Subgroups — C₃⋊(C₃⋊(D₂₇⋊C₃)) #13091560

Order 1458.

452 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃×C₃⋊(C₃⋊D₉)	—	3	1	no	maximal
3	C₃⋊(C₃⋊D₂₇)	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃⋊(D₂₇⋊C₃)	—	3	12	no	maximal
5	C₃³×C₉	D₃	1	1	yes	characteristic
6	C₃×C₂₇⋊C₃	—	2	12	no	—
7	C₃×C₂₇⋊C₃	D₃	1	12	yes	complemented
8	C₃²×C₂₇	—	2	1	no	—
9	C₃²×C₂₇	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×C₃⋊(C₃⋊D₃)	—	9	1	no	—
11	C₃⋊(C₃⋊D₉)	—	3	1	no	—
12	C₃×C₃⋊D₉	—	9	8	no	—
13	C₃×C₃⋊D₉	—	9	4	no	—
14	C₃⋊D₂₇	—	3	12	no	—
15	D₂₇⋊C₃	—	9	9	no	—
16	C₃⁴	D₉	1	1	yes	characteristic
17	C₃²×C₉	—	2	1	no	—
18	C₃²×C₉	—	2	8	no	—
19	C₃²×C₉	—	2	4	no	—
20	C₃²×C₉	D₉	1	8	yes	—
21	C₃²×C₉	C₃×D₃	1	1	yes	characteristic
22	C₃²×C₉	C₃⋊D₃	1	4	yes	—
23	C₂₇⋊C₃	—	2	36	no	—
24	C₂₇⋊C₃	C₃⋊D₃	1	9	yes	complemented
25	C₃×C₂₇	—	2	12	no	—
26	C₃×C₂₇	C₃×D₃	1	12	yes	complemented
27	C₃⋊(C₃⋊D₃)	—	9	1	no	—
28	C₃×C₃⋊D₃	—	27	9	no	—
29	C₃×C₃⋊D₃	—	27	4	no	—
30	C₃⋊D₉	—	9	8	no	—
31	C₃⋊D₉	—	9	4	no	—
32	C₃×D₉	—	27	8	no	—
33	C₃×D₉	—	27	1	no	—
34	D₂₇	—	9	9	no	—
35	C₃³	—	2	4	no	—
36	C₃³	—	3	9	no	—
37	C₃³	C₃×D₉	1	1	yes	characteristic
38	C₃³	C₃⋊D₉	1	4	yes	—
39	C₃×C₉	—	2	8	no	—
40	C₃×C₉	—	2	4	no	—
41	C₃×C₉	—	2	24	no	—
42	C₃×C₉	—	2	8	no	—
43	C₃×C₉	—	2	4	no	—
44	C₃×C₉	C₃×D₉	1	8	yes	—
45	C₃×C₉	C₃⋊D₉	1	8	yes	—
46	C₃×C₉	C₃×C₃⋊D₃	1	4	yes	—
47	C₃×C₉	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
48	C₂₇	—	2	9	no	—
49	C₂₇	C₃×C₃⋊D₃	1	9	yes	complemented
50	C₃⋊D₃	—	27	9	no	—
51	C₃⋊D₃	—	27	4	no	—
52	C₃×D₃	—	81	12	no	—
53	C₃×D₃	—	81	1	no	—
54	D₉	—	27	8	no	—
55	D₉	—	27	1	no	—
56	C₃²	—	2	4	no	—
57	C₃²	—	3	12	no	—
58	C₃²	—	6	12	no	—
59	C₃²	D₂₇⋊C₃	1	9	yes	complemented
60	C₃²	C₃×C₃⋊D₉	1	4	yes	—
61	C₃²	C₃⋊(C₃⋊D₉)	1	1	yes	characteristic
62	C₉	—	2	8	no	—
63	C₉	—	2	1	no	—
64	C₉	C₃×C₃⋊D₉	1	8	yes	—
65	C₉	C₃×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
66	C₂×C₃	—	243	1	no	—
67	D₃	—	81	12	no	—
68	D₃	—	81	1	no	—
69	C₃	—	3	1	no	—
70	C₃	—	6	4	no	—
71	C₃	C₃⋊(D₂₇⋊C₃)	1	12	yes	complemented
72	C₃	C₃×C₃⋊(C₃⋊D₉)	1	1	yes	characteristic
73	C₂	—	243	1	no	Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₃²×C₂₇⋊C₃	C₂	semidirect
3. C₃⋊(C₃⋊D₂₇)	C₃	semidirect
7. C₃×C₂₇⋊C₃	D₃	semidirect
9. C₃²×C₂₇	C₂×C₃	semidirect
24. C₂₇⋊C₃	C₃⋊D₃	semidirect
26. C₃×C₂₇	C₃×D₃	semidirect
49. C₂₇	C₃×C₃⋊D₃	semidirect
59. C₃²	D₂₇⋊C₃	semidirect
71. C₃	C₃⋊(D₂₇⋊C₃)	semidirect

Maximal subgroups

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

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

Subgroups — C3⋊(C3⋊(D27⋊C3)) #13091560

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₃⋊(D₂₇⋊C₃)) #13091560