Subgroups — #44532361

Order 31347.

524 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#11923958	C₃	1	2	yes	maximal
2	C₃×C₃²⋊(C₄₃⋊C₉)	C₃	1	1	yes	maximal, characteristic
3	C₄₃⋊#6855	C₃	1	9	yes	maximal, complemented
4	C₃×C₄₃×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic
5	C₃×#11923958	—	3	18	no	—
6	C₃×#11923958	—	3	6	no	—
7	C₃²×C₄₃⋊C₉	C₃²	1	3	yes	—
8	C₃²×C₄₃⋊C₉	C₃²	1	6	yes	—
9	C₃²⋊(C₄₃⋊C₉)	—	3	3	no	—
10	C₃⁴×C₄₃	C₃²	1	1	yes	characteristic
11	C₃²×C₉×C₄₃	C₃²	1	3	yes	—
12	C₄₃×C₃²⋊C₉	—	3	3	no	—
13	#11923958	—	3	54	no	—
14	C₃×C₄₃⋊C₉	—	3	6	no	—
15	C₃×C₄₃⋊C₉	—	3	12	no	—
16	C₃×C₄₃⋊C₉	—	3	3	no	—
17	C₃×C₄₃⋊C₉	—	3	9	no	—
18	C₃×C₄₃⋊C₉	3₋¹⁺²	1	18	yes	complemented
19	C₃³×C₄₃	—	3	6	no	—
20	C₃³×C₄₃	—	3	3	no	—
21	C₃³×C₄₃	—	3	3	no	—
22	C₃³×C₄₃	H(3,𝔽₃)	1	3	yes	—
23	C₃³×C₄₃	C₃³	1	1	yes	characteristic
24	C₃×C₉×C₄₃	—	3	3	no	—
25	C₃×C₉×C₄₃	—	3	9	no	—
26	#10624567	—	43	1	no	maximal, Sylow
27	C₃²×C₄₃	—	3	6	no	—
28	C₃²×C₄₃	—	3	3	no	—
29	C₃²×C₄₃	—	3	3	no	—
30	C₃²×C₄₃	—	9	9	no	—
31	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
32	C₃²×C₄₃	C₃×3₋¹⁺²	1	6	yes	—
33	C₃²×C₄₃	#737	1	3	yes	—
34	C₃²×C₄₃	#737	1	3	yes	—
35	C₉×C₄₃	—	9	3	no	—
36	C₄₃⋊C₉	—	3	18	no	—
37	C₄₃⋊C₉	—	9	3	no	—
38	C₃²×3₋¹⁺²	—	43	2	no	—
39	C₃×C₃²⋊C₉	—	43	1	no	—
40	C₃×C₃²⋊C₉	C₄₃⋊C₃	1	1	yes	characteristic
41	#6855	—	43	9	no	—
42	C₃×C₄₃	—	9	3	no	—
43	C₃×C₄₃	#6891	1	2	yes	—
44	C₃×C₄₃	#6893	1	1	yes	characteristic
45	C₃×C₄₃	#6893	1	1	yes	characteristic
46	C₃×C₄₃	#6896	1	9	yes	—
47	C₃⁴	C₃×C₄₃⋊C₃	1	1	yes	characteristic
48	C₃×3₋¹⁺²	—	129	18	no	—
49	C₃×3₋¹⁺²	—	129	6	no	—
50	C₃²×C₉	—	43	6	no	—
51	C₃²×C₉	—	43	3	no	—
52	C₃²×C₉	C₃×C₄₃⋊C₃	1	3	yes	—
53	C₃²⋊C₉	—	3	3	no	—
54	C₃²⋊C₉	—	129	3	no	—
55	C₄₃	#10624567	1	1	yes	characteristic, complemented, Sylow
56	C₃³	—	3	6	no	—
57	C₃³	—	3	3	no	—
58	C₃³	—	3	3	no	—
59	C₃³	C₃²⋊(C₄₃⋊C₃)	1	3	yes	—
60	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
61	3₋¹⁺²	—	129	54	no	—
62	C₃×C₉	—	3	3	no	—
63	C₃×C₉	—	3	9	no	—
64	C₃×C₉	—	43	18	no	—
65	C₃×C₉	—	129	6	no	—
66	C₃×C₉	—	129	12	no	—
67	C₃×C₉	—	129	3	no	—
68	C₃×C₉	—	129	9	no	—
69	C₃²	—	3	6	no	—
70	C₃²	—	3	3	no	—
71	C₃²	—	3	3	no	—
72	C₃²	—	9	9	no	—
73	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
74	C₃²	3₋¹⁺²×C₄₃⋊C₃	1	6	yes	—
75	C₃²	#16812524	1	3	yes	—
76	C₃²	#16812525	1	3	yes	—
77	C₉	—	9	3	no	—
78	C₉	—	129	18	no	—
79	C₉	—	387	3	no	—
80	C₃	—	9	3	no	—
81	C₃	#23782795	1	2	yes	—
82	C₃	#23782806	1	1	yes	characteristic
83	C₃	#23782808	1	1	yes	characteristic
84	C₃	#23782823	1	9	yes	—

	subgroup	G/H
center, Frattini	C₃³	C₃²×C₄₃⋊C₃
commutator, socle, cosocle	C₃³×C₄₃	C₃³
Fitting	C₃×C₄₃×C₃²⋊C₉	C₃
prime radical	C₃⁴×C₄₃	C₃²
hypercenter	C₃×C₃²⋊C₉	C₄₃⋊C₃
hypocenter	C₄₃	#10624567
LCS	G ▷ C₃³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃³ ◁ C₃×C₃²⋊C₉

Complements

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

N	H ≅ G/N	type
3. C₄₃⋊#6855	C₃	semidirect
18. C₃×C₄₃⋊C₉	3₋¹⁺²	semidirect
55. C₄₃	#10624567	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#11923958	3
C₃×C₃²⋊(C₄₃⋊C₉)	3
C₄₃⋊#6855	3
C₃×C₄₃×C₃²⋊C₉	3
#10624567	43