Subgroups — #36382364

Order 22599.

662 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21419356	C₃	1	1	yes	maximal, characteristic, complemented
2	#21419355	C₃	1	1	yes	maximal, characteristic, complemented
3	#21419354	C₃	1	1	yes	maximal, characteristic, complemented
4	#21419353	C₃	1	1	yes	maximal, characteristic, complemented
5	#21419351	C₃	1	1	yes	maximal, characteristic, complemented
6	#21419350	C₃	1	1	yes	maximal, characteristic, complemented
7	#21419350	C₃	1	1	yes	maximal, characteristic, complemented
8	#21419348	C₃	1	1	yes	maximal, characteristic, complemented
9	#21419347	C₃	1	1	yes	maximal, characteristic, complemented
10	#21419347	C₃	1	1	yes	maximal, characteristic, complemented
11	#21419346	C₃	1	1	yes	maximal, characteristic, complemented
12	#21419346	C₃	1	1	yes	maximal, characteristic, complemented
13	#21419343	C₃	1	1	yes	maximal, characteristic, complemented
14	#21419343	C₃	1	1	yes	maximal, characteristic, complemented
15	#21419342	C₃	1	1	yes	maximal, characteristic, complemented
16	#21419341	C₃	1	1	yes	maximal, characteristic, complemented
17	#21419338	C₃	1	1	yes	maximal, characteristic, complemented
18	#21419335	C₃	1	1	yes	maximal, characteristic, complemented
19	#21419335	C₃	1	1	yes	maximal, characteristic, complemented
20	#21419328	C₃	1	1	yes	maximal, characteristic, complemented
21	#21419327	C₃	1	1	yes	maximal, characteristic, complemented
22	#21419325	C₃	1	1	yes	maximal, characteristic, complemented
23	#21419324	C₃	1	1	yes	maximal, characteristic, complemented
24	#21419321	C₃	1	1	yes	maximal, characteristic
25	#21419315	C₃	1	1	yes	maximal, characteristic
26	#21419313	C₃	1	1	yes	maximal, characteristic
27	#21419306	C₃	1	1	yes	maximal, characteristic, complemented
28	3₋¹⁺²×C₃₁⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
29	#11719686⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
30	#11719686⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
31	#11719686⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
32	#11719687⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
33	#11719687⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
34	#11719687⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
35	#21419297	C₃	1	1	yes	maximal, characteristic
36	#21419295	C₃	1	1	yes	maximal, characteristic, complemented
37	#21419295	C₃	1	1	yes	maximal, characteristic, complemented
38	#21419293	C₃	1	1	yes	maximal, characteristic, complemented
39	C₉²×C₃₁⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
40	C₃₁×#6899	C₃	1	1	yes	maximal, characteristic, complemented
41	C₃×#11719689	C₃²	1	1	yes	characteristic
42	C₃×#11719686	C₃²	1	1	yes	characteristic
43	C₃×#11719686	C₃²	1	1	yes	characteristic
44	C₃×#11719686	C₃²	1	1	yes	characteristic
45	C₃×#11719687	C₃²	1	1	yes	characteristic
46	C₃×#11719687	C₃²	1	1	yes	characteristic
