Subgroups — C₃₁×#21804 #21478563

Order 7936.

1366 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#431	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2285	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1981	C₂	1	4	yes	maximal, complemented
5	C₃₁×#1956	C₂	1	4	yes	maximal, complemented
6	C₃₁×#1787	C₂	1	4	yes	maximal
7	C₂³×Q₈×C₃₁	C₂²	1	2	yes	—
8	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
9	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
10	C₂×C₃₁×C₄⋊Q₈	—	2	4	no	—
11	C₂×C₃₁×C₄⋊Q₈	C₄	1	8	yes	complemented
12	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
13	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₃₁×#117	—	2	1	no	—
15	C₂²×C₄⋊C₄×C₃₁	—	2	1	no	—
16	C₂²×C₄⋊C₄×C₃₁	—	2	1	no	—
17	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
18	C₃₁×#431	—	2	4	no	—
19	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₃₁×#103	C₂²	1	16	yes	—
21	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
23	C₃₁×#384	C₂²	1	2	yes	—
24	C₃₁×#382	—	2	1	no	—
25	C₃₁×#380	—	2	1	no	—
26	C₃₁×#380	C₂²	1	2	yes	—
27	C₄×C₄⋊C₄×C₃₁	—	2	1	no	—
28	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
29	C₂²×Q₈×C₃₁	—	2	4	no	—
30	C₂²×Q₈×C₃₁	—	2	2	no	—
31	C₂²×Q₈×C₃₁	—	4	8	no	—
32	C₂²×Q₈×C₃₁	C₂×C₄	1	8	yes	—
33	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
34	C₂³×C₄×C₃₁	—	2	2	no	—
35	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
38	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
39	C₃₁×C₄⋊Q₈	—	2	8	no	—
40	C₃₁×C₄⋊Q₈	—	2	8	no	—
41	C₃₁×C₄⋊Q₈	—	2	4	no	—
42	C₃₁×C₄⋊Q₈	—	2	4	no	—
43	C₃₁×C₄⋊Q₈	C₂×C₄	1	8	yes	—
44	C₃₁×C₄⋊Q₈	C₂×C₄	1	8	yes	—
45	C₃₁×#117	—	4	4	no	—
46	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
47	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
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	2	no	—
52	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
53	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
54	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
55	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
56	C₂×C₄²×C₃₁	—	2	2	no	—
57	C₂×C₄²×C₃₁	C₂×C₄	1	4	yes	—
58	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₃₁	D₄	1	4	yes	—
61	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
63	C₃₁×C₄⋊C₈	—	2	4	no	—
64	C₃₁×#103	—	4	16	no	—
65	C₃₁×C₂²⋊C₈	—	2	4	no	—
66	C₄×C₈×C₃₁	—	2	4	no	—
67	C₃₁×#95	—	2	2	no	—
68	C₃₁×#95	—	2	2	no	—
69	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
70	C₂×Q₈×C₃₁	—	2	8	no	—
71	C₂×Q₈×C₃₁	—	2	4	no	—
72	C₂×Q₈×C₃₁	—	2	16	no	—
73	C₂×Q₈×C₃₁	—	4	16	no	—
74	C₂×Q₈×C₃₁	—	4	8	no	—
75	C₂×Q₈×C₃₁	—	4	16	no	—
76	C₂×Q₈×C₃₁	C₂²×C₄	1	8	yes	—
77	C₂²×C₄×C₃₁	—	2	4	no	—
78	C₂²×C₄×C₃₁	—	2	4	no	—
79	C₂²×C₄×C₃₁	—	2	8	no	—
80	C₂²×C₄×C₃₁	—	2	4	no	—
81	C₂²×C₄×C₃₁	—	2	4	no	—
82	C₂²×C₄×C₃₁	—	4	8	no	—
83	C₂²×C₄×C₃₁	C₂²⋊C₄	1	4	yes	—
84	C₂²×C₄×C₃₁	C₂²⋊C₄	1	4	yes	—
85	C₂²×C₄×C₃₁	SD₁₆	1	4	yes	—
86	C₂²×C₄×C₃₁	Q₁₆	1	4	yes	—
87	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
95	C₂×C₈×C₃₁	—	2	4	no	—
