Subgroups — #36382329

Order 22599.

824 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₉×C₃₁⋊C₃	C₃	1	1	yes	maximal, characteristic
2	#21419335	C₃	1	3	yes	maximal, complemented
3	#21419335	C₃	1	3	yes	maximal, complemented
4	#21419332	C₃	1	1	yes	maximal, characteristic, complemented
5	#21419331	C₃	1	1	yes	maximal, characteristic, complemented
6	#21419330	C₃	1	1	yes	maximal, characteristic, complemented
7	#21419329	C₃	1	1	yes	maximal, characteristic, complemented
8	#21419328	C₃	1	3	yes	maximal, complemented
9	#21419327	C₃	1	3	yes	maximal, complemented
10	#21419326	C₃	1	1	yes	maximal, characteristic, complemented
11	#21419325	C₃	1	3	yes	maximal, complemented
12	#21419324	C₃	1	3	yes	maximal, complemented
13	#21419311	C₃	1	1	yes	maximal, characteristic
14	#21419310	C₃	1	1	yes	maximal, characteristic
15	#21419309	C₃	1	1	yes	maximal, characteristic
16	#21419306	C₃	1	1	yes	maximal, characteristic, complemented
17	#21419306	C₃	1	1	yes	maximal, characteristic, complemented
18	3₋¹⁺²×C₃₁⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
19	#11719686⋊C₉	C₃	1	3	yes	maximal, complemented
20	#11719687⋊C₉	C₃	1	3	yes	maximal, complemented
21	#21419295	C₃	1	3	yes	maximal, complemented
22	C₃₁×#6894	C₃	1	1	yes	maximal, characteristic, complemented
23	C₃³×C₃₁⋊C₃	C₃²	1	1	yes	characteristic
24	C₃×#11719689	C₃²	1	1	yes	characteristic
25	C₃×#11719689	C₃²	1	1	yes	characteristic
26	C₃×#11719686	C₃²	1	3	yes	—
27	C₃×#11719687	C₃²	1	3	yes	—
28	C₃²×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
29	C₃²×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
30	C₃×C₉×C₃₁⋊C₃	—	3	9	no	—
31	C₃×C₉×C₃₁⋊C₃	C₃²	1	1	yes	characteristic
32	C₃×C₉×C₃₁⋊C₃	C₃²	1	1	yes	characteristic
33	C₃×C₉×C₃₁⋊C₃	C₃²	1	1	yes	characteristic
34	C₃×C₉×C₃₁⋊C₃	C₃²	1	1	yes	characteristic
35	C₃×C₉×C₃₁⋊C₃	C₃²	1	1	yes	characteristic
36	C₃×C₉×C₃₁⋊C₃	C₃²	1	1	yes	characteristic
37	C₃×C₉×C₃₁⋊C₃	C₃²	1	1	yes	characteristic
38	C₃×C₉×C₃₁⋊C₃	C₃²	1	1	yes	characteristic
39	C₃×C₉×C₃₁⋊C₃	C₃²	1	1	yes	characteristic
40	#14578887	C₃²	1	3	yes	complemented
41	#14578887	C₃²	1	3	yes	complemented
42	#14578887	C₃²	1	3	yes	complemented
