Subgroups — C₂×C₃₁×#1772 #21477201

Order 7936.

1102 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×#108	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#427	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₁×#405	C₂	1	2	yes	maximal
4	C₂²×C₄×C₈×C₃₁	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#1772	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃₁×#339	C₂	1	2	yes	maximal
7	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
8	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
9	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
10	C₂×C₃₁×#117	C₂²	1	2	yes	—
11	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
12	C₂×C₃₁×#108	C₄	1	8	yes	complemented
13	C₂×C₃₁×#108	C₂²	1	4	yes	—
14	C₃₁×#427	C₄	1	4	yes	complemented
15	C₃₁×#427	C₂²	1	4	yes	—
16	C₂×C₃₁×#107	C₄	1	2	yes	complemented
17	C₂×C₃₁×#106	C₄	1	2	yes	complemented
18	C₃₁×#405	—	2	4	no	—
19	C₃₁×#405	C₂²	1	8	yes	—
20	C₂×C₃₁×#97	—	2	2	no	—
21	C₂×C₄×C₈×C₃₁	—	2	2	no	—
22	C₂×C₄×C₈×C₃₁	C₄	1	8	yes	complemented
23	C₂×C₄×C₈×C₃₁	C₂²	1	4	yes	—
24	C₃₁×#339	C₂²	1	8	yes	—
25	C₂³×C₄×C₃₁	—	2	1	no	—
26	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
27	C₂×M₁₆×C₃₁	—	2	2	no	—
28	C₂×M₁₆×C₃₁	—	2	4	no	—
29	C₂×M₁₆×C₃₁	C₂×C₄	1	8	yes	—
30	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
31	C₂²×C₈×C₃₁	—	2	2	no	—
32	C₂²×C₈×C₃₁	C₂×C₄	1	4	yes	—
33	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₈×C₃₁	C₂×C₄	1	2	yes	—
36	C₂²×C₈×C₃₁	C₂×C₄	1	4	yes	—
37	C₂²×C₈×C₃₁	C₂×C₄	1	4	yes	—
38	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
39	C₂²×C₈×C₃₁	D₄	1	2	yes	—
40	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₃₁	Q₈	1	4	yes	—
42	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
43	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
44	C₃₁×#117	—	2	2	no	—
45	C₃₁×#117	—	2	2	no	—
46	C₃₁×#117	C₂×C₄	1	4	yes	—
47	C₃₁×#117	C₂³	1	4	yes	—
48	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	4	yes	—
49	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
50	C₂×C₄²×C₃₁	—	2	2	no	—
51	C₂×C₄²×C₃₁	—	2	1	no	—
52	C₂×C₄²×C₃₁	—	2	2	no	—
53	C₂×C₄²×C₃₁	C₂×C₄	1	4	yes	—
54	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
55	C₃₁×#108	C₂×C₄	1	16	yes	complemented
56	C₃₁×#107	C₂×C₄	1	8	yes	complemented
57	C₃₁×#106	C₂×C₄	1	8	yes	complemented
58	C₃₁×#97	—	2	8	no	—
59	C₄×C₈×C₃₁	—	2	8	no	—
60	C₄×C₈×C₃₁	C₂×C₄	1	16	yes	complemented
61	C₂⁴×C₃₁	#41	1	1	yes	characteristic
62	C₂²×C₄×C₃₁	—	2	8	no	—
63	C₂²×C₄×C₃₁	—	2	4	no	—
64	C₂²×C₄×C₃₁	—	2	2	no	—
65	C₂²×C₄×C₃₁	—	2	4	no	—
66	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
67	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
68	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₃₁	C₂×Q₈	1	2	yes	—
73	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
74	C₂²×C₄×C₃₁	#41	1	2	yes	—
75	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
76	M₁₆×C₃₁	—	2	8	no	—
77	M₁₆×C₃₁	—	2	4	no	—
78	M₁₆×C₃₁	C₂²×C₄	1	8	yes	—
79	C₂×C₈×C₃₁	—	2	8	no	—
80	C₂×C₈×C₃₁	—	2	4	no	—
81	C₂×C₈×C₃₁	C₄²	1	4	yes	—
82	C₂×C₈×C₃₁	C₄²	1	4	yes	—
83	C₂×C₈×C₃₁	C₄²	1	8	yes	—
84	C₂×C₈×C₃₁	C₄⋊C₄	1	4	yes	—
85	C₂×C₈×C₃₁	C₄⋊C₄	1	8	yes	—
86	C₂×C₈×C₃₁	C₄⋊C₄	1	4	yes	—
87	C₂×C₈×C₃₁	C₂²×C₄	1	4	yes	—
88	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
89	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
90	C₂×C₈×C₃₁	C₂²×C₄	1	4	yes	—
91	C₂×C₈×C₃₁	C₂²×C₄	1	4	yes	—
