Subgroups — C₂×D₁₀₈ #88398

Order 432.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₂₇	C₂	1	2	yes	maximal, complemented
2	C₂×C₄×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₀₈	C₂	1	4	yes	maximal, direct product factor
4	C₂×D₃₆	—	3	1	no	maximal
5	C₂²×C₂₇	C₂²	1	1	yes	characteristic
6	C₂×D₂₇	—	2	4	no	—
7	C₂×D₂₇	C₂²	1	4	yes	complemented
8	C₄×C₂₇	C₂²	1	2	yes	complemented
9	C₂²×D₉	—	3	2	no	—
10	C₂×C₄×C₉	D₃	1	1	yes	characteristic
11	D₃₆	—	3	4	no	—
12	C₂×C₂₇	D₄	1	2	yes	complemented
13	C₂×C₂₇	C₂³	1	1	yes	characteristic
14	D₂₇	—	2	4	no	—
15	C₂×D₁₂	—	9	1	no	—
16	C₂²×C₉	C₂×D₃	1	1	yes	characteristic
17	C₂×D₉	—	3	4	no	—
18	C₂×D₉	—	6	4	no	—
19	C₄×C₉	C₂×D₃	1	2	yes	—
20	C₂₇	C₂×D₄	1	1	yes	characteristic, complemented, Sylow
21	C₂²×D₃	—	9	2	no	—
22	C₂×C₃×C₄	D₉	1	1	yes	characteristic
23	D₁₂	—	9	4	no	—
24	C₂×C₉	D₁₂	1	2	yes	—
25	C₂×C₉	C₂²×D₃	1	1	yes	characteristic
26	D₉	—	6	4	no	—
27	C₂×D₄	—	27	1	no	Sylow
28	C₂²×C₃	C₂×D₉	1	1	yes	characteristic
29	C₂×D₃	—	9	4	no	—
30	C₂×D₃	—	18	4	no	—
31	C₃×C₄	C₂×D₉	1	2	yes	—
32	C₉	C₂×D₁₂	1	1	yes	characteristic
33	C₂³	—	27	2	no	—
34	D₄	—	27	4	no	—
35	C₂×C₄	D₂₇	1	1	yes	characteristic, complemented
36	C₂×C₃	D₃₆	1	2	yes	—
37	C₂×C₃	C₂²×D₉	1	1	yes	characteristic
38	D₃	—	18	4	no	—
39	C₂²	—	27	4	no	—
40	C₂²	—	54	4	no	—
41	C₂²	C₂×D₂₇	1	1	yes	characteristic
42	C₄	C₂×D₂₇	1	2	yes	complemented
43	C₃	C₂×D₃₆	1	1	yes	characteristic
44	C₂	—	54	4	no	—
45	C₂	D₁₀₈	1	2	yes	direct product factor
46	C₂	C₂²×D₂₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₂₇
commutator, cosocle	C₂×C₂₇	C₂³
Frattini	C₂×C₉	C₂²×D₃
Fitting	C₂×C₄×C₂₇	C₂
socle	C₂²×C₃	C₂×D₉
hypercenter	C₂×C₄	D₂₇
hypocenter	C₂₇	C₂×D₄
LCS	G ▷ C₂×C₂₇ ▷ C₂₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×D₂₇	C₂	semidirect
2. C₂×C₄×C₂₇	C₂	semidirect
3. D₁₀₈	C₂	direct (N × H)
7. C₂×D₂₇	C₂²	semidirect
8. C₄×C₂₇	C₂²	semidirect
12. C₂×C₂₇	D₄	semidirect
20. C₂₇	C₂×D₄	semidirect
35. C₂×C₄	D₂₇	semidirect
42. C₄	C₂×D₂₇	semidirect
45. C₂	D₁₀₈	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×D₂₇	2
C₂×C₄×C₂₇	2
D₁₀₈	2
C₂×D₃₆	3

Subgroups — C2×D108 #88398

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₀₈ #88398