Subgroups — #44533503

Order 31347.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782780	C₃	1	1	yes	maximal, characteristic
2	(C₄₃⋊C₉)⋊C₂₇	C₃	1	6	yes	maximal, complemented
3	(C₃×C₄₃⋊C₃)⋊C₂₇	C₃	1	3	yes	maximal
4	#23782708	C₃	1	2	yes	maximal, complemented
5	C₉×C₂₇×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃×C₉×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
7	C₃×C₄₃⋊C₂₇	C₃²	1	6	yes	—
8	(C₄₃⋊C₉)⋊C₉	C₉	1	6	yes	—
9	(C₃×C₄₃⋊C₃)⋊C₉	C₉	1	3	yes	—
10	C₉×C₄₃⋊C₉	C₃²	1	2	yes	—
11	C₃×C₂₇×C₄₃	C₃²	1	3	yes	—
12	C₉²×C₄₃	C₃²	1	1	yes	characteristic
13	C₃²×C₄₃⋊C₃	C₃×C₉	1	1	yes	characteristic
14	C₃×C₄₃⋊C₉	C₃×C₉	1	6	yes	—
15	C₃×C₄₃⋊C₉	C₃×C₉	1	2	yes	—
16	C₉×C₄₃⋊C₃	—	3	3	no	—
17	C₄₃⋊C₂₇	—	3	6	no	—
18	C₃×C₉×C₄₃	C₃×C₉	1	3	yes	—
19	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
20	C₂₇×C₄₃	—	3	3	no	—
21	#10624713	—	43	1	no	maximal, Sylow
22	C₃²×C₄₃	C₃²×C₉	1	1	yes	characteristic
23	C₃×C₄₃⋊C₃	—	3	1	no	—
24	C₃×C₄₃⋊C₃	—	3	3	no	—
25	C₉×C₄₃	—	3	3	no	—
26	C₉×C₄₃	#737	1	3	yes	—
27	C₄₃⋊C₉	—	3	2	no	—
28	C₄₃⋊C₉	—	3	6	no	—
29	#6887	—	43	1	no	—
30	C₉⋊C₂₇	—	43	6	no	—
31	C₃²⋊C₂₇	—	43	3	no	—
32	#6864	—	43	2	no	—
33	C₉×C₂₇	C₄₃⋊C₃	1	1	yes	characteristic, complemented
34	C₃×C₄₃	#6887	1	1	yes	characteristic
35	C₃×C₄₃	#6903	1	3	yes	—
36	C₄₃⋊C₃	—	9	1	no	—
37	C₃²×C₉	—	43	1	no	—
38	C₃×C₂₇	—	43	6	no	—
39	C₃×C₂₇	C₃×C₄₃⋊C₃	1	3	yes	—
40	C₉⋊C₉	—	43	6	no	—
41	C₃²⋊C₉	—	43	3	no	—
42	C₉²	—	43	2	no	—
43	C₉²	C₃×C₄₃⋊C₃	1	1	yes	characteristic
44	C₄₃	#10624713	1	1	yes	characteristic, complemented, Sylow
45	C₃³	—	43	1	no	—
46	C₃×C₉	—	43	6	no	—
47	C₃×C₉	—	43	2	no	—
48	C₃×C₉	—	129	3	no	—
49	C₃×C₉	C₉×C₄₃⋊C₃	1	3	yes	—
50	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
51	C₂₇	—	3	3	no	—
52	C₂₇	—	129	6	no	—
53	C₃²	—	129	1	no	—
54	C₃²	—	129	3	no	—
55	C₃²	C₃×C₉×C₄₃⋊C₃	1	1	yes	characteristic
56	C₉	—	3	3	no	—
57	C₉	—	129	2	no	—
58	C₉	—	129	6	no	—
59	C₉	#16812525	1	3	yes	—
60	C₃	—	387	1	no	—
61	C₃	#23782780	1	1	yes	characteristic
62	C₃	#23782856	1	3	yes	—

	subgroup	G/H
center, Frattini	C₃×C₉	C₃²×C₄₃⋊C₃
commutator, socle	C₃²×C₄₃	C₃²×C₉
Fitting	C₉×C₂₇×C₄₃	C₃
prime radical	C₃²×C₄₃⋊C₃	C₃×C₉
cosocle	C₃×C₉×C₄₃	C₃³
hypercenter	C₉×C₂₇	C₄₃⋊C₃
hypocenter	C₄₃	#10624713
LCS	G ▷ C₃²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃×C₉ ◁ C₉×C₂₇

Complements

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

N	H ≅ G/N	type
2. (C₄₃⋊C₉)⋊C₂₇	C₃	semidirect
4. #23782708	C₃	semidirect
5. C₉×C₂₇×C₄₃	C₃	semidirect
33. C₉×C₂₇	C₄₃⋊C₃	semidirect
44. C₄₃	#10624713	semidirect

Maximal subgroups

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

subgroup	index
#23782780	3
(C₄₃⋊C₉)⋊C₂₇	3
(C₃×C₄₃⋊C₃)⋊C₂₇	3
#23782708	3
C₉×C₂₇×C₄₃	3
#10624713	43