Subgroups — C₂²×D₂₇ #6186

Order 216.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₂₇	C₂	1	6	yes	maximal, direct product factor
3	C₂²×D₉	—	3	1	no	maximal
4	C₂×C₂₇	C₂²	1	3	yes	complemented
5	D₂₇	C₂²	1	4	yes	direct product factor
6	C₂²×C₉	D₃	1	1	yes	characteristic
7	C₂×D₉	—	3	6	no	—
8	C₂₇	C₂³	1	1	yes	characteristic, complemented, Sylow
9	C₂²×D₃	—	9	1	no	—
10	C₂×C₉	C₂×D₃	1	3	yes	—
11	D₉	—	3	4	no	—
12	C₂²×C₃	D₉	1	1	yes	characteristic
13	C₂×D₃	—	9	6	no	—
14	C₉	C₂²×D₃	1	1	yes	characteristic
15	C₂³	—	27	1	no	Sylow
16	C₂×C₃	C₂×D₉	1	3	yes	—
17	D₃	—	9	4	no	—
18	C₂²	—	27	6	no	—
19	C₂²	D₂₇	1	1	yes	characteristic, direct product factor
20	C₃	C₂²×D₉	1	1	yes	characteristic
21	C₂	—	27	4	no	—
22	C₂	C₂×D₂₇	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²	D₂₇
commutator, cosocle, hypocenter	C₂₇	C₂³
Frattini	C₉	C₂²×D₃
Fitting	C₂²×C₂₇	C₂
socle	C₂²×C₃	D₉
LCS	G ▷ C₂₇
UCS	C₁ ◁ C₂²

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

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