Subgroups — C₂×C₃₁×#1969 #21477981

Order 7936.

1614 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	C₂³×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃₁×#107	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃₁×#103	C₂	1	2	yes	maximal
4	C₂²×C₄×C₈×C₃₁	C₂	1	1	yes	maximal, characteristic
5	C₂×C₃₁×#391	C₂	1	2	yes	maximal
6	C₃₁×#1969	C₂	1	8	yes	maximal, direct product factor
7	C₂³×Q₈×C₃₁	C₂²	1	2	yes	—
8	C₂²×Q₁₆×C₃₁	—	2	4	no	—
9	C₂²×Q₁₆×C₃₁	—	2	4	no	—
10	C₂²×Q₁₆×C₃₁	C₄	1	8	yes	complemented
11	C₂²×Q₁₆×C₃₁	C₂²	1	4	yes	—
12	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
15	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
16	C₂×C₃₁×#107	—	2	4	no	—
17	C₂×C₃₁×#107	C₂²	1	4	yes	—
18	C₂×C₃₁×#103	—	2	8	no	—
19	C₂×C₃₁×#103	C₂²	1	8	yes	—
20	C₂×C₄×C₈×C₃₁	—	2	4	no	—
21	C₂×C₄×C₈×C₃₁	C₂²	1	4	yes	—
22	C₃₁×#391	—	2	4	no	—
23	C₃₁×#391	C₂²	1	8	yes	—
24	C₂×C₃₁×#95	—	2	4	no	—
25	C₂²×Q₈×C₃₁	—	2	2	no	—
26	C₂²×Q₈×C₃₁	—	2	4	no	—
27	C₂²×Q₈×C₃₁	—	2	4	no	—
28	C₂²×Q₈×C₃₁	—	2	4	no	—
29	C₂²×Q₈×C₃₁	—	2	4	no	—
30	C₂²×Q₈×C₃₁	—	2	4	no	—
31	C₂²×Q₈×C₃₁	C₂×C₄	1	8	yes	—
32	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
33	C₂³×C₄×C₃₁	—	2	2	no	—
34	C₂³×C₄×C₃₁	—	2	2	no	—
35	C₂³×C₄×C₃₁	D₄	1	2	yes	—
36	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
37	C₂×Q₁₆×C₃₁	—	2	32	no	—
38	C₂×Q₁₆×C₃₁	—	2	8	no	—
39	C₂×Q₁₆×C₃₁	—	2	8	no	—
40	C₂×Q₁₆×C₃₁	C₂×C₄	1	16	yes	complemented
41	C₂²×C₈×C₃₁	—	2	2	no	—
42	C₂²×C₈×C₃₁	—	2	2	no	—
43	C₂²×C₈×C₃₁	C₂×C₄	1	4	yes	—
44	C₂²×C₈×C₃₁	D₄	1	4	yes	—
45	C₂²×C₈×C₃₁	D₄	1	4	yes	—
46	C₂²×C₈×C₃₁	D₄	1	4	yes	—
47	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
48	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
49	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
50	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
51	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
52	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
53	C₂×C₄²×C₃₁	—	2	2	no	—
54	C₂×C₄²×C₃₁	—	2	2	no	—
55	C₂×C₄²×C₃₁	D₄	1	2	yes	—
56	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
57	C₃₁×#107	—	2	8	no	—
58	C₃₁×#103	—	2	16	no	—
59	C₄×C₈×C₃₁	—	2	8	no	—
60	C₃₁×#95	—	2	16	no	—
61	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
62	C₂×Q₈×C₃₁	—	2	8	no	—
63	C₂×Q₈×C₃₁	—	2	4	no	—
64	C₂×Q₈×C₃₁	—	2	16	no	—
65	C₂×Q₈×C₃₁	—	2	16	no	—
66	C₂×Q₈×C₃₁	—	2	4	no	—
67	C₂×Q₈×C₃₁	—	2	4	no	—
68	C₂×Q₈×C₃₁	—	2	4	no	—
69	C₂×Q₈×C₃₁	—	2	4	no	—
70	C₂×Q₈×C₃₁	—	4	4	no	—
