Subgroups — C₃₁×#11388 #21468147

Order 7936.

878 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#544	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#1742	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#1740	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1736	C₂	1	2	yes	maximal
5	C₃₁×#1733	C₂	1	2	yes	maximal
6	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
7	C₃₁×#544	—	2	4	no	—
8	C₃₁×#544	—	2	4	no	—
9	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
10	C₂×C₃₁×C₄⋊Q₈	C₄	1	2	yes	complemented
11	C₂×C₃₁×#125	—	2	1	no	—
12	C₂×C₃₁×#125	C₄	1	2	yes	complemented
13	C₂×C₃₁×C₂²⋊Q₈	—	2	2	no	—
14	C₂×C₃₁×#117	C₂²	1	2	yes	—
15	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
16	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
18	C₃₁×#343	—	2	1	no	—
19	C₃₁×#343	—	2	1	no	—
20	C₃₁×#342	—	2	2	no	—
21	C₃₁×#340	—	2	4	no	—
22	C₃₁×#339	—	2	4	no	—
23	C₂²×Q₈×C₃₁	—	2	2	no	—
24	C₂³×C₄×C₃₁	—	2	1	no	—
25	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
30	C₂×M₁₆×C₃₁	—	2	2	no	—
31	C₂×M₁₆×C₃₁	Q₈	1	4	yes	complemented
32	C₂²×C₈×C₃₁	—	2	2	no	—
33	C₃₁×C₄⋊Q₈	—	2	8	no	—
34	C₃₁×C₄⋊Q₈	—	2	4	no	—
35	C₃₁×C₄⋊Q₈	—	2	4	no	—
36	C₃₁×#125	—	2	8	no	—
37	C₃₁×#125	—	2	4	no	—
38	C₃₁×#125	—	2	4	no	—
39	C₃₁×C₂²⋊Q₈	—	2	16	no	—
40	C₃₁×#117	—	2	2	no	—
41	C₃₁×#117	—	2	2	no	—
42	C₃₁×#117	—	2	2	no	—
43	C₃₁×#117	—	2	2	no	—
44	C₃₁×#117	—	2	2	no	—
45	C₃₁×#117	—	2	2	no	—
46	C₃₁×#117	D₄	1	4	yes	—
47	C₃₁×#117	Q₈	1	4	yes	complemented
48	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
49	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
50	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
51	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
52	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
53	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
54	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₃₁	D₄	1	4	yes	—
60	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
61	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
63	C₂×C₄²×C₃₁	—	2	1	no	—
64	C₂×C₄²×C₃₁	—	2	2	no	—
65	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
66	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
67	C₂×Q₈×C₃₁	—	2	8	no	—
68	C₂×Q₈×C₃₁	—	8	4	no	—
69	C₂²×C₄×C₃₁	—	2	1	no	—
70	C₂²×C₄×C₃₁	—	2	1	no	—
71	C₂²×C₄×C₃₁	—	2	2	no	—
72	C₂²×C₄×C₃₁	—	2	4	no	—
