Group #13143322 — subgroups

Subgroups — #10588835⋊C₃ #13143322

Order 1728.

428 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 100 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×D₈×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic
2	#63498⋊C₃	C₂	1	2	yes	maximal, complemented
3	C₂×#3672⋊C₃	C₂	1	2	yes	maximal, complemented
4	C₂×Dic₃₆⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×3₋¹⁺²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5155	—	3	1	no	maximal
7	#10588835	C₃	1	1	yes	maximal, characteristic, complemented
8	C₂×D₄×3₋¹⁺²	C₂²	1	2	yes	—
9	C₂×3₋¹⁺²⋊Q₈	C₂²	1	2	yes	—
10	D₈×3₋¹⁺²	—	2	2	no	—
11	C₂×C₈×3₋¹⁺²	C₂²	1	1	yes	characteristic
12	#3676⋊C₃	—	2	4	no	—
13	#3672⋊C₃	—	2	4	no	—
14	C₄×3₋¹⁺²⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×3₋¹⁺²⋊C₈	C₂²	1	1	yes	characteristic
16	Dic₃₆⋊C₃	—	2	2	no	—
17	C₂×C₃²×D₈	D₃	1	1	yes	characteristic
18	C₃×#936	—	3	2	no	—
19	C₂×C₃×#214	—	3	2	no	—
20	C₂×C₃×Dic₁₂	—	3	1	no	—
21	C₃×C₈×Dic₃	—	3	1	no	—
22	C₂×C₉×D₈	—	2	1	no	—
23	C₂×C₉×D₈	C₂×C₃	1	1	yes	characteristic
24	#63498	C₂×C₃	1	2	yes	complemented
25	C₂×#3672	C₂×C₃	1	2	yes	complemented
26	C₂×Dic₃₆	C₂×C₃	1	1	yes	characteristic, complemented
27	C₈×Dic₉	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂³×3₋¹⁺²	—	2	2	no	—
29	D₄×3₋¹⁺²	—	2	2	no	—
30	D₄×3₋¹⁺²	—	2	2	no	—
31	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
32	C₂×3₋¹⁺²⋊C₄	—	2	2	no	—
33	C₂×3₋¹⁺²⋊C₄	D₄	1	2	yes	—
34	3₋¹⁺²⋊Q₈	—	2	2	no	—
35	3₋¹⁺²⋊Q₈	—	2	2	no	—
36	C₈×3₋¹⁺²	D₄	1	2	yes	—
37	3₋¹⁺²⋊C₈	D₄	1	2	yes	—
38	C₃×#495	—	9	1	no	—
39	#5155	—	3	1	no	—
40	C₂×C₃²×D₄	C₂×D₃	1	2	yes	—
41	C₂×C₃×Dic₆	—	3	2	no	—
42	C₃²×D₈	—	2	2	no	—
43	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
44	C₃×#217	—	6	4	no	—
45	C₃×#214	—	6	4	no	—
46	C₃×C₄×Dic₃	—	3	1	no	—
47	C₂×C₃×C₃⋊C₈	—	3	1	no	—
48	C₃×Dic₁₂	—	6	2	no	—
49	C₂×D₄×C₉	—	2	2	no	—
50	C₂×D₄×C₉	C₂²×C₃	1	2	yes	—
51	C₂×Dic₁₈	C₂²×C₃	1	2	yes	—
52	C₉×D₈	—	2	4	no	—
53	C₉×D₈	—	2	2	no	—
54	C₂×C₈×C₉	—	2	1	no	—
55	C₂×C₈×C₉	C₂²×C₃	1	1	yes	characteristic
56	#3676	—	2	4	no	—
57	#3672	—	2	4	no	—
58	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
59	C₂×C₉⋊C₈	C₂²×C₃	1	1	yes	characteristic
60	Dic₃₆	—	2	2	no	—
61	C₂²×3₋¹⁺²	—	4	2	no	—
62	C₂²×3₋¹⁺²	—	4	4	no	—
63	C₂²×3₋¹⁺²	C₂×D₄	1	1	yes	characteristic
