Subgroups — C₄×C₉×#121 #11767021

Order 1152.

1236 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#121	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₄×C₉	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄²×C₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#390	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#389	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#388	C₂	1	2	yes	maximal, complemented
8	C₉×#386	C₂	1	2	yes	maximal, complemented
9	C₉×#380	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₉×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
12	C₃×C₄×#121	C₃	1	1	yes	maximal, characteristic
13	C₂²×D₄×C₉	C₂²	1	2	yes	—
14	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
15	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
16	C₂³×C₄×C₉	C₂²	1	2	yes	—
17	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
18	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
19	C₉×#121	C₄	1	8	yes	direct product factor
20	C₄×D₄×C₉	—	2	8	no	—
21	C₄×D₄×C₉	—	2	4	no	—
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	2	yes	—
25	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₂×C₄²×C₉	—	2	4	no	—
32	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
33	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
34	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
35	C₂×C₄²×C₉	C₂²	1	2	yes	—
36	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
37	C₉×#95	C₂²	1	2	yes	—
38	C₉×#95	C₂²	1	2	yes	—
39	C₉×#95	C₂²	1	2	yes	—
40	C₂×C₃×#121	C₂×C₃	1	1	yes	characteristic
41	C₂×C₃×C₄×D₄	C₂×C₃	1	2	yes	—
42	C₂×C₃×C₄×D₄	C₂×C₃	1	1	yes	characteristic
43	C₂²×C₃×C₄²	C₂×C₃	1	1	yes	characteristic
44	C₃×#390	C₂×C₃	1	1	yes	characteristic
45	C₃×#389	C₂×C₃	1	1	yes	characteristic
46	C₃×#388	C₂×C₃	1	2	yes	—
47	C₃×#386	C₂×C₃	1	2	yes	—
48	C₃×#380	C₂×C₃	1	1	yes	characteristic
49	C₃×C₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
50	C₃×C₄×C₂²⋊C₄	C₂×C₃	1	2	yes	—
51	C₂⁴×C₉	C₂³	1	2	yes	—
52	C₂⁴×C₉	C₂³	1	1	yes	characteristic
53	C₂×D₄×C₉	—	2	4	no	—
54	C₂×D₄×C₉	—	2	4	no	—
55	C₂×D₄×C₉	—	2	2	no	—
56	C₂×D₄×C₉	—	2	2	no	—
57	C₂×D₄×C₉	C₂×C₄	1	8	yes	complemented
58	C₂×D₄×C₉	C₂×C₄	1	4	yes	complemented
59	C₂²×C₄×C₉	—	2	2	no	—
60	C₂²×C₄×C₉	—	2	2	no	—
61	C₂²×C₄×C₉	—	2	2	no	—
62	C₂²×C₄×C₉	—	2	2	no	—
63	C₂²×C₄×C₉	—	2	2	no	—
64	C₂²×C₄×C₉	—	2	2	no	—
65	C₂²×C₄×C₉	—	2	2	no	—
66	C₂²×C₄×C₉	—	2	4	no	—
67	C₂²×C₄×C₉	—	2	4	no	—
68	C₂²×C₄×C₉	—	2	4	no	—
69	C₂²×C₄×C₉	C₂×C₄	1	4	yes	complemented
70	C₂²×C₄×C₉	D₄	1	4	yes	complemented
71	C₂²×C₄×C₉	C₂³	1	2	yes	—
72	C₂²×C₄×C₉	C₂³	1	2	yes	—
73	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
74	C₂²×C₄×C₉	C₂³	1	2	yes	—
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	C₉×C₄⋊C₄	—	2	4	no	—
81	C₉×C₄⋊C₄	—	2	2	no	—
82	C₉×C₄⋊C₄	—	2	2	no	—
83	C₉×C₄⋊C₄	C₂×C₄	1	4	yes	complemented
84	C₉×C₂²⋊C₄	—	2	4	no	—
85	C₉×C₂²⋊C₄	—	2	4	no	—
86	C₉×C₂²⋊C₄	—	2	4	no	—
87	C₉×C₂²⋊C₄	—	2	4	no	—
88	C₉×C₂²⋊C₄	C₂×C₄	1	8	yes	complemented
89	C₄²×C₉	—	2	2	no	—
90	C₄²×C₉	—	2	2	no	—
91	C₄²×C₉	—	2	2	no	—
92	C₄²×C₉	—	2	4	no	—
93	C₄²×C₉	D₄	1	4	yes	complemented
