Finite Group Databasebeta

← #7624115

Subgroups — #7624115

Order 512.

1270 conjugacy classes of subgroups.

The subgroup lattice has 1205 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#61487C211yesmaximal, characteristic, complemented
2#61477C211yesmaximal, characteristic, complemented
3#33965C211yesmaximal, characteristic, complemented
4#33956C211yesmaximal, characteristic, complemented
5#33943C211yesmaximal, characteristic, complemented
6#33939C211yesmaximal, characteristic, complemented
7#33916C211yesmaximal, characteristic, complemented
8#33911C211yesmaximal, characteristic, complemented
9#33904C211yesmaximal, characteristic, complemented
10#33882C211yesmaximal, characteristic, complemented
11#33882C211yesmaximal, characteristic, complemented
12#33881C211yesmaximal, characteristic, complemented
13#33874C211yesmaximal, characteristic, complemented
14#33869C211yesmaximal, characteristic, complemented
15#33863C211yesmaximal, characteristic, complemented
16#33849C211yesmaximal, characteristic, complemented
17#33833C211yesmaximal, characteristic, complemented
18#33833C211yesmaximal, characteristic, complemented
19#33747C211yesmaximal, characteristic, complemented
20#33745C211yesmaximal, characteristic, complemented
21#33741C211yesmaximal, characteristic, complemented
22#33684C211yesmaximal, characteristic, complemented
23#33683C211yesmaximal, characteristic, complemented
24#33680C211yesmaximal, characteristic, complemented
25#33680C211yesmaximal, characteristic, complemented
26#33667C211yesmaximal, characteristic, complemented
27#33662C211yesmaximal, characteristic, complemented
28#33482C211yesmaximal, characteristic, complemented
29#33460C211yesmaximal, characteristic, complemented
30#33454C211yesmaximal, characteristic, complemented
31#33451C211yesmaximal, characteristic, complemented
32#3521—21no—
33#3515—21no—
34C2×#509C2211yescharacteristic
35C2×#508C2211yescharacteristic
36C2×#508C2211yescharacteristic
37#3395C2211yescharacteristic, complemented
38#3393C2211yescharacteristic
39#3380C2211yescharacteristic
40#3380C2211yescharacteristic, complemented
41#3376—21no—
42#3372—21no—
43#3342C2211yescharacteristic
44#3339C2211yescharacteristic
45#3338C2211yescharacteristic
46#3336C2211yescharacteristic
47#3336C2211yescharacteristic
48#3336C2211yescharacteristic, complemented
49#3331—21no—
50#3323—21no—
51#3315—21no—
52#3315—21no—
53#3311—21no—
54#3307—21no—
55#3283C2211yescharacteristic
56#3283C2211yescharacteristic
57#3283C2211yescharacteristic
58#3283C2211yescharacteristic, complemented
59#3280C2211yescharacteristic
60#3280C2211yescharacteristic
61#3177C2211yescharacteristic
62#3177C2211yescharacteristic
63#3177C2211yescharacteristic, complemented
64#3175C2211yescharacteristic
65#3170C2211yescharacteristic, complemented
66#3168C2211yescharacteristic
67#3125—21no—
68#3123—21no—
69#3120—21no—
70#3120—21no—
71#3116—21no—
72#3111—21no—
73#2966C2211yescharacteristic
74#2951C2211yescharacteristic
75#2951C2211yescharacteristic
76#2951C2211yescharacteristic, complemented
77#2948C2211yescharacteristic
78C4×#135C2211yescharacteristic
79C4×#135C2211yescharacteristic, complemented
80#2255C2211yescharacteristic, complemented
81#2255C2211yescharacteristic, complemented
82#2253C2211yescharacteristic, complemented
83#2251C2211yescharacteristic
84#2251C2211yescharacteristic
85#2247C2211yescharacteristic, complemented
86#2245C2211yescharacteristic, complemented
87#2245C2211yescharacteristic, complemented
88#2245C2211yescharacteristic, complemented
89#2243C2211yescharacteristic
90#2242C2211yescharacteristic
91#2241C2211yescharacteristic, complemented
92#2237C2211yescharacteristic
93#2237C2211yescharacteristic
94#2237C2211yescharacteristic, complemented
