Subgroups — C₉×#3097 #11767818

Order 1152.

579 conjugacy classes of subgroups.

The subgroup lattice has 381 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#536	C₂	1	1	yes	maximal, characteristic
2	C₉×#520	C₂	1	1	yes	maximal, characteristic
3	C₉×#485	C₂	1	2	yes	maximal, complemented
4	C₉×#485	C₂	1	2	yes	maximal, complemented
5	C₉×#484	C₂	1	2	yes	maximal, complemented
6	C₉×#483	C₂	1	2	yes	maximal, complemented
7	C₉×#428	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#427	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#419	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#408	C₂	1	1	yes	maximal, characteristic
12	C₃×#3097	C₃	1	1	yes	maximal, characteristic
13	C₂×C₉×#41	C₂²	1	1	yes	characteristic
14	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
17	C₉×C₄⋊Q₈	—	2	1	no	—
18	C₉×#124	—	2	1	no	—
19	C₉×#123	—	2	2	no	—
20	C₉×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₉×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₄×Q₈×C₉	—	2	1	no	—
23	C₄×D₄×C₉	—	2	2	no	—
24	C₄×D₄×C₉	—	2	1	no	—
25	C₉×#117	C₂²	1	1	yes	characteristic
26	C₉×#117	C₂²	1	2	yes	—
27	C₉×#117	C₂²	1	1	yes	characteristic
28	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
30	C₉×#107	C₂²	1	1	yes	characteristic
31	C₉×#107	C₂²	1	1	yes	characteristic
32	C₉×#107	C₂²	1	2	yes	—
33	C₉×#106	C₂²	1	1	yes	characteristic
34	C₉×#106	C₂²	1	1	yes	characteristic
35	C₉×#106	C₂²	1	2	yes	—
36	C₉×#103	C₂²	1	2	yes	—
37	C₉×#103	C₂²	1	2	yes	—
38	C₉×#103	C₂²	1	2	yes	—
39	C₉×#103	C₂²	1	2	yes	—
40	C₉×C₂²⋊C₈	C₂²	1	2	yes	—
41	C₉×C₂²⋊C₈	C₂²	1	2	yes	—
42	C₃×#536	C₂×C₃	1	1	yes	characteristic
43	C₃×#520	C₂×C₃	1	1	yes	characteristic
44	C₃×#485	C₂×C₃	1	2	yes	—
45	C₃×#485	C₂×C₃	1	2	yes	—
46	C₃×#484	C₂×C₃	1	2	yes	—
47	C₃×#483	C₂×C₃	1	2	yes	—
48	C₃×#428	C₂×C₃	1	1	yes	characteristic
49	C₃×#427	C₂×C₃	1	1	yes	characteristic
50	C₃×#419	C₂×C₃	1	1	yes	characteristic
51	C₂×C₃×#103	C₂×C₃	1	1	yes	characteristic
52	C₃×#408	C₂×C₃	1	1	yes	characteristic
53	C₉×#41	—	2	2	no	—
54	C₉×#41	—	2	2	no	—
55	C₂×Q₈×C₉	—	2	1	no	—
56	C₂×Q₈×C₉	—	2	2	no	—
57	C₂×Q₈×C₉	—	2	2	no	—
58	C₂×Q₈×C₉	D₄	1	1	yes	characteristic
59	C₂×Q₈×C₉	C₂³	1	2	yes	—
60	C₂×D₄×C₉	D₄	1	2	yes	—
61	C₂×D₄×C₉	D₄	1	1	yes	characteristic
62	C₂²×C₄×C₉	—	2	1	no	—
63	C₂²×C₄×C₉	—	2	2	no	—
64	C₂²×C₄×C₉	—	2	1	no	—
65	C₂²×C₄×C₉	C₂³	1	2	yes	—
66	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
67	C₉×M₁₆	—	2	2	no	—
68	C₂×C₈×C₉	—	2	2	no	—
69	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
70	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
71	C₂×C₈×C₉	C₂³	1	2	yes	—
72	C₉×C₄⋊C₄	—	2	2	no	—
73	C₉×C₄⋊C₄	—	2	1	no	—
74	C₉×C₄⋊C₄	—	2	2	no	—
75	C₉×C₄⋊C₄	—	2	2	no	—
76	C₉×C₄⋊C₄	C₂³	1	2	yes	—
77	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₉×C₂²⋊C₄	—	2	2	no	—
82	C₉×C₂²⋊C₄	—	2	1	no	—
83	C₉×C₂²⋊C₄	—	2	1	no	—
84	C₉×C₂²⋊C₄	—	2	2	no	—
85	C₉×C₂²⋊C₄	—	2	2	no	—
86	C₄²×C₉	—	2	2	no	—
87	C₄²×C₉	—	2	1	no	—
88	C₄²×C₉	—	2	1	no	—
89	#3097	C₉	1	1	yes	characteristic, direct product factor, Sylow
90	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
91	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
93	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
94	C₃×C₄⋊Q₈	—	2	1	no	—
95	C₃×#124	—	2	1	no	—
