Subgroups — C₉×#2497 #11767218

Order 1152.

642 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#400	C₂	1	2	yes	maximal, complemented
2	C₉×#396	C₂	1	2	yes	maximal
3	C₉×#389	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#389	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#388	C₂	1	2	yes	maximal
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×#2497	C₃	1	1	yes	maximal, characteristic
13	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
14	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	2	yes	—
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×C₂²⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
27	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
28	C₂×C₄²×C₉	C₂²	1	2	yes	—
29	C₉×#95	C₂²	1	1	yes	characteristic
30	C₉×#95	C₂²	1	1	yes	characteristic
31	C₉×#95	C₂²	1	2	yes	—
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	C₃×#400	C₂×C₃	1	2	yes	—
37	C₃×#396	C₂×C₃	1	2	yes	—
38	C₃×#389	C₂×C₃	1	1	yes	characteristic
39	C₃×#389	C₂×C₃	1	1	yes	characteristic
40	C₃×#388	C₂×C₃	1	2	yes	—
41	C₃×#387	C₂×C₃	1	2	yes	—
42	C₃×#384	C₂×C₃	1	1	yes	characteristic
43	C₃×#380	C₂×C₃	1	1	yes	characteristic
44	C₃×#380	C₂×C₃	1	1	yes	characteristic
45	C₃×C₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
46	C₃×C₄×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
47	C₂⁴×C₉	C₂³	1	1	yes	characteristic
48	C₂²×C₄×C₉	—	2	2	no	—
49	C₂²×C₄×C₉	—	2	2	no	—
50	C₂²×C₄×C₉	—	2	2	no	—
51	C₂²×C₄×C₉	C₂³	1	2	yes	—
52	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
53	C₂²×C₄×C₉	C₂³	1	2	yes	—
54	C₂²×C₄×C₉	C₂³	1	2	yes	—
55	C₂²×C₄×C₉	C₂³	1	2	yes	—
56	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
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	C₉×C₄⋊C₄	—	2	4	no	—
62	C₉×C₄⋊C₄	—	2	2	no	—
63	C₉×C₄⋊C₄	—	2	2	no	—
64	C₉×C₄⋊C₄	—	2	2	no	—
65	C₉×C₄⋊C₄	—	2	2	no	—
66	C₉×C₄⋊C₄	—	4	2	no	—
67	C₉×C₄⋊C₄	—	4	2	no	—
68	C₉×C₄⋊C₄	—	4	2	no	—
69	C₉×C₂²⋊C₄	—	2	2	no	—
70	C₉×C₂²⋊C₄	—	4	2	no	—
71	C₉×C₂²⋊C₄	—	4	2	no	—
72	C₉×C₂²⋊C₄	Q₈	1	4	yes	—
73	C₄²×C₉	—	2	2	no	—
74	C₄²×C₉	—	2	2	no	—
75	C₄²×C₉	—	4	2	no	—
76	#2497	C₉	1	1	yes	characteristic, direct product factor, Sylow
77	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
79	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
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	2	yes	—
83	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
84	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
85	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
86	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
88	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
89	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
90	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
91	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
93	C₃×#95	C₂²×C₃	1	1	yes	characteristic
94	C₃×#95	C₂²×C₃	1	1	yes	characteristic
95	C₃×#95	C₂²×C₃	1	2	yes	—
96	C₃×#95	C₂²×C₃	1	2	yes	—
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	C₂³×C₉	—	2	1	no	—
101	C₂³×C₉	—	2	1	no	—
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	C₂×Q₈	1	2	yes	—
