Subgroups — C₂×#2842 #36672

Order 256.

1647 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2842	C₂	1	16	yes	maximal, direct product factor
2	C₂×#399	C₂	1	4	yes	maximal, complemented
3	C₂×#396	C₂	1	8	yes	maximal, complemented
4	C₂×#379	C₂	1	3	yes	maximal
5	C₂⁶	C₂²	1	1	yes	characteristic
6	C₂²×C₄⋊C₄	C₂²	1	12	yes	complemented
7	C₂²×C₂²⋊C₄	C₂²	1	12	yes	—
8	C₂²×C₂²⋊C₄	C₂²	1	6	yes	—
9	#399	C₂²	1	32	yes	complemented
10	#396	C₂²	1	64	yes	complemented
11	#379	C₂²	1	24	yes	—
12	C₂×#95	C₂²	1	4	yes	complemented
13	C₂⁵	—	4	12	no	—
14	C₂⁵	Q₈	1	8	yes	—
15	C₂⁵	C₂³	1	2	yes	—
16	C₂⁵	C₂³	1	1	yes	characteristic
17	C₂⁵	C₂³	1	4	yes	—
18	C₂³×C₄	C₂³	1	12	yes	—
19	C₂×C₄⋊C₄	—	4	24	no	—
20	C₂×C₄⋊C₄	C₂³	1	48	yes	complemented
21	C₂×C₂²⋊C₄	—	4	24	no	—
22	C₂×C₂²⋊C₄	—	4	12	no	—
23	C₂×C₂²⋊C₄	C₂³	1	48	yes	—
24	C₂×C₂²⋊C₄	C₂³	1	24	yes	—
25	#95	C₂³	1	16	yes	complemented
26	C₂⁴	—	2	24	no	—
27	C₂⁴	—	2	12	no	—
28	C₂⁴	—	4	48	no	—
29	C₂⁴	—	4	24	no	—
30	C₂⁴	—	4	64	no	—
31	C₂⁴	C₂×Q₈	1	8	yes	—
32	C₂⁴	C₂×Q₈	1	4	yes	—
33	C₂⁴	C₂×Q₈	1	16	yes	—
34	C₂⁴	C₂⁴	1	4	yes	—
35	C₂⁴	C₂⁴	1	2	yes	—
36	C₂⁴	C₂⁴	1	1	yes	characteristic
37	C₂²×C₄	—	2	48	no	—
38	C₂²×C₄	—	2	24	no	—
39	C₂²×C₄	C₂⁴	1	24	yes	—
40	C₄⋊C₄	—	4	48	no	—
41	C₂²⋊C₄	—	4	48	no	—
42	C₂²⋊C₄	—	4	24	no	—
43	C₂³	—	2	48	no	—
44	C₂³	—	2	24	no	—
45	C₂³	—	2	24	no	—
46	C₂³	—	2	12	no	—
47	C₂³	—	4	48	no	—
48	C₂³	—	4	128	no	—
49	C₂³	—	4	64	no	—
50	C₂³	—	4	32	no	—
51	C₂³	—	4	16	no	—
52	C₂³	C₂²×Q₈	1	8	yes	—
53	C₂³	C₂²×Q₈	1	4	yes	—
54	C₂³	C₂²×Q₈	1	2	yes	—
55	C₂³	H(5,𝔽₂)	1	12	yes	—
56	C₂³	C₂⁵	1	1	yes	characteristic
57	C₂×C₄	—	2	48	no	—
58	C₂×C₄	—	2	24	no	—
59	C₂×C₄	—	4	48	no	—
60	C₂²	—	2	24	no	—
61	C₂²	—	2	12	no	—
62	C₂²	—	4	64	no	—
63	C₂²	—	4	32	no	—
64	C₂²	—	4	16	no	—
65	C₂²	—	4	16	no	—
66	C₂²	—	4	8	no	—
67	C₂²	#543	1	12	yes	—
68	C₂²	#560	1	16	yes	—
69	C₂²	C₂³×Q₈	1	1	yes	characteristic
70	C₂²	C₂×H(5,𝔽₂)	1	6	yes	—
71	C₄	—	4	24	no	—
72	C₂	—	4	8	no	—
73	C₂	—	4	4	no	—
74	C₂	#2842	1	8	yes	direct product factor
75	C₂	C₂×#543	1	3	yes	—
76	C₂	C₂×#560	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. #2842	C₂	direct (N × H)
2. C₂×#399	C₂	semidirect
3. C₂×#396	C₂	semidirect
6. C₂²×C₄⋊C₄	C₂²	semidirect
9. #399	C₂²	semidirect
10. #396	C₂²	semidirect
12. C₂×#95	C₂²	semidirect
20. C₂×C₄⋊C₄	C₂³	semidirect
25. #95	C₂³	semidirect
74. C₂	#2842	direct (N × H)

Maximal subgroups

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

subgroup	index
#2842	2
C₂×#399	2
C₂×#396	2
C₂×#379	2

Subgroups — C2×#2842 #36672

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#2842 #36672