Finite Group Databasebeta

← #7688684

Subgroups — #7688684

Order 512.

5552 conjugacy classes of subgroups.

The subgroup lattice has 1370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59902C213yesmaximal, complemented
2#59486C213yesmaximal, complemented
3#59381C213yesmaximal, complemented
4#59282C213yesmaximal, complemented
5#59202C213yesmaximal, complemented
6#45192C213yesmaximal, complemented
7#45188C213yesmaximal, complemented
8#44992C213yesmaximal, complemented
9#44961C213yesmaximal, complemented
10#39070C213yesmaximal, complemented
11#39042C213yesmaximal, complemented
12#38063C213yesmaximal, complemented
13#37859C213yesmaximal, complemented
14#36585C211yesmaximal, characteristic, complemented
15#36578C211yesmaximal, characteristic, complemented
16#36456C211yesmaximal, characteristic, complemented
17#36432C211yesmaximal, characteristic, complemented
18#36428C211yesmaximal, characteristic
19#36381C213yesmaximal, complemented
20#36204C213yesmaximal, complemented
21#35948C211yesmaximal, characteristic, complemented
22#35898C211yesmaximal, characteristic, complemented
23#35723C211yesmaximal, characteristic, complemented
24#35711C211yesmaximal, characteristic, complemented
25#34849C213yesmaximal, complemented
26#34291C211yesmaximal, characteristic, complemented
27#34262C211yesmaximal, characteristic, complemented
28#34197C211yesmaximal, characteristic, complemented
29#34174C211yesmaximal, characteristic, complemented
30C4×#548C211yesmaximal, characteristic, complemented
31C22⋊C4×#41C211yesmaximal, characteristic, complemented
32C23×#41C2211yescharacteristic
33C2×Q82C2211yescharacteristic, 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#2857C2213yescomplemented
44#2855C2213yescomplemented
45#2854C2213yescomplemented
46#2848C2213yes—
47#2786C2216yescomplemented
48#2761C2216yescomplemented
49#2751C2216yescomplemented
50#2751C2216yescomplemented
51#2749C2216yescomplemented
52#2745C2216yescomplemented
53#2740C2216yescomplemented
54#2739C2216yescomplemented
55#2737C2216yescomplemented
56#2736C2216yes—
57#2735C2216yes—
58#2735C2216yes—
59#2723C2216yescomplemented
60#2684C2216yes—
61#2644C2213yescomplemented
62#2640C2213yescomplemented
63#2628C2213yes—
64#2625C2213yes—
65#2597C2216yescomplemented
66#2595C2216yescomplemented
67#2592C2213yescomplemented
68#2581C2213yescomplemented
69#2578C2213yescomplemented
70#2577C2213yescomplemented
71#2576C2213yes—
72#2576C2216yescomplemented
73#2575C2213yes—
74#2574C2216yescomplemented
75#2574C2213yescomplemented
76#2573C2213yes—
77#2572C2211yescharacteristic
78#2569C2213yescomplemented
79#2568C2213yescomplemented
80#2564C2213yescomplemented
81#2563C2213yescomplemented
82#2561C2213yes—
83#2561C2216yes—
84#2560C2216yescomplemented
85#2557C2216yescomplemented
86#2553C2213yescomplemented
87#2547C2213yescomplemented
88#2538C2213yescomplemented
89#2534C2213yes—
90#2531C2216yescomplemented
91#2530C2216yescomplemented
92#2527C2216yes—
93#2527C2216yescomplemented
94#2526C2216yescomplemented
95#2523C2216yescomplemented
96#2517C2216yescomplemented
97#2513C2213yescomplemented
98#2513C2213yescomplemented
99#2513C2213yescomplemented
100#2513C2213yescomplemented
101#2512C2213yescomplemented
102#2512C2213yescomplemented
103#2504C2213yescomplemented
104#2499C2213yes—
105#2499C2213yescomplemented
106#2497C2213yescomplemented
