Subgroups — #733×C₁₂₇⋊C₃ #44525100

Order 30861.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	3₋¹⁺²×C₁₂₇⋊C₃	C₃	1	3	yes	maximal
2	C₃×C₉×C₁₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
3	#23779850	C₃	1	2	yes	maximal, complemented
4	#23779849	C₃	1	6	yes	maximal, complemented
5	#733×C₁₂₇	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃²×C₁₂₇⋊C₃	C₃²	1	1	yes	characteristic
7	#16812184	C₃²	1	6	yes	—
8	#16812183	—	3	3	no	—
9	#16812182	—	3	3	no	—
10	C₃×#11765917	C₃²	1	2	yes	—
11	C₉×C₁₂₇⋊C₃	—	3	1	no	—
12	C₉×C₁₂₇⋊C₃	—	3	1	no	—
13	C₉×C₁₂₇⋊C₃	—	3	1	no	—
14	C₉×C₁₂₇⋊C₃	—	3	3	no	—
15	3₋¹⁺²×C₁₂₇	C₃²	1	3	yes	—
16	C₃×C₉×C₁₂₇	C₃²	1	1	yes	characteristic
17	C₃²×C₁₂₇	C₃³	1	1	yes	characteristic
18	C₃×C₁₂₇⋊C₃	—	3	3	no	—
19	C₃×C₁₂₇⋊C₃	H(3,𝔽₃)	1	1	yes	characteristic
20	C₃×C₁₂₇⋊C₃	H(3,𝔽₃)	1	1	yes	characteristic
21	C₃×C₁₂₇⋊C₃	H(3,𝔽₃)	1	1	yes	characteristic
22	C₉×C₁₂₇	—	3	1	no	—
23	C₉×C₁₂₇	—	3	3	no	—
24	#11765917	—	3	2	no	—
25	#11765917	—	3	6	no	—
26	C₃×C₁₂₇	—	3	1	no	—
27	C₃×C₁₂₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
28	C₁₂₇⋊C₃	—	3	1	no	—
29	C₁₂₇⋊C₃	—	3	1	no	—
30	C₁₂₇⋊C₃	#733	1	3	yes	direct product factor
31	C₃×#733	—	127	1	no	maximal, Sylow
32	C₁₂₇	C₃×#733	1	1	yes	characteristic, complemented, Sylow
33	C₃×3₋¹⁺²	—	127	3	no	—
34	C₃²×C₉	—	127	1	no	—
35	#733	—	127	6	no	—
36	#733	—	127	2	no	—
37	#733	C₁₂₇⋊C₃	1	1	yes	characteristic, direct product factor
38	C₃³	—	127	1	no	—
39	3₋¹⁺²	—	381	3	no	—
40	3₋¹⁺²	—	381	3	no	—
41	3₋¹⁺²	—	127	6	no	—
42	3₋¹⁺²	C₃×C₁₂₇⋊C₃	1	3	yes	—
43	C₃×C₉	—	381	1	no	—
44	C₃×C₉	—	381	1	no	—
45	C₃×C₉	—	381	1	no	—
46	C₃×C₉	—	381	3	no	—
47	C₃×C₉	—	127	2	no	—
48	C₃×C₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
49	C₃²	—	381	3	no	—
50	C₃²	—	127	1	no	—
51	C₃²	—	127	1	no	—
52	C₃²	—	127	1	no	—
53	C₃²	C₃²×C₁₂₇⋊C₃	1	1	yes	characteristic
54	C₉	—	3	1	no	—
55	C₉	—	3	3	no	—
56	C₉	—	381	2	no	—
57	C₉	—	381	6	no	—
58	C₃	—	3	1	no	—
59	C₃	—	381	1	no	—
60	C₃	—	381	1	no	—
61	C₃	—	127	3	no	—
62	C₃	H(3,𝔽₃)×C₁₂₇⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃	H(3,𝔽₃)×C₁₂₇⋊C₃
commutator, cosocle	C₃²×C₁₂₇	C₃³
Frattini	C₃²	C₃²×C₁₂₇⋊C₃
Fitting	#733×C₁₂₇	C₃
socle	C₃×C₁₂₇	C₃×H(3,𝔽₃)
prime radical	C₃²×C₁₂₇⋊C₃	C₃²
hypercenter	#733	C₁₂₇⋊C₃
hypocenter	C₁₂₇	C₃×#733
LCS	G ▷ C₃²×C₁₂₇ ▷ C₃×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₃ ◁ C₃² ◁ #733

Complements

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

N	H ≅ G/N	type
3. #23779850	C₃	semidirect
4. #23779849	C₃	semidirect
5. #733×C₁₂₇	C₃	semidirect
30. C₁₂₇⋊C₃	#733	direct (N × H)
32. C₁₂₇	C₃×#733	semidirect
37. #733	C₁₂₇⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
3₋¹⁺²×C₁₂₇⋊C₃	3
C₃×C₉×C₁₂₇⋊C₃	3
#23779850	3
#23779849	3
#733×C₁₂₇	3
C₃×#733	127

Subgroups — #733×C127⋊C3 #44525100

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #733×C₁₂₇⋊C₃ #44525100