73	C₂²×C₄×C₃₁	—	4	2	no	—
74	C₂²×C₄×C₃₁	—	8	2	no	—
75	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
76	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
77	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
79	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
80	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₃₁	C₂×Q₈	1	2	yes	—
82	C₂²×C₄×C₃₁	C₂×Q₈	1	2	yes	—
83	C₂²×C₄×C₃₁	#41	1	2	yes	—
84	C₂²×C₄×C₃₁	#41	1	2	yes	—
85	M₁₆×C₃₁	—	2	4	no	—
86	M₁₆×C₃₁	—	2	4	no	—
87	M₁₆×C₃₁	—	4	2	no	—
88	M₁₆×C₃₁	—	4	2	no	—
89	C₂×C₈×C₃₁	—	2	4	no	—
90	C₂×C₈×C₃₁	—	4	2	no	—
91	C₂×C₈×C₃₁	—	4	2	no	—
92	C₄⋊C₄×C₃₁	—	2	8	no	—
93	C₄⋊C₄×C₃₁	—	2	8	no	—
94	C₄⋊C₄×C₃₁	—	2	8	no	—
95	C₄⋊C₄×C₃₁	—	2	2	no	—
96	C₄⋊C₄×C₃₁	—	2	1	no	—
97	C₄⋊C₄×C₃₁	—	2	1	no	—
98	C₄⋊C₄×C₃₁	—	2	4	no	—
99	C₄⋊C₄×C₃₁	—	2	2	no	—
100	C₄⋊C₄×C₃₁	—	2	2	no	—
101	C₄⋊C₄×C₃₁	—	2	4	no	—
102	C₄⋊C₄×C₃₁	—	4	2	no	—
103	C₄⋊C₄×C₃₁	C₂²⋊C₄	1	4	yes	—
104	C₄⋊C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
105	C₄⋊C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
106	C₂²⋊C₄×C₃₁	—	2	4	no	—
107	C₂²⋊C₄×C₃₁	—	2	4	no	—
108	C₂²⋊C₄×C₃₁	—	2	4	no	—
109	C₂²⋊C₄×C₃₁	—	4	2	no	—
110	C₄²×C₃₁	—	2	2	no	—
111	C₄²×C₃₁	—	2	2	no	—
112	C₄²×C₃₁	—	2	4	no	—
113	C₄²×C₃₁	—	2	4	no	—
114	C₄²×C₃₁	—	4	2	no	—
115	#11388	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂³×C₃₁	—	4	1	no	—
117	C₂³×C₃₁	—	4	1	no	—
118	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
119	C₂³×C₃₁	#120	1	2	yes	—
120	C₂³×C₃₁	C₂²⋊Q₈	1	2	yes	—
121	C₂³×C₃₁	#124	1	1	yes	characteristic
122	C₂³×C₃₁	C₄⋊Q₈	1	1	yes	characteristic
123	Q₈×C₃₁	—	8	8	no	—
124	C₂×C₄×C₃₁	—	2	2	no	—
125	C₂×C₄×C₃₁	—	2	2	no	—
126	C₂×C₄×C₃₁	—	2	2	no	—
127	C₂×C₄×C₃₁	—	2	2	no	—
128	C₂×C₄×C₃₁	—	2	4	no	—
129	C₂×C₄×C₃₁	—	4	2	no	—
130	C₂×C₄×C₃₁	—	4	4	no	—
131	C₂×C₄×C₃₁	—	4	2	no	—
132	C₂×C₄×C₃₁	—	4	2	no	—
133	C₂×C₄×C₃₁	—	4	2	no	—
134	C₂×C₄×C₃₁	—	4	4	no	—
135	C₂×C₄×C₃₁	—	8	4	no	—
136	C₂×C₄×C₃₁	—	8	2	no	—
137	C₂×C₄×C₃₁	—	8	2	no	—
138	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₃₁	C₄×Q₈	1	2	yes	—
141	C₂×C₄×C₃₁	C₄×Q₈	1	2	yes	—
142	C₂×C₄×C₃₁	#120	1	2	yes	—
143	C₂×C₄×C₃₁	C₂²⋊Q₈	1	2	yes	—
144	C₂×C₄×C₃₁	C₂²⋊Q₈	1	2	yes	—
145	C₂×C₄×C₃₁	C₂²⋊Q₈	1	2	yes	—
146	C₂×C₄×C₃₁	C₂²⋊Q₈	1	2	yes	—
147	C₂×C₄×C₃₁	C₂²⋊Q₈	1	2	yes	—
148	C₂×C₄×C₃₁	#124	1	2	yes	—
149	C₂×C₄×C₃₁	#124	1	2	yes	—
150	C₂×C₄×C₃₁	#124	1	1	yes	characteristic
