Finite Group Databasebeta

← #7624618

Subgroups — #7624618

Order 512.

1305 conjugacy classes of subgroups.

The subgroup lattice has 1266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62434C211yesmaximal, characteristic, complemented
2#61487C211yesmaximal, characteristic, complemented
3#33968C211yesmaximal, characteristic, complemented
4#33960C211yesmaximal, characteristic, complemented
5#33943C211yesmaximal, characteristic, complemented
6#33928C211yesmaximal, characteristic, complemented
7#33894C211yesmaximal, characteristic, complemented
8#33880C211yesmaximal, characteristic, complemented
9#33874C211yesmaximal, characteristic, complemented
10#33871C211yesmaximal, characteristic, complemented
11#33864C211yesmaximal, characteristic, complemented
12#33863C211yesmaximal, characteristic, complemented
13#33849C211yesmaximal, characteristic, complemented
14#33848C211yesmaximal, characteristic, complemented
15#33848C211yesmaximal, characteristic, complemented
16#33839C211yesmaximal, characteristic, complemented
17#33834C211yesmaximal, characteristic, complemented
18#33833C211yesmaximal, characteristic, complemented
19#33826C211yesmaximal, characteristic, complemented
20#33824C211yesmaximal, characteristic, complemented
21#33816C211yesmaximal, characteristic, complemented
22#33790C211yesmaximal, characteristic, complemented
23#33789C211yesmaximal, characteristic, complemented
24#33778C211yesmaximal, characteristic, complemented
25#33682C211yesmaximal, characteristic, complemented
26#33680C211yesmaximal, characteristic, complemented
27#33662C211yesmaximal, characteristic, complemented
28#33589C211yesmaximal, characteristic, complemented
29#33586C211yesmaximal, characteristic, complemented
30#33579C211yesmaximal, characteristic, complemented
31#33508C211yesmaximal, characteristic, complemented
32#3562—21no—
33#3521—21no—
34C2×#509C2211yescharacteristic
35C2×#509C2211yescharacteristic
36C2×#508C2211yescharacteristic
37C2×#508C2211yescharacteristic
38C2×#508C2211yescharacteristic, complemented
39C22×SD32C2211yescharacteristic, complemented
40#3401—21no—
41#3396C2211yescharacteristic, complemented
42#3393C2211yescharacteristic, complemented
43#3393C2211yescharacteristic, complemented
44#3380C2211yescharacteristic, complemented
45#3376—21no—
46#3342C2211yescharacteristic, complemented
47#3339C2211yescharacteristic
48#3336C2211yescharacteristic
49#3323—21no—
50#3311—21no—
51#3307—21no—
52#3287C2211yescharacteristic
53#3285C2211yescharacteristic
54#3285C2211yescharacteristic
55#3283C2211yescharacteristic
56#3283C2211yescharacteristic, complemented
57#3280C2211yescharacteristic
58#3280C2211yescharacteristic
59#3280C2211yescharacteristic, complemented
60#3280C2211yescharacteristic, complemented
61#3275—21no—
62#3271—21no—
63#3267—21no—
64#3222—21no—
65#3221—21no—
66#3219—21no—
67#3177C2211yescharacteristic, complemented
68#3177C2211yescharacteristic, complemented
69#3176C2211yescharacteristic
70#3175C2211yescharacteristic
71#3168C2211yescharacteristic, complemented
72#3168C2211yescharacteristic, complemented
73#3156C2211yescharacteristic