71	C₂×Q₈×C₃₁	—	4	8	no	—
72	C₂×Q₈×C₃₁	—	4	8	no	—
73	C₂×Q₈×C₃₁	—	4	4	no	—
74	C₂×Q₈×C₃₁	C₂²×C₄	1	8	yes	—
75	C₂²×C₄×C₃₁	—	2	4	no	—
76	C₂²×C₄×C₃₁	—	2	4	no	—
77	C₂²×C₄×C₃₁	—	2	8	no	—
78	C₂²×C₄×C₃₁	—	2	4	no	—
79	C₂²×C₄×C₃₁	—	2	4	no	—
80	C₂²×C₄×C₃₁	—	4	4	no	—
81	C₂²×C₄×C₃₁	—	4	4	no	—
82	C₂²×C₄×C₃₁	—	4	4	no	—
83	C₂²×C₄×C₃₁	—	4	8	no	—
84	C₂²×C₄×C₃₁	Q₁₆	1	8	yes	complemented
85	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
87	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₃₁	#41	1	2	yes	—
92	C₂²×C₄×C₃₁	#41	1	2	yes	—
93	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
94	Q₁₆×C₃₁	—	2	32	no	—
95	C₂×C₈×C₃₁	—	2	8	no	—
96	C₂×C₈×C₃₁	—	2	2	no	—
97	C₂×C₈×C₃₁	—	2	2	no	—
98	C₂×C₈×C₃₁	C₂²⋊C₄	1	16	yes	—
99	C₂×C₈×C₃₁	C₂²×C₄	1	4	yes	—
100	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
101	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
102	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
103	C₄⋊C₄×C₃₁	—	2	4	no	—
104	C₄⋊C₄×C₃₁	—	2	4	no	—
105	C₄⋊C₄×C₃₁	—	4	4	no	—
106	C₄²×C₃₁	—	2	4	no	—
107	C₄²×C₃₁	—	2	2	no	—
108	C₄²×C₃₁	—	2	2	no	—
109	C₂×#1969	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₂³×C₃₁	C₄×D₄	1	2	yes	—
111	C₂³×C₃₁	#121	1	2	yes	—
112	C₂³×C₃₁	#127	1	2	yes	—
113	C₂³×C₃₁	C₂×Q₁₆	1	4	yes	—
114	C₂³×C₃₁	#135	1	4	yes	—
115	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
116	Q₈×C₃₁	—	2	8	no	—
117	Q₈×C₃₁	—	2	8	no	—
118	Q₈×C₃₁	—	4	4	no	—
119	Q₈×C₃₁	—	4	4	no	—
120	Q₈×C₃₁	—	4	16	no	—
121	C₂×C₄×C₃₁	—	2	4	no	—
122	C₂×C₄×C₃₁	—	2	4	no	—
123	C₂×C₄×C₃₁	—	2	16	no	—
124	C₂×C₄×C₃₁	—	2	8	no	—
125	C₂×C₄×C₃₁	—	4	4	no	—
126	C₂×C₄×C₃₁	—	4	4	no	—
127	C₂×C₄×C₃₁	—	4	16	no	—
128	C₂×C₄×C₃₁	—	4	4	no	—
129	C₂×C₄×C₃₁	—	4	8	no	—
130	C₂×C₄×C₃₁	—	8	8	no	—
131	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	4	yes	—
132	C₂×C₄×C₃₁	C₄×D₄	1	4	yes	—
133	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
134	C₂×C₄×C₃₁	#121	1	4	yes	—
135	C₂×C₄×C₃₁	#121	1	2	yes	—
136	C₂×C₄×C₃₁	#124	1	4	yes	—
137	C₂×C₄×C₃₁	#127	1	2	yes	—
138	C₂×C₄×C₃₁	C₂×Q₁₆	1	8	yes	complemented
139	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
140	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
141	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
142	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
143	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
144	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
145	C₈×C₃₁	—	2	4	no	—
146	C₈×C₃₁	C₂×C₂²⋊C₄	1	8	yes	—
