Subgroups — C₃₁×#33788 #21490547

Order 7936.

594 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3177	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3155	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2251	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2248	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2244	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2242	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2211	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2207	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2189	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2187	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2164	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×AGL(1,ℤ/8)	—	2	1	no	—
13	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
14	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
15	C₃₁×#541	—	2	1	no	—
16	C₃₁×#535	—	2	1	no	—
17	C₂×C₃₁×Q₃₂	C₂²	1	2	yes	complemented
18	C₂×C₃₁×SD₃₂	C₂²	1	2	yes	—
19	C₂×C₃₁×SD₃₂	C₂²	1	2	yes	—
20	C₂×C₃₁×SD₃₂	C₂²	1	2	yes	complemented
21	C₃₁×#499	C₂²	1	1	yes	characteristic, complemented
22	C₃₁×#496	—	2	1	no	—
23	C₃₁×#496	—	2	1	no	—
24	C₃₁×#495	C₂²	1	1	yes	characteristic
25	C₃₁×#495	C₂²	1	1	yes	characteristic
26	C₃₁×#494	C₂²	1	1	yes	characteristic, complemented
27	C₃₁×#493	C₂²	1	1	yes	characteristic
28	C₃₁×#493	C₂²	1	1	yes	characteristic
29	C₃₁×#491	—	2	1	no	—
30	C₃₁×#470	—	2	1	no	—
31	C₃₁×#467	C₂²	1	2	yes	—
32	C₃₁×#441	—	2	1	no	—
33	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
34	C₃₁×#405	C₂²	1	1	yes	characteristic
35	C₃₁×C₄⋊C₁₆	C₂²	1	2	yes	complemented
36	C₃₁×#358	C₂²	1	2	yes	complemented
37	C₃₁×#357	C₂²	1	2	yes	—
38	C₃₁×#357	C₂²	1	2	yes	—
39	C₃₁×#357	C₂²	1	2	yes	complemented
40	C₃₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
41	C₃₁×#346	C₂²	1	1	yes	characteristic, complemented
42	C₄×C₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
43	C₂×#41×C₃₁	—	2	1	no	—
44	C₂²×D₄×C₃₁	—	2	1	no	—
45	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
46	C₃₁×#135	—	4	2	no	—
47	C₂×Q₁₆×C₃₁	—	2	1	no	—
48	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
49	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
50	C₂×SD₁₆×C₃₁	—	2	1	no	—
51	C₂×SD₁₆×C₃₁	—	2	1	no	—
52	C₂×SD₁₆×C₃₁	—	2	1	no	—
53	C₂×D₈×C₃₁	—	2	1	no	—
54	C₂×D₈×C₃₁	—	2	1	no	—
55	C₂×D₈×C₃₁	—	2	1	no	—
56	C₂×D₈×C₃₁	—	4	2	no	—
57	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
58	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
59	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
60	C₂×M₁₆×C₃₁	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
62	C₃₁×C₄⋊Q₈	—	2	1	no	—
63	C₃₁×#127	—	2	1	no	—
64	C₃₁×#127	—	2	1	no	—
65	C₃₁×#126	—	4	2	no	—
66	C₃₁×#125	—	2	1	no	—
67	C₃₁×#125	—	4	2	no	—
