Subgroups — C₂²×C₄⋊C₈ #2902

Order 128.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₈	C₂	1	2	yes	maximal
2	C₂²×C₄²	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊C₈	C₂	1	12	yes	maximal, direct product factor
4	C₂³×C₄	C₄	1	1	yes	characteristic
5	C₂³×C₄	C₄	1	1	yes	characteristic
6	C₂³×C₄	C₂²	1	1	yes	characteristic
7	C₂²×C₈	—	2	8	no	—
8	C₂²×C₈	C₂²	1	12	yes	—
9	C₂×C₄²	C₄	1	6	yes	—
10	C₂×C₄²	C₂²	1	6	yes	—
11	C₄⋊C₈	C₂²	1	16	yes	direct product factor
12	C₂⁴	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₄	—	2	4	no	—
14	C₂²×C₄	C₈	1	8	yes	complemented
15	C₂²×C₄	C₂×C₄	1	6	yes	—
16	C₂²×C₄	C₂×C₄	1	3	yes	—
17	C₂²×C₄	C₂×C₄	1	6	yes	—
18	C₂²×C₄	D₄	1	4	yes	—
19	C₂²×C₄	Q₈	1	4	yes	—
20	C₂²×C₄	C₂³	1	3	yes	—
21	C₂×C₈	—	2	24	no	—
22	C₂×C₈	C₂³	1	8	yes	—
23	C₄²	C₂×C₄	1	12	yes	—
24	C₄²	C₂³	1	4	yes	—
25	C₂³	C₄⋊C₄	1	4	yes	—
26	C₂³	C₂×C₈	1	4	yes	—
27	C₂³	M₁₆	1	4	yes	—
28	C₂³	C₂²×C₄	1	3	yes	—
29	C₂×C₄	—	2	12	no	—
30	C₂×C₄	C₄⋊C₄	1	12	yes	—
31	C₂×C₄	C₂×C₈	1	24	yes	complemented
32	C₂×C₄	C₂²×C₄	1	4	yes	—
33	C₂×C₄	C₂²×C₄	1	3	yes	—
34	C₂×C₄	C₂²×C₄	1	4	yes	—
35	C₂×C₄	C₂×D₄	1	6	yes	—
36	C₂×C₄	C₂×Q₈	1	6	yes	—
37	C₂×C₄	C₂⁴	1	1	yes	characteristic
38	C₈	—	2	8	no	—
39	C₂²	C₄⋊C₈	1	16	yes	direct product factor
40	C₂²	C₂×C₄⋊C₄	1	6	yes	—
41	C₂²	C₂²×C₈	1	6	yes	—
42	C₂²	C₂×M₁₆	1	6	yes	—
43	C₂²	C₂³×C₄	1	1	yes	characteristic
44	C₄	—	2	4	no	—
45	C₄	C₂×C₄⋊C₄	1	6	yes	—
46	C₄	C₂²×C₈	1	8	yes	complemented
47	C₄	C₂²×D₄	1	1	yes	characteristic
48	C₄	C₂²×Q₈	1	1	yes	characteristic
49	C₂	C₂×C₄⋊C₈	1	12	yes	direct product factor
50	C₂	C₂²×C₄⋊C₄	1	1	yes	characteristic
51	C₂	C₂³×C₈	1	1	yes	characteristic
52	C₂	C₂²×M₁₆	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₂×C₄⋊C₈	C₂	direct (N × H)
11. C₄⋊C₈	C₂²	direct (N × H)
14. C₂²×C₄	C₈	semidirect
31. C₂×C₄	C₂×C₈	semidirect
39. C₂²	C₄⋊C₈	direct (N × H)
46. C₄	C₂²×C₈	semidirect
49. C₂	C₂×C₄⋊C₈	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₈	2
C₂²×C₄²	2
C₂×C₄⋊C₈	2

Subgroups — C22×C4⋊C8 #2902

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄⋊C₈ #2902