Subgroups — #44533594

Order 31347.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782857	C₃	1	3	yes	maximal, complemented
2	C₃×#16812505	C₃	1	1	yes	maximal, characteristic, complemented
3	#23782730	C₃	1	3	yes	maximal, complemented
4	#23782727	C₃	1	3	yes	maximal, complemented
5	#23782718	C₃	1	2	yes	maximal, complemented
6	C₄₃×#6908	C₃	1	1	yes	maximal, characteristic
7	#16812505	—	3	3	no	—
8	#16812505	—	3	6	no	—
9	#16812505	C₃²	1	6	yes	—
10	C₃×C₄₃⋊C₂₇	—	3	3	no	—
11	C₃×C₄₃⋊C₂₇	C₃²	1	1	yes	characteristic
12	C₃×C₄₃⋊C₂₇	C₃²	1	1	yes	characteristic
13	C₃×C₄₃⋊C₂₇	C₃²	1	1	yes	characteristic
14	C₄₃×#737	C₃²	1	3	yes	—
15	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
16	C₄₃×#733	C₉	1	2	yes	—
17	C₄₃×#732	C₉	1	1	yes	characteristic
18	C₄₃×#731	C₉	1	3	yes	—
19	C₄₃×AΣL(1,𝔽₂₇)	C₉	1	3	yes	—
20	C₄₃⋊C₂₇	—	3	6	no	—
21	C₄₃⋊C₂₇	—	3	1	no	—
22	C₄₃⋊C₂₇	—	3	1	no	—
23	C₄₃⋊C₂₇	H(3,𝔽₃)	1	3	yes	—
24	C₃³×C₄₃	C₃×C₉	1	1	yes	characteristic
25	3₋¹⁺²×C₄₃	—	3	6	no	—
26	3₋¹⁺²×C₄₃	C₃×C₉	1	6	yes	—
27	H(3,𝔽₃)×C₄₃	C₃×C₉	1	3	yes	—
28	C₃×C₉×C₄₃	—	3	1	no	—
29	C₃×C₉×C₄₃	—	3	3	no	—
30	C₃×C₉×C₄₃	—	3	2	no	—
31	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
32	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
33	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
34	#10624725	—	43	1	no	maximal, Sylow
35	C₃²×C₄₃	—	3	1	no	—
36	C₃²×C₄₃	—	3	3	no	—
37	C₃²×C₄₃	—	9	1	no	—
38	C₃²×C₄₃	C₃²×C₉	1	1	yes	characteristic
39	C₉×C₄₃	—	3	1	no	—
40	C₉×C₄₃	—	3	1	no	—
41	C₉×C₄₃	—	3	6	no	—
42	C₉×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
43	C₉×C₄₃	#737	1	2	yes	—
44	#6908	C₄₃⋊C₃	1	1	yes	characteristic
45	#6903	—	43	3	no	—
46	C₃×C₂₇⋊C₃	—	43	1	no	—
47	#6873	—	43	3	no	—
48	#6872	—	43	3	no	—
49	#6869	—	43	2	no	—
50	C₃×C₄₃	—	3	1	no	—
51	C₃×C₄₃	—	9	3	no	—
52	C₃×C₄₃	—	9	1	no	—
53	C₃×C₄₃	C₉×H(3,𝔽₃)	1	1	yes	characteristic
54	#737	C₃×C₄₃⋊C₃	1	3	yes	—
55	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
56	#733	C₄₃⋊C₉	1	2	yes	—
57	#732	C₄₃⋊C₉	1	1	yes	characteristic
58	#731	C₄₃⋊C₉	1	3	yes	—
59	AΣL(1,𝔽₂₇)	C₄₃⋊C₉	1	3	yes	—
60	C₂₇⋊C₃	—	43	6	no	—
61	C₂₇⋊C₃	—	129	3	no	—
62	C₂₇⋊C₃	—	129	6	no	—
63	C₃×C₂₇	—	43	1	no	—
64	C₃×C₂₇	—	43	1	no	—
65	C₃×C₂₇	—	43	1	no	—
66	C₃×C₂₇	—	129	3	no	—
67	C₄₃	#10624725	1	1	yes	characteristic, complemented, Sylow
68	C₃³	C₃×C₄₃⋊C₉	1	1	yes	characteristic
69	3₋¹⁺²	—	3	6	no	—
70	3₋¹⁺²	C₃×C₄₃⋊C₉	1	6	yes	—
71	H(3,𝔽₃)	C₃×C₄₃⋊C₉	1	3	yes	—
72	C₃×C₉	—	3	3	no	—
73	C₃×C₉	—	3	1	no	—
74	C₃×C₉	—	3	2	no	—
75	C₃×C₉	C₃×C₄₃⋊C₉	1	1	yes	characteristic
76	C₃×C₉	C₃×C₄₃⋊C₉	1	1	yes	characteristic
77	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
78	C₂₇	—	43	3	no	—
79	C₂₇	—	129	1	no	—
80	C₂₇	—	129	1	no	—
81	C₂₇	—	129	6	no	—
82	C₃²	—	3	1	no	—
83	C₃²	—	3	3	no	—
84	C₃²	—	9	1	no	—
85	C₃²	C₃²×C₄₃⋊C₉	1	1	yes	characteristic
86	C₉	—	3	1	no	—
87	C₉	—	3	1	no	—
88	C₉	—	3	6	no	—
89	C₉	H(3,𝔽₃)×C₄₃⋊C₃	1	1	yes	characteristic
90	C₉	#16812524	1	2	yes	—
91	C₃	—	3	1	no	—
92	C₃	—	9	3	no	—
93	C₃	—	9	1	no	—
94	C₃	H(3,𝔽₃)×C₄₃⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₉	H(3,𝔽₃)×C₄₃⋊C₃
commutator	C₃²×C₄₃	C₃²×C₉
Frattini	C₃×C₉	C₃²×C₄₃⋊C₃
Fitting, prime radical	C₄₃×#6908	C₃
socle	C₃×C₄₃	C₉×H(3,𝔽₃)
cosocle	C₃×C₉×C₄₃	C₃³
hypercenter	#6908	C₄₃⋊C₃
hypocenter	C₄₃	#10624725
LCS	G ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₉ ◁ C₃×C₉ ◁ #6908

Complements

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

N	H ≅ G/N	type
1. #23782857	C₃	semidirect
2. C₃×#16812505	C₃	semidirect
3. #23782730	C₃	semidirect
4. #23782727	C₃	semidirect
5. #23782718	C₃	semidirect
67. C₄₃	#10624725	semidirect

Maximal subgroups

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

subgroup	index
#23782857	3
C₃×#16812505	3
#23782730	3
#23782727	3
#23782718	3
C₄₃×#6908	3
#10624725	43