94	C₄×#121	C₉	1	1	yes	characteristic, direct product factor, Sylow
95	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
96	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
97	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
98	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
99	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
100	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
101	C₃×#121	C₃×C₄	1	8	yes	—
102	C₃×C₄×D₄	—	2	8	no	—
103	C₃×C₄×D₄	—	2	4	no	—
104	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
105	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
107	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
108	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
109	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
110	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
111	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
112	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
113	C₂×C₃×C₄²	—	2	4	no	—
114	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
115	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
116	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
117	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
118	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
119	C₃×#95	C₂²×C₃	1	2	yes	—
120	C₃×#95	C₂²×C₃	1	2	yes	—
121	C₃×#95	C₂²×C₃	1	2	yes	—
122	C₂³×C₉	—	2	1	no	—
123	C₂³×C₉	—	2	1	no	—
124	C₂³×C₉	—	2	1	no	—
125	C₂³×C₉	—	2	1	no	—
126	C₂³×C₉	—	2	2	no	—
127	C₂³×C₉	—	2	2	no	—
128	C₂³×C₉	—	2	2	no	—
129	C₂³×C₉	—	2	2	no	—
130	C₂³×C₉	—	2	2	no	—
131	C₂³×C₉	—	2	2	no	—
132	C₂³×C₉	C₂²×C₄	1	4	yes	—
133	C₂³×C₉	C₂²×C₄	1	2	yes	—
134	C₂³×C₉	C₂×D₄	1	2	yes	—
135	C₂³×C₉	#41	1	2	yes	—
136	C₂³×C₉	C₂⁴	1	1	yes	characteristic
137	D₄×C₉	—	2	16	no	—
138	D₄×C₉	—	2	8	no	—
139	C₂×C₄×C₉	—	2	8	no	—
140	C₂×C₄×C₉	—	2	1	no	—
141	C₂×C₄×C₉	—	2	1	no	—
142	C₂×C₄×C₉	—	2	1	no	—
143	C₂×C₄×C₉	—	2	2	no	—
144	C₂×C₄×C₉	—	2	1	no	—
145	C₂×C₄×C₉	—	2	1	no	—
146	C₂×C₄×C₉	—	2	1	no	—
147	C₂×C₄×C₉	—	2	1	no	—
148	C₂×C₄×C₉	—	2	1	no	—
149	C₂×C₄×C₉	—	2	2	no	—
150	C₂×C₄×C₉	—	2	8	no	—
151	C₂×C₄×C₉	—	2	8	no	—
152	C₂×C₄×C₉	—	2	2	no	—
153	C₂×C₄×C₉	—	2	2	no	—
154	C₂×C₄×C₉	—	2	2	no	—
155	C₂×C₄×C₉	—	2	2	no	—
156	C₂×C₄×C₉	—	2	2	no	—
157	C₂×C₄×C₉	—	2	2	no	—
158	C₂×C₄×C₉	—	4	8	no	—
159	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
160	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
161	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
162	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
163	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
164	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
165	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
166	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
167	C₂×C₄×C₉	#41	1	2	yes	—
168	C₂×C₄×C₉	#41	1	2	yes	—
169	C₂×C₄×C₉	#41	1	2	yes	—
170	C₂×#121	C₂×C₉	1	1	yes	characteristic
171	C₂×C₄×D₄	C₂×C₉	1	2	yes	complemented
172	C₂×C₄×D₄	C₂×C₉	1	1	yes	characteristic, complemented
173	C₂²×C₄²	C₂×C₉	1	1	yes	characteristic, complemented
174	#390	C₂×C₉	1	1	yes	characteristic, complemented