95#2237C2211yescharacteristic, complemented
96#2237C2211yescharacteristic, complemented
97#2236C2211yescharacteristic
98#2236C2211yescharacteristic, complemented
99#2236C2211yescharacteristic, complemented
100#2235C2211yescharacteristic
101#2235C2211yescharacteristic, complemented
102#2234C2211yescharacteristic
103#2232C2211yescharacteristic
104#2229C2211yescharacteristic, complemented
105#2229C2211yescharacteristic, complemented
106#2229C2211yescharacteristic, complemented
107#2228C2211yescharacteristic
108#2228C2211yescharacteristic
109#2228C2211yescharacteristic
110#2228C2211yescharacteristic, complemented
111#2228C2211yescharacteristic, complemented
112#2227C2211yescharacteristic, complemented
113#2225C2211yescharacteristic, complemented
114#2224C2211yescharacteristic
115#2224C2211yescharacteristic, complemented
116#2220C2211yescharacteristic
117#2219C2211yescharacteristic
118#2219C2211yescharacteristic
119#2219C2211yescharacteristic, complemented
120#2217C2211yescharacteristic
121#2217C2211yescharacteristic
122#2217C2211yescharacteristic
123#2216C2211yescharacteristic
124#2216C2211yescharacteristic
125#2216C2211yescharacteristic, complemented
126#2216C2211yescharacteristic, complemented
127#2216C2211yescharacteristic, complemented
128#2211C2211yescharacteristic
129#2211C2211yescharacteristic
130#2210C2211yescharacteristic
131#2210C2211yescharacteristic
132#2209C2211yescharacteristic, complemented
133#2209C2211yescharacteristic, complemented
134#2209C2211yescharacteristic, complemented
135#2208C2211yescharacteristic
136#2208C2211yescharacteristic
137#2208C2211yescharacteristic
138#2208C2211yescharacteristic
139#2208C2211yescharacteristic, complemented
140#2189C2211yescharacteristic
141#2189C2211yescharacteristic
142#2189C2211yescharacteristic
143#2189C2211yescharacteristic
144#2189C2211yescharacteristic
145#2189C2211yescharacteristic
146#2189C2211yescharacteristic, complemented
147#2189C2211yescharacteristic, complemented
148#2187C2211yescharacteristic
149#2187C2211yescharacteristic
150#2186C2211yescharacteristic
151#2186C2211yescharacteristic
152#2183C2211yescharacteristic, complemented
153#2183C2211yescharacteristic, complemented
154#2177C2211yescharacteristic
155#2177C2211yescharacteristic
156#2177C2211yescharacteristic
157#2177C2211yescharacteristic
158#2176C2211yescharacteristic, complemented
159#2176C2211yescharacteristic, complemented
160#2176C2211yescharacteristic, complemented
161#2176C2211yescharacteristic, complemented
162#2176C2211yescharacteristic, complemented
163#2175C2211yescharacteristic
164#2175C2211yescharacteristic
165#2175C2211yescharacteristic
166#2175C2211yescharacteristic
167#2175C2211yescharacteristic
168#2175C2211yescharacteristic, complemented
169#2175C2211yescharacteristic, complemented
170C4×Q32C2211yescharacteristic, complemented
171C4×Q32C2211yescharacteristic, complemented
172C4×Q32C2211yescharacteristic, complemented
173C4×SD32C2211yescharacteristic
174C4×SD32C2211yescharacteristic
175C4×SD32C2211yescharacteristic
176C4×SD32C2211yescharacteristic
177C4×SD32C2211yescharacteristic
178C4×SD32C2211yescharacteristic, complemented
179C4×SD32C2211yescharacteristic, complemented
180C4×D16C2211yescharacteristic
181C4×D16C2211yescharacteristic
182#2168C2211yescharacteristic
183#2168C2211yescharacteristic
184#2168C2211yescharacteristic
185#2168C2211yescharacteristic, complemented
186D4×C16C2211yescharacteristic
187D4×C16C2211yescharacteristic, complemented
188#2164C2211yescharacteristic
189#2164C2211yescharacteristic, complemented
190#2162C2211yescharacteristic, complemented
191#2159C2211yescharacteristic
192#2158C2211yescharacteristic, complemented
193C2×#367C2211yescharacteristic, complemented
