Subgroups — C₄×C₃₁×#393 #21470618

Order 7936.

2158 conjugacy classes of subgroups.

The subgroup lattice has 360 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, complemented
2	C₂×C₃₁×#393	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₂²⋊C₄×C₃₁	C₂	1	3	yes	maximal
4	C₃₁×#1446	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1442	C₂	1	3	yes	maximal, complemented
6	C₃₁×#1439	C₂	1	3	yes	maximal
7	C₄×C₃₁×#95	C₂	1	3	yes	maximal, complemented
8	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₃₁	—	2	12	no	—
11	C₂²×C₄⋊C₄×C₃₁	C₂²	1	3	yes	—
12	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	3	yes	—
13	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	3	yes	—
14	C₂²×C₄²×C₃₁	C₂²	1	3	yes	—
15	C₂²×C₄²×C₃₁	C₂²	1	3	yes	—
16	C₃₁×#393	C₄	1	8	yes	direct product factor
17	C₄×C₂²⋊C₄×C₃₁	—	2	12	no	—
18	C₂×C₃₁×#95	C₂²	1	6	yes	—
19	C₂×C₃₁×#95	C₂²	1	3	yes	—
20	C₂×C₃₁×#95	C₂²	1	3	yes	—
21	C₂×C₃₁×#95	C₂²	1	3	yes	—
22	C₂×C₃₁×#95	C₂²	1	3	yes	—
23	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
24	C₂²×Q₈×C₃₁	—	2	6	no	—
25	C₂²×Q₈×C₃₁	—	2	6	no	—
26	C₂²×Q₈×C₃₁	C₂×C₄	1	4	yes	complemented
27	C₂³×C₄×C₃₁	—	2	6	no	—
28	C₂³×C₄×C₃₁	—	2	6	no	—
29	C₂³×C₄×C₃₁	Q₈	1	4	yes	complemented
30	C₂³×C₄×C₃₁	C₂³	1	3	yes	—
31	C₂³×C₄×C₃₁	C₂³	1	3	yes	—
32	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
33	C₂³×C₄×C₃₁	C₂³	1	3	yes	—
34	C₂³×C₄×C₃₁	C₂³	1	3	yes	—
35	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
36	C₄×Q₈×C₃₁	—	2	32	no	—
37	C₂×C₄⋊C₄×C₃₁	—	2	12	no	—
38	C₂×C₄⋊C₄×C₃₁	—	2	6	no	—
39	C₂×C₂²⋊C₄×C₃₁	—	2	6	no	—
40	C₂×C₂²⋊C₄×C₃₁	—	2	6	no	—
41	C₂×C₂²⋊C₄×C₃₁	—	2	6	no	—
42	C₂×C₂²⋊C₄×C₃₁	—	2	6	no	—
43	C₂×C₂²⋊C₄×C₃₁	—	2	6	no	—
44	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	12	yes	—
45	C₂×C₄²×C₃₁	—	2	12	no	—
46	C₂×C₄²×C₃₁	—	2	6	no	—
47	C₂×C₄²×C₃₁	—	2	12	no	—
48	C₂×C₄²×C₃₁	D₄	1	12	yes	—
49	C₃₁×#95	—	2	6	no	—
50	C₃₁×#95	—	2	6	no	—
51	C₃₁×#95	—	2	12	no	—
52	C₃₁×#95	—	2	6	no	—
