Group #11771274 — subgroups

Subgroups — C₉⋊#1309 #11771274

Order 1152.

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

normal subgroups only

This group has 219 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	C₉×#423	C₂	1	1	yes	maximal, characteristic
2	#10588604	C₂	1	2	yes	maximal
3	C₃⋊#1309	—	3	1	no	maximal
4	C₂×C₉×M₁₆	C₄	1	2	yes	—
5	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
6	C₂×#3667	C₄	1	4	yes	—
7	C₉×C₄⋊C₈	—	2	2	no	—
8	C₄⋊(C₉⋊C₈)	—	2	2	no	—
9	C₄⋊(C₉⋊C₈)	—	2	2	no	—
10	C₃×#423	D₃	1	1	yes	characteristic
11	#4924	—	3	2	no	—
12	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
13	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
14	C₉×M₁₆	—	4	2	no	—
15	C₂×C₈×C₉	—	2	2	no	—
16	C₄²×C₉	D₄	1	1	yes	characteristic
17	C₄²×C₉	D₄	1	2	yes	—
18	C₄²×C₉	Q₈	1	1	yes	characteristic
19	#3667	—	4	4	no	—
20	C₂×C₉⋊C₈	—	2	4	no	—
21	#1309	—	9	1	no	Sylow
22	C₂×C₃×M₁₆	Dic₃	1	2	yes	—
23	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
24	C₂×#208	—	3	4	no	—
25	C₃×C₄⋊C₈	—	2	2	no	—
26	C₄⋊(C₃⋊C₈)	—	6	2	no	—
27	C₄⋊(C₃⋊C₈)	—	6	2	no	—
28	C₂³×C₉	C₄²	1	1	yes	characteristic
29	C₂×C₄×C₉	—	2	2	no	—
30	C₂×C₄×C₉	—	2	1	no	—
31	C₂×C₄×C₉	—	2	2	no	—
32	C₂×C₄×C₉	—	2	1	no	—
33	C₂×C₄×C₉	C₂²⋊C₄	1	2	yes	—
34	C₂×C₄×C₉	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₉	C₄⋊C₄	1	2	yes	—
36	C₂×C₄×C₉	C₄⋊C₄	1	1	yes	characteristic
37	C₈×C₉	—	4	2	no	—
38	C₉⋊C₈	—	4	4	no	—
39	#423	—	9	2	no	—
40	#423	D₉	1	1	yes	characteristic
41	C₂²×C₃×C₄	C₄×D₃	1	2	yes	—
42	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
43	C₃×M₁₆	—	4	2	no	—
44	C₂×C₃×C₈	—	2	2	no	—
45	C₃×C₄²	Dic₆	1	1	yes	characteristic
46	C₃×C₄²	D₁₂	1	1	yes	characteristic
47	C₃×C₄²	#67	1	2	yes	—
48	#208	—	12	4	no	—
49	C₂×C₃⋊C₈	—	6	4	no	—
50	C₂²×C₉	—	2	1	no	—
51	C₂²×C₉	—	2	2	no	—
52	C₂²×C₉	#95	1	1	yes	characteristic
53	C₄×C₉	—	2	1	no	—
54	C₄×C₉	—	2	2	no	—
55	C₄×C₉	#100	1	2	yes	—
56	C₄×C₉	#100	1	1	yes	characteristic
57	C₄×C₉	#101	1	2	yes	—
58	C₄×C₉	#101	1	1	yes	characteristic
