Subgroups — C₉×#3094 #11767815

Order 1152.

693 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×#121	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#482	C₂	1	4	yes	maximal, complemented
4	C₉×#481	C₂	1	2	yes	maximal, complemented
5	C₉×#480	C₂	1	2	yes	maximal, complemented
6	C₉×#428	C₂	1	2	yes	maximal, complemented
7	C₉×#418	C₂	1	2	yes	maximal, complemented
8	C₉×#407	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#3094	C₃	1	1	yes	maximal, characteristic
10	C₂²×D₄×C₉	—	2	1	no	—
11	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
12	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
13	C₂×C₉×M₁₆	C₂²	1	2	yes	—
14	C₉×#121	—	2	1	no	—
15	C₉×#121	—	2	1	no	—
16	C₉×#121	C₂²	1	2	yes	—
17	C₉×#121	C₂²	1	2	yes	—
18	C₉×#117	—	2	1	no	—
19	C₉×#117	—	2	1	no	—
20	C₉×#117	C₂²	1	2	yes	—
21	C₉×#117	C₂²	1	2	yes	complemented
22	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
26	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
27	C₂×C₄²×C₉	—	2	1	no	—
28	C₉×#107	C₂²	1	4	yes	complemented
29	C₉×#106	C₂²	1	4	yes	complemented
30	C₉×#102	C₂²	1	4	yes	complemented
31	C₉×#102	C₂²	1	4	yes	complemented
32	C₉×C₂²⋊C₈	C₂²	1	2	yes	complemented
33	C₉×C₂²⋊C₈	C₂²	1	2	yes	complemented
34	C₂×C₃×#121	C₂×C₃	1	1	yes	characteristic
35	C₂×C₃×#117	C₂×C₃	1	1	yes	characteristic
36	C₃×#482	C₂×C₃	1	4	yes	—
37	C₃×#481	C₂×C₃	1	2	yes	—
38	C₃×#480	C₂×C₃	1	2	yes	—
39	C₃×#428	C₂×C₃	1	2	yes	—
40	C₃×#418	C₂×C₃	1	2	yes	—
41	C₃×#407	C₂×C₃	1	1	yes	characteristic
42	C₂⁴×C₉	—	2	1	no	—
43	C₂⁴×C₉	D₄	1	1	yes	characteristic
44	C₂×D₄×C₉	—	2	2	no	—
45	C₂×D₄×C₉	—	2	2	no	—
46	C₂×D₄×C₉	—	2	1	no	—
47	C₂×D₄×C₉	—	2	4	no	—
48	C₂×D₄×C₉	—	4	4	no	—
49	C₂×D₄×C₉	C₂³	1	2	yes	—
50	C₂²×C₄×C₉	—	2	4	no	—
51	C₂²×C₄×C₉	—	2	1	no	—
52	C₂²×C₄×C₉	—	2	1	no	—
53	C₂²×C₄×C₉	—	2	1	no	—
54	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
55	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
56	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
57	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
58	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
59	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
60	C₉×M₁₆	—	2	4	no	—
61	C₂×C₈×C₉	C₂³	1	4	yes	—
62	C₉×C₄⋊C₄	—	2	1	no	—
63	C₉×C₄⋊C₄	—	2	1	no	—
64	C₉×C₄⋊C₄	—	2	1	no	—
65	C₉×C₄⋊C₄	C₂³	1	2	yes	—
66	C₉×C₄⋊C₄	C₂³	1	2	yes	—
67	C₉×C₄⋊C₄	C₂³	1	2	yes	—
68	C₉×C₂²⋊C₄	—	2	2	no	—
69	C₉×C₂²⋊C₄	—	2	2	no	—
70	C₉×C₂²⋊C₄	—	2	2	no	—
71	C₉×C₂²⋊C₄	—	2	2	no	—
72	C₄²×C₉	—	2	2	no	—
73	C₄²×C₉	—	2	2	no	—
74	#3094	C₉	1	1	yes	characteristic, direct product factor, Sylow
75	C₂²×C₃×D₄	—	2	1	no	—
76	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
77	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
79	C₃×#121	—	2	1	no	—
80	C₃×#121	—	2	1	no	—
81	C₃×#121	C₂²×C₃	1	2	yes	—
82	C₃×#121	C₂²×C₃	1	2	yes	—
83	C₃×#117	—	2	1	no	—
84	C₃×#117	—	2	1	no	—
85	C₃×#117	C₂²×C₃	1	2	yes	—
86	C₃×#117	C₂²×C₃	1	2	yes	—
87	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
89	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
90	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
91	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
92	C₂×C₃×C₄²	—	2	1	no	—
