Finite Group Databasebeta

← #7624697

Subgroups — #7624697

Order 512.

1224 conjugacy classes of subgroups.

The subgroup lattice has 1175 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62475C211yesmaximal, characteristic, complemented
2#61427C211yesmaximal, characteristic, complemented
3#33956C211yesmaximal, characteristic, complemented
4#33955C211yesmaximal, characteristic, complemented
5#33944C211yesmaximal, characteristic, complemented
6#33943C211yesmaximal, characteristic, complemented
7#33915C211yesmaximal, characteristic, complemented
8#33914C211yesmaximal, characteristic, complemented
9#33911C211yesmaximal, characteristic, complemented
10#33910C211yesmaximal, characteristic, complemented
11#33904C211yesmaximal, characteristic, complemented
12#33903C211yesmaximal, characteristic, complemented
13#33882C211yesmaximal, characteristic, complemented
14#33881C211yesmaximal, characteristic, complemented
15#33874C211yesmaximal, characteristic, complemented
16#33873C211yesmaximal, characteristic, complemented
17#33864C211yesmaximal, characteristic, complemented
18#33863C211yesmaximal, characteristic, complemented
19#33822C211yesmaximal, characteristic, complemented
20#33816C211yesmaximal, characteristic, complemented
21#33814C211yesmaximal, characteristic, complemented
22#33806C211yesmaximal, characteristic, complemented
23#33802C211yesmaximal, characteristic, complemented
24#33798C211yesmaximal, characteristic, complemented
25#33674C211yesmaximal, characteristic, complemented
26#33671C211yesmaximal, characteristic, complemented
27#33662C211yesmaximal, characteristic, complemented
28#33630C211yesmaximal, characteristic, complemented
29#33626C211yesmaximal, characteristic, complemented
30C2×#2228C211yesmaximal, characteristic, complemented
31#33504C211yesmaximal, characteristic, complemented
32#3515—21no—
33#3475—21no—
34#3393C2211yescharacteristic
35#3383C2211yescharacteristic, complemented
36#3381—21no—
37#3380C2211yescharacteristic
38#3380C2211yescharacteristic, complemented
39#3360—21no—
40#3341C2211yescharacteristic
41#3339C2211yescharacteristic
42#3339C2211yescharacteristic, complemented
43#3338C2211yescharacteristic
44#3337—21no—
45#3337—21no—
46#3336C2211yescharacteristic
47#3336C2211yescharacteristic
48#3336C2211yescharacteristic
49#3336C2211yescharacteristic, complemented
50#3335—21no—
51#3334C2211yescharacteristic
52#3303—21no—
53#3296—21no—
54#3296—21no—
55#3283C2211yescharacteristic
56#3280C2211yescharacteristic
57#3280C2211yescharacteristic
58#3233—21no—
59#3232—21no—
60#3232—21no—
61#3170C2211yescharacteristic
62#3168C2211yescharacteristic
63#3168C2211yescharacteristic
64#3168C2211yescharacteristic
65#3168C2211yescharacteristic, complemented
66#3168C2211yescharacteristic, complemented
67#3160C2211yescharacteristic, complemented
68C2×#499C2211yescharacteristic
69C2×#499C2211yescharacteristic, complemented
70#3102—21no—
71#3102—21no—
72#3101—21no—
73C8×#41C2211yescharacteristic
74C4×#135C2211yescharacteristic
75C4×#135C2211yescharacteristic
76C2×C4×D8C2211yescharacteristic
77#2255C2211yescharacteristic, complemented
78#2255C2211yescharacteristic, complemented
79#2255C2211yescharacteristic, complemented
80#2255C2211yescharacteristic, complemented
81#2253C2211yescharacteristic, complemented
82#2253C2211yescharacteristic, complemented
83#2245C2211yescharacteristic, complemented
84#2245C2211yescharacteristic, complemented
85#2243C2211yescharacteristic
86#2243C2211yescharacteristic
87#2242C2211yescharacteristic
