Subgroups — C₉×#2496 #11767217

Order 1152.

702 conjugacy classes of subgroups.

The subgroup lattice has 411 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	2	yes	maximal
2	C₉×#400	C₂	1	2	yes	maximal, complemented
3	C₉×#397	C₂	1	2	yes	maximal
4	C₉×#389	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#389	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#387	C₂	1	2	yes	maximal, complemented
7	C₉×#384	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#380	C₂	1	1	yes	maximal, characteristic
9	C₉×#380	C₂	1	1	yes	maximal, characteristic
10	C₄×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₃×#2496	C₃	1	1	yes	maximal, characteristic
13	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
14	C₉×#126	—	2	8	no	—
15	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
22	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
23	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
28	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
29	C₂×C₄²×C₉	C₂²	1	2	yes	—
30	C₉×#95	C₂²	1	1	yes	characteristic
31	C₉×#95	C₂²	1	1	yes	characteristic
32	C₉×#95	C₂²	1	2	yes	—
33	C₉×#95	C₂²	1	2	yes	—
34	C₉×#95	C₂²	1	2	yes	—
35	C₉×#95	C₂²	1	2	yes	—
36	C₉×#95	C₂²	1	2	yes	—
37	C₂×C₃×#126	C₂×C₃	1	2	yes	—
38	C₃×#400	C₂×C₃	1	2	yes	—
39	C₃×#397	C₂×C₃	1	2	yes	—
40	C₃×#389	C₂×C₃	1	1	yes	characteristic
41	C₃×#389	C₂×C₃	1	1	yes	characteristic
42	C₃×#387	C₂×C₃	1	2	yes	—
43	C₃×#384	C₂×C₃	1	1	yes	characteristic
44	C₃×#380	C₂×C₃	1	1	yes	characteristic
45	C₃×#380	C₂×C₃	1	1	yes	characteristic
46	C₃×C₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
47	C₃×C₄×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
48	C₂⁴×C₉	C₂³	1	1	yes	characteristic
49	C₂²×C₄×C₉	—	2	2	no	—
50	C₂²×C₄×C₉	—	2	2	no	—
51	C₂²×C₄×C₉	—	2	2	no	—
52	C₂²×C₄×C₉	C₂³	1	2	yes	—
53	C₂²×C₄×C₉	C₂³	1	2	yes	—
54	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
55	C₂²×C₄×C₉	C₂³	1	2	yes	—
56	C₂²×C₄×C₉	C₂³	1	2	yes	—
57	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
58	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
59	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
60	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
62	C₉×C₄⋊C₄	—	2	4	no	—
63	C₉×C₄⋊C₄	—	2	4	no	—
64	C₉×C₄⋊C₄	—	2	4	no	—
65	C₉×C₄⋊C₄	—	2	4	no	—
66	C₉×C₄⋊C₄	—	2	2	no	—
67	C₉×C₄⋊C₄	—	2	2	no	—
68	C₉×C₄⋊C₄	—	2	2	no	—
69	C₉×C₄⋊C₄	—	2	2	no	—
70	C₉×C₂²⋊C₄	—	2	4	no	—
71	C₉×C₂²⋊C₄	—	2	4	no	—
72	C₉×C₂²⋊C₄	—	2	2	no	—
73	C₉×C₂²⋊C₄	D₄	1	4	yes	—
74	C₄²×C₉	—	2	4	no	—
75	C₄²×C₉	—	2	2	no	—
76	C₄²×C₉	—	2	2	no	—
77	#2496	C₉	1	1	yes	characteristic, direct product factor, Sylow
78	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
79	C₃×#126	—	2	8	no	—
80	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
85	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
86	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
87	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
88	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
89	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
90	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
91	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
93	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
95	C₃×#95	C₂²×C₃	1	1	yes	characteristic
96	C₃×#95	C₂²×C₃	1	1	yes	characteristic
97	C₃×#95	C₂²×C₃	1	2	yes	—
98	C₃×#95	C₂²×C₃	1	2	yes	—
99	C₃×#95	C₂²×C₃	1	2	yes	—
100	C₃×#95	C₂²×C₃	1	2	yes	—
101	C₃×#95	C₂²×C₃	1	2	yes	—
