Subgroups — C₃₁×#33433 #21490192

Order 7936.

682 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#504	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃₁×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2929	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#2169	C₂	1	4	yes	maximal, complemented
5	C₃₁×#2168	C₂	1	4	yes	maximal, complemented
6	C₃₁×#2151	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2113	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2112	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#2108	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
12	C₃₁×#525	C₄	1	1	yes	characteristic
13	C₃₁×#504	—	2	4	no	—
14	C₂×C₃₁×M₃₂	—	2	4	no	—
15	C₂×C₃₁×M₃₂	C₂²	1	1	yes	characteristic
16	C₂×C₃₁×M₃₂	C₂²	1	1	yes	characteristic
17	C₂×C₃₁×M₃₂	C₂²	1	2	yes	—
18	C₂×C₃₁×M₃₂	C₂²	1	2	yes	—
19	C₂×C₃₁×M₃₂	C₂²	1	2	yes	complemented
20	C₂²×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
21	C₂²×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
22	C₂²×C₁₆×C₃₁	C₂²	1	2	yes	complemented
23	C₃₁×#435	C₄	1	4	yes	—
24	C₈×D₄×C₃₁	C₂²	1	4	yes	—
25	C₃₁×#424	C₄	1	1	yes	characteristic
26	C₃₁×#408	C₄	1	1	yes	characteristic
27	C₃₁×#407	C₄	1	1	yes	characteristic
28	C₃₁×#405	C₂²	1	1	yes	characteristic
29	C₃₁×C₄⋊C₁₆	C₂²	1	4	yes	complemented
30	C₃₁×C₂²⋊C₁₆	C₂²	1	4	yes	—
31	C₃₁×C₂²⋊C₁₆	C₂²	1	4	yes	complemented
32	C₃₁×#346	C₂²	1	2	yes	complemented
33	C₄×C₁₆×C₃₁	C₂²	1	2	yes	complemented
34	C₂×#41×C₃₁	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
36	C₃₁×#131	—	2	2	no	—
37	C₃₁×#131	—	2	2	no	—
38	C₂×M₁₆×C₃₁	C₂×C₄	1	1	yes	characteristic
39	C₂×M₁₆×C₃₁	C₂×C₄	1	1	yes	characteristic
40	C₂×M₁₆×C₃₁	C₂×C₄	1	2	yes	—
41	C₂²×C₈×C₃₁	—	2	2	no	—
42	C₂²×C₈×C₃₁	—	2	2	no	—
43	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₃₁	C₂×C₄	1	2	yes	—
45	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
46	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
47	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
48	C₃₁×#123	C₈	1	2	yes	—
49	C₃₁×C₂²⋊Q₈	C₈	1	2	yes	—
50	C₃₁×#121	C₈	1	2	yes	—
51	C₃₁×#120	C₈	1	2	yes	—
52	C₄×D₄×C₃₁	C₂×C₄	1	4	yes	—
53	C₃₁×#117	C₂×C₄	1	1	yes	characteristic
54	C₃₁×M₃₂	—	2	2	no	—
55	C₃₁×M₃₂	—	2	2	no	—
56	C₃₁×M₃₂	—	2	4	no	—
57	C₃₁×M₃₂	—	2	4	no	—
58	C₃₁×M₃₂	—	2	4	no	—
59	C₂×C₁₆×C₃₁	—	2	2	no	—
60	C₂×C₁₆×C₃₁	—	2	4	no	—
61	C₂×C₁₆×C₃₁	D₄	1	4	yes	complemented
62	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
63	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