107#2496C2213yescomplemented
108#2494C2213yescomplemented
109#2494C2213yescomplemented
110#2494C2213yescomplemented
111#2494C2213yescomplemented
112#2493C2213yescomplemented
113#2493C2216yescomplemented
114#2492C2213yescomplemented
115#2492C2213yescomplemented
116#2491C2213yescomplemented
117#2491C2213yescomplemented
118#2487C2213yescomplemented
119#2485C2213yes—
120#2485C2213yescomplemented
121#2480C2213yes—
122#2480C2216yes—
123#2467C2216yescomplemented
124#2461C2216yescomplemented
125#2452C2213yescomplemented
126#2452C2213yescomplemented
127#2451C2213yescomplemented
128#2451C2213yescomplemented
129#2448C2213yescomplemented
130#2448C2213yescomplemented
131#2447C2213yescomplemented
132#2447C2213yescomplemented
133#2446C2213yescomplemented
134#2446C2213yescomplemented
135#2439C2213yes—
136#2439C2213yes—
137#2439C2213yescomplemented
138#2439C2213yescomplemented
139#2435C2213yes—
140#2432C2213yes—
141#2432C2213yes—
142#2423C2213yescomplemented
143#2422C2213yescomplemented
144#2421C2213yescomplemented
145#2421C2213yescomplemented
146#2421C2213yescomplemented
147#2420C2213yescomplemented
148#2419C2213yescomplemented
149#2418C2213yes—
150#2408C2213yes—
151#2407C2213yes—
152#2407C2213yes—
153#2401C2213yescomplemented
154#2398C2213yescomplemented
155#2396C2213yes—
156#2395C2213yes—
157#2373C2216yescomplemented
158#2372C2216yescomplemented
159#2368C2216yescomplemented
160#2367C2213yescomplemented
161#2365C2213yescomplemented
162#2362C2213yes—
163#2362C2213yescomplemented
164#2361C2213yescomplemented
165#2360C2213yescomplemented
166#2357C2213yescomplemented
167#2357C2213yescomplemented
168#2356C2213yescomplemented
169#2355C2213yescomplemented
170#2352C2213yes—
171#2352C2213yescomplemented
172#2351C2211yescharacteristic, complemented
173#2351C2211yescharacteristic, complemented
174#2351C2211yescharacteristic, complemented
175#2351C2211yescharacteristic, complemented
176#2351C2211yescharacteristic, complemented
177#2351C2211yescharacteristic, complemented
178Q8×C4⋊C4C2211yescharacteristic, complemented
179Q8×C4⋊C4C2211yescharacteristic, complemented
180#2347C2213yes—
181#2346C2213yes—
182#2346C2213yescomplemented
183#2346C2213yescomplemented
184#2341C2213yes—
185#2341C2211yescharacteristic
186#2341C2211yescharacteristic
187#2341C2211yescharacteristic
188#2341C2211yescharacteristic
189#2341C2211yescharacteristic
190#2341C2211yescharacteristic
191#2341C2213yes—
192#2341C2211yescharacteristic
193#2341C2211yescharacteristic
194#2341C2213yes—
195#2341C2213yes—
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#2283C2213yescomplemented
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—
249Q82—44no—
250D4×Q8—28no—
251#548—28no—
252#548—44no—
253C2×C4⋊Q8C2313yes—
254C2×C4⋊Q8C2313yes—
255C2×C4⋊Q8C2313yes—
256C2×C4⋊Q8C2313yes—
257C2×#126C2313yes—
258C2×#126C2316yes—
259C2×#124C2313yes—
260C2×#124C2313yes—
261C2×#124C2316yes—
262C2×#123C2313yes—
263C2×#123C2313yes—
264C2×C22⋊Q8C2313yes—
265C2×C22⋊Q8C2313yes—
266C2×C22⋊Q8C2313yes—
267C2×C22⋊Q8C2316yes—
268C2×C22⋊Q8C2313yes—
269C2×C22⋊Q8C2313yes—
270C2×#121C2313yes—
271C2×#121C2313yes—
272C2×#120C2313yes—
273#519—28no—
274#519—44no—
275C4×#41—28no—
276C4×#41—44no—
277C2×C4×Q8—44no—
278C2×C4×Q8C2313yes—
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×Q8C2311yescharacteristic
290C2×C4×Q8C2313yes—
291C2×C4×Q8C2313yes—
