Subgroups — C₂×#2840 #36671

Order 256.

1775 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2840	C₂	1	16	yes	maximal, direct product factor
2	C₂×#393	C₂	1	12	yes	maximal, complemented
3	C₂×#379	C₂	1	3	yes	maximal
4	C₂⁶	C₂²	1	1	yes	characteristic
5	C₂³×Q₈	C₂²	1	4	yes	complemented
6	C₂²×C₂²⋊C₄	C₂²	1	18	yes	—
7	#393	C₂²	1	96	yes	complemented
8	#379	C₂²	1	24	yes	—
9	C₂×#95	C₂²	1	12	yes	complemented
10	C₂⁵	—	4	12	no	—
11	C₂⁵	Q₈	1	8	yes	complemented
12	C₂⁵	C₂³	1	3	yes	—
13	C₂⁵	C₂³	1	4	yes	—
14	C₂²×Q₈	—	4	24	no	—
15	C₂²×Q₈	C₂³	1	16	yes	complemented
16	C₂³×C₄	C₂³	1	12	yes	—
17	C₂×C₂²⋊C₄	—	4	36	no	—
18	C₂×C₂²⋊C₄	C₂³	1	72	yes	—
19	#95	C₂³	1	48	yes	complemented
20	C₂⁴	—	2	36	no	—
21	C₂⁴	—	4	48	no	—
22	C₂⁴	—	4	24	no	—
23	C₂⁴	—	4	64	no	—
24	C₂⁴	C₂×Q₈	1	12	yes	—
25	C₂⁴	C₂×Q₈	1	16	yes	complemented
26	C₂⁴	C₂⁴	1	6	yes	—
27	C₂⁴	C₂⁴	1	1	yes	characteristic
28	C₂×Q₈	—	4	48	no	—
29	C₂×Q₈	—	4	64	no	—
30	C₂²×C₄	—	2	72	no	—
31	C₂²×C₄	C₂⁴	1	24	yes	—
32	C₂²⋊C₄	—	4	72	no	—
33	C₂³	—	2	72	no	—
34	C₂³	—	2	36	no	—
35	C₂³	—	4	48	no	—
36	C₂³	—	4	128	no	—
37	C₂³	—	4	64	no	—
38	C₂³	—	4	48	no	—
39	C₂³	C₂²×Q₈	1	12	yes	—
40	C₂³	C₂²×Q₈	1	2	yes	—
41	C₂³	H(5,𝔽₂)	1	12	yes	—
42	C₂³	C₂⁵	1	1	yes	characteristic
43	Q₈	—	4	64	no	—
44	C₂×C₄	—	2	72	no	—
45	C₂×C₄	—	4	48	no	—
46	C₂²	—	2	36	no	—
47	C₂²	—	4	64	no	—
48	C₂²	—	4	48	no	—
49	C₂²	—	4	24	no	—
50	C₂²	#543	1	12	yes	—
51	C₂²	H(3,𝔽₄)	1	16	yes	—
52	C₂²	C₂³×Q₈	1	1	yes	characteristic
53	C₂²	C₂×H(5,𝔽₂)	1	6	yes	—
54	C₄	—	4	24	no	—
55	C₂	—	4	12	no	—
56	C₂	#2840	1	8	yes	direct product factor
57	C₂	C₂×#543	1	3	yes	—
58	C₂	C₂×H(3,𝔽₄)	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵
prime radical	C₂⁶	C₂²
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. #2840	C₂	direct (N × H)
2. C₂×#393	C₂	semidirect
5. C₂³×Q₈	C₂²	semidirect
7. #393	C₂²	semidirect
9. C₂×#95	C₂²	semidirect
11. C₂⁵	Q₈	semidirect
15. C₂²×Q₈	C₂³	semidirect
19. #95	C₂³	semidirect
25. C₂⁴	C₂×Q₈	semidirect
56. C₂	#2840	direct (N × H)

Maximal subgroups

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

subgroup	index
#2840	2
C₂×#393	2
C₂×#379	2

Subgroups — C2×#2840 #36671

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#2840 #36671