Subgroups — C₂×C₃₁×#1773 #21477202

Order 7936.

1062 conjugacy classes of subgroups.

The subgroup lattice has 318 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×C₃₁×#97	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#1773	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×C₃₁×#97	C₄	1	8	yes	complemented
22	C₂×C₃₁×#97	C₂²	1	4	yes	—
23	C₂×C₄×C₈×C₃₁	—	2	2	no	—
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	2	yes	—
39	C₂²×C₈×C₃₁	D₄	1	2	yes	—
40	C₂²×C₈×C₃₁	Q₈	1	4	yes	—
41	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
42	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
43	C₃₁×#117	—	2	2	no	—
44	C₃₁×#117	—	2	2	no	—
45	C₃₁×#117	C₂×C₄	1	4	yes	—
46	C₃₁×#117	C₂³	1	4	yes	—
47	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	4	yes	—
48	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
49	C₂×C₄²×C₃₁	—	2	2	no	—
50	C₂×C₄²×C₃₁	—	2	1	no	—
51	C₂×C₄²×C₃₁	—	2	2	no	—
52	C₂×C₄²×C₃₁	C₂×C₄	1	4	yes	—
53	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
54	C₃₁×#108	C₂×C₄	1	16	yes	complemented
55	C₃₁×#107	C₂×C₄	1	8	yes	complemented
56	C₃₁×#106	C₂×C₄	1	8	yes	complemented
57	C₃₁×#97	—	2	8	no	—
58	C₃₁×#97	C₂×C₄	1	16	yes	complemented
59	C₄×C₈×C₃₁	—	2	8	no	—
60	C₂⁴×C₃₁	#41	1	1	yes	characteristic
61	C₂²×C₄×C₃₁	—	2	4	no	—
62	C₂²×C₄×C₃₁	—	2	4	no	—
63	C₂²×C₄×C₃₁	—	2	2	no	—
64	C₂²×C₄×C₃₁	—	4	4	no	—
65	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
66	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
67	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₃₁	C₂×Q₈	1	2	yes	—
72	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
73	C₂²×C₄×C₃₁	#41	1	2	yes	—
74	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
75	M₁₆×C₃₁	—	2	8	no	—
76	M₁₆×C₃₁	—	2	4	no	—
77	M₁₆×C₃₁	C₂²×C₄	1	8	yes	—
78	C₂×C₈×C₃₁	—	2	8	no	—
79	C₂×C₈×C₃₁	—	2	4	no	—
80	C₂×C₈×C₃₁	C₄²	1	4	yes	—
81	C₂×C₈×C₃₁	C₄²	1	4	yes	—
82	C₂×C₈×C₃₁	C₄²	1	8	yes	—
83	C₂×C₈×C₃₁	C₄⋊C₄	1	8	yes	—
84	C₂×C₈×C₃₁	C₄⋊C₄	1	8	yes	—
85	C₂×C₈×C₃₁	C₂²×C₄	1	4	yes	—
86	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
87	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
88	C₂×C₈×C₃₁	C₂²×C₄	1	4	yes	—
89	C₂×C₈×C₃₁	C₂²×C₄	1	4	yes	—
90	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
91	C₂×C₈×C₃₁	C₂×Q₈	1	4	yes	—
92	C₄⋊C₄×C₃₁	—	2	4	no	—
93	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
94	C₂²⋊C₄×C₃₁	—	2	4	no	—
95	C₂²⋊C₄×C₃₁	—	2	4	no	—
96	C₄²×C₃₁	—	2	4	no	—
97	C₄²×C₃₁	—	2	4	no	—
98	C₄²×C₃₁	—	2	4	no	—
99	C₄²×C₃₁	—	2	2	no	—
100	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
101	C₂×#1773	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂³×C₃₁	—	2	4	no	—
103	C₂³×C₃₁	#117	1	2	yes	—
104	C₂³×C₃₁	C₄×D₄	1	1	yes	characteristic
105	C₂³×C₃₁	C₄×D₄	1	1	yes	characteristic
106	C₂³×C₃₁	C₄×Q₈	1	2	yes	—
107	C₂³×C₃₁	C₂×#41	1	1	yes	characteristic
108	C₂×C₄×C₃₁	—	2	4	no	—
109	C₂×C₄×C₃₁	—	2	8	no	—
110	C₂×C₄×C₃₁	—	4	4	no	—
111	C₂×C₄×C₃₁	—	4	8	no	—
112	C₂×C₄×C₃₁	—	4	8	no	—
