Subgroups — C₃₁×#18054 #21474813

Order 7936.

726 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2974	C₂	1	2	yes	maximal, complemented
2	C₂×C₄×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#1589	C₂	1	2	yes	maximal, complemented
4	C₃₁×#1586	C₂	1	4	yes	maximal, complemented
5	C₈×D₈×C₃₁	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1568	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1490	C₂	1	2	yes	maximal, complemented
8	C₈×M₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×D₈×C₃₁	C₄	1	1	yes	characteristic
10	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
11	C₄×D₈×C₃₁	C₄	1	2	yes	—
12	C₄×D₈×C₃₁	C₄	1	1	yes	characteristic
13	C₄×D₈×C₃₁	C₄	1	1	yes	characteristic
14	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
15	C₄×D₈×C₃₁	C₂²	1	2	yes	—
16	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
17	C₃₁×#436	C₂²	1	4	yes	complemented
18	C₃₁×#435	—	2	4	no	—
19	C₈×D₄×C₃₁	C₂²	1	4	yes	complemented
20	C₃₁×#432	C₂²	1	2	yes	—
21	C₃₁×#431	C₂²	1	1	yes	characteristic
22	C₂×C₃₁×#107	C₄	1	1	yes	characteristic
23	C₂×C₃₁×#102	C₄	1	2	yes	—
24	C₃₁×#407	—	2	2	no	—
25	C₂×C₃₁×C₂²⋊C₈	—	2	2	no	—
26	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
28	C₃₁×#335	C₂²	1	2	yes	complemented
29	C₃₁×#334	C₂²	1	2	yes	complemented
30	C₃₁×D₄⋊C₈	C₂²	1	4	yes	complemented
31	C₃₁×D₄⋊C₈	C₂²	1	4	yes	complemented
32	C₃₁×#322	C₂²	1	2	yes	complemented
33	C₈²×C₃₁	C₂²	1	2	yes	complemented
34	C₂²×D₄×C₃₁	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₃₁	—	2	2	no	—
36	C₂×D₈×C₃₁	—	2	4	no	—
37	C₂×D₈×C₃₁	C₂×C₄	1	2	yes	—
38	C₂×D₈×C₃₁	C₂×C₄	1	1	yes	characteristic
39	C₂×D₈×C₃₁	C₂×C₄	1	1	yes	characteristic
40	C₂×M₁₆×C₃₁	—	2	1	no	—
41	C₂×M₁₆×C₃₁	—	2	4	no	—
42	C₂²×C₈×C₃₁	—	2	4	no	—
43	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
45	C₄×D₄×C₃₁	—	2	2	no	—
46	C₄×D₄×C₃₁	—	2	2	no	—
47	C₄×D₄×C₃₁	C₂×C₄	1	2	yes	—
48	C₄×D₄×C₃₁	C₂×C₄	1	2	yes	—
49	C₄×D₄×C₃₁	C₂³	1	2	yes	—
50	C₄×D₄×C₃₁	C₂³	1	2	yes	—
51	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
52	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
53	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
54	C₃₁×#107	C₂×C₄	1	2	yes	—
55	C₃₁×#107	C₂×C₄	1	1	yes	characteristic
56	C₃₁×#107	C₂×C₄	1	1	yes	characteristic
57	C₃₁×C₄⋊C₈	D₄	1	2	yes	—
58	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
59	C₃₁×#102	C₂×C₄	1	2	yes	—
60	C₃₁×#102	C₂×C₄	1	2	yes	—
61	C₃₁×#102	C₂×C₄	1	2	yes	—
62	C₃₁×#102	C₂×C₄	1	2	yes	—
63	C₃₁×C₂²⋊C₈	—	2	2	no	—
64	C₃₁×C₂²⋊C₈	—	2	4	no	—
65	C₃₁×C₂²⋊C₈	—	2	4	no	—
66	C₃₁×C₂²⋊C₈	D₄	1	1	yes	characteristic
67	C₃₁×C₂²⋊C₈	D₄	1	1	yes	characteristic
68	C₃₁×#97	—	2	2	no	—
