Finite Group Databasebeta

← #7624766

Subgroups — #7624766

Order 512.

1191 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62490C211yesmaximal, characteristic, complemented
2#61487C211yesmaximal, characteristic, complemented
3#33956C211yesmaximal, characteristic, complemented
4#33948C211yesmaximal, characteristic, complemented
5#33944C211yesmaximal, characteristic, complemented
6#33927C211yesmaximal, characteristic, complemented
7#33918C211yesmaximal, characteristic, complemented
8#33917C211yesmaximal, characteristic, complemented
9#33916C211yesmaximal, characteristic, complemented
10#33907C211yesmaximal, characteristic, complemented
11#33906C211yesmaximal, characteristic, complemented
12#33903C211yesmaximal, characteristic, complemented
13#33890C211yesmaximal, characteristic, complemented
14#33886C211yesmaximal, characteristic, complemented
15#33874C211yesmaximal, characteristic, complemented
16#33869C211yesmaximal, characteristic, complemented
17#33864C211yesmaximal, characteristic, complemented
18#33863C211yesmaximal, characteristic, complemented
19#33828C211yesmaximal, characteristic, complemented
20#33824C211yesmaximal, characteristic, complemented
21#33816C211yesmaximal, characteristic, complemented
22#33810C211yesmaximal, characteristic, complemented
23#33808C211yesmaximal, characteristic, complemented
24#33799C211yesmaximal, characteristic, complemented
25#33685C211yesmaximal, characteristic, complemented
26#33678C211yesmaximal, characteristic, complemented
27#33662C211yesmaximal, characteristic, complemented
28#33633C211yesmaximal, characteristic, complemented
29#33631C211yesmaximal, characteristic, complemented
30#33626C211yesmaximal, characteristic, complemented
31#33508C211yesmaximal, characteristic, complemented
32#3565—21no—
33#3521—21no—
34#3393C2211yescharacteristic
35#3388—21no—
36#3383C2211yescharacteristic, complemented
37#3380C2211yescharacteristic
38#3380C2211yescharacteristic, complemented
39#3376—21no—
40#3351—21no—
41#3350—21no—
42#3348—21no—
43#3342C2211yescharacteristic
44#3342C2211yescharacteristic, complemented
45#3341C2211yescharacteristic
46#3339C2211yescharacteristic
47#3339C2211yescharacteristic
48#3339C2211yescharacteristic, complemented
49#3336C2211yescharacteristic
50#3336C2211yescharacteristic
51#3336C2211yescharacteristic
52#3323—21no—
53#3311—21no—
54#3307—21no—
55#3283C2211yescharacteristic
56#3280C2211yescharacteristic
57#3280C2211yescharacteristic
58#3244—21no—
59#3244—21no—
60#3240—21no—
61#3177C2211yescharacteristic
62#3175C2211yescharacteristic
63#3175C2211yescharacteristic
64#3175C2211yescharacteristic, complemented
65#3168C2211yescharacteristic
66#3168C2211yescharacteristic, complemented
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#2254C2211yescharacteristic, complemented
80#2253C2211yescharacteristic, complemented
81#2253C2211yescharacteristic, complemented
82#2253C2211yescharacteristic, complemented
83#2245C2211yescharacteristic, complemented
84#2243C2211yescharacteristic
85#2242C2211yescharacteristic
86#2242C2211yescharacteristic
87#2242C2211yescharacteristic
88#2241C2211yescharacteristic, complemented
89#2237C2211yescharacteristic
90#2237C2211yescharacteristic
91#2237C2211yescharacteristic
92#2237C2211yescharacteristic, complemented
93#2237C2211yescharacteristic, complemented
94#2237C2211yescharacteristic, complemented
95#2237C2211yescharacteristic, complemented
96#2236C2211yescharacteristic
97#2235C2211yescharacteristic
98#2235C2211yescharacteristic, complemented
99#2235C2211yescharacteristic, complemented
100#2234C2211yescharacteristic
101#2234C2211yescharacteristic
102#2234C2211yescharacteristic
103#2234C2211yescharacteristic
104#2234C2211yescharacteristic, complemented
105#2233C2211yescharacteristic
106#2233C2211yescharacteristic, complemented
107#2229C2211yescharacteristic, complemented