88#2242C2211yescharacteristic
89#2237C2211yescharacteristic, complemented
90#2237C2211yescharacteristic, complemented
91#2237C2211yescharacteristic, complemented
92#2237C2211yescharacteristic, complemented
93#2236C2211yescharacteristic
94#2236C2211yescharacteristic
95#2236C2211yescharacteristic, complemented
96#2235C2211yescharacteristic
97#2235C2211yescharacteristic
98#2235C2211yescharacteristic
99#2235C2211yescharacteristic, complemented
100#2234C2211yescharacteristic
101#2234C2211yescharacteristic
102#2234C2211yescharacteristic, complemented
103#2234C2211yescharacteristic, complemented
104#2233C2211yescharacteristic
105#2232C2211yescharacteristic
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#2229C2211yescharacteristic, complemented
117#2228C2211yescharacteristic
118#2228C2211yescharacteristic
119#2228C2211yescharacteristic
120#2228C2211yescharacteristic
121#2228C2211yescharacteristic
122#2228C2211yescharacteristic
123#2228C2211yescharacteristic
124#2228C2211yescharacteristic
125#2228C2211yescharacteristic
126#2228C2211yescharacteristic
127#2228C2211yescharacteristic
128#2228C2211yescharacteristic
129#2228C2211yescharacteristic, complemented
130#2228C2211yescharacteristic, complemented
131#2227C2211yescharacteristic, complemented
132#2226C2211yescharacteristic
133#2225C2211yescharacteristic, complemented
134#2225C2211yescharacteristic, complemented
135#2224C2211yescharacteristic
136#2224C2211yescharacteristic, complemented
137#2220C2211yescharacteristic
138#2220C2211yescharacteristic, complemented
139#2219C2211yescharacteristic, complemented
140#2218C2211yescharacteristic
141#2217C2211yescharacteristic
142#2217C2211yescharacteristic
143#2217C2211yescharacteristic
144#2217C2211yescharacteristic, complemented
145#2216C2211yescharacteristic
146#2216C2211yescharacteristic
147#2216C2211yescharacteristic, complemented
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
166#2183C2211yescharacteristic, complemented
167#2177C2211yescharacteristic
168#2177C2211yescharacteristic
169#2177C2211yescharacteristic
170#2176C2211yescharacteristic, complemented
171#2175C2211yescharacteristic
172#2175C2211yescharacteristic
173#2175C2211yescharacteristic
174#2175C2211yescharacteristic, complemented
175C4×Q32C2211yescharacteristic, complemented
176C4×SD32C2211yescharacteristic
177C4×SD32C2211yescharacteristic, complemented
178C4×D16C2211yescharacteristic
179#2168C2211yescharacteristic
180#2168C2211yescharacteristic
181#2168C2211yescharacteristic, complemented
182#2168C2211yescharacteristic, complemented
183D4×C16C2211yescharacteristic
184D4×C16C2211yescharacteristic
185#2163C2211yescharacteristic
186#2163C2211yescharacteristic, complemented
187#2162C2211yescharacteristic, complemented
188#2159C2211yescharacteristic, complemented
189#2159C2211yescharacteristic, complemented
190#2158C2211yescharacteristic, complemented
191#2158C2211yescharacteristic, complemented
192C2×#367C2211yescharacteristic
193C2×#366C2211yescharacteristic
194#2150C2211yescharacteristic, complemented
195C2×C4⋊C16C2211yescharacteristic
196C2×C4⋊C16C2211yescharacteristic, complemented
197#2139C2211yescharacteristic
198#2139C2211yescharacteristic
199#2138C2211yescharacteristic
200#2138C2211yescharacteristic
201C2×#357C2211yescharacteristic
202C2×#357C2211yescharacteristic
203C2×#135C2311yescharacteristic
204C2×#135C2311yescharacteristic
205C22×D8C2311yescharacteristic
206#557—21no—
207#556—21no—
208#555—21no—
209#554—21no—
210#554—21no—
211#554—21no—
212#553—21no—
213#553—21no—
214#553—41no—
