Subgroups — C₃₁×#12554 #21469313

Order 7936.

586 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃₁×M₃₂	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₁×#405	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1379	C₂	1	4	yes	maximal, complemented
5	C₂²×M₁₆×C₃₁	C₄	1	1	yes	characteristic
6	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
7	C₂×C₃₁×#117	C₄	1	1	yes	characteristic
8	C₂×C₃₁×M₃₂	—	2	2	no	—
9	C₂×C₃₁×M₃₂	—	2	2	no	—
10	C₂×C₃₁×M₃₂	—	2	1	no	—
11	C₂×C₃₁×M₃₂	—	2	1	no	—
12	C₂×C₃₁×M₃₂	—	2	1	no	—
13	C₂×C₃₁×M₃₂	C₄	1	4	yes	complemented
14	C₂×C₃₁×M₃₂	C₄	1	4	yes	complemented
15	C₂×C₃₁×M₃₂	C₂²	1	2	yes	—
16	C₂²×C₁₆×C₃₁	—	2	1	no	—
17	C₂²×C₁₆×C₃₁	C₂²	1	2	yes	—
18	C₃₁×#405	—	2	1	no	—
19	C₃₁×#405	—	2	1	no	—
20	C₃₁×#405	C₄	1	2	yes	—
21	C₃₁×#405	C₂²	1	2	yes	—
22	C₂×C₃₁×#97	—	2	1	no	—
23	C₂×C₄×C₈×C₃₁	—	2	1	no	—
24	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
25	C₂×M₁₆×C₃₁	—	2	1	no	—
26	C₂×M₁₆×C₃₁	—	2	2	no	—
27	C₂×M₁₆×C₃₁	C₈	1	4	yes	—
28	C₂×M₁₆×C₃₁	C₂×C₄	1	2	yes	—
29	C₂²×C₈×C₃₁	—	2	1	no	—
30	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₈×C₃₁	C₂×C₄	1	2	yes	—
32	C₂²×C₈×C₃₁	C₂×C₄	1	2	yes	—
33	C₂²×C₈×C₃₁	D₄	1	2	yes	—
34	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
35	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
36	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
37	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
38	C₂²×C₈×C₃₁	Q₈	1	2	yes	—
39	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
40	C₃₁×#117	—	2	1	no	—
41	C₃₁×#117	—	2	1	no	—
42	C₃₁×#117	C₈	1	2	yes	—
43	C₃₁×#117	C₂×C₄	1	2	yes	—
44	C₂×C₄⋊C₄×C₃₁	C₈	1	2	yes	—
45	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
46	C₂×C₄²×C₃₁	—	2	1	no	—
47	C₃₁×M₃₂	—	2	4	no	—
48	C₃₁×M₃₂	—	2	4	no	—
49	C₃₁×M₃₂	—	2	4	no	—
50	C₃₁×M₃₂	—	2	2	no	—
51	C₃₁×M₃₂	C₂×C₄	1	4	yes	complemented
52	C₂×C₁₆×C₃₁	—	2	4	no	—
53	C₂×C₁₆×C₃₁	—	2	2	no	—
54	C₂×C₁₆×C₃₁	—	2	2	no	—
55	C₂×C₁₆×C₃₁	—	2	2	no	—
56	C₂×C₁₆×C₃₁	C₂×C₄	1	4	yes	complemented
57	C₃₁×#97	—	2	2	no	—
58	C₃₁×#97	—	2	2	no	—
59	C₄×C₈×C₃₁	—	2	2	no	—
60	C₄×C₈×C₃₁	—	2	2	no	—
61	C₂⁴×C₃₁	M₁₆	1	1	yes	characteristic
62	C₂²×C₄×C₃₁	—	2	2	no	—
63	C₂²×C₄×C₃₁	C₄²	1	2	yes	—
64	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₃₁	C₄⋊C₄	1	2	yes	—
67	C₂²×C₄×C₃₁	C₂×C₈	1	2	yes	—
68	C₂²×C₄×C₃₁	C₂×C₈	1	1	yes	characteristic
69	C₂²×C₄×C₃₁	C₂×C₈	1	1	yes	characteristic
