Finite Group Databasebeta

← #7624639

Subgroups — #7624639

Order 512.

1289 conjugacy classes of subgroups.

The subgroup lattice has 1249 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62432C211yesmaximal, characteristic, complemented
2#61487C211yesmaximal, characteristic, complemented
3#33969C211yesmaximal, characteristic, complemented
4#33965C211yesmaximal, characteristic, complemented
5#33943C211yesmaximal, characteristic, complemented
6#33939C211yesmaximal, characteristic, complemented
7#33895C211yesmaximal, characteristic, complemented
8#33893C211yesmaximal, characteristic, complemented
9#33887C211yesmaximal, characteristic, complemented
10#33882C211yesmaximal, characteristic, complemented
11#33880C211yesmaximal, characteristic, complemented
12#33879C211yesmaximal, characteristic, complemented
13#33842C211yesmaximal, characteristic, complemented
14#33841C211yesmaximal, characteristic, complemented
15#33835C211yesmaximal, characteristic, complemented
16#33833C211yesmaximal, characteristic, complemented
17#33832C211yesmaximal, characteristic, complemented
18#33832C211yesmaximal, characteristic, complemented
19#33827C211yesmaximal, characteristic, complemented
20#33824C211yesmaximal, characteristic, complemented
21#33822C211yesmaximal, characteristic, complemented
22#33791C211yesmaximal, characteristic, complemented
23#33789C211yesmaximal, characteristic, complemented
24#33784C211yesmaximal, characteristic, complemented
25#33683C211yesmaximal, characteristic, complemented
26#33680C211yesmaximal, characteristic, complemented
27#33671C211yesmaximal, characteristic, complemented
28#33590C211yesmaximal, characteristic, complemented
29#33586C211yesmaximal, characteristic, complemented
30#33583C211yesmaximal, characteristic, complemented
31#33509C211yesmaximal, characteristic, complemented
32#3552—21no—
33#3521—21no—
34C2×#510C2211yescharacteristic
35C2×#510C2211yescharacteristic
36C2×#510C2211yescharacteristic
37C2×#509C2211yescharacteristic
38C2×#508C2211yescharacteristic
39C22×SD32C2211yescharacteristic
40#3398—21no—
41#3395C2211yescharacteristic, complemented
42#3393C2211yescharacteristic
43#3393C2211yescharacteristic, complemented
44#3380C2211yescharacteristic
45#3376—21no—
46#3342C2211yescharacteristic
47#3339C2211yescharacteristic
48#3336C2211yescharacteristic
49#3323—21no—
50#3311—21no—
51#3307—21no—
52D4×Q16C2211yescharacteristic
53D4×Q16C2211yescharacteristic
54D4×Q16C2211yescharacteristic, complemented
55#3285C2211yescharacteristic
56#3285C2211yescharacteristic, complemented
57#3283C2211yescharacteristic
58#3283C2211yescharacteristic
59#3280C2211yescharacteristic
60#3280C2211yescharacteristic
61#3276—21no—
62#3270—21no—
63#3270—21no—
64#3223—21no—
65#3223—21no—
66#3218—21no—
67#3177C2211yescharacteristic
68#3177C2211yescharacteristic
69#3177C2211yescharacteristic, complemented
70#3175C2211yescharacteristic
71#3168C2211yescharacteristic
72#3168C2211yescharacteristic, complemented
73#3156C2211yescharacteristic
74#3156C2211yescharacteristic, complemented
75C2×#494C2211yescharacteristic, complemented
76#3125—21no—
77#3123—21no—
78#3111—21no—
79#2966C2211yescharacteristic
80#2951C2211yescharacteristic
81#2948C2211yescharacteristic
82C4×#135C2211yescharacteristic
83#2251C2211yescharacteristic
84#2251C2211yescharacteristic
85#2251C2211yescharacteristic
86#2251C2211yescharacteristic, complemented
87#2249C2211yescharacteristic
88#2247C2211yescharacteristic, complemented
89#2245C2211yescharacteristic, complemented
90#2245C2211yescharacteristic, complemented
91#2245C2211yescharacteristic, complemented
92#2243C2211yescharacteristic, complemented
93#2242C2211yescharacteristic, complemented
94#2241C2211yescharacteristic, complemented
95#2237C2211yescharacteristic
