Subgroups — C₉×#1883 #11766604

Order 1152.

555 conjugacy classes of subgroups.

The subgroup lattice has 399 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
2	C₉×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉×#104	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#418	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#390	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#343	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#339	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#1883	C₃	1	1	yes	maximal, characteristic
9	C₂×C₉×#41	C₂²	1	1	yes	characteristic
10	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
11	C₉×AGL(1,ℤ/8)	—	2	2	no	—
12	C₉×AGL(1,ℤ/8)	C₄	1	4	yes	complemented
13	C₂×C₉×SD₁₆	—	2	1	no	—
14	C₂×C₉×D₈	—	2	1	no	—
15	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
16	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
17	C₄×Q₈×C₉	—	2	1	no	—
18	C₄×D₄×C₉	—	2	1	no	—
19	C₄×D₄×C₉	—	2	2	no	—
20	C₉×#117	—	2	1	no	—
21	C₉×#117	C₂²	1	1	yes	characteristic
22	C₂×C₉×C₄⋊C₄	—	2	1	no	—
23	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₉×C₂²⋊C₄	—	2	2	no	—
25	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
26	C₉×#104	—	2	2	no	—
27	C₉×#102	—	2	1	no	—
28	C₉×#102	—	2	1	no	—
29	C₂×C₃×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic
30	C₃×#520	C₂×C₃	1	1	yes	characteristic
31	C₂×C₃×#104	C₂×C₃	1	1	yes	characteristic
32	C₃×#418	C₂×C₃	1	1	yes	characteristic
33	C₃×#390	C₂×C₃	1	1	yes	characteristic
34	C₃×#343	C₂×C₃	1	1	yes	characteristic
35	C₃×#339	C₂×C₃	1	1	yes	characteristic
36	C₂⁴×C₉	—	2	1	no	—
37	C₉×#41	—	2	1	no	—
38	C₉×#41	—	2	1	no	—
39	C₉×#41	C₂×C₄	1	2	yes	—
40	C₉×#41	D₄	1	2	yes	—
41	C₂×Q₈×C₉	D₄	1	1	yes	characteristic
42	C₂×D₄×C₉	—	2	1	no	—
43	C₂×D₄×C₉	—	2	1	no	—
44	C₂×D₄×C₉	—	2	1	no	—
45	C₂×D₄×C₉	—	2	1	no	—
46	C₂×D₄×C₉	—	2	1	no	—
47	C₂×D₄×C₉	—	2	1	no	—
48	C₂×D₄×C₉	C₂×C₄	1	2	yes	complemented
49	C₂×D₄×C₉	D₄	1	1	yes	characteristic
50	C₂²×C₄×C₉	—	2	1	no	—
51	C₂²×C₄×C₉	—	2	1	no	—
52	C₂²×C₄×C₉	—	2	2	no	—
53	C₂²×C₄×C₉	D₄	1	2	yes	—
54	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
55	C₉×SD₁₆	—	2	4	no	—
56	C₉×D₈	—	2	4	no	—
57	C₉×M₁₆	—	2	1	no	—
58	C₉×M₁₆	—	2	1	no	—
59	C₉×M₁₆	—	2	1	no	—
60	C₉×M₁₆	C₂×C₄	1	2	yes	complemented
61	C₂×C₈×C₉	—	2	1	no	—
62	C₂×C₈×C₉	—	2	1	no	—
63	C₉×C₄⋊C₄	—	2	2	no	—
64	C₉×C₄⋊C₄	—	2	1	no	—
65	C₉×C₄⋊C₄	—	2	1	no	—
66	C₉×C₄⋊C₄	D₄	1	1	yes	characteristic
67	C₉×C₄⋊C₄	D₄	1	1	yes	characteristic
68	C₉×C₂²⋊C₄	—	2	2	no	—
69	C₉×C₂²⋊C₄	—	2	1	no	—
70	C₉×C₂²⋊C₄	—	4	4	no	—
71	C₄²×C₉	—	2	2	no	—
72	C₄²×C₉	—	2	1	no	—
73	C₄²×C₉	—	2	1	no	—
74	C₄²×C₉	—	2	1	no	—
75	#1883	C₉	1	1	yes	characteristic, direct product factor, Sylow
