Subgroups — C₃₁×#33737 #21490496

Order 7936.

554 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3169	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3168	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2255	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2250	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2244	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2243	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2220	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2218	C₂	1	2	yes	maximal, complemented
9	C₄×C₃₁×SD₃₂	C₂	1	2	yes	maximal, complemented
10	C₄×C₃₁×D₁₆	C₂	1	2	yes	maximal, complemented
11	C₄×C₃₁×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#532	—	2	1	no	—
13	C₃₁×#529	—	2	1	no	—
14	C₂×C₃₁×SD₃₂	C₂²	1	2	yes	—
15	C₂×C₃₁×D₁₆	C₂²	1	2	yes	—
16	C₂×C₃₁×M₃₂	C₂²	1	2	yes	—
17	C₃₁×#500	C₂²	1	1	yes	characteristic
18	C₃₁×#499	C₂²	1	1	yes	characteristic
19	C₃₁×#495	C₂²	1	1	yes	characteristic
20	C₃₁×#493	C₂²	1	1	yes	characteristic
21	C₃₁×#488	—	2	1	no	—
22	C₃₁×#486	—	2	1	no	—
23	C₃₁×#467	C₂²	1	1	yes	characteristic
24	C₃₁×#466	—	2	1	no	—
25	C₃₁×#466	C₂²	1	1	yes	characteristic
26	C₃₁×#466	C₂²	1	2	yes	—
27	C₃₁×#465	—	2	1	no	—
28	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
29	C₄×SD₁₆×C₃₁	—	2	1	no	—
30	C₄×D₈×C₃₁	—	2	1	no	—
31	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
32	C₄×D₈×C₃₁	C₂²	1	2	yes	—
33	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
34	C₃₁×#367	C₂²	1	2	yes	—
35	C₃₁×#366	C₂²	1	2	yes	—
36	C₃₁×#358	C₂²	1	2	yes	—
37	C₃₁×#357	C₂²	1	2	yes	—
38	C₃₁×#357	C₂²	1	2	yes	—
39	C₃₁×#357	C₂²	1	2	yes	—
40	C₃₁×#346	C₂²	1	1	yes	characteristic
41	C₃₁×#346	C₂²	1	1	yes	characteristic
42	C₄×C₁₆×C₃₁	C₂²	1	2	yes	—
43	C₂×#41×C₃₁	—	4	1	no	—
44	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
45	C₂×SD₁₆×C₃₁	—	2	1	no	—
46	C₂×D₈×C₃₁	—	2	1	no	—
47	C₂×D₈×C₃₁	C₂³	1	2	yes	—
48	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
51	C₃₁×C₄⋊Q₈	—	2	1	no	—
52	C₃₁×#127	—	2	1	no	—
53	C₃₁×#126	—	4	1	no	—
54	C₃₁×#125	—	2	1	no	—
55	C₃₁×#124	—	2	1	no	—
56	C₃₁×#124	—	4	1	no	—
57	C₃₁×#123	—	4	1	no	—
58	C₃₁×C₂²⋊Q₈	—	2	1	no	—
59	C₃₁×#121	—	2	1	no	—
60	C₃₁×#121	—	2	2	no	—
61	C₃₁×#121	—	4	1	no	—
62	C₄×Q₈×C₃₁	—	2	1	no	—
63	C₄×D₄×C₃₁	—	2	2	no	—
64	C₄×D₄×C₃₁	—	2	1	no	—
65	C₄×D₄×C₃₁	—	4	1	no	—
66	C₄×D₄×C₃₁	—	4	1	no	—
67	C₃₁×#117	—	4	1	no	—
68	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
69	C₃₁×SD₃₂	—	2	4	no	—
70	C₃₁×D₁₆	—	2	4	no	—
71	C₃₁×M₃₂	—	2	4	no	—
72	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
73	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
74	C₃₁×#107	—	2	1	no	—
