Subgroups — C₄₇×#10624599 #46804240

Order 34263.

344 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×C₃²⋊H(3,𝔽₃)	C₃	1	2	yes	maximal, complemented
2	C₃×C₄₇×C₃²⋊C₉	C₃	1	2	yes	maximal, complemented
3	C₄₇×#6856	C₃	1	9	yes	maximal, complemented
4	C₃⁴×C₄₇	C₃²	1	1	yes	characteristic
5	C₃×H(3,𝔽₃)×C₄₇	—	3	2	no	—
6	C₃×H(3,𝔽₃)×C₄₇	—	3	4	no	—
7	C₃×H(3,𝔽₃)×C₄₇	C₃²	1	6	yes	—
8	C₃²×C₉×C₄₇	—	3	2	no	—
9	C₄₇×C₃²⋊C₉	—	3	2	no	—
10	C₄₇×C₃²⋊C₉	—	3	2	no	—
11	C₄₇×C₃²⋊C₉	C₃²	1	6	yes	—
12	C₃³×C₄₇	—	3	6	no	—
13	C₃³×C₄₇	—	3	6	no	—
14	C₃³×C₄₇	—	9	2	no	—
15	C₃³×C₄₇	H(3,𝔽₃)	1	1	yes	characteristic
16	C₃³×C₄₇	H(3,𝔽₃)	1	2	yes	—
17	C₃³×C₄₇	C₃³	1	1	yes	characteristic
18	H(3,𝔽₃)×C₄₇	—	9	6	no	—
19	H(3,𝔽₃)×C₄₇	—	9	6	no	—
20	H(3,𝔽₃)×C₄₇	—	9	12	no	—
21	C₃×C₉×C₄₇	—	3	6	no	—
22	C₃×C₉×C₄₇	—	9	6	no	—
23	#10624599	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	C₃²×C₄₇	—	3	2	no	—
25	C₃²×C₄₇	—	3	4	no	—
26	C₃²×C₄₇	—	3	2	no	—
27	C₃²×C₄₇	—	3	2	no	—
28	C₃²×C₄₇	—	3	2	no	—
29	C₃²×C₄₇	—	3	2	no	—
30	C₃²×C₄₇	—	9	9	no	—
31	C₃²×C₄₇	—	9	12	no	—
32	C₃²×C₄₇	—	9	6	no	—
33	C₃²×C₄₇	—	9	6	no	—
34	C₃²×C₄₇	#732	1	6	yes	—
35	C₃²×C₄₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
36	C₉×C₄₇	—	9	6	no	—
37	C₃²⋊H(3,𝔽₃)	C₃×C₄₇	1	2	yes	complemented
38	C₃×C₃²⋊C₉	C₃×C₄₇	1	2	yes	complemented
39	#6856	C₃×C₄₇	1	9	yes	complemented
40	C₃×C₄₇	—	3	6	no	—
41	C₃×C₄₇	—	9	1	no	—
42	C₃×C₄₇	—	9	1	no	—
43	C₃×C₄₇	—	27	6	no	—
44	C₃×C₄₇	C₃×#732	1	2	yes	—
45	C₃×C₄₇	#6909	1	2	yes	—
46	C₃⁴	C₃²×C₄₇	1	1	yes	characteristic
47	C₃×H(3,𝔽₃)	—	3	2	no	—
48	C₃×H(3,𝔽₃)	—	3	4	no	—
49	C₃×H(3,𝔽₃)	C₃²×C₄₇	1	6	yes	—
50	C₃²×C₉	—	3	2	no	—
51	C₃²⋊C₉	—	3	2	no	—
52	C₃²⋊C₉	—	3	2	no	—
53	C₃²⋊C₉	C₃²×C₄₇	1	6	yes	—
54	C₄₇	#10624599	1	1	yes	characteristic, direct product factor, Sylow
55	C₃³	—	3	6	no	—
56	C₃³	—	3	6	no	—
57	C₃³	—	9	2	no	—
58	C₃³	H(3,𝔽₃)×C₄₇	1	1	yes	characteristic
59	C₃³	H(3,𝔽₃)×C₄₇	1	2	yes	—
60	C₃³	C₃³×C₄₇	1	1	yes	characteristic
61	H(3,𝔽₃)	—	9	6	no	—
62	H(3,𝔽₃)	—	9	6	no	—
63	H(3,𝔽₃)	—	9	12	no	—
64	C₃×C₉	—	3	6	no	—
65	C₃×C₉	—	9	6	no	—
66	C₃²	—	3	2	no	—
67	C₃²	—	3	4	no	—
68	C₃²	—	3	2	no	—
69	C₃²	—	3	2	no	—
70	C₃²	—	3	2	no	—
71	C₃²	—	3	2	no	—
72	C₃²	—	9	9	no	—
73	C₃²	—	9	12	no	—
74	C₃²	—	9	6	no	—
75	C₃²	—	9	6	no	—
76	C₃²	C₄₇×#732	1	6	yes	—
77	C₃²	C₃×H(3,𝔽₃)×C₄₇	1	1	yes	characteristic
78	C₉	—	9	6	no	—
79	C₃	—	3	6	no	—
80	C₃	—	9	1	no	—
81	C₃	—	9	1	no	—
82	C₃	—	27	6	no	—
83	C₃	C₃×C₄₇×#732	1	2	yes	—
84	C₃	C₄₇×#6909	1	2	yes	—

	subgroup	G/H
center, socle	C₃²×C₄₇	C₃×H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₃³×C₄₇
LCS	G ▷ C₃³ ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃²×C₄₇ ◁ C₃⁴×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₇×C₃²⋊H(3,𝔽₃)	C₃	semidirect
2. C₃×C₄₇×C₃²⋊C₉	C₃	semidirect
3. C₄₇×#6856	C₃	semidirect
23. #10624599	C₄₇	direct (N × H)
37. C₃²⋊H(3,𝔽₃)	C₃×C₄₇	semidirect
38. C₃×C₃²⋊C₉	C₃×C₄₇	semidirect
39. #6856	C₃×C₄₇	semidirect
54. C₄₇	#10624599	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₇×C₃²⋊H(3,𝔽₃)	3
C₃×C₄₇×C₃²⋊C₉	3
C₄₇×#6856	3
#10624599	47

Subgroups — C47×#10624599 #46804240

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#10624599 #46804240