Subgroups — C₃₁×#7901 #21464660

Order 7936.

818 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#431	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#423	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1279	C₂	1	4	yes	maximal, complemented
5	C₂²×M₁₆×C₃₁	—	2	1	no	—
6	C₂²×C₄⋊C₄×C₃₁	C₄	1	2	yes	—
7	C₂²×C₄²×C₃₁	—	2	1	no	—
8	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
9	C₃₁×#431	—	2	2	no	—
10	C₃₁×#431	C₄	1	4	yes	complemented
11	C₃₁×#423	—	2	2	no	—
12	C₃₁×#423	C₄	1	4	yes	complemented
13	C₂×C₃₁×C₄⋊C₈	—	2	1	no	—
14	C₂×C₃₁×C₄⋊C₈	—	2	1	no	—
15	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₃₁×C₂²⋊C₈	—	2	1	no	—
17	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
18	C₄×C₄⋊C₄×C₃₁	—	2	1	no	—
19	C₄×C₄⋊C₄×C₃₁	—	2	1	no	—
20	C₄×C₄⋊C₄×C₃₁	C₄	1	2	yes	—
21	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
22	C₂×C₃₁×#95	—	2	1	no	—
23	C₂³×C₄×C₃₁	—	2	2	no	—
24	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
26	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
27	C₂×M₁₆×C₃₁	—	2	4	no	—
28	C₂×M₁₆×C₃₁	—	4	2	no	—
29	C₂×M₁₆×C₃₁	—	4	2	no	—
30	C₂²×C₈×C₃₁	—	2	2	no	—
31	C₂²×C₈×C₃₁	—	2	2	no	—
32	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
33	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
34	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	4	yes	—
35	C₂×C₄²×C₃₁	—	2	2	no	—
36	C₂×C₄²×C₃₁	—	2	2	no	—
37	C₂×C₄²×C₃₁	—	4	2	no	—
38	C₂×C₄²×C₃₁	—	4	2	no	—
39	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
41	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
42	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₃₁	D₄	1	2	yes	—
45	C₂×C₄²×C₃₁	Q₈	1	2	yes	—
46	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
47	C₃₁×C₄⋊C₈	—	2	4	no	—
48	C₃₁×C₄⋊C₈	—	2	4	no	—
49	C₃₁×C₄⋊C₈	—	2	2	no	—
50	C₃₁×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
51	C₃₁×C₂²⋊C₈	—	2	4	no	—
52	C₄×C₈×C₃₁	—	2	2	no	—
53	C₄×C₈×C₃₁	C₂×C₄	1	4	yes	complemented
54	C₃₁×#95	—	2	2	no	—
55	C₃₁×#95	—	2	2	no	—
56	C₂⁴×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
57	C₂²×C₄×C₃₁	—	2	4	no	—
58	C₂²×C₄×C₃₁	—	2	8	no	—
59	C₂²×C₄×C₃₁	—	2	4	no	—
60	C₂²×C₄×C₃₁	—	4	2	no	—
61	C₂²×C₄×C₃₁	—	4	4	no	—
62	C₂²×C₄×C₃₁	—	4	4	no	—
63	C₂²×C₄×C₃₁	C₄²	1	2	yes	—
64	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
67	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
69	C₂²×C₄×C₃₁	C₄⋊C₄	1	2	yes	—
70	C₂²×C₄×C₃₁	C₄⋊C₄	1	2	yes	—
71	C₂²×C₄×C₃₁	C₄⋊C₄	1	2	yes	—
72	C₂²×C₄×C₃₁	D₈	1	2	yes	—
73	C₂²×C₄×C₃₁	SD₁₆	1	2	yes	—
74	C₂²×C₄×C₃₁	SD₁₆	1	2	yes	—
75	C₂²×C₄×C₃₁	Q₁₆	1	2	yes	—
76	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
79	M₁₆×C₃₁	—	4	8	no	—
80	C₂×C₈×C₃₁	—	2	4	no	—
81	C₂×C₈×C₃₁	—	2	4	no	—
82	C₂×C₈×C₃₁	—	4	4	no	—
83	C₂×C₈×C₃₁	—	4	2	no	—
84	C₂×C₈×C₃₁	—	4	2	no	—
85	C₄⋊C₄×C₃₁	—	2	8	no	—
86	C₄⋊C₄×C₃₁	—	2	4	no	—
87	C₄⋊C₄×C₃₁	M₁₆	1	8	yes	complemented
88	C₄²×C₃₁	—	4	4	no	—
89	C₄²×C₃₁	—	4	2	no	—
90	C₄²×C₃₁	—	4	2	no	—
91	C₄²×C₃₁	C₄²	1	2	yes	—
92	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
