Subgroups — C₂×C₂²⋊C₃₂ #13552

Order 256.

171 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃₂	C₂	1	2	yes	maximal, complemented
3	C₂²⋊C₃₂	C₂	1	4	yes	maximal, direct product factor
4	C₂³×C₈	C₄	1	1	yes	characteristic
5	C₂²×C₁₆	—	2	4	no	—
6	C₂²×C₁₆	C₄	1	1	yes	characteristic
7	C₂²×C₁₆	C₄	1	2	yes	—
8	C₂²×C₁₆	C₂²	1	2	yes	—
9	C₂²×C₁₆	C₂²	1	1	yes	characteristic
10	C₂×C₃₂	—	2	4	no	—
11	C₂×C₃₂	C₂²	1	4	yes	complemented
12	C₂³×C₄	C₈	1	1	yes	characteristic
13	C₂²×C₈	—	2	2	no	—
14	C₂²×C₈	—	2	2	no	—
15	C₂²×C₈	C₈	1	1	yes	characteristic
16	C₂²×C₈	C₈	1	2	yes	—
17	C₂²×C₈	C₂×C₄	1	2	yes	—
18	C₂²×C₈	C₂×C₄	1	1	yes	characteristic
19	C₂×C₁₆	—	2	2	no	—
20	C₂×C₁₆	—	2	4	no	—
21	C₂×C₁₆	—	2	4	no	—
22	C₂×C₁₆	C₂×C₄	1	2	yes	—
23	C₂×C₁₆	C₂×C₄	1	1	yes	characteristic
24	C₂×C₁₆	D₄	1	4	yes	—
25	C₂×C₁₆	C₂³	1	1	yes	characteristic
26	C₃₂	—	2	4	no	—
27	C₂⁴	C₁₆	1	1	yes	characteristic
28	C₂²×C₄	—	2	2	no	—
29	C₂²×C₄	—	2	2	no	—
30	C₂²×C₄	C₁₆	1	1	yes	characteristic
31	C₂²×C₄	C₁₆	1	2	yes	—
32	C₂²×C₄	C₂×C₈	1	2	yes	—
33	C₂²×C₄	C₂×C₈	1	1	yes	characteristic
34	C₂×C₈	—	2	2	no	—
35	C₂×C₈	—	2	4	no	—
36	C₂×C₈	—	2	2	no	—
37	C₂×C₈	—	2	2	no	—
38	C₂×C₈	C₂²⋊C₄	1	2	yes	—
39	C₂×C₈	C₂×C₈	1	2	yes	—
40	C₂×C₈	C₂×C₈	1	1	yes	characteristic
41	C₂×C₈	M₁₆	1	2	yes	—
42	C₂×C₈	C₂²×C₄	1	1	yes	characteristic
43	C₁₆	—	2	2	no	—
44	C₁₆	C₂²⋊C₄	1	2	yes	—
45	C₁₆	C₂×D₄	1	2	yes	—
46	C₂³	—	2	2	no	—
47	C₂³	—	2	2	no	—
48	C₂³	C₃₂	1	4	yes	complemented
49	C₂³	C₂×C₁₆	1	2	yes	—
50	C₂³	C₂×C₁₆	1	1	yes	characteristic
51	C₂×C₄	—	2	2	no	—
52	C₂×C₄	—	2	4	no	—
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	—	2	2	no	—
55	C₂×C₄	C₂²⋊C₈	1	2	yes	—
56	C₂×C₄	C₂×C₁₆	1	2	yes	—
57	C₂×C₄	C₂×C₁₆	1	1	yes	characteristic
58	C₂×C₄	M₃₂	1	2	yes	—
59	C₂×C₄	C₂²×C₈	1	1	yes	characteristic
60	C₈	—	2	2	no	—
61	C₈	C₂²⋊C₈	1	2	yes	—
62	C₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
63	C₈	C₂×M₁₆	1	1	yes	characteristic
64	C₂²	—	2	2	no	—
65	C₂²	—	2	8	no	—
66	C₂²	—	2	2	no	—
67	C₂²	C₂²⋊C₁₆	1	2	yes	—
68	C₂²	C₂×C₃₂	1	2	yes	—
69	C₂²	C₂×C₃₂	1	4	yes	complemented
70	C₂²	M₆₄	1	2	yes	—
71	C₂²	C₂²×C₁₆	1	1	yes	characteristic
72	C₄	—	2	2	no	—
73	C₄	C₂²⋊C₁₆	1	2	yes	—
74	C₄	C₂×C₂²⋊C₈	1	1	yes	characteristic
75	C₄	C₂×M₃₂	1	1	yes	characteristic
76	C₂	—	2	4	no	—
77	C₂	C₂²⋊C₃₂	1	4	yes	direct product factor
78	C₂	C₂×C₂²⋊C₁₆	1	1	yes	characteristic
79	C₂	C₂²×C₃₂	1	1	yes	characteristic
80	C₂	C₂×M₆₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₁₆	C₂²
commutator	C₂	C₂²×C₃₂
Frattini, cosocle	C₂×C₁₆	C₂³
socle	C₂³	C₂×C₁₆
prime radical	C₂⁴	C₁₆
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₆ ◁ G
LECS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃₂	C₂	semidirect
3. C₂²⋊C₃₂	C₂	direct (N × H)
11. C₂×C₃₂	C₂²	semidirect
48. C₂³	C₃₂	semidirect
69. C₂²	C₂×C₃₂	semidirect
77. C₂	C₂²⋊C₃₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₁₆	2
C₂²×C₃₂	2
C₂²⋊C₃₂	2

Subgroups — C2×C22⋊C32 #13552

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂²⋊C₃₂ #13552