Subgroups — Dic₂₇⋊C₄ #88365

Order 432.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₂₇	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₂₇	C₂	1	1	yes	maximal, characteristic
3	C₂×Dic₂₇	C₂	1	1	yes	maximal, characteristic
4	Dic₉⋊C₄	—	3	1	no	maximal
5	C₂²×C₂₇	C₂²	1	1	yes	characteristic
6	C₄×C₂₇	—	2	1	no	—
7	Dic₂₇	—	2	1	no	—
8	Dic₂₇	C₄	1	2	yes	complemented
9	C₂×C₄×C₉	D₃	1	1	yes	characteristic
10	C₂×Dic₉	—	3	1	no	—
11	C₂×Dic₉	—	3	1	no	—
12	C₂×C₂₇	C₂×C₄	1	1	yes	characteristic
13	C₂×C₂₇	D₄	1	1	yes	characteristic
14	C₂×C₂₇	Q₈	1	1	yes	characteristic
15	Dic₃⋊C₄	—	9	1	no	—
16	C₂²×C₉	C₂×D₃	1	1	yes	characteristic
17	C₄×C₉	—	2	1	no	—
18	Dic₉	—	3	2	no	—
19	Dic₉	—	6	1	no	—
20	C₂₇	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃×C₄	D₉	1	1	yes	characteristic
22	C₂×Dic₃	—	9	1	no	—
23	C₂×Dic₃	—	9	1	no	—
24	C₂×C₉	Dic₆	1	1	yes	characteristic
25	C₂×C₉	C₄×D₃	1	1	yes	characteristic
26	C₂×C₉	#67	1	1	yes	characteristic
27	C₄⋊C₄	—	27	1	no	Sylow
28	C₂²×C₃	C₂×D₉	1	1	yes	characteristic
29	C₃×C₄	—	2	1	no	—
30	Dic₃	—	9	2	no	—
31	Dic₃	—	18	1	no	—
32	C₉	Dic₃⋊C₄	1	1	yes	characteristic
33	C₂×C₄	—	27	1	no	—
34	C₂×C₄	—	27	1	no	—
35	C₂×C₄	D₂₇	1	1	yes	characteristic
36	C₂×C₃	Dic₁₈	1	1	yes	characteristic
37	C₂×C₃	C₄×D₉	1	1	yes	characteristic
38	C₂×C₃	#611	1	1	yes	characteristic
39	C₂²	C₂×D₂₇	1	1	yes	characteristic
40	C₄	—	2	1	no	—
41	C₄	—	27	2	no	—
42	C₄	—	54	1	no	—
43	C₃	Dic₉⋊C₄	1	1	yes	characteristic
44	C₂	Dic₅₄	1	1	yes	characteristic
45	C₂	C₄×D₂₇	1	1	yes	characteristic
46	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, prime radical	C₂²×C₃	C₂×D₉
cosocle	C₂²×C₂₇	C₂²
hypercenter	C₂×C₄	D₂₇
hypocenter	C₂₇	C₄⋊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
8. Dic₂₇	C₄	semidirect
20. C₂₇	C₄⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₂₇	2
C₂×Dic₂₇	2
Dic₉⋊C₄	3

Subgroups — Dic27⋊C4 #88365

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₂₇⋊C₄ #88365