Subgroups — C₃₁×#19647 #21476406

Order 7936.

840 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	C₃₁×#3207	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3184	C₂	1	2	yes	maximal, complemented
3	C₃₁×#3169	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3147	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1717	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1715	C₂	1	2	yes	maximal, complemented
7	C₃₁×#1712	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1709	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#1707	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#1706	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×M₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×#135	—	2	2	no	—
13	C₃₁×#532	C₂²	1	2	yes	—
14	C₃₁×#532	C₂²	1	2	yes	—
15	C₃₁×#500	C₂²	1	1	yes	characteristic
16	C₃₁×#498	C₂²	1	2	yes	—
17	C₃₁×#495	—	2	2	no	—
18	C₃₁×#494	C₂²	1	1	yes	characteristic
19	C₃₁×#493	C₂²	1	1	yes	characteristic
20	C₃₁×#493	C₂²	1	1	yes	characteristic
21	C₃₁×#493	C₂²	1	2	yes	—
22	C₃₁×#493	C₂²	1	2	yes	—
23	C₃₁×#492	C₂²	1	2	yes	—
24	C₃₁×#492	C₂²	1	2	yes	—
25	C₃₁×#487	C₂²	1	2	yes	—
26	C₃₁×#486	C₂²	1	2	yes	—
27	C₃₁×#486	C₂²	1	2	yes	—
28	C₃₁×#486	C₂²	1	2	yes	—
29	C₃₁×#486	C₂²	1	2	yes	—
30	C₃₁×#469	—	2	4	no	—
31	C₃₁×#466	—	2	2	no	—
32	C₃₁×#463	—	2	4	no	—
33	C₃₁×#449	—	2	4	no	—
34	C₃₁×#442	—	2	4	no	—
35	C₄×D₈×C₃₁	—	2	2	no	—
36	C₃₁×#431	C₂²	1	1	yes	characteristic
37	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
39	C₃₁×#322	C₂²	1	1	yes	characteristic
40	C₃₁×#322	C₂²	1	1	yes	characteristic
41	C₈²×C₃₁	C₂²	1	1	yes	characteristic
42	C₈²×C₃₁	C₂²	1	1	yes	characteristic
43	C₂×#41×C₃₁	—	2	2	no	—
44	C₂×#41×C₃₁	—	2	2	no	—
45	C₃₁×#135	—	4	8	no	—
46	C₂×Q₁₆×C₃₁	—	2	2	no	—
47	C₂×SD₁₆×C₃₁	—	2	4	no	—
48	C₂×SD₁₆×C₃₁	—	2	4	no	—
49	C₂×D₈×C₃₁	—	2	2	no	—
50	C₂×D₈×C₃₁	—	2	4	no	—
51	C₂×D₈×C₃₁	—	2	2	no	—
52	C₂×D₈×C₃₁	—	2	4	no	—
53	C₂×M₁₆×C₃₁	D₄	1	2	yes	—
54	C₂²×C₈×C₃₁	D₄	1	2	yes	—
55	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
56	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
57	C₃₁×#127	C₂³	1	2	yes	—
58	C₃₁×#127	C₂³	1	2	yes	—
59	C₃₁×#124	—	2	2	no	—
60	C₃₁×#124	—	2	2	no	—
61	C₃₁×#121	—	2	2	no	—
62	C₃₁×#121	—	2	2	no	—
63	C₃₁×#121	—	2	2	no	—
64	C₃₁×#121	—	2	2	no	—
65	C₄×D₄×C₃₁	—	2	2	no	—
66	C₄×D₄×C₃₁	—	2	2	no	—
67	C₄×D₄×C₃₁	—	2	2	no	—
68	C₄×D₄×C₃₁	—	2	2	no	—
69	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
70	C₃₁×#107	—	2	2	no	—
71	C₃₁×#106	—	2	4	no	—
72	C₃₁×C₄⋊C₈	D₄	1	2	yes	—
73	C₃₁×#103	—	2	4	no	—
74	C₃₁×#102	—	2	4	no	—
75	C₃₁×#102	—	2	4	no	—
76	C₃₁×#102	—	2	4	no	—
77	C₃₁×#102	—	2	4	no	—
78	C₃₁×C₂²⋊C₈	D₄	1	2	yes	—
79	C₃₁×#97	D₄	1	2	yes	—
80	C₄×C₈×C₃₁	D₄	1	2	yes	—
81	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
82	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
83	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
84	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
85	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
86	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
87	#41×C₃₁	—	4	8	no	—