215#552—21no—
216#552—21no—
217#552—21no—
218#552—21no—
219#552—41no—
220#552—41no—
221#552—41no—
222#552—41no—
223#551—41no—
224#551—41no—
225#547—21no—
226#547—21no—
227#547—41no—
228#546—21no—
229#546—21no—
230#541—41no—
231#539—41no—
232#539—41no—
233#533—21no—
234#533—21no—
235#529—21no—
236#529—21no—
237#529—21no—
238#529—21no—
239#529—21no—
240#529—41no—
241#529—41no—
242C2×#125—21no—
243C2×#125—21no—
244#525—41no—
245#520—41no—
246C4×#41—21no—
247C4×#41—21no—
248C4×#41D411yescharacteristic
249C2×C4×D4—21no—
250C2×#117—41no—
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#500C2311yescharacteristic
266#500C2311yescharacteristic
267#500C2311yescharacteristic
268#499—21no—
269#499—21no—
270#499—21no—
271#499—21no—
272#499—21no—
273#499C2311yescharacteristic
274#499C2311yescharacteristic
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#488—21no—
288#488—21no—
289#488—21no—
290#488—21no—
291#488—21no—
292#487—21no—
293#485—21no—
294#485—21no—
295#485—21no—
296#485—21no—
297#484—21no—
298#484—21no—
299#483—21no—
300#483—21no—
301#483—21no—
302#483—21no—
303#482—21no—
304#482—21no—
305#482—21no—
306#482—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#477—21no—
324#476—21no—
325#476—21no—
326#476—21no—
327#475—21no—
328#474—21no—
329#467—21no—
330#467C2311yescharacteristic
331#467C2311yescharacteristic
332#467C2311yescharacteristic
333#467C2311yescharacteristic
334#467C2311yescharacteristic
335#467C2311yescharacteristic
336#467C2311yescharacteristic
337#466C2311yescharacteristic
338#466C2311yescharacteristic
339#466C2311yescharacteristic
340#466C2311yescharacteristic
341#466C2311yescharacteristic
342#465—21no—
343#465—21no—
344#465—21no—
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—
359C8×Q8D411yescharacteristic
360C8×Q8C2311yescharacteristic
361C4×Q16—21no—
362C4×Q16C2311yescharacteristic
363C4×Q16C2311yescharacteristic
364C4×Q16C2311yescharacteristic
365C4×Q16C2311yescharacteristic
366C4×Q16C2311yescharacteristic
367C4×Q16C2311yescharacteristic
368C4×Q16C2311yescharacteristic
369C4×SD16—21no—
370C4×SD16—21no—
371C4×SD16—21no—
372C4×SD16—21no—
373C4×SD16—21no—
374C4×SD16—21no—
375C4×SD16—21no—
376C4×SD16—21no—
377C4×SD16—21no—
378C4×D8—21no—
379C4×D8—21no—
380C4×D8C2311yescharacteristic
381C4×D8C2311yescharacteristic
382C4×D8C2311yescharacteristic
383C4×D8C2311yescharacteristic
384C4×D8C2311yescharacteristic
385C4×D8C2311yescharacteristic
386C4×D8C2311yescharacteristic
387C4×D8C2311yescharacteristic
388C4×D8C2311yescharacteristic
389C8×D4D411yescharacteristic
390C8×D4D411yescharacteristic
391C8×D4D411yescharacteristic
392C8×D4C2311yescharacteristic
393C8×D4C2311yescharacteristic
394C8×D4C2311yescharacteristic
395#431D411yescharacteristic
396#431D411yescharacteristic
397#431D411yescharacteristic
398#427—21no—
399#427C2311yescharacteristic
400#427C2311yescharacteristic
401#427C2311yescharacteristic
402#427C2311yescharacteristic
403C2×#107C2311yescharacteristic
404C2×#107C2311yescharacteristic
405C2×#107C2311yescharacteristic
406C2×#107C2311yescharacteristic
407C2×#107C2311yescharacteristic
408C2×#106—21no—
409C2×#106—21no—
410#416—21no—
411#416—21no—
412C2×#102—21no—
413C2×C4×C8C2311yescharacteristic
414C2×C4×C8C2311yescharacteristic
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
490#346C2311yescharacteristic
491#346C2311yescharacteristic
492C4×C16C2311yescharacteristic
493C4×C16C2311yescharacteristic
494C2×#41—21no—
495C2×#41—21no—
496C2×#41—41no—
497C2×#41D811yescharacteristic
498C22×D4—21no—
499C23×C4—41no—
