Subgroups — C₉×#5693 #13153168

Order 1728.

698 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#898	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#898	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#896	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#896	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#894	C₂	1	1	yes	maximal, characteristic
7	C₉×#894	C₂	1	1	yes	maximal, characteristic
8	C₉×#893	C₂	1	1	yes	maximal, characteristic
9	C₉×#892	C₂	1	1	yes	maximal, characteristic, complemented
10	D₃×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#889	C₂	1	1	yes	maximal, characteristic, complemented
12	C₉×#889	C₂	1	1	yes	maximal, characteristic, complemented
13	C₉×#887	C₂	1	1	yes	maximal, characteristic, complemented
14	C₉×#872	C₂	1	1	yes	maximal, characteristic, complemented
15	C₉×#872	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5693	C₃	1	1	yes	maximal, characteristic
17	C₉×#552	—	3	1	no	maximal
18	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
23	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
24	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
31	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
32	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
33	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
34	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
35	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
36	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
37	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
38	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
39	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
40	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
41	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
42	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
43	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
44	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
45	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
46	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
47	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
48	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
49	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
50	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
51	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
52	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
53	C₃²×#125	C₂×C₃	1	1	yes	characteristic
54	C₃×#898	C₂×C₃	1	1	yes	characteristic
55	C₃×#898	C₂×C₃	1	1	yes	characteristic
56	C₃×#896	C₂×C₃	1	1	yes	characteristic
57	C₃×#896	C₂×C₃	1	1	yes	characteristic
58	C₃×#894	C₂×C₃	1	1	yes	characteristic
59	C₃×#894	C₂×C₃	1	1	yes	characteristic
60	C₃×#893	C₂×C₃	1	1	yes	characteristic
61	C₃×#892	C₂×C₃	1	1	yes	characteristic
62	C₃×D₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
63	C₃×#889	C₂×C₃	1	1	yes	characteristic
64	C₃×#889	C₂×C₃	1	1	yes	characteristic
65	C₃×#887	C₂×C₃	1	1	yes	characteristic
66	C₃×#872	C₂×C₃	1	1	yes	characteristic
67	C₃×#872	C₂×C₃	1	1	yes	characteristic
68	C₉×#126	—	3	1	no	—
69	C₉×#126	—	3	1	no	—
70	C₉×#125	—	2	1	no	—
71	C₉×#125	—	3	1	no	—
72	C₉×#125	—	3	1	no	—
73	C₉×#125	D₃	1	1	yes	characteristic, complemented
74	C₉×#123	—	3	1	no	—
75	C₉×#123	—	3	1	no	—
76	C₉×C₂²⋊Q₈	—	3	1	no	—
77	C₉×C₂²⋊Q₈	—	3	1	no	—
78	C₄×Q₈×C₉	—	3	1	no	—
79	C₄×D₄×C₉	—	3	1	no	—
80	C₉×#117	—	3	1	no	—
81	C₉×#117	—	3	1	no	—
82	C₉×#117	—	3	1	no	—
83	C₂×C₉×C₄⋊C₄	—	3	1	no	—
84	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