75	C₃₁×#107	C₂³	1	2	yes	—
76	C₃₁×#107	C₂³	1	1	yes	characteristic
77	C₃₁×#107	C₂³	1	1	yes	characteristic
78	C₃₁×#106	—	2	1	no	—
79	C₃₁×#103	—	2	1	no	—
80	C₃₁×#103	—	2	1	no	—
81	C₃₁×#102	—	2	2	no	—
82	C₃₁×#102	—	2	1	no	—
83	C₃₁×#102	—	2	2	no	—
84	C₃₁×#102	—	2	1	no	—
85	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
86	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
87	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
89	#41×C₃₁	—	8	4	no	—
90	C₂×Q₈×C₃₁	—	2	1	no	—
91	C₂×Q₈×C₃₁	—	4	1	no	—
92	C₂×D₄×C₃₁	—	2	1	no	—
93	C₂×D₄×C₃₁	—	2	2	no	—
94	C₂×D₄×C₃₁	—	4	1	no	—
95	C₂×D₄×C₃₁	—	4	2	no	—
96	C₂×D₄×C₃₁	—	4	1	no	—
97	C₂×D₄×C₃₁	—	4	1	no	—
98	C₂²×C₄×C₃₁	—	4	1	no	—
99	C₂²×C₄×C₃₁	—	4	2	no	—
100	C₂²×C₄×C₃₁	D₈	1	1	yes	characteristic
101	C₂²×C₄×C₃₁	D₈	1	1	yes	characteristic
102	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
103	Q₁₆×C₃₁	—	2	2	no	—
104	SD₁₆×C₃₁	—	4	2	no	—
105	D₈×C₃₁	—	2	2	no	—
106	D₈×C₃₁	—	2	2	no	—
107	D₈×C₃₁	—	2	2	no	—
108	D₈×C₃₁	—	4	2	no	—
109	C₂×C₈×C₃₁	—	2	2	no	—
110	C₂×C₈×C₃₁	—	2	2	no	—
111	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
115	C₄⋊C₄×C₃₁	—	2	2	no	—
116	C₄⋊C₄×C₃₁	—	2	1	no	—
117	C₄⋊C₄×C₃₁	—	2	1	no	—
118	C₄⋊C₄×C₃₁	—	4	1	no	—
119	C₄⋊C₄×C₃₁	—	4	1	no	—
120	C₄⋊C₄×C₃₁	—	4	1	no	—
121	C₄⋊C₄×C₃₁	—	4	1	no	—
122	C₄⋊C₄×C₃₁	—	4	1	no	—
123	C₂²⋊C₄×C₃₁	—	4	1	no	—
124	C₂²⋊C₄×C₃₁	—	4	1	no	—
125	C₂²⋊C₄×C₃₁	—	4	1	no	—
126	C₂²⋊C₄×C₃₁	—	4	2	no	—
127	C₂²⋊C₄×C₃₁	—	4	1	no	—
128	C₂²⋊C₄×C₃₁	—	4	2	no	—
129	C₂²⋊C₄×C₃₁	—	4	1	no	—
130	C₄²×C₃₁	—	4	1	no	—
131	C₄²×C₃₁	D₈	1	1	yes	characteristic
132	C₄²×C₃₁	D₈	1	1	yes	characteristic
133	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
135	C₁₆×C₃₁	—	2	2	no	—
136	C₁₆×C₃₁	#41	1	4	yes	complemented
137	#33737	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
138	C₂³×C₃₁	—	4	1	no	—
139	C₂³×C₃₁	—	4	2	no	—
140	C₂³×C₃₁	C₂×D₈	1	1	yes	characteristic
141	Q₈×C₃₁	—	4	1	no	—
142	Q₈×C₃₁	—	4	1	no	—
143	Q₈×C₃₁	—	8	2	no	—
144	D₄×C₃₁	—	4	1	no	—
145	D₄×C₃₁	—	4	2	no	—
146	D₄×C₃₁	—	4	2	no	—
147	D₄×C₃₁	—	4	1	no	—
148	D₄×C₃₁	—	8	2	no	—
149	D₄×C₃₁	—	8	2	no	—
150	D₄×C₃₁	—	8	2	no	—
151	D₄×C₃₁	—	8	4	no	—
152	C₂×C₄×C₃₁	—	2	1	no	—
153	C₂×C₄×C₃₁	—	2	1	no	—
154	C₂×C₄×C₃₁	—	2	2	no	—
155	C₂×C₄×C₃₁	—	4	1	no	—
156	C₂×C₄×C₃₁	—	4	1	no	—
157	C₂×C₄×C₃₁	—	4	1	no	—
158	C₂×C₄×C₃₁	—	4	1	no	—
159	C₂×C₄×C₃₁	—	4	2	no	—
160	C₂×C₄×C₃₁	—	8	2	no	—
161	C₂×C₄×C₃₁	—	8	4	no	—
162	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
163	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
164	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
165	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
