Finite Group Databasebeta

← #7624721

Subgroups — #7624721

Order 512.

1209 conjugacy classes of subgroups.

The subgroup lattice has 1182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62490C211yesmaximal, characteristic, complemented
2#61479C211yesmaximal, characteristic, complemented
3#33957C211yesmaximal, characteristic, complemented
4#33955C211yesmaximal, characteristic, complemented
5#33935C211yesmaximal, characteristic, complemented
6#33933C211yesmaximal, characteristic, complemented
7#33917C211yesmaximal, characteristic, complemented
8#33914C211yesmaximal, characteristic, complemented
9#33912C211yesmaximal, characteristic, complemented
10#33910C211yesmaximal, characteristic, complemented
11#33906C211yesmaximal, characteristic, complemented
12#33904C211yesmaximal, characteristic, complemented
13#33884C211yesmaximal, characteristic, complemented
14#33884C211yesmaximal, characteristic, complemented
15#33876C211yesmaximal, characteristic, complemented
16#33876C211yesmaximal, characteristic, complemented
17#33872C211yesmaximal, characteristic, complemented
18#33871C211yesmaximal, characteristic, complemented
19#33823C211yesmaximal, characteristic, complemented
20#33823C211yesmaximal, characteristic, complemented
21#33813C211yesmaximal, characteristic, complemented
22#33807C211yesmaximal, characteristic, complemented
23#33807C211yesmaximal, characteristic, complemented
24#33801C211yesmaximal, characteristic, complemented
25#33685C211yesmaximal, characteristic, complemented
26#33684C211yesmaximal, characteristic, complemented
27#33671C211yesmaximal, characteristic, complemented
28#33634C211yesmaximal, characteristic, complemented
29#33633C211yesmaximal, characteristic, complemented
30#33626C211yesmaximal, characteristic, complemented
31#33506C211yesmaximal, characteristic, complemented
32#3565—21no—
33#3517—21no—
34#3391C2211yescharacteristic
35#3388—21no—
36#3383C2211yescharacteristic
37#3383C2211yescharacteristic
38#3380C2211yescharacteristic
39#3368—21no—
40#3351—21no—
41#3350—21no—
42#3348—21no—
43#3342C2211yescharacteristic
44#3341C2211yescharacteristic
45#3339C2211yescharacteristic
46#3339C2211yescharacteristic
47#3339C2211yescharacteristic
48#3339C2211yescharacteristic
49#3336C2211yescharacteristic
50#3336C2211yescharacteristic
51#3334C2211yescharacteristic
52#3332—21no—
53#3309—21no—
54#3309—21no—
55#3287C2211yescharacteristic
56#3287C2211yescharacteristic
57#3287C2211yescharacteristic
58#3244—21no—
59#3244—21no—
60#3240—21no—
61#3176C2211yescharacteristic
62#3176C2211yescharacteristic
63#3175C2211yescharacteristic
64#3175C2211yescharacteristic
65#3169C2211yescharacteristic
66#3168C2211yescharacteristic
67#3164C2211yescharacteristic
68#3164C2211yescharacteristic
69#3160C2211yescharacteristic
70#3119—21no—
71#3119—21no—
72#3115—21no—
73#2966C2211yescharacteristic
74#2951C2211yescharacteristic
75#2951C2211yescharacteristic
76C4×#135C2211yescharacteristic
77#2255C2211yescharacteristic
