Subgroups — C₃₁×#21303 #21478062

Order 7936.

1386 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×Q₈×C₃₁	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×#1985	C₂	1	4	yes	maximal, complemented
5	C₃₁×#1984	C₂	1	4	yes	maximal, complemented
6	C₃₁×#1728	C₂	1	4	yes	maximal
7	C₂³×Q₈×C₃₁	C₄	1	1	yes	characteristic
8	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
9	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
10	C₂×C₄×Q₈×C₃₁	—	2	4	no	—
11	C₂×C₄×Q₈×C₃₁	—	2	4	no	—
12	C₂×C₄×Q₈×C₃₁	C₄	1	2	yes	—
13	C₂×C₄×Q₈×C₃₁	C₄	1	2	yes	—
14	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₃₁	C₄	1	2	yes	—
17	C₂²×C₄⋊C₄×C₃₁	C₄	1	1	yes	characteristic
18	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
19	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
20	C₃₁×#423	—	2	4	no	—
21	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
22	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
23	C₄×M₁₆×C₃₁	—	2	4	no	—
24	C₂×C₃₁×#97	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
26	C₃₁×#336	C₂²	1	16	yes	—
27	C₂²×Q₈×C₃₁	—	2	8	no	—
28	C₂²×Q₈×C₃₁	—	2	4	no	—
29	C₂²×Q₈×C₃₁	C₂×C₄	1	2	yes	—
30	C₂²×Q₈×C₃₁	C₂×C₄	1	2	yes	—
31	C₂³×C₄×C₃₁	C₂×C₄	1	2	yes	—
32	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₃₁	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
36	C₂×M₁₆×C₃₁	—	2	4	no	—
37	C₂×M₁₆×C₃₁	—	2	4	no	—
38	C₂×M₁₆×C₃₁	—	2	4	no	—
39	C₂×M₁₆×C₃₁	—	2	8	no	—
40	C₂×M₁₆×C₃₁	Q₈	1	8	yes	complemented
41	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
42	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
43	C₄×Q₈×C₃₁	—	2	8	no	—
44	C₄×Q₈×C₃₁	—	2	8	no	—
45	C₄×Q₈×C₃₁	—	2	4	no	—
46	C₄×Q₈×C₃₁	—	2	4	no	—
47	C₄×Q₈×C₃₁	—	2	4	no	—
48	C₄×Q₈×C₃₁	—	2	4	no	—
49	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
50	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
51	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
52	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
53	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	4	yes	—
54	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	4	yes	—
55	C₂×C₄²×C₃₁	—	2	4	no	—
56	C₂×C₄²×C₃₁	—	2	4	no	—
57	C₂×C₄²×C₃₁	C₂×C₄	1	4	yes	—
58	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₃₁	D₄	1	4	yes	—
61	C₂×C₄²×C₃₁	D₄	1	4	yes	—
62	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
63	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
65	C₃₁×C₄⋊C₈	—	2	4	no	—
66	C₃₁×C₄⋊C₈	—	2	4	no	—
67	C₃₁×#97	—	2	4	no	—
68	C₄×C₈×C₃₁	—	2	4	no	—
69	C₂⁴×C₃₁	C₂²×C₄	1	1	yes	characteristic
70	C₂×Q₈×C₃₁	—	2	32	no	—
71	C₂×Q₈×C₃₁	—	2	4	no	—
72	C₂×Q₈×C₃₁	—	2	4	no	—
73	C₂×Q₈×C₃₁	—	2	8	no	—
74	C₂×Q₈×C₃₁	—	2	4	no	—
75	C₂×Q₈×C₃₁	M₁₆	1	8	yes	complemented
76	C₂²×C₄×C₃₁	—	2	4	no	—
77	C₂²×C₄×C₃₁	—	2	8	no	—
78	C₂²×C₄×C₃₁	—	2	4	no	—
79	C₂²×C₄×C₃₁	—	2	4	no	—
80	C₂²×C₄×C₃₁	—	4	2	no	—
81	C₂²×C₄×C₃₁	—	4	4	no	—
82	C₂²×C₄×C₃₁	C₂²⋊C₄	1	4	yes	—
83	C₂²×C₄×C₃₁	C₂²⋊C₄	1	4	yes	—
84	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
85	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
89	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₃₁	C₂×Q₈	1	4	yes	—
