Finite Group Databasebeta

← #7624731

Subgroups — #7624731

Order 512.

1184 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62496C211yesmaximal, characteristic, complemented
2#61487C211yesmaximal, characteristic
3#33955C211yesmaximal, characteristic, complemented
4#33952C211yesmaximal, characteristic, complemented
5#33944C211yesmaximal, characteristic, complemented
6#33936C211yesmaximal, characteristic, complemented
7#33917C211yesmaximal, characteristic, complemented
8#33916C211yesmaximal, characteristic, complemented
9#33916C211yesmaximal, characteristic, complemented
10#33911C211yesmaximal, characteristic, complemented
11#33909C211yesmaximal, characteristic, complemented
12#33904C211yesmaximal, characteristic, complemented
13#33882C211yesmaximal, characteristic, complemented
14#33881C211yesmaximal, characteristic, complemented
15#33878C211yesmaximal, characteristic, complemented
16#33878C211yesmaximal, characteristic, complemented
17#33869C211yesmaximal, characteristic, complemented
18#33863C211yesmaximal, characteristic, complemented
19#33827C211yesmaximal, characteristic, complemented
20#33824C211yesmaximal, characteristic, complemented
21#33814C211yesmaximal, characteristic, complemented
22#33809C211yesmaximal, characteristic, complemented
23#33808C211yesmaximal, characteristic, complemented
24#33806C211yesmaximal, characteristic, complemented
25#33683C211yesmaximal, characteristic, complemented
26#33680C211yesmaximal, characteristic, complemented
27#33676C211yesmaximal, characteristic, complemented
28#33634C211yesmaximal, characteristic, complemented
29#33631C211yesmaximal, characteristic, complemented
30#33626C211yesmaximal, characteristic, complemented
31#33506C211yesmaximal, characteristic, complemented
32#3555—21no—
33#3521—21no—
34#3393C2211yescharacteristic
35#3387—21no—
36#3383C2211yescharacteristic, complemented
37Q8×Q16C2211yescharacteristic, complemented
38#3380C2211yescharacteristic
39#3376—21no—
40#3356—21no—
41#3349—21no—
42#3349—21no—
43#3342C2211yescharacteristic
44#3342C2211yescharacteristic
45#3342C2211yescharacteristic
46#3342C2211yescharacteristic, complemented
47#3339C2211yescharacteristic
48#3338C2211yescharacteristic
49#3336C2211yescharacteristic
50#3336C2211yescharacteristic
51#3336C2211yescharacteristic, complemented
52#3323—21no—
53#3311—21no—
54#3307—21no—
55#3283C2211yescharacteristic
56#3280C2211yescharacteristic
57#3280C2211yescharacteristic
58#3242—21no—
59#3242—21no—
60#3237—21no—
61#3177C2211yescharacteristic
62#3177C2211yescharacteristic
63#3177C2211yescharacteristic, complemented
64#3175C2211yescharacteristic
65#3170C2211yescharacteristic, complemented
66#3168C2211yescharacteristic
67#3164C2211yescharacteristic
68#3164C2211yescharacteristic, complemented
69#3160C2211yescharacteristic, complemented
70#3125—21no—
71#3123—21no—
72#3111—21no—
73#2966C2211yescharacteristic
74#2951C2211yescharacteristic
75#2948C2211yescharacteristic
76C4×#135C2211yescharacteristic
77#2255C2211yescharacteristic, complemented
78#2255C2211yescharacteristic, complemented
79#2255C2211yescharacteristic, complemented
80#2255C2211yescharacteristic, complemented
81#2253C2211yescharacteristic, complemented
82#2252C2211yescharacteristic, complemented
83#2245C2211yescharacteristic, complemented
84#2243C2211yescharacteristic
85#2243C2211yescharacteristic
86#2243C2211yescharacteristic
87#2242C2211yescharacteristic
88#2241C2211yescharacteristic, complemented
89#2237C2211yescharacteristic
