Finite Group Databasebeta

← #7647739

Subgroups — #7647739

Order 512.

4996 conjugacy classes of subgroups.

The subgroup lattice has 1029 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41042C218yesmaximal, complemented
2#41013C218yesmaximal, complemented
3#39810C214yesmaximal, complemented
4#39070C214yesmaximal, complemented
5#38250C214yesmaximal, complemented
6#38238C214yesmaximal, complemented
7#37629C212yesmaximal, complemented
8#37622C211yesmaximal, characteristic, complemented
9#37614C211yesmaximal, characteristic
10#37432C212yesmaximal, complemented
11#37371C214yesmaximal, complemented
12#37322C212yesmaximal, complemented
13#35611C214yesmaximal, complemented
14#35331C212yesmaximal, complemented
15#35296C212yesmaximal, complemented
16#35285C211yesmaximal, characteristic, complemented
17#35198C212yesmaximal, complemented
18#35197C212yesmaximal, complemented
19#35192C211yesmaximal, characteristic, complemented
20#34954C212yesmaximal, complemented
21#34210C211yesmaximal, characteristic, complemented
22#34151C211yesmaximal, characteristic, complemented
23#34085C211yesmaximal, characteristic, complemented
24C2×#542C2214yescomplemented
25C2×#533C2211yescharacteristic
26C22×#127C2211yescharacteristic
27C2×#529C2211yescharacteristic
28C2×#518C2212yes—
29#2864C2212yescomplemented
30#2862C2212yescomplemented
31#2860C2214yescomplemented
32#2858C2212yes—
33#2858C2212yes—
34#2858C2214yescomplemented
35#2854C2214yescomplemented
36#2850C2214yescomplemented
37#2830C2218yescomplemented
38#2818C2214yes—
39#2814C2214yes—
40#2808C2218yescomplemented
41#2800C2218yescomplemented
42#2797C2218yescomplemented
43#2797C2218yescomplemented
44#2786C2218yescomplemented
45#2752C2218yescomplemented
46#2751C2218yescomplemented
47#2740C2218yescomplemented
48#2736C2218yes—
49#2735C2218yes—
50#2730C2218yescomplemented
51#2712C2218yescomplemented
52#2710C2218yescomplemented
53#2700C2218yescomplemented
54#2697C2218yes—
55#2684C2218yes—
56#2665C2214yes—
57#2664C2214yescomplemented
58#2662C2218yescomplemented
59#2657C2212yes—
60#2648C2218yescomplemented
61#2644C2214yescomplemented
62#2644C2214yescomplemented
63#2641C2214yes—
64#2641C2212yes—
65#2640C2214yescomplemented
66#2640C2214yescomplemented
67#2638C2218yescomplemented
68#2628C2212yescomplemented
69#2625C2212yes—
70#2624C2212yes—
71#2621C2212yescomplemented
72#2619C2212yes—
73#2619C2212yes—
74#2613C2214yes—
75#2605C2214yescomplemented
76#2602C2218yescomplemented
77#2595C2218yescomplemented
78#2593C2218yescomplemented
79#2592C2212yescomplemented
80#2584C2212yescomplemented
81#2582C2212yescomplemented
82#2571C2212yescomplemented
83#2561C2218yes—
84#2560C2218yescomplemented
85#2560C2218yescomplemented
86#2557C2218yescomplemented
87#2557C2218yescomplemented
88#2557C2218yescomplemented
89#2551C2212yescomplemented
90#2548C2214yes—
91#2548C2212yes—
92#2548C2212yes—