113	C₂×C₄×C₃₁	C₂×C₄²	1	2	yes	—
114	C₂×C₄×C₃₁	C₂×C₄²	1	2	yes	—
115	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	2	yes	—
116	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	2	yes	—
117	C₂×C₄×C₃₁	#117	1	2	yes	—
118	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
119	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
120	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
121	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
122	C₂×C₄×C₃₁	C₄×Q₈	1	2	yes	—
123	C₂×C₄×C₃₁	C₄×Q₈	1	2	yes	—
124	C₂×C₄×C₃₁	C₄×Q₈	1	2	yes	—
125	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
126	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
127	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
128	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
129	C₂×C₄×C₃₁	C₂²×Q₈	1	1	yes	characteristic
130	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
131	C₈×C₃₁	—	2	8	no	—
132	C₈×C₃₁	C₂×C₄²	1	4	yes	—
133	C₈×C₃₁	C₂×C₄²	1	4	yes	—
134	C₈×C₃₁	C₂×C₄⋊C₄	1	8	yes	—
135	C₂²×#108	C₂×C₃₁	1	1	yes	characteristic
136	C₂×#427	C₂×C₃₁	1	1	yes	characteristic
137	C₂×#405	C₂×C₃₁	1	2	yes	—
138	C₂²×#97	C₂×C₃₁	1	1	yes	characteristic
139	#1773	C₂×C₃₁	1	8	yes	direct product factor
140	C₂×#339	C₂×C₃₁	1	2	yes	—
141	C₂²×C₃₁	—	2	2	no	—
142	C₂²×C₃₁	—	2	2	no	—
143	C₂²×C₃₁	—	2	4	no	—
144	C₂²×C₃₁	—	2	4	no	—
145	C₂²×C₃₁	C₄×C₄⋊C₄	1	2	yes	—
146	C₂²×C₃₁	C₄×C₄⋊C₄	1	2	yes	—
147	C₂²×C₃₁	#444	1	4	yes	—
148	C₂²×C₃₁	C₂×#117	1	1	yes	characteristic
149	C₂²×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
150	C₂²×C₃₁	C₂×C₄×Q₈	1	1	yes	characteristic
151	C₄×C₃₁	—	4	4	no	—
152	C₄×C₃₁	—	4	8	no	—
153	C₄×C₃₁	C₄×C₄⋊C₄	1	2	yes	—
154	C₄×C₃₁	C₄×C₄⋊C₄	1	2	yes	—
155	C₄×C₃₁	C₂²×C₄²	1	1	yes	characteristic
156	C₄×C₃₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
157	C₄×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
158	C₄×C₃₁	C₂×C₄×Q₈	1	1	yes	characteristic
159	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
160	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
161	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
162	C₂×#117	C₂²×C₃₁	1	2	yes	—
163	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
164	C₂×#108	C₄×C₃₁	1	8	yes	complemented
165	C₂×#108	C₂²×C₃₁	1	4	yes	—
166	#427	C₄×C₃₁	1	4	yes	complemented
167	#427	C₂²×C₃₁	1	4	yes	—
168	C₂×#107	C₄×C₃₁	1	2	yes	complemented
169	C₂×#106	C₄×C₃₁	1	2	yes	complemented
170	#405	—	2	4	no	—
171	#405	C₂²×C₃₁	1	8	yes	—
172	C₂×#97	—	2	2	no	—
173	C₂×#97	C₄×C₃₁	1	8	yes	complemented
174	C₂×#97	C₂²×C₃₁	1	4	yes	—
175	C₂×C₄×C₈	—	2	2	no	—
176	#339	C₂²×C₃₁	1	8	yes	—
177	C₂×C₃₁	—	2	1	no	—
178	C₂×C₃₁	—	2	1	no	—
179	C₂×C₃₁	—	2	2	no	—
180	C₂×C₃₁	#1773	1	4	yes	direct product factor
181	C₂×C₃₁	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
182	C₂×C₃₁	C₂×#444	1	2	yes	—
183	C₂³×C₄	—	2	1	no	—
184	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
185	C₂×M₁₆	—	2	2	no	—
186	C₂×M₁₆	—	2	4	no	—