47	C₃×#11719687	C₃²	1	1	yes	characteristic
48	C₃×C₃²⋊(C₃₁⋊C₃)	C₃²	1	1	yes	characteristic
49	C₃²×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
50	C₃×C₉×C₃₁⋊C₃	C₃²	1	1	yes	characteristic
51	C₃×C₉×C₃₁⋊C₃	C₃²	1	1	yes	characteristic
52	C₃×C₉×C₃₁⋊C₃	C₃²	1	1	yes	characteristic
53	C₃×C₉×C₃₁⋊C₃	C₃²	1	1	yes	characteristic
54	C₃×C₉×C₃₁⋊C₃	C₃²	1	1	yes	characteristic
55	C₃×C₉×C₃₁⋊C₃	C₃²	1	1	yes	characteristic
56	#14578887	C₃²	1	1	yes	characteristic
57	#14578887	C₃²	1	1	yes	characteristic
58	#14578887	C₃²	1	1	yes	characteristic
59	#14578887	C₃²	1	1	yes	characteristic
60	#14578887	C₃²	1	1	yes	characteristic
61	#14578887	C₃²	1	1	yes	characteristic
62	#14578887	C₃²	1	1	yes	characteristic
63	#14578887	C₃²	1	1	yes	characteristic
64	#14578886	C₃²	1	1	yes	characteristic
65	#14578886	C₃²	1	1	yes	characteristic
66	#14578886	C₃²	1	1	yes	characteristic
67	#14578886	C₃²	1	1	yes	characteristic
68	#14578886	C₃²	1	1	yes	characteristic
69	#14578886	C₃²	1	1	yes	characteristic
70	#14578886	C₃²	1	1	yes	characteristic
71	#14578886	C₃²	1	1	yes	characteristic
72	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
73	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
74	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
75	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
76	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
77	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
78	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
79	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
80	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
81	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
82	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
83	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
84	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
85	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
86	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
87	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
88	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
89	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
90	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
91	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
92	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
93	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
94	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
95	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
96	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
97	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
98	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
99	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
100	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
101	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
102	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