500#135—22no—
501#135—22no—
502#135—41no—
503#135—41no—
504C2×Q16—21no—
505C2×Q16C2411yescharacteristic
506C2×Q16C2411yescharacteristic
507C2×Q16C2411yescharacteristic
508C2×SD16—21no—
509C2×SD16—21no—
510C2×SD16—21no—
511C2×SD16—21no—
512C2×SD16—21no—
513C2×D8—22no—
514C2×D8—21no—
515C2×D8—41no—
516C2×D8C2411yescharacteristic
517C2×D8C2411yescharacteristic
518C2×D8C2411yescharacteristic
519C22×C8C2×D411yescharacteristic
520C22×C8C2×D411yescharacteristic
521C22×C8C2×D411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C4⋊Q8—21no—
526C4⋊Q8—21no—
527C4⋊Q8—21no—
528C4⋊Q8—21no—
529C4⋊Q8—41no—
530#126—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#125—21no—
544#125—21no—
545#125—21no—
546#125—21no—
547#125—21no—
548#125—21no—
549#125—21no—
550#125—21no—
551#125—21no—
552#125—41no—
553#125—41no—
554#125—41no—
555#125—41no—
556#125—41no—
557#125—41no—
558#125—41no—
559#125—41no—
560#125—41no—
561#125—41no—
562#125—41no—
563#125—41no—
564#124—21no—
565#124—21no—
566#124—21no—
567#124—41no—
568#124—41no—
569#123—41no—
570#123—41no—
571#123—41no—
572#123—41no—
573#123—41no—
574#123—41no—
575#123—41no—
576#123—41no—
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—
586C22⋊Q8—21no—
587C22⋊Q8—21no—
588C22⋊Q8—21no—
589C22⋊Q8—21no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8—21no—
593C22⋊Q8—41no—
594C22⋊Q8—41no—
595C22⋊Q8—41no—
596C22⋊Q8—41no—
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—
606#121—21no—
607#121—21no—
608#121—21no—
609#121—21no—
610#121—21no—
611#121—41no—
612#121—41no—
613#121—41no—
614#121—41no—
615#121—41no—
616#121—41no—
617#120—41no—
618#120—41no—
619C4×Q8—21no—
620C4×Q8—21no—
621C4×Q8—21no—
622C4×Q8—21no—
623C4×Q8—21no—
624C4×Q8—21no—
625C4×Q8—21no—
626C4×Q8—41no—
627C4×Q8—41no—
628C4×Q8—41no—
629C4×Q8—41no—
630C4×Q8D811yescharacteristic
631C4×Q8C2×D411yescharacteristic
632C4×D4—21no—
633C4×D4—21no—
634C4×D4—21no—
635C4×D4—21no—
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—41no—
642C4×D4—41no—
643C4×D4—41no—
644C4×D4—41no—
645C4×D4—41no—
646C4×D4—41no—
647C4×D4—41no—
648C4×D4—41no—
649C4×D4—41no—
650C4×D4—41no—
651C4×D4—41no—
652C4×D4—41no—
653C4×D4—41no—
654C4×D4—41no—
655C4×D4D811yescharacteristic
656C4×D4D811yescharacteristic
657C4×D4D811yescharacteristic
658C4×D4C2×D411yescharacteristic
659C4×D4C2×D411yescharacteristic
660C4×D4C2×D411yescharacteristic
661#117—21no—
662#117—21no—
663#117—21no—
664#117—21no—
665#117—41no—
666#117—41no—
667#117—41no—
668#117—41no—
669#117—41no—
670#117—41no—
671#117—41no—
672#117—41no—
673#117—41no—
674#117—41no—
675#117—41no—
676#117—41no—
677#117—41no—
678#117—41no—
679#117D811yescharacteristic
680#117D811yescharacteristic
681#117D811yescharacteristic
682C2×C4⋊C4—21no—
683C2×C4⋊C4—21no—
684C2×C4⋊C4—21no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—41no—
688C2×C4⋊C4—41no—
689C2×C4⋊C4—41no—
690C2×C4⋊C4—41no—
691C2×C4⋊C4—41no—
692C2×C4⋊C4—41no—
693C2×C4⋊C4—41no—
694C2×C22⋊C4—41no—
695C2×C22⋊C4—41no—
696C2×C22⋊C4—41no—
697C2×C42—41no—
698C2×C42—41no—
699C2×C42C2×D411yescharacteristic
700C2×C42C2×D411yescharacteristic
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
795C4×C8C2×D411yescharacteristic
796C4×C8C2×D411yescharacteristic
797C4×C8C2×D411yescharacteristic
798C4×C8C2×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—42no—
809#41—81no—
810#41—81no—
811#41—84no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
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×C4—41no—
850C22×C4—41no—
851C22×C4—84no—
852C22×C4C2×D811yescharacteristic
