Finite Group Databasebeta

← #7637141

Subgroups — #7637141

Order 512.

5306 conjugacy classes of subgroups.

The subgroup lattice has 1054 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52275C218yesmaximal, complemented
2#39203C212yesmaximal, complemented
3#39202C212yesmaximal, complemented
4#39201C212yesmaximal, complemented
5#39200C212yesmaximal, complemented
6#39199C214yesmaximal, complemented
7#39198C214yesmaximal, complemented
8#39197C214yesmaximal, complemented
9#39196C214yesmaximal, complemented
10#39195C218yesmaximal, complemented
11#36639C211yesmaximal, characteristic, complemented
12#34954C214yesmaximal, complemented
13#34946C211yesmaximal, characteristic, complemented
14#34936C211yesmaximal, characteristic
15#34918C214yesmaximal, complemented
16#34813C212yesmaximal, complemented
17#34742C212yesmaximal, complemented
18#34635C212yesmaximal, complemented
19#34145C211yesmaximal, characteristic, complemented
20#34141C211yesmaximal, characteristic, complemented
21#34065C212yesmaximal, complemented
22C4×#533C211yesmaximal, characteristic, complemented
23C2×#2293C211yesmaximal, characteristic, complemented
24C2×#533C2211yescharacteristic
25C2×#533C2211yescharacteristic
26C2×#532C2211yescharacteristic
27C2×#525C2212yes—
28C2×#525C2212yes—
29C2×C4×#41C2212yes—
30C22×C4×D4C2211yescharacteristic
31C22×#117C2212yes—
32#2862C2211yescharacteristic, complemented
33#2862C2211yescharacteristic, complemented
34#2861C2212yescomplemented
35#2861C2212yescomplemented
36#2858C2211yescharacteristic, complemented
37#2858C2211yescharacteristic, complemented
38#2850C2214yes—
39#2850C2214yes—
40#2807C2218yescomplemented
41#2803C2218yes—
42#2803C2218yes—
43#2798C2218yescomplemented
44#2798C2218yescomplemented
45#2797C2218yes—
46#2797C2218yescomplemented
47#2773C2218yescomplemented
48#2773C2218yescomplemented
49#2771C2218yescomplemented
50#2754C2218yescomplemented
51#2754C2218yescomplemented
52#2752C2218yescomplemented
53#2712C2218yescomplemented
54#2710C2218yes—
55#2710C2218yescomplemented
56#2625C2214yescomplemented
57#2625C2214yescomplemented
58#2624C2214yescomplemented
59#2624C2214yescomplemented
60#2623C2218yes—
61#2622C2218yes—
62#2597C2218yescomplemented
63#2595C2218yescomplemented
64#2593C2218yescomplemented
65#2593C2218yescomplemented
66#2592C2214yes—
67#2582C2214yescomplemented
68#2580C2214yescomplemented
69#2571C2214yescomplemented
70#2570C2214yescomplemented
71#2563C2212yes—
72#2562C2214yes—
73#2561C2214yes—
74#2548C2214yes—
75#2548C2214yes—
76#2547C2212yes—
77#2544C2214yes—
78#2542C2212yes—
79#2541C2212yes—
80#2540C2214yes—
81#2539C2214yes—
82#2516C2218yescomplemented
83#2513C2214yes—
84#2513C2214yes—
85#2513C2218yescomplemented
86#2513C2214yescomplemented