69	C₃₁×#97	—	2	1	no	—
70	C₄×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
71	C₄×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
72	C₄×C₈×C₃₁	C₂³	1	2	yes	—
73	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
74	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
75	C₄×C₈×C₃₁	C₂³	1	2	yes	—
76	C₂⁴×C₃₁	—	2	2	no	—
77	C₂×D₄×C₃₁	—	2	4	no	—
78	C₂×D₄×C₃₁	—	2	2	no	—
79	C₂×D₄×C₃₁	—	4	2	no	—
80	C₂×D₄×C₃₁	C₂²×C₄	1	2	yes	—
81	C₂×D₄×C₃₁	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₃₁	—	2	2	no	—
83	C₂²×C₄×C₃₁	—	2	2	no	—
84	C₂²×C₄×C₃₁	—	2	2	no	—
85	C₂²×C₄×C₃₁	—	2	2	no	—
86	C₂²×C₄×C₃₁	—	2	2	no	—
87	C₂²×C₄×C₃₁	—	8	4	no	—
88	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
91	D₈×C₃₁	—	2	4	no	—
92	D₈×C₃₁	—	2	2	no	—
93	D₈×C₃₁	M₁₆	1	4	yes	complemented
94	M₁₆×C₃₁	—	2	4	no	—
95	M₁₆×C₃₁	—	8	4	no	—
96	C₂×C₈×C₃₁	—	2	2	no	—
97	C₂×C₈×C₃₁	—	2	2	no	—
98	C₂×C₈×C₃₁	—	2	4	no	—
99	C₂×C₈×C₃₁	—	4	1	no	—
100	C₂×C₈×C₃₁	—	8	4	no	—
101	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
106	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
107	C₄⋊C₄×C₃₁	—	2	2	no	—
108	C₄⋊C₄×C₃₁	C₂²×C₄	1	2	yes	—
109	C₄⋊C₄×C₃₁	C₂²×C₄	1	2	yes	—
110	C₂²⋊C₄×C₃₁	—	2	2	no	—
111	C₂²⋊C₄×C₃₁	—	2	2	no	—
112	C₂²⋊C₄×C₃₁	—	2	2	no	—
113	C₂²⋊C₄×C₃₁	—	2	2	no	—
114	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₃₁	#41	1	1	yes	characteristic
117	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
118	#18054	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₂³×C₃₁	—	2	2	no	—
120	C₂³×C₃₁	—	2	2	no	—
121	C₂³×C₃₁	—	4	4	no	—
122	C₂³×C₃₁	—	4	4	no	—
123	C₂³×C₃₁	—	8	2	no	—
124	C₂³×C₃₁	C₄×D₄	1	1	yes	characteristic
125	D₄×C₃₁	—	2	2	no	—
126	D₄×C₃₁	—	2	2	no	—
127	D₄×C₃₁	—	2	2	no	—
128	D₄×C₃₁	—	4	4	no	—
129	D₄×C₃₁	C₂×M₁₆	1	4	yes	—
130	C₂×C₄×C₃₁	—	2	2	no	—
131	C₂×C₄×C₃₁	—	2	1	no	—
132	C₂×C₄×C₃₁	—	2	1	no	—
133	C₂×C₄×C₃₁	—	2	2	no	—
134	C₂×C₄×C₃₁	—	2	2	no	—
135	C₂×C₄×C₃₁	—	2	2	no	—
136	C₂×C₄×C₃₁	—	4	4	no	—
137	C₂×C₄×C₃₁	—	4	4	no	—
138	C₂×C₄×C₃₁	—	8	2	no	—
139	C₂×C₄×C₃₁	—	8	2	no	—
140	C₂×C₄×C₃₁	—	8	2	no	—
141	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
142	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
144	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
145	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
146	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
147	C₈×C₃₁	—	2	4	no	—
148	C₈×C₃₁	—	2	1	no	—
149	C₈×C₃₁	—	2	1	no	—
150	C₈×C₃₁	—	2	1	no	—
151	C₈×C₃₁	—	2	2	no	—
152	C₈×C₃₁	—	2	2	no	—
153	C₈×C₃₁	—	4	4	no	—
154	C₈×C₃₁	C₂×M₁₆	1	2	yes	—
155	#2974	C₂×C₃₁	1	2	yes	complemented
156	C₂×C₄×D₈	C₂×C₃₁	1	1	yes	characteristic
157	#1589	C₂×C₃₁	1	2	yes	complemented
