Subgroups — C₂×C₃₁×#2503 #21491532

Order 7936.

2918 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2503	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃₁×#400	C₂	1	4	yes	maximal, complemented
5	C₂×C₃₁×#391	C₂	1	2	yes	maximal, complemented
6	C₂×C₃₁×#382	C₂	1	2	yes	maximal, complemented
7	C₂×C₃₁×#381	C₂	1	4	yes	maximal
8	C₂×C₄×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
9	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₃₁	C₂²	1	2	yes	—
11	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
12	C₂×C₃₁×C₂²⋊Q₈	—	2	8	no	—
13	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	8	yes	—
14	C₂²×C₄⋊C₄×C₃₁	—	2	8	no	—
15	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₃₁	C₂²	1	8	yes	—
18	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
21	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
22	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
23	C₃₁×#400	C₂²	1	32	yes	complemented
24	C₃₁×#391	C₂²	1	16	yes	complemented
25	C₃₁×#382	C₂²	1	16	yes	complemented
26	C₃₁×#381	C₂²	1	32	yes	—
27	C₄×C₂²⋊C₄×C₃₁	C₂²	1	8	yes	—
28	C₂×C₃₁×#95	C₂²	1	2	yes	—
29	C₂×C₃₁×#95	C₂²	1	8	yes	—
30	C₂×C₃₁×#95	C₂²	1	8	yes	—
31	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
32	C₂²×Q₈×C₃₁	—	2	4	no	—
33	C₂²×Q₈×C₃₁	—	2	8	no	—
34	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
35	C₂³×C₄×C₃₁	—	2	8	no	—
36	C₂³×C₄×C₃₁	—	2	8	no	—
37	C₂³×C₄×C₃₁	—	2	16	no	—
38	C₂³×C₄×C₃₁	D₄	1	8	yes	—
39	C₂³×C₄×C₃₁	C₂³	1	8	yes	—
40	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
41	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
42	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
43	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
44	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
45	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
47	C₃₁×C₂²⋊Q₈	—	2	32	no	—
48	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
49	C₂×C₄⋊C₄×C₃₁	—	2	32	no	—
50	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
51	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
52	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
53	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
54	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
55	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
56	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
57	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
58	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
59	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
60	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
61	C₂×C₄²×C₃₁	—	2	8	no	—
62	C₂×C₄²×C₃₁	C₂³	1	8	yes	—
63	C₃₁×#95	C₂³	1	8	yes	—
64	C₃₁×#95	C₂³	1	32	yes	—
65	C₃₁×#95	C₂³	1	32	yes	—
66	C₂⁴×C₃₁	—	2	4	no	—
67	C₂⁴×C₃₁	—	2	4	no	—
68	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
69	C₂⁴×C₃₁	#41	1	8	yes	—
70	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
71	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
72	C₂×Q₈×C₃₁	—	2	8	no	—
73	C₂×Q₈×C₃₁	—	2	16	no	—
74	C₂×Q₈×C₃₁	—	4	16	no	—
75	C₂²×C₄×C₃₁	—	2	4	no	—
76	C₂²×C₄×C₃₁	—	2	32	no	—
77	C₂²×C₄×C₃₁	—	2	16	no	—
78	C₂²×C₄×C₃₁	—	2	4	no	—
79	C₂²×C₄×C₃₁	—	2	4	no	—
80	C₂²×C₄×C₃₁	—	2	16	no	—
81	C₂²×C₄×C₃₁	—	2	8	no	—
82	C₂²×C₄×C₃₁	—	2	8	no	—