93#2548C2212yes—
94#2541C2212yes—
95#2538C2212yescomplemented
96#2513C2214yescomplemented
97#2513C2214yescomplemented
98#2513C2214yescomplemented
99#2491C2214yescomplemented
100#2480C2218yes—
101#2474C2218yescomplemented
102#2472C2218yes—
103#2471C2218yescomplemented
104#2466C2218yescomplemented
105#2461C2218yescomplemented
106#2459C2218yescomplemented
107#2457C2218yescomplemented
108#2452C2214yescomplemented
109#2452C2214yescomplemented
110#2452C2214yescomplemented
111#2448C2214yescomplemented
112#2448C2214yescomplemented
113#2447C2214yescomplemented
114#2447C2214yescomplemented
115#2445C2214yescomplemented
116#2445C2214yescomplemented
117#2439C2214yes—
118#2439C2214yes—
119#2435C2214yes—
120#2435C2214yes—
121#2435C2212yes—
122#2433C2212yes—
123#2427C2214yescomplemented
124#2426C2214yescomplemented
125#2420C2214yescomplemented
126#2415C2214yes—
127#2415C2218yescomplemented
128#2411C2218yes—
129#2408C2214yes—
130#2395C2218yescomplemented
131#2374C2214yes—
132#2373C2214yescomplemented
133#2370C2212yescomplemented
134#2367C2212yescomplemented
135#2366C2214yes—
136#2366C2214yes—
137#2363C2212yes—
138#2362C2212yes—
139D4×C22⋊C4C2214yes—
140D4×C22⋊C4C2214yes—
141#2336C2214yescomplemented
142#2332C2214yes—
143#2331C2211yescharacteristic, complemented
144#2331C2211yescharacteristic, complemented
145#2331C2214yescomplemented
146#2328C2212yes—
147#2328C2212yes—
148#2328C2214yescomplemented
149#2327C2211yescharacteristic, complemented
150#2327C2211yescharacteristic, complemented
151#2324C2214yescomplemented
152#2323C2212yes—
153#2323C2212yes—
154#2319C2214yescomplemented
155#2309C2214yes—
156#2309C2212yes—
157C4×#127C2212yes—
158C4×#127C2212yes—
159C4×#124C2214yescomplemented
160C4×#124C2214yescomplemented
161#2298C2214yes—
162#2298C2212yescomplemented
163#2295C2214yescomplemented
164#2295C2212yescomplemented
165#2295C2211yescharacteristic, complemented
166#2293C2212yes—
167#2293C2214yescomplemented
168#2293C2214yescomplemented
169#2293C2211yescharacteristic, complemented
170#2290C2212yes—
171#2285C2211yescharacteristic
172#2283C2211yescharacteristic
173C42×Q8C2212yescomplemented
174C42×Q8C2211yescharacteristic, complemented
175C42×D4C2211yescharacteristic, complemented
176C4×#117C2211yescharacteristic
177C4×#117C2211yescharacteristic
178C4×#117C2212yescomplemented
179C23×D4C2312yes—
180C23×D4C2312yes—
181C23×D4C2312yes—
182#542—416no—
183#533—28no—
184C2×C4⋊Q8C2311yescharacteristic
185C2×C4⋊Q8C2311yescharacteristic
186C2×C4⋊Q8C2314yes—
187C2×C4⋊Q8C2314yes—
188C2×#127—28no—
189C2×#127C2312yes—
190C2×#127C2312yes—
191C2×#127C2312yes—
192C2×#127C2312yes—
193C2×#127C2314yes—
194#529—28no—
195C2×#126C2312yes—
196C2×#126C2318yes—
197C2×#125C2311yescharacteristic
198C2×#125C2312yes—
199C2×#124C2311yescharacteristic
200C2×#124C2314yes—
201C2×#124C2314yes—
202C2×#124C2318yes—
203C2×#124C2314yes—
