Subgroups — C₁₃₁×#33783 #45719667

Order 33536.

688 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3168×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#493×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#2250×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#2244×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#2207×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2206×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#2187×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#2184×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	#2163×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×D₈×C₁₃₁	—	2	1	no	—
11	C₂²×D₈×C₁₃₁	C₂²	1	2	yes	—
12	C₂×#127×C₁₃₁	—	2	1	no	—
13	#529×C₁₃₁	—	2	1	no	—
14	C₂×SD₃₂×C₁₃₁	C₂²	1	4	yes	complemented
15	C₂×D₁₆×C₁₃₁	C₂²	1	4	yes	complemented
16	#499×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
17	#495×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
18	#493×C₁₃₁	—	2	1	no	—
19	#493×C₁₃₁	—	2	1	no	—
20	#493×C₁₃₁	C₂²	1	2	yes	—
21	#493×C₁₃₁	C₂²	1	2	yes	—
22	#488×C₁₃₁	—	2	1	no	—
23	#467×C₁₃₁	C₂²	1	1	yes	characteristic
24	#466×C₁₃₁	C₂²	1	1	yes	characteristic
25	#465×C₁₃₁	—	2	1	no	—
26	C₄×Q₁₆×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
27	C₄×SD₁₆×C₁₃₁	—	2	1	no	—
28	C₄×D₈×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
30	C₄⋊C₁₆×C₁₃₁	C₂²	1	2	yes	complemented
31	#357×C₁₃₁	C₂²	1	4	yes	complemented
32	#357×C₁₃₁	C₂²	1	4	yes	complemented
33	C₂²⋊C₁₆×C₁₃₁	C₂²	1	2	yes	—
34	#346×C₁₃₁	C₂²	1	2	yes	complemented
35	C₂²×D₄×C₁₃₁	—	2	2	no	—
36	C₂²×D₄×C₁₃₁	—	4	1	no	—
37	C₂²×D₄×C₁₃₁	—	4	1	no	—
38	C₂×Q₁₆×C₁₃₁	C₂³	1	1	yes	characteristic
39	C₂×SD₁₆×C₁₃₁	—	2	1	no	—
40	C₂×D₈×C₁₃₁	—	2	2	no	—
41	C₂×D₈×C₁₃₁	—	2	2	no	—
42	C₂×D₈×C₁₃₁	—	2	2	no	—
43	C₂×D₈×C₁₃₁	—	4	4	no	—
44	C₂×D₈×C₁₃₁	—	4	4	no	—
45	C₂×D₈×C₁₃₁	C₂³	1	1	yes	characteristic
46	C₂×D₈×C₁₃₁	C₂³	1	4	yes	—
47	C₂²×C₈×C₁₃₁	D₄	1	1	yes	characteristic
48	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
49	#127×C₁₃₁	—	2	2	no	—
50	#127×C₁₃₁	—	2	2	no	—
51	#127×C₁₃₁	—	4	1	no	—
52	#127×C₁₃₁	—	4	1	no	—
53	#126×C₁₃₁	—	4	1	no	—
54	#125×C₁₃₁	—	2	1	no	—
55	#124×C₁₃₁	—	2	1	no	—
56	#123×C₁₃₁	—	4	1	no	—
57	C₂²⋊Q₈×C₁₃₁	—	2	1	no	—
58	#121×C₁₃₁	—	2	1	no	—
59	C₄×Q₈×C₁₃₁	—	2	1	no	—
60	C₄×D₄×C₁₃₁	—	2	1	no	—
61	C₄×D₄×C₁₃₁	—	4	1	no	—
62	#117×C₁₃₁	—	4	1	no	—
63	C₂×C₄²×C₁₃₁	D₄	1	1	yes	characteristic
64	SD₃₂×C₁₃₁	—	4	4	no	—
65	D₁₆×C₁₃₁	—	4	4	no	—
66	C₂×C₁₆×C₁₃₁	C₂³	1	4	yes	—