194#2139C2211yescharacteristic
195#2139C2211yescharacteristic, complemented
196#2138C2211yescharacteristic
197#2138C2211yescharacteristic
198#2138C2211yescharacteristic, complemented
199C2×#357C2211yescharacteristic
200#2108C2211yescharacteristic
201#2108C2211yescharacteristic, complemented
202C2×#346C2211yescharacteristic, complemented
203C2×#135C2311yescharacteristic
204C2×#135C2311yescharacteristic
205C2×#135C2311yescharacteristic
206C2×#135C2311yescharacteristic
207C2×#135C2311yescharacteristic
208C22×D8C2311yescharacteristic
209#557—21no—
210#556—21no—
211#556—21no—
212#554—21no—
213#554—21no—
214#554—21no—
215#553—21no—
216#553—41no—
217#553—41no—
218#552—21no—
219#552—21no—
220#552—21no—
221#552—41no—
222#552—41no—
223#552—41no—
224#552—41no—
225#551—41no—
226#551—41no—
227#547—21no—
228#547—21no—
229#547—21no—
230#547—21no—
231#546—21no—
232#546—21no—
233#542—21no—
234#541—21no—
235#541—21no—
236#541—21no—
237#539—41no—
238#539—41no—
239#539—41no—
240#538—41no—
241#533—21no—
242#529—21no—
243#529—41no—
244#529—41no—
245#529D411yescharacteristic
246C2×#126—41no—
247C2×#125—41no—
248#520—21no—
249#520—21no—
250#520—21no—
251#518—21no—
252C4×#41—21no—
253C4×#41—21no—
254#509—24no—
255#508—24no—
256#508—24no—
257C2×Q32C2311yescharacteristic
258C2×Q32C2311yescharacteristic
259C2×Q32C2311yescharacteristic
260C2×Q32C2311yescharacteristic
261C2×Q32C2311yescharacteristic
262C2×Q32C2311yescharacteristic
263C2×SD32C2311yescharacteristic
264C2×SD32C2311yescharacteristic
265C2×SD32C2311yescharacteristic
266C2×SD32C2311yescharacteristic
267C2×SD32C2311yescharacteristic
268C2×SD32C2311yescharacteristic
269C2×SD32C2311yescharacteristic
270C2×SD32C2311yescharacteristic
271C2×D16C2311yescharacteristic
272C2×D16C2311yescharacteristic
273C2×M32C2311yescharacteristic
274C2×M32C2311yescharacteristic
275C22×C16C2311yescharacteristic
276C22×C16C2311yescharacteristic
277C22×C16C2311yescharacteristic
278C22×C16C2311yescharacteristic
279#500C2311yescharacteristic
280#500C2311yescharacteristic
281#499C2311yescharacteristic
282#499C2311yescharacteristic
283#499C2311yescharacteristic
284#499C2311yescharacteristic
285#495C2311yescharacteristic
286#495C2311yescharacteristic
287#494C2311yescharacteristic
288#494C2311yescharacteristic
289#494C2311yescharacteristic
290#494C2311yescharacteristic
291#491—21no—
292#491—21no—
293#491—21no—
294#489—21no—
295#488—21no—
296#487—21no—
297#485—21no—
298#485—21no—
299#485—21no—
300#485—21no—
301#485—21no—
302#484—21no—
303#484—21no—
304#483—21no—
305#483—21no—
306#483—21no—
307#482—21no—
308#481—21no—
309#479—21no—
310#479—21no—
311#479—21no—
312#478—21no—
313#478—21no—
314#478—21no—
315#478—21no—
316#478—21no—
317#477—21no—
318#476—21no—
319#476—21no—
320#475—21no—
321#470—21no—
322#470—21no—
323#470—21no—
324#468—21no—
325#467—21no—
326#467C2311yescharacteristic
327#467C2311yescharacteristic
328#467C2311yescharacteristic
329#467C2311yescharacteristic
330#467C2311yescharacteristic
331#467C2311yescharacteristic
332#467C2311yescharacteristic
333#467C2311yescharacteristic
334#467C2311yescharacteristic
335#467C2311yescharacteristic
336#466C2311yescharacteristic
337#466C2311yescharacteristic
338#465—21no—
339#464—21no—
340#464—21no—
341#463—21no—
342#463—21no—
343#462—21no—
344#462—21no—
345#462—21no—
346#461—21no—
347#461—21no—
348#461—21no—
349#461—21no—
350#461—21no—
351#452—21no—
352#452—21no—
353#452—21no—
354#452—21no—
355#452—21no—
356#452—21no—
357#452—21no—
358#452—21no—
359#450—21no—
360#450—21no—
361#449—21no—
362#449—21no—
363#446D411yescharacteristic
364C8×Q8C2311yescharacteristic
365#442—21no—
366#442—21no—
367#441—21no—
368#441—21no—
369#441—21no—
370#440—21no—
371#440—21no—
372#440—21no—
373#440—21no—
374#440—21no—
