Subgroups — C₉×#2538 #11767259

Order 1152.

930 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×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
2	C₂×C₄×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic
4	C₉×#396	C₂	1	4	yes	maximal, complemented
5	C₉×#390	C₂	1	2	yes	maximal
6	C₉×#389	C₂	1	2	yes	maximal, complemented
7	C₉×#384	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#380	C₂	1	2	yes	maximal, complemented
9	C₃×#2538	C₃	1	1	yes	maximal, characteristic
10	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
11	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
12	C₂³×C₄×C₉	C₂²	1	2	yes	—
13	C₉×C₂²⋊Q₈	—	2	8	no	—
14	C₄×Q₈×C₉	—	2	4	no	—
15	C₄×D₄×C₉	—	2	4	no	—
16	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂×C₉×C₄⋊C₄	C₂²	1	4	yes	—
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	1	yes	characteristic
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	4	yes	—
24	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂×C₉×C₂²⋊C₄	C₂²	1	4	yes	—
26	C₂×C₄²×C₉	C₂²	1	2	yes	—
27	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
28	C₉×#95	C₂²	1	4	yes	—
29	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	2	yes	—
30	C₂×C₃×C₄×Q₈	C₂×C₃	1	1	yes	characteristic
31	C₂×C₃×C₄×D₄	C₂×C₃	1	1	yes	characteristic
32	C₃×#396	C₂×C₃	1	4	yes	—
33	C₃×#390	C₂×C₃	1	2	yes	—
34	C₃×#389	C₂×C₃	1	2	yes	—
35	C₃×#384	C₂×C₃	1	1	yes	characteristic
36	C₃×#380	C₂×C₃	1	2	yes	—
37	C₂⁴×C₉	C₂³	1	2	yes	—
38	C₂×Q₈×C₉	—	2	2	no	—
39	C₂×Q₈×C₉	—	2	2	no	—
40	C₂×Q₈×C₉	D₄	1	4	yes	complemented
41	C₂×D₄×C₉	—	2	2	no	—
42	C₂×D₄×C₉	—	2	2	no	—
43	C₂×D₄×C₉	Q₈	1	4	yes	complemented
44	C₂²×C₄×C₉	—	2	4	no	—
45	C₂²×C₄×C₉	—	2	4	no	—
46	C₂²×C₄×C₉	—	2	4	no	—
47	C₂²×C₄×C₉	C₂³	1	2	yes	—
48	C₂²×C₄×C₉	C₂³	1	4	yes	—
49	C₂²×C₄×C₉	C₂³	1	2	yes	—
50	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
51	C₂²×C₄×C₉	C₂³	1	2	yes	—
52	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
53	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
54	C₉×C₄⋊C₄	—	2	2	no	—
55	C₉×C₄⋊C₄	—	2	4	no	—
56	C₉×C₄⋊C₄	—	2	2	no	—
57	C₉×C₄⋊C₄	—	2	4	no	—
58	C₉×C₄⋊C₄	—	2	8	no	—
59	C₉×C₄⋊C₄	—	2	4	no	—
60	C₉×C₄⋊C₄	—	4	2	no	—
61	C₉×C₂²⋊C₄	—	2	4	no	—
62	C₉×C₂²⋊C₄	—	2	8	no	—
63	C₉×C₂²⋊C₄	—	4	4	no	—
64	C₄²×C₉	—	2	4	no	—
65	C₄²×C₉	D₄	1	4	yes	—
66	#2538	C₉	1	1	yes	characteristic, direct product factor, Sylow
67	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
68	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
69	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
70	C₃×C₂²⋊Q₈	—	2	8	no	—
71	C₃×C₄×Q₈	—	2	4	no	—
72	C₃×C₄×D₄	—	2	4	no	—
73	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
75	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
76	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
78	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
79	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
80	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
81	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
82	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
83	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
84	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
85	C₃×#95	C₂²×C₃	1	4	yes	—
86	C₂³×C₉	—	2	2	no	—
