Subgroups — C₃₁×#33738 #21490497

Order 7936.

510 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3170	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3168	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2255	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2251	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2245	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2243	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2220	C₂	1	2	yes	maximal
8	C₃₁×#2219	C₂	1	2	yes	maximal, complemented
9	C₄×C₃₁×Q₃₂	C₂	1	2	yes	maximal, complemented
10	C₄×C₃₁×SD₃₂	C₂	1	2	yes	maximal, complemented
11	C₄×C₃₁×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#533	—	2	1	no	—
13	C₃₁×#529	—	2	1	no	—
14	C₂×C₃₁×Q₃₂	C₂²	1	2	yes	—
15	C₂×C₃₁×SD₃₂	C₂²	1	2	yes	—
16	C₂×C₃₁×M₃₂	C₂²	1	2	yes	—
17	C₃₁×#500	C₂²	1	1	yes	characteristic
18	C₃₁×#499	C₂²	1	1	yes	characteristic
19	C₃₁×#495	C₂²	1	1	yes	characteristic
20	C₃₁×#494	C₂²	1	1	yes	characteristic
21	C₃₁×#488	—	2	1	no	—
22	C₃₁×#487	—	2	1	no	—
23	C₃₁×#467	—	2	1	no	—
24	C₃₁×#467	C₂²	1	1	yes	characteristic
25	C₃₁×#467	C₂²	1	2	yes	—
26	C₃₁×#466	C₂²	1	1	yes	characteristic
27	C₃₁×#465	—	2	1	no	—
28	C₄×Q₁₆×C₃₁	—	2	1	no	—
29	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
30	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
31	C₄×SD₁₆×C₃₁	—	2	1	no	—
32	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
34	C₃₁×#367	C₂²	1	2	yes	—
35	C₃₁×#366	C₂²	1	2	yes	—
36	C₃₁×#358	C₂²	1	2	yes	—
37	C₃₁×#358	C₂²	1	2	yes	—
38	C₃₁×#358	C₂²	1	2	yes	—
39	C₃₁×#357	C₂²	1	2	yes	—
40	C₃₁×#346	C₂²	1	1	yes	characteristic
41	C₃₁×#346	C₂²	1	1	yes	characteristic
42	C₄×C₁₆×C₃₁	C₂²	1	2	yes	—
43	C₂×Q₁₆×C₃₁	—	2	1	no	—
44	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
45	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
46	C₂×SD₁₆×C₃₁	—	2	1	no	—
47	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
49	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
50	C₃₁×C₄⋊Q₈	—	2	1	no	—
51	C₃₁×C₄⋊Q₈	—	2	1	no	—
52	C₃₁×#126	—	4	1	no	—
53	C₃₁×#125	—	2	1	no	—
54	C₃₁×#125	—	4	1	no	—
55	C₃₁×#124	—	2	1	no	—
56	C₃₁×#123	—	4	1	no	—
57	C₃₁×C₂²⋊Q₈	—	2	1	no	—
58	C₃₁×C₂²⋊Q₈	—	2	2	no	—
59	C₃₁×C₂²⋊Q₈	—	4	1	no	—
60	C₃₁×#121	—	2	1	no	—
61	C₄×Q₈×C₃₁	—	2	1	no	—
62	C₄×Q₈×C₃₁	—	2	2	no	—
63	C₄×Q₈×C₃₁	—	4	1	no	—
64	C₄×D₄×C₃₁	—	2	1	no	—
65	C₄×D₄×C₃₁	—	4	1	no	—
66	C₃₁×#117	—	4	1	no	—
67	C₃₁×#117	—	4	1	no	—
68	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
69	C₃₁×Q₃₂	—	2	4	no	—
70	C₃₁×SD₃₂	—	2	4	no	—
71	C₃₁×M₃₂	—	2	4	no	—
72	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