94	C₂²×C₄×C₃₁	#41	1	4	yes	—
95	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
96	M₁₆×C₃₁	—	2	16	no	—
97	M₁₆×C₃₁	—	4	8	no	—
98	C₂×C₈×C₃₁	—	2	4	no	—
99	C₂×C₈×C₃₁	—	2	4	no	—
100	C₂×C₈×C₃₁	—	2	4	no	—
101	C₂×C₈×C₃₁	—	2	8	no	—
102	C₂×C₈×C₃₁	C₂×Q₈	1	8	yes	complemented
103	C₄⋊C₄×C₃₁	—	2	8	no	—
104	C₄⋊C₄×C₃₁	—	2	8	no	—
105	C₄⋊C₄×C₃₁	—	2	4	no	—
106	C₄⋊C₄×C₃₁	—	2	4	no	—
107	C₄²×C₃₁	—	2	8	no	—
108	C₄²×C₃₁	—	2	4	no	—
109	C₄²×C₃₁	—	2	4	no	—
110	C₄²×C₃₁	C₂²⋊C₄	1	4	yes	—
111	C₄²×C₃₁	C₂²⋊C₄	1	4	yes	—
112	C₄²×C₃₁	C₂×D₄	1	2	yes	—
113	C₄²×C₃₁	C₂×D₄	1	2	yes	—
114	C₄²×C₃₁	C₂×D₄	1	2	yes	—
115	C₄²×C₃₁	C₂×D₄	1	2	yes	—
116	#21303	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
117	C₂³×C₃₁	—	2	2	no	—
118	C₂³×C₃₁	—	2	2	no	—
119	C₂³×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
120	C₂³×C₃₁	C₄×Q₈	1	4	yes	—
121	C₂³×C₃₁	C₂³×C₄	1	1	yes	characteristic
122	Q₈×C₃₁	—	2	16	no	—
123	Q₈×C₃₁	—	2	16	no	—
124	C₂×C₄×C₃₁	—	2	16	no	—
125	C₂×C₄×C₃₁	—	2	4	no	—
126	C₂×C₄×C₃₁	—	2	2	no	—
127	C₂×C₄×C₃₁	—	2	4	no	—
128	C₂×C₄×C₃₁	—	2	2	no	—
129	C₂×C₄×C₃₁	—	2	2	no	—
130	C₂×C₄×C₃₁	—	2	8	no	—
131	C₂×C₄×C₃₁	—	2	4	no	—
132	C₂×C₄×C₃₁	—	2	8	no	—
133	C₂×C₄×C₃₁	—	4	4	no	—
134	C₂×C₄×C₃₁	—	4	8	no	—
135	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
136	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
137	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
138	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
139	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
140	C₂×C₄×C₃₁	C₄×Q₈	1	4	yes	—
141	C₂×C₄×C₃₁	C₂²⋊Q₈	1	8	yes	—
142	C₂×C₄×C₃₁	#124	1	4	yes	—
143	C₂×C₄×C₃₁	C₄⋊Q₈	1	4	yes	—
144	C₂×C₄×C₃₁	C₂×M₁₆	1	8	yes	—
145	C₂×C₄×C₃₁	C₂×M₁₆	1	4	yes	—
146	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₃₁	C₂²×Q₈	1	2	yes	—
149	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
150	C₈×C₃₁	—	2	8	no	—
151	C₈×C₃₁	—	4	4	no	—
152	C₂²×C₄×Q₈	C₂×C₃₁	1	1	yes	characteristic
153	C₂×#423	C₂×C₃₁	1	1	yes	characteristic
154	C₂×C₄×M₁₆	C₂×C₃₁	1	1	yes	characteristic
155	#1985	C₂×C₃₁	1	4	yes	complemented
156	#1984	C₂×C₃₁	1	4	yes	complemented
157	#1728	C₂×C₃₁	1	4	yes	—
158	C₂²×C₃₁	—	2	2	no	—
159	C₂²×C₃₁	—	2	2	no	—
160	C₂²×C₃₁	—	2	8	no	—
161	C₂²×C₃₁	#391	1	4	yes	—
162	C₂²×C₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
163	C₂²×C₃₁	C₂×C₄×Q₈	1	2	yes	—
164	C₂²×C₃₁	C₂²×M₁₆	1	2	yes	—
165	C₂²×C₃₁	#568	1	2	yes	—
166	C₄×C₃₁	—	2	2	no	—
167	C₄×C₃₁	—	2	8	no	—
168	C₄×C₃₁	—	2	2	no	—
169	C₄×C₃₁	—	2	2	no	—
170	C₄×C₃₁	—	4	4	no	—
171	C₄×C₃₁	#391	1	4	yes	—
172	C₄×C₃₁	#407	1	4	yes	—
173	C₄×C₃₁	C₂×C₂²⋊Q₈	1	2	yes	—
174	C₄×C₃₁	C₂×#124	1	1	yes	characteristic
175	C₄×C₃₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
176	C₂³×Q₈	C₄×C₃₁	1	1	yes	characteristic
177	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
178	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
179	C₂×C₄×Q₈	—	2	4	no	—
180	C₂×C₄×Q₈	—	2	4	no	—
181	C₂×C₄×Q₈	C₄×C₃₁	1	2	yes	—
182	C₂×C₄×Q₈	C₄×C₃₁	1	2	yes	—
183	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
184	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
185	C₂²×C₄⋊C₄	C₄×C₃₁	1	2	yes	—
186	C₂²×C₄⋊C₄	C₄×C₃₁	1	1	yes	characteristic