87#2511C2214yescomplemented
88#2503C2212yes—
89#2501C2212yes—
90#2492C2214yescomplemented
91#2491C2214yescomplemented
92#2490C2214yescomplemented
93#2489C2214yescomplemented
94#2488C2218yes—
95#2472C2218yes—
96#2458C2218yescomplemented
97#2448C2214yes—
98#2448C2218yescomplemented
99#2448C2214yescomplemented
100#2447C2214yescomplemented
101#2445C2214yes—
102#2435C2212yes—
103#2433C2212yes—
104#2423C2214yescomplemented
105#2422C2214yescomplemented
106#2421C2214yescomplemented
107#2420C2214yescomplemented
108#2419C2218yes—
109#2418C2218yes—
110#2398C2214yes—
111#2398C2218yescomplemented
112#2397C2214yes—
113#2395C2218yescomplemented
114#2395C2218yescomplemented
115#2395C2218yescomplemented
116#2370C2214yescomplemented
117#2369C2212yescomplemented
118#2368C2214yes—
119#2367C2214yescomplemented
120#2366C2212yescomplemented
121#2365C2212yescomplemented
122#2365C2212yescomplemented
123#2364C2214yes—
124#2361C2214yes—
125#2360C2214yes—
126#2324C2214yescomplemented
127#2324C2214yescomplemented
128#2323C2214yescomplemented
129#2323C2214yescomplemented
130#2322C2218yes—
131#2321C2218yes—
132C4×C4⋊Q8C2212yescomplemented
133C4×C4⋊Q8C2212yescomplemented
134C4×#127C2214yes—
135C4×#125C2212yescomplemented
136C4×#125C2212yescomplemented
137C4×#124C2214yes—
138C4×#124C2214yescomplemented
139C4×#124C2214yescomplemented
140C4×#124C2218yescomplemented
141C4×C22⋊Q8C2214yes—
142C4×C22⋊Q8C2214yes—
143C4×#123C2218yescomplemented
144#2297C2212yes—
145#2297C2212yes—
146#2297C2212yes—
147#2296C2211yescharacteristic
148#2296C2211yescharacteristic
149#2296C2212yes—
150#2295C2214yescomplemented
151#2295C2214yescomplemented
152#2295C2212yescomplemented
153#2293C2212yes—
154#2293C2212yes—
155#2293C2212yes—
156#2293C2212yes—
157#2293C2214yes—
158#2293C2212yes—
159#2293C2212yes—
160#2293C2218yescomplemented
161#2293C2212yescomplemented
162C2×#390C2212yes—
163C2×#389C2212yes—
164#2290C2218yescomplemented
165#2290C2214yescomplemented
166C2×#388C2214yes—
167#2285C2211yescharacteristic
168#2280C2212yes—
169#2280C2212yes—
170C42×Q8C2212yescomplemented
171C42×Q8C2214yescomplemented
172C42×D4C2212yescomplemented
173C4×#117C2212yes—
174C4×#117C2211yescharacteristic
175C4×#117C2211yescharacteristic
176C2×C4×C4⋊C4C2211yescharacteristic
177C2×C4×C22⋊C4C2212yes—
178C2×C43C2211yescharacteristic
179C22×#41C2312yes—
180C23×D4C2311yescharacteristic
181C24×C4C2312yes—
182#533—28no—
183#533—28no—
184#532—28no—
185C2×C4⋊Q8C2312yes—
186C2×C4⋊Q8C2311yescharacteristic
187C2×C4⋊Q8C2311yescharacteristic
188C2×C4⋊Q8C2311yescharacteristic
189C2×#127C2311yescharacteristic
190C2×#127C2314yes—
191C2×#125C2312yes—
192C2×#125C2312yes—
193C2×#124C2312yes—
194C2×#124C2314yes—
195C2×#124C2314yes—
196C2×#124C2314yes—
197C2×#124C2318yes—
198#525—216no—
