Subgroups — C₂×C₃₁×#2210 #21490334

Order 7936.

786 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃₁×D₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₁×#495	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2210	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃₁×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃₁×#358	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃₁×#357	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
10	C₂²×SD₁₆×C₃₁	—	2	1	no	—
11	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
12	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×#124	—	2	1	no	—
14	C₂×C₄×D₄×C₃₁	—	2	1	no	—
15	C₂×C₃₁×SD₃₂	—	2	4	no	—
16	C₂×C₃₁×SD₃₂	C₂²	1	4	yes	complemented
17	C₂×C₃₁×D₁₆	—	2	4	no	—
18	C₂×C₃₁×D₁₆	C₂²	1	4	yes	—
19	C₂²×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
20	C₂²×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
21	C₃₁×#495	—	2	2	no	—
22	C₃₁×#495	C₂²	1	4	yes	complemented
23	C₄×D₈×C₃₁	—	2	2	no	—
24	C₄×D₈×C₃₁	C₂²	1	4	yes	complemented
25	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#102	—	2	1	no	—
27	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
28	C₃₁×C₄⋊C₁₆	C₂²	1	4	yes	complemented
29	C₃₁×#358	C₂²	1	4	yes	complemented
30	C₃₁×#357	C₂²	1	4	yes	complemented
31	C₂²×Q₈×C₃₁	—	2	1	no	—
32	C₂²×D₄×C₃₁	—	2	1	no	—
33	C₂²×D₄×C₃₁	—	2	1	no	—
34	C₂³×C₄×C₃₁	—	4	1	no	—
35	C₂×Q₁₆×C₃₁	—	2	2	no	—
36	C₂×Q₁₆×C₃₁	—	2	1	no	—
37	C₂×Q₁₆×C₃₁	—	2	2	no	—
38	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
39	C₂×SD₁₆×C₃₁	—	2	4	no	—
40	C₂×SD₁₆×C₃₁	—	4	4	no	—
41	C₂×D₈×C₃₁	—	2	1	no	—
42	C₂×D₈×C₃₁	—	2	2	no	—
43	C₂×D₈×C₃₁	—	2	1	no	—
44	C₂×D₈×C₃₁	—	2	2	no	—
45	C₂×D₈×C₃₁	—	2	2	no	—
46	C₂×D₈×C₃₁	D₄	1	4	yes	—
47	C₂×D₈×C₃₁	C₂³	1	2	yes	—
48	C₂×D₈×C₃₁	C₂³	1	2	yes	—
49	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
51	C₃₁×#124	—	2	4	no	—
52	C₃₁×#124	—	4	2	no	—
53	C₄×D₄×C₃₁	—	2	4	no	—
54	C₄×D₄×C₃₁	—	4	2	no	—
55	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
56	C₂×C₂²⋊C₄×C₃₁	—	4	1	no	—
57	C₂×C₂²⋊C₄×C₃₁	—	4	1	no	—
58	C₂×C₂²⋊C₄×C₃₁	—	4	1	no	—
59	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
60	C₃₁×SD₃₂	—	2	8	no	—
61	C₃₁×D₁₆	—	2	8	no	—
62	C₂×C₁₆×C₃₁	—	2	2	no	—
63	C₂×C₁₆×C₃₁	—	2	2	no	—
64	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
65	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
66	C₃₁×#107	—	2	1	no	—
67	C₃₁×#107	C₂³	1	2	yes	—
68	C₃₁×#102	—	2	4	no	—
69	C₄×C₈×C₃₁	D₄	1	2	yes	—
70	C₄×C₈×C₃₁	C₂³	1	2	yes	—