76	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
77	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
78	C₃×AGL(1,ℤ/8)	—	2	2	no	—
79	C₃×AGL(1,ℤ/8)	C₃×C₄	1	4	yes	—
80	C₂×C₃×SD₁₆	—	2	1	no	—
81	C₂×C₃×D₈	—	2	1	no	—
82	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
84	C₃×C₄×Q₈	—	2	1	no	—
85	C₃×C₄×D₄	—	2	1	no	—
86	C₃×C₄×D₄	—	2	2	no	—
87	C₃×#117	—	2	1	no	—
88	C₃×#117	C₂²×C₃	1	1	yes	characteristic
89	C₂×C₃×C₄⋊C₄	—	2	1	no	—
90	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
91	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
92	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
93	C₃×#104	—	2	2	no	—
94	C₃×#102	—	2	1	no	—
95	C₃×#102	—	2	1	no	—
96	C₂³×C₉	—	2	1	no	—
97	C₂³×C₉	—	2	2	no	—
98	C₂³×C₉	—	4	2	no	—
99	C₂³×C₉	—	4	2	no	—
100	C₂³×C₉	—	4	1	no	—
101	C₂³×C₉	—	4	1	no	—
102	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
103	Q₈×C₉	—	2	1	no	—
104	Q₈×C₉	C₂²⋊C₄	1	2	yes	complemented
105	D₄×C₉	—	2	2	no	—
106	D₄×C₉	—	2	2	no	—
107	D₄×C₉	—	2	2	no	—
108	D₄×C₉	—	2	2	no	—
109	D₄×C₉	—	2	1	no	—
110	D₄×C₉	—	4	1	no	—
111	D₄×C₉	—	4	1	no	—
112	D₄×C₉	C₂²⋊C₄	1	2	yes	complemented
113	C₂×C₄×C₉	—	2	1	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	1	no	—
118	C₂×C₄×C₉	—	2	2	no	—
119	C₂×C₄×C₉	—	2	1	no	—
120	C₂×C₄×C₉	—	4	1	no	—
121	C₂×C₄×C₉	—	4	1	no	—
122	C₂×C₄×C₉	—	4	2	no	—
123	C₂×C₄×C₉	—	8	2	no	—
124	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
126	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
127	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
128	C₂×C₄×C₉	#41	1	1	yes	characteristic
129	C₂×C₄×C₉	#41	1	1	yes	characteristic
130	C₈×C₉	—	2	2	no	—
131	C₈×C₉	—	4	1	no	—
132	C₂×AGL(1,ℤ/8)	C₂×C₉	1	1	yes	characteristic
133	#520	C₂×C₉	1	1	yes	characteristic, complemented
134	C₂×#104	C₂×C₉	1	1	yes	characteristic, complemented
135	#418	C₂×C₉	1	1	yes	characteristic, complemented
136	#390	C₂×C₉	1	1	yes	characteristic, complemented
137	#343	C₂×C₉	1	1	yes	characteristic, complemented
138	#339	C₂×C₉	1	1	yes	characteristic, complemented
139	C₂⁴×C₃	—	2	1	no	—
140	C₃×#41	—	2	1	no	—
141	C₃×#41	—	2	1	no	—
142	C₃×#41	C₂×C₃×C₄	1	2	yes	—
143	C₃×#41	C₃×D₄	1	2	yes	—
144	C₂×C₃×Q₈	C₃×D₄	1	1	yes	characteristic
145	C₂×C₃×D₄	—	2	1	no	—
146	C₂×C₃×D₄	—	2	1	no	—
147	C₂×C₃×D₄	—	2	1	no	—
148	C₂×C₃×D₄	—	2	1	no	—
149	C₂×C₃×D₄	—	2	1	no	—
150	C₂×C₃×D₄	—	2	1	no	—
151	C₂×C₃×D₄	C₂×C₃×C₄	1	2	yes	—
152	C₂×C₃×D₄	C₃×D₄	1	1	yes	characteristic
153	C₂²×C₃×C₄	—	2	1	no	—
154	C₂²×C₃×C₄	—	2	1	no	—
155	C₂²×C₃×C₄	—	2	2	no	—
156	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
157	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