43	#14578886	C₃²	1	3	yes	complemented
44	#14578886	C₃²	1	3	yes	complemented
45	#14578886	C₃²	1	3	yes	complemented
46	(C₃₁⋊C₉)⋊C₉	C₃²	1	3	yes	complemented
47	(C₃₁⋊C₉)⋊C₉	C₃²	1	3	yes	complemented
48	(C₃₁⋊C₉)⋊C₉	C₃²	1	3	yes	complemented
49	(C₃₁⋊C₉)⋊C₉	C₃²	1	3	yes	complemented
50	(C₃₁⋊C₉)⋊C₉	C₃²	1	3	yes	complemented
51	(C₃₁⋊C₉)⋊C₉	C₃²	1	3	yes	complemented
52	(C₃₁⋊C₉)⋊C₉	C₃²	1	3	yes	complemented
53	(C₃₁⋊C₉)⋊C₉	C₃²	1	3	yes	complemented
54	(C₃₁⋊C₉)⋊C₉	C₃²	1	3	yes	complemented
55	(C₃₁⋊C₉)⋊C₉	C₃²	1	3	yes	complemented
56	(C₃₁⋊C₉)⋊C₉	C₃²	1	3	yes	complemented
57	(C₃₁⋊C₉)⋊C₉	C₃²	1	3	yes	complemented
58	(C₃₁⋊C₉)⋊C₉	C₃²	1	3	yes	complemented
59	(C₃₁⋊C₉)⋊C₉	C₃²	1	3	yes	complemented
60	(C₃₁⋊C₉)⋊C₉	C₃²	1	3	yes	complemented
61	C₃²⋊(C₃₁⋊C₉)	C₃²	1	1	yes	characteristic
62	C₃²⋊(C₃₁⋊C₉)	C₃²	1	1	yes	characteristic
63	C₃²⋊(C₃₁⋊C₉)	C₃²	1	1	yes	characteristic
64	C₃²⋊(C₃₁⋊C₉)	C₃²	1	1	yes	characteristic
65	(C₃×C₃₁⋊C₃)⋊C₉	C₃²	1	3	yes	—
66	(C₃×C₃₁⋊C₃)⋊C₉	C₃²	1	3	yes	—
67	(C₃×C₃₁⋊C₃)⋊C₉	C₃²	1	3	yes	—
68	(C₃×C₃₁⋊C₃)⋊C₉	C₃²	1	3	yes	—
69	(C₃×C₃₁⋊C₃)⋊C₉	C₃²	1	3	yes	—
70	(C₃×C₃₁⋊C₃)⋊C₉	C₃²	1	3	yes	—
71	(C₃×C₃₁⋊C₃)⋊C₉	C₃²	1	3	yes	—
72	C₉×C₃₁⋊C₉	C₃²	1	3	yes	complemented
73	C₉×C₃₁⋊C₉	C₃²	1	3	yes	complemented
74	C₉×C₃₁⋊C₉	C₃²	1	3	yes	complemented
75	C₃×3₋¹⁺²×C₃₁	C₃²	1	1	yes	characteristic
76	C₃²×C₉×C₃₁	C₃²	1	1	yes	characteristic
77	C₃₁×C₉⋊C₉	C₃²	1	3	yes	complemented
78	C₃₁×C₉⋊C₉	C₃²	1	3	yes	complemented
79	C₃₁×C₉⋊C₉	C₃²	1	3	yes	complemented
80	C₃₁×C₃²⋊C₉	C₃²	1	1	yes	characteristic
81	C₃₁×C₃²⋊C₉	C₃²	1	1	yes	characteristic
82	C₃³×C₃₁	C₃³	1	1	yes	characteristic
83	C₃²×C₃₁⋊C₃	—	3	3	no	—
84	C₃²×C₃₁⋊C₃	—	3	3	no	—
85	C₃²×C₃₁⋊C₃	—	3	3	no	—
86	C₃²×C₃₁⋊C₃	—	3	3	no	—
87	C₃²×C₃₁⋊C₃	C₃³	1	1	yes	characteristic
88	C₃²×C₃₁⋊C₃	C₃³	1	1	yes	characteristic
89	C₃²×C₃₁⋊C₃	C₃³	1	1	yes	characteristic
90	3₋¹⁺²×C₃₁	—	3	3	no	—
91	C₃×C₉×C₃₁	—	3	3	no	—
92	C₃×C₉×C₃₁	C₃³	1	3	yes	—
93	C₃×C₉×C₃₁	C₃³	1	3	yes	—
94	C₃×C₉×C₃₁	C₃³	1	1	yes	characteristic
95	C₃×C₉×C₃₁	C₃³	1	1	yes	characteristic
96	C₃×C₉×C₃₁	C₃³	1	3	yes	—
97	C₃×C₉×C₃₁	C₃³	1	1	yes	characteristic
98	#11719689	—	3	3	no	—
99	#11719689	—	3	3	no	—
