Subgroups — C₃₁×#19905 #21476664

Order 7936.

604 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3341	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3329	C₂	1	2	yes	maximal, complemented
4	C₃₁×#1710	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1703	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1676	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1673	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1646	C₂	1	2	yes	maximal, complemented
9	C₃₁×#1637	C₂	1	2	yes	maximal, complemented
10	C₃₁×#1589	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#555	C₂²	1	2	yes	—
13	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
14	C₃₁×#500	—	2	1	no	—
15	C₃₁×#500	C₂²	1	1	yes	characteristic
16	C₃₁×#500	C₂²	1	1	yes	characteristic
17	C₃₁×#487	C₂²	1	2	yes	—
18	C₃₁×#487	C₂²	1	2	yes	—
19	C₃₁×#485	—	2	2	no	—
20	C₃₁×#482	—	2	2	no	—
21	C₃₁×#477	C₂²	1	2	yes	—
22	C₃₁×#476	C₂²	1	2	yes	—
23	C₃₁×#474	—	2	2	no	—
24	C₃₁×#474	C₂²	1	2	yes	—
25	C₃₁×#468	—	2	2	no	—
26	C₃₁×#466	—	2	1	no	—
27	C₃₁×#461	C₂²	1	2	yes	—
28	C₃₁×#448	—	2	2	no	—
29	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
30	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
31	C₄×D₈×C₃₁	—	2	1	no	—
32	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
33	C₃₁×#436	C₂²	1	2	yes	—
34	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
35	C₃₁×#427	—	2	1	no	—
36	C₃₁×#419	—	2	2	no	—
37	C₃₁×#335	C₂²	1	1	yes	characteristic
38	C₃₁×#334	C₂²	1	1	yes	characteristic
39	C₃₁×#333	C₂²	1	2	yes	—
40	C₃₁×#332	C₂²	1	2	yes	—
41	C₃₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
42	C₃₁×D₄⋊C₈	C₂²	1	1	yes	characteristic
43	C₃₁×D₄⋊C₈	C₂²	1	2	yes	—
44	C₈²×C₃₁	C₂²	1	1	yes	characteristic
45	C₂²×Q₈×C₃₁	—	2	2	no	—
46	C₂×SD₁₆×C₃₁	—	2	2	no	—
47	C₂×SD₁₆×C₃₁	D₄	1	1	yes	characteristic
48	C₂×D₈×C₃₁	D₄	1	1	yes	characteristic
49	C₂×M₁₆×C₃₁	—	2	2	no	—
50	C₂²×C₈×C₃₁	—	2	1	no	—
51	C₃₁×C₄⋊Q₈	—	2	2	no	—
52	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
53	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
54	C₃₁×#124	—	4	2	no	—
55	C₃₁×C₂²⋊Q₈	—	2	2	no	—
56	C₃₁×C₂²⋊Q₈	—	4	2	no	—
57	C₃₁×#121	—	2	2	no	—
58	C₃₁×#121	—	2	2	no	—
59	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
60	C₄×D₄×C₃₁	—	2	2	no	—
61	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
62	C₄×D₄×C₃₁	C₂³	1	2	yes	—
63	C₃₁×#117	—	2	2	no	—
64	C₃₁×#117	—	2	2	no	—
65	C₃₁×#107	—	2	1	no	—
66	C₃₁×#107	—	2	1	no	—
67	C₃₁×#107	—	2	1	no	—
68	C₃₁×#107	—	2	1	no	—
69	C₃₁×#107	—	2	2	no	—
70	C₃₁×#107	—	2	2	no	—
71	C₃₁×#107	D₄	1	1	yes	characteristic
72	C₃₁×#106	—	2	2	no	—
73	C₃₁×#106	D₄	1	1	yes	characteristic
74	C₃₁×C₄⋊C₈	—	2	1	no	—
75	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
76	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
77	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
78	C₃₁×#103	—	2	2	no	—
79	C₃₁×#103	—	2	2	no	—
80	C₃₁×#103	—	2	2	no	—
81	C₃₁×#103	—	2	2	no	—
82	C₃₁×#103	—	4	2	no	—
83	C₃₁×#103	D₄	1	1	yes	characteristic
84	C₃₁×#102	—	2	2	no	—
85	C₃₁×#102	—	2	2	no	—
86	C₃₁×#102	D₄	1	2	yes	—
87	C₃₁×#102	D₄	1	1	yes	characteristic
88	C₃₁×C₂²⋊C₈	—	2	1	no	—
89	C₃₁×C₂²⋊C₈	—	2	2	no	—
90	C₄×C₈×C₃₁	—	2	1	no	—