375#440—21no—
376#440—21no—
377C4×Q16—21no—
378C4×Q16C2311yescharacteristic
379C4×Q16C2311yescharacteristic
380C4×Q16C2311yescharacteristic
381C4×Q16C2311yescharacteristic
382C4×Q16C2311yescharacteristic
383C4×Q16C2311yescharacteristic
384C4×Q16C2311yescharacteristic
385C4×Q16C2311yescharacteristic
386C4×Q16C2311yescharacteristic
387C4×Q16C2311yescharacteristic
388C4×SD16—21no—
389C4×SD16—21no—
390C4×SD16—21no—
391C4×SD16—21no—
392C4×SD16—21no—
393C4×D8C2311yescharacteristic
394C4×D8C2311yescharacteristic
395C4×D8C2311yescharacteristic
396C4×D8C2311yescharacteristic
397C4×D8C2311yescharacteristic
398C4×D8C2311yescharacteristic
399C4×D8C2311yescharacteristic
400C4×D8C2311yescharacteristic
401C4×D8C2311yescharacteristic
402C4×D8C2311yescharacteristic
403#436D411yescharacteristic
404#435D411yescharacteristic
405#435D411yescharacteristic
406C8×D4C2311yescharacteristic
407C8×D4C2311yescharacteristic
408C8×D4C2311yescharacteristic
409#433D411yescharacteristic
410#433D411yescharacteristic
411#432D411yescharacteristic
412#427C2311yescharacteristic
413#427C2311yescharacteristic
414#427C2311yescharacteristic
415C2×#107C2311yescharacteristic
416C2×#107C2311yescharacteristic
417C2×#107C2311yescharacteristic
418#418—21no—
419#417—21no—
420#417—21no—
421#417—21no—
422#416—21no—
423#416—21no—
424#405C2311yescharacteristic
425#405C2311yescharacteristic
426C2×C4×C8C2311yescharacteristic
427#367C2311yescharacteristic
428#367C2311yescharacteristic
429#367C2311yescharacteristic
430#367C2311yescharacteristic
431#367C2311yescharacteristic
432#367C2311yescharacteristic
433#367C2311yescharacteristic
434#367C2311yescharacteristic
435#366C2311yescharacteristic
436#366C2311yescharacteristic
437#366C2311yescharacteristic
438#366C2311yescharacteristic
439#366C2311yescharacteristic
440#366C2311yescharacteristic
441#366C2311yescharacteristic
442#366C2311yescharacteristic
443C4⋊C16C2311yescharacteristic
444C4⋊C16C2311yescharacteristic
445C4⋊C16C2311yescharacteristic
446C4⋊C16C2311yescharacteristic
447C4⋊C16C2311yescharacteristic
448C4⋊C16C2311yescharacteristic
449#358C2311yescharacteristic
450#358C2311yescharacteristic
451#358C2311yescharacteristic
452#358C2311yescharacteristic
453#358C2311yescharacteristic
454#358C2311yescharacteristic
455#358C2311yescharacteristic
456#358C2311yescharacteristic
457#358C2311yescharacteristic
458#358C2311yescharacteristic
459#358C2311yescharacteristic
460#358C2311yescharacteristic
461#358C2311yescharacteristic
462#358C2311yescharacteristic
463#358C2311yescharacteristic
464#358C2311yescharacteristic
465#358C2311yescharacteristic
466#358C2311yescharacteristic
467#358C2311yescharacteristic
468#358C2311yescharacteristic
469#357C2311yescharacteristic
470#357C2311yescharacteristic
471#357C2311yescharacteristic
472#357C2311yescharacteristic
473#357C2311yescharacteristic
474#357C2311yescharacteristic
475#357C2311yescharacteristic
476#357C2311yescharacteristic
477#357C2311yescharacteristic
478#357C2311yescharacteristic
479#357C2311yescharacteristic
480#357C2311yescharacteristic
481C22⋊C16C2311yescharacteristic
482C22⋊C16C2311yescharacteristic
483C22⋊C16C2311yescharacteristic
484C22⋊C16C2311yescharacteristic
485C22⋊C16C2311yescharacteristic
486C22⋊C16C2311yescharacteristic
487#346C2311yescharacteristic
488#346C2311yescharacteristic
489#346C2311yescharacteristic
490#346C2311yescharacteristic
491#346C2311yescharacteristic
492#346C2311yescharacteristic
493C4×C16C2311yescharacteristic
494C4×C16C2311yescharacteristic
495C4×C16C2311yescharacteristic
496C4×C16C2311yescharacteristic
497C2×#41—21no—
498C2×#41—21no—
499C2×#41—21no—
500C2×#41—21no—
501C2×#41—21no—
502C22×D4—21no—
503#135—22no—
504#135—22no—
505#135—22no—
506#135—22no—
507#135—22no—
508#135—41no—
