Subgroups — C₂×(C₂²⋊C₂₇)⋊C₂ #88577

Order 432.

79 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂²⋊C₂₇	C₂	1	1	yes	maximal, characteristic, complemented
2	(C₂²⋊C₂₇)⋊C₂	C₂	1	2	yes	maximal, direct product factor
3	C₂×#611	—	3	1	no	maximal
4	C₂×D₂₇	—	4	1	no	maximal
5	C₂²⋊C₂₇	C₂²	1	1	yes	characteristic, complemented
6	C₂³×C₉	D₃	1	1	yes	characteristic
7	C₂²×D₉	—	3	1	no	—
8	#611	—	3	2	no	—
9	#611	—	3	2	no	—
10	C₂×Dic₉	—	3	1	no	—
11	C₂×C₂₇	—	4	1	no	—
12	D₂₇	—	4	2	no	—
13	C₂×#67	—	9	1	no	—
14	C₂²×C₉	—	3	1	no	—
15	C₂²×C₉	—	3	1	no	—
16	C₂²×C₉	C₂×D₃	1	1	yes	characteristic
17	C₂×D₉	—	3	2	no	—
18	C₂×D₉	—	6	1	no	—
19	C₂×D₉	—	6	1	no	—
20	Dic₉	—	3	2	no	—
21	C₂₇	—	4	1	no	Sylow
22	C₂³×C₃	D₉	1	1	yes	characteristic
23	C₂²×D₃	—	9	1	no	—
24	#67	—	9	2	no	—
25	#67	—	9	2	no	—
26	C₂×Dic₃	—	9	1	no	—
27	C₂×C₉	—	3	1	no	—
28	C₂×C₉	—	3	1	no	—
29	C₂×C₉	S₄	1	1	yes	characteristic
30	D₉	—	6	2	no	—
31	C₂×D₄	—	27	1	no	Sylow
32	C₂²×C₃	—	3	1	no	—
33	C₂²×C₃	—	3	1	no	—
34	C₂²×C₃	C₂×D₉	1	1	yes	characteristic
35	C₂×D₃	—	9	2	no	—
36	C₂×D₃	—	18	1	no	—
37	C₂×D₃	—	18	1	no	—
38	Dic₃	—	9	2	no	—
39	C₉	C₂×S₄	1	1	yes	characteristic
40	C₂³	—	27	1	no	—
41	C₂³	D₂₇	1	1	yes	characteristic, complemented
42	D₄	—	27	2	no	—
43	D₄	—	27	2	no	—
44	C₂×C₄	—	27	1	no	—
45	C₂×C₃	—	3	1	no	—
46	C₂×C₃	—	3	1	no	—
47	C₂×C₃	(C₂²⋊C₉)⋊C₂	1	1	yes	characteristic
48	D₃	—	18	2	no	—
49	C₂²	—	3	1	no	—
50	C₂²	—	3	1	no	—
51	C₂²	—	27	2	no	—
52	C₂²	—	54	1	no	—
53	C₂²	—	54	1	no	—
54	C₂²	C₂×D₂₇	1	1	yes	characteristic, complemented
55	C₄	—	27	2	no	—
56	C₃	C₂×(C₂²⋊C₉)⋊C₂	1	1	yes	characteristic
57	C₂	—	3	1	no	—
58	C₂	—	3	1	no	—
59	C₂	—	54	2	no	—
60	C₂	(C₂²⋊C₂₇)⋊C₂	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	(C₂²⋊C₂₇)⋊C₂
commutator, cosocle, hypocenter	C₂²⋊C₂₇	C₂²
Frattini	C₉	C₂×S₄
Fitting	C₂³×C₉	D₃
socle	C₂³×C₃	D₉
LCS	G ▷ C₂²⋊C₂₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₂²⋊C₂₇	C₂	semidirect
2. (C₂²⋊C₂₇)⋊C₂	C₂	direct (N × H)
5. C₂²⋊C₂₇	C₂²	semidirect
41. C₂³	D₂₇	semidirect
54. C₂²	C₂×D₂₇	semidirect
60. C₂	(C₂²⋊C₂₇)⋊C₂	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×C₂²⋊C₂₇	2
(C₂²⋊C₂₇)⋊C₂	2
C₂×#611	3
C₂×D₂₇	4

Subgroups — C2×(C22⋊C27)⋊C2 #88577

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×(C₂²⋊C₂₇)⋊C₂ #88577