59	C₂×M₁₆	—	9	4	no	—
60	C₂×M₁₆	Dic₉	1	2	yes	—
61	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
62	C₄⋊C₈	—	2	2	no	—
63	C₄⋊C₈	—	18	2	no	—
64	C₄⋊C₈	—	18	2	no	—
65	C₂³×C₃	C₄×Dic₃	1	1	yes	characteristic
66	C₂×C₃×C₄	—	2	2	no	—
67	C₂×C₃×C₄	—	2	2	no	—
68	C₂×C₃×C₄	—	2	1	no	—
69	C₂×C₃×C₄	—	2	1	no	—
70	C₂×C₃×C₄	Dic₃⋊C₄	1	2	yes	—
71	C₂×C₃×C₄	C₄⋊Dic₃	1	1	yes	characteristic
72	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	2	yes	—
73	C₂×C₃×C₄	#217	1	1	yes	characteristic
74	C₃×C₈	—	4	2	no	—
75	C₃⋊C₈	—	12	4	no	—
76	C₂×C₉	—	4	1	no	—
77	C₂×C₉	#343	1	1	yes	characteristic
78	C₂×C₉	#343	1	2	yes	—
79	C₂²×C₄	C₄×D₉	1	2	yes	—
80	C₂²×C₄	C₂×Dic₉	1	1	yes	characteristic
81	M₁₆	—	4	2	no	—
82	M₁₆	—	36	4	no	—
83	C₂×C₈	—	2	2	no	—
84	C₂×C₈	—	18	4	no	—
85	C₄²	Dic₁₈	1	1	yes	characteristic
86	C₄²	D₃₆	1	1	yes	characteristic
87	C₄²	#611	1	2	yes	—
88	C₂²×C₃	—	2	1	no	—
89	C₂²×C₃	—	2	2	no	—
90	C₂²×C₃	C₃⋊#95	1	1	yes	characteristic
91	C₃×C₄	—	2	1	no	—
92	C₃×C₄	—	2	2	no	—
93	C₃×C₄	#823	1	2	yes	—
94	C₃×C₄	#824	1	2	yes	—
95	C₃×C₄	#833	1	1	yes	characteristic
96	C₃×C₄	#836	1	1	yes	characteristic
97	C₉	#1309	1	1	yes	characteristic, complemented, Sylow
98	C₂³	C₄×Dic₉	1	1	yes	characteristic
99	C₂×C₄	—	2	2	no	—
100	C₂×C₄	—	2	2	no	—
101	C₂×C₄	—	2	1	no	—
102	C₂×C₄	—	2	1	no	—
103	C₂×C₄	Dic₉⋊C₄	1	2	yes	—
104	C₂×C₄	C₄⋊Dic₉	1	1	yes	characteristic
105	C₂×C₄	(C₂×D₉)⋊C₄	1	2	yes	—
106	C₂×C₄	#3676	1	1	yes	characteristic
107	C₈	—	4	2	no	—
108	C₈	—	36	4	no	—
109	C₂×C₃	—	4	1	no	—
110	C₂×C₃	#4530	1	1	yes	characteristic
111	C₂×C₃	#4554	1	2	yes	—
112	C₂²	—	2	1	no	—
113	C₂²	—	2	2	no	—
114	C₂²	C₉⋊#95	1	1	yes	characteristic
115	C₄	—	2	1	no	—
116	C₄	—	2	2	no	—
117	C₄	#63382	1	2	yes	—
118	C₄	#63383	1	2	yes	—
119	C₄	#63391	1	1	yes	characteristic
120	C₄	#63394	1	1	yes	characteristic
121	C₃	C₃⋊#1309	1	1	yes	characteristic
122	C₂	—	4	1	no	—
123	C₂	#10588207	1	1	yes	characteristic
124	C₂	#10588234	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₉×#423