78#2255C2211yescharacteristic
79#2255C2211yescharacteristic
80#2255C2211yescharacteristic
81#2253C2211yescharacteristic
82#2253C2211yescharacteristic
83#2244C2211yescharacteristic
84#2244C2211yescharacteristic
85#2244C2211yescharacteristic
86#2244C2211yescharacteristic
87#2240C2211yescharacteristic
88#2240C2211yescharacteristic
89#2237C2211yescharacteristic
90#2236C2211yescharacteristic
91#2235C2211yescharacteristic
92#2234C2211yescharacteristic
93#2234C2211yescharacteristic
94#2234C2211yescharacteristic
95#2234C2211yescharacteristic
96#2234C2211yescharacteristic
97#2234C2211yescharacteristic
98#2234C2211yescharacteristic
99#2234C2211yescharacteristic
100#2234C2211yescharacteristic
101#2233C2211yescharacteristic
102#2233C2211yescharacteristic
103#2233C2211yescharacteristic
104#2232C2211yescharacteristic
105#2232C2211yescharacteristic
106#2232C2211yescharacteristic
107#2229C2211yescharacteristic
108#2229C2211yescharacteristic
109#2229C2211yescharacteristic
110#2229C2211yescharacteristic
111#2229C2211yescharacteristic
112#2229C2211yescharacteristic
113#2229C2211yescharacteristic
114#2228C2211yescharacteristic
115#2228C2211yescharacteristic
116#2228C2211yescharacteristic
117#2228C2211yescharacteristic
118#2228C2211yescharacteristic
119#2228C2211yescharacteristic
120#2228C2211yescharacteristic
121#2228C2211yescharacteristic
122#2228C2211yescharacteristic
123#2227C2211yescharacteristic
124#2227C2211yescharacteristic
125#2227C2211yescharacteristic
126#2226C2211yescharacteristic
127#2226C2211yescharacteristic
128#2226C2211yescharacteristic
129#2226C2211yescharacteristic
130#2226C2211yescharacteristic
131#2225C2211yescharacteristic
132#2225C2211yescharacteristic
133#2224C2211yescharacteristic
134#2224C2211yescharacteristic
135#2224C2211yescharacteristic
136#2224C2211yescharacteristic
137#2220C2211yescharacteristic
138#2220C2211yescharacteristic
139#2218C2211yescharacteristic
140#2218C2211yescharacteristic
141#2217C2211yescharacteristic
142#2217C2211yescharacteristic
143#2217C2211yescharacteristic
144#2217C2211yescharacteristic
145#2215C2211yescharacteristic
146#2215C2211yescharacteristic
147#2215C2211yescharacteristic
148#2215C2211yescharacteristic
149#2211C2211yescharacteristic
150#2210C2211yescharacteristic
151#2210C2211yescharacteristic
152#2210C2211yescharacteristic
153#2207C2211yescharacteristic
154#2207C2211yescharacteristic
155#2207C2211yescharacteristic
156#2206C2211yescharacteristic
157#2206C2211yescharacteristic
158#2206C2211yescharacteristic
159#2189C2211yescharacteristic
160#2189C2211yescharacteristic
161#2189C2211yescharacteristic
162#2186C2211yescharacteristic
163#2186C2211yescharacteristic
164#2186C2211yescharacteristic
165#2183C2211yescharacteristic
166#2183C2211yescharacteristic
167#2177C2211yescharacteristic
168#2177C2211yescharacteristic
169#2176C2211yescharacteristic
170#2176C2211yescharacteristic
171#2175C2211yescharacteristic
172#2175C2211yescharacteristic
173#2175C2211yescharacteristic
