Finite Group Databasebeta

← #7628511

Subgroups — #7628511

Order 512.

5516 conjugacy classes of subgroups.

The subgroup lattice has 1067 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36641C212yesmaximal, complemented
2#36639C212yesmaximal, complemented
3#35243C214yesmaximal, complemented
4#35230C214yesmaximal, complemented
5#35199C212yesmaximal, complemented
6#35198C212yesmaximal, complemented
7#35186C212yesmaximal, complemented
8#35184C212yesmaximal, complemented
9#35117C214yesmaximal, complemented
10#35114C214yesmaximal, complemented
11#35060C218yesmaximal, complemented
12#34974C214yesmaximal, complemented
13#34968C214yesmaximal, complemented
14#34955C211yesmaximal, characteristic, complemented
15#34952C211yesmaximal, characteristic, complemented
16#34938C211yesmaximal, characteristic, complemented
17#34937C211yesmaximal, characteristic
18#34745C212yesmaximal, complemented
19#34744C212yesmaximal, complemented
20#34603C214yesmaximal, complemented
21C4×#542C214yesmaximal, complemented
22C4×#532C211yesmaximal, characteristic, complemented
23#34026C211yesmaximal, characteristic, complemented
24C2×C42×Q8C211yesmaximal, characteristic, complemented
25C2×#542C2214yes—
26C2×#533C2212yes—
27C2×#532C2211yescharacteristic
28C2×#532C2212yes—
29C2×C4×#41C2211yescharacteristic
30C2×C4×#41C2212yes—
31C22×C4×Q8C2211yescharacteristic
32C22×C4×Q8C2212yes—
33#2863C2214yes—
34#2863C2214yes—
35#2862C2214yes—
36#2861C2214yes—
37#2861C2214yes—
38#2860C2214yes—
39#2860C2214yes—
40#2858C2214yes—
41#2852C2218yes—
42#2852C2218yes—
43#2850C2218yes—
44#2850C2218yes—
45#2666C2218yes—
46#2662C2218yes—
47#2654C2218yes—
48#2651C2218yes—
49#2651C2218yes—
50#2650C2218yes—
51#2637C2218yes—
52#2632C2218yes—
53#2592C2214yes—
54#2591C2214yes—
55#2582C2212yes—
56#2581C2212yes—
57#2580C2212yes—
58#2579C2214yes—
59#2568C2212yes—
60#2552C2212yes—
61#2551C2212yes—
62#2550C2214yes—
63#2549C2214yes—
64#2548C2211yescharacteristic
65#2548C2212yes—
66#2547C2211yescharacteristic
67#2546C2211yescharacteristic
68#2545C2212yes—
69#2544C2212yes—
70#2543C2214yes—
71#2541C2211yescharacteristic
72#2538C2212yes—
73#2532C2218yes—
74#2529C2218yes—
75#2525C2218yes—
76#2521C2218yes—
77#2520C2218yes—
78#2515C2218yes—
79#2512C2214yes—
80#2508C2214yes—
81#2504C2212yes—
82#2495C2214yes—
83#2491C2214yes—
84#2487C2212yes—
85#2479C2218yes—
86#2474C2218yes—
87#2468C2218yes—
88#2465C2218yes—
89#2461C2218yes—
90#2458C2218yes—
91#2454C2214yes—
92#2453C2214yes—
93#2452C2214yes—
94#2451C2214yes—
95#2451C2214yes—
96#2450C2218yes—
97#2449C2218yes—
98#2448C2214yes—
99#2448C2214yes—
100#2447C2214yes—
101#2446C2214yes—
102#2445C2214yes—
103#2444C2218yes—
104#2443C2218yes—
105#2440C2214yes—
106#2436C2212yes—
107#2426C2214yes—
108#2423C2214yes—
109#2416C2214yes—
110#2409C2212yes—
111#2399C2214yes—
112#2398C2214yes—
113#2396C2214yes—
114#2396C2218yes—
115#2395C2218yes—