204C2×#124C2318yes—
205C2×#124C2318yes—
206C2×#123C2312yes—
207C2×#123C2318yes—
208C2×#123C2318yes—
209C2×C22⋊Q8C2312yes—
210C2×C22⋊Q8C2312yes—
211C2×C22⋊Q8C2311yescharacteristic
212C2×C22⋊Q8C2318yes—
213C2×C22⋊Q8C2314yes—
214C2×C22⋊Q8C2318yes—
215C2×#121C2311yescharacteristic
216C2×#121C2314yes—
217C2×#121C2314yes—
218C2×#120C2318yes—
219#518—48no—
220C2×C4×Q8C2312yes—
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2312yes—
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2312yes—
226C2×C4×D4C2314yes—
227C2×C4×D4C2312yes—
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2314yes—
230C2×C4×D4C2314yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2312yes—
233C2×C4×D4C2318yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2314yes—
236C2×#117C2312yes—
237C2×#117C2311yescharacteristic
238C2×#117C2312yes—
239C2×#117C2312yes—
240C2×#117C2311yescharacteristic
241C2×#117C2312yes—
242C2×#117C2312yes—
243C2×#117C2318yes—
244C22×C22⋊C4C2318yes—
245C22×C42C2312yes—
246C22×C42C2311yescharacteristic
247#400C2318yes—
248#400C2314yes—
249#399C2314yes—
250#399C2318yes—
251#398C2314yes—
252#398C2314yes—
253#398C2318yes—
254#397C2318yes—
255#397C2318yes—
256#397C2318yes—
257#397C2318yes—
258#397C2318yes—
259#397C2318yes—
260#397C2318yes—
261#397C2314yes—
262#397C2318yes—
263#397C2314yes—
264#397C2318yes—
265#397C2318yes—
266#397C2318yes—
267#397C2318yes—
268#397C2318yes—
269#396C2318yes—
270#396C2318yes—
271#396C2318yes—
272#396C2318yes—
273#396C2318yes—
274#395C2318yes—
275#395C2314yes—
276#394C2314yes—
277#394C2314yes—
278#394C2318yes—
279#394C2314yes—
280#394C2318yes—
281#394C2318yes—
282#394C2318yes—
283#394C2318yes—
284#394C2318yes—
285#394C2314yes—
286#394C2318yes—
287#394C2318yes—
288#394C2318yes—
289#394C2318yes—
290#394C2318yes—
291#393C2318yes—
292#393C2318yes—
293#393C2318yes—
294#393C2318yes—
295#393C2314yes—
296#393C2318yes—
297#392C2318yes—
298#392C2318yes—
299#392C2314yes—
300#392C2314yes—
301#392C2314yes—
302#392C2314yes—
303#391C2318yes—
304#391C2318yes—
305#391C2312yes—
306#391C2312yes—
307#391C2314yes—
308#391C2314yes—
309#391C2314yes—
310#391C2314yes—
311#391C2318yes—
312#391C2312yes—
313#390C2318yes—
314#390C2318yes—
315#390C2314yes—
316#390C2314yes—
317#390C2314yes—
318#390C2314yes—
319#390C2314yes—
320#390C2314yes—
321#390C2314yes—
322#390C2314yes—
323#390C2318yes—
324#390C2314yes—
325#390C2314yes—
326#390C2318yes—
327#390C2314yes—
328#390C2318yes—
329#390C2314yes—
330#390C2314yes—
331#390C2314yes—
332#390C2312yes—
333#390C2318yes—
334#390C2314yes—
335#390C2314yes—
336#390C2314yes—
337#390C2314yes—
338#389C2314yes—
339#389C2314yes—
340#389C2314yes—
341#389C2312yes—
342#389C2312yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2318yes—
349#389C2314yes—
350#389C2312yes—
351#389C2312yes—
352#389C2314yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2314yes—
