Subgroups — C₂×C₃₁×#1546 #21474461

Order 7936.

1246 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#431	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₁×#423	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1546	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃₁×#332	C₂	1	4	yes	maximal, complemented
6	C₂³×Q₈×C₃₁	—	2	1	no	—
7	C₂²×M₁₆×C₃₁	—	2	1	no	—
8	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
9	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
10	C₂×C₃₁×C₄⋊Q₈	—	2	2	no	—
11	C₂×C₃₁×C₄⋊Q₈	—	2	2	no	—
12	C₂×C₃₁×C₄⋊Q₈	C₄	1	4	yes	—
13	C₂×C₃₁×C₄⋊Q₈	C₄	1	2	yes	—
14	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₃₁×C₄⋊Q₈	C₂²	1	4	yes	—
16	C₂²×C₄⋊C₄×C₃₁	—	2	1	no	—
17	C₂²×C₄⋊C₄×C₃₁	C₄	1	2	yes	—
18	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
19	C₃₁×#431	—	2	2	no	—
20	C₃₁×#431	C₂²	1	4	yes	—
21	C₃₁×#423	—	2	2	no	—
22	C₃₁×#423	C₂²	1	4	yes	—
23	C₂×C₃₁×C₄⋊C₈	—	2	1	no	—
24	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
25	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
26	C₂×C₃₁×C₂²⋊C₈	—	2	1	no	—
27	C₂×C₄×C₈×C₃₁	—	2	1	no	—
28	C₃₁×#332	C₂²	1	16	yes	complemented
29	C₂²×Q₈×C₃₁	—	2	4	no	—
30	C₂²×Q₈×C₃₁	—	2	2	no	—
31	C₂²×Q₈×C₃₁	—	2	4	no	—
32	C₂²×Q₈×C₃₁	—	2	2	no	—
33	C₂²×Q₈×C₃₁	—	4	4	no	—
34	C₂²×Q₈×C₃₁	—	4	4	no	—
35	C₂³×C₄×C₃₁	—	2	2	no	—
36	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
39	C₂×M₁₆×C₃₁	—	2	4	no	—
40	C₂×M₁₆×C₃₁	—	4	4	no	—
41	C₂²×C₈×C₃₁	—	2	2	no	—
42	C₂²×C₈×C₃₁	—	2	2	no	—
43	C₃₁×C₄⋊Q₈	—	2	4	no	—
44	C₃₁×C₄⋊Q₈	—	2	4	no	—
45	C₃₁×C₄⋊Q₈	—	2	4	no	—
46	C₃₁×C₄⋊Q₈	—	2	4	no	—
47	C₃₁×C₄⋊Q₈	—	2	2	no	—
48	C₃₁×C₄⋊Q₈	—	2	4	no	—
49	C₃₁×C₄⋊Q₈	—	2	2	no	—
50	C₃₁×C₄⋊Q₈	C₂×C₄	1	4	yes	—
51	C₃₁×C₄⋊Q₈	C₂×C₄	1	8	yes	—
52	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
53	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
54	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
55	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
56	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
58	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	8	yes	—
60	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	4	yes	—
61	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
62	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₃₁	D₄	1	2	yes	—
66	C₂×C₄²×C₃₁	D₄	1	2	yes	—
67	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
69	C₃₁×C₄⋊C₈	—	2	4	no	—
70	C₃₁×C₄⋊C₈	—	2	2	no	—
71	C₃₁×C₄⋊C₈	—	2	2	no	—
72	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
73	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
74	C₃₁×C₂²⋊C₈	—	2	4	no	—
75	C₄×C₈×C₃₁	—	2	4	no	—
76	C₂⁴×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
77	C₂×Q₈×C₃₁	—	2	8	no	—
78	C₂×Q₈×C₃₁	—	2	4	no	—
79	C₂×Q₈×C₃₁	—	2	4	no	—
80	C₂×Q₈×C₃₁	—	4	16	no	—
81	C₂×Q₈×C₃₁	—	4	8	no	—
82	C₂×Q₈×C₃₁	—	4	4	no	—
83	C₂×Q₈×C₃₁	—	4	8	no	—
84	C₂×Q₈×C₃₁	—	4	8	no	—
85	C₂×Q₈×C₃₁	—	4	4	no	—
86	C₂²×C₄×C₃₁	—	2	4	no	—
87	C₂²×C₄×C₃₁	—	2	4	no	—
88	C₂²×C₄×C₃₁	—	2	8	no	—
89	C₂²×C₄×C₃₁	—	2	4	no	—
90	C₂²×C₄×C₃₁	—	4	8	no	—
91	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
92	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
93	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
96	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