166	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
167	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
168	C₈×C₃₁	—	2	1	no	—
169	C₈×C₃₁	—	2	1	no	—
170	C₈×C₃₁	#135	1	2	yes	—
171	C₈×C₃₁	C₂×#41	1	2	yes	—
172	#3169	C₂×C₃₁	1	1	yes	characteristic, complemented
173	#3168	C₂×C₃₁	1	1	yes	characteristic, complemented
174	#2255	C₂×C₃₁	1	1	yes	characteristic, complemented
175	#2250	C₂×C₃₁	1	1	yes	characteristic, complemented
176	#2244	C₂×C₃₁	1	1	yes	characteristic, complemented
177	#2243	C₂×C₃₁	1	1	yes	characteristic, complemented
178	#2220	C₂×C₃₁	1	2	yes	complemented
179	#2218	C₂×C₃₁	1	2	yes	complemented
180	C₄×SD₃₂	C₂×C₃₁	1	2	yes	complemented
181	C₄×D₁₆	C₂×C₃₁	1	2	yes	complemented
182	C₄×M₃₂	C₂×C₃₁	1	1	yes	characteristic, complemented
183	C₂²×C₃₁	—	2	1	no	—
184	C₂²×C₃₁	—	2	1	no	—
185	C₂²×C₃₁	—	2	1	no	—
186	C₂²×C₃₁	—	8	2	no	—
187	C₂²×C₃₁	—	8	1	no	—
188	C₂²×C₃₁	—	8	2	no	—
189	C₂²×C₃₁	—	8	1	no	—
190	C₂²×C₃₁	—	8	2	no	—
191	C₂²×C₃₁	—	8	1	no	—
192	C₂²×C₃₁	C₂²×D₈	1	1	yes	characteristic
193	C₄×C₃₁	—	2	1	no	—
194	C₄×C₃₁	—	2	1	no	—
195	C₄×C₃₁	—	2	1	no	—
196	C₄×C₃₁	—	2	1	no	—
197	C₄×C₃₁	—	8	1	no	—
198	C₄×C₃₁	—	8	2	no	—
199	C₄×C₃₁	—	8	1	no	—
200	C₄×C₃₁	—	8	1	no	—
201	C₄×C₃₁	#509	1	2	yes	—
202	C₄×C₃₁	#532	1	1	yes	characteristic
203	C₄×C₃₁	C₂×#135	1	1	yes	characteristic
204	#532	—	2	1	no	—
205	#529	—	2	1	no	—
206	C₂×SD₃₂	C₂²×C₃₁	1	2	yes	—
207	C₂×D₁₆	C₂²×C₃₁	1	2	yes	—
208	C₂×M₃₂	C₂²×C₃₁	1	2	yes	—
209	#500	C₂²×C₃₁	1	1	yes	characteristic
210	#499	C₂²×C₃₁	1	1	yes	characteristic
211	#495	C₂²×C₃₁	1	1	yes	characteristic
212	#493	C₂²×C₃₁	1	1	yes	characteristic
213	#488	—	2	1	no	—
214	#486	—	2	1	no	—
215	#467	C₂²×C₃₁	1	1	yes	characteristic
216	#466	—	2	1	no	—
217	#466	C₂²×C₃₁	1	1	yes	characteristic
218	#466	C₂²×C₃₁	1	2	yes	—
219	#465	—	2	1	no	—
220	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
221	C₄×SD₁₆	—	2	1	no	—
222	C₄×D₈	—	2	1	no	—
223	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
224	C₄×D₈	C₂²×C₃₁	1	2	yes	—
225	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
226	#367	C₂²×C₃₁	1	2	yes	—
227	#366	C₂²×C₃₁	1	2	yes	—
228	#358	C₂²×C₃₁	1	2	yes	—
229	#357	C₂²×C₃₁	1	2	yes	—
230	#357	C₂²×C₃₁	1	2	yes	—
231	#357	C₂²×C₃₁	1	2	yes	—
232	#346	C₂²×C₃₁	1	1	yes	characteristic
233	#346	C₂²×C₃₁	1	1	yes	characteristic
234	C₄×C₁₆	C₂²×C₃₁	1	2	yes	—
235	C₂×C₃₁	—	4	1	no	—
236	C₂×C₃₁	—	16	2	no	—
237	C₂×C₃₁	—	16	1	no	—
238	C₂×C₃₁	#3169	1	1	yes	characteristic
239	C₂×C₃₁	C₂×#509	1	1	yes	characteristic
240	C₂×C₃₁	#3414	1	1	yes	characteristic
241	C₂×#41	—	4	1	no	—
242	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
243	C₂×SD₁₆	—	2	1	no	—
244	C₂×D₈	—	2	1	no	—