187	C₂×M₁₆	C₂×C₄×C₃₁	1	8	yes	—
188	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
189	C₂²×C₈	—	2	2	no	—
190	C₂²×C₈	C₂×C₄×C₃₁	1	4	yes	—
191	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
192	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
193	C₂²×C₈	C₂×C₄×C₃₁	1	2	yes	—
194	C₂²×C₈	C₂×C₄×C₃₁	1	4	yes	—
195	C₂²×C₈	C₂×C₄×C₃₁	1	4	yes	—
196	C₂²×C₈	D₄×C₃₁	1	2	yes	—
197	C₂²×C₈	D₄×C₃₁	1	2	yes	—
198	C₂²×C₈	Q₈×C₃₁	1	4	yes	—
199	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
200	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
201	#117	—	2	2	no	—
202	#117	—	2	2	no	—
203	#117	C₂×C₄×C₃₁	1	4	yes	—
204	#117	C₂³×C₃₁	1	4	yes	—
205	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
206	C₂×C₂²⋊C₄	—	2	2	no	—
207	C₂×C₄²	—	2	2	no	—
208	C₂×C₄²	—	2	1	no	—
209	C₂×C₄²	—	2	2	no	—
210	C₂×C₄²	C₂×C₄×C₃₁	1	4	yes	—
211	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
212	#108	C₂×C₄×C₃₁	1	16	yes	complemented
213	#107	C₂×C₄×C₃₁	1	8	yes	complemented
214	#106	C₂×C₄×C₃₁	1	8	yes	complemented
215	#97	—	2	8	no	—
216	#97	C₂×C₄×C₃₁	1	16	yes	complemented
217	C₄×C₈	—	2	8	no	—
218	C₃₁	C₂×#1773	1	1	yes	characteristic, direct product factor, Sylow
219	C₂⁴	#41×C₃₁	1	1	yes	characteristic
220	C₂²×C₄	—	2	4	no	—
221	C₂²×C₄	—	2	4	no	—
222	C₂²×C₄	—	2	2	no	—
223	C₂²×C₄	—	4	4	no	—
224	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
225	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
226	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
227	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
228	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
229	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
230	C₂²×C₄	C₂×Q₈×C₃₁	1	2	yes	—
231	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
232	C₂²×C₄	#41×C₃₁	1	2	yes	—
233	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
234	M₁₆	—	2	8	no	—
235	M₁₆	—	2	4	no	—
236	M₁₆	C₂²×C₄×C₃₁	1	8	yes	—
237	C₂×C₈	—	2	8	no	—
238	C₂×C₈	—	2	4	no	—
239	C₂×C₈	C₄²×C₃₁	1	4	yes	—
240	C₂×C₈	C₄²×C₃₁	1	4	yes	—
241	C₂×C₈	C₄²×C₃₁	1	8	yes	—
242	C₂×C₈	C₄⋊C₄×C₃₁	1	8	yes	—
243	C₂×C₈	C₄⋊C₄×C₃₁	1	8	yes	—
244	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
245	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
246	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
247	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
248	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
249	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
250	C₂×C₈	C₂×Q₈×C₃₁	1	4	yes	—
251	C₄⋊C₄	—	2	4	no	—
252	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
253	C₂²⋊C₄	—	2	4	no	—
254	C₂²⋊C₄	—	2	4	no	—
255	C₄²	—	2	4	no	—
256	C₄²	—	2	4	no	—
257	C₄²	—	2	4	no	—
258	C₄²	—	2	2	no	—
259	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
260	C₂³	—	2	4	no	—
261	C₂³	C₃₁×#117	1	2	yes	—
262	C₂³	C₄×D₄×C₃₁	1	1	yes	characteristic
263	C₂³	C₄×D₄×C₃₁	1	1	yes	characteristic
264	C₂³	C₄×Q₈×C₃₁	1	2	yes	—
265	C₂³	C₂×#41×C₃₁	1	1	yes	characteristic
