Group #36475445 — subgroups

Subgroups — #36475445

Order 22784.

232 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 71 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	C₂×#19151438	C₂	1	2	yes	maximal, complemented
2	C₂×#19151436	C₂	1	2	yes	maximal
3	#26022505	C₂	1	1	yes	maximal, characteristic, complemented
4	#26018386	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2249	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₇₁₂	—	2	1	no	—
7	C₂×Dic₇₁₂	C₂²	1	2	yes	—
8	#19151978	—	2	1	no	—
9	#19151438	—	2	4	no	—
10	#19151436	—	2	4	no	—
11	C₂×#15667918	C₂²	1	2	yes	—
12	C₂×Q₃₂×C₈₉	C₂²	1	1	yes	characteristic
13	C₂×SD₃₂×C₈₉	—	2	1	no	—
14	C₂×D₁₆×C₈₉	C₂²	1	1	yes	characteristic
15	#495×C₈₉	—	2	1	no	—
16	C₄×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
17	C₂×Dic₃₅₆	—	2	2	no	—
18	C₂×Dic₃₅₆	—	4	1	no	—
19	#15668012	—	4	1	no	—
20	Dic₇₁₂	—	2	2	no	—
21	Dic₇₁₂	—	2	2	no	—
22	Dic₇₁₂	—	4	2	no	—
23	#15667918	D₄	1	4	yes	—
24	C₂×Q₁₆×C₈₉	—	2	1	no	—
25	C₂×SD₁₆×C₈₉	—	4	1	no	—
26	C₂×D₈×C₈₉	—	2	1	no	—
27	#124×C₈₉	—	4	1	no	—
28	Q₃₂×C₈₉	—	2	2	no	—
29	SD₃₂×C₈₉	—	4	2	no	—
30	D₁₆×C₈₉	—	2	2	no	—
31	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
32	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
33	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
34	C₂×Dic₁₇₈	—	4	2	no	—
35	Dic₃₅₆	—	4	2	no	—
36	Dic₃₅₆	—	4	2	no	—
37	Dic₃₅₆	—	8	2	no	—
38	C₄⋊Dic₈₉	—	8	2	no	—
39	C₂×Q₈×C₈₉	—	4	1	no	—
40	C₂×D₄×C₈₉	—	4	1	no	—
41	Q₁₆×C₈₉	—	4	1	no	—
42	Q₁₆×C₈₉	—	4	1	no	—
43	SD₁₆×C₈₉	—	8	2	no	—
44	D₈×C₈₉	—	4	1	no	—
45	D₈×C₈₉	—	4	1	no	—
46	C₂×C₈×C₈₉	D₈	1	1	yes	characteristic
47	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
48	C₂²⋊C₄×C₈₉	—	8	2	no	—
49	C₄²×C₈₉	D₈	1	1	yes	characteristic
50	C₁₆×C₈₉	D₈	1	2	yes	—
51	C₁₆×C₈₉	C₂×D₄	1	2	yes	—
52	C₂³×C₈₉	—	8	1	no	—
53	Q₈×C₈₉	—	8	1	no	—
54	Q₈×C₈₉	—	8	1	no	—
55	D₄×C₈₉	—	8	1	no	—
56	D₄×C₈₉	—	8	1	no	—
57	C₂×C₄×C₈₉	—	8	1	no	—
58	C₂×C₄×C₈₉	D₁₆	1	2	yes	—
59	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
60	C₂×Dic₈₉	—	8	2	no	—
61	Dic₁₇₈	—	8	2	no	—
62	Dic₁₇₈	—	8	2	no	—
63	C₈×C₈₉	D₁₆	1	2	yes	—
64	C₈×C₈₉	#127	1	1	yes	characteristic
65	C₈×C₈₉	C₂×D₈	1	1	yes	characteristic
66	C₂²×C₈₉	—	16	1	no	—
67	C₂²×C₈₉	—	16	2	no	—
68	C₂²×C₈₉	C₂×D₁₆	1	1	yes	characteristic
69	C₄×C₈₉	—	2	2	no	—
70	C₄×C₈₉	—	16	1	no	—
71	C₄×C₈₉	#493	1	1	yes	characteristic
