Subgroups — #44534552

Order 31347.

188 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782877	C₃	1	3	yes	maximal, complemented
2	#23782767	C₃	1	3	yes	maximal, complemented
3	#23782762	C₃	1	3	yes	maximal, complemented
4	#23782757	C₃	1	3	yes	maximal, complemented
5	C₄₃×#6887	C₃	1	1	yes	maximal, characteristic, complemented
6	#16812525	—	3	3	no	—
7	#16812515	C₃²	1	3	yes	—
8	#16812515	C₃²	1	3	yes	—
9	#16812513	C₃²	1	3	yes	—
10	#16812510	—	3	3	no	—
11	#16812507	—	3	3	no	—
12	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
13	C₄₃×C₉⋊C₉	—	3	1	no	—
14	C₄₃×C₉⋊C₉	C₃²	1	3	yes	—
15	C₄₃×C₃²⋊C₉	—	3	1	no	—
16	C₉²×C₄₃	—	3	1	no	—
17	#11923958	—	3	3	no	—
18	#11923958	—	3	3	no	—
19	#11923957	—	9	3	no	—
20	#11923956	—	9	3	no	—
21	C₃²⋊(C₄₃⋊C₃)	—	3	3	no	—
22	C₉×C₄₃⋊C₃	—	9	3	no	—
23	C₃³×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
24	C₃×C₉×C₄₃	—	3	3	no	—
25	C₃×C₉×C₄₃	—	3	3	no	—
26	C₃×C₉×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
27	C₃×C₉×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
28	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
29	#10624849	—	43	1	no	maximal, Sylow
30	C₃²×C₄₃	—	3	1	no	—
31	C₃²×C₄₃	—	9	1	no	—
32	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
33	C₃×C₄₃⋊C₃	—	9	3	no	—
34	C₉×C₄₃	—	3	1	no	—
35	C₉×C₄₃	—	3	1	no	—
36	C₉×C₄₃	—	9	3	no	—
37	C₉×C₄₃	#732	1	3	yes	—
38	C₄₃⋊C₉	—	9	3	no	—
39	C₄₃⋊C₉	—	9	3	no	—
40	#6908	—	43	3	no	—
41	#6887	C₄₃⋊C₃	1	1	yes	characteristic, complemented
42	#6883	—	43	3	no	—
43	#6882	—	43	3	no	—
44	#6881	—	43	3	no	—
45	C₃×C₄₃	—	3	1	no	—
46	C₃×C₄₃	—	9	1	no	—
47	C₃×C₄₃	C₃×#732	1	1	yes	characteristic
48	C₄₃⋊C₃	—	27	3	no	—
49	#737	—	129	3	no	—
50	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
51	#733	—	43	3	no	—
52	#733	—	43	3	no	—
53	#732	—	43	3	no	—
54	#731	—	129	3	no	—
55	AΣL(1,𝔽₂₇)	—	129	3	no	—
56	C₉⋊C₉	—	3	1	no	—
57	C₉⋊C₉	C₃×C₄₃⋊C₃	1	3	yes	—
58	C₃²⋊C₉	—	3	1	no	—
59	C₉²	—	3	1	no	—
60	C₄₃	#10624849	1	1	yes	characteristic, complemented, Sylow
61	C₃³	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
62	3₋¹⁺²	—	129	3	no	—
63	3₋¹⁺²	—	129	3	no	—
64	3₋¹⁺²	—	387	3	no	—
65	3₋¹⁺²	—	387	3	no	—
66	H(3,𝔽₃)	—	129	3	no	—
67	C₃×C₉	—	3	3	no	—
68	C₃×C₉	—	3	3	no	—
69	C₃×C₉	—	387	3	no	—
70	C₃×C₉	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
71	C₃×C₉	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
72	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
73	C₃²	—	3	1	no	—
74	C₃²	—	9	1	no	—
75	C₃²	—	387	3	no	—
76	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
77	C₉	—	3	1	no	—
78	C₉	—	3	1	no	—
79	C₉	—	9	3	no	—
80	C₉	—	387	3	no	—
81	C₉	—	387	3	no	—
82	C₉	#16812513	1	3	yes	—
83	C₃	—	3	1	no	—
84	C₃	—	9	1	no	—
85	C₃	—	1161	3	no	—
86	C₃	C₃×#16812513	1	1	yes	characteristic

	subgroup	G/H
center	C₃	C₃×#16812513
commutator, cosocle	C₃×C₉×C₄₃	C₃³
Frattini	C₃×C₉	C₃²×C₄₃⋊C₃
Fitting	C₄₃×#6887	C₃
socle	C₃×C₄₃	C₃×#732
hypercenter	#6887	C₄₃⋊C₃
hypocenter	C₄₃	#10624849
LCS	G ▷ C₃×C₉×C₄₃ ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃ ◁ C₃×C₉ ◁ C₃²×C₉ ◁ #6887

Complements

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

N	H ≅ G/N	type
1. #23782877	C₃	semidirect
2. #23782767	C₃	semidirect
3. #23782762	C₃	semidirect
4. #23782757	C₃	semidirect
5. C₄₃×#6887	C₃	semidirect
41. #6887	C₄₃⋊C₃	semidirect
60. C₄₃	#10624849	semidirect

Maximal subgroups

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

subgroup	index
#23782877	3
#23782767	3
#23782762	3
#23782757	3
C₄₃×#6887	3
#10624849	43