Subgroups — C₉×#4802 #13141881

Order 1728.

492 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×Q₈×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic
3	C₉×#892	C₂	1	1	yes	maximal, characteristic
4	C₃×C₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#835	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#816	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#810	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4802	C₃	1	1	yes	maximal, characteristic
9	C₉×#419	—	3	1	no	maximal
10	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
11	D₃×Q₈×C₉	—	2	2	no	—
12	D₃×Q₈×C₉	C₄	1	4	yes	complemented
13	C₂×C₄×D₃×C₉	—	2	1	no	—
14	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₉×Dic₆	—	2	1	no	—
16	C₂×C₉×Dic₆	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	C₉×ΓL(1,𝔽₂₅)	—	2	2	no	—
24	C₂×C₃×D₃×Q₈	C₂×C₃	1	1	yes	characteristic
25	C₂×C₃×ΓL(1,𝔽₂₅)	C₂×C₃	1	1	yes	characteristic
26	C₃×#892	C₂×C₃	1	1	yes	characteristic
27	C₂²×Q₈×C₉	—	3	1	no	—
28	C₃²×#103	C₂×C₃	1	1	yes	characteristic
29	C₃×#835	C₂×C₃	1	1	yes	characteristic
30	C₃×#816	C₂×C₃	1	1	yes	characteristic
31	C₃×#810	C₂×C₃	1	1	yes	characteristic
32	C₂×C₉×M₁₆	—	3	1	no	—
33	C₉×#117	—	3	1	no	—
34	C₉×#103	—	2	1	no	—
35	C₉×#103	—	3	1	no	—
36	C₉×#103	—	3	1	no	—
37	C₉×#103	—	3	1	no	—
38	C₉×#103	D₃	1	1	yes	characteristic, complemented
39	C₂²×D₃×C₉	D₄	1	1	yes	characteristic
40	C₃×Q₈×C₉	—	2	1	no	—
41	C₃×Q₈×C₉	C₂×C₄	1	2	yes	—
42	C₂×C₃×C₄×C₉	—	2	1	no	—
43	C₂×C₃×C₄×C₉	—	2	1	no	—
44	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
45	C₂×C₉×Dic₃	—	2	1	no	—
46	C₂×C₉×Dic₃	—	2	1	no	—
47	C₂×C₉×Dic₃	D₄	1	1	yes	characteristic
48	C₄×D₃×C₉	—	2	4	no	—
49	C₄×D₃×C₉	C₂×C₄	1	2	yes	—
50	C₄×D₃×C₉	D₄	1	2	yes	—
51	C₉×Dic₆	—	2	1	no	—
52	C₉×Dic₆	—	2	4	no	—
53	C₉×Dic₆	C₂×C₄	1	2	yes	—
54	C₃×C₈×C₉	—	2	1	no	—
55	C₉×C₃⋊C₈	—	2	1	no	—
56	C₃×#419	—	3	1	no	—
57	#4802	C₉	1	1	yes	characteristic, direct product factor
58	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
59	C₃×D₃×Q₈	—	2	2	no	—
60	C₃×D₃×Q₈	C₃×C₄	1	4	yes	—
61	C₂×C₃×C₄×D₃	—	2	1	no	—
62	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
63	C₂×C₃×Dic₆	—	2	1	no	—
64	C₂×C₃×Dic₆	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×ΓL(1,𝔽₂₅)	—	2	2	no	—
72	C₂×Q₈×C₉	—	2	1	no	—
73	C₂×Q₈×C₉	—	3	4	no	—
74	C₂×Q₈×C₉	—	3	1	no	—
75	C₂×Q₈×C₉	—	6	1	no	—
76	C₂×Q₈×C₉	—	6	2	no	—
