Subgroups — C₉×#2334 #11767055

Order 1152.

714 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#126	C₂	1	1	yes	maximal, characteristic
2	C₉×#389	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#389	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#388	C₂	1	1	yes	maximal, characteristic
5	C₉×#388	C₂	1	1	yes	maximal, characteristic
6	C₉×#388	C₂	1	1	yes	maximal, characteristic
7	C₉×#387	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#387	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#387	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#385	C₂	1	1	yes	maximal, characteristic
11	C₉×#385	C₂	1	1	yes	maximal, characteristic
12	C₉×#382	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
16	C₃×#2334	C₃	1	1	yes	maximal, characteristic
17	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
18	C₉×#126	C₄	1	8	yes	complemented
19	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
36	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
37	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
38	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
39	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
40	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
41	C₉×#95	C₂²	1	1	yes	characteristic
42	C₉×#95	C₂²	1	1	yes	characteristic
43	C₉×#95	C₂²	1	1	yes	characteristic
44	C₉×#95	C₂²	1	1	yes	characteristic
45	C₉×#95	C₂²	1	1	yes	characteristic
46	C₉×#95	C₂²	1	1	yes	characteristic
47	C₉×#95	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	C₂×C₃×#126	C₂×C₃	1	1	yes	characteristic
54	C₃×#389	C₂×C₃	1	1	yes	characteristic
55	C₃×#389	C₂×C₃	1	1	yes	characteristic
56	C₃×#388	C₂×C₃	1	1	yes	characteristic
57	C₃×#388	C₂×C₃	1	1	yes	characteristic
58	C₃×#388	C₂×C₃	1	1	yes	characteristic
59	C₃×#387	C₂×C₃	1	1	yes	characteristic
60	C₃×#387	C₂×C₃	1	1	yes	characteristic
61	C₃×#387	C₂×C₃	1	1	yes	characteristic
62	C₃×#385	C₂×C₃	1	1	yes	characteristic
63	C₃×#385	C₂×C₃	1	1	yes	characteristic
64	C₃×#382	C₂×C₃	1	1	yes	characteristic
65	C₃×C₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
66	C₃×C₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
67	C₃×C₄×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
68	C₂⁴×C₉	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₉	—	2	2	no	—
70	C₂²×C₄×C₉	—	4	1	no	—
71	C₂²×C₄×C₉	—	4	1	no	—
72	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
74	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
75	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
76	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
77	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
78	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
79	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
80	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
81	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
82	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
83	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
84	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
85	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
86	C₉×C₄⋊C₄	—	2	2	no	—
87	C₉×C₄⋊C₄	—	2	2	no	—
88	C₉×C₄⋊C₄	—	2	2	no	—
89	C₉×C₄⋊C₄	—	4	1	no	—
90	C₉×C₄⋊C₄	—	4	1	no	—
