Subgroups — C₉×#5816 #13153651

Order 1728.

966 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#235	C₂	1	1	yes	maximal, characteristic
3	C₉×#947	C₂	1	2	yes	maximal, complemented
4	C₉×#946	C₂	1	4	yes	maximal, complemented
5	C₉×#944	C₂	1	2	yes	maximal, complemented
6	C₉×#929	C₂	1	4	yes	maximal, complemented
7	C₉×#926	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#5816	C₃	1	1	yes	maximal, characteristic
9	C₉×#536	—	3	1	no	maximal
10	C₂×C₃×Q₈×C₉	—	2	4	no	—
11	C₂×C₃×Q₈×C₉	C₂²	1	2	yes	—
12	C₂×C₃×Q₈×C₉	C₂²	1	2	yes	—
13	C₂²×C₃×C₄×C₉	C₂²	1	2	yes	—
14	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₉×#67	C₂²	1	2	yes	—
16	C₉×#235	—	2	4	no	—
17	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
19	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
20	C₉×#217	C₂²	1	2	yes	—
21	C₉×(C₂×D₃)⋊C₄	C₂²	1	8	yes	—
22	C₉×C₄⋊Dic₃	C₂²	1	2	yes	—
23	C₉×Dic₃⋊C₄	C₂²	1	8	yes	—
24	C₄×C₉×Dic₃	C₂²	1	2	yes	—
25	C₂²×C₃²×Q₈	C₂×C₃	1	1	yes	characteristic
26	C₂×C₃×#235	C₂×C₃	1	1	yes	characteristic
27	C₃×#947	C₂×C₃	1	2	yes	—
28	C₃×#946	C₂×C₃	1	4	yes	—
29	C₃×#944	C₂×C₃	1	2	yes	—
30	C₃×#929	C₂×C₃	1	4	yes	—
31	C₃×#926	C₂×C₃	1	1	yes	characteristic
32	C₂×C₉×#41	—	3	1	no	—
33	C₂²×Q₈×C₉	—	2	1	no	—
34	C₂²×Q₈×C₉	D₃	1	1	yes	characteristic, complemented
35	C₉×C₄⋊Q₈	—	3	2	no	—
36	C₉×#124	—	3	2	no	—
37	C₉×#123	—	3	4	no	—
38	C₉×C₂²⋊Q₈	—	3	4	no	—
39	C₉×#117	—	3	1	no	—
40	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
41	C₂²×D₃×C₉	C₂³	1	2	yes	—
42	C₃×Q₈×C₉	—	2	4	no	—
43	C₃×Q₈×C₉	—	2	4	no	—
44	C₂×C₃×C₄×C₉	—	2	4	no	—
45	C₂×C₃×C₄×C₉	D₄	1	4	yes	—
46	C₂×C₃×C₄×C₉	C₂³	1	4	yes	—
47	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
48	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
49	C₉×#67	—	2	4	no	—
50	C₂×C₉×Dic₃	C₂³	1	2	yes	—
51	C₂×C₉×Dic₃	C₂³	1	4	yes	—
52	C₉×D₁₂	—	2	2	no	—
53	C₄×D₃×C₉	—	2	4	no	—
54	C₉×Dic₆	—	2	2	no	—
55	C₃×#536	—	3	1	no	—
56	#5816	C₉	1	1	yes	characteristic, direct product factor
57	C₂×C₃²×Q₈	—	2	4	no	—
58	C₂×C₃²×Q₈	C₂²×C₃	1	2	yes	—
59	C₂×C₃²×Q₈	C₂²×C₃	1	2	yes	—
60	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
61	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
62	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
63	C₃×#235	—	2	4	no	—
64	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
65	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
66	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
67	C₃×#217	C₂²×C₃	1	2	yes	—
68	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