100	C₃×C₃₁⋊C₉	—	3	3	no	—
101	C₃×C₃₁⋊C₉	—	3	3	no	—
102	C₃×C₃₁⋊C₉	C₃³	1	3	yes	—
103	C₃×C₃₁⋊C₉	C₃³	1	3	yes	—
104	C₃×C₃₁⋊C₉	C₃³	1	3	yes	—
105	C₃×C₃₁⋊C₉	C₃³	1	3	yes	—
106	C₃×C₃₁⋊C₉	C₃³	1	3	yes	—
107	C₃×C₃₁⋊C₉	C₃³	1	3	yes	—
108	C₃×C₃₁⋊C₉	C₃³	1	1	yes	characteristic
109	C₃×C₃₁⋊C₉	C₃³	1	1	yes	characteristic
110	C₃×C₃₁⋊C₉	C₃³	1	1	yes	characteristic
111	C₃×C₃₁⋊C₉	C₃³	1	1	yes	characteristic
112	C₃×C₃₁⋊C₉	C₃³	1	1	yes	characteristic
113	C₃×C₃₁⋊C₉	C₃³	1	1	yes	characteristic
114	#11719687	—	3	9	no	—
115	#11719686	—	3	9	no	—
116	C₉×C₃₁⋊C₃	—	3	3	no	—
117	C₉×C₃₁⋊C₃	—	3	3	no	—
118	C₉×C₃₁⋊C₃	—	3	3	no	—
119	C₉×C₃₁⋊C₃	—	3	3	no	—
120	C₉×C₃₁⋊C₃	—	3	3	no	—
121	C₉×C₃₁⋊C₃	—	3	3	no	—
122	C₉×C₃₁⋊C₃	—	3	3	no	—
123	C₉×C₃₁⋊C₃	—	3	3	no	—
124	C₉×C₃₁⋊C₃	3₋¹⁺²	1	9	yes	complemented
125	#10624872	—	31	1	no	maximal, Sylow
126	C₃²×C₃₁	—	3	1	no	—
127	C₃²×C₃₁	—	3	1	no	—
128	C₃²×C₃₁	—	3	1	no	—
129	C₃²×C₃₁	#737	1	3	yes	—
130	C₃²×C₃₁	C₃⁴	1	1	yes	characteristic
131	C₃×C₃₁⋊C₃	—	3	27	no	—
132	C₃×C₃₁⋊C₃	—	3	1	no	—
133	C₃×C₃₁⋊C₃	—	3	1	no	—
134	C₃×C₃₁⋊C₃	—	3	1	no	—
135	C₃×C₃₁⋊C₃	—	3	1	no	—
136	C₃×C₃₁⋊C₃	—	3	1	no	—
137	C₃×C₃₁⋊C₃	—	3	1	no	—
138	C₃×C₃₁⋊C₃	—	3	1	no	—
139	C₃×C₃₁⋊C₃	—	3	1	no	—
140	C₃×C₃₁⋊C₃	—	3	1	no	—
141	C₃×C₃₁⋊C₃	C₃×3₋¹⁺²	1	3	yes	—
142	C₃×C₃₁⋊C₃	#737	1	3	yes	—
143	C₃×C₃₁⋊C₃	#737	1	3	yes	—
144	C₉×C₃₁	—	3	1	no	—
145	C₉×C₃₁	—	3	1	no	—
146	C₉×C₃₁	—	3	3	no	—
147	C₉×C₃₁	—	3	3	no	—
148	C₉×C₃₁	—	3	3	no	—
149	C₉×C₃₁	C₃×3₋¹⁺²	1	3	yes	—
150	C₃₁⋊C₉	—	3	1	no	—
151	C₃₁⋊C₉	—	3	1	no	—
152	C₃₁⋊C₉	—	3	1	no	—
153	C₃₁⋊C₉	—	3	1	no	—
154	C₃₁⋊C₉	—	3	3	no	—
155	C₃₁⋊C₉	—	3	3	no	—
156	C₃₁⋊C₉	—	3	3	no	—
157	C₃₁⋊C₉	—	3	3	no	—
158	C₃₁⋊C₉	—	3	3	no	—
159	C₃₁⋊C₉	—	3	3	no	—
160	C₃₁⋊C₉	C₃×3₋¹⁺²	1	3	yes	—
161	C₃₁⋊C₉	C₃×3₋¹⁺²	1	3	yes	—
162	C₃³×C₉	—	31	1	no	—
163	#6895	—	31	3	no	—
164	#6895	—	31	3	no	—
165	#6894	—	31	1	no	—
166	#6894	—	31	1	no	—
167	#6894	—	31	1	no	—
168	#6894	—	31	3	no	—
169	#6894	—	31	3	no	—
170	#6894	—	31	3	no	—
171	#6894	—	31	3	no	—
172	#6894	—	31	1	no	—
173	#6894	—	31	1	no	—
174	#6894	C₃₁⋊C₃	1	1	yes	characteristic, complemented
175	#6891	—	31	1	no	—
176	#6891	—	31	1	no	—
177	#6891	—	31	1	no	—
