Subgroups — C₉×#2337 #11767058

Order 1152.

810 conjugacy classes of subgroups.

The subgroup lattice has 357 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#124	C₂	1	1	yes	maximal, characteristic
2	C₉×#391	C₂	1	2	yes	maximal, complemented
3	C₉×#388	C₂	1	2	yes	maximal, complemented
4	C₉×#388	C₂	1	2	yes	maximal, complemented
5	C₉×#386	C₂	1	2	yes	maximal
6	C₉×#385	C₂	1	2	yes	maximal, complemented
7	C₉×#383	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₉×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₃×#2337	C₃	1	1	yes	maximal, characteristic
11	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
12	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
13	C₂³×C₄×C₉	C₂²	1	2	yes	—
14	C₉×#124	C₄	1	8	yes	complemented
15	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
18	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
19	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
23	C₂×C₄²×C₉	C₂²	1	2	yes	—
24	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
25	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
26	C₉×#95	C₂²	1	2	yes	—
27	C₉×#95	C₂²	1	2	yes	—
28	C₉×#95	C₂²	1	2	yes	—
29	C₉×#95	C₂²	1	1	yes	characteristic
30	C₉×#95	C₂²	1	2	yes	—
31	C₉×#95	C₂²	1	1	yes	characteristic
32	C₉×#95	C₂²	1	2	yes	—
33	C₂×C₃×#124	C₂×C₃	1	1	yes	characteristic
34	C₃×#391	C₂×C₃	1	2	yes	—
35	C₃×#388	C₂×C₃	1	2	yes	—
36	C₃×#388	C₂×C₃	1	2	yes	—
37	C₃×#386	C₂×C₃	1	2	yes	—
38	C₃×#385	C₂×C₃	1	2	yes	—
39	C₃×#383	C₂×C₃	1	1	yes	characteristic
40	C₃×C₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
41	C₃×C₄×C₂²⋊C₄	C₂×C₃	1	2	yes	—
42	C₂⁴×C₉	C₂³	1	2	yes	—
43	C₂×Q₈×C₉	—	4	2	no	—
44	C₂×Q₈×C₉	C₂×C₄	1	4	yes	complemented
45	C₂×D₄×C₉	—	4	2	no	—
46	C₂×D₄×C₉	C₂×C₄	1	4	yes	—
47	C₂²×C₄×C₉	—	2	4	no	—
48	C₂²×C₄×C₉	—	4	2	no	—
49	C₂²×C₄×C₉	—	4	2	no	—
50	C₂²×C₄×C₉	C₂³	1	2	yes	—
51	C₂²×C₄×C₉	C₂³	1	2	yes	—
52	C₂²×C₄×C₉	C₂³	1	2	yes	—
53	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
54	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
55	C₂²×C₄×C₉	C₂³	1	2	yes	—
56	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
57	C₂²×C₄×C₉	C₂³	1	2	yes	—
58	C₉×C₄⋊C₄	—	2	4	no	—
59	C₉×C₄⋊C₄	—	4	2	no	—
60	C₉×C₂²⋊C₄	—	2	4	no	—
61	C₉×C₂²⋊C₄	—	4	2	no	—
62	C₉×C₂²⋊C₄	—	4	2	no	—
63	C₉×C₂²⋊C₄	C₂×C₄	1	8	yes	complemented
64	C₉×C₂²⋊C₄	C₂×C₄	1	8	yes	complemented
65	C₄²×C₉	—	4	1	no	—
66	C₄²×C₉	—	4	1	no	—
67	C₄²×C₉	—	4	2	no	—
68	C₄²×C₉	C₂×C₄	1	4	yes	complemented
69	#2337	C₉	1	1	yes	characteristic, direct product factor, Sylow
70	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
71	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
72	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
73	C₃×#124	C₃×C₄	1	8	yes	—
74	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
75	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
76	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
77	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
78	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
79	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
80	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
81	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