358#388C2314yes—
359#388C2318yes—
360#388C2318yes—
361#388C2314yes—
362#388C2314yes—
363#388C2314yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2314yes—
373#388C2318yes—
374#388C2318yes—
375#388C2314yes—
376#388C2314yes—
377#388C2314yes—
378#388C2314yes—
379#387C2314yes—
380#387C2314yes—
381#387C2314yes—
382#387C2314yes—
383#387C2314yes—
384#387C2314yes—
385#387C2314yes—
386#387C2314yes—
387#387C2314yes—
388#387C2314yes—
389#387C2318yes—
390#387C2318yes—
391#387C2314yes—
392#387C2318yes—
393#387C2314yes—
394#387C2314yes—
395#387C2314yes—
396#386C2318yes—
397#386C2318yes—
398#386C2318yes—
399#386C2318yes—
400#386C2318yes—
401#386C2318yes—
402#386C2318yes—
403#386C2318yes—
404#386C2318yes—
405#386C2318yes—
406#386C2314yes—
407#385C2318yes—
408#385C2318yes—
409#385C2314yes—
410#385C2318yes—
411#384C2312yes—
412#383C2312yes—
413#382C2314yes—
414#382C2314yes—
415#382C2311yescharacteristic
416#382C2311yescharacteristic
417#382C2312yes—
418#381C2318yes—
419#381C2318yes—
420#381C2312yes—
421#380C2318yes—
422#380C2312yes—
423#380C2314yes—
424#380C2312yes—
425#380C2312yes—
426#379C2318yes—
427#379C2318yes—
428#379C2318yes—
429#379C2318yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2312yes—
434C4×C4⋊C4C2312yes—
435C4×C4⋊C4C2312yes—
436C4×C4⋊C4C2312yes—
437C4×C4⋊C4C2312yes—
438C4×C4⋊C4C2312yes—
439C4×C4⋊C4C2314yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2312yes—
442C4×C4⋊C4C2314yes—
443C4×C4⋊C4C2312yes—
444C4×C4⋊C4C2312yes—
445C4×C4⋊C4C2312yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2312yes—
449C4×C4⋊C4C2312yes—
450C4×C4⋊C4C2311yescharacteristic
451C4×C22⋊C4C2318yes—
452C4×C22⋊C4C2318yes—
453C4×C22⋊C4C2318yes—
454C4×C22⋊C4C2312yes—
455C4×C22⋊C4C2312yes—
456C4×C22⋊C4C2314yes—
457C4×C22⋊C4C2314yes—
458C4×C22⋊C4C2314yes—
459C4×C22⋊C4C2312yes—
460C4×C22⋊C4C2312yes—
461C4×C22⋊C4C2312yes—
462C4×C22⋊C4C2312yes—
463C4×C22⋊C4C2312yes—
464#376C2314yes—
465#376C2311yescharacteristic
466#376C2311yescharacteristic
467#376C2312yes—
468#376C2312yes—
469#376C2312yes—
470C43C2311yescharacteristic
471C43C2311yescharacteristic
472C43C2312yes—
473C43C2314yes—
474C43C2312yes—
475C25C2414yes—
476C22×Q8C2412yes—
477C22×Q8C2411yescharacteristic
478C22×Q8C2412yes—
479C22×Q8C2418yes—
480C22×D4—28no—
481C22×D4—28no—
482C22×D4—28no—
483C22×D4—44no—
484C22×D4—44no—
485C22×D4—48no—
486C22×D4—84no—
487C22×D4C2411yescharacteristic
488C22×D4C2414yes—
489C22×D4C2414yes—
490C22×D4C2414yes—
491C22×D4C2414yes—
492C22×D4C2412yes—
493C22×D4C2414yes—
494C22×D4C2414yes—
495C22×D4C2418yes—
496C22×D4C2418yes—
497C23×C4C2412yes—
498C23×C4C2411yescharacteristic
499C23×C4C2411yescharacteristic
500C23×C4C2418yes—
501C23×C4C2418yes—
502C23×C4C2414yes—
503C23×C4C2411yescharacteristic
504C4⋊Q8—24no—
505C4⋊Q8—24no—
506C4⋊Q8—48no—
507C4⋊Q8—48no—
508#127—28no—
509#127—28no—
510#127—28no—
511#127—28no—
512#127—48no—
513#126—28no—