158	#1586	C₂×C₃₁	1	4	yes	complemented
159	C₈×D₈	C₂×C₃₁	1	2	yes	complemented
160	#1568	C₂×C₃₁	1	1	yes	characteristic, complemented
161	#1490	C₂×C₃₁	1	2	yes	complemented
162	C₈×M₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
163	C₂²×C₃₁	—	2	1	no	—
164	C₂²×C₃₁	—	2	1	no	—
165	C₂²×C₃₁	—	2	4	no	—
166	C₂²×C₃₁	—	4	2	no	—
167	C₂²×C₃₁	—	4	2	no	—
168	C₂²×C₃₁	—	4	2	no	—
169	C₂²×C₃₁	—	4	2	no	—
170	C₂²×C₃₁	—	4	2	no	—
171	C₂²×C₃₁	—	8	8	no	—
172	C₂²×C₃₁	#443	1	2	yes	—
173	C₂²×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
174	C₄×C₃₁	—	2	1	no	—
175	C₄×C₃₁	—	2	1	no	—
176	C₄×C₃₁	—	2	1	no	—
177	C₄×C₃₁	—	2	1	no	—
178	C₄×C₃₁	—	4	2	no	—
179	C₄×C₃₁	—	4	2	no	—
180	C₄×C₃₁	C₂²×M₁₆	1	1	yes	characteristic
181	C₄×C₃₁	#568	1	1	yes	characteristic
182	C₄×C₃₁	#576	1	2	yes	—
183	C₂²×D₈	C₄×C₃₁	1	1	yes	characteristic
184	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
185	C₄×D₈	C₄×C₃₁	1	2	yes	—
186	C₄×D₈	C₄×C₃₁	1	1	yes	characteristic
187	C₄×D₈	C₄×C₃₁	1	1	yes	characteristic
188	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
189	C₄×D₈	C₂²×C₃₁	1	2	yes	—
190	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
191	#436	C₂²×C₃₁	1	4	yes	complemented
192	#435	—	2	4	no	—
193	C₈×D₄	C₂²×C₃₁	1	4	yes	complemented
194	#432	C₂²×C₃₁	1	2	yes	—
195	#431	C₂²×C₃₁	1	1	yes	characteristic
196	C₂×#107	C₄×C₃₁	1	1	yes	characteristic
197	C₂×#102	C₄×C₃₁	1	2	yes	—
198	#407	—	2	2	no	—
199	C₂×C₂²⋊C₈	—	2	2	no	—
200	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
201	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
202	#335	C₂²×C₃₁	1	2	yes	complemented
203	#334	C₂²×C₃₁	1	2	yes	complemented
204	D₄⋊C₈	C₂²×C₃₁	1	4	yes	complemented
205	D₄⋊C₈	C₂²×C₃₁	1	4	yes	complemented
206	#322	C₂²×C₃₁	1	2	yes	complemented
207	C₈²	C₂²×C₃₁	1	2	yes	complemented
208	C₂×C₃₁	—	2	2	no	—
209	C₂×C₃₁	—	4	4	no	—
210	C₂×C₃₁	—	8	2	no	—
211	C₂×C₃₁	D₄×M₁₆	1	1	yes	characteristic
212	C₂×C₃₁	#2948	1	1	yes	characteristic
213	C₂×C₃₁	C₂×#443	1	1	yes	characteristic
214	C₂²×D₄	C₂×C₄×C₃₁	1	2	yes	—
215	C₂³×C₄	—	2	2	no	—
216	C₂×D₈	—	2	4	no	—
217	C₂×D₈	C₂×C₄×C₃₁	1	2	yes	—
218	C₂×D₈	C₂×C₄×C₃₁	1	1	yes	characteristic
219	C₂×D₈	C₂×C₄×C₃₁	1	1	yes	characteristic
220	C₂×M₁₆	—	2	1	no	—
221	C₂×M₁₆	—	2	4	no	—
222	C₂²×C₈	—	2	4	no	—
223	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
224	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
225	C₄×D₄	—	2	2	no	—
226	C₄×D₄	—	2	2	no	—
227	C₄×D₄	C₂×C₄×C₃₁	1	2	yes	—
228	C₄×D₄	C₂×C₄×C₃₁	1	2	yes	—
229	C₄×D₄	C₂³×C₃₁	1	2	yes	—
230	C₄×D₄	C₂³×C₃₁	1	2	yes	—
231	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
232	C₂×C₂²⋊C₄	—	2	2	no	—