69	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
70	C₃×Dic₃⋊C₄	C₂²×C₃	1	8	yes	—
71	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
72	C₉×#41	—	6	4	no	—
73	C₂×Q₈×C₉	—	2	8	no	—
74	C₂×Q₈×C₉	—	2	2	no	—
75	C₂×Q₈×C₉	—	2	2	no	—
76	C₂×Q₈×C₉	—	2	4	no	—
77	C₂×Q₈×C₉	—	3	1	no	—
78	C₂×Q₈×C₉	C₂×D₃	1	2	yes	—
79	C₂×Q₈×C₉	C₂×D₃	1	2	yes	—
80	C₂×D₄×C₉	—	3	2	no	—
81	C₂×D₄×C₉	—	3	1	no	—
82	C₂²×C₄×C₉	—	2	2	no	—
83	C₂²×C₄×C₉	—	2	1	no	—
84	C₂²×C₄×C₉	—	3	2	no	—
85	C₂²×C₄×C₉	C₂×D₃	1	2	yes	—
86	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
87	C₉×C₄⋊C₄	—	3	2	no	—
88	C₉×C₄⋊C₄	—	3	8	no	—
89	C₉×C₂²⋊C₄	—	3	2	no	—
90	C₉×C₂²⋊C₄	—	3	8	no	—
91	C₄²×C₉	—	3	2	no	—
92	C₂²×C₃×C₉	—	2	2	no	—
93	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
94	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
95	C₂×D₃×C₉	—	2	2	no	—
96	C₂×D₃×C₉	—	2	4	no	—
97	C₃×C₄×C₉	—	2	4	no	—
98	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
99	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
100	C₉×Dic₃	—	2	2	no	—
101	C₉×Dic₃	—	2	4	no	—
102	C₂×C₃×#41	—	3	1	no	—
103	C₂²×C₃×Q₈	—	2	1	no	—
104	C₂²×C₃×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
105	C₂²×C₃×Q₈	C₃×D₃	1	1	yes	characteristic
106	C₂×#235	C₂×C₉	1	1	yes	characteristic
107	C₃×C₄⋊Q₈	—	3	2	no	—
108	C₃×#124	—	3	2	no	—
109	C₃×#123	—	3	4	no	—
110	C₃×C₂²⋊Q₈	—	3	4	no	—
111	C₃×#117	—	3	1	no	—
112	#947	C₂×C₉	1	2	yes	complemented
113	#946	C₂×C₉	1	4	yes	complemented
114	#944	C₂×C₉	1	2	yes	complemented
115	#929	C₂×C₉	1	4	yes	complemented
116	#926	C₂×C₉	1	1	yes	characteristic, complemented
117	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
118	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
119	C₃²×Q₈	—	2	4	no	—
120	C₃²×Q₈	—	2	4	no	—
121	C₂×C₃²×C₄	—	2	4	no	—
122	C₂×C₃²×C₄	C₃×D₄	1	4	yes	—
123	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
124	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
125	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
126	C₃×#67	—	2	4	no	—
127	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
128	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
129	C₃×D₁₂	—	2	2	no	—
130	C₃×C₄×D₃	—	2	4	no	—
131	C₃×Dic₆	—	2	2	no	—
132	C₂³×C₉	—	2	1	no	—
133	C₂³×C₉	—	3	2	no	—
134	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
135	Q₈×C₉	—	2	8	no	—
136	Q₈×C₉	—	2	8	no	—
137	Q₈×C₉	—	2	4	no	—
138	Q₈×C₉	—	2	4	no	—
139	Q₈×C₉	—	6	2	no	—
140	D₄×C₉	—	6	4	no	—
141	D₄×C₉	—	6	2	no	—
142	C₂×C₄×C₉	—	2	8	no	—
143	C₂×C₄×C₉	—	2	4	no	—
144	C₂×C₄×C₉	—	2	4	no	—
145	C₂×C₄×C₉	—	2	4	no	—