116#2392C2214yes—
117#2337C2218yes—
118#2335C2218yes—
119#2334C2218yes—
120#2332C2218yes—
121#2331C2214yes—
122#2326C2214yes—
123#2324C2214yes—
124#2323C2214yes—
125#2320C2214yes—
126#2319C2214yes—
127#2314C2214yes—
128C4×C4⋊Q8C2214yes—
129C4×C4⋊Q8C2212yes—
130C4×#127C2212yes—
131C4×#126C2218yes—
132C4×#126C2218yes—
133C4×#124C2218yes—
134C4×#124C2218yes—
135C4×#124C2214yes—
136C4×#124C2214yes—
137C4×C22⋊Q8C2214yes—
138C4×C22⋊Q8C2218yes—
139C4×#123C2218yes—
140C4×#121C2214yes—
141C4×#121C2214yes—
142C4×#121C2214yes—
143#2298C2212yes—
144#2298C2212yes—
145#2297C2211yescharacteristic
146#2297C2212yes—
147#2297C2212yes—
148#2297C2212yes—
149#2297C2212yes—
150#2297C2212yes—
151#2297C2211yescharacteristic
152#2296C2211yescharacteristic
153#2296C2212yes—
154#2296C2212yes—
155#2296C2211yescharacteristic
156#2295C2212yes—
157#2295C2212yes—
158#2293C2212yes—
159#2293C2212yes—
160#2293C2212yes—
161#2293C2212yes—
162#2290C2214yes—
163#2290C2214yes—
164#2285C2211yescharacteristic
165C42×Q8C2214yes—
166C42×Q8C2212yes—
167C42×Q8C2212yes—
168C42×Q8C2212yes—
169C42×Q8C2212yes—
170C42×Q8C2212yes—
171C42×Q8C2212yes—
172C42×D4C2212yes—
173C42×D4C2212yes—
174C4×#117C2212yes—
175C4×#117C2211yescharacteristic
176C4×#117C2212yes—
177C2×C4×C4⋊C4C2211yescharacteristic
178C2×C4×C4⋊C4C2212yes—
179C2×C4×C4⋊C4C2212yes—
180C2×C4×C4⋊C4C2214yes—
181C2×C43C2212yes—
182C2×C43C2211yescharacteristic
183C22×#41C2311yescharacteristic
184C22×#41C2312yes—
185C23×Q8C2311yescharacteristic
186#542—232no—
187#533—48no—
188#532—28no—
189#532—48no—
190C2×C4⋊Q8C2311yescharacteristic
191C2×C4⋊Q8C2314yes—
192C2×C4⋊Q8C2314yes—
193C2×C4⋊Q8C2312yes—
194C2×#127C2311yescharacteristic
195C2×#127C2312yes—
196C2×#126C2318yes—
197C2×#126C2318yes—
198C2×#125C2314yes—
199C2×#124C2314yes—
200C2×#124C2312yes—
201C2×#124C2318yes—
202C2×#124C2318yes—
203C2×#124C2312yes—
204C2×#124C2312yes—
205C2×#123C2318yes—
206C2×C22⋊Q8C2314yes—
207C2×C22⋊Q8C2318yes—
208C2×C22⋊Q8C2318yes—
209C2×#121C2314yes—
210C2×#121C2312yes—
211C2×#121C2312yes—
212C2×#121C2318yes—
213C4×#41—28no—
214C4×#41—48no—
215C2×C4×Q8—216no—
216C2×C4×Q8—28no—
217C2×C4×Q8C2312yes—
218C2×C4×Q8C2312yes—
219C2×C4×Q8C2312yes—
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2314yes—
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2312yes—
226C2×C4×Q8C2314yes—
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2318yes—
229C2×C4×Q8C2314yes—
230C2×C4×Q8C2312yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2312yes—
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2312yes—
235C2×C4×D4C2312yes—
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2312yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C2318yes—
241C2×C4×D4C2318yes—
242C2×#117C2314yes—
243C2×#117C2312yes—
244C2×#117C2312yes—
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2314yes—
249C2×#117C2314yes—
250C22×C4⋊C4C2312yes—