199#525—48no—
200C2×#123C2314yes—
201C2×#123C2314yes—
202C2×#123C2318yes—
203C2×C22⋊Q8C2312yes—
204C2×C22⋊Q8C2314yes—
205C2×C22⋊Q8C2312yes—
206C2×C22⋊Q8C2314yes—
207C2×C22⋊Q8C2314yes—
208C2×#121C2314yes—
209C2×#121C2312yes—
210C2×#121C2312yes—
211C2×#121C2314yes—
212C2×#120C2314yes—
213C2×#120C2314yes—
214C4×#41—48no—
215C2×C4×Q8C2312yes—
216C2×C4×Q8C2314yes—
217C2×C4×Q8C2312yes—
218C2×C4×Q8C2314yes—
219C2×C4×Q8C2314yes—
220C2×C4×Q8C2314yes—
221C2×C4×Q8C2314yes—
222C2×C4×D4—28no—
223C2×C4×D4C2312yes—
224C2×C4×D4C2312yes—
225C2×C4×D4C2318yes—
226C2×C4×D4C2312yes—
227C2×C4×D4C2312yes—
228C2×C4×D4C2312yes—
229C2×C4×D4C2312yes—
230C2×C4×D4C2318yes—
231C2×C4×D4C2318yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2314yes—
234C2×#117—48no—
235C2×#117C2311yescharacteristic
236C2×#117C2311yescharacteristic
237C2×#117C2312yes—
238C2×#117C2311yescharacteristic
239C2×#117C2314yes—
240C2×#117C2314yes—
241C2×#117C2314yes—
242C2×#117C2314yes—
243C2×#117C2314yes—
244C2×#117C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2314yes—
247C22×C4⋊C4C2312yes—
248C22×C22⋊C4C2312yes—
249C22×C22⋊C4C2314yes—
250C22×C22⋊C4C2314yes—
251C22×C42C2311yescharacteristic
252C22×C42C2312yes—
253C22×C42C2311yescharacteristic
254C22×C42C2312yes—
255C22×C42C2312yes—
256C22×C42C2314yes—
257C22×C42C2311yescharacteristic
258#400C2318yes—
259#400C2318yes—
260#400C2318yes—
261#400C2318yes—
262#400C2318yes—
263#400C2318yes—
264#399C2318yes—
265#399C2318yes—
266#399C2318yes—
267#399C2318yes—
268#399C2318yes—
269#398C2318yes—
270#398C2318yes—
271#398C2318yes—
272#397C2318yes—
273#397C2318yes—
274#397C2318yes—
275#397C2318yes—
276#397C2318yes—
277#397C2318yes—
278#397C2318yes—
279#397C2318yes—
280#397C2318yes—
281#397C2318yes—
282#397C2318yes—
283#397C2318yes—
284#394C2318yes—
285#394C2318yes—
286#394C2318yes—
287#394C2318yes—
288#394C2318yes—
289#394C2318yes—
290#394C2318yes—
291#394C2318yes—
292#394C2318yes—
293#393C2318yes—
294#393C2318yes—
295#393C2318yes—
296#392C2318yes—
297#392C2318yes—
298#391C2314yes—
299#391C2314yes—
300#391C2312yes—
301#391C2312yes—
302#391C2314yes—
303#391C2314yes—
304#391C2318yes—
305#391C2314yes—
306#391C2314yes—
307#391C2312yes—
308#391C2312yes—
309#391C2314yes—
310#391C2318yes—
311#390C2314yes—
312#390C2314yes—
313#390C2318yes—
314#390C2318yes—
315#390C2314yes—
316#390C2318yes—
317#390C2318yes—
318#390C2312yes—
319#390C2312yes—
320#390C2314yes—
321#390C2312yes—
322#390C2314yes—
323#390C2312yes—
324#390C2312yes—
325#390C2314yes—
326#390C2314yes—
327#390C2312yes—
328#390C2314yes—
329#390C2318yes—
330#390C2312yes—
331#390C2312yes—
332#390C2314yes—
333#389C2312yes—
334#389C2312yes—
335#389C2312yes—
336#389C2312yes—
337#389C2314yes—
338#389C2314yes—
339#389C2312yes—
340#389C2314yes—