96#2237C2211yescharacteristic
97#2237C2211yescharacteristic, complemented
98#2236C2211yescharacteristic, complemented
99#2235C2211yescharacteristic, complemented
100#2234C2211yescharacteristic, complemented
101#2229C2211yescharacteristic, complemented
102#2229C2211yescharacteristic, complemented
103#2229C2211yescharacteristic, complemented
104#2229C2211yescharacteristic, complemented
105#2229C2211yescharacteristic, complemented
106#2228C2211yescharacteristic
107#2228C2211yescharacteristic
108#2228C2211yescharacteristic, complemented
109#2227C2211yescharacteristic, complemented
110#2225C2211yescharacteristic, complemented
111#2220C2211yescharacteristic
112#2220C2211yescharacteristic
113#2220C2211yescharacteristic, complemented
114#2219C2211yescharacteristic
115#2219C2211yescharacteristic
116#2219C2211yescharacteristic, complemented
117#2219C2211yescharacteristic, complemented
118#2218C2211yescharacteristic
119#2217C2211yescharacteristic
120#2216C2211yescharacteristic
121#2216C2211yescharacteristic
122#2216C2211yescharacteristic, complemented
123#2211C2211yescharacteristic
124#2211C2211yescharacteristic
125#2211C2211yescharacteristic
126#2211C2211yescharacteristic, complemented
127#2211C2211yescharacteristic, complemented
128#2211C2211yescharacteristic, complemented
129#2210C2211yescharacteristic
130#2210C2211yescharacteristic
131#2210C2211yescharacteristic
132#2210C2211yescharacteristic
133#2210C2211yescharacteristic
134#2210C2211yescharacteristic
135#2209C2211yescharacteristic, complemented
136#2209C2211yescharacteristic, complemented
137#2209C2211yescharacteristic, complemented
138#2209C2211yescharacteristic, complemented
139#2209C2211yescharacteristic, complemented
140#2209C2211yescharacteristic, complemented
141#2209C2211yescharacteristic, complemented
142#2209C2211yescharacteristic, complemented
143#2209C2211yescharacteristic, complemented
144#2208C2211yescharacteristic
145#2208C2211yescharacteristic
146#2208C2211yescharacteristic
147#2208C2211yescharacteristic
148#2208C2211yescharacteristic
149#2208C2211yescharacteristic
150#2208C2211yescharacteristic
151#2208C2211yescharacteristic
152#2208C2211yescharacteristic
153#2189C2211yescharacteristic
154#2189C2211yescharacteristic
155#2189C2211yescharacteristic
156#2189C2211yescharacteristic
157#2189C2211yescharacteristic
158#2189C2211yescharacteristic, complemented
159#2188C2211yescharacteristic
160#2188C2211yescharacteristic
161#2188C2211yescharacteristic, complemented
162#2188C2211yescharacteristic, complemented
163#2188C2211yescharacteristic, complemented
164#2187C2211yescharacteristic
165#2187C2211yescharacteristic
166#2186C2211yescharacteristic
167#2186C2211yescharacteristic
168#2185C2211yescharacteristic
169#2185C2211yescharacteristic
170#2185C2211yescharacteristic
171#2183C2211yescharacteristic, complemented
172#2183C2211yescharacteristic, complemented
173#2177C2211yescharacteristic
174#2176C2211yescharacteristic, complemented
175#2176C2211yescharacteristic, complemented
176#2175C2211yescharacteristic
177#2175C2211yescharacteristic
178#2175C2211yescharacteristic
179#2175C2211yescharacteristic
180#2175C2211yescharacteristic, complemented
181C4×Q32C2211yescharacteristic, complemented
182C4×SD32C2211yescharacteristic
183C4×SD32C2211yescharacteristic
184C4×SD32C2211yescharacteristic
185#2169C2211yescharacteristic
186#2169C2211yescharacteristic, complemented
187#2168C2211yescharacteristic
188#2168C2211yescharacteristic
189#2168C2211yescharacteristic
190#2168C2211yescharacteristic, complemented
191#2164C2211yescharacteristic
192#2164C2211yescharacteristic, complemented
193#2163C2211yescharacteristic, complemented
194#2151C2211yescharacteristic
195#2151C2211yescharacteristic, complemented