103	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
104	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
105	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
106	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
107	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
108	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
109	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
110	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
111	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
112	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
113	(C₃₁⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
114	C₃²⋊(C₃₁⋊C₉)	C₃²	1	1	yes	characteristic
115	C₃²⋊(C₃₁⋊C₉)	C₃²	1	1	yes	characteristic
116	C₃²⋊(C₃₁⋊C₉)	C₃²	1	1	yes	characteristic
117	C₃²⋊(C₃₁⋊C₉)	C₃²	1	1	yes	characteristic
118	C₃²⋊(C₃₁⋊C₉)	C₃²	1	1	yes	characteristic
119	C₃²⋊(C₃₁⋊C₉)	C₃²	1	1	yes	characteristic
120	(C₃×C₃₁⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
121	(C₃×C₃₁⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
122	(C₃×C₃₁⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
123	(C₃×C₃₁⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
124	(C₃×C₃₁⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
125	(C₃×C₃₁⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
126	(C₃×C₃₁⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
127	(C₃×C₃₁⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
128	(C₃×C₃₁⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
129	(C₃×C₃₁⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
130	(C₃×C₃₁⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
131	(C₃×C₃₁⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
132	(C₃×C₃₁⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
133	(C₃×C₃₁⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
134	(C₃×C₃₁⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
135	(C₃×C₃₁⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
136	(C₃×C₃₁⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
137	(C₃×C₃₁⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
138	(C₃×C₃₁⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
139	(C₃×C₃₁⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
140	(C₃×C₃₁⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
141	(C₃×C₃₁⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
142	(C₃×C₃₁⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
143	(C₃×C₃₁⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
144	C₉×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
145	C₉×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
146	C₉×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
147	C₉×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
148	C₉×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