71	C₂⁴×C₃₁	—	4	1	no	—
72	C₂⁴×C₃₁	—	4	1	no	—
73	C₂×Q₈×C₃₁	—	2	2	no	—
74	C₂×Q₈×C₃₁	—	4	1	no	—
75	C₂×Q₈×C₃₁	—	4	2	no	—
76	C₂×Q₈×C₃₁	—	4	2	no	—
77	C₂×D₄×C₃₁	—	2	4	no	—
78	C₂×D₄×C₃₁	—	2	2	no	—
79	C₂×D₄×C₃₁	—	2	2	no	—
80	C₂×D₄×C₃₁	—	4	2	no	—
81	C₂×D₄×C₃₁	—	4	1	no	—
82	C₂×D₄×C₃₁	—	4	1	no	—
83	C₂×D₄×C₃₁	—	4	2	no	—
84	C₂×D₄×C₃₁	—	4	2	no	—
85	C₂²×C₄×C₃₁	—	4	1	no	—
86	C₂²×C₄×C₃₁	—	4	1	no	—
87	C₂²×C₄×C₃₁	—	4	4	no	—
88	C₂²×C₄×C₃₁	—	8	4	no	—
89	C₂²×C₄×C₃₁	D₈	1	1	yes	characteristic
90	C₂²×C₄×C₃₁	D₈	1	1	yes	characteristic
91	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
92	Q₁₆×C₃₁	—	2	2	no	—
93	Q₁₆×C₃₁	—	2	2	no	—
94	Q₁₆×C₃₁	—	4	2	no	—
95	SD₁₆×C₃₁	—	4	8	no	—
96	D₈×C₃₁	—	2	4	no	—
97	D₈×C₃₁	—	2	2	no	—
98	D₈×C₃₁	—	2	2	no	—
99	D₈×C₃₁	—	2	2	no	—
100	D₈×C₃₁	—	4	2	no	—
101	D₈×C₃₁	C₂×D₄	1	4	yes	—
102	C₂×C₈×C₃₁	—	2	2	no	—
103	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
104	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
105	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
106	C₂×C₈×C₃₁	#41	1	2	yes	—
107	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
108	C₄⋊C₄×C₃₁	—	2	2	no	—
109	C₄⋊C₄×C₃₁	—	4	1	no	—
110	C₂²⋊C₄×C₃₁	—	4	4	no	—
111	C₂²⋊C₄×C₃₁	—	4	4	no	—
112	C₂²⋊C₄×C₃₁	—	4	4	no	—
113	C₄²×C₃₁	D₈	1	2	yes	—
114	C₄²×C₃₁	C₂×D₄	1	2	yes	—
115	C₁₆×C₃₁	—	2	2	no	—
116	C₁₆×C₃₁	—	2	2	no	—
117	C₂×#2210	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₂³×C₃₁	—	4	2	no	—
119	C₂³×C₃₁	—	4	4	no	—
120	C₂³×C₃₁	—	4	2	no	—
121	C₂³×C₃₁	—	8	2	no	—
122	C₂³×C₃₁	—	8	2	no	—
123	C₂³×C₃₁	—	8	2	no	—
124	C₂³×C₃₁	—	8	2	no	—
125	C₂³×C₃₁	—	8	2	no	—
126	C₂³×C₃₁	C₂×D₈	1	1	yes	characteristic
127	Q₈×C₃₁	—	4	2	no	—
128	Q₈×C₃₁	—	4	2	no	—
129	Q₈×C₃₁	—	8	2	no	—
130	D₄×C₃₁	—	2	4	no	—
131	D₄×C₃₁	—	4	2	no	—
132	D₄×C₃₁	—	4	2	no	—
133	D₄×C₃₁	—	4	2	no	—
134	D₄×C₃₁	—	4	4	no	—
135	D₄×C₃₁	—	8	2	no	—
136	C₂×C₄×C₃₁	—	2	2	no	—
137	C₂×C₄×C₃₁	—	2	2	no	—
138	C₂×C₄×C₃₁	—	4	2	no	—
139	C₂×C₄×C₃₁	—	4	2	no	—
140	C₂×C₄×C₃₁	—	8	8	no	—
141	C₂×C₄×C₃₁	—	8	2	no	—
142	C₂×C₄×C₃₁	—	8	2	no	—
143	C₂×C₄×C₃₁	#121	1	2	yes	—
144	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
145	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
146	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
147	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
148	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
149	C₈×C₃₁	—	2	2	no	—
150	C₈×C₃₁	#121	1	2	yes	—
151	C₈×C₃₁	C₂²×D₄	1	1	yes	characteristic
152	C₈×C₃₁	C₂×#41	1	1	yes	characteristic
