Group #11766608 — subgroups

Subgroups — C₉×#1887 #11766608

Order 1152.

666 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 666 conjugacy classes of subgroups — too many to draw. Only its 168 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×#127	C₂	1	1	yes	maximal, characteristic
2	C₉×#518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#418	C₂	1	2	yes	maximal, complemented
4	C₂×C₉×#100	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#339	C₂	1	2	yes	maximal, complemented
6	C₃×#1887	C₃	1	1	yes	maximal, characteristic
7	C₂²×D₄×C₉	—	2	2	no	—
8	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
9	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
10	C₂×C₉×M₁₆	C₂²	1	2	yes	—
11	C₉×#127	—	2	2	no	—
12	C₉×#127	C₄	1	4	yes	complemented
13	C₄×D₄×C₉	—	2	4	no	—
14	C₉×#117	C₂²	1	2	yes	—
15	C₂×C₉×C₂²⋊C₄	—	2	2	no	—
16	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
17	C₉×#102	—	2	4	no	—
18	C₉×#100	—	2	2	no	—
19	C₂×C₃×#127	C₂×C₃	1	1	yes	characteristic
20	C₃×#518	C₂×C₃	1	1	yes	characteristic
21	C₃×#418	C₂×C₃	1	2	yes	—
22	C₂×C₃×#100	C₂×C₃	1	1	yes	characteristic
23	C₃×#339	C₂×C₃	1	2	yes	—
24	C₂⁴×C₉	—	2	1	no	—
25	C₂⁴×C₉	D₄	1	2	yes	—
26	C₂×D₄×C₉	—	2	8	no	—
27	C₂×D₄×C₉	—	2	2	no	—
28	C₂×D₄×C₉	—	2	2	no	—
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	—	4	8	no	—
33	C₂×D₄×C₉	C₂×C₄	1	2	yes	—
34	C₂×D₄×C₉	C₂×C₄	1	2	yes	complemented
35	C₂×D₄×C₉	D₄	1	2	yes	—
36	C₂²×C₄×C₉	—	2	1	no	—
37	C₂²×C₄×C₉	—	2	4	no	—
38	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
39	C₉×M₁₆	—	2	2	no	—
40	C₉×M₁₆	—	2	2	no	—
41	C₂×C₈×C₉	—	2	2	no	—
42	C₉×C₄⋊C₄	D₄	1	4	yes	complemented
43	C₉×C₂²⋊C₄	—	2	4	no	—
44	C₉×C₂²⋊C₄	—	2	2	no	—
45	C₄²×C₉	—	2	1	no	—
46	C₄²×C₉	—	2	2	no	—
47	C₄²×C₉	C₂×C₄	1	2	yes	complemented
48	#1887	C₉	1	1	yes	characteristic, direct product factor, Sylow
49	C₂²×C₃×D₄	—	2	2	no	—
50	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
51	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
52	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
53	C₃×#127	—	2	2	no	—
54	C₃×#127	C₃×C₄	1	4	yes	—
55	C₃×C₄×D₄	—	2	4	no	—
56	C₃×#117	C₂²×C₃	1	2	yes	—
57	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
58	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
59	C₃×#102	—	2	4	no	—
60	C₃×#100	—	2	2	no	—
61	C₂³×C₉	—	2	2	no	—
62	C₂³×C₉	—	2	2	no	—
63	C₂³×C₉	—	2	2	no	—
64	C₂³×C₉	—	4	4	no	—
65	C₂³×C₉	—	4	4	no	—
66	C₂³×C₉	—	4	1	no	—
67	C₂³×C₉	—	4	1	no	—
68	C₂³×C₉	C₂²⋊C₄	1	4	yes	—
69	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
70	D₄×C₉	—	2	4	no	—
71	D₄×C₉	—	2	4	no	—
72	D₄×C₉	—	2	4	no	—
73	D₄×C₉	—	4	16	no	—
74	D₄×C₉	—	4	2	no	—
75	C₂×C₄×C₉	—	2	4	no	—
76	C₂×C₄×C₉	—	2	2	no	—
77	C₂×C₄×C₉	—	2	4	no	—
