Subgroups — C₂×C₉×#465 #11767768

Order 1152.

846 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₉×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₉×#121	C₂	1	1	yes	maximal, characteristic
5	C₉×#465	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₉×#106	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₉×#102	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#465	C₃	1	1	yes	maximal, characteristic
10	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
11	C₂²×D₄×C₉	—	2	1	no	—
12	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
13	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
14	C₂×C₉×SD₁₆	—	2	4	no	—
15	C₂×C₉×SD₁₆	C₂²	1	4	yes	complemented
16	C₂²×C₈×C₉	—	2	4	no	—
17	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
18	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
19	C₂²×C₈×C₉	C₂²	1	4	yes	complemented
20	C₉×C₂²⋊Q₈	—	2	2	no	—
21	C₉×C₂²⋊Q₈	C₂²	1	4	yes	complemented
22	C₉×#121	—	2	2	no	—
23	C₉×#121	C₂²	1	4	yes	—
24	C₂×C₉×C₄⋊C₄	—	2	1	no	—
25	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
28	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
29	C₉×#106	C₂²	1	4	yes	complemented
30	C₉×#103	C₂²	1	4	yes	complemented
31	C₉×#102	C₂²	1	4	yes	complemented
32	C₂²×C₃×SD₁₆	C₂×C₃	1	1	yes	characteristic
33	C₂³×C₃×C₈	C₂×C₃	1	1	yes	characteristic
34	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
35	C₂×C₃×#121	C₂×C₃	1	1	yes	characteristic
36	C₃×#465	C₂×C₃	1	8	yes	—
37	C₂×C₃×#106	C₂×C₃	1	1	yes	characteristic
38	C₂×C₃×#103	C₂×C₃	1	1	yes	characteristic
39	C₂×C₃×#102	C₂×C₃	1	1	yes	characteristic
40	C₂⁴×C₉	—	2	1	no	—
41	C₂⁴×C₉	D₄	1	1	yes	characteristic
42	C₂×Q₈×C₉	—	2	1	no	—
43	C₂×Q₈×C₉	—	2	2	no	—
44	C₂×Q₈×C₉	—	2	2	no	—
45	C₂×Q₈×C₉	C₂³	1	2	yes	—
46	C₂×D₄×C₉	—	2	4	no	—
47	C₂×D₄×C₉	—	2	2	no	—
48	C₂×D₄×C₉	—	2	1	no	—
49	C₂×D₄×C₉	—	2	2	no	—
50	C₂×D₄×C₉	—	4	4	no	—
51	C₂×D₄×C₉	C₂³	1	2	yes	—
52	C₂²×C₄×C₉	—	2	2	no	—
53	C₂²×C₄×C₉	—	2	2	no	—
54	C₂²×C₄×C₉	—	2	1	no	—
55	C₂²×C₄×C₉	—	2	1	no	—
56	C₂²×C₄×C₉	—	2	1	no	—
57	C₂²×C₄×C₉	D₄	1	2	yes	—
58	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
59	C₂²×C₄×C₉	C₂³	1	2	yes	—
60	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
61	C₉×SD₁₆	—	2	8	no	—
62	C₂×C₈×C₉	—	2	2	no	—
63	C₂×C₈×C₉	—	2	8	no	—
64	C₂×C₈×C₉	D₄	1	4	yes	complemented
65	C₂×C₈×C₉	C₂³	1	2	yes	—
66	C₂×C₈×C₉	C₂³	1	2	yes	—
67	C₉×C₄⋊C₄	—	2	4	no	—
68	C₉×C₄⋊C₄	—	2	1	no	—
69	C₉×C₄⋊C₄	—	2	1	no	—
70	C₉×C₄⋊C₄	C₂³	1	2	yes	—
71	C₉×C₄⋊C₄	C₂³	1	2	yes	—
72	C₉×C₂²⋊C₄	—	2	4	no	—
73	C₉×C₂²⋊C₄	—	2	4	no	—
74	C₂×#465	C₉	1	1	yes	characteristic, direct product factor, Sylow
75	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
76	C₂²×C₃×D₄	—	2	1	no	—