97	C₂²×C₄×C₃₁	D₈	1	4	yes	—
98	C₂²×C₄×C₃₁	SD₁₆	1	4	yes	—
99	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
105	M₁₆×C₃₁	—	4	8	no	—
106	C₂×C₈×C₃₁	—	2	4	no	—
107	C₂×C₈×C₃₁	—	2	4	no	—
108	C₂×C₈×C₃₁	—	4	4	no	—
109	C₂×C₈×C₃₁	—	4	4	no	—
110	C₄⋊C₄×C₃₁	—	2	8	no	—
111	C₄⋊C₄×C₃₁	—	2	4	no	—
112	C₄⋊C₄×C₃₁	—	2	4	no	—
113	C₄⋊C₄×C₃₁	—	2	8	no	—
114	C₄⋊C₄×C₃₁	—	2	4	no	—
115	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
116	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
117	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
118	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
119	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
120	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₃₁	C₂×D₄	1	2	yes	—
122	C₄²×C₃₁	C₂×D₄	1	2	yes	—
123	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
126	C₂×#1546	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂³×C₃₁	—	2	2	no	—
128	C₂³×C₃₁	—	2	2	no	—
129	C₂³×C₃₁	#102	1	4	yes	—
130	C₂³×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
131	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
132	Q₈×C₃₁	—	4	4	no	—
133	Q₈×C₃₁	—	4	4	no	—
134	Q₈×C₃₁	—	4	8	no	—
135	Q₈×C₃₁	—	4	16	no	—
136	C₂×C₄×C₃₁	—	2	2	no	—
137	C₂×C₄×C₃₁	—	2	2	no	—
138	C₂×C₄×C₃₁	—	2	4	no	—
139	C₂×C₄×C₃₁	—	2	4	no	—
140	C₂×C₄×C₃₁	—	2	4	no	—
141	C₂×C₄×C₃₁	—	2	4	no	—
142	C₂×C₄×C₃₁	—	2	8	no	—
143	C₂×C₄×C₃₁	—	4	16	no	—
144	C₂×C₄×C₃₁	—	4	8	no	—
145	C₂×C₄×C₃₁	#101	1	4	yes	—
146	C₂×C₄×C₃₁	#102	1	8	yes	—
147	C₂×C₄×C₃₁	#102	1	4	yes	—
148	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
149	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
151	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
152	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
155	C₂×C₄×C₃₁	C₂×D₈	1	4	yes	—
156	C₂×C₄×C₃₁	C₂×SD₁₆	1	4	yes	—
157	C₂×C₄×C₃₁	C₂×SD₁₆	1	2	yes	—
158	C₂×C₄×C₃₁	#137	1	4	yes	—
159	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
162	C₈×C₃₁	—	4	4	no	—
163	C₈×C₃₁	—	4	4	no	—
164	C₂²×C₄⋊Q₈	C₂×C₃₁	1	1	yes	characteristic
165	C₂×#431	C₂×C₃₁	1	1	yes	characteristic
166	C₂×#423	C₂×C₃₁	1	1	yes	characteristic
167	#1546	C₂×C₃₁	1	8	yes	direct product factor
168	C₂×#332	C₂×C₃₁	1	4	yes	complemented
169	C₂²×C₃₁	—	2	8	no	—
170	C₂²×C₃₁	—	2	2	no	—
171	C₂²×C₃₁	—	2	2	no	—
172	C₂²×C₃₁	C₂×#101	1	2	yes	—
173	C₂²×C₃₁	C₂×#102	1	4	yes	—
174	C₂²×C₃₁	C₂×#102	1	2	yes	—
175	C₂²×C₃₁	#419	1	2	yes	—
176	C₂²×C₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
177	C₄×C₃₁	—	2	1	no	—
178	C₄×C₃₁	—	2	1	no	—
179	C₄×C₃₁	—	2	2	no	—
180	C₄×C₃₁	—	4	8	no	—
181	C₄×C₃₁	C₂×#101	1	4	yes	—
182	C₄×C₃₁	C₂×#102	1	2	yes	—
183	C₄×C₃₁	C₂×#102	1	4	yes	—
184	C₄×C₃₁	#419	1	2	yes	—
185	C₄×C₃₁	C₂²×D₈	1	1	yes	characteristic
186	C₄×C₃₁	C₂²×SD₁₆	1	1	yes	characteristic
187	C₄×C₃₁	C₂×#137	1	2	yes	—
188	C₂³×Q₈	—	2	1	no	—
189	C₂²×M₁₆	—	2	1	no	—
190	C₂×C₄⋊Q₈	—	2	1	no	—
191	C₂×C₄⋊Q₈	—	2	1	no	—
192	C₂×C₄⋊Q₈	—	2	2	no	—
193	C₂×C₄⋊Q₈	—	2	2	no	—
194	C₂×C₄⋊Q₈	C₄×C₃₁	1	2	yes	—
195	C₂×C₄⋊Q₈	C₄×C₃₁	1	4	yes	—
196	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
197	C₂×C₄⋊Q₈	C₂²×C₃₁	1	4	yes	—
198	C₂²×C₄⋊C₄	—	2	1	no	—
199	C₂²×C₄⋊C₄	C₄×C₃₁	1	2	yes	—
200	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
201	#431	—	2	2	no	—
202	#431	C₂²×C₃₁	1	4	yes	—
203	#423	—	2	2	no	—
