect
49. #2757C22semidirect
50. #2751C22semidirect
51. #2744C22semidirect
52. #2740C22semidirect
53. #2740C22semidirect
54. #2738C22semidirect
55. #2737C22semidirect
59. #2706C22semidirect
61. #2644C22semidirect
62. #2640C22semidirect
65. #2603C22semidirect
66. #2602C22semidirect
67. #2597C22semidirect
68. #2595C22semidirect
69. #2592C22semidirect
70. #2582C22semidirect
71. #2580C22semidirect
72. #2578C22semidirect
73. #2577C22semidirect
74. #2577C22semidirect
77. #2574C22semidirect
80. #2572C22semidirect
81. #2569C22semidirect
82. #2566C22semidirect
83. #2565C22semidirect
84. #2564C22semidirect
85. #2563C22semidirect
87. #2560C22semidirect
88. #2553C22semidirect
90. #2531C22semidirect
91. #2523C22semidirect
92. #2522C22semidirect
93. #2517C22semidirect
95. #2515C22semidirect
96. #2513C22semidirect
97. #2513C22semidirect
98. #2513C22semidirect
99. #2513C22semidirect
100. #2512C22semidirect
101. #2512C22semidirect
102. #2505C22semidirect
103. #2501C22semidirect
105. #2499C22semidirect
106. #2497C22semidirect
107. #2496C22semidirect
108. #2495C22semidirect
109. #2495C22semidirect
110. #2495C22semidirect
111. #2495C22semidirect
112. #2493C22semidirect
113. #2490C22semidirect
114. #2490C22semidirect
115. #2489C22semidirect
116. #2489C22semidirect
117. #2486C22semidirect
119. #2485C22semidirect
123. #2479C22semidirect
124. #2471C22semidirect
125. #2454C22semidirect
126. #2453C22semidirect
127. #2452C22semidirect
128. #2451C22semidirect
129. #2448C22semidirect
130. #2448C22semidirect
131. #2447C22semidirect
132. #2447C22semidirect
133. #2446C22semidirect
134. #2446C22semidirect
136. #2441C22semidirect
138. #2439C22semidirect
142. #2423C22semidirect
143. #2423C22semidirect
144. #2423C22semidirect
145. #2422C22semidirect
146. #2421C22semidirect
147. #2420C22semidirect
148. #2419C22semidirect
153. #2401C22semidirect
154. #2398C22semidirect
157. #2374C22semidirect
158. #2373C22semidirect
159. #2367C22semidirect
160. #2365C22semidirect
162. #2362C22semidirect
163. #2361C22semidirect
164. #2360C22semidirect
165. #2356C22semidirect
166. #2355C22semidirect
167. #2354C22semidirect
168. #2354C22semidirect
170. #2352C22semidirect
171. #2351C22semidirect
172. #2351C22semidirect
173. #2351C22semidirect
174. #2351C22semidirect
175. Q8×C4⋊C4C22semidirect
176. Q8×C4⋊C4C22semidirect
177. Q8×C4⋊C4C22semidirect
178. Q8×C4⋊C4C22semidirect
180. #2347C22semidirect
181. #2347C22semidirect
183. #2343C22semidirect
199. Q8×C22⋊C4C22semidirect
200. Q8×C22⋊C4C22semidirect
201. Q8×C22⋊C4C22semidirect
206. #2327C22semidirect
208. #2320C22semidirect
209. #2319C22semidirect
210. #2319C22semidirect
214. C4×#126C22semidirect
215. C4×#124C22semidirect
216. C4×C22⋊Q8C22semidirect
217. C4×C22⋊Q8C22semidirect
218. C4×C22⋊Q8C22semidirect
219. C4×#123C22semidirect
220. C4×#123C22semidirect
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
#597692
#594822
#593802
#592772
#592012
#453652
#451822
#450222
#450192
#390702
#390462
#380632
#378562
#364832
#364582
#364322
#364312
#364282
#364012
#362072
#360592
#358542
#357862
#357232
#348492
#342912
#342622
#341932
#341742
C4×#5482
C22⋊C4×#412