73	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
74	C₃₁×#107	—	2	1	no	—
75	C₃₁×#107	C₂³	1	1	yes	characteristic
76	C₃₁×#107	C₂³	1	1	yes	characteristic
77	C₃₁×#107	C₂³	1	2	yes	—
78	C₃₁×#106	—	2	1	no	—
79	C₃₁×#103	—	2	1	no	—
80	C₃₁×#103	—	2	2	no	—
81	C₃₁×#103	—	2	1	no	—
82	C₃₁×#103	—	2	2	no	—
83	C₃₁×#102	—	2	1	no	—
84	C₃₁×#102	—	2	1	no	—
85	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
86	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
87	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
89	C₂×Q₈×C₃₁	—	2	1	no	—
90	C₂×Q₈×C₃₁	—	2	2	no	—
91	C₂×Q₈×C₃₁	—	4	1	no	—
92	C₂×D₄×C₃₁	—	2	1	no	—
93	C₂×D₄×C₃₁	—	4	1	no	—
94	C₂²×C₄×C₃₁	—	4	1	no	—
95	C₂²×C₄×C₃₁	D₈	1	1	yes	characteristic
96	C₂²×C₄×C₃₁	D₈	1	1	yes	characteristic
97	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
98	Q₁₆×C₃₁	—	2	2	no	—
99	Q₁₆×C₃₁	—	2	2	no	—
100	Q₁₆×C₃₁	—	2	2	no	—
101	Q₁₆×C₃₁	—	4	2	no	—
102	SD₁₆×C₃₁	—	4	2	no	—
103	D₈×C₃₁	—	2	2	no	—
104	C₂×C₈×C₃₁	—	2	2	no	—
105	C₂×C₈×C₃₁	—	2	2	no	—
106	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
107	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
108	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
109	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
110	C₄⋊C₄×C₃₁	—	2	1	no	—
111	C₄⋊C₄×C₃₁	—	2	1	no	—
112	C₄⋊C₄×C₃₁	—	2	2	no	—
113	C₄⋊C₄×C₃₁	—	4	1	no	—
114	C₄⋊C₄×C₃₁	—	4	1	no	—
115	C₄⋊C₄×C₃₁	—	4	1	no	—
116	C₄⋊C₄×C₃₁	—	4	1	no	—
117	C₄⋊C₄×C₃₁	—	4	1	no	—
118	C₄⋊C₄×C₃₁	—	4	2	no	—
119	C₄⋊C₄×C₃₁	—	4	1	no	—
120	C₄⋊C₄×C₃₁	—	4	2	no	—
121	C₄⋊C₄×C₃₁	—	4	1	no	—
122	C₂²⋊C₄×C₃₁	—	4	2	no	—
123	C₂²⋊C₄×C₃₁	—	4	1	no	—
124	C₂²⋊C₄×C₃₁	—	4	1	no	—
125	C₂²⋊C₄×C₃₁	—	4	1	no	—
126	C₂²⋊C₄×C₃₁	—	4	1	no	—
127	C₂²⋊C₄×C₃₁	—	4	1	no	—
128	C₄²×C₃₁	—	4	1	no	—
129	C₄²×C₃₁	—	4	2	no	—
130	C₄²×C₃₁	D₈	1	1	yes	characteristic
131	C₄²×C₃₁	D₈	1	1	yes	characteristic
132	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
134	C₁₆×C₃₁	—	2	2	no	—
135	C₁₆×C₃₁	#41	1	4	yes	—
136	#33738	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂³×C₃₁	—	4	1	no	—
138	C₂³×C₃₁	C₂×D₈	1	1	yes	characteristic
139	Q₈×C₃₁	—	4	2	no	—
140	Q₈×C₃₁	—	4	1	no	—
141	Q₈×C₃₁	—	4	1	no	—
142	Q₈×C₃₁	—	4	2	no	—
143	Q₈×C₃₁	—	8	2	no	—
144	D₄×C₃₁	—	4	1	no	—
145	D₄×C₃₁	—	4	1	no	—
146	D₄×C₃₁	—	8	2	no	—
147	C₂×C₄×C₃₁	—	2	1	no	—
148	C₂×C₄×C₃₁	—	2	1	no	—
149	C₂×C₄×C₃₁	—	2	2	no	—
150	C₂×C₄×C₃₁	—	4	1	no	—
151	C₂×C₄×C₃₁	—	4	1	no	—
152	C₂×C₄×C₃₁	—	4	1	no	—
153	C₂×C₄×C₃₁	—	4	2	no	—
154	C₂×C₄×C₃₁	—	4	2	no	—
155	C₂×C₄×C₃₁	—	4	1	no	—
156	C₂×C₄×C₃₁	—	8	2	no	—
157	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
158	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