93	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
94	C₄²×C₃₁	C₄⋊C₄	1	2	yes	—
95	C₄²×C₃₁	C₄⋊C₄	1	2	yes	—
96	C₄²×C₃₁	C₄⋊C₄	1	2	yes	—
97	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
98	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
99	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
100	C₄²×C₃₁	C₂×Q₈	1	1	yes	characteristic
101	#7901	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂³×C₃₁	—	2	2	no	—
103	C₂³×C₃₁	—	2	2	no	—
104	C₂³×C₃₁	#95	1	2	yes	—
105	C₂³×C₃₁	#102	1	2	yes	—
106	C₂³×C₃₁	#103	1	2	yes	—
107	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
108	C₂×C₄×C₃₁	—	2	2	no	—
109	C₂×C₄×C₃₁	—	2	2	no	—
110	C₂×C₄×C₃₁	—	2	2	no	—
111	C₂×C₄×C₃₁	—	2	4	no	—
112	C₂×C₄×C₃₁	—	2	4	no	—
113	C₂×C₄×C₃₁	—	2	8	no	—
114	C₂×C₄×C₃₁	—	4	2	no	—
115	C₂×C₄×C₃₁	—	4	2	no	—
116	C₂×C₄×C₃₁	—	4	16	no	—
117	C₂×C₄×C₃₁	—	4	4	no	—
118	C₂×C₄×C₃₁	—	4	4	no	—
119	C₂×C₄×C₃₁	#95	1	2	yes	—
120	C₂×C₄×C₃₁	#95	1	2	yes	—
121	C₂×C₄×C₃₁	#95	1	2	yes	—
122	C₂×C₄×C₃₁	#102	1	2	yes	—
123	C₂×C₄×C₃₁	#102	1	4	yes	—
124	C₂×C₄×C₃₁	#103	1	2	yes	—
125	C₂×C₄×C₃₁	#103	1	4	yes	—
126	C₂×C₄×C₃₁	#106	1	4	yes	—
127	C₂×C₄×C₃₁	#107	1	4	yes	—
128	C₂×C₄×C₃₁	C₂×C₄²	1	1	yes	characteristic
129	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
132	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₃₁	C₂×M₁₆	1	4	yes	—
135	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
136	C₂×C₄×C₃₁	C₂×SD₁₆	1	1	yes	characteristic
137	C₂×C₄×C₃₁	C₂×SD₁₆	1	1	yes	characteristic
138	C₂×C₄×C₃₁	C₂×Q₁₆	1	1	yes	characteristic
139	C₈×C₃₁	—	4	4	no	—
140	C₈×C₃₁	—	4	4	no	—
141	C₂×#431	C₂×C₃₁	1	1	yes	characteristic
142	C₂×#423	C₂×C₃₁	1	1	yes	characteristic
143	C₂×C₄×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic
144	#1279	C₂×C₃₁	1	4	yes	complemented
145	C₂²×C₃₁	—	2	2	no	—
146	C₂²×C₃₁	—	2	2	no	—
147	C₂²×C₃₁	—	2	4	no	—
148	C₂²×C₃₁	—	2	4	no	—
149	C₂²×C₃₁	#340	1	4	yes	—
150	C₂²×C₃₁	C₂×#95	1	1	yes	characteristic
151	C₂²×C₃₁	#407	1	2	yes	—
152	C₂²×C₃₁	C₂×#102	1	1	yes	characteristic
153	C₂²×C₃₁	C₂×#103	1	1	yes	characteristic
154	C₂²×C₃₁	#421	1	2	yes	—
155	C₄×C₃₁	—	2	2	no	—
156	C₄×C₃₁	—	2	1	no	—
157	C₄×C₃₁	—	2	2	no	—
158	C₄×C₃₁	—	2	1	no	—
159	C₄×C₃₁	—	4	8	no	—
160	C₄×C₃₁	#340	1	4	yes	—
161	C₄×C₃₁	C₄×M₁₆	1	2	yes	—
162	C₄×C₃₁	C₂×#102	1	1	yes	characteristic
163	C₄×C₃₁	C₂×#103	1	1	yes	characteristic
164	C₄×C₃₁	#423	1	2	yes	—
165	C₄×C₃₁	C₂×#106	1	1	yes	characteristic
166	C₄×C₃₁	C₂×#107	1	1	yes	characteristic
167	C₂²×M₁₆	—	2	1	no	—
168	C₂²×C₄⋊C₄	C₄×C₃₁	1	2	yes	—
169	C₂²×C₄²	—	2	1	no	—
170	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
171	#431	—	2	2	no	—
172	#431	C₄×C₃₁	1	4	yes	complemented
173	#423	—	2	2	no	—
174	#423	C₄×C₃₁	1	4	yes	complemented
175	C₂×C₄⋊C₈	—	2	1	no	—
176	C₂×C₄⋊C₈	—	2	1	no	—
177	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
178	C₂×C₂²⋊C₈	—	2	1	no	—
179	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
180	C₄×C₄⋊C₄	—	2	1	no	—
181	C₄×C₄⋊C₄	—	2	1	no	—
