Subgroups — C₃₁×#22670 #21479429

Order 7936.

1122 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#442	C₂	1	2	yes	maximal
2	C₂×C₄×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic
3	D₄×C₄⋊C₄×C₃₁	C₂	1	2	yes	maximal, complemented
4	C₃₁×#1943	C₂	1	2	yes	maximal, complemented
5	C₃₁×#1864	C₂	1	4	yes	maximal, complemented
6	C₃₁×#1844	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1802	C₂	1	2	yes	maximal, complemented
8	C₃₁×#1770	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	—
11	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
12	C₂²×C₄⋊C₄×C₃₁	—	2	2	no	—
13	C₃₁×#442	—	2	8	no	—
14	C₄×D₈×C₃₁	C₄	1	8	yes	complemented
15	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
16	C₂×C₃₁×#106	C₂²	1	2	yes	—
17	C₂×C₃₁×#106	C₂²	1	2	yes	—
18	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₃₁×#102	C₂²	1	4	yes	—
20	C₂×C₃₁×#102	C₂²	1	2	yes	—
21	C₂×C₃₁×#97	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
23	C₃₁×#389	C₂²	1	4	yes	—
24	C₃₁×#385	—	2	4	no	—
25	C₃₁×#384	C₂²	1	2	yes	—
26	C₃₁×#380	—	2	2	no	—
27	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
28	C₃₁×#340	C₂²	1	4	yes	—
29	C₃₁×#336	C₂²	1	2	yes	—
30	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
31	C₂³×C₄×C₃₁	—	2	2	no	—
32	C₂³×C₄×C₃₁	—	2	4	no	—
33	C₂×D₈×C₃₁	C₂×C₄	1	4	yes	—
34	C₂×D₈×C₃₁	D₄	1	4	yes	—
35	C₂×D₈×C₃₁	Q₈	1	4	yes	—
36	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
37	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
38	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
39	C₄×D₄×C₃₁	—	2	8	no	—
40	C₄×D₄×C₃₁	—	2	4	no	—
41	C₄×D₄×C₃₁	—	4	4	no	—
42	C₄×D₄×C₃₁	C₂×C₄	1	8	yes	complemented
43	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
44	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
45	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
46	C₂×C₄⋊C₄×C₃₁	—	4	8	no	—
47	C₂×C₄⋊C₄×C₃₁	D₄	1	2	yes	—
48	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
49	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
50	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
51	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
52	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
53	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
54	C₃₁×#107	C₂×C₄	1	4	yes	complemented
55	C₃₁×#106	—	2	4	no	—
56	C₃₁×#106	—	4	2	no	—
57	C₃₁×C₄⋊C₈	—	2	2	no	—
58	C₃₁×#102	—	2	8	no	—
59	C₃₁×#102	C₂×C₄	1	8	yes	complemented
60	C₃₁×#97	—	2	4	no	—
61	C₄×C₈×C₃₁	C₂×C₄	1	4	yes	complemented
62	C₃₁×#95	—	2	4	no	—
63	C₃₁×#95	D₄	1	2	yes	—
64	C₂⁴×C₃₁	—	2	2	no	—
65	C₂×D₄×C₃₁	—	2	2	no	—
66	C₂×D₄×C₃₁	—	2	2	no	—
67	C₂×D₄×C₃₁	—	2	2	no	—