174#2175C2211yescharacteristic
175C4×Q32C2211yescharacteristic
176C4×SD32C2211yescharacteristic
177C4×SD32C2211yescharacteristic
178C4×D16C2211yescharacteristic
179#2168C2211yescharacteristic
180#2168C2211yescharacteristic
181#2168C2211yescharacteristic
182#2168C2211yescharacteristic
183D4×C16C2211yescharacteristic
184D4×C16C2211yescharacteristic
185#2164C2211yescharacteristic
186#2164C2211yescharacteristic
187#2163C2211yescharacteristic
188#2159C2211yescharacteristic
189#2159C2211yescharacteristic
190#2158C2211yescharacteristic
191#2158C2211yescharacteristic
192C2×#367C2211yescharacteristic
193C2×#366C2211yescharacteristic
194#2151C2211yescharacteristic
195#2151C2211yescharacteristic
196C2×C4⋊C16C2211yescharacteristic
197#2139C2211yescharacteristic
198#2139C2211yescharacteristic
199#2138C2211yescharacteristic
200#2138C2211yescharacteristic
201#2138C2211yescharacteristic
202#2138C2211yescharacteristic
203C2×#135C2311yescharacteristic
204C2×#135C2311yescharacteristic
205C2×#135C2311yescharacteristic
206#563—41no—
207#562—41no—
208#557—21no—
209#557—21no—
210#556—21no—
211#556—41no—
212#555—21no—
213#554—21no—
214#553—21no—
215#553—21no—
216#553—21no—
217#553—21no—
218#553—41no—
219#553—41no—
220#552—21no—
221#552—21no—
222#552—41no—
223#550—21no—
224#550—21no—
225#550—21no—
226#550—21no—
227#550—41no—
228#547—21no—
229#547—41no—
230#544—21no—
231#544—21no—
232#542—21no—
233#542—21no—
234#542—41no—
235#542—41no—
236#541—41no—
237#540—21no—
238#540—21no—
239#540—41no—
240#540—41no—
241#539—41no—
242#533—21no—
243#532—21no—
244#532—41no—
245#529—21no—
246#529—41no—
247#529D411yescharacteristic
248#520—21no—
249#520—21no—
250C4×#41—21no—
251C2×Q32C2311yescharacteristic
252C2×SD32C2311yescharacteristic
253C2×SD32C2311yescharacteristic
254C2×SD32C2311yescharacteristic
255C2×SD32C2311yescharacteristic
256C2×D16C2311yescharacteristic
257C2×D16C2311yescharacteristic
258C2×D16C2311yescharacteristic
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#499—21no—
275#499C2311yescharacteristic
276#499C2311yescharacteristic
277#499C2311yescharacteristic
278#499C2311yescharacteristic
279#499C2311yescharacteristic
280#499C2311yescharacteristic
281#499C2311yescharacteristic
282#498—21no—
283#495C2311yescharacteristic
284#493C2311yescharacteristic
285#493C2311yescharacteristic
286#493C2311yescharacteristic
287#490—21no—
288#490—21no—
289#489—21no—
290#489—21no—
291#488—21no—
292#486—21no—
293#485—21no—
294#485—21no—
295#485—21no—
296#485—21no—
297#483—21no—
298#483—21no—
299#482—21no—
300#482—21no—
301#482—21no—
302#482—21no—
303#482—21no—
304#482—21no—
305#481—21no—
306#481—21no—
307#481—21no—
308#481—21no—
309#480—21no—
310#480—21no—
311#479—21no—
312#479—21no—
313#479—21no—
314#479—21no—
315#479—21no—
316#479—21no—
317#478—21no—
318#478—21no—
319#478—21no—
320#478—21no—
321#478—21no—
322#478—21no—
323#476—21no—
324#476—21no—
325#475—21no—
326#475—21no—
327#475—21no—
328#474—21no—
329#469—21no—
330#469—21no—