70	C₂²×C₄×C₃₁	M₁₆	1	1	yes	characteristic
71	C₂²×C₄×C₃₁	M₁₆	1	2	yes	—
72	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
73	M₁₆×C₃₁	—	2	4	no	—
74	M₁₆×C₃₁	—	2	2	no	—
75	M₁₆×C₃₁	C₂×C₈	1	4	yes	—
76	C₂×C₈×C₃₁	—	2	4	no	—
77	C₂×C₈×C₃₁	—	2	2	no	—
78	C₂×C₈×C₃₁	C₄²	1	2	yes	—
79	C₂×C₈×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
80	C₂×C₈×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₈×C₃₁	C₂²⋊C₄	1	2	yes	—
82	C₂×C₈×C₃₁	C₂²⋊C₄	1	2	yes	—
83	C₂×C₈×C₃₁	C₂²⋊C₄	1	2	yes	—
84	C₂×C₈×C₃₁	C₂²⋊C₄	1	2	yes	—
85	C₂×C₈×C₃₁	C₄⋊C₄	1	2	yes	—
86	C₂×C₈×C₃₁	C₄⋊C₄	1	2	yes	—
87	C₂×C₈×C₃₁	C₄⋊C₄	1	2	yes	—
88	C₂×C₈×C₃₁	C₄⋊C₄	1	2	yes	—
89	C₂×C₈×C₃₁	C₄⋊C₄	1	2	yes	—
90	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
93	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
94	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
95	C₂×C₈×C₃₁	C₂×Q₈	1	1	yes	characteristic
96	C₄⋊C₄×C₃₁	—	2	2	no	—
97	C₄⋊C₄×C₃₁	C₂×C₈	1	4	yes	—
98	C₂²⋊C₄×C₃₁	—	2	2	no	—
99	C₂²⋊C₄×C₃₁	—	2	2	no	—
100	C₄²×C₃₁	—	2	2	no	—
101	C₄²×C₃₁	—	2	2	no	—
102	C₁₆×C₃₁	—	2	4	no	—
103	C₁₆×C₃₁	—	2	4	no	—
104	#12554	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
105	C₂³×C₃₁	—	4	2	no	—
106	C₂³×C₃₁	#97	1	2	yes	—
107	C₂³×C₃₁	C₂²⋊C₈	1	1	yes	characteristic
108	C₂³×C₃₁	C₂²⋊C₈	1	1	yes	characteristic
109	C₂³×C₃₁	C₄⋊C₈	1	2	yes	—
110	C₂³×C₃₁	C₂×M₁₆	1	1	yes	characteristic
111	C₂×C₄×C₃₁	—	2	4	no	—
112	C₂×C₄×C₃₁	—	4	4	no	—
113	C₂×C₄×C₃₁	#95	1	2	yes	—
114	C₂×C₄×C₃₁	#95	1	2	yes	—
115	C₂×C₄×C₃₁	C₄×C₈	1	2	yes	—
116	C₂×C₄×C₃₁	C₄×C₈	1	2	yes	—
117	C₂×C₄×C₃₁	#97	1	2	yes	—
118	C₂×C₄×C₃₁	C₂²⋊C₈	1	1	yes	characteristic
119	C₂×C₄×C₃₁	C₂²⋊C₈	1	1	yes	characteristic
120	C₂×C₄×C₃₁	C₂²⋊C₈	1	2	yes	—
121	C₂×C₄×C₃₁	C₂²⋊C₈	1	2	yes	—
122	C₂×C₄×C₃₁	C₄⋊C₈	1	2	yes	—
123	C₂×C₄×C₃₁	C₄⋊C₈	1	2	yes	—
124	C₂×C₄×C₃₁	C₄⋊C₈	1	2	yes	—
125	C₂×C₄×C₃₁	C₂×C₄²	1	1	yes	characteristic
126	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
127	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
128	C₂×C₄×C₃₁	C₂²×C₈	1	1	yes	characteristic
129	C₂×C₄×C₃₁	C₂²×C₈	1	1	yes	characteristic
130	C₂×C₄×C₃₁	C₂×M₁₆	1	1	yes	characteristic
131	C₈×C₃₁	—	2	4	no	—
132	C₈×C₃₁	#95	1	2	yes	—
133	C₈×C₃₁	#95	1	2	yes	—
134	C₈×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	C₈×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	C₈×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₈×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂²×M₃₂	C₂×C₃₁	1	1	yes	characteristic