68	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
69	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
70	C₂×D₄×C₃₁	C₂×Q₈	1	4	yes	—
71	C₂²×C₄×C₃₁	—	2	2	no	—
72	C₂²×C₄×C₃₁	—	2	8	no	—
73	C₂²×C₄×C₃₁	—	2	4	no	—
74	C₂²×C₄×C₃₁	—	4	8	no	—
75	C₂²×C₄×C₃₁	—	4	8	no	—
76	C₂²×C₄×C₃₁	—	4	4	no	—
77	C₂²×C₄×C₃₁	—	4	4	no	—
78	C₂²×C₄×C₃₁	—	8	4	no	—
79	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
80	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
83	D₈×C₃₁	C₄⋊C₄	1	16	yes	complemented
84	C₂×C₈×C₃₁	—	2	1	no	—
85	C₂×C₈×C₃₁	—	2	1	no	—
86	C₂×C₈×C₃₁	—	2	2	no	—
87	C₂×C₈×C₃₁	—	2	2	no	—
88	C₂×C₈×C₃₁	—	2	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×D₄	1	2	yes	—
92	C₂×C₈×C₃₁	C₂×Q₈	1	2	yes	—
93	C₄⋊C₄×C₃₁	—	2	4	no	—
94	C₄⋊C₄×C₃₁	—	2	2	no	—
95	C₄⋊C₄×C₃₁	—	2	4	no	—
96	C₄⋊C₄×C₃₁	—	2	4	no	—
97	C₄⋊C₄×C₃₁	—	4	8	no	—
98	C₄⋊C₄×C₃₁	—	4	4	no	—
99	C₄⋊C₄×C₃₁	—	8	2	no	—
100	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
101	C₂²⋊C₄×C₃₁	—	2	8	no	—
102	C₂²⋊C₄×C₃₁	—	4	8	no	—
103	C₄²×C₃₁	—	2	2	no	—
104	C₄²×C₃₁	—	2	2	no	—
105	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
106	C₄²×C₃₁	#41	1	2	yes	—
107	#22670	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂³×C₃₁	—	2	4	no	—
109	C₂³×C₃₁	—	2	4	no	—
110	C₂³×C₃₁	—	2	4	no	—
111	C₂³×C₃₁	—	4	2	no	—
112	C₂³×C₃₁	—	4	2	no	—
113	C₂³×C₃₁	—	4	2	no	—
114	C₂³×C₃₁	—	4	2	no	—
115	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
116	D₄×C₃₁	—	2	4	no	—
117	D₄×C₃₁	—	2	4	no	—
118	D₄×C₃₁	—	2	4	no	—
119	D₄×C₃₁	C₂×C₄⋊C₄	1	8	yes	complemented
120	C₂×C₄×C₃₁	—	2	2	no	—
121	C₂×C₄×C₃₁	—	2	4	no	—
122	C₂×C₄×C₃₁	—	2	4	no	—
123	C₂×C₄×C₃₁	—	2	4	no	—
124	C₂×C₄×C₃₁	—	2	4	no	—
125	C₂×C₄×C₃₁	—	4	2	no	—
126	C₂×C₄×C₃₁	—	4	2	no	—
127	C₂×C₄×C₃₁	—	4	16	no	—
128	C₂×C₄×C₃₁	—	4	4	no	—
129	C₂×C₄×C₃₁	—	4	4	no	—
130	C₂×C₄×C₃₁	—	4	4	no	—
131	C₂×C₄×C₃₁	—	8	16	no	—
132	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
133	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
134	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	4	yes	—
135	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
136	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
137	C₂×C₄×C₃₁	C₂²×Q₈	1	1	yes	characteristic
138	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
139	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
140	C₂×C₄×C₃₁	2₋¹⁺⁴	1	1	yes	characteristic
141	C₈×C₃₁	—	2	2	no	—
142	C₈×C₃₁	—	4	2	no	—
143	C₈×C₃₁	C₂×C₄⋊C₄	1	4	yes	complemented
144	C₂×#442	C₂×C₃₁	1	2	yes	—
145	C₂×C₄×D₈	C₂×C₃₁	1	1	yes	characteristic
146	D₄×C₄⋊C₄	C₂×C₃₁	1	2	yes	complemented
147	#1943	C₂×C₃₁	1	2	yes	complemented
148	#1864	C₂×C₃₁	1	4	yes	complemented