178	C₉×3₋¹⁺²	—	31	1	no	—
179	C₉×3₋¹⁺²	—	31	3	no	—
180	C₉×3₋¹⁺²	—	31	3	no	—
181	C₉×3₋¹⁺²	—	31	1	no	—
182	C₉×3₋¹⁺²	—	31	1	no	—
183	#6887	—	31	3	no	—
184	C₃×C₃₁	—	3	3	no	—
185	C₃×C₃₁	C₃²×3₋¹⁺²	1	1	yes	characteristic
186	C₃×C₃₁	C₃×#737	1	1	yes	characteristic
187	C₃×C₃₁	C₃×#737	1	1	yes	characteristic
188	C₃×C₃₁	C₃×#737	1	1	yes	characteristic
189	C₃₁⋊C₃	—	3	3	no	—
190	C₃₁⋊C₃	—	3	3	no	—
191	C₃₁⋊C₃	—	3	3	no	—
192	C₃⁴	—	31	1	no	—
193	C₃×3₋¹⁺²	—	31	1	no	—
194	C₃×3₋¹⁺²	—	31	1	no	—
195	C₃×3₋¹⁺²	—	31	3	no	—
196	C₃×3₋¹⁺²	—	31	3	no	—
197	C₃×3₋¹⁺²	C₃×C₃₁⋊C₃	1	1	yes	characteristic
198	C₃²×C₉	—	31	1	no	—
199	C₃²×C₉	—	31	1	no	—
200	C₃²×C₉	—	31	1	no	—
201	C₃²×C₉	—	31	1	no	—
202	C₃²×C₉	—	31	1	no	—
203	C₃²×C₉	—	31	1	no	—
204	C₃²×C₉	—	31	1	no	—
205	C₃²×C₉	—	31	1	no	—
206	C₃²×C₉	—	31	1	no	—
207	C₃²×C₉	—	31	1	no	—
208	C₃²×C₉	—	31	1	no	—
209	C₃²×C₉	—	93	9	no	—
210	C₃²×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
211	C₉⋊C₉	—	31	3	no	—
212	C₉⋊C₉	—	31	3	no	—
213	C₉⋊C₉	—	31	3	no	—
214	C₉⋊C₉	—	31	3	no	—
215	C₉⋊C₉	—	31	3	no	—
216	C₉⋊C₉	—	31	3	no	—
217	C₉⋊C₉	—	31	3	no	—
218	C₉⋊C₉	—	31	3	no	—
219	C₉⋊C₉	—	31	3	no	—
220	C₉⋊C₉	—	31	3	no	—
221	C₉⋊C₉	—	31	3	no	—
222	C₉⋊C₉	—	31	3	no	—
223	C₉⋊C₉	—	31	3	no	—
224	C₉⋊C₉	—	31	3	no	—
225	C₉⋊C₉	—	31	3	no	—
226	C₉⋊C₉	—	31	3	no	—
227	C₉⋊C₉	—	31	3	no	—
228	C₉⋊C₉	—	31	3	no	—
229	C₉⋊C₉	—	31	3	no	—
230	C₉⋊C₉	—	31	3	no	—
231	C₉⋊C₉	—	31	3	no	—
232	C₉⋊C₉	C₃×C₃₁⋊C₃	1	3	yes	complemented
233	C₉⋊C₉	C₃×C₃₁⋊C₃	1	3	yes	complemented
234	C₉⋊C₉	C₃×C₃₁⋊C₃	1	3	yes	complemented
235	C₃²⋊C₉	—	31	1	no	—
236	C₃²⋊C₉	—	31	1	no	—
237	C₃²⋊C₉	—	31	1	no	—
238	C₃²⋊C₉	—	31	1	no	—
239	C₃²⋊C₉	—	31	3	no	—
240	C₃²⋊C₉	—	31	3	no	—
241	C₃²⋊C₉	—	31	3	no	—
242	C₃²⋊C₉	—	31	3	no	—
243	C₃²⋊C₉	—	31	3	no	—
244	C₃²⋊C₉	—	31	3	no	—
245	C₃²⋊C₉	—	31	3	no	—
246	C₃²⋊C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
247	C₃²⋊C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
248	C₉²	—	31	3	no	—
249	C₉²	—	31	3	no	—
250	C₉²	—	31	3	no	—
251	C₃₁	#10624872	1	1	yes	characteristic, complemented, Sylow
252	C₃³	—	31	1	no	—
253	C₃³	—	31	1	no	—
254	C₃³	—	31	1	no	—
255	C₃³	—	93	3	no	—
256	C₃³	—	93	3	no	—