251C22×C4⋊C4C2312yes—
252C22×C4⋊C4C2314yes—
253C22×C4⋊C4C2311yescharacteristic
254C22×C42C2314yes—
255C22×C42C2312yes—
256C22×C42C2312yes—
257C22×C42C2311yescharacteristic
258C22×C42C2312yes—
259C22×C42C2312yes—
260C22×C42C2311yescharacteristic
261C22×C42C2314yes—
262C22×C42C2314yes—
263C22×C42C2312yes—
264C22×C42C2311yescharacteristic
265#400C2318yes—
266#400C2314yes—
267#400C2318yes—
268#400C2318yes—
269#399C2314yes—
270#399C2318yes—
271#399C2318yes—
272#398C2318yes—
273#398C2318yes—
274#398C2318yes—
275#398C2318yes—
276#398C2314yes—
277#398C2318yes—
278#398C2318yes—
279#397C2318yes—
280#397C2318yes—
281#397C2314yes—
282#397C2318yes—
283#397C2318yes—
284#396C2318yes—
285#396C2318yes—
286#396C2318yes—
287#396C2318yes—
288#395C2314yes—
289#395C2318yes—
290#395C2318yes—
291#395C2318yes—
292#394C2318yes—
293#394C2318yes—
294#394C2318yes—
295#394C2314yes—
296#394C2318yes—
297#393C2314yes—
298#393C2318yes—
299#393C2318yes—
300#392C2314yes—
301#391C2318yes—
302#391C2314yes—
303#391C2314yes—
304#391C2314yes—
305#391C2314yes—
306#391C2314yes—
307#391C2314yes—
308#391C2318yes—
309#391C2318yes—
310#391C2318yes—
311#391C2312yes—
312#391C2312yes—
313#391C2312yes—
314#391C2312yes—
315#390C2314yes—
316#390C2314yes—
317#390C2314yes—
318#390C2314yes—
319#390C2314yes—
320#390C2318yes—
321#390C2314yes—
322#390C2314yes—
323#390C2314yes—
324#390C2318yes—
325#390C2312yes—
326#390C2312yes—
327#390C2312yes—
328#390C2312yes—
329#389C2314yes—
330#389C2314yes—
331#389C2318yes—
332#389C2314yes—
333#389C2314yes—
334#389C2314yes—
335#389C2314yes—
336#389C2318yes—
337#389C2314yes—
338#389C2314yes—
339#389C2312yes—
340#389C2312yes—
341#389C2314yes—
342#389C2314yes—
343#389C2312yes—
344#389C2312yes—
345#388C2318yes—
346#388C2318yes—
347#388C2318yes—
348#388C2318yes—
349#388C2318yes—
350#388C2318yes—
351#388C2318yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2314yes—
365#388C2318yes—
366#388C2314yes—
367#388C2314yes—
368#388C2314yes—
369#388C2318yes—
370#387C2318yes—
371#387C2318yes—
372#387C2318yes—
373#387C2318yes—
374#387C2318yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2314yes—
382#387C2314yes—
383#387C2314yes—
384#387C2314yes—
385#386C2314yes—
386#386C2314yes—
387#386C2318yes—
388#386C2318yes—
389#386C2314yes—
390#386C2314yes—
391#386C2314yes—
392#386C2314yes—
393#386C2314yes—
394#386C2318yes—
395#386C2318yes—
396#386C2314yes—
397#385C2318yes—
398#385C2314yes—
399#385C2314yes—
400#385C2318yes—
401#385C2318yes—
402#385C2318yes—
403#385C2314yes—
404#385C2318yes—
405#385C2314yes—
406#384C2312yes—
407#384C2314yes—
408#383C2318yes—
409#383C2318yes—
410#382C2314yes—
411#382C2318yes—
412#382C2312yes—
413#382C2318yes—
414#381C2318yes—
415#380C2314yes—
416#380C2314yes—
417#380C2318yes—
418#380C2312yes—
419#380C2312yes—
420C4×C4⋊C4C2312yes—
421C4×C4⋊C4C2312yes—
422C4×C4⋊C4C2318yes—
423C4×C4⋊C4C2318yes—
424C4×C4⋊C4C2312yes—