175	#389	C₂×C₉	1	1	yes	characteristic, complemented
176	#388	C₂×C₉	1	2	yes	complemented
177	#386	C₂×C₉	1	2	yes	complemented
178	#380	C₂×C₉	1	1	yes	characteristic, complemented
179	C₄×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
180	C₄×C₂²⋊C₄	C₂×C₉	1	2	yes	complemented
181	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
182	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
183	C₂×C₃×D₄	—	2	4	no	—
184	C₂×C₃×D₄	—	2	4	no	—
185	C₂×C₃×D₄	—	2	2	no	—
186	C₂×C₃×D₄	—	2	2	no	—
187	C₂×C₃×D₄	C₂×C₃×C₄	1	8	yes	—
188	C₂×C₃×D₄	C₂×C₃×C₄	1	4	yes	—
189	C₂²×C₃×C₄	—	2	2	no	—
190	C₂²×C₃×C₄	—	2	2	no	—
191	C₂²×C₃×C₄	—	2	2	no	—
192	C₂²×C₃×C₄	—	2	2	no	—
193	C₂²×C₃×C₄	—	2	2	no	—
194	C₂²×C₃×C₄	—	2	2	no	—
195	C₂²×C₃×C₄	—	2	2	no	—
196	C₂²×C₃×C₄	—	2	4	no	—
197	C₂²×C₃×C₄	—	2	4	no	—
198	C₂²×C₃×C₄	—	2	4	no	—
199	C₂²×C₃×C₄	C₂×C₃×C₄	1	4	yes	—
200	C₂²×C₃×C₄	C₃×D₄	1	4	yes	—
201	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
202	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
203	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
204	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
205	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
206	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
207	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
208	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
209	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
210	C₃×C₄⋊C₄	—	2	4	no	—
211	C₃×C₄⋊C₄	—	2	2	no	—
212	C₃×C₄⋊C₄	—	2	2	no	—
213	C₃×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
214	C₃×C₂²⋊C₄	—	2	4	no	—
215	C₃×C₂²⋊C₄	—	2	4	no	—
216	C₃×C₂²⋊C₄	—	2	4	no	—
217	C₃×C₂²⋊C₄	—	2	4	no	—
218	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	—
219	C₃×C₄²	—	2	2	no	—
220	C₃×C₄²	—	2	2	no	—
221	C₃×C₄²	—	2	2	no	—
222	C₃×C₄²	—	2	4	no	—
223	C₃×C₄²	C₃×D₄	1	4	yes	—
224	C₂²×C₉	—	2	2	no	—
225	C₂²×C₉	—	2	2	no	—
226	C₂²×C₉	—	2	2	no	—
227	C₂²×C₉	—	2	2	no	—
228	C₂²×C₉	—	2	2	no	—
229	C₂²×C₉	—	2	2	no	—
230	C₂²×C₉	—	2	4	no	—
231	C₂²×C₉	—	2	4	no	—
232	C₂²×C₉	—	2	4	no	—
233	C₂²×C₉	—	4	2	no	—
234	C₂²×C₉	—	4	2	no	—
235	C₂²×C₉	—	4	2	no	—
236	C₂²×C₉	—	4	2	no	—
237	C₂²×C₉	C₄×D₄	1	4	yes	complemented
238	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
239	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
240	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
241	C₂²×C₉	C₂×#41	1	1	yes	characteristic
242	C₂²×C₉	C₂×#41	1	1	yes	characteristic
243	C₂²×C₉	C₂×#41	1	1	yes	characteristic
244	C₂²×C₉	C₂×#41	1	1	yes	characteristic
245	C₄×C₉	—	2	2	no	—
246	C₄×C₉	—	2	4	no	—
247	C₄×C₉	—	2	2	no	—
248	C₄×C₉	—	2	2	no	—
249	C₄×C₉	—	2	2	no	—
250	C₄×C₉	—	4	2	no	—
251	C₄×C₉	—	4	2	no	—
252	C₄×C₉	C₄×D₄	1	4	yes	complemented
253	C₄×C₉	#121	1	4	yes	direct product factor
254	C₂²×D₄	C₂²×C₉	1	2	yes	—
255	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
256	C₂³×C₄	C₂²×C₉	1	2	yes	—
257	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
258	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
259	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
260	#121	C₄×C₉	1	8	yes	direct product factor
261	C₄×D₄	—	2	8	no	—
