Subgroups — #44525022

Order 30861.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812184	C₃	1	1	yes	maximal, characteristic
2	C₃²×#11765917	C₃	1	1	yes	maximal, characteristic
3	#23779833	C₃	1	6	yes	maximal, complemented
4	C₃²⋊#11765917	C₃	1	1	yes	maximal, characteristic
5	C₉×#11765917	C₃	1	3	yes	maximal, complemented
6	C₃²⋊C₉×C₁₂₇	C₃	1	1	yes	maximal, characteristic
7	#16812184	C₉	1	9	yes	complemented
8	C₃×#11765917	—	3	3	no	—
9	C₃×#11765917	C₃²	1	2	yes	—
10	C₃×#11765917	C₃²	1	3	yes	—
11	C₃×#11765917	C₃²	1	3	yes	—
12	C₃×#11765917	C₃²	1	1	yes	characteristic
13	C₃³×C₁₂₇	C₃²	1	1	yes	characteristic
14	C₃×C₉×C₁₂₇	C₃²	1	3	yes	—
15	C₃²×C₁₂₇	—	3	1	no	—
16	C₃²×C₁₂₇	—	3	1	no	—
17	C₃²×C₁₂₇	—	3	1	no	—
18	C₃²×C₁₂₇	C₃×C₉	1	3	yes	—
19	C₃²×C₁₂₇	C₃³	1	1	yes	characteristic
20	C₉×C₁₂₇	—	3	3	no	—
21	#11765917	—	3	2	no	—
22	#11765917	—	3	3	no	—
23	#11765917	C₃×C₉	1	9	yes	complemented
24	#11765917	3₋¹⁺²	1	3	yes	complemented
25	C₃×C₁₂₇	—	3	3	no	—
26	C₃×C₁₂₇	C₃²×C₉	1	1	yes	characteristic
27	C₃×C₁₂₇	C₃×3₋¹⁺²	1	1	yes	characteristic
28	C₃×C₁₂₇	#737	1	1	yes	characteristic
29	C₃×C₁₂₇	#737	1	1	yes	characteristic
30	C₉×3₋¹⁺²	—	127	1	no	maximal, Sylow
31	C₁₂₇	C₉×3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
32	C₃×3₋¹⁺²	—	127	1	no	—
33	C₃²×C₉	—	127	1	no	—
34	C₉⋊C₉	—	127	6	no	—
35	C₃²⋊C₉	—	127	1	no	—
36	C₃²⋊C₉	C₁₂₇⋊C₃	1	1	yes	characteristic
37	C₉²	—	127	3	no	—
38	C₃³	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
39	3₋¹⁺²	—	127	9	no	—
40	C₃×C₉	—	381	3	no	—
41	C₃×C₉	—	127	3	no	—
42	C₃×C₉	—	127	2	no	—
43	C₃×C₉	—	127	1	no	—
44	C₃×C₉	—	127	3	no	—
45	C₃×C₉	C₃×C₁₂₇⋊C₃	1	3	yes	—
46	C₃²	—	3	1	no	—
47	C₃²	—	3	1	no	—
48	C₃²	—	3	1	no	—
49	C₃²	C₉×C₁₂₇⋊C₃	1	3	yes	—
50	C₃²	C₃²×C₁₂₇⋊C₃	1	1	yes	characteristic
51	C₉	—	3	3	no	—
52	C₉	—	381	2	no	—
53	C₉	—	381	3	no	—
54	C₉	—	127	9	no	—
55	C₉	—	127	3	no	—
56	C₃	—	3	3	no	—
57	C₃	C₃×C₉×C₁₂₇⋊C₃	1	1	yes	characteristic
58	C₃	3₋¹⁺²×C₁₂₇⋊C₃	1	1	yes	characteristic
59	C₃	#23779859	1	1	yes	characteristic
60	C₃	#23779861	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₁₂₇⋊C₃
commutator	C₃×C₁₂₇	C₃²×C₉
Fitting	C₃²⋊C₉×C₁₂₇	C₃
socle, cosocle	C₃²×C₁₂₇	C₃³
prime radical	C₃³×C₁₂₇	C₃²
hypercenter	C₃²⋊C₉	C₁₂₇⋊C₃
hypocenter	C₁₂₇	C₉×3₋¹⁺²
LCS	G ▷ C₃×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₃² ◁ C₃²⋊C₉

Complements

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

N	H ≅ G/N	type
3. #23779833	C₃	semidirect
5. C₉×#11765917	C₃	semidirect
7. #16812184	C₉	semidirect
23. #11765917	C₃×C₉	semidirect
24. #11765917	3₋¹⁺²	semidirect
31. C₁₂₇	C₉×3₋¹⁺²	semidirect

Maximal subgroups

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

subgroup	index
C₃×#16812184	3
C₃²×#11765917	3
#23779833	3
C₃²⋊#11765917	3
C₉×#11765917	3
C₃²⋊C₉×C₁₂₇	3
C₉×3₋¹⁺²	127