Subgroups — C₉×#3040 #11767761

Order 1152.

750 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#137	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
3	C₂×C₉×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₉×#41	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#464	C₂	1	4	yes	maximal, complemented
6	C₉×#463	C₂	1	4	yes	maximal, complemented
7	C₉×#423	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#419	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#418	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#3040	C₃	1	1	yes	maximal, characteristic
11	C₂×C₉×#41	C₂²	1	1	yes	characteristic
12	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
13	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
14	C₉×#137	—	2	4	no	—
15	C₉×AGL(1,ℤ/8)	—	2	4	no	—
16	C₂×C₉×Q₁₆	C₂²	1	2	yes	complemented
17	C₂×C₉×SD₁₆	C₂²	1	2	yes	—
18	C₂×C₉×SD₁₆	C₂²	1	2	yes	complemented
19	C₂×C₉×D₈	C₂²	1	2	yes	—
20	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
22	C₉×#124	—	2	1	no	—
23	C₉×#124	—	2	1	no	—
24	C₉×#124	C₂²	1	4	yes	—
25	C₄×Q₈×C₉	C₂²	1	2	yes	complemented
26	C₄×D₄×C₉	—	2	2	no	—
27	C₄×D₄×C₉	C₂²	1	2	yes	complemented
28	C₉×#117	—	2	1	no	—
29	C₉×#117	C₂²	1	1	yes	characteristic
30	C₂×C₉×C₂²⋊C₄	—	2	2	no	—
31	C₂×C₄²×C₉	—	2	1	no	—
32	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
33	C₉×C₄⋊C₈	C₂²	1	4	yes	complemented
34	C₉×#103	C₂²	1	4	yes	complemented
35	C₉×#102	C₂²	1	4	yes	—
36	C₂×C₃×#137	C₂×C₃	1	1	yes	characteristic
37	C₂×C₃×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic
38	C₂×C₃×#124	C₂×C₃	1	1	yes	characteristic
39	C₃×C₄×#41	C₂×C₃	1	1	yes	characteristic
40	C₃×#464	C₂×C₃	1	4	yes	—
41	C₃×#463	C₂×C₃	1	4	yes	—
42	C₃×#423	C₂×C₃	1	1	yes	characteristic
43	C₃×#419	C₂×C₃	1	1	yes	characteristic
44	C₃×#418	C₂×C₃	1	1	yes	characteristic
45	C₂⁴×C₉	—	2	1	no	—
46	C₉×#41	—	2	2	no	—
47	C₉×#41	D₄	1	4	yes	—
48	C₂×Q₈×C₉	—	2	1	no	—
49	C₂×Q₈×C₉	—	2	2	no	—
50	C₂×Q₈×C₉	—	2	2	no	—
51	C₂×Q₈×C₉	C₂³	1	2	yes	—
52	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
53	C₂×D₄×C₉	—	2	1	no	—
54	C₂×D₄×C₉	—	2	2	no	—
55	C₂×D₄×C₉	—	2	1	no	—
56	C₂×D₄×C₉	—	2	2	no	—
57	C₂×D₄×C₉	C₂³	1	2	yes	—
58	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
59	C₂²×C₄×C₉	—	2	1	no	—
60	C₂²×C₄×C₉	—	2	1	no	—
61	C₂²×C₄×C₉	—	2	2	no	—
62	C₂²×C₄×C₉	D₄	1	2	yes	—
63	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
64	C₉×Q₁₆	—	2	4	no	—
65	C₉×SD₁₆	—	2	4	no	—
66	C₉×SD₁₆	—	2	4	no	—
67	C₉×D₈	—	2	4	no	—
68	C₉×M₁₆	—	2	2	no	—
69	C₉×M₁₆	—	2	2	no	—
70	C₂×C₈×C₉	C₂³	1	2	yes	—
71	C₂×C₈×C₉	C₂³	1	2	yes	—
72	C₉×C₄⋊C₄	—	2	2	no	—
73	C₉×C₄⋊C₄	C₂³	1	2	yes	—
74	C₉×C₂²⋊C₄	—	2	1	no	—
75	C₉×C₂²⋊C₄	—	2	4	no	—
