Subgroups — C₃₁×#8597 #21465356

Order 7936.

546 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×M₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#1797	C₂	1	2	yes	maximal
3	C₂×C₃₁×#335	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₁×#334	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1277	C₂	1	2	yes	maximal, complemented
6	C₂²×M₁₆×C₃₁	C₄	1	1	yes	characteristic
7	C₂²×M₁₆×C₃₁	C₄	1	1	yes	characteristic
8	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
9	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
10	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
11	C₂×C₃₁×C₂²⋊C₈	—	2	2	no	—
12	C₄×M₁₆×C₃₁	—	2	2	no	—
13	C₄×M₁₆×C₃₁	—	2	2	no	—
14	C₂×C₃₁×#97	C₄	1	1	yes	characteristic
15	C₂×C₃₁×#97	C₄	1	1	yes	characteristic
16	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
18	C₃₁×#336	—	2	2	no	—
19	C₃₁×#335	—	2	2	no	—
20	C₃₁×#334	—	2	2	no	—
21	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₃₁	Q₈	1	1	yes	characteristic
24	C₂×M₁₆×C₃₁	—	2	2	no	—
25	C₂×M₁₆×C₃₁	—	2	2	no	—
26	C₂×M₁₆×C₃₁	—	2	2	no	—
27	C₂×M₁₆×C₃₁	—	2	2	no	—
28	C₂×M₁₆×C₃₁	—	2	2	no	—
29	C₂×M₁₆×C₃₁	C₈	1	4	yes	complemented
30	C₂²×C₈×C₃₁	—	2	2	no	—
31	C₂²×C₈×C₃₁	—	2	2	no	—
32	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₃₁	—	2	1	no	—
37	C₂×C₄²×C₃₁	—	2	1	no	—
38	C₂×C₄²×C₃₁	—	2	1	no	—
39	C₂×C₄²×C₃₁	—	2	1	no	—
40	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₃₁	Q₈	1	1	yes	characteristic
43	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
44	C₃₁×C₄⋊C₈	—	2	2	no	—
45	C₃₁×C₄⋊C₈	—	2	2	no	—
46	C₃₁×C₄⋊C₈	—	2	2	no	—
47	C₃₁×C₄⋊C₈	—	2	2	no	—
48	C₃₁×C₂²⋊C₈	—	4	4	no	—
49	C₃₁×#97	—	2	2	no	—
50	C₃₁×#97	—	2	2	no	—
51	C₄×C₈×C₃₁	—	2	1	no	—
52	C₄×C₈×C₃₁	—	2	1	no	—
53	C₄×C₈×C₃₁	D₄	1	2	yes	—
54	C₄×C₈×C₃₁	D₄	1	2	yes	—
55	C₂⁴×C₃₁	C₄⋊C₄	1	1	yes	characteristic
56	C₂²×C₄×C₃₁	—	2	1	no	—
57	C₂²×C₄×C₃₁	—	2	1	no	—
58	C₂²×C₄×C₃₁	—	2	1	no	—
59	C₂²×C₄×C₃₁	—	2	1	no	—
60	C₂²×C₄×C₃₁	—	2	1	no	—
61	C₂²×C₄×C₃₁	—	2	1	no	—
62	C₂²×C₄×C₃₁	—	2	1	no	—
63	C₂²×C₄×C₃₁	—	2	1	no	—
64	C₂²×C₄×C₃₁	—	2	2	no	—
65	C₂²×C₄×C₃₁	—	2	2	no	—
66	C₂²×C₄×C₃₁	—	4	2	no	—
67	C₂²×C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₃₁	C₂×C₈	1	2	yes	—
71	C₂²×C₄×C₃₁	M₁₆	1	2	yes	—
72	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
75	M₁₆×C₃₁	—	2	8	no	—
76	M₁₆×C₃₁	—	2	8	no	—
77	C₂×C₈×C₃₁	—	2	1	no	—
78	C₂×C₈×C₃₁	—	2	1	no	—
79	C₂×C₈×C₃₁	—	2	1	no	—