53	C₃₁×#95	C₂×C₄	1	12	yes	complemented
54	C₂⁴×C₃₁	—	2	3	no	—
55	C₂⁴×C₃₁	—	2	3	no	—
56	C₂⁴×C₃₁	—	2	3	no	—
57	C₂⁴×C₃₁	—	2	3	no	—
58	C₂⁴×C₃₁	C₂²×C₄	1	2	yes	—
59	C₂⁴×C₃₁	C₂×Q₈	1	2	yes	—
60	C₂⁴×C₃₁	#41	1	2	yes	—
61	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
62	C₂×Q₈×C₃₁	—	2	8	no	—
63	C₂×Q₈×C₃₁	—	2	24	no	—
64	C₂×Q₈×C₃₁	—	2	24	no	—
65	C₂²×C₄×C₃₁	—	2	6	no	—
66	C₂²×C₄×C₃₁	—	2	6	no	—
67	C₂²×C₄×C₃₁	—	2	3	no	—
68	C₂²×C₄×C₃₁	—	2	3	no	—
69	C₂²×C₄×C₃₁	—	2	3	no	—
70	C₂²×C₄×C₃₁	—	2	6	no	—
71	C₂²×C₄×C₃₁	—	2	6	no	—
72	C₂²×C₄×C₃₁	—	2	6	no	—
73	C₂²×C₄×C₃₁	—	2	6	no	—
74	C₂²×C₄×C₃₁	—	2	6	no	—
75	C₂²×C₄×C₃₁	—	2	6	no	—
76	C₂²×C₄×C₃₁	—	2	3	no	—
77	C₂²×C₄×C₃₁	—	2	3	no	—
78	C₂²×C₄×C₃₁	—	2	3	no	—
79	C₂²×C₄×C₃₁	—	2	3	no	—
80	C₂²×C₄×C₃₁	—	2	3	no	—
81	C₂²×C₄×C₃₁	—	2	24	no	—
82	C₂²×C₄×C₃₁	—	4	4	no	—
83	C₂²×C₄×C₃₁	—	4	12	no	—
84	C₂²×C₄×C₃₁	C₂²×C₄	1	6	yes	—
85	C₂²×C₄×C₃₁	C₂²×C₄	1	6	yes	—
86	C₂²×C₄×C₃₁	C₂×D₄	1	6	yes	—
87	C₂²×C₄×C₃₁	C₂×D₄	1	6	yes	—
88	C₂²×C₄×C₃₁	C₂×D₄	1	6	yes	—
89	C₂²×C₄×C₃₁	C₂×Q₈	1	2	yes	—
90	C₂²×C₄×C₃₁	C₂×Q₈	1	2	yes	—
91	C₂²×C₄×C₃₁	#41	1	6	yes	—
92	C₂²×C₄×C₃₁	#41	1	6	yes	—
93	C₂²×C₄×C₃₁	#41	1	6	yes	—
94	C₄⋊C₄×C₃₁	—	2	24	no	—
95	C₂²⋊C₄×C₃₁	—	2	24	no	—
96	C₂²⋊C₄×C₃₁	—	2	24	no	—
97	C₄²×C₃₁	—	2	24	no	—
98	C₄²×C₃₁	—	4	12	no	—
99	C₄×#393	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
100	C₂³×C₃₁	—	2	6	no	—
101	C₂³×C₃₁	—	2	6	no	—
102	C₂³×C₃₁	—	2	6	no	—
103	C₂³×C₃₁	—	2	6	no	—
104	C₂³×C₃₁	—	2	6	no	—
105	C₂³×C₃₁	—	2	6	no	—
106	C₂³×C₃₁	—	4	1	no	—
107	C₂³×C₃₁	—	4	3	no	—
108	C₂³×C₃₁	—	4	3	no	—
109	C₂³×C₃₁	—	4	6	no	—
110	C₂³×C₃₁	—	4	3	no	—
111	C₂³×C₃₁	C₄×Q₈	1	4	yes	complemented
112	C₂³×C₃₁	C₂³×C₄	1	1	yes	characteristic
113	C₂³×C₃₁	C₂²×D₄	1	3	yes	—
114	C₂³×C₃₁	C₂²×Q₈	1	1	yes	characteristic
115	C₂³×C₃₁	C₂×#41	1	3	yes	—
116	C₂³×C₃₁	C₂×#41	1	1	yes	characteristic
117	C₂³×C₃₁	C₂×#41	1	3	yes	—
118	C₂³×C₃₁	C₂×#41	1	3	yes	—
119	Q₈×C₃₁	—	2	32	no	—
120	C₂×C₄×C₃₁	—	2	12	no	—
121	C₂×C₄×C₃₁	—	2	6	no	—
122	C₂×C₄×C₃₁	—	2	6	no	—
