Subgroups — (C₂×D₂₇)⋊C₄ #88367

Order 432.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₂₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×Dic₂₇	C₂	1	1	yes	maximal, characteristic, complemented
4	(C₂×D₉)⋊C₄	—	3	1	no	maximal
5	C₂²×C₂₇	C₂²	1	1	yes	characteristic
6	C₂×D₂₇	—	2	1	no	—
7	C₂×D₂₇	—	2	1	no	—
8	C₂×D₂₇	C₄	1	2	yes	complemented
9	C₄×C₂₇	—	2	1	no	—
10	Dic₂₇	—	2	1	no	—
11	C₂²×D₉	—	3	1	no	—
12	C₂×C₄×C₉	D₃	1	1	yes	characteristic
13	C₂×Dic₉	—	3	1	no	—
14	C₂×C₂₇	C₂×C₄	1	1	yes	characteristic
15	C₂×C₂₇	D₄	1	1	yes	characteristic
16	C₂×C₂₇	D₄	1	1	yes	characteristic
17	D₂₇	—	2	2	no	—
18	(C₂×D₃)⋊C₄	—	9	1	no	—
19	C₂²×C₉	C₂×D₃	1	1	yes	characteristic
20	C₂×D₉	—	3	2	no	—
21	C₂×D₉	—	6	1	no	—
22	C₂×D₉	—	6	1	no	—
23	C₄×C₉	—	2	1	no	—
24	Dic₉	—	6	1	no	—
25	C₂₇	C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
26	C₂²×D₃	—	9	1	no	—
27	C₂×C₃×C₄	D₉	1	1	yes	characteristic
28	C₂×Dic₃	—	9	1	no	—
29	C₂×C₉	C₄×D₃	1	1	yes	characteristic
30	C₂×C₉	D₁₂	1	1	yes	characteristic
31	C₂×C₉	#67	1	1	yes	characteristic
32	D₉	—	6	2	no	—
33	C₂²⋊C₄	—	27	1	no	Sylow
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	C₃×C₄	—	2	1	no	—
39	Dic₃	—	18	1	no	—
40	C₉	(C₂×D₃)⋊C₄	1	1	yes	characteristic
41	C₂³	—	27	1	no	—
42	C₂×C₄	—	27	1	no	—
43	C₂×C₄	D₂₇	1	1	yes	characteristic, complemented
44	C₂×C₃	C₄×D₉	1	1	yes	characteristic
45	C₂×C₃	D₃₆	1	1	yes	characteristic
46	C₂×C₃	#611	1	1	yes	characteristic
47	D₃	—	18	2	no	—
48	C₂²	—	27	2	no	—
49	C₂²	—	54	1	no	—
50	C₂²	—	54	1	no	—
51	C₂²	C₂×D₂₇	1	1	yes	characteristic
52	C₄	—	2	1	no	—
53	C₄	—	54	1	no	—
54	C₃	(C₂×D₉)⋊C₄	1	1	yes	characteristic
55	C₂	—	54	2	no	—
56	C₂	C₄×D₂₇	1	1	yes	characteristic
57	C₂	D₁₀₈	1	1	yes	characteristic
58	C₂	#6171	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₂₇
commutator	C₂×C₂₇	C₂×C₄
Frattini	C₂²×C₉	C₂×D₃
Fitting	C₂×C₄×C₂₇	C₂
socle	C₂²×C₃	C₂×D₉
prime radical	C₂²×D₂₇	C₂
cosocle	C₂²×C₂₇	C₂²
hypercenter	C₂×C₄	D₂₇
hypocenter	C₂₇	C₂²⋊C₄
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
2. C₂×C₄×C₂₇	C₂	semidirect
3. C₂×Dic₂₇	C₂	semidirect
8. C₂×D₂₇	C₄	semidirect
25. C₂₇	C₂²⋊C₄	semidirect
43. C₂×C₄	D₂₇	semidirect

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
C₂×Dic₂₇	2
(C₂×D₉)⋊C₄	3

Subgroups — (C2×D27)⋊C4 #88367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₂×D₂₇)⋊C₄ #88367