80	C₂×C₈×C₃₁	—	2	1	no	—
81	C₂×C₈×C₃₁	—	2	1	no	—
82	C₂×C₈×C₃₁	—	2	1	no	—
83	C₂×C₈×C₃₁	—	4	2	no	—
84	C₂×C₈×C₃₁	—	4	2	no	—
85	C₂×C₈×C₃₁	—	4	2	no	—
86	C₂×C₈×C₃₁	—	4	2	no	—
87	C₂×C₈×C₃₁	—	4	2	no	—
88	C₂×C₈×C₃₁	—	4	2	no	—
89	C₂×C₈×C₃₁	C₂²⋊C₄	1	2	yes	—
90	C₂×C₈×C₃₁	C₂²⋊C₄	1	2	yes	—
91	C₂×C₈×C₃₁	C₂×C₈	1	2	yes	—
92	C₂×C₈×C₃₁	C₂×C₈	1	2	yes	—
93	C₂×C₈×C₃₁	M₁₆	1	2	yes	—
94	C₂×C₈×C₃₁	M₁₆	1	2	yes	—
95	C₄²×C₃₁	—	2	1	no	—
96	C₄²×C₃₁	—	2	1	no	—
97	C₄²×C₃₁	—	2	1	no	—
98	C₄²×C₃₁	—	2	1	no	—
99	C₄²×C₃₁	—	2	1	no	—
100	C₄²×C₃₁	—	2	1	no	—
101	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
102	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
103	C₄²×C₃₁	#41	1	1	yes	characteristic
104	C₄²×C₃₁	#41	1	1	yes	characteristic
105	#8597	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
106	C₂³×C₃₁	—	2	1	no	—
107	C₂³×C₃₁	—	2	1	no	—
108	C₂³×C₃₁	—	2	2	no	—
109	C₂³×C₃₁	—	2	2	no	—
110	C₂³×C₃₁	C₄⋊C₈	1	2	yes	—
111	C₂³×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₄×C₃₁	—	2	1	no	—
113	C₂×C₄×C₃₁	—	2	1	no	—
114	C₂×C₄×C₃₁	—	2	2	no	—
115	C₂×C₄×C₃₁	—	2	2	no	—
116	C₂×C₄×C₃₁	—	2	2	no	—
117	C₂×C₄×C₃₁	—	2	2	no	—
118	C₂×C₄×C₃₁	—	2	2	no	—
119	C₂×C₄×C₃₁	—	2	1	no	—
120	C₂×C₄×C₃₁	—	2	1	no	—
121	C₂×C₄×C₃₁	—	2	2	no	—
122	C₂×C₄×C₃₁	—	2	2	no	—
123	C₂×C₄×C₃₁	—	4	2	no	—
124	C₂×C₄×C₃₁	—	4	2	no	—
125	C₂×C₄×C₃₁	—	4	2	no	—
126	C₂×C₄×C₃₁	—	4	1	no	—
127	C₂×C₄×C₃₁	—	4	1	no	—
128	C₂×C₄×C₃₁	C₄⋊C₈	1	2	yes	—
129	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₃₁	#117	1	1	yes	characteristic
131	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
132	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
133	C₂×C₄×C₃₁	C₂²⋊Q₈	1	1	yes	characteristic
134	C₂×C₄×C₃₁	C₂²⋊Q₈	1	1	yes	characteristic
135	C₂×C₄×C₃₁	C₂²×C₈	1	1	yes	characteristic
136	C₂×C₄×C₃₁	C₂×M₁₆	1	1	yes	characteristic
137	C₂×C₄×C₃₁	C₂×M₁₆	1	1	yes	characteristic
138	C₂×C₄×C₃₁	C₂×M₁₆	1	1	yes	characteristic
139	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
140	C₂×C₄×C₃₁	#137	1	2	yes	—
141	C₈×C₃₁	—	2	2	no	—
142	C₈×C₃₁	—	2	2	no	—
143	C₈×C₃₁	—	2	2	no	—
144	C₈×C₃₁	—	8	2	no	—
145	C₈×C₃₁	—	8	2	no	—
146	C₈×C₃₁	C₂²⋊C₈	1	4	yes	complemented
147	C₂×C₄×M₁₆	C₂×C₃₁	1	1	yes	characteristic
148	#1797	C₂×C₃₁	1	2	yes	—
149	C₂×#335	C₂×C₃₁	1	1	yes	characteristic, complemented
150	C₂×#334	C₂×C₃₁	1	1	yes	characteristic, complemented
151	#1277	C₂×C₃₁	1	2	yes	complemented
152	C₂²×C₃₁	—	2	2	no	—