158	C₃×SD₁₆	—	2	4	no	—
159	C₃×D₈	—	2	4	no	—
160	C₃×M₁₆	—	2	1	no	—
161	C₃×M₁₆	—	2	1	no	—
162	C₃×M₁₆	—	2	1	no	—
163	C₃×M₁₆	C₂×C₃×C₄	1	2	yes	—
164	C₂×C₃×C₈	—	2	1	no	—
165	C₂×C₃×C₈	—	2	1	no	—
166	C₃×C₄⋊C₄	—	2	2	no	—
167	C₃×C₄⋊C₄	—	2	1	no	—
168	C₃×C₄⋊C₄	—	2	1	no	—
169	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
170	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
171	C₃×C₂²⋊C₄	—	2	2	no	—
172	C₃×C₂²⋊C₄	—	2	1	no	—
173	C₃×C₂²⋊C₄	—	4	4	no	—
174	C₃×C₄²	—	2	2	no	—
175	C₃×C₄²	—	2	1	no	—
176	C₃×C₄²	—	2	1	no	—
177	C₃×C₄²	—	2	1	no	—
178	C₂²×C₉	—	2	1	no	—
179	C₂²×C₉	—	2	1	no	—
180	C₂²×C₉	—	2	2	no	—
181	C₂²×C₉	—	4	4	no	—
182	C₂²×C₉	—	4	1	no	—
183	C₂²×C₉	—	4	1	no	—
184	C₂²×C₉	—	4	2	no	—
185	C₂²×C₉	—	8	2	no	—
186	C₂²×C₉	—	8	1	no	—
187	C₂²×C₉	—	8	1	no	—
188	C₂²×C₉	C₄×D₄	1	1	yes	characteristic
189	C₂²×C₉	#120	1	1	yes	characteristic
190	C₂²×C₉	#121	1	1	yes	characteristic
191	C₄×C₉	—	2	2	no	—
192	C₄×C₉	—	4	2	no	—
193	C₄×C₉	—	4	2	no	—
194	C₄×C₉	—	4	1	no	—
195	C₄×C₉	—	4	1	no	—
196	C₄×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
197	C₄×C₉	C₄×D₄	1	1	yes	characteristic
198	C₄×C₉	#121	1	1	yes	characteristic
199	C₄×C₉	#123	1	1	yes	characteristic
200	C₂×#41	C₂²×C₉	1	1	yes	characteristic
201	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
202	AGL(1,ℤ/8)	—	2	2	no	—
203	AGL(1,ℤ/8)	C₄×C₉	1	4	yes	complemented
204	C₂×SD₁₆	—	2	1	no	—
205	C₂×D₈	—	2	1	no	—
206	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
207	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
208	C₄×Q₈	—	2	1	no	—
209	C₄×D₄	—	2	1	no	—
210	C₄×D₄	—	2	2	no	—
211	#117	—	2	1	no	—
212	#117	C₂²×C₉	1	1	yes	characteristic
213	C₂×C₄⋊C₄	—	2	1	no	—
214	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
215	C₂×C₂²⋊C₄	—	2	2	no	—
216	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
217	#104	—	2	2	no	—
218	#102	—	2	1	no	—
219	#102	—	2	1	no	—
220	C₂³×C₃	—	2	1	no	—
221	C₂³×C₃	—	2	2	no	—
222	C₂³×C₃	—	4	2	no	—
223	C₂³×C₃	—	4	2	no	—
224	C₂³×C₃	—	4	1	no	—
225	C₂³×C₃	—	4	1	no	—
226	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
227	C₃×Q₈	—	2	1	no	—
228	C₃×Q₈	C₃×C₂²⋊C₄	1	2	yes	—
229	C₃×D₄	—	2	2	no	—
230	C₃×D₄	—	2	2	no	—
231	C₃×D₄	—	2	2	no	—
232	C₃×D₄	—	2	2	no	—
233	C₃×D₄	—	2	1	no	—
234	C₃×D₄	—	4	1	no	—
235	C₃×D₄	—	4	1	no	—
236	C₃×D₄	C₃×C₂²⋊C₄	1	2	yes	—
237	C₂×C₃×C₄	—	2	1	no	—
238	C₂×C₃×C₄	—	2	2	no	—
239	C₂×C₃×C₄	—	2	2	no	—
240	C₂×C₃×C₄	—	2	2	no	—
241	C₂×C₃×C₄	—	2	1	no	—
242	C₂×C₃×C₄	—	2	2	no	—
243	C₂×C₃×C₄	—	2	1	no	—
244	C₂×C₃×C₄	—	4	1	no	—
245	C₂×C₃×C₄	—	4	1	no	—
246	C₂×C₃×C₄	—	4	2	no	—
247	C₂×C₃×C₄	—	8	2	no	—
248	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
