Subgroups — C₂²×C₃₁×#473 #21517224

Order 7936.

2630 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×#137	C₂	1	2	yes	maximal
2	C₂³×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃₁×#131	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃₁×#473	C₂	1	24	yes	maximal, direct product factor
5	C₂²×C₃₁×#108	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₃₁×#101	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
8	C₂³×Q₈×C₃₁	C₂²	1	2	yes	—
9	C₂×C₃₁×#137	—	2	12	no	—
10	C₂×C₃₁×#137	C₂²	1	24	yes	—
11	C₂²×Q₁₆×C₃₁	—	2	2	no	—
12	C₂²×Q₁₆×C₃₁	—	2	1	no	—
13	C₂²×Q₁₆×C₃₁	—	2	1	no	—
14	C₂²×Q₁₆×C₃₁	—	2	6	no	—
15	C₂²×Q₁₆×C₃₁	C₂²	1	12	yes	complemented
16	C₂²×SD₁₆×C₃₁	—	2	2	no	—
17	C₂×C₃₁×#131	—	2	6	no	—
18	C₂×C₃₁×#131	C₂²	1	12	yes	—
19	C₂²×M₁₆×C₃₁	—	2	1	no	—
20	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
22	C₂³×C₈×C₃₁	—	2	1	no	—
23	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
24	C₃₁×#473	C₂²	1	64	yes	direct product factor
25	C₂×C₃₁×#108	C₂²	1	12	yes	complemented
26	C₂×C₃₁×#101	C₂²	1	24	yes	complemented
27	C₂×#41×C₃₁	—	2	3	no	—
28	C₂×#41×C₃₁	—	2	3	no	—
29	C₂×#41×C₃₁	D₄	1	6	yes	—
30	C₂×#41×C₃₁	C₂³	1	6	yes	—
31	C₂²×Q₈×C₃₁	—	2	6	no	—
32	C₂²×Q₈×C₃₁	—	2	2	no	—
33	C₂²×Q₈×C₃₁	—	2	6	no	—
34	C₂²×Q₈×C₃₁	—	2	2	no	—
35	C₂²×Q₈×C₃₁	—	2	6	no	—
36	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
37	C₂²×Q₈×C₃₁	C₂³	1	12	yes	—
38	C₂²×D₄×C₃₁	—	2	1	no	—
39	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₃₁	—	2	1	no	—
41	C₂³×C₄×C₃₁	—	2	2	no	—
42	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
43	C₃₁×#137	—	2	48	no	—
44	C₃₁×#137	C₂³	1	32	yes	—
45	C₂×Q₁₆×C₃₁	—	2	24	no	—
46	C₂×Q₁₆×C₃₁	—	2	12	no	—
47	C₂×Q₁₆×C₃₁	—	2	12	no	—
48	C₂×Q₁₆×C₃₁	—	2	24	no	—
49	C₂×Q₁₆×C₃₁	C₂³	1	16	yes	complemented
50	C₂×SD₁₆×C₃₁	—	2	24	no	—
51	C₃₁×#131	—	2	24	no	—
52	C₃₁×#131	C₂³	1	16	yes	—
53	C₂×M₁₆×C₃₁	—	2	3	no	—
54	C₂×M₁₆×C₃₁	—	2	6	no	—
55	C₂×M₁₆×C₃₁	—	2	12	no	—
56	C₂×M₁₆×C₃₁	C₂³	1	6	yes	—
57	C₂×M₁₆×C₃₁	C₂³	1	12	yes	—
58	C₂²×C₈×C₃₁	—	2	1	no	—
59	C₂²×C₈×C₃₁	—	2	2	no	—
60	C₂²×C₈×C₃₁	—	2	12	no	—
61	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
62	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
63	C₂²×C₈×C₃₁	D₄	1	6	yes	—
64	C₂²×C₈×C₃₁	C₂³	1	6	yes	—
65	C₃₁×#108	C₂³	1	16	yes	complemented
66	C₃₁×#101	C₂³	1	32	yes	complemented
67	C₂⁴×C₃₁	—	2	1	no	—
68	C₂⁴×C₃₁	#41	1	1	yes	characteristic