96	C₃×#123	—	2	2	no	—
97	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
98	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
99	C₃×C₄×Q₈	—	2	1	no	—
100	C₃×C₄×D₄	—	2	2	no	—
101	C₃×C₄×D₄	—	2	1	no	—
102	C₃×#117	C₂²×C₃	1	1	yes	characteristic
103	C₃×#117	C₂²×C₃	1	1	yes	characteristic
104	C₃×#117	C₂²×C₃	1	2	yes	—
105	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
107	C₃×#107	C₂²×C₃	1	1	yes	characteristic
108	C₃×#107	C₂²×C₃	1	1	yes	characteristic
109	C₃×#107	C₂²×C₃	1	2	yes	—
110	C₃×#106	C₂²×C₃	1	1	yes	characteristic
111	C₃×#106	C₂²×C₃	1	1	yes	characteristic
112	C₃×#106	C₂²×C₃	1	2	yes	—
113	C₃×#103	C₂²×C₃	1	2	yes	—
114	C₃×#103	C₂²×C₃	1	2	yes	—
115	C₃×#103	C₂²×C₃	1	2	yes	—
116	C₃×#103	C₂²×C₃	1	2	yes	—
117	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
118	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
119	C₂³×C₉	C₂×D₄	1	2	yes	—
120	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
121	Q₈×C₉	—	2	2	no	—
122	Q₈×C₉	—	2	2	no	—
123	Q₈×C₉	—	2	2	no	—
124	Q₈×C₉	—	4	2	no	—
125	D₄×C₉	—	2	4	no	—
126	D₄×C₉	—	2	2	no	—
127	C₂×C₄×C₉	—	2	2	no	—
128	C₂×C₄×C₉	—	2	2	no	—
129	C₂×C₄×C₉	—	2	1	no	—
130	C₂×C₄×C₉	—	2	1	no	—
131	C₂×C₄×C₉	—	2	1	no	—
132	C₂×C₄×C₉	—	2	2	no	—
133	C₂×C₄×C₉	—	2	1	no	—
134	C₂×C₄×C₉	—	2	2	no	—
135	C₂×C₄×C₉	—	4	2	no	—
136	C₂×C₄×C₉	—	8	1	no	—
137	C₂×C₄×C₉	—	8	2	no	—
138	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
139	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
140	C₂×C₄×C₉	#41	1	2	yes	—
141	C₂×C₄×C₉	#41	1	2	yes	—
142	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
143	C₈×C₉	—	2	1	no	—
144	C₈×C₉	—	2	1	no	—
145	C₈×C₉	—	2	2	no	—
146	#536	C₂×C₉	1	1	yes	characteristic
147	#520	C₂×C₉	1	1	yes	characteristic
148	#485	C₂×C₉	1	2	yes	complemented
149	#485	C₂×C₉	1	2	yes	complemented
150	#484	C₂×C₉	1	2	yes	complemented
151	#483	C₂×C₉	1	2	yes	complemented
152	#428	C₂×C₉	1	1	yes	characteristic, complemented
153	#427	C₂×C₉	1	1	yes	characteristic, complemented
154	#419	C₂×C₉	1	1	yes	characteristic, complemented
155	C₂×#103	C₂×C₉	1	1	yes	characteristic, complemented
156	#408	C₂×C₉	1	1	yes	characteristic
157	C₃×#41	—	2	2	no	—
158	C₃×#41	—	2	2	no	—
159	C₂×C₃×Q₈	—	2	1	no	—
160	C₂×C₃×Q₈	—	2	2	no	—
161	C₂×C₃×Q₈	—	2	2	no	—
162	C₂×C₃×Q₈	C₃×D₄	1	1	yes	characteristic
163	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
164	C₂×C₃×D₄	C₃×D₄	1	2	yes	—
165	C₂×C₃×D₄	C₃×D₄	1	1	yes	characteristic
166	C₂²×C₃×C₄	—	2	1	no	—
167	C₂²×C₃×C₄	—	2	2	no	—
168	C₂²×C₃×C₄	—	2	1	no	—
169	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
170	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
171	C₃×M₁₆	—	2	2	no	—
172	C₂×C₃×C₈	—	2	2	no	—
173	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
174	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
175	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
176	C₃×C₄⋊C₄	—	2	2	no	—
177	C₃×C₄⋊C₄	—	2	1	no	—
178	C₃×C₄⋊C₄	—	2	2	no	—
179	C₃×C₄⋊C₄	—	2	2	no	—
180	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
181	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
182	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
183	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
184	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