149	#1844	C₂×C₃₁	1	1	yes	characteristic, complemented
150	#1802	C₂×C₃₁	1	2	yes	complemented
151	#1770	C₂×C₃₁	1	1	yes	characteristic, complemented
152	C₂²×C₃₁	—	2	8	no	—
153	C₂²×C₃₁	—	4	4	no	—
154	C₂²×C₃₁	—	4	4	no	—
155	C₂²×C₃₁	—	4	4	no	—
156	C₂²×C₃₁	—	4	4	no	—
157	C₂²×C₃₁	—	4	4	no	—
158	C₂²×C₃₁	—	4	4	no	—
159	C₂²×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
160	C₂²×C₃₁	D₄²	1	1	yes	characteristic
161	C₂²×C₃₁	D₄×Q₈	1	1	yes	characteristic
162	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
163	C₂²×C₃₁	#577	1	2	yes	—
164	C₄×C₃₁	—	2	2	no	—
165	C₄×C₃₁	—	4	4	no	—
166	C₄×C₃₁	—	4	4	no	—
167	C₄×C₃₁	—	8	4	no	—
168	C₄×C₃₁	#442	1	4	yes	complemented
169	C₄×C₃₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
170	C₄×C₃₁	#520	1	1	yes	characteristic
171	C₄×C₃₁	#547	1	1	yes	characteristic
172	C₄×C₃₁	#554	1	1	yes	characteristic
173	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
174	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	—
175	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
176	C₂²×C₄⋊C₄	—	2	2	no	—
177	#442	—	2	8	no	—
178	C₄×D₈	C₄×C₃₁	1	8	yes	complemented
179	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
180	C₂×#106	C₂²×C₃₁	1	2	yes	—
181	C₂×#106	C₂²×C₃₁	1	2	yes	—
182	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
183	C₂×#102	C₂²×C₃₁	1	4	yes	—
184	C₂×#102	C₂²×C₃₁	1	2	yes	—
185	C₂×#97	C₂²×C₃₁	1	2	yes	—
186	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
187	#389	C₂²×C₃₁	1	4	yes	—
188	#385	—	2	4	no	—
189	#384	C₂²×C₃₁	1	2	yes	—
190	#380	—	2	2	no	—
191	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
192	#340	C₂²×C₃₁	1	4	yes	—
193	#336	C₂²×C₃₁	1	2	yes	—
194	C₂×C₃₁	—	4	8	no	—
195	C₂×C₃₁	D₄×C₄⋊C₄	1	1	yes	characteristic
196	C₂×C₃₁	C₂×#442	1	1	yes	characteristic
197	C₂×C₃₁	#2952	1	1	yes	characteristic
198	C₂×C₃₁	#3272	1	2	yes	—
199	C₂×C₃₁	#3384	1	2	yes	—
200	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
201	C₂³×C₄	—	2	2	no	—
202	C₂³×C₄	—	2	4	no	—
203	C₂×D₈	C₂×C₄×C₃₁	1	4	yes	—
204	C₂×D₈	D₄×C₃₁	1	4	yes	—
205	C₂×D₈	Q₈×C₃₁	1	4	yes	—
206	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
207	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
208	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
209	C₄×D₄	—	2	8	no	—
210	C₄×D₄	—	2	4	no	—
211	C₄×D₄	—	4	4	no	—
212	C₄×D₄	C₂×C₄×C₃₁	1	8	yes	complemented
213	C₂×C₄⋊C₄	—	2	2	no	—
214	C₂×C₄⋊C₄	—	2	4	no	—
215	C₂×C₄⋊C₄	—	2	2	no	—
216	C₂×C₄⋊C₄	—	4	8	no	—
217	C₂×C₄⋊C₄	D₄×C₃₁	1	2	yes	—
218	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
219	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
220	C₂×C₂²⋊C₄	—	2	2	no	—
221	C₂×C₂²⋊C₄	—	2	4	no	—
