Subgroups — C₂×C₃⋊D₂₇ #66384

Order 324.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊D₂₇	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃⋊D₉	—	3	1	no	maximal
4	C₂×D₂₇	—	3	3	no	maximal
5	C₃×C₂₇	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	D₃	1	3	yes	complemented
9	D₂₇	—	3	6	no	—
10	C₂×C₃⋊D₃	—	9	1	no	—
11	C₂×D₉	—	9	2	no	—
12	C₂×D₉	—	9	1	no	—
13	C₃×C₉	C₂×D₃	1	1	yes	characteristic
14	C₂₇	C₂×D₃	1	3	yes	complemented
15	C₂×C₃²	D₉	1	1	yes	characteristic
16	C₃⋊D₃	—	9	2	no	—
17	C₂×C₉	D₉	1	2	yes	—
18	C₂×C₉	C₃⋊D₃	1	1	yes	characteristic
19	D₉	—	9	4	no	—
20	D₉	—	9	2	no	—
21	C₂×D₃	—	27	3	no	—
22	C₂×D₃	—	27	1	no	—
23	C₃²	C₂×D₉	1	1	yes	characteristic
24	C₉	C₂×D₉	1	2	yes	—
25	C₉	C₂×C₃⋊D₃	1	1	yes	characteristic
26	C₂×C₃	D₂₇	1	3	yes	complemented
27	C₂×C₃	C₃⋊D₉	1	1	yes	characteristic
28	D₃	—	27	6	no	—
29	D₃	—	27	2	no	—
30	C₂²	—	81	1	no	Sylow
31	C₃	C₂×D₂₇	1	3	yes	complemented
32	C₃	C₂×C₃⋊D₉	1	1	yes	characteristic
33	C₂	—	81	2	no	—
34	C₂	C₃⋊D₂₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊D₂₇
commutator, cosocle, hypocenter	C₃×C₂₇	C₂²
Frattini	C₉	C₂×C₃⋊D₃
Fitting	C₂×C₃×C₂₇	C₂
socle	C₂×C₃²	D₉
LCS	G ▷ C₃×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.