Subgroups — C₃₁×#19267 #21476026

Order 7936.

870 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#493	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3038	C₂	1	2	yes	maximal, complemented
3	C₈×#41×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#1668	C₂	1	4	yes	maximal, complemented
5	C₃₁×#1667	C₂	1	4	yes	maximal, complemented
6	C₃₁×#1567	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1545	C₂	1	2	yes	maximal, complemented
8	C₂×C₃₁×AGL(1,ℤ/8)	—	2	2	no	—
9	C₂²×D₈×C₃₁	—	2	2	no	—
10	C₂×C₃₁×#127	C₂²	1	2	yes	—
11	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
12	C₃₁×#493	—	2	1	no	—
13	C₃₁×#493	—	2	1	no	—
14	C₃₁×#493	C₂²	1	4	yes	—
15	C₃₁×#460	—	2	2	no	—
16	C₃₁×#460	C₂²	1	4	yes	complemented
17	C₃₁×#459	—	2	2	no	—
18	C₃₁×#459	C₂²	1	4	yes	complemented
19	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
20	C₈×D₄×C₃₁	—	2	2	no	—
21	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
22	C₃₁×#431	—	2	1	no	—
23	C₃₁×#431	C₂²	1	1	yes	characteristic
24	C₃₁×#423	C₂²	1	2	yes	—
25	C₃₁×#418	—	2	2	no	—
26	C₂×C₄×C₈×C₃₁	—	2	1	no	—
27	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
28	C₃₁×#335	C₂²	1	4	yes	complemented
29	C₃₁×#331	C₂²	1	8	yes	complemented
30	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
31	C₂²×D₄×C₃₁	—	2	2	no	—
32	C₂²×D₄×C₃₁	—	2	2	no	—
33	C₂²×D₄×C₃₁	—	2	2	no	—
34	C₃₁×AGL(1,ℤ/8)	—	4	8	no	—
35	C₂×SD₁₆×C₃₁	—	2	4	no	—
36	C₂×D₈×C₃₁	—	2	4	no	—
37	C₂×D₈×C₃₁	—	2	4	no	—
38	C₂×D₈×C₃₁	—	2	4	no	—
39	C₂×D₈×C₃₁	—	4	8	no	—
40	C₂×M₁₆×C₃₁	—	2	2	no	—
41	C₂²×C₈×C₃₁	—	2	2	no	—
42	C₂²×C₈×C₃₁	D₄	1	2	yes	—
43	C₃₁×#127	—	2	2	no	—
44	C₃₁×#127	—	2	2	no	—
45	C₃₁×#127	—	2	2	no	—
46	C₃₁×#127	C₂³	1	4	yes	—
47	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
48	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
49	C₄×D₄×C₃₁	—	2	1	no	—
50	C₄×D₄×C₃₁	—	2	1	no	—
51	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
52	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
53	C₃₁×#117	—	2	1	no	—
54	C₃₁×#117	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₃₁	—	2	1	no	—
56	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
57	C₃₁×C₄⋊C₈	—	2	2	no	—
58	C₃₁×C₄⋊C₈	—	2	2	no	—
59	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
60	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
61	C₃₁×#102	—	2	4	no	—
62	C₃₁×#102	—	2	4	no	—
63	C₃₁×C₂²⋊C₈	—	2	1	no	—
64	C₃₁×C₂²⋊C₈	—	2	2	no	—
65	C₄×C₈×C₃₁	—	2	2	no	—
66	C₄×C₈×C₃₁	—	2	1	no	—
67	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
68	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
69	C₄×C₈×C₃₁	C₂³	1	2	yes	—