249	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
250	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
251	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
252	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
253	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
254	C₃×C₈	—	2	2	no	—
255	C₃×C₈	—	4	1	no	—
256	C₂×C₉	—	2	1	no	—
257	C₂×C₉	—	2	1	no	—
258	C₂×C₉	—	4	2	no	—
259	C₂×C₉	—	8	2	no	—
260	C₂×C₉	#386	1	1	yes	characteristic
261	C₂×C₉	#453	1	1	yes	characteristic
262	C₂×C₉	#454	1	1	yes	characteristic
263	C₂⁴	—	2	1	no	—
264	#41	—	2	1	no	—
265	#41	—	2	1	no	—
266	#41	C₂×C₄×C₉	1	2	yes	—
267	#41	D₄×C₉	1	2	yes	—
268	C₂×Q₈	D₄×C₉	1	1	yes	characteristic
269	C₂×D₄	—	2	1	no	—
270	C₂×D₄	—	2	1	no	—
271	C₂×D₄	—	2	1	no	—
272	C₂×D₄	—	2	1	no	—
273	C₂×D₄	—	2	1	no	—
274	C₂×D₄	—	2	1	no	—
275	C₂×D₄	C₂×C₄×C₉	1	2	yes	complemented
276	C₂×D₄	D₄×C₉	1	1	yes	characteristic
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	D₄×C₉	1	2	yes	—
281	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
282	SD₁₆	—	2	4	no	—
283	D₈	—	2	4	no	—
284	M₁₆	—	2	1	no	—
285	M₁₆	—	2	1	no	—
286	M₁₆	—	2	1	no	—
287	M₁₆	C₂×C₄×C₉	1	2	yes	complemented
288	C₂×C₈	—	2	1	no	—
289	C₂×C₈	—	2	1	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	2	1	no	—
292	C₄⋊C₄	—	2	1	no	—
293	C₄⋊C₄	D₄×C₉	1	1	yes	characteristic
294	C₄⋊C₄	D₄×C₉	1	1	yes	characteristic
295	C₂²⋊C₄	—	2	2	no	—
296	C₂²⋊C₄	—	2	1	no	—
297	C₂²⋊C₄	—	4	4	no	—
298	C₄²	—	2	2	no	—
299	C₄²	—	2	1	no	—
300	C₄²	—	2	1	no	—
301	C₄²	—	2	1	no	—
302	C₂²×C₃	—	2	1	no	—
303	C₂²×C₃	—	2	1	no	—
304	C₂²×C₃	—	2	2	no	—
305	C₂²×C₃	—	4	4	no	—
306	C₂²×C₃	—	4	1	no	—
307	C₂²×C₃	—	4	1	no	—
308	C₂²×C₃	—	4	2	no	—
309	C₂²×C₃	—	8	2	no	—
310	C₂²×C₃	—	8	1	no	—
311	C₂²×C₃	—	8	1	no	—
312	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
313	C₂²×C₃	C₃×#120	1	1	yes	characteristic
314	C₂²×C₃	C₃×#121	1	1	yes	characteristic
315	C₃×C₄	—	2	2	no	—
316	C₃×C₄	—	4	2	no	—
317	C₃×C₄	—	4	2	no	—
318	C₃×C₄	—	4	1	no	—
319	C₃×C₄	—	4	1	no	—
320	C₃×C₄	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
321	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
322	C₃×C₄	C₃×#121	1	1	yes	characteristic
323	C₃×C₄	C₃×#123	1	1	yes	characteristic
324	C₉	#1883	1	1	yes	characteristic, direct product factor, Sylow
325	C₂³	—	2	1	no	—
326	C₂³	—	2	2	no	—
327	C₂³	—	4	2	no	—
328	C₂³	—	4	2	no	—
329	C₂³	—	4	1	no	—
330	C₂³	—	4	1	no	—
331	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
332	Q₈	—	2	1	no	—
333	Q₈	C₉×C₂²⋊C₄	1	2	yes	complemented
334	D₄	—	2	2	no	—
335	D₄	—	2	2	no	—
336	D₄	—	2	2	no	—
337	D₄	—	2	2	no	—
338	D₄	—	2	1	no	—
339	D₄	—	4	1	no	—
340	D₄	—	4	1	no	—
341	D₄	C₉×C₂²⋊C₄	1	2	yes	complemented