187	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
188	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
189	#423	—	2	4	no	—
190	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
191	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
192	C₄×M₁₆	—	2	4	no	—
193	C₂×#97	C₂²×C₃₁	1	2	yes	—
194	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
195	#336	C₂²×C₃₁	1	16	yes	—
196	C₂×C₃₁	—	2	4	no	—
197	C₂×C₃₁	C₂×#391	1	1	yes	characteristic
198	C₂×C₃₁	C₂×#407	1	1	yes	characteristic
199	C₂×C₃₁	#2879	1	1	yes	characteristic
200	C₂×C₃₁	Q₈×M₁₆	1	4	yes	—
201	C₂²×Q₈	—	2	8	no	—
202	C₂²×Q₈	—	2	4	no	—
203	C₂²×Q₈	C₂×C₄×C₃₁	1	2	yes	—
204	C₂²×Q₈	C₂×C₄×C₃₁	1	2	yes	—
205	C₂³×C₄	C₂×C₄×C₃₁	1	2	yes	—
206	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
207	C₂³×C₄	C₂×C₄×C₃₁	1	2	yes	—
208	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
209	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
210	C₂×M₁₆	—	2	4	no	—
211	C₂×M₁₆	—	2	4	no	—
212	C₂×M₁₆	—	2	4	no	—
213	C₂×M₁₆	—	2	8	no	—
214	C₂×M₁₆	Q₈×C₃₁	1	8	yes	complemented
215	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
216	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
217	C₄×Q₈	—	2	8	no	—
218	C₄×Q₈	—	2	8	no	—
219	C₄×Q₈	—	2	4	no	—
220	C₄×Q₈	—	2	4	no	—
221	C₄×Q₈	—	2	4	no	—
222	C₄×Q₈	—	2	4	no	—
223	C₂×C₄⋊C₄	—	2	8	no	—
224	C₂×C₄⋊C₄	—	2	4	no	—
225	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
226	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
227	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
228	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
229	C₂×C₄²	—	2	4	no	—
230	C₂×C₄²	—	2	4	no	—
231	C₂×C₄²	C₂×C₄×C₃₁	1	4	yes	—
232	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
233	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
234	C₂×C₄²	D₄×C₃₁	1	4	yes	—
235	C₂×C₄²	D₄×C₃₁	1	4	yes	—
236	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
237	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
238	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
239	C₄⋊C₈	—	2	4	no	—
240	C₄⋊C₈	—	2	4	no	—
241	#97	—	2	4	no	—
242	C₄×C₈	—	2	4	no	—
243	C₃₁	#21303	1	1	yes	characteristic, direct product factor, Sylow
244	C₂⁴	C₂²×C₄×C₃₁	1	1	yes	characteristic
245	C₂×Q₈	—	2	32	no	—
246	C₂×Q₈	—	2	4	no	—
247	C₂×Q₈	—	2	4	no	—
248	C₂×Q₈	—	2	8	no	—
249	C₂×Q₈	—	2	4	no	—
250	C₂×Q₈	M₁₆×C₃₁	1	8	yes	complemented
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	2	8	no	—
253	C₂²×C₄	—	2	4	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	4	2	no	—
256	C₂²×C₄	—	4	4	no	—
257	C₂²×C₄	C₂²⋊C₄×C₃₁	1	4	yes	—
258	C₂²×C₄	C₂²⋊C₄×C₃₁	1	4	yes	—
259	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
260	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
261	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
262	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
263	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
264	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
265	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
266	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
