Subgroups — C₉×#4804 #13141883

Order 1728.

516 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#239	C₂	1	1	yes	maximal, characteristic
2	C₂×D₃×C₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#892	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#835	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#821	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#809	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4804	C₃	1	1	yes	maximal, characteristic
9	C₉×#416	—	3	1	no	maximal
10	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
11	C₉×#239	—	2	2	no	—
12	C₉×#239	C₄	1	4	yes	complemented
13	C₂×C₉×D₁₂	—	2	1	no	—
14	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₃×C₉	—	2	1	no	—
16	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic
18	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₉×(C₂×D₃)⋊C₄	—	2	1	no	—
20	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
21	C₄×C₉×Dic₃	—	2	1	no	—
22	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
23	D₃×C₈×C₉	—	2	2	no	—
24	C₂×C₃×#239	C₂×C₃	1	1	yes	characteristic
25	C₂×C₃×D₃×C₈	C₂×C₃	1	1	yes	characteristic
26	C₃×#892	C₂×C₃	1	1	yes	characteristic
27	C₂×C₉×#41	—	3	1	no	—
28	C₃²×#103	C₂×C₃	1	1	yes	characteristic
29	C₃×#835	C₂×C₃	1	1	yes	characteristic
30	C₃×#821	C₂×C₃	1	1	yes	characteristic
31	C₃×#809	C₂×C₃	1	1	yes	characteristic
32	C₂²×C₈×C₉	—	3	1	no	—
33	C₉×#117	—	3	1	no	—
34	C₉×#103	—	2	1	no	—
35	C₉×#103	—	3	1	no	—
36	C₉×#103	D₃	1	1	yes	characteristic, complemented
37	C₉×#102	—	3	1	no	—
38	C₉×#102	—	3	1	no	—
39	C₂²×D₃×C₉	—	2	1	no	—
40	C₂²×D₃×C₉	D₄	1	1	yes	characteristic
41	C₃×Q₈×C₉	—	2	1	no	—
42	C₃×Q₈×C₉	C₂×C₄	1	2	yes	—
43	C₂×C₃×C₄×C₉	—	2	1	no	—
44	C₂×C₃×C₄×C₉	—	2	1	no	—
45	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
46	C₂×C₉×Dic₃	—	2	1	no	—
47	C₂×C₉×Dic₃	D₄	1	1	yes	characteristic
48	C₉×D₁₂	—	2	4	no	—
49	C₉×D₁₂	—	2	1	no	—
50	C₉×D₁₂	C₂×C₄	1	2	yes	—
51	C₄×D₃×C₉	—	2	4	no	—
52	C₄×D₃×C₉	C₂×C₄	1	2	yes	—
53	C₄×D₃×C₉	D₄	1	2	yes	—
54	C₃×C₈×C₉	—	2	1	no	—
55	C₉×C₃⋊C₈	—	2	1	no	—
56	C₃×#416	—	3	1	no	—
57	#4804	C₉	1	1	yes	characteristic, direct product factor
58	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
59	C₃×#239	—	2	2	no	—
60	C₃×#239	C₃×C₄	1	4	yes	—
61	C₂×C₃×D₁₂	—	2	1	no	—
62	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
63	C₂×C₃×C₄×D₃	—	2	1	no	—
64	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
65	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
66	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
67	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
68	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
69	C₃×C₄×Dic₃	—	2	1	no	—