68	C₃₁×#124	—	2	1	no	—
69	C₃₁×#124	—	2	1	no	—
70	C₃₁×C₂²⋊Q₈	—	2	2	no	—
71	C₃₁×#121	—	4	2	no	—
72	C₃₁×#120	—	4	2	no	—
73	C₄×Q₈×C₃₁	—	2	2	no	—
74	C₃₁×#117	D₄	1	1	yes	characteristic
75	C₃₁×Q₃₂	—	4	2	no	—
76	C₃₁×SD₃₂	—	4	2	no	—
77	C₃₁×SD₃₂	—	4	2	no	—
78	C₃₁×SD₃₂	—	4	2	no	—
79	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
80	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
81	C₃₁×#107	C₂³	1	2	yes	—
82	C₃₁×#106	—	2	1	no	—
83	C₃₁×#103	—	2	2	no	—
84	C₃₁×#103	—	2	2	no	—
85	C₃₁×#97	D₄	1	1	yes	characteristic
86	C₃₁×#97	D₄	1	1	yes	characteristic
87	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
89	C₂⁴×C₃₁	—	4	1	no	—
90	#41×C₃₁	—	4	2	no	—
91	#41×C₃₁	—	4	2	no	—
92	C₂×Q₈×C₃₁	—	2	2	no	—
93	C₂×Q₈×C₃₁	—	2	1	no	—
94	C₂×D₄×C₃₁	—	2	1	no	—
95	C₂×D₄×C₃₁	—	2	1	no	—
96	C₂×D₄×C₃₁	—	2	1	no	—
97	C₂×D₄×C₃₁	—	4	2	no	—
98	C₂×D₄×C₃₁	—	4	2	no	—
99	C₂×D₄×C₃₁	—	4	1	no	—
100	C₂×D₄×C₃₁	—	4	1	no	—
101	C₂×D₄×C₃₁	—	4	2	no	—
102	C₂×D₄×C₃₁	—	4	2	no	—
103	C₂²×C₄×C₃₁	—	4	1	no	—
104	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
105	Q₁₆×C₃₁	—	2	2	no	—
106	Q₁₆×C₃₁	—	2	2	no	—
107	Q₁₆×C₃₁	—	2	2	no	—
108	Q₁₆×C₃₁	—	4	2	no	—
109	SD₁₆×C₃₁	—	4	2	no	—
110	SD₁₆×C₃₁	—	4	2	no	—
111	SD₁₆×C₃₁	—	4	2	no	—
112	D₈×C₃₁	—	2	2	no	—
113	D₈×C₃₁	—	2	2	no	—
114	D₈×C₃₁	—	2	2	no	—
115	D₈×C₃₁	—	4	2	no	—
116	D₈×C₃₁	—	4	2	no	—
117	D₈×C₃₁	—	4	2	no	—
118	M₁₆×C₃₁	—	2	2	no	—
119	C₂×C₈×C₃₁	—	2	2	no	—
120	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
124	C₄⋊C₄×C₃₁	—	2	2	no	—
125	C₄⋊C₄×C₃₁	—	4	2	no	—
126	C₄⋊C₄×C₃₁	—	4	2	no	—
127	C₄⋊C₄×C₃₁	—	4	2	no	—
128	C₄⋊C₄×C₃₁	—	4	2	no	—
129	C₄⋊C₄×C₃₁	D₈	1	2	yes	—
130	C₂²⋊C₄×C₃₁	—	4	2	no	—
131	C₂²⋊C₄×C₃₁	—	4	2	no	—
132	C₂²⋊C₄×C₃₁	—	4	2	no	—
133	C₂²⋊C₄×C₃₁	D₈	1	2	yes	—
134	C₄²×C₃₁	—	4	2	no	—
135	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
137	C₁₆×C₃₁	—	2	2	no	—
138	C₁₆×C₃₁	—	2	2	no	—
139	#33788	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂³×C₃₁	—	4	1	no	—
141	C₂³×C₃₁	—	4	1	no	—
142	C₂³×C₃₁	—	4	1	no	—
143	C₂³×C₃₁	—	8	2	no	—
144	C₂³×C₃₁	—	16	2	no	—
145	C₂³×C₃₁	C₂×D₈	1	1	yes	characteristic
146	Q₈×C₃₁	—	4	1	no	—
147	Q₈×C₃₁	—	4	2	no	—
148	Q₈×C₃₁	—	4	1	no	—
149	Q₈×C₃₁	—	4	2	no	—
150	D₄×C₃₁	—	4	1	no	—
151	D₄×C₃₁	—	4	1	no	—
152	D₄×C₃₁	—	4	1	no	—
153	D₄×C₃₁	—	4	1	no	—
154	D₄×C₃₁	—	4	1	no	—
155	D₄×C₃₁	—	4	1	no	—
156	D₄×C₃₁	—	8	2	no	—
157	D₄×C₃₁	—	8	2	no	—
158	D₄×C₃₁	—	16	2	no	—
159	D₄×C₃₁	—	16	2	no	—
160	C₂×C₄×C₃₁	—	2	1	no	—
161	C₂×C₄×C₃₁	—	2	1	no	—
162	C₂×C₄×C₃₁	—	4	2	no	—
163	C₂×C₄×C₃₁	—	4	2	no	—
164	C₂×C₄×C₃₁	—	4	1	no	—
165	C₂×C₄×C₃₁	—	8	2	no	—
166	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
167	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
168	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
169	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