341#389C2312yes—
342#389C2318yes—
343#389C2314yes—
344#389C2318yes—
345#389C2312yes—
346#389C2312yes—
347#389C2318yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2314yes—
363#388C2314yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2314yes—
373#388C2314yes—
374#388C2318yes—
375#388C2318yes—
376#388C2314yes—
377#388C2314yes—
378#388C2314yes—
379#388C2314yes—
380#387C2314yes—
381#387C2314yes—
382#387C2314yes—
383#387C2314yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#386C2318yes—
393#386C2318yes—
394#386C2318yes—
395#386C2318yes—
396#386C2318yes—
397#386C2318yes—
398#386C2318yes—
399#385C2314yes—
400#385C2318yes—
401#385C2318yes—
402#385C2318yes—
403#385C2318yes—
404#385C2318yes—
405#385C2314yes—
406#384C2314yes—
407#384C2312yes—
408#382C2312yes—
409#382C2314yes—
410#382C2314yes—
411#382C2318yes—
412#382C2314yes—
413#381C2314yes—
414#381C2314yes—
415#381C2318yes—
416#380C2314yes—
417#380C2314yes—
418#380C2314yes—
419#380C2314yes—
420#380C2314yes—
421#379C2314yes—
422#379C2314yes—
423C4×C4⋊C4C2312yes—
424C4×C4⋊C4C2312yes—
425C4×C4⋊C4C2312yes—
426C4×C4⋊C4C2312yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2314yes—
433C4×C4⋊C4C2314yes—
434C4×C4⋊C4C2314yes—
435C4×C4⋊C4C2314yes—
436C4×C4⋊C4C2314yes—
437C4×C4⋊C4C2318yes—
438C4×C4⋊C4C2312yes—
439C4×C4⋊C4C2312yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2314yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2314yes—
448C4×C22⋊C4C2312yes—
449C4×C22⋊C4C2318yes—
450C4×C22⋊C4C2318yes—
451C4×C22⋊C4C2312yes—
452C4×C22⋊C4C2312yes—
453C4×C22⋊C4C2312yes—
454C4×C22⋊C4C2318yes—
455C4×C22⋊C4C2314yes—
456C4×C22⋊C4C2314yes—
457C4×C22⋊C4C2318yes—
458C4×C22⋊C4C2314yes—
459C4×C22⋊C4C2318yes—
460C4×C22⋊C4C2318yes—
461C4×C22⋊C4C2314yes—
462C4×C22⋊C4C2314yes—
463C4×C22⋊C4C2314yes—
464#376C2312yes—
465#376C2312yes—
466#376C2314yes—
467C2×#95C2312yes—
468C2×#95C2314yes—
469C43C2311yescharacteristic
470C43C2311yescharacteristic
471C43C2312yes—
472C43C2311yescharacteristic
473C43C2311yescharacteristic
474C43C2312yes—
475C43C2312yes—
476C43C2312yes—
477C43C2314yes—
478C25C2412yes—
479C2×#41—28no—
480C2×#41—28no—
481C2×#41—28no—
482C22×Q8C2412yes—
483C22×Q8C2412yes—
484C22×Q8C2414yes—
485C22×Q8C2412yes—
486C22×D4—24no—
487C22×D4—44no—
488C22×D4C2412yes—
489C22×D4C2414yes—
490C22×D4C2412yes—
491C22×D4C2412yes—
492C22×D4C2412yes—
493C22×D4C2418yes—
494C22×D4C2412yes—
495C22×D4C2418yes—
496C23×C4—28no—
497C23×C4—28no—
498C23×C4—28no—
499C23×C4C2412yes—
500C23×C4C2414yes—
501C23×C4C2414yes—
502C23×C4C2414yes—
503C23×C4C2412yes—
504C23×C4C2411yescharacteristic
505C23×C4C2414yes—
506C23×C4C2412yes—
507C23×C4C2418yes—
508C23×C4C2411yescharacteristic
509C23×C4C2411yescharacteristic
510C4⋊Q8—28no—
511C4⋊Q8—24no—
512C4⋊Q8—24no—