70	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
71	C₃×D₃×C₈	—	2	2	no	—
72	C₉×#41	—	3	4	no	—
73	C₉×#41	—	6	2	no	—
74	C₂×Q₈×C₉	—	2	1	no	—
75	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
76	C₂×D₄×C₉	—	3	1	no	—
77	C₂×D₄×C₉	—	6	1	no	—
78	C₂²×C₄×C₉	—	3	1	no	—
79	C₂²×C₄×C₉	—	6	1	no	—
80	C₂×C₈×C₉	—	2	1	no	—
81	C₂×C₈×C₉	—	3	1	no	—
82	C₂×C₈×C₉	—	6	2	no	—
83	C₂×C₈×C₉	C₂×D₃	1	1	yes	characteristic
84	C₉×C₄⋊C₄	—	2	1	no	—
85	C₉×C₄⋊C₄	—	3	1	no	—
86	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
87	C₉×C₂²⋊C₄	—	6	1	no	—
88	C₄²×C₉	—	6	1	no	—
89	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
90	C₂×D₃×C₉	—	2	1	no	—
91	C₂×D₃×C₉	—	2	1	no	—
92	C₂×D₃×C₉	—	2	2	no	—
93	C₂×D₃×C₉	—	4	1	no	—
94	C₂×D₃×C₉	—	4	1	no	—
95	C₂×D₃×C₉	C₂²⋊C₄	1	2	yes	—
96	C₃×C₄×C₉	—	2	2	no	—
97	C₃×C₄×C₉	—	4	1	no	—
98	C₃×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
99	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
100	C₉×Dic₃	—	4	1	no	—
101	C₉×Dic₃	C₂²⋊C₄	1	2	yes	—
102	C₂×C₃×#41	—	3	1	no	—
103	C₂×#239	C₂×C₉	1	1	yes	characteristic
104	C₂²×C₃×C₈	—	3	1	no	—
105	C₃×#117	—	3	1	no	—
106	C₂×D₃×C₈	C₂×C₉	1	1	yes	characteristic, complemented
107	#892	C₂×C₉	1	1	yes	characteristic, complemented
108	C₃×#103	—	2	1	no	—
109	C₃×#103	—	3	1	no	—
110	C₃×#103	C₂×C₉	1	1	yes	characteristic, complemented
111	C₃×#103	C₃×D₃	1	1	yes	characteristic
112	C₃×#102	—	3	1	no	—
113	C₃×#102	—	3	1	no	—
114	#835	C₂×C₉	1	1	yes	characteristic, complemented
115	#821	C₂×C₉	1	1	yes	characteristic, complemented
116	#809	C₂×C₉	1	1	yes	characteristic, complemented
117	C₂²×C₃×D₃	—	2	1	no	—
118	C₂²×C₃×D₃	C₃×D₄	1	1	yes	characteristic
119	C₃²×Q₈	—	2	1	no	—
120	C₃²×Q₈	C₂×C₃×C₄	1	2	yes	—
121	C₂×C₃²×C₄	—	2	1	no	—
122	C₂×C₃²×C₄	—	2	1	no	—
123	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
124	C₂×C₃×Dic₃	—	2	1	no	—
125	C₂×C₃×Dic₃	C₃×D₄	1	1	yes	characteristic
126	C₃×D₁₂	—	2	4	no	—
127	C₃×D₁₂	—	2	1	no	—
128	C₃×D₁₂	C₂×C₃×C₄	1	2	yes	—
129	C₃×C₄×D₃	—	2	4	no	—
130	C₃×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
131	C₃×C₄×D₃	C₃×D₄	1	2	yes	—
132	C₂³×C₉	—	3	1	no	—
133	C₂³×C₉	—	6	1	no	—
134	C₃²×C₈	—	2	1	no	—
135	C₃×C₃⋊C₈	—	2	1	no	—
136	Q₈×C₉	—	2	1	no	—
137	Q₈×C₉	—	2	2	no	—
138	Q₈×C₉	—	4	1	no	—
139	Q₈×C₉	C₄×D₃	1	2	yes	—
140	D₄×C₉	—	3	2	no	—
141	D₄×C₉	—	6	4	no	—
142	D₄×C₉	—	6	1	no	—
143	C₂×C₄×C₉	—	2	1	no	—
144	C₂×C₄×C₉	—	2	1	no	—
145	C₂×C₄×C₉	—	2	1	no	—
146	C₂×C₄×C₉	—	3	1	no	—
147	C₂×C₄×C₉	—	3	2	no	—
148	C₂×C₄×C₉	—	3	2	no	—
149	C₂×C₄×C₉	—	4	1	no	—
150	C₂×C₄×C₉	—	4	1	no	—
151	C₂×C₄×C₉	—	6	4	no	—
152	C₂×C₄×C₉	—	6	1	no	—
153	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
154	C₈×C₉	—	2	1	no	—
155	C₈×C₉	—	4	1	no	—
156	C₈×C₉	—	6	1	no	—