170	C₈×C₃₁	—	2	1	no	—
171	C₈×C₃₁	—	2	1	no	—
172	C₈×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
173	C₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
174	#3177	C₂×C₃₁	1	1	yes	characteristic, complemented
175	#3155	C₂×C₃₁	1	1	yes	characteristic
176	#2251	C₂×C₃₁	1	1	yes	characteristic, complemented
177	#2248	C₂×C₃₁	1	1	yes	characteristic, complemented
178	#2244	C₂×C₃₁	1	1	yes	characteristic, complemented
179	#2242	C₂×C₃₁	1	1	yes	characteristic, complemented
180	#2211	C₂×C₃₁	1	2	yes	complemented
181	#2207	C₂×C₃₁	1	2	yes	complemented
182	#2189	C₂×C₃₁	1	2	yes	complemented
183	#2187	C₂×C₃₁	1	2	yes	complemented
184	#2164	C₂×C₃₁	1	1	yes	characteristic, complemented
185	C₂²×C₃₁	—	2	2	no	—
186	C₂²×C₃₁	—	2	1	no	—
187	C₂²×C₃₁	—	8	2	no	—
188	C₂²×C₃₁	—	8	2	no	—
189	C₂²×C₃₁	—	8	2	no	—
190	C₂²×C₃₁	—	8	1	no	—
191	C₂²×C₃₁	—	8	1	no	—
192	C₂²×C₃₁	—	8	1	no	—
193	C₂²×C₃₁	—	16	4	no	—
194	C₂²×C₃₁	C₂²×D₈	1	1	yes	characteristic
195	C₄×C₃₁	—	2	2	no	—
196	C₄×C₃₁	—	2	2	no	—
197	C₄×C₃₁	—	2	1	no	—
198	C₄×C₃₁	—	8	2	no	—
199	C₄×C₃₁	—	8	1	no	—
200	C₄×C₃₁	—	8	2	no	—
201	C₄×C₃₁	#535	1	1	yes	characteristic
202	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
203	C₂×AGL(1,ℤ/8)	—	2	1	no	—
204	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
205	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
206	#541	—	2	1	no	—
207	#535	—	2	1	no	—
208	C₂×Q₃₂	C₂²×C₃₁	1	2	yes	complemented
209	C₂×SD₃₂	C₂²×C₃₁	1	2	yes	—
210	C₂×SD₃₂	C₂²×C₃₁	1	2	yes	—
211	C₂×SD₃₂	C₂²×C₃₁	1	2	yes	complemented
212	#499	C₂²×C₃₁	1	1	yes	characteristic, complemented
213	#496	—	2	1	no	—
214	#496	—	2	1	no	—
215	#495	C₂²×C₃₁	1	1	yes	characteristic
216	#495	C₂²×C₃₁	1	1	yes	characteristic
217	#494	C₂²×C₃₁	1	1	yes	characteristic, complemented
218	#493	C₂²×C₃₁	1	1	yes	characteristic
219	#493	C₂²×C₃₁	1	1	yes	characteristic
220	#491	—	2	1	no	—
221	#470	—	2	1	no	—
222	#467	C₂²×C₃₁	1	2	yes	—
223	#441	—	2	1	no	—
224	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
225	#405	C₂²×C₃₁	1	1	yes	characteristic
226	C₄⋊C₁₆	C₂²×C₃₁	1	2	yes	complemented
227	#358	C₂²×C₃₁	1	2	yes	complemented
228	#357	C₂²×C₃₁	1	2	yes	—
229	#357	C₂²×C₃₁	1	2	yes	—
230	#357	C₂²×C₃₁	1	2	yes	complemented
231	C₂²⋊C₁₆	C₂²×C₃₁	1	2	yes	—
232	#346	C₂²×C₃₁	1	1	yes	characteristic, complemented
233	C₄×C₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
234	C₂×C₃₁	—	4	1	no	—
235	C₂×C₃₁	—	16	1	no	—
236	C₂×C₃₁	—	16	1	no	—
237	C₂×C₃₁	—	16	1	no	—
238	C₂×C₃₁	#3205	1	1	yes	characteristic
239	C₂×C₃₁	#3416	1	2	yes	—
240	C₂×#41	—	2	1	no	—
241	C₂²×D₄	—	2	1	no	—
242	AGL(1,ℤ/8)	—	4	4	no	—
243	#135	—	4	2	no	—
244	C₂×Q₁₆	—	2	1	no	—
245	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
246	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
247	C₂×SD₁₆	—	2	1	no	—
248	C₂×SD₁₆	—	2	1	no	—