102	C₂³×C₉	—	2	1	no	—
103	C₂³×C₉	—	2	1	no	—
104	C₂³×C₉	—	2	1	no	—
105	C₂³×C₉	—	2	1	no	—
106	C₂³×C₉	—	2	1	no	—
107	C₂³×C₉	—	2	1	no	—
108	C₂³×C₉	C₂×D₄	1	2	yes	—
109	C₂³×C₉	C₂⁴	1	1	yes	characteristic
110	C₂×C₄×C₉	—	2	1	no	—
111	C₂×C₄×C₉	—	2	1	no	—
112	C₂×C₄×C₉	—	2	1	no	—
113	C₂×C₄×C₉	—	2	1	no	—
114	C₂×C₄×C₉	—	2	1	no	—
115	C₂×C₄×C₉	—	2	1	no	—
116	C₂×C₄×C₉	—	2	2	no	—
117	C₂×C₄×C₉	—	2	2	no	—
118	C₂×C₄×C₉	—	2	2	no	—
119	C₂×C₄×C₉	—	2	2	no	—
120	C₂×C₄×C₉	—	2	1	no	—
121	C₂×C₄×C₉	—	2	1	no	—
122	C₂×C₄×C₉	—	2	2	no	—
123	C₂×C₄×C₉	—	2	2	no	—
124	C₂×C₄×C₉	—	2	2	no	—
125	C₂×C₄×C₉	—	2	2	no	—
126	C₂×C₄×C₉	—	2	2	no	—
127	C₂×C₄×C₉	—	2	2	no	—
128	C₂×C₄×C₉	—	2	1	no	—
129	C₂×C₄×C₉	—	2	1	no	—
130	C₂×C₄×C₉	—	2	1	no	—
131	C₂×C₄×C₉	—	2	2	no	—
132	C₂×C₄×C₉	—	2	2	no	—
133	C₂×C₄×C₉	—	2	1	no	—
134	C₂×C₄×C₉	—	4	4	no	—
135	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
136	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
137	C₂×C₄×C₉	#41	1	2	yes	—
138	C₂×C₄×C₉	#41	1	2	yes	—
139	C₂×C₄×C₉	#41	1	2	yes	—
140	C₂×C₄×C₉	#41	1	2	yes	—
141	C₂×#126	C₂×C₉	1	2	yes	—
142	#400	C₂×C₉	1	2	yes	complemented
143	#397	C₂×C₉	1	2	yes	—
144	#389	C₂×C₉	1	1	yes	characteristic, complemented
145	#389	C₂×C₉	1	1	yes	characteristic, complemented
146	#387	C₂×C₉	1	2	yes	complemented
147	#384	C₂×C₉	1	1	yes	characteristic, complemented
148	#380	C₂×C₉	1	1	yes	characteristic
149	#380	C₂×C₉	1	1	yes	characteristic
150	C₄×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
151	C₄×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic
152	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
153	C₂²×C₃×C₄	—	2	2	no	—
154	C₂²×C₃×C₄	—	2	2	no	—
155	C₂²×C₃×C₄	—	2	2	no	—
156	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
157	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
158	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
159	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
160	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
161	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
162	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
163	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
164	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
165	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
166	C₃×C₄⋊C₄	—	2	4	no	—
167	C₃×C₄⋊C₄	—	2	4	no	—
168	C₃×C₄⋊C₄	—	2	4	no	—
169	C₃×C₄⋊C₄	—	2	4	no	—
170	C₃×C₄⋊C₄	—	2	2	no	—
171	C₃×C₄⋊C₄	—	2	2	no	—
172	C₃×C₄⋊C₄	—	2	2	no	—
173	C₃×C₄⋊C₄	—	2	2	no	—
174	C₃×C₂²⋊C₄	—	2	4	no	—
175	C₃×C₂²⋊C₄	—	2	4	no	—
176	C₃×C₂²⋊C₄	—	2	2	no	—
177	C₃×C₂²⋊C₄	C₃×D₄	1	4	yes	—
178	C₃×C₄²	—	2	4	no	—
179	C₃×C₄²	—	2	2	no	—
180	C₃×C₄²	—	2	2	no	—
181	C₂²×C₉	—	2	2	no	—
182	C₂²×C₉	—	2	2	no	—
183	C₂²×C₉	—	2	2	no	—
184	C₂²×C₉	—	4	1	no	—
185	C₂²×C₉	—	4	1	no	—
186	C₂²×C₉	—	4	1	no	—
187	C₂²×C₉	—	4	1	no	—
188	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
189	C₂²×C₉	C₂×#41	1	1	yes	characteristic
190	C₂²×C₉	C₂×#41	1	1	yes	characteristic
191	C₂²×C₉	C₂×#41	1	1	yes	characteristic
192	C₂²×C₉	C₂×#41	1	1	yes	characteristic
193	C₂²×C₉	2₋¹⁺⁴	1	1	yes	characteristic
194	C₂²×C₉	2₋¹⁺⁴	1	1	yes	characteristic
195	C₄×C₉	—	2	2	no	—
196	C₄×C₉	—	2	2	no	—
197	C₄×C₉	—	2	2	no	—
198	C₄×C₉	—	4	1	no	—
199	C₄×C₉	—	4	2	no	—
200	C₄×C₉	—	4	2	no	—
201	C₄×C₉	—	4	2	no	—
202	C₄×C₉	—	4	2	no	—
203	C₄×C₉	—	4	1	no	—
204	C₄×C₉	#126	1	4	yes	complemented
205	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