85	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
86	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
87	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
88	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
89	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
90	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
91	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
92	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
93	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
94	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
95	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
96	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
97	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
98	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
99	C₉×D₁₂	—	2	2	no	—
100	C₄×D₃×C₉	—	2	2	no	—
101	C₄×D₃×C₉	—	2	2	no	—
102	C₄×D₃×C₉	—	2	2	no	—
103	C₄×D₃×C₉	—	2	2	no	—
104	C₉×Dic₆	—	2	2	no	—
105	C₃×#552	—	3	1	no	—
106	#5693	C₉	1	1	yes	characteristic, direct product factor
107	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
108	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
109	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
110	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
111	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
112	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
113	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
114	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
115	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
116	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
117	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
118	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
119	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
120	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
121	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
122	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
123	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
124	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
125	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
126	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
127	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
128	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
129	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
130	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
131	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
132	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
133	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
134	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
135	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
136	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
137	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
138	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
139	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
140	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
141	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
142	C₂×Q₈×C₉	—	3	1	no	—
143	C₂×D₄×C₉	—	3	1	no	—
144	C₂²×C₄×C₉	—	3	1	no	—
145	C₂²×C₄×C₉	—	3	1	no	—
146	C₂²×C₄×C₉	—	3	1	no	—
147	C₂²×C₄×C₉	—	3	1	no	—
148	C₉×C₄⋊C₄	—	2	1	no	—
149	C₉×C₄⋊C₄	—	2	1	no	—
150	C₉×C₄⋊C₄	—	2	1	no	—
151	C₉×C₄⋊C₄	—	2	1	no	—
152	C₉×C₄⋊C₄	—	2	1	no	—
153	C₉×C₄⋊C₄	—	2	1	no	—
154	C₉×C₄⋊C₄	—	3	1	no	—
155	C₉×C₄⋊C₄	—	3	1	no	—
156	C₉×C₄⋊C₄	—	3	1	no	—
157	C₉×C₄⋊C₄	—	3	1	no	—