87	C₂³×C₉	—	2	2	no	—
88	C₂³×C₉	—	2	2	no	—
89	C₂³×C₉	—	2	2	no	—
90	C₂³×C₉	—	2	2	no	—
91	C₂³×C₉	—	2	2	no	—
92	C₂³×C₉	C₂×Q₈	1	4	yes	—
93	C₂³×C₉	C₂⁴	1	1	yes	characteristic
94	Q₈×C₉	—	2	8	no	—
95	D₄×C₉	—	2	8	no	—
96	C₂×C₄×C₉	—	2	2	no	—
97	C₂×C₄×C₉	—	2	2	no	—
98	C₂×C₄×C₉	—	2	1	no	—
99	C₂×C₄×C₉	—	2	1	no	—
100	C₂×C₄×C₉	—	2	2	no	—
101	C₂×C₄×C₉	—	2	4	no	—
102	C₂×C₄×C₉	—	2	2	no	—
103	C₂×C₄×C₉	—	2	2	no	—
104	C₂×C₄×C₉	—	2	4	no	—
105	C₂×C₄×C₉	—	2	2	no	—
106	C₂×C₄×C₉	—	2	2	no	—
107	C₂×C₄×C₉	—	2	4	no	—
108	C₂×C₄×C₉	—	2	2	no	—
109	C₂×C₄×C₉	—	4	8	no	—
110	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
111	C₂×C₄×C₉	C₂×D₄	1	4	yes	—
112	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
113	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
114	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
115	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
116	C₂×C₄×C₉	#41	1	2	yes	—
117	C₂×C₄×C₉	#41	1	2	yes	—
118	C₂×C₂²⋊Q₈	C₂×C₉	1	2	yes	complemented
119	C₂×C₄×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
120	C₂×C₄×D₄	C₂×C₉	1	1	yes	characteristic
121	#396	C₂×C₉	1	4	yes	complemented
122	#390	C₂×C₉	1	2	yes	—
123	#389	C₂×C₉	1	2	yes	complemented
124	#384	C₂×C₉	1	1	yes	characteristic, complemented
125	#380	C₂×C₉	1	2	yes	complemented
126	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
127	C₂×C₃×Q₈	—	2	2	no	—
128	C₂×C₃×Q₈	—	2	2	no	—
129	C₂×C₃×Q₈	C₃×D₄	1	4	yes	—
130	C₂×C₃×D₄	—	2	2	no	—
131	C₂×C₃×D₄	—	2	2	no	—
132	C₂×C₃×D₄	C₃×Q₈	1	4	yes	—
133	C₂²×C₃×C₄	—	2	4	no	—
134	C₂²×C₃×C₄	—	2	4	no	—
135	C₂²×C₃×C₄	—	2	4	no	—
136	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
137	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
138	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
139	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
140	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
141	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
142	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
143	C₃×C₄⋊C₄	—	2	2	no	—
144	C₃×C₄⋊C₄	—	2	4	no	—
145	C₃×C₄⋊C₄	—	2	2	no	—
146	C₃×C₄⋊C₄	—	2	4	no	—
147	C₃×C₄⋊C₄	—	2	8	no	—
148	C₃×C₄⋊C₄	—	2	4	no	—
149	C₃×C₄⋊C₄	—	4	2	no	—
150	C₃×C₂²⋊C₄	—	2	4	no	—
151	C₃×C₂²⋊C₄	—	2	8	no	—
152	C₃×C₂²⋊C₄	—	4	4	no	—
153	C₃×C₄²	—	2	4	no	—
154	C₃×C₄²	C₃×D₄	1	4	yes	—
155	C₂²×C₉	—	2	4	no	—
156	C₂²×C₉	—	2	4	no	—
157	C₂²×C₉	—	2	4	no	—
158	C₂²×C₉	—	4	2	no	—
159	C₂²×C₉	—	4	2	no	—
160	C₂²×C₉	—	4	2	no	—
161	C₂²×C₉	—	4	2	no	—
162	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
163	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
164	C₂²×C₉	C₂²×Q₈	1	1	yes	characteristic
165	C₂²×C₉	C₂×#41	1	1	yes	characteristic
166	C₂²×C₉	C₂×#41	1	1	yes	characteristic
167	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
168	C₂²×C₉	2₋¹⁺⁴	1	1	yes	characteristic
169	C₄×C₉	—	2	4	no	—
170	C₄×C₉	—	2	2	no	—
171	C₄×C₉	—	4	2	no	—
172	C₄×C₉	—	4	2	no	—
173	C₄×C₉	—	4	4	no	—
174	C₄×C₉	#121	1	4	yes	—
175	C₄×C₉	C₂²⋊Q₈	1	4	yes	complemented
176	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
177	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
178	C₂³×C₄	C₂²×C₉	1	2	yes	—
179	C₂²⋊Q₈	—	2	8	no	—
180	C₄×Q₈	—	2	4	no	—
181	C₄×D₄	—	2	4	no	—
182	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
