Group #11795361 — subgroups

Subgroups — #11795361

Order 1152.

333 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 333 conjugacy classes of subgroups — too many to draw. Only its 94 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	#10588808	C₂	1	3	yes	maximal
2	#10588800	C₂	1	3	yes	maximal, complemented
3	C₉×#338	C₂	1	1	yes	maximal, characteristic, complemented
4	#68721	—	3	1	no	maximal
5	C₂²×C₄×D₉	C₂²	1	1	yes	characteristic
6	C₂×C₉×M₁₆	C₂²	1	3	yes	—
7	C₂×#3667	C₂²	1	3	yes	—
8	(C₂×D₉)⋊C₈	—	2	6	no	—
9	#63372	—	2	6	no	—
10	#5126	—	3	3	no	—
11	#5125	—	3	3	no	—
12	C₃×#338	D₃	1	1	yes	characteristic
13	C₂³×D₉	Q₈	1	1	yes	characteristic
14	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
15	C₂²×Dic₉	Q₈	1	1	yes	characteristic
16	C₂×C₄×D₉	—	2	3	no	—
17	C₂×C₄×D₉	—	2	3	no	—
18	C₉×M₁₆	—	2	6	no	—
19	C₂×C₈×C₉	D₄	1	6	yes	—
20	#3667	—	2	6	no	—
21	C₂×C₉⋊C₈	—	2	3	no	—
22	#2091	—	9	1	no	Sylow
23	C₂²×C₄×D₃	—	3	1	no	—
24	C₂×C₃×M₁₆	C₂×D₃	1	3	yes	—
25	C₂×#208	—	3	3	no	—
26	(C₂×D₃)⋊C₈	—	6	6	no	—
27	#819	—	6	6	no	—
28	C₂³×C₉	C₂×Q₈	1	1	yes	characteristic
29	C₂²×D₉	—	2	3	no	—
30	C₂²×D₉	—	4	2	no	—
31	C₂×C₄×C₉	C₂×D₄	1	3	yes	—
32	C₂×C₄×C₉	#41	1	3	yes	—
33	C₂×Dic₉	—	2	3	no	—
34	C₄×D₉	—	4	3	no	—
35	C₄×D₉	—	4	1	no	—
36	C₈×C₉	—	2	6	no	—
37	C₉⋊C₈	—	4	3	no	—
38	#430	—	9	3	no	—
39	#407	—	9	3	no	—
40	#338	D₉	1	1	yes	characteristic, complemented
41	C₂³×D₃	—	3	1	no	—
42	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
43	C₂²×Dic₃	—	3	1	no	—
44	C₂×C₄×D₃	—	6	3	no	—
45	C₂×C₄×D₃	—	6	3	no	—
46	C₃×M₁₆	—	2	6	no	—
47	C₂×C₃×C₈	D₁₂	1	6	yes	—
48	#208	—	6	6	no	—
49	C₂×C₃⋊C₈	—	6	3	no	—
50	C₂²×C₉	—	4	1	no	—
51	C₂²×C₉	C₂²⋊Q₈	1	3	yes	—
52	C₂×D₉	—	2	6	no	—
53	C₂×D₉	—	4	3	no	—
54	C₂×D₉	—	4	1	no	—
55	C₄×C₉	#123	1	3	yes	—
56	C₄×C₉	#127	1	1	yes	characteristic
57	Dic₉	—	4	1	no	—
58	C₂³×C₄	—	9	1	no	—
59	C₂×M₁₆	—	9	3	no	—
60	C₂×M₁₆	C₂×D₉	1	3	yes	—
61	#108	—	18	6	no	—
62	C₂²⋊C₈	—	18	6	no	—
63	C₂³×C₃	D₃×Q₈	1	1	yes	characteristic
64	C₂²×D₃	—	6	3	no	—
65	C₂²×D₃	—	12	2	no	—
66	C₂×C₃×C₄	C₂×D₁₂	1	3	yes	—
67	C₂×C₃×C₄	#237	1	3	yes	—
68	C₂×Dic₃	—	6	3	no	—
69	C₄×D₃	—	12	1	no	—
70	C₄×D₃	—	12	3	no	—
71	C₃×C₈	—	2	6	no	—
72	C₃⋊C₈	—	12	3	no	—
73	C₂×C₉	—	2	3	no	—
74	C₂×C₉	#399	1	1	yes	characteristic
75	D₉	—	4	2	no	—
76	C₂⁴	—	9	1	no	—
77	C₂²×C₄	—	9	1	no	—
78	C₂²×C₄	—	18	3	no	—
79	C₂²×C₄	—	18	3	no	—
80	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
81	M₁₆	—	2	6	no	—
82	M₁₆	—	18	6	no	—
83	C₂×C₈	—	18	3	no	—
84	C₂×C₈	D₃₆	1	6	yes	—
85	C₂²×C₃	—	4	1	no	—
86	C₂²×C₃	#897	1	3	yes	—
87	C₂×D₃	—	6	6	no	—
88	C₂×D₃	—	12	3	no	—
89	C₂×D₃	—	12	1	no	—
90	C₃×C₄	#874	1	1	yes	characteristic
91	C₃×C₄	#886	1	3	yes	—
92	Dic₃	—	12	1	no	—
93	C₉	#2091	1	1	yes	characteristic, complemented, Sylow
94	C₂³	—	18	3	no	—
95	C₂³	—	36	2	no	—
96	C₂³	Q₈×D₉	1	1	yes	characteristic
97	C₂×C₄	—	18	3	no	—
98	C₂×C₄	—	36	1	no	—
99	C₂×C₄	—	36	3	no	—
100	C₂×C₄	C₂×D₃₆	1	3	yes	—
101	C₂×C₄	#3699	1	3	yes	—
102	C₈	—	2	6	no	—
103	C₈	—	36	3	no	—
104	C₂×C₃	—	2	3	no	—
105	C₂×C₃	#4677	1	1	yes	characteristic
106	D₃	—	12	2	no	—
107	C₂²	—	4	1	no	—
108	C₂²	—	18	6	no	—
109	C₂²	—	36	3	no	—
110	C₂²	—	36	1	no	—
111	C₂²	#63459	1	3	yes	—
112	C₄	—	36	1	no	—
113	C₄	#63436	1	1	yes	characteristic
114	C₄	#63448	1	3	yes	—
115	C₃	#68721	1	1	yes	characteristic
116	C₂	—	2	3	no	—
117	C₂	—	36	2	no	—
118	C₂	#10588357	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#10588808