78	C₂×C₄×C₉	—	8	4	no	—
79	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
80	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
81	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
82	C₂×C₄×C₉	#41	1	2	yes	—
83	C₈×C₉	—	4	2	no	—
84	C₂×#127	C₂×C₉	1	1	yes	characteristic
85	#518	C₂×C₉	1	1	yes	characteristic, complemented
86	#418	C₂×C₉	1	2	yes	complemented
87	C₂×#100	C₂×C₉	1	1	yes	characteristic, complemented
88	#339	C₂×C₉	1	2	yes	complemented
89	C₂⁴×C₃	—	2	1	no	—
90	C₂⁴×C₃	C₃×D₄	1	2	yes	—
91	C₂×C₃×D₄	—	2	8	no	—
92	C₂×C₃×D₄	—	2	2	no	—
93	C₂×C₃×D₄	—	2	2	no	—
94	C₂×C₃×D₄	—	2	1	no	—
95	C₂×C₃×D₄	—	2	2	no	—
96	C₂×C₃×D₄	—	2	2	no	—
97	C₂×C₃×D₄	—	4	8	no	—
98	C₂×C₃×D₄	C₂×C₃×C₄	1	2	yes	—
99	C₂×C₃×D₄	C₂×C₃×C₄	1	2	yes	—
100	C₂×C₃×D₄	C₃×D₄	1	2	yes	—
101	C₂²×C₃×C₄	—	2	1	no	—
102	C₂²×C₃×C₄	—	2	4	no	—
103	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
104	C₃×M₁₆	—	2	2	no	—
105	C₃×M₁₆	—	2	2	no	—
106	C₂×C₃×C₈	—	2	2	no	—
107	C₃×C₄⋊C₄	C₃×D₄	1	4	yes	—
108	C₃×C₂²⋊C₄	—	2	4	no	—
109	C₃×C₂²⋊C₄	—	2	2	no	—
110	C₃×C₄²	—	2	1	no	—
111	C₃×C₄²	—	2	2	no	—
112	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
113	C₂²×C₉	—	2	2	no	—
114	C₂²×C₉	—	2	4	no	—
115	C₂²×C₉	—	4	4	no	—
116	C₂²×C₉	—	4	4	no	—
117	C₂²×C₉	—	4	4	no	—
118	C₂²×C₉	—	4	2	no	—
119	C₂²×C₉	—	8	2	no	—
120	C₂²×C₉	—	8	2	no	—
121	C₂²×C₉	—	8	2	no	—
122	C₂²×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
123	C₂²×C₉	#120	1	1	yes	characteristic
124	C₂²×C₉	#123	1	1	yes	characteristic
125	C₄×C₉	—	2	4	no	—
126	C₄×C₉	—	4	4	no	—
127	C₄×C₉	C₄×D₄	1	2	yes	—
128	C₄×C₉	#121	1	2	yes	—
129	C₂²×D₄	—	2	2	no	—
130	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
131	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
132	C₂×M₁₆	C₂²×C₉	1	2	yes	—
133	#127	—	2	2	no	—
134	#127	C₄×C₉	1	4	yes	complemented
135	C₄×D₄	—	2	4	no	—
136	#117	C₂²×C₉	1	2	yes	—
137	C₂×C₂²⋊C₄	—	2	2	no	—
138	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
139	#102	—	2	4	no	—
140	#100	—	2	2	no	—
141	C₂³×C₃	—	2	2	no	—
142	C₂³×C₃	—	2	2	no	—
143	C₂³×C₃	—	2	2	no	—
144	C₂³×C₃	—	4	4	no	—
145	C₂³×C₃	—	4	4	no	—
146	C₂³×C₃	—	4	1	no	—
147	C₂³×C₃	—	4	1	no	—
148	C₂³×C₃	C₃×C₂²⋊C₄	1	4	yes	—
149	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
150	C₃×D₄	—	2	4	no	—
151	C₃×D₄	—	2	4	no	—
152	C₃×D₄	—	2	4	no	—
153	C₃×D₄	—	4	16	no	—
154	C₃×D₄	—	4	2	no	—
155	C₂×C₃×C₄	—	2	4	no	—
156	C₂×C₃×C₄	—	2	2	no	—
157	C₂×C₃×C₄	—	2	4	no	—
158	C₂×C₃×C₄	—	8	4	no	—
159	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
160	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
161	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
162	C₂×C₃×C₄	C₃×#41	1	2	yes	—
163	C₃×C₈	—	4	2	no	—
164	C₂×C₉	—	2	1	no	—
165	C₂×C₉	—	2	1	no	—
