Subgroups — C₃₁×#12683 #21469442

Order 7936.

936 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×#131	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#350	C₂	1	4	yes	maximal, complemented
3	C₃₁×#2112	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₁×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#41×C₃₁	C₄	1	1	yes	characteristic
6	C₂×C₃₁×#131	—	2	8	no	—
7	C₂×C₃₁×#131	—	2	1	no	—
8	C₂×C₃₁×#131	—	2	1	no	—
9	C₂×C₃₁×#131	C₄	1	2	yes	—
10	C₂×C₃₁×#131	C₂²	1	2	yes	—
11	C₂²×M₁₆×C₃₁	—	2	1	no	—
12	C₂²×M₁₆×C₃₁	C₄	1	1	yes	characteristic
13	C₂³×C₈×C₃₁	—	2	1	no	—
14	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
15	C₂×C₃₁×M₃₂	C₂²	1	2	yes	complemented
16	C₂²×C₁₆×C₃₁	C₂²	1	2	yes	complemented
17	C₃₁×#350	—	2	8	no	—
18	C₃₁×C₂²⋊C₁₆	—	2	1	no	—
19	C₃₁×C₂²⋊C₁₆	—	2	1	no	—
20	C₃₁×C₂²⋊C₁₆	—	2	1	no	—
21	C₃₁×C₂²⋊C₁₆	—	2	1	no	—
22	C₂×#41×C₃₁	—	2	4	no	—
23	C₂×#41×C₃₁	—	2	4	no	—
24	C₂×#41×C₃₁	—	2	1	no	—
25	C₂×#41×C₃₁	—	2	1	no	—
26	C₂×#41×C₃₁	C₈	1	2	yes	—
27	C₂×#41×C₃₁	C₂×C₄	1	2	yes	—
28	C₂²×Q₈×C₃₁	C₈	1	1	yes	characteristic
29	C₂²×D₄×C₃₁	—	2	1	no	—
30	C₂²×D₄×C₃₁	C₈	1	1	yes	characteristic
31	C₂³×C₄×C₃₁	—	2	1	no	—
32	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
33	C₃₁×#131	—	2	8	no	—
34	C₃₁×#131	—	2	8	no	—
35	C₃₁×#131	—	2	4	no	—
36	C₃₁×#131	—	2	4	no	—
37	C₃₁×#131	—	2	4	no	—
38	C₃₁×#131	D₄	1	8	yes	—
39	C₂×M₁₆×C₃₁	—	2	8	no	—
40	C₂×M₁₆×C₃₁	—	2	1	no	—
41	C₂×M₁₆×C₃₁	—	2	4	no	—
42	C₂×M₁₆×C₃₁	—	2	2	no	—
43	C₂×M₁₆×C₃₁	—	2	2	no	—
44	C₂×M₁₆×C₃₁	C₂×C₄	1	2	yes	—
45	C₂²×C₈×C₃₁	—	2	8	no	—
46	C₂²×C₈×C₃₁	—	2	1	no	—
47	C₂²×C₈×C₃₁	—	2	2	no	—
48	C₂²×C₈×C₃₁	—	2	4	no	—
49	C₂²×C₈×C₃₁	—	2	2	no	—
50	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
52	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
53	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
54	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
55	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
56	C₃₁×M₃₂	—	2	4	no	—
57	C₂×C₁₆×C₃₁	—	2	2	no	—
58	C₂×C₁₆×C₃₁	—	2	4	no	—
59	C₂×C₁₆×C₃₁	—	2	2	no	—
60	C₂⁴×C₃₁	—	2	1	no	—
61	C₂⁴×C₃₁	M₁₆	1	1	yes	characteristic
62	#41×C₃₁	—	2	4	no	—
63	#41×C₃₁	—	2	8	no	—
64	#41×C₃₁	—	2	4	no	—
65	#41×C₃₁	—	2	4	no	—
66	#41×C₃₁	—	2	4	no	—
67	#41×C₃₁	—	2	2	no	—
68	#41×C₃₁	—	2	2	no	—
69	#41×C₃₁	C₂²⋊C₄	1	4	yes	—