64	C₄×3₋¹⁺²	C₂×D₄	1	1	yes	characteristic
65	C₄×3₋¹⁺²	C₂×D₄	1	1	yes	characteristic
66	3₋¹⁺²⋊C₄	—	2	2	no	—
67	3₋¹⁺²⋊C₄	—	4	2	no	—
68	C₂×C₃×Q₁₆	—	9	1	no	—
69	C₂×C₃×SD₁₆	—	9	2	no	—
70	C₂×C₃×D₈	—	3	1	no	—
71	C₂×C₃×D₈	C₃×D₃	1	1	yes	characteristic
72	C₃×#124	—	9	2	no	—
73	#936	—	3	2	no	—
74	C₂×#214	—	3	2	no	—
75	C₂×Dic₁₂	—	3	1	no	—
76	C₃×C₄×C₈	—	9	1	no	—
77	C₈×Dic₃	—	3	1	no	—
78	C₂³×C₃²	—	2	2	no	—
79	C₃²×D₄	—	2	2	no	—
80	C₃²×D₄	—	2	2	no	—
81	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
82	C₂×C₃×Dic₃	—	3	2	no	—
83	C₂×C₃×Dic₃	—	6	2	no	—
84	C₃×Dic₆	—	6	2	no	—
85	C₃×Dic₆	—	6	2	no	—
86	C₂³×C₉	—	2	2	no	—
87	C₂³×C₉	—	4	2	no	—
88	C₃²×C₈	#67	1	2	yes	—
89	C₃×C₃⋊C₈	—	3	2	no	—
90	D₄×C₉	—	2	4	no	—
91	D₄×C₉	—	2	2	no	—
92	D₄×C₉	—	2	2	no	—
93	D₄×C₉	—	4	2	no	—
94	C₂×C₄×C₉	—	2	1	no	—
95	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
96	C₂×Dic₉	—	2	2	no	—
97	C₂×Dic₉	C₃×D₄	1	2	yes	—
98	Dic₁₈	—	2	2	no	—
99	Dic₁₈	—	2	2	no	—
100	C₈×C₉	—	2	2	no	—
101	C₈×C₉	C₃×D₄	1	2	yes	—
102	C₉⋊C₈	C₃×D₄	1	2	yes	—
103	#495	—	9	1	no	Sylow
104	C₂×3₋¹⁺²	—	8	2	no	—
105	C₂×3₋¹⁺²	#127	1	1	yes	characteristic
106	C₂×3₋¹⁺²	#135	1	2	yes	—
107	C₂×C₃×Q₈	—	9	2	no	—
108	C₂×C₃×D₄	—	3	2	no	—
109	C₂×C₃×D₄	C₂×C₃×D₃	1	2	yes	—
110	C₂×Dic₆	—	3	2	no	—
111	C₃×Q₁₆	—	18	2	no	—
112	C₃×SD₁₆	—	18	4	no	—
113	C₃×D₈	—	2	2	no	—
114	C₃×D₈	—	6	2	no	—
115	C₂×C₃×C₈	—	3	1	no	—
116	C₂×C₃×C₈	—	9	1	no	—
117	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
118	C₃×C₂²⋊C₄	—	18	4	no	—
119	C₃×C₄²	—	9	1	no	—
120	#217	—	6	4	no	—
121	#214	—	6	4	no	—
122	C₄×Dic₃	—	3	1	no	—
123	C₂×C₃⋊C₈	—	3	1	no	—
124	Dic₁₂	—	6	2	no	—
125	C₂²×C₃²	—	4	4	no	—
126	C₂²×C₃²	—	4	2	no	—
127	C₂²×C₃²	D₃×D₄	1	1	yes	characteristic
128	C₃²×C₄	D₃×D₄	1	1	yes	characteristic
129	C₃²×C₄	C₂×#67	1	1	yes	characteristic
130	C₃×Dic₃	—	6	2	no	—
131	C₃×Dic₃	—	12	2	no	—
132	C₂²×C₉	—	2	1	no	—
133	C₂²×C₉	—	4	4	no	—
134	C₂²×C₉	—	4	2	no	—
135	C₂²×C₉	—	4	4	no	—
136	C₂²×C₉	—	8	4	no	—
137	C₂²×C₉	C₂×C₃×D₄	1	1	yes	characteristic
138	C₄×C₉	—	2	1	no	—
139	C₄×C₉	—	2	1	no	—
140	C₄×C₉	C₂×C₃×D₄	1	1	yes	characteristic
141	C₄×C₉	C₂×C₃×D₄	1	1	yes	characteristic
142	Dic₉	—	2	2	no	—
143	Dic₉	—	4	2	no	—
144	C₂×Q₁₆	—	9	1	no	—
145	C₂×SD₁₆	—	9	2	no	—
146	C₂×D₈	AGL(1,ℤ/9)	1	1	yes	characteristic
147	#124	—	9	2	no	—
148	C₄×C₈	—	9	1	no	—
149	3₋¹⁺²	#495	1	1	yes	characteristic, complemented, Sylow