331#468—21no—
332#468—21no—
333#467C2311yescharacteristic
334#467C2311yescharacteristic
335#467C2311yescharacteristic
336#466—21no—
337#466C2311yescharacteristic
338#466C2311yescharacteristic
339#466C2311yescharacteristic
340#466C2311yescharacteristic
341#466C2311yescharacteristic
342#466C2311yescharacteristic
343#466C2311yescharacteristic
344#466C2311yescharacteristic
345#466C2311yescharacteristic
346#465—21no—
347#460—21no—
348#460—21no—
349#460—21no—
350#459—21no—
351#459—21no—
352#459—21no—
353#449—21no—
354#449—21no—
355#449—21no—
356#449—21no—
357#449—21no—
358#449—21no—
359#446D411yescharacteristic
360C8×Q8C2311yescharacteristic
361#442—21no—
362#442—21no—
363#440—21no—
364#440—21no—
365#440—21no—
366#440—21no—
367#440—21no—
368#440—21no—
369C4×Q16C2311yescharacteristic
370C4×Q16C2311yescharacteristic
371C4×Q16C2311yescharacteristic
372C4×Q16C2311yescharacteristic
373C4×Q16C2311yescharacteristic
374C4×Q16C2311yescharacteristic
375C4×Q16C2311yescharacteristic
376C4×SD16—21no—
377C4×SD16—21no—
378C4×SD16—21no—
379C4×D8—21no—
380C4×D8C2311yescharacteristic
381C4×D8C2311yescharacteristic
382C4×D8C2311yescharacteristic
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
406C2×#107C2311yescharacteristic
407C2×#107C2311yescharacteristic
408C2×#107C2311yescharacteristic
409C2×#107C2311yescharacteristic
410#417—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#357C2311yescharacteristic
461#357C2311yescharacteristic
462#357C2311yescharacteristic
463#357C2311yescharacteristic
464#357C2311yescharacteristic
465#357C2311yescharacteristic
466#357C2311yescharacteristic
467#357C2311yescharacteristic
468#357C2311yescharacteristic
469#357C2311yescharacteristic
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—
496C2×#41—21no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500#135—22no—
501#135—22no—
502#135—22no—
503#135—41no—
504#135—41no—
505#135—41no—
506C2×Q16C2411yescharacteristic
507C2×Q16C2411yescharacteristic
508C2×SD16—21no—
509C2×SD16—21no—
510C2×SD16—21no—
511C2×SD16—21no—
512C2×D8—21no—
513C2×D8—21no—
514C2×D8—21no—
515C2×D8C2411yescharacteristic
516C2×D8C2411yescharacteristic
517C2×D8C2411yescharacteristic
518C2×D8C2411yescharacteristic
519C2×M16C2×D411yescharacteristic
520C2×M16C2×D411yescharacteristic
521C22×C8C2×D411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
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—
534#127—21no—
535#127—21no—
536#127—21no—
537#127—41no—
538#127—41no—
539#127—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#126D811yescharacteristic
552#126D811yescharacteristic
553#125—21no—
554#125—21no—
555#125—21no—
556#125—21no—
557#125—21no—
558#125—21no—
559#125—21no—
560#125—41no—
561#125—41no—
562#125—41no—
563#125—41no—
564#125—41no—
565#125—41no—
566#125—41no—
567#125—41no—
568#125D811yescharacteristic
569#124—21no—
570#124—41no—
571#124—41no—
572#124—41no—
573#124—41no—
574#124—41no—
575#124—41no—
576#124D811yescharacteristic
577#123—41no—