91	C₉×C₄⋊C₄	—	4	1	no	—
92	C₉×C₄⋊C₄	—	4	1	no	—
93	C₉×C₄⋊C₄	C₂×C₄	1	4	yes	complemented
94	C₉×C₄⋊C₄	C₂×C₄	1	4	yes	complemented
95	C₉×C₄⋊C₄	C₂×C₄	1	4	yes	complemented
96	C₉×C₂²⋊C₄	—	2	2	no	—
97	C₉×C₂²⋊C₄	—	4	1	no	—
98	C₉×C₂²⋊C₄	—	4	1	no	—
99	C₉×C₂²⋊C₄	C₂×C₄	1	4	yes	—
100	C₉×C₂²⋊C₄	C₂×C₄	1	4	yes	—
101	C₉×C₂²⋊C₄	C₂×C₄	1	4	yes	—
102	C₄²×C₉	—	2	2	no	—
103	C₄²×C₉	—	4	1	no	—
104	C₄²×C₉	—	4	1	no	—
105	C₄²×C₉	—	4	1	no	—
106	C₄²×C₉	—	4	1	no	—
107	C₄²×C₉	C₂×C₄	1	4	yes	complemented
108	#2334	C₉	1	1	yes	characteristic, direct product factor, Sylow
109	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
110	C₃×#126	C₃×C₄	1	8	yes	—
111	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
112	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
113	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
114	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
115	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
116	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
117	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
118	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
119	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
120	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
121	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
122	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
123	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
124	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
125	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
126	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
128	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
129	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
130	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
131	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
132	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
133	C₃×#95	C₂²×C₃	1	1	yes	characteristic
134	C₃×#95	C₂²×C₃	1	1	yes	characteristic
135	C₃×#95	C₂²×C₃	1	1	yes	characteristic
136	C₃×#95	C₂²×C₃	1	1	yes	characteristic
137	C₃×#95	C₂²×C₃	1	1	yes	characteristic
138	C₃×#95	C₂²×C₃	1	1	yes	characteristic
139	C₃×#95	C₂²×C₃	1	1	yes	characteristic
140	C₃×#95	C₂²×C₃	1	1	yes	characteristic
141	C₃×#95	C₂²×C₃	1	1	yes	characteristic
142	C₃×#95	C₂²×C₃	1	1	yes	characteristic
143	C₃×#95	C₂²×C₃	1	1	yes	characteristic
144	C₃×#95	C₂²×C₃	1	1	yes	characteristic
145	C₂³×C₉	—	2	1	no	—
146	C₂³×C₉	—	2	1	no	—
147	C₂³×C₉	—	2	1	no	—
148	C₂³×C₉	—	2	1	no	—
149	C₂³×C₉	—	2	1	no	—
150	C₂³×C₉	—	2	1	no	—
151	C₂³×C₉	C₂²×C₄	1	2	yes	—
152	C₂³×C₉	C₂⁴	1	1	yes	characteristic
153	C₂×C₄×C₉	—	2	1	no	—
154	C₂×C₄×C₉	—	2	1	no	—
155	C₂×C₄×C₉	—	2	1	no	—
156	C₂×C₄×C₉	—	2	1	no	—
157	C₂×C₄×C₉	—	2	1	no	—
158	C₂×C₄×C₉	—	2	1	no	—
159	C₂×C₄×C₉	—	2	1	no	—
160	C₂×C₄×C₉	—	2	1	no	—
161	C₂×C₄×C₉	—	2	1	no	—
162	C₂×C₄×C₉	—	2	1	no	—
163	C₂×C₄×C₉	—	2	1	no	—
164	C₂×C₄×C₉	—	2	1	no	—
165	C₂×C₄×C₉	—	2	1	no	—
166	C₂×C₄×C₉	—	2	1	no	—
167	C₂×C₄×C₉	—	2	1	no	—
168	C₂×C₄×C₉	—	2	1	no	—
169	C₂×C₄×C₉	—	2	1	no	—
170	C₂×C₄×C₉	—	2	1	no	—
171	C₂×C₄×C₉	—	2	1	no	—
172	C₂×C₄×C₉	—	2	1	no	—
173	C₂×C₄×C₉	—	2	1	no	—
174	C₂×C₄×C₉	—	2	1	no	—
175	C₂×C₄×C₉	—	2	1	no	—
176	C₂×C₄×C₉	—	2	1	no	—
177	C₂×C₄×C₉	—	2	1	no	—