90#2237C2211yescharacteristic
91#2237C2211yescharacteristic
92#2237C2211yescharacteristic
93#2237C2211yescharacteristic, complemented
94#2237C2211yescharacteristic, complemented
95#2237C2211yescharacteristic, complemented
96#2237C2211yescharacteristic, complemented
97#2237C2211yescharacteristic, complemented
98#2236C2211yescharacteristic
99#2236C2211yescharacteristic, complemented
100#2236C2211yescharacteristic, complemented
101#2235C2211yescharacteristic
102#2235C2211yescharacteristic, complemented
103#2234C2211yescharacteristic
104#2234C2211yescharacteristic
105#2234C2211yescharacteristic
106#2232C2211yescharacteristic
107#2229C2211yescharacteristic, complemented
108#2229C2211yescharacteristic, complemented
109#2229C2211yescharacteristic, complemented
110#2229C2211yescharacteristic, complemented
111#2229C2211yescharacteristic, complemented
112#2229C2211yescharacteristic, complemented
113#2229C2211yescharacteristic, complemented
114#2229C2211yescharacteristic, complemented
115#2229C2211yescharacteristic, complemented
116#2228C2211yescharacteristic
117#2228C2211yescharacteristic
118#2228C2211yescharacteristic
119#2228C2211yescharacteristic
120#2228C2211yescharacteristic
121#2228C2211yescharacteristic
122#2228C2211yescharacteristic
123#2227C2211yescharacteristic, complemented
124#2227C2211yescharacteristic, complemented
125#2227C2211yescharacteristic, complemented
126#2226C2211yescharacteristic
127#2226C2211yescharacteristic
128#2226C2211yescharacteristic
129#2226C2211yescharacteristic
130#2225C2211yescharacteristic, complemented
131#2225C2211yescharacteristic, complemented
132#2225C2211yescharacteristic, complemented
133#2225C2211yescharacteristic, complemented
134#2224C2211yescharacteristic
135#2224C2211yescharacteristic
136#2224C2211yescharacteristic
137#2220C2211yescharacteristic
138#2219C2211yescharacteristic
139#2219C2211yescharacteristic
140#2219C2211yescharacteristic, complemented
141#2217C2211yescharacteristic
142#2217C2211yescharacteristic
143#2217C2211yescharacteristic
144#2216C2211yescharacteristic
145#2216C2211yescharacteristic
146#2216C2211yescharacteristic, complemented
147#2216C2211yescharacteristic, complemented
148#2216C2211yescharacteristic, complemented
149#2211C2211yescharacteristic
150#2211C2211yescharacteristic
151#2211C2211yescharacteristic
152#2211C2211yescharacteristic
153#2209C2211yescharacteristic, complemented
154#2209C2211yescharacteristic, complemented
155#2209C2211yescharacteristic, complemented
156#2209C2211yescharacteristic, complemented
157#2208C2211yescharacteristic
158#2208C2211yescharacteristic
159#2189C2211yescharacteristic
160#2189C2211yescharacteristic
161#2189C2211yescharacteristic
162#2189C2211yescharacteristic
163#2187C2211yescharacteristic
164#2187C2211yescharacteristic
165#2183C2211yescharacteristic, complemented
166#2183C2211yescharacteristic, complemented
167#2176C2211yescharacteristic, complemented
168#2176C2211yescharacteristic, complemented
169#2176C2211yescharacteristic, complemented
170#2175C2211yescharacteristic
171#2175C2211yescharacteristic
172#2175C2211yescharacteristic
173#2175C2211yescharacteristic
174#2175C2211yescharacteristic
175C4×Q32C2211yescharacteristic, complemented
176C4×SD32C2211yescharacteristic
177C4×SD32C2211yescharacteristic
178C4×SD32C2211yescharacteristic
179#2168C2211yescharacteristic
180#2168C2211yescharacteristic
181#2168C2211yescharacteristic
182#2168C2211yescharacteristic, complemented
183D4×C16C2211yescharacteristic
