Subgroups — C₂×D₁₁₂ #89674

Order 448.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅₆	C₂	1	2	yes	maximal, complemented
2	C₂×C₇×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₁₂	C₂	1	4	yes	maximal, direct product factor
4	C₂×D₂₈	—	2	2	no	—
5	C₂×C₇×C₈	C₂²	1	1	yes	characteristic
6	D₅₆	—	2	2	no	—
7	D₅₆	C₂²	1	4	yes	complemented
8	C₇×C₁₆	C₂²	1	2	yes	complemented
9	C₂×D₁₆	—	7	1	no	maximal, Sylow
10	C₂²×D₇	—	4	2	no	—
11	C₂×C₄×C₇	D₄	1	1	yes	characteristic
12	D₂₈	—	2	4	no	—
13	D₂₈	—	4	2	no	—
14	C₇×C₈	D₄	1	1	yes	characteristic
15	C₇×C₈	C₂³	1	1	yes	characteristic
16	C₂×D₈	—	7	2	no	—
17	D₁₆	—	7	4	no	—
18	C₂×C₁₆	D₇	1	1	yes	characteristic, complemented
19	C₂²×C₇	D₈	1	1	yes	characteristic
20	C₂×D₇	—	4	4	no	—
21	C₂×D₇	—	8	4	no	—
22	C₄×C₇	D₈	1	1	yes	characteristic
23	C₄×C₇	C₂×D₄	1	1	yes	characteristic
24	C₂×D₄	—	14	2	no	—
25	D₈	—	7	4	no	—
26	D₈	—	14	2	no	—
27	C₂×C₈	C₂×D₇	1	1	yes	characteristic
28	C₁₆	C₂×D₇	1	2	yes	complemented
29	C₂×C₇	D₁₆	1	2	yes	complemented
30	C₂×C₇	C₂×D₈	1	1	yes	characteristic
31	D₇	—	8	4	no	—
32	C₂³	—	28	2	no	—
33	D₄	—	14	4	no	—
34	D₄	—	28	2	no	—
35	C₂×C₄	D₂₈	1	1	yes	characteristic
36	C₈	D₂₈	1	1	yes	characteristic
37	C₈	C₂²×D₇	1	1	yes	characteristic
38	C₇	C₂×D₁₆	1	1	yes	characteristic, complemented, Sylow
39	C₂²	—	28	4	no	—
40	C₂²	—	56	4	no	—
41	C₂²	D₅₆	1	1	yes	characteristic
42	C₄	D₅₆	1	1	yes	characteristic
43	C₄	C₂×D₂₈	1	1	yes	characteristic
44	C₂	—	56	4	no	—
45	C₂	D₁₁₂	1	2	yes	direct product factor
46	C₂	C₂×D₅₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₅₆
commutator, cosocle	C₇×C₈	C₂³
Frattini	C₈	C₂²×D₇
Fitting	C₂×C₇×C₁₆	C₂
socle	C₂²×C₇	D₈
hypercenter	C₂×C₁₆	D₇
hypocenter	C₇	C₂×D₁₆
LCS	G ▷ C₇×C₈ ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×D₅₆	C₂	semidirect
2. C₂×C₇×C₁₆	C₂	semidirect
3. D₁₁₂	C₂	direct (N × H)
7. D₅₆	C₂²	semidirect
8. C₇×C₁₆	C₂²	semidirect
18. C₂×C₁₆	D₇	semidirect
28. C₁₆	C₂×D₇	semidirect
29. C₂×C₇	D₁₆	semidirect
38. C₇	C₂×D₁₆	semidirect
45. C₂	D₁₁₂	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×D₅₆	2
C₂×C₇×C₁₆	2
D₁₁₂	2
C₂×D₁₆	7

Subgroups — C2×D112 #89674

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₁₂ #89674