Subgroups — C₉×#2443 #11767164

Order 1152.

1011 conjugacy classes of subgroups.

The subgroup lattice has 681 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#123	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#121	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#399	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#398	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#397	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#394	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#388	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#387	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#386	C₂	1	1	yes	maximal, characteristic, complemented
12	C₉×#386	C₂	1	1	yes	maximal, characteristic, complemented
13	C₉×#386	C₂	1	1	yes	maximal, characteristic, complemented
14	C₉×#385	C₂	1	1	yes	maximal, characteristic, complemented
15	C₉×#385	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2443	C₃	1	1	yes	maximal, characteristic
17	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
18	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
19	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
20	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
21	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
22	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
23	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
24	C₉×#123	—	2	4	no	—
25	C₉×#121	—	2	4	no	—
26	C₄×D₄×C₉	—	2	4	no	—
27	C₂×C₉×C₄⋊C₄	—	2	4	no	—
28	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
43	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
45	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
46	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
47	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
48	C₉×#95	C₂²	1	1	yes	characteristic
49	C₉×#95	C₂²	1	1	yes	characteristic
50	C₉×#95	C₂²	1	1	yes	characteristic
51	C₉×#95	C₂²	1	1	yes	characteristic
52	C₉×#95	C₂²	1	1	yes	characteristic
53	C₉×#95	C₂²	1	1	yes	characteristic
54	C₉×#95	C₂²	1	1	yes	characteristic
55	C₉×#95	C₂²	1	1	yes	characteristic
56	C₂×C₃×#123	C₂×C₃	1	1	yes	characteristic
57	C₂×C₃×#121	C₂×C₃	1	1	yes	characteristic
58	C₂×C₃×C₄×D₄	C₂×C₃	1	1	yes	characteristic
59	C₂²×C₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
60	C₃×#399	C₂×C₃	1	1	yes	characteristic
61	C₃×#398	C₂×C₃	1	1	yes	characteristic
62	C₃×#397	C₂×C₃	1	1	yes	characteristic
63	C₃×#394	C₂×C₃	1	1	yes	characteristic
64	C₃×#388	C₂×C₃	1	1	yes	characteristic
65	C₃×#387	C₂×C₃	1	1	yes	characteristic
66	C₃×#386	C₂×C₃	1	1	yes	characteristic
67	C₃×#386	C₂×C₃	1	1	yes	characteristic
68	C₃×#386	C₂×C₃	1	1	yes	characteristic
69	C₃×#385	C₂×C₃	1	1	yes	characteristic
70	C₃×#385	C₂×C₃	1	1	yes	characteristic
71	C₂⁴×C₉	C₂³	1	1	yes	characteristic
72	C₂⁴×C₉	C₂³	1	1	yes	characteristic
73	C₂⁴×C₉	C₂³	1	1	yes	characteristic
74	C₂×D₄×C₉	—	2	2	no	—
75	C₂×D₄×C₉	—	2	2	no	—
76	C₂×D₄×C₉	—	2	2	no	—
77	C₂×D₄×C₉	—	2	2	no	—
78	C₂×D₄×C₉	—	2	2	no	—
79	C₂×D₄×C₉	—	2	2	no	—
80	C₂×D₄×C₉	—	2	2	no	—
81	C₂×D₄×C₉	—	4	1	no	—
82	C₂×D₄×C₉	D₄	1	4	yes	—
83	C₂²×C₄×C₉	—	2	2	no	—
84	C₂²×C₄×C₉	—	2	2	no	—
85	C₂²×C₄×C₉	—	2	2	no	—
86	C₂²×C₄×C₉	—	2	2	no	—
87	C₂²×C₄×C₉	—	2	2	no	—
88	C₂²×C₄×C₉	—	2	2	no	—
89	C₂²×C₄×C₉	—	2	2	no	—
90	C₂²×C₄×C₉	—	2	2	no	—