166	C₂×C₉	—	4	4	no	—
167	C₂×C₉	—	8	2	no	—
168	C₂×C₉	#386	1	1	yes	characteristic
169	C₂×C₉	#453	1	2	yes	—
170	C₂⁴	—	2	1	no	—
171	C₂⁴	D₄×C₉	1	2	yes	—
172	C₂×D₄	—	2	8	no	—
173	C₂×D₄	—	2	2	no	—
174	C₂×D₄	—	2	2	no	—
175	C₂×D₄	—	2	1	no	—
176	C₂×D₄	—	2	2	no	—
177	C₂×D₄	—	2	2	no	—
178	C₂×D₄	—	4	8	no	—
179	C₂×D₄	C₂×C₄×C₉	1	2	yes	—
180	C₂×D₄	C₂×C₄×C₉	1	2	yes	complemented
181	C₂×D₄	D₄×C₉	1	2	yes	—
182	C₂²×C₄	—	2	1	no	—
183	C₂²×C₄	—	2	4	no	—
184	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
185	M₁₆	—	2	2	no	—
186	M₁₆	—	2	2	no	—
187	C₂×C₈	—	2	2	no	—
188	C₄⋊C₄	D₄×C₉	1	4	yes	complemented
189	C₂²⋊C₄	—	2	4	no	—
190	C₂²⋊C₄	—	2	2	no	—
191	C₄²	—	2	1	no	—
192	C₄²	—	2	2	no	—
193	C₄²	C₂×C₄×C₉	1	2	yes	complemented
194	C₂²×C₃	—	2	2	no	—
195	C₂²×C₃	—	2	4	no	—
196	C₂²×C₃	—	4	4	no	—
197	C₂²×C₃	—	4	4	no	—
198	C₂²×C₃	—	4	4	no	—
199	C₂²×C₃	—	4	2	no	—
200	C₂²×C₃	—	8	2	no	—
201	C₂²×C₃	—	8	2	no	—
202	C₂²×C₃	—	8	2	no	—
203	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
204	C₂²×C₃	C₃×#120	1	1	yes	characteristic
205	C₂²×C₃	C₃×#123	1	1	yes	characteristic
206	C₃×C₄	—	2	4	no	—
207	C₃×C₄	—	4	4	no	—
208	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
209	C₃×C₄	C₃×#121	1	2	yes	—
210	C₉	#1887	1	1	yes	characteristic, direct product factor, Sylow
211	C₂³	—	2	2	no	—
212	C₂³	—	2	2	no	—
213	C₂³	—	2	2	no	—
214	C₂³	—	4	4	no	—
215	C₂³	—	4	4	no	—
216	C₂³	—	4	1	no	—
217	C₂³	—	4	1	no	—
218	C₂³	C₉×C₂²⋊C₄	1	4	yes	—
219	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
220	D₄	—	2	4	no	—
221	D₄	—	2	4	no	—
222	D₄	—	2	4	no	—
223	D₄	—	4	16	no	—
224	D₄	—	4	2	no	—
225	C₂×C₄	—	2	4	no	—
226	C₂×C₄	—	2	2	no	—
227	C₂×C₄	—	2	4	no	—
228	C₂×C₄	—	8	4	no	—
229	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
230	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
231	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
232	C₂×C₄	C₉×#41	1	2	yes	—
233	C₈	—	4	2	no	—
234	C₂×C₃	—	2	1	no	—
235	C₂×C₃	—	2	1	no	—
236	C₂×C₃	—	4	4	no	—
237	C₂×C₃	—	8	2	no	—
238	C₂×C₃	C₃×#386	1	1	yes	characteristic
239	C₂×C₃	C₃×#453	1	2	yes	—
240	C₂²	—	2	2	no	—
241	C₂²	—	2	4	no	—
242	C₂²	—	4	4	no	—
243	C₂²	—	4	4	no	—
244	C₂²	—	4	4	no	—
245	C₂²	—	4	2	no	—
246	C₂²	—	8	2	no	—
247	C₂²	—	8	2	no	—
248	C₂²	—	8	2	no	—
249	C₂²	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
250	C₂²	C₉×#120	1	1	yes	characteristic
251	C₂²	C₉×#123	1	1	yes	characteristic
252	C₄	—	2	4	no	—
253	C₄	—	4	4	no	—
254	C₄	C₄×D₄×C₉	1	2	yes	—
255	C₄	C₉×#121	1	2	yes	—
256	C₃	C₃×#1887	1	1	yes	characteristic
257	C₂	—	2	1	no	—
258	C₂	—	2	1	no	—
259	C₂	—	4	4	no	—
260	C₂	—	8	2	no	—
261	C₂	C₉×#386	1	1	yes	characteristic
262	C₂	C₉×#453	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₉×#127