204	#423	C₂²×C₃₁	1	4	yes	—
205	C₂×C₄⋊C₈	—	2	1	no	—
206	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
207	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
208	C₂×C₂²⋊C₈	—	2	1	no	—
209	C₂×C₄×C₈	—	2	1	no	—
210	#332	C₂²×C₃₁	1	16	yes	complemented
211	C₂×C₃₁	—	2	4	no	—
212	C₂×C₃₁	#1546	1	4	yes	direct product factor
213	C₂×C₃₁	C₂²×#101	1	1	yes	characteristic
214	C₂×C₃₁	C₂²×#102	1	1	yes	characteristic
215	C₂×C₃₁	C₂×#419	1	1	yes	characteristic
216	C₂²×Q₈	—	2	4	no	—
217	C₂²×Q₈	—	2	2	no	—
218	C₂²×Q₈	—	2	2	no	—
219	C₂²×Q₈	—	2	4	no	—
220	C₂²×Q₈	—	4	4	no	—
221	C₂²×Q₈	—	4	4	no	—
222	C₂³×C₄	—	2	2	no	—
223	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
224	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
225	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
226	C₂×M₁₆	—	2	4	no	—
227	C₂×M₁₆	—	4	4	no	—
228	C₂²×C₈	—	2	2	no	—
229	C₂²×C₈	—	2	2	no	—
230	C₄⋊Q₈	—	2	4	no	—
231	C₄⋊Q₈	—	2	4	no	—
232	C₄⋊Q₈	—	2	4	no	—
233	C₄⋊Q₈	—	2	4	no	—
234	C₄⋊Q₈	—	2	2	no	—
235	C₄⋊Q₈	—	2	4	no	—
236	C₄⋊Q₈	—	2	2	no	—
237	C₄⋊Q₈	C₂×C₄×C₃₁	1	4	yes	—
238	C₄⋊Q₈	C₂×C₄×C₃₁	1	8	yes	—
239	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
240	C₂×C₄⋊C₄	—	2	2	no	—
241	C₂×C₄⋊C₄	—	2	4	no	—
242	C₂×C₄⋊C₄	—	2	4	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	4	no	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
247	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	8	yes	—
248	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
249	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
250	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
251	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
252	C₂×C₄²	D₄×C₃₁	1	2	yes	—
253	C₂×C₄²	D₄×C₃₁	1	2	yes	—
254	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
255	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
256	C₄⋊C₈	—	2	4	no	—
257	C₄⋊C₈	—	2	2	no	—
258	C₄⋊C₈	—	2	2	no	—
259	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
260	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
261	C₂²⋊C₈	—	2	4	no	—
262	C₄×C₈	—	2	4	no	—
263	C₃₁	C₂×#1546	1	1	yes	characteristic, direct product factor, Sylow
264	C₂⁴	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
265	C₂×Q₈	—	2	8	no	—
266	C₂×Q₈	—	2	4	no	—
267	C₂×Q₈	—	2	4	no	—
268	C₂×Q₈	—	4	16	no	—
269	C₂×Q₈	—	4	8	no	—
270	C₂×Q₈	—	4	4	no	—
271	C₂×Q₈	—	4	8	no	—
272	C₂×Q₈	—	4	8	no	—
273	C₂×Q₈	—	4	4	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	8	no	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	4	8	no	—
279	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
280	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
281	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
282	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
283	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
284	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
285	C₂²×C₄	D₈×C₃₁	1	4	yes	—
286	C₂²×C₄	SD₁₆×C₃₁	1	4	yes	—
287	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
288	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
289	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
290	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
292	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
293	M₁₆	—	4	8	no	—
294	C₂×C₈	—	2	4	no	—