158	C₉×C₄⋊C₄	—	3	1	no	—
159	C₉×C₄⋊C₄	—	3	1	no	—
160	C₉×C₄⋊C₄	—	3	1	no	—
161	C₉×C₄⋊C₄	—	3	1	no	—
162	C₉×C₄⋊C₄	—	3	1	no	—
163	C₉×C₄⋊C₄	—	3	1	no	—
164	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
165	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
166	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
167	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
168	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
169	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
170	C₉×C₂²⋊C₄	—	3	1	no	—
171	C₉×C₂²⋊C₄	—	3	1	no	—
172	C₉×C₂²⋊C₄	—	3	1	no	—
173	C₉×C₂²⋊C₄	—	3	1	no	—
174	C₉×C₂²⋊C₄	—	3	1	no	—
175	C₉×C₂²⋊C₄	—	3	1	no	—
176	C₉×C₂²⋊C₄	—	3	1	no	—
177	C₉×C₂²⋊C₄	—	3	1	no	—
178	C₄²×C₉	—	2	1	no	—
179	C₄²×C₉	—	3	1	no	—
180	C₄²×C₉	—	3	1	no	—
181	C₄²×C₉	—	3	1	no	—
182	C₄²×C₉	—	3	1	no	—
183	C₄²×C₉	C₂×D₃	1	1	yes	characteristic
184	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
185	C₂×D₃×C₉	—	2	1	no	—
186	C₂×D₃×C₉	—	2	1	no	—
187	C₂×D₃×C₉	—	2	1	no	—
188	C₂×D₃×C₉	—	2	1	no	—
189	C₂×D₃×C₉	—	2	1	no	—
190	C₂×D₃×C₉	#41	1	2	yes	—
191	C₃×C₄×C₉	—	2	1	no	—
192	C₃×C₄×C₉	—	2	1	no	—
193	C₃×C₄×C₉	—	2	1	no	—
194	C₃×C₄×C₉	—	2	1	no	—
195	C₃×C₄×C₉	—	2	1	no	—
196	C₃×C₄×C₉	—	2	1	no	—
197	C₃×C₄×C₉	—	2	1	no	—
198	C₉×Dic₃	—	2	1	no	—
199	C₉×Dic₃	—	2	1	no	—
200	C₉×Dic₃	—	2	1	no	—
201	C₉×Dic₃	—	2	1	no	—
202	C₉×Dic₃	—	2	1	no	—
203	C₉×Dic₃	#41	1	2	yes	—
204	C₃×#126	—	3	1	no	—
205	C₃×#126	—	3	1	no	—
206	C₃×#125	—	2	1	no	—
207	C₃×#125	—	3	1	no	—
208	C₃×#125	—	3	1	no	—
209	C₃×#125	C₂×C₉	1	1	yes	characteristic, complemented
210	C₃×#125	C₃×D₃	1	1	yes	characteristic
211	C₃×#123	—	3	1	no	—
212	C₃×#123	—	3	1	no	—
213	C₃×C₂²⋊Q₈	—	3	1	no	—
214	C₃×C₂²⋊Q₈	—	3	1	no	—
215	C₃×C₄×Q₈	—	3	1	no	—
216	C₃×C₄×D₄	—	3	1	no	—
217	C₃×#117	—	3	1	no	—
218	C₃×#117	—	3	1	no	—
219	C₃×#117	—	3	1	no	—
220	C₂×C₃×C₄⋊C₄	—	3	1	no	—
221	#898	C₂×C₉	1	1	yes	characteristic, complemented
222	#898	C₂×C₉	1	1	yes	characteristic, complemented
223	#896	C₂×C₉	1	1	yes	characteristic, complemented
224	#896	C₂×C₉	1	1	yes	characteristic, complemented
225	#894	C₂×C₉	1	1	yes	characteristic
226	#894	C₂×C₉	1	1	yes	characteristic
227	#893	C₂×C₉	1	1	yes	characteristic
228	#892	C₂×C₉	1	1	yes	characteristic, complemented
229	D₃×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
230	#889	C₂×C₉	1	1	yes	characteristic, complemented
231	#889	C₂×C₉	1	1	yes	characteristic, complemented
232	#887	C₂×C₉	1	1	yes	characteristic, complemented
233	#872	C₂×C₉	1	1	yes	characteristic, complemented
234	#872	C₂×C₉	1	1	yes	characteristic, complemented
235	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
236	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
237	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
238	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
239	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
240	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
241	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
242	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
243	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
244	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
245	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
246	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
247	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
248	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
249	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
250	C₃×D₁₂	—	2	2	no	—
251	C₃×C₄×D₃	—	2	2	no	—
252	C₃×C₄×D₃	—	2	2	no	—