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	8	2	no	—
353	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
354	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
355	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
356	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
357	C₂×C₄	C₉×#41	1	1	yes	characteristic
358	C₂×C₄	C₉×#41	1	1	yes	characteristic
359	C₈	—	2	2	no	—
360	C₈	—	4	1	no	—
361	C₂×C₃	—	2	1	no	—
362	C₂×C₃	—	2	1	no	—
363	C₂×C₃	—	4	2	no	—
364	C₂×C₃	—	8	2	no	—
365	C₂×C₃	C₃×#386	1	1	yes	characteristic
366	C₂×C₃	C₃×#453	1	1	yes	characteristic
367	C₂×C₃	C₃×#454	1	1	yes	characteristic
368	C₂²	—	2	1	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	4	4	no	—
372	C₂²	—	4	1	no	—
373	C₂²	—	4	1	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	8	1	no	—
377	C₂²	—	8	1	no	—
378	C₂²	C₄×D₄×C₉	1	1	yes	characteristic
379	C₂²	C₉×#120	1	1	yes	characteristic
380	C₂²	C₉×#121	1	1	yes	characteristic
381	C₄	—	2	2	no	—
382	C₄	—	4	2	no	—
383	C₄	—	4	2	no	—
384	C₄	—	4	1	no	—
385	C₄	—	4	1	no	—
386	C₄	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
387	C₄	C₄×D₄×C₉	1	1	yes	characteristic
388	C₄	C₉×#121	1	1	yes	characteristic
389	C₄	C₉×#123	1	1	yes	characteristic
390	C₃	C₃×#1883	1	1	yes	characteristic
391	C₂	—	2	1	no	—
392	C₂	—	2	1	no	—
393	C₂	—	4	2	no	—
394	C₂	—	8	2	no	—
395	C₂	C₉×#386	1	1	yes	characteristic
396	C₂	C₉×#453	1	1	yes	characteristic
397	C₂	C₉×#454	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	#120
commutator	C₂×C₄	C₂²×C₄×C₉
Frattini, cosocle	C₂²×C₃×C₄	C₂³×C₃
socle	C₂²×C₃	C₃×#120
prime radical	C₂×C₃×AGL(1,ℤ/8)	C₂×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₂²×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₉×#520	C₂	semidirect
3. C₂×C₉×#104	C₂	semidirect
4. C₉×#418	C₂	semidirect
5. C₉×#390	C₂	semidirect
6. C₉×#343	C₂	semidirect
7. C₉×#339	C₂	semidirect
12. C₉×AGL(1,ℤ/8)	C₄	semidirect
48. C₂×D₄×C₉	C₂×C₄	semidirect
60. C₉×M₁₆	C₂×C₄	semidirect
75. #1883	C₉	direct (N × H)
104. Q₈×C₉	C₂²⋊C₄	semidirect
112. D₄×C₉	C₂²⋊C₄	semidirect
133. #520	C₂×C₉	semidirect
134. C₂×#104	C₂×C₉	semidirect
135. #418	C₂×C₉	semidirect
136. #390	C₂×C₉	semidirect
137. #343	C₂×C₉	semidirect
138. #339	C₂×C₉	semidirect
203. AGL(1,ℤ/8)	C₄×C₉	semidirect
275. C₂×D₄	C₂×C₄×C₉	semidirect
287. M₁₆	C₂×C₄×C₉	semidirect
324. C₉	#1883	direct (N × H)
333. Q₈	C₉×C₂²⋊C₄	semidirect
341. D₄	C₉×C₂²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×AGL(1,ℤ/8)	2
C₉×#520	2
C₂×C₉×#104	2
C₉×#418	2
C₉×#390	2
C₉×#343	2
C₉×#339	2
C₃×#1883	3

Subgroups — C9×#1883 #11766604

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#1883 #11766604