139	C₂²×M₃₂	C₂×C₃₁	1	1	yes	characteristic
140	C₂×#405	C₂×C₃₁	1	1	yes	characteristic
141	#1379	C₂×C₃₁	1	4	yes	complemented
142	C₂²×C₃₁	—	2	2	no	—
143	C₂²×C₃₁	—	2	2	no	—
144	C₂²×C₃₁	—	2	2	no	—
145	C₂²×C₃₁	—	4	2	no	—
146	C₂²×C₃₁	—	4	2	no	—
147	C₂²×C₃₁	#336	1	2	yes	—
148	C₂²×C₃₁	#336	1	2	yes	—
149	C₂²×C₃₁	C₂×#97	1	1	yes	characteristic
150	C₂²×C₃₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
151	C₂²×C₃₁	C₂×C₄⋊C₈	1	1	yes	characteristic
152	C₄×C₃₁	—	4	4	no	—
153	C₄×C₃₁	#336	1	2	yes	—
154	C₄×C₃₁	#336	1	2	yes	—
155	C₄×C₃₁	C₂×#95	1	1	yes	characteristic
156	C₄×C₃₁	C₂×C₄×C₈	1	1	yes	characteristic
157	C₄×C₃₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
158	C₄×C₃₁	C₂×C₄⋊C₈	1	1	yes	characteristic
159	C₂²×M₁₆	C₄×C₃₁	1	1	yes	characteristic
160	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
161	C₂×#117	C₄×C₃₁	1	1	yes	characteristic
162	C₂×M₃₂	—	2	2	no	—
163	C₂×M₃₂	—	2	1	no	—
164	C₂×M₃₂	—	2	2	no	—
165	C₂×M₃₂	—	2	1	no	—
166	C₂×M₃₂	—	2	1	no	—
167	C₂×M₃₂	C₄×C₃₁	1	4	yes	complemented
168	C₂×M₃₂	C₄×C₃₁	1	4	yes	complemented
169	C₂×M₃₂	C₂²×C₃₁	1	2	yes	—
170	C₂²×C₁₆	—	2	1	no	—
171	C₂²×C₁₆	C₂²×C₃₁	1	2	yes	—
172	#405	—	2	1	no	—
173	#405	—	2	1	no	—
174	#405	C₄×C₃₁	1	2	yes	—
175	#405	C₂²×C₃₁	1	2	yes	—
176	C₂×#97	—	2	1	no	—
177	C₂×C₄×C₈	—	2	1	no	—
178	C₂×C₃₁	—	2	2	no	—
179	C₂×C₃₁	—	2	2	no	—
180	C₂×C₃₁	—	2	1	no	—
181	C₂×C₃₁	—	2	1	no	—
182	C₂×C₃₁	C₂×#336	1	1	yes	characteristic
183	C₂×C₃₁	#2117	1	2	yes	—
184	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
185	C₂×M₁₆	—	2	1	no	—
186	C₂×M₁₆	—	2	2	no	—
187	C₂×M₁₆	C₈×C₃₁	1	4	yes	—
188	C₂×M₁₆	C₂×C₄×C₃₁	1	2	yes	—
189	C₂²×C₈	—	2	1	no	—
190	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
191	C₂²×C₈	C₂×C₄×C₃₁	1	2	yes	—
192	C₂²×C₈	C₂×C₄×C₃₁	1	2	yes	—
193	C₂²×C₈	D₄×C₃₁	1	2	yes	—
194	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
195	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
196	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
197	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
198	C₂²×C₈	Q₈×C₃₁	1	2	yes	—
199	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
200	#117	—	2	1	no	—
201	#117	—	2	1	no	—
202	#117	C₈×C₃₁	1	2	yes	—
203	#117	C₂×C₄×C₃₁	1	2	yes	—
204	C₂×C₄⋊C₄	C₈×C₃₁	1	2	yes	—
205	C₂×C₂²⋊C₄	—	2	1	no	—
206	C₂×C₄²	—	2	1	no	—