77	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
78	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
79	C₂×C₃×SD₁₆	—	2	4	no	—
80	C₂×C₃×SD₁₆	C₂²×C₃	1	4	yes	—
81	C₂²×C₃×C₈	—	2	4	no	—
82	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
83	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
84	C₂²×C₃×C₈	C₂²×C₃	1	4	yes	—
85	C₃×C₂²⋊Q₈	—	2	2	no	—
86	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
87	C₃×#121	—	2	2	no	—
88	C₃×#121	C₂²×C₃	1	4	yes	—
89	C₂×C₃×C₄⋊C₄	—	2	1	no	—
90	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
91	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
93	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
94	C₃×#106	C₂²×C₃	1	4	yes	—
95	C₃×#103	C₂²×C₃	1	4	yes	—
96	C₃×#102	C₂²×C₃	1	4	yes	—
97	C₂³×C₉	—	2	2	no	—
98	C₂³×C₉	—	2	2	no	—
99	C₂³×C₉	—	2	2	no	—
100	C₂³×C₉	—	4	2	no	—
101	C₂³×C₉	—	4	2	no	—
102	C₂³×C₉	—	4	2	no	—
103	C₂³×C₉	SD₁₆	1	4	yes	complemented
104	C₂³×C₉	C₂×D₄	1	2	yes	—
105	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
106	Q₈×C₉	—	2	2	no	—
107	Q₈×C₉	—	2	2	no	—
108	Q₈×C₉	—	4	2	no	—
109	D₄×C₉	—	2	2	no	—
110	D₄×C₉	—	2	2	no	—
111	D₄×C₉	—	4	8	no	—
112	D₄×C₉	—	4	2	no	—
113	C₂×C₄×C₉	—	2	2	no	—
114	C₂×C₄×C₉	—	2	4	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	—	2	2	no	—
120	C₂×C₄×C₉	—	4	2	no	—
121	C₂×C₄×C₉	—	4	2	no	—
122	C₂×C₄×C₉	—	4	2	no	—
123	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
124	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
125	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
126	C₂×C₄×C₉	#41	1	2	yes	—
127	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
128	C₈×C₉	—	2	2	no	—
129	C₈×C₉	C₂×D₄	1	4	yes	complemented
130	C₂²×SD₁₆	C₂×C₉	1	1	yes	characteristic, complemented
131	C₂³×C₈	C₂×C₉	1	1	yes	characteristic, complemented
132	C₂×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
133	C₂×#121	C₂×C₉	1	1	yes	characteristic
134	#465	C₂×C₉	1	8	yes	direct product factor
135	C₂×#106	C₂×C₉	1	1	yes	characteristic, complemented
136	C₂×#103	C₂×C₉	1	1	yes	characteristic, complemented
137	C₂×#102	C₂×C₉	1	1	yes	characteristic, complemented
138	C₂⁴×C₃	—	2	1	no	—
139	C₂⁴×C₃	C₃×D₄	1	1	yes	characteristic
140	C₂×C₃×Q₈	—	2	1	no	—
141	C₂×C₃×Q₈	—	2	2	no	—
142	C₂×C₃×Q₈	—	2	2	no	—
143	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
144	C₂×C₃×D₄	—	2	4	no	—
145	C₂×C₃×D₄	—	2	2	no	—
146	C₂×C₃×D₄	—	2	1	no	—
147	C₂×C₃×D₄	—	2	2	no	—
148	C₂×C₃×D₄	—	4	4	no	—
149	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
150	C₂²×C₃×C₄	—	2	2	no	—
151	C₂²×C₃×C₄	—	2	2	no	—
152	C₂²×C₃×C₄	—	2	1	no	—
153	C₂²×C₃×C₄	—	2	1	no	—
154	C₂²×C₃×C₄	—	2	1	no	—
155	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
