Subgroups — C₂³×D₂₇ #88580

Order 432.

268 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₂₇	C₂	1	14	yes	maximal, direct product factor
3	C₂³×D₉	—	3	1	no	maximal
4	C₂²×C₂₇	C₂²	1	7	yes	complemented
5	C₂×D₂₇	C₂²	1	28	yes	direct product factor
6	C₂³×C₉	D₃	1	1	yes	characteristic
7	C₂²×D₉	—	3	14	no	—
8	C₂×C₂₇	C₂³	1	7	yes	complemented
9	D₂₇	C₂³	1	8	yes	direct product factor
10	C₂³×D₃	—	9	1	no	—
11	C₂²×C₉	C₂×D₃	1	7	yes	—
12	C₂×D₉	—	3	28	no	—
13	C₂₇	C₂⁴	1	1	yes	characteristic, complemented, Sylow
14	C₂³×C₃	D₉	1	1	yes	characteristic
15	C₂²×D₃	—	9	14	no	—
16	C₂×C₉	C₂²×D₃	1	7	yes	—
17	D₉	—	3	8	no	—
18	C₂⁴	—	27	1	no	Sylow
19	C₂²×C₃	C₂×D₉	1	7	yes	—
20	C₂×D₃	—	9	28	no	—
21	C₉	C₂³×D₃	1	1	yes	characteristic
22	C₂³	—	27	14	no	—
23	C₂³	D₂₇	1	1	yes	characteristic, direct product factor
24	C₂×C₃	C₂²×D₉	1	7	yes	—
25	D₃	—	9	8	no	—
26	C₂²	—	27	28	no	—
27	C₂²	C₂×D₂₇	1	7	yes	direct product factor
28	C₃	C₂³×D₉	1	1	yes	characteristic
29	C₂	—	27	8	no	—
30	C₂	C₂²×D₂₇	1	7	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂³	D₂₇
commutator, cosocle, hypocenter	C₂₇	C₂⁴
Frattini	C₉	C₂³×D₃
Fitting	C₂³×C₂₇	C₂
socle	C₂³×C₃	D₉
LCS	G ▷ C₂₇
UCS	C₁ ◁ C₂³

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.