159	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
160	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
161	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
162	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
163	C₈×C₃₁	—	2	1	no	—
164	C₈×C₃₁	—	2	1	no	—
165	C₈×C₃₁	#135	1	2	yes	—
166	C₈×C₃₁	C₂×#41	1	2	yes	—
167	#3170	C₂×C₃₁	1	1	yes	characteristic, complemented
168	#3168	C₂×C₃₁	1	1	yes	characteristic
169	#2255	C₂×C₃₁	1	1	yes	characteristic, complemented
170	#2251	C₂×C₃₁	1	1	yes	characteristic, complemented
171	#2245	C₂×C₃₁	1	1	yes	characteristic, complemented
172	#2243	C₂×C₃₁	1	1	yes	characteristic, complemented
173	#2220	C₂×C₃₁	1	2	yes	—
174	#2219	C₂×C₃₁	1	2	yes	complemented
175	C₄×Q₃₂	C₂×C₃₁	1	2	yes	complemented
176	C₄×SD₃₂	C₂×C₃₁	1	2	yes	complemented
177	C₄×M₃₂	C₂×C₃₁	1	1	yes	characteristic, complemented
178	C₂²×C₃₁	—	2	1	no	—
179	C₂²×C₃₁	—	2	1	no	—
180	C₂²×C₃₁	—	2	1	no	—
181	C₂²×C₃₁	—	8	1	no	—
182	C₂²×C₃₁	—	8	1	no	—
183	C₂²×C₃₁	—	8	1	no	—
184	C₂²×C₃₁	C₂²×D₈	1	1	yes	characteristic
185	C₄×C₃₁	—	2	1	no	—
186	C₄×C₃₁	—	2	1	no	—
187	C₄×C₃₁	—	2	1	no	—
188	C₄×C₃₁	—	2	1	no	—
189	C₄×C₃₁	—	8	1	no	—
190	C₄×C₃₁	—	8	1	no	—
191	C₄×C₃₁	—	8	2	no	—
192	C₄×C₃₁	—	8	1	no	—
193	C₄×C₃₁	—	8	2	no	—
194	C₄×C₃₁	#510	1	2	yes	—
195	C₄×C₃₁	#532	1	1	yes	characteristic
196	C₄×C₃₁	C₂×#135	1	1	yes	characteristic
197	#533	—	2	1	no	—
198	#529	—	2	1	no	—
199	C₂×Q₃₂	C₂²×C₃₁	1	2	yes	—
200	C₂×SD₃₂	C₂²×C₃₁	1	2	yes	—
201	C₂×M₃₂	C₂²×C₃₁	1	2	yes	—
202	#500	C₂²×C₃₁	1	1	yes	characteristic
203	#499	C₂²×C₃₁	1	1	yes	characteristic
204	#495	C₂²×C₃₁	1	1	yes	characteristic
205	#494	C₂²×C₃₁	1	1	yes	characteristic
206	#488	—	2	1	no	—
207	#487	—	2	1	no	—
208	#467	—	2	1	no	—
209	#467	C₂²×C₃₁	1	1	yes	characteristic
210	#467	C₂²×C₃₁	1	2	yes	—
211	#466	C₂²×C₃₁	1	1	yes	characteristic
212	#465	—	2	1	no	—
213	C₄×Q₁₆	—	2	1	no	—
214	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
215	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
216	C₄×SD₁₆	—	2	1	no	—
217	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
218	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
219	#367	C₂²×C₃₁	1	2	yes	—
220	#366	C₂²×C₃₁	1	2	yes	—
221	#358	C₂²×C₃₁	1	2	yes	—
222	#358	C₂²×C₃₁	1	2	yes	—
223	#358	C₂²×C₃₁	1	2	yes	—
224	#357	C₂²×C₃₁	1	2	yes	—
225	#346	C₂²×C₃₁	1	1	yes	characteristic
226	#346	C₂²×C₃₁	1	1	yes	characteristic
227	C₄×C₁₆	C₂²×C₃₁	1	2	yes	—
228	C₂×C₃₁	—	4	1	no	—
229	C₂×C₃₁	—	16	1	no	—
230	C₂×C₃₁	#3169	1	1	yes	characteristic
231	C₂×C₃₁	C₂×#510	1	1	yes	characteristic
232	C₂×C₃₁	#3414	1	1	yes	characteristic
233	C₂×Q₁₆	—	2	1	no	—
234	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
