Group #72244258 — subgroups

Subgroups — #72244258

Order 5184.

1518 conjugacy classes of subgroups; only the 387 normal subgroups are shown.

normal subgroups only

This group has 1518 conjugacy classes of subgroups — too many to draw. Only its 387 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	#72244232	C₂	1	2	yes	maximal, complemented
2	C₄×C₄⋊(C₉⋊D₉)	C₂	1	2	yes	maximal, complemented
3	C₂×#13046732	C₂	1	1	yes	maximal, characteristic
4	#72244084	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉²×#97	C₂	1	1	yes	maximal, characteristic, complemented
6	#13143798	—	3	4	no	maximal
7	C₂×C₄⋊(C₉⋊D₉)	C₂²	1	2	yes	—
8	C₂×C₄×C₉⋊D₉	—	2	2	no	—
9	C₂×C₈×C₉²	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₉²	C₂²	1	1	yes	characteristic
11	C₄²×C₉²	C₂²	1	1	yes	characteristic
12	#13046768	—	2	2	no	—
13	C₄⋊(C₉⋊Dic₉)	C₂²	1	2	yes	—
14	#13046732	C₄	1	4	yes	complemented
15	C₂×#88525	—	3	4	no	—
16	C₄×C₄⋊(C₃⋊D₉)	—	3	8	no	—
17	C₃×C₉×#97	D₃	1	4	yes	—
18	#11720543	—	3	8	no	—
19	#11720540	—	3	4	no	—
20	C₂²×C₉⋊D₉	—	2	2	no	—
21	C₂×C₄×C₉²	D₄	1	2	yes	—
22	C₂×C₄×C₉²	C₂³	1	1	yes	characteristic
23	C₂×C₉⋊Dic₉	—	2	2	no	—
24	C₄⋊(C₉⋊D₉)	—	2	2	no	—
25	C₄⋊(C₉⋊D₉)	C₂×C₄	1	4	yes	complemented
26	C₄×C₉⋊D₉	—	4	4	no	—
27	C₈×C₉²	—	2	1	no	—
28	C₈×C₉²	C₂×C₄	1	2	yes	complemented
29	#10592410	—	9	1	no	—
30	#10588392	—	9	12	no	—
31	C₂×C₄⋊(C₃⋊D₉)	—	3	8	no	—
32	C₂×C₄×C₃⋊D₉	—	6	8	no	—
33	C₂×C₃×C₈×C₉	C₂×D₃	1	4	yes	—
34	C₂×C₃×C₈×C₉	C₂×D₃	1	4	yes	—
35	C₃×C₄²×C₉	C₂×D₃	1	4	yes	—
36	#88536	—	6	8	no	—
37	C₄⋊(C₃⋊Dic₉)	—	3	8	no	—
38	#88525	—	3	16	no	—
39	C₂²×C₉²	C₂×D₄	1	1	yes	characteristic
40	C₂×C₉⋊D₉	—	2	4	no	—
41	C₂×C₉⋊D₉	—	4	2	no	—
42	C₂×C₉⋊D₉	—	4	2	no	—
43	C₄×C₉²	—	2	2	no	—
44	C₄×C₉²	C₂²×C₄	1	1	yes	characteristic
45	C₄×C₉²	#41	1	1	yes	characteristic
46	C₉⋊Dic₉	—	4	2	no	—
47	C₂×#3745	—	9	1	no	—
48	C₄×C₄⋊(C₃⋊D₃)	—	9	2	no	—
49	C₃²×#97	C₃⋊D₃	1	1	yes	characteristic
50	#63648	—	9	2	no	—
51	#63644	—	9	1	no	—
52	C₂×D₇₂	—	9	12	no	—
53	C₄×D₃₆	—	9	24	no	—
54	C₉×#97	D₉	1	12	yes	complemented
55	#63380	—	9	24	no	—
56	#63377	—	9	12	no	—
57	C₂²×C₃⋊D₉	—	6	8	no	—
58	C₂×C₃×C₄×C₉	D₁₂	1	8	yes	—
59	C₂×C₃×C₄×C₉	C₂²×D₃	1	4	yes	—
60	C₂×C₃⋊Dic₉	—	6	8	no	—