206	#126	—	2	8	no	—
207	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
208	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
209	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
210	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
211	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
212	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
213	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
214	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
215	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
216	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
217	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
218	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
219	C₂×C₄²	C₂²×C₉	1	2	yes	—
220	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
221	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
222	#95	C₂²×C₉	1	1	yes	characteristic
223	#95	C₂²×C₉	1	1	yes	characteristic
224	#95	C₂²×C₉	1	2	yes	—
225	#95	C₂²×C₉	1	2	yes	—
226	#95	C₂²×C₉	1	2	yes	—
227	#95	C₂²×C₉	1	2	yes	—
228	#95	C₂²×C₉	1	2	yes	—
229	C₂³×C₃	—	2	1	no	—
230	C₂³×C₃	—	2	1	no	—
231	C₂³×C₃	—	2	1	no	—
232	C₂³×C₃	—	2	1	no	—
233	C₂³×C₃	—	2	1	no	—
234	C₂³×C₃	—	2	1	no	—
235	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
236	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
237	C₂×C₃×C₄	—	2	1	no	—
238	C₂×C₃×C₄	—	2	1	no	—
239	C₂×C₃×C₄	—	2	1	no	—
240	C₂×C₃×C₄	—	2	1	no	—
241	C₂×C₃×C₄	—	2	1	no	—
242	C₂×C₃×C₄	—	2	1	no	—
243	C₂×C₃×C₄	—	2	2	no	—
244	C₂×C₃×C₄	—	2	2	no	—
245	C₂×C₃×C₄	—	2	2	no	—
246	C₂×C₃×C₄	—	2	2	no	—
247	C₂×C₃×C₄	—	2	1	no	—
248	C₂×C₃×C₄	—	2	1	no	—
249	C₂×C₃×C₄	—	2	2	no	—
250	C₂×C₃×C₄	—	2	2	no	—
251	C₂×C₃×C₄	—	2	2	no	—
252	C₂×C₃×C₄	—	2	2	no	—
253	C₂×C₃×C₄	—	2	2	no	—
254	C₂×C₃×C₄	—	2	2	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	2	1	no	—
257	C₂×C₃×C₄	—	2	1	no	—
258	C₂×C₃×C₄	—	2	2	no	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	2	1	no	—
261	C₂×C₃×C₄	—	4	4	no	—
262	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
263	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
264	C₂×C₃×C₄	C₃×#41	1	2	yes	—
265	C₂×C₃×C₄	C₃×#41	1	2	yes	—
266	C₂×C₃×C₄	C₃×#41	1	2	yes	—
267	C₂×C₃×C₄	C₃×#41	1	2	yes	—
268	C₂×C₉	—	4	2	no	—
269	C₂×C₉	C₂×#126	1	1	yes	characteristic
270	C₂×C₉	#532	1	1	yes	characteristic
271	C₂×C₉	#541	1	1	yes	characteristic
272	C₂×C₉	#547	1	1	yes	characteristic
273	C₂×C₉	#547	1	1	yes	characteristic
274	C₂×C₉	#552	1	1	yes	characteristic
275	C₂×C₉	#556	1	1	yes	characteristic
276	C₂⁴	C₂³×C₉	1	1	yes	characteristic
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
281	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
282	C₂²×C₄	C₂³×C₉	1	2	yes	—
283	C₂²×C₄	C₂³×C₉	1	2	yes	—
284	C₂²×C₄	C₂³×C₉	1	2	yes	—
285	C₂²×C₄	C₂³×C₉	1	2	yes	—
286	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
287	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
288	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
289	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
290	C₄⋊C₄	—	2	4	no	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄⋊C₄	—	2	4	no	—
293	C₄⋊C₄	—	2	4	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₂²⋊C₄	—	2	4	no	—
299	C₂²⋊C₄	—	2	4	no	—
300	C₂²⋊C₄	—	2	2	no	—
301	C₂²⋊C₄	D₄×C₉	1	4	yes	—
302	C₄²	—	2	4	no	—
303	C₄²	—	2	2	no	—
304	C₄²	—	2	2	no	—
305	C₂²×C₃	—	2	2	no	—
306	C₂²×C₃	—	2	2	no	—
307	C₂²×C₃	—	2	2	no	—
308	C₂²×C₃	—	4	1	no	—