108#2229C2211yescharacteristic, complemented
109#2229C2211yescharacteristic, complemented
110#2229C2211yescharacteristic, complemented
111#2229C2211yescharacteristic, complemented
112#2229C2211yescharacteristic, complemented
113#2229C2211yescharacteristic, complemented
114#2228C2211yescharacteristic
115#2228C2211yescharacteristic
116#2228C2211yescharacteristic
117#2228C2211yescharacteristic
118#2228C2211yescharacteristic
119#2228C2211yescharacteristic
120#2228C2211yescharacteristic
121#2228C2211yescharacteristic, complemented
122#2228C2211yescharacteristic, complemented
123#2227C2211yescharacteristic, complemented
124#2227C2211yescharacteristic, complemented
125#2227C2211yescharacteristic, complemented
126#2227C2211yescharacteristic, complemented
127#2226C2211yescharacteristic
128#2226C2211yescharacteristic
129#2226C2211yescharacteristic
130#2225C2211yescharacteristic, complemented
131#2225C2211yescharacteristic, complemented
132#2224C2211yescharacteristic
133#2224C2211yescharacteristic
134#2224C2211yescharacteristic
135#2224C2211yescharacteristic
136#2224C2211yescharacteristic, complemented
137#2220C2211yescharacteristic
138#2220C2211yescharacteristic
139#2220C2211yescharacteristic, complemented
140#2219C2211yescharacteristic
141#2217C2211yescharacteristic
142#2217C2211yescharacteristic
143#2217C2211yescharacteristic, complemented
144#2216C2211yescharacteristic
145#2216C2211yescharacteristic, complemented
146#2216C2211yescharacteristic, complemented
147#2215C2211yescharacteristic
148#2215C2211yescharacteristic
149#2211C2211yescharacteristic
150#2211C2211yescharacteristic
151#2211C2211yescharacteristic, complemented
152#2211C2211yescharacteristic, complemented
153#2210C2211yescharacteristic
154#2210C2211yescharacteristic
155#2210C2211yescharacteristic
156#2210C2211yescharacteristic
157#2209C2211yescharacteristic, complemented
158#2208C2211yescharacteristic, complemented
159#2189C2211yescharacteristic
160#2189C2211yescharacteristic
161#2187C2211yescharacteristic
162#2186C2211yescharacteristic
163#2186C2211yescharacteristic
164#2184C2211yescharacteristic
165#2183C2211yescharacteristic, complemented
166Q8×C16C2211yescharacteristic, complemented
167#2177C2211yescharacteristic
168#2177C2211yescharacteristic
169#2176C2211yescharacteristic, complemented
170#2175C2211yescharacteristic
171C4×Q32C2211yescharacteristic, complemented
172C4×SD32C2211yescharacteristic
173C4×SD32C2211yescharacteristic
174C4×SD32C2211yescharacteristic
175C4×SD32C2211yescharacteristic, complemented
176C4×SD32C2211yescharacteristic, complemented
177C4×D16C2211yescharacteristic
178C4×D16C2211yescharacteristic
179#2169C2211yescharacteristic
180#2168C2211yescharacteristic
181#2168C2211yescharacteristic, complemented
182D4×C16C2211yescharacteristic
183D4×C16C2211yescharacteristic
184D4×C16C2211yescharacteristic, complemented
185#2164C2211yescharacteristic
186#2164C2211yescharacteristic, complemented
187#2162C2211yescharacteristic, complemented
188#2159C2211yescharacteristic
189#2159C2211yescharacteristic, complemented
190#2158C2211yescharacteristic
191#2158C2211yescharacteristic, complemented
192#2158C2211yescharacteristic, complemented
193C2×#366C2211yescharacteristic, 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#562—41no—
208#557—21no—
209#556—21no—
210#556—21no—
211#556—21no—
212#556—41no—
213#555—21no—
214#554—21no—
215#554—21no—
216#553—21no—
217#553—21no—
218#553—21no—
219#553—41no—
220#552—21no—
221#552—21no—
222#552—21no—
223#552—41no—
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—21no—
234#542—21no—
235#542—41no—
236#542—41no—
237#541—21no—
238#541—41no—
239#539—41no—
240#539—41no—
241#538—41no—
242#533—21no—
243#529—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×SD32C2311yescharacteristic
254C2×SD32C2311yescharacteristic