83	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
85	C₃×#95	C₂²×C₃	1	2	yes	—
86	C₃×#95	C₂²×C₃	1	2	yes	—
87	C₃×#95	C₂²×C₃	1	2	yes	—
88	C₃×#95	C₂²×C₃	1	1	yes	characteristic
89	C₃×#95	C₂²×C₃	1	2	yes	—
90	C₃×#95	C₂²×C₃	1	1	yes	characteristic
91	C₃×#95	C₂²×C₃	1	2	yes	—
92	C₂³×C₉	—	2	2	no	—
93	C₂³×C₉	—	2	2	no	—
94	C₂³×C₉	—	2	2	no	—
95	C₂³×C₉	—	2	2	no	—
96	C₂³×C₉	—	2	2	no	—
97	C₂³×C₉	—	2	2	no	—
98	C₂³×C₉	C₂²×C₄	1	4	yes	—
99	C₂³×C₉	C₂⁴	1	1	yes	characteristic
100	Q₈×C₉	—	4	4	no	—
101	D₄×C₉	—	4	4	no	—
102	C₂×C₄×C₉	—	2	2	no	—
103	C₂×C₄×C₉	—	2	1	no	—
104	C₂×C₄×C₉	—	2	2	no	—
105	C₂×C₄×C₉	—	2	2	no	—
106	C₂×C₄×C₉	—	2	2	no	—
107	C₂×C₄×C₉	—	2	2	no	—
108	C₂×C₄×C₉	—	2	2	no	—
109	C₂×C₄×C₉	—	2	1	no	—
110	C₂×C₄×C₉	—	2	2	no	—
111	C₂×C₄×C₉	—	2	2	no	—
112	C₂×C₄×C₉	—	2	2	no	—
113	C₂×C₄×C₉	—	2	2	no	—
114	C₂×C₄×C₉	—	2	2	no	—
115	C₂×C₄×C₉	—	2	2	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	—	4	8	no	—
120	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
121	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
122	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
123	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
124	C₂×C₄×C₉	#41	1	4	yes	—
125	C₂×#124	C₂×C₉	1	1	yes	characteristic
126	#391	C₂×C₉	1	2	yes	complemented
127	#388	C₂×C₉	1	2	yes	complemented
128	#388	C₂×C₉	1	2	yes	complemented
129	#386	C₂×C₉	1	2	yes	—
130	#385	C₂×C₉	1	2	yes	complemented
131	#383	C₂×C₉	1	1	yes	characteristic, complemented
132	C₄×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
133	C₄×C₂²⋊C₄	C₂×C₉	1	2	yes	complemented
134	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
135	C₂×C₃×Q₈	—	4	2	no	—
136	C₂×C₃×Q₈	C₂×C₃×C₄	1	4	yes	—
137	C₂×C₃×D₄	—	4	2	no	—
138	C₂×C₃×D₄	C₂×C₃×C₄	1	4	yes	—
139	C₂²×C₃×C₄	—	2	4	no	—
140	C₂²×C₃×C₄	—	4	2	no	—
141	C₂²×C₃×C₄	—	4	2	no	—
142	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
143	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
144	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
145	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
146	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
147	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
148	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
149	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
150	C₃×C₄⋊C₄	—	2	4	no	—
151	C₃×C₄⋊C₄	—	4	2	no	—
152	C₃×C₂²⋊C₄	—	2	4	no	—
153	C₃×C₂²⋊C₄	—	4	2	no	—
154	C₃×C₂²⋊C₄	—	4	2	no	—
155	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	—
156	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	—
157	C₃×C₄²	—	4	1	no	—
158	C₃×C₄²	—	4	1	no	—
159	C₃×C₄²	—	4	2	no	—
160	C₃×C₄²	C₂×C₃×C₄	1	4	yes	—
161	C₂²×C₉	—	2	4	no	—
162	C₂²×C₉	—	2	4	no	—
163	C₂²×C₉	—	2	4	no	—
164	C₂²×C₉	—	4	2	no	—
165	C₂²×C₉	—	4	2	no	—
166	C₂²×C₉	—	4	2	no	—
167	C₂²×C₉	—	4	2	no	—
168	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
169	C₂²×C₉	C₂×#41	1	2	yes	—
170	C₂²×C₉	H(5,𝔽₂)	1	2	yes	—
171	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
172	C₂²×C₉	2₋¹⁺⁴	1	1	yes	characteristic
173	C₄×C₉	—	2	2	no	—
174	C₄×C₉	—	2	2	no	—
175	C₄×C₉	—	2	4	no	—
176	C₄×C₉	—	2	2	no	—
177	C₄×C₉	—	2	4	no	—
178	C₄×C₉	—	4	2	no	—
179	C₄×C₉	—	4	2	no	—