257	C₃³	—	93	3	no	—
258	C₃³	—	93	3	no	—
259	C₃³	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
260	3₋¹⁺²	—	3	3	no	—
261	3₋¹⁺²	—	93	9	no	—
262	3₋¹⁺²	—	93	9	no	—
263	3₋¹⁺²	—	93	3	no	—
264	3₋¹⁺²	—	93	3	no	—
265	C₃×C₉	—	3	3	no	—
266	C₃×C₉	—	31	1	no	—
267	C₃×C₉	—	31	1	no	—
268	C₃×C₉	—	31	9	no	—
269	C₃×C₉	—	31	3	no	—
270	C₃×C₉	—	31	3	no	—
271	C₃×C₉	—	31	3	no	—
272	C₃×C₉	—	31	3	no	—
273	C₃×C₉	—	31	3	no	—
274	C₃×C₉	—	31	3	no	—
275	C₃×C₉	—	31	1	no	—
276	C₃×C₉	—	31	1	no	—
277	C₃×C₉	—	31	1	no	—
278	C₃×C₉	—	31	1	no	—
279	C₃×C₉	—	93	3	no	—
280	C₃×C₉	—	93	3	no	—
281	C₃×C₉	—	93	3	no	—
282	C₃×C₉	—	93	3	no	—
283	C₃×C₉	—	93	3	no	—
284	C₃×C₉	—	93	3	no	—
285	C₃×C₉	—	93	3	no	—
286	C₃×C₉	—	93	3	no	—
287	C₃×C₉	—	93	3	no	—
288	C₃×C₉	—	93	3	no	—
289	C₃×C₉	C₃²×C₃₁⋊C₃	1	3	yes	—
290	C₃×C₉	C₃²×C₃₁⋊C₃	1	3	yes	—
291	C₃×C₉	C₃²×C₃₁⋊C₃	1	3	yes	—
292	C₃×C₉	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
293	C₃×C₉	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
294	C₃×C₉	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
295	C₃²	—	3	1	no	—
296	C₃²	—	3	1	no	—
297	C₃²	—	3	1	no	—
298	C₃²	—	31	3	no	—
299	C₃²	—	31	3	no	—
300	C₃²	—	31	3	no	—
301	C₃²	—	93	27	no	—
302	C₃²	—	93	1	no	—
303	C₃²	—	93	1	no	—
304	C₃²	—	93	1	no	—
305	C₃²	—	93	1	no	—
306	C₃²	—	93	1	no	—
307	C₃²	—	93	1	no	—
308	C₃²	—	93	1	no	—
309	C₃²	—	93	1	no	—
310	C₃²	—	93	1	no	—
311	C₃²	#14578913	1	3	yes	—
312	C₃²	C₃³×C₃₁⋊C₃	1	1	yes	characteristic
313	C₉	—	3	1	no	—
314	C₉	—	3	1	no	—
315	C₉	—	3	3	no	—
316	C₉	—	3	3	no	—
317	C₉	—	3	3	no	—
318	C₉	—	31	3	no	—
319	C₉	—	31	3	no	—
320	C₉	—	93	1	no	—
321	C₉	—	93	1	no	—
322	C₉	—	93	1	no	—
323	C₉	—	93	1	no	—
324	C₉	—	93	3	no	—
325	C₉	—	93	3	no	—
326	C₉	—	93	3	no	—
327	C₉	—	93	3	no	—
328	C₉	—	93	3	no	—
329	C₉	—	93	3	no	—
330	C₉	3₋¹⁺²×C₃₁⋊C₃	1	3	yes	—
331	C₃	—	3	3	no	—
332	C₃	—	93	3	no	—
333	C₃	—	93	3	no	—
334	C₃	—	93	3	no	—
335	C₃	C₃×3₋¹⁺²×C₃₁⋊C₃	1	1	yes	characteristic
336	C₃	#737×C₃₁⋊C₃	1	1	yes	characteristic
337	C₃	#737×C₃₁⋊C₃	1	1	yes	characteristic
338	C₃	C₃×#14578913	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃²	C₃³×C₃₁⋊C₃
commutator, socle, cosocle	C₃²×C₃₁	C₃⁴