70	C₂⁴×C₃₁	—	4	2	no	—
71	#41×C₃₁	—	2	2	no	—
72	#41×C₃₁	D₈	1	4	yes	complemented
73	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
74	C₂×D₄×C₃₁	—	2	1	no	—
75	C₂×D₄×C₃₁	—	2	4	no	—
76	C₂×D₄×C₃₁	—	2	4	no	—
77	C₂×D₄×C₃₁	—	2	4	no	—
78	C₂×D₄×C₃₁	—	4	8	no	—
79	C₂×D₄×C₃₁	—	4	2	no	—
80	C₂×D₄×C₃₁	—	4	2	no	—
81	C₂×D₄×C₃₁	—	4	2	no	—
82	C₂×D₄×C₃₁	—	4	4	no	—
83	C₂×D₄×C₃₁	—	4	4	no	—
84	C₂×D₄×C₃₁	—	8	4	no	—
85	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₃₁	—	2	1	no	—
87	C₂²×C₄×C₃₁	—	2	1	no	—
88	C₂²×C₄×C₃₁	—	2	1	no	—
89	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
92	SD₁₆×C₃₁	—	4	8	no	—
93	D₈×C₃₁	—	4	8	no	—
94	D₈×C₃₁	—	4	8	no	—
95	D₈×C₃₁	—	4	8	no	—
96	M₁₆×C₃₁	—	4	4	no	—
97	C₂×C₈×C₃₁	—	2	4	no	—
98	C₂×C₈×C₃₁	—	2	2	no	—
99	C₂×C₈×C₃₁	—	2	4	no	—
100	C₂×C₈×C₃₁	—	4	4	no	—
101	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
102	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
103	C₄⋊C₄×C₃₁	—	2	1	no	—
104	C₄⋊C₄×C₃₁	—	2	1	no	—
105	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
106	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
107	C₂²⋊C₄×C₃₁	—	2	1	no	—
108	C₂²⋊C₄×C₃₁	—	2	1	no	—
109	C₂²⋊C₄×C₃₁	—	2	1	no	—
110	C₄²×C₃₁	—	2	1	no	—
111	C₄²×C₃₁	—	2	1	no	—
112	C₄²×C₃₁	—	2	1	no	—
113	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
115	C₄²×C₃₁	#41	1	1	yes	characteristic
116	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
117	#19267	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₂³×C₃₁	—	2	1	no	—
119	C₂³×C₃₁	—	4	4	no	—
120	C₂³×C₃₁	—	8	4	no	—
121	C₂³×C₃₁	—	8	4	no	—
122	C₂³×C₃₁	—	8	4	no	—
123	C₂³×C₃₁	#121	1	1	yes	characteristic
124	Q₈×C₃₁	—	2	1	no	—
125	Q₈×C₃₁	C₂×D₈	1	2	yes	complemented
126	D₄×C₃₁	—	2	4	no	—
127	D₄×C₃₁	—	2	1	no	—
128	D₄×C₃₁	—	4	4	no	—
129	D₄×C₃₁	—	4	4	no	—
130	D₄×C₃₁	—	4	8	no	—
131	D₄×C₃₁	—	8	4	no	—
132	D₄×C₃₁	—	8	4	no	—
133	D₄×C₃₁	—	8	4	no	—
134	D₄×C₃₁	—	8	4	no	—
135	D₄×C₃₁	C₂×D₈	1	2	yes	complemented
136	C₂×C₄×C₃₁	—	2	1	no	—
137	C₂×C₄×C₃₁	—	2	2	no	—
138	C₂×C₄×C₃₁	—	2	4	no	—
139	C₂×C₄×C₃₁	—	2	2	no	—
140	C₂×C₄×C₃₁	—	2	1	no	—
141	C₂×C₄×C₃₁	—	2	1	no	—
142	C₂×C₄×C₃₁	—	4	2	no	—
143	C₂×C₄×C₃₁	—	4	2	no	—
144	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
145	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
146	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
147	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
148	C₂×C₄×C₃₁	#135	1	2	yes	—
149	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
150	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
152	C₈×C₃₁	—	2	2	no	—
153	C₈×C₃₁	—	4	4	no	—
154	C₈×C₃₁	—	4	2	no	—