292C2×C4×Q8C2313yes—
293C2×C4×Q8C2313yes—
294C2×C4×Q8C2313yes—
295C2×C4×Q8C2313yes—
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×D4C2313yes—
305C2×#117C2313yes—
306C2×#117C2313yes—
307C2×#117C2313yes—
308C2×#117C2313yes—
309C2×#117C2313yes—
310C2×#117C2313yes—
311C22×C4⋊C4C2313yes—
312C22×C22⋊C4C2313yes—
313C22×C22⋊C4C2313yes—
314C22×C42C2313yes—
315C22×C42C2313yes—
316C22×C42C2313yes—
317#401C2313yes—
318#401C2316yes—
319#400C2313yes—
320#400C2313yes—
321#400C2316yes—
322#400C2311yescharacteristic
323#400C2313yes—
324#400C2313yes—
325#400C2313yes—
326#400C2313yes—
327#400C2316yes—
328#400C2316yes—
329#399C2313yes—
330#399C2313yes—
331#399C2316yes—
332#398C2316yes—
333#398C2313yes—
334#398C2313yes—
335#398C2313yes—
336#397C2316yes—
337#397C2313yes—
338#397C2316yes—
339#397C2316yes—
340#397C2313yes—
341#397C2313yes—
342#397C2313yes—
343#397C2313yes—
344#397C2313yes—
345#397C2313yes—
346#397C2313yes—
347#397C2316yes—
348#397C2316yes—
349#397C2316yes—
350#397C2316yes—
351#397C2316yes—
352#397C2316yes—
353#397C2316yes—
354#397C2316yes—
355#397C2316yes—
356#396C2313yes—
357#396C2316yes—
358#396C2313yes—
359#396C2313yes—
360#396C2316yes—
361#396C2316yes—
362#395C2313yes—
363#395C2316yes—
364#394C2316yes—
365#394C2311yescharacteristic
366#394C2313yes—
367#394C2316yes—
368#394C2313yes—
369#394C2316yes—
370#394C2316yes—
371#394C2313yes—
372#393C2316yes—
373#393C2311yescharacteristic
374#393C2313yes—
375#393C2316yes—
376#393C2316yes—
377#393C2316yes—
378#393C2316yes—
379#393C2311yescharacteristic
380#392C2316yes—
381#391C2316yes—
382#391C2313yes—
383#391C2313yes—
384#391C2316yes—
385#391C2311yescharacteristic
386#391C2316yes—
387#391C2313yes—
388#391C2313yes—
389#391C2313yes—
390#391C2313yes—
391#391C2313yes—
392#391C2313yes—
393#391C2313yes—
394#391C2313yes—
395#391C2313yes—
396#391C2313yes—
397#391C2316yes—
398#390C2316yes—
399#390C2313yes—
400#390C2313yes—
401#390C2313yes—
402#390C2313yes—
403#390C2313yes—
404#390C2316yes—
405#390C2316yes—
406#390C2313yes—
407#390C2313yes—
408#390C2313yes—
409#390C2313yes—
410#390C2316yes—
411#390C2313yes—
412#390C2313yes—
413#390C2313yes—
414#390C2313yes—
415#390C2313yes—
416#390C2313yes—
417#390C2313yes—
418#389C2313yes—
419#389C2313yes—
420#389C2313yes—
421#389C2313yes—
422#389C2313yes—
423#389C2313yes—
424#389C2313yes—
425#389C2313yes—
426#389C2316yes—
427#389C2313yes—
428#389C2313yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#388C2313yes—
437#388C2313yes—
438#388C2313yes—
439#388C2316yes—
440#388C2316yes—
441#388C2316yes—
442#388C2313yes—
443#388C2313yes—
444#388C2313yes—
445#388C2313yes—
446#388C2313yes—
447#388C2316yes—
448#388C2313yes—
449#388C2316yes—
450#388C2311yescharacteristic
451#388C2311yescharacteristic
452#388C2313yes—
453#388C2316yes—
454#388C2316yes—
455#388C2316yes—
456#388C2316yes—
457#388C2316yes—
458#388C2313yes—
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#387C2313yes—
474#387C2313yes—
475#387C2313yes—
476#387C2316yes—
477#387C2316yes—
478#387C2313yes—
479#387C2313yes—
480#387C2313yes—
481#387C2316yes—
482#387C2313yes—
483#387C2313yes—
484#387C2316yes—
485#387C2313yes—
486#387C2313yes—
487#387C2316yes—
488#387C2316yes—
489#387C2316yes—
490#387C2316yes—
491#387C2316yes—
492#387C2316yes—
493#387C2316yes—
494#387C2316yes—
495#387C2316yes—
496#386C2316yes—
497#386C2313yes—