92	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
93	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
94	C₂×C₈×C₃₁	C₂×Q₈	1	4	yes	—
95	C₄⋊C₄×C₃₁	—	2	4	no	—
96	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
97	C₂²⋊C₄×C₃₁	—	2	4	no	—
98	C₂²⋊C₄×C₃₁	—	2	4	no	—
99	C₄²×C₃₁	—	2	4	no	—
100	C₄²×C₃₁	—	2	4	no	—
101	C₄²×C₃₁	—	2	4	no	—
102	C₄²×C₃₁	—	2	2	no	—
103	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
104	C₂×#1772	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
105	C₂³×C₃₁	—	2	4	no	—
106	C₂³×C₃₁	#117	1	2	yes	—
107	C₂³×C₃₁	C₄×D₄	1	1	yes	characteristic
108	C₂³×C₃₁	C₄×D₄	1	1	yes	characteristic
109	C₂³×C₃₁	C₄×Q₈	1	2	yes	—
110	C₂³×C₃₁	C₂×#41	1	1	yes	characteristic
111	C₂×C₄×C₃₁	—	2	8	no	—
112	C₂×C₄×C₃₁	—	2	16	no	—
113	C₂×C₄×C₃₁	—	2	4	no	—
114	C₂×C₄×C₃₁	—	2	8	no	—
115	C₂×C₄×C₃₁	—	4	8	no	—
116	C₂×C₄×C₃₁	C₂×C₄²	1	2	yes	—
117	C₂×C₄×C₃₁	C₂×C₄²	1	2	yes	—
118	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	2	yes	—
119	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	2	yes	—
120	C₂×C₄×C₃₁	#117	1	2	yes	—
121	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
122	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
123	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
124	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
125	C₂×C₄×C₃₁	C₄×Q₈	1	2	yes	—
126	C₂×C₄×C₃₁	C₄×Q₈	1	2	yes	—
127	C₂×C₄×C₃₁	C₄×Q₈	1	2	yes	—
128	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
129	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
130	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
131	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
132	C₂×C₄×C₃₁	C₂²×Q₈	1	1	yes	characteristic
133	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
134	C₈×C₃₁	—	2	8	no	—
135	C₈×C₃₁	C₂×C₄²	1	4	yes	—
136	C₈×C₃₁	C₂×C₄²	1	4	yes	—
137	C₈×C₃₁	C₂×C₄⋊C₄	1	4	yes	—
138	C₈×C₃₁	C₂×C₄⋊C₄	1	4	yes	—
139	C₂²×#108	C₂×C₃₁	1	1	yes	characteristic
140	C₂×#427	C₂×C₃₁	1	1	yes	characteristic
141	C₂×#405	C₂×C₃₁	1	2	yes	—
142	C₂²×C₄×C₈	C₂×C₃₁	1	1	yes	characteristic
143	#1772	C₂×C₃₁	1	8	yes	direct product factor
144	C₂×#339	C₂×C₃₁	1	2	yes	—
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	C₄×C₄⋊C₄	1	2	yes	—
150	C₂²×C₃₁	C₄×C₄⋊C₄	1	2	yes	—
151	C₂²×C₃₁	#443	1	4	yes	—
152	C₂²×C₃₁	C₂×#117	1	1	yes	characteristic
153	C₂²×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
154	C₂²×C₃₁	C₂×C₄×Q₈	1	1	yes	characteristic
155	C₄×C₃₁	—	2	8	no	—
156	C₄×C₃₁	—	4	8	no	—
157	C₄×C₃₁	C₄×C₄⋊C₄	1	2	yes	—
158	C₄×C₃₁	C₄×C₄⋊C₄	1	2	yes	—
159	C₄×C₃₁	C₂²×C₄²	1	1	yes	characteristic
160	C₄×C₃₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
161	C₄×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
162	C₄×C₃₁	C₂×C₄×Q₈	1	1	yes	characteristic
163	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
164	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
165	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
166	C₂×#117	C₂²×C₃₁	1	2	yes	—
167	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
168	C₂×#108	C₄×C₃₁	1	8	yes	complemented
169	C₂×#108	C₂²×C₃₁	1	4	yes	—
170	#427	C₄×C₃₁	1	4	yes	complemented
171	#427	C₂²×C₃₁	1	4	yes	—
172	C₂×#107	C₄×C₃₁	1	2	yes	complemented
173	C₂×#106	C₄×C₃₁	1	2	yes	complemented
174	#405	—	2	4	no	—
175	#405	C₂²×C₃₁	1	8	yes	—
176	C₂×#97	—	2	2	no	—
177	C₂×C₄×C₈	—	2	2	no	—
178	C₂×C₄×C₈	C₄×C₃₁	1	8	yes	complemented
179	C₂×C₄×C₈	C₂²×C₃₁	1	4	yes	—