149	C₉×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
150	C₉×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
151	C₉×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
152	C₉×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
153	C₉×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
154	C₉×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
155	C₉×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
156	C₉×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
157	C₉×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
158	C₃×3₋¹⁺²×C₃₁	C₃²	1	1	yes	characteristic
159	C₃₁×C₉⋊C₉	C₃²	1	1	yes	characteristic
160	C₃₁×C₉⋊C₉	C₃²	1	1	yes	characteristic
161	C₃₁×C₉⋊C₉	C₃²	1	1	yes	characteristic
162	C₃₁×C₉⋊C₉	C₃²	1	1	yes	characteristic
163	C₃₁×C₉⋊C₉	C₃²	1	1	yes	characteristic
164	C₃₁×C₉⋊C₉	C₃²	1	1	yes	characteristic
165	C₃₁×C₉⋊C₉	C₃²	1	1	yes	characteristic
166	C₃₁×C₉⋊C₉	C₃²	1	1	yes	characteristic
167	C₃₁×C₃²⋊C₉	C₃²	1	1	yes	characteristic
168	C₃₁×C₃²⋊C₉	C₃²	1	1	yes	characteristic
169	C₃₁×C₃²⋊C₉	C₃²	1	1	yes	characteristic
170	C₉²×C₃₁	C₃²	1	1	yes	characteristic
171	C₃³×C₃₁	C₃³	1	1	yes	characteristic
172	C₃²×C₃₁⋊C₃	C₃³	1	1	yes	characteristic
173	C₃²×C₃₁⋊C₃	C₃³	1	1	yes	characteristic
174	C₃²×C₃₁⋊C₃	C₃³	1	1	yes	characteristic
175	3₋¹⁺²×C₃₁	—	3	3	no	—
176	C₃×C₉×C₃₁	C₃³	1	1	yes	characteristic
177	C₃×C₉×C₃₁	C₃³	1	1	yes	characteristic
178	C₃×C₉×C₃₁	C₃³	1	1	yes	characteristic
179	C₃×C₉×C₃₁	C₃³	1	1	yes	characteristic
180	C₃×C₉×C₃₁	C₃³	1	1	yes	characteristic
181	C₃×C₉×C₃₁	C₃³	1	1	yes	characteristic
182	C₃×C₉×C₃₁	C₃³	1	1	yes	characteristic
183	C₃×C₉×C₃₁	C₃³	1	1	yes	characteristic
184	C₃×C₉×C₃₁	C₃³	1	1	yes	characteristic
185	C₃×C₉×C₃₁	C₃³	1	1	yes	characteristic
186	C₃×C₉×C₃₁	C₃³	1	1	yes	characteristic
187	C₃×C₉×C₃₁	C₃³	1	1	yes	characteristic
188	C₃²⋊(C₃₁⋊C₃)	—	3	3	no	—
189	#11719689	—	3	3	no	—
190	C₃×C₃₁⋊C₉	—	3	3	no	—
191	C₃×C₃₁⋊C₉	C₃³	1	1	yes	characteristic
192	C₃×C₃₁⋊C₉	C₃³	1	1	yes	characteristic
193	C₃×C₃₁⋊C₉	C₃³	1	1	yes	characteristic
194	C₃×C₃₁⋊C₉	C₃³	1	1	yes	characteristic
195	C₃×C₃₁⋊C₉	C₃³	1	1	yes	characteristic
196	C₃×C₃₁⋊C₉	C₃³	1	1	yes	characteristic
197	C₃×C₃₁⋊C₉	C₃³	1	1	yes	characteristic
198	C₃×C₃₁⋊C₉	C₃³	1	1	yes	characteristic
199	C₃×C₃₁⋊C₉	C₃³	1	1	yes	characteristic
200	C₃×C₃₁⋊C₉	C₃³	1	1	yes	characteristic
201	C₃×C₃₁⋊C₉	C₃³	1	1	yes	characteristic
202	C₃×C₃₁⋊C₉	C₃³	1	1	yes	characteristic
203	C₃×C₃₁⋊C₉	C₃³	1	1	yes	characteristic
204	C₃×C₃₁⋊C₉	C₃³	1	1	yes	characteristic
205	C₃×C₃₁⋊C₉	C₃³	1	1	yes	characteristic
206	C₃×C₃₁⋊C₉	C₃³	1	1	yes	characteristic
207	C₃×C₃₁⋊C₉	C₃³	1	1	yes	characteristic
208	C₃×C₃₁⋊C₉	C₃³	1	1	yes	characteristic
209	C₃×C₃₁⋊C₉	C₃³	1	1	yes	characteristic
210	C₃×C₃₁⋊C₉	C₃³	1	1	yes	characteristic
211	C₃×C₃₁⋊C₉	C₃³	1	1	yes	characteristic
212	C₃×C₃₁⋊C₉	C₃³	1	1	yes	characteristic
213	C₃×C₃₁⋊C₉	C₃³	1	1	yes	characteristic