91	C₂²×C₄×C₉	—	2	2	no	—
92	C₂²×C₄×C₉	—	4	1	no	—
93	C₂²×C₄×C₉	—	4	1	no	—
94	C₂²×C₄×C₉	—	4	1	no	—
95	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
96	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
97	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
98	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
99	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
100	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
101	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
102	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
103	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
104	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
105	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
106	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
107	C₉×C₄⋊C₄	—	2	2	no	—
108	C₉×C₄⋊C₄	—	2	2	no	—
109	C₉×C₄⋊C₄	—	2	2	no	—
110	C₉×C₄⋊C₄	—	2	2	no	—
111	C₉×C₄⋊C₄	—	2	2	no	—
112	C₉×C₄⋊C₄	—	2	2	no	—
113	C₉×C₄⋊C₄	—	4	1	no	—
114	C₉×C₄⋊C₄	D₄	1	4	yes	complemented
115	C₉×C₂²⋊C₄	—	2	2	no	—
116	C₉×C₂²⋊C₄	—	2	2	no	—
117	C₉×C₂²⋊C₄	—	2	2	no	—
118	C₉×C₂²⋊C₄	—	2	2	no	—
119	C₉×C₂²⋊C₄	—	2	2	no	—
120	C₉×C₂²⋊C₄	—	2	2	no	—
121	C₉×C₂²⋊C₄	—	2	2	no	—
122	C₉×C₂²⋊C₄	—	2	2	no	—
123	C₉×C₂²⋊C₄	—	2	2	no	—
124	C₉×C₂²⋊C₄	—	2	2	no	—
125	C₉×C₂²⋊C₄	—	4	1	no	—
126	C₄²×C₉	—	2	2	no	—
127	#2443	C₉	1	1	yes	characteristic, direct product factor, Sylow
128	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
129	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
130	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
131	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
132	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
133	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
134	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
135	C₃×#123	—	2	4	no	—
136	C₃×#121	—	2	4	no	—
137	C₃×C₄×D₄	—	2	4	no	—
138	C₂×C₃×C₄⋊C₄	—	2	4	no	—
139	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
140	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
141	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
142	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
143	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
144	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
145	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
146	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
147	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
148	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
149	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
150	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
151	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
152	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
153	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
154	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
155	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
156	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
157	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
158	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
159	C₃×#95	C₂²×C₃	1	1	yes	characteristic
160	C₃×#95	C₂²×C₃	1	1	yes	characteristic
161	C₃×#95	C₂²×C₃	1	1	yes	characteristic
162	C₃×#95	C₂²×C₃	1	1	yes	characteristic