578#123—41no—
579#123—41no—
580#123—41no—
581#123—41no—
582#123—41no—
583#123—41no—
584#123—41no—
585#123—41no—
586#123—41no—
587#123—41no—
588#123—41no—
589#123—41no—
590#123—41no—
591#123—41no—
592#123D811yescharacteristic
593#123D811yescharacteristic
594C22⋊Q8—21no—
595C22⋊Q8—21no—
596C22⋊Q8—21no—
597C22⋊Q8—41no—
598C22⋊Q8—41no—
599C22⋊Q8—41no—
600C22⋊Q8—41no—
601C22⋊Q8—41no—
602C22⋊Q8—41no—
603C22⋊Q8—41no—
604C22⋊Q8—41no—
605C22⋊Q8—41no—
606C22⋊Q8—41no—
607C22⋊Q8—41no—
608C22⋊Q8—41no—
609C22⋊Q8D811yescharacteristic
610#121—21no—
611#121—21no—
612#121—21no—
613#121—21no—
614#121—21no—
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—41no—
620#121—41no—
621#121—41no—
622#121—41no—
623#121—41no—
624#121—41no—
625#121—41no—
626#121—41no—
627#121—41no—
628#121—41no—
629#121—41no—
630#121—41no—
631#121—41no—
632#121—41no—
633#121—41no—
634#121—41no—
635#121—41no—
636#121—41no—
637#121—41no—
638#121D811yescharacteristic
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×Q8C2×D411yescharacteristic
652C4×D4—21no—
653C4×D4—21no—
654C4×D4—21no—
655C4×D4—21no—
656C4×D4—21no—
657C4×D4—21no—
658C4×D4—21no—
659C4×D4—21no—
660C4×D4—21no—
661C4×D4—41no—
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×D4—41no—
672C4×D4—41no—
673C4×D4—41no—
674C4×D4—41no—
675C4×D4—41no—
676C4×D4C2×D411yescharacteristic
677C4×D4C2×D411yescharacteristic
678C4×D4C2×D411yescharacteristic
679#117—21no—
680#117—21no—
681#117—21no—
682#117—21no—
683#117—21no—
684#117—41no—
685#117—41no—
686#117—41no—
687#117—41no—
688#117—41no—
689#117—41no—
690#117—41no—
691#117C2×D411yescharacteristic
692#117C2×D411yescharacteristic
693C2×C4⋊C4—21no—
694C2×C4⋊C4—21no—
695C2×C4⋊C4—21no—
696C2×C4⋊C4—21no—
697C2×C4⋊C4—41no—
698C2×C4⋊C4—41no—
699C2×C4⋊C4—41no—
700C2×C42—41no—
701C2×C42C2×D411yescharacteristic
702Q32—22no—
703SD32—22no—
704SD32—41no—
705SD32—41no—
706SD32—41no—
707D16—41no—
708D16—41no—
709D16—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#102—21no—
772#102—21no—
773#102—21no—
774#102—21no—
775#102—21no—
776#102—21no—
777#102—21no—
778#102—21no—
779#102—21no—
780#102—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
805#41—42no—
806#41—42no—
807#41—42no—
808#41—81no—
809#41—81no—
810#41—81no—
811#41—162no—
812#41—162no—
813#41—162no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—41no—
817C2×Q8—41no—
818C2×Q8—41no—
819C2×Q8—41no—
820C2×Q8—41no—
821C2×Q8C2×D811yescharacteristic
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—41no—
827C2×D4—41no—
828C2×D4—41no—
829C2×D4—41no—
830C2×D4—41no—
831C2×D4—41no—
832C2×D4—41no—
833C2×D4—41no—
834C2×D4—41no—
835C2×D4—41no—
836C2×D4—41no—
837C2×D4—41no—
838C2×D4—41no—
839C2×D4—41no—
840C2×D4—41no—
841C2×D4—41no—
842C2×D4—41no—
843C2×D4—41no—
844C2×D4C2×D811yescharacteristic
845C2×D4C2×D811yescharacteristic
846C2×D4C2×D811yescharacteristic
847C22×C4—41no—
848C22×C4—41no—
849C22×C4—41no—
850C22×C4—41no—
851C22×C4—41no—
852C22×C4—41no—
853C22×C4—41no—
854C22×C4—41no—