61	C₄⋊(C₃⋊D₉)	—	3	16	no	—
62	C₄⋊(C₃⋊D₉)	—	6	8	no	—
63	C₄×C₃⋊D₉	—	12	16	no	—
64	C₃×C₈×C₉	—	2	4	no	—
65	C₃×C₈×C₉	C₄×D₃	1	8	yes	—
66	#4711	—	27	4	no	—
67	C₂×C₉²	C₄×D₄	1	1	yes	characteristic
68	C₂×C₉²	AGL(1,ℤ/8)	1	2	yes	—
69	C₉⋊D₉	—	4	4	no	—
70	C₂×C₄⋊(C₃⋊D₃)	—	9	2	no	—
71	C₂×C₄×C₃⋊D₃	—	18	2	no	—
72	C₂×C₃²×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
73	C₂×C₃²×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
74	C₃²×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic
75	#3752	—	18	2	no	—
76	C₄⋊(C₃⋊Dic₃)	—	9	2	no	—
77	#3745	—	9	4	no	—
78	C₂×D₃₆	—	9	24	no	—
79	C₂×C₄×D₉	—	18	24	no	—
80	C₂×C₈×C₉	C₂×D₉	1	12	yes	—
81	C₂×C₈×C₉	C₂×D₉	1	12	yes	—
82	C₄²×C₉	C₂×D₉	1	12	yes	—
83	(C₂×D₉)⋊C₄	—	18	24	no	—
84	C₄⋊Dic₉	—	9	24	no	—
85	D₇₂	—	9	48	no	—
86	C₂²×C₃×C₉	C₂×D₁₂	1	4	yes	—
87	C₂×C₃⋊D₉	—	6	16	no	—
88	C₂×C₃⋊D₉	—	12	8	no	—
89	C₂×C₃⋊D₉	—	12	8	no	—
90	C₃×C₄×C₉	—	2	8	no	—
91	C₃×C₄×C₉	C₂×C₄×D₃	1	4	yes	—
92	C₃×C₄×C₉	#235	1	4	yes	—
93	C₃⋊Dic₉	—	12	8	no	—
94	C₂×D₂₄	—	27	4	no	—
95	C₄×D₁₂	—	27	8	no	—
96	C₃×#97	C₃⋊D₉	1	4	yes	—
97	#821	—	27	8	no	—
98	#817	—	27	4	no	—
99	C₉²	#442	1	1	yes	characteristic, complemented, Sylow
100	C₂²×C₃⋊D₃	—	18	2	no	—
101	C₂×C₃²×C₄	C₄⋊(C₃⋊D₃)	1	2	yes	—
102	C₂×C₃²×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
103	C₂×C₃⋊Dic₃	—	18	2	no	—
104	C₄⋊(C₃⋊D₃)	—	9	4	no	—
105	C₄⋊(C₃⋊D₃)	—	18	2	no	—
106	C₄×C₃⋊D₃	—	36	4	no	—
107	C₂²×D₉	—	18	24	no	—
108	C₃²×C₈	—	2	1	no	—
109	C₃²×C₈	C₄×C₃⋊D₃	1	2	yes	—
110	C₂×C₄×C₉	D₃₆	1	24	yes	—
111	C₂×C₄×C₉	C₂²×D₉	1	12	yes	—
112	C₂×Dic₉	—	18	24	no	—
113	D₃₆	—	9	48	no	—
114	D₃₆	—	18	24	no	—
115	C₄×D₉	—	36	48	no	—
116	C₈×C₉	—	2	12	no	—
117	C₈×C₉	C₄×D₉	1	24	yes	complemented
118	#442	—	81	1	no	Sylow
119	C₂×C₃×C₉	C₄×D₁₂	1	4	yes	—
120	C₂×C₃×C₉	#908	1	8	yes	—
121	C₃⋊D₉	—	12	16	no	—
122	C₂×D₁₂	—	27	8	no	—
123	C₂×C₄×D₃	—	54	8	no	—
124	C₂×C₃×C₈	C₂×C₃⋊D₉	1	4	yes	—
125	C₂×C₃×C₈	C₂×C₃⋊D₉	1	4	yes	—
126	C₃×C₄²	C₂×C₃⋊D₉	1	4	yes	—
127	(C₂×D₃)⋊C₄	—	54	8	no	—
128	C₄⋊Dic₃	—	27	8	no	—
129	D₂₄	—	27	16	no	—
130	C₂²×C₃²	C₂×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
131	C₂×C₃⋊D₃	—	18	4	no	—
132	C₂×C₃⋊D₃	—	36	2	no	—
133	C₂×C₃⋊D₃	—	36	2	no	—
134	C₃²×C₄	—	2	2	no	—
