Subgroups — C₂×#2845 #36689

Order 256.

871 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2845	C₂	1	16	yes	maximal, direct product factor
2	C₂×#398	C₂	1	12	yes	maximal
3	C₂×#382	C₂	1	3	yes	maximal
4	C₂²×C₄⋊C₄	C₂²	1	12	yes	—
5	C₂²×C₄⋊C₄	C₂²	1	6	yes	—
6	C₂²×C₄²	C₂²	1	1	yes	characteristic
7	#398	C₂²	1	96	yes	—
8	#382	C₂²	1	24	yes	—
9	C₂×#95	C₂²	1	4	yes	—
10	C₂×#95	C₂²	1	12	yes	—
11	C₂³×C₄	C₂³	1	12	yes	—
12	C₂³×C₄	C₂³	1	3	yes	—
13	C₂×C₄⋊C₄	—	4	12	no	—
14	C₂×C₄⋊C₄	—	4	24	no	—
15	C₂×C₄⋊C₄	C₂³	1	24	yes	—
16	C₂×C₄⋊C₄	C₂³	1	48	yes	—
17	C₂×C₄²	Q₈	1	8	yes	—
18	C₂×C₄²	C₂³	1	4	yes	—
19	#95	C₂³	1	48	yes	—
20	#95	C₂³	1	16	yes	—
21	C₂⁴	C₂⁴	1	1	yes	characteristic
22	C₂²×C₄	—	2	6	no	—
23	C₂²×C₄	—	2	6	no	—
24	C₂²×C₄	—	2	24	no	—
25	C₂²×C₄	—	2	24	no	—
26	C₂²×C₄	—	2	24	no	—
27	C₂²×C₄	C₂×Q₈	1	12	yes	—
28	C₂²×C₄	C₂⁴	1	24	yes	—
29	C₂²×C₄	C₂⁴	1	6	yes	—
30	C₄⋊C₄	—	4	24	no	—
31	C₄⋊C₄	—	4	48	no	—
32	C₄²	C₂×Q₈	1	16	yes	—
33	C₂³	C₂²×Q₈	1	2	yes	—
34	C₂³	H(5,𝔽₂)	1	6	yes	—
35	C₂³	2₋¹⁺⁴	1	6	yes	—
36	C₂³	C₂⁵	1	1	yes	characteristic
37	C₂×C₄	—	2	24	no	—
38	C₂×C₄	—	2	6	no	—
39	C₂×C₄	—	2	6	no	—
40	C₂×C₄	—	2	24	no	—
41	C₂×C₄	—	2	24	no	—
42	C₂×C₄	—	2	24	no	—
43	C₂×C₄	—	4	48	no	—
44	C₂×C₄	C₂²×Q₈	1	12	yes	—
45	C₂²	#544	1	12	yes	—
46	C₂²	#562	1	12	yes	—
47	C₂²	#564	1	4	yes	—
48	C₂²	C₂³×Q₈	1	1	yes	characteristic
49	C₂²	C₂×H(5,𝔽₂)	1	3	yes	—
50	C₂²	C₂×2₋¹⁺⁴	1	3	yes	—
51	C₄	—	2	12	no	—
52	C₄	—	4	24	no	—
53	C₂	#2845	1	8	yes	direct product factor
54	C₂	C₂×#544	1	3	yes	—
55	C₂	C₂×#562	1	3	yes	—
56	C₂	C₂×#564	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. #2845	C₂	direct (N × H)
53. C₂	#2845	direct (N × H)

Maximal subgroups

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

subgroup	index
#2845	2
C₂×#398	2
C₂×#382	2

Subgroups — C2×#2845 #36689

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#2845 #36689