88	#41×C₃₁	—	8	4	no	—
89	C₂×Q₈×C₃₁	—	2	2	no	—
90	C₂×Q₈×C₃₁	—	2	2	no	—
91	C₂×D₄×C₃₁	—	2	2	no	—
92	C₂×D₄×C₃₁	—	2	2	no	—
93	C₂×D₄×C₃₁	—	2	2	no	—
94	C₂×D₄×C₃₁	—	2	2	no	—
95	C₂×D₄×C₃₁	—	2	2	no	—
96	C₂×D₄×C₃₁	—	2	2	no	—
97	C₂×D₄×C₃₁	—	4	2	no	—
98	C₂×D₄×C₃₁	—	4	2	no	—
99	C₂²×C₄×C₃₁	—	4	2	no	—
100	C₂²×C₄×C₃₁	—	4	2	no	—
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×D₄	1	1	yes	characteristic
104	Q₁₆×C₃₁	—	4	4	no	—
105	SD₁₆×C₃₁	—	4	8	no	—
106	SD₁₆×C₃₁	—	8	4	no	—
107	D₈×C₃₁	—	4	8	no	—
108	D₈×C₃₁	—	4	4	no	—
109	D₈×C₃₁	—	4	4	no	—
110	D₈×C₃₁	—	8	4	no	—
111	M₁₆×C₃₁	—	2	4	no	—
112	C₂×C₈×C₃₁	—	2	4	no	—
113	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
114	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
115	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
116	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
117	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
119	C₄⋊C₄×C₃₁	—	2	2	no	—
120	C₄⋊C₄×C₃₁	—	2	2	no	—
121	C₄⋊C₄×C₃₁	—	2	2	no	—
122	C₄⋊C₄×C₃₁	—	2	2	no	—
123	C₂²⋊C₄×C₃₁	—	4	2	no	—
124	C₂²⋊C₄×C₃₁	—	4	2	no	—
125	C₂²⋊C₄×C₃₁	—	4	2	no	—
126	C₂²⋊C₄×C₃₁	—	4	2	no	—
127	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
131	#19647	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₂³×C₃₁	—	4	2	no	—
133	C₂³×C₃₁	—	4	2	no	—
134	C₂³×C₃₁	#127	1	1	yes	characteristic
135	Q₈×C₃₁	—	4	4	no	—
136	Q₈×C₃₁	—	4	4	no	—
137	D₄×C₃₁	—	4	4	no	—
138	D₄×C₃₁	—	4	4	no	—
139	D₄×C₃₁	—	4	4	no	—
140	D₄×C₃₁	—	4	4	no	—
141	D₄×C₃₁	—	4	4	no	—
142	D₄×C₃₁	—	4	4	no	—
143	D₄×C₃₁	—	8	4	no	—
144	D₄×C₃₁	—	8	4	no	—
145	C₂×C₄×C₃₁	—	2	2	no	—
146	C₂×C₄×C₃₁	—	2	2	no	—
147	C₂×C₄×C₃₁	—	2	2	no	—
148	C₂×C₄×C₃₁	—	4	2	no	—
149	C₂×C₄×C₃₁	—	4	2	no	—
150	C₂×C₄×C₃₁	—	8	4	no	—
151	C₂×C₄×C₃₁	—	8	4	no	—
152	C₂×C₄×C₃₁	#127	1	1	yes	characteristic
153	C₂×C₄×C₃₁	#127	1	1	yes	characteristic
154	C₂×C₄×C₃₁	#127	1	1	yes	characteristic
155	C₂×C₄×C₃₁	C₂²×D₄	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	—	2	2	no	—
159	C₈×C₃₁	—	2	2	no	—
160	C₈×C₃₁	—	2	2	no	—
161	C₈×C₃₁	—	2	2	no	—
162	C₈×C₃₁	#135	1	4	yes	complemented
163	C₈×C₃₁	AGL(1,ℤ/8)	1	4	yes	—
164	#3207	C₂×C₃₁	1	2	yes	complemented
165	#3184	C₂×C₃₁	1	2	yes	complemented
166	#3169	C₂×C₃₁	1	1	yes	characteristic, complemented
167	#3147	C₂×C₃₁	1	1	yes	characteristic, complemented
168	#1717	C₂×C₃₁	1	2	yes	complemented
169	#1715	C₂×C₃₁	1	2	yes	complemented
170	#1712	C₂×C₃₁	1	1	yes	characteristic, complemented
171	#1709	C₂×C₃₁	1	1	yes	characteristic, complemented
172	#1707	C₂×C₃₁	1	1	yes	characteristic, complemented
173	#1706	C₂×C₃₁	1	1	yes	characteristic, complemented
174	C₈×M₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
175	C₂²×C₃₁	—	2	1	no	—
176	C₂²×C₃₁	—	2	1	no	—
177	C₂²×C₃₁	—	2	1	no	—
178	C₂²×C₃₁	—	8	2	no	—
179	C₂²×C₃₁	—	8	2	no	—
180	C₂²×C₃₁	—	8	2	no	—
181	C₂²×C₃₁	—	8	2	no	—
182	C₂²×C₃₁	—	8	2	no	—
183	C₂²×C₃₁	—	8	2	no	—
184	C₂²×C₃₁	C₂×#127	1	1	yes	characteristic
185	C₄×C₃₁	—	2	1	no	—
186	C₄×C₃₁	—	2	1	no	—
187	C₄×C₃₁	—	2	1	no	—
188	C₄×C₃₁	—	8	2	no	—
189	C₄×C₃₁	—	8	2	no	—
190	C₄×C₃₁	C₂×#135	1	2	yes	—
191	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
