Finite Group Databasebeta

← #7688395

Subgroups — #7688395

Order 512.

4623 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59821C211yesmaximal, characteristic
2#59749C214yesmaximal, complemented
3#59679C212yesmaximal
4#59653C212yesmaximal, complemented
5#59449C214yesmaximal, complemented
6#59435C212yesmaximal, complemented
7#45309C214yesmaximal, complemented
8#44111C218yesmaximal, complemented
9#40027C214yesmaximal, complemented
10#39219C214yesmaximal, complemented
11#39203C212yesmaximal, complemented
12#39192C212yesmaximal, complemented
13#36598C211yesmaximal, characteristic, complemented
14#36584C212yesmaximal, complemented
15#36563C211yesmaximal, characteristic, complemented
16#36562C212yesmaximal, complemented
17#36559C211yesmaximal, characteristic
18#36299C212yesmaximal, complemented
19#36285C212yesmaximal, complemented
20#35720C214yesmaximal, complemented
21#34954C212yesmaximal
22#34954C211yesmaximal, characteristic
23#34322C212yesmaximal, complemented
24#34317C212yesmaximal, complemented
25C4×#557C211yesmaximal, characteristic, complemented
26C4×#557C211yesmaximal, characteristic, complemented
27C2×#557C2211yescharacteristic
28C2×#557C2211yescharacteristic
29C2×#556C2212yes—
30C2×#554C2212yes—
31#2868C2211yescharacteristic
32#2863C2214yes—
33#2862C2212yes—
34#2859C2212yes—
35#2859C2214yes—
36#2859C2212yes—
37#2800C2218yes—
38#2798C2218yes—
39#2783C2218yes—
40#2777C2218yes—
41#2775C2218yes—
42#2772C2218yes—
43#2772C2218yes—
44#2754C2218yes—
45#2727C2214yes—
46#2725C2218yes—
47#2725C2218yes—
48#2652C2218yes—
49#2625C2214yes—
50#2606C2218yes—
51#2604C2218yes—
52#2593C2214yes—
53#2593C2218yes—
54#2590C2218yes—
55#2582C2212yes—
56#2582C2211yescharacteristic
57#2582C2212yes—
58#2575C2218yes—
59#2571C2214yes—
60#2571C2214yes—
61#2571C2211yescharacteristic
62#2571C2212yes—
63#2570C2214yes—
64#2570C2214yes—
65#2568C2212yes—
66#2567C2212yes—
67#2566C2214yes—
68#2566C2214yes—
69#2565C2214yes—
70#2563C2212yes—
71#2556C2218yes—
72#2556C2218yes—
73#2552C2212yes—
74#2550C2214yes—
75#2548C2211yescharacteristic
76#2548C2212yes—
77#2548C2211yescharacteristic
78#2545C2214yes—
79#2542C2212yes—
80#2538C2212yes—
81#2538C2212yes—
82#2538C2212yes—
83#2529C2218yes—
84#2519C2218yes—
85#2517C2218yes—
86#2515C2218yes—
87#2513C2214yes—
88#2513C2214yes—
89#2513C2214yes—
90#2513C2212yes—
91#2513C2212yes—
92#2512C2214yes—
93#2512C2214yes—
94#2512C2214yes—
95#2511C2214yes—
96#2509C2214yes—
97#2509C2218yes—
98#2509C2218yes—
99#2509C2214yes—
100#2507C2214yes—
101#2507C2214yes—
102#2496C2214yes—
103#2495C2214yes—
104#2489C2214yes—
105#2478C2218yes—
106#2475C2218yes—
107#2466C2218yes—
108#2452C2214yes—
109#2452C2214yes—
110#2451C2214yes—
111#2448C2214yes—
112#2448C2214yes—
113#2448C2212yes—
114#2448C2214yes—
115#2448C2212yes—
116#2447C2214yes—
117#2446C2214yes—
118#2446C2214yes—
119#2441C2214yes—
120#2429C2214yes—
121#2429C2214yes—
122#2421C2214yes—
123#2415C2214yes—
124#2395C2218yes—
125#2395C2214yes—
126#2373C2218yes—