498#386C2313yes—
499#386C2311yescharacteristic
500#386C2311yescharacteristic
501#386C2313yes—
502#386C2316yes—
503#386C2313yes—
504#386C2313yes—
505#386C2316yes—
506#386C2316yes—
507#386C2316yes—
508#386C2316yes—
509#385C2313yes—
510#385C2313yes—
511#385C2313yes—
512#385C2313yes—
513#385C2313yes—
514#385C2313yes—
515#385C2316yes—
516#385C2316yes—
517#385C2313yes—
518#385C2313yes—
519#385C2316yes—
520#385C2316yes—
521#385C2313yes—
522#384C2313yes—
523#384C2313yes—
524#383C2311yescharacteristic
525#383C2311yescharacteristic
526#383C2313yes—
527#383C2316yes—
528#382C2313yes—
529#382C2313yes—
530#382C2313yes—
531#382C2313yes—
532#382C2313yes—
533#382C2313yes—
534#382C2316yes—
535#382C2313yes—
536#382C2313yes—
537#381C2316yes—
538#381C2316yes—
539#381C2313yes—
540#381C2313yes—
541#381C2311yescharacteristic
542#381C2311yescharacteristic
543#381C2313yes—
544#381C2316yes—
545#381C2313yes—
546#380C2313yes—
547#380C2316yes—
548#380C2313yes—
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#380C2313yes—
562#380C2313yes—
563#380C2313yes—
564#380C2313yes—
565#380C2313yes—
566#380C2313yes—
567#380C2313yes—
568#379C2313yes—
569#379C2316yes—
570#379C2316yes—
571#379C2313yes—
572#379C2313yes—
573#379C2316yes—
574C4×C4⋊C4C2313yes—
575C4×C4⋊C4C2313yes—
576C4×C4⋊C4C2313yes—
577C4×C4⋊C4C2316yes—
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⋊C4C2316yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C22⋊C4C2313yes—
596C4×C22⋊C4C2313yes—
597C4×C22⋊C4C2313yes—
598C4×C22⋊C4C2313yes—
599C4×C22⋊C4C2313yes—
600C4×C22⋊C4C2316yes—
601C4×C22⋊C4C2311yescharacteristic
602C4×C22⋊C4C2311yescharacteristic
603C4×C22⋊C4C2316yes—
604C4×C22⋊C4C2313yes—
605C4×C22⋊C4C2313yes—
606C4×C22⋊C4C2313yes—
607C4×C22⋊C4C2316yes—
608C4×C22⋊C4C2316yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2316yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2316yes—
623#376C2313yes—
624#376C2313yes—
625#376C2316yes—
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×Q8C2411yescharacteristic
653C22×Q8C2416yes—
654C22×Q8C2411yescharacteristic
655C22×D4—212no—
656C22×D4—212no—
657C22×D4—46no—
658C22×D4C2413yes—
659C22×D4C2411yescharacteristic
660C22×D4C2413yes—
661C22×D4C2416yes—
662C22×D4C2413yes—
663C22×D4C2413yes—
664C23×C4—212no—
665C23×C4—212no—
666C23×C4—46no—
667C23×C4C2413yes—
668C23×C4C2413yes—
669C23×C4C2411yescharacteristic
670C23×C4C2411yescharacteristic
671C23×C4C2413yes—
672C23×C4C2413yes—
673C23×C4C2413yes—
674C23×C4C2413yes—
675C23×C4C2413yes—
676C23×C4C2413yes—
677C23×C4C2413yes—
678C23×C4C2413yes—
679C23×C4C2413yes—
680C4⋊Q8—212no—
681C4⋊Q8—46no—
682C4⋊Q8—46no—
683C4⋊Q8—46no—
684#126—46no—
685#126—412no—
686#124—212no—
687#124—46no—
688#124—412no—
689#123—46no—
690#123—46no—
691C22⋊Q8—212no—
692C22⋊Q8—212no—
693C22⋊Q8—212no—
694C22⋊Q8—412no—
695C22⋊Q8—46no—
696C22⋊Q8—46no—
697#121—212no—
698#121—46no—
699#120—46no—
700C4×Q8—24no—
701C4×Q8—24no—
702C4×Q8—212no—
703C4×Q8—212no—
704C4×Q8—24no—
705C4×Q8—24no—
706C4×Q8—24no—
707C4×Q8—24no—
708C4×Q8—24no—
709C4×Q8—24no—
710C4×Q8—24no—
711C4×Q8—24no—
712C4×Q8—24no—
713C4×Q8—46no—
714C4×Q8—46no—
715C4×Q8—46no—
716C4×Q8—46no—
717C4×Q8—46no—
718C4×D4—212no—
719C4×D4—212no—
720C4×D4—212no—
721C4×D4—212no—
722C4×D4—46no—
723C4×D4—46no—
724C4×D4—46no—
725C4×D4—46no—
726C4×D4—46no—
727#117—212no—
728#117—212no—
729#117—212no—