74#3155C2211yescharacteristic, complemented
75#3147C2211yescharacteristic, complemented
76#3125—21no—
77#3123—21no—
78#3111—21no—
79#2966C2211yescharacteristic
80#2951C2211yescharacteristic
81#2948C2211yescharacteristic, complemented
82C4×#135C2211yescharacteristic, complemented
83#2251C2211yescharacteristic, complemented
84#2250C2211yescharacteristic
85#2249C2211yescharacteristic
86#2249C2211yescharacteristic
87#2249C2211yescharacteristic, complemented
88#2247C2211yescharacteristic, complemented
89#2245C2211yescharacteristic, complemented
90#2243C2211yescharacteristic, complemented
91#2242C2211yescharacteristic, complemented
92#2242C2211yescharacteristic, complemented
93#2242C2211yescharacteristic, complemented
94#2240C2211yescharacteristic, complemented
95#2237C2211yescharacteristic, complemented
96#2236C2211yescharacteristic, complemented
97#2235C2211yescharacteristic, complemented
98#2234C2211yescharacteristic
99#2234C2211yescharacteristic, complemented
100#2234C2211yescharacteristic, complemented
101#2229C2211yescharacteristic, complemented
102#2229C2211yescharacteristic, complemented
103#2229C2211yescharacteristic, complemented
104#2228C2211yescharacteristic, complemented
105#2228C2211yescharacteristic, complemented
106#2228C2211yescharacteristic, complemented
107#2228C2211yescharacteristic, complemented
108#2228C2211yescharacteristic, complemented
109#2227C2211yescharacteristic, complemented
110#2225C2211yescharacteristic, complemented
111#2220C2211yescharacteristic
112#2220C2211yescharacteristic
113#2220C2211yescharacteristic, complemented
114#2219C2211yescharacteristic, complemented
115#2217C2211yescharacteristic
116#2217C2211yescharacteristic
117#2217C2211yescharacteristic, complemented
118#2217C2211yescharacteristic, complemented
119#2217C2211yescharacteristic, complemented
120#2216C2211yescharacteristic, complemented
121#2216C2211yescharacteristic, complemented
122#2215C2211yescharacteristic
123#2211C2211yescharacteristic, complemented
124#2211C2211yescharacteristic, complemented
125#2211C2211yescharacteristic, complemented
126#2211C2211yescharacteristic, complemented
127#2211C2211yescharacteristic, complemented
128#2211C2211yescharacteristic, complemented
129#2211C2211yescharacteristic, complemented
130#2211C2211yescharacteristic, complemented
131#2210C2211yescharacteristic
132#2210C2211yescharacteristic
133#2210C2211yescharacteristic
134#2210C2211yescharacteristic
135#2210C2211yescharacteristic
136#2210C2211yescharacteristic
137#2210C2211yescharacteristic
138#2210C2211yescharacteristic, complemented
139#2209C2211yescharacteristic, complemented
140#2209C2211yescharacteristic, complemented
141#2208C2211yescharacteristic, complemented
142#2208C2211yescharacteristic, complemented
143#2208C2211yescharacteristic, complemented
144#2208C2211yescharacteristic, complemented
145#2208C2211yescharacteristic, complemented
146#2208C2211yescharacteristic, complemented
147#2207C2211yescharacteristic, complemented
148#2207C2211yescharacteristic, complemented
149#2207C2211yescharacteristic, complemented
150#2206C2211yescharacteristic