64	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
65	C₂×C₁₆×C₃₁	C₂³	1	1	yes	characteristic
66	C₂×C₁₆×C₃₁	C₂³	1	1	yes	characteristic
67	C₃₁×C₄⋊C₈	C₂×C₄	1	4	yes	—
68	C₃₁×C₂²⋊C₈	C₂×C₄	1	4	yes	—
69	C₃₁×C₂²⋊C₈	C₂×C₄	1	4	yes	—
70	C₃₁×#97	C₂×C₄	1	2	yes	—
71	C₄×C₈×C₃₁	C₂³	1	2	yes	—
72	C₂⁴×C₃₁	C₂×C₈	1	1	yes	characteristic
73	#41×C₃₁	—	2	2	no	—
74	#41×C₃₁	—	2	2	no	—
75	C₂×Q₈×C₃₁	C₂×C₈	1	1	yes	characteristic
76	C₂×D₄×C₃₁	C₂×C₈	1	2	yes	—
77	C₂×D₄×C₃₁	C₂×C₈	1	1	yes	characteristic
78	C₂×D₄×C₃₁	C₂×C₈	1	4	yes	—
79	C₂²×C₄×C₃₁	—	2	2	no	—
80	C₂²×C₄×C₃₁	—	2	2	no	—
81	C₂²×C₄×C₃₁	C₂×C₈	1	2	yes	—
82	C₂²×C₄×C₃₁	C₂×C₈	1	1	yes	characteristic
83	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
86	M₁₆×C₃₁	—	2	2	no	—
87	M₁₆×C₃₁	—	2	2	no	—
88	M₁₆×C₃₁	—	2	4	no	—
89	C₂×C₈×C₃₁	—	2	2	no	—
90	C₂×C₈×C₃₁	—	2	4	no	—
91	C₂×C₈×C₃₁	—	2	2	no	—
92	C₂×C₈×C₃₁	—	2	2	no	—
93	C₂×C₈×C₃₁	—	2	2	no	—
94	C₂×C₈×C₃₁	—	2	2	no	—
95	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
96	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
97	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
98	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
100	C₂×C₈×C₃₁	#41	1	2	yes	—
101	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
102	C₄⋊C₄×C₃₁	C₂×C₈	1	2	yes	—
103	C₄⋊C₄×C₃₁	C₂×C₈	1	4	yes	—
104	C₂²⋊C₄×C₃₁	C₂×C₈	1	2	yes	—
105	C₂²⋊C₄×C₃₁	C₂×C₈	1	4	yes	—
106	C₂²⋊C₄×C₃₁	C₂×C₈	1	4	yes	—
107	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
108	C₁₆×C₃₁	—	2	2	no	—
109	C₁₆×C₃₁	—	2	2	no	—
110	C₁₆×C₃₁	—	2	2	no	—
111	C₁₆×C₃₁	C₂×D₄	1	2	yes	—
112	C₁₆×C₃₁	C₂×D₄	1	2	yes	—
113	#33433	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
114	C₂³×C₃₁	—	2	2	no	—
115	C₂³×C₃₁	—	4	2	no	—
116	C₂³×C₃₁	C₂²×C₈	1	2	yes	—
117	C₂³×C₃₁	C₂²×C₈	1	2	yes	—
118	C₂³×C₃₁	C₂²×C₈	1	1	yes	characteristic
119	Q₈×C₃₁	—	2	2	no	—
120	D₄×C₃₁	—	2	4	no	—
121	D₄×C₃₁	—	2	2	no	—
122	D₄×C₃₁	—	4	4	no	—
123	C₂×C₄×C₃₁	—	2	2	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	C₄×D₄	1	2	yes	—
130	C₂×C₄×C₃₁	C₂²×C₈	1	4	yes	—
131	C₂×C₄×C₃₁	C₂²×C₈	1	2	yes	—
132	C₂×C₄×C₃₁	C₂²×C₈	1	2	yes	—
133	C₂×C₄×C₃₁	C₂²×C₈	1	1	yes	characteristic
134	C₂×C₄×C₃₁	#131	1	2	yes	—
135	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
136	C₈×C₃₁	—	2	2	no	—
137	C₈×C₃₁	—	2	2	no	—
138	C₈×C₃₁	—	2	2	no	—
139	C₈×C₃₁	C₄×D₄	1	2	yes	—
140	C₈×C₃₁	C₂²×D₄	1	1	yes	characteristic
141	C₈×C₃₁	C₂×#41	1	1	yes	characteristic
142	C₂×#504	C₂×C₃₁	1	1	yes	characteristic, complemented
