Subgroups — C₂×C₃₁×#1549 #21474465

Order 7936.

1246 conjugacy classes of subgroups.

The subgroup lattice has 368 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×#1549	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	8	no	—
34	C₂³×C₄×C₃₁	—	2	2	no	—
35	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
38	C₂×M₁₆×C₃₁	—	2	4	no	—
39	C₂×M₁₆×C₃₁	—	4	4	no	—
40	C₂²×C₈×C₃₁	—	2	2	no	—
41	C₂²×C₈×C₃₁	—	2	2	no	—
42	C₃₁×C₄⋊Q₈	—	2	4	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	2	no	—
47	C₃₁×C₄⋊Q₈	—	2	2	no	—
48	C₃₁×C₄⋊Q₈	—	2	4	no	—
49	C₃₁×C₄⋊Q₈	C₂×C₄	1	4	yes	—
50	C₃₁×C₄⋊Q₈	C₂×C₄	1	8	yes	—
51	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
52	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
53	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
54	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
55	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
56	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
57	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
58	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	8	yes	—
59	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	4	yes	—
60	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
61	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₃₁	D₄	1	2	yes	—
65	C₂×C₄²×C₃₁	D₄	1	2	yes	—
66	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
68	C₃₁×C₄⋊C₈	—	2	4	no	—
69	C₃₁×C₄⋊C₈	—	2	2	no	—
70	C₃₁×C₄⋊C₈	—	2	2	no	—
71	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
72	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
73	C₃₁×C₂²⋊C₈	—	2	4	no	—
74	C₄×C₈×C₃₁	—	2	4	no	—
75	C₂⁴×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
76	C₂×Q₈×C₃₁	—	2	8	no	—
77	C₂×Q₈×C₃₁	—	2	4	no	—
78	C₂×Q₈×C₃₁	—	2	4	no	—
79	C₂×Q₈×C₃₁	—	4	8	no	—
80	C₂×Q₈×C₃₁	—	4	16	no	—
81	C₂×Q₈×C₃₁	—	4	16	no	—
82	C₂×Q₈×C₃₁	—	4	8	no	—
83	C₂²×C₄×C₃₁	—	2	4	no	—
84	C₂²×C₄×C₃₁	—	2	4	no	—
85	C₂²×C₄×C₃₁	—	2	8	no	—
86	C₂²×C₄×C₃₁	—	2	4	no	—
87	C₂²×C₄×C₃₁	—	4	8	no	—
88	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
89	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
90	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
93	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₃₁	SD₁₆	1	4	yes	—
95	C₂²×C₄×C₃₁	Q₁₆	1	4	yes	—
96	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
102	M₁₆×C₃₁	—	4	8	no	—
103	C₂×C₈×C₃₁	—	2	4	no	—
104	C₂×C₈×C₃₁	—	2	4	no	—
105	C₂×C₈×C₃₁	—	4	4	no	—
106	C₂×C₈×C₃₁	—	4	4	no	—
107	C₄⋊C₄×C₃₁	—	2	8	no	—
108	C₄⋊C₄×C₃₁	—	2	4	no	—
109	C₄⋊C₄×C₃₁	—	2	4	no	—
110	C₄⋊C₄×C₃₁	—	2	8	no	—
111	C₄⋊C₄×C₃₁	—	2	4	no	—
112	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
113	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
114	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
115	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
116	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
117	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₃₁	C₂×D₄	1	2	yes	—
119	C₄²×C₃₁	C₂×D₄	1	2	yes	—
120	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
123	C₂×#1549	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂³×C₃₁	—	2	2	no	—
125	C₂³×C₃₁	—	2	2	no	—
126	C₂³×C₃₁	#103	1	4	yes	—
127	C₂³×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
128	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
129	Q₈×C₃₁	—	4	16	no	—
130	Q₈×C₃₁	—	4	8	no	—
131	Q₈×C₃₁	—	4	8	no	—
132	C₂×C₄×C₃₁	—	2	2	no	—
133	C₂×C₄×C₃₁	—	2	2	no	—
134	C₂×C₄×C₃₁	—	2	4	no	—
135	C₂×C₄×C₃₁	—	2	4	no	—
136	C₂×C₄×C₃₁	—	2	4	no	—
137	C₂×C₄×C₃₁	—	2	4	no	—
138	C₂×C₄×C₃₁	—	2	8	no	—
139	C₂×C₄×C₃₁	—	4	16	no	—
140	C₂×C₄×C₃₁	—	4	8	no	—
141	C₂×C₄×C₃₁	#101	1	4	yes	—
142	C₂×C₄×C₃₁	#103	1	8	yes	—
143	C₂×C₄×C₃₁	#103	1	4	yes	—
144	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
145	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
147	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
148	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₃₁	C₂×SD₁₆	1	2	yes	—
151	C₂×C₄×C₃₁	C₂×SD₁₆	1	4	yes	—