151#2206C2211yescharacteristic
152#2206C2211yescharacteristic
153#2189C2211yescharacteristic
154#2189C2211yescharacteristic
155#2189C2211yescharacteristic
156#2189C2211yescharacteristic
157#2189C2211yescharacteristic, complemented
158#2189C2211yescharacteristic, complemented
159#2189C2211yescharacteristic, complemented
160#2189C2211yescharacteristic, complemented
161#2188C2211yescharacteristic, complemented
162#2188C2211yescharacteristic, complemented
163#2187C2211yescharacteristic, complemented
164#2186C2211yescharacteristic
165#2186C2211yescharacteristic
166#2186C2211yescharacteristic
167#2186C2211yescharacteristic, complemented
168#2184C2211yescharacteristic
169#2184C2211yescharacteristic
170#2184C2211yescharacteristic, complemented
171#2183C2211yescharacteristic, complemented
172Q8×C16C2211yescharacteristic, complemented
173#2177C2211yescharacteristic
174#2177C2211yescharacteristic, complemented
175#2176C2211yescharacteristic, complemented
176#2175C2211yescharacteristic, complemented
177C4×Q32C2211yescharacteristic, complemented
178C4×Q32C2211yescharacteristic, complemented
179C4×SD32C2211yescharacteristic, complemented
180C4×SD32C2211yescharacteristic, complemented
181C4×SD32C2211yescharacteristic, complemented
182C4×D16C2211yescharacteristic
183C4×D16C2211yescharacteristic
184C4×D16C2211yescharacteristic, complemented
185#2169C2211yescharacteristic
186#2168C2211yescharacteristic, complemented
187#2168C2211yescharacteristic, complemented
188D4×C16C2211yescharacteristic
189D4×C16C2211yescharacteristic, complemented
190D4×C16C2211yescharacteristic, complemented
191#2164C2211yescharacteristic, complemented
192#2164C2211yescharacteristic, complemented
193#2162C2211yescharacteristic, complemented
194#2151C2211yescharacteristic, complemented
195#2151C2211yescharacteristic, complemented
196C2×C4⋊C16C2211yescharacteristic, complemented
197#2141C2211yescharacteristic, complemented
198#2139C2211yescharacteristic, complemented
199#2138C2211yescharacteristic
200#2138C2211yescharacteristic, complemented
201#2138C2211yescharacteristic, complemented
202C2×#357C2211yescharacteristic, complemented
203C2×#137—21no—
204C2×AGL(1,ℤ/8)—21no—
205C2×#135—21no—
206C2×#135C2311yescharacteristic
207C2×#135C2311yescharacteristic
208C2×#135C2311yescharacteristic
209C2×#135C2311yescharacteristic
210C2×#135C2311yescharacteristic
211C2×#135C2311yescharacteristic
212C22×Q16C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215#562—41no—
216#560—41no—
217#559—21no—
218#556—21no—
219#556—21no—
220#556—21no—
221#554—21no—
222#553—21no—
223#553—41no—
224#553—41no—
225#552—21no—
226#552—41no—
227#551—41no—
228#551—41no—
229#551—41no—
230#550—21no—
231#548—21no—
232#548—21no—
233#547—21no—
234#547—21no—
235#546—21no—
236#546—21no—
237#546—21no—
238#546—21no—
239#542—21no—
240#541—21no—
241#541—21no—
242#540—21no—
243#540—41no—
244#539—41no—
245#539—41no—
246#538—41no—
247#538—41no—
248#538—41no—
249#536—21no—
250#535—21no—
251#532—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#509—42no—
261#509—42no—
262#508—42no—
263#508—42no—
264#508—42no—
265C2×Q32C2311yescharacteristic