730#117—46no—
731#117—46no—
732#117—46no—
733C2×C4⋊C4—46no—
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⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2416yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2416yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2416yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2416yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2411yescharacteristic
772C2×C4⋊C4C2411yescharacteristic
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2413yes—
775C2×C22⋊C4—46no—
776C2×C22⋊C4—46no—
777C2×C22⋊C4C2411yescharacteristic
778C2×C22⋊C4C2411yescharacteristic
779C2×C22⋊C4C2413yes—
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2411yescharacteristic
783C2×C22⋊C4C2416yes—
784C2×C22⋊C4C2411yescharacteristic
785C2×C22⋊C4C2411yescharacteristic
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2416yes—
791C2×C22⋊C4C2411yescharacteristic
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2413yes—
798C2×C22⋊C4C2411yescharacteristic
799C2×C22⋊C4C2416yes—
800C2×C22⋊C4C2411yescharacteristic
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2416yes—
808C2×C22⋊C4C2416yes—
809C2×C22⋊C4C2416yes—
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2413yes—
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2416yes—
816C2×C22⋊C4C2416yes—
817C2×C22⋊C4C2416yes—
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2416yes—
821C2×C22⋊C4C2411yescharacteristic
822C2×C22⋊C4C2416yes—
823C2×C22⋊C4C2411yescharacteristic
824C2×C22⋊C4C2416yes—
825C2×C22⋊C4C2413yes—
826C2×C22⋊C4C2413yes—
827C2×C42—212no—
828C2×C42—46no—
829C2×C42—46no—
830C2×C42C2413yes—
831C2×C42C2413yes—
832C2×C42C2413yes—
833C2×C42C2413yes—
834C2×C42C2416yes—
835C2×C42C2413yes—
836C2×C42C2413yes—
837C2×C42C2413yes—
838C2×C42C2413yes—
839C2×C42C2413yes—
840C2×C42C2413yes—
841C2×C42C2413yes—
842C2×C42C2413yes—
843C2×C42C2411yescharacteristic
844C2×C42C2411yescharacteristic
845C2×C42C2413yes—
846C2×C42C2416yes—
847C2×C42C2413yes—
848C2×C42C2413yes—
849C2×C42C2413yes—
850C2×C42C2413yes—
851C2×C42C2416yes—
852C2×C42C2416yes—
853C2×C42C2413yes—
854C2×C42C2411yescharacteristic
855#95C2411yescharacteristic
856#95C2411yescharacteristic
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2411yescharacteristic
864#95C2411yescharacteristic
865#95C2413yes—
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2416yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2416yes—
877#95C2416yes—
878#95C2416yes—
879#95C2411yescharacteristic
880#95C2411yescharacteristic
881#95C2411yescharacteristic
882#95C2411yescharacteristic
883#95C2413yes—
884#95C2411yescharacteristic
885#95C2413yes—
886#95C2413yes—
887#95C2411yescharacteristic
888#95C2411yescharacteristic
889#95C2413yes—
890#95C2413yes—
891#95C2413yes—
892#95C2413yes—
893#95C2413yes—
894#95C2413yes—
895#95C2416yes—
896#95C2416yes—
897#95C2416yes—
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2413yes—
902#95C2416yes—
903#95C2413yes—
904#95C2411yescharacteristic
905#95C2411yescharacteristic
906#95C2411yescharacteristic
907#95C2411yescharacteristic
908#95C2416yes—
909#95C2411yescharacteristic
910#95C2413yes—
911#95C2413yes—
912#95C2416yes—
913#95C2416yes—
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—22no—
942C2×Q8—41no—
943C2×Q8—41no—
944C2×Q8—46no—
945C2×Q8—46no—
946C2×Q8—46no—
