Subgroups — C₂×#2811 #52286

Order 256.

1175 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2811	C₂	1	16	yes	maximal, direct product factor
2	C₂×#395	C₂	1	6	yes	maximal
3	C₂×#391	C₂	1	9	yes	maximal
4	C₂³×Q₈	C₂²	1	2	yes	—
5	C₂³×Q₈	C₂²	1	3	yes	—
6	C₂²×C₄⋊C₄	C₂²	1	9	yes	—
7	C₂²×C₄²	C₂²	1	3	yes	—
8	#395	C₂²	1	48	yes	—
9	#391	C₂²	1	72	yes	—
10	C₂×#95	C₂²	1	18	yes	—
11	C₂²×Q₈	—	4	6	no	—
12	C₂²×Q₈	—	4	6	no	—
13	C₂²×Q₈	—	4	12	no	—
14	C₂²×Q₈	Q₈	1	24	yes	complemented
15	C₂²×Q₈	C₂³	1	8	yes	—
16	C₂²×Q₈	C₂³	1	12	yes	—
17	C₂³×C₄	C₂³	1	6	yes	—
18	C₂³×C₄	C₂³	1	9	yes	—
19	C₂×C₄⋊C₄	—	4	18	no	—
20	C₂×C₄⋊C₄	C₂³	1	36	yes	—
21	C₂×C₄²	—	4	6	no	—
22	C₂×C₄²	C₂³	1	12	yes	—
23	#95	C₂³	1	72	yes	—
24	C₂⁴	C₂⁴	1	1	yes	characteristic
25	C₂×Q₈	—	4	48	no	—
26	C₂×Q₈	—	4	12	no	—
27	C₂×Q₈	—	4	12	no	—
28	C₂×Q₈	—	4	24	no	—
29	C₂×Q₈	—	4	32	no	—
30	C₂×Q₈	C₂×Q₈	1	48	yes	complemented
31	C₂²×C₄	—	2	18	no	—
32	C₂²×C₄	—	2	18	no	—
33	C₂²×C₄	—	2	36	no	—
34	C₂²×C₄	C₂×Q₈	1	36	yes	—
35	C₂²×C₄	C₂⁴	1	12	yes	—
36	C₂²×C₄	C₂⁴	1	18	yes	—
37	C₄⋊C₄	—	4	36	no	—
38	C₄²	—	4	12	no	—
39	C₂³	C₂²×Q₈	1	6	yes	—
40	C₂³	H(5,𝔽₂)	1	2	yes	—
41	C₂³	H(5,𝔽₂)	1	6	yes	—
42	C₂³	C₂⁵	1	1	yes	characteristic
43	Q₈	—	4	48	no	—
44	Q₈	—	4	32	no	—
45	C₂×C₄	—	2	72	no	—
46	C₂×C₄	—	2	18	no	—
47	C₂×C₄	—	2	18	no	—
48	C₂×C₄	—	2	36	no	—
49	C₂×C₄	—	4	24	no	—
50	C₂×C₄	C₂²×Q₈	1	36	yes	—
51	C₂²	#543	1	12	yes	—
52	C₂²	Q₈²	1	12	yes	—
53	C₂²	H(3,𝔽₄)	1	4	yes	—
54	C₂²	C₂³×Q₈	1	3	yes	—
55	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
56	C₂²	C₂×H(5,𝔽₂)	1	3	yes	—
57	C₄	—	2	36	no	—
58	C₄	—	4	12	no	—
59	C₂	#2811	1	8	yes	direct product factor
60	C₂	C₂×#543	1	3	yes	—
61	C₂	C₂×Q₈²	1	3	yes	—
62	C₂	C₂×H(3,𝔽₄)	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. #2811	C₂	direct (N × H)
14. C₂²×Q₈	Q₈	semidirect
30. C₂×Q₈	C₂×Q₈	semidirect
59. C₂	#2811	direct (N × H)

Maximal subgroups

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

subgroup	index
#2811	2
C₂×#395	2
C₂×#391	2

Subgroups — C2×#2811 #52286

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#2811 #52286