178	C₂×C₄×C₉	—	2	1	no	—
179	C₂×C₄×C₉	—	2	1	no	—
180	C₂×C₄×C₉	—	2	1	no	—
181	C₂×C₄×C₉	—	2	1	no	—
182	C₂×C₄×C₉	—	2	1	no	—
183	C₂×C₄×C₉	—	2	1	no	—
184	C₂×C₄×C₉	—	2	1	no	—
185	C₂×C₄×C₉	—	2	1	no	—
186	C₂×C₄×C₉	—	2	1	no	—
187	C₂×C₄×C₉	—	4	4	no	—
188	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
189	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
190	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
191	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
192	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
193	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
194	C₂×C₄×C₉	#41	1	2	yes	—
195	C₂×C₄×C₉	#41	1	2	yes	—
196	C₂×#126	C₂×C₉	1	1	yes	characteristic
197	#389	C₂×C₉	1	1	yes	characteristic, complemented
198	#389	C₂×C₉	1	1	yes	characteristic, complemented
199	#388	C₂×C₉	1	1	yes	characteristic
200	#388	C₂×C₉	1	1	yes	characteristic
201	#388	C₂×C₉	1	1	yes	characteristic
202	#387	C₂×C₉	1	1	yes	characteristic, complemented
203	#387	C₂×C₉	1	1	yes	characteristic, complemented
204	#387	C₂×C₉	1	1	yes	characteristic, complemented
205	#385	C₂×C₉	1	1	yes	characteristic
206	#385	C₂×C₉	1	1	yes	characteristic
207	#382	C₂×C₉	1	1	yes	characteristic, complemented
208	C₄×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
209	C₄×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
210	C₄×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic
211	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
212	C₂²×C₃×C₄	—	2	2	no	—
213	C₂²×C₃×C₄	—	4	1	no	—
214	C₂²×C₃×C₄	—	4	1	no	—
215	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
216	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
217	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
218	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
219	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
220	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
221	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
222	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
223	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
224	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
225	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
226	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
227	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
228	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
229	C₃×C₄⋊C₄	—	2	2	no	—
230	C₃×C₄⋊C₄	—	2	2	no	—
231	C₃×C₄⋊C₄	—	2	2	no	—
232	C₃×C₄⋊C₄	—	4	1	no	—
233	C₃×C₄⋊C₄	—	4	1	no	—
234	C₃×C₄⋊C₄	—	4	1	no	—
235	C₃×C₄⋊C₄	—	4	1	no	—
236	C₃×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
237	C₃×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
238	C₃×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
239	C₃×C₂²⋊C₄	—	2	2	no	—
240	C₃×C₂²⋊C₄	—	4	1	no	—
241	C₃×C₂²⋊C₄	—	4	1	no	—
242	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	4	yes	—
243	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	4	yes	—
244	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	4	yes	—
245	C₃×C₄²	—	2	2	no	—
246	C₃×C₄²	—	4	1	no	—
247	C₃×C₄²	—	4	1	no	—
248	C₃×C₄²	—	4	1	no	—
249	C₃×C₄²	—	4	1	no	—
250	C₃×C₄²	C₂×C₃×C₄	1	4	yes	—
251	C₂²×C₉	—	2	2	no	—
252	C₂²×C₉	—	2	2	no	—
253	C₂²×C₉	—	2	2	no	—