91	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
94	C₂×Q₈×C₃₁	—	2	2	no	—
95	C₂×Q₈×C₃₁	—	2	2	no	—
96	C₂×Q₈×C₃₁	—	4	2	no	—
97	C₂×Q₈×C₃₁	—	4	4	no	—
98	C₂×Q₈×C₃₁	—	8	2	no	—
99	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
100	C₂×D₄×C₃₁	—	4	2	no	—
101	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
102	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₃₁	—	2	1	no	—
104	C₂²×C₄×C₃₁	—	2	2	no	—
105	C₂²×C₄×C₃₁	—	4	2	no	—
106	SD₁₆×C₃₁	—	2	2	no	—
107	SD₁₆×C₃₁	—	8	2	no	—
108	D₈×C₃₁	—	2	2	no	—
109	M₁₆×C₃₁	—	8	2	no	—
110	C₂×C₈×C₃₁	—	2	1	no	—
111	C₂×C₈×C₃₁	—	2	1	no	—
112	C₂×C₈×C₃₁	—	2	2	no	—
113	C₂×C₈×C₃₁	—	2	1	no	—
114	C₂×C₈×C₃₁	—	4	2	no	—
115	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
119	C₄⋊C₄×C₃₁	—	2	1	no	—
120	C₄⋊C₄×C₃₁	—	2	2	no	—
121	C₄⋊C₄×C₃₁	—	2	2	no	—
122	C₄⋊C₄×C₃₁	—	2	2	no	—
123	C₄⋊C₄×C₃₁	—	2	2	no	—
124	C₄⋊C₄×C₃₁	—	4	2	no	—
125	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
126	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
127	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
128	C₂²⋊C₄×C₃₁	—	2	2	no	—
129	C₂²⋊C₄×C₃₁	—	2	1	no	—
130	C₂²⋊C₄×C₃₁	—	4	2	no	—
131	C₂²⋊C₄×C₃₁	—	4	2	no	—
132	C₂²⋊C₄×C₃₁	—	4	2	no	—
133	C₄²×C₃₁	—	2	1	no	—
134	C₄²×C₃₁	—	4	2	no	—
135	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
136	#19905	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂³×C₃₁	—	2	2	no	—
138	C₂³×C₃₁	—	2	1	no	—
139	Q₈×C₃₁	—	2	1	no	—
140	Q₈×C₃₁	—	4	2	no	—
141	Q₈×C₃₁	—	4	2	no	—
142	Q₈×C₃₁	—	8	4	no	—
143	Q₈×C₃₁	—	8	2	no	—
144	Q₈×C₃₁	#135	1	2	yes	—
145	D₄×C₃₁	—	2	1	no	—
146	D₄×C₃₁	—	2	2	no	—
147	D₄×C₃₁	—	2	1	no	—
148	D₄×C₃₁	—	2	2	no	—
149	D₄×C₃₁	—	16	2	no	—
150	C₂×C₄×C₃₁	—	2	1	no	—
151	C₂×C₄×C₃₁	—	2	1	no	—
152	C₂×C₄×C₃₁	—	2	1	no	—
153	C₂×C₄×C₃₁	—	2	2	no	—
154	C₂×C₄×C₃₁	—	4	2	no	—
155	C₂×C₄×C₃₁	—	4	1	no	—
156	C₂×C₄×C₃₁	—	4	2	no	—
157	C₂×C₄×C₃₁	—	4	1	no	—
158	C₂×C₄×C₃₁	—	4	2	no	—
159	C₂×C₄×C₃₁	—	4	2	no	—
160	C₂×C₄×C₃₁	—	8	4	no	—
161	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
164	C₈×C₃₁	—	2	1	no	—
165	C₈×C₃₁	—	2	1	no	—
166	C₈×C₃₁	—	2	1	no	—
167	C₈×C₃₁	—	4	1	no	—
168	C₈×C₃₁	—	4	1	no	—
169	C₈×C₃₁	—	4	2	no	—
170	C₈×C₃₁	—	4	1	no	—
171	C₈×C₃₁	#137	1	2	yes	—
172	Q₈×D₈	C₂×C₃₁	1	1	yes	characteristic, complemented
173	#3341	C₂×C₃₁	1	1	yes	characteristic
174	#3329	C₂×C₃₁	1	2	yes	complemented
175	#1710	C₂×C₃₁	1	1	yes	characteristic, complemented
176	#1703	C₂×C₃₁	1	2	yes	complemented
177	#1676	C₂×C₃₁	1	1	yes	characteristic, complemented
178	#1673	C₂×C₃₁	1	1	yes	characteristic, complemented
179	#1646	C₂×C₃₁	1	2	yes	complemented
180	#1637	C₂×C₃₁	1	2	yes	complemented
181	#1589	C₂×C₃₁	1	1	yes	characteristic, complemented
182	C₈×SD₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
183	C₂²×C₃₁	—	4	1	no	—
184	C₂²×C₃₁	—	4	2	no	—
185	C₂²×C₃₁	—	4	2	no	—
186	C₂²×C₃₁	—	4	1	no	—
187	C₂²×C₃₁	—	4	1	no	—
188	C₂²×C₃₁	—	4	2	no	—
189	C₂²×C₃₁	D₄²	1	1	yes	characteristic
190	C₄×C₃₁	—	2	2	no	—
191	C₄×C₃₁	—	2	1	no	—
192	C₄×C₃₁	—	4	1	no	—
193	C₄×C₃₁	—	4	2	no	—
194	C₄×C₃₁	—	4	1	no	—
195	C₄×C₃₁	—	8	2	no	—
196	C₄×C₃₁	—	8	2	no	—
197	C₄×C₃₁	C₂×#135	1	1	yes	characteristic
198	C₄×C₃₁	C₂×#137	1	1	yes	characteristic
199	C₄×C₃₁	#576	1	1	yes	characteristic
200	C₄×C₃₁	#578	1	1	yes	characteristic