107	C₂³×C₉	C₂⁴	1	1	yes	characteristic
108	C₂×C₄×C₉	—	2	1	no	—
109	C₂×C₄×C₉	—	2	1	no	—
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	2	no	—
121	C₂×C₄×C₉	—	2	2	no	—
122	C₂×C₄×C₉	—	2	1	no	—
123	C₂×C₄×C₉	—	2	1	no	—
124	C₂×C₄×C₉	—	2	1	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	2	no	—
129	C₂×C₄×C₉	—	2	2	no	—
130	C₂×C₄×C₉	—	2	2	no	—
131	C₂×C₄×C₉	—	2	1	no	—
132	C₂×C₄×C₉	—	4	4	no	—
133	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
134	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
135	C₂×C₄×C₉	#41	1	2	yes	—
136	C₂×C₄×C₉	#41	1	2	yes	—
137	C₂×C₄×C₉	#41	1	2	yes	—
138	C₂×C₄×C₉	#41	1	2	yes	—
139	#400	C₂×C₉	1	2	yes	complemented
140	#396	C₂×C₉	1	2	yes	—
141	#389	C₂×C₉	1	1	yes	characteristic, complemented
142	#389	C₂×C₉	1	1	yes	characteristic, complemented
143	#388	C₂×C₉	1	2	yes	—
144	#387	C₂×C₉	1	2	yes	complemented
145	#384	C₂×C₉	1	1	yes	characteristic, complemented
146	#380	C₂×C₉	1	1	yes	characteristic
147	#380	C₂×C₉	1	1	yes	characteristic
148	C₄×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
149	C₄×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic
150	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
151	C₂²×C₃×C₄	—	2	2	no	—
152	C₂²×C₃×C₄	—	2	2	no	—
153	C₂²×C₃×C₄	—	2	2	no	—
154	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
155	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
156	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
157	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
161	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
162	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
163	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
164	C₃×C₄⋊C₄	—	2	4	no	—
165	C₃×C₄⋊C₄	—	2	2	no	—
166	C₃×C₄⋊C₄	—	2	2	no	—
167	C₃×C₄⋊C₄	—	2	2	no	—
168	C₃×C₄⋊C₄	—	2	2	no	—
169	C₃×C₄⋊C₄	—	4	2	no	—
170	C₃×C₄⋊C₄	—	4	2	no	—
171	C₃×C₄⋊C₄	—	4	2	no	—
172	C₃×C₂²⋊C₄	—	2	2	no	—
173	C₃×C₂²⋊C₄	—	4	2	no	—
174	C₃×C₂²⋊C₄	—	4	2	no	—
175	C₃×C₂²⋊C₄	C₃×Q₈	1	4	yes	—
176	C₃×C₄²	—	2	2	no	—
177	C₃×C₄²	—	2	2	no	—
178	C₃×C₄²	—	4	2	no	—
179	C₂²×C₉	—	2	2	no	—
180	C₂²×C₉	—	2	2	no	—
181	C₂²×C₉	—	2	2	no	—
182	C₂²×C₉	—	4	1	no	—
183	C₂²×C₉	—	4	1	no	—
184	C₂²×C₉	—	4	1	no	—
185	C₂²×C₉	—	4	1	no	—
186	C₂²×C₉	C₂²×Q₈	1	1	yes	characteristic
187	C₂²×C₉	C₂×#41	1	1	yes	characteristic
188	C₂²×C₉	C₂×#41	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	H(5,𝔽₂)	1	1	yes	characteristic
192	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
193	C₄×C₉	—	2	2	no	—
194	C₄×C₉	—	2	2	no	—
195	C₄×C₉	—	2	2	no	—
196	C₄×C₉	—	4	1	no	—
197	C₄×C₉	—	4	2	no	—
198	C₄×C₉	—	4	2	no	—
199	C₄×C₉	—	4	2	no	—
200	C₄×C₉	—	4	1	no	—
201	C₄×C₉	—	4	2	no	—
202	C₄×C₉	#126	1	4	yes	—
203	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
204	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
205	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
206	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
207	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
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	2	yes	—