135	C₃²×C₄	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
136	C₃²×C₄	#3828	1	1	yes	characteristic
137	C₃⋊Dic₃	—	36	2	no	—
138	C₂²×C₉	C₂×D₃₆	1	12	yes	—
139	C₂×D₉	—	18	48	no	—
140	C₂×D₉	—	36	24	no	—
141	C₂×D₉	—	36	24	no	—
142	C₄×C₉	—	2	24	no	—
143	C₄×C₉	C₂×C₄×D₉	1	12	yes	—
144	C₄×C₉	#3697	1	12	yes	—
145	Dic₉	—	36	24	no	—
146	C₂×D₈	—	81	1	no	—
147	C₄×D₄	—	81	2	no	—
148	#106	—	81	1	no	—
149	#102	—	81	2	no	—
150	#97	C₉⋊D₉	1	1	yes	characteristic, complemented
151	C₃×C₉	#4711	1	4	yes	—
152	C₂²×D₃	—	54	8	no	—
153	C₂×C₃×C₄	C₄⋊(C₃⋊D₉)	1	8	yes	—
154	C₂×C₃×C₄	C₂²×C₃⋊D₉	1	4	yes	—
155	C₂×Dic₃	—	54	8	no	—
156	D₁₂	—	27	16	no	—
157	D₁₂	—	54	8	no	—
158	C₄×D₃	—	108	16	no	—
159	C₃×C₈	—	2	4	no	—
160	C₃×C₈	C₄×C₃⋊D₉	1	8	yes	—
161	C₂×C₃²	C₄×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
162	C₂×C₃²	#64117	1	2	yes	—
163	C₃⋊D₃	—	36	4	no	—
164	C₂×C₉	C₄×D₃₆	1	12	yes	—
165	C₂×C₉	#63470	1	24	yes	—
166	D₉	—	36	48	no	—
167	C₂×D₄	—	81	2	no	—
168	C₂²×C₄	—	162	2	no	—
169	D₈	—	81	4	no	—
170	C₂×C₈	C₂×C₉⋊D₉	1	1	yes	characteristic
171	C₂×C₈	C₂×C₉⋊D₉	1	1	yes	characteristic
172	C₄⋊C₄	—	81	2	no	—
173	C₂²⋊C₄	—	162	2	no	—
174	C₄²	C₂×C₉⋊D₉	1	1	yes	characteristic
175	C₂²×C₃	C₂×C₄⋊(C₃⋊D₉)	1	4	yes	—
176	C₂×D₃	—	54	16	no	—
177	C₂×D₃	—	108	8	no	—
178	C₂×D₃	—	108	8	no	—
179	C₃×C₄	—	2	8	no	—
180	C₃×C₄	C₂×C₄×C₃⋊D₉	1	4	yes	—
181	C₃×C₄	#88736	1	4	yes	—
182	Dic₃	—	108	8	no	—
183	C₃²	#10592410	1	1	yes	characteristic
184	C₉	#10588392	1	12	yes	complemented
185	C₂³	—	162	2	no	—
186	D₄	—	81	4	no	—
187	D₄	—	162	2	no	—
188	C₂×C₄	—	324	4	no	—
189	C₂×C₄	—	162	2	no	—
190	C₂×C₄	C₄⋊(C₉⋊D₉)	1	2	yes	—
191	C₂×C₄	C₂²×C₉⋊D₉	1	1	yes	characteristic
192	C₈	—	2	1	no	—
193	C₈	C₄×C₉⋊D₉	1	2	yes	complemented
194	C₂×C₃	C₄×C₄⋊(C₃⋊D₉)	1	4	yes	—
195	C₂×C₃	#11721783	1	8	yes	—
196	D₃	—	108	16	no	—
197	C₂²	—	324	2	no	—
198	C₂²	—	324	2	no	—
199	C₂²	—	162	4	no	—
200	C₂²	C₂×C₄⋊(C₉⋊D₉)	1	1	yes	characteristic
201	C₄	—	2	2	no	—
202	C₄	—	324	2	no	—
203	C₄	C₂×C₄×C₉⋊D₉	1	1	yes	characteristic
204	C₄	#13047416	1	1	yes	characteristic
205	C₃	#13143798	1	4	yes	—
206	C₂	—	324	4	no	—
207	C₂	C₄×C₄⋊(C₉⋊D₉)	1	1	yes	characteristic
208	C₂	#72244240	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#72244232

