Group #11766739 — subgroups

Subgroups — C₉×#2018 #11766739

Order 1152.

573 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 573 conjugacy classes of subgroups — too many to draw. Only its 138 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×C₉×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
2	C₂²×C₉×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉×#100	C₂	1	2	yes	maximal, complemented
4	C₉×#408	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#341	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2018	C₃	1	1	yes	maximal, characteristic
7	C₂×C₉×#41	C₂²	1	1	yes	characteristic
8	C₂²×D₄×C₉	C₂²	1	2	yes	—
9	C₉×AGL(1,ℤ/8)	—	2	4	no	—
10	C₉×AGL(1,ℤ/8)	—	2	4	no	—
11	C₂×C₉×SD₁₆	—	2	2	no	—
12	C₂×C₉×D₈	—	2	4	no	—
13	C₂×C₉×D₈	—	2	2	no	—
14	C₂×C₉×D₈	—	2	2	no	—
15	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
16	C₂×C₉×M₁₆	C₂²	1	2	yes	—
17	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
18	C₉×#100	—	2	4	no	—
19	C₉×C₂²⋊C₈	—	2	2	no	—
20	C₂×C₃×AGL(1,ℤ/8)	C₂×C₃	1	2	yes	—
21	C₂²×C₃×D₈	C₂×C₃	1	1	yes	characteristic
22	C₂×C₃×#100	C₂×C₃	1	2	yes	—
23	C₃×#408	C₂×C₃	1	1	yes	characteristic
24	C₃×#341	C₂×C₃	1	1	yes	characteristic
25	C₂⁴×C₉	—	2	2	no	—
26	C₉×#41	—	2	2	no	—
27	C₉×#41	—	2	2	no	—
28	C₂×Q₈×C₉	D₄	1	1	yes	characteristic
29	C₂×D₄×C₉	—	2	1	no	—
30	C₂×D₄×C₉	—	2	2	no	—
31	C₂×D₄×C₉	—	2	2	no	—
32	C₂×D₄×C₉	—	2	2	no	—
33	C₂×D₄×C₉	—	2	2	no	—
34	C₂×D₄×C₉	—	2	2	no	—
35	C₂×D₄×C₉	D₄	1	1	yes	characteristic
36	C₂×D₄×C₉	D₄	1	4	yes	—
37	C₂²×C₄×C₉	—	2	1	no	—
38	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
39	C₉×SD₁₆	—	2	8	no	—
40	C₉×D₈	—	2	8	no	—
41	C₉×D₈	—	2	8	no	—
42	C₉×M₁₆	—	2	2	no	—
43	C₉×M₁₆	—	2	2	no	—
44	C₉×M₁₆	D₄	1	4	yes	—
45	C₂×C₈×C₉	—	2	2	no	—
46	C₂×C₈×C₉	—	2	2	no	—
47	C₂×C₈×C₉	—	2	1	no	—
48	C₂×C₈×C₉	D₄	1	2	yes	—
49	#2018	C₉	1	1	yes	characteristic, direct product factor, Sylow
50	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
51	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
52	C₃×AGL(1,ℤ/8)	—	2	4	no	—
53	C₃×AGL(1,ℤ/8)	—	2	4	no	—
54	C₂×C₃×SD₁₆	—	2	2	no	—
55	C₂×C₃×D₈	—	2	4	no	—
56	C₂×C₃×D₈	—	2	2	no	—
57	C₂×C₃×D₈	—	2	2	no	—
58	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
59	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
60	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
61	C₃×#100	—	2	4	no	—
62	C₃×C₂²⋊C₈	—	2	2	no	—
63	C₂³×C₉	—	2	1	no	—
64	C₂³×C₉	—	2	4	no	—
65	C₂³×C₉	—	4	2	no	—
66	C₂³×C₉	—	4	2	no	—
67	C₂³×C₉	—	8	4	no	—
68	C₂³×C₉	#41	1	1	yes	characteristic
69	Q₈×C₉	—	2	2	no	—
70	D₄×C₉	—	2	4	no	—
71	D₄×C₉	—	2	2	no	—
72	D₄×C₉	—	2	4	no	—
73	D₄×C₉	—	4	2	no	—