196#2150C2211yescharacteristic, complemented
197#2141C2211yescharacteristic
198#2141C2211yescharacteristic, complemented
199#2141C2211yescharacteristic, complemented
200#2139C2211yescharacteristic, complemented
201#2138C2211yescharacteristic
202C2×#358C2211yescharacteristic, complemented
203C2×#137—21no—
204C2×#137—21no—
205C2×#135C2311yescharacteristic
206C2×#135C2311yescharacteristic
207C2×#135C2311yescharacteristic
208C2×#135C2311yescharacteristic
209C22×Q16—21no—
210C22×Q16C2311yescharacteristic
211C22×Q16C2311yescharacteristic
212C22×Q16C2311yescharacteristic
213C22×Q16C2311yescharacteristic
214C22×D8C2311yescharacteristic
215#563—41no—
216#563—41no—
217#557—21no—
218#556—21no—
219#556—21no—
220#556—21no—
221#554—21no—
222#554—41no—
223#553—21no—
224#553—41no—
225#553—41no—
226#552—21no—
227#552—41no—
228#551—41no—
229#551—41no—
230D4×Q8—21no—
231D4×Q8—21no—
232D4×Q8—21no—
233#548—21no—
234#548—21no—
235#547—21no—
236#547—21no—
237#546—21no—
238#546—21no—
239#544—41no—
240#542—21no—
241#542—41no—
242#541—21no—
243#541—21no—
244#541—21no—
245#539—41no—
246#539—41no—
247#539—41no—
248#538—41no—
249#536—21no—
250#536—21no—
251C2×C4⋊Q8—21no—
252#529—21no—
253#529—21no—
254#529—41no—
255#529D411yescharacteristic
256C2×#126—41no—
257#520—21no—
258#518—21no—
259C4×#41—21no—
260#510—42no—
261#510—42no—
262#510—42no—
263#509—42no—
264#508—42no—
265C2×Q32C2311yescharacteristic
266C2×Q32C2311yescharacteristic
267C2×Q32C2311yescharacteristic
268C2×Q32C2311yescharacteristic
269C2×Q32C2311yescharacteristic
270C2×Q32C2311yescharacteristic
271C2×Q32C2311yescharacteristic
272C2×Q32C2311yescharacteristic
273C2×Q32C2311yescharacteristic
274C2×Q32C2311yescharacteristic
275C2×SD32—42no—
276C2×SD32C2311yescharacteristic
277C2×SD32C2311yescharacteristic
278C2×SD32C2311yescharacteristic
279C2×SD32C2311yescharacteristic
280C2×SD32C2311yescharacteristic
281C2×SD32C2311yescharacteristic
282C2×SD32C2311yescharacteristic
283C2×SD32C2311yescharacteristic
284C2×SD32C2311yescharacteristic
285C2×SD32C2311yescharacteristic
286C2×SD32C2311yescharacteristic
287C2×SD32C2311yescharacteristic
288C2×D16C2311yescharacteristic
289C2×D16C2311yescharacteristic
290C2×M32C2311yescharacteristic
291C2×M32C2311yescharacteristic
292C2×M32C2311yescharacteristic
293C2×M32C2311yescharacteristic
294C22×C16C2311yescharacteristic
295C22×C16C2311yescharacteristic
296#500C2311yescharacteristic
297#499C2311yescharacteristic
298#499C2311yescharacteristic
299#499C2311yescharacteristic
300#497—21no—
301#497—21no—
302#497—21no—
303#497—21no—
304#495C2311yescharacteristic
305#495C2311yescharacteristic
306#495C2311yescharacteristic
307#495C2311yescharacteristic
308#495C2311yescharacteristic
309#494—21no—
310#494—21no—
311#494C2311yescharacteristic
312#494C2311yescharacteristic
313#494C2311yescharacteristic
314#494C2311yescharacteristic
315#494C2311yescharacteristic
316#494C2311yescharacteristic
317#494C2311yescharacteristic
318#491—21no—
319#491—21no—
320#491—21no—
321#489—21no—
322#488—21no—
323#488—21no—
324#485—21no—
325#485—21no—
326#485—21no—
327#483—21no—
328#482—21no—
329#481—21no—
330#479—21no—
331#478—21no—
332#478—21no—
333#478—21no—
334#476—21no—
335#475—21no—
336#470—21no—
337#470—21no—
338#470—21no—
339#468—21no—
340#467C2311yescharacteristic
341#467C2311yescharacteristic
342#467C2311yescharacteristic
343#467C2311yescharacteristic
344#467C2311yescharacteristic
345#467C2311yescharacteristic
346#467C2311yescharacteristic
347#467C2311yescharacteristic
348#467C2311yescharacteristic
349#466C2311yescharacteristic
350#466C2311yescharacteristic
351#466C2311yescharacteristic
352#465—21no—
353#465—21no—
354#464—21no—
355#464—21no—
356#464—21no—
357#464—21no—
358#464—21no—
359#464—21no—
360#463—21no—
361#463—21no—
362#462—21no—