143	C₂²×M₃₂	C₂×C₃₁	1	1	yes	characteristic, complemented
144	#2929	C₂×C₃₁	1	1	yes	characteristic
145	#2169	C₂×C₃₁	1	4	yes	complemented
146	#2168	C₂×C₃₁	1	4	yes	complemented
147	#2151	C₂×C₃₁	1	1	yes	characteristic, complemented
148	#2113	C₂×C₃₁	1	1	yes	characteristic, complemented
149	#2112	C₂×C₃₁	1	1	yes	characteristic, complemented
150	#2108	C₂×C₃₁	1	1	yes	characteristic, complemented
151	C₂²×C₃₁	—	2	2	no	—
152	C₂²×C₃₁	—	2	2	no	—
153	C₂²×C₃₁	—	2	4	no	—
154	C₂²×C₃₁	—	2	2	no	—
155	C₂²×C₃₁	—	2	2	no	—
156	C₂²×C₃₁	—	2	2	no	—
157	C₂²×C₃₁	—	4	4	no	—
158	C₂²×C₃₁	C₈×D₄	1	2	yes	—
159	C₂²×C₃₁	C₂³×C₈	1	1	yes	characteristic
160	C₄×C₃₁	—	2	4	no	—
161	C₄×C₃₁	—	2	2	no	—
162	C₄×C₃₁	—	2	2	no	—
163	C₄×C₃₁	C₈×D₄	1	2	yes	—
164	C₄×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
165	C₄×C₃₁	C₂×#131	1	1	yes	characteristic
166	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic
167	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
168	#525	C₄×C₃₁	1	1	yes	characteristic
169	#504	—	2	4	no	—
170	C₂×M₃₂	—	2	4	no	—
171	C₂×M₃₂	C₂²×C₃₁	1	1	yes	characteristic
172	C₂×M₃₂	C₂²×C₃₁	1	1	yes	characteristic
173	C₂×M₃₂	C₂²×C₃₁	1	2	yes	—
174	C₂×M₃₂	C₂²×C₃₁	1	2	yes	—
175	C₂×M₃₂	C₂²×C₃₁	1	2	yes	complemented
176	C₂²×C₁₆	C₂²×C₃₁	1	1	yes	characteristic
177	C₂²×C₁₆	C₂²×C₃₁	1	1	yes	characteristic
178	C₂²×C₁₆	C₂²×C₃₁	1	2	yes	complemented
179	#435	C₄×C₃₁	1	4	yes	—
180	C₈×D₄	C₂²×C₃₁	1	4	yes	—
181	#424	C₄×C₃₁	1	1	yes	characteristic
182	#408	C₄×C₃₁	1	1	yes	characteristic
183	#407	C₄×C₃₁	1	1	yes	characteristic
184	#405	C₂²×C₃₁	1	1	yes	characteristic
185	C₄⋊C₁₆	C₂²×C₃₁	1	4	yes	complemented
186	C₂²⋊C₁₆	C₂²×C₃₁	1	4	yes	—
187	C₂²⋊C₁₆	C₂²×C₃₁	1	4	yes	complemented
188	#346	C₂²×C₃₁	1	2	yes	complemented
189	C₄×C₁₆	C₂²×C₃₁	1	2	yes	complemented
190	C₂×C₃₁	—	2	2	no	—
191	C₂×C₃₁	—	4	2	no	—
192	C₂×C₃₁	—	4	2	no	—
193	C₂×C₃₁	C₂×C₈×D₄	1	1	yes	characteristic
194	C₂×C₃₁	#3407	1	2	yes	—
195	C₂×#41	C₂×C₄×C₃₁	1	1	yes	characteristic
196	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
197	#131	—	2	2	no	—
198	#131	—	2	2	no	—
199	C₂×M₁₆	C₂×C₄×C₃₁	1	1	yes	characteristic
200	C₂×M₁₆	C₂×C₄×C₃₁	1	2	yes	—
201	C₂×M₁₆	C₂×C₄×C₃₁	1	1	yes	characteristic
202	C₂²×C₈	—	2	2	no	—
203	C₂²×C₈	—	2	2	no	—
204	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
205	C₂²×C₈	C₂×C₄×C₃₁	1	2	yes	—
206	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
207	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
208	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