255C2×SD32C2311yescharacteristic
256C2×SD32C2311yescharacteristic
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#495C2311yescharacteristic
285#495C2311yescharacteristic
286#494C2311yescharacteristic
287#491—21no—
288#489—21no—
289#489—21no—
290#489—21no—
291#488—21no—
292#488—21no—
293#485—21no—
294#485—21no—
295#485—21no—
296#485—21no—
297#485—21no—
298#485—21no—
299#485—21no—
300#483—21no—
301#483—21no—
302#483—21no—
303#482—21no—
304#482—21no—
305#482—21no—
306#482—21no—
307#482—21no—
308#481—21no—
309#481—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#478—21no—
320#478—21no—
321#478—21no—
322#478—21no—
323#476—21no—
324#476—21no—
325#476—21no—
326#475—21no—
327#475—21no—
328#475—21no—
329#470—21no—
330#468—21no—
331#468—21no—
332#468—21no—
333#467C2311yescharacteristic
334#467C2311yescharacteristic
335#467C2311yescharacteristic
336#467C2311yescharacteristic
337#467C2311yescharacteristic
338#467C2311yescharacteristic
339#467C2311yescharacteristic
340#466C2311yescharacteristic
341#466C2311yescharacteristic
342#466C2311yescharacteristic
343#466C2311yescharacteristic
344#466C2311yescharacteristic
345#465—21no—
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#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×SD16—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
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#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
490C4×C16C2311yescharacteristic
491C4×C16C2311yescharacteristic
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×Q16C2411yescharacteristic
503C2×Q16C2411yescharacteristic
504C2×Q16C2411yescharacteristic
505C2×SD16—21no—
506C2×SD16—21no—
507C2×SD16—21no—
508C2×SD16—21no—
509C2×SD16—21no—
510C2×D8—22no—
511C2×D8—21no—
512C2×D8—41no—
513C2×D8C2411yescharacteristic
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—41no—
529C4⋊Q8—41no—
530C4⋊Q8—41no—
531#126—41no—
532#126—41no—
533#126—41no—
534#126—41no—
535#126—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#126D811yescharacteristic
551#126D811yescharacteristic
552#125—21no—
553#125—21no—
554#125—21no—
555#125—21no—
556#125—21no—
557#125—21no—
558#125—21no—
559#125—41no—
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—21no—
571#124—21no—
572#124—41no—
573#124—41no—
574#124—41no—
575#124—41no—
576#124—41no—
577#124—41no—
578#124—41no—
579#124D811yescharacteristic
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#123—41no—
593#123—41no—
594#123—41no—
595#123D811yescharacteristic
596#123D811yescharacteristic
597C22⋊Q8—21no—
598C22⋊Q8—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—41no—
605C22⋊Q8—41no—
606C22⋊Q8—41no—
607C22⋊Q8—41no—
608C22⋊Q8—41no—
609C22⋊Q8—41no—
610C22⋊Q8—41no—
611C22⋊Q8—41no—
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⋊Q8D811yescharacteristic
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121—21no—
626#121—41no—
627#121—41no—
628#121—41no—
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—41no—
644C4×Q8—41no—
645C4×Q8—41no—
646C4×Q8—41no—
647C4×Q8—41no—
648C4×Q8C2×D411yescharacteristic
649C4×D4—21no—
650C4×D4—21no—
651C4×D4—21no—
652C4×D4—21no—
653C4×D4—21no—
654C4×D4—21no—
655C4×D4—21no—
656C4×D4—21no—
657C4×D4—21no—
658C4×D4—41no—
659C4×D4—41no—
660C4×D4—41no—
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×D4C2×D411yescharacteristic
670C4×D4C2×D411yescharacteristic
671C4×D4C2×D411yescharacteristic
672#117—21no—
673#117—21no—
674#117—21no—
675#117—21no—
676#117—21no—
677#117—21no—
678#117—41no—
679#117—41no—
680#117—41no—
681#117—41no—
682#117—41no—
683#117—41no—
684#117—41no—
685#117—41no—
686#117—41no—
687#117C2×D411yescharacteristic
688#117C2×D411yescharacteristic
689C2×C4⋊C4—21no—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C4⋊C4—41no—
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—
704SD32—22no—
705SD32—41no—
706SD32—41no—