156	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
157	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
158	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
159	C₃×SD₁₆	—	2	8	no	—
160	C₂×C₃×C₈	—	2	2	no	—
161	C₂×C₃×C₈	—	2	8	no	—
162	C₂×C₃×C₈	C₃×D₄	1	4	yes	—
163	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
164	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
165	C₃×C₄⋊C₄	—	2	4	no	—
166	C₃×C₄⋊C₄	—	2	1	no	—
167	C₃×C₄⋊C₄	—	2	1	no	—
168	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
169	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
170	C₃×C₂²⋊C₄	—	2	4	no	—
171	C₃×C₂²⋊C₄	—	2	4	no	—
172	C₂²×C₉	—	2	2	no	—
173	C₂²×C₉	—	2	2	no	—
174	C₂²×C₉	—	2	8	no	—
175	C₂²×C₉	—	4	2	no	—
176	C₂²×C₉	—	4	2	no	—
177	C₂²×C₉	—	4	2	no	—
178	C₂²×C₉	—	8	4	no	—
179	C₂²×C₉	#121	1	2	yes	—
180	C₂²×C₉	C₂×SD₁₆	1	2	yes	—
181	C₂²×C₉	C₂×SD₁₆	1	4	yes	complemented
182	C₂²×C₉	#135	1	2	yes	—
183	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
184	C₄×C₉	—	2	2	no	—
185	C₄×C₉	—	4	2	no	—
186	C₄×C₉	—	4	2	no	—
187	C₄×C₉	—	4	2	no	—
188	C₄×C₉	#121	1	2	yes	—
189	C₄×C₉	C₂²×D₄	1	1	yes	characteristic
190	C₄×C₉	C₂×#41	1	1	yes	characteristic
191	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
192	C₂²×D₄	—	2	1	no	—
193	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
194	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
195	C₂×SD₁₆	—	2	4	no	—
196	C₂×SD₁₆	C₂²×C₉	1	4	yes	complemented
197	C₂²×C₈	—	2	4	no	—
198	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
199	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
200	C₂²×C₈	C₂²×C₉	1	4	yes	complemented
201	C₂²⋊Q₈	—	2	2	no	—
202	C₂²⋊Q₈	C₂²×C₉	1	4	yes	complemented
203	#121	—	2	2	no	—
204	#121	C₂²×C₉	1	4	yes	—
205	C₂×C₄⋊C₄	—	2	1	no	—
206	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
207	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
208	C₂×C₂²⋊C₄	—	2	1	no	—
209	C₂×C₂²⋊C₄	—	2	1	no	—
210	#106	C₂²×C₉	1	4	yes	complemented
211	#103	C₂²×C₉	1	4	yes	complemented
212	#102	C₂²×C₉	1	4	yes	complemented
213	C₂³×C₃	—	2	2	no	—
214	C₂³×C₃	—	2	2	no	—
215	C₂³×C₃	—	2	2	no	—
216	C₂³×C₃	—	4	2	no	—
217	C₂³×C₃	—	4	2	no	—
218	C₂³×C₃	—	4	2	no	—
219	C₂³×C₃	C₃×SD₁₆	1	4	yes	—
220	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
221	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
222	C₃×Q₈	—	2	2	no	—
223	C₃×Q₈	—	2	2	no	—
224	C₃×Q₈	—	4	2	no	—
225	C₃×D₄	—	2	2	no	—
226	C₃×D₄	—	2	2	no	—
227	C₃×D₄	—	4	8	no	—
228	C₃×D₄	—	4	2	no	—
229	C₂×C₃×C₄	—	2	2	no	—
230	C₂×C₃×C₄	—	2	4	no	—
231	C₂×C₃×C₄	—	2	2	no	—
232	C₂×C₃×C₄	—	2	2	no	—
233	C₂×C₃×C₄	—	2	2	no	—
234	C₂×C₃×C₄	—	2	2	no	—
235	C₂×C₃×C₄	—	2	2	no	—
236	C₂×C₃×C₄	—	4	2	no	—
237	C₂×C₃×C₄	—	4	2	no	—