211	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
212	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
213	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
214	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
215	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
216	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
217	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
218	C₂×C₄²	C₂²×C₉	1	2	yes	—
219	#95	C₂²×C₉	1	1	yes	characteristic
220	#95	C₂²×C₉	1	1	yes	characteristic
221	#95	C₂²×C₉	1	2	yes	—
222	#95	C₂²×C₉	1	2	yes	—
223	#95	C₂²×C₉	1	2	yes	—
224	#95	C₂²×C₉	1	2	yes	—
225	#95	C₂²×C₉	1	2	yes	—
226	C₂³×C₃	—	2	1	no	—
227	C₂³×C₃	—	2	1	no	—
228	C₂³×C₃	—	2	1	no	—
229	C₂³×C₃	—	2	1	no	—
230	C₂³×C₃	—	2	1	no	—
231	C₂³×C₃	—	2	1	no	—
232	C₂³×C₃	C₂×C₃×Q₈	1	2	yes	—
233	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
234	C₂×C₃×C₄	—	2	1	no	—
235	C₂×C₃×C₄	—	2	1	no	—
236	C₂×C₃×C₄	—	2	1	no	—
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	2	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	2	no	—
248	C₂×C₃×C₄	—	2	1	no	—
249	C₂×C₃×C₄	—	2	1	no	—
250	C₂×C₃×C₄	—	2	1	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	2	no	—
256	C₂×C₃×C₄	—	2	2	no	—
257	C₂×C₃×C₄	—	2	1	no	—
258	C₂×C₃×C₄	—	4	4	no	—
259	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
260	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
261	C₂×C₃×C₄	C₃×#41	1	2	yes	—
262	C₂×C₃×C₄	C₃×#41	1	2	yes	—
263	C₂×C₃×C₄	C₃×#41	1	2	yes	—
264	C₂×C₃×C₄	C₃×#41	1	2	yes	—
265	C₂×C₉	—	4	2	no	—
266	C₂×C₉	C₂×#126	1	1	yes	characteristic
267	C₂×C₉	#533	1	1	yes	characteristic
268	C₂×C₉	#540	1	1	yes	characteristic
269	C₂×C₉	#553	1	1	yes	characteristic
270	C₂×C₉	#554	1	1	yes	characteristic
271	C₂×C₉	#554	1	1	yes	characteristic
272	C₂×C₉	#555	1	1	yes	characteristic
273	C₂⁴	C₂³×C₉	1	1	yes	characteristic
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
278	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
279	C₂²×C₄	C₂³×C₉	1	2	yes	—
280	C₂²×C₄	C₂³×C₉	1	2	yes	—
281	C₂²×C₄	C₂³×C₉	1	2	yes	—
282	C₂²×C₄	C₂³×C₉	1	2	yes	—
283	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
284	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
285	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
286	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
287	C₄⋊C₄	—	2	4	no	—
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	—	2	2	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	4	2	no	—
293	C₄⋊C₄	—	4	2	no	—
294	C₄⋊C₄	—	4	2	no	—
295	C₂²⋊C₄	—	2	2	no	—
296	C₂²⋊C₄	—	4	2	no	—
297	C₂²⋊C₄	—	4	2	no	—
298	C₂²⋊C₄	Q₈×C₉	1	4	yes	—
299	C₄²	—	2	2	no	—
300	C₄²	—	2	2	no	—
301	C₄²	—	4	2	no	—
302	C₂²×C₃	—	2	2	no	—
303	C₂²×C₃	—	2	2	no	—
304	C₂²×C₃	—	2	2	no	—
305	C₂²×C₃	—	4	1	no	—
306	C₂²×C₃	—	4	1	no	—
307	C₂²×C₃	—	4	1	no	—
308	C₂²×C₃	—	4	1	no	—
309	C₂²×C₃	C₂²×C₃×Q₈	1	1	yes	characteristic
310	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
311	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
312	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