67	#107×C₁₃₁	C₂³	1	1	yes	characteristic
68	#107×C₁₃₁	C₂³	1	1	yes	characteristic
69	#106×C₁₃₁	—	2	1	no	—
70	#103×C₁₃₁	—	2	1	no	—
71	#103×C₁₃₁	—	2	1	no	—
72	#102×C₁₃₁	—	2	1	no	—
73	#102×C₁₃₁	—	2	1	no	—
74	C₄×C₈×C₁₃₁	D₄	1	1	yes	characteristic
75	C₄×C₈×C₁₃₁	D₄	1	1	yes	characteristic
76	C₄×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
77	C₄×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
78	C₂⁴×C₁₃₁	—	4	2	no	—
79	C₂×Q₈×C₁₃₁	—	2	1	no	—
80	C₂×D₄×C₁₃₁	—	2	1	no	—
81	C₂×D₄×C₁₃₁	—	2	4	no	—
82	C₂×D₄×C₁₃₁	—	4	4	no	—
83	C₂×D₄×C₁₃₁	—	4	4	no	—
84	C₂×D₄×C₁₃₁	—	4	1	no	—
85	C₂×D₄×C₁₃₁	—	4	2	no	—
86	C₂×D₄×C₁₃₁	—	4	2	no	—
87	C₂×D₄×C₁₃₁	—	4	2	no	—
88	C₂×D₄×C₁₃₁	—	4	2	no	—
89	C₂×D₄×C₁₃₁	—	4	2	no	—
90	C₂×D₄×C₁₃₁	—	8	4	no	—
91	C₂×D₄×C₁₃₁	—	8	4	no	—
92	C₂²×C₄×C₁₃₁	—	4	1	no	—
93	C₂²×C₄×C₁₃₁	D₈	1	1	yes	characteristic
94	C₂²×C₄×C₁₃₁	D₈	1	1	yes	characteristic
95	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
96	Q₁₆×C₁₃₁	—	2	2	no	—
97	SD₁₆×C₁₃₁	—	4	2	no	—
98	D₈×C₁₃₁	—	2	2	no	—
99	D₈×C₁₃₁	—	2	4	no	—
100	D₈×C₁₃₁	—	2	4	no	—
101	D₈×C₁₃₁	—	4	4	no	—
102	D₈×C₁₃₁	—	4	4	no	—
103	D₈×C₁₃₁	—	4	4	no	—
104	C₂×C₈×C₁₃₁	—	2	2	no	—
105	C₂×C₈×C₁₃₁	—	2	2	no	—
106	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
107	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
108	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
109	C₂×C₈×C₁₃₁	C₂⁴	1	1	yes	characteristic
110	C₄⋊C₄×C₁₃₁	—	2	1	no	—
111	C₄⋊C₄×C₁₃₁	—	2	1	no	—
112	C₄⋊C₄×C₁₃₁	—	4	1	no	—
113	C₄⋊C₄×C₁₃₁	—	4	1	no	—
114	C₄⋊C₄×C₁₃₁	—	4	1	no	—
115	C₄⋊C₄×C₁₃₁	—	4	1	no	—
116	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
117	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
118	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
119	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
120	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
121	C₄²×C₁₃₁	—	4	1	no	—
122	C₄²×C₁₃₁	D₈	1	1	yes	characteristic
123	C₄²×C₁₃₁	D₈	1	1	yes	characteristic
124	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
126	C₁₆×C₁₃₁	—	2	4	no	—
127	C₂³×C₁₃₁	—	4	1	no	—
128	C₂³×C₁₃₁	—	4	4	no	—
129	C₂³×C₁₃₁	—	8	4	no	—
130	C₂³×C₁₃₁	—	8	4	no	—
131	C₂³×C₁₃₁	—	8	4	no	—
132	C₂³×C₁₃₁	C₂×D₈	1	1	yes	characteristic
133	Q₈×C₁₃₁	—	4	1	no	—
134	Q₈×C₁₃₁	—	4	1	no	—
135	D₄×C₁₃₁	—	4	4	no	—
136	D₄×C₁₃₁	—	4	1	no	—
137	D₄×C₁₃₁	—	4	4	no	—
138	D₄×C₁₃₁	—	4	1	no	—
139	D₄×C₁₃₁	—	8	4	no	—
140	D₄×C₁₃₁	—	8	4	no	—
141	D₄×C₁₃₁	—	8	4	no	—
142	D₄×C₁₃₁	—	8	4	no	—
143	D₄×C₁₃₁	—	8	2	no	—