184D4×C16C2211yescharacteristic, complemented
185#2164C2211yescharacteristic
186#2164C2211yescharacteristic, complemented
187#2163C2211yescharacteristic, complemented
188#2159C2211yescharacteristic
189#2159C2211yescharacteristic, complemented
190#2158C2211yescharacteristic
191#2158C2211yescharacteristic, complemented
192#2158C2211yescharacteristic, complemented
193C2×#367C2211yescharacteristic, complemented
194#2151C2211yescharacteristic
195#2151C2211yescharacteristic, complemented
196C2×C4⋊C16C2211yescharacteristic, complemented
197#2140C2211yescharacteristic
198#2139C2211yescharacteristic
199#2138C2211yescharacteristic
200#2138C2211yescharacteristic
201#2138C2211yescharacteristic
202C2×#357C2211yescharacteristic
203C2×#135C2311yescharacteristic
204C2×#135C2311yescharacteristic
205C22×D8C2311yescharacteristic
206#563—41no—
207#563—41no—
208Q82—21no—
209#557—21no—
210#557—41no—
211#556—21no—
212#556—21no—
213#556—21no—
214#556—21no—
215#556—21no—
216#556—41no—
217#554—21no—
218#554—21no—
219#553—21no—
220#553—41no—
221#552—21no—
222#552—21no—
223#552—21no—
224#552—41no—
225#551—41no—
226#551—41no—
227#547—21no—
228#546—21no—
229#546—21no—
230#544—21no—
231#544—21no—
232#542—21no—
233#542—41no—
234#541—21no—
235#541—21no—
236#541—21no—
237#541—41no—
238#541—41no—
239#541—41no—
240#539—41no—
241#538—41no—
242#533—21no—
243#533—21no—
244#529—21no—
245#529—41no—
246#529D411yescharacteristic
247C2×#126—41no—
248#520—21no—
249#518—21no—
250C4×#41—21no—
251C2×Q32C2311yescharacteristic
252C2×Q32C2311yescharacteristic
253C2×Q32C2311yescharacteristic
254C2×Q32C2311yescharacteristic
255C2×SD32C2311yescharacteristic
256C2×SD32C2311yescharacteristic
257C2×SD32C2311yescharacteristic
258C2×SD32C2311yescharacteristic
259C2×M32C2311yescharacteristic
260C2×M32C2311yescharacteristic
261C22×C16C2311yescharacteristic
262C22×C16C2311yescharacteristic
263C22×C16C2311yescharacteristic
264C22×C16C2311yescharacteristic
265#501—21no—
266#501—21no—
267#501—21no—
268#501—21no—
269#500C2311yescharacteristic
270#500C2311yescharacteristic
271#500C2311yescharacteristic
272#500C2311yescharacteristic
273#500C2311yescharacteristic
274#500C2311yescharacteristic
275#499—21no—
276#499C2311yescharacteristic
277#499C2311yescharacteristic
278#499C2311yescharacteristic
279#499C2311yescharacteristic
280#499C2311yescharacteristic
281#499C2311yescharacteristic
282#498—21no—
283#495C2311yescharacteristic
284#495C2311yescharacteristic
285#494C2311yescharacteristic
286#494C2311yescharacteristic
287#491—21no—
288#491—21no—
289#491—21no—
290#489—21no—
291#488—21no—
292#487—21no—
293#485—21no—
294#485—21no—
295#485—21no—
296#485—21no—
297#485—21no—
298#485—21no—
299#485—21no—
300#485—21no—
301#485—21no—
302#485—21no—
303#485—21no—
304#484—21no—
305#484—21no—
306#483—21no—
307#483—21no—
308#483—21no—
309#482—21no—
310#481—21no—
311#479—21no—
312#479—21no—
313#479—21no—
314#479—21no—
315#479—21no—
316#478—21no—
317#478—21no—
318#478—21no—
319#477—21no—
320#477—21no—
321#477—21no—
322#477—21no—
323#476—21no—
324#475—21no—
325#475—21no—
326#475—21no—
327#475—21no—
328#475—21no—
329#470—21no—
330#470—21no—
331#470—21no—
332#468—21no—
333#467—21no—
334#467C2311yescharacteristic
335#467C2311yescharacteristic
336#467C2311yescharacteristic
337#467C2311yescharacteristic
338#467C2311yescharacteristic
339#467C2311yescharacteristic
340#467C2311yescharacteristic
341#467C2311yescharacteristic
342#467C2311yescharacteristic
343#467C2311yescharacteristic
344#466C2311yescharacteristic