83	C₂²×C₄×C₃₁	—	2	8	no	—
84	C₂²×C₄×C₃₁	—	2	32	no	—
85	C₂²×C₄×C₃₁	—	2	16	no	—
86	C₂²×C₄×C₃₁	—	2	8	no	—
87	C₂²×C₄×C₃₁	—	2	8	no	—
88	C₂²×C₄×C₃₁	—	2	8	no	—
89	C₂²×C₄×C₃₁	—	4	32	no	—
90	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
91	C₂²×C₄×C₃₁	C₂×D₄	1	16	yes	—
92	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
93	C₂²×C₄×C₃₁	#41	1	8	yes	—
94	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
95	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
96	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
97	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
98	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
99	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
100	C₄⋊C₄×C₃₁	—	2	16	no	—
101	C₄⋊C₄×C₃₁	—	2	16	no	—
102	C₄⋊C₄×C₃₁	—	2	8	no	—
103	C₄⋊C₄×C₃₁	—	2	16	no	—
104	C₂²⋊C₄×C₃₁	—	2	16	no	—
105	C₂²⋊C₄×C₃₁	—	2	16	no	—
106	C₄²×C₃₁	—	2	16	no	—
107	C₂×#2503	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂³×C₃₁	—	2	8	no	—
109	C₂³×C₃₁	—	2	8	no	—
110	C₂³×C₃₁	—	2	32	no	—
111	C₂³×C₃₁	—	2	4	no	—
112	C₂³×C₃₁	—	2	4	no	—
113	C₂³×C₃₁	#124	1	16	yes	—
114	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
115	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
116	C₂³×C₃₁	C₂×#41	1	8	yes	—
117	C₂³×C₃₁	C₂×#41	1	4	yes	—
118	C₂³×C₃₁	C₂×#41	1	4	yes	—
119	C₂³×C₃₁	2₋¹⁺⁴	1	4	yes	—
120	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
121	Q₈×C₃₁	—	4	16	no	—
122	C₂×C₄×C₃₁	—	2	8	no	—
123	C₂×C₄×C₃₁	—	2	4	no	—
124	C₂×C₄×C₃₁	—	2	32	no	—
125	C₂×C₄×C₃₁	—	2	4	no	—
126	C₂×C₄×C₃₁	—	2	4	no	—
127	C₂×C₄×C₃₁	—	2	8	no	—
128	C₂×C₄×C₃₁	—	2	8	no	—
129	C₂×C₄×C₃₁	—	2	8	no	—
130	C₂×C₄×C₃₁	—	2	16	no	—
131	C₂×C₄×C₃₁	—	2	8	no	—
132	C₂×C₄×C₃₁	—	2	8	no	—
133	C₂×C₄×C₃₁	—	2	8	no	—
134	C₂×C₄×C₃₁	—	4	8	no	—
135	C₂×C₄×C₃₁	—	4	32	no	—
136	C₂×C₄×C₃₁	—	4	16	no	—
137	C₂×C₄×C₃₁	—	4	8	no	—
138	C₂×C₄×C₃₁	—	4	16	no	—
139	C₂×C₄×C₃₁	#123	1	16	yes	—
140	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
141	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
142	C₂×C₄×C₃₁	C₂×#41	1	8	yes	—
143	C₂²×C₂²⋊Q₈	C₂×C₃₁	1	1	yes	characteristic
144	C₂³×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic
145	#2503	C₂×C₃₁	1	16	yes	direct product factor
146	C₂×#400	C₂×C₃₁	1	4	yes	complemented
147	C₂×#391	C₂×C₃₁	1	2	yes	complemented
148	C₂×#382	C₂×C₃₁	1	2	yes	complemented
149	C₂×#381	C₂×C₃₁	1	4	yes	—
150	C₂×C₄×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic
151	C₂²×C₃₁	—	2	4	no	—
152	C₂²×C₃₁	—	2	4	no	—
153	C₂²×C₃₁	—	2	16	no	—
154	C₂²×C₃₁	—	2	32	no	—
155	C₂²×C₃₁	C₂×#123	1	4	yes	—
156	C₂²×C₃₁	C₂×#124	1	8	yes	—
157	C₂²×C₃₁	C₂×#124	1	4	yes	—
158	C₂²×C₃₁	#536	1	4	yes	—
159	C₂²×C₃₁	#552	1	16	yes	—
160	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
161	C₂²×C₃₁	C₂²×#41	1	2	yes	—
162	C₂²×C₃₁	C₂²×#41	1	2	yes	—
163	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	2	yes	—
164	C₄×C₃₁	—	2	4	no	—
165	C₄×C₃₁	—	4	4	no	—
166	C₄×C₃₁	—	4	8	no	—
167	C₄×C₃₁	—	4	4	no	—
168	C₄×C₃₁	—	4	8	no	—
169	C₄×C₃₁	C₂×#123	1	8	yes	—
170	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic
171	C₂⁴×C₄	C₂²×C₃₁	1	2	yes	—
172	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
173	C₂×C₂²⋊Q₈	—	2	8	no	—
174	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	8	yes	—