123	C₂×C₄×C₃₁	—	2	12	no	—
124	C₂×C₄×C₃₁	—	2	6	no	—
125	C₂×C₄×C₃₁	—	2	12	no	—
126	C₂×C₄×C₃₁	—	2	6	no	—
127	C₂×C₄×C₃₁	—	2	6	no	—
128	C₂×C₄×C₃₁	—	2	6	no	—
129	C₂×C₄×C₃₁	—	2	6	no	—
130	C₂×C₄×C₃₁	—	2	12	no	—
131	C₂×C₄×C₃₁	—	2	6	no	—
132	C₂×C₄×C₃₁	—	4	1	no	—
133	C₂×C₄×C₃₁	—	4	6	no	—
134	C₂×C₄×C₃₁	—	4	3	no	—
135	C₂×C₄×C₃₁	—	4	3	no	—
136	C₂×C₄×C₃₁	—	4	3	no	—
137	C₂×C₄×C₃₁	—	4	3	no	—
138	C₂×C₄×C₃₁	—	4	6	no	—
139	C₂×C₄×C₃₁	—	4	6	no	—
140	C₂×C₄×C₃₁	—	4	6	no	—
141	C₂×C₄×C₃₁	—	4	3	no	—
142	C₂×C₄×C₃₁	—	4	16	no	—
143	C₂×C₄×C₃₁	C₄×D₄	1	12	yes	—
144	C₂×C₄×C₃₁	#120	1	4	yes	—
145	C₂×C₄×C₃₁	C₂²⋊Q₈	1	12	yes	—
146	C₂×C₄×C₃₁	#124	1	12	yes	—
147	C₂²×C₄×Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
148	C₂×#393	C₂×C₃₁	1	1	yes	characteristic
149	C₂×C₄×C₂²⋊C₄	C₂×C₃₁	1	3	yes	—
150	#1446	C₂×C₃₁	1	1	yes	characteristic, complemented
151	#1442	C₂×C₃₁	1	3	yes	complemented
152	#1439	C₂×C₃₁	1	3	yes	—
153	C₄×#95	C₂×C₃₁	1	3	yes	complemented
154	C₂²×C₃₁	—	2	12	no	—
155	C₂²×C₃₁	—	4	2	no	—
156	C₂²×C₃₁	—	4	2	no	—
157	C₂²×C₃₁	—	4	6	no	—
158	C₂²×C₃₁	—	4	6	no	—
159	C₂²×C₃₁	—	4	2	no	—
160	C₂²×C₃₁	—	4	6	no	—
161	C₂²×C₃₁	C₂×C₄×D₄	1	3	yes	—
162	C₂²×C₃₁	C₂×C₄×Q₈	1	1	yes	characteristic
163	C₂²×C₃₁	C₄×#41	1	3	yes	—
164	C₂²×C₃₁	C₂×#120	1	1	yes	characteristic
165	C₂²×C₃₁	C₂×C₂²⋊Q₈	1	3	yes	—
166	C₂²×C₃₁	#525	1	3	yes	—
167	C₂²×C₃₁	#525	1	3	yes	—
168	C₂²×C₃₁	C₂×#124	1	3	yes	—
169	C₂²×C₃₁	#529	1	6	yes	—
170	C₂²×C₃₁	#529	1	3	yes	—
171	C₂²×C₃₁	#532	1	3	yes	—
172	C₂²×C₃₁	#533	1	3	yes	—
173	C₄×C₃₁	—	2	12	no	—
174	C₄×C₃₁	—	4	2	no	—
175	C₄×C₃₁	—	4	6	no	—
176	C₄×C₃₁	—	4	6	no	—
177	C₄×C₃₁	—	4	6	no	—
178	C₄×C₃₁	#393	1	8	yes	direct product factor
179	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic
180	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
181	C₂×C₄×Q₈	—	2	12	no	—
182	C₂²×C₄⋊C₄	C₂²×C₃₁	1	3	yes	—
183	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	3	yes	—
184	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	3	yes	—