235	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
236	C₂×SD₁₆	—	2	1	no	—
237	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
238	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
239	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
240	C₄⋊Q₈	—	2	1	no	—
241	C₄⋊Q₈	—	2	1	no	—
242	#126	—	4	1	no	—
243	#125	—	2	1	no	—
244	#125	—	4	1	no	—
245	#124	—	2	1	no	—
246	#123	—	4	1	no	—
247	C₂²⋊Q₈	—	2	1	no	—
248	C₂²⋊Q₈	—	2	2	no	—
249	C₂²⋊Q₈	—	4	1	no	—
250	#121	—	2	1	no	—
251	C₄×Q₈	—	2	1	no	—
252	C₄×Q₈	—	2	2	no	—
253	C₄×Q₈	—	4	1	no	—
254	C₄×D₄	—	2	1	no	—
255	C₄×D₄	—	4	1	no	—
256	#117	—	4	1	no	—
257	#117	—	4	1	no	—
258	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
259	Q₃₂	—	2	4	no	—
260	SD₃₂	—	2	4	no	—
261	M₃₂	—	2	4	no	—
262	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
263	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
264	#107	—	2	1	no	—
265	#107	C₂³×C₃₁	1	2	yes	—
266	#107	C₂³×C₃₁	1	1	yes	characteristic
267	#107	C₂³×C₃₁	1	1	yes	characteristic
268	#106	—	2	1	no	—
269	#103	—	2	1	no	—
270	#103	—	2	2	no	—
271	#103	—	2	1	no	—
272	#103	—	2	2	no	—
273	#102	—	2	1	no	—
274	#102	—	2	1	no	—
275	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
276	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
277	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
278	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
279	C₃₁	#33738	1	1	yes	characteristic, direct product factor, Sylow
280	C₂×Q₈	—	2	1	no	—
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	4	1	no	—
283	C₂×D₄	—	2	1	no	—
284	C₂×D₄	—	4	1	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	D₈×C₃₁	1	1	yes	characteristic
287	C₂²×C₄	D₈×C₃₁	1	1	yes	characteristic
288	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
289	Q₁₆	—	2	2	no	—
290	Q₁₆	—	2	2	no	—
291	Q₁₆	—	2	2	no	—
292	Q₁₆	—	4	2	no	—
293	SD₁₆	—	4	2	no	—
294	D₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
298	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
299	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
300	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	—	2	1	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	4	1	no	—
305	C₄⋊C₄	—	4	1	no	—
306	C₄⋊C₄	—	4	1	no	—
307	C₄⋊C₄	—	4	1	no	—
308	C₄⋊C₄	—	4	1	no	—
309	C₄⋊C₄	—	4	2	no	—
310	C₄⋊C₄	—	4	1	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₄⋊C₄	—	4	1	no	—
313	C₂²⋊C₄	—	4	2	no	—
314	C₂²⋊C₄	—	4	1	no	—
315	C₂²⋊C₄	—	4	1	no	—
316	C₂²⋊C₄	—	4	1	no	—
317	C₂²⋊C₄	—	4	1	no	—
318	C₂²⋊C₄	—	4	1	no	—
319	C₄²	—	4	1	no	—
320	C₄²	—	4	2	no	—
321	C₄²	D₈×C₃₁	1	1	yes	characteristic