262	C₄×D₄	—	2	4	no	—
263	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
264	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
265	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
266	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
267	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
268	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
269	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
270	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
271	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
272	C₂×C₄²	—	2	4	no	—
273	C₂×C₄²	C₂²×C₉	1	2	yes	—
274	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
275	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
276	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
277	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
278	#95	C₂²×C₉	1	2	yes	—
279	#95	C₂²×C₉	1	2	yes	—
280	#95	C₂²×C₉	1	2	yes	—
281	C₂³×C₃	—	2	1	no	—
282	C₂³×C₃	—	2	1	no	—
283	C₂³×C₃	—	2	1	no	—
284	C₂³×C₃	—	2	1	no	—
285	C₂³×C₃	—	2	2	no	—
286	C₂³×C₃	—	2	2	no	—
287	C₂³×C₃	—	2	2	no	—
288	C₂³×C₃	—	2	2	no	—
289	C₂³×C₃	—	2	2	no	—
290	C₂³×C₃	—	2	2	no	—
291	C₂³×C₃	C₂²×C₃×C₄	1	4	yes	—
292	C₂³×C₃	C₂²×C₃×C₄	1	2	yes	—
293	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
294	C₂³×C₃	C₃×#41	1	2	yes	—
295	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
296	C₃×D₄	—	2	16	no	—
297	C₃×D₄	—	2	8	no	—
298	C₂×C₃×C₄	—	2	8	no	—
299	C₂×C₃×C₄	—	2	1	no	—
300	C₂×C₃×C₄	—	2	1	no	—
301	C₂×C₃×C₄	—	2	1	no	—
302	C₂×C₃×C₄	—	2	2	no	—
303	C₂×C₃×C₄	—	2	1	no	—
304	C₂×C₃×C₄	—	2	1	no	—
305	C₂×C₃×C₄	—	2	1	no	—
306	C₂×C₃×C₄	—	2	1	no	—
307	C₂×C₃×C₄	—	2	1	no	—
308	C₂×C₃×C₄	—	2	2	no	—
309	C₂×C₃×C₄	—	2	8	no	—
310	C₂×C₃×C₄	—	2	8	no	—
311	C₂×C₃×C₄	—	2	2	no	—
312	C₂×C₃×C₄	—	2	2	no	—
313	C₂×C₃×C₄	—	2	2	no	—
314	C₂×C₃×C₄	—	2	2	no	—
315	C₂×C₃×C₄	—	2	2	no	—
316	C₂×C₃×C₄	—	2	2	no	—
317	C₂×C₃×C₄	—	4	8	no	—
318	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
319	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
320	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
321	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
322	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
323	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
324	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
325	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
326	C₂×C₃×C₄	C₃×#41	1	2	yes	—
327	C₂×C₃×C₄	C₃×#41	1	2	yes	—
328	C₂×C₃×C₄	C₃×#41	1	2	yes	—
329	C₂×C₉	—	2	4	no	—
330	C₂×C₉	—	4	4	no	—
331	C₂×C₉	C₂×C₄×D₄	1	1	yes	characteristic
332	C₂×C₉	C₂×C₄×D₄	1	1	yes	characteristic
333	C₂×C₉	C₄×#41	1	1	yes	characteristic
334	C₂×C₉	C₂×#121	1	1	yes	characteristic
335	C₂×C₉	#525	1	1	yes	characteristic
336	C₂×C₉	#529	1	1	yes	characteristic
337	C₂×C₉	#532	1	1	yes	characteristic
338	C₂⁴	C₂³×C₉	1	2	yes	—
339	C₂⁴	C₂³×C₉	1	1	yes	characteristic
340	C₂×D₄	—	2	4	no	—
341	C₂×D₄	—	2	4	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	C₂×C₄×C₉	1	8	yes	complemented
345	C₂×D₄	C₂×C₄×C₉	1	4	yes	complemented
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	C₂×C₄×C₉	1	4	yes	complemented