249	C₂×SD₁₆	—	2	1	no	—
250	C₂×D₈	—	2	1	no	—
251	C₂×D₈	—	2	1	no	—
252	C₂×D₈	—	2	1	no	—
253	C₂×D₈	—	4	2	no	—
254	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
255	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
256	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
257	C₂×M₁₆	D₄×C₃₁	1	1	yes	characteristic
258	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
259	C₄⋊Q₈	—	2	1	no	—
260	#127	—	2	1	no	—
261	#127	—	2	1	no	—
262	#126	—	4	2	no	—
263	#125	—	2	1	no	—
264	#125	—	4	2	no	—
265	#124	—	2	1	no	—
266	#124	—	2	1	no	—
267	C₂²⋊Q₈	—	2	2	no	—
268	#121	—	4	2	no	—
269	#120	—	4	2	no	—
270	C₄×Q₈	—	2	2	no	—
271	#117	D₄×C₃₁	1	1	yes	characteristic
272	Q₃₂	—	4	2	no	—
273	SD₃₂	—	4	2	no	—
274	SD₃₂	—	4	2	no	—
275	SD₃₂	—	4	2	no	—
276	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
277	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
278	#107	C₂³×C₃₁	1	2	yes	—
279	#106	—	2	1	no	—
280	#103	—	2	2	no	—
281	#103	—	2	2	no	—
282	#97	D₄×C₃₁	1	1	yes	characteristic
283	#97	D₄×C₃₁	1	1	yes	characteristic
284	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
285	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
286	C₃₁	#33788	1	1	yes	characteristic, direct product factor, Sylow
287	C₂⁴	—	4	1	no	—
288	#41	—	4	2	no	—
289	#41	—	4	2	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	1	no	—
292	C₂×D₄	—	2	1	no	—
293	C₂×D₄	—	2	1	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	4	2	no	—
296	C₂×D₄	—	4	2	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂×D₄	—	4	1	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
303	Q₁₆	—	2	2	no	—
304	Q₁₆	—	2	2	no	—
305	Q₁₆	—	2	2	no	—
306	Q₁₆	—	4	2	no	—
307	SD₁₆	—	4	2	no	—
308	SD₁₆	—	4	2	no	—
309	SD₁₆	—	4	2	no	—
310	D₈	—	2	2	no	—
311	D₈	—	2	2	no	—
312	D₈	—	2	2	no	—
313	D₈	—	4	2	no	—
314	D₈	—	4	2	no	—
315	D₈	—	4	2	no	—
316	M₁₆	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
319	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
320	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
321	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₄⋊C₄	—	4	2	no	—
325	C₄⋊C₄	—	4	2	no	—
326	C₄⋊C₄	—	4	2	no	—
327	C₄⋊C₄	D₈×C₃₁	1	2	yes	—
328	C₂²⋊C₄	—	4	2	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₂²⋊C₄	—	4	2	no	—
331	C₂²⋊C₄	D₈×C₃₁	1	2	yes	—
332	C₄²	—	4	2	no	—
333	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
334	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
335	C₁₆	—	2	2	no	—
336	C₁₆	—	2	2	no	—
337	C₂³	—	4	1	no	—
338	C₂³	—	4	1	no	—
339	C₂³	—	4	1	no	—
340	C₂³	—	8	2	no	—
341	C₂³	—	16	2	no	—
342	C₂³	C₂×D₈×C₃₁	1	1	yes	characteristic
343	Q₈	—	4	1	no	—
344	Q₈	—	4	2	no	—
345	Q₈	—	4	1	no	—
346	Q₈	—	4	2	no	—
347	D₄	—	4	1	no	—
348	D₄	—	4	1	no	—
349	D₄	—	4	1	no	—
350	D₄	—	4	1	no	—
351	D₄	—	4	1	no	—
352	D₄	—	4	1	no	—