69	#41×C₃₁	—	2	12	no	—
70	#41×C₃₁	—	2	6	no	—
71	#41×C₃₁	—	2	6	no	—
72	#41×C₃₁	C₂×D₄	1	12	yes	—
73	#41×C₃₁	C₂⁴	1	4	yes	—
74	C₂×Q₈×C₃₁	—	2	3	no	—
75	C₂×Q₈×C₃₁	—	2	12	no	—
76	C₂×Q₈×C₃₁	—	2	12	no	—
77	C₂×Q₈×C₃₁	—	2	12	no	—
78	C₂×Q₈×C₃₁	—	2	12	no	—
79	C₂×Q₈×C₃₁	—	2	12	no	—
80	C₂×Q₈×C₃₁	—	4	6	no	—
81	C₂×Q₈×C₃₁	—	4	6	no	—
82	C₂×Q₈×C₃₁	—	4	12	no	—
83	C₂×Q₈×C₃₁	C₂×D₄	1	6	yes	—
84	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
85	C₂×D₄×C₃₁	—	2	6	no	—
86	C₂×D₄×C₃₁	—	2	6	no	—
87	C₂×D₄×C₃₁	—	2	3	no	—
88	C₂×D₄×C₃₁	C₂×D₄	1	6	yes	—
89	C₂²×C₄×C₃₁	—	2	1	no	—
90	C₂²×C₄×C₃₁	—	2	6	no	—
91	C₂²×C₄×C₃₁	—	2	6	no	—
92	C₂²×C₄×C₃₁	—	2	12	no	—
93	C₂²×C₄×C₃₁	—	4	6	no	—
94	C₂²×C₄×C₃₁	—	4	2	no	—
95	C₂²×C₄×C₃₁	C₂×D₄	1	3	yes	—
96	C₂²×C₄×C₃₁	C₂×D₄	1	3	yes	—
97	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₃₁	#41	1	3	yes	—
100	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
101	Q₁₆×C₃₁	—	2	32	no	—
102	Q₁₆×C₃₁	—	2	16	no	—
103	Q₁₆×C₃₁	—	2	16	no	—
104	SD₁₆×C₃₁	—	2	32	no	—
105	M₁₆×C₃₁	—	2	6	no	—
106	M₁₆×C₃₁	—	2	12	no	—
107	M₁₆×C₃₁	—	2	16	no	—
108	M₁₆×C₃₁	C₂⁴	1	4	yes	—
109	M₁₆×C₃₁	C₂⁴	1	8	yes	—
110	C₂×C₈×C₃₁	—	2	6	no	—
111	C₂×C₈×C₃₁	—	2	12	no	—
112	C₂×C₈×C₃₁	—	2	16	no	—
113	C₂×C₈×C₃₁	C₂×D₄	1	6	yes	—
114	C₂×C₈×C₃₁	C₂×D₄	1	6	yes	—
115	C₂×C₈×C₃₁	C₂×D₄	1	12	yes	—
116	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
117	C₂²×#473	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₂³×C₃₁	—	2	4	no	—
119	C₂³×C₃₁	—	2	6	no	—
120	C₂³×C₃₁	—	4	4	no	—
121	C₂³×C₃₁	#121	1	3	yes	—
122	C₂³×C₃₁	#121	1	1	yes	characteristic
123	C₂³×C₃₁	C₂×#41	1	3	yes	—
124	Q₈×C₃₁	—	2	6	no	—
125	Q₈×C₃₁	—	2	8	no	—
126	Q₈×C₃₁	—	2	8	no	—
127	Q₈×C₃₁	—	4	12	no	—
128	Q₈×C₃₁	—	4	12	no	—
129	Q₈×C₃₁	C₂²×D₄	1	4	yes	—
130	D₄×C₃₁	—	2	12	no	—
131	D₄×C₃₁	—	2	4	no	—
132	D₄×C₃₁	—	2	6	no	—
133	D₄×C₃₁	C₂²×D₄	1	4	yes	—
134	C₂×C₄×C₃₁	—	2	6	no	—
135	C₂×C₄×C₃₁	—	2	12	no	—
136	C₂×C₄×C₃₁	—	2	4	no	—
137	C₂×C₄×C₃₁	—	2	8	no	—
138	C₂×C₄×C₃₁	—	4	12	no	—
139	C₂×C₄×C₃₁	—	4	12	no	—
140	C₂×C₄×C₃₁	#121	1	3	yes	—
141	C₂×C₄×C₃₁	#121	1	3	yes	—
142	C₂×C₄×C₃₁	#121	1	6	yes	—
143	C₂×C₄×C₃₁	C₂²×D₄	1	3	yes	—
144	C₂×C₄×C₃₁	C₂²×D₄	1	3	yes	—
145	C₂×C₄×C₃₁	C₂²×D₄	1	3	yes	—
146	C₂×C₄×C₃₁	C₂²×D₄	1	3	yes	—
147	C₂×C₄×C₃₁	C₂×#41	1	3	yes	—
148	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
149	C₈×C₃₁	—	2	4	no	—
150	C₈×C₃₁	—	2	8	no	—
151	C₈×C₃₁	C₂²×D₄	1	4	yes	—
152	C₈×C₃₁	C₂²×D₄	1	4	yes	—