74	D₄×C₉	—	4	2	no	—
75	D₄×C₉	—	4	2	no	—
76	C₂×C₄×C₉	—	2	1	no	—
77	C₂×C₄×C₉	—	4	1	no	—
78	C₂×C₄×C₉	—	4	1	no	—
79	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
80	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
81	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
82	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
83	C₈×C₉	—	2	2	no	—
84	C₈×C₉	—	2	4	no	—
85	C₈×C₉	—	4	1	no	—
86	C₂×AGL(1,ℤ/8)	C₂×C₉	1	2	yes	complemented
87	C₂²×D₈	C₂×C₉	1	1	yes	characteristic, complemented
88	C₂×#100	C₂×C₉	1	2	yes	complemented
89	#408	C₂×C₉	1	1	yes	characteristic, complemented
90	#341	C₂×C₉	1	1	yes	characteristic, complemented
91	C₂⁴×C₃	—	2	2	no	—
92	C₃×#41	—	2	2	no	—
93	C₃×#41	—	2	2	no	—
94	C₂×C₃×Q₈	C₃×D₄	1	1	yes	characteristic
95	C₂×C₃×D₄	—	2	1	no	—
96	C₂×C₃×D₄	—	2	2	no	—
97	C₂×C₃×D₄	—	2	2	no	—
98	C₂×C₃×D₄	—	2	2	no	—
99	C₂×C₃×D₄	—	2	2	no	—
100	C₂×C₃×D₄	—	2	2	no	—
101	C₂×C₃×D₄	C₃×D₄	1	1	yes	characteristic
102	C₂×C₃×D₄	C₃×D₄	1	4	yes	—
103	C₂²×C₃×C₄	—	2	1	no	—
104	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
105	C₃×SD₁₆	—	2	8	no	—
106	C₃×D₈	—	2	8	no	—
107	C₃×D₈	—	2	8	no	—
108	C₃×M₁₆	—	2	2	no	—
109	C₃×M₁₆	—	2	2	no	—
110	C₃×M₁₆	C₃×D₄	1	4	yes	—
111	C₂×C₃×C₈	—	2	2	no	—
112	C₂×C₃×C₈	—	2	2	no	—
113	C₂×C₃×C₈	—	2	1	no	—
114	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
115	C₂²×C₉	—	2	2	no	—
116	C₂²×C₉	—	4	1	no	—
117	C₂²×C₉	—	4	4	no	—
118	C₂²×C₉	—	4	2	no	—
119	C₂²×C₉	—	8	4	no	—
120	C₂²×C₉	—	8	4	no	—
121	C₂²×C₉	—	8	4	no	—
122	C₂²×C₉	#121	1	2	yes	—
123	C₂²×C₉	#121	1	1	yes	characteristic
124	C₄×C₉	—	4	1	no	—
125	C₄×C₉	#120	1	1	yes	characteristic
126	C₄×C₉	#120	1	2	yes	—
127	C₄×C₉	#127	1	1	yes	characteristic
128	C₂×#41	C₂²×C₉	1	1	yes	characteristic
129	C₂²×D₄	C₂²×C₉	1	2	yes	—
130	AGL(1,ℤ/8)	—	2	4	no	—
131	AGL(1,ℤ/8)	—	2	4	no	—
132	C₂×SD₁₆	—	2	2	no	—
133	C₂×D₈	—	2	4	no	—
134	C₂×D₈	—	2	2	no	—
135	C₂×D₈	—	2	2	no	—
136	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
137	C₂×M₁₆	C₂²×C₉	1	2	yes	—
138	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
139	#100	—	2	4	no	—
140	C₂²⋊C₈	—	2	2	no	—
141	C₂³×C₃	—	2	1	no	—
142	C₂³×C₃	—	2	4	no	—
143	C₂³×C₃	—	4	2	no	—
144	C₂³×C₃	—	4	2	no	—
145	C₂³×C₃	—	8	4	no	—
146	C₂³×C₃	C₃×#41	1	1	yes	characteristic
147	C₃×Q₈	—	2	2	no	—
148	C₃×D₄	—	2	4	no	—
149	C₃×D₄	—	2	2	no	—
150	C₃×D₄	—	2	4	no	—
151	C₃×D₄	—	4	2	no	—
152	C₃×D₄	—	4	2	no	—
153	C₃×D₄	—	4	2	no	—
154	C₂×C₃×C₄	—	2	1	no	—
155	C₂×C₃×C₄	—	4	1	no	—
156	C₂×C₃×C₄	—	4	1	no	—
157	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
158	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
159	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
