Subgroups — C₂×C₄⋊C₁₆ #2149

Order 128.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₆	C₂	1	2	yes	maximal
2	C₂×C₄×C₈	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₁₆	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₈	C₄	1	1	yes	characteristic
5	C₂²×C₈	C₂²	1	1	yes	characteristic
6	C₂×C₄²	C₄	1	1	yes	characteristic
7	C₂×C₁₆	—	2	4	no	—
8	C₂×C₁₆	C₂²	1	4	yes	—
9	C₄×C₈	C₄	1	2	yes	—
10	C₄×C₈	C₂²	1	2	yes	—
11	C₂²×C₄	C₈	1	1	yes	characteristic
12	C₂²×C₄	C₈	1	1	yes	characteristic
13	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈	—	2	2	no	—
15	C₂×C₈	C₂×C₄	1	2	yes	—
16	C₂×C₈	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈	D₄	1	2	yes	—
18	C₂×C₈	Q₈	1	2	yes	—
19	C₂×C₈	C₂³	1	1	yes	characteristic
20	C₄²	C₈	1	2	yes	—
21	C₄²	C₂×C₄	1	2	yes	—
22	C₁₆	—	2	4	no	—
23	C₂³	C₂×C₈	1	1	yes	characteristic
24	C₂×C₄	—	2	2	no	—
25	C₂×C₄	C₁₆	1	4	yes	complemented
26	C₂×C₄	C₄⋊C₄	1	2	yes	—
27	C₂×C₄	C₂×C₈	1	2	yes	—
28	C₂×C₄	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄	C₂×C₈	1	2	yes	—
30	C₂×C₄	M₁₆	1	2	yes	—
31	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
32	C₈	—	2	2	no	—
33	C₈	C₄⋊C₄	1	2	yes	—
34	C₈	C₂×D₄	1	1	yes	characteristic
35	C₈	C₂×Q₈	1	1	yes	characteristic
36	C₂²	C₄⋊C₈	1	2	yes	—
37	C₂²	C₂×C₁₆	1	2	yes	—
38	C₂²	M₃₂	1	2	yes	—
39	C₂²	C₂²×C₈	1	1	yes	characteristic
40	C₄	—	2	2	no	—
41	C₄	C₄⋊C₈	1	2	yes	—
42	C₄	C₂×C₁₆	1	4	yes	complemented
43	C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
44	C₄	C₂×M₁₆	1	1	yes	characteristic
45	C₂	C₄⋊C₁₆	1	4	yes	direct product factor
46	C₂	C₂×C₄⋊C₈	1	1	yes	characteristic
47	C₂	C₂²×C₁₆	1	1	yes	characteristic
48	C₂	C₂×M₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈	C₂²
commutator	C₂	C₂²×C₁₆
Frattini, cosocle	C₂×C₈	C₂³
socle, prime radical	C₂³	C₂×C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈ ◁ G
LECS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
3. C₄⋊C₁₆	C₂	direct (N × H)
25. C₂×C₄	C₁₆	semidirect
42. C₄	C₂×C₁₆	semidirect
45. C₂	C₄⋊C₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₆	2
C₂×C₄×C₈	2
C₄⋊C₁₆	2

Subgroups — C2×C4⋊C16 #2149

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄⋊C₁₆ #2149