Subgroups — C₂×#501 #3161

Order 128.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#125	C₂	1	1	yes	maximal, characteristic
3	#501	C₂	1	8	yes	maximal, direct product factor
4	C₂×#107	C₂	1	2	yes	maximal
5	C₂×#106	C₂	1	2	yes	maximal
6	C₂×#97	C₂	1	1	yes	maximal, characteristic
7	C₂²×Q₈	—	2	1	no	—
8	C₂²×C₈	C₂²	1	2	yes	—
9	C₄⋊Q₈	—	2	2	no	—
10	C₄⋊Q₈	C₂²	1	4	yes	—
11	#125	—	2	2	no	—
12	#125	C₂²	1	4	yes	—
13	C₂×C₄⋊C₄	—	2	1	no	—
14	C₂×C₄⋊C₄	—	2	1	no	—
15	C₂×C₄⋊C₄	—	2	1	no	—
16	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₄²	C₂²	1	1	yes	characteristic
20	#107	C₂²	1	8	yes	—
21	#106	C₂²	1	8	yes	—
22	#97	C₂²	1	4	yes	—
23	C₂×Q₈	—	2	4	no	—
24	C₂×Q₈	—	4	4	no	—
25	C₂²×C₄	—	2	1	no	—
26	C₂²×C₄	—	2	1	no	—
27	C₂²×C₄	—	2	2	no	—
28	C₂²×C₄	D₄	1	1	yes	characteristic
29	C₂²×C₄	D₄	1	1	yes	characteristic
30	C₂²×C₄	C₂³	1	1	yes	characteristic
31	C₂×C₈	Q₈	1	8	yes	complemented
32	C₂×C₈	C₂³	1	4	yes	—
33	C₄⋊C₄	—	2	4	no	—
34	C₄⋊C₄	—	2	4	no	—
35	C₄⋊C₄	—	2	4	no	—
36	C₄⋊C₄	—	2	1	no	—
37	C₄⋊C₄	—	2	1	no	—
38	C₄⋊C₄	—	2	2	no	—
39	C₄⋊C₄	C₂³	1	2	yes	—
40	C₄⋊C₄	C₂³	1	4	yes	—
41	C₄⋊C₄	C₂³	1	2	yes	—
42	C₄²	D₄	1	2	yes	—
43	C₄²	C₂³	1	2	yes	—
44	C₂³	C₂×D₄	1	1	yes	characteristic
45	Q₈	—	4	8	no	—
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	—	2	2	no	—
48	C₂×C₄	—	2	2	no	—
49	C₂×C₄	—	2	2	no	—
50	C₂×C₄	—	2	4	no	—
51	C₂×C₄	—	4	2	no	—
52	C₂×C₄	—	4	4	no	—
53	C₂×C₄	—	4	2	no	—
54	C₂×C₄	C₂×D₄	1	2	yes	—
55	C₂×C₄	C₂×D₄	1	2	yes	—
56	C₂×C₄	C₂×D₄	1	1	yes	characteristic
57	C₂×C₄	C₂×Q₈	1	4	yes	—
58	C₂×C₄	C₂⁴	1	1	yes	characteristic
59	C₈	C₂×Q₈	1	8	yes	complemented
60	C₂²	C₄⋊Q₈	1	2	yes	—
61	C₂²	AGL(1,ℤ/8)	1	2	yes	—
62	C₂²	#137	1	2	yes	—
63	C₂²	C₂²×D₄	1	1	yes	characteristic
64	C₄	—	2	2	no	—
65	C₄	—	2	2	no	—
66	C₄	—	4	2	no	—
67	C₄	—	4	4	no	—
68	C₄	—	4	2	no	—
69	C₄	C₄⋊Q₈	1	2	yes	—
70	C₄	C₂²×Q₈	1	2	yes	—
71	C₂	#501	1	4	yes	direct product factor
72	C₂	C₂×C₄⋊Q₈	1	1	yes	characteristic
73	C₂	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
74	C₂	C₂×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴
LCS	G ▷ C₂×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
3. #501	C₂	direct (N × H)
31. C₂×C₈	Q₈	semidirect
59. C₈	C₂×Q₈	semidirect
71. C₂	#501	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄⋊Q₈	2
C₂×#125	2
#501	2
C₂×#107	2
C₂×#106	2
C₂×#97	2

Subgroups — C2×#501 #3161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#501 #3161