207	M₃₂	—	2	4	no	—
208	M₃₂	—	2	4	no	—
209	M₃₂	—	2	4	no	—
210	M₃₂	—	2	2	no	—
211	M₃₂	C₂×C₄×C₃₁	1	4	yes	complemented
212	C₂×C₁₆	—	2	4	no	—
213	C₂×C₁₆	—	2	2	no	—
214	C₂×C₁₆	—	2	2	no	—
215	C₂×C₁₆	—	2	2	no	—
216	C₂×C₁₆	C₂×C₄×C₃₁	1	4	yes	complemented
217	#97	—	2	2	no	—
218	#97	—	2	2	no	—
219	C₄×C₈	—	2	2	no	—
220	C₄×C₈	—	2	2	no	—
221	C₃₁	#12554	1	1	yes	characteristic, direct product factor, Sylow
222	C₂⁴	M₁₆×C₃₁	1	1	yes	characteristic
223	C₂²×C₄	—	2	2	no	—
224	C₂²×C₄	C₄²×C₃₁	1	2	yes	—
225	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
226	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
227	C₂²×C₄	C₄⋊C₄×C₃₁	1	2	yes	—
228	C₂²×C₄	C₂×C₈×C₃₁	1	2	yes	—
229	C₂²×C₄	C₂×C₈×C₃₁	1	1	yes	characteristic
230	C₂²×C₄	C₂×C₈×C₃₁	1	1	yes	characteristic
231	C₂²×C₄	M₁₆×C₃₁	1	1	yes	characteristic
232	C₂²×C₄	M₁₆×C₃₁	1	2	yes	—
233	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
234	M₁₆	—	2	4	no	—
235	M₁₆	—	2	2	no	—
236	M₁₆	C₂×C₈×C₃₁	1	4	yes	—
237	C₂×C₈	—	2	4	no	—
238	C₂×C₈	—	2	2	no	—
239	C₂×C₈	C₄²×C₃₁	1	2	yes	—
240	C₂×C₈	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
241	C₂×C₈	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
242	C₂×C₈	C₂²⋊C₄×C₃₁	1	2	yes	—
243	C₂×C₈	C₂²⋊C₄×C₃₁	1	2	yes	—
244	C₂×C₈	C₂²⋊C₄×C₃₁	1	2	yes	—
245	C₂×C₈	C₂²⋊C₄×C₃₁	1	2	yes	—
246	C₂×C₈	C₄⋊C₄×C₃₁	1	2	yes	—
247	C₂×C₈	C₄⋊C₄×C₃₁	1	2	yes	—
248	C₂×C₈	C₄⋊C₄×C₃₁	1	2	yes	—
249	C₂×C₈	C₄⋊C₄×C₃₁	1	2	yes	—
250	C₂×C₈	C₄⋊C₄×C₃₁	1	2	yes	—
251	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
252	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
253	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
254	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
255	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
256	C₂×C₈	C₂×Q₈×C₃₁	1	1	yes	characteristic
257	C₄⋊C₄	—	2	2	no	—
258	C₄⋊C₄	C₂×C₈×C₃₁	1	4	yes	—
259	C₂²⋊C₄	—	2	2	no	—
260	C₂²⋊C₄	—	2	2	no	—
261	C₄²	—	2	2	no	—
262	C₄²	—	2	2	no	—
263	C₁₆	—	2	4	no	—
264	C₁₆	—	2	4	no	—
265	C₂³	—	4	2	no	—
266	C₂³	C₃₁×#97	1	2	yes	—
267	C₂³	C₃₁×C₂²⋊C₈	1	1	yes	characteristic
268	C₂³	C₃₁×C₂²⋊C₈	1	1	yes	characteristic
269	C₂³	C₃₁×C₄⋊C₈	1	2	yes	—
270	C₂³	C₂×M₁₆×C₃₁	1	1	yes	characteristic
271	C₂×C₄	—	2	4	no	—
272	C₂×C₄	—	4	4	no	—
273	C₂×C₄	C₃₁×#95	1	2	yes	—
274	C₂×C₄	C₃₁×#95	1	2	yes	—
275	C₂×C₄	C₄×C₈×C₃₁	1	2	yes	—
276	C₂×C₄	C₄×C₈×C₃₁	1	2	yes	—
277	C₂×C₄	C₃₁×#97	1	2	yes	—