180	#339	C₂²×C₃₁	1	8	yes	—
181	C₂×C₃₁	—	2	1	no	—
182	C₂×C₃₁	—	2	1	no	—
183	C₂×C₃₁	—	2	2	no	—
184	C₂×C₃₁	#1772	1	4	yes	direct product factor
185	C₂×C₃₁	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
186	C₂×C₃₁	C₂×#443	1	2	yes	—
187	C₂³×C₄	—	2	1	no	—
188	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
189	C₂×M₁₆	—	2	2	no	—
190	C₂×M₁₆	—	2	4	no	—
191	C₂×M₁₆	C₂×C₄×C₃₁	1	8	yes	—
192	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
193	C₂²×C₈	—	2	2	no	—
194	C₂²×C₈	C₂×C₄×C₃₁	1	4	yes	—
195	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
196	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
197	C₂²×C₈	C₂×C₄×C₃₁	1	2	yes	—
198	C₂²×C₈	C₂×C₄×C₃₁	1	4	yes	—
199	C₂²×C₈	C₂×C₄×C₃₁	1	4	yes	—
200	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
201	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
202	C₂²×C₈	D₄×C₃₁	1	2	yes	—
203	C₂²×C₈	Q₈×C₃₁	1	4	yes	—
204	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
205	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
206	#117	—	2	2	no	—
207	#117	—	2	2	no	—
208	#117	C₂×C₄×C₃₁	1	4	yes	—
209	#117	C₂³×C₃₁	1	4	yes	—
210	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
211	C₂×C₂²⋊C₄	—	2	2	no	—
212	C₂×C₄²	—	2	2	no	—
213	C₂×C₄²	—	2	1	no	—
214	C₂×C₄²	—	2	2	no	—
215	C₂×C₄²	C₂×C₄×C₃₁	1	4	yes	—
216	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
217	#108	C₂×C₄×C₃₁	1	16	yes	complemented
218	#107	C₂×C₄×C₃₁	1	8	yes	complemented
219	#106	C₂×C₄×C₃₁	1	8	yes	complemented
220	#97	—	2	8	no	—
221	C₄×C₈	—	2	8	no	—
222	C₄×C₈	C₂×C₄×C₃₁	1	16	yes	complemented
223	C₃₁	C₂×#1772	1	1	yes	characteristic, direct product factor, Sylow
224	C₂⁴	#41×C₃₁	1	1	yes	characteristic
225	C₂²×C₄	—	2	8	no	—
226	C₂²×C₄	—	2	4	no	—
227	C₂²×C₄	—	2	2	no	—
228	C₂²×C₄	—	2	4	no	—
229	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
230	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
231	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
232	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
233	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
234	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
235	C₂²×C₄	C₂×Q₈×C₃₁	1	2	yes	—
236	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
237	C₂²×C₄	#41×C₃₁	1	2	yes	—
238	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
239	M₁₆	—	2	8	no	—
240	M₁₆	—	2	4	no	—
241	M₁₆	C₂²×C₄×C₃₁	1	8	yes	—
242	C₂×C₈	—	2	8	no	—
243	C₂×C₈	—	2	4	no	—
244	C₂×C₈	C₄²×C₃₁	1	4	yes	—
245	C₂×C₈	C₄²×C₃₁	1	4	yes	—
246	C₂×C₈	C₄²×C₃₁	1	8	yes	—
247	C₂×C₈	C₄⋊C₄×C₃₁	1	4	yes	—
248	C₂×C₈	C₄⋊C₄×C₃₁	1	8	yes	—
249	C₂×C₈	C₄⋊C₄×C₃₁	1	4	yes	—
250	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
251	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
252	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
253	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
254	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
255	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
256	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
257	C₂×C₈	C₂×Q₈×C₃₁	1	4	yes	—
258	C₄⋊C₄	—	2	4	no	—
259	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
260	C₂²⋊C₄	—	2	4	no	—
261	C₂²⋊C₄	—	2	4	no	—
262	C₄²	—	2	4	no	—
263	C₄²	—	2	4	no	—
264	C₄²	—	2	4	no	—
265	C₄²	—	2	2	no	—
266	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
267	C₂³	—	2	4	no	—
268	C₂³	C₃₁×#117	1	2	yes	—