163	C₃×#95	C₂²×C₃	1	1	yes	characteristic
164	C₃×#95	C₂²×C₃	1	1	yes	characteristic
165	C₃×#95	C₂²×C₃	1	1	yes	characteristic
166	C₃×#95	C₂²×C₃	1	1	yes	characteristic
167	C₂³×C₉	—	2	1	no	—
168	C₂³×C₉	—	2	1	no	—
169	C₂³×C₉	—	2	1	no	—
170	C₂³×C₉	—	2	1	no	—
171	C₂³×C₉	—	2	1	no	—
172	C₂³×C₉	—	2	1	no	—
173	C₂³×C₉	—	2	1	no	—
174	C₂³×C₉	—	2	1	no	—
175	C₂³×C₉	—	2	1	no	—
176	C₂³×C₉	—	2	1	no	—
177	C₂³×C₉	—	2	1	no	—
178	C₂³×C₉	—	2	1	no	—
179	C₂³×C₉	—	2	1	no	—
180	C₂³×C₉	—	2	1	no	—
181	C₂³×C₉	—	2	1	no	—
182	C₂³×C₉	—	2	1	no	—
183	C₂³×C₉	—	2	1	no	—
184	C₂³×C₉	C₂×D₄	1	2	yes	—
185	C₂³×C₉	C₂×D₄	1	2	yes	—
186	C₂³×C₉	#41	1	2	yes	—
187	C₂³×C₉	#41	1	2	yes	—
188	C₂³×C₉	C₂⁴	1	1	yes	characteristic
189	D₄×C₉	—	2	8	no	—
190	D₄×C₉	—	4	4	no	—
191	D₄×C₉	—	4	4	no	—
192	C₂×C₄×C₉	—	2	8	no	—
193	C₂×C₄×C₉	—	2	1	no	—
194	C₂×C₄×C₉	—	2	1	no	—
195	C₂×C₄×C₉	—	2	1	no	—
196	C₂×C₄×C₉	—	2	1	no	—
197	C₂×C₄×C₉	—	2	1	no	—
198	C₂×C₄×C₉	—	2	1	no	—
199	C₂×C₄×C₉	—	2	1	no	—
200	C₂×C₄×C₉	—	2	1	no	—
201	C₂×C₄×C₉	—	2	1	no	—
202	C₂×C₄×C₉	—	2	1	no	—
203	C₂×C₄×C₉	—	2	1	no	—
204	C₂×C₄×C₉	—	2	1	no	—
205	C₂×C₄×C₉	—	2	1	no	—
206	C₂×C₄×C₉	—	2	1	no	—
207	C₂×C₄×C₉	—	2	1	no	—
208	C₂×C₄×C₉	—	2	1	no	—
209	C₂×C₄×C₉	—	2	1	no	—
210	C₂×C₄×C₉	—	2	1	no	—
211	C₂×C₄×C₉	—	2	1	no	—
212	C₂×C₄×C₉	—	2	1	no	—
213	C₂×C₄×C₉	—	2	1	no	—
214	C₂×C₄×C₉	—	2	1	no	—
215	C₂×C₄×C₉	—	2	1	no	—
216	C₂×C₄×C₉	—	2	1	no	—
217	C₂×C₄×C₉	—	2	1	no	—
218	C₂×C₄×C₉	—	2	1	no	—
219	C₂×C₄×C₉	—	2	1	no	—
220	C₂×C₄×C₉	—	2	1	no	—
221	C₂×C₄×C₉	—	2	1	no	—
222	C₂×C₄×C₉	—	2	1	no	—
223	C₂×C₄×C₉	—	2	1	no	—
224	C₂×C₄×C₉	—	4	4	no	—
225	C₂×C₄×C₉	—	4	4	no	—
226	C₂×C₄×C₉	—	4	4	no	—
227	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
228	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
229	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
230	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
231	C₂×C₄×C₉	#41	1	2	yes	—
232	C₂×#123	C₂×C₉	1	1	yes	characteristic, complemented
233	C₂×#121	C₂×C₉	1	1	yes	characteristic
234	C₂×C₄×D₄	C₂×C₉	1	1	yes	characteristic, complemented
235	C₂²×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
236	#399	C₂×C₉	1	1	yes	characteristic, complemented
237	#398	C₂×C₉	1	1	yes	characteristic, complemented
238	#397	C₂×C₉	1	1	yes	characteristic, complemented
239	#394	C₂×C₉	1	1	yes	characteristic, complemented
240	#388	C₂×C₉	1	1	yes	characteristic, complemented
241	#387	C₂×C₉	1	1	yes	characteristic, complemented
242	#386	C₂×C₉	1	1	yes	characteristic, complemented
243	#386	C₂×C₉	1	1	yes	characteristic, complemented
244	#386	C₂×C₉	1	1	yes	characteristic, complemented
245	#385	C₂×C₉	1	1	yes	characteristic, complemented
246	#385	C₂×C₉	1	1	yes	characteristic, complemented
247	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
248	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
249	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
250	C₂×C₃×D₄	—	2	2	no	—
251	C₂×C₃×D₄	—	2	2	no	—
252	C₂×C₃×D₄	—	2	2	no	—
253	C₂×C₃×D₄	—	2	2	no	—
254	C₂×C₃×D₄	—	2	2	no	—
255	C₂×C₃×D₄	—	2	2	no	—
256	C₂×C₃×D₄	—	2	2	no	—
257	C₂×C₃×D₄	—	4	1	no	—
258	C₂×C₃×D₄	C₃×D₄	1	4	yes	—
259	C₂²×C₃×C₄	—	2	2	no	—
260	C₂²×C₃×C₄	—	2	2	no	—
261	C₂²×C₃×C₄	—	2	2	no	—
262	C₂²×C₃×C₄	—	2	2	no	—
263	C₂²×C₃×C₄	—	2	2	no	—
264	C₂²×C₃×C₄	—	2	2	no	—
265	C₂²×C₃×C₄	—	2	2	no	—
