Subgroups — C₈×#401 #359418

Order 512.

964 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#401	C₂	1	1	yes	maximal, characteristic
2	#11298	C₂	1	7	yes	maximal
3	C₈×#95	C₂	1	7	yes	maximal
4	C₂²×C₄×C₈	C₂²	1	7	yes	—
5	C₂×#401	C₄	1	1	yes	characteristic
6	C₂×#336	C₂²	1	21	yes	—
7	#1443	C₄	1	7	yes	—
8	C₄×#95	C₂²	1	7	yes	—
9	C₂³×C₈	C₂³	1	7	yes	—
10	C₂³×C₈	C₂³	1	1	yes	characteristic
11	C₂²×C₄²	C₂³	1	7	yes	—
12	C₂×C₄×C₈	—	2	42	no	—
13	#401	C₈	1	8	yes	direct product factor
14	C₂×#95	C₂×C₄	1	21	yes	—
15	C₂×#95	C₂×C₄	1	7	yes	—
16	#336	—	2	42	no	—
17	C₂³×C₄	C₂²×C₄	1	7	yes	—
18	C₂³×C₄	C₂²×C₄	1	7	yes	—
19	C₂³×C₄	C₂⁴	1	1	yes	characteristic
20	C₂²×C₈	—	2	21	no	—
21	C₂²×C₈	—	2	21	no	—
22	C₂²×C₈	#41	1	14	yes	—
23	C₂²×C₈	#41	1	14	yes	—
24	C₂×C₄²	—	2	21	no	—
25	C₂×C₄²	—	2	21	no	—
26	C₄×C₈	—	4	28	no	—
27	#95	—	2	42	no	—
28	#95	C₂×C₈	1	28	yes	—
29	C₂⁴	C₂³×C₄	1	1	yes	characteristic
30	C₂²×C₄	—	2	21	no	—
31	C₂²×C₄	—	2	21	no	—
32	C₂²×C₄	—	2	21	no	—
33	C₂²×C₄	—	2	21	no	—
34	C₂²×C₄	C₂²×C₈	1	14	yes	—
35	C₂²×C₄	#131	1	14	yes	—
36	C₂²×C₄	C₂×#41	1	7	yes	—
37	C₂²×C₄	C₂×#41	1	7	yes	—
38	C₂×C₈	—	2	42	no	—
39	C₂×C₈	—	4	7	no	—
40	C₂×C₈	—	4	21	no	—
41	C₂×C₈	#126	1	28	yes	—
42	C₄²	—	4	7	no	—
43	C₄²	—	4	21	no	—
44	C₂³	C₄×#41	1	7	yes	—
45	C₂³	C₂³×C₈	1	1	yes	characteristic
46	C₂³	C₂×#131	1	7	yes	—
47	C₂×C₄	—	2	42	no	—
48	C₂×C₄	—	2	42	no	—
49	C₂×C₄	—	4	7	no	—
50	C₂×C₄	—	4	7	no	—
51	C₂×C₄	—	4	21	no	—
52	C₂×C₄	—	4	21	no	—
53	C₂×C₄	C₂×#126	1	7	yes	—
54	C₂×C₄	#529	1	21	yes	—
55	C₈	—	4	14	no	—
56	C₈	#401	1	8	yes	direct product factor
57	C₂²	C₄×#126	1	7	yes	—
58	C₂²	C₈×#41	1	7	yes	—
59	C₂²	#2966	1	21	yes	—
60	C₄	—	4	14	no	—
61	C₄	—	4	14	no	—
62	C₄	C₂×#401	1	1	yes	characteristic
63	C₄	#2401	1	7	yes	—
64	C₂	C₄×#401	1	1	yes	characteristic
65	C₂	C₈×#126	1	7	yes	—
66	C₂	#21668	1	7	yes	—

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

Complements

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

N	H ≅ G/N	type
13. #401	C₈	direct (N × H)
56. C₈	#401	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×#401	2
#11298	2
C₈×#95	2

Subgroups — C8×#401 #359418

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#401 #359418