146	C₂×C₄×C₉	—	2	1	no	—
147	C₂×C₄×C₉	—	2	1	no	—
148	C₂×C₄×C₉	—	3	4	no	—
149	C₂×C₄×C₉	—	3	2	no	—
150	C₂×C₄×C₉	—	6	4	no	—
151	C₂×C₄×C₉	#67	1	4	yes	—
152	C₂×C₄×C₉	C₂²×D₃	1	4	yes	—
153	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
154	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
155	#536	—	3	1	no	Sylow
156	C₂×C₃×C₉	—	2	2	no	—
157	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₃×C₉	2₋¹⁺⁴	1	2	yes	—
159	D₃×C₉	—	4	2	no	—
160	C₃×#41	—	6	4	no	—
161	C₂×C₃×Q₈	—	2	8	no	—
162	C₂×C₃×Q₈	—	2	4	no	—
163	C₂×C₃×Q₈	—	2	4	no	—
164	C₂×C₃×Q₈	—	2	2	no	—
165	C₂×C₃×Q₈	—	2	2	no	—
166	C₂×C₃×Q₈	—	3	1	no	—
167	C₂×C₃×Q₈	C₂²×C₉	1	2	yes	—
168	C₂×C₃×Q₈	C₂²×C₉	1	2	yes	—
169	C₂×C₃×Q₈	C₂×C₃×D₃	1	2	yes	—
170	C₂×C₃×Q₈	C₂×C₃×D₃	1	2	yes	—
171	C₂×C₃×D₄	—	3	2	no	—
172	C₂×C₃×D₄	—	3	1	no	—
173	C₂²×C₃×C₄	—	2	2	no	—
174	C₂²×C₃×C₄	—	2	1	no	—
175	C₂²×C₃×C₄	—	3	2	no	—
176	C₂²×C₃×C₄	C₂²×C₉	1	2	yes	—
177	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
178	C₂²×C₃×C₄	C₂×C₃×D₃	1	2	yes	—
179	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
180	C₂×#67	C₂²×C₉	1	2	yes	—
181	#235	—	2	4	no	—
182	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
183	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
184	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
185	C₃×C₄⋊C₄	—	3	8	no	—
186	C₃×C₄⋊C₄	—	3	2	no	—
187	C₃×C₂²⋊C₄	—	3	2	no	—
188	C₃×C₂²⋊C₄	—	3	8	no	—
189	C₃×C₄²	—	3	2	no	—
190	#217	C₂²×C₉	1	2	yes	—
191	(C₂×D₃)⋊C₄	C₂²×C₉	1	8	yes	—
192	C₄⋊Dic₃	C₂²×C₉	1	2	yes	—
193	Dic₃⋊C₄	C₂²×C₉	1	8	yes	—
194	C₄×Dic₃	C₂²×C₉	1	2	yes	—
195	C₂²×C₃²	—	2	2	no	—
196	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
197	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
198	C₂×C₃×D₃	—	2	2	no	—
199	C₂×C₃×D₃	—	2	4	no	—
200	C₃²×C₄	—	2	4	no	—
201	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
202	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
203	C₃×Dic₃	—	2	2	no	—
204	C₃×Dic₃	—	2	4	no	—
205	C₂²×C₉	—	2	4	no	—
206	C₂²×C₉	—	2	2	no	—
207	C₂²×C₉	—	2	1	no	—
208	C₂²×C₉	—	2	2	no	—
209	C₂²×C₉	—	6	4	no	—
210	C₂²×C₉	—	6	2	no	—
211	C₂²×C₉	C₂×#67	1	2	yes	—
212	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
213	C₄×C₉	—	2	8	no	—
214	C₄×C₉	—	2	4	no	—
215	C₄×C₉	—	2	2	no	—
216	C₄×C₉	—	2	2	no	—
217	C₄×C₉	—	6	4	no	—
218	C₄×C₉	—	6	2	no	—
219	C₄×C₉	C₂×#67	1	2	yes	—
220	C₄×C₉	C₂×#67	1	2	yes	—
221	C₂×#41	—	3	1	no	—
222	C₂²×Q₈	D₃×C₉	1	1	yes	characteristic, complemented
223	C₄⋊Q₈	—	3	2	no	—
224	#124	—	3	2	no	—
225	#123	—	3	4	no	—
226	C₂²⋊Q₈	—	3	4	no	—