947C2×Q8—416no—
948C2×Q8C2×#41112yes—
949C2×Q8C2×#4114yes—
950C2×Q8C2×#4114yes—
951C2×Q8H(5,𝔽2)14yes—
952C2×D4—22no—
953C2×D4—26no—
954C2×D4—212no—
955C2×D4—26no—
956C2×D4—22no—
957C2×D4—26no—
958C2×D4—26no—
959C2×D4—212no—
960C2×D4—26no—
961C2×D4—26no—
962C2×D4—26no—
963C2×D4—26no—
964C2×D4—448no—
965C2×D4—43no—
966C2×D4—46no—
967C2×D4—41no—
968C2×D4—43no—
969C2×D4—43no—
970C2×D4C2×#41112yes—
971C22×C4—26no—
972C22×C4—26no—
973C22×C4—26no—
974C22×C4—26no—
975C22×C4—22no—
976C22×C4—26no—
977C22×C4—22no—
978C22×C4—26no—
979C22×C4—26no—
980C22×C4—26no—
981C22×C4—26no—
982C22×C4—22no—
983C22×C4—26no—
984C22×C4—26no—
985C22×C4—26no—
986C22×C4—26no—
987C22×C4—26no—
988C22×C4—26no—
989C22×C4—26no—
990C22×C4—22no—
991C22×C4—26no—
992C22×C4—26no—
993C22×C4—41no—
994C22×C4—41no—
995C22×C4—43no—
996C22×C4—43no—
997C22×C4—448no—
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×C4—43no—
1007C22×C4—43no—
1008C22×C4—43no—
1009C22×C4C2×#41112yes—
1010C22×C4C2×#41112yes—
1011C22×C4C2511yescharacteristic
1012C22×C4C2511yescharacteristic
1013C22×C4C2511yescharacteristic
1014C22×C4C2511yescharacteristic
1015C22×C4C2513yes—
1016C22×C4C2511yescharacteristic
1017C22×C4C2513yes—
1018C22×C4C2513yes—
1019C22×C4C2513yes—
1020C22×C4C2511yescharacteristic
1021C22×C4C2513yes—
1022C22×C4C2513yes—
1023C22×C4C2513yes—
1024C22×C4C2513yes—
1025C22×C4C2511yescharacteristic
1026C22×C4C2513yes—
1027C22×C4C2513yes—
1028C22×C4C2513yes—
1029C22×C4C2511yescharacteristic
1030C22×C4C2511yescharacteristic
1031C22×C4C2513yes—
1032C22×C4C2511yescharacteristic
1033C22×C4C2511yescharacteristic
1034C22×C4C2513yes—
1035C22×C4C2511yescharacteristic
1036C22×C4C2511yescharacteristic
1037C22×C4C2513yes—
1038C4⋊C4—26no—
1039C4⋊C4—26no—
1040C4⋊C4—26no—
1041C4⋊C4—26no—
1042C4⋊C4—26no—
1043C4⋊C4—26no—
1044C4⋊C4—26no—
1045C4⋊C4—26no—
1046C4⋊C4—26no—
1047C4⋊C4—26no—
1048C4⋊C4—212no—
1049C4⋊C4—26no—
1050C4⋊C4—26no—
1051C4⋊C4—26no—
1052C4⋊C4—26no—
1053C4⋊C4—26no—
1054C4⋊C4—26no—
1055C4⋊C4—26no—
1056C4⋊C4—26no—
1057C4⋊C4—26no—
1058C4⋊C4—46no—
1059C4⋊C4—41no—
1060C4⋊C4—41no—
1061C4⋊C4—43no—
1062C4⋊C4—43no—
1063C4⋊C4—43no—
1064C4⋊C4—43no—
1065C4⋊C4—43no—
1066C4⋊C4—43no—
1067C4⋊C4—43no—
1068C4⋊C4—43no—
1069C4⋊C4—43no—
1070C4⋊C4—43no—
1071C4⋊C4—43no—
1072C4⋊C4—46no—
1073C4⋊C4—43no—
1074C4⋊C4—43no—
1075C4⋊C4—43no—
1076C4⋊C4—43no—
1077C4⋊C4—43no—
1078C4⋊C4—46no—
1079C22⋊C4—26no—
1080C22⋊C4—22no—
1081C22⋊C4—212no—
1082C22⋊C4—26no—
1083C22⋊C4—26no—
1084C22⋊C4—212no—
1085C22⋊C4—26no—
1086C22⋊C4—22no—
1087C22⋊C4—26no—
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—41no—
1100C22⋊C4—43no—
1101C22⋊C4—46no—
1102C22⋊C4—46no—
1103C22⋊C4—41no—
1104C22⋊C4—43no—
1105C22⋊C4—41no—
1106C22⋊C4—43no—
1107C22⋊C4—46no—
1108C22⋊C4—43no—
1109C22⋊C4—43no—
1110C22⋊C4—41no—
1111C22⋊C4—43no—
1112C22⋊C4—43no—
1113C22⋊C4—43no—
1114C22⋊C4—43no—
1115C22⋊C4—46no—
1116C22⋊C4—43no—
1117C22⋊C4—46no—
1118C22⋊C4—43no—
1119C22⋊C4—46no—
1120C22⋊C4—43no—
1121C22⋊C4—43no—
1122C22⋊C4—43no—
1123C22⋊C4—46no—
1124C22⋊C4—46no—
1125C22⋊C4—43no—
1126C22⋊C4—43no—
1127C22⋊C4—46no—
1128C22⋊C4—46no—
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—22no—
1144C42—41no—
1145C42—43no—
1146C42—43no—
1147C42—43no—
1148C42—43no—
1149C42—46no—
1150C42—43no—
1151C42—43no—
1152C42—46no—
1153C42—46no—
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—23no—