363#462—21no—
364#462—21no—
365#462—21no—
366#462—21no—
367#462—21no—
368#461—21no—
369#461—21no—
370#461—21no—
371#461—21no—
372#452—21no—
373#452—21no—
374#452—21no—
375#452—21no—
376#452—21no—
377#452—21no—
378#451—21no—
379#451—21no—
380#451—21no—
381#451—21no—
382#451—21no—
383#451—21no—
384#450—21no—
385#450—21no—
386#449—21no—
387#449—21no—
388#448—21no—
389#448—21no—
390#446D411yescharacteristic
391C8×Q8C2311yescharacteristic
392#442—21no—
393#442—21no—
394#441—21no—
395#441—21no—
396#441—21no—
397#440—21no—
398#440—21no—
399#440—21no—
400C4×Q16C2311yescharacteristic
401C4×Q16C2311yescharacteristic
402C4×Q16C2311yescharacteristic
403C4×Q16C2311yescharacteristic
404C4×Q16C2311yescharacteristic
405C4×Q16C2311yescharacteristic
406C4×Q16C2311yescharacteristic
407C4×Q16C2311yescharacteristic
408C4×Q16C2311yescharacteristic
409C4×SD16—21no—
410C4×SD16—21no—
411C4×SD16—21no—
412C4×SD16—21no—
413C4×D8C2311yescharacteristic
414C4×D8C2311yescharacteristic
415C4×D8C2311yescharacteristic
416C4×D8C2311yescharacteristic
417C4×D8C2311yescharacteristic
418C4×D8C2311yescharacteristic
419C4×D8C2311yescharacteristic
420#436D411yescharacteristic
421#435D411yescharacteristic
422#435D411yescharacteristic
423C8×D4C2311yescharacteristic
424C8×D4C2311yescharacteristic
425C8×D4C2311yescharacteristic
426#433D411yescharacteristic
427#433D411yescharacteristic
428#432D411yescharacteristic
429#427C2311yescharacteristic
430#427C2311yescharacteristic
431C2×#107C2311yescharacteristic
432#418—21no—
433#417—21no—
434#416—21no—
435#405C2311yescharacteristic
436#405C2311yescharacteristic
437C2×C4×C8C2311yescharacteristic
438#367C2311yescharacteristic
439#367C2311yescharacteristic
440#367C2311yescharacteristic
441#367C2311yescharacteristic
442#366C2311yescharacteristic
443#366C2311yescharacteristic
444#366C2311yescharacteristic
445#366C2311yescharacteristic
446C4⋊C16C2311yescharacteristic
447C4⋊C16C2311yescharacteristic
448C4⋊C16C2311yescharacteristic
449C4⋊C16C2311yescharacteristic
450C4⋊C16C2311yescharacteristic
451C4⋊C16C2311yescharacteristic
452C4⋊C16C2311yescharacteristic
453C4⋊C16C2311yescharacteristic
454C4⋊C16C2311yescharacteristic
455C4⋊C16C2311yescharacteristic
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#358C2311yescharacteristic
471#358C2311yescharacteristic
472#358C2311yescharacteristic
473#358C2311yescharacteristic
474#358C2311yescharacteristic
475#358C2311yescharacteristic
476#358C2311yescharacteristic
477#358C2311yescharacteristic
478#358C2311yescharacteristic
479#358C2311yescharacteristic
480#357C2311yescharacteristic
481#357C2311yescharacteristic
482#357C2311yescharacteristic
483#357C2311yescharacteristic
484#357C2311yescharacteristic
485#357C2311yescharacteristic
486#357C2311yescharacteristic
487#357C2311yescharacteristic
488C22⋊C16C2311yescharacteristic
489C22⋊C16C2311yescharacteristic
490C22⋊C16C2311yescharacteristic
491C22⋊C16C2311yescharacteristic
492C22⋊C16C2311yescharacteristic
493C22⋊C16C2311yescharacteristic
494#346C2311yescharacteristic
495#346C2311yescharacteristic
496#346C2311yescharacteristic
497#346C2311yescharacteristic
498C4×C16C2311yescharacteristic
499C4×C16C2311yescharacteristic
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—21no—
503C2×#41—21no—
504C22×Q8—21no—
505C22×Q8—21no—
506C22×Q8—21no—
507C22×Q8—21no—
508C22×D4—21no—
509#137—82no—
510#137—82no—
511#135—22no—
512#135—22no—
513#135—41no—
514#135—41no—
515#135—41no—
516#135—41no—
517#135—41no—
518#135—41no—
519C2×Q16—21no—
520C2×Q16—21no—
521C2×Q16—21no—
522C2×Q16—21no—
523C2×Q16—21no—
524C2×Q16—21no—
525C2×Q16—21no—
526C2×Q16—21no—
527C2×Q16—21no—
528C2×Q16—21no—
529C2×Q16—21no—
530C2×Q16—41no—
531C2×Q16—41no—
532C2×Q16—41no—
533C2×Q16—41no—
534C2×Q16—41no—
535C2×Q16—41no—