357	C₂²×C₄	D₄×C₉	1	4	yes	complemented
358	C₂²×C₄	C₂³×C₉	1	2	yes	—
359	C₂²×C₄	C₂³×C₉	1	2	yes	—
360	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
361	C₂²×C₄	C₂³×C₉	1	2	yes	—
362	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
363	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
364	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
365	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
366	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	C₂×C₄×C₉	1	4	yes	complemented
371	C₂²⋊C₄	—	2	4	no	—
372	C₂²⋊C₄	—	2	4	no	—
373	C₂²⋊C₄	—	2	4	no	—
374	C₂²⋊C₄	—	2	4	no	—
375	C₂²⋊C₄	C₂×C₄×C₉	1	8	yes	complemented
376	C₄²	—	2	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	2	no	—
379	C₄²	—	2	4	no	—
380	C₄²	D₄×C₉	1	4	yes	complemented
381	C₂²×C₃	—	2	2	no	—
382	C₂²×C₃	—	2	2	no	—
383	C₂²×C₃	—	2	2	no	—
384	C₂²×C₃	—	2	2	no	—
385	C₂²×C₃	—	2	2	no	—
386	C₂²×C₃	—	2	2	no	—
387	C₂²×C₃	—	2	4	no	—
388	C₂²×C₃	—	2	4	no	—
389	C₂²×C₃	—	2	4	no	—
390	C₂²×C₃	—	4	2	no	—
391	C₂²×C₃	—	4	2	no	—
392	C₂²×C₃	—	4	2	no	—
393	C₂²×C₃	—	4	2	no	—
394	C₂²×C₃	C₃×C₄×D₄	1	4	yes	—
395	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
396	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
397	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
398	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
399	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
400	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
401	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
402	C₃×C₄	—	2	2	no	—
403	C₃×C₄	—	2	4	no	—
404	C₃×C₄	—	2	2	no	—
405	C₃×C₄	—	2	2	no	—
406	C₃×C₄	—	2	2	no	—
407	C₃×C₄	—	4	2	no	—
408	C₃×C₄	—	4	2	no	—
409	C₃×C₄	C₃×C₄×D₄	1	4	yes	—
410	C₃×C₄	C₃×#121	1	4	yes	—
411	C₉	C₄×#121	1	1	yes	characteristic, direct product factor, Sylow
412	C₂³	—	2	1	no	—
413	C₂³	—	2	1	no	—
414	C₂³	—	2	1	no	—
415	C₂³	—	2	1	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	2	2	no	—
418	C₂³	—	2	2	no	—
419	C₂³	—	2	2	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	2	2	no	—
422	C₂³	C₂²×C₄×C₉	1	4	yes	—
423	C₂³	C₂²×C₄×C₉	1	2	yes	—
424	C₂³	C₂×D₄×C₉	1	2	yes	—
425	C₂³	C₉×#41	1	2	yes	—
426	C₂³	C₂⁴×C₉	1	1	yes	characteristic
427	D₄	—	2	16	no	—
428	D₄	—	2	8	no	—
429	C₂×C₄	—	2	8	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	8	no	—
441	C₂×C₄	—	2	8	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	4	8	no	—
449	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
450	C₂×C₄	C₂²×C₄×C₉	1	4	yes	—
451	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
452	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
453	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
454	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
455	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
456	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
457	C₂×C₄	C₉×#41	1	2	yes	—
458	C₂×C₄	C₉×#41	1	2	yes	—
459	C₂×C₄	C₉×#41	1	2	yes	—
460	C₂×C₃	—	2	4	no	—
461	C₂×C₃	—	4	4	no	—
462	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
463	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
464	C₂×C₃	C₃×C₄×#41	1	1	yes	characteristic
