Subgroups — #44531892

Order 31347.

136 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	C₃²×C₉×C₄₃	C₉	1	2	yes	—
5	C₃²×C₉×C₄₃	C₉	1	1	yes	characteristic
6	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
7	C₉²×C₄₃	—	3	1	no	—
8	C₉²×C₄₃	—	3	2	no	—
9	C₄₃⋊C₂₇	—	9	3	no	—
10	C₃³×C₄₃	C₃×C₉	1	1	yes	characteristic
11	C₃×C₉×C₄₃	—	3	1	no	—
12	C₃×C₉×C₄₃	—	3	2	no	—
13	C₃×C₉×C₄₃	—	3	2	no	—
14	C₃×C₉×C₄₃	—	3	1	no	—
15	C₃×C₉×C₄₃	—	3	2	no	—
16	C₃×C₉×C₄₃	—	3	6	no	—
17	C₃×C₉×C₄₃	C₂₇	1	3	yes	complemented
18	C₃×C₉×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
19	C₃×C₉×C₄₃	3₋¹⁺²	1	2	yes	—
20	#10624446	—	43	1	no	maximal, Sylow
21	C₃²×C₄₃	—	3	1	no	—
22	C₃²×C₄₃	—	3	2	no	—
23	C₃²×C₄₃	C₃²⋊C₉	1	1	yes	characteristic
24	C₃²×C₄₃	C₃×C₂₇	1	1	yes	characteristic
25	C₃²×C₄₃	C₂₇⋊C₃	1	2	yes	—
26	C₉×C₄₃	—	3	3	no	—
27	C₉×C₄₃	—	3	2	no	—
28	C₉×C₄₃	—	3	6	no	—
29	C₉×C₄₃	#732	1	1	yes	characteristic
30	C₉×C₄₃	#733	1	2	yes	—
31	C₃×C₉²	C₄₃⋊C₃	1	1	yes	characteristic
32	C₃²⋊C₂₇	—	43	3	no	—
33	C₃×C₄₃	—	3	1	no	—
34	C₃×C₄₃	—	3	2	no	—
35	C₃×C₄₃	C₃²⋊C₂₇	1	1	yes	characteristic
36	C₃×C₄₃	#6868	1	1	yes	characteristic
37	C₃×C₄₃	#6869	1	2	yes	—
38	C₃²×C₉	C₄₃⋊C₉	1	2	yes	—
39	C₃²×C₉	C₄₃⋊C₉	1	1	yes	characteristic
40	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
41	C₃×C₂₇	—	129	3	no	—
42	C₉²	—	3	1	no	—
43	C₉²	—	3	2	no	—
44	C₄₃	#10624446	1	1	yes	characteristic, complemented, Sylow
45	C₃³	C₃×C₄₃⋊C₉	1	1	yes	characteristic
46	C₃×C₉	—	3	1	no	—
47	C₃×C₉	—	3	2	no	—
48	C₃×C₉	—	3	2	no	—
49	C₃×C₉	—	3	1	no	—
50	C₃×C₉	—	3	2	no	—
51	C₃×C₉	—	3	6	no	—
52	C₃×C₉	C₄₃⋊C₂₇	1	3	yes	complemented
53	C₃×C₉	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
54	C₃×C₉	#11923958	1	2	yes	—
55	C₂₇	—	387	3	no	—
56	C₃²	—	3	1	no	—
57	C₃²	—	3	2	no	—
58	C₃²	C₃²⋊(C₄₃⋊C₉)	1	1	yes	characteristic
59	C₃²	C₃×C₄₃⋊C₂₇	1	1	yes	characteristic
60	C₃²	#16812505	1	2	yes	—
61	C₉	—	3	3	no	—
62	C₉	—	3	2	no	—
63	C₉	—	3	6	no	—
64	C₉	#16812513	1	1	yes	characteristic
65	C₉	#16812515	1	2	yes	—
66	C₃	—	3	1	no	—
67	C₃	—	3	2	no	—
68	C₃	C₃²⋊(C₄₃⋊C₂₇)	1	1	yes	characteristic
69	C₃	#23782716	1	1	yes	characteristic
70	C₃	#23782718	1	2	yes	—

	subgroup	G/H
center	C₃×C₉	C₃²⋊(C₄₃⋊C₃)
commutator	C₃²×C₄₃	C₃×C₂₇
Frattini	C₃²×C₉	C₃×C₄₃⋊C₃
Fitting	C₃×C₉²×C₄₃	C₃
socle	C₃²×C₄₃	C₃²⋊C₉
prime radical	C₃³×C₄₃	C₃×C₉
cosocle	C₃²×C₉×C₄₃	C₃²
hypercenter	C₃×C₉²	C₄₃⋊C₃
hypocenter	C₄₃	#10624446
LCS	G ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉ ◁ C₃×C₉²

Complements

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

N	H ≅ G/N	type
17. C₃×C₉×C₄₃	C₂₇	semidirect
44. C₄₃	#10624446	semidirect
52. 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
#10624446	43