269	C₂³	C₄×D₄×C₃₁	1	1	yes	characteristic
270	C₂³	C₄×D₄×C₃₁	1	1	yes	characteristic
271	C₂³	C₄×Q₈×C₃₁	1	2	yes	—
272	C₂³	C₂×#41×C₃₁	1	1	yes	characteristic
273	C₂×C₄	—	2	8	no	—
274	C₂×C₄	—	2	16	no	—
275	C₂×C₄	—	2	4	no	—
276	C₂×C₄	—	2	8	no	—
277	C₂×C₄	—	4	8	no	—
278	C₂×C₄	C₂×C₄²×C₃₁	1	2	yes	—
279	C₂×C₄	C₂×C₄²×C₃₁	1	2	yes	—
280	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	2	yes	—
281	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	2	yes	—
282	C₂×C₄	C₃₁×#117	1	2	yes	—
283	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
284	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
285	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
286	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
287	C₂×C₄	C₄×Q₈×C₃₁	1	2	yes	—
288	C₂×C₄	C₄×Q₈×C₃₁	1	2	yes	—
289	C₂×C₄	C₄×Q₈×C₃₁	1	2	yes	—
290	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
291	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
292	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
293	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
294	C₂×C₄	C₂²×Q₈×C₃₁	1	1	yes	characteristic
295	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
296	C₈	—	2	8	no	—
297	C₈	C₂×C₄²×C₃₁	1	4	yes	—
298	C₈	C₂×C₄²×C₃₁	1	4	yes	—
299	C₈	C₂×C₄⋊C₄×C₃₁	1	4	yes	—
300	C₈	C₂×C₄⋊C₄×C₃₁	1	4	yes	—
301	C₂²	—	2	2	no	—
302	C₂²	—	2	2	no	—
303	C₂²	—	2	4	no	—
304	C₂²	—	2	4	no	—
305	C₂²	C₄×C₄⋊C₄×C₃₁	1	2	yes	—
306	C₂²	C₄×C₄⋊C₄×C₃₁	1	2	yes	—
307	C₂²	C₃₁×#443	1	4	yes	—
308	C₂²	C₂×C₃₁×#117	1	1	yes	characteristic
309	C₂²	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
310	C₂²	C₂×C₄×Q₈×C₃₁	1	1	yes	characteristic
311	C₄	—	2	8	no	—
312	C₄	—	4	8	no	—
313	C₄	C₄×C₄⋊C₄×C₃₁	1	2	yes	—
314	C₄	C₄×C₄⋊C₄×C₃₁	1	2	yes	—
315	C₄	C₂²×C₄²×C₃₁	1	1	yes	characteristic
316	C₄	C₂²×C₄⋊C₄×C₃₁	1	1	yes	characteristic
317	C₄	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
318	C₄	C₂×C₄×Q₈×C₃₁	1	1	yes	characteristic
319	C₂	—	2	1	no	—
320	C₂	—	2	1	no	—
321	C₂	—	2	2	no	—
322	C₂	C₃₁×#1772	1	4	yes	direct product factor
323	C₂	C₂×C₄×C₄⋊C₄×C₃₁	1	1	yes	characteristic
324	C₂	C₂×C₃₁×#443	1	2	yes	—

	subgroup	G/H
center	C₂²×C₈×C₃₁	D₄
commutator	C₄	C₂²×C₄²×C₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
socle	C₂³×C₃₁	C₄×D₄
prime radical	C₂⁴×C₃₁	#41
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₃₁ ◁ C₂³×C₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₃₁×#1772	C₂	direct (N × H)
12. C₂×C₃₁×#108	C₄	semidirect
14. C₃₁×#427	C₄	semidirect
16. C₂×C₃₁×#107	C₄	semidirect
17. C₂×C₃₁×#106	C₄	semidirect
22. C₂×C₄×C₈×C₃₁	C₄	semidirect
55. C₃₁×#108	C₂×C₄	semidirect
56. C₃₁×#107	C₂×C₄	semidirect
57. C₃₁×#106	C₂×C₄	semidirect
60. C₄×C₈×C₃₁	C₂×C₄	semidirect
104. C₂×#1772	C₃₁	direct (N × H)
143. #1772	C₂×C₃₁	direct (N × H)
168. C₂×#108	C₄×C₃₁	semidirect
170. #427	C₄×C₃₁	semidirect
172. C₂×#107	C₄×C₃₁	semidirect
173. C₂×#106	C₄×C₃₁	semidirect
178. C₂×C₄×C₈	C₄×C₃₁	semidirect
184. C₂×C₃₁	#1772	direct (N × H)
217. #108	C₂×C₄×C₃₁	semidirect
218. #107	C₂×C₄×C₃₁	semidirect
219. #106	C₂×C₄×C₃₁	semidirect
222. C₄×C₈	C₂×C₄×C₃₁	semidirect
223. C₃₁	C₂×#1772	direct (N × H)
322. C₂	C₃₁×#1772	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×#108	2
C₂×C₃₁×#427	2
C₂×C₃₁×#405	2
C₂²×C₄×C₈×C₃₁	2
C₃₁×#1772	2
C₂×C₃₁×#339	2
C₂×#1772	31

Subgroups — C2×C31×#1772 #21477201

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#1772 #21477201