Group #36485624 — subgroups

Subgroups — #36485624

Order 22784.

1422 conjugacy classes of subgroups; only the 555 normal subgroups are shown.

normal subgroups only

This group has 1422 conjugacy classes of subgroups — too many to draw. Only its 555 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×#19151466	C₂	1	2	yes	maximal
2	#26018482	C₂	1	6	yes	maximal
3	#26018479	C₂	1	6	yes	maximal
4	C₂×C₄³×C₈₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄⋊Dic₈₉	C₂²	1	4	yes	—
6	#19151466	—	2	8	no	—
7	C₂×#15667919	C₂²	1	12	yes	—
8	C₂×#15667919	C₂²	1	12	yes	—
9	C₂²×C₄²×C₈₉	C₂²	1	3	yes	—
10	C₂²×C₄²×C₈₉	C₂²	1	3	yes	—
11	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
12	C₄³×C₈₉	C₄	1	8	yes	complemented
13	C₂³×Dic₈₉	C₂³	1	8	yes	—
14	C₂×C₄⋊Dic₈₉	—	2	24	no	—
15	#15667919	—	2	24	no	—
16	#15667919	—	2	24	no	—
17	C₂³×C₄×C₈₉	C₂³	1	3	yes	—
18	C₂³×C₄×C₈₉	C₂³	1	3	yes	—
19	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
20	C₂×C₄²×C₈₉	—	2	12	no	—
21	C₂×C₄²×C₈₉	—	2	12	no	—
22	C₂×C₄²×C₈₉	C₂×C₄	1	12	yes	—
23	C₂×C₄²×C₈₉	C₂×C₄	1	12	yes	—
24	C₂×C₄²×C₈₉	C₂×C₄	1	4	yes	—
25	C₂×C₄²×C₈₉	D₄	1	4	yes	—
26	C₂×C₄²×C₈₉	Q₈	1	4	yes	—
27	C₂²×Dic₈₉	—	2	8	no	—
28	C₂²×Dic₈₉	—	2	24	no	—
29	C₂²×Dic₈₉	—	2	24	no	—
30	C₄⋊Dic₈₉	—	4	16	no	—
31	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
32	C₂²×C₄×C₈₉	—	2	6	no	—
33	C₂²×C₄×C₈₉	—	2	6	no	—
34	C₂²×C₄×C₈₉	—	2	6	no	—
35	C₂²×C₄×C₈₉	—	2	6	no	—
36	C₂²×C₄×C₈₉	C₂²×C₄	1	6	yes	—
37	C₂²×C₄×C₈₉	C₂²×C₄	1	6	yes	—
38	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
39	C₂²×C₄×C₈₉	C₂×D₄	1	6	yes	—
40	C₂²×C₄×C₈₉	C₂×Q₈	1	6	yes	—
41	C₂²×C₄×C₈₉	#41	1	12	yes	—
42	C₂²×C₄×C₈₉	#41	1	12	yes	—
43	C₄²×C₈₉	—	2	24	no	—
44	C₄²×C₈₉	—	2	24	no	—
45	C₄²×C₈₉	C₄⋊C₄	1	16	yes	complemented
46	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
47	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
48	C₂³×C₈₉	C₂²×Q₈	1	1	yes	characteristic
49	C₂³×C₈₉	C₂×#41	1	6	yes	—
50	C₂³×C₈₉	C₂×#41	1	6	yes	—
51	C₂×C₄×C₈₉	—	2	6	no	—
52	C₂×C₄×C₈₉	—	2	6	no	—
53	C₂×C₄×C₈₉	—	2	6	no	—
54	C₂×C₄×C₈₉	—	2	6	no	—
55	C₂×C₄×C₈₉	—	2	24	no	—
56	C₂×C₄×C₈₉	—	2	12	no	—
57	C₂×C₄×C₈₉	—	2	12	no	—
58	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	12	yes	—
59	C₂×C₄×C₈₉	#117	1	12	yes	—
60	C₂×C₄×C₈₉	#117	1	12	yes	—
61	C₂×C₄×C₈₉	#126	1	16	yes	—
62	C₂×Dic₈₉	—	4	8	no	—
63	C₂×Dic₈₉	—	4	24	no	—
64	C₂×Dic₈₉	—	4	24	no	—
65	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
66	C₂²×C₈₉	C₂×#117	1	3	yes	—
67	C₂²×C₈₉	C₂×#117	1	3	yes	—
68	C₂²×C₈₉	C₂×#126	1	4	yes	—
69	C₂²×C₈₉	#529	1	12	yes	—
70	C₂²×C₈₉	#532	1	6	yes	—
71	C₂²×C₈₉	#533	1	6	yes	—
72	C₄×C₈₉	—	2	12	no	—
73	C₄×C₈₉	—	2	12	no	—
