Subgroups — #46798618

Order 33777.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26014629	C₃	1	1	yes	maximal, characteristic
2	#26014609	C₃	1	1	yes	maximal, characteristic, complemented
3	#26014608	C₃	1	3	yes	maximal, complemented
4	#26014607	C₃	1	3	yes	maximal, complemented
5	C₃×C₁₃₉⋊C₂₇	C₃	1	1	yes	maximal, characteristic, complemented
6	C₂₇×C₁₃₉⋊C₃	C₃	1	3	yes	maximal, complemented
7	C₂₇⋊C₃×C₁₃₉	C₃	1	1	yes	maximal, characteristic, complemented
8	#16836730	C₉	1	2	yes	—
9	#16836729	C₉	1	3	yes	—
10	#16836728	C₉	1	3	yes	—
11	C₃²⋊(C₁₃₉⋊C₃)	C₉	1	1	yes	characteristic
12	C₉×C₁₃₉⋊C₃	C₃²	1	3	yes	—
13	C₁₃₉⋊C₂₇	C₃²	1	1	yes	characteristic
14	C₁₃₉⋊C₂₇	C₃²	1	3	yes	—
15	C₁₃₉⋊C₂₇	C₃²	1	1	yes	characteristic
16	C₁₃₉⋊C₂₇	C₃²	1	1	yes	characteristic
17	C₃×C₉×C₁₃₉	C₃²	1	1	yes	characteristic
18	C₂₇×C₁₃₉	C₃²	1	3	yes	—
19	C₃²×C₁₃₉	C₃×C₉	1	1	yes	characteristic
20	C₃×C₁₃₉⋊C₃	C₃×C₉	1	3	yes	—
21	C₉×C₁₃₉	C₃×C₉	1	1	yes	characteristic
22	C₉×C₁₃₉	C₃×C₉	1	1	yes	characteristic
23	C₉×C₁₃₉	C₃³	1	1	yes	characteristic
24	C₁₃₉⋊C₉	C₃×C₉	1	6	yes	—
25	C₃×C₁₃₉	—	3	1	no	—
26	C₃×C₁₃₉	C₃²×C₉	1	1	yes	characteristic
27	C₁₃₉⋊C₃	—	3	3	no	—
28	#6903	—	139	1	no	maximal, Sylow
29	C₁₃₉	#6903	1	1	yes	characteristic, complemented, Sylow
30	#737	—	139	1	no	—
31	C₂₇⋊C₃	—	139	1	no	—
32	C₂₇⋊C₃	—	139	3	no	—
33	C₂₇⋊C₃	—	139	3	no	—
34	C₂₇⋊C₃	C₁₃₉⋊C₃	1	1	yes	characteristic, complemented
35	C₃×C₂₇	—	139	1	no	—
36	C₃×C₂₇	—	139	3	no	—
37	3₋¹⁺²	—	139	2	no	—
38	3₋¹⁺²	—	139	3	no	—
39	3₋¹⁺²	—	139	3	no	—
40	H(3,𝔽₃)	—	139	1	no	—
41	C₃×C₉	—	139	3	no	—
42	C₃×C₉	C₃×C₁₃₉⋊C₃	1	1	yes	characteristic
43	C₂₇	—	139	1	no	—
44	C₂₇	—	139	3	no	—
45	C₂₇	—	139	1	no	—
46	C₂₇	—	139	1	no	—
47	C₂₇	C₃×C₁₃₉⋊C₃	1	3	yes	—
48	C₃²	—	139	3	no	—
49	C₃²	C₉×C₁₃₉⋊C₃	1	1	yes	characteristic
50	C₉	—	139	6	no	—
51	C₉	C₉×C₁₃₉⋊C₃	1	1	yes	characteristic
52	C₉	C₉×C₁₃₉⋊C₃	1	1	yes	characteristic
53	C₉	C₃²×C₁₃₉⋊C₃	1	1	yes	characteristic
54	C₃	—	3	1	no	—
55	C₃	—	417	3	no	—
56	C₃	C₃×C₉×C₁₃₉⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₉	C₃²×C₁₃₉⋊C₃
commutator, socle	C₃×C₁₃₉	C₃²×C₉
Fitting	C₂₇⋊C₃×C₁₃₉	C₃
prime radical	C₃²⋊(C₁₃₉⋊C₃)	C₉
cosocle	C₉×C₁₃₉	C₃³
hypercenter	C₂₇⋊C₃	C₁₃₉⋊C₃
hypocenter	C₁₃₉	#6903
LCS	G ▷ C₃×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₉ ◁ C₂₇⋊C₃

Complements

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

N	H ≅ G/N	type
2. #26014609	C₃	semidirect
3. #26014608	C₃	semidirect
4. #26014607	C₃	semidirect
5. C₃×C₁₃₉⋊C₂₇	C₃	semidirect
6. C₂₇×C₁₃₉⋊C₃	C₃	semidirect
7. C₂₇⋊C₃×C₁₃₉	C₃	semidirect
29. C₁₃₉	#6903	semidirect
34. 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
#26014629	3
#26014609	3
#26014608	3
#26014607	3
C₃×C₁₃₉⋊C₂₇	3
C₂₇×C₁₃₉⋊C₃	3
C₂₇⋊C₃×C₁₃₉	3
#6903	139