465	C₂×C₃	C₂×C₃×#121	1	1	yes	characteristic
466	C₂×C₃	C₃×#525	1	1	yes	characteristic
467	C₂×C₃	C₃×#529	1	1	yes	characteristic
468	C₂×C₃	C₃×#532	1	1	yes	characteristic
469	C₂²	—	2	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	4	no	—
476	C₂²	—	2	4	no	—
477	C₂²	—	2	4	no	—
478	C₂²	—	4	2	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	4	2	no	—
481	C₂²	—	4	2	no	—
482	C₂²	C₄×D₄×C₉	1	4	yes	complemented
483	C₂²	C₂³×C₄×C₉	1	1	yes	characteristic
484	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
485	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
486	C₂²	C₂×C₉×#41	1	1	yes	characteristic
487	C₂²	C₂×C₉×#41	1	1	yes	characteristic
488	C₂²	C₂×C₉×#41	1	1	yes	characteristic
489	C₂²	C₂×C₉×#41	1	1	yes	characteristic
490	C₄	—	2	2	no	—
491	C₄	—	2	2	no	—
492	C₄	—	2	2	no	—
493	C₄	—	2	2	no	—
494	C₄	—	2	4	no	—
495	C₄	—	4	2	no	—
496	C₄	—	4	2	no	—
497	C₄	C₄×D₄×C₉	1	4	yes	complemented
498	C₄	C₉×#121	1	4	yes	direct product factor
499	C₃	C₃×C₄×#121	1	1	yes	characteristic
500	C₂	—	2	4	no	—
501	C₂	—	4	4	no	—
502	C₂	C₂×C₄×D₄×C₉	1	1	yes	characteristic
503	C₂	C₂×C₄×D₄×C₉	1	1	yes	characteristic
504	C₂	C₄×C₉×#41	1	1	yes	characteristic
505	C₂	C₂×C₉×#121	1	1	yes	characteristic
506	C₂	C₉×#525	1	1	yes	characteristic
507	C₂	C₉×#529	1	1	yes	characteristic
508	C₂	C₉×#532	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₉	C₂³
commutator	C₂²	C₂³×C₄×C₉
Frattini, socle, cosocle	C₂³×C₃	C₂⁴×C₃
prime radical	C₂×C₃×#121	C₂×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×D₄×C₉	C₂	semidirect
3. C₂×C₄×D₄×C₉	C₂	semidirect
4. C₂²×C₄²×C₉	C₂	semidirect
5. C₉×#390	C₂	semidirect
6. C₉×#389	C₂	semidirect
7. C₉×#388	C₂	semidirect
8. C₉×#386	C₂	semidirect
9. C₉×#380	C₂	semidirect
10. C₄×C₉×C₄⋊C₄	C₂	semidirect
11. C₄×C₉×C₂²⋊C₄	C₂	semidirect
19. C₉×#121	C₄	direct (N × H)
57. C₂×D₄×C₉	C₂×C₄	semidirect
58. C₂×D₄×C₉	C₂×C₄	semidirect
69. C₂²×C₄×C₉	C₂×C₄	semidirect
70. C₂²×C₄×C₉	D₄	semidirect
83. C₉×C₄⋊C₄	C₂×C₄	semidirect
88. C₉×C₂²⋊C₄	C₂×C₄	semidirect
93. C₄²×C₉	D₄	semidirect
94. C₄×#121	C₉	direct (N × H)
171. C₂×C₄×D₄	C₂×C₉	semidirect
172. C₂×C₄×D₄	C₂×C₉	semidirect
173. C₂²×C₄²	C₂×C₉	semidirect
174. #390	C₂×C₉	semidirect
175. #389	C₂×C₉	semidirect
176. #388	C₂×C₉	semidirect
177. #386	C₂×C₉	semidirect
178. #380	C₂×C₉	semidirect
179. C₄×C₄⋊C₄	C₂×C₉	semidirect
180. C₄×C₂²⋊C₄	C₂×C₉	semidirect
237. C₂²×C₉	C₄×D₄	semidirect
252. C₄×C₉	C₄×D₄	semidirect
253. C₄×C₉	#121	direct (N × H)
260. #121	C₄×C₉	direct (N × H)
344. C₂×D₄	C₂×C₄×C₉	semidirect
345. C₂×D₄	C₂×C₄×C₉	semidirect
356. C₂²×C₄	C₂×C₄×C₉	semidirect
357. C₂²×C₄	D₄×C₉	semidirect
370. C₄⋊C₄	C₂×C₄×C₉	semidirect
375. C₂²⋊C₄	C₂×C₄×C₉	semidirect
380. C₄²	D₄×C₉	semidirect
411. C₉	C₄×#121	direct (N × H)
482. C₂²	C₄×D₄×C₉	semidirect
497. C₄	C₄×D₄×C₉	semidirect
498. C₄	C₉×#121	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×#121	2
C₂×C₄×D₄×C₉	2
C₂²×C₄²×C₉	2
C₉×#390	2
C₉×#389	2
C₉×#388	2
C₉×#386	2
C₉×#380	2
C₄×C₉×C₄⋊C₄	2
C₄×C₉×C₂²⋊C₄	2
C₃×C₄×#121	3

Subgroups — C4×C9×#121 #11767021

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₉×#121 #11767021