254	C₂²×C₉	—	4	1	no	—
255	C₂²×C₉	—	4	1	no	—
256	C₂²×C₉	—	4	1	no	—
257	C₂²×C₉	—	4	1	no	—
258	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
259	C₂²×C₉	C₂×#41	1	1	yes	characteristic
260	C₂²×C₉	C₂×#41	1	1	yes	characteristic
261	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
262	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
263	C₂²×C₉	2₋¹⁺⁴	1	1	yes	characteristic
264	C₂²×C₉	2₋¹⁺⁴	1	1	yes	characteristic
265	C₄×C₉	—	2	2	no	—
266	C₄×C₉	—	2	2	no	—
267	C₄×C₉	—	2	2	no	—
268	C₄×C₉	—	2	2	no	—
269	C₄×C₉	—	2	2	no	—
270	C₄×C₉	—	2	2	no	—
271	C₄×C₉	—	2	2	no	—
272	C₄×C₉	—	2	2	no	—
273	C₄×C₉	—	4	1	no	—
274	C₄×C₉	—	4	1	no	—
275	C₄×C₉	—	4	1	no	—
276	C₄×C₉	—	4	1	no	—
277	C₄×C₉	—	4	1	no	—
278	C₄×C₉	—	4	1	no	—
279	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
280	#126	C₄×C₉	1	8	yes	complemented
281	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
282	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
283	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
291	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
292	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
293	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
294	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
295	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
296	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
297	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
298	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
299	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
300	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
301	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
302	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
303	#95	C₂²×C₉	1	1	yes	characteristic
304	#95	C₂²×C₉	1	1	yes	characteristic
305	#95	C₂²×C₉	1	1	yes	characteristic
306	#95	C₂²×C₉	1	1	yes	characteristic
307	#95	C₂²×C₉	1	1	yes	characteristic
308	#95	C₂²×C₉	1	1	yes	characteristic
309	#95	C₂²×C₉	1	1	yes	characteristic
310	#95	C₂²×C₉	1	1	yes	characteristic
311	#95	C₂²×C₉	1	1	yes	characteristic
312	#95	C₂²×C₉	1	1	yes	characteristic
313	#95	C₂²×C₉	1	1	yes	characteristic
314	#95	C₂²×C₉	1	1	yes	characteristic
315	C₂³×C₃	—	2	1	no	—
316	C₂³×C₃	—	2	1	no	—
317	C₂³×C₃	—	2	1	no	—
318	C₂³×C₃	—	2	1	no	—
319	C₂³×C₃	—	2	1	no	—
320	C₂³×C₃	—	2	1	no	—
321	C₂³×C₃	C₂²×C₃×C₄	1	2	yes	—
322	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
323	C₂×C₃×C₄	—	2	1	no	—
324	C₂×C₃×C₄	—	2	1	no	—
325	C₂×C₃×C₄	—	2	1	no	—
326	C₂×C₃×C₄	—	2	1	no	—
327	C₂×C₃×C₄	—	2	1	no	—
328	C₂×C₃×C₄	—	2	1	no	—
329	C₂×C₃×C₄	—	2	1	no	—
330	C₂×C₃×C₄	—	2	1	no	—
331	C₂×C₃×C₄	—	2	1	no	—
332	C₂×C₃×C₄	—	2	1	no	—
333	C₂×C₃×C₄	—	2	1	no	—
334	C₂×C₃×C₄	—	2	1	no	—
335	C₂×C₃×C₄	—	2	1	no	—
336	C₂×C₃×C₄	—	2	1	no	—
337	C₂×C₃×C₄	—	2	1	no	—
338	C₂×C₃×C₄	—	2	1	no	—
339	C₂×C₃×C₄	—	2	1	no	—
340	C₂×C₃×C₄	—	2	1	no	—
341	C₂×C₃×C₄	—	2	1	no	—
342	C₂×C₃×C₄	—	2	1	no	—
343	C₂×C₃×C₄	—	2	1	no	—
344	C₂×C₃×C₄	—	2	1	no	—
345	C₂×C₃×C₄	—	2	1	no	—
346	C₂×C₃×C₄	—	2	1	no	—
347	C₂×C₃×C₄	—	2	1	no	—
348	C₂×C₃×C₄	—	2	1	no	—
349	C₂×C₃×C₄	—	2	1	no	—
350	C₂×C₃×C₄	—	2	1	no	—
351	C₂×C₃×C₄	—	2	1	no	—
352	C₂×C₃×C₄	—	2	1	no	—
353	C₂×C₃×C₄	—	2	1	no	—
354	C₂×C₃×C₄	—	2	1	no	—