147	C₂³×Q₁₆	C₂×C₃₁	1	1	yes	characteristic
148	C₂²×#107	C₂×C₃₁	1	1	yes	characteristic
149	C₂²×#103	C₂×C₃₁	1	2	yes	—
150	C₂²×C₄×C₈	C₂×C₃₁	1	1	yes	characteristic
151	C₂×#391	C₂×C₃₁	1	2	yes	—
152	#1969	C₂×C₃₁	1	8	yes	direct product factor
153	C₂²×C₃₁	#390	1	4	yes	—
154	C₂²×C₃₁	C₄×Q₁₆	1	8	yes	—
155	C₂²×C₃₁	#467	1	8	yes	—
156	C₂²×C₃₁	#494	1	4	yes	—
157	C₂²×C₃₁	#495	1	4	yes	—
158	C₂²×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
159	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
160	C₂²×C₃₁	C₂×#127	1	1	yes	characteristic
161	C₂²×C₃₁	C₂²×Q₁₆	1	2	yes	—
162	C₂²×C₃₁	C₂×#135	1	2	yes	—
163	C₄×C₃₁	—	2	8	no	—
164	C₄×C₃₁	—	4	8	no	—
165	C₄×C₃₁	—	8	4	no	—
166	C₄×C₃₁	#390	1	4	yes	—
167	C₄×C₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
168	C₄×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
169	C₄×C₃₁	C₂×#121	1	1	yes	characteristic
170	C₄×C₃₁	C₂×#124	1	1	yes	characteristic
171	C₂³×Q₈	C₂²×C₃₁	1	2	yes	—
172	C₂²×Q₁₆	—	2	4	no	—
173	C₂²×Q₁₆	—	2	4	no	—
174	C₂²×Q₁₆	C₄×C₃₁	1	8	yes	complemented
175	C₂²×Q₁₆	C₂²×C₃₁	1	4	yes	—
176	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
177	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
178	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
179	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
180	C₂×#107	—	2	4	no	—
181	C₂×#107	C₂²×C₃₁	1	4	yes	—
182	C₂×#103	—	2	8	no	—
183	C₂×#103	C₂²×C₃₁	1	8	yes	—
184	C₂×C₄×C₈	—	2	4	no	—
185	C₂×C₄×C₈	C₂²×C₃₁	1	4	yes	—
186	#391	—	2	4	no	—
187	#391	C₂²×C₃₁	1	8	yes	—
188	C₂×#95	—	2	4	no	—
189	C₂×C₃₁	#1969	1	8	yes	direct product factor
190	C₂×C₃₁	C₂×#390	1	1	yes	characteristic
191	C₂×C₃₁	C₂×C₄×Q₁₆	1	2	yes	—
192	C₂×C₃₁	C₂×#467	1	2	yes	—
193	C₂×C₃₁	C₂×#494	1	1	yes	characteristic
194	C₂×C₃₁	C₂×#495	1	1	yes	characteristic
195	C₂²×Q₈	—	2	2	no	—
196	C₂²×Q₈	—	2	4	no	—
197	C₂²×Q₈	—	2	4	no	—
198	C₂²×Q₈	—	2	4	no	—
199	C₂²×Q₈	—	2	4	no	—
200	C₂²×Q₈	—	2	4	no	—
201	C₂²×Q₈	C₂×C₄×C₃₁	1	8	yes	—
202	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
203	C₂³×C₄	—	2	2	no	—
204	C₂³×C₄	—	2	2	no	—
205	C₂³×C₄	D₄×C₃₁	1	2	yes	—
206	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
207	C₂×Q₁₆	—	2	32	no	—
208	C₂×Q₁₆	—	2	8	no	—
209	C₂×Q₁₆	—	2	8	no	—
210	C₂×Q₁₆	C₂×C₄×C₃₁	1	16	yes	complemented
211	C₂²×C₈	—	2	2	no	—
212	C₂²×C₈	—	2	2	no	—
213	C₂²×C₈	C₂×C₄×C₃₁	1	4	yes	—
214	C₂²×C₈	D₄×C₃₁	1	4	yes	—
215	C₂²×C₈	D₄×C₃₁	1	4	yes	—
216	C₂²×C₈	D₄×C₃₁	1	4	yes	—
217	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