209	#123	C₈×C₃₁	1	2	yes	—
210	C₂²⋊Q₈	C₈×C₃₁	1	2	yes	—
211	#121	C₈×C₃₁	1	2	yes	—
212	#120	C₈×C₃₁	1	2	yes	—
213	C₄×D₄	C₂×C₄×C₃₁	1	4	yes	—
214	#117	C₂×C₄×C₃₁	1	1	yes	characteristic
215	M₃₂	—	2	2	no	—
216	M₃₂	—	2	2	no	—
217	M₃₂	—	2	4	no	—
218	M₃₂	—	2	4	no	—
219	M₃₂	—	2	4	no	—
220	C₂×C₁₆	—	2	2	no	—
221	C₂×C₁₆	—	2	4	no	—
222	C₂×C₁₆	D₄×C₃₁	1	4	yes	complemented
223	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
224	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
225	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
226	C₂×C₁₆	C₂³×C₃₁	1	1	yes	characteristic
227	C₂×C₁₆	C₂³×C₃₁	1	1	yes	characteristic
228	C₄⋊C₈	C₂×C₄×C₃₁	1	4	yes	—
229	C₂²⋊C₈	C₂×C₄×C₃₁	1	4	yes	—
230	C₂²⋊C₈	C₂×C₄×C₃₁	1	4	yes	—
231	#97	C₂×C₄×C₃₁	1	2	yes	—
232	C₄×C₈	C₂³×C₃₁	1	2	yes	—
233	C₃₁	#33433	1	1	yes	characteristic, direct product factor, Sylow
234	C₂⁴	C₂×C₈×C₃₁	1	1	yes	characteristic
235	#41	—	2	2	no	—
236	#41	—	2	2	no	—
237	C₂×Q₈	C₂×C₈×C₃₁	1	1	yes	characteristic
238	C₂×D₄	C₂×C₈×C₃₁	1	2	yes	—
239	C₂×D₄	C₂×C₈×C₃₁	1	1	yes	characteristic
240	C₂×D₄	C₂×C₈×C₃₁	1	4	yes	—
241	C₂²×C₄	—	2	2	no	—
242	C₂²×C₄	—	2	2	no	—
243	C₂²×C₄	C₂×C₈×C₃₁	1	2	yes	—
244	C₂²×C₄	C₂×C₈×C₃₁	1	1	yes	characteristic
245	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
246	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
247	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
248	M₁₆	—	2	2	no	—
249	M₁₆	—	2	2	no	—
250	M₁₆	—	2	4	no	—
251	C₂×C₈	—	2	2	no	—
252	C₂×C₈	—	2	4	no	—
253	C₂×C₈	—	2	2	no	—
254	C₂×C₈	—	2	2	no	—
255	C₂×C₈	—	2	2	no	—
256	C₂×C₈	—	2	2	no	—
257	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
258	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
259	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
260	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
261	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
262	C₂×C₈	#41×C₃₁	1	2	yes	—
263	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
264	C₄⋊C₄	C₂×C₈×C₃₁	1	2	yes	—
265	C₄⋊C₄	C₂×C₈×C₃₁	1	4	yes	—
266	C₂²⋊C₄	C₂×C₈×C₃₁	1	2	yes	—
267	C₂²⋊C₄	C₂×C₈×C₃₁	1	4	yes	—
268	C₂²⋊C₄	C₂×C₈×C₃₁	1	4	yes	—
269	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
270	C₁₆	—	2	2	no	—
271	C₁₆	—	2	2	no	—
272	C₁₆	—	2	2	no	—
273	C₁₆	C₂×D₄×C₃₁	1	2	yes	—
274	C₁₆	C₂×D₄×C₃₁	1	2	yes	—
275	C₂³	—	2	2	no	—
276	C₂³	—	4	2	no	—
277	C₂³	C₂²×C₈×C₃₁	1	2	yes	—
278	C₂³	C₂²×C₈×C₃₁	1	2	yes	—
279	C₂³	C₂²×C₈×C₃₁	1	1	yes	characteristic
280	Q₈	—	2	2	no	—
281	D₄	—	2	4	no	—
282	D₄	—	2	2	no	—