227	#117	—	3	1	no	—
228	C₃×C₉	#536	1	1	yes	characteristic, complemented, Sylow
229	C₂³×C₃	—	2	1	no	—
230	C₂³×C₃	—	3	2	no	—
231	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
232	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
233	C₂²×D₃	C₂³×C₉	1	2	yes	—
234	C₃×Q₈	—	2	8	no	—
235	C₃×Q₈	—	2	8	no	—
236	C₃×Q₈	—	2	4	no	—
237	C₃×Q₈	—	2	4	no	—
238	C₃×Q₈	—	2	4	no	—
239	C₃×Q₈	—	2	4	no	—
240	C₃×Q₈	—	6	2	no	—
241	C₃×D₄	—	6	4	no	—
242	C₃×D₄	—	6	2	no	—
243	C₂×C₃×C₄	—	2	8	no	—
244	C₂×C₃×C₄	—	2	4	no	—
245	C₂×C₃×C₄	—	2	4	no	—
246	C₂×C₃×C₄	—	2	4	no	—
247	C₂×C₃×C₄	—	2	4	no	—
248	C₂×C₃×C₄	—	2	1	no	—
249	C₂×C₃×C₄	—	2	1	no	—
250	C₂×C₃×C₄	—	3	4	no	—
251	C₂×C₃×C₄	—	3	2	no	—
252	C₂×C₃×C₄	—	6	4	no	—
253	C₂×C₃×C₄	D₄×C₉	1	4	yes	—
254	C₂×C₃×C₄	C₂³×C₉	1	4	yes	—
255	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
256	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
257	C₂×C₃×C₄	C₃×#67	1	4	yes	—
258	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
259	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
261	#67	—	2	4	no	—
262	C₂×Dic₃	C₂³×C₉	1	4	yes	—
263	C₂×Dic₃	C₂³×C₉	1	2	yes	—
264	D₁₂	—	2	2	no	—
265	C₄×D₃	—	2	4	no	—
266	Dic₆	—	2	2	no	—
267	C₂×C₃²	—	2	2	no	—
268	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
269	C₂×C₃²	C₃×2₋¹⁺⁴	1	2	yes	—
270	C₃×D₃	—	4	2	no	—
271	C₂×C₉	—	2	4	no	—
272	C₂×C₉	—	2	2	no	—
273	C₂×C₉	—	2	2	no	—
274	C₂×C₉	—	2	1	no	—
275	C₂×C₉	—	12	2	no	—
276	C₂×C₉	#1007	1	2	yes	—
277	C₂×C₉	C₂²×#67	1	1	yes	characteristic
278	#41	—	6	4	no	—
279	C₂×Q₈	—	2	4	no	—
280	C₂×Q₈	—	3	1	no	—
281	C₂×Q₈	C₂×D₃×C₉	1	2	yes	—
282	C₂×Q₈	C₂×D₃×C₉	1	2	yes	—
283	C₂×D₄	—	3	2	no	—
284	C₂×D₄	—	3	1	no	—
285	C₂²×C₄	—	3	2	no	—
286	C₂²×C₄	C₂×D₃×C₉	1	2	yes	—
287	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
288	C₄⋊C₄	—	3	2	no	—
289	C₄⋊C₄	—	3	8	no	—
290	C₂²⋊C₄	—	3	2	no	—
291	C₂²⋊C₄	—	3	8	no	—
292	C₄²	—	3	2	no	—
293	C₂²×C₃	—	2	4	no	—
294	C₂²×C₃	—	2	2	no	—
295	C₂²×C₃	—	2	2	no	—
296	C₂²×C₃	—	2	1	no	—
297	C₂²×C₃	—	2	2	no	—
298	C₂²×C₃	—	6	4	no	—
299	C₂²×C₃	—	6	2	no	—
300	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
301	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
302	C₂²×C₃	C₂×C₃×#67	1	2	yes	—
303	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
304	C₂×D₃	—	2	2	no	—
305	C₂×D₃	—	2	4	no	—
306	C₃×C₄	—	2	8	no	—
307	C₃×C₄	—	2	4	no	—
308	C₃×C₄	—	2	4	no	—
309	C₃×C₄	—	2	2	no	—
310	C₃×C₄	—	2	2	no	—
311	C₃×C₄	—	6	4	no	—
312	C₃×C₄	—	6	2	no	—
313	C₃×C₄	C₂×D₄×C₉	1	2	yes	—
314	C₃×C₄	C₂×D₄×C₉	1	2	yes	—
