Group #11786107 — subgroups

Subgroups — #11786107

Order 1152.

270 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 118 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	1	yes	maximal, characteristic
3	C₂×#63362	C₂	1	1	yes	maximal, characteristic
4	#10588231	C₂	1	4	yes	maximal
5	#70517	—	3	1	no	maximal
6	C₂×C₉×M₁₆	C₂²	1	2	yes	—
7	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
8	C₂×#3667	C₂²	1	2	yes	—
9	C₂²×C₉⋊C₈	C₂²	1	2	yes	—
10	C₉×C₄⋊C₈	—	2	2	no	—
11	C₄⋊(C₉⋊C₈)	—	2	2	no	—
12	#63362	C₄	1	4	yes	—
13	C₃×#423	D₃	1	1	yes	characteristic
14	#4924	—	3	1	no	—
15	C₂×#803	—	3	1	no	—
16	#4558	—	3	4	no	—
17	C₂²×C₄×C₉	Q₈	1	2	yes	—
18	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
19	C₉×M₁₆	—	2	4	no	—
20	C₂×C₈×C₉	—	2	2	no	—
21	C₄²×C₉	C₂×C₄	1	2	yes	—
22	C₄²×C₉	D₄	1	2	yes	—
23	#3667	—	2	4	no	—
24	C₂×C₉⋊C₈	—	2	2	no	—
25	C₂×C₉⋊C₈	—	2	2	no	—
26	C₂×C₉⋊C₈	—	2	2	no	—
27	C₂×C₉⋊C₈	C₂×C₄	1	4	yes	—
28	#1838	—	9	1	no	Sylow
29	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
30	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
31	C₂×#208	—	3	2	no	—
32	C₂²×C₃⋊C₈	—	3	2	no	—
33	C₃×C₄⋊C₈	—	2	2	no	—
34	C₄⋊(C₃⋊C₈)	—	6	2	no	—
35	#803	—	3	4	no	—
36	C₂³×C₉	C₂×Q₈	1	1	yes	characteristic
37	C₂×C₄×C₉	—	4	2	no	—
38	C₂×C₄×C₉	C₄⋊C₄	1	4	yes	—
39	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₉	#41	1	2	yes	—
42	C₂×C₄×C₉	#41	1	2	yes	—
43	C₈×C₉	—	4	2	no	—
44	C₉⋊C₈	—	2	4	no	—
45	C₉⋊C₈	—	4	2	no	—
46	#423	—	9	1	no	—
47	#423	D₉	1	1	yes	characteristic
48	C₂×#97	—	9	1	no	—
49	#341	—	9	4	no	—
50	C₂²×C₃×C₄	Dic₆	1	2	yes	—
51	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
52	C₃×M₁₆	—	2	4	no	—
53	C₂×C₃×C₈	—	2	2	no	—
54	C₃×C₄²	C₄×D₃	1	2	yes	—
55	C₃×C₄²	#67	1	2	yes	—
56	#208	—	6	4	no	—
57	C₂×C₃⋊C₈	—	3	4	no	—
58	C₂×C₃⋊C₈	—	6	2	no	—
59	C₂×C₃⋊C₈	—	6	2	no	—
60	C₂×C₃⋊C₈	—	6	2	no	—
61	C₂²×C₉	—	2	2	no	—
62	C₂²×C₉	C₂×C₄⋊C₄	1	1	yes	characteristic
63	C₂²×C₉	#125	1	2	yes	—
64	C₄×C₉	—	2	4	no	—
65	C₄×C₉	#117	1	2	yes	—
66	C₄×C₉	#124	1	1	yes	characteristic
67	C₄×C₉	#124	1	1	yes	characteristic
68	C₂×M₁₆	—	9	2	no	—
69	C₂×M₁₆	C₂×D₉	1	2	yes	—
70	C₂²×C₈	—	9	2	no	—
71	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
72	C₄⋊C₈	—	2	2	no	—
73	C₄⋊C₈	—	18	2	no	—
74	#97	—	9	4	no	—
75	C₂³×C₃	C₂×Dic₆	1	1	yes	characteristic
76	C₂×C₃×C₄	—	4	2	no	—
77	C₂×C₃×C₄	Dic₃⋊C₄	1	4	yes	—
78	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
79	C₂×C₃×C₄	#237	1	2	yes	—
80	C₂×C₃×C₄	#239	1	2	yes	—
81	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
82	C₃×C₈	—	4	2	no	—
83	C₃⋊C₈	—	6	4	no	—
84	C₃⋊C₈	—	12	2	no	—
85	C₂×C₉	—	2	2	no	—
86	C₂×C₉	#382	1	1	yes	characteristic
87	C₂×C₉	#430	1	2	yes	—
88	C₂²×C₄	Dic₁₈	1	2	yes	—
89	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
90	M₁₆	—	2	4	no	—
91	M₁₆	—	18	4	no	—
92	C₂×C₈	—	2	2	no	—
93	C₂×C₈	—	9	4	no	—
94	C₂×C₈	—	18	2	no	—
95	C₂×C₈	—	18	2	no	—
96	C₂×C₈	—	18	2	no	—
97	C₄²	C₄×D₉	1	2	yes	—
98	C₄²	#611	1	2	yes	—
99	C₂²×C₃	—	2	2	no	—
100	C₂²×C₃	#890	1	2	yes	—
101	C₂²×C₃	C₂×Dic₃⋊C₄	1	1	yes	characteristic
102	C₃×C₄	—	2	4	no	—
103	C₃×C₄	#892	1	2	yes	—
104	C₃×C₄	#936	1	1	yes	characteristic
105	C₃×C₄	#947	1	1	yes	characteristic
106	C₉	#1838	1	1	yes	characteristic, complemented, Sylow
107	C₂³	C₂×Dic₁₈	1	1	yes	characteristic
108	C₂×C₄	—	4	2	no	—
109	C₂×C₄	Dic₉⋊C₄	1	4	yes	—
110	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
111	C₂×C₄	#3699	1	2	yes	—
112	C₂×C₄	#3701	1	2	yes	—
113	C₂×C₄	C₂×#611	1	1	yes	characteristic
114	C₈	—	4	2	no	—
115	C₈	—	18	4	no	—
116	C₈	—	36	2	no	—
117	C₂×C₃	—	2	2	no	—
118	C₂×C₃	#4977	1	1	yes	characteristic
119	C₂×C₃	#5124	1	2	yes	—
120	C₂²	—	2	2	no	—
121	C₂²	#63452	1	2	yes	—
122	C₂²	C₂×Dic₉⋊C₄	1	1	yes	characteristic
123	C₄	—	2	4	no	—
124	C₄	#63454	1	2	yes	—
125	C₄	#63498	1	1	yes	characteristic
126	C₄	#63509	1	1	yes	characteristic
127	C₃	#70517	1	1	yes	characteristic
128	C₂	—	2	2	no	—
129	C₂	#10588657	1	1	yes	characteristic
130	C₂	#10588799	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₉×#423