1170C23—21no—
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—44no—
1192Q8—412no—
1193Q8—166no—
1194Q8#551116yes—
1195D4—224no—
1196D4—424no—
1197D4—44no—
1198D4—412no—
1199D4—412no—
1200D4—86no—
1201C2×C4—21no—
1202C2×C4—23no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—23no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—224no—
1210C2×C4—224no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—23no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—23no—
1218C2×C4—21no—
1219C2×C4—23no—
1220C2×C4—23no—
1221C2×C4—23no—
1222C2×C4—23no—
1223C2×C4—23no—
1224C2×C4—23no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—23no—
1231C2×C4—23no—
1232C2×C4—23no—
1233C2×C4—23no—
1234C2×C4—23no—
1235C2×C4—23no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—23no—
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—23no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—23no—
1254C2×C4—23no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—23no—
1258C2×C4—23no—
1259C2×C4—23no—
1260C2×C4—23no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—23no—
1266C2×C4—23no—
1267C2×C4—21no—
1268C2×C4—23no—
1269C2×C4—23no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—23no—
1273C2×C4—23no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—412no—
1278C2×C4—44no—
1279C2×C4—44no—
1280C2×C4—412no—
1281C2×C4—412no—
1282C2×C4—412no—
1283C2×C4—86no—
1284C2×C4—86no—
1285C2×C4—86no—
1286C2×C4—86no—
1287C2×C4—86no—
1288C2×C4C22×#4112yes—
1289C2×C4C22×#4116yes—
1290C2×C4C22×#4116yes—
1291C2×C4C22×#4116yes—
1292C2×C4C2×H(5,𝔽2)16yes—
1293C2×C4#58512yes—
1294C2×C4#58512yes—
1295C22—22no—
1296C22—22no—
1297C22—26no—
1298C22—22no—
1299C22—22no—
1300C22—26no—
1301C22—22no—
1302C22—22no—
1303C22—26no—
1304C22—43no—
1305C22—41no—
1306C22—41no—
1307C22—43no—
1308C22—41no—
1309C22—41no—
1310C22—43no—
1311C22—41no—
1312C22—41no—
1313C22—43no—
1314C22—41no—
1315C22—41no—
1316C22—43no—
1317C22—43no—
1318C22—43no—
1319C22—43no—
1320C22—43no—
1321C22—43no—
1322C22—43no—
1323C22—824no—
1324C22C23×#4111yescharacteristic
1325C22C23×#4111yescharacteristic
1326C22C22×H(5,𝔽2)11yescharacteristic
1327C22C2×#58511yescharacteristic
1328C22C2×#58511yescharacteristic
1329C22C2×#58511yescharacteristic
1330C222−1+611yescharacteristic
1331C4—22no—
1332C4—22no—
1333C4—22no—
1334C4—26no—
1335C4—43no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—43no—
1340C4—41no—
1341C4—41no—
1342C4—43no—
1343C4—43no—
1344C4—43no—
1345C4—41no—
1346C4—43no—
1347C4—43no—
1348C4—43no—
1349C4—41no—
1350C4—43no—
1351C4—43no—
1352C4—43no—
1353C4—41no—
1354C4—41no—
1355C4—41no—
1356C4—43no—
1357C4C2×#551112yes—
1358C2—42no—
1359C2—46no—
1360C2—42no—
1361C2—83no—
1362C2C22×#55111yescharacteristic
1363C2#6279311yescharacteristic
1364C2#6281611yescharacteristic
1365C2#6289711yescharacteristic
1366C2#6300511yescharacteristic
1367C2#6300911yescharacteristic
1368C2#6302011yescharacteristic
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. #59902C2semidirect
2. #59486C2semidirect
3. #59381C2semidirect
4. #59282C2semidirect
5. #59202C2semidirect
6. #45192C2semidirect
7. #45188C2semidirect
8. #44992C2semidirect
9. #44961C2semidirect
10. #39070C2semidirect
11. #39042C2semidirect
12. #38063C2semidirect
13. #37859C2semidirect
14. #36585C2semidirect
15. #36578C2semidirect
16. #36456C2semidirect