175	C₂²×C₄⋊C₄	—	2	8	no	—
176	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
177	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
178	C₂²×C₄⋊C₄	C₂²×C₃₁	1	8	yes	—
179	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
180	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
181	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
182	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
183	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
184	#400	C₂²×C₃₁	1	32	yes	complemented
185	#391	C₂²×C₃₁	1	16	yes	complemented
186	#382	C₂²×C₃₁	1	16	yes	complemented
187	#381	C₂²×C₃₁	1	32	yes	—
188	C₄×C₂²⋊C₄	C₂²×C₃₁	1	8	yes	—
189	C₂×#95	C₂²×C₃₁	1	2	yes	—
190	C₂×#95	C₂²×C₃₁	1	8	yes	—
191	C₂×#95	C₂²×C₃₁	1	8	yes	—
192	C₂×C₃₁	—	2	8	no	—
193	C₂×C₃₁	#2503	1	8	yes	direct product factor
194	C₂×C₃₁	C₂²×#123	1	1	yes	characteristic
195	C₂×C₃₁	C₂²×#124	1	1	yes	characteristic
196	C₂×C₃₁	C₂×#536	1	1	yes	characteristic
197	C₂×C₃₁	C₂×#552	1	4	yes	—
198	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
199	C₂²×Q₈	—	2	4	no	—
200	C₂²×Q₈	—	2	8	no	—
201	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
202	C₂³×C₄	—	2	8	no	—
203	C₂³×C₄	—	2	8	no	—
204	C₂³×C₄	—	2	16	no	—
205	C₂³×C₄	D₄×C₃₁	1	8	yes	—
206	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
207	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
208	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
209	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
210	C₂³×C₄	C₂³×C₃₁	1	8	yes	—
211	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
212	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
213	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
214	C₂²⋊Q₈	—	2	32	no	—
215	C₂×C₄⋊C₄	—	2	8	no	—
216	C₂×C₄⋊C₄	—	2	32	no	—
217	C₂×C₄⋊C₄	—	2	8	no	—
218	C₂×C₄⋊C₄	—	2	4	no	—
219	C₂×C₄⋊C₄	—	2	8	no	—
220	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
221	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
222	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
223	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
224	C₂×C₂²⋊C₄	—	2	8	no	—
225	C₂×C₂²⋊C₄	—	2	8	no	—
226	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
227	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
228	C₂×C₄²	—	2	8	no	—
229	C₂×C₄²	C₂³×C₃₁	1	8	yes	—
230	#95	C₂³×C₃₁	1	8	yes	—
231	#95	C₂³×C₃₁	1	32	yes	—
232	#95	C₂³×C₃₁	1	32	yes	—
233	C₃₁	C₂×#2503	1	1	yes	characteristic, direct product factor, Sylow
234	C₂⁴	—	2	4	no	—
235	C₂⁴	—	2	4	no	—
236	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
237	C₂⁴	#41×C₃₁	1	8	yes	—
238	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
239	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
240	C₂×Q₈	—	2	8	no	—
241	C₂×Q₈	—	2	16	no	—
242	C₂×Q₈	—	4	16	no	—
243	C₂²×C₄	—	2	4	no	—
244	C₂²×C₄	—	2	32	no	—
245	C₂²×C₄	—	2	16	no	—
246	C₂²×C₄	—	2	4	no	—
247	C₂²×C₄	—	2	4	no	—
248	C₂²×C₄	—	2	16	no	—
249	C₂²×C₄	—	2	8	no	—
250	C₂²×C₄	—	2	8	no	—
251	C₂²×C₄	—	2	8	no	—
252	C₂²×C₄	—	2	32	no	—
253	C₂²×C₄	—	2	16	no	—
254	C₂²×C₄	—	2	8	no	—
255	C₂²×C₄	—	2	8	no	—
256	C₂²×C₄	—	2	8	no	—
257	C₂²×C₄	—	4	32	no	—
258	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
259	C₂²×C₄	C₂×D₄×C₃₁	1	16	yes	—
260	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