425C4×C4⋊C4C2312yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2312yes—
429C4×C4⋊C4C2312yes—
430C4×C4⋊C4C2312yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2314yes—
433C4×C4⋊C4C2314yes—
434C4×C4⋊C4C2312yes—
435C4×C4⋊C4C2312yes—
436C4×C4⋊C4C2314yes—
437C4×C4⋊C4C2314yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2312yes—
440C4×C4⋊C4C2312yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2314yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2312yes—
450C4×C4⋊C4C2312yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2312yes—
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2312yes—
457C4×C22⋊C4C2318yes—
458C4×C22⋊C4C2318yes—
459C4×C22⋊C4C2314yes—
460C4×C22⋊C4C2314yes—
461C4×C22⋊C4C2318yes—
462C4×C22⋊C4C2314yes—
463C4×C22⋊C4C2312yes—
464C4×C22⋊C4C2312yes—
465C4×C22⋊C4C2318yes—
466C4×C22⋊C4C2318yes—
467C4×C22⋊C4C2314yes—
468C4×C22⋊C4C2312yes—
469C4×C22⋊C4C2318yes—
470C4×C22⋊C4C2312yes—
471C4×C22⋊C4C2312yes—
472C4×C22⋊C4C2312yes—
473#376C2314yes—
474#376C2312yes—
475#376C2314yes—
476C2×#95C2314yes—
477C2×#95C2312yes—
478C43C2314yes—
479C43C2314yes—
480C43C2312yes—
481C43C2312yes—
482C43C2314yes—
483C43C2314yes—
484C43C2311yescharacteristic
485C43C2311yescharacteristic
486C43C2311yescharacteristic
487C43C2311yescharacteristic
488C43C2312yes—
489C2×#41—24no—
490C2×#41—28no—
491C2×#41—28no—
492C2×#41—24no—
493C2×#41—24no—
494C2×#41—28no—
495C22×Q8—28no—
496C22×Q8—24no—
497C22×Q8C2412yes—
498C22×Q8C2411yescharacteristic
499C22×Q8C2412yes—
500C22×Q8C2412yes—
501C22×Q8C2418yes—
502C22×D4C2412yes—
503C22×D4C2412yes—
504C22×D4C2414yes—
505C22×D4C2411yescharacteristic
506C22×D4C2412yes—
507C22×D4C2412yes—
508C22×D4C2418yes—
509C23×C4C2412yes—
510C23×C4C2412yes—
511C23×C4C2412yes—
512C23×C4C2412yes—
513C23×C4C2414yes—
514C23×C4C2412yes—
515C23×C4C2414yes—
516C23×C4C2411yescharacteristic
517C23×C4C2412yes—
518C23×C4C2412yes—
519C23×C4C2418yes—
520C23×C4C2411yescharacteristic
521C23×C4C2411yescharacteristic
522C4⋊Q8—216no—
523C4⋊Q8—24no—
524C4⋊Q8—48no—
525C4⋊Q8—44no—
526#127—24no—
527#127—44no—
528#126—232no—
529#126—416no—
530#125—48no—
531#124—216no—
532#124—28no—
533#124—232no—
534#124—416no—
535#124—44no—
536#124—44no—
537#123—232no—
538C22⋊Q8—216no—
539C22⋊Q8—232no—
540C22⋊Q8—416no—
541#121—28no—
542#121—28no—
543#121—216no—
544#121—416no—
545C4×Q8—28no—
546C4×Q8—28no—
547C4×Q8—216no—
548C4×Q8—28no—
549C4×Q8—28no—
550C4×Q8—216no—
551C4×Q8—28no—
552C4×Q8—28no—
553C4×Q8—28no—
554C4×Q8—24no—
555C4×Q8—24no—
556C4×Q8—416no—
557C4×Q8—48no—
558C4×Q8#41116yescomplemented
559C4×D4—28no—
560C4×D4—28no—
561C4×D4—24no—
562C4×D4—24no—
563C4×D4—28no—
564C4×D4—28no—
565C4×D4—216no—
566C4×D4—48no—
567C4×D4—48no—
568C4×D4—416no—
569C4×D4—416no—
570#117—24no—
571#117—28no—
572#117—24no—
573#117—24no—
574#117—28no—
575#117—216no—
576#117—48no—
577#117—48no—
578C2×C4⋊C4—28no—
579C2×C4⋊C4—24no—
580C2×C4⋊C4—28no—