345#466C2311yescharacteristic
346#465—21no—
347#464—21no—
348#464—21no—
349#463—21no—
350#463—21no—
351#461—21no—
352#461—21no—
353#452—21no—
354#452—21no—
355#450—21no—
356#450—21no—
357#449—21no—
358#449—21no—
359#446D411yescharacteristic
360C8×Q8C2311yescharacteristic
361#442—21no—
362#442—21no—
363#441—21no—
364#441—21no—
365#441—21no—
366#440—21no—
367#440—21no—
368#440—21no—
369C4×Q16—21no—
370C4×Q16C2311yescharacteristic
371C4×Q16C2311yescharacteristic
372C4×Q16C2311yescharacteristic
373C4×Q16C2311yescharacteristic
374C4×Q16C2311yescharacteristic
375C4×Q16C2311yescharacteristic
376C4×Q16C2311yescharacteristic
377C4×Q16C2311yescharacteristic
378C4×Q16C2311yescharacteristic
379C4×Q16C2311yescharacteristic
380C4×SD16—21no—
381C4×SD16—21no—
382C4×SD16—21no—
383C4×D8C2311yescharacteristic
384C4×D8C2311yescharacteristic
385C4×D8C2311yescharacteristic
386C4×D8C2311yescharacteristic
387C4×D8C2311yescharacteristic
388C4×D8C2311yescharacteristic
389#436D411yescharacteristic
390#435D411yescharacteristic
391#435D411yescharacteristic
392C8×D4C2311yescharacteristic
393C8×D4C2311yescharacteristic
394C8×D4C2311yescharacteristic
395#433D411yescharacteristic
396#433D411yescharacteristic
397#432D411yescharacteristic
398#428—21no—
399#428—21no—
400#427—21no—
401#427C2311yescharacteristic
402#427C2311yescharacteristic
403#427C2311yescharacteristic
404#427C2311yescharacteristic
405#427C2311yescharacteristic
406#427C2311yescharacteristic
407C2×#107C2311yescharacteristic
408C2×#107C2311yescharacteristic
409C2×#107C2311yescharacteristic
410#418—21no—
411#417—21no—
412#416—21no—
413#405C2311yescharacteristic
414#405C2311yescharacteristic
415C2×C4×C8C2311yescharacteristic
416#367C2311yescharacteristic
417#367C2311yescharacteristic
418#367C2311yescharacteristic
419#367C2311yescharacteristic
420#367C2311yescharacteristic
421#367C2311yescharacteristic
422#367C2311yescharacteristic
423#367C2311yescharacteristic
424#367C2311yescharacteristic
425#367C2311yescharacteristic
426#367C2311yescharacteristic
427#367C2311yescharacteristic
428#366C2311yescharacteristic
429#366C2311yescharacteristic
430#366C2311yescharacteristic
431#366C2311yescharacteristic
432#366C2311yescharacteristic
433#366C2311yescharacteristic
434#366C2311yescharacteristic
435#366C2311yescharacteristic
436#366C2311yescharacteristic
437#366C2311yescharacteristic
438#366C2311yescharacteristic
439#366C2311yescharacteristic
440C4⋊C16C2311yescharacteristic
441C4⋊C16C2311yescharacteristic
442C4⋊C16C2311yescharacteristic
443C4⋊C16C2311yescharacteristic
444C4⋊C16C2311yescharacteristic
445C4⋊C16C2311yescharacteristic
446C4⋊C16C2311yescharacteristic
447C4⋊C16C2311yescharacteristic
448C4⋊C16C2311yescharacteristic
449C4⋊C16C2311yescharacteristic
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#358C2311yescharacteristic
470#357C2311yescharacteristic
471#357C2311yescharacteristic
472#357C2311yescharacteristic
473#357C2311yescharacteristic
474#357C2311yescharacteristic
475#357C2311yescharacteristic
476#357C2311yescharacteristic
477#357C2311yescharacteristic
478#357C2311yescharacteristic
479#357C2311yescharacteristic
480#357C2311yescharacteristic
481#357C2311yescharacteristic
482C22⋊C16C2311yescharacteristic
483C22⋊C16C2311yescharacteristic
484C22⋊C16C2311yescharacteristic
485C22⋊C16C2311yescharacteristic
486C22⋊C16C2311yescharacteristic
487C22⋊C16C2311yescharacteristic
488#346C2311yescharacteristic
489#346C2311yescharacteristic
490#346C2311yescharacteristic