152	C₂×C₄×C₃₁	C₂×Q₁₆	1	4	yes	—
153	C₂×C₄×C₃₁	C₂×Q₁₆	1	2	yes	—
154	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	4	yes	—
155	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
158	C₈×C₃₁	—	4	4	no	—
159	C₈×C₃₁	—	4	4	no	—
160	C₂²×C₄⋊Q₈	C₂×C₃₁	1	1	yes	characteristic
161	C₂×#431	C₂×C₃₁	1	1	yes	characteristic
162	C₂×#423	C₂×C₃₁	1	1	yes	characteristic
163	#1549	C₂×C₃₁	1	8	yes	direct product factor
164	C₂×#332	C₂×C₃₁	1	4	yes	complemented
165	C₂²×C₃₁	—	2	8	no	—
166	C₂²×C₃₁	—	2	2	no	—
167	C₂²×C₃₁	—	2	2	no	—
168	C₂²×C₃₁	C₂×#101	1	2	yes	—
169	C₂²×C₃₁	C₂×#103	1	4	yes	—
170	C₂²×C₃₁	C₂×#103	1	2	yes	—
171	C₂²×C₃₁	#418	1	2	yes	—
172	C₂²×C₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
173	C₄×C₃₁	—	2	1	no	—
174	C₄×C₃₁	—	2	1	no	—
175	C₄×C₃₁	—	2	2	no	—
176	C₄×C₃₁	—	4	8	no	—
177	C₄×C₃₁	C₂×#101	1	4	yes	—
178	C₄×C₃₁	C₂×#103	1	2	yes	—
179	C₄×C₃₁	C₂×#103	1	4	yes	—
180	C₄×C₃₁	#418	1	2	yes	—
181	C₄×C₃₁	C₂²×SD₁₆	1	1	yes	characteristic
182	C₄×C₃₁	C₂²×Q₁₆	1	1	yes	characteristic
183	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
184	C₂³×Q₈	—	2	1	no	—
185	C₂²×M₁₆	—	2	1	no	—
186	C₂×C₄⋊Q₈	—	2	1	no	—
187	C₂×C₄⋊Q₈	—	2	1	no	—
188	C₂×C₄⋊Q₈	—	2	2	no	—
189	C₂×C₄⋊Q₈	—	2	2	no	—
190	C₂×C₄⋊Q₈	C₄×C₃₁	1	2	yes	—
191	C₂×C₄⋊Q₈	C₄×C₃₁	1	4	yes	—
192	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
193	C₂×C₄⋊Q₈	C₂²×C₃₁	1	4	yes	—
194	C₂²×C₄⋊C₄	—	2	1	no	—
195	C₂²×C₄⋊C₄	C₄×C₃₁	1	2	yes	—
196	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
197	#431	—	2	2	no	—
198	#431	C₂²×C₃₁	1	4	yes	—
199	#423	—	2	2	no	—
200	#423	C₂²×C₃₁	1	4	yes	—
201	C₂×C₄⋊C₈	—	2	1	no	—
202	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
203	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
204	C₂×C₂²⋊C₈	—	2	1	no	—
205	C₂×C₄×C₈	—	2	1	no	—
206	#332	C₂²×C₃₁	1	16	yes	complemented
207	C₂×C₃₁	—	2	4	no	—
208	C₂×C₃₁	#1549	1	4	yes	direct product factor
209	C₂×C₃₁	C₂²×#101	1	1	yes	characteristic
210	C₂×C₃₁	C₂²×#103	1	1	yes	characteristic
211	C₂×C₃₁	C₂×#418	1	1	yes	characteristic
212	C₂²×Q₈	—	2	4	no	—
213	C₂²×Q₈	—	2	2	no	—
214	C₂²×Q₈	—	2	4	no	—
215	C₂²×Q₈	—	2	2	no	—
216	C₂²×Q₈	—	4	8	no	—
217	C₂³×C₄	—	2	2	no	—
218	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
219	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
220	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
221	C₂×M₁₆	—	2	4	no	—
222	C₂×M₁₆	—	4	4	no	—
223	C₂²×C₈	—	2	2	no	—
224	C₂²×C₈	—	2	2	no	—
225	C₄⋊Q₈	—	2	4	no	—
226	C₄⋊Q₈	—	2	4	no	—
227	C₄⋊Q₈	—	2	4	no	—
228	C₄⋊Q₈	—	2	4	no	—
229	C₄⋊Q₈	—	2	2	no	—
230	C₄⋊Q₈	—	2	2	no	—
231	C₄⋊Q₈	—	2	4	no	—
232	C₄⋊Q₈	C₂×C₄×C₃₁	1	4	yes	—
233	C₄⋊Q₈	C₂×C₄×C₃₁	1	8	yes	—
234	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
235	C₂×C₄⋊C₄	—	2	4	no	—
236	C₂×C₄⋊C₄	—	2	2	no	—
237	C₂×C₄⋊C₄	—	2	4	no	—
238	C₂×C₄⋊C₄	—	2	2	no	—
239	C₂×C₄⋊C₄	—	2	2	no	—
240	C₂×C₄⋊C₄	—	2	4	no	—
241	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
242	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	8	yes	—
243	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
244	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
245	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
246	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
247	C₂×C₄²	D₄×C₃₁	1	2	yes	—
248	C₂×C₄²	D₄×C₃₁	1	2	yes	—
249	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
250	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
251	C₄⋊C₈	—	2	4	no	—
252	C₄⋊C₈	—	2	2	no	—
253	C₄⋊C₈	—	2	2	no	—
254	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
255	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
256	C₂²⋊C₈	—	2	4	no	—
257	C₄×C₈	—	2	4	no	—
258	C₃₁	C₂×#1549	1	1	yes	characteristic, direct product factor, Sylow
259	C₂⁴	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
260	C₂×Q₈	—	2	8	no	—
261	C₂×Q₈	—	2	4	no	—
262	C₂×Q₈	—	2	4	no	—
263	C₂×Q₈	—	4	8	no	—
264	C₂×Q₈	—	4	16	no	—
265	C₂×Q₈	—	4	16	no	—
266	C₂×Q₈	—	4	8	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	8	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	4	8	no	—
