Subgroups — #44531928

Order 31347.

208 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812525	C₃	1	1	yes	maximal, characteristic
2	C₃²⋊(C₄₃⋊C₂₇)	C₃	1	2	yes	maximal, complemented
3	C₄₃×C₃²⋊C₂₇	C₃	1	1	yes	maximal, characteristic, complemented
4	#16812525	—	3	3	no	—
5	#16812525	—	3	6	no	—
6	C₃×#11923958	C₉	1	2	yes	—
7	C₃×#11923957	—	3	1	no	—
8	C₃×#11923956	—	3	1	no	—
9	C₃×C₃²⋊(C₄₃⋊C₃)	C₉	1	1	yes	characteristic
10	C₃×C₉×C₄₃⋊C₃	—	3	1	no	—
11	C₃×C₄₃⋊C₂₇	—	3	2	no	—
12	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
13	C₃×C₂₇×C₄₃	—	3	1	no	—
14	C₃²×C₄₃⋊C₃	—	3	1	no	—
15	#11923958	—	3	6	no	—
16	#11923957	—	3	9	no	—
17	#11923956	—	3	9	no	—
18	C₃²⋊(C₄₃⋊C₃)	—	3	3	no	—
19	C₃×C₄₃⋊C₉	—	3	2	no	—
20	C₉×C₄₃⋊C₃	—	3	3	no	—
21	C₉×C₄₃⋊C₃	—	3	6	no	—
22	C₄₃⋊C₂₇	—	9	2	no	—
23	C₃³×C₄₃	C₃×C₉	1	1	yes	characteristic
24	C₃×C₉×C₄₃	—	3	1	no	—
25	C₃×C₉×C₄₃	—	3	2	no	—
26	C₃×C₉×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
27	C₃×C₉×C₄₃	3₋¹⁺²	1	1	yes	characteristic
28	C₃×C₉×C₄₃	3₋¹⁺²	1	1	yes	characteristic
29	C₂₇×C₄₃	—	9	1	no	—
30	#10624459	—	43	1	no	maximal, Sylow
31	C₃²×C₄₃	—	3	1	no	—
32	C₃²×C₄₃	—	3	2	no	—
33	C₃²×C₄₃	—	3	1	no	—
34	C₃²×C₄₃	C₃²⋊C₉	1	1	yes	characteristic
35	C₃×C₄₃⋊C₃	—	3	3	no	—
36	C₃×C₄₃⋊C₃	—	9	2	no	—
37	C₃×C₄₃⋊C₃	—	9	1	no	—
38	C₉×C₄₃	—	3	1	no	—
39	C₉×C₄₃	—	3	1	no	—
40	C₉×C₄₃	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
41	C₉×C₄₃	AΣL(1,𝔽₂₇)	1	2	yes	—
42	C₄₃⋊C₉	—	3	6	no	—
43	C₃×#737	—	43	1	no	—
44	C₃²⋊C₂₇	—	43	2	no	—
45	C₃²⋊C₂₇	C₄₃⋊C₃	1	1	yes	characteristic, complemented
46	C₃×C₄₃	—	9	1	no	—
47	C₃×C₄₃	#6866	1	1	yes	characteristic
48	C₃×C₄₃	#6873	1	2	yes	—
49	C₃×C₄₃	#6873	1	1	yes	characteristic
50	C₄₃⋊C₃	—	9	3	no	—
51	#737	—	129	3	no	—
52	#737	—	129	6	no	—
53	C₃×3₋¹⁺²	—	43	2	no	—
54	C₃×3₋¹⁺²	—	129	1	no	—
55	C₃×3₋¹⁺²	—	129	1	no	—
56	C₃×H(3,𝔽₃)	—	43	1	no	—
57	C₃²×C₉	—	129	1	no	—
58	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
59	C₃×C₂₇	—	3	1	no	—
60	C₃×C₂₇	—	129	2	no	—
61	C₄₃	#10624459	1	1	yes	characteristic, complemented, Sylow
62	C₃³	—	129	1	no	—
63	C₃³	C₉×C₄₃⋊C₃	1	1	yes	characteristic
64	3₋¹⁺²	—	129	9	no	—
65	3₋¹⁺²	—	129	9	no	—
66	3₋¹⁺²	—	129	6	no	—
67	H(3,𝔽₃)	—	129	3	no	—
68	C₃×C₉	—	3	1	no	—
69	C₃×C₉	—	3	2	no	—
70	C₃×C₉	—	129	2	no	—
71	C₃×C₉	—	129	3	no	—
72	C₃×C₉	—	129	6	no	—
73	C₃×C₉	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
74	C₃×C₉	#11923956	1	1	yes	characteristic
75	C₃×C₉	#11923957	1	1	yes	characteristic
76	C₂₇	—	9	1	no	—
77	C₂₇	—	387	2	no	—
78	C₃²	—	3	1	no	—
79	C₃²	—	3	2	no	—
80	C₃²	—	3	1	no	—
81	C₃²	—	129	3	no	—
82	C₃²	—	387	2	no	—
83	C₃²	—	387	1	no	—
84	C₃²	(C₃×C₄₃⋊C₃)⋊C₉	1	1	yes	characteristic
85	C₉	—	3	1	no	—
86	C₉	—	3	1	no	—
87	C₉	—	129	6	no	—
88	C₉	#16812506	1	1	yes	characteristic
89	C₉	#16812508	1	2	yes	—
90	C₃	—	9	1	no	—
91	C₃	—	387	3	no	—
92	C₃	#23782711	1	1	yes	characteristic
93	C₃	#23782729	1	2	yes	—
94	C₃	#23782731	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₉	C₃²⋊(C₄₃⋊C₃)
commutator	C₃³×C₄₃	C₃×C₉
Frattini	C₃²×C₉	C₃×C₄₃⋊C₃
Fitting	C₄₃×C₃²⋊C₂₇	C₃
socle	C₃²×C₄₃	C₃²⋊C₉
prime radical	C₃×C₃²⋊(C₄₃⋊C₃)	C₉
cosocle	C₃²×C₉×C₄₃	C₃²
hypercenter	C₃²⋊C₂₇	C₄₃⋊C₃
hypocenter	C₄₃	#10624459
LCS	G ▷ C₃³×C₄₃ ▷ C₃²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉ ◁ C₃²⋊C₂₇

Complements

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

N	H ≅ G/N	type
2. C₃²⋊(C₄₃⋊C₂₇)	C₃	semidirect
3. C₄₃×C₃²⋊C₂₇	C₃	semidirect
45. C₃²⋊C₂₇	C₄₃⋊C₃	semidirect
61. C₄₃	#10624459	semidirect

Maximal subgroups

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

subgroup	index
C₃×#16812525	3
C₃²⋊(C₄₃⋊C₂₇)	3
C₄₃×C₃²⋊C₂₇	3
#10624459	43