513C4⋊Q8—24no—
514#127—24no—
515#127—48no—
516#125—28no—
517#125—28no—
518#124—28no—
519#124—48no—
520#124—48no—
521#124—48no—
522#124—416no—
523#123—216no—
524#123—416no—
525#123—48no—
526C22⋊Q8—28no—
527C22⋊Q8—28no—
528C22⋊Q8—216no—
529C22⋊Q8—216no—
530C22⋊Q8—48no—
531#121—28no—
532#121—28no—
533#121—216no—
534#121—48no—
535#120—216no—
536#120—48no—
537C4×Q8—216no—
538C4×Q8—28no—
539C4×Q8—28no—
540C4×Q8—48no—
541C4×Q8—48no—
542C4×Q8—48no—
543C4×Q8—48no—
544C4×D4—28no—
545C4×D4—28no—
546C4×D4—28no—
547C4×D4—28no—
548C4×D4—232no—
549C4×D4—28no—
550C4×D4—28no—
551C4×D4—48no—
552C4×D4—48no—
553C4×D4—416no—
554C4×D4—416no—
555#117—24no—
556#117—28no—
557#117—24no—
558#117—24no—
559#117—48no—
560#117—48no—
561#117—48no—
562#117—48no—
563#117—48no—
564#117#4118yes—
565C2×C4⋊C4—24no—
566C2×C4⋊C4—44no—
567C2×C4⋊C4—48no—
568C2×C4⋊C4C2412yes—
569C2×C4⋊C4C2412yes—
570C2×C4⋊C4C2412yes—
571C2×C4⋊C4C2412yes—
572C2×C4⋊C4C2412yes—
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C2412yes—
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2418yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2418yes—
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2418yes—
602C2×C4⋊C4C2412yes—
603C2×C22⋊C4—28no—
604C2×C22⋊C4—48no—
605C2×C22⋊C4—48no—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2412yes—
611C2×C22⋊C4C2412yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2412yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2414yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2418yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C2418yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2412yes—
638C2×C42—24no—
639C2×C42—24no—
640C2×C42—28no—
641C2×C42—48no—
642C2×C42—44no—
643C2×C42—44no—
644C2×C42#4118yes—
645C2×C42C2411yescharacteristic
646C2×C42C2411yescharacteristic
647C2×C42C2414yes—
648C2×C42C2414yes—
649C2×C42C2414yes—
650C2×C42C2412yes—
651C2×C42C2412yes—
652C2×C42C2412yes—
653C2×C42C2412yes—
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2412yes—
657C2×C42C2412yes—
658C2×C42C2412yes—
659C2×C42C2412yes—
660C2×C42C2412yes—
661C2×C42C2414yes—
662C2×C42C2412yes—
663C2×C42C2412yes—
664C2×C42C2418yes—
665C2×C42C2414yes—
666C2×C42C2414yes—
667C2×C42C2418yes—
668C2×C42C2418yes—
669C2×C42C2412yes—
670C2×C42C2412yes—
671C2×C42C2412yes—
672C2×C42C2412yes—
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675C2×C42C2412yes—
676C2×C42C2411yescharacteristic
677C2×C42C2411yescharacteristic
678#95C2412yes—
679#95C2414yes—
680#95C2414yes—
681#95C2414yes—
682#95C2414yes—
683#95C2412yes—
684#95C2414yes—
685#95C2414yes—
686#95C2418yes—
687#95C2418yes—
688#95C2414yes—
689#95C2414yes—
690#95C2414yes—
691#95C2418yes—
692#95C2418yes—
693#95C2418yes—
694#95C2418yes—