153	C₂²×C₃₁	—	2	4	no	—
154	C₂²×C₃₁	—	4	1	no	—
155	C₂²×C₃₁	—	4	1	no	—
156	C₂²×C₃₁	—	4	2	no	—
157	C₂²×C₃₁	#380	1	1	yes	characteristic
158	C₂²×C₃₁	C₂×C₄⋊C₈	1	1	yes	characteristic
159	C₂²×C₃₁	#423	1	1	yes	characteristic
160	C₂²×C₃₁	#428	1	2	yes	—
161	C₂²×C₃₁	#430	1	2	yes	—
162	C₄×C₃₁	—	2	2	no	—
163	C₄×C₃₁	—	2	1	no	—
164	C₄×C₃₁	—	2	1	no	—
165	C₄×C₃₁	—	4	1	no	—
166	C₄×C₃₁	—	4	1	no	—
167	C₄×C₃₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
168	C₄×C₃₁	#407	1	1	yes	characteristic
169	C₄×C₃₁	#431	1	1	yes	characteristic
170	C₄×C₃₁	#432	1	1	yes	characteristic
171	C₄×C₃₁	#468	1	2	yes	—
172	C₄×C₃₁	#469	1	1	yes	characteristic
173	C₄×C₃₁	#470	1	1	yes	characteristic
174	C₂²×M₁₆	C₄×C₃₁	1	1	yes	characteristic
175	C₂²×M₁₆	C₄×C₃₁	1	1	yes	characteristic
176	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
177	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
178	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
179	C₂×C₂²⋊C₈	—	2	2	no	—
180	C₄×M₁₆	—	2	2	no	—
181	C₄×M₁₆	—	2	2	no	—
182	C₂×#97	C₄×C₃₁	1	1	yes	characteristic
183	C₂×#97	C₄×C₃₁	1	1	yes	characteristic
184	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
185	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
186	#336	—	2	2	no	—
187	#335	—	2	2	no	—
188	#334	—	2	2	no	—
189	C₂×C₃₁	—	4	2	no	—
190	C₂×C₃₁	#1565	1	2	yes	—
191	C₂×C₃₁	#1569	1	2	yes	—
192	C₂×C₃₁	#1797	1	1	yes	characteristic
193	C₂×C₃₁	#1809	1	1	yes	characteristic
194	C₂×C₃₁	#1811	1	1	yes	characteristic
195	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
196	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
197	C₂³×C₄	Q₈×C₃₁	1	1	yes	characteristic
198	C₂×M₁₆	—	2	2	no	—
199	C₂×M₁₆	—	2	2	no	—
200	C₂×M₁₆	—	2	2	no	—
201	C₂×M₁₆	—	2	2	no	—
202	C₂×M₁₆	—	2	2	no	—
203	C₂×M₁₆	C₈×C₃₁	1	4	yes	complemented
204	C₂²×C₈	—	2	2	no	—
205	C₂²×C₈	—	2	2	no	—
206	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
207	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
208	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
209	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
210	C₂×C₄²	—	2	1	no	—
211	C₂×C₄²	—	2	1	no	—
212	C₂×C₄²	—	2	1	no	—
213	C₂×C₄²	—	2	1	no	—
214	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
215	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
216	C₂×C₄²	Q₈×C₃₁	1	1	yes	characteristic
217	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
