Subgroups — C₂×#487 #3129

Order 128.

212 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×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	#487	C₂	1	8	yes	maximal, direct product factor
4	C₂×#103	C₂	1	4	yes	maximal
5	C₂×C₄×C₈	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₈	—	2	1	no	—
7	C₂²×Q₈	C₂²	1	2	yes	—
8	C₂²×C₈	C₂²	1	2	yes	—
9	C₄⋊Q₈	—	2	2	no	—
10	C₄⋊Q₈	—	2	2	no	—
11	C₄⋊Q₈	C₂²	1	4	yes	—
12	C₄⋊Q₈	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	2	yes	—
17	C₂×C₄²	C₂²	1	1	yes	characteristic
18	#103	C₂²	1	16	yes	—
19	C₄×C₈	C₂²	1	4	yes	—
20	C₂×Q₈	—	2	2	no	—
21	C₂×Q₈	—	2	4	no	—
22	C₂×Q₈	—	2	8	no	—
23	C₂×Q₈	—	4	4	no	—
24	C₂×Q₈	C₂³	1	4	yes	—
25	C₂²×C₄	—	2	2	no	—
26	C₂²×C₄	—	2	2	no	—
27	C₂²×C₄	D₄	1	1	yes	characteristic
28	C₂²×C₄	D₄	1	1	yes	characteristic
29	C₂²×C₄	C₂³	1	1	yes	characteristic
30	C₂×C₈	—	2	4	no	—
31	C₂×C₈	C₂³	1	4	yes	—
32	C₄⋊C₄	—	2	4	no	—
33	C₄⋊C₄	—	2	4	no	—
34	C₄⋊C₄	—	2	4	no	—
35	C₄⋊C₄	—	2	2	no	—
36	C₄⋊C₄	C₂³	1	4	yes	—
37	C₄²	D₄	1	2	yes	—
38	C₄²	C₂³	1	2	yes	—
39	C₂³	C₂×D₄	1	1	yes	characteristic
40	Q₈	—	2	8	no	—
41	Q₈	—	4	4	no	—
42	Q₈	—	4	8	no	—
43	C₂×C₄	—	2	4	no	—
44	C₂×C₄	—	2	4	no	—
45	C₂×C₄	—	4	4	no	—
46	C₂×C₄	—	4	4	no	—
47	C₂×C₄	SD₁₆	1	4	yes	—
48	C₂×C₄	Q₁₆	1	4	yes	—
49	C₂×C₄	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄	C₂×D₄	1	2	yes	—
51	C₂×C₄	C₂×D₄	1	2	yes	—
52	C₂×C₄	#41	1	4	yes	—
53	C₂×C₄	C₂⁴	1	1	yes	characteristic
54	C₈	—	2	4	no	—
55	C₂²	#124	1	2	yes	—
56	C₂²	C₂×SD₁₆	1	2	yes	—
57	C₂²	C₂×Q₁₆	1	2	yes	—
58	C₂²	C₂²×D₄	1	1	yes	characteristic
59	C₄	—	4	4	no	—
60	C₄	—	4	4	no	—
61	C₄	#124	1	2	yes	—
62	C₄	C₂×SD₁₆	1	4	yes	—
63	C₄	C₂×Q₁₆	1	4	yes	—
64	C₄	C₂×#41	1	2	yes	—
65	C₂	#487	1	4	yes	direct product factor
66	C₂	C₂×#124	1	1	yes	characteristic
67	C₂	C₂²×SD₁₆	1	1	yes	characteristic
68	C₂	C₂²×Q₁₆	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. #487	C₂	direct (N × H)
65. C₂	#487	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
#487	2
C₂×#103	2
C₂×C₄×C₈	2

Subgroups — C2×#487 #3129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#487 #3129