509#135—41no—
510#135—41no—
511#135—41no—
512#135—41no—
513C2×Q16—21no—
514C2×Q16—21no—
515C2×Q16—21no—
516C2×Q16—21no—
517C2×Q16C2411yescharacteristic
518C2×Q16C2411yescharacteristic
519C2×Q16C2411yescharacteristic
520C2×Q16C2411yescharacteristic
521C2×Q16C2411yescharacteristic
522C2×SD16—21no—
523C2×SD16—21no—
524C2×SD16—21no—
525C2×SD16—21no—
526C2×SD16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×D8—22no—
530C2×D8—21no—
531C2×D8—41no—
532C2×D8C2411yescharacteristic
533C2×D8C2411yescharacteristic
534C2×D8C2411yescharacteristic
535C2×M16C2×D411yescharacteristic
536C2×M16C2×D411yescharacteristic
537C22×C8C2×D411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C4⋊Q8—21no—
542C4⋊Q8—21no—
543C4⋊Q8—21no—
544C4⋊Q8—21no—
545C4⋊Q8—21no—
546C4⋊Q8—21no—
547#126—41no—
548#126—41no—
549#126—41no—
550#126—41no—
551#126—41no—
552#126—41no—
553#126—41no—
554#126—41no—
555#126—41no—
556#126—41no—
557#126—41no—
558#126—41no—
559#126—41no—
560#126—41no—
561#126—41no—
562#126—41no—
563#126D811yescharacteristic
564#126D811yescharacteristic
565#125—21no—
566#125—21no—
567#125—21no—
568#125—21no—
569#125—41no—
570#125—41no—
571#125—41no—
572#125—41no—
573#125—41no—
574#125—41no—
575#125—41no—
576#125—41no—
577#125—41no—
578#125—41no—
579#125—41no—
580#125—41no—
581#125—41no—
582#125—41no—
583#125D811yescharacteristic
584#124—21no—
585#124—21no—
586#124—41no—
587#124—41no—
588#124D811yescharacteristic
589#123—41no—
590#123—41no—
591#123—41no—
592#123—41no—
593#123—41no—
594#123—41no—
595#123—41no—
596#123—41no—
597#123—41no—
598#123—41no—
599#123—41no—
600#123—41no—
601#123—41no—
602#123—41no—
603#123—41no—
604#123—41no—
605#123D811yescharacteristic
606#123D811yescharacteristic
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612C22⋊Q8—21no—
613C22⋊Q8—21no—
614C22⋊Q8—21no—
615C22⋊Q8—21no—
616C22⋊Q8—21no—
617C22⋊Q8—41no—
618C22⋊Q8—41no—
619C22⋊Q8—41no—
620C22⋊Q8—41no—
621C22⋊Q8—41no—
622C22⋊Q8—41no—
623C22⋊Q8—41no—
624C22⋊Q8—41no—
625C22⋊Q8—41no—
626C22⋊Q8—41no—
627C22⋊Q8—41no—
628C22⋊Q8D811yescharacteristic
629#121—21no—
630#121—21no—
631#121—41no—
632#121—41no—
633#121—41no—
634#121—41no—
635#121—41no—
636#121—41no—
637#121—41no—
638#121D811yescharacteristic
639#120—41no—
640#120—41no—
641C4×Q8—21no—
642C4×Q8—21no—
643C4×Q8—21no—
644C4×Q8—21no—
645C4×Q8—21no—
646C4×Q8—21no—
647C4×Q8—21no—
648C4×Q8—21no—
649C4×Q8—21no—
650C4×Q8—21no—
651C4×Q8—41no—
652C4×Q8—41no—
653C4×Q8—41no—
654C4×Q8C2×D411yescharacteristic
655C4×D4—21no—
656C4×D4—21no—
657C4×D4—21no—
658C4×D4—21no—
659C4×D4—21no—
660C4×D4—21no—
661C4×D4—21no—
662C4×D4—21no—
663C4×D4—21no—
664C4×D4—21no—
665C4×D4—41no—
666C4×D4—41no—
667C4×D4—41no—
668C4×D4—41no—
669C4×D4—41no—
670C4×D4—41no—
671C4×D4—41no—
672C4×D4—41no—
673C4×D4—41no—
674C4×D4—41no—
675C4×D4—41no—
676C4×D4—41no—
677C4×D4—41no—
678C4×D4—41no—
679C4×D4—41no—
680C4×D4C2×D411yescharacteristic
681C4×D4C2×D411yescharacteristic
682C4×D4C2×D411yescharacteristic
683#117—21no—
684#117—21no—
685#117—21no—
686#117—41no—
687#117—41no—
688#117—41no—
689#117—41no—
690#117—41no—
691#117—41no—
692#117—41no—
693#117—41no—
694#117—41no—
695#117—41no—
696#117—41no—
697#117C2×D411yescharacteristic
698#117C2×D411yescharacteristic
699C2×C4⋊C4—21no—
700C2×C4⋊C4—21no—
701C2×C4⋊C4—21no—
702C2×C4⋊C4—41no—
703C2×C4⋊C4—41no—
704C2×C4⋊C4—41no—
705C2×C4⋊C4—41no—
706C2×C4⋊C4—41no—
707C2×C4⋊C4—41no—
708C2×C4⋊C4—41no—
709C2×C4⋊C4—41no—
710C2×C4⋊C4—41no—
711C2×C22⋊C4—41no—
712C2×C22⋊C4—41no—
713C2×C22⋊C4—41no—
714C2×C22⋊C4—41no—
715C2×C42—41no—
716C2×C42—41no—
717C2×C42C2×D411yescharacteristic
718Q32—22no—
719Q32—22no—
720Q32—41no—
721Q32—41no—
722Q32—41no—
723Q32—41no—
724SD32—22no—
725SD32—22no—
726SD32—22no—
727SD32—22no—
728SD32—22no—
729SD32—22no—