127#2370C2214yes—
128#2370C2214yes—
129#2370C2214yes—
130#2370C2212yes—
131#2370C2212yes—
132#2369C2212yes—
133#2367C2214yes—
134#2365C2211yescharacteristic
135#2365C2211yescharacteristic
136#2365C2212yes—
137#2365C2212yes—
138#2365C2212yes—
139#2362C2214yes—
140#2362C2218yes—
141#2360C2214yes—
142#2360C2214yes—
143#2357C2214yes—
144#2356C2214yes—
145#2355C2211yescharacteristic
146#2355C2212yes—
147#2355C2212yes—
148#2355C2212yes—
149#2355C2212yes—
150#2355C2212yes—
151#2355C2211yescharacteristic
152#2354C2212yes—
153#2351C2214yes—
154#2351C2214yes—
155#2351C2212yes—
156#2351C2212yes—
157Q8×C4⋊C4C2211yescharacteristic
158Q8×C4⋊C4C2212yes—
159Q8×C4⋊C4C2211yescharacteristic
160Q8×C4⋊C4C2212yes—
161D4×C4⋊C4C2212yes—
162D4×C4⋊C4C2212yes—
163#2346C2214yes—
164#2344C2214yes—
165#2334C2218yes—
166#2332C2218yes—
167#2323C2214yes—
168#2323C2214yes—
169C4×C4⋊Q8C2212yes—
170C4×C4⋊Q8C2212yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2211yescharacteristic
174C4×C4⋊Q8C2211yescharacteristic
175C4×#127C2212yes—
176C4×#127C2211yescharacteristic
177C4×#125C2214yes—
178C4×#125C2212yes—
179C4×#125C2212yes—
180C4×#125C2214yes—
181C4×#125C2214yes—
182C4×#124C2212yes—
183C4×#124C2214yes—
184C4×#124C2212yes—
185C4×#124C2214yes—
186#2295C2214yes—
187#2293C2212yes—
188#2293C2214yes—
189#2293C2212yes—
190#2293C2214yes—
191#2274C2214yes—
192C42×Q8C2212yes—
193C42×Q8C2212yes—
194C42×Q8C2211yescharacteristic
195C42×Q8C2212yes—
196C42×Q8C2211yescharacteristic
197C42×Q8C2212yes—
198C42×Q8C2211yescharacteristic
199#557—28no—
200#557—28no—
201#556—216no—
202#554—216no—
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2311yescharacteristic
210C2×#127C2311yescharacteristic
211C2×#126C2318yes—
212C2×#126C2318yes—
213C2×#125C2314yes—
214C2×#125C2312yes—
215C2×#125C2312yes—
216C2×#125C2314yes—
217C2×#125C2314yes—
218C2×#125C2314yes—
219C2×#124C2314yes—
220C2×#124C2312yes—
221C2×#124C2312yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2318yes—
225C2×C22⋊Q8C2314yes—
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2314yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2311yescharacteristic
248C2×C4×D4C2312yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2312yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2314yes—
254C2×#117C2314yes—
255C2×#117C2314yes—
256C2×#117C2318yes—
257C22×C4⋊C4C2314yes—
258#400C2318yes—
259#400C2318yes—
260#400C2318yes—
261#400C2318yes—
262#400C2314yes—
263#400C2318yes—
264#400C2318yes—
265#400C2318yes—
266#399C2314yes—
267#399C2318yes—
268#399C2318yes—
269#398C2318yes—
270#398C2318yes—
271#398C2318yes—
272#398C2318yes—
273#398C2314yes—
274#398C2318yes—
275#398C2318yes—
276#397C2318yes—
277#397C2318yes—
278#397C2318yes—
279#397C2314yes—
280#397C2318yes—
281#397C2314yes—
282#397C2314yes—
283#397C2318yes—
284#397C2318yes—
285#397C2318yes—
286#396C2318yes—
287#396C2318yes—
288#396C2318yes—
289#396C2318yes—
290#396C2318yes—
291#396C2318yes—
292#395C2318yes—
293#394C2314yes—
