Subgroups — C₃×C₈×C₂₇⋊C₃ #14516396

Order 1944.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₂₇⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₈×C₉	C₃	1	1	yes	maximal, characteristic
3	C₈×C₂₇⋊C₃	C₃	1	9	yes	maximal, direct product factor
4	C₃×C₈×C₂₇	C₃	1	3	yes	maximal, complemented
5	C₂×C₃×C₂₇⋊C₃	C₄	1	1	yes	characteristic
6	C₃²×C₄×C₉	C₂×C₃	1	1	yes	characteristic
7	C₄×C₂₇⋊C₃	C₂×C₃	1	9	yes	—
8	C₃×C₄×C₂₇	C₂×C₃	1	3	yes	—
9	C₃×C₂₇⋊C₃	C₈	1	1	yes	characteristic, direct product factor, Sylow
10	C₃³×C₈	C₉	1	1	yes	characteristic
11	C₃×C₈×C₉	C₉	1	2	yes	—
12	C₃×C₈×C₉	C₉	1	6	yes	—
13	C₃×C₈×C₉	C₃²	1	3	yes	—
14	C₃×C₈×C₉	C₃²	1	1	yes	characteristic
15	C₈×C₂₇	C₃²	1	9	yes	complemented
16	C₂×C₃²×C₉	C₃×C₄	1	1	yes	characteristic
17	C₂×C₂₇⋊C₃	C₃×C₄	1	9	yes	—
18	C₂×C₃×C₂₇	C₃×C₄	1	3	yes	—
19	C₃³×C₄	C₂×C₉	1	1	yes	characteristic
20	C₃×C₄×C₉	C₂×C₉	1	6	yes	—
21	C₃×C₄×C₉	C₂×C₉	1	2	yes	—
22	C₃×C₄×C₉	C₂×C₃²	1	1	yes	characteristic
23	C₃×C₄×C₉	C₂×C₃²	1	3	yes	—
24	C₄×C₂₇	C₂×C₃²	1	9	yes	—
25	C₃²×C₉	C₃×C₈	1	1	yes	characteristic
26	C₂₇⋊C₃	C₃×C₈	1	9	yes	direct product factor
27	C₃×C₂₇	C₃×C₈	1	3	yes	complemented
28	C₃²×C₈	—	3	3	no	—
29	C₃²×C₈	C₃×C₉	1	3	yes	—
30	C₃²×C₈	C₃×C₉	1	1	yes	characteristic
31	C₈×C₉	C₃×C₉	1	6	yes	—
32	C₈×C₉	C₃×C₉	1	2	yes	—
33	C₈×C₉	C₃³	1	1	yes	characteristic
34	C₂×C₃³	C₄×C₉	1	1	yes	characteristic
35	C₂×C₃×C₉	C₄×C₉	1	6	yes	—
36	C₂×C₃×C₉	C₄×C₉	1	2	yes	—
37	C₂×C₃×C₉	C₃²×C₄	1	1	yes	characteristic
38	C₂×C₃×C₉	C₃²×C₄	1	3	yes	—
39	C₂×C₂₇	C₃²×C₄	1	9	yes	—
40	C₃²×C₄	—	3	3	no	—
41	C₃²×C₄	C₂×C₃×C₉	1	3	yes	—
42	C₃²×C₄	C₂×C₃×C₉	1	1	yes	characteristic
43	C₄×C₉	C₂×C₃×C₉	1	2	yes	—
44	C₄×C₉	C₂×C₃×C₉	1	6	yes	—
45	C₄×C₉	C₂×C₃³	1	1	yes	characteristic
46	C₃³	C₈×C₉	1	1	yes	characteristic
47	C₃×C₉	C₈×C₉	1	6	yes	—
48	C₃×C₉	C₈×C₉	1	2	yes	—
49	C₃×C₉	C₃²×C₈	1	1	yes	characteristic
50	C₃×C₉	C₃²×C₈	1	3	yes	—
51	C₂₇	C₃²×C₈	1	9	yes	complemented
52	C₃×C₈	—	3	3	no	—
53	C₃×C₈	C₂₇⋊C₃	1	3	yes	direct product factor
54	C₃×C₈	C₃²×C₉	1	1	yes	characteristic
55	C₂×C₃²	—	3	3	no	—
56	C₂×C₃²	C₃×C₄×C₉	1	3	yes	—
57	C₂×C₃²	C₃×C₄×C₉	1	1	yes	characteristic
58	C₂×C₉	C₃×C₄×C₉	1	2	yes	—
59	C₂×C₉	C₃×C₄×C₉	1	6	yes	—
60	C₂×C₉	C₃³×C₄	1	1	yes	characteristic
61	C₃×C₄	—	3	3	no	—
62	C₃×C₄	C₂×C₂₇⋊C₃	1	3	yes	—
63	C₃×C₄	C₂×C₃²×C₉	1	1	yes	characteristic
64	C₃²	—	3	3	no	—
65	C₃²	C₃×C₈×C₉	1	3	yes	—
66	C₃²	C₃×C₈×C₉	1	1	yes	characteristic
67	C₉	C₃×C₈×C₉	1	2	yes	—
68	C₉	C₃×C₈×C₉	1	6	yes	—
69	C₉	C₃³×C₈	1	1	yes	characteristic
70	C₈	C₃×C₂₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
71	C₂×C₃	—	3	3	no	—
72	C₂×C₃	C₄×C₂₇⋊C₃	1	3	yes	—
73	C₂×C₃	C₃²×C₄×C₉	1	1	yes	characteristic
74	C₄	C₂×C₃×C₂₇⋊C₃	1	1	yes	characteristic
75	C₃	—	3	3	no	—
76	C₃	C₈×C₂₇⋊C₃	1	3	yes	direct product factor
77	C₃	C₃²×C₈×C₉	1	1	yes	characteristic
78	C₂	C₃×C₄×C₂₇⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₈×C₉	C₃²
commutator	C₃	C₃²×C₈×C₉
Frattini, cosocle	C₄×C₉	C₂×C₃³
socle	C₂×C₃²	C₃×C₄×C₉
prime radical	C₂×C₃³	C₄×C₉
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₈×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₈×C₂₇⋊C₃	C₃	direct (N × H)
4. C₃×C₈×C₂₇	C₃	semidirect
9. C₃×C₂₇⋊C₃	C₈	direct (N × H)
15. C₈×C₂₇	C₃²	semidirect
26. C₂₇⋊C₃	C₃×C₈	direct (N × H)
27. C₃×C₂₇	C₃×C₈	semidirect
51. C₂₇	C₃²×C₈	semidirect
53. C₃×C₈	C₂₇⋊C₃	direct (N × H)
70. C₈	C₃×C₂₇⋊C₃	direct (N × H)
76. C₃	C₈×C₂₇⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₄×C₂₇⋊C₃	2
C₃²×C₈×C₉	3
C₈×C₂₇⋊C₃	3
C₃×C₈×C₂₇	3

Subgroups — C3×C8×C27⋊C3 #14516396

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₈×C₂₇⋊C₃ #14516396