514#126—416no—
515#125—24no—
516#125—28no—
517#124—24no—
518#124—416no—
519#124—48no—
520#124—48no—
521#124—48no—
522#124—88no—
523#124—88no—
524#123—28no—
525#123—416no—
526#123—88no—
527C22⋊Q8—24no—
528C22⋊Q8—28no—
529C22⋊Q8—28no—
530C22⋊Q8—416no—
531C22⋊Q8—48no—
532C22⋊Q8—88no—
533#121—24no—
534#121—48no—
535#121—48no—
536#120—88no—
537C4×Q8—24no—
538C4×Q8—28no—
539C4×Q8—28no—
540C4×Q8—28no—
541C4×Q8—44no—
542C4×Q8—44no—
543C4×D4—28no—
544C4×D4—24no—
545C4×D4—216no—
546C4×D4—44no—
547C4×D4—48no—
548C4×D4—48no—
549C4×D4—48no—
550C4×D4—416no—
551C4×D4—84no—
552C4×D4—84no—
553#117—28no—
554#117—28no—
555#117—24no—
556#117—28no—
557#117—42no—
558#117—44no—
559#117—44no—
560#117—88no—
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2412yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2412yes—
567C2×C4⋊C4C2412yes—
568C2×C4⋊C4C2412yes—
569C2×C4⋊C4C2412yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2411yescharacteristic
572C2×C4⋊C4C2412yes—
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C2412yes—
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2418yes—
583C2×C4⋊C4C2418yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2418yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2418yes—
593C2×C4⋊C4C2418yes—
594C2×C22⋊C4—416no—
595C2×C22⋊C4C2412yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2412yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2414yes—
600C2×C22⋊C4C2412yes—
601C2×C22⋊C4C2412yes—
602C2×C22⋊C4C2412yes—
603C2×C22⋊C4C2412yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2412yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2418yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2418yes—
618C2×C22⋊C4C2418yes—
619C2×C22⋊C4C2418yes—
620C2×C22⋊C4C2418yes—
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2418yes—
623C2×C22⋊C4C2418yes—
624C2×C22⋊C4C2418yes—
625C2×C22⋊C4C2414yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C2418yes—
631C2×C42—44no—
632C2×C42#4118yes—
633C2×C42C2411yescharacteristic
634C2×C42C2412yes—
635C2×C42C2411yescharacteristic
636C2×C42C2414yes—
637C2×C42C2412yes—
638C2×C42C2411yescharacteristic
639C2×C42C2412yes—
640C2×C42C2412yes—
641C2×C42C2414yes—
642C2×C42C2412yes—
643C2×C42C2414yes—
644C2×C42C2414yes—
645C2×C42C2414yes—
646C2×C42C2414yes—
647C2×C42C2414yes—
648C2×C42C2412yes—
649C2×C42C2412yes—
650C2×C42C2414yes—
651C2×C42C2414yes—
652C2×C42C2414yes—
653C2×C42C2414yes—
654C2×C42C2414yes—
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660#95C2412yes—
661#95C2412yes—
662#95C2412yes—
663#95C2414yes—
664#95C2414yes—
665#95C2412yes—
666#95C2412yes—
667#95C2414yes—
668#95C2412yes—
669#95C2414yes—
670#95C2414yes—
671#95C2414yes—
672#95C2412yes—
673#95C2412yes—
674#95C2414yes—
675#95C2414yes—
676#95C2414yes—
677#95C2418yes—
678#95C2418yes—
679#95C2418yes—
680#95C2412yes—
681#95C2412yes—
682#95C2418yes—