214	C₃×C₃₁⋊C₉	C₃³	1	1	yes	characteristic
215	#11719687	—	3	3	no	—
216	#11719687	—	3	3	no	—
217	#11719687	—	3	3	no	—
218	#11719686	—	3	3	no	—
219	#11719686	—	3	3	no	—
220	#11719686	—	3	3	no	—
221	C₉×C₃₁⋊C₃	—	3	3	no	—
222	C₉×C₃₁⋊C₃	—	3	3	no	—
223	C₉×C₃₁⋊C₃	—	3	3	no	—
224	C₉×C₃₁⋊C₃	—	3	3	no	—
225	C₉×C₃₁⋊C₃	—	3	3	no	—
226	C₉×C₃₁⋊C₃	—	3	3	no	—
227	#10624877	—	31	1	no	maximal, Sylow
228	C₃²×C₃₁	—	3	1	no	—
229	C₃²×C₃₁	—	3	1	no	—
230	C₃²×C₃₁	—	3	1	no	—
231	C₃²×C₃₁	—	3	1	no	—
232	C₃²×C₃₁	C₃⁴	1	1	yes	characteristic
233	C₃×C₃₁⋊C₃	—	3	1	no	—
234	C₃×C₃₁⋊C₃	—	3	1	no	—
235	C₃×C₃₁⋊C₃	—	3	1	no	—
236	C₃×C₃₁⋊C₃	—	3	1	no	—
237	C₃×C₃₁⋊C₃	—	3	1	no	—
238	C₃×C₃₁⋊C₃	—	3	1	no	—
239	C₃×C₃₁⋊C₃	—	3	1	no	—
240	C₃×C₃₁⋊C₃	—	3	1	no	—
241	C₃×C₃₁⋊C₃	—	3	1	no	—
242	C₃×C₃₁⋊C₃	—	3	1	no	—
243	C₃×C₃₁⋊C₃	—	3	1	no	—
244	C₃×C₃₁⋊C₃	#737	1	3	yes	—
245	C₉×C₃₁	—	3	1	no	—
246	C₉×C₃₁	—	3	1	no	—
247	C₉×C₃₁	—	3	1	no	—
248	C₉×C₃₁	—	3	1	no	—
249	C₉×C₃₁	—	3	1	no	—
250	C₉×C₃₁	—	3	1	no	—
251	C₉×C₃₁	—	3	1	no	—
252	C₉×C₃₁	—	3	1	no	—
253	C₉×C₃₁	—	3	1	no	—
254	C₉×C₃₁	—	3	1	no	—
255	C₉×C₃₁	—	3	1	no	—
256	C₉×C₃₁	#737	1	3	yes	—
257	C₃₁⋊C₉	—	3	1	no	—
258	C₃₁⋊C₉	—	3	1	no	—
259	C₃₁⋊C₉	—	3	1	no	—
260	C₃₁⋊C₉	—	3	1	no	—
261	C₃₁⋊C₉	—	3	1	no	—
262	C₃₁⋊C₉	—	3	1	no	—
263	C₃₁⋊C₉	—	3	1	no	—
264	C₃₁⋊C₉	—	3	1	no	—
265	C₃₁⋊C₉	—	3	1	no	—
266	C₃₁⋊C₉	—	3	1	no	—
267	C₃₁⋊C₉	—	3	1	no	—
268	C₃₁⋊C₉	—	3	1	no	—
269	C₃₁⋊C₉	—	3	1	no	—
270	C₃₁⋊C₉	—	3	1	no	—
271	C₃₁⋊C₉	—	3	1	no	—
272	C₃₁⋊C₉	—	3	1	no	—
273	C₃₁⋊C₉	—	3	1	no	—
274	C₃₁⋊C₉	—	3	1	no	—
275	C₃₁⋊C₉	—	3	1	no	—
276	C₃₁⋊C₉	—	3	1	no	—
277	C₃₁⋊C₉	—	3	1	no	—
278	C₃₁⋊C₉	—	3	1	no	—
279	C₃₁⋊C₉	#737	1	3	yes	—
280	C₃₁⋊C₉	#737	1	3	yes	—
281	#6899	—	31	1	no	—
282	#6899	—	31	1	no	—
283	#6899	—	31	1	no	—
284	#6899	—	31	1	no	—
285	#6899	—	31	1	no	—
286	#6899	C₃₁⋊C₃	1	1	yes	characteristic, complemented
287	#6898	—	31	1	no	—
288	#6898	—	31	1	no	—
289	#6898	—	31	1	no	—
290	#6897	—	31	1	no	—
291	#6897	—	31	1	no	—
292	#6897	—	31	1	no	—
293	#6897	—	31	1	no	—
294	#6897	—	31	1	no	—
295	#6897	—	31	1	no	—
296	#6896	—	31	1	no	—
297	#6896	—	31	1	no	—
298	#6896	—	31	1	no	—
299	#6895	—	31	1	no	—
300	#6895	—	31	1	no	—
301	#6894	—	31	1	no	—
302	#6894	—	31	1	no	—
303	#6894	—	31	1	no	—
304	#6894	—	31	1	no	—
305	#6893	—	31	1	no	—
306	C₉⋊H(3,𝔽₃)	—	31	1	no	—
307	C₉⋊H(3,𝔽₃)	—	31	1	no	—
308	C₉×3₋¹⁺²	—	31	1	no	—
309	C₉×3₋¹⁺²	—	31	1	no	—
310	C₉×3₋¹⁺²	—	31	1	no	—
311	C₉×3₋¹⁺²	—	31	1	no	—
312	C₉×3₋¹⁺²	—	31	1	no	—
313	C₉×3₋¹⁺²	—	31	1	no	—
314	C₉×3₋¹⁺²	—	31	1	no	—
315	C₉×3₋¹⁺²	—	31	1	no	—
316	C₉×H(3,𝔽₃)	—	31	1	no	—
317	#6887	—	31	1	no	—
318	#6887	—	31	1	no	—
319	#6887	—	31	1	no	—
320	C₃×C₉²	—	31	1	no	—
321	C₃×C₃₁	—	9	1	no	—
322	C₃×C₃₁	C₃×#737	1	1	yes	characteristic
323	C₃×C₃₁	C₃×#737	1	1	yes	characteristic
324	C₃×C₃₁	C₃×#737	1	1	yes	characteristic
325	C₃×C₃₁	C₃×#737	1	1	yes	characteristic
326	C₃₁⋊C₃	—	3	3	no	—
327	C₃₁⋊C₃	—	9	1	no	—