278	C₂×C₄	C₃₁×C₂²⋊C₈	1	2	yes	—
279	C₂×C₄	C₃₁×C₂²⋊C₈	1	2	yes	—
280	C₂×C₄	C₃₁×C₂²⋊C₈	1	1	yes	characteristic
281	C₂×C₄	C₃₁×C₂²⋊C₈	1	1	yes	characteristic
282	C₂×C₄	C₃₁×C₄⋊C₈	1	2	yes	—
283	C₂×C₄	C₃₁×C₄⋊C₈	1	2	yes	—
284	C₂×C₄	C₃₁×C₄⋊C₈	1	2	yes	—
285	C₂×C₄	C₂×C₄²×C₃₁	1	1	yes	characteristic
286	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
287	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
288	C₂×C₄	C₂²×C₈×C₃₁	1	1	yes	characteristic
289	C₂×C₄	C₂²×C₈×C₃₁	1	1	yes	characteristic
290	C₂×C₄	C₂×M₁₆×C₃₁	1	1	yes	characteristic
291	C₈	—	2	4	no	—
292	C₈	C₃₁×#95	1	2	yes	—
293	C₈	C₃₁×#95	1	2	yes	—
294	C₈	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
295	C₈	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
296	C₈	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
297	C₈	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
298	C₂²	—	2	2	no	—
299	C₂²	—	2	2	no	—
300	C₂²	—	2	2	no	—
301	C₂²	—	4	2	no	—
302	C₂²	—	4	2	no	—
303	C₂²	C₃₁×#336	1	2	yes	—
304	C₂²	C₃₁×#336	1	2	yes	—
305	C₂²	C₂×C₃₁×#97	1	1	yes	characteristic
306	C₂²	C₂×C₃₁×C₂²⋊C₈	1	1	yes	characteristic
307	C₂²	C₂×C₃₁×C₄⋊C₈	1	1	yes	characteristic
308	C₄	—	4	4	no	—
309	C₄	C₃₁×#336	1	2	yes	—
310	C₄	C₃₁×#336	1	2	yes	—
311	C₄	C₂×C₃₁×#95	1	1	yes	characteristic
312	C₄	C₂×C₄×C₈×C₃₁	1	1	yes	characteristic
313	C₄	C₂×C₃₁×C₂²⋊C₈	1	1	yes	characteristic
314	C₄	C₂×C₃₁×C₄⋊C₈	1	1	yes	characteristic
315	C₂	—	2	1	no	—
316	C₂	—	2	1	no	—
317	C₂	—	2	2	no	—
318	C₂	—	2	2	no	—
319	C₂	C₂×C₃₁×#336	1	1	yes	characteristic
320	C₂	C₃₁×#2117	1	2	yes	—

	subgroup	G/H
center	C₂×C₈×C₃₁	C₂×D₄
commutator	C₄	C₂×C₄×C₈×C₃₁
Frattini, cosocle	C₂²×C₈	C₂³×C₃₁
socle	C₂²×C₃₁	C₂×C₂²⋊C₈
prime radical	C₂⁴×C₃₁	M₁₆
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₃₁ ◁ C₂³×C₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₃₁×#1379	C₂	semidirect
13. C₂×C₃₁×M₃₂	C₄	semidirect
14. C₂×C₃₁×M₃₂	C₄	semidirect
51. C₃₁×M₃₂	C₂×C₄	semidirect
56. C₂×C₁₆×C₃₁	C₂×C₄	semidirect
104. #12554	C₃₁	direct (N × H)
141. #1379	C₂×C₃₁	semidirect
167. C₂×M₃₂	C₄×C₃₁	semidirect
168. C₂×M₃₂	C₄×C₃₁	semidirect
211. M₃₂	C₂×C₄×C₃₁	semidirect
216. C₂×C₁₆	C₂×C₄×C₃₁	semidirect
221. C₃₁	#12554	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×C₃₁×M₃₂	2
C₂×C₃₁×#405	2
C₃₁×#1379	2
#12554	31

Subgroups — C31×#12554 #21469313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#12554 #21469313