185	C₂²×C₄²	C₂²×C₃₁	1	3	yes	—
186	C₂²×C₄²	C₂²×C₃₁	1	3	yes	—
187	#393	C₄×C₃₁	1	8	yes	direct product factor
188	C₄×C₂²⋊C₄	—	2	12	no	—
189	C₂×#95	C₂²×C₃₁	1	6	yes	—
190	C₂×#95	C₂²×C₃₁	1	3	yes	—
191	C₂×#95	C₂²×C₃₁	1	3	yes	—
192	C₂×#95	C₂²×C₃₁	1	3	yes	—
193	C₂×#95	C₂²×C₃₁	1	3	yes	—
194	C₂×C₃₁	—	4	4	no	—
195	C₂×C₃₁	C₄×#120	1	1	yes	characteristic
196	C₂×C₃₁	C₄×C₂²⋊Q₈	1	3	yes	—
197	C₂×C₃₁	C₄×#124	1	3	yes	—
198	C₂×C₃₁	C₂×#393	1	1	yes	characteristic
199	C₂×C₃₁	#2388	1	1	yes	characteristic
200	C₂×C₃₁	#2396	1	3	yes	—
201	C₂×C₃₁	#2398	1	3	yes	—
202	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
203	C₂²×Q₈	—	2	6	no	—
204	C₂²×Q₈	—	2	6	no	—
205	C₂²×Q₈	C₂×C₄×C₃₁	1	4	yes	complemented
206	C₂³×C₄	—	2	6	no	—
207	C₂³×C₄	—	2	6	no	—
208	C₂³×C₄	Q₈×C₃₁	1	4	yes	complemented
209	C₂³×C₄	C₂³×C₃₁	1	3	yes	—
210	C₂³×C₄	C₂³×C₃₁	1	3	yes	—
211	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
212	C₂³×C₄	C₂³×C₃₁	1	3	yes	—
213	C₂³×C₄	C₂³×C₃₁	1	3	yes	—
214	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
215	C₄×Q₈	—	2	32	no	—
216	C₂×C₄⋊C₄	—	2	12	no	—
217	C₂×C₄⋊C₄	—	2	6	no	—
218	C₂×C₂²⋊C₄	—	2	6	no	—
219	C₂×C₂²⋊C₄	—	2	6	no	—
220	C₂×C₂²⋊C₄	—	2	6	no	—
221	C₂×C₂²⋊C₄	—	2	6	no	—
222	C₂×C₂²⋊C₄	—	2	6	no	—
223	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	12	yes	—
224	C₂×C₄²	—	2	12	no	—
225	C₂×C₄²	—	2	6	no	—
226	C₂×C₄²	—	2	12	no	—
227	C₂×C₄²	D₄×C₃₁	1	12	yes	—
228	#95	—	2	6	no	—
229	#95	—	2	6	no	—
230	#95	—	2	12	no	—
231	#95	—	2	6	no	—
232	#95	C₂×C₄×C₃₁	1	12	yes	complemented
233	C₃₁	C₄×#393	1	1	yes	characteristic, direct product factor, Sylow
234	C₂⁴	—	2	3	no	—
235	C₂⁴	—	2	3	no	—
236	C₂⁴	—	2	3	no	—
237	C₂⁴	—	2	3	no	—
238	C₂⁴	C₂²×C₄×C₃₁	1	2	yes	—
239	C₂⁴	C₂×Q₈×C₃₁	1	2	yes	—
240	C₂⁴	#41×C₃₁	1	2	yes	—
241	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
242	C₂×Q₈	—	2	8	no	—
243	C₂×Q₈	—	2	24	no	—
244	C₂×Q₈	—	2	24	no	—
245	C₂²×C₄	—	2	6	no	—
246	C₂²×C₄	—	2	6	no	—
247	C₂²×C₄	—	2	3	no	—
248	C₂²×C₄	—	2	3	no	—
249	C₂²×C₄	—	2	3	no	—