491#346C2311yescharacteristic
492C4×C16C2311yescharacteristic
493C4×C16C2311yescharacteristic
494C2×#41—21no—
495C2×#41—21no—
496C22×D4—21no—
497#135—22no—
498#135—22no—
499#135—41no—
500#135—41no—
501C2×Q16—21no—
502C2×Q16—21no—
503C2×Q16C2411yescharacteristic
504C2×Q16C2411yescharacteristic
505C2×Q16C2411yescharacteristic
506C2×Q16C2411yescharacteristic
507C2×SD16—21no—
508C2×SD16—21no—
509C2×SD16—21no—
510C2×SD16—21no—
511C2×D8—22no—
512C2×D8—21no—
513C2×D8—41no—
514C2×D8C2411yescharacteristic
515C2×D8C2411yescharacteristic
516C2×M16C2×D411yescharacteristic
517C2×M16C2×D411yescharacteristic
518C22×C8C2×D411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C4⋊Q8—21no—
523C4⋊Q8—21no—
524C4⋊Q8—21no—
525C4⋊Q8—21no—
526C4⋊Q8—21no—
527C4⋊Q8—21no—
528C4⋊Q8—21no—
529C4⋊Q8—21no—
530C4⋊Q8—41no—
531C4⋊Q8—41no—
532C4⋊Q8—41no—
533C4⋊Q8—41no—
534C4⋊Q8—41no—
535C4⋊Q8—41no—
536#126—41no—
537#126—41no—
538#126—41no—
539#126—41no—
540#126—41no—
541#126—41no—
542#126—41no—
543#126—41no—
544#126—41no—
545#126—41no—
546#126—41no—
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#126D811yescharacteristic
559#126D811yescharacteristic
560#125—21no—
561#125—21no—
562#125—21no—
563#125—21no—
564#125—21no—
565#125—21no—
566#125—41no—
567#125—41no—
568#125—41no—
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#125D811yescharacteristic
582#124—21no—
583#124—21no—
584#124—41no—
585#124—41no—
586#124—41no—
587#124—41no—
588#124—41no—
589#124D811yescharacteristic
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#123D811yescharacteristic
601#123D811yescharacteristic
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612C22⋊Q8—41no—
613C22⋊Q8—41no—
614C22⋊Q8—41no—
615C22⋊Q8—41no—
616C22⋊Q8—41no—
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⋊Q8D811yescharacteristic
627#121—21no—
628#121—21no—
629#121—41no—
630#121—41no—
631#121—41no—
632#121—41no—
633#121D811yescharacteristic
634#120—41no—
635#120—41no—
636C4×Q8—21no—
637C4×Q8—21no—
638C4×Q8—21no—
639C4×Q8—21no—
640C4×Q8—21no—
641C4×Q8—21no—
642C4×Q8—21no—
643C4×Q8—21no—
644C4×Q8—21no—
645C4×Q8—21no—
646C4×Q8—41no—
647C4×Q8—41no—
648C4×Q8—41no—
649C4×Q8—41no—
650C4×Q8—41no—
651C4×Q8—41no—
652C4×Q8—41no—
653C4×Q8—41no—
654C4×Q8—41no—
655C4×Q8C2×D411yescharacteristic
656C4×D4—21no—
657C4×D4—21no—
658C4×D4—21no—
659C4×D4—21no—
660C4×D4—21no—
661C4×D4—21no—
662C4×D4—41no—
663C4×D4—41no—
664C4×D4—41no—
665C4×D4—41no—
666C4×D4—41no—
667C4×D4—41no—
668C4×D4—41no—
669C4×D4—41no—
670C4×D4—41no—
671C4×D4C2×D411yescharacteristic
672C4×D4C2×D411yescharacteristic
673C4×D4C2×D411yescharacteristic
674#117—21no—
675#117—21no—
676#117—21no—
677#117—21no—
678#117—21no—
679#117—21no—
680#117—41no—
681#117—41no—
682#117—41no—
683#117—41no—
684#117—41no—
685#117—41no—
686#117—41no—
687#117—41no—
688#117C2×D411yescharacteristic
689#117C2×D411yescharacteristic
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C4⋊C4—21no—
693C2×C4⋊C4—41no—
694C2×C4⋊C4—41no—
695C2×C4⋊C4—41no—
696C2×C22⋊C4—41no—
697C2×C22⋊C4—41no—
698C2×C22⋊C4—41no—
699C2×C22⋊C4—41no—
700C2×C42—41no—
701C2×C42C2×D411yescharacteristic
702Q32—41no—
703Q32—41no—
704Q32—41no—
705Q32—41no—
706SD32—22no—
707SD32—22no—
708SD32—41no—
709SD32—41no—
710M32—41no—
711M32—41no—
712C2×C16—41no—
713C2×C16—41no—
714C2×C16—41no—
715C2×C16—41no—
716C2×C16C2411yescharacteristic
717C2×C16C2411yescharacteristic
718C2×C16C2411yescharacteristic
719C2×C16C2411yescharacteristic
720C2×C16C2411yescharacteristic
721C2×C16C2411yescharacteristic
