Subgroups — C₄₇×#10624711 #46804352

Order 34263.

206 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉²×C₄₇	C₃	1	1	yes	maximal, characteristic
2	C₄₇×C₉⋊C₂₇	C₃	1	6	yes	maximal, complemented
3	C₄₇×C₃²⋊C₂₇	C₃	1	3	yes	maximal
4	C₄₇×#6864	C₃	1	3	yes	maximal, complemented
5	C₃²×C₉×C₄₇	C₉	1	1	yes	characteristic
6	C₃²×C₉×C₄₇	C₉	1	2	yes	—
7	C₃²×C₉×C₄₇	C₃²	1	1	yes	characteristic
8	C₃×C₂₇×C₄₇	C₃²	1	9	yes	—
9	C₉²×C₄₇	C₉	1	2	yes	—
10	C₉²×C₄₇	C₉	1	1	yes	characteristic
11	C₉²×C₄₇	C₉	1	2	yes	—
12	C₉²×C₄₇	C₉	1	1	yes	characteristic
13	C₉²×C₄₇	C₃²	1	1	yes	characteristic
14	C₉²×C₄₇	C₃²	1	2	yes	—
15	C₃³×C₄₇	C₃×C₉	1	1	yes	characteristic
16	C₃×C₉×C₄₇	—	3	3	no	—
17	C₃×C₉×C₄₇	—	3	6	no	—
18	C₃×C₉×C₄₇	—	3	3	no	—
19	C₃×C₉×C₄₇	C₃×C₉	1	1	yes	characteristic
20	C₃×C₉×C₄₇	C₃×C₉	1	1	yes	characteristic
21	C₃×C₉×C₄₇	C₃×C₉	1	1	yes	characteristic
22	C₃×C₉×C₄₇	C₃×C₉	1	2	yes	—
23	C₃×C₉×C₄₇	C₃×C₉	1	2	yes	—
24	C₃×C₉×C₄₇	C₃×C₉	1	2	yes	—
25	C₃×C₉×C₄₇	C₃×C₉	1	2	yes	—
26	C₃×C₉×C₄₇	C₃³	1	1	yes	characteristic
27	C₂₇×C₄₇	—	3	9	no	—
28	#10624711	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
29	C₃²×C₄₇	—	3	1	no	—
30	C₃²×C₄₇	—	3	2	no	—
31	C₃²×C₄₇	C₂₇⋊C₃	1	3	yes	—
32	C₃²×C₄₇	C₃²×C₉	1	1	yes	characteristic
33	C₉×C₄₇	—	3	1	no	—
34	C₉×C₄₇	—	3	1	no	—
35	C₉×C₄₇	—	3	1	no	—
36	C₉×C₄₇	—	3	2	no	—
37	C₉×C₄₇	—	3	2	no	—
38	C₉×C₄₇	—	3	2	no	—
39	C₉×C₄₇	C₂₇⋊C₃	1	6	yes	—
40	C₉×C₄₇	#737	1	3	yes	—
41	C₃×C₉²	C₃×C₄₇	1	1	yes	characteristic
42	C₉⋊C₂₇	C₃×C₄₇	1	6	yes	complemented
43	C₃²⋊C₂₇	C₃×C₄₇	1	3	yes	—
44	#6864	C₃×C₄₇	1	3	yes	complemented
45	C₃×C₄₇	—	3	3	no	—
46	C₃×C₄₇	#6887	1	1	yes	characteristic
47	C₃×C₄₇	C₃×C₂₇⋊C₃	1	1	yes	characteristic
48	C₃×C₄₇	C₃×C₂₇⋊C₃	1	2	yes	—
49	C₃²×C₉	C₉×C₄₇	1	1	yes	characteristic
50	C₃²×C₉	C₉×C₄₇	1	2	yes	—
51	C₃²×C₉	C₃²×C₄₇	1	1	yes	characteristic
52	C₃×C₂₇	C₃²×C₄₇	1	9	yes	—
53	C₉²	C₉×C₄₇	1	2	yes	—
54	C₉²	C₉×C₄₇	1	1	yes	characteristic
55	C₉²	C₉×C₄₇	1	2	yes	—
56	C₉²	C₉×C₄₇	1	1	yes	characteristic
57	C₉²	C₃²×C₄₇	1	1	yes	characteristic
58	C₉²	C₃²×C₄₇	1	2	yes	—
59	C₄₇	#10624711	1	1	yes	characteristic, direct product factor, Sylow
60	C₃³	C₃×C₉×C₄₇	1	1	yes	characteristic
61	C₃×C₉	—	3	3	no	—
62	C₃×C₉	—	3	6	no	—
63	C₃×C₉	—	3	3	no	—
64	C₃×C₉	C₃×C₉×C₄₇	1	1	yes	characteristic
65	C₃×C₉	C₃×C₉×C₄₇	1	1	yes	characteristic
66	C₃×C₉	C₃×C₉×C₄₇	1	1	yes	characteristic
67	C₃×C₉	C₃×C₉×C₄₇	1	2	yes	—
68	C₃×C₉	C₃×C₉×C₄₇	1	2	yes	—
69	C₃×C₉	C₃×C₉×C₄₇	1	2	yes	—
70	C₃×C₉	C₃×C₉×C₄₇	1	2	yes	—
71	C₃×C₉	C₃³×C₄₇	1	1	yes	characteristic
72	C₂₇	—	3	9	no	—
73	C₃²	—	3	1	no	—
74	C₃²	—	3	2	no	—
75	C₃²	C₄₇×C₂₇⋊C₃	1	3	yes	—
76	C₃²	C₃²×C₉×C₄₇	1	1	yes	characteristic
77	C₉	—	3	1	no	—
78	C₉	—	3	1	no	—
79	C₉	—	3	1	no	—
80	C₉	—	3	2	no	—
81	C₉	—	3	2	no	—
82	C₉	—	3	2	no	—
83	C₉	C₄₇×C₂₇⋊C₃	1	6	yes	—
84	C₉	C₄₇×#737	1	3	yes	—
85	C₃	—	3	3	no	—
86	C₃	C₄₇×#6887	1	1	yes	characteristic
87	C₃	C₃×C₄₇×C₂₇⋊C₃	1	1	yes	characteristic
88	C₃	C₃×C₄₇×C₂₇⋊C₃	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
2. C₄₇×C₉⋊C₂₇	C₃	semidirect
4. C₄₇×#6864	C₃	semidirect
28. #10624711	C₄₇	direct (N × H)
42. C₉⋊C₂₇	C₃×C₄₇	semidirect
44. #6864	C₃×C₄₇	semidirect
59. C₄₇	#10624711	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×C₉²×C₄₇	3
C₄₇×C₉⋊C₂₇	3
C₄₇×C₃²⋊C₂₇	3
C₄₇×#6864	3
#10624711	47

Subgroups — C47×#10624711 #46804352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#10624711 #46804352