70	#41×C₃₁	M₁₆	1	4	yes	—
71	C₂×Q₈×C₃₁	—	2	4	no	—
72	C₂×Q₈×C₃₁	—	2	1	no	—
73	C₂×Q₈×C₃₁	C₂×C₈	1	2	yes	—
74	C₂×D₄×C₃₁	—	2	8	no	—
75	C₂×D₄×C₃₁	—	2	2	no	—
76	C₂×D₄×C₃₁	—	2	2	no	—
77	C₂×D₄×C₃₁	—	2	4	no	—
78	C₂×D₄×C₃₁	—	2	1	no	—
79	C₂×D₄×C₃₁	C₂×C₈	1	2	yes	—
80	C₂²×C₄×C₃₁	—	2	4	no	—
81	C₂²×C₄×C₃₁	—	2	4	no	—
82	C₂²×C₄×C₃₁	—	2	1	no	—
83	C₂²×C₄×C₃₁	—	2	2	no	—
84	C₂²×C₄×C₃₁	—	2	2	no	—
85	C₂²×C₄×C₃₁	—	2	2	no	—
86	C₂²×C₄×C₃₁	—	2	2	no	—
87	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₃₁	C₂×C₈	1	1	yes	characteristic
90	C₂²×C₄×C₃₁	C₂×C₈	1	1	yes	characteristic
91	C₂²×C₄×C₃₁	M₁₆	1	1	yes	characteristic
92	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
93	M₁₆×C₃₁	—	2	4	no	—
94	M₁₆×C₃₁	—	2	8	no	—
95	M₁₆×C₃₁	—	2	2	no	—
96	M₁₆×C₃₁	—	2	8	no	—
97	M₁₆×C₃₁	C₂²⋊C₄	1	4	yes	—
98	C₂×C₈×C₃₁	—	2	4	no	—
99	C₂×C₈×C₃₁	—	2	8	no	—
100	C₂×C₈×C₃₁	—	2	2	no	—
101	C₂×C₈×C₃₁	—	2	2	no	—
102	C₂×C₈×C₃₁	—	2	2	no	—
103	C₂×C₈×C₃₁	—	2	8	no	—
104	C₂×C₈×C₃₁	—	2	2	no	—
105	C₂×C₈×C₃₁	—	2	2	no	—
106	C₂×C₈×C₃₁	—	2	2	no	—
107	C₂×C₈×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
108	C₂×C₈×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
109	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
110	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
111	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
112	C₁₆×C₃₁	—	4	2	no	—
113	C₁₆×C₃₁	—	4	2	no	—
114	#12683	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
115	C₂³×C₃₁	—	2	4	no	—
116	C₂³×C₃₁	—	2	2	no	—
117	C₂³×C₃₁	—	2	2	no	—
118	C₂³×C₃₁	—	2	2	no	—
119	C₂³×C₃₁	—	4	1	no	—
120	C₂³×C₃₁	—	4	2	no	—
121	C₂³×C₃₁	—	4	2	no	—
122	C₂³×C₃₁	C₂²⋊C₈	1	1	yes	characteristic
123	C₂³×C₃₁	C₂²⋊C₈	1	1	yes	characteristic
124	C₂³×C₃₁	C₂×M₁₆	1	1	yes	characteristic
125	Q₈×C₃₁	—	2	4	no	—
126	Q₈×C₃₁	—	2	2	no	—
127	Q₈×C₃₁	C₂²⋊C₈	1	4	yes	—
128	D₄×C₃₁	—	2	8	no	—
129	D₄×C₃₁	—	2	4	no	—
130	D₄×C₃₁	—	2	4	no	—
131	D₄×C₃₁	—	2	4	no	—
132	D₄×C₃₁	—	2	2	no	—
133	D₄×C₃₁	C₂²⋊C₈	1	4	yes	—
134	C₂×C₄×C₃₁	—	2	4	no	—
135	C₂×C₄×C₃₁	—	2	8	no	—
136	C₂×C₄×C₃₁	—	2	2	no	—
137	C₂×C₄×C₃₁	—	2	2	no	—
138	C₂×C₄×C₃₁	—	2	1	no	—
139	C₂×C₄×C₃₁	—	2	4	no	—
140	C₂×C₄×C₃₁	—	2	1	no	—
141	C₂×C₄×C₃₁	—	2	2	no	—
142	C₂×C₄×C₃₁	—	2	2	no	—
143	C₂×C₄×C₃₁	—	2	1	no	—
144	C₂×C₄×C₃₁	—	2	4	no	—
145	C₂×C₄×C₃₁	—	2	1	no	—
146	C₂×C₄×C₃₁	C₂²⋊C₈	1	1	yes	characteristic