160	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
161	C₃×C₈	—	2	2	no	—
162	C₃×C₈	—	2	4	no	—
163	C₃×C₈	—	4	1	no	—
164	C₂×C₉	—	2	2	no	—
165	C₂×C₉	—	8	1	no	—
166	C₂×C₉	—	8	4	no	—
167	C₂×C₉	#392	1	1	yes	characteristic
168	C₂×C₉	#472	1	2	yes	—
169	C₂⁴	—	2	2	no	—
170	#41	—	2	2	no	—
171	#41	—	2	2	no	—
172	C₂×Q₈	D₄×C₉	1	1	yes	characteristic
173	C₂×D₄	—	2	1	no	—
174	C₂×D₄	—	2	2	no	—
175	C₂×D₄	—	2	2	no	—
176	C₂×D₄	—	2	2	no	—
177	C₂×D₄	—	2	2	no	—
178	C₂×D₄	—	2	2	no	—
179	C₂×D₄	D₄×C₉	1	1	yes	characteristic
180	C₂×D₄	D₄×C₉	1	4	yes	—
181	C₂²×C₄	—	2	1	no	—
182	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
183	SD₁₆	—	2	8	no	—
184	D₈	—	2	8	no	—
185	D₈	—	2	8	no	—
186	M₁₆	—	2	2	no	—
187	M₁₆	—	2	2	no	—
188	M₁₆	D₄×C₉	1	4	yes	—
189	C₂×C₈	—	2	2	no	—
190	C₂×C₈	—	2	2	no	—
191	C₂×C₈	—	2	1	no	—
192	C₂×C₈	D₄×C₉	1	2	yes	—
193	C₂²×C₃	—	2	2	no	—
194	C₂²×C₃	—	4	1	no	—
195	C₂²×C₃	—	4	4	no	—
196	C₂²×C₃	—	4	2	no	—
197	C₂²×C₃	—	8	4	no	—
198	C₂²×C₃	—	8	4	no	—
199	C₂²×C₃	—	8	4	no	—
200	C₂²×C₃	C₃×#121	1	2	yes	—
201	C₂²×C₃	C₃×#121	1	1	yes	characteristic
202	C₃×C₄	—	4	1	no	—
203	C₃×C₄	C₃×#120	1	1	yes	characteristic
204	C₃×C₄	C₃×#120	1	2	yes	—
205	C₃×C₄	C₃×#127	1	1	yes	characteristic
206	C₉	#2018	1	1	yes	characteristic, direct product factor, Sylow
207	C₂³	—	2	1	no	—
208	C₂³	—	2	4	no	—
209	C₂³	—	4	2	no	—
210	C₂³	—	4	2	no	—
211	C₂³	—	8	4	no	—
212	C₂³	C₉×#41	1	1	yes	characteristic
213	Q₈	—	2	2	no	—
214	D₄	—	2	4	no	—
215	D₄	—	2	2	no	—
216	D₄	—	2	4	no	—
217	D₄	—	4	2	no	—
218	D₄	—	4	2	no	—
219	D₄	—	4	2	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	4	1	no	—
222	C₂×C₄	—	4	1	no	—
223	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
224	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
225	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
226	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
227	C₈	—	2	2	no	—
228	C₈	—	2	4	no	—
229	C₈	—	4	1	no	—
230	C₂×C₃	—	2	2	no	—
231	C₂×C₃	—	8	1	no	—
232	C₂×C₃	—	8	4	no	—
233	C₂×C₃	C₃×#392	1	1	yes	characteristic
234	C₂×C₃	C₃×#472	1	2	yes	—
235	C₂²	—	2	2	no	—
236	C₂²	—	4	1	no	—
237	C₂²	—	4	4	no	—
238	C₂²	—	4	2	no	—
239	C₂²	—	8	4	no	—
240	C₂²	—	8	4	no	—
241	C₂²	—	8	4	no	—
242	C₂²	C₉×#121	1	2	yes	—
243	C₂²	C₉×#121	1	1	yes	characteristic
244	C₄	—	4	1	no	—
245	C₄	C₉×#120	1	1	yes	characteristic
246	C₄	C₉×#120	1	2	yes	—
247	C₄	C₉×#127	1	1	yes	characteristic
248	C₃	C₃×#2018	1	1	yes	characteristic
249	C₂	—	2	2	no	—
250	C₂	—	8	1	no	—
251	C₂	—	8	4	no	—
252	C₂	C₉×#392	1	1	yes	characteristic
253	C₂	C₉×#472	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₉×AGL(1,ℤ/8)