309	C₂²×C₃	—	4	1	no	—
310	C₂²×C₃	—	4	1	no	—
311	C₂²×C₃	—	4	1	no	—
312	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
313	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
314	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
315	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
316	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
317	C₂²×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
318	C₂²×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
319	C₃×C₄	—	2	2	no	—
320	C₃×C₄	—	2	2	no	—
321	C₃×C₄	—	2	2	no	—
322	C₃×C₄	—	4	1	no	—
323	C₃×C₄	—	4	2	no	—
324	C₃×C₄	—	4	2	no	—
325	C₃×C₄	—	4	2	no	—
326	C₃×C₄	—	4	2	no	—
327	C₃×C₄	—	4	1	no	—
328	C₃×C₄	C₃×#126	1	4	yes	—
329	C₉	#2496	1	1	yes	characteristic, direct product factor, Sylow
330	C₂³	—	2	1	no	—
331	C₂³	—	2	1	no	—
332	C₂³	—	2	1	no	—
333	C₂³	—	2	1	no	—
334	C₂³	—	2	1	no	—
335	C₂³	—	2	1	no	—
336	C₂³	C₂×D₄×C₉	1	2	yes	—
337	C₂³	C₂⁴×C₉	1	1	yes	characteristic
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
364	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
365	C₂×C₄	C₉×#41	1	2	yes	—
366	C₂×C₄	C₉×#41	1	2	yes	—
367	C₂×C₄	C₉×#41	1	2	yes	—
368	C₂×C₄	C₉×#41	1	2	yes	—
369	C₂×C₃	—	4	2	no	—
370	C₂×C₃	C₂×C₃×#126	1	1	yes	characteristic
371	C₂×C₃	C₃×#532	1	1	yes	characteristic
372	C₂×C₃	C₃×#541	1	1	yes	characteristic
373	C₂×C₃	C₃×#547	1	1	yes	characteristic
374	C₂×C₃	C₃×#547	1	1	yes	characteristic
375	C₂×C₃	C₃×#552	1	1	yes	characteristic
376	C₂×C₃	C₃×#556	1	1	yes	characteristic
377	C₂²	—	2	2	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	4	1	no	—
381	C₂²	—	4	1	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	4	1	no	—
384	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
385	C₂²	C₂×C₉×#41	1	1	yes	characteristic
386	C₂²	C₂×C₉×#41	1	1	yes	characteristic
387	C₂²	C₂×C₉×#41	1	1	yes	characteristic
388	C₂²	C₂×C₉×#41	1	1	yes	characteristic
389	C₂²	C₉×2₋¹⁺⁴	1	1	yes	characteristic
390	C₂²	C₉×2₋¹⁺⁴	1	1	yes	characteristic
391	C₄	—	2	2	no	—
392	C₄	—	2	2	no	—
393	C₄	—	2	2	no	—
394	C₄	—	4	1	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	2	no	—
397	C₄	—	4	2	no	—
398	C₄	—	4	2	no	—
399	C₄	—	4	1	no	—
400	C₄	C₉×#126	1	4	yes	complemented
401	C₃	C₃×#2496	1	1	yes	characteristic
402	C₂	—	4	2	no	—
403	C₂	C₂×C₉×#126	1	1	yes	characteristic
404	C₂	C₉×#532	1	1	yes	characteristic
405	C₂	C₉×#541	1	1	yes	characteristic
406	C₂	C₉×#547	1	1	yes	characteristic
407	C₂	C₉×#547	1	1	yes	characteristic
408	C₂	C₉×#552	1	1	yes	characteristic
409	C₂	C₉×#556	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂⁴
commutator	C₂³	C₂⁴×C₉
Frattini, socle, cosocle	C₂³×C₃	C₂⁴×C₃
prime radical	C₂⁴×C₃	C₂³×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
2. C₉×#400	C₂	semidirect
4. C₉×#389	C₂	semidirect
5. C₉×#389	C₂	semidirect
6. C₉×#387	C₂	semidirect
7. C₉×#384	C₂	semidirect
10. C₄×C₉×C₄⋊C₄	C₂	semidirect
77. #2496	C₉	direct (N × H)
142. #400	C₂×C₉	semidirect
144. #389	C₂×C₉	semidirect
145. #389	C₂×C₉	semidirect
146. #387	C₂×C₉	semidirect
147. #384	C₂×C₉	semidirect
150. C₄×C₄⋊C₄	C₂×C₉	semidirect
204. C₄×C₉	#126	semidirect
329. C₉	#2496	direct (N × H)
400. C₄	C₉×#126	semidirect

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×#400	2
C₉×#397	2
C₉×#389	2
C₉×#387	2
C₉×#384	2
C₉×#380	2
C₄×C₉×C₄⋊C₄	2
C₄×C₉×C₂²⋊C₄	2
C₃×#2496	3

Subgroups — C9×#2496 #11767217

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2496 #11767217