253	C₃×C₄×D₃	—	2	2	no	—
254	C₃×C₄×D₃	—	2	2	no	—
255	C₃×Dic₆	—	2	2	no	—
256	C₂³×C₉	—	3	1	no	—
257	C₂³×C₉	—	3	1	no	—
258	Q₈×C₉	—	6	2	no	—
259	D₄×C₉	—	6	2	no	—
260	C₂×C₄×C₉	—	2	1	no	—
261	C₂×C₄×C₉	—	2	1	no	—
262	C₂×C₄×C₉	—	2	1	no	—
263	C₂×C₄×C₉	—	2	1	no	—
264	C₂×C₄×C₉	—	2	1	no	—
265	C₂×C₄×C₉	—	2	1	no	—
266	C₂×C₄×C₉	—	2	1	no	—
267	C₂×C₄×C₉	—	3	1	no	—
268	C₂×C₄×C₉	—	3	1	no	—
269	C₂×C₄×C₉	—	3	1	no	—
270	C₂×C₄×C₉	—	3	1	no	—
271	C₂×C₄×C₉	—	3	1	no	—
272	C₂×C₄×C₉	—	3	1	no	—
273	C₂×C₄×C₉	—	6	2	no	—
274	C₂×C₄×C₉	—	6	2	no	—
275	C₂×C₄×C₉	—	6	2	no	—
276	C₂×C₄×C₉	—	6	2	no	—
277	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
278	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
279	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
280	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
281	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
282	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
283	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
284	#552	—	3	1	no	Sylow
285	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
286	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
287	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
288	D₃×C₉	—	2	2	no	—
289	D₃×C₉	—	4	1	no	—
290	C₂×C₃×Q₈	—	3	1	no	—
291	C₂×C₃×D₄	—	3	1	no	—
292	C₂²×C₃×C₄	—	3	1	no	—
293	C₂²×C₃×C₄	—	3	1	no	—
294	C₂²×C₃×C₄	—	3	1	no	—
295	C₂²×C₃×C₄	—	3	1	no	—
296	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
297	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
298	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
299	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
300	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
301	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
302	C₃×C₄⋊C₄	—	2	1	no	—
303	C₃×C₄⋊C₄	—	2	1	no	—
304	C₃×C₄⋊C₄	—	2	1	no	—
305	C₃×C₄⋊C₄	—	2	1	no	—
306	C₃×C₄⋊C₄	—	2	1	no	—
307	C₃×C₄⋊C₄	—	2	1	no	—
308	C₃×C₄⋊C₄	—	3	1	no	—
309	C₃×C₄⋊C₄	—	3	1	no	—
310	C₃×C₄⋊C₄	—	3	1	no	—
311	C₃×C₄⋊C₄	—	3	1	no	—
312	C₃×C₄⋊C₄	—	3	1	no	—
313	C₃×C₄⋊C₄	—	3	1	no	—
314	C₃×C₄⋊C₄	—	3	1	no	—
315	C₃×C₄⋊C₄	—	3	1	no	—
316	C₃×C₄⋊C₄	—	3	1	no	—
317	C₃×C₄⋊C₄	—	3	1	no	—
318	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
319	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
320	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
321	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
322	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
323	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
324	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
325	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
326	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
327	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
328	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
329	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
330	C₃×C₂²⋊C₄	—	3	1	no	—
331	C₃×C₂²⋊C₄	—	3	1	no	—
332	C₃×C₂²⋊C₄	—	3	1	no	—
333	C₃×C₂²⋊C₄	—	3	1	no	—
334	C₃×C₂²⋊C₄	—	3	1	no	—
335	C₃×C₂²⋊C₄	—	3	1	no	—
336	C₃×C₂²⋊C₄	—	3	1	no	—
337	C₃×C₂²⋊C₄	—	3	1	no	—
338	C₃×C₄²	—	2	1	no	—
339	C₃×C₄²	—	3	1	no	—
340	C₃×C₄²	—	3	1	no	—
341	C₃×C₄²	—	3	1	no	—
342	C₃×C₄²	—	3	1	no	—
343	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic
344	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
345	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
346	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
347	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
348	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
