Subgroups — #44534466

Order 31347.

154 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782856	C₃	1	1	yes	maximal, characteristic
2	#23782744	C₃	1	1	yes	maximal, characteristic, complemented
3	#23782743	C₃	1	3	yes	maximal, complemented
4	#23782742	C₃	1	3	yes	maximal, complemented
5	C₃×C₄₃⋊C₈₁	C₃	1	1	yes	maximal, characteristic, complemented
6	C₈₁×C₄₃⋊C₃	C₃	1	3	yes	maximal, complemented
7	C₄₃×C₈₁⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
8	#16812525	C₉	1	1	yes	characteristic
9	#16812505	C₉	1	2	yes	—
10	#16812504	C₉	1	3	yes	—
11	#16812503	C₉	1	3	yes	—
12	C₂₇×C₄₃⋊C₃	C₃²	1	3	yes	—
13	C₄₃⋊C₈₁	C₃²	1	1	yes	characteristic
14	C₄₃⋊C₈₁	C₃²	1	3	yes	—
15	C₄₃⋊C₈₁	C₃²	1	1	yes	characteristic
16	C₄₃⋊C₈₁	C₃²	1	1	yes	characteristic
17	C₃×C₂₇×C₄₃	C₃²	1	1	yes	characteristic
18	C₄₃×C₈₁	C₃²	1	3	yes	—
19	#11923958	C₂₇	1	2	yes	—
20	#11923957	C₂₇	1	3	yes	—
21	#11923956	C₂₇	1	3	yes	—
22	C₃²⋊(C₄₃⋊C₃)	C₂₇	1	1	yes	characteristic
23	C₉×C₄₃⋊C₃	C₃×C₉	1	3	yes	—
24	C₄₃⋊C₂₇	C₃×C₉	1	6	yes	—
25	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
26	C₂₇×C₄₃	C₃×C₉	1	1	yes	characteristic
27	C₂₇×C₄₃	C₃×C₉	1	1	yes	characteristic
28	C₂₇×C₄₃	C₃³	1	1	yes	characteristic
29	#10624833	—	43	1	no	maximal, Sylow
30	C₃²×C₄₃	C₃×C₂₇	1	1	yes	characteristic
31	C₃×C₄₃⋊C₃	C₃×C₂₇	1	3	yes	—
32	C₉×C₄₃	C₃×C₂₇	1	1	yes	characteristic
33	C₉×C₄₃	C₃×C₂₇	1	1	yes	characteristic
34	C₉×C₄₃	C₃²×C₉	1	1	yes	characteristic
35	C₄₃⋊C₉	C₃×C₂₇	1	6	yes	—
36	#6903	—	43	1	no	—
37	C₈₁⋊C₃	—	43	1	no	—
38	C₈₁⋊C₃	—	43	3	no	—
39	C₈₁⋊C₃	—	43	3	no	—
40	C₈₁⋊C₃	C₄₃⋊C₃	1	1	yes	characteristic, complemented
41	C₃×C₈₁	—	43	1	no	—
42	C₃×C₈₁	—	43	3	no	—
43	C₃×C₄₃	—	3	1	no	—
44	C₃×C₄₃	C₃²×C₂₇	1	1	yes	characteristic
45	C₄₃⋊C₃	—	3	3	no	—
46	#737	—	43	1	no	—
47	C₂₇⋊C₃	—	43	2	no	—
48	C₂₇⋊C₃	—	43	3	no	—
49	C₂₇⋊C₃	—	43	3	no	—
50	C₃×C₂₇	—	43	3	no	—
51	C₃×C₂₇	C₃×C₄₃⋊C₃	1	1	yes	characteristic
52	C₈₁	—	43	1	no	—
53	C₈₁	—	43	3	no	—
54	C₈₁	—	43	1	no	—
55	C₈₁	—	43	1	no	—
56	C₈₁	C₃×C₄₃⋊C₃	1	3	yes	—
57	C₄₃	#10624833	1	1	yes	characteristic, complemented, Sylow
58	3₋¹⁺²	—	43	2	no	—
59	3₋¹⁺²	—	43	3	no	—
60	3₋¹⁺²	—	43	3	no	—
61	H(3,𝔽₃)	—	43	1	no	—
62	C₃×C₉	—	43	3	no	—
63	C₃×C₉	C₉×C₄₃⋊C₃	1	1	yes	characteristic
64	C₂₇	—	43	6	no	—
65	C₂₇	C₉×C₄₃⋊C₃	1	1	yes	characteristic
66	C₂₇	C₉×C₄₃⋊C₃	1	1	yes	characteristic
67	C₂₇	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
68	C₃²	—	43	3	no	—
69	C₃²	C₂₇×C₄₃⋊C₃	1	1	yes	characteristic
70	C₉	—	43	6	no	—
71	C₉	C₂₇×C₄₃⋊C₃	1	1	yes	characteristic
72	C₉	C₂₇×C₄₃⋊C₃	1	1	yes	characteristic
73	C₉	C₃×C₉×C₄₃⋊C₃	1	1	yes	characteristic
74	C₃	—	3	1	no	—
75	C₃	—	129	3	no	—
76	C₃	C₃×C₂₇×C₄₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂₇	C₃²×C₄₃⋊C₃
commutator, socle	C₃×C₄₃	C₃²×C₂₇
Fitting	C₄₃×C₈₁⋊C₃	C₃
prime radical	C₃²⋊(C₄₃⋊C₃)	C₂₇
cosocle	C₂₇×C₄₃	C₃³
hypercenter	C₈₁⋊C₃	C₄₃⋊C₃
hypocenter	C₄₃	#10624833
LCS	G ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂₇ ◁ C₈₁⋊C₃

Complements

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

N	H ≅ G/N	type
2. #23782744	C₃	semidirect
3. #23782743	C₃	semidirect
4. #23782742	C₃	semidirect
5. C₃×C₄₃⋊C₈₁	C₃	semidirect
6. C₈₁×C₄₃⋊C₃	C₃	semidirect
7. C₄₃×C₈₁⋊C₃	C₃	semidirect
40. C₈₁⋊C₃	C₄₃⋊C₃	semidirect
57. C₄₃	#10624833	semidirect

Maximal subgroups

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

subgroup	index
#23782856	3
#23782744	3
#23782743	3
#23782742	3
C₃×C₄₃⋊C₈₁	3
C₈₁×C₄₃⋊C₃	3
C₄₃×C₈₁⋊C₃	3
#10624833	43