Group #11777846 — subgroups

Subgroups — #11777846

Order 1152.

262 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 58 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	#10593835	C₂	1	2	yes	maximal
2	Q₁₆×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
3	Q₈⋊#622	C₂	1	2	yes	maximal
4	#10590171	C₂	1	1	yes	maximal, characteristic
5	C₈×#622	C₂	1	1	yes	maximal, characteristic
6	C₂×C₃²×Q₁₆	C₄	1	1	yes	characteristic
7	Q₈×C₃⋊Dic₃	C₂²	1	2	yes	—
8	#63779	—	2	2	no	—
9	#63777	—	2	2	no	—
10	C₄⋊#622	C₂²	1	2	yes	—
11	C₄×#622	C₂²	1	1	yes	characteristic
12	C₄×#622	C₂²	1	1	yes	characteristic
13	#63662	C₄	1	2	yes	—
14	#63645	C₄	1	1	yes	characteristic
15	C₈×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
16	Dic₃×Q₁₆	—	6	2	no	—
17	C₂×C₃²×Q₈	C₂×C₄	1	2	yes	—
18	C₂×#622	—	2	1	no	—
19	C₂×#622	—	2	2	no	—
20	C₂×#622	D₄	1	1	yes	characteristic
21	C₂×#622	D₄	1	1	yes	characteristic
22	C₃²×Q₁₆	—	2	2	no	—
23	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
24	C₄⋊(C₃⋊Dic₃)	—	2	2	no	—
25	C₄⋊(C₃⋊Dic₃)	C₂×C₄	1	2	yes	—
26	C₄×C₃⋊Dic₃	—	2	2	no	—
27	C₄×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
28	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
29	#1591	—	9	1	no	maximal, Sylow
30	C₂×C₃×Q₁₆	—	2	2	no	—
31	Q₈×Dic₃	—	6	4	no	—
32	#835	—	6	4	no	—
33	#818	—	6	2	no	—
34	C₈×Dic₃	—	6	2	no	—
35	C₃²×Q₈	—	2	2	no	—
36	C₃²×Q₈	—	2	2	no	—
37	C₂×C₃²×C₄	—	2	2	no	—
38	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₃⋊Dic₃	—	2	2	no	—
40	C₂×C₃⋊Dic₃	C₂×D₄	1	1	yes	characteristic
41	C₂×C₃⋊Dic₃	#41	1	1	yes	characteristic
42	#622	—	2	2	no	—
43	#622	—	2	1	no	—
44	#622	—	4	2	no	—
45	#622	Q₁₆	1	2	yes	complemented
46	C₃²×C₈	M₁₆	1	2	yes	—
47	C₃⋊(C₃⋊C₈)	—	2	1	no	—
48	#446	—	9	2	no	—
49	C₄×Q₁₆	—	9	1	no	—
50	#335	—	9	1	no	—
51	Q₈⋊C₈	—	9	2	no	—
52	C₈²	—	9	1	no	—
53	C₂×C₃×Q₈	—	2	4	no	—
54	C₃×Q₁₆	—	2	8	no	—
55	C₂×C₃×C₈	—	2	2	no	—
56	C₄⋊Dic₃	—	6	4	no	—
57	C₄⋊Dic₃	—	12	4	no	—
58	C₄×Dic₃	—	6	2	no	—
59	C₄×Dic₃	—	12	4	no	—
60	C₂×C₃⋊C₈	—	6	2	no	—
61	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
62	C₃²×C₄	—	4	2	no	—
63	C₃²×C₄	C₂×M₁₆	1	1	yes	characteristic
64	C₃²×C₄	#131	1	1	yes	characteristic
65	C₃⋊Dic₃	—	2	1	no	—
66	C₃⋊Dic₃	—	4	2	no	—
67	C₃⋊Dic₃	C₂×Q₁₆	1	1	yes	characteristic
68	C₃⋊Dic₃	#135	1	1	yes	characteristic
69	C₂×Q₁₆	#157	1	1	yes	characteristic
70	C₄×Q₈	—	9	2	no	—
71	#107	—	9	1	no	—
72	C₄⋊C₈	—	9	2	no	—
73	C₄⋊C₈	—	18	2	no	—
74	#103	—	9	2	no	—
75	#97	—	18	2	no	—
76	C₄×C₈	—	9	1	no	—
77	C₄×C₈	—	9	1	no	—
78	C₄×C₈	—	9	1	no	—
79	C₃×Q₈	—	2	8	no	—
80	C₃×Q₈	—	4	4	no	—
81	C₂×C₃×C₄	—	2	2	no	—
82	C₂×C₃×C₄	—	4	4	no	—
83	C₂×Dic₃	—	6	2	no	—
84	C₂×Dic₃	—	6	2	no	—
85	C₂×Dic₃	—	12	4	no	—
86	C₃×C₈	—	2	4	no	—
87	C₃⋊C₈	—	12	2	no	—
88	C₂×C₃²	#436	1	1	yes	characteristic
89	C₂×C₃²	C₄×Q₁₆	1	1	yes	characteristic
90	C₂×C₃²	#443	1	1	yes	characteristic
91	C₂×Q₈	C₂×#157	1	2	yes	—
92	Q₁₆	—	2	2	no	—
93	C₂×C₈	—	9	1	no	—
94	C₂×C₈	—	9	1	no	—
95	C₂×C₈	—	9	1	no	—
96	C₂×C₈	—	18	1	no	—
97	C₂×C₈	—	18	2	no	—
98	C₂×C₈	C₂×#157	1	1	yes	characteristic
99	C₄⋊C₄	—	9	2	no	—
100	C₄⋊C₄	—	18	2	no	—
101	C₄²	—	9	1	no	—
102	C₄²	—	18	2	no	—
103	C₂²×C₃	—	2	2	no	—
104	C₃×C₄	—	2	2	no	—
105	C₃×C₄	—	2	2	no	—
106	C₃×C₄	—	4	8	no	—
107	Dic₃	—	6	2	no	—
108	Dic₃	—	6	2	no	—
109	Dic₃	—	12	2	no	—
110	Dic₃	—	24	4	no	—
111	C₃²	#1591	1	1	yes	characteristic, complemented, Sylow
112	Q₈	—	2	2	no	—
113	Q₈	—	2	2	no	—
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	9	1	no	—
116	C₂×C₄	—	9	1	no	—
117	C₂×C₄	—	18	2	no	—
118	C₂×C₄	C₂²×#157	1	1	yes	characteristic
119	C₈	—	9	2	no	—
120	C₈	—	18	1	no	—
121	C₈	—	18	2	no	—
122	C₈	—	18	1	no	—
123	C₈	—	36	2	no	—
124	C₈	#3792	1	2	yes	—
125	C₂×C₃	—	2	2	no	—
126	C₂×C₃	—	2	2	no	—
127	C₂×C₃	—	2	2	no	—
128	C₂²	D₄×#157	1	1	yes	characteristic
129	C₄	—	4	2	no	—
130	C₄	—	9	1	no	—
131	C₄	—	9	1	no	—
132	C₄	—	18	1	no	—
133	C₄	—	36	2	no	—
134	C₄	#64287	1	1	yes	characteristic
135	C₄	C₂×#3792	1	1	yes	characteristic
136	C₃	—	2	2	no	—
137	C₂	Q₁₆×#157	1	1	yes	characteristic
138	C₂	#10593787	1	1	yes	characteristic
139	C₂	#10593821	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#10593835