683#95C2418yes—
684#95C2418yes—
685#95C2414yes—
686#95C2414yes—
687#95C2414yes—
688#95C2414yes—
689#95C2414yes—
690#95C2414yes—
691#95C2414yes—
692#95C2414yes—
693#95C2414yes—
694#95C2414yes—
695#95C2418yes—
696#95C2418yes—
697C24—28no—
698C24—44no—
699C24—44no—
700C24—48no—
701C24—48no—
702C24C2518yes—
703C24C2512yes—
704C24C2511yescharacteristic
705C2×Q8—22no—
706C2×Q8—24no—
707C2×Q8—24no—
708C2×Q8—24no—
709C2×Q8—24no—
710C2×Q8—24no—
711C2×Q8—44no—
712C2×Q8—48no—
713C2×Q8—48no—
714C2×Q8—48no—
715C2×D4—24no—
716C2×D4—22no—
717C2×D4—28no—
718C2×D4—28no—
719C2×D4—28no—
720C2×D4—28no—
721C2×D4—28no—
722C2×D4—28no—
723C2×D4—28no—
724C2×D4—28no—
725C2×D4—24no—
726C2×D4—28no—
727C2×D4—28no—
728C2×D4—44no—
729C2×D4—44no—
730C2×D4—44no—
731C2×D4—44no—
732C2×D4—432no—
733C2×D4—44no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—48no—
737C2×D4—48no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—816no—
743C2×D4—816no—
744C22×C4—22no—
745C22×C4—24no—
746C22×C4—22no—
747C22×C4—24no—
748C22×C4—24no—
749C22×C4—24no—
750C22×C4—216no—
751C22×C4—42no—
752C22×C4—44no—
753C22×C4—48no—
754C22×C4—48no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—48no—
758C22×C4—48no—
759C22×C4—48no—
760C22×C4C2×#4114yes—
761C22×C4C2×#4114yes—
762C22×C4C2×#4114yes—
763C22×C4C2512yes—
764C22×C4C2512yes—
765C22×C4C2514yes—
766C22×C4C2512yes—
767C22×C4C2514yes—
768C22×C4C2514yes—
769C22×C4C2518yes—
770C22×C4C2512yes—
771C22×C4C2514yes—
772C22×C4C2514yes—
773C22×C4C2514yes—
774C22×C4C2512yes—
775C22×C4C2512yes—
776C22×C4C2511yescharacteristic
777C22×C4C2511yescharacteristic
778C22×C4C2511yescharacteristic
779C22×C4C2511yescharacteristic
780C22×C4C2512yes—
781C22×C4C2511yescharacteristic
782C22×C4C2511yescharacteristic
783C4⋊C4—24no—
784C4⋊C4—24no—
785C4⋊C4—24no—
786C4⋊C4—24no—
787C4⋊C4—22no—
788C4⋊C4—24no—
789C4⋊C4—22no—
790C4⋊C4—28no—
791C4⋊C4—28no—
792C4⋊C4—24no—
793C4⋊C4—24no—
794C4⋊C4—24no—
795C4⋊C4—24no—
796C4⋊C4—28no—
797C4⋊C4—28no—
798C4⋊C4—24no—
799C4⋊C4—28no—
800C4⋊C4—24no—
801C4⋊C4—24no—
802C4⋊C4—28no—
803C4⋊C4—24no—
804C4⋊C4—42no—
805C4⋊C4—48no—
806C4⋊C4—48no—
807C4⋊C4—44no—
808C4⋊C4—44no—
809C4⋊C4—44no—
810C4⋊C4—48no—
811C4⋊C4—44no—
812C4⋊C4—44no—
813C4⋊C4—48no—
814C4⋊C4—44no—
815C4⋊C4—48no—
816C22⋊C4—28no—
817C22⋊C4—24no—
818C22⋊C4—24no—
819C22⋊C4—24no—
820C22⋊C4—24no—
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—216no—
824C22⋊C4—28no—
825C22⋊C4—44no—
826C22⋊C4—48no—
827C22⋊C4—42no—
828C22⋊C4—44no—
829C22⋊C4—48no—
830C22⋊C4—48no—
831C22⋊C4—48no—
832C22⋊C4—48no—
833C22⋊C4—44no—
834C22⋊C4—48no—
835C22⋊C4—48no—
836C22⋊C4—44no—
837C22⋊C4—48no—
838C22⋊C4—48no—
839C22⋊C4—48no—
840C22⋊C4—48no—
841C22⋊C4—48no—
842C22⋊C4—48no—
843C22⋊C4—48no—
844C22⋊C4—48no—
845C22⋊C4—48no—
846C22⋊C4—48no—
847C22⋊C4—48no—
848C22⋊C4—48no—
849C22⋊C4—48no—
850C22⋊C4—44no—
851C22⋊C4—48no—
852C42—24no—
853C42—28no—