147	C₂×C₄×C₃₁	C₂²⋊C₈	1	1	yes	characteristic
148	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
149	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₃₁	C₂²×C₈	1	1	yes	characteristic
151	C₂×C₄×C₃₁	C₂×M₁₆	1	2	yes	—
152	C₈×C₃₁	—	2	1	no	—
153	C₈×C₃₁	—	2	4	no	—
154	C₈×C₃₁	—	2	1	no	—
155	C₈×C₃₁	#120	1	2	yes	—
156	C₈×C₃₁	#120	1	2	yes	—
157	C₂²×#131	C₂×C₃₁	1	1	yes	characteristic
158	C₂×#350	C₂×C₃₁	1	4	yes	complemented
159	#2112	C₂×C₃₁	1	1	yes	characteristic, complemented
160	C₂×C₂²⋊C₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
161	C₂²×C₃₁	—	2	1	no	—
162	C₂²×C₃₁	—	2	1	no	—
163	C₂²×C₃₁	—	2	1	no	—
164	C₂²×C₃₁	—	2	1	no	—
165	C₂²×C₃₁	—	2	1	no	—
166	C₂²×C₃₁	—	2	1	no	—
167	C₂²×C₃₁	—	2	1	no	—
168	C₂²×C₃₁	—	2	4	no	—
169	C₂²×C₃₁	—	4	4	no	—
170	C₂²×C₃₁	—	4	8	no	—
171	C₂²×C₃₁	—	4	2	no	—
172	C₂²×C₃₁	—	4	2	no	—
173	C₂²×C₃₁	#350	1	2	yes	complemented
174	C₂²×C₃₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
175	C₂²×C₃₁	#407	1	2	yes	—
176	C₄×C₃₁	—	2	1	no	—
177	C₄×C₃₁	—	2	4	no	—
178	C₄×C₃₁	—	2	1	no	—
179	C₄×C₃₁	#379	1	1	yes	characteristic
180	C₄×C₃₁	C₂×C₂²⋊C₈	1	2	yes	—
181	C₄×C₃₁	#407	1	1	yes	characteristic
182	C₂²×#41	C₄×C₃₁	1	1	yes	characteristic
183	C₂×#131	—	2	8	no	—
184	C₂×#131	—	2	1	no	—
185	C₂×#131	—	2	1	no	—
186	C₂×#131	C₄×C₃₁	1	2	yes	—
187	C₂×#131	C₂²×C₃₁	1	2	yes	—
188	C₂²×M₁₆	—	2	1	no	—
189	C₂²×M₁₆	C₄×C₃₁	1	1	yes	characteristic
190	C₂³×C₈	—	2	1	no	—
191	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
192	C₂×M₃₂	C₂²×C₃₁	1	2	yes	complemented
193	C₂²×C₁₆	C₂²×C₃₁	1	2	yes	complemented
194	#350	—	2	8	no	—
195	C₂²⋊C₁₆	—	2	1	no	—
196	C₂²⋊C₁₆	—	2	1	no	—
197	C₂²⋊C₁₆	—	2	1	no	—
198	C₂²⋊C₁₆	—	2	1	no	—
199	C₂×C₃₁	—	2	2	no	—
200	C₂×C₃₁	—	2	2	no	—
201	C₂×C₃₁	—	4	1	no	—
202	C₂×C₃₁	—	4	4	no	—
203	C₂×C₃₁	#1779	1	1	yes	characteristic
204	C₂×C₃₁	C₂×#350	1	1	yes	characteristic
205	C₂×C₃₁	#2117	1	1	yes	characteristic
206	C₂×#41	—	2	4	no	—
207	C₂×#41	—	2	4	no	—
208	C₂×#41	—	2	1	no	—
209	C₂×#41	—	2	1	no	—
210	C₂×#41	C₈×C₃₁	1	2	yes	—
211	C₂×#41	C₂×C₄×C₃₁	1	2	yes	—
212	C₂²×Q₈	C₈×C₃₁	1	1	yes	characteristic
213	C₂²×D₄	—	2	1	no	—
214	C₂²×D₄	C₈×C₃₁	1	1	yes	characteristic
215	C₂³×C₄	—	2	1	no	—
216	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
217	#131	—	2	8	no	—
218	#131	—	2	8	no	—
219	#131	—	2	4	no	—
