Subgroups — C₂×C₈×Q₈ #2958

Order 128.

220 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	C₈×Q₈	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄⋊C₈	C₂	1	3	yes	maximal
4	C₂×C₄×C₈	C₂	1	3	yes	maximal
5	C₂²×Q₈	C₄	1	1	yes	characteristic
6	C₂²×C₈	C₂²	1	3	yes	—
7	C₂²×C₈	C₂²	1	1	yes	characteristic
8	C₄×Q₈	C₄	1	4	yes	—
9	C₄×Q₈	C₂²	1	4	yes	—
10	C₂×C₄⋊C₄	C₄	1	3	yes	—
11	C₂×C₄²	C₂²	1	3	yes	—
12	C₄⋊C₈	C₂²	1	12	yes	—
13	C₄×C₈	C₂²	1	12	yes	—
14	C₂×Q₈	C₈	1	8	yes	direct product factor
15	C₂×Q₈	C₂×C₄	1	4	yes	—
16	C₂²×C₄	C₂×C₄	1	3	yes	—
17	C₂²×C₄	C₂×C₄	1	3	yes	—
18	C₂²×C₄	C₂³	1	1	yes	characteristic
19	C₂×C₈	—	2	6	no	—
20	C₂×C₈	Q₈	1	4	yes	direct product factor
21	C₂×C₈	C₂³	1	6	yes	—
22	C₂×C₈	C₂³	1	2	yes	—
23	C₄⋊C₄	C₂×C₄	1	12	yes	—
24	C₄²	C₂×C₄	1	6	yes	—
25	C₄²	C₂³	1	6	yes	—
26	C₂³	C₂²×C₄	1	1	yes	characteristic
27	Q₈	C₂×C₈	1	16	yes	direct product factor
28	C₂×C₄	—	2	6	no	—
29	C₂×C₄	C₂×C₈	1	12	yes	—
30	C₂×C₄	C₂²×C₄	1	6	yes	—
31	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄	C₂²×C₄	1	6	yes	—
33	C₂×C₄	C₂×Q₈	1	2	yes	—
34	C₂×C₄	#41	1	2	yes	—
35	C₂×C₄	C₂⁴	1	1	yes	characteristic
36	C₈	—	2	6	no	—
37	C₈	C₂×Q₈	1	4	yes	direct product factor
38	C₂²	C₄×Q₈	1	2	yes	—
39	C₂²	C₂²×C₈	1	2	yes	—
40	C₂²	#131	1	2	yes	—
41	C₂²	C₂³×C₄	1	1	yes	characteristic
42	C₄	—	2	6	no	—
43	C₄	C₄×Q₈	1	2	yes	—
44	C₄	C₂²×C₈	1	12	yes	—
45	C₄	C₂²×Q₈	1	1	yes	characteristic
46	C₄	C₂×#41	1	1	yes	characteristic
47	C₂	C₈×Q₈	1	4	yes	direct product factor
48	C₂	C₂×C₄×Q₈	1	1	yes	characteristic
49	C₂	C₂³×C₈	1	1	yes	characteristic
50	C₂	C₂×#131	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈	C₂²
commutator	C₂	C₂³×C₈
Frattini, cosocle	C₂×C₄	C₂⁴
socle, prime radical	C₂³	C₂²×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈ ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. C₈×Q₈	C₂	direct (N × H)
14. C₂×Q₈	C₈	direct (N × H)
20. C₂×C₈	Q₈	direct (N × H)
27. Q₈	C₂×C₈	direct (N × H)
37. C₈	C₂×Q₈	direct (N × H)
47. C₂	C₈×Q₈	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
C₈×Q₈	2
C₂×C₄⋊C₈	2
C₂×C₄×C₈	2

Subgroups — C2×C8×Q8 #2958

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈×Q₈ #2958