182	C₄×C₄⋊C₄	C₄×C₃₁	1	2	yes	—
183	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
184	C₂×#95	—	2	1	no	—
185	C₂×C₃₁	—	2	4	no	—
186	C₂×C₃₁	#1486	1	2	yes	—
187	C₂×C₃₁	#1487	1	2	yes	—
188	C₂×C₃₁	#1728	1	1	yes	characteristic
189	C₂×C₃₁	#1733	1	1	yes	characteristic
190	C₂×C₃₁	C₂×#340	1	1	yes	characteristic
191	C₂³×C₄	—	2	2	no	—
192	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
193	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
194	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
195	C₂×M₁₆	—	2	4	no	—
196	C₂×M₁₆	—	4	2	no	—
197	C₂×M₁₆	—	4	2	no	—
198	C₂²×C₈	—	2	2	no	—
199	C₂²×C₈	—	2	2	no	—
200	C₂×C₄⋊C₄	—	2	2	no	—
201	C₂×C₄⋊C₄	—	2	8	no	—
202	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
203	C₂×C₄²	—	2	2	no	—
204	C₂×C₄²	—	2	2	no	—
205	C₂×C₄²	—	4	2	no	—
206	C₂×C₄²	—	4	2	no	—
207	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
208	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
209	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
210	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
211	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
212	C₂×C₄²	D₄×C₃₁	1	2	yes	—
213	C₂×C₄²	Q₈×C₃₁	1	2	yes	—
214	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
215	C₄⋊C₈	—	2	4	no	—
216	C₄⋊C₈	—	2	4	no	—
217	C₄⋊C₈	—	2	2	no	—
218	C₄⋊C₈	C₂×C₄×C₃₁	1	4	yes	complemented
219	C₂²⋊C₈	—	2	4	no	—
220	C₄×C₈	—	2	2	no	—
221	C₄×C₈	C₂×C₄×C₃₁	1	4	yes	complemented
222	#95	—	2	2	no	—
223	#95	—	2	2	no	—
224	C₃₁	#7901	1	1	yes	characteristic, direct product factor, Sylow
225	C₂⁴	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
226	C₂²×C₄	—	2	4	no	—
227	C₂²×C₄	—	2	8	no	—
228	C₂²×C₄	—	2	4	no	—
229	C₂²×C₄	—	4	2	no	—
230	C₂²×C₄	—	4	4	no	—
231	C₂²×C₄	—	4	4	no	—
232	C₂²×C₄	C₄²×C₃₁	1	2	yes	—
233	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
234	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
235	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
236	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
237	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
238	C₂²×C₄	C₄⋊C₄×C₃₁	1	2	yes	—
239	C₂²×C₄	C₄⋊C₄×C₃₁	1	2	yes	—
240	C₂²×C₄	C₄⋊C₄×C₃₁	1	2	yes	—
241	C₂²×C₄	D₈×C₃₁	1	2	yes	—
242	C₂²×C₄	SD₁₆×C₃₁	1	2	yes	—
243	C₂²×C₄	SD₁₆×C₃₁	1	2	yes	—
244	C₂²×C₄	Q₁₆×C₃₁	1	2	yes	—
245	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
246	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
247	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
248	M₁₆	—	4	8	no	—
249	C₂×C₈	—	2	4	no	—
250	C₂×C₈	—	2	4	no	—
251	C₂×C₈	—	4	4	no	—
252	C₂×C₈	—	4	2	no	—
253	C₂×C₈	—	4	2	no	—
254	C₄⋊C₄	—	2	8	no	—
255	C₄⋊C₄	—	2	4	no	—
256	C₄⋊C₄	M₁₆×C₃₁	1	8	yes	complemented
257	C₄²	—	4	4	no	—
258	C₄²	—	4	2	no	—
259	C₄²	—	4	2	no	—
260	C₄²	C₄²×C₃₁	1	2	yes	—
261	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
262	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
263	C₄²	C₄⋊C₄×C₃₁	1	2	yes	—
264	C₄²	C₄⋊C₄×C₃₁	1	2	yes	—
265	C₄²	C₄⋊C₄×C₃₁	1	2	yes	—
