Subgroups — C₉×#2036 #11766757

Order 1152.

474 conjugacy classes of subgroups.

The subgroup lattice has 390 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	1	yes	maximal, characteristic
2	C₂×C₉×#107	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
6	C₉×#380	C₂	1	1	yes	maximal, characteristic
7	C₉×#340	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2036	C₃	1	1	yes	maximal, characteristic
9	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
10	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
11	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
12	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
13	C₉×C₂²⋊Q₈	—	2	2	no	—
14	C₉×C₂²⋊Q₈	—	2	2	no	—
15	C₂×C₉×C₄⋊C₄	—	2	1	no	—
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×C₂²⋊C₄	—	2	1	no	—
20	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
21	C₉×#107	—	2	2	no	—
22	C₉×#103	—	2	2	no	—
23	C₉×#103	—	2	2	no	—
24	C₉×C₂²⋊C₈	—	2	2	no	—
25	C₉×#95	—	2	1	no	—
26	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
27	C₂×C₃×#107	C₂×C₃	1	1	yes	characteristic
28	C₂×C₃×#103	C₂×C₃	1	1	yes	characteristic
29	C₂×C₃×#103	C₂×C₃	1	1	yes	characteristic
30	C₂×C₃×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic
31	C₃×#380	C₂×C₃	1	1	yes	characteristic
32	C₃×#340	C₂×C₃	1	1	yes	characteristic
33	C₂⁴×C₉	D₄	1	1	yes	characteristic
34	C₂×Q₈×C₉	—	2	1	no	—
35	C₂×Q₈×C₉	—	2	1	no	—
36	C₂×Q₈×C₉	—	2	1	no	—
37	C₂×Q₈×C₉	—	2	1	no	—
38	C₂×Q₈×C₉	—	2	1	no	—
39	C₂×Q₈×C₉	D₄	1	2	yes	—
40	C₂²×C₄×C₉	—	2	1	no	—
41	C₂²×C₄×C₉	—	2	1	no	—
42	C₂²×C₄×C₉	—	2	1	no	—
43	C₂²×C₄×C₉	—	2	1	no	—
44	C₂²×C₄×C₉	—	2	1	no	—
45	C₂²×C₄×C₉	—	2	1	no	—
46	C₂²×C₄×C₉	—	2	1	no	—
47	C₂²×C₄×C₉	—	2	1	no	—
48	C₂²×C₄×C₉	—	2	1	no	—
49	C₂²×C₄×C₉	—	2	1	no	—
50	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
51	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
52	C₂×C₈×C₉	—	2	1	no	—
53	C₂×C₈×C₉	—	2	1	no	—
54	C₂×C₈×C₉	—	2	1	no	—
55	C₂×C₈×C₉	—	2	1	no	—
56	C₂×C₈×C₉	—	2	1	no	—
57	C₂×C₈×C₉	D₄	1	2	yes	—
58	C₉×C₄⋊C₄	—	2	4	no	—
59	C₉×C₄⋊C₄	—	2	1	no	—
60	C₉×C₄⋊C₄	—	2	1	no	—
61	C₉×C₄⋊C₄	—	2	1	no	—
62	C₉×C₄⋊C₄	—	2	1	no	—
63	C₉×C₄⋊C₄	—	2	1	no	—
64	C₉×C₄⋊C₄	D₄	1	2	yes	—
65	C₉×C₂²⋊C₄	—	2	4	no	—
66	C₉×C₂²⋊C₄	—	4	2	no	—
67	#2036	C₉	1	1	yes	characteristic, direct product factor, Sylow
68	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
69	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
70	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
