Subgroups — C₂²⋊C₄×C₂₇ #88374

Order 432.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂²×C₂₇	C₂²
commutator	C₂	C₂×C₄×C₂₇
Frattini, cosocle	C₂²×C₉	C₂²×C₃
socle	C₂²×C₃	C₂²×C₉
prime radical	C₂³×C₃	C₂×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
2. C₂×C₄×C₂₇	C₂	semidirect
5. C₂²×C₂₇	C₄	semidirect
18. C₂₇	C₂²⋊C₄	direct (N × H)
24. C₂²⋊C₄	C₂₇	direct (N × H)
31. C₂×C₄	C₂×C₂₇	semidirect
36. C₂²	C₄×C₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₂₇	2
C₂×C₄×C₂₇	2
C₉×C₂²⋊C₄	3

Subgroups — C22⋊C4×C27 #88374

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊C₄×C₂₇ #88374