96	C₂×C₈×C₃₁	—	2	8	no	—
97	C₄⋊C₄×C₃₁	—	2	8	no	—
98	C₄⋊C₄×C₃₁	—	2	8	no	—
99	C₄⋊C₄×C₃₁	—	2	8	no	—
100	C₄⋊C₄×C₃₁	—	2	8	no	—
101	C₄⋊C₄×C₃₁	—	2	8	no	—
102	C₄⋊C₄×C₃₁	—	4	4	no	—
103	C₄⋊C₄×C₃₁	—	4	4	no	—
104	C₂²⋊C₄×C₃₁	—	4	4	no	—
105	C₄²×C₃₁	—	4	4	no	—
106	C₄²×C₃₁	C₂²⋊C₄	1	4	yes	—
107	C₄²×C₃₁	C₂²⋊C₄	1	4	yes	—
108	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
109	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
110	C₄²×C₃₁	C₂×D₄	1	2	yes	—
111	C₄²×C₃₁	C₂×D₄	1	2	yes	—
112	#21804	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
113	C₂³×C₃₁	—	2	2	no	—
114	C₂³×C₃₁	—	2	2	no	—
115	C₂³×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
116	C₂³×C₃₁	C₂×SD₁₆	1	2	yes	—
117	C₂³×C₃₁	C₂×Q₁₆	1	2	yes	—
118	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
119	Q₈×C₃₁	—	2	16	no	—
120	Q₈×C₃₁	—	4	16	no	—
121	Q₈×C₃₁	—	4	8	no	—
122	C₂×C₄×C₃₁	—	2	2	no	—
123	C₂×C₄×C₃₁	—	2	2	no	—
124	C₂×C₄×C₃₁	—	2	4	no	—
125	C₂×C₄×C₃₁	—	2	4	no	—
126	C₂×C₄×C₃₁	—	2	8	no	—
127	C₂×C₄×C₃₁	—	2	8	no	—
128	C₂×C₄×C₃₁	—	4	16	no	—
129	C₂×C₄×C₃₁	—	4	8	no	—
130	C₂×C₄×C₃₁	—	4	4	no	—
131	C₂×C₄×C₃₁	—	4	4	no	—
132	C₂×C₄×C₃₁	—	4	4	no	—
133	C₂×C₄×C₃₁	#103	1	16	yes	complemented
134	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
135	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
136	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
137	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
138	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
139	C₂×C₄×C₃₁	C₂×SD₁₆	1	2	yes	—
140	C₂×C₄×C₃₁	C₂×SD₁₆	1	2	yes	—
141	C₂×C₄×C₃₁	C₂×Q₁₆	1	2	yes	—
142	C₂×C₄×C₃₁	C₂×Q₁₆	1	2	yes	—
143	C₂×C₄×C₃₁	#137	1	4	yes	—
144	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
145	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
146	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
147	C₈×C₃₁	—	4	4	no	—
148	C₂²×C₄⋊Q₈	C₂×C₃₁	1	1	yes	characteristic
149	C₂×#431	C₂×C₃₁	1	1	yes	characteristic
150	#2285	C₂×C₃₁	1	1	yes	characteristic
151	#1981	C₂×C₃₁	1	4	yes	complemented
152	#1956	C₂×C₃₁	1	4	yes	complemented
153	#1787	C₂×C₃₁	1	4	yes	—
154	C₂²×C₃₁	—	2	2	no	—
155	C₂²×C₃₁	—	2	2	no	—
156	C₂²×C₃₁	—	2	4	no	—
157	C₂²×C₃₁	—	2	4	no	—
158	C₂²×C₃₁	C₂×#103	1	4	yes	—
159	C₂²×C₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
160	C₂²×C₃₁	#535	1	2	yes	—
161	C₂²×C₃₁	C₂²×SD₁₆	1	1	yes	characteristic
162	C₂²×C₃₁	C₂²×Q₁₆	1	1	yes	characteristic
163	C₂²×C₃₁	C₂×#137	1	2	yes	—
164	C₄×C₃₁	—	2	2	no	—
165	C₄×C₃₁	—	2	2	no	—
166	C₄×C₃₁	—	4	8	no	—
167	C₄×C₃₁	—	8	4	no	—
168	C₄×C₃₁	C₂×#103	1	4	yes	—
169	C₄×C₃₁	C₂×#103	1	4	yes	—
170	C₄×C₃₁	#419	1	4	yes	—
171	C₄×C₃₁	#518	1	2	yes	—
172	C₄×C₃₁	#535	1	2	yes	—
173	C₂³×Q₈	C₂²×C₃₁	1	2	yes	—
174	C₂×C₄⋊Q₈	—	2	1	no	—
175	C₂×C₄⋊Q₈	—	2	1	no	—
176	C₂×C₄⋊Q₈	—	2	4	no	—
177	C₂×C₄⋊Q₈	C₄×C₃₁	1	8	yes	complemented
178	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
179	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
180	C₂×#117	—	2	1	no	—
181	C₂²×C₄⋊C₄	—	2	1	no	—
182	C₂²×C₄⋊C₄	—	2	1	no	—
183	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