294#394C2318yes—
295#394C2314yes—
296#393C2318yes—
297#391C2314yes—
298#391C2312yes—
299#391C2314yes—
300#391C2312yes—
301#391C2312yes—
302#391C2312yes—
303#391C2312yes—
304#391C2312yes—
305#391C2312yes—
306#391C2314yes—
307#391C2314yes—
308#391C2314yes—
309#391C2314yes—
310#391C2314yes—
311#391C2312yes—
312#391C2318yes—
313#391C2314yes—
314#390C2314yes—
315#390C2312yes—
316#390C2312yes—
317#390C2314yes—
318#390C2312yes—
319#390C2314yes—
320#390C2312yes—
321#390C2314yes—
322#390C2314yes—
323#390C2312yes—
324#390C2312yes—
325#390C2314yes—
326#390C2312yes—
327#390C2312yes—
328#390C2312yes—
329#389C2312yes—
330#389C2314yes—
331#389C2312yes—
332#389C2312yes—
333#389C2312yes—
334#389C2314yes—
335#389C2312yes—
336#389C2314yes—
337#389C2314yes—
338#389C2314yes—
339#389C2314yes—
340#389C2312yes—
341#389C2314yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2312yes—
346#389C2314yes—
347#389C2312yes—
348#389C2314yes—
349#389C2312yes—
350#389C2314yes—
351#389C2312yes—
352#389C2314yes—
353#389C2318yes—
354#389C2314yes—
355#389C2318yes—
356#389C2312yes—
357#389C2314yes—
358#389C2318yes—
359#389C2314yes—
360#389C2312yes—
361#389C2318yes—
362#389C2314yes—
363#389C2318yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2318yes—
368#389C2314yes—
369#389C2318yes—
370#389C2318yes—
371#389C2314yes—
372#389C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2314yes—
380#388C2318yes—
381#388C2318yes—
382#388C2314yes—
383#388C2318yes—
384#388C2318yes—
385#388C2314yes—
386#388C2318yes—
387#388C2318yes—
388#388C2314yes—
389#388C2314yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2314yes—
394#388C2314yes—
395#388C2314yes—
396#387C2314yes—
397#387C2318yes—
398#387C2314yes—
399#387C2314yes—
400#387C2318yes—
401#387C2314yes—
402#387C2314yes—
403#387C2314yes—
404#387C2314yes—
405#387C2314yes—
406#387C2314yes—
407#387C2314yes—
408#387C2314yes—
409#387C2314yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#385C2318yes—
423#385C2318yes—
424#385C2318yes—
425#385C2318yes—
426#384C2311yescharacteristic
427#384C2312yes—
428#384C2311yescharacteristic
429#384C2312yes—
430#384C2311yescharacteristic
431#384C2312yes—
432#384C2312yes—
433#384C2314yes—
434#384C2312yes—
435#384C2314yes—
436#384C2312yes—
437#383C2318yes—
438#382C2312yes—
439#382C2314yes—
440#382C2312yes—
441#382C2314yes—
442#382C2314yes—
443#382C2314yes—
444#382C2314yes—
445#382C2314yes—
446#382C2312yes—
447#382C2318yes—
448#382C2312yes—
449#382C2318yes—
450#382C2314yes—
451#381C2318yes—
452#380C2314yes—
453#380C2314yes—
454#380C2314yes—
455C4×C4⋊C4C2312yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2312yes—
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2318yes—
474C4×C4⋊C4C2318yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2318yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2314yes—
508C4×C4⋊C4C2311yescharacteristic
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2318yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2318yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2318yes—
