Subgroups — #44531938

Order 31347.

230 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄₃⋊C₂₇	C₃	1	3	yes	maximal
2	C₃×C₉²×C₄₃	C₃	1	1	yes	maximal, characteristic
3	C₃×C₄₃⋊C₂₇	—	3	3	no	—
4	C₃×C₄₃⋊C₂₇	—	3	3	no	—
5	C₃×C₄₃⋊C₂₇	—	3	3	no	—
6	C₃×C₄₃⋊C₂₇	C₉	1	9	yes	complemented
7	C₃²×C₉×C₄₃	C₉	1	3	yes	—
8	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
9	C₉²×C₄₃	—	3	1	no	—
10	C₉²×C₄₃	—	3	2	no	—
11	C₄₃⋊C₂₇	—	3	9	no	—
12	C₃³×C₄₃	C₃×C₉	1	1	yes	characteristic
13	C₃×C₉×C₄₃	—	3	3	no	—
14	C₃×C₉×C₄₃	—	3	6	no	—
15	C₃×C₉×C₄₃	C₂₇	1	9	yes	complemented
16	C₃×C₉×C₄₃	C₃×C₉	1	3	yes	—
17	C₃×C₉×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
18	C₃×C₉×C₄₃	3₋¹⁺²	1	3	yes	—
19	C₃×C₉×C₄₃	3₋¹⁺²	1	3	yes	—
20	C₃×C₉×C₄₃	3₋¹⁺²	1	2	yes	—
21	#10624463	—	43	1	no	maximal, Sylow
22	C₃²×C₄₃	C₉²	1	1	yes	characteristic
23	C₃²×C₄₃	C₃²⋊C₉	1	1	yes	characteristic
24	C₃²×C₄₃	C₉⋊C₉	1	1	yes	characteristic
25	C₃²×C₄₃	C₉⋊C₉	1	1	yes	characteristic
26	C₃²×C₄₃	C₃×C₂₇	1	3	yes	—
27	C₃²×C₄₃	C₂₇⋊C₃	1	6	yes	—
28	C₉×C₄₃	—	3	9	no	—
29	C₉×C₄₃	C₃²⋊C₉	1	3	yes	—
30	C₉×C₄₃	C₉⋊C₉	1	6	yes	—
31	C₃²×C₂₇	—	43	3	no	—
32	C₃×C₉²	C₄₃⋊C₃	1	1	yes	characteristic
33	C₃×C₄₃	#6855	1	1	yes	characteristic
34	C₃×C₄₃	C₉×C₂₇	1	1	yes	characteristic
35	C₃×C₄₃	#6864	1	2	yes	—
36	C₃×C₄₃	C₃²⋊C₂₇	1	3	yes	—
37	C₃×C₄₃	C₉⋊C₂₇	1	3	yes	—
38	C₃×C₄₃	C₉⋊C₂₇	1	3	yes	—
39	C₃²×C₉	C₄₃⋊C₉	1	3	yes	—
40	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
41	C₃×C₂₇	—	43	9	no	—
42	C₃×C₂₇	—	129	3	no	—
43	C₃×C₂₇	—	129	3	no	—
44	C₃×C₂₇	—	129	3	no	—
45	C₉²	—	3	1	no	—
46	C₉²	—	3	2	no	—
47	C₄₃	#10624463	1	1	yes	characteristic, complemented, Sylow
48	C₃³	C₃×C₄₃⋊C₉	1	1	yes	characteristic
49	C₃×C₉	—	3	3	no	—
50	C₃×C₉	—	3	6	no	—
51	C₃×C₉	C₄₃⋊C₂₇	1	9	yes	complemented
52	C₃×C₉	C₉×C₄₃⋊C₃	1	3	yes	—
53	C₃×C₉	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
54	C₃×C₉	#11923956	1	3	yes	—
55	C₃×C₉	#11923957	1	3	yes	—
56	C₃×C₉	#11923958	1	2	yes	—
57	C₂₇	—	129	9	no	—
58	C₃²	C₉×C₄₃⋊C₉	1	1	yes	characteristic
59	C₃²	C₃²⋊(C₄₃⋊C₉)	1	1	yes	characteristic
60	C₃²	#16812499	1	1	yes	characteristic
61	C₃²	#16812500	1	1	yes	characteristic
62	C₃²	C₃×C₄₃⋊C₂₇	1	3	yes	—
63	C₃²	#16812505	1	6	yes	—
64	C₉	—	3	9	no	—
65	C₉	(C₃×C₄₃⋊C₃)⋊C₉	1	3	yes	—
66	C₉	(C₄₃⋊C₉)⋊C₉	1	6	yes	—
67	C₃	C₄₃⋊#6855	1	1	yes	characteristic
68	C₃	C₉×C₄₃⋊C₂₇	1	1	yes	characteristic
69	C₃	#23782708	1	2	yes	—
70	C₃	C₃²⋊(C₄₃⋊C₂₇)	1	3	yes	—
71	C₃	#23782733	1	3	yes	—
72	C₃	#23782734	1	3	yes	—

	subgroup	G/H
center, Frattini	C₃²×C₉	C₃×C₄₃⋊C₃
commutator	C₃×C₄₃	C₉×C₂₇
Fitting	C₃×C₉²×C₄₃	C₃
socle, prime radical	C₃³×C₄₃	C₃×C₉
cosocle	C₃²×C₉×C₄₃	C₃²
hypercenter	C₃×C₉²	C₄₃⋊C₃
hypocenter	C₄₃	#10624463
LCS	G ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃²×C₉ ◁ C₃×C₉²

Complements

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

N	H ≅ G/N	type
6. C₃×C₄₃⋊C₂₇	C₉	semidirect
15. C₃×C₉×C₄₃	C₂₇	semidirect
47. C₄₃	#10624463	semidirect
51. C₃×C₉	C₄₃⋊C₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₄₃⋊C₂₇	3
C₃×C₉²×C₄₃	3
#10624463	43