Group #41005110 — subgroups

Subgroups — #41005110

Order 26973.

290 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#66524	C₃	1	1	yes	maximal, characteristic
2	#22582441	C₃	1	3	yes	maximal
3	#22582441	C₃	1	6	yes	maximal
4	#22582441	C₃	1	1	yes	maximal, characteristic
5	#22582441	C₃	1	1	yes	maximal, characteristic
6	C₃₇×#6855	C₃	1	1	yes	maximal, characteristic
7	C₃²×#66524	C₃²	1	3	yes	—
8	C₃²×#66524	C₃²	1	3	yes	—
9	C₃²×#66524	C₃²	1	1	yes	characteristic
10	C₃²×#66524	C₃²	1	2	yes	—
11	C₉×#66524	C₉	1	9	yes	complemented
12	C₃²×C₉×C₃₇	C₃²	1	3	yes	—
13	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
14	C₃³×C₃₇	C₃³	1	1	yes	characteristic
15	C₃×C₉×C₃₇	—	3	1	no	—
16	C₃×C₉×C₃₇	—	3	1	no	—
17	C₃×C₉×C₃₇	—	3	1	no	—
18	C₃×C₉×C₃₇	—	3	3	no	—
19	C₃×C₉×C₃₇	—	3	3	no	—
20	C₃×C₉×C₃₇	—	3	6	no	—
21	C₃×C₉×C₃₇	C₃×C₉	1	3	yes	—
22	C₃×#66524	—	3	3	no	—
23	C₃×#66524	—	3	6	no	—
24	C₃×#66524	—	3	3	no	—
25	C₃×#66524	—	3	3	no	—
26	C₃×#66524	—	3	3	no	—
27	C₃×#66524	—	3	6	no	—
28	C₃×#66524	—	3	3	no	—
29	C₃×#66524	—	3	6	no	—
30	C₃×#66524	C₃×C₉	1	3	yes	—
31	C₃×#66524	C₃×C₉	1	6	yes	—
32	#10624551	—	37	1	no	maximal, Sylow
33	C₃²×C₃₇	C₃²×C₉	1	1	yes	characteristic
34	C₃²×C₃₇	#737	1	1	yes	characteristic
35	C₃²×C₃₇	#737	1	3	yes	—
36	C₃²×C₃₇	#737	1	1	yes	characteristic
37	C₃²×C₃₇	#737	1	1	yes	characteristic
38	C₃²×C₃₇	#737	1	6	yes	—
39	C₉×C₃₇	—	3	3	no	—
40	C₉×C₃₇	—	9	3	no	—
41	#66524	—	3	3	no	—
42	#66524	—	3	6	no	—
43	#66524	—	9	3	no	—
44	#66524	—	9	3	no	—
45	C₃×C₉²	—	37	1	no	—
46	#6855	—	37	3	no	—
47	#6855	—	37	6	no	—
48	#6855	—	37	1	no	—
49	#6855	—	37	1	no	—
50	#6855	C₃₇⋊C₃	1	1	yes	characteristic
51	C₃×C₃₇	#6887	1	1	yes	characteristic
52	C₃×C₃₇	#6887	1	1	yes	characteristic
53	C₃×C₃₇	#6887	1	2	yes	—
54	C₃×C₃₇	#6897	1	3	yes	—
55	C₃×C₃₇	#6897	1	3	yes	—
56	C₃×C₃₇	#6897	1	3	yes	—
57	C₃²×C₉	—	37	1	no	—
58	C₃²×C₉	—	37	2	no	—
59	C₃²×C₉	—	37	3	no	—
60	C₃²×C₉	—	37	3	no	—
61	C₃²×C₉	C₃×C₃₇⋊C₃	1	3	yes	—
62	C₃²×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
63	C₉²	—	37	9	no	—
64	C₃₇	#10624551	1	1	yes	characteristic, complemented, Sylow
65	C₃³	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
66	C₃×C₉	—	3	1	no	—
67	C₃×C₉	—	3	1	no	—
68	C₃×C₉	—	3	1	no	—
69	C₃×C₉	—	3	3	no	—
70	C₃×C₉	—	3	3	no	—
71	C₃×C₉	—	3	6	no	—
72	C₃×C₉	—	37	3	no	—
73	C₃×C₉	—	37	6	no	—
74	C₃×C₉	—	111	3	no	—
75	C₃×C₉	—	111	3	no	—
76	C₃×C₉	—	111	3	no	—
77	C₃×C₉	—	111	6	no	—
78	C₃×C₉	—	111	3	no	—
79	C₃×C₉	—	111	6	no	—
80	C₃×C₉	—	111	3	no	—
81	C₃×C₉	—	111	6	no	—
82	C₃×C₉	C₉×C₃₇⋊C₃	1	3	yes	—
83	C₃²	C₃×C₉×C₃₇⋊C₃	1	1	yes	characteristic
84	C₃²	#15688530	1	1	yes	characteristic
85	C₃²	#15688531	1	3	yes	—
86	C₃²	#15688532	1	1	yes	characteristic
87	C₃²	#15688532	1	1	yes	characteristic
88	C₃²	#15688532	1	6	yes	—
89	C₉	—	3	3	no	—
90	C₉	—	9	3	no	—
91	C₉	—	333	3	no	—
92	C₉	—	333	3	no	—
93	C₉	—	111	3	no	—
94	C₉	—	111	6	no	—
95	C₃	#22582535	1	1	yes	characteristic
96	C₃	#22582536	1	1	yes	characteristic
97	C₃	#22582537	1	2	yes	—
98	C₃	#22582585	1	3	yes	—
99	C₃	#22582588	1	3	yes	—
100	C₃	#22582589	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×C₉×#66524