17. #36432C2semidirect
19. #36381C2semidirect
20. #36204C2semidirect
21. #35948C2semidirect
22. #35898C2semidirect
23. #35723C2semidirect
24. #35711C2semidirect
25. #34849C2semidirect
26. #34291C2semidirect
27. #34262C2semidirect
28. #34197C2semidirect
29. #34174C2semidirect
30. C4×#548C2semidirect
31. C22⋊C4×#41C2semidirect
33. C2×Q82C22semidirect
41. C22×C4×Q8C22semidirect
42. #2860C22semidirect
43. #2857C22semidirect
44. #2855C22semidirect
45. #2854C22semidirect
47. #2786C22semidirect
48. #2761C22semidirect
49. #2751C22semidirect
50. #2751C22semidirect
51. #2749C22semidirect
52. #2745C22semidirect
53. #2740C22semidirect
54. #2739C22semidirect
55. #2737C22semidirect
59. #2723C22semidirect
61. #2644C22semidirect
62. #2640C22semidirect
65. #2597C22semidirect
66. #2595C22semidirect
67. #2592C22semidirect
68. #2581C22semidirect
69. #2578C22semidirect
70. #2577C22semidirect
72. #2576C22semidirect
74. #2574C22semidirect
75. #2574C22semidirect
78. #2569C22semidirect
79. #2568C22semidirect
80. #2564C22semidirect
81. #2563C22semidirect
84. #2560C22semidirect
85. #2557C22semidirect
86. #2553C22semidirect
87. #2547C22semidirect
88. #2538C22semidirect
90. #2531C22semidirect
91. #2530C22semidirect
93. #2527C22semidirect
94. #2526C22semidirect
95. #2523C22semidirect
96. #2517C22semidirect
97. #2513C22semidirect
98. #2513C22semidirect
99. #2513C22semidirect
100. #2513C22semidirect
101. #2512C22semidirect
102. #2512C22semidirect
103. #2504C22semidirect
105. #2499C22semidirect
106. #2497C22semidirect
107. #2496C22semidirect
108. #2494C22semidirect
109. #2494C22semidirect
110. #2494C22semidirect
111. #2494C22semidirect
112. #2493C22semidirect
113. #2493C22semidirect
114. #2492C22semidirect
115. #2492C22semidirect
116. #2491C22semidirect
117. #2491C22semidirect
118. #2487C22semidirect
120. #2485C22semidirect
123. #2467C22semidirect
124. #2461C22semidirect
125. #2452C22semidirect
126. #2452C22semidirect
127. #2451C22semidirect
128. #2451C22semidirect
129. #2448C22semidirect
130. #2448C22semidirect
131. #2447C22semidirect
132. #2447C22semidirect
133. #2446C22semidirect
134. #2446C22semidirect
137. #2439C22semidirect
138. #2439C22semidirect
142. #2423C22semidirect
143. #2422C22semidirect
144. #2421C22semidirect
145. #2421C22semidirect
146. #2421C22semidirect
147. #2420C22semidirect
148. #2419C22semidirect
153. #2401C22semidirect
154. #2398C22semidirect
157. #2373C22semidirect
158. #2372C22semidirect
159. #2368C22semidirect
160. #2367C22semidirect
161. #2365C22semidirect
163. #2362C22semidirect
164. #2361C22semidirect
165. #2360C22semidirect
166. #2357C22semidirect
167. #2357C22semidirect
168. #2356C22semidirect
169. #2355C22semidirect
171. #2352C22semidirect
172. #2351C22semidirect
173. #2351C22semidirect
174. #2351C22semidirect
175. #2351C22semidirect
176. #2351C22semidirect
177. #2351C22semidirect
178. Q8×C4⋊C4C22semidirect
179. Q8×C4⋊C4C22semidirect
182. #2346C22semidirect
183. #2346C22semidirect
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. #2283C22semidirect
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
#599022
#594862
#593812
#592822
#592022
#451922
#451882
#449922
#449612
#390702
#390422
#380632
#378592
#365852
#365782
#364562
#364322
#364282
#363812
#362042
#359482
#358982
#357232
#357112
#348492
#342912
#342622
#341972
#341742
C4×#5482
C22⋊C4×#412