Subgroups — C₂×D₄×C₂₇ #88407

Order 432.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂²×C₂₇	C₂²
commutator	C₂	C₂³×C₂₇
Frattini, cosocle	C₂×C₉	C₂³×C₃
socle	C₂²×C₃	C₂²×C₉
prime radical	C₂×C₃×D₄	C₉
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₂₇	C₂	semidirect
2. D₄×C₂₇	C₂	direct (N × H)
3. C₂×C₄×C₂₇	C₂	semidirect
7. C₂²×C₂₇	C₂²	semidirect
8. C₄×C₂₇	C₂²	semidirect
13. C₂×C₂₇	D₄	direct (N × H)
20. C₂₇	C₂×D₄	direct (N × H)
27. C₂×D₄	C₂₇	direct (N × H)
33. C₂³	C₂×C₂₇	semidirect
34. D₄	C₂×C₂₇	direct (N × H)
35. C₂×C₄	C₂×C₂₇	semidirect
41. C₂²	C₂²×C₂₇	semidirect
42. C₄	C₂²×C₂₇	semidirect
45. C₂	D₄×C₂₇	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×C₂₇	2
D₄×C₂₇	2
C₂×C₄×C₂₇	2
C₂×D₄×C₉	3

Subgroups — C2×D4×C27 #88407

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄×C₂₇ #88407