C₂

yes

maximal

Q₁₆×C₃⋊Dic₃

C₂

yes

maximal, characteristic

Q₈⋊#622

C₂

yes

maximal

#10590171

C₂

yes

maximal, characteristic

C₈×#622

C₂

yes

maximal, characteristic

C₂×C₃²×Q₁₆

C₄

yes

characteristic

Q₈×C₃⋊Dic₃

C₂²

yes

—

#63779

—

#63777

—

C₄⋊#622

C₂²

yes

—

C₄×#622

C₂²

yes

characteristic

C₄×#622

C₂²

yes

characteristic

#63662

C₄

yes

—

#63645

C₄

yes

characteristic

C₈×C₃⋊Dic₃

C₂²

yes

characteristic

Dic₃×Q₁₆

—

C₂×C₃²×Q₈

C₂×C₄

yes

—

C₂×#622

—

C₂×#622

—

C₂×#622

D₄

yes

characteristic

C₂×#622

D₄

yes

characteristic

C₃²×Q₁₆

—

C₂×C₃²×C₈

C₂×C₄

yes

characteristic

C₄⋊(C₃⋊Dic₃)

—

C₄⋊(C₃⋊Dic₃)

C₂×C₄

yes

—

C₄×C₃⋊Dic₃

—

C₄×C₃⋊Dic₃

C₂³

yes

characteristic

C₂×C₃⋊(C₃⋊C₈)