76	C₉×C₂²⋊C₄	—	2	4	no	—
77	C₉×C₂²⋊C₄	—	2	2	no	—
78	C₄²×C₉	—	2	1	no	—
79	C₄²×C₉	—	2	2	no	—
80	C₄²×C₉	D₄	1	1	yes	characteristic
81	C₄²×C₉	D₄	1	1	yes	characteristic
82	C₄²×C₉	C₂³	1	2	yes	—
83	#3040	C₉	1	1	yes	characteristic, direct product factor, Sylow
84	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
85	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
86	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
87	C₃×#137	—	2	4	no	—
88	C₃×AGL(1,ℤ/8)	—	2	4	no	—
89	C₂×C₃×Q₁₆	C₂²×C₃	1	2	yes	—
90	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
91	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
92	C₂×C₃×D₈	C₂²×C₃	1	2	yes	—
93	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
95	C₃×#124	—	2	1	no	—
96	C₃×#124	—	2	1	no	—
97	C₃×#124	C₂²×C₃	1	4	yes	—
98	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	—
99	C₃×C₄×D₄	—	2	2	no	—
100	C₃×C₄×D₄	C₂²×C₃	1	2	yes	—
101	C₃×#117	—	2	1	no	—
102	C₃×#117	C₂²×C₃	1	1	yes	characteristic
103	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
104	C₂×C₃×C₄²	—	2	1	no	—
105	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
106	C₃×C₄⋊C₈	C₂²×C₃	1	4	yes	—
107	C₃×#103	C₂²×C₃	1	4	yes	—
108	C₃×#102	C₂²×C₃	1	4	yes	—
109	C₂³×C₉	—	2	1	no	—
110	C₂³×C₉	—	2	2	no	—
111	C₂³×C₉	—	4	4	no	—
112	C₂³×C₉	—	4	2	no	—
113	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
114	Q₈×C₉	—	2	1	no	—
115	Q₈×C₉	—	2	2	no	—
116	Q₈×C₉	—	2	2	no	—
117	Q₈×C₉	—	4	2	no	—
118	Q₈×C₉	C₂×D₄	1	2	yes	—
119	D₄×C₉	—	2	4	no	—
120	D₄×C₉	—	2	2	no	—
121	D₄×C₉	—	2	1	no	—
122	D₄×C₉	—	2	2	no	—
123	D₄×C₉	—	4	2	no	—
124	D₄×C₉	C₂×D₄	1	2	yes	—
125	C₂×C₄×C₉	—	2	1	no	—
126	C₂×C₄×C₉	—	2	4	no	—
127	C₂×C₄×C₉	—	2	2	no	—
128	C₂×C₄×C₉	—	2	2	no	—
129	C₂×C₄×C₉	—	4	2	no	—
130	C₂×C₄×C₉	—	4	4	no	—
131	C₂×C₄×C₉	—	4	2	no	—
132	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
133	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
134	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
135	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
136	C₂×C₄×C₉	#41	1	2	yes	—
137	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
138	C₈×C₉	—	2	2	no	—
139	C₈×C₉	—	2	2	no	—
140	C₂×#137	C₂×C₉	1	1	yes	characteristic, complemented
141	C₂×AGL(1,ℤ/8)	C₂×C₉	1	1	yes	characteristic
142	C₂×#124	C₂×C₉	1	1	yes	characteristic, complemented
143	C₄×#41	C₂×C₉	1	1	yes	characteristic, complemented
144	#464	C₂×C₉	1	4	yes	complemented
145	#463	C₂×C₉	1	4	yes	complemented
146	#423	C₂×C₉	1	1	yes	characteristic, complemented
147	#419	C₂×C₉	1	1	yes	characteristic, complemented
148	#418	C₂×C₉	1	1	yes	characteristic, complemented
149	C₂⁴×C₃	—	2	1	no	—
150	C₃×#41	—	2	2	no	—
151	C₃×#41	C₃×D₄	1	4	yes	—
