Subgroups — (C₃×A₄)⋊C₂₇ #11757426

Order 972.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×A₄	C₃	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₂₇	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×C₂²⋊C₂₇	C₃	1	2	yes	maximal, complemented
4	C₃²⋊C₂₇	—	4	1	no	maximal, Sylow
5	C₂×C₃×C₂₇	—	3	1	no	—
6	C₃²×A₄	C₉	1	1	yes	characteristic
7	C₂²×C₃×C₉	C₃²	1	1	yes	characteristic
8	C₃×C₂²⋊C₉	C₉	1	2	yes	—
9	C₉×A₄	—	3	1	no	—
10	C₉×A₄	—	3	2	no	—
11	C₂²×C₂₇	—	3	1	no	—
12	C₂²⋊C₂₇	—	3	2	no	—
13	C₃²×C₉	—	4	1	no	—
14	C₃×C₂₇	—	4	2	no	—
15	C₃×C₂₇	A₄	1	1	yes	characteristic, complemented
16	C₂×C₃×C₉	—	3	1	no	—
17	C₂×C₂₇	—	3	3	no	—
18	C₂²×C₃²	C₃×C₉	1	1	yes	characteristic
19	C₃×A₄	—	3	1	no	—
20	C₃×A₄	—	3	2	no	—
21	C₃×A₄	C₂₇	1	3	yes	complemented
22	C₂²×C₉	H(3,𝔽₃)	1	1	yes	characteristic
23	C₂²×C₉	3₋¹⁺²	1	2	yes	—
24	C₂²⋊C₉	—	3	2	no	—
25	C₃³	—	4	1	no	—
26	C₃×C₉	—	4	2	no	—
27	C₃×C₉	—	12	2	no	—
28	C₃×C₉	—	12	1	no	—
29	C₃×C₉	C₃×A₄	1	1	yes	characteristic
30	C₂₇	—	3	1	no	—
31	C₂₇	—	12	2	no	—
32	C₂×C₃²	—	3	1	no	—
33	C₂×C₉	—	3	2	no	—
34	C₂×C₉	—	3	1	no	—
35	C₂²×C₃	C₃²⋊C₉	1	1	yes	characteristic
36	C₂²×C₃	C₃×C₂₇	1	1	yes	characteristic
37	C₂²×C₃	C₂₇⋊C₃	1	2	yes	—
38	A₄	—	3	3	no	—
39	C₃²	—	4	3	no	—
40	C₃²	—	12	2	no	—
41	C₃²	—	12	1	no	—
42	C₃²	C₉×A₄	1	1	yes	characteristic
43	C₉	—	12	2	no	—
44	C₉	C₉⋊A₄	1	2	yes	—
45	C₉	C₂²⋊H(3,𝔽₃)	1	1	yes	characteristic
46	C₂×C₃	—	3	1	no	—
47	C₂×C₃	—	3	2	no	—
48	C₂×C₃	—	3	1	no	—
49	C₂²	C₃²⋊C₂₇	1	1	yes	characteristic, complemented, Sylow
50	C₃	—	12	3	no	—
51	C₃	A₄×C₂₇	1	1	yes	characteristic
52	C₃	C₂₇⋊A₄	1	2	yes	—
53	C₃	(C₃×A₄)⋊C₉	1	1	yes	characteristic
54	C₂	—	3	1	no	—

	subgroup	G/H
center, Frattini	C₃×C₉	C₃×A₄
commutator	C₂²×C₃	C₃×C₂₇
Fitting	C₂²×C₃×C₂₇	C₃
socle	C₂²×C₃²	C₃×C₉
prime radical	C₃²×A₄	C₉
cosocle	C₂²×C₃×C₉	C₃²
hypercenter	C₃×C₂₇	A₄
hypocenter	C₂²	C₃²⋊C₂₇
LCS	G ▷ C₂²×C₃ ▷ C₂²
UCS	C₁ ◁ C₃×C₉ ◁ C₃×C₂₇

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×C₂₇	C₃	semidirect
3. C₃×C₂²⋊C₂₇	C₃	semidirect
15. C₃×C₂₇	A₄	semidirect
21. C₃×A₄	C₂₇	semidirect
49. C₂²	C₃²⋊C₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×A₄	3
C₂²×C₃×C₂₇	3
C₃×C₂²⋊C₂₇	3
C₃²⋊C₂₇	4

Subgroups — (C3×A4)⋊C27 #11757426

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₃×A₄)⋊C₂₇ #11757426