536C2×Q16—41no—
537C2×Q16—41no—
538C2×Q16—82no—
539C2×Q16C2411yescharacteristic
540C2×Q16C2411yescharacteristic
541C2×Q16C2411yescharacteristic
542C2×Q16C2411yescharacteristic
543C2×Q16C2411yescharacteristic
544C2×Q16C2411yescharacteristic
545C2×Q16C2411yescharacteristic
546C2×SD16—21no—
547C2×SD16—21no—
548C2×SD16—21no—
549C2×SD16—21no—
550C2×SD16—21no—
551C2×SD16—21no—
552C2×SD16—21no—
553C2×SD16—21no—
554C2×SD16—21no—
555C2×D8—22no—
556C2×D8—21no—
557C2×D8—41no—
558C2×D8C2411yescharacteristic
559C2×D8C2411yescharacteristic
560C2×D8C2411yescharacteristic
561C2×M16C2×D411yescharacteristic
562C2×M16C2×D411yescharacteristic
563C22×C8C2×D411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C4⋊Q8—21no—
568C4⋊Q8—21no—
569C4⋊Q8—21no—
570C4⋊Q8—21no—
571C4⋊Q8—21no—
572C4⋊Q8—21no—
573C4⋊Q8—21no—
574C4⋊Q8—21no—
575C4⋊Q8—41no—
576C4⋊Q8—41no—
577C4⋊Q8—41no—
578C4⋊Q8—41no—
579C4⋊Q8—41no—
580#126—41no—
581#126—41no—
582#126—41no—
583#126—41no—
584#126—41no—
585#126—41no—
586#126—41no—
587#126—41no—
588#126—41no—
589#126—41no—
590#126—41no—
591#126—41no—
592#126—41no—
593#126—41no—
594#126—41no—
595#126—41no—
596#126—41no—
597#126D811yescharacteristic
598#126D811yescharacteristic
599#125—21no—
600#125—21no—
601#125—21no—
602#125—41no—
603#125—41no—
604#125—41no—
605#125—41no—
606#125—41no—
607#125—41no—
608#125—41no—
609#125—41no—
610#125—41no—
611#125—41no—
612#125D811yescharacteristic
613#124—21no—
614#124—21no—
615#124—21no—
616#124—21no—
617#124—21no—
618#124—41no—
619#124—41no—
620#124—41no—
621#124—41no—
622#124D811yescharacteristic
623#123—41no—
624#123—41no—
625#123—41no—
626#123—41no—
627#123—41no—
628#123—41no—
629#123—41no—
630#123—41no—
631#123—41no—
632#123—41no—
633#123—41no—
634#123—41no—
635#123—41no—
636#123—41no—
637#123—41no—
638#123D811yescharacteristic
639#123D811yescharacteristic
640C22⋊Q8—21no—
641C22⋊Q8—21no—
642C22⋊Q8—21no—
643C22⋊Q8—21no—
644C22⋊Q8—21no—
645C22⋊Q8—21no—
646C22⋊Q8—21no—
647C22⋊Q8—21no—
648C22⋊Q8—21no—
649C22⋊Q8—41no—
650C22⋊Q8—41no—
651C22⋊Q8—41no—
652C22⋊Q8—41no—
653C22⋊Q8—41no—
654C22⋊Q8—41no—
655C22⋊Q8—41no—
656C22⋊Q8—41no—
657C22⋊Q8—41no—
658C22⋊Q8—41no—
659C22⋊Q8—41no—
660C22⋊Q8—41no—
661C22⋊Q8—41no—
662C22⋊Q8—41no—
663C22⋊Q8—41no—
664C22⋊Q8—41no—
665C22⋊Q8—41no—
666C22⋊Q8—41no—
667C22⋊Q8D811yescharacteristic
668#121—21no—
669#121—21no—
670#121—21no—
671#121—41no—
672#121—41no—
673#121—41no—
674#121—41no—
675#121—41no—
676#121—41no—
677#121—41no—
678#121D811yescharacteristic
679#120—41no—
680#120—41no—
681C4×Q8—21no—
682C4×Q8—21no—
683C4×Q8—21no—
684C4×Q8—21no—
685C4×Q8—21no—
686C4×Q8—21no—
687C4×Q8—21no—
688C4×Q8—21no—
689C4×Q8—21no—
690C4×Q8—41no—
691C4×Q8—41no—
692C4×Q8C2×D411yescharacteristic
693C4×D4—21no—
694C4×D4—21no—
695C4×D4—21no—
696C4×D4—21no—
697C4×D4—21no—
698C4×D4—21no—
699C4×D4—21no—
700C4×D4—41no—
701C4×D4—41no—
702C4×D4—41no—
703C4×D4—41no—
704C4×D4—41no—
705C4×D4—41no—
706C4×D4—41no—
707C4×D4—41no—
708C4×D4—41no—
709C4×D4—41no—
710C4×D4—41no—
711C4×D4—41no—
712C4×D4—41no—
713C4×D4—41no—
714C4×D4C2×D411yescharacteristic
715C4×D4C2×D411yescharacteristic
716C4×D4C2×D411yescharacteristic
717#117—21no—
718#117—21no—
719#117—41no—
720#117—41no—
721#117—41no—
722#117—41no—
723#117—41no—
724#117—41no—
725#117—41no—
726#117C2×D411yescharacteristic
727#117C2×D411yescharacteristic
728C2×C4⋊C4—21no—
729C2×C4⋊C4—41no—
730C2×C4⋊C4—41no—
731C2×C4⋊C4—41no—
732C2×C4⋊C4—41no—
733C2×C4⋊C4—41no—
734C2×C4⋊C4—41no—
735C2×C22⋊C4—41no—
736C2×C22⋊C4—41no—
737C2×C22⋊C4—41no—
738C2×C22⋊C4—41no—
739C2×C42—41no—
740C2×C42C2×D411yescharacteristic
741Q32—41no—
742Q32—41no—
743Q32—41no—
744Q32—41no—
745Q32—41no—
746Q32—41no—
747Q32—41no—
748Q32—41no—
749Q32—41no—
750Q32—41no—
751SD32—22no—
752SD32—22no—
753SD32—22no—
754SD32—22no—
755SD32—22no—
