Subgroups — C₂×C₃₁×#1997 #21478094

Order 7936.

1342 conjugacy classes of subgroups.

The subgroup lattice has 392 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×#423	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×M₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1997	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃₁×#343	C₂	1	4	yes	maximal
6	C₂³×Q₈×C₃₁	C₄	1	2	yes	—
7	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
8	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
9	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
10	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
11	C₂×C₃₁×C₄⋊Q₈	—	2	2	no	—
12	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
13	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
14	C₂×C₃₁×C₄⋊Q₈	—	2	2	no	—
15	C₂×C₃₁×C₄⋊Q₈	C₄	1	4	yes	—
16	C₂×C₃₁×C₄⋊Q₈	C₂²	1	4	yes	—
17	C₂²×C₄⋊C₄×C₃₁	C₄	1	2	yes	—
18	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
19	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
20	C₃₁×#423	—	2	2	no	—
21	C₃₁×#423	C₂²	1	4	yes	—
22	C₂×C₃₁×C₄⋊C₈	—	2	1	no	—
23	C₂×C₃₁×C₄⋊C₈	—	2	1	no	—
24	C₄×M₁₆×C₃₁	—	2	2	no	—
25	C₄×M₁₆×C₃₁	C₂²	1	4	yes	—
26	C₂×C₃₁×#97	—	2	1	no	—
27	C₂×C₄×C₈×C₃₁	—	2	1	no	—
28	C₃₁×#343	C₂²	1	16	yes	—
29	C₂²×Q₈×C₃₁	—	2	4	no	—
30	C₂²×Q₈×C₃₁	—	2	2	no	—
31	C₂²×Q₈×C₃₁	—	2	2	no	—
32	C₂²×Q₈×C₃₁	—	4	8	no	—
33	C₂²×Q₈×C₃₁	C₂×C₄	1	8	yes	—
34	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₃₁	C₂×C₄	1	4	yes	—
37	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
38	C₂×M₁₆×C₃₁	—	2	2	no	—
39	C₂×M₁₆×C₃₁	—	2	4	no	—
40	C₂×M₁₆×C₃₁	—	2	2	no	—
41	C₂×M₁₆×C₃₁	—	2	8	no	—
42	C₂×M₁₆×C₃₁	Q₈	1	8	yes	complemented
43	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
44	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
45	C₂²×C₈×C₃₁	—	2	2	no	—
46	C₂²×C₈×C₃₁	—	2	2	no	—
47	C₃₁×C₄⋊Q₈	—	2	4	no	—
48	C₃₁×C₄⋊Q₈	—	2	4	no	—
49	C₃₁×C₄⋊Q₈	—	2	4	no	—
50	C₃₁×C₄⋊Q₈	—	2	4	no	—
51	C₃₁×C₄⋊Q₈	—	2	4	no	—
52	C₃₁×C₄⋊Q₈	—	2	4	no	—
53	C₃₁×C₄⋊Q₈	—	2	4	no	—
54	C₃₁×C₄⋊Q₈	—	2	4	no	—
55	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
56	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
58	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	8	yes	—
63	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	4	yes	—
64	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
65	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₃₁	D₄	1	2	yes	—
69	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₃₁	D₄	1	2	yes	—
72	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
73	C₃₁×C₄⋊C₈	—	2	4	no	—
74	C₃₁×C₄⋊C₈	—	2	4	no	—
75	C₃₁×#97	—	2	4	no	—
76	C₄×C₈×C₃₁	—	2	4	no	—
77	C₂⁴×C₃₁	C₂²×C₄	1	1	yes	characteristic
78	C₂×Q₈×C₃₁	—	2	8	no	—
79	C₂×Q₈×C₃₁	—	2	8	no	—
80	C₂×Q₈×C₃₁	—	4	8	no	—
81	C₂×Q₈×C₃₁	—	4	16	no	—
82	C₂×Q₈×C₃₁	—	4	16	no	—
83	C₂×Q₈×C₃₁	—	4	8	no	—
84	C₂²×C₄×C₃₁	—	2	4	no	—
85	C₂²×C₄×C₃₁	—	2	4	no	—
86	C₂²×C₄×C₃₁	—	2	4	no	—
87	C₂²×C₄×C₃₁	—	2	4	no	—
88	C₂²×C₄×C₃₁	—	4	8	no	—
89	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
90	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
91	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
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	2	yes	—
97	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