151	C₂×C₄×C₃₁	C₄⋊Q₈	1	2	yes	—
152	C₂×C₄×C₃₁	C₄⋊Q₈	1	2	yes	—
153	C₂×C₄×C₃₁	C₄⋊Q₈	1	1	yes	characteristic
154	C₈×C₃₁	—	4	4	no	—
155	C₂×#544	C₂×C₃₁	1	1	yes	characteristic
156	#1742	C₂×C₃₁	1	1	yes	characteristic
157	#1740	C₂×C₃₁	1	1	yes	characteristic
158	#1736	C₂×C₃₁	1	2	yes	—
159	#1733	C₂×C₃₁	1	2	yes	—
160	C₂²×C₃₁	—	2	1	no	—
161	C₂²×C₃₁	—	2	2	no	—
162	C₂²×C₃₁	—	2	1	no	—
163	C₂²×C₃₁	—	2	2	no	—
164	C₂²×C₃₁	—	4	2	no	—
165	C₂²×C₃₁	—	4	1	no	—
166	C₂²×C₃₁	—	4	1	no	—
167	C₂²×C₃₁	#379	1	1	yes	characteristic
168	C₂²×C₃₁	#391	1	1	yes	characteristic
169	C₂²×C₃₁	#391	1	1	yes	characteristic
170	C₂²×C₃₁	#393	1	2	yes	—
171	C₂²×C₃₁	#395	1	2	yes	—
172	C₄×C₃₁	—	4	4	no	—
173	C₄×C₃₁	—	4	2	no	—
174	C₄×C₃₁	—	4	2	no	—
175	C₄×C₃₁	—	4	2	no	—
176	C₄×C₃₁	—	4	2	no	—
177	C₄×C₃₁	—	8	4	no	—
178	C₄×C₃₁	#391	1	2	yes	—
179	C₄×C₃₁	#391	1	2	yes	—
180	C₄×C₃₁	#393	1	2	yes	—
181	C₄×C₃₁	#395	1	2	yes	—
182	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
183	#544	—	2	4	no	—
184	#544	—	2	4	no	—
185	C₂×C₄⋊Q₈	—	2	1	no	—
186	C₂×C₄⋊Q₈	C₄×C₃₁	1	2	yes	complemented
187	C₂×#125	—	2	1	no	—
188	C₂×#125	C₄×C₃₁	1	2	yes	complemented
189	C₂×C₂²⋊Q₈	—	2	2	no	—
190	C₂×#117	C₂²×C₃₁	1	2	yes	—
191	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
192	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
193	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
194	#343	—	2	1	no	—
195	#343	—	2	1	no	—
196	#342	—	2	2	no	—
197	#340	—	2	4	no	—
198	#339	—	2	4	no	—
199	C₂×C₃₁	—	2	2	no	—
200	C₂×C₃₁	—	2	1	no	—
201	C₂×C₃₁	—	2	1	no	—
202	C₂×C₃₁	—	2	2	no	—
203	C₂×C₃₁	#1446	1	1	yes	characteristic
204	C₂×C₃₁	#1795	1	1	yes	characteristic
205	C₂×C₃₁	#1796	1	1	yes	characteristic
206	C₂²×Q₈	—	2	2	no	—
207	C₂³×C₄	—	2	1	no	—
208	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
209	C₂×M₁₆	—	2	2	no	—
210	C₂×M₁₆	—	2	2	no	—
211	C₂×M₁₆	—	2	2	no	—
212	C₂×M₁₆	—	2	2	no	—
213	C₂×M₁₆	—	2	2	no	—
214	C₂×M₁₆	Q₈×C₃₁	1	4	yes	complemented
215	C₂²×C₈	—	2	2	no	—
216	C₄⋊Q₈	—	2	8	no	—
217	C₄⋊Q₈	—	2	4	no	—
218	C₄⋊Q₈	—	2	4	no	—
219	#125	—	2	8	no	—
220	#125	—	2	4	no	—
221	#125	—	2	4	no	—
222	C₂²⋊Q₈	—	2	16	no	—
223	#117	—	2	2	no	—
224	#117	—	2	2	no	—
225	#117	—	2	2	no	—
226	#117	—	2	2	no	—
227	#117	—	2	2	no	—
228	#117	—	2	2	no	—
229	#117	D₄×C₃₁	1	4	yes	—
230	#117	Q₈×C₃₁	1	4	yes	complemented
231	C₂×C₄⋊C₄	—	2	2	no	—
232	C₂×C₄⋊C₄	—	2	2	no	—