220	#131	—	2	4	no	—
221	#131	—	2	4	no	—
222	#131	D₄×C₃₁	1	8	yes	—
223	C₂×M₁₆	—	2	8	no	—
224	C₂×M₁₆	—	2	1	no	—
225	C₂×M₁₆	—	2	4	no	—
226	C₂×M₁₆	—	2	2	no	—
227	C₂×M₁₆	—	2	2	no	—
228	C₂×M₁₆	C₂×C₄×C₃₁	1	2	yes	—
229	C₂²×C₈	—	2	8	no	—
230	C₂²×C₈	—	2	1	no	—
231	C₂²×C₈	—	2	2	no	—
232	C₂²×C₈	—	2	2	no	—
233	C₂²×C₈	—	2	4	no	—
234	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
235	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
236	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
237	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
238	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
239	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
240	M₃₂	—	2	4	no	—
241	C₂×C₁₆	—	2	2	no	—
242	C₂×C₁₆	—	2	2	no	—
243	C₂×C₁₆	—	2	4	no	—
244	C₃₁	#12683	1	1	yes	characteristic, direct product factor, Sylow
245	C₂⁴	—	2	1	no	—
246	C₂⁴	M₁₆×C₃₁	1	1	yes	characteristic
247	#41	—	2	4	no	—
248	#41	—	2	8	no	—
249	#41	—	2	4	no	—
250	#41	—	2	4	no	—
251	#41	—	2	4	no	—
252	#41	—	2	2	no	—
253	#41	—	2	2	no	—
254	#41	C₂²⋊C₄×C₃₁	1	4	yes	—
255	#41	M₁₆×C₃₁	1	4	yes	—
256	C₂×Q₈	—	2	4	no	—
257	C₂×Q₈	—	2	1	no	—
258	C₂×Q₈	C₂×C₈×C₃₁	1	2	yes	—
259	C₂×D₄	—	2	8	no	—
260	C₂×D₄	—	2	2	no	—
261	C₂×D₄	—	2	2	no	—
262	C₂×D₄	—	2	4	no	—
263	C₂×D₄	—	2	1	no	—
264	C₂×D₄	C₂×C₈×C₃₁	1	2	yes	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
273	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
274	C₂²×C₄	C₂×C₈×C₃₁	1	1	yes	characteristic
275	C₂²×C₄	C₂×C₈×C₃₁	1	1	yes	characteristic
276	C₂²×C₄	M₁₆×C₃₁	1	1	yes	characteristic
277	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
278	M₁₆	—	2	4	no	—
279	M₁₆	—	2	8	no	—
280	M₁₆	—	2	2	no	—
281	M₁₆	—	2	8	no	—
282	M₁₆	C₂²⋊C₄×C₃₁	1	4	yes	—
283	C₂×C₈	—	2	4	no	—
284	C₂×C₈	—	2	8	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	8	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
293	C₂×C₈	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
294	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
295	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
296	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
297	C₁₆	—	4	2	no	—
298	C₁₆	—	4	2	no	—
299	C₂³	—	2	4	no	—
300	C₂³	—	2	2	no	—
301	C₂³	—	2	2	no	—
302	C₂³	—	2	2	no	—
303	C₂³	—	4	1	no	—
304	C₂³	—	4	2	no	—
305	C₂³	—	4	2	no	—