756SD32—41no—
757SD32—41no—
758SD32—41no—
759SD32—41no—
760SD32—41no—
761SD32—41no—
762SD32—41no—
763D16—22no—
764D16—41no—
765M32—41no—
766M32—41no—
767M32—41no—
768M32—41no—
769C2×C16—41no—
770C2×C16—41no—
771C2×C16C2411yescharacteristic
772C2×C16C2411yescharacteristic
773C2×C16C2411yescharacteristic
774C2×C16C2411yescharacteristic
775C2×C16C2411yescharacteristic
776C2×C16C2411yescharacteristic
777C2×C16C2411yescharacteristic
778C2×C16C2411yescharacteristic
779#107—21no—
780#107—21no—
781#107C2411yescharacteristic
782#107C2411yescharacteristic
783#107C2411yescharacteristic
784#107C2411yescharacteristic
785#107C2411yescharacteristic
786#107C2411yescharacteristic
787#106—21no—
788#106—21no—
789#106—21no—
790#106—21no—
791#106—21no—
792C4⋊C8C2×D411yescharacteristic
793C4⋊C8C2×D411yescharacteristic
794C4⋊C8C2×D411yescharacteristic
795C4⋊C8C2×D411yescharacteristic
796C4⋊C8C2×D411yescharacteristic
797C4⋊C8C2×D411yescharacteristic
798#103—21no—
799#103—21no—
800#103—21no—
801#103—21no—
802#103—21no—
803#103—21no—
804#103—21no—
805#103—21no—
806#103—21no—
807#103—21no—
808#103—21no—
809#103—21no—
810#103—21no—
811#103—21no—
812#103—21no—
813#103—21no—
814#103—21no—
815#103—21no—
816#102—21no—
817#102—21no—
818#102—21no—
819#102—21no—
820#102—21no—
821#102—21no—
822#102—21no—
823#102—21no—
824#102—21no—
825#102—21no—
826C22⋊C8C2×D411yescharacteristic
827C22⋊C8C2×D411yescharacteristic
828C22⋊C8C2×D411yescharacteristic
829C22⋊C8C2×D411yescharacteristic
830C22⋊C8C2×D411yescharacteristic
831C22⋊C8C2×D411yescharacteristic
832#97C2×D411yescharacteristic
833#97C2×D411yescharacteristic
834#97C2×D411yescharacteristic
835#97C2×D411yescharacteristic
836C4×C8C2×D411yescharacteristic
837C4×C8C2×D411yescharacteristic
838C4×C8C2411yescharacteristic
839C4×C8C2411yescharacteristic
840C4×C8C2411yescharacteristic
841C4×C8C2411yescharacteristic
842C24—41no—
843#41—42no—
844#41—42no—
845#41—81no—
846#41—81no—
847#41—81no—
848#41—81no—
849#41—81no—
850#41—81no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—41no—
859C2×Q8—41no—
860C2×Q8—41no—
861C2×Q8—41no—
862C2×Q8—41no—
863C2×Q8—81no—
864C2×Q8—81no—
865C2×Q8—81no—
866C2×Q8—81no—
867C2×Q8—81no—
868C2×Q8—81no—
869C2×Q8—81no—
870C2×Q8—81no—
871C2×Q8C2×D811yescharacteristic
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—42no—
876C2×D4—41no—
877C2×D4—41no—
878C2×D4—41no—
879C2×D4—41no—
880C2×D4—41no—
881C2×D4—41no—
882C2×D4—41no—
883C2×D4—41no—
884C2×D4—81no—
885C2×D4C2×D811yescharacteristic
886C2×D4C2×D811yescharacteristic
887C2×D4C2×D811yescharacteristic
888C22×C4—41no—
889C22×C4—41no—
890C22×C4—41no—
891C22×C4—41no—
892C22×C4—41no—
893C22×C4—41no—
894C22×C4—41no—
895C22×C4—41no—
896C22×C4—41no—
897C22×C4—41no—
898C22×C4—41no—
899C22×C4—41no—
900C22×C4—41no—
901C22×C4—41no—
902C22×C4—41no—
903C22×C4—41no—
904C22×C4C2×D811yescharacteristic
905C22×C4C2×D811yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909Q16—21no—
910Q16—21no—
911Q16—21no—
912Q16—21no—
913Q16—21no—
914Q16—21no—
915Q16—21no—
916Q16—21no—
917Q16—21no—
918Q16—21no—
919Q16—21no—
920Q16—21no—
921Q16—21no—
922Q16—21no—
923Q16—42no—
924Q16—42no—
925Q16—81no—
926Q16—81no—
927Q16—81no—
928Q16—81no—
929Q16—81no—
930Q16—81no—
931Q16—81no—
932Q16—81no—
933Q16—81no—
934SD16—42no—
935SD16—42no—
936SD16—42no—
937SD16—81no—
938SD16—81no—
939SD16—81no—
940SD16—81no—
941SD16—81no—
942SD16—81no—
943D8—21no—
944D8—21no—
945D8—21no—
946D8—21no—
947D8—21no—
948D8—42no—
949D8H(5,𝔽2)12yes—
950M16—41no—
951M16—41no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—41no—
959C2×C8C22×D411yescharacteristic
960C2×C8C22×D411yescharacteristic
961C2×C8C22×D411yescharacteristic
962C2×C8C22×D411yescharacteristic
963C2×C8C22×D411yescharacteristic
964C2×C8C22×D411yescharacteristic