74	C₄×C₈₉	#383	1	8	yes	complemented
75	Dic₈₉	—	8	8	no	—
76	#14688	—	89	1	no	maximal, Sylow
77	C₂×C₈₉	C₂×#383	1	1	yes	characteristic
78	C₂×C₈₉	#2283	1	3	yes	—
79	C₂×C₈₉	#2285	1	3	yes	—
80	C₂×C₈₉	#2860	1	4	yes	—
81	C₂×C₈₉	#2863	1	4	yes	—
82	C₂×#383	—	89	2	no	—
83	C₂×C₄³	D₈₉	1	1	yes	characteristic
84	C₄⋊#95	—	89	6	no	—
85	#1434	—	89	6	no	—
86	C₈₉	#14688	1	1	yes	characteristic, complemented, Sylow
87	C₂²×C₄⋊C₄	—	89	4	no	—
88	C₂²×C₄²	C₂×D₈₉	1	3	yes	—
89	C₂²×C₄²	C₂×D₈₉	1	3	yes	—
90	C₂²×C₄²	C₂×D₈₉	1	1	yes	characteristic
91	#383	—	178	8	no	—
92	C₂×#95	—	89	12	no	—
93	C₂×#95	—	89	12	no	—
94	C₄³	Dic₈₉	1	8	yes	complemented
95	C₂³×C₄	—	89	8	no	—
96	C₂³×C₄	C₂²×D₈₉	1	3	yes	—
97	C₂³×C₄	C₂²×D₈₉	1	3	yes	—
98	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
99	C₂×C₄⋊C₄	—	178	24	no	—
100	C₂×C₄²	—	2	12	no	—
101	C₂×C₄²	—	2	12	no	—
102	C₂×C₄²	Dic₁₇₈	1	4	yes	—
103	C₂×C₄²	D₃₅₆	1	4	yes	—
104	C₂×C₄²	C₂×Dic₈₉	1	12	yes	—
105	C₂×C₄²	C₂×Dic₈₉	1	12	yes	—
106	C₂×C₄²	C₂×Dic₈₉	1	4	yes	—
107	#95	—	178	24	no	—
108	#95	—	178	24	no	—
109	C₂⁴	C₂³×D₈₉	1	1	yes	characteristic
110	C₂²×C₄	—	2	6	no	—
111	C₂²×C₄	—	2	6	no	—
112	C₂²×C₄	—	2	6	no	—
113	C₂²×C₄	—	2	6	no	—
114	C₂²×C₄	—	178	8	no	—
115	C₂²×C₄	—	178	24	no	—
116	C₂²×C₄	—	178	24	no	—
117	C₂²×C₄	C₂²×Dic₈₉	1	6	yes	—
118	C₂²×C₄	C₂²×Dic₈₉	1	6	yes	—
119	C₂²×C₄	C₂²×Dic₈₉	1	2	yes	—
120	C₂²×C₄	C₂×D₃₅₆	1	6	yes	—
121	C₂²×C₄	C₂×Dic₁₇₈	1	6	yes	—
122	C₂²×C₄	#13083574	1	12	yes	—
123	C₂²×C₄	#13083574	1	12	yes	—
124	C₄⋊C₄	—	356	16	no	—
125	C₄²	—	2	24	no	—
126	C₄²	—	2	24	no	—
127	C₄²	C₄⋊Dic₈₉	1	16	yes	complemented
128	C₂³	C₂³×Dic₈₉	1	1	yes	characteristic
129	C₂³	C₂²×D₃₅₆	1	1	yes	characteristic
130	C₂³	C₂²×Dic₁₇₈	1	1	yes	characteristic
131	C₂³	C₂×#13083574	1	6	yes	—
132	C₂³	C₂×#13083574	1	6	yes	—
133	C₂×C₄	—	2	24	no	—
134	C₂×C₄	—	2	12	no	—
135	C₂×C₄	—	2	12	no	—
136	C₂×C₄	—	2	6	no	—
137	C₂×C₄	—	2	6	no	—
138	C₂×C₄	—	2	6	no	—
139	C₂×C₄	—	2	6	no	—
140	C₂×C₄	—	356	24	no	—
141	C₂×C₄	—	356	24	no	—
142	C₂×C₄	—	356	8	no	—
143	C₂×C₄	C₂×C₄⋊Dic₈₉	1	12	yes	—
144	C₂×C₄	#15667971	1	12	yes	—
145	C₂×C₄	#15667971	1	12	yes	—
146	C₂×C₄	#15668006	1	16	yes	—
147	C₂²	C₂²×C₄⋊Dic₈₉	1	1	yes	characteristic
148	C₂²	C₂×#15667971	1	3	yes	—
149	C₂²	C₂×#15667971	1	3	yes	—
150	C₂²	C₂×#15668006	1	4	yes	—
151	C₂²	#19152132	1	12	yes	—
152	C₂²	#19152148	1	6	yes	—
153	C₂²	#19152155	1	6	yes	—
154	C₄	—	2	12	no	—
155	C₄	—	2	12	no	—
156	C₄	—	712	8	no	—
157	C₄	#19151466	1	8	yes	complemented
158	C₂	C₂×#19151466	1	1	yes	characteristic
159	C₂	#26022650	1	3	yes	—
160	C₂	#26022659	1	3	yes	—
161	C₂	#26028619	1	4	yes	—
162	C₂	#26028634	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19151466