266	C₂²×C₃×C₄	—	2	2	no	—
267	C₂²×C₃×C₄	—	2	2	no	—
268	C₂²×C₃×C₄	—	4	1	no	—
269	C₂²×C₃×C₄	—	4	1	no	—
270	C₂²×C₃×C₄	—	4	1	no	—
271	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
272	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
273	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
274	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
275	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
276	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
277	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
278	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
279	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
280	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
281	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
282	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
283	C₃×C₄⋊C₄	—	2	2	no	—
284	C₃×C₄⋊C₄	—	2	2	no	—
285	C₃×C₄⋊C₄	—	2	2	no	—
286	C₃×C₄⋊C₄	—	2	2	no	—
287	C₃×C₄⋊C₄	—	2	2	no	—
288	C₃×C₄⋊C₄	—	2	2	no	—
289	C₃×C₄⋊C₄	—	4	1	no	—
290	C₃×C₄⋊C₄	C₃×D₄	1	4	yes	—
291	C₃×C₂²⋊C₄	—	2	2	no	—
292	C₃×C₂²⋊C₄	—	2	2	no	—
293	C₃×C₂²⋊C₄	—	2	2	no	—
294	C₃×C₂²⋊C₄	—	2	2	no	—
295	C₃×C₂²⋊C₄	—	2	2	no	—
296	C₃×C₂²⋊C₄	—	2	2	no	—
297	C₃×C₂²⋊C₄	—	2	2	no	—
298	C₃×C₂²⋊C₄	—	2	2	no	—
299	C₃×C₂²⋊C₄	—	2	2	no	—
300	C₃×C₂²⋊C₄	—	2	2	no	—
301	C₃×C₂²⋊C₄	—	4	1	no	—
302	C₃×C₄²	—	2	2	no	—
303	C₂²×C₉	—	2	2	no	—
304	C₂²×C₉	—	2	2	no	—
305	C₂²×C₉	—	2	2	no	—
306	C₂²×C₉	—	2	2	no	—
307	C₂²×C₉	—	2	2	no	—
308	C₂²×C₉	—	2	2	no	—
309	C₂²×C₉	—	2	2	no	—
310	C₂²×C₉	—	2	2	no	—
311	C₂²×C₉	—	2	2	no	—
312	C₂²×C₉	—	4	1	no	—
313	C₂²×C₉	—	4	1	no	—
314	C₂²×C₉	—	4	1	no	—
315	C₂²×C₉	—	4	1	no	—
316	C₂²×C₉	—	4	1	no	—
317	C₂²×C₉	—	4	1	no	—
318	C₂²×C₉	—	4	1	no	—
319	C₂²×C₉	—	4	1	no	—
320	C₂²×C₉	—	4	1	no	—
321	C₂²×C₉	—	4	1	no	—
322	C₂²×C₉	—	4	1	no	—
323	C₂²×C₉	#123	1	4	yes	complemented
324	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
325	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
326	C₂²×C₉	C₂×#41	1	1	yes	characteristic
327	C₂²×C₉	C₂×#41	1	1	yes	characteristic
328	C₂²×C₉	C₂×#41	1	1	yes	characteristic
329	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
330	C₂²×C₉	2₋¹⁺⁴	1	1	yes	characteristic
331	C₄×C₉	—	2	2	no	—
332	C₄×C₉	—	2	2	no	—
333	C₄×C₉	—	2	2	no	—
334	C₄×C₉	—	2	2	no	—
335	C₄×C₉	—	2	2	no	—
336	C₄×C₉	—	4	1	no	—
337	C₄×C₉	—	4	1	no	—
338	C₄×C₉	—	4	1	no	—
339	C₄×C₉	—	4	1	no	—
340	C₄×C₉	—	4	1	no	—
341	C₄×C₉	—	4	1	no	—
342	C₄×C₉	—	4	1	no	—
343	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
344	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
345	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
346	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
347	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
348	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
349	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
350	#123	—	2	4	no	—
351	#121	—	2	4	no	—
352	C₄×D₄	—	2	4	no	—
353	C₂×C₄⋊C₄	—	2	4	no	—
354	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
355	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
356	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
358	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
359	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