322	C₄²	D₈×C₃₁	1	1	yes	characteristic
323	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
324	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
325	C₁₆	—	2	2	no	—
326	C₁₆	#41×C₃₁	1	4	yes	—
327	C₂³	—	4	1	no	—
328	C₂³	C₂×D₈×C₃₁	1	1	yes	characteristic
329	Q₈	—	4	2	no	—
330	Q₈	—	4	1	no	—
331	Q₈	—	4	1	no	—
332	Q₈	—	4	2	no	—
333	Q₈	—	8	2	no	—
334	D₄	—	4	1	no	—
335	D₄	—	4	1	no	—
336	D₄	—	8	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	8	2	no	—
347	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
348	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
349	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
350	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
351	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
352	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
353	C₈	—	2	1	no	—
354	C₈	—	2	1	no	—
355	C₈	C₃₁×#135	1	2	yes	—
356	C₈	C₂×#41×C₃₁	1	2	yes	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	8	1	no	—
361	C₂²	—	8	1	no	—
362	C₂²	—	8	1	no	—
363	C₂²	C₂²×D₈×C₃₁	1	1	yes	characteristic
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	8	1	no	—
369	C₄	—	8	1	no	—
370	C₄	—	8	2	no	—
371	C₄	—	8	1	no	—
372	C₄	—	8	2	no	—
373	C₄	C₃₁×#510	1	2	yes	—
374	C₄	C₃₁×#532	1	1	yes	characteristic
375	C₄	C₂×C₃₁×#135	1	1	yes	characteristic
376	C₂	—	4	1	no	—
377	C₂	—	16	1	no	—
378	C₂	C₃₁×#3169	1	1	yes	characteristic
379	C₂	C₂×C₃₁×#510	1	1	yes	characteristic
380	C₂	C₃₁×#3414	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₁	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₃₁
socle	C₂²×C₃₁	C₂²×D₈
prime radical	C₃₁×#466	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ C₂×C₄²×C₃₁ ◁ C₂×C₄×C₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3170	C₂	semidirect
3. C₃₁×#2255	C₂	semidirect
4. C₃₁×#2251	C₂	semidirect
5. C₃₁×#2245	C₂	semidirect
6. C₃₁×#2243	C₂	semidirect
8. C₃₁×#2219	C₂	semidirect
9. C₄×C₃₁×Q₃₂	C₂	semidirect
10. C₄×C₃₁×SD₃₂	C₂	semidirect
11. C₄×C₃₁×M₃₂	C₂	semidirect
136. #33738	C₃₁	direct (N × H)
167. #3170	C₂×C₃₁	semidirect
169. #2255	C₂×C₃₁	semidirect
170. #2251	C₂×C₃₁	semidirect
171. #2245	C₂×C₃₁	semidirect
172. #2243	C₂×C₃₁	semidirect
174. #2219	C₂×C₃₁	semidirect
175. C₄×Q₃₂	C₂×C₃₁	semidirect
176. C₄×SD₃₂	C₂×C₃₁	semidirect
177. C₄×M₃₂	C₂×C₃₁	semidirect
279. C₃₁	#33738	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#3170	2
C₃₁×#3168	2
C₃₁×#2255	2
C₃₁×#2251	2
C₃₁×#2245	2
C₃₁×#2243	2
C₃₁×#2220	2
C₃₁×#2219	2
C₄×C₃₁×Q₃₂	2
C₄×C₃₁×SD₃₂	2
C₄×C₃₁×M₃₂	2
#33738	31

Subgroups — C31×#33738 #21490497

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33738 #21490497