Subgroups — #41004769

Order 26973.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15688511	C₃	1	1	yes	maximal, characteristic
2	C₉×#11758608	C₃	1	1	yes	maximal, characteristic
3	C₃²⋊#11758601	C₃	1	1	yes	maximal, characteristic
4	C₃₇×C₃²⋊C₂₇	C₃	1	1	yes	maximal, characteristic
5	C₃×#11758608	C₉	1	1	yes	characteristic
6	#15688511	—	3	3	no	—
7	C₃×#11758601	—	3	1	no	—
8	C₃×#11758601	—	3	1	no	—
9	#15688504	—	3	1	no	—
10	#15688504	—	3	1	no	—
11	C₃²⋊#66524	C₉	1	1	yes	characteristic
12	C₃²⋊#66524	C₉	1	1	yes	characteristic
13	C₉×#66524	—	3	1	no	—
14	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
15	C₃×C₂₇×C₃₇	—	3	1	no	—
16	C₃³×C₃₇	C₃×C₉	1	1	yes	characteristic
17	C₃×C₉×C₃₇	—	3	1	no	—
18	C₃×C₉×C₃₇	—	3	1	no	—
19	C₃×C₉×C₃₇	—	3	1	no	—
20	C₃×C₉×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
21	C₃×C₉×C₃₇	3₋¹⁺²	1	1	yes	characteristic
22	C₃×C₉×C₃₇	3₋¹⁺²	1	1	yes	characteristic
23	#11758608	—	3	3	no	—
24	C₃×#66524	—	3	1	no	—
25	C₃×#66524	—	3	1	no	—
26	C₃×#66524	—	3	1	no	—
27	C₂₇×C₃₇	—	9	1	no	—
28	#11758601	—	3	3	no	—
29	#11758601	—	9	1	no	—
30	#10624454	—	37	1	no	maximal, Sylow
31	C₃²×C₃₇	—	3	1	no	—
32	C₃²×C₃₇	—	3	1	no	—
33	C₃²×C₃₇	—	3	1	no	—
34	C₃²×C₃₇	—	3	1	no	—
35	C₃²×C₃₇	C₃²⋊C₉	1	1	yes	characteristic
36	C₉×C₃₇	—	3	1	no	—
37	C₉×C₃₇	—	3	1	no	—
38	C₉×C₃₇	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
39	C₉×C₃₇	#731	1	1	yes	characteristic
40	C₉×C₃₇	#733	1	1	yes	characteristic
41	#66524	—	3	3	no	—
42	#66524	—	9	1	no	—
43	#66524	—	9	1	no	—
44	C₃×C₂₇⋊C₃	—	37	1	no	—
45	C₉×3₋¹⁺²	—	37	1	no	—
46	C₃²⋊C₂₇	—	37	1	no	—
47	C₃²⋊C₂₇	C₃₇⋊C₃	1	1	yes	characteristic
48	C₃×C₃₇	—	9	1	no	—
49	C₃×C₃₇	#6869	1	1	yes	characteristic
50	C₃×C₃₇	3₋¹⁺²⋊C₉	1	1	yes	characteristic
51	C₃×C₃₇	#6872	1	1	yes	characteristic
52	C₃×C₃₇	#6873	1	1	yes	characteristic
53	C₃×3₋¹⁺²	—	37	1	no	—
54	C₃²×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
55	C₂₇⋊C₃	—	111	3	no	—
56	C₃×C₂₇	—	3	1	no	—
57	C₃×C₂₇	—	111	1	no	—
58	C₃×C₂₇	—	111	1	no	—
59	C₉⋊C₉	—	111	1	no	—
60	C₉⋊C₉	—	111	1	no	—
61	C₃²⋊C₉	—	37	1	no	—
62	C₃²⋊C₉	—	37	1	no	—
63	C₉²	—	111	1	no	—
64	C₃₇	#10624454	1	1	yes	characteristic, complemented, Sylow
65	C₃³	C₉×C₃₇⋊C₃	1	1	yes	characteristic
66	3₋¹⁺²	—	111	3	no	—
67	C₃×C₉	—	3	1	no	—
68	C₃×C₉	—	3	1	no	—
69	C₃×C₉	—	3	1	no	—
70	C₃×C₉	—	111	1	no	—
71	C₃×C₉	—	111	1	no	—
72	C₃×C₉	—	111	1	no	—
73	C₃×C₉	#11758605	1	1	yes	characteristic
74	C₃×C₉	#11758606	1	1	yes	characteristic
75	C₃×C₉	C₃²⋊(C₃₇⋊C₃)	1	1	yes	characteristic
76	C₂₇	—	9	1	no	—
77	C₂₇	—	333	1	no	—
78	C₂₇	—	111	3	no	—
79	C₃²	—	3	1	no	—
80	C₃²	—	3	1	no	—
81	C₃²	—	3	1	no	—
82	C₃²	—	3	1	no	—
83	C₃²	#15688502	1	1	yes	characteristic
84	C₉	—	3	1	no	—
85	C₉	—	3	1	no	—
86	C₉	—	333	1	no	—
87	C₉	—	333	1	no	—
88	C₉	—	111	3	no	—
89	C₉	#15688512	1	1	yes	characteristic
90	C₉	#15688517	1	1	yes	characteristic
91	C₉	#15688520	1	1	yes	characteristic
92	C₃	—	9	1	no	—
93	C₃	#22582473	1	1	yes	characteristic
94	C₃	#22582478	1	1	yes	characteristic
95	C₃	#22582482	1	1	yes	characteristic
96	C₃	#22582487	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₉	C₃²⋊(C₃₇⋊C₃)
commutator, prime radical	C₃³×C₃₇	C₃×C₉
Frattini	C₃²×C₉	C₃×C₃₇⋊C₃
Fitting	C₃₇×C₃²⋊C₂₇	C₃
socle	C₃²×C₃₇	C₃²⋊C₉
cosocle	C₃²×C₉×C₃₇	C₃²
hypercenter	C₃²⋊C₂₇	C₃₇⋊C₃
hypocenter	C₃₇	#10624454
LCS	G ▷ C₃³×C₃₇ ▷ C₃²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉ ◁ C₃²⋊C₂₇

Complements

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

N	H ≅ G/N	type
64. C₃₇	#10624454	semidirect

Maximal subgroups

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

subgroup	index
C₃×#15688511	3
C₉×#11758608	3
C₃²⋊#11758601	3
C₃₇×C₃²⋊C₂₇	3
#10624454	37