360	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
362	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
363	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
364	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
365	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
366	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
367	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
368	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
369	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
370	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
371	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
372	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
373	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
374	#95	C₂²×C₉	1	1	yes	characteristic
375	#95	C₂²×C₉	1	1	yes	characteristic
376	#95	C₂²×C₉	1	1	yes	characteristic
377	#95	C₂²×C₉	1	1	yes	characteristic
378	#95	C₂²×C₉	1	1	yes	characteristic
379	#95	C₂²×C₉	1	1	yes	characteristic
380	#95	C₂²×C₉	1	1	yes	characteristic
381	#95	C₂²×C₉	1	1	yes	characteristic
382	C₂³×C₃	—	2	1	no	—
383	C₂³×C₃	—	2	1	no	—
384	C₂³×C₃	—	2	1	no	—
385	C₂³×C₃	—	2	1	no	—
386	C₂³×C₃	—	2	1	no	—
387	C₂³×C₃	—	2	1	no	—
388	C₂³×C₃	—	2	1	no	—
389	C₂³×C₃	—	2	1	no	—
390	C₂³×C₃	—	2	1	no	—
391	C₂³×C₃	—	2	1	no	—
392	C₂³×C₃	—	2	1	no	—
393	C₂³×C₃	—	2	1	no	—
394	C₂³×C₃	—	2	1	no	—
395	C₂³×C₃	—	2	1	no	—
396	C₂³×C₃	—	2	1	no	—
397	C₂³×C₃	—	2	1	no	—
398	C₂³×C₃	—	2	1	no	—
399	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
400	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
401	C₂³×C₃	C₃×#41	1	2	yes	—
402	C₂³×C₃	C₃×#41	1	2	yes	—
403	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
404	C₃×D₄	—	2	8	no	—
405	C₃×D₄	—	4	4	no	—
406	C₃×D₄	—	4	4	no	—
407	C₂×C₃×C₄	—	2	8	no	—
408	C₂×C₃×C₄	—	2	1	no	—
409	C₂×C₃×C₄	—	2	1	no	—
410	C₂×C₃×C₄	—	2	1	no	—
411	C₂×C₃×C₄	—	2	1	no	—
412	C₂×C₃×C₄	—	2	1	no	—
413	C₂×C₃×C₄	—	2	1	no	—
414	C₂×C₃×C₄	—	2	1	no	—
415	C₂×C₃×C₄	—	2	1	no	—
416	C₂×C₃×C₄	—	2	1	no	—
417	C₂×C₃×C₄	—	2	1	no	—
418	C₂×C₃×C₄	—	2	1	no	—
419	C₂×C₃×C₄	—	2	1	no	—
420	C₂×C₃×C₄	—	2	1	no	—
421	C₂×C₃×C₄	—	2	1	no	—
422	C₂×C₃×C₄	—	2	1	no	—
423	C₂×C₃×C₄	—	2	1	no	—
424	C₂×C₃×C₄	—	2	1	no	—
425	C₂×C₃×C₄	—	2	1	no	—
426	C₂×C₃×C₄	—	2	1	no	—
427	C₂×C₃×C₄	—	2	1	no	—
428	C₂×C₃×C₄	—	2	1	no	—
429	C₂×C₃×C₄	—	2	1	no	—
430	C₂×C₃×C₄	—	2	1	no	—
431	C₂×C₃×C₄	—	2	1	no	—
432	C₂×C₃×C₄	—	2	1	no	—
433	C₂×C₃×C₄	—	2	1	no	—
434	C₂×C₃×C₄	—	2	1	no	—
435	C₂×C₃×C₄	—	2	1	no	—
436	C₂×C₃×C₄	—	2	1	no	—
437	C₂×C₃×C₄	—	2	1	no	—
438	C₂×C₃×C₄	—	2	1	no	—
439	C₂×C₃×C₄	—	4	4	no	—
440	C₂×C₃×C₄	—	4	4	no	—
441	C₂×C₃×C₄	—	4	4	no	—
442	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
443	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
444	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
445	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
446	C₂×C₃×C₄	C₃×#41	1	2	yes	—
447	C₂×C₉	—	2	4	no	—
448	C₂×C₉	—	4	2	no	—
449	C₂×C₉	—	8	1	no	—
450	C₂×C₉	C₂×#123	1	1	yes	characteristic
451	C₂×C₉	#525	1	1	yes	characteristic
452	C₂×C₉	#539	1	1	yes	characteristic
453	C₂×C₉	D₄²	1	1	yes	characteristic
454	C₂×C₉	#547	1	1	yes	characteristic
455	C₂×C₉	#548	1	1	yes	characteristic
456	C₂×C₉	#553	1	1	yes	characteristic
457	C₂⁴	C₂³×C₉	1	1	yes	characteristic