183	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
184	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
185	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
186	C₂×C₄⋊C₄	C₂²×C₉	1	4	yes	—
187	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
188	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
189	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
190	C₂×C₂²⋊C₄	C₂²×C₉	1	4	yes	—
191	C₂×C₂²⋊C₄	C₂²×C₉	1	4	yes	—
192	C₂×C₄²	C₂²×C₉	1	2	yes	—
193	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
194	#95	C₂²×C₉	1	4	yes	—
195	C₂³×C₃	—	2	2	no	—
196	C₂³×C₃	—	2	2	no	—
197	C₂³×C₃	—	2	2	no	—
198	C₂³×C₃	—	2	2	no	—
199	C₂³×C₃	—	2	2	no	—
200	C₂³×C₃	—	2	2	no	—
201	C₂³×C₃	C₂×C₃×Q₈	1	4	yes	—
202	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
203	C₃×Q₈	—	2	8	no	—
204	C₃×D₄	—	2	8	no	—
205	C₂×C₃×C₄	—	2	2	no	—
206	C₂×C₃×C₄	—	2	2	no	—
207	C₂×C₃×C₄	—	2	1	no	—
208	C₂×C₃×C₄	—	2	1	no	—
209	C₂×C₃×C₄	—	2	2	no	—
210	C₂×C₃×C₄	—	2	4	no	—
211	C₂×C₃×C₄	—	2	2	no	—
212	C₂×C₃×C₄	—	2	2	no	—
213	C₂×C₃×C₄	—	2	4	no	—
214	C₂×C₃×C₄	—	2	2	no	—
215	C₂×C₃×C₄	—	2	2	no	—
216	C₂×C₃×C₄	—	2	4	no	—
217	C₂×C₃×C₄	—	2	2	no	—
218	C₂×C₃×C₄	—	4	8	no	—
219	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
220	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
221	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
222	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
223	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
224	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
225	C₂×C₃×C₄	C₃×#41	1	2	yes	—
226	C₂×C₃×C₄	C₃×#41	1	2	yes	—
227	C₂×C₉	—	4	4	no	—
228	C₂×C₉	C₂×#121	1	1	yes	characteristic
229	C₂×C₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
230	C₂×C₉	#537	1	1	yes	characteristic
231	C₂×C₉	D₄×Q₈	1	1	yes	characteristic
232	C₂×C₉	#550	1	1	yes	characteristic
233	C₂×C₉	#554	1	1	yes	characteristic
234	C₂×C₉	#556	1	1	yes	characteristic
235	C₂⁴	C₂³×C₉	1	2	yes	—
236	C₂×Q₈	—	2	2	no	—
237	C₂×Q₈	—	2	2	no	—
238	C₂×Q₈	D₄×C₉	1	4	yes	complemented
239	C₂×D₄	—	2	2	no	—
240	C₂×D₄	—	2	2	no	—
241	C₂×D₄	Q₈×C₉	1	4	yes	complemented
242	C₂²×C₄	—	2	4	no	—
243	C₂²×C₄	—	2	4	no	—
244	C₂²×C₄	—	2	4	no	—
245	C₂²×C₄	C₂³×C₉	1	2	yes	—
246	C₂²×C₄	C₂³×C₉	1	2	yes	—
247	C₂²×C₄	C₂³×C₉	1	4	yes	—
248	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
249	C₂²×C₄	C₂³×C₉	1	2	yes	—
250	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
251	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
252	C₄⋊C₄	—	2	2	no	—
253	C₄⋊C₄	—	2	4	no	—
254	C₄⋊C₄	—	2	2	no	—
255	C₄⋊C₄	—	2	4	no	—
256	C₄⋊C₄	—	2	8	no	—
257	C₄⋊C₄	—	2	4	no	—
258	C₄⋊C₄	—	4	2	no	—
259	C₂²⋊C₄	—	2	4	no	—
260	C₂²⋊C₄	—	2	8	no	—
261	C₂²⋊C₄	—	4	4	no	—
262	C₄²	—	2	4	no	—
263	C₄²	D₄×C₉	1	4	yes	—
264	C₂²×C₃	—	2	4	no	—
265	C₂²×C₃	—	2	4	no	—
266	C₂²×C₃	—	2	4	no	—
267	C₂²×C₃	—	4	2	no	—
268	C₂²×C₃	—	4	2	no	—
269	C₂²×C₃	—	4	2	no	—
270	C₂²×C₃	—	4	2	no	—
271	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
272	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
273	C₂²×C₃	C₂²×C₃×Q₈	1	1	yes	characteristic
274	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
275	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