516#376C2318yes—
517C43C2314yes—
518C43C2312yes—
519C43C2312yes—
520C43C2314yes—
521C43C2311yescharacteristic
522C43C2312yes—
523C22×Q8C2412yes—
524C22×Q8C2411yescharacteristic
525C22×Q8C2411yescharacteristic
526C22×Q8C2412yes—
527C22×Q8C2411yescharacteristic
528C22×Q8C2414yes—
529C22×D4C2412yes—
530C22×D4C2412yes—
531C22×D4C2412yes—
532C23×C4C2414yes—
533C23×C4C2418yes—
534C4⋊Q8—28no—
535C4⋊Q8—28no—
536C4⋊Q8—28no—
537C4⋊Q8—24no—
538C4⋊Q8—44no—
539C4⋊Q8—82no—
540C4⋊Q8#4118yes—
541#127—24no—
542#126—232no—
543#126—88no—
544#125—216no—
545#125—28no—
546#125—216no—
547#125—216no—
548#125—28no—
549#125—84no—
550#124—216no—
551#124—28no—
552#124—44no—
553C22⋊Q8—216no—
554C22⋊Q8—232no—
555C22⋊Q8—216no—
556C22⋊Q8—48no—
557C4×Q8—216no—
558C4×Q8—28no—
559C4×Q8—28no—
560C4×Q8—24no—
561C4×Q8—28no—
562C4×Q8—28no—
563C4×Q8—28no—
564C4×Q8—24no—
565C4×Q8—28no—
566C4×Q8—24no—
567C4×Q8—24no—
568C4×Q8—28no—
569C4×Q8—24no—
570C4×Q8—24no—
571C4×Q8—44no—
572C4×Q8—44no—
573C4×Q8—42no—
574C4×Q8—44no—
575C4×Q8—48no—
576C4×Q8—42no—
577C4×Q8—84no—
578C4×Q8#4118yes—
579C4×D4—216no—
580C4×D4—28no—
581C4×D4—28no—
582C4×D4—48no—
583C4×D4—44no—
584C4×D4—84no—
585#117—216no—
586#117—48no—
587#117—88no—
588C2×C4⋊C4—216no—
589C2×C4⋊C4C2418yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2412yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2418yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C42C2412yes—
669C2×C42C2412yes—
670C2×C42C2418yes—
671C2×C42C2412yes—
672C2×C42C2411yescharacteristic
673C2×C42C2412yes—
674C2×C42C2414yes—
675C2×C42C2414yes—
676C2×C42C2412yes—
677C2×C42C2414yes—
678C2×C42C2412yes—
679C2×C42C2412yes—
680C2×C42C2411yescharacteristic
681C2×C42C2412yes—
682C2×C42C2414yes—
683C2×C42C2412yes—
684C2×C42C2412yes—
685C2×C42C2411yescharacteristic
686C2×C42C2414yes—
687C2×C42C2412yes—
688C2×C42C2412yes—
689C2×C42C2414yes—
690C2×C42C2414yes—
691C2×C42C2412yes—
692C2×C42C2412yes—
693C2×C42C2418yes—
694C2×C42C2414yes—
695C2×C42C2412yes—
696C2×C42C2414yes—
697C2×C42C2414yes—
698C2×C42C2412yes—
699C2×C42C2418yes—
700C2×C42C2412yes—
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2412yes—
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706#95C2414yes—
707#95C2414yes—
708#95C2418yes—
709#95C2418yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2418yes—
714#95C2418yes—
715#95C2414yes—
716#95C2418yes—
717#95C2418yes—
718#95C2414yes—
719#95C2418yes—
720#95C2414yes—
721#95C2414yes—
722#95C2412yes—
723#95C2412yes—
724#95C2414yes—
725#95C2412yes—
726#95C2412yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2412yes—
731#95C2412yes—
732#95C2414yes—
733#95C2412yes—
734#95C2412yes—
735#95C2414yes—
736#95C2412yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2418yes—
741#95C2418yes—
742#95C2418yes—
743#95C2414yes—
744#95C2414yes—
745#95C2418yes—
746#95C2414yes—
747#95C2414yes—
748#95C2418yes—
749#95C2418yes—
750C24C2514yes—
751C2×Q8—22no—