328	C₃₁⋊C₃	—	9	1	no	—
329	C₃×3₋¹⁺²	—	31	1	no	—
330	C₃×3₋¹⁺²	—	31	1	no	—
331	C₃×3₋¹⁺²	—	31	1	no	—
332	C₃×3₋¹⁺²	—	31	1	no	—
333	C₃×3₋¹⁺²	—	31	1	no	—
334	C₃×3₋¹⁺²	—	31	1	no	—
335	C₃×3₋¹⁺²	—	31	1	no	—
336	C₃×3₋¹⁺²	C₃×C₃₁⋊C₃	1	1	yes	characteristic
337	C₃×H(3,𝔽₃)	—	31	1	no	—
338	C₃²×C₉	—	31	1	no	—
339	C₃²×C₉	—	31	1	no	—
340	C₃²×C₉	—	31	1	no	—
341	C₃²×C₉	—	31	1	no	—
342	C₃²×C₉	—	31	1	no	—
343	C₃²×C₉	—	31	1	no	—
344	C₃²×C₉	—	31	1	no	—
345	C₉⋊C₉	—	31	1	no	—
346	C₉⋊C₉	—	31	1	no	—
347	C₉⋊C₉	—	31	1	no	—
348	C₉⋊C₉	—	31	1	no	—
349	C₉⋊C₉	—	31	1	no	—
350	C₉⋊C₉	—	31	1	no	—
351	C₉⋊C₉	—	31	1	no	—
352	C₉⋊C₉	—	31	1	no	—
353	C₉⋊C₉	—	31	1	no	—
354	C₉⋊C₉	—	31	1	no	—
355	C₉⋊C₉	—	31	1	no	—
356	C₉⋊C₉	—	31	1	no	—
357	C₉⋊C₉	—	31	1	no	—
358	C₉⋊C₉	—	31	1	no	—
359	C₉⋊C₉	—	31	1	no	—
360	C₉⋊C₉	—	31	1	no	—
361	C₉⋊C₉	—	31	1	no	—
362	C₉⋊C₉	—	31	1	no	—
363	C₉⋊C₉	—	31	1	no	—
364	C₉⋊C₉	—	31	1	no	—
365	C₉⋊C₉	—	31	1	no	—
366	C₉⋊C₉	—	31	1	no	—
367	C₉⋊C₉	—	31	1	no	—
368	C₉⋊C₉	—	31	1	no	—
369	C₉⋊C₉	—	31	1	no	—
370	C₉⋊C₉	—	31	1	no	—
371	C₉⋊C₉	—	31	1	no	—
372	C₉⋊C₉	—	31	1	no	—
373	C₉⋊C₉	—	31	1	no	—
374	C₉⋊C₉	—	31	1	no	—
375	C₉⋊C₉	—	31	1	no	—
376	C₉⋊C₉	—	31	1	no	—
377	C₉⋊C₉	—	31	1	no	—
378	C₉⋊C₉	—	31	1	no	—
379	C₉⋊C₉	—	31	1	no	—
380	C₉⋊C₉	—	31	1	no	—
381	C₉⋊C₉	—	31	1	no	—
382	C₉⋊C₉	—	31	1	no	—
383	C₉⋊C₉	—	31	1	no	—
384	C₉⋊C₉	—	31	1	no	—
385	C₉⋊C₉	—	31	1	no	—
386	C₉⋊C₉	—	31	1	no	—
387	C₉⋊C₉	—	31	1	no	—
388	C₉⋊C₉	—	31	1	no	—
389	C₉⋊C₉	—	31	1	no	—
390	C₉⋊C₉	—	31	1	no	—
391	C₉⋊C₉	—	31	1	no	—
392	C₉⋊C₉	—	31	1	no	—
393	C₉⋊C₉	—	31	1	no	—
394	C₉⋊C₉	—	31	1	no	—
395	C₉⋊C₉	—	31	1	no	—
396	C₉⋊C₉	—	31	1	no	—
397	C₉⋊C₉	—	31	1	no	—
398	C₉⋊C₉	—	31	1	no	—
399	C₉⋊C₉	—	31	1	no	—
400	C₉⋊C₉	—	31	1	no	—
401	C₉⋊C₉	—	31	1	no	—
402	C₉⋊C₉	—	31	1	no	—
403	C₉⋊C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
404	C₉⋊C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
405	C₉⋊C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
406	C₉⋊C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
407	C₉⋊C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
408	C₉⋊C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
409	C₉⋊C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
410	C₉⋊C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
411	C₃²⋊C₉	—	31	1	no	—
412	C₃²⋊C₉	—	31	1	no	—
413	C₃²⋊C₉	—	31	1	no	—
414	C₃²⋊C₉	—	31	1	no	—
415	C₃²⋊C₉	—	31	1	no	—
416	C₃²⋊C₉	—	31	1	no	—
417	C₃²⋊C₉	—	31	1	no	—
418	C₃²⋊C₉	—	31	1	no	—
419	C₃²⋊C₉	—	31	1	no	—
420	C₃²⋊C₉	—	31	1	no	—
421	C₃²⋊C₉	—	31	1	no	—
422	C₃²⋊C₉	—	31	1	no	—
423	C₃²⋊C₉	—	31	1	no	—
424	C₃²⋊C₉	—	31	1	no	—
425	C₃²⋊C₉	—	31	1	no	—
426	C₃²⋊C₉	—	31	1	no	—
427	C₃²⋊C₉	—	31	1	no	—
428	C₃²⋊C₉	—	31	1	no	—
429	C₃²⋊C₉	—	31	1	no	—
430	C₃²⋊C₉	—	31	1	no	—
431	C₃²⋊C₉	—	31	1	no	—
432	C₃²⋊C₉	—	31	1	no	—
433	C₃²⋊C₉	—	31	1	no	—
434	C₃²⋊C₉	—	31	1	no	—
435	C₃²⋊C₉	—	31	1	no	—
436	C₃²⋊C₉	—	31	1	no	—