458	C₂⁴	C₂³×C₉	1	1	yes	characteristic
459	C₂⁴	C₂³×C₉	1	1	yes	characteristic
460	C₂×D₄	—	2	2	no	—
461	C₂×D₄	—	2	2	no	—
462	C₂×D₄	—	2	2	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	—	2	2	no	—
467	C₂×D₄	—	4	1	no	—
468	C₂×D₄	D₄×C₉	1	4	yes	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	4	1	no	—
479	C₂²×C₄	—	4	1	no	—
480	C₂²×C₄	—	4	1	no	—
481	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
482	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
483	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
484	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
485	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
486	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
487	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
488	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
489	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
490	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
491	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
492	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	2	2	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	4	1	no	—
500	C₄⋊C₄	D₄×C₉	1	4	yes	complemented
501	C₂²⋊C₄	—	2	2	no	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	2	2	no	—
506	C₂²⋊C₄	—	2	2	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	—	4	1	no	—
512	C₄²	—	2	2	no	—
513	C₂²×C₃	—	2	2	no	—
514	C₂²×C₃	—	2	2	no	—
515	C₂²×C₃	—	2	2	no	—
516	C₂²×C₃	—	2	2	no	—
517	C₂²×C₃	—	2	2	no	—
518	C₂²×C₃	—	2	2	no	—
519	C₂²×C₃	—	2	2	no	—
520	C₂²×C₃	—	2	2	no	—
521	C₂²×C₃	—	2	2	no	—
522	C₂²×C₃	—	4	1	no	—
523	C₂²×C₃	—	4	1	no	—
524	C₂²×C₃	—	4	1	no	—
525	C₂²×C₃	—	4	1	no	—
526	C₂²×C₃	—	4	1	no	—
527	C₂²×C₃	—	4	1	no	—
528	C₂²×C₃	—	4	1	no	—
529	C₂²×C₃	—	4	1	no	—
530	C₂²×C₃	—	4	1	no	—
531	C₂²×C₃	—	4	1	no	—
532	C₂²×C₃	—	4	1	no	—
533	C₂²×C₃	C₃×#123	1	4	yes	—
534	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
535	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
536	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
537	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
538	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
539	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
540	C₂²×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
541	C₃×C₄	—	2	2	no	—
542	C₃×C₄	—	2	2	no	—
543	C₃×C₄	—	2	2	no	—
544	C₃×C₄	—	2	2	no	—
545	C₃×C₄	—	2	2	no	—
546	C₃×C₄	—	4	1	no	—
547	C₃×C₄	—	4	1	no	—
548	C₃×C₄	—	4	1	no	—
549	C₃×C₄	—	4	1	no	—
550	C₃×C₄	—	4	1	no	—
551	C₃×C₄	—	4	1	no	—
552	C₃×C₄	—	4	1	no	—
553	C₉	#2443	1	1	yes	characteristic, direct product factor, Sylow
554	C₂³	—	2	1	no	—
555	C₂³	—	2	1	no	—
556	C₂³	—	2	1	no	—
557	C₂³	—	2	1	no	—
558	C₂³	—	2	1	no	—
559	C₂³	—	2	1	no	—
560	C₂³	—	2	1	no	—
561	C₂³	—	2	1	no	—
562	C₂³	—	2	1	no	—
563	C₂³	—	2	1	no	—
564	C₂³	—	2	1	no	—
565	C₂³	—	2	1	no	—
566	C₂³	—	2	1	no	—
567	C₂³	—	2	1	no	—
568	C₂³	—	2	1	no	—
569	C₂³	—	2	1	no	—
570	C₂³	—	2	1	no	—
571	C₂³	C₂×D₄×C₉	1	2	yes	—
572	C₂³	C₂×D₄×C₉	1	2	yes	—
573	C₂³	C₉×#41	1	2	yes	—
574	C₂³	C₉×#41	1	2	yes	—
575	C₂³	C₂⁴×C₉	1	1	yes	characteristic
576	D₄	—	2	8	no	—
577	D₄	—	4	4	no	—
578	D₄	—	4	4	no	—
579	C₂×C₄	—	2	8	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	4	4	no	—
612	C₂×C₄	—	4	4	no	—
613	C₂×C₄	—	4	4	no	—