854C42—22no—
855C42—24no—
856C42—28no—
857C42—22no—
858C42—24no—
859C42—22no—
860C42—24no—
861C42—24no—
862C42—28no—
863C42—44no—
864C42—44no—
865C42—44no—
866C42—44no—
867C42—44no—
868C42—42no—
869C42—42no—
870C42—44no—
871C42—44no—
872C42—44no—
873C42—44no—
874C42C2×#4114yes—
875C42C2×#4114yes—
876C42C2×#4114yes—
877C42C2×#4114yes—
878C42H(5,𝔽2)14yes—
879C23—21no—
880C23—22no—
881C23—21no—
882C23—22no—
883C23—22no—
884C23—28no—
885C23—22no—
886C23—28no—
887C23—28no—
888C23—28no—
889C23—24no—
890C23—28no—
891C23—22no—
892C23—28no—
893C23—28no—
894C23—24no—
895C23—416no—
896C23—88no—
897C23—88no—
898C23—168no—
899C23—168no—
900C23C22×#4112yes—
901C23C2611yescharacteristic
902Q8—48no—
903Q8—44no—
904Q8—84no—
905Q8—168no—
906D4—416no—
907D4—416no—
908D4—416no—
909D4—44no—
910D4—416no—
911D4—88no—
912D4—88no—
913D4—84no—
914D4—168no—
915D4—168no—
916C2×C4—21no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—21no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—28no—
924C2×C4—28no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—22no—
930C2×C4—24no—
931C2×C4—22no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—28no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—24no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—24no—
942C2×C4—22no—
943C2×C4—24no—
944C2×C4—22no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—28no—
951C2×C4—22no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—22no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—22no—
961C2×C4—28no—
962C2×C4—44no—
963C2×C4—48no—
964C2×C4—816no—
965C2×C4—88no—
966C2×C4—168no—
967C2×C4C22×#4112yes—
968C2×C4C22×#4112yes—
969C2×C4C22×#4112yes—
970C2×C4C22×#4112yes—
971C2×C4C22×#4112yes—
972C2×C4C22×#4112yes—
973C2×C4C2×H(5,𝔽2)14yes—
974C2×C4C2×H(5,𝔽2)12yes—
975C2×C4#58512yes—
976C2×C4#58514yes—
977C22—22no—
978C22—22no—
979C22—22no—
980C22—42no—
981C22—42no—
982C22—48no—
983C22—42no—
984C22—48no—
985C22—42no—
986C22—42no—
987C22—48no—
988C22—48no—
989C22—48no—
990C22—44no—
991C22—44no—
992C22—48no—
993C22—48no—
994C22—1616no—
995C22C23×#4111yescharacteristic
996C22C22×H(5,𝔽2)11yescharacteristic
997C22C2×#58512yes—
998C22C2×#58511yescharacteristic
999C22H(7,𝔽2)12yes—
1000C4—22no—
1001C4—22no—
1002C4—22no—
1003C4—22no—
1004C4—24no—
1005C4—42no—
1006C4—42no—
1007C4—44no—
1008C4—42no—
1009C4—44no—
1010C4—48no—
1011C4—42no—
1012C4—44no—
1013C4—44no—
1014C4—42no—
1015C4—44no—
1016C4—42no—
1017C4—44no—
1018C4#346014yes—
1019C4#351014yes—
1020C2—42no—
1021C2—82no—
1022C2—88no—
1023C2C2×#346011yescharacteristic
1024C2C2×#351011yescharacteristic
1025C2#6285511yescharacteristic
1026C2#6296112yes—
1027C2#6296612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#37614C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #41042C2semidirect
2. #41013C2semidirect
3. #39810C2semidirect
4. #39070C2semidirect
