Subgroups — #44533407

Order 31347.

312 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812505	C₃	1	3	yes	maximal, complemented
2	#23782718	C₃	1	9	yes	maximal, complemented
3	C₃×C₄₃×#737	C₃	1	1	yes	maximal, characteristic
4	#16812505	—	3	6	no	—
5	#16812505	C₃²	1	9	yes	—
6	C₃×C₄₃⋊C₂₇	—	3	3	no	—
7	C₄₃×#737	—	3	3	no	—
8	C₄₃×#737	—	3	6	no	—
9	C₃×3₋¹⁺²×C₄₃	C₉	1	2	yes	—
10	C₃×3₋¹⁺²×C₄₃	C₉	1	6	yes	—
11	C₃×H(3,𝔽₃)×C₄₃	C₉	1	1	yes	characteristic
12	C₃²×C₉×C₄₃	C₃²	1	3	yes	—
13	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
14	C₄₃⋊C₂₇	—	3	9	no	—
15	C₃³×C₄₃	C₃×C₉	1	3	yes	—
16	C₃³×C₄₃	C₃×C₉	1	1	yes	characteristic
17	3₋¹⁺²×C₄₃	—	3	6	no	—
18	3₋¹⁺²×C₄₃	—	3	18	no	—
19	H(3,𝔽₃)×C₄₃	—	3	3	no	—
20	C₃×C₉×C₄₃	—	3	3	no	—
21	C₃×C₉×C₄₃	—	3	6	no	—
22	C₃×C₉×C₄₃	C₃×C₉	1	6	yes	—
23	C₃×C₉×C₄₃	C₃×C₉	1	2	yes	—
24	C₃×C₉×C₄₃	H(3,𝔽₃)	1	3	yes	—
25	C₃×C₉×C₄₃	3₋¹⁺²	1	6	yes	—
26	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
27	#10624694	—	43	1	no	maximal, Sylow
28	C₃²×C₄₃	—	3	3	no	—
29	C₃²×C₄₃	—	9	1	no	—
30	C₃²×C₄₃	—	9	3	no	—
31	C₃²×C₄₃	C₃²⋊C₉	1	3	yes	—
32	C₃²×C₄₃	C₃²×C₉	1	1	yes	characteristic
33	C₉×C₄₃	—	3	6	no	—
34	C₉×C₄₃	C₃²⋊C₉	1	6	yes	—
35	C₉×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
36	C₉×C₄₃	C₃×3₋¹⁺²	1	2	yes	—
37	C₃×#737	C₄₃⋊C₃	1	1	yes	characteristic
38	C₃×C₂₇⋊C₃	—	43	3	no	—
39	#6869	—	43	9	no	—
40	C₃×C₄₃	—	3	1	no	—
41	C₃×C₄₃	—	3	3	no	—
42	C₃×C₄₃	—	9	3	no	—
43	C₃×C₄₃	C₃×C₃²⋊C₉	1	1	yes	characteristic
44	#737	—	3	3	no	—
45	#737	—	3	6	no	—
46	C₃×3₋¹⁺²	C₄₃⋊C₉	1	2	yes	—
47	C₃×3₋¹⁺²	C₄₃⋊C₉	1	6	yes	—
48	C₃×H(3,𝔽₃)	C₄₃⋊C₉	1	1	yes	characteristic
49	C₃²×C₉	C₃×C₄₃⋊C₃	1	3	yes	—
50	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
51	C₂₇⋊C₃	—	43	9	no	—
52	C₂₇⋊C₃	—	129	6	no	—
53	C₃×C₂₇	—	129	3	no	—
54	C₄₃	#10624694	1	1	yes	characteristic, complemented, Sylow
55	C₃³	C₃×C₄₃⋊C₉	1	3	yes	—
56	C₃³	C₃×C₄₃⋊C₉	1	1	yes	characteristic
57	3₋¹⁺²	—	3	6	no	—
58	3₋¹⁺²	—	3	18	no	—
59	H(3,𝔽₃)	—	3	3	no	—
60	C₃×C₉	—	3	3	no	—
61	C₃×C₉	—	3	6	no	—
62	C₃×C₉	C₃×C₄₃⋊C₉	1	6	yes	—
63	C₃×C₉	C₃×C₄₃⋊C₉	1	2	yes	—
64	C₃×C₉	C₃²⋊(C₄₃⋊C₃)	1	3	yes	—
65	C₃×C₉	#11923958	1	6	yes	—
66	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
67	C₂₇	—	129	9	no	—
68	C₃²	—	3	3	no	—
69	C₃²	—	9	1	no	—
70	C₃²	—	9	3	no	—
71	C₃²	C₃²⋊(C₄₃⋊C₉)	1	3	yes	—
72	C₃²	C₃²×C₄₃⋊C₉	1	1	yes	characteristic
73	C₉	—	3	6	no	—
74	C₉	C₃²⋊(C₄₃⋊C₉)	1	6	yes	—
75	C₉	C₃×C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
76	C₉	C₃×#11923958	1	2	yes	—
77	C₃	—	3	1	no	—
78	C₃	—	3	3	no	—
79	C₃	—	9	3	no	—
80	C₃	C₃×C₃²⋊(C₄₃⋊C₉)	1	1	yes	characteristic

	subgroup	G/H
center	C₉	C₃×C₃²⋊(C₄₃⋊C₃)
commutator	C₃²×C₄₃	C₃²×C₉
Frattini	C₃×C₉	C₃²×C₄₃⋊C₃
Fitting	C₃×C₄₃×#737	C₃
socle	C₃×C₄₃	C₃×C₃²⋊C₉
prime radical	C₃×H(3,𝔽₃)×C₄₃	C₉
cosocle	C₃×C₉×C₄₃	C₃³
hypercenter	C₃×#737	C₄₃⋊C₃
hypocenter	C₄₃	#10624694
LCS	G ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₉ ◁ C₃²×C₉ ◁ C₃×#737

Complements

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

N	H ≅ G/N	type
1. C₃×#16812505	C₃	semidirect
2. #23782718	C₃	semidirect
54. C₄₃	#10624694	semidirect

Maximal subgroups

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

subgroup	index
C₃×#16812505	3
#23782718	3
C₃×C₄₃×#737	3
#10624694	43