349	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
350	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
351	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
352	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
353	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
354	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
355	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
356	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
357	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
358	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
359	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
360	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
361	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
362	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
363	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
364	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
365	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
366	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
367	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
368	C₂×C₃×D₃	—	2	1	no	—
369	C₂×C₃×D₃	—	2	1	no	—
370	C₂×C₃×D₃	—	2	1	no	—
371	C₂×C₃×D₃	—	2	1	no	—
372	C₂×C₃×D₃	—	2	1	no	—
373	C₂×C₃×D₃	C₃×#41	1	2	yes	—
374	C₃²×C₄	—	2	1	no	—
375	C₃²×C₄	—	2	1	no	—
376	C₃²×C₄	—	2	1	no	—
377	C₃²×C₄	—	2	1	no	—
378	C₃²×C₄	—	2	1	no	—
379	C₃²×C₄	—	2	1	no	—
380	C₃²×C₄	—	2	1	no	—
381	C₃×Dic₃	—	2	1	no	—
382	C₃×Dic₃	—	2	1	no	—
383	C₃×Dic₃	—	2	1	no	—
384	C₃×Dic₃	—	2	1	no	—
385	C₃×Dic₃	—	2	1	no	—
386	C₃×Dic₃	C₃×#41	1	2	yes	—
387	C₂²×C₉	—	2	1	no	—
388	C₂²×C₉	—	3	2	no	—
389	C₂²×C₉	—	6	1	no	—
390	C₂²×C₉	—	6	1	no	—
391	C₂²×C₉	—	6	1	no	—
392	C₂²×C₉	—	6	1	no	—
393	C₂²×C₉	—	6	1	no	—
394	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
395	C₄×C₉	—	2	2	no	—
396	C₄×C₉	—	2	1	no	—
397	C₄×C₉	—	2	1	no	—
398	C₄×C₉	—	2	1	no	—
399	C₄×C₉	—	2	1	no	—
400	C₄×C₉	—	2	1	no	—
401	C₄×C₉	—	2	1	no	—
402	C₄×C₉	—	2	1	no	—
403	C₄×C₉	—	3	2	no	—
404	C₄×C₉	—	4	1	no	—
405	C₄×C₉	—	4	1	no	—
406	C₄×C₉	—	4	1	no	—
407	C₄×C₉	—	4	1	no	—
408	C₄×C₉	—	4	1	no	—
409	C₄×C₉	—	4	1	no	—
410	C₄×C₉	—	6	1	no	—
411	C₄×C₉	—	6	1	no	—
412	C₄×C₉	—	6	1	no	—
413	C₄×C₉	—	6	1	no	—
414	C₄×C₉	—	6	1	no	—
415	#126	—	3	1	no	—
416	#126	—	3	1	no	—
417	#125	—	3	1	no	—
418	#125	—	3	1	no	—
419	#125	D₃×C₉	1	1	yes	characteristic, complemented
420	#123	—	3	1	no	—
421	#123	—	3	1	no	—
422	C₂²⋊Q₈	—	3	1	no	—
423	C₂²⋊Q₈	—	3	1	no	—
424	C₄×Q₈	—	3	1	no	—
425	C₄×D₄	—	3	1	no	—
426	#117	—	3	1	no	—
427	#117	—	3	1	no	—
428	#117	—	3	1	no	—
429	C₂×C₄⋊C₄	—	3	1	no	—
430	C₃×C₉	#552	1	1	yes	characteristic, complemented, Sylow
431	C₂³×C₃	—	3	1	no	—
432	C₂³×C₃	—	3	1	no	—
433	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
434	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
435	C₃×Q₈	—	6	2	no	—
436	C₃×D₄	—	6	2	no	—
437	C₂×C₃×C₄	—	2	1	no	—
438	C₂×C₃×C₄	—	2	1	no	—
439	C₂×C₃×C₄	—	2	1	no	—
440	C₂×C₃×C₄	—	2	1	no	—
441	C₂×C₃×C₄	—	2	1	no	—
442	C₂×C₃×C₄	—	2	1	no	—
443	C₂×C₃×C₄	—	2	1	no	—
444	C₂×C₃×C₄	—	3	1	no	—
445	C₂×C₃×C₄	—	3	1	no	—
446	C₂×C₃×C₄	—	3	1	no	—
447	C₂×C₃×C₄	—	3	1	no	—
448	C₂×C₃×C₄	—	3	1	no	—
449	C₂×C₃×C₄	—	3	1	no	—
450	C₂×C₃×C₄	—	6	2	no	—
451	C₂×C₃×C₄	—	6	2	no	—
452	C₂×C₃×C₄	—	6	2	no	—
453	C₂×C₃×C₄	—	6	2	no	—
454	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
455	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
456	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
457	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