C₂

yes

maximal, complemented

C₄×C₄⋊(C₉⋊D₉)

C₂

yes

maximal, complemented

C₂×#13046732

C₂

yes

maximal, characteristic

#72244084

C₂

yes

maximal, characteristic, complemented

C₉²×#97

C₂

yes

maximal, characteristic, complemented

#13143798

—

maximal

C₂×C₄⋊(C₉⋊D₉)

C₂²

yes

—

C₂×C₄×C₉⋊D₉

—

C₂×C₈×C₉²

C₂²

yes

characteristic

C₂×C₈×C₉²

C₂²

yes

characteristic

C₄²×C₉²

C₂²

yes

characteristic

#13046768

—

C₄⋊(C₉⋊Dic₉)

C₂²

yes

—

#13046732

C₄

yes

complemented

C₂×#88525

—

C₄×C₄⋊(C₃⋊D₉)

—

C₃×C₉×#97

D₃

yes

—

#11720543

—

#11720540

—

C₂²×C₉⋊D₉

—

C₂×C₄×C₉²

D₄

yes

—

C₂×C₄×C₉²

C₂³

yes

characteristic

C₂×C₉⋊Dic₉

—

C₄⋊(C₉⋊D₉)

—

C₄⋊(C₉⋊D₉)

C₂×C₄

yes

complemented

C₄×C₉⋊D₉

—

C₈×C₉²

—

C₈×C₉²

C₂×C₄

yes

complemented

#10592410

—

#10588392

—

C₂×C₄⋊(C₃⋊D₉)

—

C₂×C₄×C₃⋊D₉

—

C₂×C₃×C₈×C₉

C₂×D₃

yes

—

C₂×C₃×C₈×C₉

C₂×D₃

yes

—

C₃×C₄²×C₉

C₂×D₃

yes

—

#88536

—

C₄⋊(C₃⋊Dic₉)

—

#88525

—

C₂²×C₉²

C₂×D₄

yes

characteristic

C₂×C₉⋊D₉

—

C₂×C₉⋊D₉

—

C₂×C₉⋊D₉

—

C₄×C₉²

—

C₄×C₉²

C₂²×C₄

yes

characteristic

C₄×C₉²

#41

yes

characteristic

C₉⋊Dic₉

—

C₂×#3745

—

C₄×C₄⋊(C₃⋊D₃)

—

C₃²×#97

C₃⋊D₃

yes

characteristic

#63648

—

#63644

—

C₂×D₇₂

—

C₄×D₃₆

—

C₉×#97

D₉

yes

complemented

#63380

—

#63377

—

C₂²×C₃⋊D₉

—

C₂×C₃×C₄×C₉

D₁₂

yes

—

C₂×C₃×C₄×C₉

C₂²×D₃

yes

—

C₂×C₃⋊Dic₉

—

C₄⋊(C₃⋊D₉)

—

C₄⋊(C₃⋊D₉)

—

C₄×C₃⋊D₉

—

C₃×C₈×C₉

—

C₃×C₈×C₉

C₄×D₃

yes

—

#4711

—

C₂×C₉²

C₄×D₄

yes

characteristic

C₂×C₉²

AGL(1,ℤ/8)

yes

—

C₉⋊D₉

—

C₂×C₄⋊(C₃⋊D₃)

—

C₂×C₄×C₃⋊D₃

—

C₂×C₃²×C₈

C₂×C₃⋊D₃

yes

characteristic

C₂×C₃²×C₈

C₂×C₃⋊D₃

yes

characteristic

C₃²×C₄²

C₂×C₃⋊D₃

yes

characteristic

#3752

—

C₄⋊(C₃⋊Dic₃)