152	C₂×C₃×Q₈	—	2	1	no	—
153	C₂×C₃×Q₈	—	2	2	no	—
154	C₂×C₃×Q₈	—	2	2	no	—
155	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
156	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
157	C₂×C₃×D₄	—	2	1	no	—
158	C₂×C₃×D₄	—	2	2	no	—
159	C₂×C₃×D₄	—	2	1	no	—
160	C₂×C₃×D₄	—	2	2	no	—
161	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
162	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
163	C₂²×C₃×C₄	—	2	1	no	—
164	C₂²×C₃×C₄	—	2	1	no	—
165	C₂²×C₃×C₄	—	2	2	no	—
166	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
167	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
168	C₃×Q₁₆	—	2	4	no	—
169	C₃×SD₁₆	—	2	4	no	—
170	C₃×SD₁₆	—	2	4	no	—
171	C₃×D₈	—	2	4	no	—
172	C₃×M₁₆	—	2	2	no	—
173	C₃×M₁₆	—	2	2	no	—
174	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
175	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
176	C₃×C₄⋊C₄	—	2	2	no	—
177	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
178	C₃×C₂²⋊C₄	—	2	1	no	—
179	C₃×C₂²⋊C₄	—	2	4	no	—
180	C₃×C₂²⋊C₄	—	2	4	no	—
181	C₃×C₂²⋊C₄	—	2	2	no	—
182	C₃×C₄²	—	2	1	no	—
183	C₃×C₄²	—	2	2	no	—
184	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
185	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
186	C₃×C₄²	C₂³×C₃	1	2	yes	—
187	C₂²×C₉	—	2	2	no	—
188	C₂²×C₉	—	2	2	no	—
189	C₂²×C₉	—	4	2	no	—
190	C₂²×C₉	—	4	2	no	—
191	C₂²×C₉	—	4	4	no	—
192	C₂²×C₉	—	8	4	no	—
193	C₂²×C₉	#121	1	2	yes	—
194	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
195	C₄×C₉	—	2	2	no	—
196	C₄×C₉	—	2	2	no	—
197	C₄×C₉	—	2	2	no	—
198	C₄×C₉	—	4	2	no	—
199	C₄×C₉	—	4	2	no	—
200	C₄×C₉	#121	1	2	yes	—
201	C₄×C₉	C₂²×D₄	1	1	yes	characteristic
202	C₄×C₉	C₂×#41	1	1	yes	characteristic
203	C₂×#41	C₂²×C₉	1	1	yes	characteristic
204	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
205	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
206	#137	—	2	4	no	—
207	AGL(1,ℤ/8)	—	2	4	no	—
208	C₂×Q₁₆	C₂²×C₉	1	2	yes	complemented
209	C₂×SD₁₆	C₂²×C₉	1	2	yes	—
210	C₂×SD₁₆	C₂²×C₉	1	2	yes	complemented
211	C₂×D₈	C₂²×C₉	1	2	yes	—
212	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
213	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
214	#124	—	2	1	no	—
215	#124	—	2	1	no	—
216	#124	C₂²×C₉	1	4	yes	—
217	C₄×Q₈	C₂²×C₉	1	2	yes	complemented
218	C₄×D₄	—	2	2	no	—
219	C₄×D₄	C₂²×C₉	1	2	yes	complemented
220	#117	—	2	1	no	—
221	#117	C₂²×C₉	1	1	yes	characteristic
222	C₂×C₂²⋊C₄	—	2	2	no	—
223	C₂×C₄²	—	2	1	no	—
224	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
225	C₄⋊C₈	C₂²×C₉	1	4	yes	complemented
226	#103	C₂²×C₉	1	4	yes	complemented
227	#102	C₂²×C₉	1	4	yes	—
228	C₂³×C₃	—	2	1	no	—
229	C₂³×C₃	—	2	2	no	—
230	C₂³×C₃	—	4	4	no	—