458	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
459	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
460	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
461	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
462	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
463	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
464	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
465	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
466	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
467	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
468	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
469	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
470	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
471	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
472	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
473	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
474	D₁₂	—	2	2	no	—
475	C₄×D₃	—	2	2	no	—
476	C₄×D₃	—	2	2	no	—
477	C₄×D₃	—	2	2	no	—
478	C₄×D₃	—	2	2	no	—
479	Dic₆	—	2	2	no	—
480	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
481	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
482	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
483	C₃×D₃	—	2	2	no	—
484	C₃×D₃	—	4	1	no	—
485	C₂×C₉	—	2	1	no	—
486	C₂×C₉	—	2	1	no	—
487	C₂×C₉	—	2	1	no	—
488	C₂×C₉	—	6	2	no	—
489	C₂×C₉	—	12	1	no	—
490	C₂×C₉	#1007	1	1	yes	characteristic
491	C₂×C₉	D₃×#41	1	1	yes	characteristic
492	C₂×C₉	D₃×#41	1	1	yes	characteristic
493	C₂×Q₈	—	3	1	no	—
494	C₂×D₄	—	3	1	no	—
495	C₂²×C₄	—	3	1	no	—
496	C₂²×C₄	—	3	1	no	—
497	C₂²×C₄	—	3	1	no	—
498	C₂²×C₄	—	3	1	no	—
499	C₄⋊C₄	—	3	1	no	—
500	C₄⋊C₄	—	3	1	no	—
501	C₄⋊C₄	—	3	1	no	—
502	C₄⋊C₄	—	3	1	no	—
503	C₄⋊C₄	—	3	1	no	—
504	C₄⋊C₄	—	3	1	no	—
505	C₄⋊C₄	—	3	1	no	—
506	C₄⋊C₄	—	3	1	no	—
507	C₄⋊C₄	—	3	1	no	—
508	C₄⋊C₄	—	3	1	no	—
509	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
510	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
511	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
512	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
513	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
514	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
515	C₂²⋊C₄	—	3	1	no	—
516	C₂²⋊C₄	—	3	1	no	—
517	C₂²⋊C₄	—	3	1	no	—
518	C₂²⋊C₄	—	3	1	no	—
519	C₂²⋊C₄	—	3	1	no	—
520	C₂²⋊C₄	—	3	1	no	—
521	C₂²⋊C₄	—	3	1	no	—
522	C₂²⋊C₄	—	3	1	no	—
523	C₄²	—	3	1	no	—
524	C₄²	—	3	1	no	—
525	C₄²	—	3	1	no	—
526	C₄²	—	3	1	no	—
527	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
528	C₂²×C₃	—	2	1	no	—
529	C₂²×C₃	—	3	2	no	—
530	C₂²×C₃	—	6	1	no	—
531	C₂²×C₃	—	6	1	no	—
532	C₂²×C₃	—	6	1	no	—
533	C₂²×C₃	—	6	1	no	—
534	C₂²×C₃	—	6	1	no	—
535	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
536	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
537	C₂×D₃	—	2	1	no	—
538	C₂×D₃	—	2	1	no	—
539	C₂×D₃	—	2	1	no	—
540	C₂×D₃	—	2	1	no	—
541	C₂×D₃	—	2	1	no	—
542	C₂×D₃	C₉×#41	1	2	yes	—
543	C₃×C₄	—	2	2	no	—
544	C₃×C₄	—	2	1	no	—
545	C₃×C₄	—	2	1	no	—
546	C₃×C₄	—	2	1	no	—
547	C₃×C₄	—	2	1	no	—
548	C₃×C₄	—	2	1	no	—
549	C₃×C₄	—	2	1	no	—
550	C₃×C₄	—	2	1	no	—
551	C₃×C₄	—	2	1	no	—
552	C₃×C₄	—	2	1	no	—
553	C₃×C₄	—	2	1	no	—
554	C₃×C₄	—	2	1	no	—
555	C₃×C₄	—	2	1	no	—
556	C₃×C₄	—	2	1	no	—
557	C₃×C₄	—	2	1	no	—
558	C₃×C₄	—	3	2	no	—
559	C₃×C₄	—	4	1	no	—
560	C₃×C₄	—	4	1	no	—
561	C₃×C₄	—	4	1	no	—
562	C₃×C₄	—	4	1	no	—
563	C₃×C₄	—	4	1	no	—
564	C₃×C₄	—	4	1	no	—
565	C₃×C₄	—	6	1	no	—
566	C₃×C₄	—	6	1	no	—
567	C₃×C₄	—	6	1	no	—
568	C₃×C₄	—	6	1	no	—
569	C₃×C₄	—	6	1	no	—