315	C₃×C₄	C₂×C₃×#67	1	2	yes	—
316	C₃×C₄	C₂×C₃×#67	1	2	yes	—
317	Dic₃	—	2	2	no	—
318	Dic₃	—	2	4	no	—
319	C₃²	C₃×#536	1	1	yes	characteristic
320	C₉	—	2	1	no	—
321	C₉	#5816	1	1	yes	characteristic, direct product factor
322	C₂³	—	3	2	no	—
323	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
324	Q₈	—	2	4	no	—
325	Q₈	—	2	4	no	—
326	Q₈	—	6	2	no	—
327	D₄	—	6	4	no	—
328	D₄	—	6	2	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	3	4	no	—
331	C₂×C₄	—	3	2	no	—
332	C₂×C₄	—	6	4	no	—
333	C₂×C₄	C₉×#67	1	4	yes	—
334	C₂×C₄	C₂²×D₃×C₉	1	4	yes	—
335	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
336	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
337	C₂×C₃	—	2	4	no	—
338	C₂×C₃	—	2	2	no	—
339	C₂×C₃	—	2	2	no	—
340	C₂×C₃	—	2	2	no	—
341	C₂×C₃	—	2	1	no	—
342	C₂×C₃	—	12	2	no	—
343	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
344	C₂×C₃	C₉×2₋¹⁺⁴	1	2	yes	—
345	C₂×C₃	C₃×#1007	1	2	yes	—
346	C₂×C₃	C₂²×C₃×#67	1	1	yes	characteristic
347	D₃	—	4	2	no	—
348	C₂²	—	2	2	no	—
349	C₂²	—	6	4	no	—
350	C₂²	—	6	2	no	—
351	C₂²	C₂×C₉×#67	1	2	yes	—
352	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
353	C₄	—	2	4	no	—
354	C₄	—	6	4	no	—
355	C₄	—	6	2	no	—
356	C₄	C₂×C₉×#67	1	2	yes	—
357	C₄	C₂×C₉×#67	1	2	yes	—
358	C₃	—	2	1	no	—
359	C₃	C₉×#536	1	1	yes	characteristic, complemented
360	C₃	C₃×#5816	1	1	yes	characteristic
361	C₂	—	2	2	no	—
362	C₂	—	12	2	no	—
363	C₂	C₉×#1007	1	2	yes	—
364	C₂	C₂²×C₉×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂³×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₂²×C₃×Q₈×C₉	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₂×C₃×#235	C₂×C₃
hypercenter	C₂²×Q₈×C₉	D₃
hypocenter	C₃	C₉×#536
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₂²×Q₈×C₉

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×Q₈×C₉	C₂	semidirect
3. C₉×#947	C₂	semidirect
4. C₉×#946	C₂	semidirect
5. C₉×#944	C₂	semidirect
6. C₉×#929	C₂	semidirect
7. C₉×#926	C₂	semidirect
34. C₂²×Q₈×C₉	D₃	semidirect
56. #5816	C₉	direct (N × H)
104. C₂²×C₃×Q₈	C₂×C₉	semidirect
112. #947	C₂×C₉	semidirect
113. #946	C₂×C₉	semidirect
114. #944	C₂×C₉	semidirect
115. #929	C₂×C₉	semidirect
116. #926	C₂×C₉	semidirect
222. C₂²×Q₈	D₃×C₉	semidirect
228. C₃×C₉	#536	semidirect
321. C₉	#5816	direct (N × H)
359. C₃	C₉×#536	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×Q₈×C₉	2
C₂×C₉×#235	2
C₉×#947	2
C₉×#946	2
C₉×#944	2
C₉×#929	2
C₉×#926	2
C₃×#5816	3
C₉×#536	3

Subgroups — C9×#5816 #13153651

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5816 #13153651