218	C₄⋊C₈	—	2	2	no	—
219	C₄⋊C₈	—	2	2	no	—
220	C₄⋊C₈	—	2	2	no	—
221	C₄⋊C₈	—	2	2	no	—
222	C₂²⋊C₈	—	4	4	no	—
223	#97	—	2	2	no	—
224	#97	—	2	2	no	—
225	C₄×C₈	—	2	1	no	—
226	C₄×C₈	—	2	1	no	—
227	C₄×C₈	D₄×C₃₁	1	2	yes	—
228	C₄×C₈	D₄×C₃₁	1	2	yes	—
229	C₃₁	#8597	1	1	yes	characteristic, direct product factor, Sylow
230	C₂⁴	C₄⋊C₄×C₃₁	1	1	yes	characteristic
231	C₂²×C₄	—	2	1	no	—
232	C₂²×C₄	—	2	1	no	—
233	C₂²×C₄	—	2	1	no	—
234	C₂²×C₄	—	2	1	no	—
235	C₂²×C₄	—	2	1	no	—
236	C₂²×C₄	—	2	1	no	—
237	C₂²×C₄	—	2	1	no	—
238	C₂²×C₄	—	2	1	no	—
239	C₂²×C₄	—	2	2	no	—
240	C₂²×C₄	—	2	2	no	—
241	C₂²×C₄	—	4	2	no	—
242	C₂²×C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
243	C₂²×C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
244	C₂²×C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
245	C₂²×C₄	C₂×C₈×C₃₁	1	2	yes	—
246	C₂²×C₄	M₁₆×C₃₁	1	2	yes	—
247	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
248	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
249	C₂²×C₄	C₂×Q₈×C₃₁	1	1	yes	characteristic
250	M₁₆	—	2	8	no	—
251	M₁₆	—	2	8	no	—
252	C₂×C₈	—	2	1	no	—
253	C₂×C₈	—	2	1	no	—
254	C₂×C₈	—	2	1	no	—
255	C₂×C₈	—	2	1	no	—
256	C₂×C₈	—	2	1	no	—
257	C₂×C₈	—	2	1	no	—
258	C₂×C₈	—	4	2	no	—
259	C₂×C₈	—	4	2	no	—
260	C₂×C₈	—	4	2	no	—
261	C₂×C₈	—	4	2	no	—
262	C₂×C₈	—	4	2	no	—
263	C₂×C₈	—	4	2	no	—
264	C₂×C₈	C₂²⋊C₄×C₃₁	1	2	yes	—
265	C₂×C₈	C₂²⋊C₄×C₃₁	1	2	yes	—
266	C₂×C₈	C₂×C₈×C₃₁	1	2	yes	—
267	C₂×C₈	C₂×C₈×C₃₁	1	2	yes	—
268	C₂×C₈	M₁₆×C₃₁	1	2	yes	—
269	C₂×C₈	M₁₆×C₃₁	1	2	yes	—
270	C₄²	—	2	1	no	—
271	C₄²	—	2	1	no	—
272	C₄²	—	2	1	no	—
273	C₄²	—	2	1	no	—
274	C₄²	—	2	1	no	—
275	C₄²	—	2	1	no	—
276	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
277	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
278	C₄²	#41×C₃₁	1	1	yes	characteristic
279	C₄²	#41×C₃₁	1	1	yes	characteristic
280	C₂³	—	2	1	no	—
281	C₂³	—	2	2	no	—
282	C₂³	—	2	2	no	—
283	C₂³	—	2	1	no	—
284	C₂³	C₃₁×C₄⋊C₈	1	2	yes	—
285	C₂³	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
286	C₂×C₄	—	2	1	no	—
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	2	1	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	1	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	4	2	no	—
298	C₂×C₄	—	4	2	no	—
299	C₂×C₄	—	4	2	no	—
300	C₂×C₄	—	4	1	no	—
301	C₂×C₄	—	4	1	no	—
302	C₂×C₄	C₃₁×C₄⋊C₈	1	2	yes	—
303	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