C₂

yes

maximal

#26018482

C₂

yes

maximal

#26018479

C₂

yes

maximal

C₂×C₄³×C₈₉

C₂

yes

maximal, characteristic

C₂²×C₄⋊Dic₈₉

C₂²

yes

—

#19151466

—

C₂×#15667919

C₂²

yes

—

C₂×#15667919

C₂²

yes

—

C₂²×C₄²×C₈₉

C₂²

yes

—

C₂²×C₄²×C₈₉

C₂²

yes

—

C₂²×C₄²×C₈₉

C₂²

yes

characteristic

C₄³×C₈₉

C₄

yes

complemented

C₂³×Dic₈₉

C₂³

yes

—

C₂×C₄⋊Dic₈₉

—

#15667919

—

#15667919

—

C₂³×C₄×C₈₉

C₂³

yes

—

C₂³×C₄×C₈₉

C₂³

yes

—

C₂³×C₄×C₈₉

C₂³

yes

characteristic

C₂×C₄²×C₈₉

—

C₂×C₄²×C₈₉

—

C₂×C₄²×C₈₉

C₂×C₄

yes

—

C₂×C₄²×C₈₉

C₂×C₄

yes

—

C₂×C₄²×C₈₉

C₂×C₄

yes

—

C₂×C₄²×C₈₉

D₄

yes

—

C₂×C₄²×C₈₉

Q₈

yes

—

C₂²×Dic₈₉

—

C₂²×Dic₈₉

—

C₂²×Dic₈₉

—

C₄⋊Dic₈₉

—

C₂⁴×C₈₉

C₂⁴

yes

characteristic

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

C₂²×C₄

yes

—

C₂²×C₄×C₈₉

C₂²×C₄

yes

—

C₂²×C₄×C₈₉

C₂²×C₄

yes

—

C₂²×C₄×C₈₉

C₂×D₄

yes

—

C₂²×C₄×C₈₉

C₂×Q₈

yes

—

C₂²×C₄×C₈₉

#41

yes

—

C₂²×C₄×C₈₉

#41

yes

—

C₄²×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

C₄⋊C₄

yes

complemented

C₂³×C₈₉

C₂³×C₄

yes

characteristic

C₂³×C₈₉

C₂²×D₄

yes

characteristic

C₂³×C₈₉

C₂²×Q₈

yes

characteristic

C₂³×C₈₉

C₂×#41

yes

—

C₂³×C₈₉

C₂×#41

yes

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₈₉

#117

yes

—

C₂×C₄×C₈₉

#117

yes

—

C₂×C₄×C₈₉

#126

yes

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂²×C₈₉

C₂²×C₄⋊C₄

yes

characteristic

C₂²×C₈₉

C₂×#117

yes

—

C₂²×C₈₉

C₂×#117

yes

—

C₂²×C₈₉

C₂×#126

yes

—

C₂²×C₈₉

#529

yes

—

C₂²×C₈₉

#532

yes

—

C₂²×C₈₉

#533

yes

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

#383

yes

complemented

Dic₈₉

—

—

C₂×C₈₉

yes

C₂×C₈₉

yes

—

C₂×C₈₉

#2285

yes

—

C₂×C₈₉

#2860

yes

—

C₂×C₈₉

#2863

yes

—

C₂×#383

—

C₂×C₄³

D₈₉

yes

characteristic

C₄⋊#95

—

#1434

—

C₈₉

#14688

yes

characteristic, complemented, Sylow

C₂²×C₄⋊C₄

—

C₂²×C₄²

C₂×D₈₉

yes

—

C₂²×C₄²

C₂×D₈₉

yes

—

C₂²×C₄²

C₂×D₈₉

yes

characteristic

#383

—

178

—

C₂×#95

—

C₂×#95

—

C₄³

Dic₈₉

yes

complemented

C₂³×C₄

—

C₂³×C₄

C₂²×D₈₉

yes

—

C₂³×C₄

C₂²×D₈₉

yes

—

C₂³×C₄

C₂²×D₈₉

yes

characteristic

C₂×C₄⋊C₄

—

178

—

100

C₂×C₄²

—

101

C₂×C₄²

—

102

C₂×C₄²

Dic₁₇₈

yes

—

103

C₂×C₄²

D₃₅₆

yes

—

104

C₂×C₄²

C₂×Dic₈₉

yes

—

105

C₂×C₄²

C₂×Dic₈₉

yes

—

106

C₂×C₄²

C₂×Dic₈₉

yes

—

107

#95

—

178

—

108

#95

—

178

—

109

C₂⁴

C₂³×D₈₉

yes

characteristic