233	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
234	#107	C₂×C₄×C₃₁	1	2	yes	—
235	#107	C₂×C₄×C₃₁	1	1	yes	characteristic
236	#107	C₂×C₄×C₃₁	1	1	yes	characteristic
237	C₄⋊C₈	D₄×C₃₁	1	2	yes	—
238	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
239	#102	C₂×C₄×C₃₁	1	2	yes	—
240	#102	C₂×C₄×C₃₁	1	2	yes	—
241	#102	C₂×C₄×C₃₁	1	2	yes	—
242	#102	C₂×C₄×C₃₁	1	2	yes	—
243	C₂²⋊C₈	—	2	2	no	—
244	C₂²⋊C₈	—	2	4	no	—
245	C₂²⋊C₈	—	2	4	no	—
246	C₂²⋊C₈	D₄×C₃₁	1	1	yes	characteristic
247	C₂²⋊C₈	D₄×C₃₁	1	1	yes	characteristic
248	#97	—	2	2	no	—
249	#97	—	2	1	no	—
250	C₄×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
251	C₄×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
252	C₄×C₈	C₂³×C₃₁	1	2	yes	—
253	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
254	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
255	C₄×C₈	C₂³×C₃₁	1	2	yes	—
256	C₃₁	#18054	1	1	yes	characteristic, direct product factor, Sylow
257	C₂⁴	—	2	2	no	—
258	C₂×D₄	—	2	4	no	—
259	C₂×D₄	—	2	2	no	—
260	C₂×D₄	—	4	2	no	—
261	C₂×D₄	C₂²×C₄×C₃₁	1	2	yes	—
262	C₂×D₄	C₂²×C₄×C₃₁	1	2	yes	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	8	4	no	—
269	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
270	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
271	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
272	D₈	—	2	4	no	—
273	D₈	—	2	2	no	—
274	D₈	M₁₆×C₃₁	1	4	yes	complemented
275	M₁₆	—	2	4	no	—
276	M₁₆	—	8	4	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	4	no	—
280	C₂×C₈	—	4	1	no	—
281	C₂×C₈	—	8	4	no	—
282	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
283	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
284	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
285	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
286	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
287	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	C₂²×C₄×C₃₁	1	2	yes	—
290	C₄⋊C₄	C₂²×C₄×C₃₁	1	2	yes	—
291	C₂²⋊C₄	—	2	2	no	—
292	C₂²⋊C₄	—	2	2	no	—
293	C₂²⋊C₄	—	2	2	no	—
294	C₂²⋊C₄	—	2	2	no	—
295	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
296	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
297	C₄²	#41×C₃₁	1	1	yes	characteristic
298	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
299	C₂³	—	2	2	no	—
300	C₂³	—	2	2	no	—
301	C₂³	—	4	4	no	—
302	C₂³	—	4	4	no	—
303	C₂³	—	8	2	no	—
304	C₂³	C₄×D₄×C₃₁	1	1	yes	characteristic
305	D₄	—	2	2	no	—
306	D₄	—	2	2	no	—
307	D₄	—	2	2	no	—
308	D₄	—	4	4	no	—
309	D₄	C₂×M₁₆×C₃₁	1	4	yes	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	4	4	no	—
317	C₂×C₄	—	4	4	no	—
318	C₂×C₄	—	8	2	no	—
319	C₂×C₄	—	8	2	no	—
320	C₂×C₄	—	8	2	no	—