730SD32—41no—
731SD32—41no—
732D16—22no—
733D16#4114yes—
734M32—22no—
735M32—41no—
736C2×C16—22no—
737C2×C16—22no—
738C2×C16—41no—
739C2×C16—41no—
740C2×C16C2411yescharacteristic
741C2×C16C2411yescharacteristic
742C2×C16C2411yescharacteristic
743C2×C16C2411yescharacteristic
744C2×C16C2411yescharacteristic
745C2×C16C2411yescharacteristic
746C2×C16C2411yescharacteristic
747C2×C16C2411yescharacteristic
748#107—21no—
749#107—21no—
750#107—21no—
751#107—21no—
752#107—21no—
753#107C2411yescharacteristic
754#107C2411yescharacteristic
755#107C2411yescharacteristic
756#107C2411yescharacteristic
757#107C2411yescharacteristic
758#107C2411yescharacteristic
759#107C2411yescharacteristic
760#107C2411yescharacteristic
761#106—21no—
762#106—21no—
763#106—21no—
764#106—21no—
765#106—21no—
766#106—21no—
767#106—21no—
768C4⋊C8C2×D411yescharacteristic
769C4⋊C8C2×D411yescharacteristic
770C4⋊C8C2×D411yescharacteristic
771C4⋊C8C2×D411yescharacteristic
772C4⋊C8C2×D411yescharacteristic
773C4⋊C8C2×D411yescharacteristic
774#103—21no—
775#103—21no—
776#103—21no—
777#103—21no—
778#103—21no—
779#103—21no—
780#103—21no—
781#103—21no—
782#103—21no—
783#103—21no—
784#103—21no—
785#103—21no—
786#103—21no—
787#103—21no—
788#103—21no—
789#103—21no—
790#103—21no—
791#103—21no—
792#103—21no—
793#103—21no—
794#102—21no—
795#102—21no—
796#102—21no—
797#102—21no—
798#102—21no—
799#102—21no—
800#102—21no—
801#102—21no—
802#102—21no—
803#102—21no—
804#102—21no—
805#102—21no—
806C22⋊C8C2×D411yescharacteristic
807C22⋊C8C2×D411yescharacteristic
808C22⋊C8C2×D411yescharacteristic
809C22⋊C8C2×D411yescharacteristic
810C22⋊C8C2×D411yescharacteristic
811C22⋊C8C2×D411yescharacteristic
812#97C2×D411yescharacteristic
813#97C2×D411yescharacteristic
814#97C2×D411yescharacteristic
815#97C2×D411yescharacteristic
816C4×C8C2×D411yescharacteristic
817C4×C8C2×D411yescharacteristic
818C4×C8C2411yescharacteristic
819C4×C8C2411yescharacteristic
820C4×C8C2411yescharacteristic
821C4×C8C2411yescharacteristic
822C24—41no—
823#41—42no—
824#41—42no—
825#41—42no—
826#41—42no—
827#41—42no—
828#41—81no—
829#41—81no—
830#41—81no—
831#41—81no—
832#41—81no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—41no—
839C2×Q8—41no—
840C2×Q8C2×D811yescharacteristic
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—42no—
845C2×D4—41no—
846C2×D4—41no—
847C2×D4—41no—
848C2×D4—41no—
849C2×D4—41no—
850C2×D4—41no—
851C2×D4—41no—
852C2×D4—41no—
853C2×D4—81no—
854C2×D4C2×D811yescharacteristic
855C2×D4C2×D811yescharacteristic
856C2×D4C2×D811yescharacteristic
857C22×C4—41no—
858C22×C4—41no—
859C22×C4—41no—
860C22×C4—41no—
861C22×C4—41no—
862C22×C4—41no—
863C22×C4—41no—
864C22×C4—41no—
865C22×C4—41no—
866C22×C4—41no—
867C22×C4—41no—
868C22×C4—41no—
869C22×C4—41no—
870C22×C4—41no—
871C22×C4—41no—
872C22×C4—41no—
873C22×C4—41no—
874C22×C4—41no—
875C22×C4C2×D811yescharacteristic
876C22×C4C2×D811yescharacteristic
877C22×C4C22×D411yescharacteristic
878C22×C4C22×D411yescharacteristic
879C22×C4C22×D411yescharacteristic
880Q16—21no—
881Q16—21no—
882Q16—21no—
883Q16—21no—
884Q16—21no—
885Q16—21no—
886Q16—21no—
887Q16—21no—
888Q16—21no—
889Q16—21no—
890Q16—81no—
891Q16—81no—
892Q16—81no—
893Q16—81no—
894SD16—42no—
895SD16—42no—
896SD16—42no—
897SD16—42no—
898SD16—42no—
899SD16—81no—
900SD16—81no—
901D8—21no—
902D8—21no—
903D8—21no—
904D8—21no—
905D8—42no—
906D8C2×#4112yes—
907D8C2×#4112yes—
908M16—41no—
909M16—41no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—41no—
917C2×C8C22×D411yescharacteristic
918C2×C8C22×D411yescharacteristic
919C2×C8C22×D411yescharacteristic
920C2×C8C22×D411yescharacteristic
921C2×C8C22×D411yescharacteristic
922C2×C8C22×D411yescharacteristic
923C2×C8C22×D411yescharacteristic
924C2×C8C2511yescharacteristic