581C2×C4⋊C4—216no—
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2418yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2418yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2414yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2412yes—
619C2×C22⋊C4C2412yes—
620C2×C22⋊C4C2412yes—
621C2×C22⋊C4C2412yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2412yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2414yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C2418yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2418yes—
638C2×C22⋊C4C2418yes—
639C2×C22⋊C4C2418yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2418yes—
642C2×C42—28no—
643C2×C42—24no—
644C2×C42—28no—
645C2×C42—24no—
646C2×C42—28no—
647C2×C42—216no—
648C2×C42—28no—
649C2×C42—48no—
650C2×C42—44no—
651C2×C42—48no—
652C2×C42#4118yes—
653C2×C42C2412yes—
654C2×C42C2414yes—
655C2×C42C2412yes—
656C2×C42C2412yes—
657C2×C42C2412yes—
658C2×C42C2412yes—
659C2×C42C2412yes—
660C2×C42C2412yes—
661C2×C42C2414yes—
662C2×C42C2412yes—
663C2×C42C2414yes—
664C2×C42C2414yes—
665C2×C42C2414yes—
666C2×C42C2412yes—
667C2×C42C2414yes—
668C2×C42C2414yes—
669C2×C42C2412yes—
670C2×C42C2412yes—
671C2×C42C2411yescharacteristic
672C2×C42C2414yes—
673C2×C42C2412yes—
674C2×C42C2412yes—
675C2×C42C2412yes—
676C2×C42C2414yes—
677C2×C42C2414yes—
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2414yes—
682C2×C42C2418yes—
683C2×C42C2412yes—
684C2×C42C2414yes—
685C2×C42C2412yes—
686C2×C42C2414yes—
687C2×C42C2412yes—
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2414yes—
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693#95C2414yes—
694#95C2414yes—
695#95C2414yes—
696#95C2412yes—
697#95C2414yes—
698#95C2412yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2418yes—
713#95C2418yes—
714#95C2418yes—
715#95C2418yes—
716#95C2418yes—
717#95C2418yes—
718#95C2418yes—
719#95C2418yes—
720#95C2418yes—
721#95C2418yes—
722#95C2418yes—
723#95C2418yes—
724#95C2418yes—
725#95C2418yes—
726C24C2512yes—
727C24C2514yes—
728C24C2511yescharacteristic
729#41—416no—
730#41—432no—
731C2×Q8—232no—
732C2×Q8—28no—
733C2×Q8—24no—
734C2×Q8—24no—
735C2×Q8—24no—
736C2×Q8—22no—
737C2×Q8—24no—
738C2×Q8—216no—
739C2×Q8—24no—
740C2×Q8—22no—
741C2×Q8—22no—
742C2×Q8—24no—
743C2×Q8—48no—
744C2×Q8—48no—
745C2×Q8C2×#4118yes—
746C2×D4—24no—
747C2×D4—28no—
748C2×D4—28no—
749C2×D4—24no—
750C2×D4—24no—
751C2×D4—28no—
752C2×D4—22no—
753C2×D4—28no—
754C2×D4—24no—
755C2×D4—24no—
756C2×D4—24no—
757C2×D4—216no—
758C2×D4—24no—
759C2×D4—22no—
760C2×D4—22no—
761C2×D4—24no—
762C2×D4—44no—
763C2×D4—48no—
764C2×D4—48no—
765C22×C4—24no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—28no—
769C22×C4—24no—
770C22×C4—24no—
771C22×C4—24no—
772C22×C4—24no—
773C22×C4—28no—
774C22×C4—24no—
775C22×C4—28no—
776C22×C4—24no—
777C22×C4—24no—
778C22×C4—24no—
779C22×C4—28no—
780C22×C4—28no—
