Subgroups — C₃×C₄₇×C₃²⋊C₂₇ #46804323

Order 34263.

464 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₉×C₄₇	C₃	1	1	yes	maximal, characteristic
2	C₃²×C₂₇×C₄₇	C₃	1	3	yes	maximal, complemented
3	C₄₇×C₃²⋊C₂₇	C₃	1	9	yes	maximal, direct product factor
4	C₃⁴×C₄₇	C₉	1	1	yes	characteristic
5	C₃²×C₉×C₄₇	—	3	3	no	—
6	C₃²×C₉×C₄₇	—	3	6	no	—
7	C₃²×C₉×C₄₇	C₉	1	2	yes	—
8	C₃²×C₉×C₄₇	C₉	1	6	yes	—
9	C₃²×C₉×C₄₇	C₃²	1	3	yes	—
10	C₃²×C₉×C₄₇	C₃²	1	1	yes	characteristic
11	C₃×C₂₇×C₄₇	—	3	9	no	—
12	C₃×C₂₇×C₄₇	C₃²	1	9	yes	complemented
13	C₃³×C₄₇	—	3	3	no	—
14	C₃³×C₄₇	—	3	6	no	—
15	C₃³×C₄₇	C₂₇	1	9	yes	complemented
16	C₃³×C₄₇	C₃×C₉	1	3	yes	—
17	C₃³×C₄₇	C₃×C₉	1	1	yes	characteristic
18	C₃×C₉×C₄₇	—	3	6	no	—
19	C₃×C₉×C₄₇	—	3	18	no	—
20	C₃×C₉×C₄₇	—	3	3	no	—
21	C₃×C₉×C₄₇	—	3	6	no	—
22	C₃×C₉×C₄₇	C₃×C₉	1	6	yes	—
23	C₃×C₉×C₄₇	C₃×C₉	1	2	yes	—
24	C₃×C₉×C₄₇	H(3,𝔽₃)	1	3	yes	—
25	C₃×C₉×C₄₇	3₋¹⁺²	1	6	yes	—
26	C₃×C₉×C₄₇	C₃³	1	1	yes	characteristic
27	C₂₇×C₄₇	—	3	9	no	—
28	C₃×C₃²⋊C₂₇	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
29	C₃²×C₄₇	—	3	27	no	—
30	C₃²×C₄₇	—	3	3	no	—
31	C₃²×C₄₇	—	3	6	no	—
32	C₃²×C₄₇	C₃²⋊C₉	1	3	yes	—
33	C₃²×C₄₇	C₃×C₂₇	1	3	yes	—
34	C₃²×C₄₇	C₃×C₂₇	1	9	yes	complemented
35	C₃²×C₄₇	C₂₇⋊C₃	1	6	yes	—
36	C₃²×C₄₇	C₃²×C₉	1	1	yes	characteristic
37	C₉×C₄₇	—	3	6	no	—
38	C₉×C₄₇	C₃²⋊C₉	1	6	yes	—
39	C₉×C₄₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
40	C₉×C₄₇	C₃×3₋¹⁺²	1	2	yes	—
41	C₃³×C₉	C₃×C₄₇	1	1	yes	characteristic
42	C₃²×C₂₇	C₃×C₄₇	1	3	yes	complemented
43	C₃²⋊C₂₇	C₃×C₄₇	1	9	yes	direct product factor
44	C₃×C₄₇	—	3	9	no	—
45	C₃×C₄₇	C₃²⋊C₂₇	1	9	yes	direct product factor
46	C₃×C₄₇	C₃×C₃²⋊C₉	1	1	yes	characteristic
47	C₃×C₄₇	C₃²×C₂₇	1	1	yes	characteristic
48	C₃×C₄₇	C₃×C₂₇⋊C₃	1	2	yes	—
49	C₃⁴	C₉×C₄₇	1	1	yes	characteristic
50	C₃²×C₉	—	3	3	no	—
51	C₃²×C₉	—	3	6	no	—
52	C₃²×C₉	C₉×C₄₇	1	2	yes	—
53	C₃²×C₉	C₉×C₄₇	1	6	yes	—
54	C₃²×C₉	C₃²×C₄₇	1	3	yes	—
55	C₃²×C₉	C₃²×C₄₇	1	1	yes	characteristic
56	C₃×C₂₇	—	3	9	no	—
57	C₃×C₂₇	C₃²×C₄₇	1	9	yes	complemented
58	C₄₇	C₃×C₃²⋊C₂₇	1	1	yes	characteristic, direct product factor, Sylow
59	C₃³	—	3	3	no	—
60	C₃³	—	3	6	no	—
61	C₃³	C₂₇×C₄₇	1	9	yes	complemented
62	C₃³	C₃×C₉×C₄₇	1	3	yes	—
63	C₃³	C₃×C₉×C₄₇	1	1	yes	characteristic
64	C₃×C₉	—	3	6	no	—
65	C₃×C₉	—	3	18	no	—
66	C₃×C₉	—	3	3	no	—
67	C₃×C₉	—	3	6	no	—
68	C₃×C₉	C₃×C₉×C₄₇	1	6	yes	—
69	C₃×C₉	C₃×C₉×C₄₇	1	2	yes	—
70	C₃×C₉	H(3,𝔽₃)×C₄₇	1	3	yes	—
71	C₃×C₉	3₋¹⁺²×C₄₇	1	6	yes	—
72	C₃×C₉	C₃³×C₄₇	1	1	yes	characteristic
73	C₂₇	—	3	9	no	—
74	C₃²	—	3	27	no	—
75	C₃²	—	3	3	no	—
76	C₃²	—	3	6	no	—
77	C₃²	C₄₇×C₃²⋊C₉	1	3	yes	—
78	C₃²	C₃×C₂₇×C₄₇	1	3	yes	—
79	C₃²	C₃×C₂₇×C₄₇	1	9	yes	complemented
80	C₃²	C₄₇×C₂₇⋊C₃	1	6	yes	—
81	C₃²	C₃²×C₉×C₄₇	1	1	yes	characteristic
82	C₉	—	3	6	no	—
83	C₉	C₄₇×C₃²⋊C₉	1	6	yes	—
84	C₉	C₃×H(3,𝔽₃)×C₄₇	1	1	yes	characteristic
85	C₉	C₃×3₋¹⁺²×C₄₇	1	2	yes	—
86	C₃	—	3	9	no	—
87	C₃	C₄₇×C₃²⋊C₂₇	1	9	yes	direct product factor
88	C₃	C₃×C₄₇×C₃²⋊C₉	1	1	yes	characteristic
89	C₃	C₃²×C₂₇×C₄₇	1	1	yes	characteristic
90	C₃	C₃×C₄₇×C₂₇⋊C₃	1	2	yes	—