153	C₂²×#137	C₂×C₃₁	1	2	yes	—
154	C₂³×Q₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
155	C₂²×#131	C₂×C₃₁	1	1	yes	characteristic
156	C₂×#473	C₂×C₃₁	1	24	yes	direct product factor
157	C₂²×#108	C₂×C₃₁	1	1	yes	characteristic, complemented
158	C₂²×#101	C₂×C₃₁	1	2	yes	complemented
159	C₂²×C₃₁	—	2	6	no	—
160	C₂²×C₃₁	—	2	6	no	—
161	C₂²×C₃₁	—	2	4	no	—
162	C₂²×C₃₁	—	4	12	no	—
163	C₂²×C₃₁	#473	1	4	yes	direct product factor
164	C₂²×C₃₁	C₂×#121	1	3	yes	—
165	C₂²×C₃₁	C₂×#121	1	3	yes	—
166	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
167	C₄×C₃₁	—	2	4	no	—
168	C₄×C₃₁	—	4	8	no	—
169	C₄×C₃₁	C₂×#121	1	3	yes	—
170	C₄×C₃₁	C₂×#121	1	3	yes	—
171	C₄×C₃₁	C₂³×D₄	1	1	yes	characteristic
172	C₄×C₃₁	C₂³×D₄	1	1	yes	characteristic
173	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
174	C₂³×Q₈	C₂²×C₃₁	1	2	yes	—
175	C₂×#137	—	2	12	no	—
176	C₂×#137	C₂²×C₃₁	1	24	yes	—
177	C₂²×Q₁₆	—	2	2	no	—
178	C₂²×Q₁₆	—	2	1	no	—
179	C₂²×Q₁₆	—	2	1	no	—
180	C₂²×Q₁₆	—	2	6	no	—
181	C₂²×Q₁₆	C₂²×C₃₁	1	12	yes	complemented
182	C₂²×SD₁₆	—	2	2	no	—
183	C₂×#131	—	2	6	no	—
184	C₂×#131	C₂²×C₃₁	1	12	yes	—
185	C₂²×M₁₆	—	2	1	no	—
186	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
187	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
188	C₂³×C₈	—	2	1	no	—
189	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
190	#473	C₂²×C₃₁	1	64	yes	direct product factor
191	C₂×#108	C₂²×C₃₁	1	12	yes	complemented
192	C₂×#101	C₂²×C₃₁	1	24	yes	complemented
193	C₂×C₃₁	—	2	3	no	—
194	C₂×C₃₁	—	2	1	no	—
195	C₂×C₃₁	—	4	4	no	—
196	C₂×C₃₁	C₂×#473	1	6	yes	direct product factor
197	C₂×C₃₁	C₂²×#121	1	1	yes	characteristic
198	C₂×#41	—	2	3	no	—
199	C₂×#41	—	2	3	no	—
200	C₂×#41	D₄×C₃₁	1	6	yes	—
201	C₂×#41	C₂³×C₃₁	1	6	yes	—
202	C₂²×Q₈	—	2	6	no	—
203	C₂²×Q₈	—	2	2	no	—
204	C₂²×Q₈	—	2	2	no	—
205	C₂²×Q₈	—	2	6	no	—
206	C₂²×Q₈	—	2	6	no	—
207	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
208	C₂²×Q₈	C₂³×C₃₁	1	12	yes	—
209	C₂²×D₄	—	2	1	no	—
210	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
211	C₂³×C₄	—	2	1	no	—
212	C₂³×C₄	—	2	2	no	—
213	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
214	#137	—	2	48	no	—
215	#137	C₂³×C₃₁	1	32	yes	—
216	C₂×Q₁₆	—	2	24	no	—
217	C₂×Q₁₆	—	2	12	no	—
218	C₂×Q₁₆	—	2	12	no	—
219	C₂×Q₁₆	—	2	24	no	—
220	C₂×Q₁₆	C₂³×C₃₁	1	16	yes	complemented
221	C₂×SD₁₆	—	2	24	no	—
222	#131	—	2	24	no	—
223	#131	C₂³×C₃₁	1	16	yes	—