266C2×Q32C2311yescharacteristic
267C2×Q32C2311yescharacteristic
268C2×Q32C2311yescharacteristic
269C2×Q32C2311yescharacteristic
270C2×Q32C2311yescharacteristic
271C2×SD32—42no—
272C2×SD32C2311yescharacteristic
273C2×SD32C2311yescharacteristic
274C2×SD32C2311yescharacteristic
275C2×SD32C2311yescharacteristic
276C2×SD32C2311yescharacteristic
277C2×SD32C2311yescharacteristic
278C2×SD32C2311yescharacteristic
279C2×SD32C2311yescharacteristic
280C2×SD32C2311yescharacteristic
281C2×SD32C2311yescharacteristic
282C2×SD32C2311yescharacteristic
283C2×SD32C2311yescharacteristic
284C2×D16C2311yescharacteristic
285C2×D16C2311yescharacteristic
286C2×D16C2311yescharacteristic
287C2×D16C2311yescharacteristic
288C2×D16C2311yescharacteristic
289C2×D16C2311yescharacteristic
290C2×M32C2311yescharacteristic
291C2×M32C2311yescharacteristic
292C22×C16C2311yescharacteristic
293C22×C16C2311yescharacteristic
294C22×C16C2311yescharacteristic
295C22×C16C2311yescharacteristic
296#500C2311yescharacteristic
297#499C2311yescharacteristic
298#499C2311yescharacteristic
299#499C2311yescharacteristic
300#497—21no—
301#497—21no—
302#496—21no—
303#496—21no—
304#495—21no—
305#495C2311yescharacteristic
306#495C2311yescharacteristic
307#495C2311yescharacteristic
308#495C2311yescharacteristic
309#495C2311yescharacteristic
310#495C2311yescharacteristic
311#495C2311yescharacteristic
312#494C2311yescharacteristic
313#494C2311yescharacteristic
314#494C2311yescharacteristic
315#493C2311yescharacteristic
316#493C2311yescharacteristic
317#492—21no—
318#491—21no—
319#491—21no—
320#490—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#469—21no—
339#468—21no—
340#467C2311yescharacteristic
341#467C2311yescharacteristic
342#467C2311yescharacteristic
343#467C2311yescharacteristic
344#467C2311yescharacteristic
345#467C2311yescharacteristic
346#467C2311yescharacteristic
347#466C2311yescharacteristic
348#466C2311yescharacteristic
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#463—21no—
363#463—21no—
364#463—21no—
365#463—21no—
366#461—21no—
367#461—21no—
368#461—21no—
369#461—21no—
370#460—21no—
371#460—21no—
372#452—21no—
373#452—21no—
374#452—21no—
375#452—21no—
376#452—21no—
377#452—21no—
378#450—21no—
379#450—21no—
380#450—21no—
381#450—21no—
382#449—21no—
383#449—21no—
384#449—21no—
385#449—21no—
386#449—21no—
387#449—21no—
388#448—21no—
389#448—21no—
390#446D411yescharacteristic
391C8×Q8C2311yescharacteristic
392#442—21no—
393#442—21no—
394#442—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×SD16—21no—
408C4×SD16—21no—
409C4×SD16—21no—
410C4×SD16—21no—
411C4×D8C2311yescharacteristic
412C4×D8C2311yescharacteristic
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#357C2311yescharacteristic
473#357C2311yescharacteristic
474#357C2311yescharacteristic
475#357C2311yescharacteristic
476#357C2311yescharacteristic
477#357C2311yescharacteristic
478#357C2311yescharacteristic
479#357C2311yescharacteristic
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
496C4×C16C2311yescharacteristic
497C4×C16C2311yescharacteristic
498C4×C16C2311yescharacteristic