C₂

yes

maximal, characteristic

#10588604

C₂

yes

maximal

C₃⋊#1309

—

maximal

C₂×C₉×M₁₆

C₄

yes

—

C₂×C₄²×C₉

C₂²

yes

characteristic

C₂×#3667

C₄

yes

—

C₉×C₄⋊C₈

—

C₄⋊(C₉⋊C₈)

—

C₄⋊(C₉⋊C₈)

—

C₃×#423

D₃

yes

characteristic

#4924

—

C₂²×C₄×C₉

C₂×C₄

yes

—

C₂²×C₄×C₉

C₂×C₄

yes

characteristic

C₉×M₁₆

—

C₂×C₈×C₉

—

C₄²×C₉

D₄

yes

characteristic

C₄²×C₉

D₄

yes

—

C₄²×C₉

Q₈

yes

characteristic

#3667

—

C₂×C₉⋊C₈

—

#1309

—

Sylow

C₂×C₃×M₁₆

Dic₃

yes

—

C₂×C₃×C₄²

C₂×D₃

yes

characteristic

C₂×#208

—

C₃×C₄⋊C₈

—

C₄⋊(C₃⋊C₈)

—

C₄⋊(C₃⋊C₈)

—

C₂³×C₉

C₄²

yes

characteristic

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₂²⋊C₄

yes

—

C₂×C₄×C₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₉

C₄⋊C₄

yes

—

C₂×C₄×C₉

C₄⋊C₄

yes

characteristic

C₈×C₉

—

C₉⋊C₈

—

#423

—

#423

D₉

yes

characteristic

C₂²×C₃×C₄

C₄×D₃

yes

—

C₂²×C₃×C₄

C₂×Dic₃

yes

characteristic

C₃×M₁₆

—

C₂×C₃×C₈

—

C₃×C₄²

Dic₆

yes

characteristic

C₃×C₄²

D₁₂

yes

characteristic

C₃×C₄²

#67

yes

—

#208

—

C₂×C₃⋊C₈

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

#95

yes

characteristic

C₄×C₉

—

C₄×C₉

—

C₄×C₉

#100

yes

—

C₄×C₉

#100

yes

characteristic

C₄×C₉

#101

yes

—

C₄×C₉

#101

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

Dic₉

yes

—

C₂×C₄²

C₂×D₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂³×C₃

C₄×Dic₃

yes

characteristic

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

Dic₃⋊C₄

yes

—

C₂×C₃×C₄

C₄⋊Dic₃

yes

characteristic

C₂×C₃×C₄

(C₂×D₃)⋊C₄

yes

—

C₂×C₃×C₄

#217

yes

characteristic

C₃×C₈

—

C₃⋊C₈

—

C₂×C₉

—

C₂×C₉

#343

yes

characteristic

C₂×C₉

#343

yes

—

C₂²×C₄

C₄×D₉

yes

—

C₂²×C₄

C₂×Dic₉

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₄²

Dic₁₈

yes

characteristic

C₄²

D₃₆

yes

characteristic

C₄²

#611

yes

—

C₂²×C₃

—

C₂²×C₃

—

C₂²×C₃

C₃⋊#95

yes

characteristic

C₃×C₄

—

C₃×C₄

—

C₃×C₄

#823

yes

—

C₃×C₄

#824

yes

—

C₃×C₄

yes

C₃×C₄

yes

C₉

yes

characteristic, complemented, Sylow

C₂³

C₄×Dic₉

yes

characteristic

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

Dic₉⋊C₄

yes

—

104

C₂×C₄

C₄⋊Dic₉

yes

characteristic

105

C₂×C₄

(C₂×D₉)⋊C₄

yes

—

106

C₂×C₄

#3676

yes

characteristic

107

C₈

—

108

C₈

—

109

C₂×C₃

—

110

C₂×C₃

#4530

yes

characteristic

111

C₂×C₃

#4554

yes

—

112

C₂²

—

113

C₂²

—

114

C₂²

C₉⋊#95

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

#63382

yes

—

118

C₄

#63383

yes

—

119

C₄

#63391

yes

characteristic

120

C₄

#63394

yes

characteristic

121

C₃

C₃⋊#1309

yes

characteristic

122

C₂

—

123

C₂

#10588207

yes

characteristic

124

C₂

#10588234

yes

—

	subgroup	G/H
center	C₂²	C₉⋊#95
commutator	C₂³×C₉	C₄²
Frattini	C₂×C₃×C₄²	C₂×D₃
Fitting	C₉×#423	C₂
socle	C₂²×C₃	C₃⋊#95
prime radical	C₂³×C₃	C₄×Dic₃
cosocle	C₂×C₄²×C₉	C₂²
hypercenter	#423	D₉
hypocenter	C₉	#1309
LCS	G ▷ C₂³×C₉ ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #423

subgroup

G/H

center

C₂²

C₉⋊#95

commutator

C₂³×C₉

C₄²

Frattini

C₂×C₃×C₄²

C₂×D₃

C₂

C₂²×C₃

C₂³×C₃

C₄×Dic₃

cosocle

C₂×C₄²×C₉

C₂²

D₉

C₉

G ▷ C₂³×C₉ ▷ C₂²×C₉ ▷ C₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #423

N	H ≅ G/N	type
97. C₉	#1309	semidirect

H ≅ G/N

type

97. C₉

#1309

semidirect

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

subgroup	index
C₉×#423	2
#10588604	2
C₃⋊#1309	3

subgroup

index

C₉×#423

#10588604

C₃⋊#1309

Subgroups — C₉⋊#1309 #11771274

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C9⋊#1309 #11771274

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉⋊#1309 #11771274