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—41no—
934C4⋊C4—41no—
935C4⋊C4—41no—
936C4⋊C4—41no—
937C4⋊C4—41no—
938C4⋊C4—41no—
939C4⋊C4—41no—
940C4⋊C4—41no—
941C4⋊C4—41no—
942C4⋊C4—41no—
943C4⋊C4—41no—
944C4⋊C4—41no—
945C4⋊C4—41no—
946C4⋊C4—41no—
947C4⋊C4—41no—
948C4⋊C4—41no—
949C4⋊C4—41no—
950C4⋊C4—41no—
951C4⋊C4—41no—
952C4⋊C4—41no—
953C4⋊C4—41no—
954C4⋊C4—41no—
955C4⋊C4—41no—
956C4⋊C4—41no—
957C4⋊C4—41no—
958C4⋊C4—41no—
959C4⋊C4—41no—
960C4⋊C4—41no—
961C4⋊C4—41no—
962C4⋊C4—41no—
963C4⋊C4—41no—
964C4⋊C4—41no—
965C4⋊C4—41no—
966C4⋊C4—41no—
967C4⋊C4—41no—
968C4⋊C4—41no—
969C4⋊C4—41no—
970C4⋊C4—41no—
971C4⋊C4—41no—
972C4⋊C4—41no—
973C4⋊C4—41no—
974C4⋊C4C2×D811yescharacteristic
975C4⋊C4C2×D811yescharacteristic
976C4⋊C4C2×D811yescharacteristic
977C4⋊C4C2×D811yescharacteristic
978C4⋊C4C2×D811yescharacteristic
979C4⋊C4C2×D811yescharacteristic
980C4⋊C4C2×D811yescharacteristic
981C4⋊C4C2×D811yescharacteristic
982C4⋊C4C2×D811yescharacteristic
983C4⋊C4C2×D811yescharacteristic
984C22⋊C4—41no—
985C22⋊C4—41no—
986C22⋊C4—41no—
987C22⋊C4—41no—
988C22⋊C4—41no—
989C22⋊C4—41no—
990C22⋊C4—41no—
991C22⋊C4—41no—
992C22⋊C4—41no—
993C22⋊C4—41no—
994C22⋊C4—41no—
995C22⋊C4—41no—
996C22⋊C4—41no—
997C22⋊C4—41no—
998C22⋊C4—41no—
999C22⋊C4—41no—
1000C22⋊C4—41no—
1001C22⋊C4—41no—
1002C22⋊C4—41no—
1003C22⋊C4—41no—
1004C22⋊C4—41no—
1005C22⋊C4—41no—
1006C22⋊C4—41no—
1007C22⋊C4—41no—
1008C22⋊C4—41no—
1009C22⋊C4—41no—
1010C22⋊C4—41no—
1011C22⋊C4—41no—
1012C22⋊C4—41no—
1013C22⋊C4C2×D811yescharacteristic
1014C22⋊C4C2×D811yescharacteristic
1015C22⋊C4C2×D811yescharacteristic
1016C22⋊C4C2×D811yescharacteristic
1017C22⋊C4C2×D811yescharacteristic
1018C22⋊C4C2×D811yescharacteristic
1019C22⋊C4C2×D811yescharacteristic
1020C22⋊C4C2×D811yescharacteristic
1021C22⋊C4C2×D811yescharacteristic
1022C22⋊C4C2×D811yescharacteristic
1023C42—41no—
1024C42—41no—
1025C42—41no—
1026C42—41no—
1027C42—41no—
1028C42—41no—
1029C42—41no—
1030C42—41no—
1031C42—41no—
1032C42—41no—
1033C42—41no—
1034C42—41no—
1035C42—41no—
1036C42C2×D811yescharacteristic
1037C42C2×D811yescharacteristic
1038C42C22×D411yescharacteristic
1039C42C22×D411yescharacteristic
1040C42C22×D411yescharacteristic
1041C42C22×D411yescharacteristic
1042C16—21no—
1043C16—21no—
1044C16—21no—
1045C16—21no—
1046C16—21no—
1047C16—21no—
1048C16—21no—
1049C16C2×#4112yes—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—82no—
1054C23—161no—
1055C23—161no—
1056C23C22×D811yescharacteristic
1057C23C22×D811yescharacteristic
1058C23C22×D811yescharacteristic
1059Q8—41no—
1060Q8—41no—
1061Q8—41no—
1062Q8—41no—
1063Q8—41no—
1064Q8—41no—
1065Q8—41no—
1066Q8—41no—
1067Q8—41no—
1068Q8—41no—
1069Q8—41no—
1070Q8—161no—
1071Q8—161no—
1072D4—22no—
1073D4—22no—
1074D4—41no—
1075D4—41no—
1076D4—41no—
1077D4—41no—
1078D4—41no—
1079D4—41no—
1080D4—41no—
1081D4—82no—
1082D4—82no—
1083D4—82no—
1084D4—82no—
1085D4—82no—
1086D4—82no—
1087D4—161no—
1088D4—161no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—82no—
1111C2×C4—82no—
1112C2×C4—82no—
1113C2×C4—82no—
1114C2×C4—82no—
1115C2×C4—82no—
1116C2×C4—161no—
1117C2×C4—161no—
1118C2×C4—161no—
1119C2×C4—161no—
1120C2×C4—161no—
1121C2×C4—161no—
1122C2×C4—161no—
1123C2×C4—161no—
1124C2×C4—161no—
1125C2×C4—161no—
1126C2×C4—161no—
1127C2×C4—161no—
1128C2×C4C22×D811yescharacteristic
1129C2×C4C22×D811yescharacteristic
1130C2×C4C22×D811yescharacteristic
1131C2×C4C22×D811yescharacteristic
1132C2×C4C22×D811yescharacteristic
1133C2×C4C22×D811yescharacteristic
1134C2×C4C22×D811yescharacteristic
1135C2×C4C22×D811yescharacteristic
1136C2×C4C22×D811yescharacteristic
1137C2×C4C22×D811yescharacteristic
1138C2×C4C22×D811yescharacteristic
1139C2×C4C23×D411yescharacteristic
1140C8—21no—
1141C8—21no—
1142C8—21no—
