Subgroups — #46798570

Order 33777.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16836728	C₃	1	1	yes	maximal, characteristic
2	C₃×C₉×C₁₃₉⋊C₃	C₃	1	1	yes	maximal, characteristic
3	#26014604	C₃	1	2	yes	maximal, complemented
4	#26014604	C₃	1	1	yes	maximal, characteristic, complemented
5	#26014603	C₃	1	1	yes	maximal, characteristic, complemented
6	(C₁₃₉⋊C₉)⋊C₉	C₃	1	2	yes	maximal, complemented
7	(C₁₃₉⋊C₉)⋊C₉	C₃	1	2	yes	maximal, complemented
8	(C₃×C₁₃₉⋊C₃)⋊C₉	C₃	1	2	yes	maximal
9	C₉⋊C₉×C₁₃₉	C₃	1	1	yes	maximal, characteristic, complemented
10	C₃²×C₁₃₉⋊C₃	C₃²	1	1	yes	characteristic
11	#16836728	—	3	3	no	—
12	C₃×C₁₃₉⋊C₉	C₃²	1	2	yes	—
13	C₃×C₁₃₉⋊C₉	C₃²	1	2	yes	—
14	C₃×C₁₃₉⋊C₉	C₃²	1	1	yes	characteristic
15	C₃×C₁₃₉⋊C₉	C₃²	1	2	yes	—
16	C₃×C₁₃₉⋊C₉	C₃²	1	1	yes	characteristic
17	C₉×C₁₃₉⋊C₃	—	3	3	no	—
18	C₃×C₉×C₁₃₉	C₃²	1	2	yes	—
19	C₃×C₉×C₁₃₉	C₃²	1	1	yes	characteristic
20	C₃×C₉×C₁₃₉	C₃²	1	1	yes	characteristic
21	C₃²×C₁₃₉	C₃³	1	1	yes	characteristic
22	C₃×C₁₃₉⋊C₃	—	3	1	no	—
23	C₃×C₁₃₉⋊C₃	—	3	2	no	—
24	C₃×C₁₃₉⋊C₃	3₋¹⁺²	1	3	yes	—
25	C₉×C₁₃₉	—	3	1	no	—
26	C₉×C₁₃₉	—	3	2	no	—
27	C₉×C₁₃₉	3₋¹⁺²	1	3	yes	complemented
28	C₁₃₉⋊C₉	—	3	2	no	—
29	C₁₃₉⋊C₉	—	3	1	no	—
30	C₁₃₉⋊C₉	—	3	1	no	—
31	C₁₃₉⋊C₉	—	3	2	no	—
32	C₁₃₉⋊C₉	—	3	2	no	—
33	C₃×C₁₃₉	C₃×3₋¹⁺²	1	1	yes	characteristic
34	C₃×C₁₃₉	C₃×3₋¹⁺²	1	1	yes	characteristic
35	C₃×C₁₃₉	#737	1	2	yes	—
36	C₁₃₉⋊C₃	—	3	3	no	—
37	#6894	—	139	1	no	maximal, Sylow
38	C₁₃₉	#6894	1	1	yes	characteristic, complemented, Sylow
39	C₃×3₋¹⁺²	—	139	1	no	—
40	C₃²×C₉	—	139	1	no	—
41	C₉⋊C₉	—	139	2	no	—
42	C₉⋊C₉	—	139	2	no	—
43	C₉⋊C₉	—	139	1	no	—
44	C₉⋊C₉	—	139	1	no	—
45	C₉⋊C₉	—	139	2	no	—
46	C₉⋊C₉	C₁₃₉⋊C₃	1	1	yes	characteristic, complemented
47	C₃²⋊C₉	—	139	2	no	—
48	C₃³	—	139	1	no	—
49	3₋¹⁺²	—	417	3	no	—
50	C₃×C₉	—	139	2	no	—
51	C₃×C₉	—	139	2	no	—
52	C₃×C₉	—	139	2	no	—
53	C₃×C₉	—	139	1	no	—
54	C₃×C₉	—	139	1	no	—
55	C₃×C₉	—	417	3	no	—
56	C₃×C₉	C₃×C₁₃₉⋊C₃	1	2	yes	—
57	C₃×C₉	C₃×C₁₃₉⋊C₃	1	1	yes	characteristic
58	C₃×C₉	C₃×C₁₃₉⋊C₃	1	1	yes	characteristic
59	C₃²	—	139	3	no	—
60	C₃²	—	417	1	no	—
61	C₃²	—	417	2	no	—
62	C₃²	C₃²×C₁₃₉⋊C₃	1	1	yes	characteristic
63	C₉	—	3	1	no	—
64	C₉	—	3	2	no	—
65	C₉	—	417	1	no	—
66	C₉	—	417	1	no	—
67	C₉	—	417	2	no	—
68	C₉	—	417	2	no	—
69	C₉	—	417	2	no	—
70	C₉	#16836728	1	3	yes	complemented
71	C₃	—	417	3	no	—
72	C₃	3₋¹⁺²×C₁₃₉⋊C₃	1	1	yes	characteristic
73	C₃	C₃×#16836728	1	1	yes	characteristic
74	C₃	#26014630	1	2	yes	—

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₁₃₉⋊C₃
commutator, socle, cosocle	C₃²×C₁₃₉	C₃³
Fitting	C₉⋊C₉×C₁₃₉	C₃
prime radical	C₃²×C₁₃₉⋊C₃	C₃²
hypercenter	C₉⋊C₉	C₁₃₉⋊C₃
hypocenter	C₁₃₉	#6894
LCS	G ▷ C₃²×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₃² ◁ C₉⋊C₉

Complements

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

N	H ≅ G/N	type
3. #26014604	C₃	semidirect
4. #26014604	C₃	semidirect
5. #26014603	C₃	semidirect
6. (C₁₃₉⋊C₉)⋊C₉	C₃	semidirect
7. (C₁₃₉⋊C₉)⋊C₉	C₃	semidirect
9. C₉⋊C₉×C₁₃₉	C₃	semidirect
27. C₉×C₁₃₉	3₋¹⁺²	semidirect
38. C₁₃₉	#6894	semidirect
46. C₉⋊C₉	C₁₃₉⋊C₃	semidirect
70. C₉	#16836728	semidirect

Maximal subgroups

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

subgroup	index
C₃×#16836728	3
C₃×C₉×C₁₃₉⋊C₃	3
#26014604	3
#26014603	3
(C₁₃₉⋊C₉)⋊C₉	3
(C₃×C₁₃₉⋊C₃)⋊C₉	3
C₉⋊C₉×C₁₃₉	3
#6894	139