77	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
78	C₂²×C₄×C₉	—	3	1	no	—
79	C₂²×C₄×C₉	—	6	1	no	—
80	C₉×M₁₆	—	6	2	no	—
81	C₂×C₈×C₉	—	2	1	no	—
82	C₂×C₈×C₉	—	3	1	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	C₂²⋊C₄	1	2	yes	—
93	C₃×C₄×C₉	—	2	2	no	—
94	C₃×C₄×C₉	—	4	1	no	—
95	C₃×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
96	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
97	C₉×Dic₃	—	2	2	no	—
98	C₉×Dic₃	—	4	1	no	—
99	C₉×Dic₃	C₂²⋊C₄	1	2	yes	—
100	C₂²×C₃×Q₈	—	3	1	no	—
101	C₂×D₃×Q₈	C₂×C₉	1	1	yes	characteristic
102	C₂×C₃×M₁₆	—	3	1	no	—
103	C₃×#117	—	3	1	no	—
104	C₂×ΓL(1,𝔽₂₅)	C₂×C₉	1	1	yes	characteristic
105	#892	C₂×C₉	1	1	yes	characteristic
106	C₃×#103	—	2	1	no	—
107	C₃×#103	—	3	1	no	—
108	C₃×#103	—	3	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	#835	C₂×C₉	1	1	yes	characteristic, complemented
113	#816	C₂×C₉	1	1	yes	characteristic, complemented
114	#810	C₂×C₉	1	1	yes	characteristic, complemented
115	C₂²×C₃×D₃	C₃×D₄	1	1	yes	characteristic
116	C₃²×Q₈	—	2	1	no	—
117	C₃²×Q₈	C₂×C₃×C₄	1	2	yes	—
118	C₂×C₃²×C₄	—	2	1	no	—
119	C₂×C₃²×C₄	—	2	1	no	—
120	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
121	C₂×C₃×Dic₃	—	2	1	no	—
122	C₂×C₃×Dic₃	—	2	1	no	—
123	C₂×C₃×Dic₃	C₃×D₄	1	1	yes	characteristic
124	C₃×C₄×D₃	—	2	4	no	—
125	C₃×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
126	C₃×C₄×D₃	C₃×D₄	1	2	yes	—
127	C₃×Dic₆	—	2	1	no	—
128	C₃×Dic₆	—	2	4	no	—
129	C₃×Dic₆	C₂×C₃×C₄	1	2	yes	—
130	C₂³×C₉	—	3	1	no	—
131	C₃²×C₈	—	2	1	no	—
132	C₃×C₃⋊C₈	—	2	1	no	—
133	Q₈×C₉	—	2	1	no	—
134	Q₈×C₉	—	2	2	no	—
135	Q₈×C₉	—	3	2	no	—
136	Q₈×C₉	—	4	1	no	—
137	Q₈×C₉	—	6	4	no	—
138	Q₈×C₉	—	6	1	no	—
139	Q₈×C₉	C₄×D₃	1	2	yes	—
140	C₂×C₄×C₉	—	2	1	no	—
141	C₂×C₄×C₉	—	2	1	no	—
142	C₂×C₄×C₉	—	2	1	no	—
143	C₂×C₄×C₉	—	3	1	no	—
144	C₂×C₄×C₉	—	3	2	no	—
145	C₂×C₄×C₉	—	3	2	no	—
146	C₂×C₄×C₉	—	4	1	no	—
147	C₂×C₄×C₉	—	4	1	no	—
148	C₂×C₄×C₉	—	6	4	no	—
149	C₂×C₄×C₉	—	6	1	no	—
150	C₂×C₄×C₉	—	6	1	no	—
151	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
152	C₈×C₉	—	2	1	no	—
153	C₈×C₉	—	4	1	no	—
154	C₈×C₉	—	6	1	no	—
155	#419	—	3	1	no	Sylow
156	C₂×C₃×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
157	C₂×C₃×C₉	#137	1	1	yes	characteristic
158	C₂×C₃×C₉	#137	1	1	yes	characteristic
159	D₃×C₉	—	2	2	no	—
160	C₂×C₃×Q₈	—	2	1	no	—
161	C₂×C₃×Q₈	—	3	4	no	—
162	C₂×C₃×Q₈	—	3	1	no	—