71	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
72	C₃×C₂²⋊Q₈	—	2	2	no	—
73	C₃×C₂²⋊Q₈	—	2	2	no	—
74	C₂×C₃×C₄⋊C₄	—	2	1	no	—
75	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
79	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
80	C₃×#107	—	2	2	no	—
81	C₃×#103	—	2	2	no	—
82	C₃×#103	—	2	2	no	—
83	C₃×C₂²⋊C₈	—	2	2	no	—
84	C₃×#95	—	2	1	no	—
85	C₂³×C₉	—	2	1	no	—
86	C₂³×C₉	—	2	1	no	—
87	C₂³×C₉	—	2	1	no	—
88	C₂³×C₉	—	2	1	no	—
89	C₂³×C₉	—	2	1	no	—
90	C₂³×C₉	—	2	1	no	—
91	C₂³×C₉	Q₁₆	1	2	yes	—
92	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
93	Q₈×C₉	—	2	2	no	—
94	Q₈×C₉	—	2	2	no	—
95	Q₈×C₉	—	4	1	no	—
96	Q₈×C₉	—	4	1	no	—
97	C₂×C₄×C₉	—	2	2	no	—
98	C₂×C₄×C₉	—	2	2	no	—
99	C₂×C₄×C₉	—	2	1	no	—
100	C₂×C₄×C₉	—	2	1	no	—
101	C₂×C₄×C₉	—	2	1	no	—
102	C₂×C₄×C₉	—	4	1	no	—
103	C₂×C₄×C₉	—	4	1	no	—
104	C₂×C₄×C₉	—	4	1	no	—
105	C₂×C₄×C₉	—	4	1	no	—
106	C₂×C₄×C₉	—	4	1	no	—
107	C₂×C₄×C₉	—	4	1	no	—
108	C₂×C₄×C₉	—	4	1	no	—
109	C₂×C₄×C₉	—	4	1	no	—
110	C₂×C₄×C₉	—	4	1	no	—
111	C₂×C₄×C₉	—	4	1	no	—
112	C₂×C₄×C₉	—	4	1	no	—
113	C₂×C₄×C₉	—	4	1	no	—
114	C₂×C₄×C₉	—	4	1	no	—
115	C₂×C₄×C₉	—	4	1	no	—
116	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
117	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
118	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
119	C₂×C₄×C₉	#41	1	1	yes	characteristic
120	C₂×C₄×C₉	#41	1	1	yes	characteristic
121	C₂×C₄×C₉	#41	1	1	yes	characteristic
122	C₈×C₉	—	2	2	no	—
123	C₈×C₉	—	4	1	no	—
124	C₂×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic
125	C₂×#107	C₂×C₉	1	1	yes	characteristic, complemented
126	C₂×#103	C₂×C₉	1	1	yes	characteristic, complemented
127	C₂×#103	C₂×C₉	1	1	yes	characteristic, complemented
128	C₂×C₂²⋊C₈	C₂×C₉	1	1	yes	characteristic
129	#380	C₂×C₉	1	1	yes	characteristic
130	#340	C₂×C₉	1	1	yes	characteristic, complemented
131	C₂⁴×C₃	C₃×D₄	1	1	yes	characteristic
132	C₂×C₃×Q₈	—	2	1	no	—
133	C₂×C₃×Q₈	—	2	1	no	—
134	C₂×C₃×Q₈	—	2	1	no	—
135	C₂×C₃×Q₈	—	2	1	no	—
136	C₂×C₃×Q₈	—	2	1	no	—
137	C₂×C₃×Q₈	C₃×D₄	1	2	yes	—
138	C₂²×C₃×C₄	—	2	1	no	—
139	C₂²×C₃×C₄	—	2	1	no	—
140	C₂²×C₃×C₄	—	2	1	no	—
141	C₂²×C₃×C₄	—	2	1	no	—
142	C₂²×C₃×C₄	—	2	1	no	—
143	C₂²×C₃×C₄	—	2	1	no	—
144	C₂²×C₃×C₄	—	2	1	no	—
145	C₂²×C₃×C₄	—	2	1	no	—
146	C₂²×C₃×C₄	—	2	1	no	—
147	C₂²×C₃×C₄	—	2	1	no	—
148	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
149	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
150	C₂×C₃×C₈	—	2	1	no	—
151	C₂×C₃×C₈	—	2	1	no	—
152	C₂×C₃×C₈	—	2	1	no	—