C₂

yes

maximal, characteristic

#10588604

C₂

yes

maximal, characteristic

C₂×#63362

C₂

yes

maximal, characteristic

#10588231

C₂

yes

maximal

#70517

—

maximal

C₂×C₉×M₁₆

C₂²

yes

—

C₂×C₄²×C₉

C₂²

yes

characteristic

C₂×#3667

C₂²

yes

—

C₂²×C₉⋊C₈

C₂²

yes

—

C₉×C₄⋊C₈

—

C₄⋊(C₉⋊C₈)

—

#63362

C₄

yes

—

C₃×#423

D₃

yes

—

—

—

C₂²×C₄×C₉

Q₈

yes

—

C₂²×C₄×C₉

C₂³

yes

characteristic

C₉×M₁₆

—

C₂×C₈×C₉

—

C₄²×C₉

C₂×C₄

yes

—

C₄²×C₉

D₄

yes

—

#3667

—

C₂×C₉⋊C₈

—

C₂×C₉⋊C₈

—

C₂×C₉⋊C₈

—

C₂×C₉⋊C₈

C₂×C₄

yes

—

#1838

—

Sylow

C₂×C₃×M₁₆

C₂×D₃

yes

—

C₂×C₃×C₄²

C₂×D₃

yes

characteristic

C₂×#208

—

C₂²×C₃⋊C₈

—

C₃×C₄⋊C₈

—

C₄⋊(C₃⋊C₈)