150	C₂³×C₃	—	2	2	no	—
151	C₂³×C₃	—	6	2	no	—
152	C₃×Q₈	—	18	2	no	—
153	C₃×Q₈	—	18	2	no	—
154	C₃×D₄	—	2	2	no	—
155	C₃×D₄	—	2	2	no	—
156	C₃×D₄	—	6	2	no	—
157	C₃×D₄	—	6	2	no	—
158	C₂×C₃×C₄	—	3	1	no	—
159	C₂×C₃×C₄	—	9	2	no	—
160	C₂×C₃×C₄	—	18	2	no	—
161	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
162	C₂×Dic₃	—	3	2	no	—
163	C₂×Dic₃	—	6	2	no	—
164	Dic₆	—	6	2	no	—
165	Dic₆	—	6	2	no	—
166	C₃×C₈	—	3	2	no	—
167	C₃×C₈	—	9	2	no	—
168	C₃×C₈	C₃×#67	1	2	yes	—
169	C₃⋊C₈	—	3	2	no	—
170	C₂×C₃²	—	8	2	no	—
171	C₂×C₃²	#912	1	2	yes	—
172	C₂×C₃²	#940	1	1	yes	characteristic
173	C₂×C₉	—	2	2	no	—
174	C₂×C₉	—	2	1	no	—
175	C₂×C₉	—	8	4	no	—
176	C₂×C₉	—	8	2	no	—
177	C₂×C₉	C₃×#127	1	1	yes	characteristic
178	C₂×C₉	C₃×#135	1	2	yes	—
179	C₂×Q₈	—	9	2	no	—
180	C₂×D₄	C₂×AGL(1,ℤ/9)	1	2	yes	—
181	Q₁₆	—	18	2	no	—
182	SD₁₆	—	18	4	no	—
183	D₈	—	2	2	no	—
184	C₂×C₈	—	9	1	no	—
185	C₂×C₈	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
186	C₂²⋊C₄	—	18	4	no	—
187	C₄²	—	9	1	no	—
188	C₂²×C₃	—	3	1	no	—
189	C₂²×C₃	—	4	4	no	—
190	C₂²×C₃	—	4	2	no	—
191	C₂²×C₃	—	12	2	no	—
192	C₂²×C₃	—	12	4	no	—
193	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
194	C₃×C₄	—	3	1	no	—
195	C₃×C₄	—	3	1	no	—
196	C₃×C₄	—	18	2	no	—
197	C₃×C₄	—	36	2	no	—
198	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
199	C₃×C₄	C₂×C₃×#67	1	1	yes	characteristic
200	Dic₃	—	6	2	no	—
201	Dic₃	—	12	2	no	—
202	C₃²	#5155	1	1	yes	characteristic
203	C₉	—	2	1	no	—
204	C₉	C₃×#495	1	1	yes	characteristic, complemented
205	C₂³	—	2	2	no	—
206	Q₈	—	18	2	no	—
207	Q₈	—	18	2	no	—
208	D₄	—	2	2	no	—
209	D₄	—	2	2	no	—
210	C₂×C₄	—	9	2	no	—
211	C₂×C₄	—	18	2	no	—
212	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
213	C₈	—	9	2	no	—
214	C₈	#611⋊C₃	1	2	yes	—
215	C₂×C₃	—	3	2	no	—
216	C₂×C₃	—	3	1	no	—
217	C₂×C₃	—	8	2	no	—
218	C₂×C₃	—	24	2	no	—
219	C₂×C₃	C₃×#912	1	2	yes	—
220	C₂×C₃	C₃×#940	1	1	yes	characteristic
221	C₂²	—	4	4	no	—
222	C₂²	—	4	2	no	—
223	C₂²	D₄×AGL(1,ℤ/9)	1	1	yes	characteristic
224	C₄	—	18	2	no	—
225	C₄	—	36	2	no	—
226	C₄	D₄×AGL(1,ℤ/9)	1	1	yes	characteristic
227	C₄	C₂×#611⋊C₃	1	1	yes	characteristic
228	C₃	—	3	1	no	—
229	C₃	C₃×#5155	1	1	yes	characteristic
230	C₂	—	8	2	no	—
231	C₂	#63474⋊C₃	1	2	yes	—
232	C₂	#63502⋊C₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₈×3₋¹⁺²