752C2×Q8—22no—
753C2×Q8—24no—
754C2×Q8—24no—
755C2×Q8—22no—
756C2×Q8—28no—
757C2×Q8—24no—
758C2×Q8—22no—
759C2×Q8—22no—
760C2×Q8—22no—
761C2×Q8—24no—
762C2×Q8—24no—
763C2×Q8—22no—
764C2×Q8—44no—
765C2×Q8—44no—
766C2×Q8C2×#4118yes—
767C2×Q8C2×#4114yes—
768C2×Q82−1+414yes—
769C2×D4—24no—
770C2×D4—24no—
771C2×D4—24no—
772C2×D4—24no—
773C2×D4—24no—
774C2×D4—24no—
775C2×D4—24no—
776C2×D4—42no—
777C2×D4—42no—
778C22×C4—28no—
779C22×C4—28no—
780C22×C4—28no—
781C22×C4—216no—
782C22×C4—48no—
783C22×C4—48no—
784C22×C4C2512yes—
785C22×C4C2512yes—
786C22×C4C2512yes—
787C22×C4C2512yes—
788C22×C4C2511yescharacteristic
789C22×C4C2514yes—
790C22×C4C2512yes—
791C22×C4C2512yes—
792C22×C4C2512yes—
793C22×C4C2512yes—
794C22×C4C2514yes—
795C22×C4C2514yes—
796C22×C4C2514yes—
797C22×C4C2518yes—
798C22×C4C2512yes—
799C22×C4C2512yes—
800C22×C4C2514yes—
801C22×C4C2511yescharacteristic
802C22×C4C2511yescharacteristic
803C22×C4C2512yes—
804C22×C4C2512yes—
805C22×C4C2511yescharacteristic
806C22×C4C2511yescharacteristic
807C22×C4C2511yescharacteristic
808C22×C4C2511yescharacteristic
809C4⋊C4—216no—
810C4⋊C4—28no—
811C4⋊C4—24no—
812C4⋊C4—24no—
813C4⋊C4—24no—
814C4⋊C4—28no—
815C4⋊C4—22no—
816C4⋊C4—216no—
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—28no—
820C4⋊C4—24no—
821C4⋊C4—22no—
822C4⋊C4—22no—
823C4⋊C4—28no—
824C4⋊C4—28no—
825C4⋊C4—28no—
826C4⋊C4—24no—
827C4⋊C4—28no—
828C4⋊C4—216no—
829C4⋊C4—28no—
830C4⋊C4—28no—
831C4⋊C4—24no—
832C4⋊C4—24no—
833C4⋊C4—28no—
834C4⋊C4—24no—
835C4⋊C4—28no—
836C4⋊C4—22no—
837C4⋊C4—24no—
838C4⋊C4—22no—
839C4⋊C4—22no—
840C4⋊C4—24no—
841C4⋊C4—24no—
842C4⋊C4—28no—
843C4⋊C4—22no—
844C4⋊C4—22no—
845C4⋊C4—24no—
846C4⋊C4—44no—
847C4⋊C4—44no—
848C4⋊C4—48no—
849C4⋊C4—48no—
850C4⋊C4—42no—
851C4⋊C4—44no—
852C4⋊C4—44no—
853C4⋊C4—42no—
854C4⋊C4—44no—
855C4⋊C4—48no—
856C4⋊C4—44no—
857C4⋊C4—42no—
858C4⋊C4—42no—
859C4⋊C4—48no—
860C4⋊C4—42no—
861C4⋊C4—48no—
862C4⋊C4—44no—
863C4⋊C4—44no—
864C4⋊C4—44no—
865C4⋊C4—44no—
866C4⋊C4C2×#4114yes—
867C4⋊C4C2×#4118yes—
868C4⋊C4C2×#4118yes—
869C4⋊C4C2×#4118yes—
870C22⋊C4—216no—
871C22⋊C4—28no—
872C22⋊C4—216no—
873C22⋊C4—28no—
874C22⋊C4—216no—
875C22⋊C4—28no—
876C22⋊C4—28no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C22⋊C4—48no—
881C22⋊C4—48no—
882C22⋊C4—44no—
883C22⋊C4—48no—
884C22⋊C4—48no—
885C22⋊C4—44no—
886C22⋊C4—44no—
887C22⋊C4—44no—
888C42—216no—
889C42—28no—
890C42—28no—
891C42—28no—
892C42—24no—
893C42—24no—
894C42—24no—
895C42—24no—
896C42—22no—
897C42—24no—
898C42—28no—
899C42—28no—
900C42—24no—
901C42—24no—
902C42—24no—
903C42—24no—
904C42—24no—
905C42—22no—
906C42—24no—
907C42—24no—
908C42—22no—
909C42—44no—
910C42—44no—
911C42—42no—
912C42—42no—
913C42—44no—
914C42—42no—
915C42—48no—
916C42—44no—
917C42—44no—
918C42—42no—
919C42—48no—
920C42—42no—
921C42—41no—
922C42C2×#4114yes—
923C42C2×#4118yes—
924C42C2×#4114yes—
925C422−1+414yes—
926C23—24no—
927C23—24no—
928C23—24no—
929C23—24no—
930C23—24no—
931C23—24no—
932C23—24no—
933C23C2611yescharacteristic