153	C₂²×SD₃₂	C₂×C₃₁	1	1	yes	characteristic, complemented
154	C₂²×D₁₆	C₂×C₃₁	1	1	yes	characteristic
155	C₂×#495	C₂×C₃₁	1	1	yes	characteristic, complemented
156	C₂×C₄×D₈	C₂×C₃₁	1	1	yes	characteristic, complemented
157	#2210	C₂×C₃₁	1	8	yes	direct product factor
158	C₂×C₄⋊C₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
159	C₂×#358	C₂×C₃₁	1	1	yes	characteristic, complemented
160	C₂×#357	C₂×C₃₁	1	1	yes	characteristic, complemented
161	C₂²×C₃₁	—	4	4	no	—
162	C₂²×C₃₁	—	8	2	no	—
163	C₂²×C₃₁	—	8	2	no	—
164	C₂²×C₃₁	—	8	8	no	—
165	C₂²×C₃₁	—	8	2	no	—
166	C₂²×C₃₁	—	8	2	no	—
167	C₂²×C₃₁	—	8	2	no	—
168	C₂²×C₃₁	—	16	4	no	—
169	C₂²×C₃₁	#459	1	2	yes	—
170	C₂²×C₃₁	#508	1	2	yes	—
171	C₂²×C₃₁	#509	1	2	yes	—
172	C₂²×C₃₁	C₂²×D₈	1	1	yes	characteristic
173	C₄×C₃₁	—	2	2	no	—
174	C₄×C₃₁	—	2	2	no	—
175	C₄×C₃₁	—	8	2	no	—
176	C₄×C₃₁	—	8	2	no	—
177	C₄×C₃₁	#459	1	2	yes	—
178	C₄×C₃₁	C₂×#121	1	1	yes	characteristic
179	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
180	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
181	C₂²×SD₁₆	—	2	1	no	—
182	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
183	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
184	C₂×#124	—	2	1	no	—
185	C₂×C₄×D₄	—	2	1	no	—
186	C₂×SD₃₂	—	2	4	no	—
187	C₂×SD₃₂	C₂²×C₃₁	1	4	yes	complemented
188	C₂×D₁₆	—	2	4	no	—
189	C₂×D₁₆	C₂²×C₃₁	1	4	yes	—
190	C₂²×C₁₆	C₂²×C₃₁	1	1	yes	characteristic
191	C₂²×C₁₆	C₂²×C₃₁	1	1	yes	characteristic
192	#495	—	2	2	no	—
193	#495	C₂²×C₃₁	1	4	yes	complemented
194	C₄×D₈	—	2	2	no	—
195	C₄×D₈	C₂²×C₃₁	1	4	yes	complemented
196	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
197	C₂×#102	—	2	1	no	—
198	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
199	C₄⋊C₁₆	C₂²×C₃₁	1	4	yes	complemented
200	#358	C₂²×C₃₁	1	4	yes	complemented
201	#357	C₂²×C₃₁	1	4	yes	complemented
202	C₂×C₃₁	—	8	4	no	—
203	C₂×C₃₁	—	16	2	no	—
204	C₂×C₃₁	#2210	1	4	yes	direct product factor
205	C₂×C₃₁	C₂×#459	1	1	yes	characteristic
206	C₂×C₃₁	C₂×#508	1	1	yes	characteristic
207	C₂×C₃₁	C₂×#509	1	1	yes	characteristic
208	C₂²×Q₈	—	2	1	no	—
209	C₂²×D₄	—	2	1	no	—
210	C₂²×D₄	—	2	1	no	—
211	C₂³×C₄	—	4	1	no	—
212	C₂×Q₁₆	—	2	2	no	—
213	C₂×Q₁₆	—	2	1	no	—
214	C₂×Q₁₆	—	2	2	no	—
215	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
216	C₂×SD₁₆	—	2	4	no	—
217	C₂×SD₁₆	—	4	4	no	—
218	C₂×D₈	—	2	1	no	—
219	C₂×D₈	—	2	2	no	—
220	C₂×D₈	—	2	1	no	—
221	C₂×D₈	—	2	2	no	—
222	C₂×D₈	—	2	2	no	—
223	C₂×D₈	D₄×C₃₁	1	4	yes	—
224	C₂×D₈	C₂³×C₃₁	1	2	yes	—