722C2×C16C2411yescharacteristic
723C2×C16C2411yescharacteristic
724#107—21no—
725#107—21no—
726#107—21no—
727#107—21no—
728#107—21no—
729#107—21no—
730#107—21no—
731#107—21no—
732#107—21no—
733#107C2411yescharacteristic
734#107C2411yescharacteristic
735#107C2411yescharacteristic
736#107C2411yescharacteristic
737#107C2411yescharacteristic
738#107C2411yescharacteristic
739#107C2411yescharacteristic
740#107C2411yescharacteristic
741#107C2411yescharacteristic
742#107C2411yescharacteristic
743#106—21no—
744#106—21no—
745#106—21no—
746#106—21no—
747#106—21no—
748#106—21no—
749#106—21no—
750#106—21no—
751#106—21no—
752#106—21no—
753#106—21no—
754#106—21no—
755C4⋊C8C2×D411yescharacteristic
756C4⋊C8C2×D411yescharacteristic
757C4⋊C8C2×D411yescharacteristic
758C4⋊C8C2×D411yescharacteristic
759C4⋊C8C2×D411yescharacteristic
760C4⋊C8C2×D411yescharacteristic
761#103—21no—
762#103—21no—
763#103—21no—
764#103—21no—
765#103—21no—
766#103—21no—
767#103—21no—
768#103—21no—
769#103—21no—
770#103—21no—
771#103—21no—
772#103—21no—
773#103—21no—
774#103—21no—
775#103—21no—
776#103—21no—
777#103—21no—
778#103—21no—
779#103—21no—
780#103—21no—
781#102—21no—
782#102—21no—
783#102—21no—
784#102—21no—
785#102—21no—
786#102—21no—
787#102—21no—
788#102—21no—
789C22⋊C8C2×D411yescharacteristic
790C22⋊C8C2×D411yescharacteristic
791C22⋊C8C2×D411yescharacteristic
792C22⋊C8C2×D411yescharacteristic
793C22⋊C8C2×D411yescharacteristic
794C22⋊C8C2×D411yescharacteristic
795#97C2×D411yescharacteristic
796#97C2×D411yescharacteristic
797#97C2×D411yescharacteristic
798#97C2×D411yescharacteristic
799C4×C8C2×D411yescharacteristic
800C4×C8C2×D411yescharacteristic
801C4×C8C2411yescharacteristic
802C4×C8C2411yescharacteristic
803C4×C8C2411yescharacteristic
804C4×C8C2411yescharacteristic
805C24—41no—
806#41—42no—
807#41—42no—
808#41—81no—
809#41—81no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—41no—
815C2×Q8—41no—
816C2×Q8—41no—
817C2×Q8—41no—
818C2×Q8—41no—
819C2×Q8—41no—
820C2×Q8C2×D811yescharacteristic
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—42no—
824C2×D4—41no—
825C2×D4—41no—
826C2×D4—41no—
827C2×D4—41no—
828C2×D4—41no—
829C2×D4—81no—
830C2×D4C2×D811yescharacteristic
831C2×D4C2×D811yescharacteristic
832C2×D4C2×D811yescharacteristic
833C22×C4—41no—
834C22×C4—41no—
835C22×C4—41no—
836C22×C4—41no—
837C22×C4—41no—
838C22×C4—41no—
839C22×C4—41no—
840C22×C4—41no—
841C22×C4—41no—
842C22×C4—41no—
843C22×C4—41no—
844C22×C4C2×D811yescharacteristic
845C22×C4C2×D811yescharacteristic
846C22×C4C22×D411yescharacteristic
847C22×C4C22×D411yescharacteristic
848C22×C4C22×D411yescharacteristic
849Q16—21no—
850Q16—21no—
851Q16—21no—
852Q16—21no—
853Q16—21no—
854Q16—21no—
855Q16—21no—
856Q16—21no—
857Q16—42no—
858Q16—81no—
859SD16—42no—
860SD16—42no—
861SD16—81no—
862SD16—81no—
863D8—21no—
864D8—21no—
865D8—21no—
866D8—42no—
867D82−1+412yes—
868M16—41no—
869M16—41no—
870C2×C8—21no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—41no—
877C2×C8C22×D411yescharacteristic
878C2×C8C22×D411yescharacteristic
879C2×C8C22×D411yescharacteristic
880C2×C8C22×D411yescharacteristic
881C2×C8C22×D411yescharacteristic
882C2×C8C22×D411yescharacteristic
883C2×C8C22×D411yescharacteristic
884C2×C8C2511yescharacteristic
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—41no—
896C4⋊C4—41no—
897C4⋊C4—41no—
898C4⋊C4—41no—
899C4⋊C4—41no—
900C4⋊C4—41no—
901C4⋊C4—41no—
902C4⋊C4—41no—
903C4⋊C4—41no—
904C4⋊C4—41no—
905C4⋊C4—41no—
906C4⋊C4—41no—
907C4⋊C4—41no—