185	C₃×C₂²⋊C₄	—	2	2	no	—
186	C₃×C₂²⋊C₄	—	2	1	no	—
187	C₃×C₂²⋊C₄	—	2	1	no	—
188	C₃×C₂²⋊C₄	—	2	2	no	—
189	C₃×C₂²⋊C₄	—	2	2	no	—
190	C₃×C₄²	—	2	2	no	—
191	C₃×C₄²	—	2	1	no	—
192	C₃×C₄²	—	2	1	no	—
193	C₂²×C₉	—	2	1	no	—
194	C₂²×C₉	—	2	1	no	—
195	C₂²×C₉	—	2	2	no	—
196	C₂²×C₉	—	2	2	no	—
197	C₂²×C₉	—	2	2	no	—
198	C₂²×C₉	#123	1	2	yes	—
199	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
200	C₄×C₉	—	2	2	no	—
201	C₄×C₉	—	4	2	no	—
202	C₄×C₉	—	4	1	no	—
203	C₄×C₉	—	4	2	no	—
204	C₄×C₉	—	4	1	no	—
205	C₄×C₉	—	4	1	no	—
206	C₄×C₉	—	4	1	no	—
207	C₄×C₉	#123	1	2	yes	—
208	C₄×C₉	C₂×#41	1	1	yes	characteristic
209	C₄×C₉	C₂×#41	1	1	yes	characteristic
210	C₂×#41	C₂²×C₉	1	1	yes	characteristic
211	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
212	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
213	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
214	C₄⋊Q₈	—	2	1	no	—
215	#124	—	2	1	no	—
216	#123	—	2	2	no	—
217	C₂²⋊Q₈	C₂²×C₉	1	2	yes	—
218	C₂²⋊Q₈	C₂²×C₉	1	2	yes	—
219	C₄×Q₈	—	2	1	no	—
220	C₄×D₄	—	2	2	no	—
221	C₄×D₄	—	2	1	no	—
222	#117	C₂²×C₉	1	1	yes	characteristic
223	#117	C₂²×C₉	1	2	yes	—
224	#117	C₂²×C₉	1	1	yes	characteristic
225	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
226	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
227	#107	C₂²×C₉	1	1	yes	characteristic
228	#107	C₂²×C₉	1	1	yes	characteristic
229	#107	C₂²×C₉	1	2	yes	—
230	#106	C₂²×C₉	1	1	yes	characteristic
231	#106	C₂²×C₉	1	1	yes	characteristic
232	#106	C₂²×C₉	1	2	yes	—
233	#103	C₂²×C₉	1	2	yes	—
234	#103	C₂²×C₉	1	2	yes	—
235	#103	C₂²×C₉	1	2	yes	—
236	#103	C₂²×C₉	1	2	yes	—
237	C₂²⋊C₈	C₂²×C₉	1	2	yes	—
238	C₂²⋊C₈	C₂²×C₉	1	2	yes	—
239	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
240	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
241	C₃×Q₈	—	2	2	no	—
242	C₃×Q₈	—	2	2	no	—
243	C₃×Q₈	—	2	2	no	—
244	C₃×Q₈	—	4	2	no	—
245	C₃×D₄	—	2	4	no	—
246	C₃×D₄	—	2	2	no	—
247	C₂×C₃×C₄	—	2	2	no	—
248	C₂×C₃×C₄	—	2	2	no	—
249	C₂×C₃×C₄	—	2	1	no	—
250	C₂×C₃×C₄	—	2	1	no	—
251	C₂×C₃×C₄	—	2	1	no	—
252	C₂×C₃×C₄	—	2	2	no	—
253	C₂×C₃×C₄	—	2	1	no	—
254	C₂×C₃×C₄	—	2	2	no	—
255	C₂×C₃×C₄	—	4	2	no	—
256	C₂×C₃×C₄	—	8	1	no	—
257	C₂×C₃×C₄	—	8	2	no	—
258	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
259	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
260	C₂×C₃×C₄	C₃×#41	1	2	yes	—
261	C₂×C₃×C₄	C₃×#41	1	2	yes	—
262	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
263	C₃×C₈	—	2	1	no	—
264	C₃×C₈	—	2	1	no	—
265	C₃×C₈	—	2	2	no	—
266	C₂×C₉	—	2	2	no	—
267	C₂×C₉	—	4	2	no	—
268	C₂×C₉	C₂×#123	1	1	yes	characteristic
269	C₂×C₉	#577	1	1	yes	characteristic
270	C₂×C₉	#578	1	1	yes	characteristic
271	#41	—	2	2	no	—
272	#41	—	2	2	no	—
273	C₂×Q₈	—	2	1	no	—
274	C₂×Q₈	—	2	2	no	—
275	C₂×Q₈	—	2	2	no	—
276	C₂×Q₈	D₄×C₉	1	1	yes	characteristic
277	C₂×Q₈	C₂³×C₉	1	2	yes	—
278	C₂×D₄	D₄×C₉	1	2	yes	—
279	C₂×D₄	D₄×C₉	1	1	yes	characteristic
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	C₂³×C₉	1	2	yes	—
284	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
285	M₁₆	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
288	C₂×C₈	C₂³×C₉	1	2	yes	—
289	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	2	1	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	C₂³×C₉	1	2	yes	—
