Subgroups — #44532196

Order 31347.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782877	C₃	1	1	yes	maximal, characteristic
2	C₃×#16812505	C₃	1	1	yes	maximal, characteristic, complemented
3	#23782718	C₃	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#6869	C₃	1	1	yes	maximal, characteristic, complemented
5	#16812525	—	3	1	no	—
6	#16812515	C₉	1	2	yes	—
7	#16812513	C₉	1	1	yes	characteristic
8	#16812510	—	3	1	no	—
9	#16812507	—	3	1	no	—
10	#16812505	—	3	3	no	—
11	#16812505	—	3	1	no	—
12	C₃×C₄₃⋊C₂₇	—	3	1	no	—
13	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
14	C₄₃×C₂₇⋊C₃	—	3	1	no	—
15	#11923958	—	3	2	no	—
16	#11923957	—	9	1	no	—
17	#11923956	—	9	1	no	—
18	C₃²⋊(C₄₃⋊C₃)	—	3	1	no	—
19	C₉×C₄₃⋊C₃	—	9	1	no	—
20	C₄₃⋊C₂₇	—	3	3	no	—
21	C₄₃⋊C₂₇	—	9	1	no	—
22	C₃³×C₄₃	3₋¹⁺²	1	1	yes	characteristic
23	C₃×C₉×C₄₃	—	3	1	no	—
24	C₃×C₉×C₄₃	—	3	1	no	—
25	C₃×C₉×C₄₃	—	3	1	no	—
26	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
27	C₃×C₉×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
28	C₃×C₉×C₄₃	3₋¹⁺²	1	1	yes	characteristic
29	C₂₇×C₄₃	—	9	1	no	—
30	#10624530	—	43	1	no	maximal, Sylow
31	C₃²×C₄₃	—	3	1	no	—
32	C₃²×C₄₃	—	9	1	no	—
33	C₃²×C₄₃	C₃²⋊C₉	1	1	yes	characteristic
34	C₃×C₄₃⋊C₃	—	9	1	no	—
35	C₉×C₄₃	—	3	1	no	—
36	C₉×C₄₃	—	3	1	no	—
37	C₉×C₄₃	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
38	C₉×C₄₃	#731	1	1	yes	characteristic
39	C₉×C₄₃	#732	1	1	yes	characteristic
40	C₄₃⋊C₉	—	9	2	no	—
41	#6908	—	43	1	no	—
42	C₃×C₂₇⋊C₃	—	43	1	no	—
43	#6869	—	43	1	no	—
44	#6869	C₄₃⋊C₃	1	1	yes	characteristic, complemented
45	C₃×C₄₃	—	3	1	no	—
46	C₃×C₄₃	—	9	1	no	—
47	C₃×C₄₃	H(3,𝔽₃)⋊C₉	1	1	yes	characteristic
48	C₄₃⋊C₃	—	27	1	no	—
49	#737	—	129	1	no	—
50	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
51	#733	—	43	2	no	—
52	#732	—	43	1	no	—
53	#731	—	129	1	no	—
54	AΣL(1,𝔽₂₇)	—	129	1	no	—
55	C₂₇⋊C₃	—	3	1	no	—
56	C₂₇⋊C₃	—	129	3	no	—
57	C₂₇⋊C₃	—	129	1	no	—
58	C₃×C₂₇	—	129	1	no	—
59	C₄₃	#10624530	1	1	yes	characteristic, complemented, Sylow
60	C₃³	#11923956	1	1	yes	characteristic
61	3₋¹⁺²	—	129	2	no	—
62	3₋¹⁺²	—	387	1	no	—
63	3₋¹⁺²	—	387	1	no	—
64	H(3,𝔽₃)	—	129	1	no	—
65	C₃×C₉	—	3	1	no	—
66	C₃×C₉	—	3	1	no	—
67	C₃×C₉	—	3	1	no	—
68	C₃×C₉	—	387	1	no	—
69	C₃×C₉	C₉×C₄₃⋊C₃	1	1	yes	characteristic
70	C₃×C₉	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
71	C₃×C₉	#11923957	1	1	yes	characteristic
72	C₂₇	—	9	1	no	—
73	C₂₇	—	129	3	no	—
74	C₂₇	—	387	1	no	—
75	C₃²	—	3	1	no	—
76	C₃²	—	9	1	no	—
77	C₃²	—	387	1	no	—
78	C₃²	(C₃×C₄₃⋊C₃)⋊C₉	1	1	yes	characteristic
79	C₉	—	3	1	no	—
80	C₉	—	3	1	no	—
81	C₉	—	387	2	no	—
82	C₉	#16812508	1	1	yes	characteristic
83	C₉	#16812511	1	1	yes	characteristic
84	C₉	#16812512	1	1	yes	characteristic
85	C₃	—	3	1	no	—
86	C₃	—	9	1	no	—
87	C₃	—	1161	1	no	—
88	C₃	#23782719	1	1	yes	characteristic

	subgroup	G/H
center	C₉	#16812512
commutator	C₃×C₉×C₄₃	C₃×C₉
Frattini	C₃²×C₉	C₃×C₄₃⋊C₃
Fitting	C₄₃×#6869	C₃
socle	C₃×C₄₃	H(3,𝔽₃)⋊C₉
prime radical	#23782877	C₃
cosocle	C₃²×C₉×C₄₃	C₃²
hypercenter	#6869	C₄₃⋊C₃
hypocenter	C₄₃	#10624530
LCS	G ▷ C₃×C₉×C₄₃ ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₉ ◁ C₃×C₉ ◁ C₃²×C₉ ◁ #6869

Complements

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

N	H ≅ G/N	type
2. C₃×#16812505	C₃	semidirect
3. #23782718	C₃	semidirect
4. C₄₃×#6869	C₃	semidirect
44. #6869	C₄₃⋊C₃	semidirect
59. C₄₃	#10624530	semidirect

Maximal subgroups

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

subgroup	index
#23782877	3
C₃×#16812505	3
#23782718	3
C₄₃×#6869	3
#10624530	43