Fitting	C₃₁×#6894	C₃
prime radical	C₃³×C₃₁⋊C₃	C₃²
hypercenter	#6894	C₃₁⋊C₃
hypocenter	C₃₁	#10624872
LCS	G ▷ C₃²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃² ◁ #6894

Complements

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

N	H ≅ G/N	type
2. #21419335	C₃	semidirect
3. #21419335	C₃	semidirect
4. #21419332	C₃	semidirect
5. #21419331	C₃	semidirect
6. #21419330	C₃	semidirect
7. #21419329	C₃	semidirect
8. #21419328	C₃	semidirect
9. #21419327	C₃	semidirect
10. #21419326	C₃	semidirect
11. #21419325	C₃	semidirect
12. #21419324	C₃	semidirect
16. #21419306	C₃	semidirect
17. #21419306	C₃	semidirect
18. 3₋¹⁺²×C₃₁⋊C₉	C₃	semidirect
19. #11719686⋊C₉	C₃	semidirect
20. #11719687⋊C₉	C₃	semidirect
21. #21419295	C₃	semidirect
22. C₃₁×#6894	C₃	semidirect
40. #14578887	C₃²	semidirect
41. #14578887	C₃²	semidirect
42. #14578887	C₃²	semidirect
43. #14578886	C₃²	semidirect
44. #14578886	C₃²	semidirect
45. #14578886	C₃²	semidirect
46. (C₃₁⋊C₉)⋊C₉	C₃²	semidirect
47. (C₃₁⋊C₉)⋊C₉	C₃²	semidirect
48. (C₃₁⋊C₉)⋊C₉	C₃²	semidirect
49. (C₃₁⋊C₉)⋊C₉	C₃²	semidirect
50. (C₃₁⋊C₉)⋊C₉	C₃²	semidirect
51. (C₃₁⋊C₉)⋊C₉	C₃²	semidirect
52. (C₃₁⋊C₉)⋊C₉	C₃²	semidirect
53. (C₃₁⋊C₉)⋊C₉	C₃²	semidirect
54. (C₃₁⋊C₉)⋊C₉	C₃²	semidirect
55. (C₃₁⋊C₉)⋊C₉	C₃²	semidirect
56. (C₃₁⋊C₉)⋊C₉	C₃²	semidirect
57. (C₃₁⋊C₉)⋊C₉	C₃²	semidirect
58. (C₃₁⋊C₉)⋊C₉	C₃²	semidirect
59. (C₃₁⋊C₉)⋊C₉	C₃²	semidirect
60. (C₃₁⋊C₉)⋊C₉	C₃²	semidirect
72. C₉×C₃₁⋊C₉	C₃²	semidirect
73. C₉×C₃₁⋊C₉	C₃²	semidirect
74. C₉×C₃₁⋊C₉	C₃²	semidirect
77. C₃₁×C₉⋊C₉	C₃²	semidirect
78. C₃₁×C₉⋊C₉	C₃²	semidirect
79. C₃₁×C₉⋊C₉	C₃²	semidirect
124. C₉×C₃₁⋊C₃	3₋¹⁺²	semidirect
174. #6894	C₃₁⋊C₃	semidirect
232. C₉⋊C₉	C₃×C₃₁⋊C₃	semidirect
233. C₉⋊C₉	C₃×C₃₁⋊C₃	semidirect
234. C₉⋊C₉	C₃×C₃₁⋊C₃	semidirect
251. C₃₁	#10624872	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₉×C₃₁⋊C₃	3
#21419335	3
#21419332	3
#21419331	3
#21419330	3
#21419329	3
#21419328	3
#21419327	3
#21419326	3
#21419325	3
#21419324	3
#21419311	3
#21419310	3
#21419309	3
#21419306	3
3₋¹⁺²×C₃₁⋊C₉	3
#11719686⋊C₉	3
#11719687⋊C₉	3
#21419295	3
C₃₁×#6894	3
#10624872	31