C₂×C₄

yes

characteristic

#1591

—

maximal, Sylow

C₂×C₃×Q₁₆

—

Q₈×Dic₃

—

#835

—

#818

—

C₈×Dic₃

—

C₃²×Q₈

—

C₃²×Q₈

—

C₂×C₃²×C₄

—

C₂×C₃²×C₄

C₂²×C₄

yes

characteristic

C₂×C₃⋊Dic₃

—

C₂×C₃⋊Dic₃

C₂×D₄

yes

C₂×C₃⋊Dic₃

yes

—

—

—

Q₁₆

yes

complemented

C₃²×C₈

M₁₆

yes

—

C₃⋊(C₃⋊C₈)

—

#446

—

C₄×Q₁₆

—

#335

—

Q₈⋊C₈

—

C₈²

—

C₂×C₃×Q₈

—

C₃×Q₁₆

—

C₂×C₃×C₈

—

C₄⋊Dic₃

—

C₄⋊Dic₃

—

C₄×Dic₃

—

C₄×Dic₃

—

C₂×C₃⋊C₈

—

C₂²×C₃²

C₄×D₄

yes

characteristic

C₃²×C₄

—

C₃²×C₄

C₂×M₁₆

yes

characteristic

C₃²×C₄

#131

yes

characteristic

C₃⋊Dic₃

—

C₃⋊Dic₃

—

C₃⋊Dic₃

C₂×Q₁₆

yes

C₃⋊Dic₃

yes

C₂×Q₁₆

yes

C₄×Q₈

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

#103

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₃×Q₈

—

C₃×Q₈

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×Dic₃

—

C₂×Dic₃

—

C₂×Dic₃

—

C₃×C₈

—

C₃⋊C₈

—

C₂×C₃²

#436

yes

characteristic

C₂×C₃²

C₄×Q₁₆

yes

C₂×C₃²

yes

C₂×Q₈

yes

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#157

yes

characteristic

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄²

—

102

C₄²

—

103

C₂²×C₃

—

104

C₃×C₄

—

105

C₃×C₄

—

106

C₃×C₄

—

107

Dic₃

—

108

Dic₃

—

109

Dic₃

—

110

Dic₃

—

111

C₃²

#1591

yes

characteristic, complemented, Sylow

112

Q₈

—

113

Q₈

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

C₂²×#157

yes

characteristic

119

C₈

—

120

C₈

—

121

C₈

—

122

C₈

—

123

C₈

—

124

C₈

#3792

yes

—

125

C₂×C₃

—

126

C₂×C₃

—

127

C₂×C₃

—

128

C₂²

D₄×#157

yes

characteristic

129

C₄

—

130

C₄

—

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

#64287

yes

characteristic

135

C₄

C₂×#3792

yes

characteristic

136

C₃

—

137

C₂

Q₁₆×#157

yes

characteristic

138

C₂

#10593787

yes

characteristic

139

C₂

#10593821

yes

characteristic

	subgroup	G/H
center	C₂²	D₄×#157
commutator	C₂×C₃²×C₄	C₂²×C₄
Frattini	C₂×C₄	C₂²×#157
Fitting	C₂×C₃²×Q₁₆	C₄
socle, prime radical	C₂²×C₃²	C₄×D₄
cosocle	C₄×C₃⋊Dic₃	C₂³
hypercenter	C₂×Q₁₆	#157
hypocenter	C₃²	#1591
LCS	G ▷ C₂×C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

subgroup

G/H

center

C₂²

D₄×#157

commutator

C₂×C₃²×C₄

C₂²×C₄

Frattini

C₂×C₄

C₂²×#157

Fitting

C₂×C₃²×Q₁₆

C₄

socle, prime radical

C₂²×C₃²

C₄×D₄

cosocle

C₄×C₃⋊Dic₃

C₂³

C₂×Q₁₆

C₃²

G ▷ C₂×C₃²×C₄ ▷ C₂×C₃² ▷ C₃²

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

N	H ≅ G/N	type
45. #622	Q₁₆	semidirect
111. C₃²	#1591	semidirect

H ≅ G/N

type

45. #622

Q₁₆

semidirect

111. C₃²

#1591

semidirect

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

subgroup	index
#10593835	2
Q₁₆×C₃⋊Dic₃	2
Q₈⋊#622	2
#10590171	2
C₈×#622	2
#1591	9

subgroup

index

Q₁₆×C₃⋊Dic₃

Subgroups — #11777846

Conjugacy classes of subgroups

Complements

Maximal subgroups