C₃

yes

maximal, characteristic

#22582441

C₃

yes

maximal

#22582441

C₃

yes

maximal

#22582441

C₃

yes

maximal, characteristic

#22582441

C₃

yes

maximal, characteristic

C₃₇×#6855

C₃

yes

maximal, characteristic

C₃²×#66524

C₃²

yes

—

C₃²×#66524

C₃²

yes

—

C₃²×#66524

C₃²

yes

characteristic

C₃²×#66524

C₃²

yes

—

C₉×#66524

C₉

yes

complemented

C₃²×C₉×C₃₇

C₃²

yes

—

C₃²×C₉×C₃₇

C₃²

yes

characteristic

C₃³×C₃₇

C₃³

yes

characteristic

C₃×C₉×C₃₇

—

C₃×C₉×C₃₇

—

C₃×C₉×C₃₇

—

C₃×C₉×C₃₇

—

C₃×C₉×C₃₇

—

C₃×C₉×C₃₇

—

C₃×C₉×C₃₇

C₃×C₉

yes

—

—

—

—

—

—

—

—

—

C₃×C₉

yes

—

C₃×#66524

C₃×C₉

yes

—

#10624551

—

maximal, Sylow

C₃²×C₃₇

C₃²×C₉

yes

C₃²×C₃₇

yes

C₃²×C₃₇

yes

—

C₃²×C₃₇

yes

C₃²×C₃₇

yes

C₃²×C₃₇

yes

—

C₉×C₃₇

—

C₉×C₃₇

—

—

—

—

—

C₃×C₉²

—

—

—

—

—

C₃₇⋊C₃

yes

C₃×C₃₇

yes

C₃×C₃₇

yes

C₃×C₃₇

yes

—

C₃×C₃₇

#6897

yes

—

C₃×C₃₇

#6897

yes

—

C₃×C₃₇

#6897

yes

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

C₃×C₃₇⋊C₃

yes

—

C₃²×C₉

C₃×C₃₇⋊C₃

yes

characteristic

C₉²

—

C₃₇

#10624551

yes

characteristic, complemented, Sylow

C₃³

C₃²×C₃₇⋊C₃

yes

characteristic

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

111

—

C₃×C₉

—

111

—

C₃×C₉

—

111

—

C₃×C₉

—

111

—

C₃×C₉

—

111

—

C₃×C₉

—

111

—

C₃×C₉

—

111

—

C₃×C₉

—

111

—

C₃×C₉

C₉×C₃₇⋊C₃

yes

—

C₃²

C₃×C₉×C₃₇⋊C₃

yes

C₃²

yes

C₃²

yes

—

C₃²

yes

C₃²

yes

C₃²

yes

—

C₉

—

C₉

—

C₉

—

333

—

C₉

—

333

—

C₉

—

111

—

C₉

—

111

—

C₃

yes

C₃

yes

C₃

yes

—

C₃

#22582585

yes

—

C₃

#22582588

yes

—

100

C₃

#22582589

yes

—

	subgroup	G/H
center, Frattini	C₃³	C₃²×C₃₇⋊C₃
commutator	C₃²×C₃₇	C₃²×C₉
Fitting	C₃₇×#6855	C₃
socle, prime radical, cosocle	C₃³×C₃₇	C₃³
hypercenter	#6855	C₃₇⋊C₃
hypocenter	C₃₇	#10624551
LCS	G ▷ C₃²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃³ ◁ #6855

subgroup

G/H

center, Frattini

C₃³

C₃²×C₃₇⋊C₃

commutator

C₃²×C₃₇

C₃²×C₉

Fitting

C₃₇×#6855

C₃

socle, prime radical, cosocle

C₃³×C₃₇

C₃³

C₃₇⋊C₃

C₃₇

G ▷ C₃²×C₃₇ ▷ C₃₇

C₁ ◁ C₃³ ◁ #6855

N	H ≅ G/N	type
11. C₉×#66524	C₉	semidirect
64. C₃₇	#10624551	semidirect

H ≅ G/N

type

11. C₉×#66524

C₉

semidirect

64. C₃₇

#10624551

semidirect

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

subgroup	index
C₃×C₉×#66524	3
#22582441	3
C₃₇×#6855	3
#10624551	37

subgroup

index

C₃×C₉×#66524

#22582441

C₃₇×#6855

#10624551

Subgroups — #41005110

Conjugacy classes of subgroups

Complements

Maximal subgroups