695#95C2418yes—
696#95C2418yes—
697#95C2418yes—
698#95C2418yes—
699#95C2418yes—
700#95C2418yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2418yes—
708#95C2418yes—
709C24—24no—
710C24—24no—
711C24—24no—
712C24—44no—
713C24—44no—
714C24C2514yes—
715C24C2514yes—
716C24C2511yescharacteristic
717#41—432no—
718C2×Q8—28no—
719C2×Q8—24no—
720C2×Q8—24no—
721C2×Q8—24no—
722C2×Q8—24no—
723C2×Q8—24no—
724C2×Q8—28no—
725C2×Q8—28no—
726C2×Q8—44no—
727C2×Q8—44no—
728C2×D4—28no—
729C2×D4—28no—
730C2×D4—28no—
731C2×D4—24no—
732C2×D4—24no—
733C2×D4—24no—
734C2×D4—24no—
735C2×D4—24no—
736C2×D4—216no—
737C2×D4—24no—
738C2×D4—24no—
739C2×D4—28no—
740C2×D4—24no—
741C2×D4—24no—
742C2×D4—44no—
743C2×D4—416no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4—44no—
747C2×D4—48no—
748C2×D4—48no—
749C2×D4—48no—
750C22×C4—24no—
751C22×C4—24no—
752C22×C4—24no—
753C22×C4—24no—
754C22×C4—24no—
755C22×C4—24no—
756C22×C4—28no—
757C22×C4—28no—
758C22×C4—28no—
759C22×C4—28no—
760C22×C4—28no—
761C22×C4—28no—
762C22×C4—28no—
763C22×C4—28no—
764C22×C4—28no—
765C22×C4—28no—
766C22×C4—24no—
767C22×C4—42no—
768C22×C4—42no—
769C22×C4—42no—
770C22×C4—42no—
771C22×C4—48no—
772C22×C4—44no—
773C22×C4—44no—
774C22×C4—48no—
775C22×C4—48no—
776C22×C4—432no—
777C22×C4C2×#4114yes—
778C22×C4C2×#4114yes—
779C22×C4C2×#4114yes—
780C22×C4C2×#4114yes—
781C22×C4H(5,𝔽2)14yes—
782C22×C4C2512yes—
783C22×C4C2514yes—
784C22×C4C2514yes—
785C22×C4C2514yes—
786C22×C4C2514yes—
787C22×C4C2514yes—
788C22×C4C2514yes—
789C22×C4C2514yes—
790C22×C4C2514yes—
791C22×C4C2512yes—
792C22×C4C2512yes—
793C22×C4C2514yes—
794C22×C4C2511yescharacteristic
795C22×C4C2514yes—
796C22×C4C2511yescharacteristic
797C22×C4C2511yescharacteristic
798C22×C4C2512yes—
799C22×C4C2511yescharacteristic
800C22×C4C2511yescharacteristic
801C22×C4C2511yescharacteristic
802C4⋊C4—24no—
803C4⋊C4—24no—
804C4⋊C4—24no—
805C4⋊C4—24no—
806C4⋊C4—24no—
807C4⋊C4—24no—
808C4⋊C4—24no—
809C4⋊C4—216no—
810C4⋊C4—28no—
811C4⋊C4—28no—
812C4⋊C4—28no—
813C4⋊C4—28no—
814C4⋊C4—28no—
815C4⋊C4—24no—
816C4⋊C4—24no—
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—24no—
820C4⋊C4—24no—
821C4⋊C4—28no—
822C4⋊C4—44no—
823C4⋊C4—44no—
824C4⋊C4—44no—
825C4⋊C4—44no—
826C4⋊C4—44no—
827C4⋊C4—48no—
828C4⋊C4—48no—
829C4⋊C4—44no—
830C4⋊C4—44no—
831C4⋊C4—44no—
832C4⋊C4—44no—
833C4⋊C4—44no—
834C4⋊C4—48no—
835C4⋊C4—48no—
836C4⋊C4C2×#4118yes—
837C22⋊C4—28no—
838C22⋊C4—24no—
839C22⋊C4—24no—
840C22⋊C4—24no—
841C22⋊C4—28no—
842C22⋊C4—28no—
843C22⋊C4—216no—
844C22⋊C4—216no—
845C22⋊C4—28no—
846C22⋊C4—28no—
847C22⋊C4—28no—
848C22⋊C4—28no—
849C22⋊C4—216no—
850C22⋊C4—44no—
851C22⋊C4—44no—
852C22⋊C4—44no—
853C22⋊C4—44no—
854C22⋊C4—44no—
855C22⋊C4—44no—
856C22⋊C4—48no—
857C22⋊C4—48no—
858C22⋊C4—48no—
859C22⋊C4—48no—