233	C₂×C₄⋊C₄	—	2	2	no	—
234	C₂×C₄⋊C₄	—	2	1	no	—
235	C₂×C₄⋊C₄	—	2	2	no	—
236	C₂×C₄⋊C₄	—	2	2	no	—
237	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
238	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
239	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
240	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
241	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
242	C₂×C₄⋊C₄	D₄×C₃₁	1	4	yes	—
243	C₂×C₂²⋊C₄	—	2	1	no	—
244	C₂×C₂²⋊C₄	—	2	2	no	—
245	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
246	C₂×C₄²	—	2	1	no	—
247	C₂×C₄²	—	2	2	no	—
248	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
249	C₃₁	#11388	1	1	yes	characteristic, direct product factor, Sylow
250	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
251	C₂×Q₈	—	2	8	no	—
252	C₂×Q₈	—	8	4	no	—
253	C₂²×C₄	—	2	1	no	—
254	C₂²×C₄	—	2	1	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	4	2	no	—
258	C₂²×C₄	—	8	2	no	—
259	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
260	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
261	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
262	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
263	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
264	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
265	C₂²×C₄	C₂×Q₈×C₃₁	1	2	yes	—
266	C₂²×C₄	C₂×Q₈×C₃₁	1	2	yes	—
267	C₂²×C₄	#41×C₃₁	1	2	yes	—
268	C₂²×C₄	#41×C₃₁	1	2	yes	—
269	M₁₆	—	2	4	no	—
270	M₁₆	—	2	4	no	—
271	M₁₆	—	4	2	no	—
272	M₁₆	—	4	2	no	—
273	C₂×C₈	—	2	4	no	—
274	C₂×C₈	—	4	2	no	—
275	C₂×C₈	—	4	2	no	—
276	C₄⋊C₄	—	2	8	no	—
277	C₄⋊C₄	—	2	8	no	—
278	C₄⋊C₄	—	2	8	no	—
279	C₄⋊C₄	—	2	2	no	—
280	C₄⋊C₄	—	2	1	no	—
281	C₄⋊C₄	—	2	1	no	—
282	C₄⋊C₄	—	2	4	no	—
283	C₄⋊C₄	—	2	2	no	—
284	C₄⋊C₄	—	2	2	no	—
285	C₄⋊C₄	—	2	4	no	—
286	C₄⋊C₄	—	4	2	no	—
287	C₄⋊C₄	C₂²⋊C₄×C₃₁	1	4	yes	—
288	C₄⋊C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
289	C₄⋊C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
290	C₂²⋊C₄	—	2	4	no	—
291	C₂²⋊C₄	—	2	4	no	—
292	C₂²⋊C₄	—	2	4	no	—
293	C₂²⋊C₄	—	4	2	no	—
294	C₄²	—	2	2	no	—
295	C₄²	—	2	2	no	—
296	C₄²	—	2	4	no	—
297	C₄²	—	2	4	no	—
298	C₄²	—	4	2	no	—
299	C₂³	—	4	1	no	—
300	C₂³	—	4	1	no	—
301	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
302	C₂³	C₃₁×#120	1	2	yes	—
303	C₂³	C₃₁×C₂²⋊Q₈	1	2	yes	—
304	C₂³	C₃₁×#124	1	1	yes	characteristic