192	C₄×C₃₁	#576	1	2	yes	—
193	C₂×#135	—	2	2	no	—
194	#532	C₂²×C₃₁	1	2	yes	—
195	#532	C₂²×C₃₁	1	2	yes	—
196	#500	C₂²×C₃₁	1	1	yes	characteristic
197	#498	C₂²×C₃₁	1	2	yes	—
198	#495	—	2	2	no	—
199	#494	C₂²×C₃₁	1	1	yes	characteristic
200	#493	C₂²×C₃₁	1	1	yes	characteristic
201	#493	C₂²×C₃₁	1	1	yes	characteristic
202	#493	C₂²×C₃₁	1	2	yes	—
203	#493	C₂²×C₃₁	1	2	yes	—
204	#492	C₂²×C₃₁	1	2	yes	—
205	#492	C₂²×C₃₁	1	2	yes	—
206	#487	C₂²×C₃₁	1	2	yes	—
207	#486	C₂²×C₃₁	1	2	yes	—
208	#486	C₂²×C₃₁	1	2	yes	—
209	#486	C₂²×C₃₁	1	2	yes	—
210	#486	C₂²×C₃₁	1	2	yes	—
211	#469	—	2	4	no	—
212	#466	—	2	2	no	—
213	#463	—	2	4	no	—
214	#449	—	2	4	no	—
215	#442	—	2	4	no	—
216	C₄×D₈	—	2	2	no	—
217	#431	C₂²×C₃₁	1	1	yes	characteristic
218	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
219	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
220	#322	C₂²×C₃₁	1	1	yes	characteristic
221	#322	C₂²×C₃₁	1	1	yes	characteristic
222	C₈²	C₂²×C₃₁	1	1	yes	characteristic
223	C₈²	C₂²×C₃₁	1	1	yes	characteristic
224	C₂×C₃₁	—	4	1	no	—
225	C₂×C₃₁	—	16	2	no	—
226	C₂×C₃₁	—	16	2	no	—
227	C₂×C₃₁	#3147	1	1	yes	characteristic
228	C₂×C₃₁	#3151	1	1	yes	characteristic
229	C₂×C₃₁	#3155	1	1	yes	characteristic
230	C₂×#41	—	2	2	no	—
231	C₂×#41	—	2	2	no	—
232	#135	—	4	8	no	—
233	C₂×Q₁₆	—	2	2	no	—
234	C₂×SD₁₆	—	2	4	no	—
235	C₂×SD₁₆	—	2	4	no	—
236	C₂×D₈	—	2	2	no	—
237	C₂×D₈	—	2	2	no	—
238	C₂×D₈	—	2	4	no	—
239	C₂×D₈	—	2	4	no	—
240	C₂×M₁₆	D₄×C₃₁	1	2	yes	—
241	C₂²×C₈	D₄×C₃₁	1	2	yes	—
242	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
243	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
244	#127	C₂³×C₃₁	1	2	yes	—
245	#127	C₂³×C₃₁	1	2	yes	—
246	#124	—	2	2	no	—
247	#124	—	2	2	no	—
248	#121	—	2	2	no	—
249	#121	—	2	2	no	—
250	#121	—	2	2	no	—
251	#121	—	2	2	no	—
252	C₄×D₄	—	2	2	no	—
253	C₄×D₄	—	2	2	no	—
254	C₄×D₄	—	2	2	no	—
255	C₄×D₄	—	2	2	no	—
256	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
257	#107	—	2	2	no	—
258	#106	—	2	4	no	—
259	C₄⋊C₈	D₄×C₃₁	1	2	yes	—
260	#103	—	2	4	no	—
261	#102	—	2	4	no	—
262	#102	—	2	4	no	—
263	#102	—	2	4	no	—
264	#102	—	2	4	no	—
265	C₂²⋊C₈	D₄×C₃₁	1	2	yes	—
266	#97	D₄×C₃₁	1	2	yes	—
267	C₄×C₈	D₄×C₃₁	1	2	yes	—
268	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
269	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
270	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
271	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
272	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
273	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
274	C₃₁	#19647	1	1	yes	characteristic, direct product factor, Sylow
275	#41	—	4	8	no	—
276	#41	—	8	4	no	—
277	C₂×Q₈	—	2	2	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	4	2	no	—
286	C₂×D₄	—	4	2	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
292	Q₁₆	—	4	4	no	—
293	SD₁₆	—	4	8	no	—
294	SD₁₆	—	8	4	no	—
295	D₈	—	4	8	no	—
296	D₈	—	4	4	no	—
297	D₈	—	4	4	no	—
298	D₈	—	8	4	no	—
299	M₁₆	—	2	4	no	—
300	C₂×C₈	—	2	4	no	—
301	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
302	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