860C22⋊C4—48no—
861C22⋊C4—48no—
862C22⋊C4—48no—
863C22⋊C4—48no—
864C22⋊C4—48no—
865C22⋊C4—48no—
866C22⋊C4—48no—
867C22⋊C4—48no—
868C22⋊C4C2×#4118yes—
869C42—24no—
870C42—22no—
871C42—22no—
872C42—28no—
873C42—24no—
874C42—24no—
875C42—24no—
876C42—24no—
877C42—22no—
878C42—22no—
879C42—28no—
880C42—24no—
881C42—24no—
882C42—24no—
883C42—24no—
884C42—24no—
885C42—24no—
886C42—28no—
887C42—28no—
888C42—42no—
889C42—42no—
890C42—42no—
891C42—42no—
892C42—48no—
893C42—44no—
894C42—44no—
895C42—48no—
896C42—48no—
897C42C2×#4114yes—
898C42C2×#4114yes—
899C42C2×#4114yes—
900C42C2×#4114yes—
901C42C2×#4118yes—
902C23—22no—
903C23—22no—
904C23—24no—
905C23—24no—
906C23—24no—
907C23—24no—
908C23—24no—
909C23—24no—
910C23—24no—
911C23—24no—
912C23—28no—
913C23—24no—
914C23—28no—
915C23—24no—
916C23—48no—
917C23—48no—
918C23—48no—
919C23—88no—
920C23—88no—
921C23C22×#4112yes—
922C23C22×#4112yes—
923C23C2×H(5,𝔽2)12yes—
924C23C2611yescharacteristic
925Q8—416no—
926Q8—48no—
927Q8—48no—
928Q8—84no—
929D4—48no—
930D4—416no—
931D4—48no—
932D4—48no—
933D4—48no—
934D4—84no—
935D4—816no—
936D4—816no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—24no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—24no—
943C2×C4—22no—
944C2×C4—28no—
945C2×C4—22no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—22no—
971C2×C4—24no—
972C2×C4—28no—
973C2×C4—24no—
974C2×C4—28no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—44no—
980C2×C4—48no—
981C2×C4—48no—
982C2×C4—48no—
983C2×C4—416no—
984C2×C4—416no—
985C2×C4—416no—
986C2×C4—88no—
987C2×C4—816no—
988C2×C4#559116yes—
989C2×C4C22×#4112yes—
990C2×C4C22×#4112yes—
991C2×C4C22×#4112yes—
992C2×C4C22×#4118yes—
993C2×C4C22×#4112yes—
994C2×C4C22×#4112yes—
995C2×C4C22×#4112yes—
996C2×C4C22×#4112yes—
997C2×C4C22×#4112yes—
998C2×C4C2×H(5,𝔽2)12yes—
999C2×C4C2×H(5,𝔽2)12yes—
1000C2×C4#58514yes—
1001C2×C4#58514yes—
1002C22—24no—
1003C22—22no—
1004C22—24no—
1005C22—22no—
1006C22—48no—
1007C22—44no—
1008C22—44no—
1009C22—44no—
1010C22—44no—
1011C22—44no—
1012C22—48no—
1013C22—44no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22—816no—
1019C22C2×#55914yes—
1020C22C23×#4111yescharacteristic
1021C22C23×#4111yescharacteristic
1022C22C22×H(5,𝔽2)11yescharacteristic
1023C22C2×#58512yes—
1024C22C2×#58512yes—
1025C4—22no—
1026C4—22no—
1027C4—24no—
1028C4—28no—
1029C4—22no—
1030C4—42no—
1031C4—42no—
1032C4—44no—
1033C4—44no—
1034C4—44no—
1035C4—44no—
1036C4—44no—
1037C4—42no—
1038C4—44no—
1039C4—44no—
1040C4—44no—
1041C4—44no—
1042C4#345514yes—
1043C4C2×#55914yes—
1044C4C2×#55914yes—
1045C2—24no—
1046C2—84no—
1047C2—84no—
1048C2C2×#345511yescharacteristic
1049C2C22×#55911yescharacteristic
1050C2#6275912yes—
1051C2#6281511yescharacteristic
1052C2#6281612yes—