283	D₄	—	4	4	no	—
284	C₂×C₄	—	2	2	no	—
285	C₂×C₄	—	2	4	no	—
286	C₂×C₄	—	2	2	no	—
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
291	C₂×C₄	C₂²×C₈×C₃₁	1	4	yes	—
292	C₂×C₄	C₂²×C₈×C₃₁	1	2	yes	—
293	C₂×C₄	C₂²×C₈×C₃₁	1	2	yes	—
294	C₂×C₄	C₂²×C₈×C₃₁	1	1	yes	characteristic
295	C₂×C₄	C₃₁×#131	1	2	yes	—
296	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
297	C₈	—	2	2	no	—
298	C₈	—	2	2	no	—
299	C₈	—	2	2	no	—
300	C₈	C₄×D₄×C₃₁	1	2	yes	—
301	C₈	C₂²×D₄×C₃₁	1	1	yes	characteristic
302	C₈	C₂×#41×C₃₁	1	1	yes	characteristic
303	C₂²	—	2	2	no	—
304	C₂²	—	2	2	no	—
305	C₂²	—	2	4	no	—
306	C₂²	—	2	2	no	—
307	C₂²	—	2	2	no	—
308	C₂²	—	2	2	no	—
309	C₂²	—	4	4	no	—
310	C₂²	C₈×D₄×C₃₁	1	2	yes	—
311	C₂²	C₂³×C₈×C₃₁	1	1	yes	characteristic
312	C₄	—	2	4	no	—
313	C₄	—	2	2	no	—
314	C₄	—	2	2	no	—
315	C₄	C₈×D₄×C₃₁	1	2	yes	—
316	C₄	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
317	C₄	C₂×C₃₁×#131	1	1	yes	characteristic
318	C₂	—	2	2	no	—
319	C₂	—	4	2	no	—
320	C₂	—	4	2	no	—
321	C₂	C₂×C₈×D₄×C₃₁	1	1	yes	characteristic
322	C₂	C₃₁×#3407	1	2	yes	—

	subgroup	G/H
center	C₂×C₈×C₃₁	C₂⁴
commutator	C₂²	C₂³×C₈×C₃₁
Frattini, cosocle	C₂×C₈	C₂⁴×C₃₁
socle	C₂²×C₃₁	C₂³×C₈
prime radical	C₃₁×#525	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#504	C₂	semidirect
2. C₂²×C₃₁×M₃₂	C₂	semidirect
4. C₃₁×#2169	C₂	semidirect
5. C₃₁×#2168	C₂	semidirect
6. C₃₁×#2151	C₂	semidirect
7. C₃₁×#2113	C₂	semidirect
8. C₃₁×#2112	C₂	semidirect
9. C₃₁×#2108	C₂	semidirect
19. C₂×C₃₁×M₃₂	C₂²	semidirect
22. C₂²×C₁₆×C₃₁	C₂²	semidirect
29. C₃₁×C₄⋊C₁₆	C₂²	semidirect
31. C₃₁×C₂²⋊C₁₆	C₂²	semidirect
32. C₃₁×#346	C₂²	semidirect
33. C₄×C₁₆×C₃₁	C₂²	semidirect
61. C₂×C₁₆×C₃₁	D₄	semidirect
113. #33433	C₃₁	direct (N × H)
142. C₂×#504	C₂×C₃₁	semidirect
143. C₂²×M₃₂	C₂×C₃₁	semidirect
145. #2169	C₂×C₃₁	semidirect
146. #2168	C₂×C₃₁	semidirect
147. #2151	C₂×C₃₁	semidirect
148. #2113	C₂×C₃₁	semidirect
149. #2112	C₂×C₃₁	semidirect
150. #2108	C₂×C₃₁	semidirect
175. C₂×M₃₂	C₂²×C₃₁	semidirect
178. C₂²×C₁₆	C₂²×C₃₁	semidirect
185. C₄⋊C₁₆	C₂²×C₃₁	semidirect
187. C₂²⋊C₁₆	C₂²×C₃₁	semidirect
188. #346	C₂²×C₃₁	semidirect
189. C₄×C₁₆	C₂²×C₃₁	semidirect
222. C₂×C₁₆	D₄×C₃₁	semidirect
233. C₃₁	#33433	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×#504	2
C₂²×C₃₁×M₃₂	2
C₃₁×#2929	2
C₃₁×#2169	2
C₃₁×#2168	2
C₃₁×#2151	2
C₃₁×#2113	2
C₃₁×#2112	2
C₃₁×#2108	2
#33433	31

Subgroups — C31×#33433 #21490192

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33433 #21490192