Subgroups — #41007299

Order 26973.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15688505	C₃	1	1	yes	maximal, characteristic
2	#22582495	C₃	1	6	yes	maximal, complemented
3	#22582492	C₃	1	3	yes	maximal, complemented
4	#22582474	C₃	1	2	yes	maximal
5	C₃₇×#6869	C₃	1	1	yes	maximal, characteristic
6	C₃²×#66524	—	3	1	no	—
7	#15688511	C₃²	1	6	yes	—
8	#15688505	—	3	2	no	—
9	#15688505	C₃²	1	1	yes	characteristic
10	#15688505	C₃²	1	2	yes	—
11	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
12	C₃₇×C₂₇⋊C₃	C₃²	1	3	yes	—
13	C₃³×C₃₇	3₋¹⁺²	1	1	yes	characteristic
14	C₃×C₉×C₃₇	—	3	1	no	—
15	C₃×C₉×C₃₇	—	3	2	no	—
16	C₃×C₉×C₃₇	3₋¹⁺²	1	2	yes	—
17	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
18	C₃×#66524	—	3	1	no	—
19	C₃×#66524	—	3	2	no	—
20	C₃×#66524	—	9	3	no	—
21	C₂₇×C₃₇	—	3	3	no	—
22	#11758601	—	3	6	no	—
23	#10624828	—	37	1	no	maximal, Sylow
24	C₃²×C₃₇	—	3	3	no	—
25	C₃²×C₃₇	—	3	1	no	—
26	C₃²×C₃₇	C₃×3₋¹⁺²	1	1	yes	characteristic
27	C₉×C₃₇	—	3	2	no	—
28	C₉×C₃₇	#737	1	1	yes	characteristic
29	C₉×C₃₇	#737	1	2	yes	—
30	#66524	—	9	1	no	—
31	#66524	—	9	2	no	—
32	C₃×C₉⋊C₉	—	37	1	no	—
33	#6875	—	37	3	no	—
34	#6875	—	37	6	no	—
35	#6869	—	37	2	no	—
36	#6869	C₃₇⋊C₃	1	1	yes	characteristic
37	C₃×C₃₇	—	3	1	no	—
38	C₃×C₃₇	—	3	3	no	—
39	C₃×C₃₇	#6895	1	1	yes	characteristic
40	C₃²×C₉	—	111	1	no	—
41	C₃²×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
42	C₂₇⋊C₃	—	37	6	no	—
43	C₂₇⋊C₃	C₃×C₃₇⋊C₃	1	3	yes	—
44	C₉⋊C₉	—	37	1	no	—
45	C₉⋊C₉	—	37	2	no	—
46	C₉⋊C₉	—	111	2	no	—
47	C₃₇	#10624828	1	1	yes	characteristic, complemented, Sylow
48	C₃³	#11758605	1	1	yes	characteristic
49	C₃×C₉	—	3	1	no	—
50	C₃×C₉	—	3	2	no	—
51	C₃×C₉	—	333	3	no	—
52	C₃×C₉	—	111	1	no	—
53	C₃×C₉	—	111	2	no	—
54	C₃×C₉	#11758605	1	2	yes	—
55	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
56	C₂₇	—	3	3	no	—
57	C₂₇	—	111	6	no	—
58	C₃²	—	3	3	no	—
59	C₃²	—	3	1	no	—
60	C₃²	C₃×#11758605	1	1	yes	characteristic
61	C₉	—	3	2	no	—
62	C₉	—	333	1	no	—
63	C₉	—	333	2	no	—
64	C₉	#15688530	1	1	yes	characteristic
65	C₉	#15688532	1	2	yes	—
66	C₃	—	3	1	no	—
67	C₃	—	3	3	no	—
68	C₃	#22582576	1	1	yes	characteristic

	subgroup	G/H
center	C₃	#22582576
commutator, cosocle	C₃×C₉×C₃₇	C₃³
Frattini	C₃×C₉	C₃²×C₃₇⋊C₃
Fitting	C₃₇×#6869	C₃
socle	C₃×C₃₇	#6895
prime radical	C₃³×C₃₇	3₋¹⁺²
hypercenter	#6869	C₃₇⋊C₃
hypocenter	C₃₇	#10624828
LCS	G ▷ C₃×C₉×C₃₇ ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃ ◁ C₃×C₉ ◁ #6869

Complements

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

N	H ≅ G/N	type
2. #22582495	C₃	semidirect
3. #22582492	C₃	semidirect
47. C₃₇	#10624828	semidirect

Maximal subgroups

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

subgroup	index
C₃×#15688505	3
#22582495	3
#22582492	3
#22582474	3
C₃₇×#6869	3
#10624828	37