245	C₂×D₈	C₂³×C₃₁	1	2	yes	—
246	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
247	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
248	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
249	C₄⋊Q₈	—	2	1	no	—
250	#127	—	2	1	no	—
251	#126	—	4	1	no	—
252	#125	—	2	1	no	—
253	#124	—	2	1	no	—
254	#124	—	4	1	no	—
255	#123	—	4	1	no	—
256	C₂²⋊Q₈	—	2	1	no	—
257	#121	—	2	1	no	—
258	#121	—	2	2	no	—
259	#121	—	4	1	no	—
260	C₄×Q₈	—	2	1	no	—
261	C₄×D₄	—	2	1	no	—
262	C₄×D₄	—	2	2	no	—
263	C₄×D₄	—	4	1	no	—
264	C₄×D₄	—	4	1	no	—
265	#117	—	4	1	no	—
266	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
267	SD₃₂	—	2	4	no	—
268	D₁₆	—	2	4	no	—
269	M₃₂	—	2	4	no	—
270	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
271	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
272	#107	—	2	1	no	—
273	#107	C₂³×C₃₁	1	1	yes	characteristic
274	#107	C₂³×C₃₁	1	1	yes	characteristic
275	#107	C₂³×C₃₁	1	2	yes	—
276	#106	—	2	1	no	—
277	#103	—	2	1	no	—
278	#103	—	2	1	no	—
279	#102	—	2	2	no	—
280	#102	—	2	1	no	—
281	#102	—	2	2	no	—
282	#102	—	2	1	no	—
283	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
284	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
285	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
286	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
287	C₃₁	#33737	1	1	yes	characteristic, direct product factor, Sylow
288	#41	—	8	4	no	—
289	C₂×Q₈	—	2	1	no	—
290	C₂×Q₈	—	4	1	no	—
291	C₂×D₄	—	2	1	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	4	1	no	—
294	C₂×D₄	—	4	2	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂²×C₄	—	4	1	no	—
298	C₂²×C₄	—	4	2	no	—
299	C₂²×C₄	D₈×C₃₁	1	1	yes	characteristic
300	C₂²×C₄	D₈×C₃₁	1	1	yes	characteristic
301	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
302	Q₁₆	—	2	2	no	—
303	SD₁₆	—	4	2	no	—
304	D₈	—	2	2	no	—
305	D₈	—	2	2	no	—
306	D₈	—	2	2	no	—
307	D₈	—	4	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	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	C₂⁴×C₃₁	1	1	yes	characteristic
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	—	4	1	no	—
322	C₂²⋊C₄	—	4	1	no	—
323	C₂²⋊C₄	—	4	1	no	—
324	C₂²⋊C₄	—	4	1	no	—
325	C₂²⋊C₄	—	4	2	no	—
326	C₂²⋊C₄	—	4	1	no	—
327	C₂²⋊C₄	—	4	2	no	—
328	C₂²⋊C₄	—	4	1	no	—
329	C₄²	—	4	1	no	—
330	C₄²	D₈×C₃₁	1	1	yes	characteristic
331	C₄²	D₈×C₃₁	1	1	yes	characteristic
332	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
333	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
334	C₁₆	—	2	2	no	—
335	C₁₆	#41×C₃₁	1	4	yes	complemented
336	C₂³	—	4	1	no	—
337	C₂³	—	4	2	no	—
338	C₂³	C₂×D₈×C₃₁	1	1	yes	characteristic
339	Q₈	—	4	1	no	—