266	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
267	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
268	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
269	C₄²	C₂×Q₈×C₃₁	1	1	yes	characteristic
270	C₂³	—	2	2	no	—
271	C₂³	—	2	2	no	—
272	C₂³	C₃₁×#95	1	2	yes	—
273	C₂³	C₃₁×#102	1	2	yes	—
274	C₂³	C₃₁×#103	1	2	yes	—
275	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
276	C₂×C₄	—	2	2	no	—
277	C₂×C₄	—	2	2	no	—
278	C₂×C₄	—	2	2	no	—
279	C₂×C₄	—	2	4	no	—
280	C₂×C₄	—	2	4	no	—
281	C₂×C₄	—	2	8	no	—
282	C₂×C₄	—	4	2	no	—
283	C₂×C₄	—	4	2	no	—
284	C₂×C₄	—	4	16	no	—
285	C₂×C₄	—	4	4	no	—
286	C₂×C₄	—	4	4	no	—
287	C₂×C₄	C₃₁×#95	1	2	yes	—
288	C₂×C₄	C₃₁×#95	1	2	yes	—
289	C₂×C₄	C₃₁×#95	1	2	yes	—
290	C₂×C₄	C₃₁×#102	1	4	yes	—
291	C₂×C₄	C₃₁×#102	1	2	yes	—
292	C₂×C₄	C₃₁×#103	1	4	yes	—
293	C₂×C₄	C₃₁×#103	1	2	yes	—
294	C₂×C₄	C₃₁×#106	1	4	yes	—
295	C₂×C₄	C₃₁×#107	1	4	yes	—
296	C₂×C₄	C₂×C₄²×C₃₁	1	1	yes	characteristic
297	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
298	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
299	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
300	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
301	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
302	C₂×C₄	C₂×M₁₆×C₃₁	1	4	yes	—
303	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
304	C₂×C₄	C₂×SD₁₆×C₃₁	1	1	yes	characteristic
305	C₂×C₄	C₂×SD₁₆×C₃₁	1	1	yes	characteristic
306	C₂×C₄	C₂×Q₁₆×C₃₁	1	1	yes	characteristic
307	C₈	—	4	4	no	—
308	C₈	—	4	4	no	—
309	C₂²	—	2	2	no	—
310	C₂²	—	2	2	no	—
311	C₂²	—	2	4	no	—
312	C₂²	—	2	4	no	—
313	C₂²	C₃₁×#340	1	4	yes	—
314	C₂²	C₂×C₃₁×#95	1	1	yes	characteristic
315	C₂²	C₃₁×#407	1	2	yes	—
316	C₂²	C₂×C₃₁×#102	1	1	yes	characteristic
317	C₂²	C₂×C₃₁×#103	1	1	yes	characteristic
318	C₂²	C₃₁×#421	1	2	yes	—
319	C₄	—	2	2	no	—
320	C₄	—	2	1	no	—
321	C₄	—	2	2	no	—
322	C₄	—	2	1	no	—
323	C₄	—	4	8	no	—
324	C₄	C₃₁×#340	1	4	yes	—
325	C₄	C₄×M₁₆×C₃₁	1	2	yes	—
326	C₄	C₂×C₃₁×#102	1	1	yes	characteristic
327	C₄	C₂×C₃₁×#103	1	1	yes	characteristic
328	C₄	C₃₁×#423	1	2	yes	—
329	C₄	C₂×C₃₁×#106	1	1	yes	characteristic
330	C₄	C₂×C₃₁×#107	1	1	yes	characteristic
331	C₂	—	2	4	no	—
332	C₂	C₃₁×#1486	1	2	yes	—
333	C₂	C₃₁×#1487	1	2	yes	—
334	C₂	C₃₁×#1728	1	1	yes	characteristic
335	C₂	C₃₁×#1733	1	1	yes	characteristic
336	C₂	C₂×C₃₁×#340	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₃₁×#1279	C₂	semidirect
10. C₃₁×#431	C₄	semidirect
12. C₃₁×#423	C₄	semidirect
50. C₃₁×C₄⋊C₈	C₂×C₄	semidirect
53. C₄×C₈×C₃₁	C₂×C₄	semidirect
87. C₄⋊C₄×C₃₁	M₁₆	semidirect
101. #7901	C₃₁	direct (N × H)
144. #1279	C₂×C₃₁	semidirect
172. #431	C₄×C₃₁	semidirect
174. #423	C₄×C₃₁	semidirect
218. C₄⋊C₈	C₂×C₄×C₃₁	semidirect
221. C₄×C₈	C₂×C₄×C₃₁	semidirect
224. C₃₁	#7901	direct (N × H)
256. C₄⋊C₄	M₁₆×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#431	2
C₂×C₃₁×#423	2
C₂×C₄×C₄⋊C₄×C₃₁	2
C₃₁×#1279	2
#7901	31

Subgroups — C31×#7901 #21464660

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#7901 #21464660