155	C₈×C₃₁	AGL(1,ℤ/8)	1	4	yes	complemented
156	C₂×#493	C₂×C₃₁	1	1	yes	characteristic, complemented
157	#3038	C₂×C₃₁	1	2	yes	complemented
158	C₈×#41	C₂×C₃₁	1	1	yes	characteristic, complemented
159	#1668	C₂×C₃₁	1	4	yes	complemented
160	#1667	C₂×C₃₁	1	4	yes	complemented
161	#1567	C₂×C₃₁	1	1	yes	characteristic, complemented
162	#1545	C₂×C₃₁	1	2	yes	complemented
163	C₂²×C₃₁	—	2	1	no	—
164	C₂²×C₃₁	—	2	1	no	—
165	C₂²×C₃₁	—	2	2	no	—
166	C₂²×C₃₁	—	4	1	no	—
167	C₂²×C₃₁	—	4	1	no	—
168	C₂²×C₃₁	—	8	4	no	—
169	C₂²×C₃₁	—	8	4	no	—
170	C₂²×C₃₁	—	8	4	no	—
171	C₂²×C₃₁	—	16	8	no	—
172	C₂²×C₃₁	#466	1	2	yes	—
173	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
174	C₄×C₃₁	—	2	1	no	—
175	C₄×C₃₁	—	2	2	no	—
176	C₄×C₃₁	—	2	1	no	—
177	C₄×C₃₁	—	4	1	no	—
178	C₄×C₃₁	—	4	1	no	—
179	C₄×C₃₁	#466	1	2	yes	—
180	C₄×C₃₁	#472	1	2	yes	—
181	C₄×C₃₁	C₂²×D₈	1	1	yes	characteristic
182	C₄×C₃₁	C₂×#135	1	1	yes	characteristic
183	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
184	C₂×AGL(1,ℤ/8)	—	2	2	no	—
185	C₂²×D₈	—	2	2	no	—
186	C₂×#127	C₂²×C₃₁	1	2	yes	—
187	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
188	#493	—	2	1	no	—
189	#493	—	2	1	no	—
190	#493	C₂²×C₃₁	1	4	yes	—
191	#460	—	2	2	no	—
192	#460	C₂²×C₃₁	1	4	yes	complemented
193	#459	—	2	2	no	—
194	#459	C₂²×C₃₁	1	4	yes	complemented
195	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
196	C₈×D₄	—	2	2	no	—
197	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
198	#431	—	2	1	no	—
199	#431	C₂²×C₃₁	1	1	yes	characteristic
200	#423	C₂²×C₃₁	1	2	yes	—
201	#418	—	2	2	no	—
202	C₂×C₄×C₈	—	2	1	no	—
203	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
204	#335	C₂²×C₃₁	1	4	yes	complemented
205	#331	C₂²×C₃₁	1	8	yes	complemented
206	C₂×C₃₁	—	2	2	no	—
207	C₂×C₃₁	—	4	2	no	—
208	C₂×C₃₁	—	16	4	no	—
209	C₂×C₃₁	#3038	1	1	yes	characteristic
210	C₂×C₃₁	C₂×#466	1	1	yes	characteristic
211	C₂×C₃₁	C₂×#472	1	1	yes	characteristic
212	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
213	C₂²×D₄	—	2	2	no	—
214	C₂²×D₄	—	2	2	no	—
215	C₂²×D₄	—	2	2	no	—
216	AGL(1,ℤ/8)	—	4	8	no	—
217	C₂×SD₁₆	—	2	4	no	—
218	C₂×D₈	—	2	4	no	—
219	C₂×D₈	—	2	4	no	—
220	C₂×D₈	—	2	4	no	—
221	C₂×D₈	—	4	8	no	—
222	C₂×M₁₆	—	2	2	no	—
223	C₂²×C₈	—	2	2	no	—
224	C₂²×C₈	D₄×C₃₁	1	2	yes	—
225	#127	—	2	2	no	—
226	#127	—	2	2	no	—
227	#127	—	2	2	no	—
228	#127	C₂³×C₃₁	1	4	yes	—
229	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
230	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
231	C₄×D₄	—	2	1	no	—
232	C₄×D₄	—	2	1	no	—
233	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
234	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