614	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
615	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
616	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
617	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
618	C₂×C₄	C₉×#41	1	2	yes	—
619	C₂×C₃	—	2	4	no	—
620	C₂×C₃	—	4	2	no	—
621	C₂×C₃	—	8	1	no	—
622	C₂×C₃	C₂×C₃×#123	1	1	yes	characteristic
623	C₂×C₃	C₃×#525	1	1	yes	characteristic
624	C₂×C₃	C₃×#539	1	1	yes	characteristic
625	C₂×C₃	C₃×D₄²	1	1	yes	characteristic
626	C₂×C₃	C₃×#547	1	1	yes	characteristic
627	C₂×C₃	C₃×#548	1	1	yes	characteristic
628	C₂×C₃	C₃×#553	1	1	yes	characteristic
629	C₂²	—	2	2	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	4	1	no	—
639	C₂²	—	4	1	no	—
640	C₂²	—	4	1	no	—
641	C₂²	—	4	1	no	—
642	C₂²	—	4	1	no	—
643	C₂²	—	4	1	no	—
644	C₂²	—	4	1	no	—
645	C₂²	—	4	1	no	—
646	C₂²	—	4	1	no	—
647	C₂²	—	4	1	no	—
648	C₂²	—	4	1	no	—
649	C₂²	C₉×#123	1	4	yes	complemented
650	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
651	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
652	C₂²	C₂×C₉×#41	1	1	yes	characteristic
653	C₂²	C₂×C₉×#41	1	1	yes	characteristic
654	C₂²	C₂×C₉×#41	1	1	yes	characteristic
655	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
656	C₂²	C₉×2₋¹⁺⁴	1	1	yes	characteristic
657	C₄	—	2	2	no	—
658	C₄	—	2	2	no	—
659	C₄	—	2	2	no	—
660	C₄	—	2	2	no	—
661	C₄	—	2	2	no	—
662	C₄	—	4	1	no	—
663	C₄	—	4	1	no	—
664	C₄	—	4	1	no	—
665	C₄	—	4	1	no	—
666	C₄	—	4	1	no	—
667	C₄	—	4	1	no	—
668	C₄	—	4	1	no	—
669	C₃	C₃×#2443	1	1	yes	characteristic
670	C₂	—	2	4	no	—
671	C₂	—	4	2	no	—
672	C₂	—	8	1	no	—
673	C₂	C₂×C₉×#123	1	1	yes	characteristic
674	C₂	C₉×#525	1	1	yes	characteristic
675	C₂	C₉×#539	1	1	yes	characteristic
676	C₂	D₄²×C₉	1	1	yes	characteristic
677	C₂	C₉×#547	1	1	yes	characteristic
678	C₂	C₉×#548	1	1	yes	characteristic
679	C₂	C₉×#553	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂⁴
commutator	C₂³	C₂⁴×C₉
Frattini, socle, cosocle	C₂³×C₃	C₂⁴×C₃
prime radical	C₂×C₃×#121	C₂×C₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₉×#123	C₂	semidirect
3. C₂×C₄×D₄×C₉	C₂	semidirect
4. C₂²×C₉×C₄⋊C₄	C₂	semidirect
5. C₉×#399	C₂	semidirect
6. C₉×#398	C₂	semidirect
7. C₉×#397	C₂	semidirect
8. C₉×#394	C₂	semidirect
9. C₉×#388	C₂	semidirect
10. C₉×#387	C₂	semidirect
11. C₉×#386	C₂	semidirect
12. C₉×#386	C₂	semidirect
13. C₉×#386	C₂	semidirect
14. C₉×#385	C₂	semidirect
15. C₉×#385	C₂	semidirect
114. C₉×C₄⋊C₄	D₄	semidirect
127. #2443	C₉	direct (N × H)
232. C₂×#123	C₂×C₉	semidirect
234. C₂×C₄×D₄	C₂×C₉	semidirect
235. C₂²×C₄⋊C₄	C₂×C₉	semidirect
236. #399	C₂×C₉	semidirect
237. #398	C₂×C₉	semidirect
238. #397	C₂×C₉	semidirect
239. #394	C₂×C₉	semidirect
240. #388	C₂×C₉	semidirect
241. #387	C₂×C₉	semidirect
242. #386	C₂×C₉	semidirect
243. #386	C₂×C₉	semidirect
244. #386	C₂×C₉	semidirect
245. #385	C₂×C₉	semidirect
246. #385	C₂×C₉	semidirect
323. C₂²×C₉	#123	semidirect
500. C₄⋊C₄	D₄×C₉	semidirect
553. C₉	#2443	direct (N × H)
649. C₂²	C₉×#123	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×#123	2
C₂×C₉×#121	2
C₂×C₄×D₄×C₉	2
C₂²×C₉×C₄⋊C₄	2
C₉×#399	2
C₉×#398	2
C₉×#397	2
C₉×#394	2
C₉×#388	2
C₉×#387	2
C₉×#386	2
C₉×#385	2
C₃×#2443	3

Subgroups — C9×#2443 #11767164

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2443 #11767164