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂²×C₄

—

113

C₂²×C₄

—

114

C₂²×C₄

—

178

—

115

C₂²×C₄

—

178

—

116

C₂²×C₄

—

178

—

117

C₂²×C₄

C₂²×Dic₈₉

yes

—

118

C₂²×C₄

C₂²×Dic₈₉

yes

—

119

C₂²×C₄

C₂²×Dic₈₉

yes

—

120

C₂²×C₄

C₂×D₃₅₆

yes

—

121

C₂²×C₄

C₂×Dic₁₇₈

yes

—

122

C₂²×C₄

#13083574

yes

—

123

C₂²×C₄

#13083574

yes

—

124

C₄⋊C₄

—

356

—

125

C₄²

—

126

C₄²

—

127

C₄²

C₄⋊Dic₈₉

yes

complemented

128

C₂³

C₂³×Dic₈₉

yes

characteristic

129

C₂³

C₂²×D₃₅₆

yes

characteristic

130

C₂³

C₂²×Dic₁₇₈

yes

characteristic

131

C₂³

C₂×#13083574

yes

—

132

C₂³

C₂×#13083574

yes

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

356

—

141

C₂×C₄

—

356

—

142

C₂×C₄

—

356

—

143

C₂×C₄

C₂×C₄⋊Dic₈₉

yes

—

144

C₂×C₄

#15667971

yes

—

145

C₂×C₄

#15667971

yes

—

146

C₂×C₄

#15668006

yes

—

147

C₂²

C₂²×C₄⋊Dic₈₉

yes

characteristic

148

C₂²

C₂×#15667971

yes

—

149

C₂²

C₂×#15667971

yes

—

150

C₂²

C₂×#15668006

yes

—

151

C₂²

#19152132

yes

—

152

C₂²

#19152148

yes

—

153

C₂²

#19152155

yes

—

154

C₄

—

155

C₄

—

156

C₄

—

712

—

157

C₄

#19151466

yes

complemented

158

C₂

C₂×#19151466

yes

characteristic

159

C₂

#26022650

yes

—

160

C₂

#26022659

yes

—

161

C₂

#26028619

yes

—

162

C₂

#26028634

yes

—

	subgroup	G/H
center, Frattini	C₂⁴	C₂³×D₈₉
commutator	C₂³×C₈₉	C₂³×C₄
Fitting	C₂×C₄³×C₈₉	C₂
socle, prime radical, cosocle	C₂⁴×C₈₉	C₂⁴
hypercenter	C₂×C₄³	D₈₉
hypocenter	C₈₉	#14688
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂⁴ ◁ C₂×C₄³

subgroup

G/H

center, Frattini

C₂⁴

C₂³×D₈₉

commutator

C₂³×C₈₉

C₂³×C₄

Fitting

C₂×C₄³×C₈₉

C₂

socle, prime radical, cosocle

C₂⁴×C₈₉

C₂⁴

hypercenter

C₂×C₄³

D₈₉

C₈₉

G ▷ C₂³×C₈₉ ▷ C₈₉

C₁ ◁ C₂⁴ ◁ C₂×C₄³

N	H ≅ G/N	type
12. C₄³×C₈₉	C₄	semidirect
45. C₄²×C₈₉	C₄⋊C₄	semidirect
74. C₄×C₈₉	#383	semidirect
86. C₈₉	#14688	semidirect
94. C₄³	Dic₈₉	semidirect
127. C₄²	C₄⋊Dic₈₉	semidirect
157. C₄	#19151466	semidirect

H ≅ G/N

type

12. C₄³×C₈₉

C₄

semidirect

45. C₄²×C₈₉

C₄⋊C₄

semidirect

74. C₄×C₈₉

#383

semidirect

86. C₈₉

#14688

semidirect

94. C₄³

Dic₈₉

semidirect

127. C₄²

C₄⋊Dic₈₉

semidirect

157. C₄

#19151466

semidirect

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

subgroup	index
C₂×#19151466	2
#26018482	2
#26018479	2
C₂×C₄³×C₈₉	2
#14688	89

subgroup

index

C₂×C₄³×C₈₉

Subgroups — #36485624

Conjugacy classes of subgroups

Complements

Maximal subgroups