570	Dic₃	—	2	1	no	—
571	Dic₃	—	2	1	no	—
572	Dic₃	—	2	1	no	—
573	Dic₃	—	2	1	no	—
574	Dic₃	—	2	1	no	—
575	Dic₃	C₉×#41	1	2	yes	—
576	C₃²	C₃×#552	1	1	yes	characteristic
577	C₉	—	2	1	no	—
578	C₉	#5693	1	1	yes	characteristic, direct product factor
579	C₂³	—	3	1	no	—
580	C₂³	—	3	1	no	—
581	Q₈	—	6	2	no	—
582	D₄	—	6	2	no	—
583	C₂×C₄	—	3	1	no	—
584	C₂×C₄	—	3	1	no	—
585	C₂×C₄	—	3	1	no	—
586	C₂×C₄	—	3	1	no	—
587	C₂×C₄	—	3	1	no	—
588	C₂×C₄	—	3	1	no	—
589	C₂×C₄	—	6	2	no	—
590	C₂×C₄	—	6	2	no	—
591	C₂×C₄	—	6	2	no	—
592	C₂×C₄	—	6	2	no	—
593	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
594	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
595	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
596	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
597	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
598	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
599	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
600	C₂×C₃	—	2	1	no	—
601	C₂×C₃	—	2	1	no	—
602	C₂×C₃	—	2	1	no	—
603	C₂×C₃	—	6	2	no	—
604	C₂×C₃	—	12	1	no	—
605	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
606	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
607	C₂×C₃	C₉×2₋¹⁺⁴	1	1	yes	characteristic
608	C₂×C₃	C₃×#1007	1	1	yes	characteristic
609	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
610	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
611	D₃	—	2	2	no	—
612	D₃	—	4	1	no	—
613	C₂²	—	3	2	no	—
614	C₂²	—	6	1	no	—
615	C₂²	—	6	1	no	—
616	C₂²	—	6	1	no	—
617	C₂²	—	6	1	no	—
618	C₂²	—	6	1	no	—
619	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
620	C₄	—	2	1	no	—
621	C₄	—	2	1	no	—
622	C₄	—	2	1	no	—
623	C₄	—	2	1	no	—
624	C₄	—	2	1	no	—
625	C₄	—	2	1	no	—
626	C₄	—	2	1	no	—
627	C₄	—	3	2	no	—
628	C₄	—	6	1	no	—
629	C₄	—	6	1	no	—
630	C₄	—	6	1	no	—
631	C₄	—	6	1	no	—
632	C₄	—	6	1	no	—
633	C₃	—	2	1	no	—
634	C₃	C₉×#552	1	1	yes	characteristic, complemented
635	C₃	C₃×#5693	1	1	yes	characteristic
636	C₂	—	6	2	no	—
637	C₂	—	12	1	no	—
638	C₂	C₉×#1007	1	1	yes	characteristic
639	C₂	D₃×C₉×#41	1	1	yes	characteristic
640	C₂	D₃×C₉×#41	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂³×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×#125	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₂×C₃×D₁₂	C₂²×C₃
hypercenter	C₉×#125	D₃
hypocenter	C₃	C₉×#552
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#125

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×#125	C₂	semidirect
2. C₉×#898	C₂	semidirect
3. C₉×#898	C₂	semidirect
4. C₉×#896	C₂	semidirect
5. C₉×#896	C₂	semidirect
9. C₉×#892	C₂	semidirect
10. D₃×C₉×C₄⋊C₄	C₂	semidirect
11. C₉×#889	C₂	semidirect
12. C₉×#889	C₂	semidirect
13. C₉×#887	C₂	semidirect
14. C₉×#872	C₂	semidirect
15. C₉×#872	C₂	semidirect
73. C₉×#125	D₃	semidirect
106. #5693	C₉	direct (N × H)
209. C₃×#125	C₂×C₉	semidirect
221. #898	C₂×C₉	semidirect
222. #898	C₂×C₉	semidirect
223. #896	C₂×C₉	semidirect
224. #896	C₂×C₉	semidirect
228. #892	C₂×C₉	semidirect
229. D₃×C₄⋊C₄	C₂×C₉	semidirect
230. #889	C₂×C₉	semidirect
231. #889	C₂×C₉	semidirect
232. #887	C₂×C₉	semidirect
233. #872	C₂×C₉	semidirect
234. #872	C₂×C₉	semidirect
419. #125	D₃×C₉	semidirect
430. C₃×C₉	#552	semidirect
578. C₉	#5693	direct (N × H)
634. C₃	C₉×#552	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×#125	2
C₉×#898	2
C₉×#896	2
C₉×#894	2
C₉×#893	2
C₉×#892	2
D₃×C₉×C₄⋊C₄	2
C₉×#889	2
C₉×#887	2
C₉×#872	2
C₃×#5693	3
C₉×#552	3

Subgroups — C9×#5693 #13153168

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5693 #13153168