238	C₂×C₃×C₄	—	4	2	no	—
239	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
240	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
241	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
242	C₂×C₃×C₄	C₃×#41	1	2	yes	—
243	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
244	C₃×C₈	—	2	2	no	—
245	C₃×C₈	C₂×C₃×D₄	1	4	yes	—
246	C₂×C₉	—	2	4	no	—
247	C₂×C₉	—	8	2	no	—
248	C₂×C₉	#465	1	4	yes	direct product factor
249	C₂×C₉	C₂×#121	1	1	yes	characteristic
250	C₂×C₉	C₂²×SD₁₆	1	1	yes	characteristic
251	C₂×C₉	C₂×#135	1	1	yes	characteristic
252	C₂⁴	—	2	1	no	—
253	C₂⁴	D₄×C₉	1	1	yes	characteristic
254	C₂×Q₈	—	2	1	no	—
255	C₂×Q₈	—	2	2	no	—
256	C₂×Q₈	—	2	2	no	—
257	C₂×Q₈	C₂³×C₉	1	2	yes	—
258	C₂×D₄	—	2	4	no	—
259	C₂×D₄	—	2	2	no	—
260	C₂×D₄	—	2	1	no	—
261	C₂×D₄	—	2	2	no	—
262	C₂×D₄	—	4	4	no	—
263	C₂×D₄	C₂³×C₉	1	2	yes	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	2	1	no	—
269	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
270	C₂²×C₄	D₄×C₉	1	2	yes	—
271	C₂²×C₄	C₂³×C₉	1	2	yes	—
272	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
273	SD₁₆	—	2	8	no	—
274	C₂×C₈	—	2	2	no	—
275	C₂×C₈	—	2	8	no	—
276	C₂×C₈	D₄×C₉	1	4	yes	complemented
277	C₂×C₈	C₂³×C₉	1	2	yes	—
278	C₂×C₈	C₂³×C₉	1	2	yes	—
279	C₄⋊C₄	—	2	4	no	—
280	C₄⋊C₄	—	2	1	no	—
281	C₄⋊C₄	—	2	1	no	—
282	C₄⋊C₄	C₂³×C₉	1	2	yes	—
283	C₄⋊C₄	C₂³×C₉	1	2	yes	—
284	C₂²⋊C₄	—	2	4	no	—
285	C₂²⋊C₄	—	2	4	no	—
286	C₂²×C₃	—	2	2	no	—
287	C₂²×C₃	—	2	8	no	—
288	C₂²×C₃	—	2	2	no	—
289	C₂²×C₃	—	4	2	no	—
290	C₂²×C₃	—	4	2	no	—
291	C₂²×C₃	—	4	2	no	—
292	C₂²×C₃	—	8	4	no	—
293	C₂²×C₃	C₃×#121	1	2	yes	—
294	C₂²×C₃	C₂×C₃×SD₁₆	1	2	yes	—
295	C₂²×C₃	C₂×C₃×SD₁₆	1	4	yes	—
296	C₂²×C₃	C₃×#135	1	2	yes	—
297	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
298	C₃×C₄	—	2	2	no	—
299	C₃×C₄	—	4	2	no	—
300	C₃×C₄	—	4	2	no	—
301	C₃×C₄	—	4	2	no	—
302	C₃×C₄	C₃×#121	1	2	yes	—
303	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
304	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
305	C₉	C₂×#465	1	1	yes	characteristic, direct product factor, Sylow
306	C₂³	—	2	2	no	—
307	C₂³	—	2	2	no	—
308	C₂³	—	2	2	no	—
309	C₂³	—	4	2	no	—
310	C₂³	—	4	2	no	—
311	C₂³	—	4	2	no	—
312	C₂³	C₉×SD₁₆	1	4	yes	complemented
313	C₂³	C₂×D₄×C₉	1	2	yes	—
314	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
315	Q₈	—	2	2	no	—
316	Q₈	—	2	2	no	—
317	Q₈	—	4	2	no	—
318	D₄	—	2	2	no	—
319	D₄	—	2	2	no	—
320	D₄	—	4	8	no	—
321	D₄	—	4	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
333	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
334	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
335	C₂×C₄	C₉×#41	1	2	yes	—
336	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