C₂

yes

maximal, complemented

C₂²×C₉×D₈

C₂

yes

maximal, characteristic, complemented

C₂×C₉×#100

C₂

yes

maximal, complemented

C₉×#408

C₂

yes

maximal, characteristic, complemented

C₉×#341

C₂

yes

maximal, characteristic, complemented

C₃×#2018

C₃

yes

maximal, characteristic

C₂×C₉×#41

C₂²

yes

characteristic

C₂²×D₄×C₉

C₂²

yes

—

C₉×AGL(1,ℤ/8)

—

C₉×AGL(1,ℤ/8)

—

C₂×C₉×SD₁₆

—

C₂×C₉×D₈

—

C₂×C₉×D₈

—

C₂×C₉×D₈

—

C₂×C₉×M₁₆

C₂²

yes

characteristic

C₂×C₉×M₁₆

C₂²

yes

—

C₂²×C₈×C₉

C₂²

yes

characteristic

C₉×#100

—

C₉×C₂²⋊C₈

—

C₂×C₃×AGL(1,ℤ/8)

C₂×C₃

yes

—

C₂²×C₃×D₈

C₂×C₃

yes

characteristic

C₂×C₃×#100

C₂×C₃

yes

—

C₃×#408

C₂×C₃

yes

characteristic

C₃×#341

C₂×C₃

yes

characteristic

C₂⁴×C₉

—

C₉×#41

—

C₉×#41

—

C₂×Q₈×C₉

D₄

yes

characteristic

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

D₄

yes

characteristic

C₂×D₄×C₉

D₄

yes

—

C₂²×C₄×C₉

—

C₂²×C₄×C₉

C₂³

yes

characteristic

C₉×SD₁₆

—

C₉×D₈

—

C₉×D₈

—

C₉×M₁₆

—

C₉×M₁₆

—

C₉×M₁₆

D₄

yes

—

C₂×C₈×C₉

—

C₂×C₈×C₉

—

C₂×C₈×C₉

—

C₂×C₈×C₉

D₄

yes

—

#2018

C₉

yes

characteristic, direct product factor, Sylow

C₂×C₃×#41

C₂²×C₃

yes

characteristic

C₂²×C₃×D₄

C₂²×C₃

yes

—

C₃×AGL(1,ℤ/8)

—

C₃×AGL(1,ℤ/8)

—

C₂×C₃×SD₁₆

—

C₂×C₃×D₈

—

C₂×C₃×D₈

—

C₂×C₃×D₈

—

C₂×C₃×M₁₆

C₂²×C₃

yes

characteristic

C₂×C₃×M₁₆

C₂²×C₃

yes

—

C₂²×C₃×C₈

C₂²×C₃

yes

characteristic

C₃×#100

—

C₃×C₂²⋊C₈

—

C₂³×C₉

—

C₂³×C₉

—

C₂³×C₉

—

C₂³×C₉

—

C₂³×C₉

—

C₂³×C₉

#41

yes

characteristic

Q₈×C₉

—

D₄×C₉

—

D₄×C₉

—

D₄×C₉

—

D₄×C₉

—

D₄×C₉

—

D₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₂×D₄

yes

—

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

C₂×D₄

yes

—

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₈×C₉

—

C₈×C₉

—

C₈×C₉

—

C₂×AGL(1,ℤ/8)