72	C₄×C₈₉	C₂×D₁₆	1	1	yes	characteristic
73	Dic₈₉	—	16	2	no	—
74	#13730	—	89	1	no	maximal, Sylow
75	C₂×C₈₉	—	32	1	no	—
76	C₂×C₈₉	#2246	1	1	yes	characteristic
77	C₂×C₈₉	#2264	1	2	yes	—
78	C₂×Q₆₄	—	89	2	no	—
79	C₂×SD₆₄	—	89	2	no	—
80	#2249	D₈₉	1	1	yes	characteristic
81	#2247	—	89	1	no	—
82	#1397	—	89	1	no	—
83	C₈₉	#13730	1	1	yes	characteristic, complemented, Sylow
84	C₂×Q₃₂	—	89	2	no	—
85	C₂×Q₃₂	—	178	1	no	—
86	C₂×Q₃₂	C₂×D₈₉	1	1	yes	characteristic
87	C₂×SD₃₂	—	2	1	no	—
88	C₂×D₁₆	C₂×D₈₉	1	1	yes	characteristic
89	#495	—	2	1	no	—
90	#494	—	178	1	no	—
91	Q₆₄	—	178	4	no	—
92	SD₆₄	—	178	4	no	—
93	C₂×C₃₂	—	89	2	no	—
94	C₄×C₁₆	C₂×D₈₉	1	1	yes	characteristic
95	C₂×Q₁₆	—	2	1	no	—
96	C₂×Q₁₆	—	356	1	no	—
97	C₂×Q₁₆	—	178	2	no	—
98	C₂×SD₁₆	—	4	1	no	—
99	C₂×D₈	—	2	1	no	—
100	C₄⋊Q₈	—	356	1	no	—
101	#124	—	4	1	no	—
102	Q₃₂	—	2	2	no	—
103	Q₃₂	—	356	2	no	—
104	Q₃₂	—	178	2	no	—
105	Q₃₂	—	178	2	no	—
106	SD₃₂	—	4	2	no	—
107	D₁₆	—	2	2	no	—
108	C₂×C₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
109	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
110	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
111	C₃₂	—	89	4	no	—
112	C₂×Q₈	—	4	1	no	—
113	C₂×Q₈	—	356	2	no	—
114	C₂×D₄	—	4	1	no	—
115	Q₁₆	—	4	1	no	—
116	Q₁₆	—	4	1	no	—
117	Q₁₆	—	356	2	no	—
118	Q₁₆	—	356	2	no	—
119	Q₁₆	—	712	2	no	—
120	SD₁₆	—	8	2	no	—
121	D₈	—	4	1	no	—
122	D₈	—	4	1	no	—
123	C₂×C₈	#13083559	1	1	yes	characteristic
124	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
125	C₄⋊C₄	—	712	2	no	—
126	C₂²⋊C₄	—	8	2	no	—
127	C₄²	#13083559	1	1	yes	characteristic
128	C₁₆	#13083559	1	2	yes	—
129	C₁₆	D₄×D₈₉	1	2	yes	—
130	C₂³	—	8	1	no	—
131	Q₈	—	8	1	no	—
132	Q₈	—	8	1	no	—
133	Q₈	—	712	2	no	—
134	Q₈	—	712	2	no	—
135	D₄	—	8	1	no	—
136	D₄	—	8	1	no	—
137	C₂×C₄	—	8	1	no	—
138	C₂×C₄	—	712	2	no	—
139	C₂×C₄	#15667953	1	2	yes	—
140	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
141	C₈	#15667953	1	2	yes	—
142	C₈	#15668008	1	1	yes	characteristic
143	C₈	C₂×#13083559	1	1	yes	characteristic
144	C₂²	—	16	1	no	—
145	C₂²	—	16	2	no	—
146	C₂²	C₂×#15667953	1	1	yes	characteristic
147	C₄	—	2	2	no	—
148	C₄	—	16	1	no	—
149	C₄	—	1424	2	no	—
150	C₄	#19151974	1	1	yes	characteristic
151	C₄	C₂×#15667953	1	1	yes	characteristic
152	C₂	—	32	1	no	—
153	C₂	#26022501	1	1	yes	characteristic
154	C₂	#26022569	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19151438