235	#117	—	2	1	no	—
236	#117	D₄×C₃₁	1	1	yes	characteristic
237	C₂×C₄²	—	2	1	no	—
238	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
239	C₄⋊C₈	—	2	2	no	—
240	C₄⋊C₈	—	2	2	no	—
241	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
242	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
243	#102	—	2	4	no	—
244	#102	—	2	4	no	—
245	C₂²⋊C₈	—	2	1	no	—
246	C₂²⋊C₈	—	2	2	no	—
247	C₄×C₈	—	2	2	no	—
248	C₄×C₈	—	2	1	no	—
249	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
250	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
251	C₄×C₈	C₂³×C₃₁	1	2	yes	—
252	C₃₁	#19267	1	1	yes	characteristic, direct product factor, Sylow
253	C₂⁴	—	4	2	no	—
254	#41	—	2	2	no	—
255	#41	D₈×C₃₁	1	4	yes	complemented
256	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
257	C₂×D₄	—	2	1	no	—
258	C₂×D₄	—	2	4	no	—
259	C₂×D₄	—	2	4	no	—
260	C₂×D₄	—	2	4	no	—
261	C₂×D₄	—	4	8	no	—
262	C₂×D₄	—	4	2	no	—
263	C₂×D₄	—	4	2	no	—
264	C₂×D₄	—	4	2	no	—
265	C₂×D₄	—	4	4	no	—
266	C₂×D₄	—	4	4	no	—
267	C₂×D₄	—	8	4	no	—
268	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
269	C₂²×C₄	—	2	1	no	—
270	C₂²×C₄	—	2	1	no	—
271	C₂²×C₄	—	2	1	no	—
272	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
274	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
275	SD₁₆	—	4	8	no	—
276	D₈	—	4	8	no	—
277	D₈	—	4	8	no	—
278	D₈	—	4	8	no	—
279	M₁₆	—	4	4	no	—
280	C₂×C₈	—	2	4	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	4	no	—
283	C₂×C₈	—	4	4	no	—
284	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
285	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
286	C₄⋊C₄	—	2	1	no	—
287	C₄⋊C₄	—	2	1	no	—
288	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
289	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
290	C₂²⋊C₄	—	2	1	no	—
291	C₂²⋊C₄	—	2	1	no	—
292	C₂²⋊C₄	—	2	1	no	—
293	C₄²	—	2	1	no	—
294	C₄²	—	2	1	no	—
295	C₄²	—	2	1	no	—
296	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
297	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
298	C₄²	#41×C₃₁	1	1	yes	characteristic
299	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
300	C₂³	—	2	1	no	—
301	C₂³	—	4	4	no	—
302	C₂³	—	8	4	no	—
303	C₂³	—	8	4	no	—
304	C₂³	—	8	4	no	—
305	C₂³	C₃₁×#121	1	1	yes	characteristic
306	Q₈	—	2	1	no	—
307	Q₈	C₂×D₈×C₃₁	1	2	yes	complemented
308	D₄	—	2	4	no	—
309	D₄	—	2	1	no	—
310	D₄	—	4	4	no	—
311	D₄	—	4	4	no	—
312	D₄	—	4	8	no	—
313	D₄	—	8	4	no	—
314	D₄	—	8	4	no	—
315	D₄	—	8	4	no	—
316	D₄	—	8	4	no	—
317	D₄	C₂×D₈×C₃₁	1	2	yes	complemented
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