304	C₂×C₄	C₃₁×#117	1	1	yes	characteristic
305	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
306	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
307	C₂×C₄	C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
308	C₂×C₄	C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
309	C₂×C₄	C₂²×C₈×C₃₁	1	1	yes	characteristic
310	C₂×C₄	C₂×M₁₆×C₃₁	1	1	yes	characteristic
311	C₂×C₄	C₂×M₁₆×C₃₁	1	1	yes	characteristic
312	C₂×C₄	C₂×M₁₆×C₃₁	1	1	yes	characteristic
313	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
314	C₂×C₄	C₃₁×#137	1	2	yes	—
315	C₈	—	2	2	no	—
316	C₈	—	2	2	no	—
317	C₈	—	2	2	no	—
318	C₈	—	8	2	no	—
319	C₈	—	8	2	no	—
320	C₈	C₃₁×C₂²⋊C₈	1	4	yes	complemented
321	C₂²	—	2	2	no	—
322	C₂²	—	2	4	no	—
323	C₂²	—	4	1	no	—
324	C₂²	—	4	1	no	—
325	C₂²	—	4	2	no	—
326	C₂²	C₃₁×#380	1	1	yes	characteristic
327	C₂²	C₂×C₃₁×C₄⋊C₈	1	1	yes	characteristic
328	C₂²	C₃₁×#423	1	1	yes	characteristic
329	C₂²	C₃₁×#428	1	2	yes	—
330	C₂²	C₃₁×#430	1	2	yes	—
331	C₄	—	2	2	no	—
332	C₄	—	2	1	no	—
333	C₄	—	2	1	no	—
334	C₄	—	4	1	no	—
335	C₄	—	4	1	no	—
336	C₄	C₂×C₃₁×C₂²⋊C₈	1	1	yes	characteristic
337	C₄	C₃₁×#407	1	1	yes	characteristic
338	C₄	C₃₁×#431	1	1	yes	characteristic
339	C₄	C₃₁×#432	1	1	yes	characteristic
340	C₄	C₃₁×#468	1	2	yes	—
341	C₄	C₃₁×#469	1	1	yes	characteristic
342	C₄	C₃₁×#470	1	1	yes	characteristic
343	C₂	—	4	2	no	—
344	C₂	C₃₁×#1565	1	2	yes	—
345	C₂	C₃₁×#1569	1	2	yes	—
346	C₂	C₃₁×#1797	1	1	yes	characteristic
347	C₂	C₃₁×#1809	1	1	yes	characteristic
348	C₂	C₃₁×#1811	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂×D₄
commutator	C₂×C₄	C₂²×C₈×C₃₁
Frattini, cosocle	C₂×C₄²	C₂³×C₃₁
socle	C₂³×C₃₁	C₂×C₄⋊C₄
prime radical	C₂⁴×C₃₁	C₄⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₁ ◁ C₂²×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₃₁×#335	C₂	semidirect
4. C₂×C₃₁×#334	C₂	semidirect
5. C₃₁×#1277	C₂	semidirect
29. C₂×M₁₆×C₃₁	C₈	semidirect
105. #8597	C₃₁	direct (N × H)
146. C₈×C₃₁	C₂²⋊C₈	semidirect
149. C₂×#335	C₂×C₃₁	semidirect
150. C₂×#334	C₂×C₃₁	semidirect
151. #1277	C₂×C₃₁	semidirect
203. C₂×M₁₆	C₈×C₃₁	semidirect
229. C₃₁	#8597	direct (N × H)
320. C₈	C₃₁×C₂²⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×M₁₆×C₃₁	2
C₃₁×#1797	2
C₂×C₃₁×#335	2
C₂×C₃₁×#334	2
C₃₁×#1277	2
#8597	31

Subgroups — C31×#8597 #21465356

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#8597 #21465356