853C22×C4C2×D811yescharacteristic
854C22×C4C2×D811yescharacteristic
855C22×C4C2×D811yescharacteristic
856C22×C4C2×D811yescharacteristic
857C22×C4C2×D811yescharacteristic
858C22×C4C22×D411yescharacteristic
859C22×C4C22×D411yescharacteristic
860C22×C4C22×D411yescharacteristic
861Q16—21no—
862Q16—21no—
863Q16—21no—
864Q16—21no—
865Q16—21no—
866Q16—21no—
867Q16—81no—
868SD16—42no—
869SD16—42no—
870SD16—42no—
871SD16—81no—
872SD16—81no—
873D8—21no—
874D8—21no—
875D8—21no—
876D8—21no—
877D8—21no—
878D8—42no—
879D82−1+412yes—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—41no—
887C2×C8—41no—
888C2×C8—41no—
889C2×C8C22×D411yescharacteristic
890C2×C8C22×D411yescharacteristic
891C2×C8C22×D411yescharacteristic
892C2×C8C22×D411yescharacteristic
893C2×C8C22×D411yescharacteristic
894C2×C8C22×D411yescharacteristic
895C2×C8C22×D411yescharacteristic
896C2×C8C2511yescharacteristic
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
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⋊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⋊C4C2×D811yescharacteristic
950C4⋊C4C2×D811yescharacteristic
951C4⋊C4C2×D811yescharacteristic
952C4⋊C4C2×D811yescharacteristic
953C4⋊C4C2×D811yescharacteristic
954C4⋊C4C2×D811yescharacteristic
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⋊C4—41no—
982C22⋊C4—41no—
983C22⋊C4—41no—
984C22⋊C4—41no—
985C22⋊C4—41no—
986C22⋊C4C2×D811yescharacteristic
987C22⋊C4C2×D811yescharacteristic
988C22⋊C4C2×D811yescharacteristic
989C22⋊C4C2×D811yescharacteristic
990C22⋊C4C2×D811yescharacteristic
991C22⋊C4C2×D811yescharacteristic
992C42—41no—
993C42—41no—
994C42—41no—
995C42—41no—
996C42—41no—
997C42—41no—
998C42—41no—
999C42—41no—
1000C42—41no—
1001C42—41no—
1002C42—41no—
1003C42C2×D811yescharacteristic
1004C42C2×D811yescharacteristic
1005C42C2×D811yescharacteristic
1006C42C2×D811yescharacteristic
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—82no—
1025C23—82no—
1026C23—161no—
1027C23C22×D811yescharacteristic
1028C23C22×D811yescharacteristic
1029C23C22×D811yescharacteristic
1030Q8—41no—
1031Q8—41no—
1032Q8—41no—
1033Q8—41no—
1034Q8—41no—
1035Q8—41no—
1036Q8—41no—
1037Q8—82no—
1038Q8—161no—
1039Q8—161no—
1040D4—22no—
1041D4—22no—
1042D4—22no—
1043D4—41no—
1044D4—41no—
1045D4—41no—
1046D4—41no—
1047D4—41no—
1048D4—41no—
1049D4—82no—
1050D4—82no—
1051D4—82no—
1052D4—82no—
1053D4—82no—
1054D4—161no—
1055D4—161no—
1056D4—161no—
1057C2×C4—22no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
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—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—82no—
1083C2×C4—82no—
1084C2×C4—82no—
1085C2×C4—82no—
1086C2×C4—82no—
1087C2×C4—82no—
1088C2×C4—82no—
1089C2×C4—82no—
1090C2×C4—82no—
1091C2×C4—82no—
1092C2×C4—161no—
1093C2×C4—161no—
1094C2×C4—161no—
1095C2×C4—161no—
1096C2×C4—161no—
1097C2×C4—161no—
1098C2×C4C22×D811yescharacteristic
1099C2×C4C22×D811yescharacteristic
1100C2×C4C22×D811yescharacteristic
1101C2×C4C22×D811yescharacteristic
1102C2×C4C22×D811yescharacteristic
1103C2×C4C22×D811yescharacteristic
1104C2×C4C22×D811yescharacteristic
1105C2×C4C22×D811yescharacteristic
1106C2×C4C22×D811yescharacteristic
1107C2×C4C22×D811yescharacteristic
1108C2×C4C22×D811yescharacteristic
1109C2×C4C23×D411yescharacteristic
1110C8—21no—
1111C8—21no—
1112C8—21no—
1113C8—21no—
1114C8—21no—
1115C8—21no—
1116C8—21no—
1117C8C2×2−1+411yescharacteristic
1118C8#58511yescharacteristic
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—21no—
1124C22—21no—
1125C22—21no—
1126C22—21no—
1127C22—42no—