327	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
328	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
329	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
330	C₂×C₄	C₃₁×#135	1	2	yes	—
331	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
332	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
333	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
334	C₈	—	2	2	no	—
335	C₈	—	4	4	no	—
336	C₈	—	4	2	no	—
337	C₈	C₃₁×AGL(1,ℤ/8)	1	4	yes	complemented
338	C₂²	—	2	1	no	—
339	C₂²	—	2	1	no	—
340	C₂²	—	2	2	no	—
341	C₂²	—	4	1	no	—
342	C₂²	—	4	1	no	—
343	C₂²	—	8	4	no	—
344	C₂²	—	8	4	no	—
345	C₂²	—	8	4	no	—
346	C₂²	—	16	8	no	—
347	C₂²	C₃₁×#466	1	2	yes	—
348	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
349	C₄	—	2	1	no	—
350	C₄	—	2	2	no	—
351	C₄	—	2	1	no	—
352	C₄	—	4	1	no	—
353	C₄	—	4	1	no	—
354	C₄	C₃₁×#466	1	2	yes	—
355	C₄	C₃₁×#472	1	2	yes	—
356	C₄	C₂²×D₈×C₃₁	1	1	yes	characteristic
357	C₄	C₂×C₃₁×#135	1	1	yes	characteristic
358	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
359	C₂	—	2	2	no	—
360	C₂	—	4	2	no	—
361	C₂	—	16	4	no	—
362	C₂	C₃₁×#3038	1	1	yes	characteristic
363	C₂	C₂×C₃₁×#466	1	1	yes	characteristic
364	C₂	C₂×C₃₁×#472	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₁
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#493	C₂	semidirect
2. C₃₁×#3038	C₂	semidirect
3. C₈×#41×C₃₁	C₂	semidirect
4. C₃₁×#1668	C₂	semidirect
5. C₃₁×#1667	C₂	semidirect
6. C₃₁×#1567	C₂	semidirect
7. C₃₁×#1545	C₂	semidirect
16. C₃₁×#460	C₂²	semidirect
18. C₃₁×#459	C₂²	semidirect
19. C₈×Q₈×C₃₁	C₂²	semidirect
21. C₈×D₄×C₃₁	C₂²	semidirect
28. C₃₁×#335	C₂²	semidirect
29. C₃₁×#331	C₂²	semidirect
72. #41×C₃₁	D₈	semidirect
117. #19267	C₃₁	direct (N × H)
125. Q₈×C₃₁	C₂×D₈	semidirect
135. D₄×C₃₁	C₂×D₈	semidirect
155. C₈×C₃₁	AGL(1,ℤ/8)	semidirect
156. C₂×#493	C₂×C₃₁	semidirect
157. #3038	C₂×C₃₁	semidirect
158. C₈×#41	C₂×C₃₁	semidirect
159. #1668	C₂×C₃₁	semidirect
160. #1667	C₂×C₃₁	semidirect
161. #1567	C₂×C₃₁	semidirect
162. #1545	C₂×C₃₁	semidirect
192. #460	C₂²×C₃₁	semidirect
194. #459	C₂²×C₃₁	semidirect
195. C₈×Q₈	C₂²×C₃₁	semidirect
197. C₈×D₄	C₂²×C₃₁	semidirect
204. #335	C₂²×C₃₁	semidirect
205. #331	C₂²×C₃₁	semidirect
252. C₃₁	#19267	direct (N × H)
255. #41	D₈×C₃₁	semidirect
307. Q₈	C₂×D₈×C₃₁	semidirect
317. D₄	C₂×D₈×C₃₁	semidirect
337. C₈	C₃₁×AGL(1,ℤ/8)	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#493	2
C₃₁×#3038	2
C₈×#41×C₃₁	2
C₃₁×#1668	2
C₃₁×#1667	2
C₃₁×#1567	2
C₃₁×#1545	2
#19267	31

Subgroups — C31×#19267 #21476026

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#19267 #21476026