231	C₂³×C₃	—	4	2	no	—
232	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
233	C₃×Q₈	—	2	1	no	—
234	C₃×Q₈	—	2	2	no	—
235	C₃×Q₈	—	2	2	no	—
236	C₃×Q₈	—	4	2	no	—
237	C₃×Q₈	C₂×C₃×D₄	1	2	yes	—
238	C₃×D₄	—	2	4	no	—
239	C₃×D₄	—	2	2	no	—
240	C₃×D₄	—	2	1	no	—
241	C₃×D₄	—	2	2	no	—
242	C₃×D₄	—	4	2	no	—
243	C₃×D₄	C₂×C₃×D₄	1	2	yes	—
244	C₂×C₃×C₄	—	2	1	no	—
245	C₂×C₃×C₄	—	2	4	no	—
246	C₂×C₃×C₄	—	2	2	no	—
247	C₂×C₃×C₄	—	2	2	no	—
248	C₂×C₃×C₄	—	4	2	no	—
249	C₂×C₃×C₄	—	4	4	no	—
250	C₂×C₃×C₄	—	4	2	no	—
251	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
252	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
253	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
254	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
255	C₂×C₃×C₄	C₃×#41	1	2	yes	—
256	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
257	C₃×C₈	—	2	2	no	—
258	C₃×C₈	—	2	2	no	—
259	C₂×C₉	—	2	2	no	—
260	C₂×C₉	—	4	2	no	—
261	C₂×C₉	—	8	2	no	—
262	C₂×C₉	C₂×#121	1	1	yes	characteristic
263	C₂×C₉	#575	1	2	yes	—
264	C₂⁴	—	2	1	no	—
265	#41	—	2	2	no	—
266	#41	D₄×C₉	1	4	yes	—
267	C₂×Q₈	—	2	1	no	—
268	C₂×Q₈	—	2	2	no	—
269	C₂×Q₈	—	2	2	no	—
270	C₂×Q₈	C₂³×C₉	1	2	yes	—
271	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
272	C₂×D₄	—	2	1	no	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	2	1	no	—
275	C₂×D₄	—	2	2	no	—
276	C₂×D₄	C₂³×C₉	1	2	yes	—
277	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	D₄×C₉	1	2	yes	—
282	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
283	Q₁₆	—	2	4	no	—
284	SD₁₆	—	2	4	no	—
285	SD₁₆	—	2	4	no	—
286	D₈	—	2	4	no	—
287	M₁₆	—	2	2	no	—
288	M₁₆	—	2	2	no	—
289	C₂×C₈	C₂³×C₉	1	2	yes	—
290	C₂×C₈	C₂³×C₉	1	2	yes	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	C₂³×C₉	1	2	yes	—
293	C₂²⋊C₄	—	2	1	no	—
294	C₂²⋊C₄	—	2	4	no	—
295	C₂²⋊C₄	—	2	4	no	—
296	C₂²⋊C₄	—	2	2	no	—
297	C₄²	—	2	1	no	—
298	C₄²	—	2	2	no	—
299	C₄²	D₄×C₉	1	1	yes	characteristic
300	C₄²	D₄×C₉	1	1	yes	characteristic
301	C₄²	C₂³×C₉	1	2	yes	—
302	C₂²×C₃	—	2	2	no	—
303	C₂²×C₃	—	2	2	no	—
304	C₂²×C₃	—	4	2	no	—
305	C₂²×C₃	—	4	4	no	—
306	C₂²×C₃	—	4	2	no	—
307	C₂²×C₃	—	8	4	no	—
308	C₂²×C₃	C₃×#121	1	2	yes	—
309	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
310	C₃×C₄	—	2	2	no	—
311	C₃×C₄	—	2	2	no	—
312	C₃×C₄	—	2	2	no	—
313	C₃×C₄	—	4	2	no	—
314	C₃×C₄	—	4	2	no	—
315	C₃×C₄	C₃×#121	1	2	yes	—
316	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
317	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
318	C₉	#3040	1	1	yes	characteristic, direct product factor, Sylow
319	C₂³	—	2	1	no	—
320	C₂³	—	2	2	no	—
321	C₂³	—	4	4	no	—
322	C₂³	—	4	2	no	—
323	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
324	Q₈	—	2	1	no	—