—

#803

—

C₂³×C₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₉

—

C₂×C₄×C₉

C₄⋊C₄

yes

—

C₂×C₄×C₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

#41

yes

—

C₂×C₄×C₉

#41

yes

—

C₈×C₉

—

C₉⋊C₈

—

C₉⋊C₈

—

#423

—

#423

D₉

yes

characteristic

C₂×#97

—

#341

—

C₂²×C₃×C₄

Dic₆

yes

—

C₂²×C₃×C₄

C₂²×D₃

yes

characteristic

C₃×M₁₆

—

C₂×C₃×C₈

—

C₃×C₄²

C₄×D₃

yes

—

C₃×C₄²

#67

yes

—

#208

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

C₂²×C₉

—

C₂²×C₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₉

#125

yes

—

C₄×C₉

—

C₄×C₉

#117

yes

—

C₄×C₉

yes

C₄×C₉

yes

C₂×M₁₆

—

C₂×M₁₆

C₂×D₉

yes

—

C₂²×C₈

—

C₂×C₄²

C₂×D₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

#97

—

C₂³×C₃

C₂×Dic₆

yes

characteristic

C₂×C₃×C₄

—

C₂×C₃×C₄

Dic₃⋊C₄

yes

—

C₂×C₃×C₄

C₂×C₄×D₃

yes

characteristic

C₂×C₃×C₄

#237

yes

—

C₂×C₃×C₄

#239

yes

—

C₂×C₃×C₄

C₂×#67

yes

characteristic

C₃×C₈

—

C₃⋊C₈

—

C₃⋊C₈

—

C₂×C₉

—

C₂×C₉

#382

yes

characteristic

C₂×C₉

#430

yes

—

C₂²×C₄

Dic₁₈

yes

—

C₂²×C₄

C₂²×D₉

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

C₄×D₉

yes

—

C₄²

#611

yes

—

C₂²×C₃

—

100

C₂²×C₃

#890

yes

—

101

C₂²×C₃

C₂×Dic₃⋊C₄

yes

characteristic

102

C₃×C₄

—

103

C₃×C₄

#892

yes

—

104

C₃×C₄

#936

yes

characteristic

105

C₃×C₄

#947

yes

characteristic

106

C₉

#1838

yes

characteristic, complemented, Sylow

107

C₂³

C₂×Dic₁₈

yes

characteristic

108

C₂×C₄

—

109

C₂×C₄

Dic₉⋊C₄

yes

—

110

C₂×C₄

C₂×C₄×D₉

yes

characteristic

111

C₂×C₄

#3699

yes

—

112

C₂×C₄

#3701

yes

—

113

C₂×C₄

C₂×#611

yes

characteristic

114

C₈

—

115

C₈

—

116

C₈

—

117

C₂×C₃

—

118

C₂×C₃

#4977

yes

characteristic

119

C₂×C₃

#5124

yes

—

120

C₂²

—

121

C₂²

#63452

yes

—

122

C₂²

C₂×Dic₉⋊C₄

yes

characteristic

123

C₄

—

124

C₄

#63454

yes

—

125

C₄

#63498

yes

characteristic

126

C₄

#63509

yes

characteristic

127

C₃

#70517

yes

characteristic

128

C₂

—

129

C₂

#10588657

yes

characteristic

130

C₂

#10588799

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×#611
commutator	C₂×C₄×C₉	C₂²×C₄
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₉×#423	C₂
socle	C₂²×C₃	C₂×Dic₃⋊C₄
prime radical	C₂³×C₃	C₂×Dic₆
cosocle	C₂²×C₄×C₉	C₂³
hypercenter	#423	D₉
hypocenter	C₉	#1838
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #423

subgroup

G/H

center

C₂×C₄

C₂×#611

commutator

C₂×C₄×C₉

C₂²×C₄

Frattini

C₂²×C₃×C₄

C₂²×D₃

Fitting

C₉×#423

C₂

socle

C₂²×C₃

C₂×Dic₃⋊C₄

prime radical

C₂³×C₃

C₂×Dic₆

cosocle

C₂²×C₄×C₉

C₂³

D₉

C₉

G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #423

N	H ≅ G/N	type
106. C₉	#1838	semidirect

H ≅ G/N

type

106. C₉

#1838

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
C₂×#63362	2
#10588231	2
#70517	3

subgroup

index

Subgroups — #11786107

Conjugacy classes of subgroups

Complements

Maximal subgroups