1128C22—81no—
1129C22—81no—
1130C22—81no—
1131C22—81no—
1132C22—81no—
1133C22—81no—
1134C22—81no—
1135C22—81no—
1136C22—164no—
1137C22#341412yes—
1138C22C23×D811yescharacteristic
1139C4—21no—
1140C4—21no—
1141C4—21no—
1142C4—21no—
1143C4—21no—
1144C4—21no—
1145C4—21no—
1146C4—21no—
1147C4—21no—
1148C4—21no—
1149C4—21no—
1150C4—81no—
1151C4—81no—
1152C4—81no—
1153C4—81no—
1154C4—81no—
1155C4—81no—
1156C4—81no—
1157C4—81no—
1158C4—81no—
1159C4—81no—
1160C4—81no—
1161C4—81no—
1162C4—81no—
1163C4#348911yescharacteristic
1164C4#358611yescharacteristic
1165C2—22no—
1166C2—41no—
1167C2—41no—
1168C2—82no—
1169C2—161no—
1170C2—161no—
1171C2#6209511yescharacteristic
1172C2C2×#341411yescharacteristic
1173C2#6263511yescharacteristic
subgroupG/H
center, socleC22C23×D8
commutator, Frattini, cosocleC2×C8C25
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C4×#41 ◁ C8×#41 ◁ G
LECSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62475C2semidirect
2. #61427C2semidirect
3. #33956C2semidirect
4. #33955C2semidirect
5. #33944C2semidirect
6. #33943C2semidirect
7. #33915C2semidirect
8. #33914C2semidirect
9. #33911C2semidirect
10. #33910C2semidirect
11. #33904C2semidirect
12. #33903C2semidirect
13. #33882C2semidirect
14. #33881C2semidirect
15. #33874C2semidirect
16. #33873C2semidirect
17. #33864C2semidirect
18. #33863C2semidirect
19. #33822C2semidirect
20. #33816C2semidirect
21. #33814C2semidirect
22. #33806C2semidirect
23. #33802C2semidirect
24. #33798C2semidirect
25. #33674C2semidirect
26. #33671C2semidirect
27. #33662C2semidirect
28. #33630C2semidirect
29. #33626C2semidirect
30. C2×#2228C2semidirect
31. #33504C2semidirect
35. #3383C22semidirect
38. #3380C22semidirect
42. #3339C22semidirect
49. #3336C22semidirect
65. #3168C22semidirect
66. #3168C22semidirect
67. #3160C22semidirect
69. C2×#499C22semidirect
77. #2255C22semidirect
78. #2255C22semidirect
79. #2255C22semidirect
80. #2255C22semidirect
81. #2253C22semidirect
82. #2253C22semidirect
83. #2245C22semidirect
84. #2245C22semidirect
89. #2237C22semidirect
90. #2237C22semidirect
91. #2237C22semidirect
92. #2237C22semidirect
95. #2236C22semidirect
99. #2235C22semidirect
102. #2234C22semidirect
103. #2234C22semidirect
107. #2229C22semidirect
108. #2229C22semidirect
109. #2229C22semidirect
110. #2229C22semidirect
111. #2229C22semidirect
112. #2229C22semidirect
113. #2229C22semidirect
114. #2229C22semidirect
115. #2229C22semidirect
116. #2229C22semidirect
129. #2228C22semidirect
130. #2228C22semidirect
131. #2227C22semidirect
133. #2225C22semidirect
134. #2225C22semidirect
136. #2224C22semidirect
138. #2220C22semidirect
139. #2219C22semidirect
144. #2217C22semidirect
147. #2216C22semidirect
151. #2211C22semidirect
152. #2211C22semidirect
157. #2209C22semidirect
158. #2208C22semidirect
165. #2183C22semidirect
166. #2183C22semidirect
170. #2176C22semidirect
174. #2175C22semidirect
175. C4×Q32C22semidirect
177. C4×SD32C22semidirect
181. #2168C22semidirect
182. #2168C22semidirect
186. #2163C22semidirect
187. #2162C22semidirect
188. #2159C22semidirect
189. #2159C22semidirect
190. #2158C22semidirect
191. #2158C22semidirect
194. #2150C22semidirect
196. C2×C4⋊C16C22semidirect

Maximal subgroups

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

subgroupindex
#624752
#614272
#339562
#339552
#339442
#339432
#339152
#339142
#339112
#339102
#339042
#339032
#338822
#338812
#338742
#338732
#338642
#338632
#338222
#338162
#338142
#338062
#338022
#337982
#336742
#336712
#336622
#336302
#336262
C2×#22282
#335042