163	C₂×C₃×Q₈	—	6	1	no	—
164	C₂×C₃×Q₈	—	6	2	no	—
165	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
166	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
167	C₂²×C₃×C₄	—	3	1	no	—
168	C₂²×C₃×C₄	—	6	1	no	—
169	D₃×Q₈	—	2	2	no	—
170	D₃×Q₈	C₄×C₉	1	4	yes	complemented
171	C₂×C₄×D₃	—	2	1	no	—
172	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
173	C₂×Dic₆	—	2	1	no	—
174	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
175	C₃×M₁₆	—	6	2	no	—
176	C₂×C₃×C₈	—	2	1	no	—
177	C₂×C₃×C₈	—	3	1	no	—
178	C₂×C₃×C₈	C₂²×C₉	1	1	yes	characteristic
179	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
180	C₃×C₄⋊C₄	—	2	1	no	—
181	C₃×C₄⋊C₄	—	3	1	no	—
182	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
183	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
184	C₃×C₂²⋊C₄	—	6	1	no	—
185	C₃×C₄²	—	6	1	no	—
186	(C₂×D₃)⋊C₄	—	2	1	no	—
187	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
188	C₄×Dic₃	—	2	1	no	—
189	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic
190	ΓL(1,𝔽₂₅)	—	2	2	no	—
191	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
192	C₂×C₃×D₃	—	2	1	no	—
193	C₂×C₃×D₃	—	2	1	no	—
194	C₂×C₃×D₃	C₃×C₂²⋊C₄	1	2	yes	—
195	C₃²×C₄	—	2	2	no	—
196	C₃²×C₄	—	4	1	no	—
197	C₃²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
198	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
199	C₃×Dic₃	—	2	2	no	—
200	C₃×Dic₃	—	4	1	no	—
201	C₃×Dic₃	C₃×C₂²⋊C₄	1	2	yes	—
202	C₂²×C₉	—	2	1	no	—
203	C₂²×C₉	—	3	2	no	—
204	C₂²×C₉	—	6	1	no	—
205	C₂²×C₉	—	6	1	no	—
206	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
207	C₄×C₉	—	2	2	no	—
208	C₄×C₉	—	2	1	no	—
209	C₄×C₉	—	2	1	no	—
210	C₄×C₉	—	3	2	no	—
211	C₄×C₉	—	4	2	no	—
212	C₄×C₉	—	4	1	no	—
213	C₄×C₉	—	6	2	no	—
214	C₄×C₉	—	8	1	no	—
215	C₄×C₉	—	12	1	no	—
216	C₄×C₉	C₂×C₄×D₃	1	1	yes	characteristic
217	C₄×C₉	D₃×D₄	1	1	yes	characteristic
218	C₂²×Q₈	—	3	1	no	—
219	C₂×M₁₆	—	3	1	no	—
220	#117	—	3	1	no	—
221	#103	—	3	1	no	—
222	#103	—	3	1	no	—
223	#103	—	3	1	no	—
224	#103	D₃×C₉	1	1	yes	characteristic, complemented
225	C₃×C₉	#419	1	1	yes	characteristic, complemented, Sylow
226	C₂³×C₃	—	3	1	no	—
227	C₂²×D₃	D₄×C₉	1	1	yes	characteristic
228	C₃×Q₈	—	2	1	no	—
229	C₃×Q₈	—	2	1	no	—
230	C₃×Q₈	—	2	2	no	—
231	C₃×Q₈	—	3	2	no	—
232	C₃×Q₈	—	4	1	no	—
233	C₃×Q₈	—	6	4	no	—
234	C₃×Q₈	—	6	1	no	—
235	C₃×Q₈	C₂×C₄×C₉	1	2	yes	—
236	C₃×Q₈	C₃×C₄×D₃	1	2	yes	—