353	D₄	—	8	2	no	—
354	D₄	—	8	2	no	—
355	D₄	—	16	2	no	—
356	D₄	—	16	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	8	2	no	—
363	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
364	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
365	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
366	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
367	C₈	—	2	1	no	—
368	C₈	—	2	1	no	—
369	C₈	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
370	C₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
371	C₂²	—	2	2	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	8	1	no	—
377	C₂²	—	8	1	no	—
378	C₂²	—	8	1	no	—
379	C₂²	—	16	4	no	—
380	C₂²	C₂²×D₈×C₃₁	1	1	yes	characteristic
381	C₄	—	2	2	no	—
382	C₄	—	2	2	no	—
383	C₄	—	2	1	no	—
384	C₄	—	8	2	no	—
385	C₄	—	8	1	no	—
386	C₄	—	8	2	no	—
387	C₄	C₃₁×#535	1	1	yes	characteristic
388	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
389	C₂	—	4	1	no	—
390	C₂	—	16	1	no	—
391	C₂	—	16	1	no	—
392	C₂	—	16	1	no	—
393	C₂	C₃₁×#3205	1	1	yes	characteristic
394	C₂	C₃₁×#3416	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₃₁
prime radical	C₃₁×#3155	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#117 ◁ C₃₁×#405 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3177	C₂	semidirect
3. C₃₁×#2251	C₂	semidirect
4. C₃₁×#2248	C₂	semidirect
5. C₃₁×#2244	C₂	semidirect
6. C₃₁×#2242	C₂	semidirect
7. C₃₁×#2211	C₂	semidirect
8. C₃₁×#2207	C₂	semidirect
9. C₃₁×#2189	C₂	semidirect
10. C₃₁×#2187	C₂	semidirect
11. C₃₁×#2164	C₂	semidirect
17. C₂×C₃₁×Q₃₂	C₂²	semidirect
20. C₂×C₃₁×SD₃₂	C₂²	semidirect
21. C₃₁×#499	C₂²	semidirect
26. C₃₁×#494	C₂²	semidirect
33. C₄×Q₁₆×C₃₁	C₂²	semidirect
35. C₃₁×C₄⋊C₁₆	C₂²	semidirect
36. C₃₁×#358	C₂²	semidirect
39. C₃₁×#357	C₂²	semidirect
41. C₃₁×#346	C₂²	semidirect
42. C₄×C₁₆×C₃₁	C₂²	semidirect
139. #33788	C₃₁	direct (N × H)
174. #3177	C₂×C₃₁	semidirect
176. #2251	C₂×C₃₁	semidirect
177. #2248	C₂×C₃₁	semidirect
178. #2244	C₂×C₃₁	semidirect
179. #2242	C₂×C₃₁	semidirect
180. #2211	C₂×C₃₁	semidirect
181. #2207	C₂×C₃₁	semidirect
182. #2189	C₂×C₃₁	semidirect
183. #2187	C₂×C₃₁	semidirect
184. #2164	C₂×C₃₁	semidirect
208. C₂×Q₃₂	C₂²×C₃₁	semidirect
211. C₂×SD₃₂	C₂²×C₃₁	semidirect
212. #499	C₂²×C₃₁	semidirect
217. #494	C₂²×C₃₁	semidirect
224. C₄×Q₁₆	C₂²×C₃₁	semidirect
226. C₄⋊C₁₆	C₂²×C₃₁	semidirect
227. #358	C₂²×C₃₁	semidirect
230. #357	C₂²×C₃₁	semidirect
232. #346	C₂²×C₃₁	semidirect
233. C₄×C₁₆	C₂²×C₃₁	semidirect
286. C₃₁	#33788	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#3177	2
C₃₁×#3155	2
C₃₁×#2251	2
C₃₁×#2248	2
C₃₁×#2244	2
C₃₁×#2242	2
C₃₁×#2211	2
C₃₁×#2207	2
C₃₁×#2189	2
C₃₁×#2187	2
C₃₁×#2164	2
#33788	31

Subgroups — C31×#33788 #21490547

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33788 #21490547