355	C₂×C₃×C₄	—	2	1	no	—
356	C₂×C₃×C₄	—	2	1	no	—
357	C₂×C₃×C₄	—	4	4	no	—
358	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
359	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
360	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
361	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
362	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
363	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
364	C₂×C₃×C₄	C₃×#41	1	2	yes	—
365	C₂×C₃×C₄	C₃×#41	1	2	yes	—
366	C₂×C₉	—	4	2	no	—
367	C₂×C₉	C₄×#41	1	1	yes	characteristic
368	C₂×C₉	#520	1	1	yes	characteristic
369	C₂×C₉	#520	1	1	yes	characteristic
370	C₂×C₉	#538	1	1	yes	characteristic
371	C₂×C₉	#539	1	1	yes	characteristic
372	C₂×C₉	#541	1	1	yes	characteristic
373	C₂×C₉	#542	1	1	yes	characteristic
374	C₂⁴	C₂³×C₉	1	1	yes	characteristic
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	4	1	no	—
377	C₂²×C₄	—	4	1	no	—
378	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
379	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
380	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
381	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
382	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
383	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
384	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
385	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
386	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
387	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
388	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
389	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
390	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
391	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	4	1	no	—
396	C₄⋊C₄	—	4	1	no	—
397	C₄⋊C₄	—	4	1	no	—
398	C₄⋊C₄	—	4	1	no	—
399	C₄⋊C₄	C₂×C₄×C₉	1	4	yes	complemented
400	C₄⋊C₄	C₂×C₄×C₉	1	4	yes	complemented
401	C₄⋊C₄	C₂×C₄×C₉	1	4	yes	complemented
402	C₂²⋊C₄	—	2	2	no	—
403	C₂²⋊C₄	—	4	1	no	—
404	C₂²⋊C₄	—	4	1	no	—
405	C₂²⋊C₄	C₂×C₄×C₉	1	4	yes	—
406	C₂²⋊C₄	C₂×C₄×C₉	1	4	yes	—
407	C₂²⋊C₄	C₂×C₄×C₉	1	4	yes	—
408	C₄²	—	2	2	no	—
409	C₄²	—	4	1	no	—
410	C₄²	—	4	1	no	—
411	C₄²	—	4	1	no	—
412	C₄²	—	4	1	no	—
413	C₄²	C₂×C₄×C₉	1	4	yes	complemented
414	C₂²×C₃	—	2	2	no	—
415	C₂²×C₃	—	2	2	no	—
416	C₂²×C₃	—	2	2	no	—
417	C₂²×C₃	—	4	1	no	—
418	C₂²×C₃	—	4	1	no	—
419	C₂²×C₃	—	4	1	no	—
420	C₂²×C₃	—	4	1	no	—
421	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
422	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
423	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
424	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
425	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
426	C₂²×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
427	C₂²×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
428	C₃×C₄	—	2	2	no	—
429	C₃×C₄	—	2	2	no	—
430	C₃×C₄	—	2	2	no	—
431	C₃×C₄	—	2	2	no	—
432	C₃×C₄	—	2	2	no	—
433	C₃×C₄	—	2	2	no	—
434	C₃×C₄	—	2	2	no	—
435	C₃×C₄	—	2	2	no	—
436	C₃×C₄	—	4	1	no	—
437	C₃×C₄	—	4	1	no	—
438	C₃×C₄	—	4	1	no	—
439	C₃×C₄	—	4	1	no	—
440	C₃×C₄	—	4	1	no	—
441	C₃×C₄	—	4	1	no	—
442	C₉	#2334	1	1	yes	characteristic, direct product factor, Sylow
443	C₂³	—	2	1	no	—