707SD32—41no—
708D16—22no—
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#107C2411yescharacteristic
733#107C2411yescharacteristic
734#107C2411yescharacteristic
735#107C2411yescharacteristic
736#107C2411yescharacteristic
737#107C2411yescharacteristic
738#107C2411yescharacteristic
739#107C2411yescharacteristic
740#107C2411yescharacteristic
741#107C2411yescharacteristic
742#106—21no—
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#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
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—41no—
814C2×Q8—41no—
815C2×Q8—41no—
816C2×Q8—41no—
817C2×Q8—41no—
818C2×Q8C2×D811yescharacteristic
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—42no—
823C2×D4—41no—
824C2×D4—41no—
825C2×D4—41no—
826C2×D4—41no—
827C2×D4—41no—
828C2×D4—41no—
829C2×D4—41no—
830C2×D4—41no—
831C2×D4—81no—
832C2×D4C2×D811yescharacteristic
833C2×D4C2×D811yescharacteristic
834C2×D4C2×D811yescharacteristic
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×C4—41no—
845C22×C4—41no—
846C22×C4—41no—
847C22×C4—41no—
848C22×C4—41no—
849C22×C4C2×D811yescharacteristic
850C22×C4C2×D811yescharacteristic
851C22×C4C22×D411yescharacteristic
852C22×C4C22×D411yescharacteristic
853C22×C4C22×D411yescharacteristic
854Q16—21no—
855Q16—21no—
856Q16—21no—
857Q16—21no—
858Q16—21no—
859Q16—21no—
860Q16—81no—
861SD16—42no—
862SD16—42no—
863SD16—42no—
864SD16—81no—
865SD16—81no—
866D8—21no—
867D8—21no—
868D8—21no—
869D8—21no—
870D8—21no—
871D8—42no—
872D82−1+412yes—
873M16—41no—
874M16—41no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—41no—
882C2×C8C22×D411yescharacteristic
883C2×C8C22×D411yescharacteristic
884C2×C8C22×D411yescharacteristic
885C2×C8C22×D411yescharacteristic
886C2×C8C22×D411yescharacteristic
887C2×C8C22×D411yescharacteristic
888C2×C8C22×D411yescharacteristic
889C2×C8C2511yescharacteristic
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
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⋊C4C2×D811yescharacteristic
939C4⋊C4C2×D811yescharacteristic
940C4⋊C4C2×D811yescharacteristic
941C4⋊C4C2×D811yescharacteristic
942C4⋊C4C2×D811yescharacteristic
943C4⋊C4C2×D811yescharacteristic
944C4⋊C4C2×D811yescharacteristic
945C4⋊C4C2×D811yescharacteristic
946C4⋊C4C2×D811yescharacteristic
947C4⋊C4C2×D811yescharacteristic
948C22⋊C4—41no—
949C22⋊C4—41no—
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⋊C4—41no—
979C22⋊C4—41no—
980C22⋊C4—41no—
981C22⋊C4C2×D811yescharacteristic
982C22⋊C4C2×D811yescharacteristic
983C22⋊C4C2×D811yescharacteristic
984C22⋊C4C2×D811yescharacteristic
985C22⋊C4C2×D811yescharacteristic
986C22⋊C4C2×D811yescharacteristic
987C22⋊C4C2×D811yescharacteristic
988C22⋊C4C2×D811yescharacteristic
989C22⋊C4C2×D811yescharacteristic
990C22⋊C4C2×D811yescharacteristic
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—41no—
1021C23—82no—
1022C23—161no—
1023C23—161no—
1024C23C22×D811yescharacteristic
1025C23C22×D811yescharacteristic
1026C23C22×D811yescharacteristic
1027Q8—41no—
1028Q8—41no—
1029Q8—41no—
1030Q8—41no—
1031Q8—41no—
1032Q8—41no—
1033Q8—41no—
1034Q8—161no—
1035Q8—161no—
1036Q8—161no—
1037Q8—161no—
1038Q8—161no—
1039D4—22no—
1040D4—41no—
1041D4—41no—
1042D4—41no—
1043D4—41no—
1044D4—41no—
1045D4—41no—
1046D4—41no—
1047D4—41no—
1048D4—82no—
1049D4—82no—
1050D4—82no—
1051D4—161no—
1052D4—161no—
1053D4—161no—
1054D4—161no—
1055D4—161no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
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—41no—
1076C2×C4—41no—
1077C2×C4—82no—
1078C2×C4—82no—
1079C2×C4—161no—
1080C2×C4—161no—
1081C2×C4—161no—
1082C2×C4—161no—
1083C2×C4—161no—
1084C2×C4—161no—
1085C2×C4—161no—
1086C2×C4—161no—
1087C2×C4—161no—
1088C2×C4—161no—
1089C2×C4—161no—
1090C2×C4—161no—
1091C2×C4C22×D811yescharacteristic
1092C2×C4C22×D811yescharacteristic
1093C2×C4C22×D811yescharacteristic
