Subgroups — C₂₇×#127 #11720216

Order 864.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₂₇	C₂	1	6	yes	maximal, complemented
2	C₄²×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#127	C₃	1	1	yes	maximal, characteristic
4	C₂³×C₂₇	C₂²	1	4	yes	—
5	D₄×C₂₇	—	2	12	no	—
6	C₂×C₄×C₂₇	C₂²	1	3	yes	—
7	C₂×D₄×C₉	C₂×C₃	1	6	yes	—
8	C₄²×C₉	C₂×C₃	1	1	yes	characteristic
9	C₂²×C₂₇	—	2	12	no	—
10	C₂²×C₂₇	C₂³	1	1	yes	characteristic
11	C₄×C₂₇	D₄	1	6	yes	complemented
12	C₃×#127	C₉	1	1	yes	characteristic
13	C₂³×C₉	C₂²×C₃	1	4	yes	—
14	D₄×C₉	—	2	12	no	—
15	C₂×C₄×C₉	C₂²×C₃	1	3	yes	—
16	C₂×C₂₇	—	4	4	no	—
17	C₂×C₂₇	C₂×D₄	1	3	yes	—
18	C₂×C₃×D₄	C₂×C₉	1	6	yes	—
19	C₃×C₄²	C₂×C₉	1	1	yes	characteristic
20	C₂²×C₉	—	2	12	no	—
21	C₂²×C₉	C₂³×C₃	1	1	yes	characteristic
22	C₄×C₉	C₃×D₄	1	6	yes	—
23	#127	C₂₇	1	1	yes	characteristic, direct product factor, Sylow
24	C₂₇	#127	1	1	yes	characteristic, direct product factor, Sylow
25	C₂³×C₃	C₂²×C₉	1	4	yes	—
26	C₃×D₄	—	2	12	no	—
27	C₂×C₃×C₄	C₂²×C₉	1	3	yes	—
28	C₂×C₉	—	4	4	no	—
29	C₂×C₉	C₂×C₃×D₄	1	3	yes	—
30	C₂×D₄	C₂×C₂₇	1	6	yes	complemented
31	C₄²	C₂×C₂₇	1	1	yes	characteristic, complemented
32	C₂²×C₃	—	2	12	no	—
33	C₂²×C₃	C₂³×C₉	1	1	yes	characteristic
34	C₃×C₄	D₄×C₉	1	6	yes	—
35	C₉	C₃×#127	1	1	yes	characteristic
36	C₂³	C₂²×C₂₇	1	4	yes	—
37	D₄	—	2	12	no	—
38	C₂×C₄	C₂²×C₂₇	1	3	yes	—
39	C₂×C₃	—	4	4	no	—
40	C₂×C₃	C₂×D₄×C₉	1	3	yes	—
41	C₂²	—	2	12	no	—
42	C₂²	C₂³×C₂₇	1	1	yes	characteristic
43	C₄	D₄×C₂₇	1	6	yes	complemented
44	C₃	C₉×#127	1	1	yes	characteristic
45	C₂	—	4	4	no	—
46	C₂	C₂×D₄×C₂₇	1	3	yes	—

	subgroup	G/H
center	C₂²×C₂₇	C₂³
commutator	C₂²	C₂³×C₂₇
Frattini, cosocle	C₂²×C₉	C₂³×C₃
socle	C₂²×C₃	C₂³×C₉
prime radical	C₃×#127	C₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×D₄×C₂₇	C₂	semidirect
2. C₄²×C₂₇	C₂	semidirect
11. C₄×C₂₇	D₄	semidirect
23. #127	C₂₇	direct (N × H)
24. C₂₇	#127	direct (N × H)
30. C₂×D₄	C₂×C₂₇	semidirect
31. C₄²	C₂×C₂₇	semidirect
43. C₄	D₄×C₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×C₂₇	2
C₄²×C₂₇	2
C₉×#127	3

Subgroups — C27×#127 #11720216

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₇×#127 #11720216