855C22×C4—41no—
856C22×C4—41no—
857C22×C4—41no—
858C22×C4—41no—
859C22×C4—41no—
860C22×C4—41no—
861C22×C4—41no—
862C22×C4—41no—
863C22×C4C2×D811yescharacteristic
864C22×C4C2×D811yescharacteristic
865C22×C4C22×D411yescharacteristic
866C22×C4C22×D411yescharacteristic
867C22×C4C22×D411yescharacteristic
868Q16—21no—
869Q16—21no—
870Q16—21no—
871Q162−1+412yes—
872SD16—42no—
873SD16—42no—
874SD16—42no—
875SD16—42no—
876D8—21no—
877D8—21no—
878D8—21no—
879D8—21no—
880D8—21no—
881D8—21no—
882D8—21no—
883D8—21no—
884D8—81no—
885D8—81no—
886D8—81no—
887M16—41no—
888M16—41no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—41no—
896C2×C8C22×D411yescharacteristic
897C2×C8C22×D411yescharacteristic
898C2×C8C22×D411yescharacteristic
899C2×C8C22×D411yescharacteristic
900C2×C8C22×D411yescharacteristic
901C2×C8C22×D411yescharacteristic
902C2×C8C22×D411yescharacteristic
903C2×C8C2511yescharacteristic
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
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⋊C4—41no—
941C4⋊C4—41no—
942C4⋊C4—41no—
943C4⋊C4—41no—
944C4⋊C4—41no—
945C4⋊C4—41no—
946C4⋊C4—41no—
947C4⋊C4C2×D811yescharacteristic
948C4⋊C4C2×D811yescharacteristic
949C4⋊C4C2×D811yescharacteristic
950C4⋊C4C2×D811yescharacteristic
951C4⋊C4C2×D811yescharacteristic
952C4⋊C4C2×D811yescharacteristic
953C4⋊C4C2×D811yescharacteristic
954C4⋊C4C2×D811yescharacteristic
955C4⋊C4C2×D811yescharacteristic
956C4⋊C4C2×D811yescharacteristic
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⋊C4—41no—
979C22⋊C4—41no—
980C22⋊C4—41no—
981C22⋊C4—41no—
982C22⋊C4—41no—
983C22⋊C4—41no—
984C22⋊C4—41no—
985C22⋊C4C2×D811yescharacteristic
986C22⋊C4C2×D811yescharacteristic
987C22⋊C4C2×D811yescharacteristic
988C22⋊C4C2×D811yescharacteristic
989C22⋊C4C2×D811yescharacteristic
990C22⋊C4C2×D811yescharacteristic
991C22⋊C4C2×D811yescharacteristic
992C22⋊C4C2×D811yescharacteristic
993C22⋊C4C2×D811yescharacteristic
994C22⋊C4C2×D811yescharacteristic
995C42—41no—
996C42—41no—
997C42—41no—
998C42—41no—
999C42—41no—
1000C42—41no—
1001C42—41no—
1002C42—41no—
1003C42—41no—
1004C42—41no—
1005C42—41no—
1006C42—41no—
1007C42C2×D811yescharacteristic
1008C42C2×D811yescharacteristic
1009C42C22×D411yescharacteristic
1010C42C22×D411yescharacteristic
1011C42C22×D411yescharacteristic
1012C42C22×D411yescharacteristic
1013C16—21no—
1014C16—21no—
1015C16—21no—
1016C16—21no—
1017C16—21no—
1018C16—21no—
1019C16—21no—
1020C16—21no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23C22×D811yescharacteristic
1026C23C22×D811yescharacteristic
1027C23C22×D811yescharacteristic
1028Q8—22no—
1029Q8—41no—
1030Q8—41no—
1031Q8—41no—
1032Q8—41no—
1033Q8—82no—
1034Q8—161no—
1035Q8—161no—
1036Q8—161no—
1037Q8—161no—
1038D4—41no—
1039D4—41no—
1040D4—41no—
1041D4—41no—
1042D4—41no—
1043D4—41no—
1044D4—41no—
1045D4—41no—
1046D4—41no—
1047D4—41no—
1048D4—41no—
1049D4—82no—
1050D4—82no—
1051D4—82no—
1052D4—82no—
1053D4—161no—
1054D4—161no—
1055D4—161no—
1056D4—161no—
1057D4—161no—