340	Q₈	—	4	1	no	—
341	Q₈	—	8	2	no	—
342	D₄	—	4	1	no	—
343	D₄	—	4	2	no	—
344	D₄	—	4	2	no	—
345	D₄	—	4	1	no	—
346	D₄	—	8	2	no	—
347	D₄	—	8	2	no	—
348	D₄	—	8	2	no	—
349	D₄	—	8	4	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	8	2	no	—
359	C₂×C₄	—	8	4	no	—
360	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
361	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
362	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
363	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
364	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
365	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
366	C₈	—	2	1	no	—
367	C₈	—	2	1	no	—
368	C₈	C₃₁×#135	1	2	yes	—
369	C₈	C₂×#41×C₃₁	1	2	yes	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	1	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	8	1	no	—
377	C₂²	—	8	2	no	—
378	C₂²	—	8	1	no	—
379	C₂²	C₂²×D₈×C₃₁	1	1	yes	characteristic
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	2	1	no	—
384	C₄	—	8	2	no	—
385	C₄	—	8	1	no	—
386	C₄	—	8	1	no	—
387	C₄	—	8	1	no	—
388	C₄	C₃₁×#509	1	2	yes	—
389	C₄	C₃₁×#532	1	1	yes	characteristic
390	C₄	C₂×C₃₁×#135	1	1	yes	characteristic
391	C₂	—	4	1	no	—
392	C₂	—	16	2	no	—
393	C₂	—	16	1	no	—
394	C₂	C₃₁×#3169	1	1	yes	characteristic
395	C₂	C₂×C₃₁×#509	1	1	yes	characteristic
396	C₂	C₃₁×#3414	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₁	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₃₁
socle	C₂²×C₃₁	C₂²×D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ C₂×C₄²×C₃₁ ◁ C₂×C₄×C₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3169	C₂	semidirect
2. C₃₁×#3168	C₂	semidirect
3. C₃₁×#2255	C₂	semidirect
4. C₃₁×#2250	C₂	semidirect
5. C₃₁×#2244	C₂	semidirect
6. C₃₁×#2243	C₂	semidirect
7. C₃₁×#2220	C₂	semidirect
8. C₃₁×#2218	C₂	semidirect
9. C₄×C₃₁×SD₃₂	C₂	semidirect
10. C₄×C₃₁×D₁₆	C₂	semidirect
11. C₄×C₃₁×M₃₂	C₂	semidirect
136. C₁₆×C₃₁	#41	semidirect
137. #33737	C₃₁	direct (N × H)
172. #3169	C₂×C₃₁	semidirect
173. #3168	C₂×C₃₁	semidirect
174. #2255	C₂×C₃₁	semidirect
175. #2250	C₂×C₃₁	semidirect
176. #2244	C₂×C₃₁	semidirect
177. #2243	C₂×C₃₁	semidirect
178. #2220	C₂×C₃₁	semidirect
179. #2218	C₂×C₃₁	semidirect
180. C₄×SD₃₂	C₂×C₃₁	semidirect
181. C₄×D₁₆	C₂×C₃₁	semidirect
182. C₄×M₃₂	C₂×C₃₁	semidirect
287. C₃₁	#33737	direct (N × H)
335. C₁₆	#41×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3169	2
C₃₁×#3168	2
C₃₁×#2255	2
C₃₁×#2250	2
C₃₁×#2244	2
C₃₁×#2243	2
C₃₁×#2220	2
C₃₁×#2218	2
C₄×C₃₁×SD₃₂	2
C₄×C₃₁×D₁₆	2
C₄×C₃₁×M₃₂	2
#33737	31

Subgroups — C31×#33737 #21490496

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33737 #21490496