Subgroups — #44533605

Order 31347.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#11923958	C₃	1	1	yes	maximal, characteristic
2	(C₄₃⋊C₉)⋊C₂₇	C₃	1	6	yes	maximal, complemented
3	C₃²⋊(C₄₃⋊C₂₇)	C₃	1	2	yes	maximal
4	#23782707	C₃	1	3	yes	maximal, complemented
5	C₃²×C₂₇×C₄₃	C₃	1	1	yes	maximal, characteristic
6	C₃×#11923958	C₉	1	1	yes	characteristic
7	C₃×C₄₃⋊C₂₇	C₃²	1	6	yes	—
8	(C₄₃⋊C₉)⋊C₉	C₉	1	6	yes	—
9	C₃²⋊(C₄₃⋊C₉)	C₉	1	2	yes	—
10	C₉×C₄₃⋊C₉	C₃²	1	3	yes	—
11	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
12	C₃×C₂₇×C₄₃	—	3	3	no	—
13	C₃×C₂₇×C₄₃	C₃²	1	2	yes	—
14	C₃×C₂₇×C₄₃	C₃²	1	1	yes	characteristic
15	#11923958	—	3	3	no	—
16	C₃×C₄₃⋊C₉	C₃×C₉	1	6	yes	—
17	C₃×C₄₃⋊C₉	C₃×C₉	1	3	yes	—
18	C₄₃⋊C₂₇	—	3	6	no	—
19	C₃³×C₄₃	C₃×C₉	1	1	yes	characteristic
20	C₃×C₉×C₄₃	—	3	1	no	—
21	C₃×C₉×C₄₃	—	3	2	no	—
22	C₃×C₉×C₄₃	C₃×C₉	1	2	yes	—
23	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
24	C₂₇×C₄₃	—	3	2	no	—
25	C₂₇×C₄₃	3₋¹⁺²	1	3	yes	complemented
26	#10624727	—	43	1	no	maximal, Sylow
27	C₃²×C₄₃	—	3	1	no	—
28	C₃²×C₄₃	—	3	2	no	—
29	C₃²×C₄₃	C₂₇⋊C₃	1	3	yes	—
30	C₃²×C₄₃	C₃²×C₉	1	1	yes	characteristic
31	C₉×C₄₃	—	3	2	no	—
32	C₉×C₄₃	C₃×3₋¹⁺²	1	1	yes	characteristic
33	C₉×C₄₃	#737	1	2	yes	—
34	C₄₃⋊C₉	—	3	3	no	—
35	C₄₃⋊C₉	—	3	6	no	—
36	C₃²×C₂₇	C₄₃⋊C₃	1	1	yes	characteristic
37	C₉×3₋¹⁺²	—	43	1	no	—
38	C₉⋊C₂₇	—	43	6	no	—
39	C₃²⋊C₂₇	—	43	2	no	—
40	#6864	—	43	3	no	—
41	C₃×C₄₃	—	3	3	no	—
42	C₃×C₄₃	C₉×3₋¹⁺²	1	1	yes	characteristic
43	C₃×C₄₃	C₃×C₂₇⋊C₃	1	1	yes	characteristic
44	C₃×C₄₃	#6903	1	2	yes	—
45	C₃×3₋¹⁺²	—	43	1	no	—
46	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
47	C₃×C₂₇	—	3	3	no	—
48	C₃×C₂₇	—	43	6	no	—
49	C₃×C₂₇	C₃×C₄₃⋊C₃	1	2	yes	—
50	C₃×C₂₇	C₃×C₄₃⋊C₃	1	1	yes	characteristic
51	C₉⋊C₉	—	43	6	no	—
52	C₃²⋊C₉	—	43	2	no	—
53	C₉²	—	43	3	no	—
54	C₄₃	#10624727	1	1	yes	characteristic, complemented, Sylow
55	C₃³	C₉×C₄₃⋊C₃	1	1	yes	characteristic
56	3₋¹⁺²	—	129	3	no	—
57	C₃×C₉	—	3	1	no	—
58	C₃×C₉	—	3	2	no	—
59	C₃×C₉	—	43	6	no	—
60	C₃×C₉	—	43	3	no	—
61	C₃×C₉	C₉×C₄₃⋊C₃	1	2	yes	—
62	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
63	C₂₇	—	3	2	no	—
64	C₂₇	—	129	6	no	—
65	C₂₇	#11923958	1	3	yes	complemented
66	C₃²	—	3	1	no	—
67	C₃²	—	3	2	no	—
68	C₃²	#16812504	1	3	yes	—
69	C₃²	C₃×C₉×C₄₃⋊C₃	1	1	yes	characteristic
70	C₉	—	3	2	no	—
71	C₉	—	129	3	no	—
72	C₉	—	129	6	no	—
73	C₉	C₃×#11923958	1	1	yes	characteristic
74	C₉	#16812525	1	2	yes	—
75	C₃	—	3	3	no	—
76	C₃	C₉×#11923958	1	1	yes	characteristic
77	C₃	C₃×#16812504	1	1	yes	characteristic
78	C₃	#23782856	1	2	yes	—

	subgroup	G/H
center, Frattini	C₃×C₉	C₃²×C₄₃⋊C₃
commutator, socle	C₃²×C₄₃	C₃²×C₉
Fitting	C₃²×C₂₇×C₄₃	C₃
prime radical	C₃³×C₄₃	C₃×C₉
cosocle	C₃×C₉×C₄₃	C₃³
hypercenter	C₃²×C₂₇	C₄₃⋊C₃
hypocenter	C₄₃	#10624727
LCS	G ▷ C₃²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₂₇

Complements

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

N	H ≅ G/N	type
2. (C₄₃⋊C₉)⋊C₂₇	C₃	semidirect
4. #23782707	C₃	semidirect
25. C₂₇×C₄₃	3₋¹⁺²	semidirect
54. C₄₃	#10624727	semidirect
65. C₂₇	#11923958	semidirect

Maximal subgroups

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

subgroup	index
C₉×#11923958	3
(C₄₃⋊C₉)⋊C₂₇	3
C₃²⋊(C₄₃⋊C₂₇)	3
#23782707	3
C₃²×C₂₇×C₄₃	3
#10624727	43