Subgroups — #46798477

Order 33777.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×C₁₃₉⋊C₃	C₃	1	1	yes	maximal, characteristic
2	#26014609	C₃	1	2	yes	maximal, complemented
3	C₂₇⋊C₃×C₁₃₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃²×C₁₃₉⋊C₃	C₉	1	1	yes	characteristic
5	C₃×C₁₃₉⋊C₉	C₉	1	2	yes	—
6	C₉×C₁₃₉⋊C₃	—	3	1	no	—
7	C₉×C₁₃₉⋊C₃	—	3	1	no	—
8	C₉×C₁₃₉⋊C₃	—	3	1	no	—
9	C₁₃₉⋊C₂₇	—	3	2	no	—
10	C₃×C₉×C₁₃₉	C₃²	1	1	yes	characteristic
11	C₂₇×C₁₃₉	—	3	1	no	—
12	C₃²×C₁₃₉	C₃×C₉	1	1	yes	characteristic
13	C₃×C₁₃₉⋊C₃	—	3	1	no	—
14	C₃×C₁₃₉⋊C₃	—	3	3	no	—
15	C₉×C₁₃₉	H(3,𝔽₃)	1	1	yes	characteristic
16	C₉×C₁₃₉	3₋¹⁺²	1	1	yes	characteristic
17	C₉×C₁₃₉	3₋¹⁺²	1	1	yes	characteristic
18	C₁₃₉⋊C₉	—	3	2	no	—
19	C₃×C₁₃₉	—	3	1	no	—
20	C₃×C₁₃₉	C₃²⋊C₉	1	1	yes	characteristic
21	C₁₃₉⋊C₃	—	3	3	no	—
22	#6869	—	139	1	no	maximal, Sylow
23	C₁₃₉	#6869	1	1	yes	characteristic, complemented, Sylow
24	C₃²×C₉	—	139	1	no	—
25	C₂₇⋊C₃	—	139	2	no	—
26	C₂₇⋊C₃	C₁₃₉⋊C₃	1	1	yes	characteristic, complemented
27	C₃³	—	139	1	no	—
28	C₃×C₉	—	139	2	no	—
29	C₃×C₉	—	417	1	no	—
30	C₃×C₉	—	417	1	no	—
31	C₃×C₉	—	417	1	no	—
32	C₃×C₉	C₃×C₁₃₉⋊C₃	1	1	yes	characteristic
33	C₂₇	—	3	1	no	—
34	C₂₇	—	417	2	no	—
35	C₃²	—	417	3	no	—
36	C₃²	—	417	1	no	—
37	C₃²	C₉×C₁₃₉⋊C₃	1	1	yes	characteristic
38	C₉	—	417	2	no	—
39	C₉	C₃²⋊(C₁₃₉⋊C₃)	1	1	yes	characteristic
40	C₉	#16836728	1	1	yes	characteristic
41	C₉	#16836729	1	1	yes	characteristic
42	C₃	—	3	1	no	—
43	C₃	—	417	3	no	—
44	C₃	(C₃×C₁₃₉⋊C₃)⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₉	C₃²⋊(C₁₃₉⋊C₃)
commutator	C₃²×C₁₃₉	C₃×C₉
Frattini	C₃×C₉	C₃×C₁₃₉⋊C₃
Fitting	C₂₇⋊C₃×C₁₃₉	C₃
socle	C₃×C₁₃₉	C₃²⋊C₉
prime radical	C₃²×C₁₃₉⋊C₃	C₉
cosocle	C₃×C₉×C₁₃₉	C₃²
hypercenter	C₂₇⋊C₃	C₁₃₉⋊C₃
hypocenter	C₁₃₉	#6869
LCS	G ▷ C₃²×C₁₃₉ ▷ C₃×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₉ ◁ C₃×C₉ ◁ C₂₇⋊C₃

Complements

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

N	H ≅ G/N	type
2. #26014609	C₃	semidirect
3. C₂₇⋊C₃×C₁₃₉	C₃	semidirect
23. C₁₃₉	#6869	semidirect
26. C₂₇⋊C₃	C₁₃₉⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×C₁₃₉⋊C₃	3
#26014609	3
C₂₇⋊C₃×C₁₃₉	3
#6869	139