337	C₈	—	2	2	no	—
338	C₈	C₂×D₄×C₉	1	4	yes	complemented
339	C₂×C₃	—	2	4	no	—
340	C₂×C₃	—	8	2	no	—
341	C₂×C₃	C₃×#465	1	4	yes	—
342	C₂×C₃	C₂×C₃×#121	1	1	yes	characteristic
343	C₂×C₃	C₂²×C₃×SD₁₆	1	1	yes	characteristic
344	C₂×C₃	C₂×C₃×#135	1	1	yes	characteristic
345	C₂²	—	2	2	no	—
346	C₂²	—	2	2	no	—
347	C₂²	—	2	8	no	—
348	C₂²	—	4	2	no	—
349	C₂²	—	4	2	no	—
350	C₂²	—	4	2	no	—
351	C₂²	—	8	4	no	—
352	C₂²	C₉×#121	1	2	yes	—
353	C₂²	C₂×C₉×SD₁₆	1	2	yes	—
354	C₂²	C₂×C₉×SD₁₆	1	4	yes	complemented
355	C₂²	C₉×#135	1	2	yes	—
356	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
357	C₄	—	2	2	no	—
358	C₄	—	4	2	no	—
359	C₄	—	4	2	no	—
360	C₄	—	4	2	no	—
361	C₄	C₉×#121	1	2	yes	—
362	C₄	C₂²×D₄×C₉	1	1	yes	characteristic
363	C₄	C₂×C₉×#41	1	1	yes	characteristic
364	C₃	C₂×C₃×#465	1	1	yes	characteristic
365	C₂	—	2	4	no	—
366	C₂	—	8	2	no	—
367	C₂	C₉×#465	1	4	yes	direct product factor
368	C₂	C₂×C₉×#121	1	1	yes	characteristic
369	C₂	C₂²×C₉×SD₁₆	1	1	yes	characteristic
370	C₂	C₂×C₉×#135	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂×D₄
commutator	C₂×C₄	C₂⁴×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃
socle	C₂³×C₃	C₂×C₃×D₄
prime radical	C₂×C₃×#121	C₂×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₉ ◁ C₂³×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₉×SD₁₆	C₂	semidirect
2. C₂³×C₈×C₉	C₂	semidirect
3. C₂×C₉×C₂²⋊Q₈	C₂	semidirect
5. C₉×#465	C₂	direct (N × H)
6. C₂×C₉×#106	C₂	semidirect
7. C₂×C₉×#103	C₂	semidirect
8. C₂×C₉×#102	C₂	semidirect
15. C₂×C₉×SD₁₆	C₂²	semidirect
19. C₂²×C₈×C₉	C₂²	semidirect
21. C₉×C₂²⋊Q₈	C₂²	semidirect
29. C₉×#106	C₂²	semidirect
30. C₉×#103	C₂²	semidirect
31. C₉×#102	C₂²	semidirect
64. C₂×C₈×C₉	D₄	semidirect
74. C₂×#465	C₉	direct (N × H)
103. C₂³×C₉	SD₁₆	semidirect
129. C₈×C₉	C₂×D₄	semidirect
130. C₂²×SD₁₆	C₂×C₉	semidirect
131. C₂³×C₈	C₂×C₉	semidirect
132. C₂×C₂²⋊Q₈	C₂×C₉	semidirect
134. #465	C₂×C₉	direct (N × H)
135. C₂×#106	C₂×C₉	semidirect
136. C₂×#103	C₂×C₉	semidirect
137. C₂×#102	C₂×C₉	semidirect
181. C₂²×C₉	C₂×SD₁₆	semidirect
196. C₂×SD₁₆	C₂²×C₉	semidirect
200. C₂²×C₈	C₂²×C₉	semidirect
202. C₂²⋊Q₈	C₂²×C₉	semidirect
210. #106	C₂²×C₉	semidirect
211. #103	C₂²×C₉	semidirect
212. #102	C₂²×C₉	semidirect
248. C₂×C₉	#465	direct (N × H)
276. C₂×C₈	D₄×C₉	semidirect
305. C₉	C₂×#465	direct (N × H)
312. C₂³	C₉×SD₁₆	semidirect
338. C₈	C₂×D₄×C₉	semidirect
354. C₂²	C₂×C₉×SD₁₆	semidirect
367. C₂	C₉×#465	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₉×SD₁₆	2
C₂³×C₈×C₉	2
C₂×C₉×C₂²⋊Q₈	2
C₂×C₉×#121	2
C₉×#465	2
C₂×C₉×#106	2
C₂×C₉×#103	2
C₂×C₉×#102	2
C₂×C₃×#465	3

Subgroups — C2×C9×#465 #11767768

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#465 #11767768