499C4×C16C2311yescharacteristic
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—21no—
503C2×#41—21no—
504C2×#41—21no—
505C2×#41—21no—
506C22×Q8—21no—
507C22×D4—21no—
508C22×D4—21no—
509#137—82no—
510AGL(1,ℤ/8)—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—
519#135—41no—
520#135—41no—
521#135—41no—
522#135—41no—
523#135—82no—
524C2×Q16—21no—
525C2×Q16—21no—
526C2×Q16—21no—
527C2×Q16—21no—
528C2×Q16—41no—
529C2×Q16—41no—
530C2×Q16C2411yescharacteristic
531C2×Q16C2411yescharacteristic
532C2×Q16C2411yescharacteristic
533C2×Q16C2411yescharacteristic
534C2×Q16C2411yescharacteristic
535C2×SD16—21no—
536C2×SD16—21no—
537C2×SD16—21no—
538C2×SD16—21no—
539C2×SD16—21no—
540C2×SD16—21no—
541C2×SD16—21no—
542C2×SD16—21no—
543C2×SD16—21no—
544C2×SD16—21no—
545C2×SD16—21no—
546C2×SD16—21no—
547C2×SD16—21no—
548C2×D8—22no—
549C2×D8—21no—
550C2×D8—21no—
551C2×D8—21no—
552C2×D8—21no—
553C2×D8—41no—
554C2×D8—41no—
555C2×D8—41no—
556C2×D8C2411yescharacteristic
557C2×D8C2411yescharacteristic
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—
571#127—21no—
572#127—21no—
573#127—41no—
574#126—41no—
575#126—41no—
576#126—41no—
577#126—41no—
578#126—41no—
579#126—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#126D811yescharacteristic
590#126D811yescharacteristic
591#125—21no—
592#125—21no—
593#125—21no—
594#125—41no—
595#125—41no—
596#125—41no—
597#125—41no—
598#125—41no—
599#125D811yescharacteristic
600#124—21no—
601#124—21no—
602#124—21no—
603#124—21no—
604#124—21no—
605#124—21no—
606#124—21no—
607#124—41no—
608#124—41no—
609#124—41no—
610#124—41no—
611#124—41no—
612#124D811yescharacteristic
613#123—41no—
614#123—41no—
615#123—41no—
616#123—41no—
617#123—41no—
618#123—41no—
619#123—41no—
620#123—41no—
621#123—41no—
622#123—41no—
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#123D811yescharacteristic
633#123D811yescharacteristic
634C22⋊Q8—21no—
635C22⋊Q8—21no—
636C22⋊Q8—21no—
637C22⋊Q8—21no—
638C22⋊Q8—21no—
639C22⋊Q8—21no—
640C22⋊Q8—21no—
641C22⋊Q8—41no—
642C22⋊Q8—41no—
643C22⋊Q8—41no—
644C22⋊Q8—41no—
645C22⋊Q8—41no—
646C22⋊Q8—41no—
647C22⋊Q8—41no—
648C22⋊Q8—41no—
649C22⋊Q8—41no—
650C22⋊Q8—41no—
651C22⋊Q8D811yescharacteristic
652#121—21no—
653#121—21no—
654#121—21no—
655#121—21no—
656#121—21no—
657#121—41no—
658#121—41no—
659#121—41no—
660#121—41no—
661#121—41no—
662#121—41no—
663#121—41no—
664#121—41no—
665#121—41no—
666#121—41no—
667#121—41no—
668#121—41no—
669#121—41no—
670#121—41no—
671#121—41no—
672#121—41no—
673#121—41no—
674#121D811yescharacteristic
675#120—41no—
676#120—41no—
677#120—41no—
678#120—41no—
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—41no—
689C4×Q8C2×D411yescharacteristic
690C4×D4—21no—
691C4×D4—21no—
692C4×D4—21no—
693C4×D4—21no—
694C4×D4—21no—
695C4×D4—21no—
696C4×D4—21no—
697C4×D4—21no—
698C4×D4—21no—
699C4×D4—41no—
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×C22⋊C4—41no—
734C2×C22⋊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—
747SD32—22no—
748SD32—22no—
749SD32—22no—
750SD32—41no—
751SD32—41no—
752SD32—41no—
753SD32—41no—
754SD32—41no—
755SD32—41no—
756SD32—41no—
757SD32—41no—
758SD32—41no—