98	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₃₁	C₂×Q₈	1	4	yes	—
104	C₂²×C₄×C₃₁	#41	1	4	yes	—
105	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
106	M₁₆×C₃₁	—	2	8	no	—
107	M₁₆×C₃₁	—	2	4	no	—
108	M₁₆×C₃₁	—	2	8	no	—
109	M₁₆×C₃₁	—	4	4	no	—
110	M₁₆×C₃₁	C₂×Q₈	1	8	yes	complemented
111	C₂×C₈×C₃₁	—	2	8	no	—
112	C₂×C₈×C₃₁	—	2	4	no	—
113	C₂×C₈×C₃₁	—	2	4	no	—
114	C₂×C₈×C₃₁	—	4	4	no	—
115	C₄⋊C₄×C₃₁	—	2	8	no	—
116	C₄⋊C₄×C₃₁	—	2	4	no	—
117	C₄⋊C₄×C₃₁	—	2	4	no	—
118	C₄⋊C₄×C₃₁	—	2	8	no	—
119	C₄⋊C₄×C₃₁	—	2	4	no	—
120	C₄⋊C₄×C₃₁	—	2	4	no	—
121	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
122	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
123	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
124	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
125	C₄²×C₃₁	C₂×D₄	1	2	yes	—
126	C₄²×C₃₁	C₂×D₄	1	2	yes	—
127	C₄²×C₃₁	C₂×D₄	1	2	yes	—
128	C₄²×C₃₁	C₂×D₄	1	2	yes	—
129	C₂×#1997	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂³×C₃₁	—	2	2	no	—
131	C₂³×C₃₁	—	2	2	no	—
132	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₂³×C₃₁	C₄×Q₈	1	4	yes	—
135	C₂³×C₃₁	C₂³×C₄	1	1	yes	characteristic
136	Q₈×C₃₁	—	4	16	no	—
137	Q₈×C₃₁	—	4	16	no	—
138	C₂×C₄×C₃₁	—	2	2	no	—
139	C₂×C₄×C₃₁	—	2	2	no	—
140	C₂×C₄×C₃₁	—	2	4	no	—
141	C₂×C₄×C₃₁	—	2	4	no	—
142	C₂×C₄×C₃₁	—	2	4	no	—
143	C₂×C₄×C₃₁	—	2	4	no	—
144	C₂×C₄×C₃₁	—	2	8	no	—
145	C₂×C₄×C₃₁	—	4	8	no	—
146	C₂×C₄×C₃₁	—	4	8	no	—
147	C₂×C₄×C₃₁	—	4	8	no	—
148	C₂×C₄×C₃₁	#100	1	4	yes	—
149	C₂×C₄×C₃₁	#101	1	4	yes	—
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×C₂²⋊C₄	1	2	yes	—
155	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
156	C₂×C₄×C₃₁	C₄×Q₈	1	4	yes	—
157	C₂×C₄×C₃₁	C₂²⋊Q₈	1	4	yes	—
158	C₂×C₄×C₃₁	C₂²⋊Q₈	1	4	yes	—
159	C₂×C₄×C₃₁	#124	1	2	yes	—
160	C₂×C₄×C₃₁	#124	1	2	yes	—
161	C₂×C₄×C₃₁	C₄⋊Q₈	1	2	yes	—
162	C₂×C₄×C₃₁	C₄⋊Q₈	1	2	yes	—
163	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₃₁	C₂²×Q₈	1	2	yes	—
166	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
167	C₈×C₃₁	—	2	8	no	—
168	C₈×C₃₁	—	4	4	no	—
169	C₂²×C₄⋊Q₈	C₂×C₃₁	1	1	yes	characteristic
170	C₂×#423	C₂×C₃₁	1	1	yes	characteristic
171	C₂×C₄×M₁₆	C₂×C₃₁	1	1	yes	characteristic
172	#1997	C₂×C₃₁	1	8	yes	direct product factor
173	C₂×#343	C₂×C₃₁	1	4	yes	—
174	C₂²×C₃₁	—	2	1	no	—
175	C₂²×C₃₁	—	2	1	no	—
176	C₂²×C₃₁	—	2	1	no	—
177	C₂²×C₃₁	—	2	1	no	—
178	C₂²×C₃₁	—	2	8	no	—
179	C₂²×C₃₁	#391	1	2	yes	—
180	C₂²×C₃₁	#391	1	2	yes	—
181	C₂²×C₃₁	C₂×#100	1	2	yes	—
182	C₂²×C₃₁	C₂×#101	1	2	yes	—
183	C₂²×C₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
184	C₂²×C₃₁	C₂×C₄×Q₈	1	2	yes	—
185	C₄×C₃₁	—	2	2	no	—
186	C₄×C₃₁	—	2	2	no	—
187	C₄×C₃₁	—	4	8	no	—
188	C₄×C₃₁	#391	1	2	yes	—
189	C₄×C₃₁	#391	1	2	yes	—
190	C₄×C₃₁	C₂×#100	1	4	yes	—
191	C₄×C₃₁	C₂×#101	1	4	yes	—
192	C₄×C₃₁	C₂×C₂²⋊Q₈	1	2	yes	—
193	C₄×C₃₁	C₂×#124	1	1	yes	characteristic
194	C₄×C₃₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
195	C₂³×Q₈	C₄×C₃₁	1	2	yes	—
196	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
197	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
198	C₂×C₄⋊Q₈	—	2	1	no	—
199	C₂×C₄⋊Q₈	—	2	1	no	—
200	C₂×C₄⋊Q₈	—	2	2	no	—
201	C₂×C₄⋊Q₈	—	2	1	no	—
202	C₂×C₄⋊Q₈	—	2	1	no	—
203	C₂×C₄⋊Q₈	—	2	2	no	—
204	C₂×C₄⋊Q₈	C₄×C₃₁	1	4	yes	—