261	C₂²×C₄	#41×C₃₁	1	8	yes	—
262	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
263	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
264	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
265	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
266	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
267	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
268	C₄⋊C₄	—	2	16	no	—
269	C₄⋊C₄	—	2	16	no	—
270	C₄⋊C₄	—	2	8	no	—
271	C₄⋊C₄	—	2	16	no	—
272	C₂²⋊C₄	—	2	16	no	—
273	C₂²⋊C₄	—	2	16	no	—
274	C₄²	—	2	16	no	—
275	C₂³	—	2	8	no	—
276	C₂³	—	2	8	no	—
277	C₂³	—	2	32	no	—
278	C₂³	—	2	4	no	—
279	C₂³	—	2	4	no	—
280	C₂³	C₃₁×#124	1	16	yes	—
281	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
282	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
283	C₂³	C₂×#41×C₃₁	1	8	yes	—
284	C₂³	C₂×#41×C₃₁	1	4	yes	—
285	C₂³	C₂×#41×C₃₁	1	4	yes	—
286	C₂³	C₃₁×2₋¹⁺⁴	1	4	yes	—
287	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
288	Q₈	—	4	16	no	—
289	C₂×C₄	—	2	8	no	—
290	C₂×C₄	—	2	4	no	—
291	C₂×C₄	—	2	32	no	—
292	C₂×C₄	—	2	4	no	—
293	C₂×C₄	—	2	4	no	—
294	C₂×C₄	—	2	8	no	—
295	C₂×C₄	—	2	8	no	—
296	C₂×C₄	—	2	8	no	—
297	C₂×C₄	—	2	16	no	—
298	C₂×C₄	—	2	8	no	—
299	C₂×C₄	—	2	8	no	—
300	C₂×C₄	—	2	8	no	—
301	C₂×C₄	—	4	8	no	—
302	C₂×C₄	—	4	32	no	—
303	C₂×C₄	—	4	16	no	—
304	C₂×C₄	—	4	8	no	—
305	C₂×C₄	—	4	16	no	—
306	C₂×C₄	C₃₁×#123	1	16	yes	—
307	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
308	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
309	C₂×C₄	C₂×#41×C₃₁	1	8	yes	—
310	C₂²	—	2	4	no	—
311	C₂²	—	2	4	no	—
312	C₂²	—	2	16	no	—
313	C₂²	—	2	32	no	—
314	C₂²	C₂×C₃₁×#123	1	4	yes	—
315	C₂²	C₂×C₃₁×#124	1	8	yes	—
316	C₂²	C₂×C₃₁×#124	1	4	yes	—
317	C₂²	C₃₁×#536	1	4	yes	—
318	C₂²	C₃₁×#552	1	16	yes	—
319	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
320	C₂²	C₂²×#41×C₃₁	1	2	yes	—
321	C₂²	C₂²×#41×C₃₁	1	2	yes	—
322	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	2	yes	—
323	C₄	—	2	4	no	—
324	C₄	—	4	4	no	—
325	C₄	—	4	8	no	—
326	C₄	—	4	4	no	—
327	C₄	—	4	8	no	—
328	C₄	C₂×C₃₁×#123	1	8	yes	—
329	C₂	—	2	8	no	—
330	C₂	C₃₁×#2503	1	8	yes	direct product factor
331	C₂	C₂²×C₃₁×#123	1	1	yes	characteristic
332	C₂	C₂²×C₃₁×#124	1	1	yes	characteristic
333	C₂	C₂×C₃₁×#536	1	1	yes	characteristic
334	C₂	C₂×C₃₁×#552	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂⁵×C₃₁	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃₁×#2503	C₂	direct (N × H)
4. C₂×C₃₁×#400	C₂	semidirect
5. C₂×C₃₁×#391	C₂	semidirect
6. C₂×C₃₁×#382	C₂	semidirect
23. C₃₁×#400	C₂²	semidirect
24. C₃₁×#391	C₂²	semidirect
25. C₃₁×#382	C₂²	semidirect
107. C₂×#2503	C₃₁	direct (N × H)
145. #2503	C₂×C₃₁	direct (N × H)
146. C₂×#400	C₂×C₃₁	semidirect
147. C₂×#391	C₂×C₃₁	semidirect
148. C₂×#382	C₂×C₃₁	semidirect
184. #400	C₂²×C₃₁	semidirect
185. #391	C₂²×C₃₁	semidirect
186. #382	C₂²×C₃₁	semidirect
193. C₂×C₃₁	#2503	direct (N × H)
233. C₃₁	C₂×#2503	direct (N × H)
330. C₂	C₃₁×#2503	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×C₂²⋊Q₈	2
C₂³×C₄⋊C₄×C₃₁	2
C₃₁×#2503	2
C₂×C₃₁×#400	2
C₂×C₃₁×#391	2
C₂×C₃₁×#382	2
C₂×C₃₁×#381	2
C₂×C₄×C₂²⋊C₄×C₃₁	2
C₂×#2503	31

Subgroups — C2×C31×#2503 #21491532

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#2503 #21491532