C₂

yes

maximal, characteristic

#63498⋊C₃

C₂

yes

maximal, complemented

C₂×#3672⋊C₃

C₂

yes

maximal, complemented

C₂×Dic₃₆⋊C₃

C₂

yes

maximal, characteristic, complemented

C₈×3₋¹⁺²⋊C₄

C₂

yes

maximal, characteristic, complemented

C₃×#5155

—

maximal

#10588835

C₃

yes

maximal, characteristic, complemented

C₂×D₄×3₋¹⁺²

C₂²

yes

—

C₂×3₋¹⁺²⋊Q₈

C₂²

yes

—

D₈×3₋¹⁺²

—

C₂×C₈×3₋¹⁺²

C₂²

yes

characteristic

#3676⋊C₃

—

#3672⋊C₃

—

C₄×3₋¹⁺²⋊C₄

C₂²

yes

characteristic

C₂×3₋¹⁺²⋊C₈

C₂²

yes

characteristic

Dic₃₆⋊C₃

—

C₂×C₃²×D₈

D₃

yes

characteristic

C₃×#936

—

C₂×C₃×#214

—

C₂×C₃×Dic₁₂

—

C₃×C₈×Dic₃

—

C₂×C₉×D₈

—

C₂×C₉×D₈

C₂×C₃

yes

characteristic

#63498

C₂×C₃

yes

complemented

C₂×#3672

C₂×C₃

yes

complemented

C₂×Dic₃₆

C₂×C₃

yes

characteristic, complemented

C₈×Dic₉

C₂×C₃

yes

characteristic, complemented

C₂³×3₋¹⁺²

—

D₄×3₋¹⁺²

—

D₄×3₋¹⁺²

—

C₂×C₄×3₋¹⁺²

C₂³

yes

characteristic

C₂×3₋¹⁺²⋊C₄

—

C₂×3₋¹⁺²⋊C₄

D₄

yes

—

3₋¹⁺²⋊Q₈

—

3₋¹⁺²⋊Q₈

—

C₈×3₋¹⁺²

D₄

yes

—

3₋¹⁺²⋊C₈

D₄

yes

—

C₃×#495

—

#5155

—

C₂×C₃²×D₄

C₂×D₃

yes

—

C₂×C₃×Dic₆

—

C₃²×D₈

—

C₂×C₃²×C₈

C₂×D₃

yes

characteristic

C₃×#217

—

C₃×#214

—

C₃×C₄×Dic₃

—

C₂×C₃×C₃⋊C₈

—

C₃×Dic₁₂

—

C₂×D₄×C₉

—

C₂×D₄×C₉

C₂²×C₃

yes

—

C₂×Dic₁₈

C₂²×C₃

yes

—

C₉×D₈

—

C₉×D₈

—

C₂×C₈×C₉

—

C₂×C₈×C₉

C₂²×C₃

yes

characteristic

#3676

—

#3672

—

C₄×Dic₉

C₂²×C₃

yes

characteristic

C₂×C₉⋊C₈

C₂²×C₃

yes

characteristic

Dic₃₆

—

C₂²×3₋¹⁺²

—

C₂²×3₋¹⁺²

—

C₂²×3₋¹⁺²

C₂×D₄

yes

characteristic

C₄×3₋¹⁺²

C₂×D₄

yes

characteristic

C₄×3₋¹⁺²

C₂×D₄

yes

characteristic

3₋¹⁺²⋊C₄

—

3₋¹⁺²⋊C₄

—

C₂×C₃×Q₁₆

—

C₂×C₃×SD₁₆

—

C₂×C₃×D₈

—

C₂×C₃×D₈

C₃×D₃

yes

—

—

—

C₂×Dic₁₂

—

C₃×C₄×C₈

—

C₈×Dic₃

—

C₂³×C₃²

—

C₃²×D₄

—

C₃²×D₄

—

C₂×C₃²×C₄

C₂²×D₃

yes

characteristic

C₂×C₃×Dic₃

—

C₂×C₃×Dic₃

—

C₃×Dic₆

—

C₃×Dic₆

—

C₂³×C₉

—

C₂³×C₉

—

C₃²×C₈

#67

yes

—

C₃×C₃⋊C₈

—

D₄×C₉

—

D₄×C₉

—

D₄×C₉

—

D₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₂³×C₃

yes

characteristic

C₂×Dic₉

—

C₂×Dic₉

C₃×D₄

yes

—

Dic₁₈

—

Dic₁₈

—

100

C₈×C₉

—

101

C₈×C₉

C₃×D₄

yes

—

102

C₉⋊C₈

C₃×D₄

yes

—

103

#495

—

Sylow

104

C₂×3₋¹⁺²

—

105

C₂×3₋¹⁺²

#127

yes

characteristic

106

C₂×3₋¹⁺²

#135

yes

—

107

C₂×C₃×Q₈

—

108

C₂×C₃×D₄

—

109

C₂×C₃×D₄

C₂×C₃×D₃

yes

—

110

C₂×Dic₆

—

111

C₃×Q₁₆

—

112

C₃×SD₁₆

—

113

C₃×D₈

—

114

C₃×D₈

—

115

C₂×C₃×C₈

—

116

C₂×C₃×C₈

—

117

C₂×C₃×C₈

C₂×C₃×D₃

yes

characteristic

118

C₃×C₂²⋊C₄

—

119

C₃×C₄²

—

120

#217

—

121

#214

—

122

C₄×Dic₃

—

123

C₂×C₃⋊C₈

—

124

Dic₁₂

—

125

C₂²×C₃²

—

126

C₂²×C₃²

—

127

C₂²×C₃²

D₃×D₄

yes

characteristic

128

C₃²×C₄

D₃×D₄

yes

characteristic

129

C₃²×C₄

C₂×#67

yes

characteristic

130

C₃×Dic₃

—

131

C₃×Dic₃

—

132

C₂²×C₉

—

133

C₂²×C₉

—

134

C₂²×C₉

—

135

C₂²×C₉

—

136

C₂²×C₉

—

137

C₂²×C₉

C₂×C₃×D₄

yes

characteristic

138

C₄×C₉

—

139

C₄×C₉

—

140

C₄×C₉

C₂×C₃×D₄

yes

characteristic

141

C₄×C₉

C₂×C₃×D₄

yes

characteristic

142

Dic₉

—

143

Dic₉

—

144

C₂×Q₁₆

—

145

C₂×SD₁₆

—

146

C₂×D₈

AGL(1,ℤ/9)

yes

characteristic

147

#124

—

148

C₄×C₈

—

149

3₋¹⁺²

#495

yes

characteristic, complemented, Sylow

150

C₂³×C₃

—

151

C₂³×C₃

—

152

C₃×Q₈

—

153

C₃×Q₈

—

154

C₃×D₄

—

155

C₃×D₄

—

156

C₃×D₄

—

157

C₃×D₄

—

158

C₂×C₃×C₄

—

159

C₂×C₃×C₄

—

160

C₂×C₃×C₄

—

161

C₂×C₃×C₄

C₂²×C₃×D₃

yes

characteristic

162

C₂×Dic₃

—

163

C₂×Dic₃

—

164

Dic₆

—

165

Dic₆

—

166

C₃×C₈

—

167

C₃×C₈

—

168

C₃×C₈

C₃×#67

yes

—

169

C₃⋊C₈

—

170

C₂×C₃²

—

171

C₂×C₃²

#912

yes

—

172

C₂×C₃²

#940

yes

characteristic

173

C₂×C₉

—

174

C₂×C₉

—

175

C₂×C₉

—

176

C₂×C₉

—

177

C₂×C₉

C₃×#127

yes

characteristic

178

C₂×C₉

C₃×#135

yes

—

179

C₂×Q₈

—

180

C₂×D₄

C₂×AGL(1,ℤ/9)

yes

—

181

Q₁₆

—

182

SD₁₆

—

183

D₈

—

184

C₂×C₈

—

185

C₂×C₈

C₂×AGL(1,ℤ/9)