908C4⋊C4—41no—
909C4⋊C4—41no—
910C4⋊C4—41no—
911C4⋊C4—41no—
912C4⋊C4—41no—
913C4⋊C4—41no—
914C4⋊C4—41no—
915C4⋊C4—41no—
916C4⋊C4—41no—
917C4⋊C4—41no—
918C4⋊C4—41no—
919C4⋊C4—41no—
920C4⋊C4—41no—
921C4⋊C4—41no—
922C4⋊C4—41no—
923C4⋊C4—41no—
924C4⋊C4—41no—
925C4⋊C4—41no—
926C4⋊C4—41no—
927C4⋊C4—41no—
928C4⋊C4—41no—
929C4⋊C4—41no—
930C4⋊C4—41no—
931C4⋊C4—41no—
932C4⋊C4—41no—
933C4⋊C4—41no—
934C4⋊C4—41no—
935C4⋊C4—41no—
936C4⋊C4—41no—
937C4⋊C4—41no—
938C4⋊C4—41no—
939C4⋊C4—41no—
940C4⋊C4C2×D811yescharacteristic
941C4⋊C4C2×D811yescharacteristic
942C4⋊C4C2×D811yescharacteristic
943C4⋊C4C2×D811yescharacteristic
944C4⋊C4C2×D811yescharacteristic
945C4⋊C4C2×D811yescharacteristic
946C4⋊C4C2×D811yescharacteristic
947C4⋊C4C2×D811yescharacteristic
948C4⋊C4C2×D811yescharacteristic
949C4⋊C4C2×D811yescharacteristic
950C22⋊C4—41no—
951C22⋊C4—41no—
952C22⋊C4—41no—
953C22⋊C4—41no—
954C22⋊C4—41no—
955C22⋊C4—41no—
956C22⋊C4—41no—
957C22⋊C4—41no—
958C22⋊C4—41no—
959C22⋊C4—41no—
960C22⋊C4—41no—
961C22⋊C4—41no—
962C22⋊C4—41no—
963C22⋊C4—41no—
964C22⋊C4—41no—
965C22⋊C4—41no—
966C22⋊C4—41no—
967C22⋊C4—41no—
968C22⋊C4—41no—
969C22⋊C4—41no—
970C22⋊C4—41no—
971C22⋊C4—41no—
972C22⋊C4—41no—
973C22⋊C4—41no—
974C22⋊C4—41no—
975C22⋊C4—41no—
976C22⋊C4—41no—
977C22⋊C4—41no—
978C22⋊C4C2×D811yescharacteristic
979C22⋊C4C2×D811yescharacteristic
980C22⋊C4C2×D811yescharacteristic
981C22⋊C4C2×D811yescharacteristic
982C22⋊C4C2×D811yescharacteristic
983C22⋊C4C2×D811yescharacteristic
984C22⋊C4C2×D811yescharacteristic
985C22⋊C4C2×D811yescharacteristic
986C22⋊C4C2×D811yescharacteristic
987C22⋊C4C2×D811yescharacteristic
988C42—41no—
989C42—41no—
990C42—41no—
991C42—41no—
992C42—41no—
993C42—41no—
994C42—41no—
995C42—41no—
996C42—41no—
997C42—41no—
998C42—41no—
999C42—41no—
1000C42—41no—
1001C42—41no—
1002C42—41no—
1003C42—41no—
1004C42C2×D811yescharacteristic
1005C42C2×D811yescharacteristic
1006C42C22×D411yescharacteristic
1007C42C22×D411yescharacteristic
1008C42C22×D411yescharacteristic
1009C42C22×D411yescharacteristic
1010C16—21no—
1011C16—21no—
1012C16—21no—
1013C16—21no—
1014C16—21no—
1015C16—21no—
1016C16—21no—
1017C16—21no—
1018C23—41no—
1019C23—41no—
1020C23—82no—
1021C23—161no—
1022C23—161no—
1023C23C22×D811yescharacteristic
1024C23C22×D811yescharacteristic
1025C23C22×D811yescharacteristic
1026Q8—41no—
1027Q8—41no—
1028Q8—41no—
1029Q8—41no—
1030Q8—41no—
1031Q8—41no—
1032Q8—41no—
1033Q8—41no—
1034Q8—41no—
1035Q8—82no—
1036Q8—161no—
1037Q8—161no—
1038Q8—161no—
1039Q8—161no—
1040Q8—161no—
1041D4—22no—
1042D4—41no—
1043D4—41no—
1044D4—41no—
1045D4—41no—
1046D4—41no—
1047D4—41no—
1048D4—82no—
1049D4—82no—
1050D4—82no—
1051D4—161no—
1052D4—161no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—82no—
1076C2×C4—82no—
1077C2×C4—161no—
1078C2×C4—161no—
1079C2×C4—161no—
1080C2×C4—161no—
1081C2×C4—161no—
1082C2×C4—161no—
1083C2×C4—161no—
1084C2×C4—161no—
1085C2×C4—161no—
1086C2×C4C22×D811yescharacteristic
1087C2×C4C22×D811yescharacteristic
1088C2×C4C22×D811yescharacteristic
1089C2×C4C22×D811yescharacteristic
1090C2×C4C22×D811yescharacteristic
1091C2×C4C22×D811yescharacteristic
1092C2×C4C22×D811yescharacteristic
1093C2×C4C22×D811yescharacteristic
1094C2×C4C22×D811yescharacteristic
1095C2×C4C22×D811yescharacteristic
1096C2×C4C22×D811yescharacteristic
1097C2×C4C23×D411yescharacteristic
1098C8—21no—
1099C8—21no—
1100C8—21no—
1101C8—21no—
1102C8—21no—
1103C8—21no—
1104C8—21no—
1105C8C2×2−1+411yescharacteristic
1106C8#58511yescharacteristic
1107C22—21no—