267	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
268	C₂²×C₄	C₂×Q₈×C₃₁	1	4	yes	—
269	C₂²×C₄	#41×C₃₁	1	4	yes	—
270	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
271	M₁₆	—	2	16	no	—
272	M₁₆	—	4	8	no	—
273	C₂×C₈	—	2	4	no	—
274	C₂×C₈	—	2	4	no	—
275	C₂×C₈	—	2	4	no	—
276	C₂×C₈	—	2	8	no	—
277	C₂×C₈	C₂×Q₈×C₃₁	1	8	yes	complemented
278	C₄⋊C₄	—	2	8	no	—
279	C₄⋊C₄	—	2	8	no	—
280	C₄⋊C₄	—	2	4	no	—
281	C₄⋊C₄	—	2	4	no	—
282	C₄²	—	2	8	no	—
283	C₄²	—	2	4	no	—
284	C₄²	—	2	4	no	—
285	C₄²	C₂²⋊C₄×C₃₁	1	4	yes	—
286	C₄²	C₂²⋊C₄×C₃₁	1	4	yes	—
287	C₄²	C₂×D₄×C₃₁	1	2	yes	—
288	C₄²	C₂×D₄×C₃₁	1	2	yes	—
289	C₄²	C₂×D₄×C₃₁	1	2	yes	—
290	C₄²	C₂×D₄×C₃₁	1	2	yes	—
291	C₂³	—	2	2	no	—
292	C₂³	—	2	2	no	—
293	C₂³	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
294	C₂³	C₄×Q₈×C₃₁	1	4	yes	—
295	C₂³	C₂³×C₄×C₃₁	1	1	yes	characteristic
296	Q₈	—	2	16	no	—
297	Q₈	—	2	16	no	—
298	C₂×C₄	—	2	16	no	—
299	C₂×C₄	—	2	4	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	8	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	8	no	—
307	C₂×C₄	—	4	4	no	—
308	C₂×C₄	—	4	8	no	—
309	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
310	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
311	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
312	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
313	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
314	C₂×C₄	C₄×Q₈×C₃₁	1	4	yes	—
315	C₂×C₄	C₃₁×C₂²⋊Q₈	1	8	yes	—
316	C₂×C₄	C₃₁×#124	1	4	yes	—
317	C₂×C₄	C₃₁×C₄⋊Q₈	1	4	yes	—
318	C₂×C₄	C₂×M₁₆×C₃₁	1	8	yes	—
319	C₂×C₄	C₂×M₁₆×C₃₁	1	4	yes	—
320	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
321	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
322	C₂×C₄	C₂²×Q₈×C₃₁	1	2	yes	—
323	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
324	C₈	—	2	8	no	—
325	C₈	—	4	4	no	—
326	C₂²	—	2	2	no	—
327	C₂²	—	2	2	no	—
328	C₂²	—	2	8	no	—
329	C₂²	C₃₁×#391	1	4	yes	—
330	C₂²	C₂²×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
331	C₂²	C₂×C₄×Q₈×C₃₁	1	2	yes	—
332	C₂²	C₂²×M₁₆×C₃₁	1	2	yes	—
333	C₂²	C₃₁×#568	1	2	yes	—
334	C₄	—	2	2	no	—
335	C₄	—	2	8	no	—
336	C₄	—	2	2	no	—
337	C₄	—	2	2	no	—
338	C₄	—	4	4	no	—
339	C₄	C₃₁×#391	1	4	yes	—
340	C₄	C₃₁×#407	1	4	yes	—
341	C₄	C₂×C₃₁×C₂²⋊Q₈	1	2	yes	—
342	C₄	C₂×C₃₁×#124	1	1	yes	characteristic
343	C₄	C₂×C₃₁×C₄⋊Q₈	1	1	yes	characteristic
344	C₂	—	2	4	no	—
345	C₂	C₂×C₃₁×#391	1	1	yes	characteristic
346	C₂	C₂×C₃₁×#407	1	1	yes	characteristic
347	C₂	C₃₁×#2879	1	1	yes	characteristic
348	C₂	Q₈×M₁₆×C₃₁	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
4. C₃₁×#1985	C₂	semidirect
5. C₃₁×#1984	C₂	semidirect
40. C₂×M₁₆×C₃₁	Q₈	semidirect
75. C₂×Q₈×C₃₁	M₁₆	semidirect
102. C₂×C₈×C₃₁	C₂×Q₈	semidirect
116. #21303	C₃₁	direct (N × H)
155. #1985	C₂×C₃₁	semidirect
156. #1984	C₂×C₃₁	semidirect
214. C₂×M₁₆	Q₈×C₃₁	semidirect
243. C₃₁	#21303	direct (N × H)
250. C₂×Q₈	M₁₆×C₃₁	semidirect
277. C₂×C₈	C₂×Q₈×C₃₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₄×Q₈×C₃₁	2
C₂×C₃₁×#423	2
C₂×C₄×M₁₆×C₃₁	2
C₃₁×#1985	2
C₃₁×#1984	2
C₃₁×#1728	2
#21303	31

Subgroups — C31×#21303 #21478062

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#21303 #21478062