153	C₂×C₃×C₈	—	2	1	no	—
154	C₂×C₃×C₈	—	2	1	no	—
155	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
156	C₃×C₄⋊C₄	—	2	4	no	—
157	C₃×C₄⋊C₄	—	2	1	no	—
158	C₃×C₄⋊C₄	—	2	1	no	—
159	C₃×C₄⋊C₄	—	2	1	no	—
160	C₃×C₄⋊C₄	—	2	1	no	—
161	C₃×C₄⋊C₄	—	2	1	no	—
162	C₃×C₄⋊C₄	C₃×D₄	1	2	yes	—
163	C₃×C₂²⋊C₄	—	2	4	no	—
164	C₃×C₂²⋊C₄	—	4	2	no	—
165	C₂²×C₉	—	2	2	no	—
166	C₂²×C₉	—	2	2	no	—
167	C₂²×C₉	—	2	2	no	—
168	C₂²×C₉	—	4	1	no	—
169	C₂²×C₉	—	4	1	no	—
170	C₂²×C₉	—	4	1	no	—
171	C₂²×C₉	—	4	1	no	—
172	C₂²×C₉	#120	1	1	yes	characteristic
173	C₂²×C₉	#121	1	1	yes	characteristic
174	C₂²×C₉	#123	1	1	yes	characteristic
175	C₂²×C₉	C₂×Q₁₆	1	1	yes	characteristic
176	C₂²×C₉	#135	1	1	yes	characteristic
177	C₂²×C₉	AGL(1,ℤ/8)	1	1	yes	characteristic
178	C₂²×C₉	#137	1	1	yes	characteristic
179	C₄×C₉	—	4	1	no	—
180	C₄×C₉	—	4	2	no	—
181	C₄×C₉	—	4	2	no	—
182	C₄×C₉	—	8	1	no	—
183	C₄×C₉	—	8	1	no	—
184	C₄×C₉	#121	1	1	yes	characteristic
185	C₄×C₉	#121	1	1	yes	characteristic
186	C₄×C₉	#123	1	1	yes	characteristic
187	C₄×C₉	#124	1	1	yes	characteristic
188	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
189	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
190	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
191	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
192	C₂²⋊Q₈	—	2	2	no	—
193	C₂²⋊Q₈	—	2	2	no	—
194	C₂×C₄⋊C₄	—	2	1	no	—
195	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
196	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
197	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
198	C₂×C₂²⋊C₄	—	2	1	no	—
199	C₂×C₂²⋊C₄	—	2	1	no	—
200	#107	—	2	2	no	—
201	#103	—	2	2	no	—
202	#103	—	2	2	no	—
203	C₂²⋊C₈	—	2	2	no	—
204	#95	—	2	1	no	—
205	C₂³×C₃	—	2	1	no	—
206	C₂³×C₃	—	2	1	no	—
207	C₂³×C₃	—	2	1	no	—
208	C₂³×C₃	—	2	1	no	—
209	C₂³×C₃	—	2	1	no	—
210	C₂³×C₃	—	2	1	no	—
211	C₂³×C₃	C₃×Q₁₆	1	2	yes	—
212	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
213	C₃×Q₈	—	2	2	no	—
214	C₃×Q₈	—	2	2	no	—
215	C₃×Q₈	—	4	1	no	—
216	C₃×Q₈	—	4	1	no	—
217	C₂×C₃×C₄	—	2	2	no	—
218	C₂×C₃×C₄	—	2	2	no	—
219	C₂×C₃×C₄	—	2	1	no	—
220	C₂×C₃×C₄	—	2	1	no	—
221	C₂×C₃×C₄	—	2	1	no	—
222	C₂×C₃×C₄	—	4	1	no	—
223	C₂×C₃×C₄	—	4	1	no	—
224	C₂×C₃×C₄	—	4	1	no	—
225	C₂×C₃×C₄	—	4	1	no	—
226	C₂×C₃×C₄	—	4	1	no	—
227	C₂×C₃×C₄	—	4	1	no	—
228	C₂×C₃×C₄	—	4	1	no	—
229	C₂×C₃×C₄	—	4	1	no	—
230	C₂×C₃×C₄	—	4	1	no	—
231	C₂×C₃×C₄	—	4	1	no	—
232	C₂×C₃×C₄	—	4	1	no	—
233	C₂×C₃×C₄	—	4	1	no	—
234	C₂×C₃×C₄	—	4	1	no	—
235	C₂×C₃×C₄	—	4	1	no	—