444	C₂³	—	2	1	no	—
445	C₂³	—	2	1	no	—
446	C₂³	—	2	1	no	—
447	C₂³	—	2	1	no	—
448	C₂³	—	2	1	no	—
449	C₂³	C₂²×C₄×C₉	1	2	yes	—
450	C₂³	C₂⁴×C₉	1	1	yes	characteristic
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	4	4	no	—
486	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
487	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
488	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
489	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
490	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
491	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
492	C₂×C₄	C₉×#41	1	2	yes	—
493	C₂×C₄	C₉×#41	1	2	yes	—
494	C₂×C₃	—	4	2	no	—
495	C₂×C₃	C₃×C₄×#41	1	1	yes	characteristic
496	C₂×C₃	C₃×#520	1	1	yes	characteristic
497	C₂×C₃	C₃×#520	1	1	yes	characteristic
498	C₂×C₃	C₃×#538	1	1	yes	characteristic
499	C₂×C₃	C₃×#539	1	1	yes	characteristic
500	C₂×C₃	C₃×#541	1	1	yes	characteristic
501	C₂×C₃	C₃×#542	1	1	yes	characteristic
502	C₂²	—	2	2	no	—
503	C₂²	—	2	2	no	—
504	C₂²	—	2	2	no	—
505	C₂²	—	4	1	no	—
506	C₂²	—	4	1	no	—
507	C₂²	—	4	1	no	—
508	C₂²	—	4	1	no	—
509	C₂²	C₂³×C₄×C₉	1	1	yes	characteristic
510	C₂²	C₂×C₉×#41	1	1	yes	characteristic
511	C₂²	C₂×C₉×#41	1	1	yes	characteristic
512	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
513	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
514	C₂²	C₉×2₋¹⁺⁴	1	1	yes	characteristic
515	C₂²	C₉×2₋¹⁺⁴	1	1	yes	characteristic
516	C₄	—	2	2	no	—
517	C₄	—	2	2	no	—
518	C₄	—	2	2	no	—
519	C₄	—	2	2	no	—
520	C₄	—	2	2	no	—
521	C₄	—	2	2	no	—
522	C₄	—	2	2	no	—
523	C₄	—	2	2	no	—
524	C₄	—	4	1	no	—
525	C₄	—	4	1	no	—
526	C₄	—	4	1	no	—
527	C₄	—	4	1	no	—
528	C₄	—	4	1	no	—
529	C₄	—	4	1	no	—
530	C₃	C₃×#2334	1	1	yes	characteristic
531	C₂	—	4	2	no	—
532	C₂	C₄×C₉×#41	1	1	yes	characteristic
533	C₂	C₉×#520	1	1	yes	characteristic
534	C₂	C₉×#520	1	1	yes	characteristic
535	C₂	C₉×#538	1	1	yes	characteristic
536	C₂	C₉×#539	1	1	yes	characteristic
537	C₂	C₉×#541	1	1	yes	characteristic
538	C₂	C₉×#542	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₉
Frattini, socle, cosocle	C₂³×C₃	C₂⁴×C₃
prime radical	C₂⁴×C₃	C₂³×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₉×#389	C₂	semidirect
3. C₉×#389	C₂	semidirect
7. C₉×#387	C₂	semidirect
8. C₉×#387	C₂	semidirect
9. C₉×#387	C₂	semidirect
12. C₉×#382	C₂	semidirect
13. C₄×C₉×C₄⋊C₄	C₂	semidirect
14. C₄×C₉×C₄⋊C₄	C₂	semidirect
18. C₉×#126	C₄	semidirect
93. C₉×C₄⋊C₄	C₂×C₄	semidirect
94. C₉×C₄⋊C₄	C₂×C₄	semidirect
95. C₉×C₄⋊C₄	C₂×C₄	semidirect
107. C₄²×C₉	C₂×C₄	semidirect
108. #2334	C₉	direct (N × H)
197. #389	C₂×C₉	semidirect
198. #389	C₂×C₉	semidirect
202. #387	C₂×C₉	semidirect
203. #387	C₂×C₉	semidirect
204. #387	C₂×C₉	semidirect
207. #382	C₂×C₉	semidirect
208. C₄×C₄⋊C₄	C₂×C₉	semidirect
209. C₄×C₄⋊C₄	C₂×C₉	semidirect
280. #126	C₄×C₉	semidirect
399. C₄⋊C₄	C₂×C₄×C₉	semidirect
400. C₄⋊C₄	C₂×C₄×C₉	semidirect
401. C₄⋊C₄	C₂×C₄×C₉	semidirect
413. C₄²	C₂×C₄×C₉	semidirect
442. C₉	#2334	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₉×#126	2
C₉×#389	2
C₉×#388	2
C₉×#387	2
C₉×#385	2
C₉×#382	2
C₄×C₉×C₄⋊C₄	2
C₄×C₉×C₂²⋊C₄	2
C₃×#2334	3

Subgroups — C9×#2334 #11767055

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2334 #11767055