93	C₃×#107	C₂²×C₃	1	4	yes	—
94	C₃×#106	C₂²×C₃	1	4	yes	—
95	C₃×#102	C₂²×C₃	1	4	yes	—
96	C₃×#102	C₂²×C₃	1	4	yes	—
97	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
98	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
99	C₂³×C₉	—	2	2	no	—
100	C₂³×C₉	—	2	2	no	—
101	C₂³×C₉	—	2	2	no	—
102	C₂³×C₉	—	4	1	no	—
103	C₂³×C₉	—	4	2	no	—
104	C₂³×C₉	—	4	2	no	—
105	C₂³×C₉	—	4	2	no	—
106	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
107	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
108	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
109	D₄×C₉	—	2	4	no	—
110	D₄×C₉	—	4	4	no	—
111	D₄×C₉	—	4	4	no	—
112	D₄×C₉	—	4	2	no	—
113	C₂×C₄×C₉	—	2	2	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	2	no	—
118	C₂×C₄×C₉	—	2	2	no	—
119	C₂×C₄×C₉	—	2	2	no	—
120	C₂×C₄×C₉	—	2	2	no	—
121	C₂×C₄×C₉	—	4	2	no	—
122	C₂×C₄×C₉	—	4	2	no	—
123	C₂×C₄×C₉	—	4	2	no	—
124	C₂×C₄×C₉	C₂×D₄	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	#41	1	4	yes	—
128	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
129	C₈×C₉	—	2	4	no	—
130	C₂×#121	C₂×C₉	1	1	yes	characteristic
131	C₂×#117	C₂×C₉	1	1	yes	characteristic, complemented
132	#482	C₂×C₉	1	4	yes	complemented
133	#481	C₂×C₉	1	2	yes	complemented
134	#480	C₂×C₉	1	2	yes	complemented
135	#428	C₂×C₉	1	2	yes	complemented
136	#418	C₂×C₉	1	2	yes	complemented
137	#407	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×D₄	—	2	2	no	—
141	C₂×C₃×D₄	—	2	2	no	—
142	C₂×C₃×D₄	—	2	1	no	—
143	C₂×C₃×D₄	—	2	4	no	—
144	C₂×C₃×D₄	—	4	4	no	—
145	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
146	C₂²×C₃×C₄	—	2	4	no	—
147	C₂²×C₃×C₄	—	2	1	no	—
148	C₂²×C₃×C₄	—	2	1	no	—
149	C₂²×C₃×C₄	—	2	1	no	—
150	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
151	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
152	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
153	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
154	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
155	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
156	C₃×M₁₆	—	2	4	no	—
157	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
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	C₂³×C₃	1	2	yes	—
162	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
163	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
164	C₃×C₂²⋊C₄	—	2	2	no	—
165	C₃×C₂²⋊C₄	—	2	2	no	—
166	C₃×C₂²⋊C₄	—	2	2	no	—
167	C₃×C₂²⋊C₄	—	2	2	no	—
168	C₃×C₄²	—	2	2	no	—
169	C₃×C₄²	—	2	2	no	—
170	C₂²×C₉	—	2	1	no	—
171	C₂²×C₉	—	2	1	no	—
172	C₂²×C₉	—	2	1	no	—
173	C₂²×C₉	—	2	1	no	—
174	C₂²×C₉	—	2	1	no	—
175	C₂²×C₉	—	2	1	no	—
176	C₂²×C₉	—	2	1	no	—
177	C₂²×C₉	—	4	4	no	—
178	C₂²×C₉	—	4	2	no	—
179	C₂²×C₉	—	4	2	no	—
180	C₂²×C₉	—	4	2	no	—
181	C₂²×C₉	—	8	4	no	—
182	C₂²×C₉	#123	1	2	yes	—
183	C₂²×C₉	AGL(1,ℤ/8)	1	2	yes	—
184	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
185	C₄×C₉	—	2	1	no	—
186	C₄×C₉	—	2	1	no	—
187	C₄×C₉	—	4	2	no	—
188	C₄×C₉	—	4	2	no	—
189	C₄×C₉	—	4	2	no	—
190	C₄×C₉	#123	1	2	yes	—
191	C₄×C₉	C₂×#41	1	2	yes	—
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×M₁₆	C₂²×C₉	1	2	yes	—
196	#121	—	2	1	no	—
197	#121	—	2	1	no	—
198	#121	C₂²×C₉	1	2	yes	—