184	#431	—	2	4	no	—
185	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
186	C₂×#103	C₂²×C₃₁	1	16	yes	—
187	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
188	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
189	#384	C₂²×C₃₁	1	2	yes	—
190	#382	—	2	1	no	—
191	#380	—	2	1	no	—
192	#380	C₂²×C₃₁	1	2	yes	—
193	C₄×C₄⋊C₄	—	2	1	no	—
194	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
195	C₂×C₃₁	—	2	4	no	—
196	C₂×C₃₁	#2309	1	1	yes	characteristic
197	C₂×C₃₁	C₂²×#103	1	1	yes	characteristic
198	C₂×C₃₁	C₂×#419	1	1	yes	characteristic
199	C₂×C₃₁	#3206	1	2	yes	—
200	C₂×C₃₁	#3209	1	2	yes	—
201	C₂²×Q₈	—	2	4	no	—
202	C₂²×Q₈	—	2	2	no	—
203	C₂²×Q₈	—	4	8	no	—
204	C₂²×Q₈	C₂×C₄×C₃₁	1	8	yes	—
205	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
206	C₂³×C₄	—	2	2	no	—
207	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
208	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
209	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
210	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
211	C₄⋊Q₈	—	2	8	no	—
212	C₄⋊Q₈	—	2	8	no	—
213	C₄⋊Q₈	—	2	4	no	—
214	C₄⋊Q₈	—	2	4	no	—
215	C₄⋊Q₈	C₂×C₄×C₃₁	1	8	yes	—
216	C₄⋊Q₈	C₂×C₄×C₃₁	1	8	yes	—
217	#117	—	4	4	no	—
218	C₂×C₄⋊C₄	—	2	8	no	—
219	C₂×C₄⋊C₄	—	2	8	no	—
220	C₂×C₄⋊C₄	—	2	2	no	—
221	C₂×C₄⋊C₄	—	2	2	no	—
222	C₂×C₄⋊C₄	—	2	2	no	—
223	C₂×C₄⋊C₄	—	2	2	no	—
224	C₂×C₄⋊C₄	—	2	2	no	—
225	C₂×C₄⋊C₄	—	2	2	no	—
226	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
227	C₂×C₂²⋊C₄	—	2	2	no	—
228	C₂×C₄²	—	2	2	no	—
229	C₂×C₄²	C₂×C₄×C₃₁	1	4	yes	—
230	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
231	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
232	C₂×C₄²	D₄×C₃₁	1	4	yes	—
233	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
234	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
235	C₄⋊C₈	—	2	4	no	—
236	#103	—	4	16	no	—
237	C₂²⋊C₈	—	2	4	no	—
238	C₄×C₈	—	2	4	no	—
239	#95	—	2	2	no	—
240	#95	—	2	2	no	—
241	C₃₁	#21804	1	1	yes	characteristic, direct product factor, Sylow
242	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
243	C₂×Q₈	—	2	8	no	—
244	C₂×Q₈	—	2	4	no	—
245	C₂×Q₈	—	2	16	no	—
246	C₂×Q₈	—	4	16	no	—
247	C₂×Q₈	—	4	8	no	—
248	C₂×Q₈	—	4	16	no	—
249	C₂×Q₈	C₂²×C₄×C₃₁	1	8	yes	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	2	8	no	—
253	C₂²×C₄	—	2	4	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	4	8	no	—
256	C₂²×C₄	C₂²⋊C₄×C₃₁	1	4	yes	—
257	C₂²×C₄	C₂²⋊C₄×C₃₁	1	4	yes	—
258	C₂²×C₄	SD₁₆×C₃₁	1	4	yes	—
259	C₂²×C₄	Q₁₆×C₃₁	1	4	yes	—
260	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
261	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
262	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
263	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
264	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
265	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
266	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
267	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