759D16—22no—
760D16—22no—
761D16—22no—
762D16—41no—
763D16—41no—
764D16—41no—
765M32—41no—
766M32—41no—
767C2×C16—41no—
768C2×C16—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#102—21no—
813#102—21no—
814#102—21no—
815#102—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—
843C24—41no—
844#41—42no—
845#41—42no—
846#41—81no—
847#41—81no—
848#41—81no—
849#41—81no—
850#41—81no—
851#41—81no—
852#41—81no—
853#41—81no—
854#41—81no—
855#41—81no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—41no—
862C2×Q8—41no—
863C2×Q8—81no—
864C2×Q8—81no—
865C2×Q8C2×D811yescharacteristic
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—42no—
872C2×D4—41no—
873C2×D4—41no—
874C2×D4—41no—
875C2×D4—41no—
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—41no—
885C2×D4—41no—
886C2×D4—41no—
887C2×D4—41no—
888C2×D4—41no—
889C2×D4—81no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4C2×D811yescharacteristic
893C2×D4C2×D811yescharacteristic
894C2×D4C2×D811yescharacteristic
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×C4—41no—
905C22×C4—41no—
906C22×C4—41no—
907C22×C4—41no—
908C22×C4—41no—
909C22×C4—41no—
910C22×C4—41no—
911C22×C4—41no—
912C22×C4C2×D811yescharacteristic
913C22×C4C2×D811yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917Q16—21no—
918Q16—21no—
919Q16—21no—
920Q16—21no—
921Q16—21no—
922Q16—21no—
923Q16—21no—
924Q16—21no—
925Q16—21no—
926Q16—21no—
927Q16—42no—
928Q16—81no—
929Q16—81no—
930Q16—81no—
931SD16—42no—
932SD16—42no—
933SD16—42no—
934SD16—81no—
935SD16—81no—
936SD16—81no—
937SD16—81no—
938SD16—81no—
939SD16—81no—
940SD16—81no—
941SD16—81no—
942SD16—81no—
943SD16—81no—
944D8—21no—
945D8—21no—
946D8—21no—
947D8—21no—
948D8—21no—
949D8—21no—
950D8—21no—
951D8—21no—
952D8—21no—
953D8—42no—
954D8—42no—
955D8—81no—
956D8—81no—
957D8H(5,𝔽2)12yes—
958M16—41no—
959M16—41no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—41no—
967C2×C8C22×D411yescharacteristic
968C2×C8C22×D411yescharacteristic
969C2×C8C22×D411yescharacteristic
970C2×C8C22×D411yescharacteristic
971C2×C8C22×D411yescharacteristic
972C2×C8C22×D411yescharacteristic
973C2×C8C22×D411yescharacteristic
974C2×C8C2511yescharacteristic
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
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⋊C4C2×D811yescharacteristic
1010C4⋊C4C2×D811yescharacteristic
1011C4⋊C4C2×D811yescharacteristic
1012C4⋊C4C2×D811yescharacteristic
1013C4⋊C4C2×D811yescharacteristic
1014C4⋊C4C2×D811yescharacteristic
1015C4⋊C4C2×D811yescharacteristic
1016C4⋊C4C2×D811yescharacteristic
1017C4⋊C4C2×D811yescharacteristic
1018C4⋊C4C2×D811yescharacteristic
1019C22⋊C4—41no—
1020C22⋊C4—41no—
1021C22⋊C4—41no—
1022C22⋊C4—41no—
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⋊C4—41no—
1055C22⋊C4—41no—
1056C22⋊C4C2×D811yescharacteristic
1057C22⋊C4C2×D811yescharacteristic
1058C22⋊C4C2×D811yescharacteristic
1059C22⋊C4C2×D811yescharacteristic
1060C22⋊C4C2×D811yescharacteristic
1061C22⋊C4C2×D811yescharacteristic
1062C22⋊C4C2×D811yescharacteristic
1063C22⋊C4C2×D811yescharacteristic
1064C22⋊C4C2×D811yescharacteristic
1065C22⋊C4C2×D811yescharacteristic