222	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
223	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
224	#107	C₂×C₄×C₃₁	1	4	yes	complemented
225	#106	—	2	4	no	—
226	#106	—	4	2	no	—
227	C₄⋊C₈	—	2	2	no	—
228	#102	—	2	8	no	—
229	#102	C₂×C₄×C₃₁	1	8	yes	complemented
230	#97	—	2	4	no	—
231	C₄×C₈	C₂×C₄×C₃₁	1	4	yes	complemented
232	#95	—	2	4	no	—
233	#95	D₄×C₃₁	1	2	yes	—
234	C₃₁	#22670	1	1	yes	characteristic, direct product factor, Sylow
235	C₂⁴	—	2	2	no	—
236	C₂×D₄	—	2	2	no	—
237	C₂×D₄	—	2	2	no	—
238	C₂×D₄	—	2	2	no	—
239	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
240	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
241	C₂×D₄	C₂×Q₈×C₃₁	1	4	yes	—
242	C₂²×C₄	—	2	2	no	—
243	C₂²×C₄	—	2	8	no	—
244	C₂²×C₄	—	2	4	no	—
245	C₂²×C₄	—	4	8	no	—
246	C₂²×C₄	—	4	8	no	—
247	C₂²×C₄	—	4	4	no	—
248	C₂²×C₄	—	4	4	no	—
249	C₂²×C₄	—	8	4	no	—
250	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
251	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
252	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
253	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
254	D₈	C₄⋊C₄×C₃₁	1	16	yes	complemented
255	C₂×C₈	—	2	1	no	—
256	C₂×C₈	—	2	1	no	—
257	C₂×C₈	—	2	2	no	—
258	C₂×C₈	—	2	2	no	—
259	C₂×C₈	—	2	2	no	—
260	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
261	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
262	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
263	C₂×C₈	C₂×Q₈×C₃₁	1	2	yes	—
264	C₄⋊C₄	—	2	4	no	—
265	C₄⋊C₄	—	2	2	no	—
266	C₄⋊C₄	—	2	4	no	—
267	C₄⋊C₄	—	2	4	no	—
268	C₄⋊C₄	—	4	8	no	—
269	C₄⋊C₄	—	4	4	no	—
270	C₄⋊C₄	—	8	2	no	—
271	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
272	C₂²⋊C₄	—	2	8	no	—
273	C₂²⋊C₄	—	4	8	no	—
274	C₄²	—	2	2	no	—
275	C₄²	—	2	2	no	—
276	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
277	C₄²	#41×C₃₁	1	2	yes	—
278	C₂³	—	2	4	no	—
279	C₂³	—	2	4	no	—
280	C₂³	—	2	4	no	—
281	C₂³	—	4	2	no	—
282	C₂³	—	4	2	no	—
283	C₂³	—	4	2	no	—
284	C₂³	—	4	2	no	—
285	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
286	D₄	—	2	4	no	—
287	D₄	—	2	4	no	—
288	D₄	—	2	4	no	—
289	D₄	C₂×C₄⋊C₄×C₃₁	1	8	yes	complemented
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	4	no	—
292	C₂×C₄	—	2	4	no	—
293	C₂×C₄	—	2	4	no	—
294	C₂×C₄	—	2	4	no	—
295	C₂×C₄	—	4	2	no	—
296	C₂×C₄	—	4	2	no	—
297	C₂×C₄	—	4	16	no	—
298	C₂×C₄	—	4	4	no	—
299	C₂×C₄	—	4	4	no	—
300	C₂×C₄	—	4	4	no	—
301	C₂×C₄	—	8	16	no	—
302	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
303	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
304	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	4	yes	—
305	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