subgroupG/H
centerC22×C4C25
commutator, Frattini, socle, cosocleC23C26
prime radical#34936C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52275C2semidirect
2. #39203C2semidirect
3. #39202C2semidirect
4. #39201C2semidirect
5. #39200C2semidirect
6. #39199C2semidirect
7. #39198C2semidirect
8. #39197C2semidirect
9. #39196C2semidirect
10. #39195C2semidirect
11. #36639C2semidirect
12. #34954C2semidirect
13. #34946C2semidirect
15. #34918C2semidirect
16. #34813C2semidirect
17. #34742C2semidirect
18. #34635C2semidirect
19. #34145C2semidirect
20. #34141C2semidirect
21. #34065C2semidirect
22. C4×#533C2semidirect
23. C2×#2293C2semidirect
32. #2862C22semidirect
33. #2862C22semidirect
34. #2861C22semidirect
35. #2861C22semidirect
36. #2858C22semidirect
37. #2858C22semidirect
40. #2807C22semidirect
43. #2798C22semidirect
44. #2798C22semidirect
46. #2797C22semidirect
47. #2773C22semidirect
48. #2773C22semidirect
49. #2771C22semidirect
50. #2754C22semidirect
51. #2754C22semidirect
52. #2752C22semidirect
53. #2712C22semidirect
55. #2710C22semidirect
56. #2625C22semidirect
57. #2625C22semidirect
58. #2624C22semidirect
59. #2624C22semidirect
62. #2597C22semidirect
63. #2595C22semidirect
64. #2593C22semidirect
65. #2593C22semidirect
67. #2582C22semidirect
68. #2580C22semidirect
69. #2571C22semidirect
70. #2570C22semidirect
82. #2516C22semidirect
85. #2513C22semidirect
86. #2513C22semidirect
87. #2511C22semidirect
90. #2492C22semidirect
91. #2491C22semidirect
92. #2490C22semidirect
93. #2489C22semidirect
96. #2458C22semidirect
98. #2448C22semidirect
99. #2448C22semidirect
100. #2447C22semidirect
104. #2423C22semidirect
105. #2422C22semidirect
106. #2421C22semidirect
107. #2420C22semidirect
111. #2398C22semidirect
113. #2395C22semidirect
114. #2395C22semidirect
115. #2395C22semidirect
116. #2370C22semidirect
117. #2369C22semidirect
119. #2367C22semidirect
120. #2366C22semidirect
121. #2365C22semidirect
122. #2365C22semidirect
126. #2324C22semidirect
127. #2324C22semidirect
128. #2323C22semidirect
129. #2323C22semidirect
132. C4×C4⋊Q8C22semidirect
133. C4×C4⋊Q8C22semidirect
135. C4×#125C22semidirect
136. C4×#125C22semidirect
138. C4×#124C22semidirect
139. C4×#124C22semidirect
140. C4×#124C22semidirect
143. C4×#123C22semidirect
150. #2295C22semidirect
151. #2295C22semidirect
152. #2295C22semidirect
160. #2293C22semidirect
161. #2293C22semidirect
164. #2290C22semidirect
165. #2290C22semidirect
170. C42×Q8C22semidirect
171. C42×Q8C22semidirect
172. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#522752
#392032
#392022
#392012
#392002
#391992
#391982
#391972
#391962
#391952
#366392
#349542
#349462
#349362
#349182
#348132
#347422
#346352
#341452
#341412
#340652
C4×#5332
C2×#22932