268	C₂×C₈	—	2	4	no	—
269	C₂×C₈	—	2	8	no	—
270	C₄⋊C₄	—	2	8	no	—
271	C₄⋊C₄	—	2	8	no	—
272	C₄⋊C₄	—	2	8	no	—
273	C₄⋊C₄	—	2	8	no	—
274	C₄⋊C₄	—	2	8	no	—
275	C₄⋊C₄	—	4	4	no	—
276	C₄⋊C₄	—	4	4	no	—
277	C₂²⋊C₄	—	4	4	no	—
278	C₄²	—	4	4	no	—
279	C₄²	C₂²⋊C₄×C₃₁	1	4	yes	—
280	C₄²	C₂²⋊C₄×C₃₁	1	4	yes	—
281	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
282	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
283	C₄²	C₂×D₄×C₃₁	1	2	yes	—
284	C₄²	C₂×D₄×C₃₁	1	2	yes	—
285	C₂³	—	2	2	no	—
286	C₂³	—	2	2	no	—
287	C₂³	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
288	C₂³	C₂×SD₁₆×C₃₁	1	2	yes	—
289	C₂³	C₂×Q₁₆×C₃₁	1	2	yes	—
290	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
291	Q₈	—	2	16	no	—
292	Q₈	—	4	16	no	—
293	Q₈	—	4	8	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	8	no	—
297	C₂×C₄	—	2	4	no	—
298	C₂×C₄	—	2	4	no	—
299	C₂×C₄	—	2	8	no	—
300	C₂×C₄	—	4	16	no	—
301	C₂×C₄	—	4	8	no	—
302	C₂×C₄	—	4	4	no	—
303	C₂×C₄	—	4	4	no	—
304	C₂×C₄	—	4	4	no	—
305	C₂×C₄	C₃₁×#103	1	16	yes	complemented
306	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
307	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
308	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
309	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
310	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
311	C₂×C₄	C₂×SD₁₆×C₃₁	1	2	yes	—
312	C₂×C₄	C₂×SD₁₆×C₃₁	1	2	yes	—
313	C₂×C₄	C₂×Q₁₆×C₃₁	1	2	yes	—
314	C₂×C₄	C₂×Q₁₆×C₃₁	1	2	yes	—
315	C₂×C₄	C₃₁×#137	1	4	yes	—
316	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
317	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
318	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
319	C₈	—	4	4	no	—
320	C₂²	—	2	2	no	—
321	C₂²	—	2	2	no	—
322	C₂²	—	2	4	no	—
323	C₂²	—	2	4	no	—
324	C₂²	C₂×C₃₁×#103	1	4	yes	—
325	C₂²	C₂²×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
326	C₂²	C₃₁×#535	1	2	yes	—
327	C₂²	C₂²×SD₁₆×C₃₁	1	1	yes	characteristic
328	C₂²	C₂²×Q₁₆×C₃₁	1	1	yes	characteristic
329	C₂²	C₂×C₃₁×#137	1	2	yes	—
330	C₄	—	2	2	no	—
331	C₄	—	2	2	no	—
332	C₄	—	4	8	no	—
333	C₄	—	8	4	no	—
334	C₄	C₂×C₃₁×#103	1	4	yes	—
335	C₄	C₂×C₃₁×#103	1	4	yes	—
336	C₄	C₃₁×#419	1	4	yes	—
337	C₄	C₃₁×#518	1	2	yes	—
338	C₄	C₃₁×#535	1	2	yes	—
339	C₂	—	2	4	no	—
340	C₂	C₃₁×#2309	1	1	yes	characteristic
341	C₂	C₂²×C₃₁×#103	1	1	yes	characteristic
342	C₂	C₂×C₃₁×#419	1	1	yes	characteristic
343	C₂	C₃₁×#3206	1	2	yes	—
344	C₂	C₃₁×#3209	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
4. C₃₁×#1981	C₂	semidirect
5. C₃₁×#1956	C₂	semidirect
11. C₂×C₃₁×C₄⋊Q₈	C₄	semidirect
112. #21804	C₃₁	direct (N × H)
133. C₂×C₄×C₃₁	#103	semidirect
151. #1981	C₂×C₃₁	semidirect
152. #1956	C₂×C₃₁	semidirect
177. C₂×C₄⋊Q₈	C₄×C₃₁	semidirect
241. C₃₁	#21804	direct (N × H)
305. C₂×C₄	C₃₁×#103	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃₁×C₄⋊Q₈	2
C₂×C₃₁×#431	2
C₃₁×#2285	2
C₃₁×#1981	2
C₃₁×#1956	2
C₃₁×#1787	2
#21804	31

Subgroups — C31×#21804 #21478563

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#21804 #21478563