Subgroups — C₈×M₃₂ #11398

Order 256.

177 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×M₃₂	C₂	1	2	yes	maximal
2	C₂×C₈²	C₂	1	1	yes	maximal, characteristic
3	#1311	C₂	1	2	yes	maximal, complemented
4	C₈×C₁₆	C₂	1	2	yes	maximal, complemented
5	C₂×M₃₂	C₄	1	4	yes	—
6	C₂×C₄×C₈	C₄	1	2	yes	—
7	C₂×C₄×C₈	C₂²	1	1	yes	characteristic
8	#346	C₄	1	4	yes	—
9	C₄×C₁₆	C₂²	1	4	yes	—
10	C₈²	C₄	1	2	yes	—
11	C₈²	C₂²	1	1	yes	characteristic
12	C₈²	C₂²	1	1	yes	characteristic
13	C₂²×C₈	C₈	1	4	yes	—
14	C₂²×C₈	C₂×C₄	1	2	yes	—
15	C₂×C₄²	C₂×C₄	1	1	yes	characteristic
16	M₃₂	C₈	1	16	yes	direct product factor
17	C₂×C₁₆	C₂×C₄	1	8	yes	—
18	C₄×C₈	C₈	1	4	yes	—
19	C₄×C₈	C₂×C₄	1	2	yes	—
20	C₄×C₈	C₂×C₄	1	1	yes	characteristic
21	C₄×C₈	C₂×C₄	1	2	yes	—
22	C₄×C₈	C₂×C₄	1	2	yes	—
23	C₄×C₈	C₂³	1	1	yes	characteristic
24	C₂²×C₄	C₄²	1	1	yes	characteristic
25	C₂²×C₄	C₂×C₈	1	2	yes	—
26	C₂×C₈	—	2	8	no	—
27	C₂×C₈	C₄²	1	2	yes	—
28	C₂×C₈	C₂×C₈	1	4	yes	—
29	C₂×C₈	C₂×C₈	1	8	yes	—
30	C₂×C₈	C₂×C₈	1	4	yes	—
31	C₂×C₈	C₂²×C₄	1	2	yes	—
32	C₄²	C₄²	1	1	yes	characteristic
33	C₄²	C₂×C₈	1	2	yes	—
34	C₄²	C₂²×C₄	1	1	yes	characteristic
35	C₁₆	C₂×C₈	1	16	yes	complemented
36	C₂³	C₄×C₈	1	1	yes	characteristic
37	C₂×C₄	—	2	4	no	—
38	C₂×C₄	C₄×C₈	1	2	yes	—
39	C₂×C₄	C₄×C₈	1	1	yes	characteristic
40	C₂×C₄	C₄×C₈	1	4	yes	—
41	C₂×C₄	C₂×C₄²	1	1	yes	characteristic
42	C₂×C₄	C₂²×C₈	1	2	yes	—
43	C₈	—	2	4	no	—
44	C₈	C₄×C₈	1	4	yes	—
45	C₈	M₃₂	1	8	yes	direct product factor
46	C₈	C₂²×C₈	1	4	yes	—
47	C₂²	—	2	2	no	—
48	C₂²	C₈²	1	2	yes	—
49	C₂²	C₂×C₄×C₈	1	1	yes	characteristic
50	C₄	—	2	2	no	—
51	C₄	C₈²	1	2	yes	—
52	C₄	C₂×C₄×C₈	1	2	yes	—
53	C₄	C₂×M₃₂	1	4	yes	—
54	C₂	—	2	2	no	—
55	C₂	C₂×C₈²	1	1	yes	characteristic
56	C₂	C₄×M₃₂	1	2	yes	—

	subgroup	G/H
center	C₈²	C₂²
commutator	C₂	C₂×C₈²
Frattini, cosocle	C₄×C₈	C₂³
socle	C₂²	C₂×C₄×C₈
prime radical	C₂³	C₄×C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈² ◁ G
LECS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
3. #1311	C₂	semidirect
4. C₈×C₁₆	C₂	semidirect
16. M₃₂	C₈	direct (N × H)
35. C₁₆	C₂×C₈	semidirect
45. C₈	M₃₂	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×M₃₂	2
C₂×C₈²	2
#1311	2
C₈×C₁₆	2

Subgroups — C8×M32 #11398

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×M₃₂ #11398