266	C₂×C₄	—	2	4	no	—
267	C₂×C₄	—	2	8	no	—
268	C₂×C₄	—	4	4	no	—
269	C₂×C₄	—	4	8	no	—
270	C₂×C₄	—	4	8	no	—
271	C₂×C₄	C₂×C₄²×C₃₁	1	2	yes	—
272	C₂×C₄	C₂×C₄²×C₃₁	1	2	yes	—
273	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	2	yes	—
274	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	2	yes	—
275	C₂×C₄	C₃₁×#117	1	2	yes	—
276	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
277	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
278	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
279	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
280	C₂×C₄	C₄×Q₈×C₃₁	1	2	yes	—
281	C₂×C₄	C₄×Q₈×C₃₁	1	2	yes	—
282	C₂×C₄	C₄×Q₈×C₃₁	1	2	yes	—
283	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
284	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
285	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
286	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
287	C₂×C₄	C₂²×Q₈×C₃₁	1	1	yes	characteristic
288	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
289	C₈	—	2	8	no	—
290	C₈	C₂×C₄²×C₃₁	1	4	yes	—
291	C₈	C₂×C₄²×C₃₁	1	4	yes	—
292	C₈	C₂×C₄⋊C₄×C₃₁	1	8	yes	—
293	C₂²	—	2	2	no	—
294	C₂²	—	2	2	no	—
295	C₂²	—	2	4	no	—
296	C₂²	—	2	4	no	—
297	C₂²	C₄×C₄⋊C₄×C₃₁	1	2	yes	—
298	C₂²	C₄×C₄⋊C₄×C₃₁	1	2	yes	—
299	C₂²	C₃₁×#444	1	4	yes	—
300	C₂²	C₂×C₃₁×#117	1	1	yes	characteristic
301	C₂²	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
302	C₂²	C₂×C₄×Q₈×C₃₁	1	1	yes	characteristic
303	C₄	—	4	4	no	—
304	C₄	—	4	8	no	—
305	C₄	C₄×C₄⋊C₄×C₃₁	1	2	yes	—
306	C₄	C₄×C₄⋊C₄×C₃₁	1	2	yes	—
307	C₄	C₂²×C₄²×C₃₁	1	1	yes	characteristic
308	C₄	C₂²×C₄⋊C₄×C₃₁	1	1	yes	characteristic
309	C₄	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
310	C₄	C₂×C₄×Q₈×C₃₁	1	1	yes	characteristic
311	C₂	—	2	1	no	—
312	C₂	—	2	1	no	—
313	C₂	—	2	2	no	—
314	C₂	C₃₁×#1773	1	4	yes	direct product factor
315	C₂	C₂×C₄×C₄⋊C₄×C₃₁	1	1	yes	characteristic
316	C₂	C₂×C₃₁×#444	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂×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×C₄×C₃₁ ◁ C₂³×C₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₃₁×#1773	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
21. C₂×C₃₁×#97	C₄	semidirect
54. C₃₁×#108	C₂×C₄	semidirect
55. C₃₁×#107	C₂×C₄	semidirect
56. C₃₁×#106	C₂×C₄	semidirect
58. C₃₁×#97	C₂×C₄	semidirect
101. C₂×#1773	C₃₁	direct (N × H)
139. #1773	C₂×C₃₁	direct (N × H)
164. C₂×#108	C₄×C₃₁	semidirect
166. #427	C₄×C₃₁	semidirect
168. C₂×#107	C₄×C₃₁	semidirect
169. C₂×#106	C₄×C₃₁	semidirect
173. C₂×#97	C₄×C₃₁	semidirect
180. C₂×C₃₁	#1773	direct (N × H)
212. #108	C₂×C₄×C₃₁	semidirect
213. #107	C₂×C₄×C₃₁	semidirect
214. #106	C₂×C₄×C₃₁	semidirect
216. #97	C₂×C₄×C₃₁	semidirect
218. C₃₁	C₂×#1773	direct (N × H)
314. C₂	C₃₁×#1773	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×C₃₁×#97	2
C₃₁×#1773	2
C₂×C₃₁×#339	2
C₂×#1773	31

Subgroups — C2×C31×#1773 #21477202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#1773 #21477202