437	C₃²⋊C₉	—	31	1	no	—
438	C₃²⋊C₉	—	31	1	no	—
439	C₃²⋊C₉	—	31	1	no	—
440	C₃²⋊C₉	—	31	1	no	—
441	C₃²⋊C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
442	C₃²⋊C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
443	C₃²⋊C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
444	C₉²	—	31	1	no	—
445	C₉²	—	31	1	no	—
446	C₉²	—	31	1	no	—
447	C₉²	—	31	1	no	—
448	C₉²	—	31	1	no	—
449	C₉²	—	31	1	no	—
450	C₉²	—	31	1	no	—
451	C₉²	—	31	1	no	—
452	C₉²	—	31	1	no	—
453	C₉²	—	31	1	no	—
454	C₉²	—	31	1	no	—
455	C₉²	—	31	1	no	—
456	C₉²	—	31	1	no	—
457	C₉²	—	31	1	no	—
458	C₉²	C₃×C₃₁⋊C₃	1	1	yes	characteristic
459	C₃₁	#10624877	1	1	yes	characteristic, complemented, Sylow
460	C₃³	—	31	1	no	—
461	C₃³	—	31	1	no	—
462	C₃³	—	31	1	no	—
463	C₃³	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
464	3₋¹⁺²	—	3	3	no	—
465	3₋¹⁺²	—	93	3	no	—
466	3₋¹⁺²	—	93	3	no	—
467	3₋¹⁺²	—	93	3	no	—
468	3₋¹⁺²	—	93	3	no	—
469	3₋¹⁺²	—	93	3	no	—
470	3₋¹⁺²	—	93	3	no	—
471	3₋¹⁺²	—	93	3	no	—
472	H(3,𝔽₃)	—	93	3	no	—
473	C₃×C₉	—	31	1	no	—
474	C₃×C₉	—	31	1	no	—
475	C₃×C₉	—	31	1	no	—
476	C₃×C₉	—	31	1	no	—
477	C₃×C₉	—	31	1	no	—
478	C₃×C₉	—	31	1	no	—
479	C₃×C₉	—	31	1	no	—
480	C₃×C₉	—	31	1	no	—
481	C₃×C₉	—	31	1	no	—
482	C₃×C₉	—	31	1	no	—
483	C₃×C₉	—	31	1	no	—
484	C₃×C₉	—	31	1	no	—
485	C₃×C₉	—	31	1	no	—
486	C₃×C₉	—	31	1	no	—
487	C₃×C₉	—	31	1	no	—
488	C₃×C₉	—	31	1	no	—
489	C₃×C₉	—	31	1	no	—
490	C₃×C₉	—	31	1	no	—
491	C₃×C₉	—	31	1	no	—
492	C₃×C₉	—	31	1	no	—
493	C₃×C₉	—	31	1	no	—
494	C₃×C₉	—	31	1	no	—
495	C₃×C₉	—	31	1	no	—
496	C₃×C₉	—	31	1	no	—
497	C₃×C₉	—	93	3	no	—
498	C₃×C₉	—	93	3	no	—
499	C₃×C₉	—	93	3	no	—
500	C₃×C₉	—	93	3	no	—
501	C₃×C₉	—	93	3	no	—
502	C₃×C₉	—	93	3	no	—
503	C₃×C₉	—	93	3	no	—
504	C₃×C₉	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
505	C₃×C₉	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
506	C₃×C₉	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
507	C₃×C₉	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
508	C₃×C₉	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
509	C₃×C₉	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
510	C₃×C₉	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
511	C₃×C₉	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
512	C₃×C₉	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
513	C₃×C₉	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
514	C₃×C₉	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
515	C₃×C₉	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
516	C₃²	—	3	1	no	—
517	C₃²	—	3	1	no	—
518	C₃²	—	3	1	no	—
519	C₃²	—	3	1	no	—
520	C₃²	—	31	3	no	—
521	C₃²	—	93	1	no	—
522	C₃²	—	93	1	no	—
523	C₃²	—	93	1	no	—
524	C₃²	—	93	1	no	—
525	C₃²	—	93	1	no	—
526	C₃²	—	93	1	no	—
527	C₃²	—	93	1	no	—
528	C₃²	—	93	1	no	—
529	C₃²	—	93	1	no	—
530	C₃²	—	93	1	no	—
531	C₃²	—	93	1	no	—
532	C₃²	C₃³×C₃₁⋊C₃	1	1	yes	characteristic
533	C₉	—	3	1	no	—