781C22×C4—28no—
782C22×C4—24no—
783C22×C4—24no—
784C22×C4—28no—
785C22×C4—216no—
786C22×C4—42no—
787C22×C4—42no—
788C22×C4—44no—
789C22×C4—44no—
790C22×C4—44no—
791C22×C4—48no—
792C22×C4—48no—
793C22×C4C2×#4114yes—
794C22×C4C2×#4114yes—
795C22×C4C2×#4114yes—
796C22×C4H(5,𝔽2)14yes—
797C22×C42−1+414yes—
798C22×C4C2512yes—
799C22×C4C2514yes—
800C22×C4C2514yes—
801C22×C4C2514yes—
802C22×C4C2512yes—
803C22×C4C2512yes—
804C22×C4C2514yes—
805C22×C4C2518yes—
806C22×C4C2514yes—
807C22×C4C2512yes—
808C22×C4C2512yes—
809C22×C4C2511yescharacteristic
810C22×C4C2512yes—
811C22×C4C2514yes—
812C22×C4C2511yescharacteristic
813C22×C4C2511yescharacteristic
814C22×C4C2514yes—
815C22×C4C2512yes—
816C22×C4C2511yescharacteristic
817C22×C4C2511yescharacteristic
818C22×C4C2511yescharacteristic
819C4⋊C4—28no—
820C4⋊C4—28no—
821C4⋊C4—28no—
822C4⋊C4—28no—
823C4⋊C4—28no—
824C4⋊C4—28no—
825C4⋊C4—24no—
826C4⋊C4—24no—
827C4⋊C4—24no—
828C4⋊C4—22no—
829C4⋊C4—22no—
830C4⋊C4—24no—
831C4⋊C4—24no—
832C4⋊C4—28no—
833C4⋊C4—28no—
834C4⋊C4—24no—
835C4⋊C4—24no—
836C4⋊C4—28no—
837C4⋊C4—216no—
838C4⋊C4—216no—
839C4⋊C4—28no—
840C4⋊C4—24no—
841C4⋊C4—24no—
842C4⋊C4—28no—
843C4⋊C4—44no—
844C4⋊C4—48no—
845C4⋊C4—44no—
846C4⋊C4—48no—
847C4⋊C4—48no—
848C4⋊C4—48no—
849C4⋊C4—48no—
850C4⋊C4—48no—
851C4⋊C4—48no—
852C4⋊C4C2×#4118yes—
853C4⋊C4C2×#41116yes—
854C22⋊C4—24no—
855C22⋊C4—28no—
856C22⋊C4—24no—
857C22⋊C4—24no—
858C22⋊C4—24no—
859C22⋊C4—24no—
860C22⋊C4—28no—
861C22⋊C4—28no—
862C22⋊C4—28no—
863C22⋊C4—28no—
864C22⋊C4—216no—
865C22⋊C4—216no—
866C22⋊C4—216no—
867C22⋊C4—216no—
868C22⋊C4—216no—
869C22⋊C4—28no—
870C22⋊C4—216no—
871C22⋊C4—44no—
872C22⋊C4—48no—
873C22⋊C4—48no—
874C22⋊C4—48no—
875C22⋊C4—48no—
876C22⋊C4—48no—
877C22⋊C4—48no—
878C22⋊C4—48no—
879C42—24no—
880C42—24no—
881C42—24no—
882C42—24no—
883C42—28no—
884C42—28no—
885C42—24no—
886C42—24no—
887C42—28no—
888C42—28no—
889C42—28no—
890C42—28no—
891C42—22no—
892C42—22no—
893C42—24no—
894C42—28no—
895C42—24no—
896C42—24no—
897C42—28no—
898C42—24no—
899C42—22no—
900C42—22no—
901C42—24no—
902C42—24no—
903C42—24no—
904C42—24no—
905C42—28no—
906C42—28no—
907C42—42no—
908C42—42no—
909C42—44no—
910C42—44no—
911C42—48no—
912C42—44no—
913C42C2×#4114yes—
914C42C2×#4118yes—
915C42C2×#41116yes—
916C42C2×#4114yes—
917C42C2×#4114yes—
918C42C2×#4114yes—
919C23—22no—
920C23—22no—
921C23—28no—
922C23—24no—
923C23—22no—
924C23—24no—
925C23—24no—
926C23—22no—
927C23—22no—
928C23—24no—
929C23—28no—
930C23—24no—
931C23C22×#4112yes—
932C23C2×H(5,𝔽2)12yes—
933C23C2×2−1+412yes—
934C23C2611yescharacteristic
935Q8—216no—
936Q8—216no—
937Q8—44no—
938Q8—48no—
939Q8—816no—
940D4—48no—
941D4—48no—
942D4—416no—
943D4—48no—
944D4—44no—
945D4—48no—
946D4—816no—
947C2×C4—216no—
948C2×C4—216no—
949C2×C4—22no—
950C2×C4—24no—
951C2×C4—22no—
952C2×C4—24no—
953C2×C4—22no—
954C2×C4—24no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—24no—