303	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
304	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
305	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
306	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₂²⋊C₄	—	4	2	no	—
312	C₂²⋊C₄	—	4	2	no	—
313	C₂²⋊C₄	—	4	2	no	—
314	C₂²⋊C₄	—	4	2	no	—
315	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
316	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
317	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
318	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
319	C₂³	—	4	2	no	—
320	C₂³	—	4	2	no	—
321	C₂³	C₃₁×#127	1	1	yes	characteristic
322	Q₈	—	4	4	no	—
323	Q₈	—	4	4	no	—
324	D₄	—	4	4	no	—
325	D₄	—	4	4	no	—
326	D₄	—	4	4	no	—
327	D₄	—	4	4	no	—
328	D₄	—	4	4	no	—
329	D₄	—	4	4	no	—
330	D₄	—	8	4	no	—
331	D₄	—	8	4	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	8	4	no	—
338	C₂×C₄	—	8	4	no	—
339	C₂×C₄	C₃₁×#127	1	1	yes	characteristic
340	C₂×C₄	C₃₁×#127	1	1	yes	characteristic
341	C₂×C₄	C₃₁×#127	1	1	yes	characteristic
342	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
343	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
344	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
345	C₈	—	2	2	no	—
346	C₈	—	2	2	no	—
347	C₈	—	2	2	no	—
348	C₈	—	2	2	no	—
349	C₈	C₃₁×#135	1	4	yes	complemented
350	C₈	C₃₁×AGL(1,ℤ/8)	1	4	yes	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	8	2	no	—
355	C₂²	—	8	2	no	—
356	C₂²	—	8	2	no	—
357	C₂²	—	8	2	no	—
358	C₂²	—	8	2	no	—
359	C₂²	—	8	2	no	—
360	C₂²	C₂×C₃₁×#127	1	1	yes	characteristic
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	8	2	no	—
365	C₄	—	8	2	no	—
366	C₄	C₂×C₃₁×#135	1	2	yes	—
367	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
368	C₄	C₃₁×#576	1	2	yes	—
369	C₂	—	4	1	no	—
370	C₂	—	16	2	no	—
371	C₂	—	16	2	no	—
372	C₂	C₃₁×#3147	1	1	yes	characteristic
373	C₂	C₃₁×#3151	1	1	yes	characteristic
374	C₂	C₃₁×#3155	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₁
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3207	C₂	semidirect
2. C₃₁×#3184	C₂	semidirect
3. C₃₁×#3169	C₂	semidirect
4. C₃₁×#3147	C₂	semidirect
5. C₃₁×#1717	C₂	semidirect
6. C₃₁×#1715	C₂	semidirect
7. C₃₁×#1712	C₂	semidirect
8. C₃₁×#1709	C₂	semidirect
9. C₃₁×#1707	C₂	semidirect
10. C₃₁×#1706	C₂	semidirect
11. C₈×M₁₆×C₃₁	C₂	semidirect
131. #19647	C₃₁	direct (N × H)
162. C₈×C₃₁	#135	semidirect
164. #3207	C₂×C₃₁	semidirect
165. #3184	C₂×C₃₁	semidirect
166. #3169	C₂×C₃₁	semidirect
167. #3147	C₂×C₃₁	semidirect
168. #1717	C₂×C₃₁	semidirect
169. #1715	C₂×C₃₁	semidirect
170. #1712	C₂×C₃₁	semidirect
171. #1709	C₂×C₃₁	semidirect
172. #1707	C₂×C₃₁	semidirect
173. #1706	C₂×C₃₁	semidirect
174. C₈×M₁₆	C₂×C₃₁	semidirect
274. C₃₁	#19647	direct (N × H)
349. C₈	C₃₁×#135	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3207	2
C₃₁×#3184	2
C₃₁×#3169	2
C₃₁×#3147	2
C₃₁×#1717	2
C₃₁×#1715	2
C₃₁×#1712	2
C₃₁×#1709	2
C₃₁×#1707	2
C₃₁×#1706	2
C₈×M₁₆×C₃₁	2
#19647	31

Subgroups — C31×#19647 #21476406

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#19647 #21476406