Subgroups — C₄₇×#10624727 #46804368

Order 34263.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₇×C₄₇	C₃	1	1	yes	maximal, characteristic
2	C₉×3₋¹⁺²×C₄₇	C₃	1	1	yes	maximal, characteristic
3	C₄₇×C₉⋊C₂₇	C₃	1	6	yes	maximal, complemented
4	C₄₇×C₃²⋊C₂₇	C₃	1	2	yes	maximal
5	C₄₇×#6864	C₃	1	3	yes	maximal, complemented
6	C₃×3₋¹⁺²×C₄₇	C₉	1	1	yes	characteristic
7	C₃²×C₉×C₄₇	C₃²	1	1	yes	characteristic
8	C₃×C₂₇×C₄₇	—	3	3	no	—
9	C₃×C₂₇×C₄₇	C₃²	1	6	yes	—
10	C₃×C₂₇×C₄₇	C₃²	1	2	yes	—
11	C₃×C₂₇×C₄₇	C₃²	1	1	yes	characteristic
12	C₄₇×C₉⋊C₉	C₉	1	6	yes	—
13	C₄₇×C₃²⋊C₉	C₉	1	2	yes	—
14	C₉²×C₄₇	C₃²	1	3	yes	—
15	C₃³×C₄₇	C₃×C₉	1	1	yes	characteristic
16	3₋¹⁺²×C₄₇	—	3	3	no	—
17	C₃×C₉×C₄₇	—	3	1	no	—
18	C₃×C₉×C₄₇	—	3	2	no	—
19	C₃×C₉×C₄₇	C₃×C₉	1	6	yes	—
20	C₃×C₉×C₄₇	C₃×C₉	1	3	yes	—
21	C₃×C₉×C₄₇	C₃×C₉	1	2	yes	—
22	C₃×C₉×C₄₇	C₃³	1	1	yes	characteristic
23	C₂₇×C₄₇	—	3	2	no	—
24	C₂₇×C₄₇	—	3	6	no	—
25	C₂₇×C₄₇	3₋¹⁺²	1	3	yes	complemented
26	#10624727	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
27	C₃²×C₄₇	—	3	1	no	—
28	C₃²×C₄₇	—	3	2	no	—
29	C₃²×C₄₇	C₂₇⋊C₃	1	3	yes	—
30	C₃²×C₄₇	C₃²×C₉	1	1	yes	characteristic
31	C₉×C₄₇	—	3	2	no	—
32	C₉×C₄₇	—	3	3	no	—
33	C₉×C₄₇	—	3	6	no	—
34	C₉×C₄₇	C₃×3₋¹⁺²	1	1	yes	characteristic
35	C₉×C₄₇	#737	1	2	yes	—
36	C₃²×C₂₇	C₃×C₄₇	1	1	yes	characteristic
37	C₉×3₋¹⁺²	C₃×C₄₇	1	1	yes	characteristic
38	C₉⋊C₂₇	C₃×C₄₇	1	6	yes	complemented
39	C₃²⋊C₂₇	C₃×C₄₇	1	2	yes	—
40	#6864	C₃×C₄₇	1	3	yes	complemented
41	C₃×C₄₇	—	3	3	no	—
42	C₃×C₄₇	C₉×3₋¹⁺²	1	1	yes	characteristic
43	C₃×C₄₇	C₃×C₂₇⋊C₃	1	1	yes	characteristic
44	C₃×C₄₇	#6903	1	2	yes	—
45	C₃×3₋¹⁺²	C₉×C₄₇	1	1	yes	characteristic
46	C₃²×C₉	C₃²×C₄₇	1	1	yes	characteristic
47	C₃×C₂₇	—	3	3	no	—
48	C₃×C₂₇	C₃²×C₄₇	1	6	yes	—
49	C₃×C₂₇	C₃²×C₄₇	1	2	yes	—
50	C₃×C₂₇	C₃²×C₄₇	1	1	yes	characteristic
51	C₉⋊C₉	C₉×C₄₇	1	6	yes	—
52	C₃²⋊C₉	C₉×C₄₇	1	2	yes	—
53	C₉²	C₃²×C₄₇	1	3	yes	—
54	C₄₇	#10624727	1	1	yes	characteristic, direct product factor, Sylow
55	C₃³	C₃×C₉×C₄₇	1	1	yes	characteristic
56	3₋¹⁺²	—	3	3	no	—
57	C₃×C₉	—	3	1	no	—
58	C₃×C₉	—	3	2	no	—
59	C₃×C₉	C₃×C₉×C₄₇	1	6	yes	—
60	C₃×C₉	C₃×C₉×C₄₇	1	3	yes	—
61	C₃×C₉	C₃×C₉×C₄₇	1	2	yes	—
62	C₃×C₉	C₃³×C₄₇	1	1	yes	characteristic
63	C₂₇	—	3	2	no	—
64	C₂₇	—	3	6	no	—
65	C₂₇	3₋¹⁺²×C₄₇	1	3	yes	complemented
66	C₃²	—	3	1	no	—
67	C₃²	—	3	2	no	—
68	C₃²	C₄₇×C₂₇⋊C₃	1	3	yes	—
69	C₃²	C₃²×C₉×C₄₇	1	1	yes	characteristic
70	C₉	—	3	2	no	—
71	C₉	—	3	3	no	—
72	C₉	—	3	6	no	—
73	C₉	C₃×3₋¹⁺²×C₄₇	1	1	yes	characteristic
74	C₉	C₄₇×#737	1	2	yes	—
75	C₃	—	3	3	no	—
76	C₃	C₉×3₋¹⁺²×C₄₇	1	1	yes	characteristic
77	C₃	C₃×C₄₇×C₂₇⋊C₃	1	1	yes	characteristic
78	C₃	C₄₇×#6903	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₄₇×C₉⋊C₂₇	C₃	semidirect
5. C₄₇×#6864	C₃	semidirect
25. C₂₇×C₄₇	3₋¹⁺²	semidirect
26. #10624727	C₄₇	direct (N × H)
38. C₉⋊C₂₇	C₃×C₄₇	semidirect
40. #6864	C₃×C₄₇	semidirect
54. C₄₇	#10624727	direct (N × H)
65. C₂₇	3₋¹⁺²×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₂₇×C₄₇	3
C₉×3₋¹⁺²×C₄₇	3
C₄₇×C₉⋊C₂₇	3
C₄₇×C₃²⋊C₂₇	3
C₄₇×#6864	3
#10624727	47

Subgroups — C47×#10624727 #46804368

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#10624727 #46804368