—

#3745

—

C₂×D₃₆

—

C₂×C₄×D₉

—

C₂×C₈×C₉

C₂×D₉

yes

—

C₂×C₈×C₉

C₂×D₉

yes

—

C₄²×C₉

C₂×D₉

yes

—

(C₂×D₉)⋊C₄

—

C₄⋊Dic₉

—

D₇₂

—

C₂²×C₃×C₉

C₂×D₁₂

yes

—

C₂×C₃⋊D₉

—

C₂×C₃⋊D₉

—

C₂×C₃⋊D₉

—

C₃×C₄×C₉

—

C₃×C₄×C₉

C₂×C₄×D₃

yes

—

C₃×C₄×C₉

#235

yes

—

C₃⋊Dic₉

—

C₂×D₂₄

—

C₄×D₁₂

—

C₃×#97

C₃⋊D₉

yes

—

#821

—

#817

—

C₉²

#442

yes

characteristic, complemented, Sylow

100

C₂²×C₃⋊D₃

—

101

C₂×C₃²×C₄

C₄⋊(C₃⋊D₃)

yes

—

102

C₂×C₃²×C₄

C₂²×C₃⋊D₃

yes

characteristic

103

C₂×C₃⋊Dic₃

—

104

C₄⋊(C₃⋊D₃)

—

105

C₄⋊(C₃⋊D₃)

—

106

C₄×C₃⋊D₃

—

107

C₂²×D₉

—

108

C₃²×C₈

—

109

C₃²×C₈

C₄×C₃⋊D₃

yes

—

110

C₂×C₄×C₉

D₃₆

yes

—

111

C₂×C₄×C₉

C₂²×D₉

yes

—

112

C₂×Dic₉

—

113

D₃₆

—

114

D₃₆

—

115

C₄×D₉

—

116

C₈×C₉

—

117

C₈×C₉

C₄×D₉

yes

complemented

118

#442

—

Sylow

119

C₂×C₃×C₉

C₄×D₁₂

yes

—

120

C₂×C₃×C₉

#908

yes

—

121

C₃⋊D₉

—

122

C₂×D₁₂

—

123

C₂×C₄×D₃

—

124

C₂×C₃×C₈

C₂×C₃⋊D₉

yes

—

125

C₂×C₃×C₈

C₂×C₃⋊D₉

yes

—

126

C₃×C₄²

C₂×C₃⋊D₉

yes

—

127

(C₂×D₃)⋊C₄

—

128

C₄⋊Dic₃

—

129

D₂₄

—

130

C₂²×C₃²

C₂×C₄⋊(C₃⋊D₃)

yes

characteristic

131

C₂×C₃⋊D₃

—

132

C₂×C₃⋊D₃

—

133

C₂×C₃⋊D₃

—

134

C₃²×C₄

—

135

C₃²×C₄

C₂×C₄×C₃⋊D₃

yes

characteristic

136

C₃²×C₄

#3828

yes

characteristic

137

C₃⋊Dic₃

—

138

C₂²×C₉

C₂×D₃₆

yes

—

139

C₂×D₉

—

140

C₂×D₉

—

141

C₂×D₉

—

142

C₄×C₉

—

143

C₄×C₉

C₂×C₄×D₉

yes

—

144

C₄×C₉

#3697

yes

—

145

Dic₉

—

146

C₂×D₈

—

147

C₄×D₄

—

148

#106

—

149

#102

—

150

#97

C₉⋊D₉

yes

characteristic, complemented

151

C₃×C₉

#4711

yes

—

152

C₂²×D₃

—

153

C₂×C₃×C₄

C₄⋊(C₃⋊D₉)

yes

—

154

C₂×C₃×C₄

C₂²×C₃⋊D₉

yes

—

155

C₂×Dic₃

—

156

D₁₂

—

157

D₁₂

—

158

C₄×D₃

—

108

—

159

C₃×C₈

—

160

C₃×C₈

C₄×C₃⋊D₉

yes

—

161

C₂×C₃²

C₄×C₄⋊(C₃⋊D₃)

yes

characteristic

162

C₂×C₃²

#64117

yes

—

163

C₃⋊D₃

—

164

C₂×C₉

C₄×D₃₆

yes

—

165

C₂×C₉

#63470

yes

—

166

D₉

—

167

C₂×D₄

—

168

C₂²×C₄

—

162

—

169

D₈

—

170

C₂×C₈

C₂×C₉⋊D₉

yes

characteristic

171

C₂×C₈

C₂×C₉⋊D₉

yes

characteristic

172

C₄⋊C₄

—

173

C₂²⋊C₄

—

162

—

174

C₄²

C₂×C₉⋊D₉

yes

characteristic

175

C₂²×C₃

C₂×C₄⋊(C₃⋊D₉)

