Subgroups — C₄⋊(C₃⋊(C₃⋊D₂₇)) #14517733

Order 1944.

576 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊(C₃⋊D₂₇)	C₂	1	2	yes	maximal, complemented
2	C₃²×C₄×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊(C₃⋊(C₃⋊D₉))	—	3	1	no	maximal
4	C₄⋊(C₃⋊D₂₇)	—	3	12	no	maximal
5	C₂×C₃²×C₂₇	C₂²	1	1	yes	characteristic
6	C₃⋊(C₃⋊D₂₇)	—	2	2	no	—
7	C₂×C₃⋊(C₃⋊D₉)	—	3	2	no	—
8	C₃²×C₄×C₉	D₃	1	1	yes	characteristic
9	C₂×C₃⋊D₂₇	—	3	24	no	—
10	C₃×C₄×C₂₇	D₃	1	12	yes	complemented
11	C₃²×C₂₇	D₄	1	1	yes	characteristic, complemented, Sylow
12	C₄⋊(C₃⋊(C₃⋊D₃))	—	9	1	no	—
13	C₄⋊(C₃⋊D₉)	—	9	8	no	—
14	C₄⋊(C₃⋊D₉)	—	9	4	no	—
15	D₁₀₈	—	9	9	no	—
16	C₂×C₃²×C₉	C₂×D₃	1	1	yes	characteristic
17	C₃⋊(C₃⋊D₉)	—	6	2	no	—
18	C₂×C₃×C₂₇	C₂×D₃	1	12	yes	—
19	C₃⋊D₂₇	—	6	24	no	—
20	C₂×C₃⋊(C₃⋊D₃)	—	9	2	no	—
21	C₃³×C₄	D₉	1	1	yes	characteristic
22	C₂×C₃⋊D₉	—	9	16	no	—
23	C₂×C₃⋊D₉	—	9	8	no	—
24	C₃×C₄×C₉	D₉	1	8	yes	—
25	C₃×C₄×C₉	C₃⋊D₃	1	4	yes	—
26	C₂×D₂₇	—	9	18	no	—
27	C₄×C₂₇	C₃⋊D₃	1	9	yes	complemented
28	C₃²×C₉	D₁₂	1	1	yes	characteristic
29	C₃×C₂₇	D₁₂	1	12	yes	complemented
30	C₄⋊(C₃⋊D₃)	—	27	9	no	—
31	C₄⋊(C₃⋊D₃)	—	27	4	no	—
32	D₃₆	—	27	8	no	—
33	D₃₆	—	27	1	no	—
34	C₂×C₃³	C₂×D₉	1	1	yes	characteristic
35	C₃⋊(C₃⋊D₃)	—	18	2	no	—
36	C₂×C₃×C₉	C₂×D₉	1	8	yes	—
37	C₂×C₃×C₉	C₂×C₃⋊D₃	1	4	yes	—
38	C₃⋊D₉	—	18	16	no	—
39	C₃⋊D₉	—	18	8	no	—
40	C₂×C₂₇	C₂×C₃⋊D₃	1	9	yes	—
41	D₂₇	—	18	18	no	—
42	C₂×C₃⋊D₃	—	27	18	no	—
43	C₂×C₃⋊D₃	—	27	8	no	—
44	C₃²×C₄	D₂₇	1	9	yes	complemented
45	C₃²×C₄	C₃⋊D₉	1	4	yes	—
46	C₂×D₉	—	27	16	no	—
47	C₂×D₉	—	27	2	no	—
48	C₄×C₉	C₃⋊D₉	1	8	yes	—
49	C₄×C₉	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
50	C₃³	D₃₆	1	1	yes	characteristic
51	C₃×C₉	D₃₆	1	8	yes	—
52	C₃×C₉	C₄⋊(C₃⋊D₃)	1	4	yes	—
53	C₂₇	C₄⋊(C₃⋊D₃)	1	9	yes	complemented
54	D₁₂	—	81	12	no	—
55	D₁₂	—	81	1	no	—
56	C₂×C₃²	C₂×D₂₇	1	9	yes	—
57	C₂×C₃²	C₂×C₃⋊D₉	1	4	yes	—
58	C₃⋊D₃	—	54	18	no	—
59	C₃⋊D₃	—	54	8	no	—
60	C₂×C₉	C₂×C₃⋊D₉	1	8	yes	—
61	C₂×C₉	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
62	D₉	—	54	16	no	—
63	D₉	—	54	2	no	—
64	C₂×D₃	—	81	24	no	—
65	C₂×D₃	—	81	2	no	—
66	C₃×C₄	C₃⋊D₂₇	1	12	yes	complemented
67	C₃×C₄	C₃⋊(C₃⋊D₉)	1	1	yes	characteristic
68	C₃²	D₁₀₈	1	9	yes	complemented
69	C₃²	C₄⋊(C₃⋊D₉)	1	4	yes	—
70	C₉	C₄⋊(C₃⋊D₉)	1	8	yes	—
71	C₉	C₄⋊(C₃⋊(C₃⋊D₃))	1	1	yes	characteristic
72	D₄	—	243	1	no	Sylow
73	C₂×C₃	C₂×C₃⋊D₂₇	1	12	yes	—
74	C₂×C₃	C₂×C₃⋊(C₃⋊D₉)	1	1	yes	characteristic
75	D₃	—	162	24	no	—
76	D₃	—	162	2	no	—
77	C₂²	—	243	2	no	—
78	C₄	C₃⋊(C₃⋊D₂₇)	1	1	yes	characteristic, complemented
79	C₃	C₄⋊(C₃⋊D₂₇)	1	12	yes	complemented
80	C₃	C₄⋊(C₃⋊(C₃⋊D₉))	1	1	yes	characteristic
81	C₂	—	486	2	no	—
82	C₂	C₂×C₃⋊(C₃⋊D₂₇)	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₃⋊(C₃⋊D₂₇)
commutator, cosocle	C₂×C₃²×C₂₇	C₂²
Frattini	C₂×C₉	C₂×C₃⋊(C₃⋊D₃)
Fitting	C₃²×C₄×C₂₇	C₂
socle	C₂×C₃³	C₂×D₉
hypercenter	C₄	C₃⋊(C₃⋊D₂₇)
hypocenter	C₃²×C₂₇	D₄
LCS	G ▷ C₂×C₃²×C₂₇ ▷ C₃²×C₂₇
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₃⋊(C₃⋊D₂₇)	C₂	semidirect
2. C₃²×C₄×C₂₇	C₂	semidirect
10. C₃×C₄×C₂₇	D₃	semidirect
11. C₃²×C₂₇	D₄	semidirect
27. C₄×C₂₇	C₃⋊D₃	semidirect
29. C₃×C₂₇	D₁₂	semidirect
44. C₃²×C₄	D₂₇	semidirect
53. C₂₇	C₄⋊(C₃⋊D₃)	semidirect
66. C₃×C₄	C₃⋊D₂₇	semidirect
68. C₃²	D₁₀₈	semidirect
78. C₄	C₃⋊(C₃⋊D₂₇)	semidirect
79. C₃	C₄⋊(C₃⋊D₂₇)	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃⋊(C₃⋊D₂₇)	2
C₃²×C₄×C₂₇	2
C₄⋊(C₃⋊(C₃⋊D₉))	3
C₄⋊(C₃⋊D₂₇)	3

Subgroups — C4⋊(C3⋊(C3⋊D27)) #14517733

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊(C₃⋊(C₃⋊D₂₇)) #14517733