Subgroups — C₂×#427 #2909

Order 128.

256 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#117	C₂	1	2	yes	maximal
3	#427	C₂	1	8	yes	maximal, direct product factor
4	C₂×#107	C₂	1	2	yes	maximal, complemented
5	C₂×#106	C₂	1	2	yes	maximal, complemented
6	C₂³×C₄	C₂²	1	1	yes	characteristic
7	C₂²×C₈	C₄	1	8	yes	complemented
8	C₂²×C₈	C₂²	1	1	yes	characteristic
9	C₂²×C₈	C₂²	1	1	yes	characteristic
10	C₂²×C₈	C₂²	1	4	yes	—
11	#117	—	2	4	no	—
12	#117	C₂²	1	8	yes	—
13	C₂×C₄⋊C₄	C₂²	1	4	yes	—
14	C₂×C₂²⋊C₄	—	2	2	no	—
15	C₂×C₄²	—	2	2	no	—
16	#107	C₂²	1	8	yes	complemented
17	#106	C₂²	1	8	yes	complemented
18	C₂⁴	D₄	1	1	yes	characteristic
19	C₂²×C₄	—	2	4	no	—
20	C₂²×C₄	C₂×C₄	1	4	yes	—
21	C₂²×C₄	D₄	1	2	yes	—
22	C₂²×C₄	D₄	1	1	yes	characteristic
23	C₂²×C₄	Q₈	1	4	yes	—
24	C₂²×C₄	C₂³	1	1	yes	characteristic
25	C₂²×C₄	C₂³	1	2	yes	—
26	C₂×C₈	C₂×C₄	1	4	yes	—
27	C₂×C₈	C₂×C₄	1	4	yes	—
28	C₂×C₈	C₂×C₄	1	16	yes	complemented
29	C₂×C₈	C₂³	1	2	yes	—
30	C₂×C₈	C₂³	1	2	yes	—
31	C₄⋊C₄	—	2	4	no	—
32	C₄⋊C₄	C₂³	1	8	yes	—
33	C₂²⋊C₄	—	2	8	no	—
34	C₄²	—	2	8	no	—
35	C₂³	—	2	4	no	—
36	C₂³	C₄⋊C₄	1	4	yes	—
37	C₂³	C₂×D₄	1	2	yes	—
38	C₂³	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄	—	2	8	no	—
40	C₂×C₄	—	4	8	no	—
41	C₂×C₄	C₄⋊C₄	1	8	yes	—
42	C₂×C₄	C₄⋊C₄	1	4	yes	—
43	C₂×C₄	C₂²×C₄	1	2	yes	—
44	C₂×C₄	C₂²×C₄	1	4	yes	—
45	C₂×C₄	C₂×D₄	1	2	yes	—
46	C₂×C₄	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄	C₂×Q₈	1	4	yes	—
48	C₂×C₄	C₂×Q₈	1	2	yes	—
49	C₂×C₄	C₂⁴	1	1	yes	characteristic
50	C₈	C₂²×C₄	1	4	yes	—
51	C₈	C₂²×C₄	1	4	yes	—
52	C₂²	—	2	4	no	—
53	C₂²	—	2	8	no	—
54	C₂²	C₂×C₄⋊C₄	1	4	yes	—
55	C₂²	C₂×C₄⋊C₄	1	2	yes	—
56	C₂²	#135	1	4	yes	—
57	C₂²	C₂²×D₄	1	1	yes	characteristic
58	C₄	—	4	8	no	—
59	C₄	C₂×C₄⋊C₄	1	2	yes	—
60	C₄	C₂×C₄⋊C₄	1	4	yes	—
61	C₄	C₂³×C₄	1	1	yes	characteristic
62	C₄	C₂²×Q₈	1	1	yes	characteristic
63	C₂	—	2	4	no	—
64	C₂	#427	1	4	yes	direct product factor
65	C₂	C₂²×C₄⋊C₄	1	1	yes	characteristic
66	C₂	C₂×#135	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄
commutator	C₄	C₂³×C₄
Frattini, cosocle	C₂×C₄	C₂⁴
socle	C₂³	C₂×D₄
prime radical	C₂⁴	D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
3. #427	C₂	direct (N × H)
4. C₂×#107	C₂	semidirect
5. C₂×#106	C₂	semidirect
7. C₂²×C₈	C₄	semidirect
16. #107	C₂²	semidirect
17. #106	C₂²	semidirect
28. C₂×C₈	C₂×C₄	semidirect
64. C₂	#427	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₈	2
C₂×#117	2
#427	2
C₂×#107	2
C₂×#106	2

Subgroups — C2×#427 #2909

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#427 #2909