1108C22—21no—
1109C22—21no—
1110C22—21no—
1111C22—21no—
1112C22—21no—
1113C22—21no—
1114C22—21no—
1115C22—21no—
1116C22—42no—
1117C22—81no—
1118C22—81no—
1119C22—81no—
1120C22—81no—
1121C22—81no—
1122C22—322no—
1123C22C23×D811yescharacteristic
1124C4—21no—
1125C4—21no—
1126C4—21no—
1127C4—21no—
1128C4—21no—
1129C4—21no—
1130C4—21no—
1131C4—21no—
1132C4—21no—
1133C4—21no—
1134C4—21no—
1135C4—81no—
1136C4—81no—
1137C4—81no—
1138C4—81no—
1139C4—81no—
1140C4—81no—
1141C4—81no—
1142C4—81no—
1143C4—81no—
1144C4—81no—
1145C4—81no—
1146C4—81no—
1147C4—81no—
1148C4—81no—
1149C4#348911yescharacteristic
1150C4#358611yescharacteristic
1151C2—41no—
1152C2—41no—
1153C2—41no—
1154C2—82no—
1155C2—161no—
1156C2#6209511yescharacteristic
1157C2#6263511yescharacteristic
1158C2#6263711yescharacteristic
subgroupG/H
center, socleC22C23×D8
commutator, Frattini, cosocleC2×C8C25
prime radical#61487C2
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. #62496C2semidirect
3. #33955C2semidirect
4. #33952C2semidirect
5. #33944C2semidirect
6. #33936C2semidirect
7. #33917C2semidirect
8. #33916C2semidirect
9. #33916C2semidirect
10. #33911C2semidirect
11. #33909C2semidirect
12. #33904C2semidirect
13. #33882C2semidirect
14. #33881C2semidirect
15. #33878C2semidirect
16. #33878C2semidirect
17. #33869C2semidirect
18. #33863C2semidirect
19. #33827C2semidirect
20. #33824C2semidirect
21. #33814C2semidirect
22. #33809C2semidirect
23. #33808C2semidirect
24. #33806C2semidirect
25. #33683C2semidirect
26. #33680C2semidirect
27. #33676C2semidirect
28. #33634C2semidirect
29. #33631C2semidirect
30. #33626C2semidirect
31. #33506C2semidirect
36. #3383C22semidirect
37. Q8×Q16C22semidirect
46. #3342C22semidirect
51. #3336C22semidirect
63. #3177C22semidirect
65. #3170C22semidirect
68. #3164C22semidirect
69. #3160C22semidirect
77. #2255C22semidirect
78. #2255C22semidirect
79. #2255C22semidirect
80. #2255C22semidirect
81. #2253C22semidirect
82. #2252C22semidirect
83. #2245C22semidirect
88. #2241C22semidirect
93. #2237C22semidirect
94. #2237C22semidirect
95. #2237C22semidirect
96. #2237C22semidirect
97. #2237C22semidirect
99. #2236C22semidirect
100. #2236C22semidirect
102. #2235C22semidirect
107. #2229C22semidirect
108. #2229C22semidirect
109. #2229C22semidirect
110. #2229C22semidirect
111. #2229C22semidirect
112. #2229C22semidirect
113. #2229C22semidirect
114. #2229C22semidirect
115. #2229C22semidirect
123. #2227C22semidirect
124. #2227C22semidirect
125. #2227C22semidirect
130. #2225C22semidirect
131. #2225C22semidirect
132. #2225C22semidirect
133. #2225C22semidirect
140. #2219C22semidirect
146. #2216C22semidirect
147. #2216C22semidirect
148. #2216C22semidirect
153. #2209C22semidirect
154. #2209C22semidirect
155. #2209C22semidirect
156. #2209C22semidirect
165. #2183C22semidirect
166. #2183C22semidirect
167. #2176C22semidirect
168. #2176C22semidirect
169. #2176C22semidirect
175. C4×Q32C22semidirect
182. #2168C22semidirect
184. D4×C16C22semidirect
186. #2164C22semidirect
187. #2163C22semidirect
189. #2159C22semidirect
191. #2158C22semidirect
192. #2158C22semidirect
193. C2×#367C22semidirect
195. #2151C22semidirect
196. C2×C4⋊C16C22semidirect

Maximal subgroups

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

subgroupindex
#624962
#614872
#339552
#339522
#339442
#339362
#339172
#339162
#339112
#339092
#339042
#338822
#338812
#338782
#338692
#338632
#338272
#338242
#338142
#338092
#338082
#338062
#336832
#336802
#336762
#336342
#336312
#336262
#335062