250	C₂²×C₄	—	2	6	no	—
251	C₂²×C₄	—	2	6	no	—
252	C₂²×C₄	—	2	6	no	—
253	C₂²×C₄	—	2	6	no	—
254	C₂²×C₄	—	2	6	no	—
255	C₂²×C₄	—	2	6	no	—
256	C₂²×C₄	—	2	3	no	—
257	C₂²×C₄	—	2	3	no	—
258	C₂²×C₄	—	2	3	no	—
259	C₂²×C₄	—	2	3	no	—
260	C₂²×C₄	—	2	3	no	—
261	C₂²×C₄	—	2	24	no	—
262	C₂²×C₄	—	4	4	no	—
263	C₂²×C₄	—	4	12	no	—
264	C₂²×C₄	C₂²×C₄×C₃₁	1	6	yes	—
265	C₂²×C₄	C₂²×C₄×C₃₁	1	6	yes	—
266	C₂²×C₄	C₂×D₄×C₃₁	1	6	yes	—
267	C₂²×C₄	C₂×D₄×C₃₁	1	6	yes	—
268	C₂²×C₄	C₂×D₄×C₃₁	1	6	yes	—
269	C₂²×C₄	C₂×Q₈×C₃₁	1	2	yes	—
270	C₂²×C₄	C₂×Q₈×C₃₁	1	2	yes	—
271	C₂²×C₄	#41×C₃₁	1	6	yes	—
272	C₂²×C₄	#41×C₃₁	1	6	yes	—
273	C₂²×C₄	#41×C₃₁	1	6	yes	—
274	C₄⋊C₄	—	2	24	no	—
275	C₂²⋊C₄	—	2	24	no	—
276	C₂²⋊C₄	—	2	24	no	—
277	C₄²	—	2	24	no	—
278	C₄²	—	4	12	no	—
279	C₂³	—	2	6	no	—
280	C₂³	—	2	6	no	—
281	C₂³	—	2	6	no	—
282	C₂³	—	2	6	no	—
283	C₂³	—	2	6	no	—
284	C₂³	—	2	6	no	—
285	C₂³	—	4	1	no	—
286	C₂³	—	4	3	no	—
287	C₂³	—	4	3	no	—
288	C₂³	—	4	6	no	—
289	C₂³	—	4	3	no	—
290	C₂³	C₄×Q₈×C₃₁	1	4	yes	complemented
291	C₂³	C₂³×C₄×C₃₁	1	1	yes	characteristic
292	C₂³	C₂²×D₄×C₃₁	1	3	yes	—
293	C₂³	C₂²×Q₈×C₃₁	1	1	yes	characteristic
294	C₂³	C₂×#41×C₃₁	1	3	yes	—
295	C₂³	C₂×#41×C₃₁	1	1	yes	characteristic
296	C₂³	C₂×#41×C₃₁	1	3	yes	—
297	C₂³	C₂×#41×C₃₁	1	3	yes	—
298	Q₈	—	2	32	no	—
299	C₂×C₄	—	2	12	no	—
300	C₂×C₄	—	2	6	no	—
301	C₂×C₄	—	2	6	no	—
302	C₂×C₄	—	2	12	no	—
303	C₂×C₄	—	2	6	no	—
304	C₂×C₄	—	2	12	no	—
305	C₂×C₄	—	2	6	no	—
306	C₂×C₄	—	2	6	no	—
307	C₂×C₄	—	2	6	no	—
308	C₂×C₄	—	2	6	no	—
309	C₂×C₄	—	2	12	no	—
310	C₂×C₄	—	2	6	no	—
311	C₂×C₄	—	4	1	no	—
312	C₂×C₄	—	4	6	no	—
313	C₂×C₄	—	4	3	no	—
314	C₂×C₄	—	4	3	no	—
315	C₂×C₄	—	4	3	no	—
316	C₂×C₄	—	4	3	no	—
317	C₂×C₄	—	4	6	no	—
318	C₂×C₄	—	4	6	no	—
319	C₂×C₄	—	4	6	no	—
320	C₂×C₄	—	4	3	no	—
321	C₂×C₄	—	4	16	no	—
322	C₂×C₄	C₄×D₄×C₃₁	1	12	yes	—
323	C₂×C₄	C₃₁×#120	1	4	yes	—
324	C₂×C₄	C₃₁×C₂²⋊Q₈	1	12	yes	—
325	C₂×C₄	C₃₁×#124	1	12	yes	—
326	C₂²	—	2	12	no	—
327	C₂²	—	4	2	no	—
328	C₂²	—	4	2	no	—
329	C₂²	—	4	6	no	—