199	#121	C₂²×C₉	1	2	yes	—
200	#117	—	2	1	no	—
201	#117	—	2	1	no	—
202	#117	C₂²×C₉	1	2	yes	—
203	#117	C₂²×C₉	1	2	yes	complemented
204	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
205	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
206	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
207	C₂×C₂²⋊C₄	—	2	1	no	—
208	C₂×C₂²⋊C₄	—	2	1	no	—
209	C₂×C₄²	—	2	1	no	—
210	#107	C₂²×C₉	1	4	yes	complemented
211	#106	C₂²×C₉	1	4	yes	complemented
212	#102	C₂²×C₉	1	4	yes	complemented
213	#102	C₂²×C₉	1	4	yes	complemented
214	C₂²⋊C₈	C₂²×C₉	1	2	yes	complemented
215	C₂²⋊C₈	C₂²×C₉	1	2	yes	complemented
216	C₂³×C₃	—	2	2	no	—
217	C₂³×C₃	—	2	2	no	—
218	C₂³×C₃	—	2	2	no	—
219	C₂³×C₃	—	4	1	no	—
220	C₂³×C₃	—	4	2	no	—
221	C₂³×C₃	—	4	2	no	—
222	C₂³×C₃	—	4	2	no	—
223	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
224	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
225	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
226	C₃×D₄	—	2	4	no	—
227	C₃×D₄	—	4	4	no	—
228	C₃×D₄	—	4	4	no	—
229	C₃×D₄	—	4	2	no	—
230	C₂×C₃×C₄	—	2	2	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	—	2	2	no	—
237	C₂×C₃×C₄	—	2	2	no	—
238	C₂×C₃×C₄	—	4	2	no	—
239	C₂×C₃×C₄	—	4	2	no	—
240	C₂×C₃×C₄	—	4	2	no	—
241	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
242	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
243	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
244	C₂×C₃×C₄	C₃×#41	1	4	yes	—
245	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
246	C₃×C₈	—	2	4	no	—
247	C₂×C₉	—	2	2	no	—
248	C₂×C₉	—	2	2	no	—
249	C₂×C₉	—	4	1	no	—
250	C₂×C₉	—	8	2	no	—
251	C₂×C₉	C₂×#123	1	1	yes	characteristic
252	C₂×C₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
253	C₂×C₉	#575	1	1	yes	characteristic
254	C₂⁴	—	2	1	no	—
255	C₂⁴	D₄×C₉	1	1	yes	characteristic
256	C₂×D₄	—	2	2	no	—
257	C₂×D₄	—	2	2	no	—
258	C₂×D₄	—	2	1	no	—
259	C₂×D₄	—	2	4	no	—
260	C₂×D₄	—	4	4	no	—
261	C₂×D₄	C₂³×C₉	1	2	yes	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	2	1	no	—
265	C₂²×C₄	—	2	1	no	—
266	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
267	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
268	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
269	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
270	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
271	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
272	M₁₆	—	2	4	no	—
273	C₂×C₈	C₂³×C₉	1	4	yes	—
274	C₄⋊C₄	—	2	1	no	—
275	C₄⋊C₄	—	2	1	no	—
276	C₄⋊C₄	—	2	1	no	—
277	C₄⋊C₄	C₂³×C₉	1	2	yes	—
278	C₄⋊C₄	C₂³×C₉	1	2	yes	—
279	C₄⋊C₄	C₂³×C₉	1	2	yes	—
280	C₂²⋊C₄	—	2	2	no	—
281	C₂²⋊C₄	—	2	2	no	—
282	C₂²⋊C₄	—	2	2	no	—
283	C₂²⋊C₄	—	2	2	no	—
284	C₄²	—	2	2	no	—
285	C₄²	—	2	2	no	—
286	C₂²×C₃	—	2	1	no	—
287	C₂²×C₃	—	2	1	no	—
288	C₂²×C₃	—	2	1	no	—
289	C₂²×C₃	—	2	1	no	—
290	C₂²×C₃	—	2	1	no	—
291	C₂²×C₃	—	2	1	no	—
292	C₂²×C₃	—	2	1	no	—
293	C₂²×C₃	—	4	4	no	—
294	C₂²×C₃	—	4	2	no	—
295	C₂²×C₃	—	4	2	no	—
296	C₂²×C₃	—	4	2	no	—
297	C₂²×C₃	—	8	4	no	—
298	C₂²×C₃	C₃×#123	1	2	yes	—
299	C₂²×C₃	C₃×AGL(1,ℤ/8)	1	2	yes	—
300	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
301	C₃×C₄	—	2	1	no	—
302	C₃×C₄	—	2	1	no	—
303	C₃×C₄	—	4	2	no	—
