Subgroups — C₄₇×#10624510 #46804151

Order 34263.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₇×#737	C₃	1	1	yes	maximal, characteristic
2	C₄₇×#6869	C₃	1	3	yes	maximal, complemented
3	C₄₇×#737	—	3	9	no	—
4	C₃×3₋¹⁺²×C₄₇	—	3	1	no	—
5	C₃×3₋¹⁺²×C₄₇	—	3	1	no	—
6	C₃×3₋¹⁺²×C₄₇	C₉	1	2	yes	—
7	C₃×H(3,𝔽₃)×C₄₇	C₉	1	1	yes	characteristic
8	C₃²×C₉×C₄₇	—	3	1	no	—
9	C₃²×C₉×C₄₇	C₃²	1	1	yes	characteristic
10	C₄₇×C₂₇⋊C₃	—	3	3	no	—
11	C₃³×C₄₇	—	3	1	no	—
12	C₃³×C₄₇	C₃×C₉	1	1	yes	characteristic
13	3₋¹⁺²×C₄₇	—	3	9	no	—
14	3₋¹⁺²×C₄₇	—	3	9	no	—
15	3₋¹⁺²×C₄₇	—	3	6	no	—
16	H(3,𝔽₃)×C₄₇	—	3	3	no	—
17	C₃×C₉×C₄₇	—	3	9	no	—
18	C₃×C₉×C₄₇	—	3	2	no	—
19	C₃×C₉×C₄₇	—	3	3	no	—
20	C₃×C₉×C₄₇	H(3,𝔽₃)	1	1	yes	characteristic
21	C₃×C₉×C₄₇	3₋¹⁺²	1	1	yes	characteristic
22	C₃×C₉×C₄₇	3₋¹⁺²	1	1	yes	characteristic
23	C₂₇×C₄₇	—	9	3	no	—
24	#10624510	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₃²×C₄₇	—	3	1	no	—
26	C₃²×C₄₇	—	3	3	no	—
27	C₃²×C₄₇	—	9	1	no	—
28	C₃²×C₄₇	—	9	3	no	—
29	C₃²×C₄₇	C₃²⋊C₉	1	1	yes	characteristic
30	C₉×C₄₇	—	3	1	no	—
31	C₉×C₄₇	—	3	6	no	—
32	C₉×C₄₇	—	3	1	no	—
33	C₉×C₄₇	AΣL(1,𝔽₂₇)	1	3	yes	—
34	C₃×#737	C₃×C₄₇	1	1	yes	characteristic
35	#6869	C₃×C₄₇	1	3	yes	complemented
36	C₃×C₄₇	—	3	1	no	—
37	C₃×C₄₇	—	9	1	no	—
38	C₃×C₄₇	—	9	3	no	—
39	C₃×C₄₇	#6866	1	1	yes	characteristic
40	#737	—	3	9	no	—
41	C₃×3₋¹⁺²	—	3	1	no	—
42	C₃×3₋¹⁺²	—	3	1	no	—
43	C₃×3₋¹⁺²	C₉×C₄₇	1	2	yes	—
44	C₃×H(3,𝔽₃)	C₉×C₄₇	1	1	yes	characteristic
45	C₃²×C₉	—	3	1	no	—
46	C₃²×C₉	C₃²×C₄₇	1	1	yes	characteristic
47	C₂₇⋊C₃	—	3	3	no	—
48	C₄₇	#10624510	1	1	yes	characteristic, direct product factor, Sylow
49	C₃³	—	3	1	no	—
50	C₃³	C₃×C₉×C₄₇	1	1	yes	characteristic
51	3₋¹⁺²	—	3	9	no	—
52	3₋¹⁺²	—	3	9	no	—
53	3₋¹⁺²	—	3	6	no	—
54	H(3,𝔽₃)	—	3	3	no	—
55	C₃×C₉	—	3	9	no	—
56	C₃×C₉	—	3	2	no	—
57	C₃×C₉	—	3	3	no	—
58	C₃×C₉	H(3,𝔽₃)×C₄₇	1	1	yes	characteristic
59	C₃×C₉	3₋¹⁺²×C₄₇	1	1	yes	characteristic
60	C₃×C₉	3₋¹⁺²×C₄₇	1	1	yes	characteristic
61	C₂₇	—	9	3	no	—
62	C₃²	—	3	1	no	—
63	C₃²	—	3	3	no	—
64	C₃²	—	9	1	no	—
65	C₃²	—	9	3	no	—
66	C₃²	C₄₇×C₃²⋊C₉	1	1	yes	characteristic
67	C₉	—	3	1	no	—
68	C₉	—	3	6	no	—
69	C₉	—	3	1	no	—
70	C₉	C₄₇×AΣL(1,𝔽₂₇)	1	3	yes	—
71	C₃	—	3	1	no	—
72	C₃	—	9	3	no	—
73	C₃	—	9	1	no	—
74	C₃	C₄₇×#6866	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃×C₄₇	#6866
commutator	C₃³	C₃×C₉×C₄₇
Frattini, cosocle	C₃²×C₉	C₃²×C₄₇
prime radical	C₃×H(3,𝔽₃)×C₄₇	C₉
LCS	G ▷ C₃³ ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₄₇ ◁ C₃×C₉×C₄₇ ◁ C₃²×C₉×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₇×#6869	C₃	semidirect
24. #10624510	C₄₇	direct (N × H)
35. #6869	C₃×C₄₇	semidirect
48. C₄₇	#10624510	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×C₄₇×#737	3
C₄₇×#6869	3
#10624510	47

Subgroups — C47×#10624510 #46804151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#10624510 #46804151