Subgroups — C₈×#564 #6408073

Order 512.

1352 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#564	C₂	1	1	yes	maximal, characteristic
2	#23369	C₂	1	15	yes	maximal
3	C₈×#125	C₂	1	15	yes	maximal
4	C₂×#564	C₄	1	1	yes	characteristic
5	#2382	C₄	1	15	yes	—
6	C₄×#125	C₂²	1	15	yes	—
7	#1939	C₂²	1	30	yes	—
8	#1916	C₂²	1	60	yes	—
9	#1831	C₂²	1	15	yes	—
10	C₈×C₄⋊C₄	C₂²	1	30	yes	—
11	C₄²×C₈	C₂²	1	5	yes	—
12	#564	C₈	1	16	yes	direct product factor
13	C₂×#125	C₂×C₄	1	15	yes	—
14	C₂×C₄⋊C₈	C₂³	1	30	yes	—
15	C₂×C₄×C₈	C₂³	1	15	yes	—
16	C₂×C₄×C₈	C₂³	1	15	yes	—
17	#389	C₂×C₄	1	30	yes	—
18	#387	C₂×C₄	1	60	yes	—
19	#382	C₂×C₄	1	15	yes	—
20	C₄×C₄⋊C₄	C₂³	1	30	yes	—
21	C₄³	C₂³	1	5	yes	—
22	#336	C₂³	1	60	yes	—
23	C₂²×C₈	C₂⁴	1	15	yes	—
24	C₂²×C₈	C₂⁴	1	1	yes	characteristic
25	#125	C₂×C₈	1	120	yes	—
26	C₂×C₄⋊C₄	C₂²×C₄	1	30	yes	—
27	C₂×C₄⋊C₄	C₂²×C₄	1	30	yes	—
28	C₂×C₄²	C₂²×C₄	1	15	yes	—
29	C₂×C₄²	C₂²×C₄	1	5	yes	—
30	C₂×C₄²	C₂⁴	1	15	yes	—
31	C₄⋊C₈	—	4	30	no	—
32	C₄×C₈	—	2	30	no	—
33	C₄×C₈	—	4	15	no	—
34	#95	C₂²×C₄	1	60	yes	—
35	C₂²×C₄	C₂³×C₄	1	15	yes	—
36	C₂²×C₄	C₂³×C₄	1	15	yes	—
37	C₂²×C₄	C₂⁵	1	1	yes	characteristic
38	C₂×C₈	—	2	15	no	—
39	C₂×C₈	—	2	30	no	—
40	C₂×C₈	2₋¹⁺⁴	1	6	yes	—
41	C₄⋊C₄	—	4	30	no	—
42	C₄⋊C₄	C₂²×C₈	1	120	yes	—
43	C₄²	—	2	15	no	—
44	C₄²	—	2	15	no	—
45	C₄²	—	4	15	no	—
46	C₄²	C₂²×C₈	1	20	yes	—
47	C₂³	C₂⁴×C₄	1	1	yes	characteristic
48	C₂×C₄	—	2	15	no	—
49	C₂×C₄	—	2	15	no	—
50	C₂×C₄	—	2	15	no	—
51	C₂×C₄	—	2	30	no	—
52	C₂×C₄	C₂³×C₈	1	30	yes	—
53	C₂×C₄	C₂×2₋¹⁺⁴	1	3	yes	—
54	C₂×C₄	#585	1	3	yes	—
55	C₈	—	4	15	no	—
56	C₈	#564	1	4	yes	direct product factor
57	C₂²	C₄×2₋¹⁺⁴	1	3	yes	—
58	C₂²	C₂⁴×C₈	1	1	yes	characteristic
59	C₂²	#3573	1	3	yes	—
60	C₄	—	2	30	no	—
61	C₄	—	4	15	no	—
62	C₄	C₂×#564	1	1	yes	characteristic
63	C₄	#3531	1	3	yes	—
64	C₂	C₄×#564	1	1	yes	characteristic
65	C₂	C₈×2₋¹⁺⁴	1	3	yes	—
66	C₂	#60332	1	3	yes	—

	subgroup	G/H
center	C₂²×C₈	C₂⁴
commutator	C₂²	C₂⁴×C₈
Frattini, cosocle	C₂²×C₄	C₂⁵
socle, prime radical	C₂³	C₂⁴×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈ ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
12. #564	C₈	direct (N × H)
56. C₈	#564	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×#564	2
#23369	2
C₈×#125	2

Subgroups — C8×#564 #6408073

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#564 #6408073