C₂

yes

maximal, characteristic

C₉×#518

C₂

yes

maximal, characteristic, complemented

C₉×#418

C₂

yes

maximal, complemented

C₂×C₉×#100

C₂

yes

maximal, characteristic, complemented

C₉×#339

C₂

yes

maximal, complemented

C₃×#1887

C₃

yes

maximal, characteristic

C₂²×D₄×C₉

—

C₂²×D₄×C₉

C₂²

yes

characteristic

C₂²×D₄×C₉

C₂²

yes

characteristic

C₂×C₉×M₁₆

C₂²

yes

—

C₉×#127

—

C₉×#127

C₄

yes

complemented

C₄×D₄×C₉

—

C₉×#117

C₂²

yes

—

C₂×C₉×C₂²⋊C₄

—

C₂×C₄²×C₉

C₂²

yes

characteristic

C₉×#102

—

C₉×#100

—

C₂×C₃×#127

C₂×C₃

yes

characteristic

C₃×#518

C₂×C₃

yes

characteristic

C₃×#418

C₂×C₃

yes

—

C₂×C₃×#100

C₂×C₃

yes

characteristic

C₃×#339

C₂×C₃

yes

—

C₂⁴×C₉

—

C₂⁴×C₉

D₄

yes

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

C₂×C₄

yes

—

C₂×D₄×C₉

C₂×C₄

yes

complemented

C₂×D₄×C₉

D₄

yes

—

C₂²×C₄×C₉

—

C₂²×C₄×C₉

—

C₂²×C₄×C₉

C₂³

yes

characteristic

C₉×M₁₆

—

C₉×M₁₆

—

C₂×C₈×C₉

—

C₉×C₄⋊C₄

D₄

yes

complemented

C₉×C₂²⋊C₄

—

C₉×C₂²⋊C₄

—

C₄²×C₉

—

C₄²×C₉

—

C₄²×C₉

C₂×C₄

yes

complemented

#1887

C₉

yes

characteristic, direct product factor, Sylow

C₂²×C₃×D₄

—

C₂²×C₃×D₄

C₂²×C₃

yes

characteristic

C₂²×C₃×D₄

C₂²×C₃

yes

characteristic

C₂×C₃×M₁₆

C₂²×C₃

yes

—

C₃×#127

—

C₃×#127

C₃×C₄

yes

—

C₃×C₄×D₄

—

C₃×#117

C₂²×C₃

yes

—

C₂×C₃×C₂²⋊C₄

—

C₂×C₃×C₄²

C₂²×C₃

yes

characteristic

C₃×#102

—

C₃×#100

—

C₂³×C₉

—

C₂³×C₉

—

C₂³×C₉

—

C₂³×C₉

—

C₂³×C₉

—

C₂³×C₉

—

C₂³×C₉

—

C₂³×C₉

C₂²⋊C₄

yes

—

C₂³×C₉

C₂×D₄

yes

characteristic

D₄×C₉

—

D₄×C₉

—

D₄×C₉

—

D₄×C₉

—

D₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₉

C₂×D₄

yes

—

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

#41

yes

—

C₈×C₉

—

C₂×#127

C₂×C₉

yes

characteristic

#518

C₂×C₉

yes

characteristic, complemented

#418

C₂×C₉

yes

complemented

C₂×#100

C₂×C₉

yes

characteristic, complemented

#339

C₂×C₉

yes

complemented

C₂⁴×C₃

—

C₂⁴×C₃

C₃×D₄

yes

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×C₃×D₄

C₂×C₃×C₄

yes

—

C₂×C₃×D₄

C₂×C₃×C₄

yes

—

100

C₂×C₃×D₄

C₃×D₄

yes

—

101

C₂²×C₃×C₄

—

102

C₂²×C₃×C₄

—

103

C₂²×C₃×C₄

C₂³×C₃

yes

characteristic

104

C₃×M₁₆

—

105

C₃×M₁₆

—

106

C₂×C₃×C₈

—

107

C₃×C₄⋊C₄

C₃×D₄

yes

—

108

C₃×C₂²⋊C₄

—

109

C₃×C₂²⋊C₄

—

110

C₃×C₄²

—

111

C₃×C₄²

—

112

C₃×C₄²

C₂×C₃×C₄

yes

—

113

C₂²×C₉

—

114

C₂²×C₉

—

115

C₂²×C₉

—

116

C₂²×C₉

—

117

C₂²×C₉

—

118

C₂²×C₉

—

119

C₂²×C₉

—

120