313	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
314	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
315	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
316	C₃×C₄	—	2	2	no	—
317	C₃×C₄	—	2	2	no	—
318	C₃×C₄	—	2	2	no	—
319	C₃×C₄	—	4	1	no	—
320	C₃×C₄	—	4	2	no	—
321	C₃×C₄	—	4	2	no	—
322	C₃×C₄	—	4	2	no	—
323	C₃×C₄	—	4	1	no	—
324	C₃×C₄	—	4	2	no	—
325	C₃×C₄	C₃×#126	1	4	yes	—
326	C₉	#2497	1	1	yes	characteristic, direct product factor, Sylow
327	C₂³	—	2	1	no	—
328	C₂³	—	2	1	no	—
329	C₂³	—	2	1	no	—
330	C₂³	—	2	1	no	—
331	C₂³	—	2	1	no	—
332	C₂³	—	2	1	no	—
333	C₂³	C₂×Q₈×C₉	1	2	yes	—
334	C₂³	C₂⁴×C₉	1	1	yes	characteristic
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
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	2	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	2	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	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	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
361	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
362	C₂×C₄	C₉×#41	1	2	yes	—
363	C₂×C₄	C₉×#41	1	2	yes	—
364	C₂×C₄	C₉×#41	1	2	yes	—
365	C₂×C₄	C₉×#41	1	2	yes	—
366	C₂×C₃	—	4	2	no	—
367	C₂×C₃	C₂×C₃×#126	1	1	yes	characteristic
368	C₂×C₃	C₃×#533	1	1	yes	characteristic
369	C₂×C₃	C₃×#540	1	1	yes	characteristic
370	C₂×C₃	C₃×#553	1	1	yes	characteristic
371	C₂×C₃	C₃×#554	1	1	yes	characteristic
372	C₂×C₃	C₃×#554	1	1	yes	characteristic
373	C₂×C₃	C₃×#555	1	1	yes	characteristic
374	C₂²	—	2	2	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	4	1	no	—
378	C₂²	—	4	1	no	—
379	C₂²	—	4	1	no	—
380	C₂²	—	4	1	no	—
381	C₂²	C₂²×Q₈×C₉	1	1	yes	characteristic
382	C₂²	C₂×C₉×#41	1	1	yes	characteristic
383	C₂²	C₂×C₉×#41	1	1	yes	characteristic
384	C₂²	C₂×C₉×#41	1	1	yes	characteristic
385	C₂²	C₂×C₉×#41	1	1	yes	characteristic
386	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
387	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	—	2	2	no	—
391	C₄	—	4	1	no	—
392	C₄	—	4	2	no	—
393	C₄	—	4	2	no	—
394	C₄	—	4	2	no	—
395	C₄	—	4	1	no	—
396	C₄	—	4	2	no	—
397	C₄	C₉×#126	1	4	yes	—
398	C₃	C₃×#2497	1	1	yes	characteristic
399	C₂	—	4	2	no	—
400	C₂	C₂×C₉×#126	1	1	yes	characteristic
401	C₂	C₉×#533	1	1	yes	characteristic
402	C₂	C₉×#540	1	1	yes	characteristic
403	C₂	C₉×#553	1	1	yes	characteristic
404	C₂	C₉×#554	1	1	yes	characteristic
405	C₂	C₉×#554	1	1	yes	characteristic
406	C₂	C₉×#555	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
1. C₉×#400	C₂	semidirect
3. C₉×#389	C₂	semidirect
4. C₉×#389	C₂	semidirect
6. C₉×#387	C₂	semidirect
7. C₉×#384	C₂	semidirect
10. C₄×C₉×C₄⋊C₄	C₂	semidirect
76. #2497	C₉	direct (N × H)
139. #400	C₂×C₉	semidirect
141. #389	C₂×C₉	semidirect
142. #389	C₂×C₉	semidirect
144. #387	C₂×C₉	semidirect
145. #384	C₂×C₉	semidirect
148. C₄×C₄⋊C₄	C₂×C₉	semidirect
326. C₉	#2497	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×#400	2
C₉×#396	2
C₉×#389	2
C₉×#388	2
C₉×#387	2
C₉×#384	2
C₉×#380	2
C₄×C₉×C₄⋊C₄	2
C₄×C₉×C₂²⋊C₄	2
C₃×#2497	3

Subgroups — C9×#2497 #11767218

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2497 #11767218