965C2×C8C22×D411yescharacteristic
966C2×C8C2511yescharacteristic
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—41no—
974C4⋊C4—41no—
975C4⋊C4—41no—
976C4⋊C4—41no—
977C4⋊C4—41no—
978C4⋊C4—41no—
979C4⋊C4—41no—
980C4⋊C4—41no—
981C4⋊C4—41no—
982C4⋊C4—41no—
983C4⋊C4—41no—
984C4⋊C4—41no—
985C4⋊C4—41no—
986C4⋊C4—41no—
987C4⋊C4—41no—
988C4⋊C4—41no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—41no—
992C4⋊C4—41no—
993C4⋊C4—41no—
994C4⋊C4—41no—
995C4⋊C4—41no—
996C4⋊C4—41no—
997C4⋊C4—41no—
998C4⋊C4—41no—
999C4⋊C4—41no—
1000C4⋊C4—41no—
1001C4⋊C4—41no—
1002C4⋊C4—41no—
1003C4⋊C4—41no—
1004C4⋊C4—41no—
1005C4⋊C4—41no—
1006C4⋊C4—41no—
1007C4⋊C4—41no—
1008C4⋊C4—41no—
1009C4⋊C4—41no—
1010C4⋊C4—41no—
1011C4⋊C4—41no—
1012C4⋊C4—41no—
1013C4⋊C4C2×D811yescharacteristic
1014C4⋊C4C2×D811yescharacteristic
1015C4⋊C4C2×D811yescharacteristic
1016C4⋊C4C2×D811yescharacteristic
1017C4⋊C4C2×D811yescharacteristic
1018C4⋊C4C2×D811yescharacteristic
1019C4⋊C4C2×D811yescharacteristic
1020C4⋊C4C2×D811yescharacteristic
1021C4⋊C4C2×D811yescharacteristic
1022C4⋊C4C2×D811yescharacteristic
1023C22⋊C4—41no—
1024C22⋊C4—41no—
1025C22⋊C4—41no—
1026C22⋊C4—41no—
1027C22⋊C4—41no—
1028C22⋊C4—41no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
1032C22⋊C4—41no—
1033C22⋊C4—41no—
1034C22⋊C4—41no—
1035C22⋊C4—41no—
1036C22⋊C4—41no—
1037C22⋊C4—41no—
1038C22⋊C4—41no—
1039C22⋊C4—41no—
1040C22⋊C4—41no—
1041C22⋊C4—41no—
1042C22⋊C4—41no—
1043C22⋊C4—41no—
1044C22⋊C4—41no—
1045C22⋊C4—41no—
1046C22⋊C4—41no—
1047C22⋊C4—41no—
1048C22⋊C4—41no—
1049C22⋊C4—41no—
1050C22⋊C4—41no—
1051C22⋊C4—41no—
1052C22⋊C4—41no—
1053C22⋊C4—41no—
1054C22⋊C4C2×D811yescharacteristic
1055C22⋊C4C2×D811yescharacteristic
1056C22⋊C4C2×D811yescharacteristic
1057C22⋊C4C2×D811yescharacteristic
1058C22⋊C4C2×D811yescharacteristic
1059C22⋊C4C2×D811yescharacteristic
1060C22⋊C4C2×D811yescharacteristic
1061C22⋊C4C2×D811yescharacteristic
1062C22⋊C4C2×D811yescharacteristic
1063C22⋊C4C2×D811yescharacteristic
1064C42—41no—
1065C42—41no—
1066C42—41no—
1067C42—41no—
1068C42—41no—
1069C42—41no—
1070C42—41no—
1071C42—41no—
1072C42—41no—
1073C42—41no—
1074C42—41no—
1075C42C2×D811yescharacteristic
1076C42C2×D811yescharacteristic
1077C42C22×D411yescharacteristic
1078C42C22×D411yescharacteristic
1079C42C22×D411yescharacteristic
1080C42C22×D411yescharacteristic
1081C16—21no—
1082C16—21no—
1083C16—21no—
1084C16—21no—
1085C16—21no—
1086C16—21no—
1087C16—21no—
1088C16—21no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—82no—
1093C23—161no—
1094C23—161no—
1095C23C22×D811yescharacteristic
1096C23C22×D811yescharacteristic
1097C23C22×D811yescharacteristic
1098Q8—41no—
1099Q8—41no—
1100Q8—41no—
1101Q8—41no—
1102Q8—41no—
1103Q8—41no—
1104Q8—41no—
1105Q8—41no—
1106Q8—41no—
1107Q8—41no—
1108Q8—41no—
1109Q8—41no—
1110Q8—41no—
1111Q8—41no—
1112Q8—41no—
1113Q8—161no—
1114Q8—161no—
1115Q8—161no—
1116Q8—161no—
1117Q8—161no—
1118D4—22no—
1119D4—41no—
1120D4—41no—
1121D4—41no—
1122D4—41no—
1123D4—41no—
1124D4—41no—
1125D4—41no—
1126D4—41no—
1127D4—82no—
1128D4—82no—
1129D4—82no—
1130D4—82no—
1131D4—161no—
1132D4—161no—
1133D4—161no—
1134D4—161no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—82no—
1157C2×C4—82no—
1158C2×C4—82no—
1159C2×C4—161no—
1160C2×C4—161no—
1161C2×C4—161no—
1162C2×C4—161no—
1163C2×C4—161no—
1164C2×C4—161no—
1165C2×C4—161no—
1166C2×C4—161no—
1167C2×C4—161no—
1168C2×C4—161no—
1169C2×C4—161no—
1170C2×C4—161no—
1171C2×C4—161no—
1172C2×C4C22×D811yescharacteristic
1173C2×C4C22×D811yescharacteristic
1174C2×C4C22×D811yescharacteristic
1175C2×C4C22×D811yescharacteristic
1176C2×C4C22×D811yescharacteristic
1177C2×C4C22×D811yescharacteristic
1178C2×C4C22×D811yescharacteristic
1179C2×C4C22×D811yescharacteristic
1180C2×C4C22×D811yescharacteristic