237	C₂×C₃×C₄	—	2	1	no	—
238	C₂×C₃×C₄	—	2	1	no	—
239	C₂×C₃×C₄	—	2	1	no	—
240	C₂×C₃×C₄	—	2	1	no	—
241	C₂×C₃×C₄	—	2	1	no	—
242	C₂×C₃×C₄	—	3	1	no	—
243	C₂×C₃×C₄	—	3	2	no	—
244	C₂×C₃×C₄	—	3	2	no	—
245	C₂×C₃×C₄	—	4	1	no	—
246	C₂×C₃×C₄	—	4	1	no	—
247	C₂×C₃×C₄	—	6	4	no	—
248	C₂×C₃×C₄	—	6	1	no	—
249	C₂×C₃×C₄	—	6	1	no	—
250	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
251	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
252	C₂×Dic₃	—	2	1	no	—
253	C₂×Dic₃	—	2	1	no	—
254	C₂×Dic₃	D₄×C₉	1	1	yes	characteristic
255	C₄×D₃	—	2	4	no	—
256	C₄×D₃	C₂×C₄×C₉	1	2	yes	—
257	C₄×D₃	D₄×C₉	1	2	yes	—
258	Dic₆	—	2	1	no	—
259	Dic₆	—	2	4	no	—
260	Dic₆	C₂×C₄×C₉	1	2	yes	—
261	C₃×C₈	—	2	1	no	—
262	C₃×C₈	—	2	1	no	—
263	C₃×C₈	—	4	1	no	—
264	C₃×C₈	—	6	1	no	—
265	C₃⋊C₈	—	2	1	no	—
266	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×C₃²	C₃×#137	1	1	yes	characteristic
268	C₂×C₃²	C₃×#137	1	1	yes	characteristic
269	C₃×D₃	—	2	2	no	—
270	C₂×C₉	—	2	1	no	—
271	C₂×C₉	—	2	1	no	—
272	C₂×C₉	—	2	1	no	—
273	C₂×C₉	—	6	2	no	—
274	C₂×C₉	D₃×C₂²⋊C₄	1	1	yes	characteristic
275	C₂×C₉	#915	1	1	yes	characteristic
276	C₂×C₉	#918	1	1	yes	characteristic
277	C₂×Q₈	—	3	4	no	—
278	C₂×Q₈	—	3	1	no	—
279	C₂×Q₈	—	6	1	no	—
280	C₂×Q₈	—	6	2	no	—
281	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
282	C₂²×C₄	—	3	1	no	—
283	C₂²×C₄	—	6	1	no	—
284	M₁₆	—	6	2	no	—
285	C₂×C₈	—	3	1	no	—
286	C₂×C₈	C₂×D₃×C₉	1	1	yes	characteristic
287	C₄⋊C₄	—	3	1	no	—
288	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
289	C₂²⋊C₄	—	6	1	no	—
290	C₄²	—	6	1	no	—
291	C₂²×C₃	—	2	1	no	—
292	C₂²×C₃	—	3	2	no	—
293	C₂²×C₃	—	6	1	no	—
294	C₂²×C₃	—	6	1	no	—
295	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
296	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
297	C₂×D₃	—	2	1	no	—
298	C₂×D₃	—	2	1	no	—
299	C₂×D₃	C₉×C₂²⋊C₄	1	2	yes	—
300	C₃×C₄	—	2	2	no	—
301	C₃×C₄	—	2	2	no	—
302	C₃×C₄	—	2	1	no	—
303	C₃×C₄	—	2	1	no	—
304	C₃×C₄	—	3	2	no	—
305	C₃×C₄	—	4	2	no	—
306	C₃×C₄	—	4	1	no	—
307	C₃×C₄	—	4	1	no	—
308	C₃×C₄	—	6	2	no	—
309	C₃×C₄	—	8	1	no	—
310	C₃×C₄	—	12	1	no	—
311	C₃×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
312	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
313	C₃×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
314	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
315	Dic₃	—	2	2	no	—
316	Dic₃	—	4	1	no	—
