Subgroups — #44534356

Order 31347.

208 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782822	C₃	1	2	yes	maximal, complemented
2	#23782808	C₃	1	1	yes	maximal, characteristic
3	#23782724	C₃	1	6	yes	maximal, complemented
4	#23782721	C₃	1	3	yes	maximal
5	C₃×C₄₃×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃×#11923958	C₃²	1	2	yes	—
7	C₃×C₃²⋊(C₄₃⋊C₃)	C₃²	1	1	yes	characteristic
8	(C₄₃⋊C₉)⋊C₉	—	3	6	no	—
9	C₃²⋊(C₄₃⋊C₉)	C₃²	1	6	yes	—
10	(C₃×C₄₃⋊C₃)⋊C₉	—	3	3	no	—
11	C₃²×C₉×C₄₃	C₃²	1	3	yes	—
12	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
13	C₄₃×C₉⋊C₉	—	3	3	no	—
14	C₃²×C₄₃⋊C₃	—	3	1	no	—
15	#11923958	—	3	6	no	—
16	C₃²⋊(C₄₃⋊C₃)	—	3	3	no	—
17	C₃×C₄₃⋊C₉	—	3	2	no	—
18	C₃×C₄₃⋊C₉	—	3	6	no	—
19	C₃³×C₄₃	C₃³	1	1	yes	characteristic
20	C₃×C₉×C₄₃	—	3	3	no	—
21	C₃×C₉×C₄₃	—	3	3	no	—
22	C₃×C₉×C₄₃	—	9	3	no	—
23	C₃×C₉×C₄₃	H(3,𝔽₃)	1	3	yes	—
24	#10624817	—	43	1	no	maximal, Sylow
25	C₃²×C₄₃	—	3	3	no	—
26	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
27	C₃²×C₄₃	#737	1	3	yes	—
28	C₃×C₄₃⋊C₃	—	9	3	no	—
29	C₃×C₄₃⋊C₃	—	9	1	no	—
30	C₉×C₄₃	—	3	3	no	—
31	C₉×C₄₃	—	9	3	no	—
32	C₄₃⋊C₉	—	9	6	no	—
33	C₄₃⋊C₉	—	9	2	no	—
34	#6895	—	43	2	no	—
35	#6893	—	43	1	no	—
36	C₃×C₉⋊C₉	C₄₃⋊C₃	1	1	yes	characteristic, complemented
37	3₋¹⁺²⋊C₉	—	43	6	no	—
38	H(3,𝔽₃)⋊C₉	—	43	3	no	—
39	C₃×C₄₃	—	3	3	no	—
40	C₃×C₄₃	#6893	1	1	yes	characteristic
41	C₃×C₄₃	#6913	1	3	yes	—
42	C₄₃⋊C₃	—	27	1	no	—
43	C₃×3₋¹⁺²	—	43	2	no	—
44	C₃×H(3,𝔽₃)	—	43	1	no	—
45	C₃²×C₉	C₃×C₄₃⋊C₃	1	3	yes	—
46	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
47	C₉⋊C₉	—	3	3	no	—
48	C₉⋊C₉	—	129	6	no	—
49	C₃²⋊C₉	—	43	6	no	—
50	C₃²⋊C₉	—	129	3	no	—
51	C₄₃	#10624817	1	1	yes	characteristic, complemented, Sylow
52	C₃³	—	129	1	no	—
53	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
54	3₋¹⁺²	—	129	6	no	—
55	H(3,𝔽₃)	—	129	3	no	—
56	C₃×C₉	—	3	3	no	—
57	C₃×C₉	—	3	3	no	—
58	C₃×C₉	—	9	3	no	—
59	C₃×C₉	—	129	6	no	—
60	C₃×C₉	—	129	2	no	—
61	C₃×C₉	C₃²⋊(C₄₃⋊C₃)	1	3	yes	—
62	C₃²	—	3	3	no	—
63	C₃²	—	387	1	no	—
64	C₃²	—	387	3	no	—
65	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
66	C₃²	#16812525	1	3	yes	—
67	C₉	—	3	3	no	—
68	C₉	—	9	3	no	—
69	C₉	—	387	2	no	—
70	C₉	—	387	6	no	—
71	C₃	—	3	3	no	—
72	C₃	—	1161	1	no	—
73	C₃	#23782808	1	1	yes	characteristic
74	C₃	#23782905	1	3	yes	—

	subgroup	G/H
center	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)
commutator, cosocle	C₃³×C₄₃	C₃³
Frattini	C₃³	C₃²×C₄₃⋊C₃
Fitting	C₃×C₄₃×C₉⋊C₉	C₃
socle	C₃²×C₄₃	C₃×H(3,𝔽₃)
prime radical	C₃×C₃²⋊(C₄₃⋊C₃)	C₃²
hypercenter	C₃×C₉⋊C₉	C₄₃⋊C₃
hypocenter	C₄₃	#10624817
LCS	G ▷ C₃³×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ C₃²×C₉ ◁ C₃×C₉⋊C₉

Complements

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

N	H ≅ G/N	type
1. #23782822	C₃	semidirect
3. #23782724	C₃	semidirect
5. C₃×C₄₃×C₉⋊C₉	C₃	semidirect
36. C₃×C₉⋊C₉	C₄₃⋊C₃	semidirect
51. C₄₃	#10624817	semidirect

Maximal subgroups

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

subgroup	index
#23782822	3
#23782808	3
#23782724	3
#23782721	3
C₃×C₄₃×C₉⋊C₉	3
#10624817	43