Subgroups — #41004738

Order 26973.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#11758601	C₃	1	1	yes	maximal, characteristic
2	C₉×#11758601	C₃	1	1	yes	maximal, characteristic
3	C₉×#11758601	C₃	1	1	yes	maximal, characteristic
4	C₉×C₂₇×C₃₇	C₃	1	1	yes	maximal, characteristic
5	C₃×#11758601	C₉	1	3	yes	—
6	C₃×#11758601	C₉	1	3	yes	—
7	C₃×#11758601	C₉	1	3	yes	—
8	C₃×C₂₇×C₃₇	C₉	1	3	yes	—
9	C₉²×C₃₇	C₃²	1	1	yes	characteristic
10	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
11	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
12	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
13	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
14	C₂₇×C₃₇	—	3	3	no	—
15	#11758601	—	3	3	no	—
16	#11758601	—	3	3	no	—
17	#11758601	C₂₇	1	9	yes	complemented
18	#10624443	—	37	1	no	maximal, Sylow
19	C₃²×C₃₇	C₉²	1	1	yes	characteristic
20	C₉×C₃₇	C₃×C₂₇	1	3	yes	—
21	C₉×C₃₇	C₂₇⋊C₃	1	3	yes	—
22	C₉×C₃₇	C₂₇⋊C₃	1	3	yes	—
23	C₉×C₃₇	C₂₇⋊C₃	1	3	yes	—
24	C₉×C₂₇	—	37	1	no	—
25	C₉×C₂₇	—	37	1	no	—
26	C₉×C₂₇	—	37	1	no	—
27	C₉×C₂₇	C₃₇⋊C₃	1	1	yes	characteristic
28	C₃×C₃₇	C₉×C₂₇	1	1	yes	characteristic
29	C₃×C₃₇	#6864	1	1	yes	characteristic
30	C₃×C₃₇	#6864	1	1	yes	characteristic
31	C₃×C₃₇	#6864	1	1	yes	characteristic
32	C₃×C₂₇	—	37	3	no	—
33	C₃×C₂₇	—	37	3	no	—
34	C₃×C₂₇	—	37	3	no	—
35	C₃×C₂₇	#66524	1	3	yes	—
36	C₉²	C₃×C₃₇⋊C₃	1	1	yes	characteristic
37	C₃₇	#10624443	1	1	yes	characteristic, complemented, Sylow
38	C₃×C₉	C₉×C₃₇⋊C₃	1	1	yes	characteristic
39	C₃×C₉	C₉×C₃₇⋊C₃	1	1	yes	characteristic
40	C₃×C₉	C₉×C₃₇⋊C₃	1	1	yes	characteristic
41	C₃×C₉	C₃×#66524	1	1	yes	characteristic
42	C₂₇	—	3	3	no	—
43	C₂₇	—	37	9	no	—
44	C₂₇	—	111	3	no	—
45	C₂₇	—	111	3	no	—
46	C₃²	C₉×#66524	1	1	yes	characteristic
47	C₉	C₂₇×C₃₇⋊C₃	1	3	yes	—
48	C₉	#15688509	1	3	yes	—
49	C₉	#15688510	1	3	yes	—
50	C₉	#15688511	1	3	yes	—
51	C₃	C₂₇×#66524	1	1	yes	characteristic
52	C₃	#22582462	1	1	yes	characteristic
53	C₃	#22582463	1	1	yes	characteristic
54	C₃	#22582464	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₉²	C₃×C₃₇⋊C₃
commutator	C₃×C₃₇	C₉×C₂₇
Fitting	C₉×C₂₇×C₃₇	C₃
socle, prime radical	C₃²×C₃₇	C₉²
cosocle	C₉²×C₃₇	C₃²
hypercenter	C₉×C₂₇	C₃₇⋊C₃
hypocenter	C₃₇	#10624443
LCS	G ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₉² ◁ C₉×C₂₇

Complements

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

N	H ≅ G/N	type
17. #11758601	C₂₇	semidirect
37. C₃₇	#10624443	semidirect

Maximal subgroups

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

subgroup	index
C₉×#11758601	3
C₉×C₂₇×C₃₇	3
#10624443	37