157	#416	—	3	1	no	Sylow
158	C₂×C₃×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₃×C₉	#135	1	1	yes	characteristic
160	C₂×C₃×C₉	#135	1	1	yes	characteristic
161	D₃×C₉	—	2	2	no	—
162	D₃×C₉	—	4	2	no	—
163	C₃×#41	—	3	4	no	—
164	C₃×#41	—	6	2	no	—
165	C₂×C₃×Q₈	—	2	1	no	—
166	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
167	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
168	C₂×C₃×D₄	—	3	1	no	—
169	C₂×C₃×D₄	—	6	1	no	—
170	C₂²×C₃×C₄	—	3	1	no	—
171	C₂²×C₃×C₄	—	6	1	no	—
172	#239	—	2	2	no	—
173	#239	C₄×C₉	1	4	yes	complemented
174	C₂×D₁₂	—	2	1	no	—
175	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
176	C₂×C₄×D₃	—	2	1	no	—
177	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
178	C₂×C₃×C₈	—	2	1	no	—
179	C₂×C₃×C₈	—	3	1	no	—
180	C₂×C₃×C₈	—	6	2	no	—
181	C₂×C₃×C₈	C₂²×C₉	1	1	yes	characteristic
182	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
183	C₃×C₄⋊C₄	—	2	1	no	—
184	C₃×C₄⋊C₄	—	3	1	no	—
185	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
186	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
187	C₃×C₂²⋊C₄	—	6	1	no	—
188	C₃×C₄²	—	6	1	no	—
189	(C₂×D₃)⋊C₄	—	2	1	no	—
190	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
191	C₄×Dic₃	—	2	1	no	—
192	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic
193	D₃×C₈	—	2	2	no	—
194	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
195	C₂×C₃×D₃	—	2	1	no	—
196	C₂×C₃×D₃	—	2	1	no	—
197	C₂×C₃×D₃	—	2	2	no	—
198	C₂×C₃×D₃	—	4	1	no	—
199	C₂×C₃×D₃	—	4	1	no	—
200	C₂×C₃×D₃	C₃×C₂²⋊C₄	1	2	yes	—
201	C₃²×C₄	—	2	2	no	—
202	C₃²×C₄	—	4	1	no	—
203	C₃²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
204	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
205	C₃×Dic₃	—	4	1	no	—
206	C₃×Dic₃	C₃×C₂²⋊C₄	1	2	yes	—
207	C₂²×C₉	—	2	1	no	—
208	C₂²×C₉	—	3	2	no	—
209	C₂²×C₉	—	6	1	no	—
210	C₂²×C₉	—	6	1	no	—
211	C₂²×C₉	—	6	2	no	—
212	C₂²×C₉	—	12	1	no	—
213	C₂²×C₉	—	12	1	no	—
214	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
215	C₄×C₉	—	2	2	no	—
216	C₄×C₉	—	2	1	no	—
217	C₄×C₉	—	2	1	no	—
218	C₄×C₉	—	3	2	no	—
219	C₄×C₉	—	4	2	no	—
220	C₄×C₉	—	4	1	no	—
221	C₄×C₉	—	8	1	no	—
222	C₄×C₉	—	12	1	no	—
223	C₄×C₉	C₂×C₄×D₃	1	1	yes	characteristic
224	C₄×C₉	D₃×D₄	1	1	yes	characteristic
225	C₂×#41	—	3	1	no	—
226	C₂²×C₈	—	3	1	no	—
227	#117	—	3	1	no	—
228	#103	—	3	1	no	—
229	#103	D₃×C₉	1	1	yes	characteristic, complemented
230	#102	—	3	1	no	—
231	#102	—	3	1	no	—
232	C₃×C₉	#416	1	1	yes	characteristic, complemented, Sylow
233	C₂³×C₃	—	3	1	no	—
234	C₂³×C₃	—	6	1	no	—
235	C₂²×D₃	—	2	1	no	—
236	C₂²×D₃	D₄×C₉	1	1	yes	characteristic
237	C₃×Q₈	—	2	1	no	—
238	C₃×Q₈	—	2	1	no	—
239	C₃×Q₈	—	2	2	no	—
240	C₃×Q₈	—	4	1	no	—