295	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
296	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
297	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
298	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
299	C₂²⋊C₄	—	2	2	no	—
300	C₂²⋊C₄	—	2	1	no	—
301	C₂²⋊C₄	—	2	1	no	—
302	C₂²⋊C₄	—	2	2	no	—
303	C₂²⋊C₄	—	2	2	no	—
304	C₄²	—	2	2	no	—
305	C₄²	—	2	1	no	—
306	C₄²	—	2	1	no	—
307	C₂²×C₃	—	2	1	no	—
308	C₂²×C₃	—	2	1	no	—
309	C₂²×C₃	—	2	2	no	—
310	C₂²×C₃	—	2	2	no	—
311	C₂²×C₃	—	2	2	no	—
312	C₂²×C₃	C₃×#123	1	2	yes	—
313	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
314	C₃×C₄	—	2	2	no	—
315	C₃×C₄	—	4	2	no	—
316	C₃×C₄	—	4	1	no	—
317	C₃×C₄	—	4	1	no	—
318	C₃×C₄	—	4	1	no	—
319	C₃×C₄	—	4	1	no	—
320	C₃×C₄	—	4	2	no	—
321	C₃×C₄	C₃×#123	1	2	yes	—
322	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
323	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
324	C₉	#3097	1	1	yes	characteristic, direct product factor, Sylow
325	C₂³	C₂×D₄×C₉	1	2	yes	—
326	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
327	Q₈	—	2	2	no	—
328	Q₈	—	2	2	no	—
329	Q₈	—	2	2	no	—
330	Q₈	—	4	2	no	—
331	D₄	—	2	4	no	—
332	D₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	8	1	no	—
343	C₂×C₄	—	8	2	no	—
344	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
345	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
346	C₂×C₄	C₉×#41	1	2	yes	—
347	C₂×C₄	C₉×#41	1	2	yes	—
348	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
349	C₈	—	2	1	no	—
350	C₈	—	2	1	no	—
351	C₈	—	2	2	no	—
352	C₂×C₃	—	2	2	no	—
353	C₂×C₃	—	4	2	no	—
354	C₂×C₃	C₂×C₃×#123	1	1	yes	characteristic
355	C₂×C₃	C₃×#577	1	1	yes	characteristic
356	C₂×C₃	C₃×#578	1	1	yes	characteristic
357	C₂²	—	2	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	2	no	—
362	C₂²	C₉×#123	1	2	yes	—
363	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
364	C₄	—	2	2	no	—
365	C₄	—	4	2	no	—
366	C₄	—	4	2	no	—
367	C₄	—	4	1	no	—
368	C₄	—	4	1	no	—
369	C₄	—	4	1	no	—
370	C₄	—	4	1	no	—
371	C₄	C₉×#123	1	2	yes	—
372	C₄	C₂×C₉×#41	1	1	yes	characteristic
373	C₄	C₂×C₉×#41	1	1	yes	characteristic
374	C₃	C₃×#3097	1	1	yes	characteristic
375	C₂	—	2	2	no	—
376	C₂	—	4	2	no	—
377	C₂	C₂×C₉×#123	1	1	yes	characteristic
378	C₂	C₉×#577	1	1	yes	characteristic
379	C₂	C₉×#578	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×#41	C₂²×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₉×#41 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₉×#485	C₂	semidirect
4. C₉×#485	C₂	semidirect
5. C₉×#484	C₂	semidirect
6. C₉×#483	C₂	semidirect
7. C₉×#428	C₂	semidirect
8. C₉×#427	C₂	semidirect
9. C₉×#419	C₂	semidirect
10. C₂×C₉×#103	C₂	semidirect
89. #3097	C₉	direct (N × H)
148. #485	C₂×C₉	semidirect
149. #485	C₂×C₉	semidirect
150. #484	C₂×C₉	semidirect
151. #483	C₂×C₉	semidirect
152. #428	C₂×C₉	semidirect
153. #427	C₂×C₉	semidirect
154. #419	C₂×C₉	semidirect
155. C₂×#103	C₂×C₉	semidirect
324. C₉	#3097	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×#536	2
C₉×#520	2
C₉×#485	2
C₉×#484	2
C₉×#483	2
C₉×#428	2
C₉×#427	2
C₉×#419	2
C₂×C₉×#103	2
C₉×#408	2
C₃×#3097	3

Subgroups — C9×#3097 #11767818

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3097 #11767818