224	C₂×M₁₆	—	2	3	no	—
225	C₂×M₁₆	—	2	6	no	—
226	C₂×M₁₆	—	2	12	no	—
227	C₂×M₁₆	C₂³×C₃₁	1	6	yes	—
228	C₂×M₁₆	C₂³×C₃₁	1	12	yes	—
229	C₂²×C₈	—	2	1	no	—
230	C₂²×C₈	—	2	2	no	—
231	C₂²×C₈	—	2	12	no	—
232	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
233	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
234	C₂²×C₈	D₄×C₃₁	1	6	yes	—
235	C₂²×C₈	C₂³×C₃₁	1	6	yes	—
236	#108	C₂³×C₃₁	1	16	yes	complemented
237	#101	C₂³×C₃₁	1	32	yes	complemented
238	C₃₁	C₂²×#473	1	1	yes	characteristic, direct product factor, Sylow
239	C₂⁴	—	2	1	no	—
240	C₂⁴	#41×C₃₁	1	1	yes	characteristic
241	#41	—	2	12	no	—
242	#41	—	2	6	no	—
243	#41	—	2	6	no	—
244	#41	C₂×D₄×C₃₁	1	12	yes	—
245	#41	C₂⁴×C₃₁	1	4	yes	—
246	C₂×Q₈	—	2	3	no	—
247	C₂×Q₈	—	2	12	no	—
248	C₂×Q₈	—	2	12	no	—
249	C₂×Q₈	—	2	12	no	—
250	C₂×Q₈	—	2	12	no	—
251	C₂×Q₈	—	2	12	no	—
252	C₂×Q₈	—	4	6	no	—
253	C₂×Q₈	—	4	6	no	—
254	C₂×Q₈	—	4	12	no	—
255	C₂×Q₈	C₂×D₄×C₃₁	1	6	yes	—
256	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
257	C₂×D₄	—	2	6	no	—
258	C₂×D₄	—	2	6	no	—
259	C₂×D₄	—	2	3	no	—
260	C₂×D₄	C₂×D₄×C₃₁	1	6	yes	—
261	C₂²×C₄	—	2	1	no	—
262	C₂²×C₄	—	2	6	no	—
263	C₂²×C₄	—	2	6	no	—
264	C₂²×C₄	—	2	12	no	—
265	C₂²×C₄	—	4	6	no	—
266	C₂²×C₄	—	4	2	no	—
267	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
268	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
269	C₂²×C₄	C₂×D₄×C₃₁	1	3	yes	—
270	C₂²×C₄	C₂×D₄×C₃₁	1	3	yes	—
271	C₂²×C₄	#41×C₃₁	1	3	yes	—
272	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
273	Q₁₆	—	2	32	no	—
274	Q₁₆	—	2	16	no	—
275	Q₁₆	—	2	16	no	—
276	SD₁₆	—	2	32	no	—
277	M₁₆	—	2	6	no	—
278	M₁₆	—	2	12	no	—
279	M₁₆	—	2	16	no	—
280	M₁₆	C₂⁴×C₃₁	1	4	yes	—
281	M₁₆	C₂⁴×C₃₁	1	8	yes	—
282	C₂×C₈	—	2	6	no	—
283	C₂×C₈	—	2	12	no	—
284	C₂×C₈	—	2	16	no	—
285	C₂×C₈	C₂×D₄×C₃₁	1	6	yes	—
286	C₂×C₈	C₂×D₄×C₃₁	1	6	yes	—
287	C₂×C₈	C₂×D₄×C₃₁	1	12	yes	—
288	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
289	C₂³	—	2	4	no	—
290	C₂³	—	2	6	no	—
291	C₂³	—	4	4	no	—
292	C₂³	C₃₁×#121	1	3	yes	—
293	C₂³	C₃₁×#121	1	1	yes	characteristic
294	C₂³	C₂×#41×C₃₁	1	3	yes	—
295	Q₈	—	2	6	no	—
296	Q₈	—	2	8	no	—
297	Q₈	—	2	8	no	—
298	Q₈	—	4	12	no	—
299	Q₈	—	4	12	no	—
300	Q₈	C₂²×D₄×C₃₁	1	4	yes	—
301	D₄	—	2	12	no	—
302	D₄	—	2	4	no	—
303	D₄	—	2	6	no	—
304	D₄	C₂²×D₄×C₃₁	1	4	yes	—
305	C₂×C₄	—	2	6	no	—
306	C₂×C₄	—	2	12	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	2	8	no	—