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—41no—
1093C23—41no—
1094C23—82no—
1095C23—161no—
1096C23—161no—
1097C23—161no—
1098C23—161no—
1099C23—161no—
1100C23C22×D811yescharacteristic
1101C23C22×D811yescharacteristic
1102C23C22×D811yescharacteristic
1103Q8—41no—
1104Q8—41no—
1105Q8—41no—
1106Q8—41no—
1107Q8—41no—
1108Q8—41no—
1109Q8—41no—
1110Q8—41no—
1111Q8—41no—
1112Q8—41no—
1113Q8—41no—
1114Q8—161no—
1115Q8—161no—
1116D4—22no—
1117D4—41no—
1118D4—41no—
1119D4—41no—
1120D4—41no—
1121D4—41no—
1122D4—41no—
1123D4—41no—
1124D4—41no—
1125D4—41no—
1126D4—41no—
1127D4—41no—
1128D4—41no—
1129D4—82no—
1130D4—82no—
1131D4—82no—
1132D4—161no—
1133D4—161no—
1134D4—161no—
1135D4—161no—
1136D4—161no—
1137D4—161no—
1138D4—161no—
1139D4—161no—
1140D4—161no—
1141D4—161no—
1142D4—161no—
1143D4—161no—
1144D4—161no—
1145D4—161no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—82no—
1166C2×C4—82no—
1167C2×C4—161no—
1168C2×C4—161no—
1169C2×C4—161no—
1170C2×C4—161no—
1171C2×C4—161no—
1172C2×C4—161no—
1173C2×C4—161no—
1174C2×C4—161no—
1175C2×C4—161no—
1176C2×C4—161no—
1177C2×C4—161no—
1178C2×C4—161no—
1179C2×C4—161no—
1180C2×C4—161no—
1181C2×C4—161no—
1182C2×C4C22×D811yescharacteristic
1183C2×C4C22×D811yescharacteristic
1184C2×C4C22×D811yescharacteristic
1185C2×C4C22×D811yescharacteristic
1186C2×C4C22×D811yescharacteristic
1187C2×C4C22×D811yescharacteristic
1188C2×C4C22×D811yescharacteristic
1189C2×C4C22×D811yescharacteristic
1190C2×C4C22×D811yescharacteristic
1191C2×C4C22×D811yescharacteristic
1192C2×C4C22×D811yescharacteristic
1193C2×C4C23×D411yescharacteristic
1194C8—21no—
1195C8—21no—
1196C8—21no—
1197C8—21no—
1198C8—21no—
1199C8—21no—
1200C8—21no—
1201C8C2×H(5,𝔽2)11yescharacteristic
1202C8#58511yescharacteristic
1203C22—21no—
1204C22—21no—
1205C22—21no—
1206C22—21no—
1207C22—21no—
1208C22—21no—
1209C22—21no—
1210C22—21no—
1211C22—21no—
1212C22—42no—
1213C22—81no—
1214C22—81no—
1215C22—81no—
1216C22—81no—
1217C22—81no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—322no—
1228C22—322no—
1229C22C23×D811yescharacteristic
1230C4—21no—
1231C4—21no—
1232C4—21no—
1233C4—21no—
1234C4—21no—
1235C4—21no—
1236C4—21no—
1237C4—21no—
1238C4—21no—
1239C4—21no—
1240C4—21no—
1241C4—81no—
1242C4—81no—
1243C4—81no—
1244C4—81no—
1245C4—81no—
1246C4—81no—
1247C4—81no—
1248C4—81no—
1249C4—81no—
1250C4—81no—
1251C4—81no—
1252C4#348811yescharacteristic
1253C4#358511yescharacteristic
1254C2—41no—
1255C2—41no—
1256C2—41no—
1257C2—82no—
1258C2—161no—
1259C2—161no—
1260C2—161no—
1261C2—161no—
1262C2#6194711yescharacteristic
1263C2#6263511yescharacteristic
1264C2#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. #62434C2semidirect
2. #61487C2semidirect
3. #33968C2semidirect
4. #33960C2semidirect
5. #33943C2semidirect
6. #33928C2semidirect
7. #33894C2semidirect
8. #33880C2semidirect
9. #33874C2semidirect
10. #33871C2semidirect
11. #33864C2semidirect
12. #33863C2semidirect
13. #33849C2semidirect
14. #33848C2semidirect
15. #33848C2semidirect
16. #33839C2semidirect
17. #33834C2semidirect
18. #33833C2semidirect
19. #33826C2semidirect