C₂×C₉

yes

complemented

C₂²×D₈

C₂×C₉

yes

characteristic, complemented

C₂×#100

C₂×C₉

yes

complemented

#408

C₂×C₉

yes

characteristic, complemented

#341

C₂×C₉

yes

characteristic, complemented

C₂⁴×C₃

—

C₃×#41

—

C₃×#41

—

C₂×C₃×Q₈

C₃×D₄

yes

characteristic

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

100

C₂×C₃×D₄

—

101

C₂×C₃×D₄

C₃×D₄

yes

characteristic

102

C₂×C₃×D₄

C₃×D₄

yes

—

103

C₂²×C₃×C₄

—

104

C₂²×C₃×C₄

C₂³×C₃

yes

characteristic

105

C₃×SD₁₆

—

106

C₃×D₈

—

107

C₃×D₈

—

108

C₃×M₁₆

—

109

C₃×M₁₆

—

110

C₃×M₁₆

C₃×D₄

yes

—

111

C₂×C₃×C₈

—

112

C₂×C₃×C₈

—

113

C₂×C₃×C₈

—

114

C₂×C₃×C₈

C₃×D₄

yes

—

115

C₂²×C₉

—

116

C₂²×C₉

—

117

C₂²×C₉

—

118

C₂²×C₉

—

119

C₂²×C₉

—

120

C₂²×C₉

—

121

C₂²×C₉

—

122

C₂²×C₉

#121

yes

—

123

C₂²×C₉

#121

yes

characteristic

124

C₄×C₉

—

125

C₄×C₉

#120

yes

characteristic

126

C₄×C₉

#120

yes

—

127

C₄×C₉

#127

yes

characteristic

128

C₂×#41

C₂²×C₉

yes

characteristic

129

C₂²×D₄

C₂²×C₉

yes

—

130

AGL(1,ℤ/8)

—

131

AGL(1,ℤ/8)