225	C₂×D₈	C₂³×C₃₁	1	2	yes	—
226	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
227	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
228	#124	—	2	4	no	—
229	#124	—	4	2	no	—
230	C₄×D₄	—	2	4	no	—
231	C₄×D₄	—	4	2	no	—
232	C₂×C₄⋊C₄	—	2	1	no	—
233	C₂×C₂²⋊C₄	—	4	1	no	—
234	C₂×C₂²⋊C₄	—	4	1	no	—
235	C₂×C₂²⋊C₄	—	4	1	no	—
236	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
237	SD₃₂	—	2	8	no	—
238	D₁₆	—	2	8	no	—
239	C₂×C₁₆	—	2	2	no	—
240	C₂×C₁₆	—	2	2	no	—
241	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
242	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
243	#107	—	2	1	no	—
244	#107	C₂³×C₃₁	1	2	yes	—
245	#102	—	2	4	no	—
246	C₄×C₈	D₄×C₃₁	1	2	yes	—
247	C₄×C₈	C₂³×C₃₁	1	2	yes	—
248	C₃₁	C₂×#2210	1	1	yes	characteristic, direct product factor, Sylow
249	C₂⁴	—	4	1	no	—
250	C₂⁴	—	4	1	no	—
251	C₂×Q₈	—	2	2	no	—
252	C₂×Q₈	—	4	1	no	—
253	C₂×Q₈	—	4	2	no	—
254	C₂×Q₈	—	4	2	no	—
255	C₂×D₄	—	2	4	no	—
256	C₂×D₄	—	2	2	no	—
257	C₂×D₄	—	2	2	no	—
258	C₂×D₄	—	4	2	no	—
259	C₂×D₄	—	4	1	no	—
260	C₂×D₄	—	4	1	no	—
261	C₂×D₄	—	4	2	no	—
262	C₂×D₄	—	4	2	no	—
263	C₂²×C₄	—	4	1	no	—
264	C₂²×C₄	—	4	1	no	—
265	C₂²×C₄	—	4	4	no	—
266	C₂²×C₄	—	8	4	no	—
267	C₂²×C₄	D₈×C₃₁	1	1	yes	characteristic
268	C₂²×C₄	D₈×C₃₁	1	1	yes	characteristic
269	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
270	Q₁₆	—	2	2	no	—
271	Q₁₆	—	2	2	no	—
272	Q₁₆	—	4	2	no	—
273	SD₁₆	—	4	8	no	—
274	D₈	—	2	4	no	—
275	D₈	—	2	2	no	—
276	D₈	—	2	2	no	—
277	D₈	—	2	2	no	—
278	D₈	—	4	2	no	—
279	D₈	C₂×D₄×C₃₁	1	4	yes	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
282	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
283	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
284	C₂×C₈	#41×C₃₁	1	2	yes	—
285	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	—	4	1	no	—
288	C₂²⋊C₄	—	4	4	no	—
289	C₂²⋊C₄	—	4	4	no	—
290	C₂²⋊C₄	—	4	4	no	—
291	C₄²	D₈×C₃₁	1	2	yes	—
292	C₄²	C₂×D₄×C₃₁	1	2	yes	—
293	C₁₆	—	2	2	no	—
294	C₁₆	—	2	2	no	—
295	C₂³	—	4	4	no	—
296	C₂³	—	4	2	no	—
297	C₂³	—	4	2	no	—
298	C₂³	—	8	2	no	—
299	C₂³	—	8	2	no	—
300	C₂³	—	8	2	no	—
301	C₂³	—	8	2	no	—
302	C₂³	—	8	2	no	—
303	C₂³	C₂×D₈×C₃₁	1	1	yes	characteristic
304	Q₈	—	4	2	no	—
305	Q₈	—	4	2	no	—
306	Q₈	—	8	2	no	—
307	D₄	—	2	4	no	—
308	D₄	—	4	4	no	—
309	D₄	—	4	2	no	—
310	D₄	—	4	2	no	—
311	D₄	—	4	2	no	—
312	D₄	—	8	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	8	8	no	—
318	C₂×C₄	—	8	2	no	—
319	C₂×C₄	—	8	2	no	—
320	C₂×C₄	C₃₁×#121	1	2	yes	—
321	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
