Subgroups — C₂²×C₂²⋊C₈ #2876

Order 128.

536 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₄	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₈	C₂	1	2	yes	maximal, complemented
3	C₂×C₂²⋊C₈	C₂	1	12	yes	maximal, direct product factor
4	C₂⁵	C₄	1	1	yes	characteristic
5	C₂³×C₄	—	2	8	no	—
6	C₂³×C₄	C₄	1	1	yes	characteristic
7	C₂³×C₄	C₄	1	6	yes	—
8	C₂³×C₄	C₂²	1	6	yes	—
9	C₂³×C₄	C₂²	1	1	yes	characteristic
10	C₂²×C₈	—	2	8	no	—
11	C₂²×C₈	C₂²	1	12	yes	complemented
12	C₂²⋊C₈	C₂²	1	16	yes	direct product factor
13	C₂⁴	—	2	4	no	—
14	C₂⁴	—	2	4	no	—
15	C₂⁴	C₈	1	8	yes	complemented
16	C₂⁴	C₂×C₄	1	6	yes	—
17	C₂⁴	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₄	—	2	4	no	—
19	C₂²×C₄	—	2	24	no	—
20	C₂²×C₄	—	2	24	no	—
21	C₂²×C₄	C₂×C₄	1	6	yes	—
22	C₂²×C₄	C₂×C₄	1	12	yes	—
23	C₂²×C₄	C₂×C₄	1	3	yes	—
24	C₂²×C₄	D₄	1	8	yes	—
25	C₂²×C₄	C₂³	1	4	yes	—
26	C₂²×C₄	C₂³	1	3	yes	—
27	C₂×C₈	—	2	24	no	—
28	C₂×C₈	C₂³	1	8	yes	complemented
29	C₂³	—	2	32	no	—
30	C₂³	—	2	12	no	—
31	C₂³	—	2	12	no	—
32	C₂³	C₂²⋊C₄	1	4	yes	—
33	C₂³	C₂×C₈	1	4	yes	—
34	C₂³	C₂×C₈	1	24	yes	complemented
35	C₂³	M₁₆	1	4	yes	—
36	C₂³	C₂²×C₄	1	4	yes	—
37	C₂³	C₂²×C₄	1	3	yes	—
38	C₂×C₄	—	2	12	no	—
39	C₂×C₄	—	2	24	no	—
40	C₂×C₄	—	2	8	no	—
41	C₂×C₄	C₂²⋊C₄	1	12	yes	—
42	C₂×C₄	C₂²×C₄	1	4	yes	—
43	C₂×C₄	C₂²×C₄	1	3	yes	—
44	C₂×C₄	C₂×D₄	1	12	yes	—
45	C₂×C₄	C₂⁴	1	1	yes	characteristic
46	C₈	—	2	8	no	—
47	C₂²	—	2	4	no	—
48	C₂²	—	2	4	no	—
49	C₂²	—	2	48	no	—
50	C₂²	C₂²⋊C₈	1	16	yes	direct product factor
51	C₂²	C₂×C₂²⋊C₄	1	6	yes	—
52	C₂²	C₂²×C₈	1	6	yes	—
53	C₂²	C₂²×C₈	1	8	yes	complemented
54	C₂²	C₂×M₁₆	1	6	yes	—
55	C₂²	C₂³×C₄	1	1	yes	characteristic
56	C₄	—	2	4	no	—
57	C₄	C₂×C₂²⋊C₄	1	6	yes	—
58	C₄	C₂²×D₄	1	2	yes	—
59	C₂	—	2	8	no	—
60	C₂	C₂×C₂²⋊C₈	1	12	yes	direct product factor
61	C₂	C₂²×C₂²⋊C₄	1	1	yes	characteristic
62	C₂	C₂³×C₈	1	1	yes	characteristic
63	C₂	C₂²×M₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	C₂²
commutator	C₂	C₂³×C₈
Frattini, cosocle	C₂×C₄	C₂⁴
socle	C₂⁴	C₂×C₄
prime radical	C₂⁵	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
2. C₂³×C₈	C₂	semidirect
3. C₂×C₂²⋊C₈	C₂	direct (N × H)
11. C₂²×C₈	C₂²	semidirect
12. C₂²⋊C₈	C₂²	direct (N × H)
15. C₂⁴	C₈	semidirect
28. C₂×C₈	C₂³	semidirect
34. C₂³	C₂×C₈	semidirect
50. C₂²	C₂²⋊C₈	direct (N × H)
53. C₂²	C₂²×C₈	semidirect
60. C₂	C₂×C₂²⋊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
C₂⁴×C₄	2
C₂³×C₈	2
C₂×C₂²⋊C₈	2

Subgroups — C22×C22⋊C8 #2876

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₂²⋊C₈ #2876