—

132

C₂×SD₁₆

—

133

C₂×D₈

—

134

C₂×D₈

—

135

C₂×D₈

—

136

C₂×M₁₆

C₂²×C₉

yes

characteristic

137

C₂×M₁₆

C₂²×C₉

yes

—

138

C₂²×C₈

C₂²×C₉

yes

characteristic

139

#100

—

140

C₂²⋊C₈

—

141

C₂³×C₃

—

142

C₂³×C₃

—

143

C₂³×C₃

—

144

C₂³×C₃

—

145

C₂³×C₃

—

146

C₂³×C₃

C₃×#41

yes

characteristic

147

C₃×Q₈

—

148

C₃×D₄

—

149

C₃×D₄

—

150

C₃×D₄

—

151

C₃×D₄

—

152

C₃×D₄

—

153

C₃×D₄

—

154

C₂×C₃×C₄

—

155

C₂×C₃×C₄

—

156

C₂×C₃×C₄

—

157

C₂×C₃×C₄

C₂×C₃×D₄

yes

characteristic

158

C₂×C₃×C₄

C₂×C₃×D₄

yes

—

159

C₂×C₃×C₄

C₂×C₃×D₄

yes

characteristic

160

C₂×C₃×C₄

C₂×C₃×D₄

yes

—

161

C₃×C₈

—

162

C₃×C₈

—

163

C₃×C₈

—

164

C₂×C₉

—

165

C₂×C₉

—

166

C₂×C₉

—

167

C₂×C₉

#392

yes

characteristic

168

C₂×C₉

#472

yes

—

169

C₂⁴

—

170

#41

—

171

#41

—

172

C₂×Q₈

D₄×C₉

yes

characteristic

173

C₂×D₄

—

174

C₂×D₄

—

175

C₂×D₄

—

176

C₂×D₄

—

177

C₂×D₄

—

178

C₂×D₄

—

179

C₂×D₄

D₄×C₉

yes

characteristic

180

C₂×D₄

D₄×C₉

yes

—

181

C₂²×C₄

—

182

C₂²×C₄

C₂³×C₉

yes

characteristic

183

SD₁₆

—

184

D₈

—

185

D₈

—

186

M₁₆

—

187

M₁₆

—

188

M₁₆

D₄×C₉

yes

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

D₄×C₉

yes

—

193

C₂²×C₃

—

194

C₂²×C₃

—

195

C₂²×C₃

—

196

C₂²×C₃

—

197

C₂²×C₃

—

198

C₂²×C₃

—

199

C₂²×C₃

—

200

C₂²×C₃

C₃×#121

yes

—

201

C₂²×C₃

C₃×#121

yes

characteristic

202

C₃×C₄

—

203

C₃×C₄

C₃×#120

yes

characteristic

204

C₃×C₄

C₃×#120

yes

—

205

C₃×C₄

C₃×#127

yes

characteristic

206

C₉

#2018

yes

characteristic, direct product factor, Sylow

207

C₂³

—

208

C₂³

—

209

C₂³

—

210

C₂³

—

211

C₂³

—

212

C₂³

C₉×#41

yes

characteristic

213

Q₈

—

214

D₄

—

215

D₄

—

216

D₄

—

217

D₄

—

218

D₄

—

219

D₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

C₂×D₄×C₉

yes

characteristic

224

C₂×C₄

C₂×D₄×C₉

yes

—

225

C₂×C₄

C₂×D₄×C₉

yes

characteristic

226

C₂×C₄

C₂×D₄×C₉

yes

—

227

C₈

—

228

C₈

—

229

C₈

—

230

C₂×C₃

—

231

C₂×C₃

—

232

C₂×C₃

—

233

C₂×C₃

C₃×#392

yes

characteristic

234

C₂×C₃

C₃×#472

yes

—

235

C₂²

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

239

C₂²

—

240

C₂²

—

241

C₂²

—

242

C₂²

C₉×#121

yes

—

243

C₂²

C₉×#121

yes

characteristic

244

C₄

—

245

C₄

C₉×#120

yes

characteristic

246

C₄

C₉×#120

yes

—

247

C₄

C₉×#127

yes

characteristic

248

C₃

C₃×#2018

yes

characteristic

249

C₂

—

250

C₂

—

251

C₂

—

252

C₂

C₉×#392

yes

characteristic

253

C₂

C₉×#472

yes

—

	subgroup	G/H
center	C₂²×C₉	#121
commutator	C₂²×C₄	C₂³×C₉
Frattini, cosocle	C₂²×C₃×C₄	C₂³×C₃
socle	C₂²×C₃	C₃×#121
prime radical	C₃×#2018	C₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₂²×C₄×C₉ ◁ G

subgroup

G/H

center

C₂²×C₉

#121

commutator

C₂²×C₄

C₂³×C₉

Frattini, cosocle

C₂²×C₃×C₄

C₂³×C₃

C₂²×C₃

C₃

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

C₁ ◁ C₂²×C₉ ◁ C₂²×C₄×C₉ ◁ G

N	H ≅ G/N	type
1. C₂×C₉×AGL(1,ℤ/8)	C₂	semidirect
2. C₂²×C₉×D₈	C₂	semidirect
3. C₂×C₉×#100	C₂	semidirect
4. C₉×#408	C₂	semidirect
5. C₉×#341	C₂	semidirect
49. #2018	C₉	direct (N × H)
86. C₂×AGL(1,ℤ/8)	C₂×C₉	semidirect
87. C₂²×D₈	C₂×C₉	semidirect
88. C₂×#100	C₂×C₉	semidirect
89. #408	C₂×C₉	semidirect
90. #341	C₂×C₉	semidirect
206. C₉	#2018	direct (N × H)

H ≅ G/N

type

1. C₂×C₉×AGL(1,ℤ/8)

C₂

semidirect

2. C₂²×C₉×D₈

C₂

semidirect

3. C₂×C₉×#100

C₂

semidirect

4. C₉×#408

C₂

semidirect

5. C₉×#341

C₂

semidirect

49. #2018

C₉

direct (N × H)

86. C₂×AGL(1,ℤ/8)

C₂×C₉

semidirect

87. C₂²×D₈

C₂×C₉

semidirect

88. C₂×#100

C₂×C₉

semidirect

89. #408

C₂×C₉

semidirect

90. #341

C₂×C₉

semidirect

206. C₉

#2018

direct (N × H)

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

subgroup	index
C₂×C₉×AGL(1,ℤ/8)	2
C₂²×C₉×D₈	2
C₂×C₉×#100	2
C₉×#408	2
C₉×#341	2
C₃×#2018	3

subgroup

index

C₂×C₉×AGL(1,ℤ/8)

C₂²×C₉×D₈

C₂×C₉×#100

C₉×#408

C₉×#341

C₃×#2018

Subgroups — C₉×#2018 #11766739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C9×#2018 #11766739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2018 #11766739