306	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
307	C₂×C₄	C₂²×Q₈×C₃₁	1	1	yes	characteristic
308	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
309	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
310	C₂×C₄	C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
311	C₈	—	2	2	no	—
312	C₈	—	4	2	no	—
313	C₈	C₂×C₄⋊C₄×C₃₁	1	4	yes	complemented
314	C₂²	—	2	8	no	—
315	C₂²	—	4	4	no	—
316	C₂²	—	4	4	no	—
317	C₂²	—	4	4	no	—
318	C₂²	—	4	4	no	—
319	C₂²	—	4	4	no	—
320	C₂²	—	4	4	no	—
321	C₂²	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
322	C₂²	D₄²×C₃₁	1	1	yes	characteristic
323	C₂²	D₄×Q₈×C₃₁	1	1	yes	characteristic
324	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
325	C₂²	C₃₁×#577	1	2	yes	—
326	C₄	—	2	2	no	—
327	C₄	—	4	4	no	—
328	C₄	—	4	4	no	—
329	C₄	—	8	4	no	—
330	C₄	C₃₁×#442	1	4	yes	complemented
331	C₄	C₂²×C₄⋊C₄×C₃₁	1	1	yes	characteristic
332	C₄	C₃₁×#520	1	1	yes	characteristic
333	C₄	C₃₁×#547	1	1	yes	characteristic
334	C₄	C₃₁×#554	1	1	yes	characteristic
335	C₂	—	4	8	no	—
336	C₂	D₄×C₄⋊C₄×C₃₁	1	1	yes	characteristic
337	C₂	C₂×C₃₁×#442	1	1	yes	characteristic
338	C₂	C₃₁×#2952	1	1	yes	characteristic
339	C₂	C₃₁×#3272	1	2	yes	—
340	C₂	C₃₁×#3384	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	C₂²×D₈×C₃₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₄×C₄⋊C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. D₄×C₄⋊C₄×C₃₁	C₂	semidirect
4. C₃₁×#1943	C₂	semidirect
5. C₃₁×#1864	C₂	semidirect
6. C₃₁×#1844	C₂	semidirect
7. C₃₁×#1802	C₂	semidirect
8. C₃₁×#1770	C₂	semidirect
14. C₄×D₈×C₃₁	C₄	semidirect
42. C₄×D₄×C₃₁	C₂×C₄	semidirect
54. C₃₁×#107	C₂×C₄	semidirect
59. C₃₁×#102	C₂×C₄	semidirect
61. C₄×C₈×C₃₁	C₂×C₄	semidirect
83. D₈×C₃₁	C₄⋊C₄	semidirect
107. #22670	C₃₁	direct (N × H)
119. D₄×C₃₁	C₂×C₄⋊C₄	semidirect
143. C₈×C₃₁	C₂×C₄⋊C₄	semidirect
146. D₄×C₄⋊C₄	C₂×C₃₁	semidirect
147. #1943	C₂×C₃₁	semidirect
148. #1864	C₂×C₃₁	semidirect
149. #1844	C₂×C₃₁	semidirect
150. #1802	C₂×C₃₁	semidirect
151. #1770	C₂×C₃₁	semidirect
168. C₄×C₃₁	#442	semidirect
178. C₄×D₈	C₄×C₃₁	semidirect
212. C₄×D₄	C₂×C₄×C₃₁	semidirect
224. #107	C₂×C₄×C₃₁	semidirect
229. #102	C₂×C₄×C₃₁	semidirect
231. C₄×C₈	C₂×C₄×C₃₁	semidirect
234. C₃₁	#22670	direct (N × H)
254. D₈	C₄⋊C₄×C₃₁	semidirect
289. D₄	C₂×C₄⋊C₄×C₃₁	semidirect
313. C₈	C₂×C₄⋊C₄×C₃₁	semidirect
330. C₄	C₃₁×#442	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#442	2
C₂×C₄×D₈×C₃₁	2
D₄×C₄⋊C₄×C₃₁	2
C₃₁×#1943	2
C₃₁×#1864	2
C₃₁×#1844	2
C₃₁×#1802	2
C₃₁×#1770	2
#22670	31

Subgroups — C31×#22670 #21479429

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#22670 #21479429