Subgroups — C₂⁵×C₃⋊C₈ #11708941

Order 768.

15454 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₃×C₄	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×C₃⋊C₈	C₂	1	62	yes	maximal, direct product factor
3	C₂⁵×C₈	—	3	1	no	maximal, Sylow
4	C₂⁶×C₃	C₄	1	1	yes	characteristic
5	C₂⁴×C₃×C₄	C₄	1	31	yes	—
6	C₂⁴×C₃×C₄	C₂²	1	31	yes	—
7	C₂³×C₃⋊C₈	C₂²	1	620	yes	direct product factor
8	C₂⁵×C₄	D₃	1	1	yes	characteristic
9	C₂⁴×C₈	—	3	62	no	—
10	C₂⁵×C₃	C₈	1	32	yes	complemented
11	C₂⁵×C₃	C₂×C₄	1	31	yes	—
12	C₂³×C₃×C₄	C₂×C₄	1	465	yes	—
13	C₂³×C₃×C₄	C₂³	1	155	yes	—
14	C₂²×C₃⋊C₈	C₂³	1	1240	yes	direct product factor
15	C₂⁶	Dic₃	1	1	yes	characteristic
16	C₂⁴×C₄	Dic₃	1	31	yes	—
17	C₂⁴×C₄	C₂×D₃	1	31	yes	—
18	C₂³×C₈	—	3	620	no	—
19	C₂⁴×C₃	C₂×C₈	1	496	yes	complemented
20	C₂⁴×C₃	C₂²×C₄	1	155	yes	—
21	C₂²×C₃×C₄	C₂²×C₄	1	1085	yes	—
22	C₂²×C₃×C₄	C₂⁴	1	155	yes	—
23	C₂×C₃⋊C₈	C₂⁴	1	496	yes	direct product factor
24	C₂⁵	C₃⋊C₈	1	32	yes	direct product factor
25	C₂⁵	C₂×Dic₃	1	31	yes	—
26	C₂³×C₄	C₂×Dic₃	1	465	yes	—
27	C₂³×C₄	C₂²×D₃	1	155	yes	—
28	C₂²×C₈	—	3	1240	no	—
29	C₂³×C₃	C₂²×C₈	1	1240	yes	complemented
30	C₂³×C₃	C₂³×C₄	1	155	yes	—
31	C₂×C₃×C₄	C₂³×C₄	1	465	yes	—
32	C₂×C₃×C₄	C₂⁵	1	31	yes	—
33	C₃⋊C₈	C₂⁵	1	32	yes	direct product factor
34	C₂⁴	C₂×C₃⋊C₈	1	496	yes	direct product factor
35	C₂⁴	C₂²×Dic₃	1	155	yes	—
36	C₂²×C₄	C₂²×Dic₃	1	1085	yes	—
37	C₂²×C₄	C₂³×D₃	1	155	yes	—
38	C₂×C₈	—	3	496	no	—
39	C₂²×C₃	C₂³×C₈	1	620	yes	complemented
40	C₂²×C₃	C₂⁴×C₄	1	31	yes	—
41	C₃×C₄	C₂⁴×C₄	1	31	yes	—
42	C₃×C₄	C₂⁶	1	1	yes	characteristic
43	C₂³	C₂²×C₃⋊C₈	1	1240	yes	direct product factor
44	C₂³	C₂³×Dic₃	1	155	yes	—
45	C₂×C₄	C₂³×Dic₃	1	465	yes	—
46	C₂×C₄	C₂⁴×D₃	1	31	yes	—
47	C₈	—	3	32	no	—
48	C₂×C₃	C₂⁴×C₈	1	62	yes	complemented
49	C₂×C₃	C₂⁵×C₄	1	1	yes	characteristic
50	C₂²	C₂³×C₃⋊C₈	1	620	yes	direct product factor
51	C₂²	C₂⁴×Dic₃	1	31	yes	—
52	C₄	C₂⁴×Dic₃	1	31	yes	—
53	C₄	C₂⁵×D₃	1	1	yes	characteristic
54	C₃	C₂⁵×C₈	1	1	yes	characteristic, complemented, Sylow
55	C₂	C₂⁴×C₃⋊C₈	1	62	yes	direct product factor
56	C₂	C₂⁵×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁵×C₄	D₃
commutator, hypocenter	C₃	C₂⁵×C₈
Frattini	C₄	C₂⁵×D₃
Fitting	C₂⁵×C₃×C₄	C₂
socle, prime radical	C₂⁶×C₃	C₄
cosocle	C₃×C₄	C₂⁶
LCS	G ▷ C₃
UCS	C₁ ◁ C₂⁵×C₄

Complements

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

N	H ≅ G/N	type
2. C₂⁴×C₃⋊C₈	C₂	direct (N × H)
7. C₂³×C₃⋊C₈	C₂²	direct (N × H)
10. C₂⁵×C₃	C₈	semidirect
14. C₂²×C₃⋊C₈	C₂³	direct (N × H)
19. C₂⁴×C₃	C₂×C₈	semidirect
23. C₂×C₃⋊C₈	C₂⁴	direct (N × H)
24. C₂⁵	C₃⋊C₈	direct (N × H)
29. C₂³×C₃	C₂²×C₈	semidirect
33. C₃⋊C₈	C₂⁵	direct (N × H)
34. C₂⁴	C₂×C₃⋊C₈	direct (N × H)
39. C₂²×C₃	C₂³×C₈	semidirect
43. C₂³	C₂²×C₃⋊C₈	direct (N × H)
48. C₂×C₃	C₂⁴×C₈	semidirect
50. C₂²	C₂³×C₃⋊C₈	direct (N × H)
54. C₃	C₂⁵×C₈	semidirect
55. C₂	C₂⁴×C₃⋊C₈	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×C₃×C₄	2
C₂⁴×C₃⋊C₈	2
C₂⁵×C₈	3

Subgroups — C25×C3⋊C8 #11708941

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×C₃⋊C₈ #11708941