Subgroups — C₂×#442 #2942

Order 128.

304 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₄	C₂	1	2	yes	maximal, complemented
3	#442	C₂	1	8	yes	maximal, direct product factor
4	C₂×#106	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#102	C₂	1	2	yes	maximal, complemented
6	C₂×#97	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×D₄	C₂²	1	2	yes	—
8	C₂³×C₄	—	2	2	no	—
9	C₂×D₈	C₄	1	8	yes	complemented
10	C₂×D₈	C₂²	1	4	yes	—
11	C₂²×C₈	C₂²	1	1	yes	characteristic
12	C₂²×C₈	C₂²	1	1	yes	characteristic
13	C₄×D₄	—	2	4	no	—
14	C₄×D₄	C₂²	1	8	yes	complemented
15	C₂×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₂²⋊C₄	—	2	2	no	—
17	C₂×C₄²	C₂²	1	1	yes	characteristic
18	#106	C₂²	1	4	yes	complemented
19	#102	C₂²	1	8	yes	complemented
20	#97	C₂²	1	4	yes	complemented
21	C₂⁴	—	2	2	no	—
22	C₂×D₄	—	2	2	no	—
23	C₂×D₄	—	2	4	no	—
24	C₂×D₄	C₂×C₄	1	8	yes	complemented
25	C₂×D₄	C₂³	1	4	yes	—
26	C₂²×C₄	—	2	2	no	—
27	C₂²×C₄	—	2	8	no	—
28	C₂²×C₄	—	4	8	no	—
29	C₂²×C₄	D₄	1	2	yes	—
30	C₂²×C₄	C₂³	1	1	yes	characteristic
31	D₈	C₂×C₄	1	16	yes	complemented
32	C₂×C₈	—	2	2	no	—
33	C₂×C₈	C₂×C₄	1	4	yes	complemented
34	C₂×C₈	C₂³	1	2	yes	—
35	C₂×C₈	C₂³	1	2	yes	—
36	C₄⋊C₄	—	2	2	no	—
37	C₄⋊C₄	C₂³	1	4	yes	—
38	C₂²⋊C₄	—	2	8	no	—
39	C₄²	D₄	1	2	yes	—
40	C₄²	C₂³	1	2	yes	—
41	C₂³	—	2	8	no	—
42	C₂³	—	2	4	no	—
43	C₂³	—	4	4	no	—
44	C₂³	—	4	4	no	—
45	C₂³	C₂×D₄	1	1	yes	characteristic
46	D₄	—	2	8	no	—
47	D₄	—	2	4	no	—
48	D₄	C₂²×C₄	1	8	yes	complemented
49	C₂×C₄	—	2	4	no	—
50	C₂×C₄	—	2	4	no	—
51	C₂×C₄	—	4	16	no	—
52	C₂×C₄	—	4	4	no	—
53	C₂×C₄	C₂²×C₄	1	2	yes	—
54	C₂×C₄	C₂×D₄	1	4	yes	—
55	C₂×C₄	C₂×D₄	1	1	yes	characteristic
56	C₂×C₄	#41	1	2	yes	—
57	C₂×C₄	C₂⁴	1	1	yes	characteristic
58	C₈	—	2	2	no	—
59	C₈	C₂²×C₄	1	4	yes	complemented
60	C₂²	—	2	8	no	—
61	C₂²	—	4	4	no	—
62	C₂²	—	4	4	no	—
63	C₂²	—	4	16	no	—
64	C₂²	C₄×D₄	1	2	yes	—
65	C₂²	AGL(1,ℤ/8)	1	4	yes	—
66	C₂²	C₂²×D₄	1	1	yes	characteristic
67	C₄	—	2	4	no	—
68	C₄	—	4	4	no	—
69	C₄	C₄×D₄	1	2	yes	—
70	C₄	C₂³×C₄	1	1	yes	characteristic
71	C₄	C₂×#41	1	1	yes	characteristic
72	C₂	—	4	8	no	—
73	C₂	#442	1	4	yes	direct product factor
74	C₂	C₂×C₄×D₄	1	1	yes	characteristic
75	C₂	C₂×AGL(1,ℤ/8)	1	2	yes	—

	subgroup	G/H
center, socle	C₂³	C₂×D₄
commutator	C₄	C₂³×C₄
Frattini, cosocle	C₂×C₄	C₂⁴
prime radical	C₂²×D₈	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×D₄	C₂	semidirect
3. #442	C₂	direct (N × H)
4. C₂×#106	C₂	semidirect
5. C₂×#102	C₂	semidirect
6. C₂×#97	C₂	semidirect
9. C₂×D₈	C₄	semidirect
14. C₄×D₄	C₂²	semidirect
18. #106	C₂²	semidirect
19. #102	C₂²	semidirect
20. #97	C₂²	semidirect
24. C₂×D₄	C₂×C₄	semidirect
31. D₈	C₂×C₄	semidirect
33. C₂×C₈	C₂×C₄	semidirect
48. D₄	C₂²×C₄	semidirect
59. C₈	C₂²×C₄	semidirect
73. C₂	#442	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×D₈	2
C₂×C₄×D₄	2
#442	2
C₂×#106	2
C₂×#102	2
C₂×#97	2

Subgroups — C2×#442 #2942

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#442 #2942