1143C8—21no—
1144C8—21no—
1145C8—21no—
1146C8—21no—
1147C8C22×#4111yescharacteristic
1148C8#58511yescharacteristic
1149C22—21no—
1150C22—21no—
1151C22—21no—
1152C22—21no—
1153C22—21no—
1154C22—21no—
1155C22—21no—
1156C22—21no—
1157C22—21no—
1158C22—42no—
1159C22—42no—
1160C22—81no—
1161C22—81no—
1162C22—81no—
1163C22—81no—
1164C22—81no—
1165C22—81no—
1166C22—81no—
1167C22—322no—
1168C22C23×D811yescharacteristic
1169C4—21no—
1170C4—21no—
1171C4—21no—
1172C4—21no—
1173C4—21no—
1174C4—21no—
1175C4—21no—
1176C4—21no—
1177C4—21no—
1178C4—21no—
1179C4—21no—
1180C4—81no—
1181C4—81no—
1182C4—81no—
1183C4—81no—
1184C4—81no—
1185C4—81no—
1186C4—81no—
1187C4—81no—
1188C4—81no—
1189C4—81no—
1190C4—81no—
1191C4—81no—
1192C4—81no—
1193C4D4×#4111yescharacteristic
1194C4#358411yescharacteristic
1195C2—41no—
1196C2—41no—
1197C2—41no—
1198C2—82no—
1199C2—82no—
1200C2—161no—
1201C2D8×#4111yescharacteristic
1202C2#6263511yescharacteristic
1203C2#6263711yescharacteristic
subgroupG/H
center, socleC22C23×D8
commutator, Frattini, cosocleC2×C8C25
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #529 ◁ #2966 ◁ G
LECSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #61487C2semidirect
2. #61477C2semidirect
3. #33965C2semidirect
4. #33956C2semidirect
5. #33943C2semidirect
6. #33939C2semidirect
7. #33916C2semidirect
8. #33911C2semidirect
9. #33904C2semidirect
10. #33882C2semidirect
11. #33882C2semidirect
12. #33881C2semidirect
13. #33874C2semidirect
14. #33869C2semidirect
15. #33863C2semidirect
16. #33849C2semidirect
17. #33833C2semidirect
18. #33833C2semidirect
19. #33747C2semidirect
20. #33745C2semidirect
21. #33741C2semidirect
22. #33684C2semidirect
23. #33683C2semidirect
24. #33680C2semidirect
25. #33680C2semidirect
26. #33667C2semidirect
27. #33662C2semidirect
28. #33482C2semidirect
29. #33460C2semidirect
30. #33454C2semidirect
31. #33451C2semidirect
37. #3395C22semidirect
40. #3380C22semidirect
48. #3336C22semidirect
58. #3283C22semidirect
63. #3177C22semidirect
65. #3170C22semidirect
76. #2951C22semidirect
79. C4×#135C22semidirect
80. #2255C22semidirect
81. #2255C22semidirect
82. #2253C22semidirect
85. #2247C22semidirect
86. #2245C22semidirect
87. #2245C22semidirect
88. #2245C22semidirect
91. #2241C22semidirect
94. #2237C22semidirect
95. #2237C22semidirect
96. #2237C22semidirect
98. #2236C22semidirect
99. #2236C22semidirect
101. #2235C22semidirect
104. #2229C22semidirect
105. #2229C22semidirect
106. #2229C22semidirect
110. #2228C22semidirect
111. #2228C22semidirect
112. #2227C22semidirect
113. #2225C22semidirect
115. #2224C22semidirect
119. #2219C22semidirect
125. #2216C22semidirect
126. #2216C22semidirect
127. #2216C22semidirect
132. #2209C22semidirect
133. #2209C22semidirect
134. #2209C22semidirect
139. #2208C22semidirect
146. #2189C22semidirect
147. #2189C22semidirect
152. #2183C22semidirect
153. #2183C22semidirect
158. #2176C22semidirect
159. #2176C22semidirect
160. #2176C22semidirect
161. #2176C22semidirect
162. #2176C22semidirect
168. #2175C22semidirect
169. #2175C22semidirect
170. C4×Q32C22semidirect
171. C4×Q32C22semidirect
172. C4×Q32C22semidirect
178. C4×SD32C22semidirect
179. C4×SD32C22semidirect
185. #2168C22semidirect
187. D4×C16C22semidirect
189. #2164C22semidirect
190. #2162C22semidirect
192. #2158C22semidirect
193. C2×#367C22semidirect
195. #2139C22semidirect
198. #2138C22semidirect
201. #2108C22semidirect
202. C2×#346C22semidirect

Maximal subgroups

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

subgroupindex
#614872
#614772
#339652
#339562
#339432
#339392
#339162
#339112
#339042
#338822
#338812
#338742
#338692
#338632
#338492
#338332
#337472
#337452
#337412
#336842
#336832
#336802
#336672
#336622
#334822
#334602
#334542
#334512