317	Dic₃	C₉×C₂²⋊C₄	1	2	yes	—
318	C₃²	C₃×#419	1	1	yes	characteristic
319	C₉	—	2	1	no	—
320	C₉	#4802	1	1	yes	characteristic, direct product factor
321	C₂³	—	3	1	no	—
322	Q₈	—	2	1	no	—
323	Q₈	—	3	2	no	—
324	Q₈	—	6	4	no	—
325	Q₈	—	6	1	no	—
326	Q₈	C₄×D₃×C₉	1	2	yes	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	3	1	no	—
330	C₂×C₄	—	3	2	no	—
331	C₂×C₄	—	3	2	no	—
332	C₂×C₄	—	6	4	no	—
333	C₂×C₄	—	6	1	no	—
334	C₂×C₄	—	6	1	no	—
335	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
336	C₈	—	2	1	no	—
337	C₈	—	6	1	no	—
338	C₂×C₃	—	2	1	no	—
339	C₂×C₃	—	2	1	no	—
340	C₂×C₃	—	2	1	no	—
341	C₂×C₃	—	6	2	no	—
342	C₂×C₃	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
343	C₂×C₃	C₉×#137	1	1	yes	characteristic
344	C₂×C₃	C₉×#137	1	1	yes	characteristic
345	C₂×C₃	C₃×D₃×C₂²⋊C₄	1	1	yes	characteristic
346	C₂×C₃	C₃×#915	1	1	yes	characteristic
347	C₂×C₃	C₃×#918	1	1	yes	characteristic
348	D₃	—	2	2	no	—
349	C₂²	—	3	2	no	—
350	C₂²	—	6	1	no	—
351	C₂²	—	6	1	no	—
352	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
353	C₄	—	2	2	no	—
354	C₄	—	3	2	no	—
355	C₄	—	4	1	no	—
356	C₄	—	6	2	no	—
357	C₄	—	12	1	no	—
358	C₄	C₂×C₄×D₃×C₉	1	1	yes	characteristic
359	C₄	D₃×D₄×C₉	1	1	yes	characteristic
360	C₃	—	2	1	no	—
361	C₃	C₉×#419	1	1	yes	characteristic, complemented
362	C₃	C₃×#4802	1	1	yes	characteristic
363	C₂	—	6	2	no	—
364	C₂	D₃×C₉×C₂²⋊C₄	1	1	yes	characteristic
365	C₂	C₉×#915	1	1	yes	characteristic
366	C₂	C₉×#918	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	C₂²×C₃×D₃	C₃×D₄
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₉×#103	D₃
hypocenter	C₃	C₉×#419
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
4. C₃×C₉×#103	C₂	semidirect
5. C₉×#835	C₂	semidirect
6. C₉×#816	C₂	semidirect
7. C₉×#810	C₂	semidirect
12. D₃×Q₈×C₉	C₄	semidirect
38. C₉×#103	D₃	semidirect
57. #4802	C₉	direct (N × H)
110. C₃×#103	C₂×C₉	semidirect
112. #835	C₂×C₉	semidirect
113. #816	C₂×C₉	semidirect
114. #810	C₂×C₉	semidirect
170. D₃×Q₈	C₄×C₉	semidirect
224. #103	D₃×C₉	semidirect
225. C₃×C₉	#419	semidirect
320. C₉	#4802	direct (N × H)
361. C₃	C₉×#419	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×Q₈×C₉	2
C₂×C₉×ΓL(1,𝔽₂₅)	2
C₉×#892	2
C₃×C₉×#103	2
C₉×#835	2
C₉×#816	2
C₉×#810	2
C₃×#4802	3
C₉×#419	3

Subgroups — C9×#4802 #13141881

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#4802 #13141881