306	C₂³	C₃₁×C₂²⋊C₈	1	1	yes	characteristic
307	C₂³	C₃₁×C₂²⋊C₈	1	1	yes	characteristic
308	C₂³	C₂×M₁₆×C₃₁	1	1	yes	characteristic
309	Q₈	—	2	4	no	—
310	Q₈	—	2	2	no	—
311	Q₈	C₃₁×C₂²⋊C₈	1	4	yes	—
312	D₄	—	2	8	no	—
313	D₄	—	2	4	no	—
314	D₄	—	2	4	no	—
315	D₄	—	2	4	no	—
316	D₄	—	2	2	no	—
317	D₄	C₃₁×C₂²⋊C₈	1	4	yes	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	8	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	C₃₁×C₂²⋊C₈	1	1	yes	characteristic
331	C₂×C₄	C₃₁×C₂²⋊C₈	1	1	yes	characteristic
332	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
333	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
334	C₂×C₄	C₂²×C₈×C₃₁	1	1	yes	characteristic
335	C₂×C₄	C₂×M₁₆×C₃₁	1	2	yes	—
336	C₈	—	2	1	no	—
337	C₈	—	2	4	no	—
338	C₈	—	2	1	no	—
339	C₈	C₃₁×#120	1	2	yes	—
340	C₈	C₃₁×#120	1	2	yes	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	4	no	—
349	C₂²	—	4	4	no	—
350	C₂²	—	4	8	no	—
351	C₂²	—	4	2	no	—
352	C₂²	—	4	2	no	—
353	C₂²	C₃₁×#350	1	2	yes	complemented
354	C₂²	C₂×C₃₁×C₂²⋊C₈	1	1	yes	characteristic
355	C₂²	C₃₁×#407	1	2	yes	—
356	C₄	—	2	1	no	—
357	C₄	—	2	4	no	—
358	C₄	—	2	1	no	—
359	C₄	C₃₁×#379	1	1	yes	characteristic
360	C₄	C₂×C₃₁×C₂²⋊C₈	1	2	yes	—
361	C₄	C₃₁×#407	1	1	yes	characteristic
362	C₂	—	2	2	no	—
363	C₂	—	2	2	no	—
364	C₂	—	4	1	no	—
365	C₂	—	4	4	no	—
366	C₂	C₃₁×#1779	1	1	yes	characteristic
367	C₂	C₂×C₃₁×#350	1	1	yes	characteristic
368	C₂	C₃₁×#2117	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₃₁	C₂×D₄
commutator	C₂×C₄	C₂²×C₈×C₃₁
Frattini, cosocle	C₂²×C₈	C₂³×C₃₁
socle	C₂²×C₃₁	C₂×C₂²⋊C₈
prime radical	C₂²×#41×C₃₁	C₄
LCS	G ▷ C₂×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
2. C₂×C₃₁×#350	C₂	semidirect
3. C₃₁×#2112	C₂	semidirect
4. C₂×C₃₁×C₂²⋊C₁₆	C₂	semidirect
15. C₂×C₃₁×M₃₂	C₂²	semidirect
16. C₂²×C₁₆×C₃₁	C₂²	semidirect
114. #12683	C₃₁	direct (N × H)
158. C₂×#350	C₂×C₃₁	semidirect
159. #2112	C₂×C₃₁	semidirect
160. C₂×C₂²⋊C₁₆	C₂×C₃₁	semidirect
173. C₂²×C₃₁	#350	semidirect
192. C₂×M₃₂	C₂²×C₃₁	semidirect
193. C₂²×C₁₆	C₂²×C₃₁	semidirect
244. C₃₁	#12683	direct (N × H)
353. C₂²	C₃₁×#350	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃₁×#131	2
C₂×C₃₁×#350	2
C₃₁×#2112	2
C₂×C₃₁×C₂²⋊C₁₆	2
#12683	31

Subgroups — C31×#12683 #21469442

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#12683 #21469442