C₂

yes

maximal

#10588800

C₂

yes

maximal, complemented

C₉×#338

C₂

yes

maximal, characteristic, complemented

#68721

—

maximal

C₂²×C₄×D₉

C₂²

yes

characteristic

C₂×C₉×M₁₆

C₂²

yes

—

C₂×#3667

C₂²

yes

—

(C₂×D₉)⋊C₈

—

—

—

—

D₃

yes

characteristic

C₂³×D₉

Q₈

yes

characteristic

C₂²×C₄×C₉

C₂³

yes

characteristic

C₂²×Dic₉

Q₈

yes

characteristic

C₂×C₄×D₉

—

C₂×C₄×D₉

—

C₉×M₁₆

—

C₂×C₈×C₉

D₄

yes

—

#3667

—

C₂×C₉⋊C₈

—

#2091

—

Sylow

C₂²×C₄×D₃

—

C₂×C₃×M₁₆

C₂×D₃

yes

—

C₂×#208

—

(C₂×D₃)⋊C₈

—

#819

—

C₂³×C₉

C₂×Q₈

yes

characteristic

C₂²×D₉

—

C₂²×D₉

—

C₂×C₄×C₉

C₂×D₄

yes

—

C₂×C₄×C₉

#41

yes

—

C₂×Dic₉

—

C₄×D₉

—

C₄×D₉

—

C₈×C₉

—

C₉⋊C₈

—

#430

—

#407

—

#338

D₉

yes

characteristic, complemented

C₂³×D₃

—

C₂²×C₃×C₄

C₂²×D₃

yes

characteristic

C₂²×Dic₃

—

C₂×C₄×D₃

—

C₂×C₄×D₃

—

C₃×M₁₆

—

C₂×C₃×C₈

D₁₂

yes

—

#208

—

C₂×C₃⋊C₈

—

C₂²×C₉

—

C₂²×C₉

C₂²⋊Q₈

yes

—

C₂×D₉

—

C₂×D₉

—

C₂×D₉

—

C₄×C₉

#123

yes

—

C₄×C₉

#127

yes

characteristic

Dic₉

—

C₂³×C₄

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₉

yes

—

#108

—

C₂²⋊C₈

—

C₂³×C₃

D₃×Q₈

yes

characteristic

C₂²×D₃

—

C₂²×D₃

—

C₂×C₃×C₄

C₂×D₁₂

yes

—

C₂×C₃×C₄

#237

yes

—

C₂×Dic₃

—

C₄×D₃

—

C₄×D₃

—

C₃×C₈

—

C₃⋊C₈

—

C₂×C₉

—

C₂×C₉

#399

yes

characteristic

D₉

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₉

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

D₃₆

yes

—

C₂²×C₃

—

C₂²×C₃

#897

yes

—

C₂×D₃

—

C₂×D₃

—

C₂×D₃

—

C₃×C₄

#874

yes

characteristic

C₃×C₄

#886

yes

—

Dic₃

—

C₉

#2091

yes

characteristic, complemented, Sylow

C₂³

—

C₂³

—

C₂³

Q₈×D₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

C₂×D₃₆

yes

—

101

C₂×C₄

#3699

yes

—

102

C₈

—

103

C₈

—

104

C₂×C₃

—

105

C₂×C₃

#4677

yes

characteristic

106

D₃

—

107

C₂²

—

108

C₂²

—

109

C₂²

—

110

C₂²

—

111

C₂²

#63459

yes

—

112

C₄

—

113

C₄

#63436

yes

characteristic

114

C₄

#63448

yes

—

115

C₃

#68721

yes

characteristic

116

C₂

—

117

C₂

—

118

C₂

#10588357

yes

characteristic

	subgroup	G/H
center	C₄	#63436
commutator, cosocle	C₂²×C₄×C₉	C₂³
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₉×#338	C₂
socle	C₂×C₃	#4677
prime radical	C₂³×D₉	Q₈
hypercenter	#338	D₉
hypocenter	C₉	#2091
LCS	G ▷ C₂²×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #338

subgroup

G/H

center

C₄

#63436

commutator, cosocle

C₂²×C₄×C₉

C₂³

Frattini

C₂²×C₃×C₄

C₂²×D₃

C₂

C₂×C₃

C₂³×D₉

Q₈

D₉

C₉

G ▷ C₂²×C₄×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #338

N	H ≅ G/N	type
2. #10588800	C₂	semidirect
3. C₉×#338	C₂	semidirect
40. #338	D₉	semidirect
93. C₉	#2091	semidirect

H ≅ G/N

type

2. #10588800

C₂

semidirect

3. C₉×#338

C₂

semidirect

40. #338

D₉

semidirect

93. C₉

#2091

semidirect

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

subgroup	index
#10588808	2
#10588800	2
C₉×#338	2
#68721	3

subgroup

index

Subgroups — #11795361

Conjugacy classes of subgroups

Complements

Maximal subgroups