C₂

yes

maximal, complemented

C₂×#19151436

C₂

yes

maximal

#26022505

C₂

yes

maximal, characteristic, complemented

#26018386

C₂

yes

maximal, characteristic, complemented

C₈₉×#2249

C₂

yes

maximal, characteristic

C₂×Dic₇₁₂

—

C₂×Dic₇₁₂

C₂²

yes

—

—

—

—

C₂²

yes

—

C₂×Q₃₂×C₈₉

C₂²

yes

characteristic

C₂×SD₃₂×C₈₉

—

C₂×D₁₆×C₈₉

C₂²

yes

characteristic

#495×C₈₉

—

C₄×C₁₆×C₈₉

C₂²

yes

characteristic

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

#15668012

—

Dic₇₁₂

—

Dic₇₁₂

—

Dic₇₁₂

—

#15667918

D₄

yes

—

C₂×Q₁₆×C₈₉

—

C₂×SD₁₆×C₈₉

—

C₂×D₈×C₈₉

—

#124×C₈₉

—

Q₃₂×C₈₉

—

SD₃₂×C₈₉

—

D₁₆×C₈₉

—

C₂×C₁₆×C₈₉

D₄

yes

characteristic

C₂×C₁₆×C₈₉

C₂³

yes

characteristic

C₄×C₈×C₈₉

D₄

yes

characteristic

C₂×Dic₁₇₈

—

Dic₃₅₆

—

Dic₃₅₆

—

Dic₃₅₆

—

C₄⋊Dic₈₉

—

C₂×Q₈×C₈₉

—

C₂×D₄×C₈₉

—

Q₁₆×C₈₉

—

Q₁₆×C₈₉

—

SD₁₆×C₈₉

—

D₈×C₈₉

—

D₈×C₈₉

—

C₂×C₈×C₈₉

D₈

yes

characteristic

C₂×C₈×C₈₉

C₂×D₄

yes

characteristic

C₂²⋊C₄×C₈₉

—

C₄²×C₈₉

D₈

yes

characteristic

C₁₆×C₈₉

D₈

yes

—

C₁₆×C₈₉

C₂×D₄

yes

—

C₂³×C₈₉

—

Q₈×C₈₉

—

Q₈×C₈₉

—

D₄×C₈₉

—

D₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

D₁₆

yes

—

C₂×C₄×C₈₉

C₂×D₈

yes

characteristic

C₂×Dic₈₉

—

Dic₁₇₈

—

Dic₁₇₈

—

C₈×C₈₉

D₁₆

yes

—

C₈×C₈₉

#127

yes

characteristic

C₈×C₈₉

C₂×D₈

yes

characteristic

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

C₂×D₁₆

yes

characteristic

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

#493

yes

characteristic

C₄×C₈₉

C₂×D₁₆

yes

characteristic

Dic₈₉

—

#13730

—

maximal, Sylow

C₂×C₈₉

—

C₂×C₈₉

#2246

yes

characteristic

C₂×C₈₉

#2264

yes

—

C₂×Q₆₄

—

C₂×SD₆₄

—

#2249

D₈₉

yes

characteristic

#2247

—

#1397

—

C₈₉

#13730

yes

characteristic, complemented, Sylow

C₂×Q₃₂

—

C₂×Q₃₂

—

178

—

C₂×Q₃₂

C₂×D₈₉

yes

characteristic

C₂×SD₃₂

—

C₂×D₁₆

C₂×D₈₉

yes

characteristic

#495

—

#494

—

178

—

Q₆₄

—

178

—

SD₆₄

—

178

—

C₂×C₃₂

—

C₄×C₁₆

C₂×D₈₉

yes

characteristic

C₂×Q₁₆

—

C₂×Q₁₆

—

356

—

C₂×Q₁₆

—

178

—

C₂×SD₁₆

—

C₂×D₈

—

100

C₄⋊Q₈

—

356

—

101

#124

—

102

Q₃₂

—

103

Q₃₂

—

356

—

104

Q₃₂

—

178

—

105

Q₃₂

—

178

—

106

SD₃₂

—

107

D₁₆

—

108