321	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
322	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
323	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
324	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
325	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
326	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
327	C₈	—	2	4	no	—
328	C₈	—	2	1	no	—
329	C₈	—	2	1	no	—
330	C₈	—	2	1	no	—
331	C₈	—	2	2	no	—
332	C₈	—	2	2	no	—
333	C₈	—	4	4	no	—
334	C₈	C₂×M₁₆×C₃₁	1	2	yes	—
335	C₂²	—	2	1	no	—
336	C₂²	—	2	1	no	—
337	C₂²	—	2	4	no	—
338	C₂²	—	4	2	no	—
339	C₂²	—	4	2	no	—
340	C₂²	—	4	2	no	—
341	C₂²	—	4	2	no	—
342	C₂²	—	4	2	no	—
343	C₂²	—	8	8	no	—
344	C₂²	C₃₁×#443	1	2	yes	—
345	C₂²	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
346	C₄	—	2	1	no	—
347	C₄	—	2	1	no	—
348	C₄	—	2	1	no	—
349	C₄	—	2	1	no	—
350	C₄	—	4	2	no	—
351	C₄	—	4	2	no	—
352	C₄	C₂²×M₁₆×C₃₁	1	1	yes	characteristic
353	C₄	C₃₁×#568	1	1	yes	characteristic
354	C₄	C₃₁×#576	1	2	yes	—
355	C₂	—	2	2	no	—
356	C₂	—	4	4	no	—
357	C₂	—	8	2	no	—
358	C₂	D₄×M₁₆×C₃₁	1	1	yes	characteristic
359	C₂	C₃₁×#2948	1	1	yes	characteristic
360	C₂	C₂×C₃₁×#443	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₃₁
Frattini, cosocle	C₄²	C₂⁴×C₃₁
socle	C₂²×C₃₁	C₂×C₄×D₄
prime radical	C₂²×D₈×C₃₁	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ C₃₁×#431 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#2974	C₂	semidirect
3. C₃₁×#1589	C₂	semidirect
4. C₃₁×#1586	C₂	semidirect
5. C₈×D₈×C₃₁	C₂	semidirect
6. C₃₁×#1568	C₂	semidirect
7. C₃₁×#1490	C₂	semidirect
8. C₈×M₁₆×C₃₁	C₂	semidirect
17. C₃₁×#436	C₂²	semidirect
19. C₈×D₄×C₃₁	C₂²	semidirect
28. C₃₁×#335	C₂²	semidirect
29. C₃₁×#334	C₂²	semidirect
30. C₃₁×D₄⋊C₈	C₂²	semidirect
31. C₃₁×D₄⋊C₈	C₂²	semidirect
32. C₃₁×#322	C₂²	semidirect
33. C₈²×C₃₁	C₂²	semidirect
93. D₈×C₃₁	M₁₆	semidirect
118. #18054	C₃₁	direct (N × H)
155. #2974	C₂×C₃₁	semidirect
157. #1589	C₂×C₃₁	semidirect
158. #1586	C₂×C₃₁	semidirect
159. C₈×D₈	C₂×C₃₁	semidirect
160. #1568	C₂×C₃₁	semidirect
161. #1490	C₂×C₃₁	semidirect
162. C₈×M₁₆	C₂×C₃₁	semidirect
191. #436	C₂²×C₃₁	semidirect
193. C₈×D₄	C₂²×C₃₁	semidirect
202. #335	C₂²×C₃₁	semidirect
203. #334	C₂²×C₃₁	semidirect
204. D₄⋊C₈	C₂²×C₃₁	semidirect
205. D₄⋊C₈	C₂²×C₃₁	semidirect
206. #322	C₂²×C₃₁	semidirect
207. C₈²	C₂²×C₃₁	semidirect
256. C₃₁	#18054	direct (N × H)
274. D₈	M₁₆×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#2974	2
C₂×C₄×D₈×C₃₁	2
C₃₁×#1589	2
C₃₁×#1586	2
C₈×D₈×C₃₁	2
C₃₁×#1568	2
C₃₁×#1490	2
C₈×M₁₆×C₃₁	2
#18054	31

Subgroups — C31×#18054 #21474813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#18054 #21474813