309	C₂×C₄	—	4	12	no	—
310	C₂×C₄	—	4	12	no	—
311	C₂×C₄	C₃₁×#121	1	3	yes	—
312	C₂×C₄	C₃₁×#121	1	3	yes	—
313	C₂×C₄	C₃₁×#121	1	6	yes	—
314	C₂×C₄	C₂²×D₄×C₃₁	1	3	yes	—
315	C₂×C₄	C₂²×D₄×C₃₁	1	3	yes	—
316	C₂×C₄	C₂²×D₄×C₃₁	1	3	yes	—
317	C₂×C₄	C₂²×D₄×C₃₁	1	3	yes	—
318	C₂×C₄	C₂×#41×C₃₁	1	3	yes	—
319	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
320	C₈	—	2	4	no	—
321	C₈	—	2	8	no	—
322	C₈	C₂²×D₄×C₃₁	1	4	yes	—
323	C₈	C₂²×D₄×C₃₁	1	4	yes	—
324	C₂²	—	2	6	no	—
325	C₂²	—	2	6	no	—
326	C₂²	—	2	4	no	—
327	C₂²	—	4	12	no	—
328	C₂²	C₃₁×#473	1	4	yes	direct product factor
329	C₂²	C₂×C₃₁×#121	1	3	yes	—
330	C₂²	C₂×C₃₁×#121	1	3	yes	—
331	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
332	C₄	—	2	4	no	—
333	C₄	—	4	8	no	—
334	C₄	C₂×C₃₁×#121	1	3	yes	—
335	C₄	C₂×C₃₁×#121	1	3	yes	—
336	C₄	C₂³×D₄×C₃₁	1	1	yes	characteristic
337	C₄	C₂³×D₄×C₃₁	1	1	yes	characteristic
338	C₂	—	2	3	no	—
339	C₂	—	2	1	no	—
340	C₂	—	4	4	no	—
341	C₂	C₂×C₃₁×#473	1	6	yes	direct product factor
342	C₂	C₂²×C₃₁×#121	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	#121
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₂²×#41×C₃₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂³×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂³×Q₁₆×C₃₁	C₂	semidirect
4. C₂×C₃₁×#473	C₂	direct (N × H)
5. C₂²×C₃₁×#108	C₂	semidirect
6. C₂²×C₃₁×#101	C₂	semidirect
15. C₂²×Q₁₆×C₃₁	C₂²	semidirect
24. C₃₁×#473	C₂²	direct (N × H)
25. C₂×C₃₁×#108	C₂²	semidirect
26. C₂×C₃₁×#101	C₂²	semidirect
49. C₂×Q₁₆×C₃₁	C₂³	semidirect
65. C₃₁×#108	C₂³	semidirect
66. C₃₁×#101	C₂³	semidirect
117. C₂²×#473	C₃₁	direct (N × H)
154. C₂³×Q₁₆	C₂×C₃₁	semidirect
156. C₂×#473	C₂×C₃₁	direct (N × H)
157. C₂²×#108	C₂×C₃₁	semidirect
158. C₂²×#101	C₂×C₃₁	semidirect
163. C₂²×C₃₁	#473	direct (N × H)
181. C₂²×Q₁₆	C₂²×C₃₁	semidirect
190. #473	C₂²×C₃₁	direct (N × H)
191. C₂×#108	C₂²×C₃₁	semidirect
192. C₂×#101	C₂²×C₃₁	semidirect
196. C₂×C₃₁	C₂×#473	direct (N × H)
220. C₂×Q₁₆	C₂³×C₃₁	semidirect
236. #108	C₂³×C₃₁	semidirect
237. #101	C₂³×C₃₁	semidirect
238. C₃₁	C₂²×#473	direct (N × H)
328. C₂²	C₃₁×#473	direct (N × H)
341. C₂	C₂×C₃₁×#473	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃₁×#137	2
C₂³×Q₁₆×C₃₁	2
C₂²×C₃₁×#131	2
C₂×C₃₁×#473	2
C₂²×C₃₁×#108	2
C₂²×C₃₁×#101	2
C₂²×#473	31

Subgroups — C22×C31×#473 #21517224

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃₁×#473 #21517224