330	C₂²	—	4	6	no	—
331	C₂²	—	4	2	no	—
332	C₂²	—	4	6	no	—
333	C₂²	C₂×C₄×D₄×C₃₁	1	3	yes	—
334	C₂²	C₂×C₄×Q₈×C₃₁	1	1	yes	characteristic
335	C₂²	C₄×#41×C₃₁	1	3	yes	—
336	C₂²	C₂×C₃₁×#120	1	1	yes	characteristic
337	C₂²	C₂×C₃₁×C₂²⋊Q₈	1	3	yes	—
338	C₂²	C₃₁×#525	1	3	yes	—
339	C₂²	C₃₁×#525	1	3	yes	—
340	C₂²	C₂×C₃₁×#124	1	3	yes	—
341	C₂²	C₃₁×#529	1	6	yes	—
342	C₂²	C₃₁×#529	1	3	yes	—
343	C₂²	C₃₁×#532	1	3	yes	—
344	C₂²	C₃₁×#533	1	3	yes	—
345	C₄	—	2	12	no	—
346	C₄	—	4	2	no	—
347	C₄	—	4	6	no	—
348	C₄	—	4	6	no	—
349	C₄	—	4	6	no	—
350	C₄	C₃₁×#393	1	8	yes	direct product factor
351	C₂	—	4	4	no	—
352	C₂	C₄×C₃₁×#120	1	1	yes	characteristic
353	C₂	C₄×C₃₁×C₂²⋊Q₈	1	3	yes	—
354	C₂	C₄×C₃₁×#124	1	3	yes	—
355	C₂	C₂×C₃₁×#393	1	1	yes	characteristic
356	C₂	C₃₁×#2388	1	1	yes	characteristic
357	C₂	C₃₁×#2396	1	3	yes	—
358	C₂	C₃₁×#2398	1	3	yes	—

	subgroup	G/H
center	C₂³×C₄×C₃₁	C₂³
commutator	C₂³	C₂³×C₄×C₃₁
Frattini, cosocle	C₂⁴	C₂⁴×C₃₁
socle	C₂⁴×C₃₁	C₂⁴
prime radical	C₂⁵×C₃₁	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₄×Q₈×C₃₁	C₂	semidirect
4. C₃₁×#1446	C₂	semidirect
5. C₃₁×#1442	C₂	semidirect
7. C₄×C₃₁×#95	C₂	semidirect
16. C₃₁×#393	C₄	direct (N × H)
26. C₂²×Q₈×C₃₁	C₂×C₄	semidirect
29. C₂³×C₄×C₃₁	Q₈	semidirect
53. C₃₁×#95	C₂×C₄	semidirect
99. C₄×#393	C₃₁	direct (N × H)
111. C₂³×C₃₁	C₄×Q₈	semidirect
147. C₂²×C₄×Q₈	C₂×C₃₁	semidirect
150. #1446	C₂×C₃₁	semidirect
151. #1442	C₂×C₃₁	semidirect
153. C₄×#95	C₂×C₃₁	semidirect
178. C₄×C₃₁	#393	direct (N × H)
187. #393	C₄×C₃₁	direct (N × H)
205. C₂²×Q₈	C₂×C₄×C₃₁	semidirect
208. C₂³×C₄	Q₈×C₃₁	semidirect
232. #95	C₂×C₄×C₃₁	semidirect
233. C₃₁	C₄×#393	direct (N × H)
290. C₂³	C₄×Q₈×C₃₁	semidirect
350. C₄	C₃₁×#393	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×C₄×Q₈×C₃₁	2
C₂×C₃₁×#393	2
C₂×C₄×C₂²⋊C₄×C₃₁	2
C₃₁×#1446	2
C₃₁×#1442	2
C₃₁×#1439	2
C₄×C₃₁×#95	2
C₄×#393	31

Subgroups — C4×C31×#393 #21470618

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₃₁×#393 #21470618