236	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
237	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
238	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
239	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
240	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
241	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
242	C₃×C₈	—	2	2	no	—
243	C₃×C₈	—	4	1	no	—
244	C₂×C₉	—	4	2	no	—
245	C₂×C₉	#394	1	1	yes	characteristic
246	C₂×C₉	#449	1	1	yes	characteristic
247	C₂×C₉	#451	1	1	yes	characteristic
248	C₂×C₉	#467	1	1	yes	characteristic
249	C₂×C₉	#468	1	1	yes	characteristic
250	C₂×C₉	#484	1	1	yes	characteristic
251	C₂×C₉	#485	1	1	yes	characteristic
252	C₂⁴	D₄×C₉	1	1	yes	characteristic
253	C₂×Q₈	—	2	1	no	—
254	C₂×Q₈	—	2	1	no	—
255	C₂×Q₈	—	2	1	no	—
256	C₂×Q₈	—	2	1	no	—
257	C₂×Q₈	—	2	1	no	—
258	C₂×Q₈	D₄×C₉	1	2	yes	—
259	C₂²×C₄	—	2	1	no	—
260	C₂²×C₄	—	2	1	no	—
261	C₂²×C₄	—	2	1	no	—
262	C₂²×C₄	—	2	1	no	—
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	2	1	no	—
265	C₂²×C₄	—	2	1	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	C₂³×C₉	1	1	yes	characteristic
271	C₂×C₈	—	2	1	no	—
272	C₂×C₈	—	2	1	no	—
273	C₂×C₈	—	2	1	no	—
274	C₂×C₈	—	2	1	no	—
275	C₂×C₈	—	2	1	no	—
276	C₂×C₈	D₄×C₉	1	2	yes	—
277	C₄⋊C₄	—	2	4	no	—
278	C₄⋊C₄	—	2	1	no	—
279	C₄⋊C₄	—	2	1	no	—
280	C₄⋊C₄	—	2	1	no	—
281	C₄⋊C₄	—	2	1	no	—
282	C₄⋊C₄	—	2	1	no	—
283	C₄⋊C₄	D₄×C₉	1	2	yes	—
284	C₂²⋊C₄	—	2	4	no	—
285	C₂²⋊C₄	—	4	2	no	—
286	C₂²×C₃	—	2	2	no	—
287	C₂²×C₃	—	2	2	no	—
288	C₂²×C₃	—	2	2	no	—
289	C₂²×C₃	—	4	1	no	—
290	C₂²×C₃	—	4	1	no	—
291	C₂²×C₃	—	4	1	no	—
292	C₂²×C₃	—	4	1	no	—
293	C₂²×C₃	C₃×#120	1	1	yes	characteristic
294	C₂²×C₃	C₃×#121	1	1	yes	characteristic
295	C₂²×C₃	C₃×#123	1	1	yes	characteristic
296	C₂²×C₃	C₂×C₃×Q₁₆	1	1	yes	characteristic
297	C₂²×C₃	C₃×#135	1	1	yes	characteristic
298	C₂²×C₃	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
299	C₂²×C₃	C₃×#137	1	1	yes	characteristic
300	C₃×C₄	—	4	1	no	—
301	C₃×C₄	—	4	2	no	—
302	C₃×C₄	—	4	2	no	—
303	C₃×C₄	—	8	1	no	—
304	C₃×C₄	—	8	1	no	—
305	C₃×C₄	C₃×#121	1	1	yes	characteristic
306	C₃×C₄	C₃×#121	1	1	yes	characteristic
307	C₃×C₄	C₃×#123	1	1	yes	characteristic
308	C₃×C₄	C₃×#124	1	1	yes	characteristic
309	C₉	#2036	1	1	yes	characteristic, direct product factor, Sylow
310	C₂³	—	2	1	no	—
311	C₂³	—	2	1	no	—
312	C₂³	—	2	1	no	—
313	C₂³	—	2	1	no	—
314	C₂³	—	2	1	no	—
315	C₂³	—	2	1	no	—
316	C₂³	C₉×Q₁₆	1	2	yes	—
317	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