961C2×C4—22no—
962C2×C4—28no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—24no—
966C2×C4—22no—
967C2×C4—24no—
968C2×C4—22no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—28no—
973C2×C4—24no—
974C2×C4—22no—
975C2×C4—24no—
976C2×C4—28no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—22no—
980C2×C4—24no—
981C2×C4—22no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—22no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—28no—
990C2×C4—24no—
991C2×C4—44no—
992C2×C4—48no—
993C2×C4—416no—
994C2×C4—48no—
995C2×C4—48no—
996C2×C4—48no—
997C2×C4—48no—
998C2×C4—416no—
999C2×C4—816no—
1000C2×C4#542116yescomplemented
1001C2×C4C22×#4114yes—
1002C2×C4C22×#4112yes—
1003C2×C4C22×#4118yes—
1004C2×C4C22×#4114yes—
1005C2×C4C22×#4118yes—
1006C2×C4C22×#4112yes—
1007C2×C4C22×#4112yes—
1008C2×C4C22×#4114yes—
1009C2×C4C22×#4112yes—
1010C2×C4C22×#4112yes—
1011C2×C4C22×#4112yes—
1012C2×C4C2×H(5,𝔽2)12yes—
1013C2×C4C2×H(5,𝔽2)12yes—
1014C2×C4C2×2−1+412yes—
1015C2×C4C2×2−1+412yes—
1016C2×C4#58514yes—
1017C22—24no—
1018C22—24no—
1019C22—22no—
1020C22—22no—
1021C22—48no—
1022C22—44no—
1023C22—48no—
1024C22—44no—
1025C22—42no—
1026C22—44no—
1027C22—42no—
1028C22—44no—
1029C22—42no—
1030C22—44no—
1031C22C2×#54214yes—
1032C22C23×#4112yes—
1033C22C23×#4111yescharacteristic
1034C22C22×H(5,𝔽2)11yescharacteristic
1035C22C22×2−1+411yescharacteristic
1036C22C2×#58512yes—
1037C4—24no—
1038C4—24no—
1039C4—24no—
1040C4—28no—
1041C4—28no—
1042C4—22no—
1043C4—22no—
1044C4—22no—
1045C4—44no—
1046C4—42no—
1047C4—44no—
1048C4—48no—
1049C4—44no—
1050C4—42no—
1051C4—42no—
1052C4—44no—
1053C4—42no—
1054C4—44no—
1055C4#344414yes—
1056C4C2×#54214yes—
1057C4C2×#54214yes—
1058C2—24no—
1059C2—84no—
1060C2—82no—
1061C2C2×#344411yescharacteristic
1062C2C22×#54211yescharacteristic
1063C2#6268611yescharacteristic
1064C2#6278812yes—
1065C2#6280012yes—
subgroupG/H
centerC22×C4C25
commutator, Frattini, socle, cosocleC23C26
prime radical#34937C2
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. #36641C2semidirect
2. #36639C2semidirect
3. #35243C2semidirect
4. #35230C2semidirect
5. #35199C2semidirect
6. #35198C2semidirect
7. #35186C2semidirect
8. #35184C2semidirect
9. #35117C2semidirect
10. #35114C2semidirect
11. #35060C2semidirect
12. #34974C2semidirect
13. #34968C2semidirect
14. #34955C2semidirect
15. #34952C2semidirect
16. #34938C2semidirect
18. #34745C2semidirect
19. #34744C2semidirect
20. #34603C2semidirect
21. C4×#542C2semidirect
22. C4×#532C2semidirect
23. #34026C2semidirect
24. C2×C42×Q8C2semidirect
558. C4×Q8#41semidirect
1000. C2×C4#542semidirect

Maximal subgroups

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

subgroupindex
#366412
#366392
#352432
#352302
#351992
#351982
#351862
#351842
#351172
#351142
#350602
#349742
#349682
#349552
#349522
#349382
#349372
#347452
#347442
#346032
C4×#5422
C4×#5322
#340262
C2×C42×Q82