201	#555	C₂²×C₃₁	1	2	yes	—
202	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
203	#500	—	2	1	no	—
204	#500	C₂²×C₃₁	1	1	yes	characteristic
205	#500	C₂²×C₃₁	1	1	yes	characteristic
206	#487	C₂²×C₃₁	1	2	yes	—
207	#487	C₂²×C₃₁	1	2	yes	—
208	#485	—	2	2	no	—
209	#482	—	2	2	no	—
210	#477	C₂²×C₃₁	1	2	yes	—
211	#476	C₂²×C₃₁	1	2	yes	—
212	#474	—	2	2	no	—
213	#474	C₂²×C₃₁	1	2	yes	—
214	#468	—	2	2	no	—
215	#466	—	2	1	no	—
216	#461	C₂²×C₃₁	1	2	yes	—
217	#448	—	2	2	no	—
218	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
219	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
220	C₄×D₈	—	2	1	no	—
221	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
222	#436	C₂²×C₃₁	1	2	yes	—
223	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
224	#427	—	2	1	no	—
225	#419	—	2	2	no	—
226	#335	C₂²×C₃₁	1	1	yes	characteristic
227	#334	C₂²×C₃₁	1	1	yes	characteristic
228	#333	C₂²×C₃₁	1	2	yes	—
229	#332	C₂²×C₃₁	1	2	yes	—
230	Q₈⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
231	D₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
232	D₄⋊C₈	C₂²×C₃₁	1	2	yes	—
233	C₈²	C₂²×C₃₁	1	1	yes	characteristic
234	C₂×C₃₁	—	8	1	no	—
235	C₂×C₃₁	—	8	2	no	—
236	C₂×C₃₁	#3276	1	1	yes	characteristic
237	C₂×C₃₁	#3280	1	1	yes	characteristic
238	C₂×C₃₁	#3290	1	1	yes	characteristic
239	C₂²×Q₈	—	2	2	no	—
240	C₂×SD₁₆	—	2	2	no	—
241	C₂×SD₁₆	D₄×C₃₁	1	1	yes	characteristic
242	C₂×D₈	D₄×C₃₁	1	1	yes	characteristic
243	C₂×M₁₆	—	2	2	no	—
244	C₂²×C₈	—	2	1	no	—
245	C₄⋊Q₈	—	2	2	no	—
246	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
247	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
248	#124	—	4	2	no	—
249	C₂²⋊Q₈	—	2	2	no	—
250	C₂²⋊Q₈	—	4	2	no	—
251	#121	—	2	2	no	—
252	#121	—	2	2	no	—
253	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
254	C₄×D₄	—	2	2	no	—
255	C₄×D₄	C₂³×C₃₁	1	2	yes	—
256	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
257	#117	—	2	2	no	—
258	#117	—	2	2	no	—
259	#107	—	2	1	no	—
260	#107	—	2	1	no	—
261	#107	—	2	1	no	—
262	#107	—	2	1	no	—
263	#107	—	2	2	no	—
264	#107	—	2	2	no	—
265	#107	D₄×C₃₁	1	1	yes	characteristic
266	#106	—	2	2	no	—
267	#106	D₄×C₃₁	1	1	yes	characteristic
268	C₄⋊C₈	—	2	1	no	—
269	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
270	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
271	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
272	#103	—	2	2	no	—
273	#103	—	2	2	no	—
274	#103	—	2	2	no	—
275	#103	—	2	2	no	—
276	#103	—	4	2	no	—
277	#103	D₄×C₃₁	1	1	yes	characteristic
278	#102	—	2	2	no	—
279	#102	—	2	2	no	—
280	#102	D₄×C₃₁	1	2	yes	—
281	#102	D₄×C₃₁	1	1	yes	characteristic
282	C₂²⋊C₈	—	2	1	no	—
283	C₂²⋊C₈	—	2	2	no	—
284	C₄×C₈	—	2	1	no	—
285	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
286	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
287	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
288	C₃₁	#19905	1	1	yes	characteristic, direct product factor, Sylow
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	4	2	no	—
292	C₂×Q₈	—	4	4	no	—
293	C₂×Q₈	—	8	2	no	—
294	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
295	C₂×D₄	—	4	2	no	—
296	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