yes

—

176

C₂×D₃

—

177

C₂×D₃

—

108

—

178

C₂×D₃

—

108

—

179

C₃×C₄

—

180

C₃×C₄

C₂×C₄×C₃⋊D₉

yes

—

181

C₃×C₄

#88736

yes

—

182

Dic₃

—

108

—

183

C₃²

#10592410

yes

characteristic

184

C₉

#10588392

yes

complemented

185

C₂³

—

162

—

186

D₄

—

187

D₄

—

162

—

188

C₂×C₄

—

324

—

189

C₂×C₄

—

162

—

190

C₂×C₄

C₄⋊(C₉⋊D₉)

yes

—

191

C₂×C₄

C₂²×C₉⋊D₉

yes

characteristic

192

C₈

—

193

C₈

C₄×C₉⋊D₉

yes

complemented

194

C₂×C₃

C₄×C₄⋊(C₃⋊D₉)

yes

—

195

C₂×C₃

#11721783

yes

—

196

D₃

—

108

—

197

C₂²

—

324

—

198

C₂²

—

324

—

199

C₂²

—

162

—

200

C₂²

C₂×C₄⋊(C₉⋊D₉)

yes

characteristic

201

C₄

—

202

C₄

—

324

—

203

C₄

C₂×C₄×C₉⋊D₉

yes

characteristic

204

C₄

#13047416

yes

characteristic

205

C₃

#13143798

yes

—

206

C₂

—

324

—

207

C₂

C₄×C₄⋊(C₉⋊D₉)

yes

characteristic

208

C₂

#72244240

yes

—

	subgroup	G/H
center	C₂²	C₂×C₄⋊(C₉⋊D₉)
commutator	C₄×C₉²	C₂²×C₄
Frattini	C₂×C₃²×C₄	C₂²×C₃⋊D₃
Fitting	C₉²×#97	C₂
socle	C₂²×C₃²	C₂×C₄⋊(C₃⋊D₃)
prime radical	C₂×#13046732	C₂
cosocle	C₂×C₄×C₉²	C₂³
hypercenter	#97	C₉⋊D₉
hypocenter	C₉²	#442
LCS	G ▷ C₄×C₉² ▷ C₂×C₉² ▷ C₉²
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

subgroup

G/H

center

C₂²

C₂×C₄⋊(C₉⋊D₉)

commutator

C₄×C₉²

C₂²×C₄

Frattini

C₂×C₃²×C₄

C₂²×C₃⋊D₃

Fitting

C₉²×#97

C₂

socle

C₂²×C₃²

C₂×C₄⋊(C₃⋊D₃)

prime radical

C₂×#13046732

C₂

cosocle

C₂×C₄×C₉²

C₂³

C₉⋊D₉

C₉²

G ▷ C₄×C₉² ▷ C₂×C₉² ▷ C₉²

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
1. #72244232	C₂	semidirect
2. C₄×C₄⋊(C₉⋊D₉)	C₂	semidirect
4. #72244084	C₂	semidirect
5. C₉²×#97	C₂	semidirect
14. #13046732	C₄	semidirect
25. C₄⋊(C₉⋊D₉)	C₂×C₄	semidirect
28. C₈×C₉²	C₂×C₄	semidirect
54. C₉×#97	D₉	semidirect
99. C₉²	#442	semidirect
117. C₈×C₉	C₄×D₉	semidirect
150. #97	C₉⋊D₉	semidirect
184. C₉	#10588392	semidirect
193. C₈	C₄×C₉⋊D₉	semidirect

H ≅ G/N

type

1. #72244232

C₂

semidirect

2. C₄×C₄⋊(C₉⋊D₉)

C₂

semidirect

4. #72244084

C₂

semidirect

5. C₉²×#97

C₂

semidirect

14. #13046732

C₄

semidirect

25. C₄⋊(C₉⋊D₉)

C₂×C₄

semidirect

28. C₈×C₉²

C₂×C₄

semidirect

54. C₉×#97

D₉

semidirect

99. C₉²

#442

semidirect

117. C₈×C₉

C₄×D₉

semidirect

150. #97

C₉⋊D₉

semidirect

184. C₉

#10588392

semidirect

193. C₈

C₄×C₉⋊D₉

semidirect

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

subgroup	index
#72244232	2
C₄×C₄⋊(C₉⋊D₉)	2
C₂×#13046732	2
#72244084	2
C₉²×#97	2
#13143798	3

subgroup

index

C₄×C₄⋊(C₉⋊D₉)

C₉²×#97

Subgroups — #72244258

Conjugacy classes of subgroups

Complements

Maximal subgroups