241	C₃×Q₈	C₂×C₄×C₉	1	2	yes	—
242	C₃×Q₈	C₃×C₄×D₃	1	2	yes	—
243	C₃×D₄	—	3	2	no	—
244	C₃×D₄	—	6	4	no	—
245	C₃×D₄	—	6	1	no	—
246	C₂×C₃×C₄	—	2	1	no	—
247	C₂×C₃×C₄	—	2	1	no	—
248	C₂×C₃×C₄	—	2	1	no	—
249	C₂×C₃×C₄	—	2	1	no	—
250	C₂×C₃×C₄	—	2	1	no	—
251	C₂×C₃×C₄	—	3	1	no	—
252	C₂×C₃×C₄	—	3	2	no	—
253	C₂×C₃×C₄	—	3	2	no	—
254	C₂×C₃×C₄	—	4	1	no	—
255	C₂×C₃×C₄	—	4	1	no	—
256	C₂×C₃×C₄	—	6	4	no	—
257	C₂×C₃×C₄	—	6	1	no	—
258	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
259	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
260	C₂×Dic₃	—	2	1	no	—
261	C₂×Dic₃	D₄×C₉	1	1	yes	characteristic
262	D₁₂	—	2	4	no	—
263	D₁₂	—	2	1	no	—
264	D₁₂	C₂×C₄×C₉	1	2	yes	—
265	C₄×D₃	—	2	4	no	—
266	C₄×D₃	C₂×C₄×C₉	1	2	yes	—
267	C₄×D₃	D₄×C₉	1	2	yes	—
268	C₃×C₈	—	2	1	no	—
269	C₃×C₈	—	2	1	no	—
270	C₃×C₈	—	4	1	no	—
271	C₃×C₈	—	6	1	no	—
272	C₃⋊C₈	—	2	1	no	—
273	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
274	C₂×C₃²	C₃×#135	1	1	yes	characteristic
275	C₂×C₃²	C₃×#135	1	1	yes	characteristic
276	C₃×D₃	—	2	2	no	—
277	C₃×D₃	—	4	2	no	—
278	C₂×C₉	—	2	1	no	—
279	C₂×C₉	—	2	1	no	—
280	C₂×C₉	—	2	1	no	—
281	C₂×C₉	—	6	2	no	—
282	C₂×C₉	—	12	2	no	—
283	C₂×C₉	D₃×C₂²⋊C₄	1	1	yes	characteristic
284	C₂×C₉	#916	1	1	yes	characteristic
285	C₂×C₉	#919	1	1	yes	characteristic
286	#41	—	3	4	no	—
287	#41	—	6	2	no	—
288	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
289	C₂×D₄	—	3	1	no	—
290	C₂×D₄	—	6	1	no	—
291	C₂²×C₄	—	3	1	no	—
292	C₂²×C₄	—	6	1	no	—
293	C₂×C₈	—	3	1	no	—
294	C₂×C₈	—	6	2	no	—
295	C₂×C₈	C₂×D₃×C₉	1	1	yes	characteristic
296	C₄⋊C₄	—	3	1	no	—
297	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
298	C₂²⋊C₄	—	6	1	no	—
299	C₄²	—	6	1	no	—
300	C₂²×C₃	—	2	1	no	—
301	C₂²×C₃	—	3	2	no	—
302	C₂²×C₃	—	6	1	no	—
303	C₂²×C₃	—	6	1	no	—
304	C₂²×C₃	—	6	2	no	—
305	C₂²×C₃	—	12	1	no	—
306	C₂²×C₃	—	12	1	no	—
307	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
308	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
309	C₂×D₃	—	2	1	no	—
310	C₂×D₃	—	2	1	no	—
311	C₂×D₃	—	2	2	no	—
312	C₂×D₃	—	4	1	no	—
313	C₂×D₃	—	4	1	no	—
314	C₂×D₃	C₉×C₂²⋊C₄	1	2	yes	—
315	C₃×C₄	—	2	2	no	—
316	C₃×C₄	—	2	2	no	—
317	C₃×C₄	—	2	1	no	—
318	C₃×C₄	—	2	1	no	—
319	C₃×C₄	—	3	2	no	—
320	C₃×C₄	—	4	2	no	—
321	C₃×C₄	—	4	1	no	—
322	C₃×C₄	—	4	1	no	—
323	C₃×C₄	—	8	1	no	—
324	C₃×C₄	—	12	1	no	—
325	C₃×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
326	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
327	C₃×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
328	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
329	Dic₃	—	4	1	no	—
330	Dic₃	C₉×C₂²⋊C₄	1	2	yes	—
331	C₃²	C₃×#416	1	1	yes	characteristic
332	C₉	—	2	1	no	—
333	C₉	#4804	1	1	yes	characteristic, direct product factor