yes

characteristic

186

C₂²⋊C₄

—

187

C₄²

—

188

C₂²×C₃

—

189

C₂²×C₃

—

190

C₂²×C₃

—

191

C₂²×C₃

—

192

C₂²×C₃

—

193

C₂²×C₃

C₃×D₃×D₄

yes

characteristic

194

C₃×C₄

—

195

C₃×C₄

—

196

C₃×C₄

—

197

C₃×C₄

—

198

C₃×C₄

C₃×D₃×D₄

yes

characteristic

199

C₃×C₄

C₂×C₃×#67

yes

characteristic

200

Dic₃

—

201

Dic₃

—

202

C₃²

#5155

yes

characteristic

203

C₉

—

204

C₉

C₃×#495

yes

characteristic, complemented

205

C₂³

—

206

Q₈

—

207

Q₈

—

208

D₄

—

209

D₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

C₂²×AGL(1,ℤ/9)

yes

characteristic

213

C₈

—

214

C₈

#611⋊C₃

yes

—

215

C₂×C₃

—

216

C₂×C₃

—

217

C₂×C₃

—

218

C₂×C₃

—

219

C₂×C₃

C₃×#912

yes

—

220

C₂×C₃

C₃×#940

yes

characteristic

221

C₂²

—

222

C₂²

—

223

C₂²

D₄×AGL(1,ℤ/9)

yes

characteristic

224

C₄

—

225

C₄

—

226

C₄

D₄×AGL(1,ℤ/9)

yes

characteristic

227

C₄

C₂×#611⋊C₃

yes

characteristic

228

C₃

—

229

C₃

C₃×#5155

yes

characteristic

230

C₂

—

231

C₂

#63474⋊C₃

yes

—

232

C₂

#63502⋊C₃

yes

characteristic

	subgroup	G/H
center	C₂²	D₄×AGL(1,ℤ/9)
commutator, cosocle	C₂×C₄×C₉	C₂³×C₃
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₂×D₈×3₋¹⁺²	C₂
socle	C₂²×C₃	C₃×D₃×D₄
prime radical	C₂×C₃²×D₈	D₃
hypercenter	C₂×D₈	AGL(1,ℤ/9)
hypocenter	C₉	C₃×#495
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₈

subgroup

G/H

center

C₂²

D₄×AGL(1,ℤ/9)

commutator, cosocle

C₂×C₄×C₉

C₂³×C₃

Frattini

C₂×C₃×C₄

C₂²×C₃×D₃

Fitting

C₂×D₈×3₋¹⁺²

C₂

socle

C₂²×C₃

C₃×D₃×D₄

prime radical

C₂×C₃²×D₈

D₃

C₂×D₈

C₉

G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₈

N	H ≅ G/N	type
2. #63498⋊C₃	C₂	semidirect
3. C₂×#3672⋊C₃	C₂	semidirect
4. C₂×Dic₃₆⋊C₃	C₂	semidirect
5. C₈×3₋¹⁺²⋊C₄	C₂	semidirect
7. #10588835	C₃	semidirect
24. #63498	C₂×C₃	semidirect
25. C₂×#3672	C₂×C₃	semidirect
26. C₂×Dic₃₆	C₂×C₃	semidirect
27. C₈×Dic₉	C₂×C₃	semidirect
149. 3₋¹⁺²	#495	semidirect
204. C₉	C₃×#495	semidirect

H ≅ G/N

type

2. #63498⋊C₃

C₂

semidirect

3. C₂×#3672⋊C₃

C₂

semidirect

4. C₂×Dic₃₆⋊C₃

C₂

semidirect

5. C₈×3₋¹⁺²⋊C₄

C₂

semidirect

7. #10588835

C₃

semidirect

24. #63498

C₂×C₃

semidirect

25. C₂×#3672

C₂×C₃

semidirect

26. C₂×Dic₃₆

C₂×C₃

semidirect

27. C₈×Dic₉

C₂×C₃

semidirect

149. 3₋¹⁺²

#495

semidirect

204. C₉

C₃×#495

semidirect

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

subgroup	index
C₂×D₈×3₋¹⁺²	2
#63498⋊C₃	2
C₂×#3672⋊C₃	2
C₂×Dic₃₆⋊C₃	2
C₈×3₋¹⁺²⋊C₄	2
C₃×#5155	3
#10588835	3

subgroup

index

C₂×D₈×3₋¹⁺²

#63498⋊C₃

C₂×#3672⋊C₃

C₂×Dic₃₆⋊C₃

C₈×3₋¹⁺²⋊C₄

C₃×#5155

#10588835

Subgroups — #10588835⋊C₃ #13143322

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10588835⋊C3 #13143322

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10588835⋊C₃ #13143322