218	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
219	C₂×C₄⋊C₄	—	2	4	no	—
220	C₂×C₄⋊C₄	—	2	4	no	—
221	C₂×C₄⋊C₄	—	2	2	no	—
222	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
223	C₂×C₄²	—	2	2	no	—
224	C₂×C₄²	—	2	2	no	—
225	C₂×C₄²	D₄×C₃₁	1	2	yes	—
226	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
227	#107	—	2	8	no	—
228	#103	—	2	16	no	—
229	C₄×C₈	—	2	8	no	—
230	#95	—	2	16	no	—
231	C₃₁	C₂×#1969	1	1	yes	characteristic, direct product factor, Sylow
232	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
233	C₂×Q₈	—	2	8	no	—
234	C₂×Q₈	—	2	4	no	—
235	C₂×Q₈	—	2	16	no	—
236	C₂×Q₈	—	2	16	no	—
237	C₂×Q₈	—	2	4	no	—
238	C₂×Q₈	—	2	4	no	—
239	C₂×Q₈	—	2	4	no	—
240	C₂×Q₈	—	2	4	no	—
241	C₂×Q₈	—	4	4	no	—
242	C₂×Q₈	—	4	8	no	—
243	C₂×Q₈	—	4	8	no	—
244	C₂×Q₈	—	4	4	no	—
245	C₂×Q₈	C₂²×C₄×C₃₁	1	8	yes	—
246	C₂²×C₄	—	2	4	no	—
247	C₂²×C₄	—	2	4	no	—
248	C₂²×C₄	—	2	8	no	—
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	4	4	no	—
252	C₂²×C₄	—	4	4	no	—
253	C₂²×C₄	—	4	4	no	—
254	C₂²×C₄	—	4	8	no	—
255	C₂²×C₄	Q₁₆×C₃₁	1	8	yes	complemented
256	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
257	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
258	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
259	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
260	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
261	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
262	C₂²×C₄	#41×C₃₁	1	2	yes	—
263	C₂²×C₄	#41×C₃₁	1	2	yes	—
264	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
265	Q₁₆	—	2	32	no	—
266	C₂×C₈	—	2	8	no	—
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	C₂²⋊C₄×C₃₁	1	16	yes	—
270	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
271	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
272	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
273	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
274	C₄⋊C₄	—	2	4	no	—
275	C₄⋊C₄	—	2	4	no	—
276	C₄⋊C₄	—	4	4	no	—
277	C₄²	—	2	4	no	—
278	C₄²	—	2	2	no	—
279	C₄²	—	2	2	no	—
280	C₂³	C₄×D₄×C₃₁	1	2	yes	—
281	C₂³	C₃₁×#121	1	2	yes	—
282	C₂³	C₃₁×#127	1	2	yes	—
283	C₂³	C₂×Q₁₆×C₃₁	1	4	yes	—
284	C₂³	C₃₁×#135	1	4	yes	—
285	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
286	Q₈	—	2	8	no	—
287	Q₈	—	2	8	no	—
288	Q₈	—	4	4	no	—
289	Q₈	—	4	4	no	—
290	Q₈	—	4	16	no	—
291	C₂×C₄	—	2	16	no	—
292	C₂×C₄	—	2	4	no	—
293	C₂×C₄	—	2	4	no	—
294	C₂×C₄	—	2	8	no	—
295	C₂×C₄	—	4	4	no	—
296	C₂×C₄	—	4	4	no	—