C₂×C₁₆

C₂²⋊D₈₉

yes

characteristic

109

C₂×C₁₆

C₂²×D₈₉

yes

characteristic

110

C₄×C₈

C₂²⋊D₈₉

yes

characteristic

111

C₃₂

—

112

C₂×Q₈

—

113

C₂×Q₈

—

356

—

114

C₂×D₄

—

115

Q₁₆

—

116

Q₁₆

—

117

Q₁₆

—

356

—

118

Q₁₆

—

356

—

119

Q₁₆

—

712

—

120

SD₁₆

—

121

D₈

—

122

D₈

—

123

C₂×C₈

#13083559

yes

characteristic

124

C₂×C₈

C₂×C₂²⋊D₈₉

yes

characteristic

125

C₄⋊C₄

—

712

—

126

C₂²⋊C₄

—

127

C₄²

#13083559

yes

characteristic

128

C₁₆

#13083559

yes

—

129

C₁₆

D₄×D₈₉

yes

—

130

C₂³

—

131

Q₈

—

132

Q₈

—

133

Q₈

—

712

—

134

Q₈

—

712

—

135

D₄

—

136

D₄

—

137

C₂×C₄

—

138

C₂×C₄

—

712

—

139

C₂×C₄

#15667953

yes

—

140

C₂×C₄

C₂×#13083559

yes

characteristic

141

C₈

#15667953

yes

—

142

C₈

#15668008

yes

characteristic

143

C₈

C₂×#13083559

yes

characteristic

144

C₂²

—

145

C₂²

—

146

C₂²

C₂×#15667953

yes

characteristic

147

C₄

—

148

C₄

—

149

C₄

—

1424

—

150

C₄

#19151974

yes

characteristic

151

C₄

C₂×#15667953

yes

characteristic

152

C₂

—

153

C₂

#26022501

yes

characteristic

154

C₂

#26022569

yes

—

	subgroup	G/H
center	C₂²	C₂×#15667953
commutator, cosocle	C₂×C₁₆×C₈₉	C₂³
Frattini	C₂×C₁₆	C₂²×D₈₉
Fitting	C₈₉×#2249	C₂
socle	C₂²×C₈₉	C₂×D₁₆
prime radical	C₂×D₁₆×C₈₉	C₂²
hypercenter	#2249	D₈₉
hypocenter	C₈₉	#13730
LCS	G ▷ C₂×C₁₆×C₈₉ ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #2249

subgroup

G/H

center

C₂²

C₂×#15667953

commutator, cosocle

C₂×C₁₆×C₈₉

C₂³

Frattini

C₂×C₁₆

C₂²×D₈₉

Fitting

C₈₉×#2249

C₂

socle

C₂²×C₈₉

C₂×D₁₆

prime radical

C₂×D₁₆×C₈₉

C₂²

D₈₉

C₈₉

G ▷ C₂×C₁₆×C₈₉ ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #2249

N	H ≅ G/N	type
1. C₂×#19151438	C₂	semidirect
3. #26022505	C₂	semidirect
4. #26018386	C₂	semidirect
83. C₈₉	#13730	semidirect

H ≅ G/N

type

1. C₂×#19151438

C₂

semidirect

3. #26022505

C₂

semidirect

4. #26018386

C₂

semidirect

83. C₈₉

#13730

semidirect

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

subgroup	index
C₂×#19151438	2
C₂×#19151436	2
#26022505	2
#26018386	2
C₈₉×#2249	2
#13730	89

subgroup

index

C₈₉×#2249

Subgroups — #36475445

Conjugacy classes of subgroups

Complements

Maximal subgroups