334	C₂³	—	3	1	no	—
335	C₂³	—	6	1	no	—
336	Q₈	—	2	1	no	—
337	Q₈	C₄×D₃×C₉	1	2	yes	—
338	D₄	—	3	2	no	—
339	D₄	—	6	4	no	—
340	D₄	—	6	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	3	1	no	—
344	C₂×C₄	—	3	2	no	—
345	C₂×C₄	—	3	2	no	—
346	C₂×C₄	—	6	4	no	—
347	C₂×C₄	—	6	1	no	—
348	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
349	C₈	—	2	1	no	—
350	C₈	—	6	1	no	—
351	C₂×C₃	—	2	1	no	—
352	C₂×C₃	—	2	1	no	—
353	C₂×C₃	—	2	1	no	—
354	C₂×C₃	—	6	2	no	—
355	C₂×C₃	—	12	2	no	—
356	C₂×C₃	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
357	C₂×C₃	C₉×#135	1	1	yes	characteristic
358	C₂×C₃	C₉×#135	1	1	yes	characteristic
359	C₂×C₃	C₃×D₃×C₂²⋊C₄	1	1	yes	characteristic
360	C₂×C₃	C₃×#916	1	1	yes	characteristic
361	C₂×C₃	C₃×#919	1	1	yes	characteristic
362	D₃	—	2	2	no	—
363	D₃	—	4	2	no	—
364	C₂²	—	3	2	no	—
365	C₂²	—	6	1	no	—
366	C₂²	—	6	1	no	—
367	C₂²	—	6	2	no	—
368	C₂²	—	12	1	no	—
369	C₂²	—	12	1	no	—
370	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
371	C₄	—	2	2	no	—
372	C₄	—	3	2	no	—
373	C₄	—	4	1	no	—
374	C₄	—	12	1	no	—
375	C₄	C₂×C₄×D₃×C₉	1	1	yes	characteristic
376	C₄	D₃×D₄×C₉	1	1	yes	characteristic
377	C₃	—	2	1	no	—
378	C₃	C₉×#416	1	1	yes	characteristic, complemented
379	C₃	C₃×#4804	1	1	yes	characteristic
380	C₂	—	6	2	no	—
381	C₂	—	12	2	no	—
382	C₂	D₃×C₉×C₂²⋊C₄	1	1	yes	characteristic
383	C₂	C₉×#916	1	1	yes	characteristic
384	C₂	C₉×#919	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	D₃×D₄
commutator	C₃×C₄	C₂²×C₄×C₉
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₃×C₉×#103	C₂
socle	C₂²×C₃²	C₂×C₃×D₄
prime radical	C₂×C₃×#239	C₂×C₃
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₉×#103	D₃
hypocenter	C₃	C₉×#416
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₄×C₉ ◁ C₉×#103

Complements

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

N	H ≅ G/N	type
2. C₂×D₃×C₈×C₉	C₂	semidirect
3. C₉×#892	C₂	semidirect
4. C₃×C₉×#103	C₂	semidirect
5. C₉×#835	C₂	semidirect
6. C₉×#821	C₂	semidirect
7. C₉×#809	C₂	semidirect
12. C₉×#239	C₄	semidirect
36. C₉×#103	D₃	semidirect
57. #4804	C₉	direct (N × H)
106. C₂×D₃×C₈	C₂×C₉	semidirect
107. #892	C₂×C₉	semidirect
110. C₃×#103	C₂×C₉	semidirect
114. #835	C₂×C₉	semidirect
115. #821	C₂×C₉	semidirect
116. #809	C₂×C₉	semidirect
173. #239	C₄×C₉	semidirect
229. #103	D₃×C₉	semidirect
232. C₃×C₉	#416	semidirect
333. C₉	#4804	direct (N × H)
378. C₃	C₉×#416	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×#239	2
C₂×D₃×C₈×C₉	2
C₉×#892	2
C₃×C₉×#103	2
C₉×#835	2
C₉×#821	2
C₉×#809	2
C₃×#4804	3
C₉×#416	3

Subgroups — C9×#4804 #13141883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#4804 #13141883