205	C₂×C₄⋊Q₈	C₂²×C₃₁	1	4	yes	—
206	C₂²×C₄⋊C₄	C₄×C₃₁	1	2	yes	—
207	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
208	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
209	#423	—	2	2	no	—
210	#423	C₂²×C₃₁	1	4	yes	—
211	C₂×C₄⋊C₈	—	2	1	no	—
212	C₂×C₄⋊C₈	—	2	1	no	—
213	C₄×M₁₆	—	2	2	no	—
214	C₄×M₁₆	C₂²×C₃₁	1	4	yes	—
215	C₂×#97	—	2	1	no	—
216	C₂×C₄×C₈	—	2	1	no	—
217	#343	C₂²×C₃₁	1	16	yes	—
218	C₂×C₃₁	—	2	2	no	—
219	C₂×C₃₁	—	2	2	no	—
220	C₂×C₃₁	#1997	1	4	yes	direct product factor
221	C₂×C₃₁	C₂×#391	1	1	yes	characteristic
222	C₂×C₃₁	C₂²×#100	1	1	yes	characteristic
223	C₂×C₃₁	C₂²×#101	1	1	yes	characteristic
224	C₂²×Q₈	—	2	4	no	—
225	C₂²×Q₈	—	2	2	no	—
226	C₂²×Q₈	—	2	2	no	—
227	C₂²×Q₈	—	4	8	no	—
228	C₂²×Q₈	C₂×C₄×C₃₁	1	8	yes	—
229	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
230	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
231	C₂³×C₄	C₂×C₄×C₃₁	1	4	yes	—
232	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
233	C₂×M₁₆	—	2	2	no	—
234	C₂×M₁₆	—	2	4	no	—
235	C₂×M₁₆	—	2	2	no	—
236	C₂×M₁₆	—	2	8	no	—
237	C₂×M₁₆	Q₈×C₃₁	1	8	yes	complemented
238	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
239	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
240	C₂²×C₈	—	2	2	no	—
241	C₂²×C₈	—	2	2	no	—
242	C₄⋊Q₈	—	2	4	no	—
243	C₄⋊Q₈	—	2	4	no	—
244	C₄⋊Q₈	—	2	4	no	—
245	C₄⋊Q₈	—	2	4	no	—
246	C₄⋊Q₈	—	2	4	no	—
247	C₄⋊Q₈	—	2	4	no	—
248	C₄⋊Q₈	—	2	4	no	—
249	C₄⋊Q₈	—	2	4	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	4	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	8	yes	—
258	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
259	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
260	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
261	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
262	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
263	C₂×C₄²	D₄×C₃₁	1	2	yes	—
264	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
265	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
266	C₂×C₄²	D₄×C₃₁	1	2	yes	—
267	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
268	C₄⋊C₈	—	2	4	no	—
269	C₄⋊C₈	—	2	4	no	—
270	#97	—	2	4	no	—
271	C₄×C₈	—	2	4	no	—
272	C₃₁	C₂×#1997	1	1	yes	characteristic, direct product factor, Sylow
273	C₂⁴	C₂²×C₄×C₃₁	1	1	yes	characteristic
274	C₂×Q₈	—	2	8	no	—
275	C₂×Q₈	—	2	8	no	—
276	C₂×Q₈	—	4	16	no	—
277	C₂×Q₈	—	4	8	no	—
278	C₂×Q₈	—	4	16	no	—
279	C₂×Q₈	—	4	8	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	4	8	no	—
285	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
286	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
287	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
288	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
289	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
290	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
291	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
292	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
293	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
294	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
299	C₂²×C₄	C₂×Q₈×C₃₁	1	4	yes	—
300	C₂²×C₄	#41×C₃₁	1	4	yes	—
301	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
302	M₁₆	—	2	8	no	—
303	M₁₆	—	2	4	no	—
304	M₁₆	—	2	8	no	—