20. #33824C2semidirect
21. #33816C2semidirect
22. #33790C2semidirect
23. #33789C2semidirect
24. #33778C2semidirect
25. #33682C2semidirect
26. #33680C2semidirect
27. #33662C2semidirect
28. #33589C2semidirect
29. #33586C2semidirect
30. #33579C2semidirect
31. #33508C2semidirect
38. C2×#508C22semidirect
39. C22×SD32C22semidirect
41. #3396C22semidirect
42. #3393C22semidirect
43. #3393C22semidirect
44. #3380C22semidirect
46. #3342C22semidirect
56. #3283C22semidirect
59. #3280C22semidirect
60. #3280C22semidirect
67. #3177C22semidirect
68. #3177C22semidirect
71. #3168C22semidirect
72. #3168C22semidirect
74. #3155C22semidirect
75. #3147C22semidirect
81. #2948C22semidirect
82. C4×#135C22semidirect
83. #2251C22semidirect
87. #2249C22semidirect
88. #2247C22semidirect
89. #2245C22semidirect
90. #2243C22semidirect
91. #2242C22semidirect
92. #2242C22semidirect
93. #2242C22semidirect
94. #2240C22semidirect
95. #2237C22semidirect
96. #2236C22semidirect
97. #2235C22semidirect
99. #2234C22semidirect
100. #2234C22semidirect
101. #2229C22semidirect
102. #2229C22semidirect
103. #2229C22semidirect
104. #2228C22semidirect
105. #2228C22semidirect
106. #2228C22semidirect
107. #2228C22semidirect
108. #2228C22semidirect
109. #2227C22semidirect
110. #2225C22semidirect
113. #2220C22semidirect
114. #2219C22semidirect
117. #2217C22semidirect
118. #2217C22semidirect
119. #2217C22semidirect
120. #2216C22semidirect
121. #2216C22semidirect
123. #2211C22semidirect
124. #2211C22semidirect
125. #2211C22semidirect
126. #2211C22semidirect
127. #2211C22semidirect
128. #2211C22semidirect
129. #2211C22semidirect
130. #2211C22semidirect
138. #2210C22semidirect
139. #2209C22semidirect
140. #2209C22semidirect
141. #2208C22semidirect
142. #2208C22semidirect
143. #2208C22semidirect
144. #2208C22semidirect
145. #2208C22semidirect
146. #2208C22semidirect
147. #2207C22semidirect
148. #2207C22semidirect
149. #2207C22semidirect
157. #2189C22semidirect
158. #2189C22semidirect
159. #2189C22semidirect
160. #2189C22semidirect
161. #2188C22semidirect
162. #2188C22semidirect
163. #2187C22semidirect
167. #2186C22semidirect
170. #2184C22semidirect
171. #2183C22semidirect
172. Q8×C16C22semidirect
174. #2177C22semidirect
175. #2176C22semidirect
176. #2175C22semidirect
177. C4×Q32C22semidirect
178. C4×Q32C22semidirect
179. C4×SD32C22semidirect
180. C4×SD32C22semidirect
181. C4×SD32C22semidirect
184. C4×D16C22semidirect
186. #2168C22semidirect
187. #2168C22semidirect
189. D4×C16C22semidirect
190. D4×C16C22semidirect
191. #2164C22semidirect
192. #2164C22semidirect
193. #2162C22semidirect
194. #2151C22semidirect
195. #2151C22semidirect
196. C2×C4⋊C16C22semidirect
197. #2141C22semidirect
198. #2139C22semidirect
200. #2138C22semidirect
201. #2138C22semidirect
202. C2×#357C22semidirect

Maximal subgroups

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

subgroupindex
#624342
#614872
#339682
#339602
#339432
#339282
#338942
#338802
#338742
#338712
#338642
#338632
#338492
#338482
#338392
#338342
#338332
#338262
#338242
#338162
#337902
#337892
#337782
#336822
#336802
#336622
#335892
#335862
#335792
#335082