1058D4—161no—
1059D4—161no—
1060D4—161no—
1061D4—161no—
1062D4—161no—
1063D4—161no—
1064D4—161no—
1065D4—161no—
1066D4—161no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—82no—
1088C2×C4—82no—
1089C2×C4—82no—
1090C2×C4—82no—
1091C2×C4—161no—
1092C2×C4—161no—
1093C2×C4—161no—
1094C2×C4—161no—
1095C2×C4—161no—
1096C2×C4—161no—
1097C2×C4—161no—
1098C2×C4—161no—
1099C2×C4—161no—
1100C2×C4—161no—
1101C2×C4—161no—
1102C2×C4—161no—
1103C2×C4C22×D811yescharacteristic
1104C2×C4C22×D811yescharacteristic
1105C2×C4C22×D811yescharacteristic
1106C2×C4C22×D811yescharacteristic
1107C2×C4C22×D811yescharacteristic
1108C2×C4C22×D811yescharacteristic
1109C2×C4C22×D811yescharacteristic
1110C2×C4C22×D811yescharacteristic
1111C2×C4C22×D811yescharacteristic
1112C2×C4C22×D811yescharacteristic
1113C2×C4C22×D811yescharacteristic
1114C2×C4C23×D411yescharacteristic
1115C8—21no—
1116C8—21no—
1117C8—21no—
1118C8—21no—
1119C8—21no—
1120C8—21no—
1121C8—21no—
1122C8C2×2−1+411yescharacteristic
1123C8#58511yescharacteristic
1124C22—21no—
1125C22—21no—
1126C22—21no—
1127C22—21no—
1128C22—21no—
1129C22—21no—
1130C22—21no—
1131C22—21no—
1132C22—21no—
1133C22—81no—
1134C22—81no—
1135C22—81no—
1136C22—81no—
1137C22—81no—
1138C22—81no—
1139C22—81no—
1140C22—81no—
1141C22—81no—
1142C22—81no—
1143C22—81no—
1144C22—81no—
1145C22C23×D811yescharacteristic
1146C4—21no—
1147C4—21no—
1148C4—21no—
1149C4—21no—
1150C4—21no—
1151C4—21no—
1152C4—21no—
1153C4—21no—
1154C4—21no—
1155C4—21no—
1156C4—21no—
1157C4—42no—
1158C4—81no—
1159C4—81no—
1160C4—81no—
1161C4—81no—
1162C4—81no—
1163C4—81no—
1164C4—81no—
1165C4—81no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4#348911yescharacteristic
1170C4#358611yescharacteristic
1171C2—41no—
1172C2—41no—
1173C2—41no—
1174C2—161no—
1175C2—161no—
1176C2—161no—
1177C2—161no—
1178C2#6209511yescharacteristic
1179C2#6263511yescharacteristic
1180C2#6263611yescharacteristic
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. #62490C2semidirect
2. #61479C2semidirect
3. #33957C2semidirect
4. #33955C2semidirect
5. #33935C2semidirect
6. #33933C2semidirect
7. #33917C2semidirect
8. #33914C2semidirect
9. #33912C2semidirect
10. #33910C2semidirect
11. #33906C2semidirect
12. #33904C2semidirect
13. #33884C2semidirect
14. #33884C2semidirect
15. #33876C2semidirect
16. #33876C2semidirect
17. #33872C2semidirect
18. #33871C2semidirect
19. #33823C2semidirect
20. #33823C2semidirect
21. #33813C2semidirect
22. #33807C2semidirect
23. #33807C2semidirect
24. #33801C2semidirect
25. #33685C2semidirect
26. #33684C2semidirect
27. #33671C2semidirect
28. #33634C2semidirect
29. #33633C2semidirect
30. #33626C2semidirect
31. #33506C2semidirect

Maximal subgroups

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

subgroupindex
#624902
#614792
#339572
#339552
#339352
#339332
#339172
#339142
#339122
#339102
#339062
#339042
#338842
#338762
#338722
#338712
#338232
#338132
#338072
#338012
#336852
#336842
#336712
#336342
#336332
#336262
#335062