295	C₂×C₈	—	2	4	no	—
296	C₂×C₈	—	4	4	no	—
297	C₂×C₈	—	4	4	no	—
298	C₄⋊C₄	—	2	8	no	—
299	C₄⋊C₄	—	2	4	no	—
300	C₄⋊C₄	—	2	4	no	—
301	C₄⋊C₄	—	2	8	no	—
302	C₄⋊C₄	—	2	4	no	—
303	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
304	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
305	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
306	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
307	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
308	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
309	C₄²	C₂×D₄×C₃₁	1	2	yes	—
310	C₄²	C₂×D₄×C₃₁	1	2	yes	—
311	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
312	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
313	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
314	C₂³	—	2	2	no	—
315	C₂³	—	2	2	no	—
316	C₂³	C₃₁×#102	1	4	yes	—
317	C₂³	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
318	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
319	Q₈	—	4	8	no	—
320	Q₈	—	4	16	no	—
321	Q₈	—	4	4	no	—
322	Q₈	—	4	4	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	8	no	—
330	C₂×C₄	—	4	16	no	—
331	C₂×C₄	—	4	8	no	—
332	C₂×C₄	C₃₁×#101	1	4	yes	—
333	C₂×C₄	C₃₁×#102	1	8	yes	—
334	C₂×C₄	C₃₁×#102	1	4	yes	—
335	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
336	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
337	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
338	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
339	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
340	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
341	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
342	C₂×C₄	C₂×D₈×C₃₁	1	4	yes	—
343	C₂×C₄	C₂×SD₁₆×C₃₁	1	4	yes	—
344	C₂×C₄	C₂×SD₁₆×C₃₁	1	2	yes	—
345	C₂×C₄	C₃₁×#137	1	4	yes	—
346	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
347	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
348	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
349	C₈	—	4	4	no	—
350	C₈	—	4	4	no	—
351	C₂²	—	2	8	no	—
352	C₂²	—	2	2	no	—
353	C₂²	—	2	2	no	—
354	C₂²	C₂×C₃₁×#101	1	2	yes	—
355	C₂²	C₂×C₃₁×#102	1	4	yes	—
356	C₂²	C₂×C₃₁×#102	1	2	yes	—
357	C₂²	C₃₁×#419	1	2	yes	—
358	C₂²	C₂²×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	2	no	—
362	C₄	—	4	8	no	—
363	C₄	C₂×C₃₁×#101	1	4	yes	—
364	C₄	C₂×C₃₁×#102	1	2	yes	—
365	C₄	C₂×C₃₁×#102	1	4	yes	—
366	C₄	C₃₁×#419	1	2	yes	—
367	C₄	C₂²×D₈×C₃₁	1	1	yes	characteristic
368	C₄	C₂²×SD₁₆×C₃₁	1	1	yes	characteristic
369	C₄	C₂×C₃₁×#137	1	2	yes	—
370	C₂	—	2	4	no	—
371	C₂	C₃₁×#1546	1	4	yes	direct product factor
372	C₂	C₂²×C₃₁×#101	1	1	yes	characteristic
373	C₂	C₂²×C₃₁×#102	1	1	yes	characteristic
374	C₂	C₂×C₃₁×#419	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₃₁×#1546	C₂	direct (N × H)
5. C₂×C₃₁×#332	C₂	semidirect
28. C₃₁×#332	C₂²	semidirect
126. C₂×#1546	C₃₁	direct (N × H)
167. #1546	C₂×C₃₁	direct (N × H)
168. C₂×#332	C₂×C₃₁	semidirect
210. #332	C₂²×C₃₁	semidirect
212. C₂×C₃₁	#1546	direct (N × H)
263. C₃₁	C₂×#1546	direct (N × H)
371. C₂	C₃₁×#1546	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×C₄⋊Q₈	2
C₂×C₃₁×#431	2
C₂×C₃₁×#423	2
C₃₁×#1546	2
C₂×C₃₁×#332	2
C₂×#1546	31

Subgroups — C2×C31×#1546 #21474461

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#1546 #21474461