1094C2×C4C22×D811yescharacteristic
1095C2×C4C22×D811yescharacteristic
1096C2×C4C22×D811yescharacteristic
1097C2×C4C22×D811yescharacteristic
1098C2×C4C22×D811yescharacteristic
1099C2×C4C22×D811yescharacteristic
1100C2×C4C22×D811yescharacteristic
1101C2×C4C22×D811yescharacteristic
1102C2×C4C23×D411yescharacteristic
1103C8—21no—
1104C8—21no—
1105C8—21no—
1106C8—21no—
1107C8—21no—
1108C8—21no—
1109C8—21no—
1110C8C2×2−1+411yescharacteristic
1111C8#58511yescharacteristic
1112C22—21no—
1113C22—21no—
1114C22—21no—
1115C22—21no—
1116C22—21no—
1117C22—21no—
1118C22—21no—
1119C22—21no—
1120C22—21no—
1121C22—42no—
1122C22—81no—
1123C22—81no—
1124C22—81no—
1125C22—81no—
1126C22—81no—
1127C22—81no—
1128C22—81no—
1129C22—81no—
1130C22—322no—
1131C22C23×D811yescharacteristic
1132C4—21no—
1133C4—21no—
1134C4—21no—
1135C4—21no—
1136C4—21no—
1137C4—21no—
1138C4—21no—
1139C4—21no—
1140C4—21no—
1141C4—21no—
1142C4—21no—
1143C4—81no—
1144C4—81no—
1145C4—81no—
1146C4—81no—
1147C4—81no—
1148C4—81no—
1149C4—81no—
1150C4—81no—
1151C4—81no—
1152C4—81no—
1153C4—81no—
1154C4—81no—
1155C4—81no—
1156C4#348911yescharacteristic
1157C4#358611yescharacteristic
1158C2—41no—
1159C2—41no—
1160C2—41no—
1161C2—82no—
1162C2—161no—
1163C2—161no—
1164C2#6209511yescharacteristic
1165C2#6263511yescharacteristic
1166C2#6263511yescharacteristic
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. #61487C2semidirect
3. #33956C2semidirect
4. #33948C2semidirect
5. #33944C2semidirect
6. #33927C2semidirect
7. #33918C2semidirect
8. #33917C2semidirect
9. #33916C2semidirect
10. #33907C2semidirect
11. #33906C2semidirect
12. #33903C2semidirect
13. #33890C2semidirect
14. #33886C2semidirect
15. #33874C2semidirect
16. #33869C2semidirect
17. #33864C2semidirect
18. #33863C2semidirect
19. #33828C2semidirect
20. #33824C2semidirect
21. #33816C2semidirect
22. #33810C2semidirect
23. #33808C2semidirect
24. #33799C2semidirect
25. #33685C2semidirect
26. #33678C2semidirect
27. #33662C2semidirect
28. #33633C2semidirect
29. #33631C2semidirect
30. #33626C2semidirect
31. #33508C2semidirect
36. #3383C22semidirect
38. #3380C22semidirect
44. #3342C22semidirect
48. #3339C22semidirect
64. #3175C22semidirect
66. #3168C22semidirect
68. #3164C22semidirect
69. #3160C22semidirect
77. #2255C22semidirect
78. #2255C22semidirect
79. #2254C22semidirect
80. #2253C22semidirect
81. #2253C22semidirect
82. #2253C22semidirect
83. #2245C22semidirect
88. #2241C22semidirect
92. #2237C22semidirect
93. #2237C22semidirect
94. #2237C22semidirect
95. #2237C22semidirect
98. #2235C22semidirect
99. #2235C22semidirect
104. #2234C22semidirect
106. #2233C22semidirect
107. #2229C22semidirect
108. #2229C22semidirect
109. #2229C22semidirect
110. #2229C22semidirect
111. #2229C22semidirect
112. #2229C22semidirect
113. #2229C22semidirect
121. #2228C22semidirect
122. #2228C22semidirect
123. #2227C22semidirect
124. #2227C22semidirect
125. #2227C22semidirect
126. #2227C22semidirect
130. #2225C22semidirect
131. #2225C22semidirect
136. #2224C22semidirect
139. #2220C22semidirect
143. #2217C22semidirect
145. #2216C22semidirect
146. #2216C22semidirect
151. #2211C22semidirect
152. #2211C22semidirect
157. #2209C22semidirect
158. #2208C22semidirect
165. #2183C22semidirect
166. Q8×C16C22semidirect
169. #2176C22semidirect
171. C4×Q32C22semidirect
175. C4×SD32C22semidirect
176. C4×SD32C22semidirect
181. #2168C22semidirect
184. D4×C16C22semidirect
186. #2164C22semidirect
187. #2162C22semidirect
189. #2159C22semidirect
191. #2158C22semidirect
192. #2158C22semidirect
193. C2×#366C22semidirect
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
#624902
#614872
#339562
#339482
#339442
#339272
#339182
#339172
#339162
#339072
#339062
#339032
#338902
#338862
#338742
#338692
#338642
#338632
#338282
#338242
#338162
#338102
#338082
#337992
#336852
#336782
#336622
#336332
#336312
#336262
#335082