322	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
323	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
324	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
325	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
326	C₈	—	2	2	no	—
327	C₈	C₃₁×#121	1	2	yes	—
328	C₈	C₂²×D₄×C₃₁	1	1	yes	characteristic
329	C₈	C₂×#41×C₃₁	1	1	yes	characteristic
330	C₂²	—	4	4	no	—
331	C₂²	—	8	2	no	—
332	C₂²	—	8	2	no	—
333	C₂²	—	8	8	no	—
334	C₂²	—	8	2	no	—
335	C₂²	—	8	2	no	—
336	C₂²	—	8	2	no	—
337	C₂²	—	16	4	no	—
338	C₂²	C₃₁×#459	1	2	yes	—
339	C₂²	C₃₁×#508	1	2	yes	—
340	C₂²	C₃₁×#509	1	2	yes	—
341	C₂²	C₂²×D₈×C₃₁	1	1	yes	characteristic
342	C₄	—	2	2	no	—
343	C₄	—	2	2	no	—
344	C₄	—	8	2	no	—
345	C₄	—	8	2	no	—
346	C₄	C₃₁×#459	1	2	yes	—
347	C₄	C₂×C₃₁×#121	1	1	yes	characteristic
348	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
349	C₂	—	8	4	no	—
350	C₂	—	16	2	no	—
351	C₂	C₃₁×#2210	1	4	yes	direct product factor
352	C₂	C₂×C₃₁×#459	1	1	yes	characteristic
353	C₂	C₂×C₃₁×#508	1	1	yes	characteristic
354	C₂	C₂×C₃₁×#509	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₃₁
prime radical	C₂²×C₃₁×D₁₆	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×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. C₂²×C₃₁×SD₃₂	C₂	semidirect
3. C₂×C₃₁×#495	C₂	semidirect
4. C₂×C₄×D₈×C₃₁	C₂	semidirect
5. C₃₁×#2210	C₂	direct (N × H)
6. C₂×C₃₁×C₄⋊C₁₆	C₂	semidirect
7. C₂×C₃₁×#358	C₂	semidirect
8. C₂×C₃₁×#357	C₂	semidirect
16. C₂×C₃₁×SD₃₂	C₂²	semidirect
22. C₃₁×#495	C₂²	semidirect
24. C₄×D₈×C₃₁	C₂²	semidirect
28. C₃₁×C₄⋊C₁₆	C₂²	semidirect
29. C₃₁×#358	C₂²	semidirect
30. C₃₁×#357	C₂²	semidirect
117. C₂×#2210	C₃₁	direct (N × H)
153. C₂²×SD₃₂	C₂×C₃₁	semidirect
155. C₂×#495	C₂×C₃₁	semidirect
156. C₂×C₄×D₈	C₂×C₃₁	semidirect
157. #2210	C₂×C₃₁	direct (N × H)
158. C₂×C₄⋊C₁₆	C₂×C₃₁	semidirect
159. C₂×#358	C₂×C₃₁	semidirect
160. C₂×#357	C₂×C₃₁	semidirect
187. C₂×SD₃₂	C₂²×C₃₁	semidirect
193. #495	C₂²×C₃₁	semidirect
195. C₄×D₈	C₂²×C₃₁	semidirect
199. C₄⋊C₁₆	C₂²×C₃₁	semidirect
200. #358	C₂²×C₃₁	semidirect
201. #357	C₂²×C₃₁	semidirect
204. C₂×C₃₁	#2210	direct (N × H)
248. C₃₁	C₂×#2210	direct (N × H)
351. C₂	C₃₁×#2210	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃₁×SD₃₂	2
C₂²×C₃₁×D₁₆	2
C₂×C₃₁×#495	2
C₂×C₄×D₈×C₃₁	2
C₃₁×#2210	2
C₂×C₃₁×C₄⋊C₁₆	2
C₂×C₃₁×#358	2
C₂×C₃₁×#357	2
C₂×#2210	31

Subgroups — C2×C31×#2210 #21490334

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#2210 #21490334