934Q8—28no—
935Q8—216no—
936Q8—28no—
937Q8—48no—
938Q8—44no—
939Q8—88no—
940D4—48no—
941D4—48no—
942D4—48no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—21no—
946C2×C4—24no—
947C2×C4—22no—
948C2×C4—21no—
949C2×C4—22no—
950C2×C4—21no—
951C2×C4—24no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—24no—
958C2×C4—22no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—28no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—24no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—24no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—21no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—21no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—28no—
993C2×C4—24no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—24no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—24no—
1001C2×C4—28no—
1002C2×C4—416no—
1003C2×C4—816no—
1004C2×C4C22×#4118yes—
1005C2×C4C22×#4114yes—
1006C2×C4C22×#4112yes—
1007C2×C4C22×#4114yes—
1008C2×C4C22×#4112yes—
1009C2×C4C22×#4112yes—
1010C2×C4C22×#4112yes—
1011C2×C4C22×#4112yes—
1012C2×C4C22×#4112yes—
1013C2×C4C2×2−1+414yes—
1014C2×C4C2×2−1+412yes—
1015C2×C4C2×2−1+412yes—
1016C2×C4C2×2−1+412yes—
1017C2×C4C2×2−1+412yes—
1018C2×C4#58512yes—
1019C2×C4#58512yes—
1020C22—44no—
1021C22—44no—
1022C22—44no—
1023C22—44no—
1024C22—44no—
1025C22—44no—
1026C22—44no—
1027C22C23×#4111yescharacteristic
1028C22C23×#4111yescharacteristic
1029C22C22×2−1+411yescharacteristic
1030C22C22×2−1+411yescharacteristic
1031C22C2×#58511yescharacteristic
1032C22C2×#58511yescharacteristic
1033C22H(7,𝔽2)11yescharacteristic
1034C4—22no—
1035C4—24no—
1036C4—22no—
1037C4—28no—
1038C4—24no—
1039C4—22no—
1040C4—24no—
1041C4—44no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—48no—
1046C4—42no—
1047C4—42no—
1048C4—42no—
1049C4—41no—
1050C4—42no—
1051C4—42no—
1052C4—42no—
1053C4—44no—
1054C4—44no—
1055C4—44no—
1056C4#348014yes—
1057C4#351514yes—
1058C4#352314yes—
1059C2—84no—
1060C2C2×#348011yescharacteristic
1061C2C2×#351511yescharacteristic
1062C2C2×#352311yescharacteristic
1063C2#6292611yescharacteristic
1064C2#6299911yescharacteristic
1065C2#6301011yescharacteristic
1066C2#6303411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #59749C2semidirect
4. #59653C2semidirect
5. #59449C2semidirect
6. #59435C2semidirect
7. #45309C2semidirect
8. #44111C2semidirect
9. #40027C2semidirect
10. #39219C2semidirect
11. #39203C2semidirect
12. #39192C2semidirect
13. #36598C2semidirect
14. #36584C2semidirect
15. #36563C2semidirect
16. #36562C2semidirect
18. #36299C2semidirect
19. #36285C2semidirect
20. #35720C2semidirect
23. #34322C2semidirect
24. #34317C2semidirect
25. C4×#557C2semidirect
26. C4×#557C2semidirect

Maximal subgroups

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

subgroupindex
#598212
#597492
#596792
#596532
#594492
#594352
#453092
#441112
#400272
#392192
#392032
#391922
#365982
#365842
#365632
#365622
#365592
#362992
#362852
#357202
#349542
#343222
#343172
C4×#5572