304	C₃×C₄	—	4	2	no	—
305	C₃×C₄	—	4	2	no	—
306	C₃×C₄	C₃×#123	1	2	yes	—
307	C₃×C₄	C₂×C₃×#41	1	2	yes	—
308	C₉	#3094	1	1	yes	characteristic, direct product factor, Sylow
309	C₂³	—	2	2	no	—
310	C₂³	—	2	2	no	—
311	C₂³	—	2	2	no	—
312	C₂³	—	4	1	no	—
313	C₂³	—	4	2	no	—
314	C₂³	—	4	2	no	—
315	C₂³	—	4	2	no	—
316	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
317	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
318	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
319	D₄	—	2	4	no	—
320	D₄	—	4	4	no	—
321	D₄	—	4	4	no	—
322	D₄	—	4	2	no	—
323	C₂×C₄	—	2	2	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	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
335	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
336	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
337	C₂×C₄	C₉×#41	1	4	yes	—
338	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
339	C₈	—	2	4	no	—
340	C₂×C₃	—	2	2	no	—
341	C₂×C₃	—	2	2	no	—
342	C₂×C₃	—	4	1	no	—
343	C₂×C₃	—	8	2	no	—
344	C₂×C₃	C₂×C₃×#123	1	1	yes	characteristic
345	C₂×C₃	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
346	C₂×C₃	C₃×#575	1	1	yes	characteristic
347	C₂²	—	2	1	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	4	4	no	—
355	C₂²	—	4	2	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	8	4	no	—
359	C₂²	C₉×#123	1	2	yes	—
360	C₂²	C₉×AGL(1,ℤ/8)	1	2	yes	—
361	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	4	2	no	—
365	C₄	—	4	2	no	—
366	C₄	—	4	2	no	—
367	C₄	C₉×#123	1	2	yes	—
368	C₄	C₂×C₉×#41	1	2	yes	—
369	C₃	C₃×#3094	1	1	yes	characteristic
370	C₂	—	2	2	no	—
371	C₂	—	2	2	no	—
372	C₂	—	4	1	no	—
373	C₂	—	8	2	no	—
374	C₂	C₂×C₉×#123	1	1	yes	characteristic
375	C₂	C₂×C₉×AGL(1,ℤ/8)	1	1	yes	characteristic
376	C₂	C₉×#575	1	1	yes	characteristic

	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×#121	C₂×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₂³×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₉×#117	C₂	semidirect
3. C₉×#482	C₂	semidirect
4. C₉×#481	C₂	semidirect
5. C₉×#480	C₂	semidirect
6. C₉×#428	C₂	semidirect
7. C₉×#418	C₂	semidirect
8. C₉×#407	C₂	semidirect
21. C₉×#117	C₂²	semidirect
23. C₂×C₉×C₄⋊C₄	C₂²	semidirect
24. C₂×C₉×C₄⋊C₄	C₂²	semidirect
28. C₉×#107	C₂²	semidirect
29. C₉×#106	C₂²	semidirect
30. C₉×#102	C₂²	semidirect
31. C₉×#102	C₂²	semidirect
32. C₉×C₂²⋊C₈	C₂²	semidirect
33. C₉×C₂²⋊C₈	C₂²	semidirect
74. #3094	C₉	direct (N × H)
131. C₂×#117	C₂×C₉	semidirect
132. #482	C₂×C₉	semidirect
133. #481	C₂×C₉	semidirect
134. #480	C₂×C₉	semidirect
135. #428	C₂×C₉	semidirect
136. #418	C₂×C₉	semidirect
137. #407	C₂×C₉	semidirect
203. #117	C₂²×C₉	semidirect
205. C₂×C₄⋊C₄	C₂²×C₉	semidirect
206. C₂×C₄⋊C₄	C₂²×C₉	semidirect
210. #107	C₂²×C₉	semidirect
211. #106	C₂²×C₉	semidirect
212. #102	C₂²×C₉	semidirect
213. #102	C₂²×C₉	semidirect
214. C₂²⋊C₈	C₂²×C₉	semidirect
215. C₂²⋊C₈	C₂²×C₉	semidirect
308. C₉	#3094	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×#121	2
C₂×C₉×#117	2
C₉×#482	2
C₉×#481	2
C₉×#480	2
C₉×#428	2
C₉×#418	2
C₉×#407	2
C₃×#3094	3

Subgroups — C9×#3094 #11767815

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3094 #11767815