534	C₉	—	3	1	no	—
535	C₉	—	3	1	no	—
536	C₉	—	3	1	no	—
537	C₉	—	3	1	no	—
538	C₉	—	3	1	no	—
539	C₉	—	3	1	no	—
540	C₉	—	3	1	no	—
541	C₉	—	3	1	no	—
542	C₉	—	3	1	no	—
543	C₉	—	3	1	no	—
544	C₉	—	31	3	no	—
545	C₉	—	31	3	no	—
546	C₉	—	93	1	no	—
547	C₉	—	93	1	no	—
548	C₉	—	93	1	no	—
549	C₉	—	93	1	no	—
550	C₉	—	93	1	no	—
551	C₉	—	93	1	no	—
552	C₉	—	93	1	no	—
553	C₉	—	93	1	no	—
554	C₉	—	93	1	no	—
555	C₉	—	93	1	no	—
556	C₉	—	93	1	no	—
557	C₉	—	93	1	no	—
558	C₉	—	93	1	no	—
559	C₉	—	93	1	no	—
560	C₉	—	93	1	no	—
561	C₉	—	93	1	no	—
562	C₉	—	93	1	no	—
563	C₉	—	93	1	no	—
564	C₉	—	93	1	no	—
565	C₉	—	93	1	no	—
566	C₉	—	93	1	no	—
567	C₉	—	93	1	no	—
568	C₉	#14578913	1	3	yes	—
569	C₃	—	9	1	no	—
570	C₃	—	279	1	no	—
571	C₃	—	279	1	no	—
572	C₃	—	93	3	no	—
573	C₃	#737×C₃₁⋊C₃	1	1	yes	characteristic
574	C₃	#737×C₃₁⋊C₃	1	1	yes	characteristic
575	C₃	#737×C₃₁⋊C₃	1	1	yes	characteristic
576	C₃	C₃×#14578913	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃²	C₃³×C₃₁⋊C₃
commutator, socle, cosocle	C₃²×C₃₁	C₃⁴
Fitting	C₃₁×#6899	C₃
prime radical	C₃×C₃²⋊(C₃₁⋊C₃)	C₃²
hypercenter	#6899	C₃₁⋊C₃
hypocenter	C₃₁	#10624877
LCS	G ▷ C₃²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃² ◁ #6899

Complements

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

N	H ≅ G/N	type
1. #21419356	C₃	semidirect
2. #21419355	C₃	semidirect
3. #21419354	C₃	semidirect
4. #21419353	C₃	semidirect
5. #21419351	C₃	semidirect
6. #21419350	C₃	semidirect
7. #21419350	C₃	semidirect
8. #21419348	C₃	semidirect
9. #21419347	C₃	semidirect
10. #21419347	C₃	semidirect
11. #21419346	C₃	semidirect
12. #21419346	C₃	semidirect
13. #21419343	C₃	semidirect
14. #21419343	C₃	semidirect
15. #21419342	C₃	semidirect
16. #21419341	C₃	semidirect
17. #21419338	C₃	semidirect
18. #21419335	C₃	semidirect
19. #21419335	C₃	semidirect
20. #21419328	C₃	semidirect
21. #21419327	C₃	semidirect
22. #21419325	C₃	semidirect
23. #21419324	C₃	semidirect
27. #21419306	C₃	semidirect
28. 3₋¹⁺²×C₃₁⋊C₉	C₃	semidirect
29. #11719686⋊C₉	C₃	semidirect
30. #11719686⋊C₉	C₃	semidirect
31. #11719686⋊C₉	C₃	semidirect
32. #11719687⋊C₉	C₃	semidirect
33. #11719687⋊C₉	C₃	semidirect
34. #11719687⋊C₉	C₃	semidirect
36. #21419295	C₃	semidirect
37. #21419295	C₃	semidirect
38. #21419293	C₃	semidirect
39. C₉²×C₃₁⋊C₃	C₃	semidirect
40. C₃₁×#6899	C₃	semidirect
286. #6899	C₃₁⋊C₃	semidirect
459. C₃₁	#10624877	semidirect

Maximal subgroups

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

subgroup	index
#21419356	3
#21419355	3
#21419354	3
#21419353	3
#21419351	3
#21419350	3
#21419348	3
#21419347	3
#21419346	3
#21419343	3
#21419342	3
#21419341	3
#21419338	3
#21419335	3
#21419328	3
#21419327	3
#21419325	3
#21419324	3
#21419321	3
#21419315	3
#21419313	3
#21419306	3
3₋¹⁺²×C₃₁⋊C₉	3
#11719686⋊C₉	3
#11719687⋊C₉	3
#21419297	3
#21419295	3
#21419293	3
C₉²×C₃₁⋊C₃	3
C₃₁×#6899	3
#10624877	31