	subgroup	G/H
center	C₃²×C₉×C₄₇	C₃²
commutator	C₃	C₃²×C₂₇×C₄₇
Frattini, cosocle	C₃×C₉	C₃³×C₄₇
socle	C₃³×C₄₇	C₃×C₉
prime radical	C₃⁴×C₄₇	C₉
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₉×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃²×C₂₇×C₄₇	C₃	semidirect
3. C₄₇×C₃²⋊C₂₇	C₃	direct (N × H)
12. C₃×C₂₇×C₄₇	C₃²	semidirect
15. C₃³×C₄₇	C₂₇	semidirect
28. C₃×C₃²⋊C₂₇	C₄₇	direct (N × H)
34. C₃²×C₄₇	C₃×C₂₇	semidirect
42. C₃²×C₂₇	C₃×C₄₇	semidirect
43. C₃²⋊C₂₇	C₃×C₄₇	direct (N × H)
45. C₃×C₄₇	C₃²⋊C₂₇	direct (N × H)
57. C₃×C₂₇	C₃²×C₄₇	semidirect
58. C₄₇	C₃×C₃²⋊C₂₇	direct (N × H)
61. C₃³	C₂₇×C₄₇	semidirect
79. C₃²	C₃×C₂₇×C₄₇	semidirect
87. C₃	C₄₇×C₃²⋊C₂₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃³×C₉×C₄₇	3
C₃²×C₂₇×C₄₇	3
C₄₇×C₃²⋊C₂₇	3
C₃×C₃²⋊C₂₇	47

Subgroups — C3×C47×C32⋊C27 #46804323

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄₇×C₃²⋊C₂₇ #46804323