Subgroups — C₂×#491 #3134

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	#491	C₂	1	8	yes	maximal, direct product factor
4	C₂×#103	C₂	1	4	yes	maximal
5	C₂×#97	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₈	C₂²	1	2	yes	—
7	C₂²×C₈	C₂²	1	2	yes	—
8	C₄⋊Q₈	—	2	2	no	—
9	C₄⋊Q₈	C₂²	1	4	yes	—
10	#125	—	2	2	no	—
11	#125	C₂²	1	4	yes	—
12	C₂×C₄⋊C₄	—	2	2	no	—
13	C₂×C₄⋊C₄	—	2	2	no	—
14	C₂×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₄²	C₂²	1	1	yes	characteristic
16	#103	C₂²	1	16	yes	—
17	#97	C₂²	1	4	yes	—
18	C₂×Q₈	—	2	2	no	—
19	C₂×Q₈	—	2	8	no	—
20	C₂×Q₈	C₂³	1	4	yes	—
21	C₂²×C₄	—	2	2	no	—
22	C₂²×C₄	—	2	2	no	—
23	C₂²×C₄	D₄	1	2	yes	—
24	C₂²×C₄	C₂³	1	1	yes	characteristic
25	C₂×C₈	—	2	4	no	—
26	C₂×C₈	C₂³	1	4	yes	—
27	C₄⋊C₄	—	2	8	no	—
28	C₄⋊C₄	—	2	8	no	—
29	C₄⋊C₄	—	2	2	no	—
30	C₄⋊C₄	C₂³	1	4	yes	—
31	C₄²	D₄	1	2	yes	—
32	C₄²	C₂³	1	2	yes	—
33	C₂³	C₂×D₄	1	1	yes	characteristic
34	Q₈	—	2	8	no	—
35	Q₈	—	4	4	no	—
36	C₂×C₄	—	2	4	no	—
37	C₂×C₄	—	2	4	no	—
38	C₂×C₄	—	2	4	no	—
39	C₂×C₄	—	4	4	no	—
40	C₂×C₄	—	4	4	no	—
41	C₂×C₄	C₂×D₄	1	4	yes	—
42	C₂×C₄	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄	#41	1	4	yes	—
44	C₂×C₄	C₂⁴	1	1	yes	characteristic
45	C₈	—	2	4	no	—
46	C₂²	#124	1	2	yes	—
47	C₂²	#137	1	4	yes	—
48	C₂²	C₂²×D₄	1	1	yes	characteristic
49	C₄	—	2	4	no	—
50	C₄	—	4	4	no	—
51	C₄	—	4	4	no	—
52	C₄	#124	1	2	yes	—
53	C₄	C₂×#41	1	2	yes	—
54	C₂	#491	1	4	yes	direct product factor
55	C₂	C₂×#124	1	1	yes	characteristic
56	C₂	C₂×#137	1	2	yes	—

	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. #491	C₂	direct (N × H)
54. C₂	#491	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
#491	2
C₂×#103	2
C₂×#97	2

Subgroups — C2×#491 #3134

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#491 #3134