180	C₄×C₉	—	4	2	no	—
181	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
182	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
183	C₂³×C₄	C₂²×C₉	1	2	yes	—
184	#124	C₄×C₉	1	8	yes	complemented
185	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
186	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
187	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
188	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
189	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
190	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
191	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
192	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
193	C₂×C₄²	C₂²×C₉	1	2	yes	—
194	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
195	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
196	#95	C₂²×C₉	1	2	yes	—
197	#95	C₂²×C₉	1	2	yes	—
198	#95	C₂²×C₉	1	2	yes	—
199	#95	C₂²×C₉	1	1	yes	characteristic
200	#95	C₂²×C₉	1	2	yes	—
201	#95	C₂²×C₉	1	1	yes	characteristic
202	#95	C₂²×C₉	1	2	yes	—
203	C₂³×C₃	—	2	2	no	—
204	C₂³×C₃	—	2	2	no	—
205	C₂³×C₃	—	2	2	no	—
206	C₂³×C₃	—	2	2	no	—
207	C₂³×C₃	—	2	2	no	—
208	C₂³×C₃	—	2	2	no	—
209	C₂³×C₃	C₂²×C₃×C₄	1	4	yes	—
210	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
211	C₃×Q₈	—	4	4	no	—
212	C₃×D₄	—	4	4	no	—
213	C₂×C₃×C₄	—	2	2	no	—
214	C₂×C₃×C₄	—	2	1	no	—
215	C₂×C₃×C₄	—	2	2	no	—
216	C₂×C₃×C₄	—	2	2	no	—
217	C₂×C₃×C₄	—	2	2	no	—
218	C₂×C₃×C₄	—	2	2	no	—
219	C₂×C₃×C₄	—	2	2	no	—
220	C₂×C₃×C₄	—	2	1	no	—
221	C₂×C₃×C₄	—	2	2	no	—
222	C₂×C₃×C₄	—	2	2	no	—
223	C₂×C₃×C₄	—	2	2	no	—
224	C₂×C₃×C₄	—	2	2	no	—
225	C₂×C₃×C₄	—	2	2	no	—
226	C₂×C₃×C₄	—	2	2	no	—
227	C₂×C₃×C₄	—	2	2	no	—
228	C₂×C₃×C₄	—	2	2	no	—
229	C₂×C₃×C₄	—	2	2	no	—
230	C₂×C₃×C₄	—	4	8	no	—
231	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
232	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
233	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
234	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
235	C₂×C₃×C₄	C₃×#41	1	4	yes	—
236	C₂×C₉	—	4	4	no	—
237	C₂×C₉	C₄×#41	1	1	yes	characteristic
238	C₂×C₉	#518	1	1	yes	characteristic
239	C₂×C₉	#520	1	1	yes	characteristic
240	C₂×C₉	#538	1	2	yes	—
241	C₂×C₉	#542	1	2	yes	—
242	C₂⁴	C₂³×C₉	1	2	yes	—
243	C₂×Q₈	—	4	2	no	—
244	C₂×Q₈	C₂×C₄×C₉	1	4	yes	complemented
245	C₂×D₄	—	4	2	no	—
246	C₂×D₄	C₂×C₄×C₉	1	4	yes	—
247	C₂²×C₄	—	2	4	no	—
248	C₂²×C₄	—	4	2	no	—
249	C₂²×C₄	—	4	2	no	—
250	C₂²×C₄	C₂³×C₉	1	2	yes	—
251	C₂²×C₄	C₂³×C₉	1	2	yes	—
252	C₂²×C₄	C₂³×C₉	1	2	yes	—
253	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
254	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
255	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
256	C₂²×C₄	C₂³×C₉	1	2	yes	—
257	C₂²×C₄	C₂³×C₉	1	2	yes	—
258	C₄⋊C₄	—	2	4	no	—
259	C₄⋊C₄	—	4	2	no	—
260	C₂²⋊C₄	—	2	4	no	—
261	C₂²⋊C₄	—	4	2	no	—
262	C₂²⋊C₄	—	4	2	no	—
263	C₂²⋊C₄	C₂×C₄×C₉	1	8	yes	complemented
264	C₂²⋊C₄	C₂×C₄×C₉	1	8	yes	complemented
265	C₄²	—	4	1	no	—
266	C₄²	—	4	1	no	—
267	C₄²	—	4	2	no	—
268	C₄²	C₂×C₄×C₉	1	4	yes	complemented
269	C₂²×C₃	—	2	4	no	—
270	C₂²×C₃	—	2	4	no	—
271	C₂²×C₃	—	2	4	no	—
272	C₂²×C₃	—	4	2	no	—
273	C₂²×C₃	—	4	2	no	—
274	C₂²×C₃	—	4	2	no	—