325	Q₈	—	2	2	no	—
326	Q₈	—	2	2	no	—
327	Q₈	—	4	2	no	—
328	Q₈	C₂×D₄×C₉	1	2	yes	—
329	D₄	—	2	4	no	—
330	D₄	—	2	2	no	—
331	D₄	—	2	1	no	—
332	D₄	—	2	2	no	—
333	D₄	—	4	2	no	—
334	D₄	C₂×D₄×C₉	1	2	yes	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
343	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
344	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
345	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
346	C₂×C₄	C₉×#41	1	2	yes	—
347	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
348	C₈	—	2	2	no	—
349	C₈	—	2	2	no	—
350	C₂×C₃	—	2	2	no	—
351	C₂×C₃	—	4	2	no	—
352	C₂×C₃	—	8	2	no	—
353	C₂×C₃	C₂×C₃×#121	1	1	yes	characteristic
354	C₂×C₃	C₃×#575	1	2	yes	—
355	C₂²	—	2	2	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	4	2	no	—
359	C₂²	—	4	4	no	—
360	C₂²	—	8	4	no	—
361	C₂²	C₉×#121	1	2	yes	—
362	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
363	C₄	—	2	2	no	—
364	C₄	—	2	2	no	—
365	C₄	—	2	2	no	—
366	C₄	—	4	2	no	—
367	C₄	—	4	2	no	—
368	C₄	C₉×#121	1	2	yes	—
369	C₄	C₂²×D₄×C₉	1	1	yes	characteristic
370	C₄	C₂×C₉×#41	1	1	yes	characteristic
371	C₃	C₃×#3040	1	1	yes	characteristic
372	C₂	—	2	2	no	—
373	C₂	—	4	2	no	—
374	C₂	—	8	2	no	—
375	C₂	C₂×C₉×#121	1	1	yes	characteristic
376	C₂	C₉×#575	1	2	yes	—

	subgroup	G/H
center	C₂²×C₉	C₂²×D₄
commutator	C₂×C₄	C₂⁴×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃
socle	C₂²×C₃	C₂²×C₃×D₄
prime radical	C₂×C₃×AGL(1,ℤ/8)	C₂×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₄²×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×#137	C₂	semidirect
3. C₂×C₉×#124	C₂	semidirect
4. C₄×C₉×#41	C₂	semidirect
5. C₉×#464	C₂	semidirect
6. C₉×#463	C₂	semidirect
7. C₉×#423	C₂	semidirect
8. C₉×#419	C₂	semidirect
9. C₉×#418	C₂	semidirect
16. C₂×C₉×Q₁₆	C₂²	semidirect
18. C₂×C₉×SD₁₆	C₂²	semidirect
25. C₄×Q₈×C₉	C₂²	semidirect
27. C₄×D₄×C₉	C₂²	semidirect
33. C₉×C₄⋊C₈	C₂²	semidirect
34. C₉×#103	C₂²	semidirect
83. #3040	C₉	direct (N × H)
140. C₂×#137	C₂×C₉	semidirect
142. C₂×#124	C₂×C₉	semidirect
143. C₄×#41	C₂×C₉	semidirect
144. #464	C₂×C₉	semidirect
145. #463	C₂×C₉	semidirect
146. #423	C₂×C₉	semidirect
147. #419	C₂×C₉	semidirect
148. #418	C₂×C₉	semidirect
208. C₂×Q₁₆	C₂²×C₉	semidirect
210. C₂×SD₁₆	C₂²×C₉	semidirect
217. C₄×Q₈	C₂²×C₉	semidirect
219. C₄×D₄	C₂²×C₉	semidirect
225. C₄⋊C₈	C₂²×C₉	semidirect
226. #103	C₂²×C₉	semidirect
318. C₉	#3040	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×#137	2
C₂×C₉×AGL(1,ℤ/8)	2
C₂×C₉×#124	2
C₄×C₉×#41	2
C₉×#464	2
C₉×#463	2
C₉×#423	2
C₉×#419	2
C₉×#418	2
C₃×#3040	3

Subgroups — C9×#3040 #11767761

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3040 #11767761