Subgroups — C₂×#1422 #13629

Order 256.

107 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₆₄	C₂	1	2	yes	maximal
2	C₂×C₄×C₁₆	C₂	1	1	yes	maximal, characteristic
3	#1422	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₁₆	C₄	1	1	yes	characteristic
5	C₂²×C₁₆	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₈	C₄	1	1	yes	characteristic
7	M₆₄	—	2	2	no	—
8	M₆₄	C₂²	1	4	yes	—
9	C₂×C₃₂	—	2	2	no	—
10	C₄×C₁₆	C₄	1	2	yes	—
11	C₄×C₁₆	C₂²	1	2	yes	—
12	C₂²×C₈	C₈	1	1	yes	characteristic
13	C₂²×C₈	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄²	C₈	1	1	yes	characteristic
15	C₂×C₁₆	—	2	1	no	—
16	C₂×C₁₆	—	2	1	no	—
17	C₂×C₁₆	C₂×C₄	1	2	yes	—
18	C₂×C₁₆	C₂×C₄	1	1	yes	characteristic
19	C₂×C₁₆	D₄	1	1	yes	characteristic
20	C₂×C₁₆	D₄	1	1	yes	characteristic
21	C₂×C₁₆	Q₈	1	1	yes	characteristic
22	C₂×C₁₆	Q₈	1	1	yes	characteristic
23	C₂×C₁₆	C₂³	1	1	yes	characteristic
24	C₄×C₈	C₈	1	2	yes	—
25	C₄×C₈	C₂×C₄	1	2	yes	—
26	C₃₂	—	2	4	no	—
27	C₂²×C₄	—	2	1	no	—
28	C₂²×C₄	C₂×C₈	1	1	yes	characteristic
29	C₂×C₈	C₁₆	1	2	yes	—
30	C₂×C₈	C₁₆	1	2	yes	—
31	C₂×C₈	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₈	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₈	C₂×C₈	1	1	yes	characteristic
34	C₂×C₈	C₂×C₈	1	2	yes	—
35	C₂×C₈	M₁₆	1	1	yes	characteristic
36	C₂×C₈	M₁₆	1	1	yes	characteristic
37	C₂×C₈	C₂²×C₄	1	1	yes	characteristic
38	C₄²	—	2	1	no	—
39	C₄²	C₂×C₈	1	2	yes	—
40	C₁₆	—	2	2	no	—
41	C₁₆	C₄⋊C₄	1	1	yes	characteristic
42	C₁₆	C₄⋊C₄	1	1	yes	characteristic
43	C₁₆	C₂×D₄	1	1	yes	characteristic
44	C₁₆	C₂×Q₈	1	1	yes	characteristic
45	C₂³	M₃₂	1	1	yes	characteristic
46	C₂×C₄	—	2	4	no	—
47	C₂×C₄	—	2	2	no	—
48	C₂×C₄	C₄⋊C₈	1	1	yes	characteristic
49	C₂×C₄	C₄⋊C₈	1	1	yes	characteristic
50	C₂×C₄	C₂×C₁₆	1	1	yes	characteristic
51	C₂×C₄	C₂×C₁₆	1	1	yes	characteristic
52	C₂×C₄	M₃₂	1	1	yes	characteristic
53	C₂×C₄	C₂²×C₈	1	1	yes	characteristic
54	C₈	C₄⋊C₈	1	1	yes	characteristic
55	C₈	C₄⋊C₈	1	1	yes	characteristic
56	C₈	C₂×C₁₆	1	4	yes	—
57	C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
58	C₈	C₂×M₁₆	1	1	yes	characteristic
59	C₂²	—	2	2	no	—
60	C₂²	C₄⋊C₁₆	1	1	yes	characteristic
61	C₂²	C₄⋊C₁₆	1	1	yes	characteristic
62	C₂²	C₂×M₃₂	1	1	yes	characteristic
63	C₄	—	2	4	no	—
64	C₄	C₄⋊C₁₆	1	1	yes	characteristic
65	C₄	C₄⋊C₁₆	1	1	yes	characteristic
66	C₄	C₂×C₄⋊C₈	1	1	yes	characteristic
67	C₄	C₂²×C₁₆	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	2	1	no	—
70	C₂	#1422	1	2	yes	direct product factor
71	C₂	C₂×C₄⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₆	D₄
commutator	C₄	C₂²×C₁₆
Frattini, cosocle	C₂×C₁₆	C₂³
socle	C₂²	C₄⋊C₁₆
prime radical	C₂³	M₃₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₆ ◁ 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
3. #1422	C₂	direct (N × H)
70. C₂	#1422	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×M₆₄	2
C₂×C₄×C₁₆	2
#1422	2

Subgroups — C2×#1422 #13629

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1422 #13629