297	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	4	2	no	—
301	SD₁₆	—	2	2	no	—
302	SD₁₆	—	8	2	no	—
303	D₈	—	2	2	no	—
304	M₁₆	—	8	2	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	4	2	no	—
310	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
311	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
312	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
313	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	4	2	no	—
320	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
321	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
322	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
323	C₂²⋊C₄	—	2	2	no	—
324	C₂²⋊C₄	—	2	1	no	—
325	C₂²⋊C₄	—	4	2	no	—
326	C₂²⋊C₄	—	4	2	no	—
327	C₂²⋊C₄	—	4	2	no	—
328	C₄²	—	2	1	no	—
329	C₄²	—	4	2	no	—
330	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
331	C₂³	—	2	2	no	—
332	C₂³	—	2	1	no	—
333	Q₈	—	2	1	no	—
334	Q₈	—	4	2	no	—
335	Q₈	—	4	2	no	—
336	Q₈	—	8	4	no	—
337	Q₈	—	8	2	no	—
338	Q₈	C₃₁×#135	1	2	yes	—
339	D₄	—	2	1	no	—
340	D₄	—	2	2	no	—
341	D₄	—	2	1	no	—
342	D₄	—	2	2	no	—
343	D₄	—	16	2	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	8	4	no	—
355	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
356	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
357	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
358	C₈	—	2	1	no	—
359	C₈	—	2	1	no	—
360	C₈	—	2	1	no	—
361	C₈	—	4	1	no	—
362	C₈	—	4	1	no	—
363	C₈	—	4	2	no	—
364	C₈	—	4	1	no	—
365	C₈	C₃₁×#137	1	2	yes	—
366	C₂²	—	4	1	no	—
367	C₂²	—	4	2	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	4	1	no	—
370	C₂²	—	4	1	no	—
371	C₂²	—	4	2	no	—
372	C₂²	D₄²×C₃₁	1	1	yes	characteristic
373	C₄	—	2	2	no	—
374	C₄	—	2	1	no	—
375	C₄	—	4	1	no	—
376	C₄	—	4	2	no	—
377	C₄	—	4	1	no	—
378	C₄	—	8	2	no	—
379	C₄	—	8	2	no	—
380	C₄	C₂×C₃₁×#135	1	1	yes	characteristic
381	C₄	C₂×C₃₁×#137	1	1	yes	characteristic
382	C₄	C₃₁×#576	1	1	yes	characteristic
383	C₄	C₃₁×#578	1	1	yes	characteristic
384	C₂	—	8	1	no	—
385	C₂	—	8	2	no	—
386	C₂	C₃₁×#3276	1	1	yes	characteristic
387	C₂	C₃₁×#3280	1	1	yes	characteristic
388	C₂	C₃₁×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₁
prime radical	C₃₁×#3341	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. Q₈×D₈×C₃₁	C₂	semidirect
3. C₃₁×#3329	C₂	semidirect
4. C₃₁×#1710	C₂	semidirect
5. C₃₁×#1703	C₂	semidirect
6. C₃₁×#1676	C₂	semidirect
7. C₃₁×#1673	C₂	semidirect
8. C₃₁×#1646	C₂	semidirect
9. C₃₁×#1637	C₂	semidirect
10. C₃₁×#1589	C₂	semidirect
11. C₈×SD₁₆×C₃₁	C₂	semidirect
136. #19905	C₃₁	direct (N × H)
172. Q₈×D₈	C₂×C₃₁	semidirect
174. #3329	C₂×C₃₁	semidirect
175. #1710	C₂×C₃₁	semidirect
176. #1703	C₂×C₃₁	semidirect
177. #1676	C₂×C₃₁	semidirect
178. #1673	C₂×C₃₁	semidirect
179. #1646	C₂×C₃₁	semidirect
180. #1637	C₂×C₃₁	semidirect
181. #1589	C₂×C₃₁	semidirect
182. C₈×SD₁₆	C₂×C₃₁	semidirect
288. C₃₁	#19905	direct (N × H)

Maximal subgroups

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

subgroup	index
Q₈×D₈×C₃₁	2
C₃₁×#3341	2
C₃₁×#3329	2
C₃₁×#1710	2
C₃₁×#1703	2
C₃₁×#1676	2
C₃₁×#1673	2
C₃₁×#1646	2
C₃₁×#1637	2
C₃₁×#1589	2
C₈×SD₁₆×C₃₁	2
#19905	31

Subgroups — C31×#19905 #21476664

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#19905 #21476664