275	C₂²×C₃	—	4	2	no	—
276	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
277	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
278	C₂²×C₃	C₃×H(5,𝔽₂)	1	2	yes	—
279	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
280	C₂²×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
281	C₃×C₄	—	2	2	no	—
282	C₃×C₄	—	2	2	no	—
283	C₃×C₄	—	2	4	no	—
284	C₃×C₄	—	2	2	no	—
285	C₃×C₄	—	2	4	no	—
286	C₃×C₄	—	4	2	no	—
287	C₃×C₄	—	4	2	no	—
288	C₃×C₄	—	4	2	no	—
289	C₉	#2337	1	1	yes	characteristic, direct product factor, Sylow
290	C₂³	—	2	2	no	—
291	C₂³	—	2	2	no	—
292	C₂³	—	2	2	no	—
293	C₂³	—	2	2	no	—
294	C₂³	—	2	2	no	—
295	C₂³	—	2	2	no	—
296	C₂³	C₂²×C₄×C₉	1	4	yes	—
297	C₂³	C₂⁴×C₉	1	1	yes	characteristic
298	Q₈	—	4	4	no	—
299	D₄	—	4	4	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	4	8	no	—
318	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
319	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
320	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
321	C₂×C₄	C₂²×C₄×C₉	1	4	yes	—
322	C₂×C₄	C₉×#41	1	4	yes	—
323	C₂×C₃	—	4	4	no	—
324	C₂×C₃	C₃×C₄×#41	1	1	yes	characteristic
325	C₂×C₃	C₃×#518	1	1	yes	characteristic
326	C₂×C₃	C₃×#520	1	1	yes	characteristic
327	C₂×C₃	C₃×#538	1	2	yes	—
328	C₂×C₃	C₃×#542	1	2	yes	—
329	C₂²	—	2	4	no	—
330	C₂²	—	2	4	no	—
331	C₂²	—	2	4	no	—
332	C₂²	—	4	2	no	—
333	C₂²	—	4	2	no	—
334	C₂²	—	4	2	no	—
335	C₂²	—	4	2	no	—
336	C₂²	C₂³×C₄×C₉	1	1	yes	characteristic
337	C₂²	C₂×C₉×#41	1	2	yes	—
338	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
339	C₂²	C₉×H(5,𝔽₂)	1	2	yes	—
340	C₂²	C₉×2₋¹⁺⁴	1	1	yes	characteristic
341	C₄	—	2	2	no	—
342	C₄	—	2	4	no	—
343	C₄	—	2	2	no	—
344	C₄	—	2	2	no	—
345	C₄	—	2	4	no	—
346	C₄	—	4	2	no	—
347	C₄	—	4	2	no	—
348	C₄	—	4	2	no	—
349	C₃	C₃×#2337	1	1	yes	characteristic
350	C₂	—	4	4	no	—
351	C₂	C₄×C₉×#41	1	1	yes	characteristic
352	C₂	C₉×#518	1	1	yes	characteristic
353	C₂	C₉×#520	1	1	yes	characteristic
354	C₂	C₉×#538	1	2	yes	—
355	C₂	C₉×#542	1	2	yes	—

	subgroup	G/H
center	C₂³×C₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₉
Frattini, socle, cosocle	C₂³×C₃	C₂⁴×C₃
prime radical	C₂²×C₃×D₄	C₂²×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×#391	C₂	semidirect
3. C₉×#388	C₂	semidirect
4. C₉×#388	C₂	semidirect
6. C₉×#385	C₂	semidirect
7. C₉×#383	C₂	semidirect
8. C₄×C₉×C₄⋊C₄	C₂	semidirect
9. C₄×C₉×C₂²⋊C₄	C₂	semidirect
14. C₉×#124	C₄	semidirect
44. C₂×Q₈×C₉	C₂×C₄	semidirect
63. C₉×C₂²⋊C₄	C₂×C₄	semidirect
64. C₉×C₂²⋊C₄	C₂×C₄	semidirect
68. C₄²×C₉	C₂×C₄	semidirect
69. #2337	C₉	direct (N × H)
126. #391	C₂×C₉	semidirect
127. #388	C₂×C₉	semidirect
128. #388	C₂×C₉	semidirect
130. #385	C₂×C₉	semidirect
131. #383	C₂×C₉	semidirect
132. C₄×C₄⋊C₄	C₂×C₉	semidirect
133. C₄×C₂²⋊C₄	C₂×C₉	semidirect
184. #124	C₄×C₉	semidirect
244. C₂×Q₈	C₂×C₄×C₉	semidirect
263. C₂²⋊C₄	C₂×C₄×C₉	semidirect
264. C₂²⋊C₄	C₂×C₄×C₉	semidirect
268. C₄²	C₂×C₄×C₉	semidirect
289. C₉	#2337	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×#124	2
C₉×#391	2
C₉×#388	2
C₉×#386	2
C₉×#385	2
C₉×#383	2
C₄×C₉×C₄⋊C₄	2
C₄×C₉×C₂²⋊C₄	2
C₃×#2337	3

Subgroups — C9×#2337 #11767058

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2337 #11767058