1181C2×C4C22×D811yescharacteristic
1182C2×C4C22×D811yescharacteristic
1183C2×C4C23×D411yescharacteristic
1184C8—21no—
1185C8—21no—
1186C8—21no—
1187C8—21no—
1188C8—21no—
1189C8—21no—
1190C8—21no—
1191C8C2×H(5,𝔽2)11yescharacteristic
1192C8#58511yescharacteristic
1193C22—21no—
1194C22—21no—
1195C22—21no—
1196C22—21no—
1197C22—21no—
1198C22—21no—
1199C22—21no—
1200C22—21no—
1201C22—21no—
1202C22—42no—
1203C22—81no—
1204C22—81no—
1205C22—81no—
1206C22—81no—
1207C22—81no—
1208C22—81no—
1209C22—81no—
1210C22—81no—
1211C22—322no—
1212C22C23×D811yescharacteristic
1213C4—21no—
1214C4—21no—
1215C4—21no—
1216C4—21no—
1217C4—21no—
1218C4—21no—
1219C4—21no—
1220C4—21no—
1221C4—21no—
1222C4—21no—
1223C4—21no—
1224C4—81no—
1225C4—81no—
1226C4—81no—
1227C4—81no—
1228C4—81no—
1229C4—81no—
1230C4—81no—
1231C4—81no—
1232C4—81no—
1233C4—81no—
1234C4—81no—
1235C4—81no—
1236C4—81no—
1237C4#348811yescharacteristic
1238C4#358511yescharacteristic
1239C2—41no—
1240C2—41no—
1241C2—41no—
1242C2—82no—
1243C2—161no—
1244C2—161no—
1245C2#6194711yescharacteristic
1246C2#6263711yescharacteristic
1247C2#6263711yescharacteristic
subgroupG/H
center, socleC22C23×D8
commutator, Frattini, cosocleC2×C8C25
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #529 ◁ #2966 ◁ G
LECSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62432C2semidirect
2. #61487C2semidirect
3. #33969C2semidirect
4. #33965C2semidirect
5. #33943C2semidirect
6. #33939C2semidirect
7. #33895C2semidirect
8. #33893C2semidirect
9. #33887C2semidirect
10. #33882C2semidirect
11. #33880C2semidirect
12. #33879C2semidirect
13. #33842C2semidirect
14. #33841C2semidirect
15. #33835C2semidirect
16. #33833C2semidirect
17. #33832C2semidirect
18. #33832C2semidirect
19. #33827C2semidirect
20. #33824C2semidirect
21. #33822C2semidirect
22. #33791C2semidirect
23. #33789C2semidirect
24. #33784C2semidirect
25. #33683C2semidirect
26. #33680C2semidirect
27. #33671C2semidirect
28. #33590C2semidirect
29. #33586C2semidirect
30. #33583C2semidirect
31. #33509C2semidirect
41. #3395C22semidirect
43. #3393C22semidirect
54. D4×Q16C22semidirect
56. #3285C22semidirect
69. #3177C22semidirect
72. #3168C22semidirect
74. #3156C22semidirect
75. C2×#494C22semidirect
86. #2251C22semidirect
88. #2247C22semidirect
89. #2245C22semidirect
90. #2245C22semidirect
91. #2245C22semidirect
92. #2243C22semidirect
93. #2242C22semidirect
94. #2241C22semidirect
97. #2237C22semidirect
98. #2236C22semidirect
99. #2235C22semidirect
100. #2234C22semidirect
101. #2229C22semidirect
102. #2229C22semidirect
103. #2229C22semidirect
104. #2229C22semidirect
105. #2229C22semidirect
108. #2228C22semidirect
109. #2227C22semidirect
110. #2225C22semidirect
113. #2220C22semidirect
116. #2219C22semidirect
117. #2219C22semidirect
122. #2216C22semidirect
126. #2211C22semidirect
127. #2211C22semidirect
128. #2211C22semidirect
135. #2209C22semidirect
136. #2209C22semidirect
137. #2209C22semidirect
138. #2209C22semidirect
139. #2209C22semidirect
140. #2209C22semidirect
141. #2209C22semidirect
142. #2209C22semidirect
143. #2209C22semidirect
158. #2189C22semidirect
161. #2188C22semidirect
162. #2188C22semidirect
163. #2188C22semidirect
171. #2183C22semidirect
172. #2183C22semidirect
174. #2176C22semidirect
175. #2176C22semidirect
180. #2175C22semidirect
181. C4×Q32C22semidirect
186. #2169C22semidirect
190. #2168C22semidirect
192. #2164C22semidirect
193. #2163C22semidirect
195. #2151C22semidirect
196. #2150C22semidirect
198. #2141C22semidirect
199. #2141C22semidirect
200. #2139C22semidirect
202. C2×#358C22semidirect

Maximal subgroups

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

subgroupindex
#624322
#614872
#339692
#339652
#339432
#339392
#338952
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