305	C₂³	C₃₁×C₄⋊Q₈	1	1	yes	characteristic
306	Q₈	—	8	8	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	4	4	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	4	4	no	—
318	C₂×C₄	—	8	4	no	—
319	C₂×C₄	—	8	2	no	—
320	C₂×C₄	—	8	2	no	—
321	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
322	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
323	C₂×C₄	C₄×Q₈×C₃₁	1	2	yes	—
324	C₂×C₄	C₄×Q₈×C₃₁	1	2	yes	—
325	C₂×C₄	C₃₁×#120	1	2	yes	—
326	C₂×C₄	C₃₁×C₂²⋊Q₈	1	2	yes	—
327	C₂×C₄	C₃₁×C₂²⋊Q₈	1	2	yes	—
328	C₂×C₄	C₃₁×C₂²⋊Q₈	1	2	yes	—
329	C₂×C₄	C₃₁×C₂²⋊Q₈	1	2	yes	—
330	C₂×C₄	C₃₁×C₂²⋊Q₈	1	2	yes	—
331	C₂×C₄	C₃₁×#124	1	2	yes	—
332	C₂×C₄	C₃₁×#124	1	2	yes	—
333	C₂×C₄	C₃₁×#124	1	1	yes	characteristic
334	C₂×C₄	C₃₁×C₄⋊Q₈	1	1	yes	characteristic
335	C₂×C₄	C₃₁×C₄⋊Q₈	1	2	yes	—
336	C₂×C₄	C₃₁×C₄⋊Q₈	1	2	yes	—
337	C₈	—	4	4	no	—
338	C₂²	—	2	1	no	—
339	C₂²	—	2	2	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	2	no	—
342	C₂²	—	4	2	no	—
343	C₂²	—	4	1	no	—
344	C₂²	—	4	1	no	—
345	C₂²	C₃₁×#379	1	1	yes	characteristic
346	C₂²	C₃₁×#391	1	1	yes	characteristic
347	C₂²	C₃₁×#391	1	1	yes	characteristic
348	C₂²	C₃₁×#393	1	2	yes	—
349	C₂²	C₃₁×#395	1	2	yes	—
350	C₄	—	4	4	no	—
351	C₄	—	4	2	no	—
352	C₄	—	4	2	no	—
353	C₄	—	4	2	no	—
354	C₄	—	4	2	no	—
355	C₄	—	8	4	no	—
356	C₄	C₃₁×#391	1	2	yes	—
357	C₄	C₃₁×#391	1	2	yes	—
358	C₄	C₃₁×#393	1	2	yes	—
359	C₄	C₃₁×#395	1	2	yes	—
360	C₂	—	2	2	no	—
361	C₂	—	2	2	no	—
362	C₂	—	2	1	no	—
363	C₂	—	2	1	no	—
364	C₂	C₃₁×#1446	1	1	yes	characteristic
365	C₂	C₃₁×#1795	1	1	yes	characteristic
366	C₂	C₃₁×#1796	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	#379
commutator	C₂²×C₄	C₂²×C₄×C₃₁
Frattini, cosocle	C₂³×C₄	C₂³×C₃₁
prime radical	C₂⁴×C₃₁	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂³×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
10. C₂×C₃₁×C₄⋊Q₈	C₄	semidirect
12. C₂×C₃₁×#125	C₄	semidirect
31. C₂×M₁₆×C₃₁	Q₈	semidirect
47. C₃₁×#117	Q₈	semidirect
115. #11388	C₃₁	direct (N × H)
186. C₂×C₄⋊Q₈	C₄×C₃₁	semidirect
188. C₂×#125	C₄×C₃₁	semidirect
214. C₂×M₁₆	Q₈×C₃₁	semidirect
230. #117	Q₈×C₃₁	semidirect
249. C₃₁	#11388	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#544	2
C₃₁×#1742	2
C₃₁×#1740	2
C₃₁×#1736	2
C₃₁×#1733	2
#11388	31

Subgroups — C31×#11388 #21468147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#11388 #21468147