C₂²×C₉

—

121

C₂²×C₉

—

122

C₂²×C₉

C₂×C₂²⋊C₄

yes

characteristic

123

C₂²×C₉

#120

yes

characteristic

124

C₂²×C₉

#123

yes

characteristic

125

C₄×C₉

—

126

C₄×C₉

—

127

C₄×C₉

C₄×D₄

yes

—

128

C₄×C₉

#121

yes

—

129

C₂²×D₄

—

130

C₂²×D₄

C₂²×C₉

yes

characteristic

131

C₂²×D₄

C₂²×C₉

yes

characteristic

132

C₂×M₁₆

C₂²×C₉

yes

—

133

#127

—

134

#127

C₄×C₉

yes

complemented

135

C₄×D₄

—

136

#117

C₂²×C₉

yes

—

137

C₂×C₂²⋊C₄

—

138

C₂×C₄²

C₂²×C₉

yes

characteristic

139

#102

—

140

#100

—

141

C₂³×C₃

—

142

C₂³×C₃

—

143

C₂³×C₃

—

144

C₂³×C₃

—

145

C₂³×C₃

—

146

C₂³×C₃

—

147

C₂³×C₃

—

148

C₂³×C₃

C₃×C₂²⋊C₄

yes

—

149

C₂³×C₃

C₂×C₃×D₄

yes

characteristic

150

C₃×D₄

—

151

C₃×D₄

—

152

C₃×D₄

—

153

C₃×D₄

—

154

C₃×D₄

—

155

C₂×C₃×C₄

—

156

C₂×C₃×C₄

—

157

C₂×C₃×C₄

—

158

C₂×C₃×C₄

—

159

C₂×C₃×C₄

C₂²×C₃×C₄

yes

characteristic

160

C₂×C₃×C₄

C₂×C₃×D₄

yes

—

161

C₂×C₃×C₄

C₂×C₃×D₄

yes

characteristic

162

C₂×C₃×C₄

C₃×#41

yes

—

163

C₃×C₈

—

164

C₂×C₉

—

165

C₂×C₉

—

166

C₂×C₉

—

167

C₂×C₉

—

168

C₂×C₉

#386

yes

characteristic

169

C₂×C₉

#453

yes

—

170

C₂⁴

—

171

C₂⁴

D₄×C₉

yes

—

172

C₂×D₄

—

173

C₂×D₄

—

174

C₂×D₄

—

175

C₂×D₄

—

176

C₂×D₄

—

177

C₂×D₄

—

178

C₂×D₄

—

179

C₂×D₄

C₂×C₄×C₉

yes

—

180

C₂×D₄

C₂×C₄×C₉

yes

complemented

181

C₂×D₄

D₄×C₉

yes

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

C₂³×C₉

yes

characteristic

185

M₁₆

—

186

M₁₆

—

187

C₂×C₈

—

188

C₄⋊C₄

D₄×C₉

yes

complemented

189

C₂²⋊C₄

—

190

C₂²⋊C₄

—

191

C₄²

—

192

C₄²

—

193

C₄²

C₂×C₄×C₉

yes

complemented

194

C₂²×C₃

—

195

C₂²×C₃

—

196

C₂²×C₃

—

197

C₂²×C₃

—

198

C₂²×C₃

—

199

C₂²×C₃

—

200

C₂²×C₃

—

201

C₂²×C₃

—

202

C₂²×C₃

—

203

C₂²×C₃

C₂×C₃×C₂²⋊C₄

yes

characteristic

204

C₂²×C₃

C₃×#120

yes

characteristic

205

C₂²×C₃

C₃×#123

yes

characteristic

206

C₃×C₄

—

207

C₃×C₄

—

208

C₃×C₄

C₃×C₄×D₄

yes

—

209

C₃×C₄

C₃×#121

yes

—

210

C₉

#1887

yes

characteristic, direct product factor, Sylow

211

C₂³

—

212

C₂³

—

213

C₂³

—

214

C₂³

—

215

C₂³

—

216

C₂³

—

217

C₂³

—

218

C₂³

C₉×C₂²⋊C₄

yes

—

219

C₂³

C₂×D₄×C₉

yes

characteristic

220

D₄

—

221

D₄

—

222

D₄

—

223

D₄

—

224

D₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

C₂²×C₄×C₉

yes

characteristic

230

C₂×C₄

C₂×D₄×C₉

yes

—

231

C₂×C₄

C₂×D₄×C₉

yes

characteristic

232

C₂×C₄