5. #38250C2semidirect
6. #38238C2semidirect
7. #37629C2semidirect
8. #37622C2semidirect
10. #37432C2semidirect
11. #37371C2semidirect
12. #37322C2semidirect
13. #35611C2semidirect
14. #35331C2semidirect
15. #35296C2semidirect
16. #35285C2semidirect
17. #35198C2semidirect
18. #35197C2semidirect
19. #35192C2semidirect
20. #34954C2semidirect
21. #34210C2semidirect
22. #34151C2semidirect
23. #34085C2semidirect
24. C2×#542C22semidirect
29. #2864C22semidirect
30. #2862C22semidirect
31. #2860C22semidirect
34. #2858C22semidirect
35. #2854C22semidirect
36. #2850C22semidirect
37. #2830C22semidirect
40. #2808C22semidirect
41. #2800C22semidirect
42. #2797C22semidirect
43. #2797C22semidirect
44. #2786C22semidirect
45. #2752C22semidirect
46. #2751C22semidirect
47. #2740C22semidirect
50. #2730C22semidirect
51. #2712C22semidirect
52. #2710C22semidirect
53. #2700C22semidirect
57. #2664C22semidirect
58. #2662C22semidirect
60. #2648C22semidirect
61. #2644C22semidirect
62. #2644C22semidirect
65. #2640C22semidirect
66. #2640C22semidirect
67. #2638C22semidirect
68. #2628C22semidirect
71. #2621C22semidirect
75. #2605C22semidirect
76. #2602C22semidirect
77. #2595C22semidirect
78. #2593C22semidirect
79. #2592C22semidirect
80. #2584C22semidirect
81. #2582C22semidirect
82. #2571C22semidirect
84. #2560C22semidirect
85. #2560C22semidirect
86. #2557C22semidirect
87. #2557C22semidirect
88. #2557C22semidirect
89. #2551C22semidirect
95. #2538C22semidirect
96. #2513C22semidirect
97. #2513C22semidirect
98. #2513C22semidirect
99. #2491C22semidirect
101. #2474C22semidirect
103. #2471C22semidirect
104. #2466C22semidirect
105. #2461C22semidirect
106. #2459C22semidirect
107. #2457C22semidirect
108. #2452C22semidirect
109. #2452C22semidirect
110. #2452C22semidirect
111. #2448C22semidirect
112. #2448C22semidirect
113. #2447C22semidirect
114. #2447C22semidirect
115. #2445C22semidirect
116. #2445C22semidirect
123. #2427C22semidirect
124. #2426C22semidirect
125. #2420C22semidirect
127. #2415C22semidirect
130. #2395C22semidirect
132. #2373C22semidirect
133. #2370C22semidirect
134. #2367C22semidirect
141. #2336C22semidirect
143. #2331C22semidirect
144. #2331C22semidirect
145. #2331C22semidirect
148. #2328C22semidirect
149. #2327C22semidirect
150. #2327C22semidirect
151. #2324C22semidirect
154. #2319C22semidirect
159. C4×#124C22semidirect
160. C4×#124C22semidirect
162. #2298C22semidirect
163. #2295C22semidirect
164. #2295C22semidirect
165. #2295C22semidirect
167. #2293C22semidirect
168. #2293C22semidirect
169. #2293C22semidirect
173. C42×Q8C22semidirect
174. C42×Q8C22semidirect
175. C42×D4C22semidirect
178. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#410422
#410132
#398102
#390702
#382502
#382382
#376292
#376222
#376142
#374322
#373712
#373222
#356112
#353312
#352962
#352852
#351982
#351972
#351922
#349542
#342102
#341512
#340852