Subgroups — C₂×D₂₇⋊C₃ #66375

Order 324.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₂₇⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×D₉	—	3	1	no	maximal
4	C₂×D₂₇	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂₇⋊C₃	C₂²	1	1	yes	characteristic, complemented, Sylow
6	C₂×C₃×C₉	D₃	1	1	yes	characteristic
7	C₃×D₉	—	3	2	no	—
8	C₂×C₂₇	—	2	1	no	—
9	C₂×C₂₇	C₂×C₃	1	1	yes	characteristic, complemented
10	D₂₇	C₂×C₃	1	2	yes	complemented
11	C₂×C₃×D₃	—	9	1	no	—
12	C₂×D₉	—	3	1	no	—
13	C₃×C₉	C₂×D₃	1	1	yes	characteristic
14	C₂₇	—	2	1	no	—
15	C₂₇	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₂×C₃²	D₉	1	1	yes	characteristic
17	C₃×D₃	—	9	2	no	—
18	C₂×C₉	—	2	1	no	—
19	C₂×C₉	C₃×D₃	1	1	yes	characteristic
20	D₉	—	3	2	no	—
21	C₂²×C₃	—	27	1	no	—
22	C₂×D₃	—	9	1	no	—
23	C₃²	C₂×D₉	1	1	yes	characteristic
24	C₉	—	2	1	no	—
25	C₉	C₂×C₃×D₃	1	1	yes	characteristic
26	C₂×C₃	—	3	1	no	—
27	C₂×C₃	—	27	2	no	—
28	C₂×C₃	C₃×D₉	1	1	yes	characteristic
29	D₃	—	9	2	no	—
30	C₂²	—	27	1	no	Sylow
31	C₃	—	3	1	no	—
32	C₃	C₂×C₃×D₉	1	1	yes	characteristic
33	C₂	—	27	2	no	—
34	C₂	D₂₇⋊C₃	1	1	yes	characteristic, direct product factor

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

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.