318	Q₈	—	2	2	no	—
319	Q₈	—	2	2	no	—
320	Q₈	—	4	1	no	—
321	Q₈	—	4	1	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
342	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
343	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
344	C₂×C₄	C₉×#41	1	1	yes	characteristic
345	C₂×C₄	C₉×#41	1	1	yes	characteristic
346	C₂×C₄	C₉×#41	1	1	yes	characteristic
347	C₈	—	2	2	no	—
348	C₈	—	4	1	no	—
349	C₂×C₃	—	4	2	no	—
350	C₂×C₃	C₃×#394	1	1	yes	characteristic
351	C₂×C₃	C₃×#449	1	1	yes	characteristic
352	C₂×C₃	C₃×#451	1	1	yes	characteristic
353	C₂×C₃	C₃×#467	1	1	yes	characteristic
354	C₂×C₃	C₃×#468	1	1	yes	characteristic
355	C₂×C₃	C₃×#484	1	1	yes	characteristic
356	C₂×C₃	C₃×#485	1	1	yes	characteristic
357	C₂²	—	2	2	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	4	1	no	—
361	C₂²	—	4	1	no	—
362	C₂²	—	4	1	no	—
363	C₂²	—	4	1	no	—
364	C₂²	C₉×#120	1	1	yes	characteristic
365	C₂²	C₉×#121	1	1	yes	characteristic
366	C₂²	C₉×#123	1	1	yes	characteristic
367	C₂²	C₂×C₉×Q₁₆	1	1	yes	characteristic
368	C₂²	C₉×#135	1	1	yes	characteristic
369	C₂²	C₉×AGL(1,ℤ/8)	1	1	yes	characteristic
370	C₂²	C₉×#137	1	1	yes	characteristic
371	C₄	—	4	1	no	—
372	C₄	—	4	2	no	—
373	C₄	—	4	2	no	—
374	C₄	—	8	1	no	—
375	C₄	—	8	1	no	—
376	C₄	C₉×#121	1	1	yes	characteristic
377	C₄	C₉×#121	1	1	yes	characteristic
378	C₄	C₉×#123	1	1	yes	characteristic
379	C₄	C₉×#124	1	1	yes	characteristic
380	C₃	C₃×#2036	1	1	yes	characteristic
381	C₂	—	4	2	no	—
382	C₂	C₉×#394	1	1	yes	characteristic
383	C₂	C₉×#449	1	1	yes	characteristic
384	C₂	C₉×#451	1	1	yes	characteristic
385	C₂	C₉×#467	1	1	yes	characteristic
386	C₂	C₉×#468	1	1	yes	characteristic
387	C₂	C₉×#484	1	1	yes	characteristic
388	C₂	C₉×#485	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂×D₄
commutator	C₂²×C₄	C₂³×C₉
Frattini, cosocle	C₂²×C₃×C₄	C₂³×C₃
socle	C₂³×C₃	C₂×C₃×D₄
prime radical	C₂⁴×C₃	C₃×D₄
LCS	G ▷ C₂²×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
2. C₂×C₉×#107	C₂	semidirect
3. C₂×C₉×#103	C₂	semidirect
4. C₂×C₉×#103	C₂	semidirect
7. C₉×#340	C₂	semidirect
67. #2036	C₉	direct (N × H)
125. C₂×#107	C₂×C₉	semidirect
126. C₂×#103	C₂×C₉	semidirect
127. C₂×#103	C₂×C₉	semidirect
130. #340	C₂×C₉	semidirect
309. C₉	#2036	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×C₂²⋊Q₈	2
C₂×C₉×#107	2
C₂×C₉×#103	2
C₂×C₉×C₂²⋊C₈	2
C₉×#380	2
C₉×#340	2
C₃×#2036	3

Subgroups — C9×#2036 #11766757

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2036 #11766757