305	M₁₆	—	4	4	no	—
306	M₁₆	C₂×Q₈×C₃₁	1	8	yes	complemented
307	C₂×C₈	—	2	8	no	—
308	C₂×C₈	—	2	4	no	—
309	C₂×C₈	—	2	4	no	—
310	C₂×C₈	—	4	4	no	—
311	C₄⋊C₄	—	2	8	no	—
312	C₄⋊C₄	—	2	8	no	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
318	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
319	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
320	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
321	C₄²	C₂×D₄×C₃₁	1	2	yes	—
322	C₄²	C₂×D₄×C₃₁	1	2	yes	—
323	C₄²	C₂×D₄×C₃₁	1	2	yes	—
324	C₄²	C₂×D₄×C₃₁	1	2	yes	—
325	C₂³	—	2	2	no	—
326	C₂³	—	2	2	no	—
327	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
328	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
329	C₂³	C₄×Q₈×C₃₁	1	4	yes	—
330	C₂³	C₂³×C₄×C₃₁	1	1	yes	characteristic
331	Q₈	—	4	16	no	—
332	Q₈	—	4	16	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	8	no	—
340	C₂×C₄	—	4	8	no	—
341	C₂×C₄	—	4	8	no	—
342	C₂×C₄	—	4	8	no	—
343	C₂×C₄	C₃₁×#100	1	4	yes	—
344	C₂×C₄	C₃₁×#101	1	4	yes	—
345	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
346	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
347	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
348	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
349	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
350	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
351	C₂×C₄	C₄×Q₈×C₃₁	1	4	yes	—
352	C₂×C₄	C₃₁×C₂²⋊Q₈	1	4	yes	—
353	C₂×C₄	C₃₁×C₂²⋊Q₈	1	4	yes	—
354	C₂×C₄	C₃₁×#124	1	2	yes	—
355	C₂×C₄	C₃₁×#124	1	2	yes	—
356	C₂×C₄	C₃₁×C₄⋊Q₈	1	2	yes	—
357	C₂×C₄	C₃₁×C₄⋊Q₈	1	2	yes	—
358	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
359	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
360	C₂×C₄	C₂²×Q₈×C₃₁	1	2	yes	—
361	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
362	C₈	—	2	8	no	—
363	C₈	—	4	4	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	8	no	—
369	C₂²	C₃₁×#391	1	2	yes	—
370	C₂²	C₃₁×#391	1	2	yes	—
371	C₂²	C₂×C₃₁×#100	1	2	yes	—
372	C₂²	C₂×C₃₁×#101	1	2	yes	—
373	C₂²	C₂²×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
374	C₂²	C₂×C₄×Q₈×C₃₁	1	2	yes	—
375	C₄	—	2	2	no	—
376	C₄	—	2	2	no	—
377	C₄	—	4	8	no	—
378	C₄	C₃₁×#391	1	2	yes	—
379	C₄	C₃₁×#391	1	2	yes	—
380	C₄	C₂×C₃₁×#100	1	4	yes	—
381	C₄	C₂×C₃₁×#101	1	4	yes	—
382	C₄	C₂×C₃₁×C₂²⋊Q₈	1	2	yes	—
383	C₄	C₂×C₃₁×#124	1	1	yes	characteristic
384	C₄	C₂×C₃₁×C₄⋊Q₈	1	1	yes	characteristic
385	C₂	—	2	2	no	—
386	C₂	—	2	2	no	—
387	C₂	C₃₁×#1997	1	4	yes	direct product factor
388	C₂	C₂×C₃₁×#391	1	1	yes	characteristic
389	C₂	C₂²×C₃₁×#100	1	1	yes	characteristic
390	C₂	C₂²×C₃₁×#101	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₂⁴×C₃₁	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ 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×#1997	C₂	direct (N × H)
42. C₂×M₁₆×C₃₁	Q₈	semidirect
110. M₁₆×C₃₁	C₂×Q₈	semidirect
129. C₂×#1997	C₃₁	direct (N × H)
172. #1997	C₂×C₃₁	direct (N × H)
220. C₂×C₃₁	#1997	direct (N × H)
237. C₂×M₁₆	Q₈×C₃₁	semidirect
272. C₃₁	C₂×#1997	direct (N × H)
306. M₁₆	C₂×Q₈×C₃₁	semidirect
387. C₂	C₃₁×#1997	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×#423	2
C₂×C₄×M₁₆×C₃₁	2
C₃₁×#1997	2
C₂×C₃₁×#343	2
C₂×#1997	31

Subgroups — C2×C31×#1997 #21478094

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#1997 #21478094