272	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
273	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
274	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
275	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
276	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
277	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
278	C₂²×C₄	SD₁₆×C₃₁	1	4	yes	—
279	C₂²×C₄	Q₁₆×C₃₁	1	4	yes	—
280	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
281	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
282	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
283	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
285	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
286	M₁₆	—	4	8	no	—
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	4	4	no	—
290	C₂×C₈	—	4	4	no	—
291	C₄⋊C₄	—	2	8	no	—
292	C₄⋊C₄	—	2	4	no	—
293	C₄⋊C₄	—	2	4	no	—
294	C₄⋊C₄	—	2	8	no	—
295	C₄⋊C₄	—	2	4	no	—
296	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
297	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
298	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
299	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
300	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
301	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
302	C₄²	C₂×D₄×C₃₁	1	2	yes	—
303	C₄²	C₂×D₄×C₃₁	1	2	yes	—
304	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
305	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
306	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
307	C₂³	—	2	2	no	—
308	C₂³	—	2	2	no	—
309	C₂³	C₃₁×#103	1	4	yes	—
310	C₂³	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
311	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
312	Q₈	—	4	16	no	—
313	Q₈	—	4	8	no	—
314	Q₈	—	4	8	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	8	no	—
322	C₂×C₄	—	4	16	no	—
323	C₂×C₄	—	4	8	no	—
324	C₂×C₄	C₃₁×#101	1	4	yes	—
325	C₂×C₄	C₃₁×#103	1	8	yes	—
326	C₂×C₄	C₃₁×#103	1	4	yes	—
327	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
328	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
329	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
330	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
331	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
332	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
333	C₂×C₄	C₂×SD₁₆×C₃₁	1	2	yes	—
334	C₂×C₄	C₂×SD₁₆×C₃₁	1	4	yes	—
335	C₂×C₄	C₂×Q₁₆×C₃₁	1	4	yes	—
336	C₂×C₄	C₂×Q₁₆×C₃₁	1	2	yes	—
337	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	4	yes	—
338	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
339	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
340	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
341	C₈	—	4	4	no	—
342	C₈	—	4	4	no	—
343	C₂²	—	2	8	no	—
344	C₂²	—	2	2	no	—
345	C₂²	—	2	2	no	—
346	C₂²	C₂×C₃₁×#101	1	2	yes	—
347	C₂²	C₂×C₃₁×#103	1	4	yes	—
348	C₂²	C₂×C₃₁×#103	1	2	yes	—
349	C₂²	C₃₁×#418	1	2	yes	—
350	C₂²	C₂²×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	2	no	—
354	C₄	—	4	8	no	—
355	C₄	C₂×C₃₁×#101	1	4	yes	—
356	C₄	C₂×C₃₁×#103	1	2	yes	—
357	C₄	C₂×C₃₁×#103	1	4	yes	—
358	C₄	C₃₁×#418	1	2	yes	—
359	C₄	C₂²×SD₁₆×C₃₁	1	1	yes	characteristic
360	C₄	C₂²×Q₁₆×C₃₁	1	1	yes	characteristic
361	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
362	C₂	—	2	4	no	—
363	C₂	C₃₁×#1549	1	4	yes	direct product factor
364	C₂	C₂²×C₃₁×#101	1	1	yes	characteristic
365	C₂	C₂²×C₃₁×#103	1	1	yes	characteristic
366	C₂	C₂×C₃₁×#418	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×#1549	C₂	direct (N × H)
5. C₂×C₃₁×#332	C₂	semidirect
28. C₃₁×#332	C₂²	semidirect
123. C₂×#1549	C₃₁	direct (N × H)
163. #1549	C₂×C₃₁	direct (N × H)
164. C₂×#332	C₂×C₃₁	semidirect
206. #332	C₂²×C₃₁	semidirect
208. C₂×C₃₁	#1549	direct (N × H)
258. C₃₁	C₂×#1549	direct (N × H)
363. C₂	C₃₁×#1549	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×#1549	2
C₂×C₃₁×#332	2
C₂×#1549	31

Subgroups — C2×C31×#1549 #21474465

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#1549 #21474465