276	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
277	C₂²×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
278	C₃×C₄	—	2	4	no	—
279	C₃×C₄	—	2	2	no	—
280	C₃×C₄	—	4	2	no	—
281	C₃×C₄	—	4	2	no	—
282	C₃×C₄	—	4	4	no	—
283	C₃×C₄	C₃×#121	1	4	yes	—
284	C₃×C₄	C₃×C₂²⋊Q₈	1	4	yes	—
285	C₉	#2538	1	1	yes	characteristic, direct product factor, Sylow
286	C₂³	—	2	2	no	—
287	C₂³	—	2	2	no	—
288	C₂³	—	2	2	no	—
289	C₂³	—	2	2	no	—
290	C₂³	—	2	2	no	—
291	C₂³	—	2	2	no	—
292	C₂³	C₂×Q₈×C₉	1	4	yes	—
293	C₂³	C₂⁴×C₉	1	1	yes	characteristic
294	Q₈	—	2	8	no	—
295	D₄	—	2	8	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	4	8	no	—
310	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
311	C₂×C₄	C₂×D₄×C₉	1	4	yes	—
312	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
313	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
314	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
315	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
316	C₂×C₄	C₉×#41	1	2	yes	—
317	C₂×C₄	C₉×#41	1	2	yes	—
318	C₂×C₃	—	4	4	no	—
319	C₂×C₃	C₂×C₃×#121	1	1	yes	characteristic
320	C₂×C₃	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
321	C₂×C₃	C₃×#537	1	1	yes	characteristic
322	C₂×C₃	C₃×D₄×Q₈	1	1	yes	characteristic
323	C₂×C₃	C₃×#550	1	1	yes	characteristic
324	C₂×C₃	C₃×#554	1	1	yes	characteristic
325	C₂×C₃	C₃×#556	1	1	yes	characteristic
326	C₂²	—	2	4	no	—
327	C₂²	—	2	4	no	—
328	C₂²	—	2	4	no	—
329	C₂²	—	4	2	no	—
330	C₂²	—	4	2	no	—
331	C₂²	—	4	2	no	—
332	C₂²	—	4	2	no	—
333	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
334	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
335	C₂²	C₂²×Q₈×C₉	1	1	yes	characteristic
336	C₂²	C₂×C₉×#41	1	1	yes	characteristic
337	C₂²	C₂×C₉×#41	1	1	yes	characteristic
338	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
339	C₂²	C₉×2₋¹⁺⁴	1	1	yes	characteristic
340	C₄	—	2	4	no	—
341	C₄	—	2	2	no	—
342	C₄	—	4	2	no	—
343	C₄	—	4	2	no	—
344	C₄	—	4	4	no	—
345	C₄	C₉×#121	1	4	yes	—
346	C₄	C₉×C₂²⋊Q₈	1	4	yes	complemented
347	C₃	C₃×#2538	1	1	yes	characteristic
348	C₂	—	4	4	no	—
349	C₂	C₂×C₉×#121	1	1	yes	characteristic
350	C₂	C₂×C₉×C₂²⋊Q₈	1	1	yes	characteristic
351	C₂	C₉×#537	1	1	yes	characteristic
352	C₂	D₄×Q₈×C₉	1	1	yes	characteristic
353	C₂	C₉×#550	1	1	yes	characteristic
354	C₂	C₉×#554	1	1	yes	characteristic
355	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	C₂²×C₃×D₄	C₂²×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. C₂×C₉×C₂²⋊Q₈	C₂	semidirect
2. C₂×C₄×Q₈×C₉	C₂	semidirect
4. C₉×#396	C₂	semidirect
6. C₉×#389	C₂	semidirect
7. C₉×#384	C₂	semidirect
8. C₉×#380	C₂	semidirect
40. C₂×Q₈×C₉	D₄	semidirect
43. C₂×D₄×C₉	Q₈	semidirect
66. #2538	C₉	direct (N × H)
118. C₂×C₂²⋊Q₈	C₂×C₉	semidirect
119. C₂×C₄×Q₈	C₂×C₉	semidirect
121. #396	C₂×C₉	semidirect
123. #389	C₂×C₉	semidirect
124. #384	C₂×C₉	semidirect
125. #380	C₂×C₉	semidirect
175. C₄×C₉	C₂²⋊Q₈	semidirect
238. C₂×Q₈	D₄×C₉	semidirect
241. C₂×D₄	Q₈×C₉	semidirect
285. C₉	#2538	direct (N × H)
346. C₄	C₉×C₂²⋊Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×C₂²⋊Q₈	2
C₂×C₄×Q₈×C₉	2
C₂×C₄×D₄×C₉	2
C₉×#396	2
C₉×#390	2
C₉×#389	2
C₉×#384	2
C₉×#380	2
C₃×#2538	3

Subgroups — C9×#2538 #11767259

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2538 #11767259