C₉×#41

yes

—

233

C₈

—

234

C₂×C₃

—

235

C₂×C₃

—

236

C₂×C₃

—

237

C₂×C₃

—

238

C₂×C₃

C₃×#386

yes

characteristic

239

C₂×C₃

C₃×#453

yes

—

240

C₂²

—

241

C₂²

—

242

C₂²

—

243

C₂²

—

244

C₂²

—

245

C₂²

—

246

C₂²

—

247

C₂²

—

248

C₂²

—

249

C₂²

C₂×C₉×C₂²⋊C₄

yes

characteristic

250

C₂²

C₉×#120

yes

characteristic

251

C₂²

C₉×#123

yes

characteristic

252

C₄

—

253

C₄

—

254

C₄

C₄×D₄×C₉

yes

—

255

C₄

C₉×#121

yes

—

256

C₃

C₃×#1887

yes

characteristic

257

C₂

—

258

C₂

—

259

C₂

—

260

C₂

—

261

C₂

C₉×#386

yes

characteristic

262

C₂

C₉×#453

yes

—

	subgroup	G/H
center	C₂²×C₉	#120
commutator	C₂×C₄	C₂²×C₄×C₉
Frattini, cosocle	C₂²×C₃×C₄	C₂³×C₃
socle	C₂²×C₃	C₃×#120
prime radical	C₂×C₃×#127	C₂×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₂²×C₄×C₉ ◁ G

subgroup

G/H

center

C₂²×C₉

#120

commutator

C₂×C₄

C₂²×C₄×C₉

Frattini, cosocle

C₂²×C₃×C₄

C₂³×C₃

socle

C₂²×C₃

C₃×#120

prime radical

C₂×C₃×#127

C₂×C₃

LCS

G ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₉ ◁ C₂²×C₄×C₉ ◁ G

N	H ≅ G/N	type
2. C₉×#518	C₂	semidirect
3. C₉×#418	C₂	semidirect
4. C₂×C₉×#100	C₂	semidirect
5. C₉×#339	C₂	semidirect
12. C₉×#127	C₄	semidirect
34. C₂×D₄×C₉	C₂×C₄	semidirect
42. C₉×C₄⋊C₄	D₄	semidirect
47. C₄²×C₉	C₂×C₄	semidirect
48. #1887	C₉	direct (N × H)
85. #518	C₂×C₉	semidirect
86. #418	C₂×C₉	semidirect
87. C₂×#100	C₂×C₉	semidirect
88. #339	C₂×C₉	semidirect
134. #127	C₄×C₉	semidirect
180. C₂×D₄	C₂×C₄×C₉	semidirect
188. C₄⋊C₄	D₄×C₉	semidirect
193. C₄²	C₂×C₄×C₉	semidirect
210. C₉	#1887	direct (N × H)

H ≅ G/N

type

2. C₉×#518

C₂

semidirect

3. C₉×#418

C₂

semidirect

4. C₂×C₉×#100

C₂

semidirect

5. C₉×#339

C₂

semidirect

12. C₉×#127

C₄

semidirect

34. C₂×D₄×C₉

C₂×C₄

semidirect

42. C₉×C₄⋊C₄

D₄

semidirect

47. C₄²×C₉

C₂×C₄

semidirect

48. #1887

C₉

direct (N × H)

85. #518

C₂×C₉

semidirect

86. #418

C₂×C₉

semidirect

87. C₂×#100

C₂×C₉

semidirect

88. #339

C₂×C₉

semidirect

134. #127

C₄×C₉

semidirect

180. C₂×D₄

C₂×C₄×C₉

semidirect

188. C₄⋊C₄

D₄×C₉

semidirect

193. C₄²

C₂×C₄×C₉

semidirect

210. C₉

#1887

direct (N × H)

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

subgroup	index
C₂×C₉×#127	2
C₉×#518	2
C₉×#418	2
C₂×C₉×#100	2
C₉×#339	2
C₃×#1887	3

subgroup

index

C₂×C₉×#127

C₂×C₉×#100

Subgroups — C₉×#1887 #11766608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C9×#1887 #11766608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#1887 #11766608