297	C₂×C₄	—	4	16	no	—
298	C₂×C₄	—	4	4	no	—
299	C₂×C₄	—	4	8	no	—
300	C₂×C₄	—	8	8	no	—
301	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	4	yes	—
302	C₂×C₄	C₄×D₄×C₃₁	1	4	yes	—
303	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
304	C₂×C₄	C₃₁×#121	1	4	yes	—
305	C₂×C₄	C₃₁×#121	1	2	yes	—
306	C₂×C₄	C₃₁×#124	1	4	yes	—
307	C₂×C₄	C₃₁×#127	1	2	yes	—
308	C₂×C₄	C₂×Q₁₆×C₃₁	1	8	yes	complemented
309	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
310	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
311	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
312	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
313	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
314	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
315	C₈	—	2	4	no	—
316	C₈	C₂×C₂²⋊C₄×C₃₁	1	8	yes	—
317	C₂²	C₃₁×#390	1	4	yes	—
318	C₂²	C₄×Q₁₆×C₃₁	1	8	yes	—
319	C₂²	C₃₁×#467	1	8	yes	—
320	C₂²	C₃₁×#494	1	4	yes	—
321	C₂²	C₃₁×#495	1	4	yes	—
322	C₂²	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
323	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
324	C₂²	C₂×C₃₁×#127	1	1	yes	characteristic
325	C₂²	C₂²×Q₁₆×C₃₁	1	2	yes	—
326	C₂²	C₂×C₃₁×#135	1	2	yes	—
327	C₄	—	2	8	no	—
328	C₄	—	4	8	no	—
329	C₄	—	8	4	no	—
330	C₄	C₃₁×#390	1	4	yes	—
331	C₄	C₂²×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
332	C₄	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
333	C₄	C₂×C₃₁×#121	1	1	yes	characteristic
334	C₄	C₂×C₃₁×#124	1	1	yes	characteristic
335	C₂	C₃₁×#1969	1	8	yes	direct product factor
336	C₂	C₂×C₃₁×#390	1	1	yes	characteristic
337	C₂	C₂×C₄×Q₁₆×C₃₁	1	2	yes	—
338	C₂	C₂×C₃₁×#467	1	2	yes	—
339	C₂	C₂×C₃₁×#494	1	1	yes	characteristic
340	C₂	C₂×C₃₁×#495	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
6. C₃₁×#1969	C₂	direct (N × H)
10. C₂²×Q₁₆×C₃₁	C₄	semidirect
40. C₂×Q₁₆×C₃₁	C₂×C₄	semidirect
84. C₂²×C₄×C₃₁	Q₁₆	semidirect
109. C₂×#1969	C₃₁	direct (N × H)
138. C₂×C₄×C₃₁	C₂×Q₁₆	semidirect
152. #1969	C₂×C₃₁	direct (N × H)
174. C₂²×Q₁₆	C₄×C₃₁	semidirect
189. C₂×C₃₁	#1969	direct (N × H)
210. C₂×Q₁₆	C₂×C₄×C₃₁	semidirect
231. C₃₁	C₂×#1969	direct (N × H)
255. C₂²×C₄	Q₁₆×C₃₁	semidirect
308. C₂×C₄	C₂×Q₁₆×C₃₁	semidirect
335. C₂	C₃₁×#1969	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×Q₁₆×C₃₁	2
C₂²×C₃₁×#107	2
C₂²×C₃₁×#103	2
C₂²×C₄×C₈×C₃₁	2
C₂×C₃₁×#391	2
C₃₁×#1969	2
C₂×#1969	31

Subgroups — C2×C31×#1969 #21477981

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#1969 #21477981