144	D₄×C₁₃₁	—	8	4	no	—
145	C₂×C₄×C₁₃₁	—	2	2	no	—
146	C₂×C₄×C₁₃₁	—	2	1	no	—
147	C₂×C₄×C₁₃₁	—	2	1	no	—
148	C₂×C₄×C₁₃₁	—	2	2	no	—
149	C₂×C₄×C₁₃₁	—	4	1	no	—
150	C₂×C₄×C₁₃₁	—	4	1	no	—
151	C₂×C₄×C₁₃₁	—	4	1	no	—
152	C₂×C₄×C₁₃₁	—	8	2	no	—
153	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
154	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
155	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
156	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
157	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
158	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
159	C₈×C₁₃₁	—	2	1	no	—
160	C₈×C₁₃₁	—	2	1	no	—
161	C₈×C₁₃₁	AGL(1,ℤ/8)	1	2	yes	—
162	C₈×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
163	C₂²×C₁₃₁	—	2	1	no	—
164	C₂²×C₁₃₁	—	2	1	no	—
165	C₂²×C₁₃₁	—	8	1	no	—
166	C₂²×C₁₃₁	—	8	4	no	—
167	C₂²×C₁₃₁	—	8	4	no	—
168	C₂²×C₁₃₁	—	8	1	no	—
169	C₂²×C₁₃₁	—	8	4	no	—
170	C₂²×C₁₃₁	—	8	1	no	—
171	C₂²×C₁₃₁	—	16	8	no	—
172	C₂²×C₁₃₁	#509	1	2	yes	—
173	C₂²×C₁₃₁	C₂²×D₈	1	1	yes	characteristic
174	C₄×C₁₃₁	—	2	1	no	—
175	C₄×C₁₃₁	—	2	1	no	—
176	C₄×C₁₃₁	—	2	1	no	—
177	C₄×C₁₃₁	—	2	1	no	—
178	C₄×C₁₃₁	—	8	1	no	—
179	C₄×C₁₃₁	—	8	1	no	—
180	C₄×C₁₃₁	—	8	1	no	—
181	C₄×C₁₃₁	#509	1	2	yes	—
182	C₄×C₁₃₁	#535	1	1	yes	characteristic
183	C₄×C₁₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
184	C₂×C₁₃₁	—	2	2	no	—
185	C₂×C₁₃₁	—	16	1	no	—
186	C₂×C₁₃₁	—	16	4	no	—
187	C₂×C₁₃₁	#3205	1	1	yes	characteristic
188	C₂×C₁₃₁	C₂×#509	1	1	yes	characteristic
189	C₂×C₁₃₁	C₂×#509	1	1	yes	characteristic
190	#33783	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₁₃₁	#33783	1	1	yes	characteristic, direct product factor, Sylow
192	#3168	C₂×C₁₃₁	1	1	yes	characteristic, complemented
193	C₂×#493	C₂×C₁₃₁	1	1	yes	characteristic, complemented
194	#2250	C₂×C₁₃₁	1	2	yes	complemented
195	#2244	C₂×C₁₃₁	1	2	yes	complemented
196	#2207	C₂×C₁₃₁	1	2	yes	complemented
197	#2206	C₂×C₁₃₁	1	2	yes	complemented
198	#2187	C₂×C₁₃₁	1	2	yes	complemented
199	#2184	C₂×C₁₃₁	1	2	yes	complemented
200	#2163	C₂×C₁₃₁	1	1	yes	characteristic, complemented
201	C₂²×D₈	—	2	1	no	—
202	C₂²×D₈	C₂²×C₁₃₁	1	2	yes	—
203	C₂×#127	—	2	1	no	—
204	#529	—	2	1	no	—
205	C₂×SD₃₂	C₂²×C₁₃₁	1	4	yes	complemented
206	C₂×D₁₆	C₂²×C₁₃₁	1	4	yes	complemented
207	#499	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
208	#495	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
209	#493	—	2	1	no	—
210	#493	—	2	1	no	—
211	#493	C₂²×C₁₃₁	1	2	yes	—
212	#493	C₂²×C₁₃₁	1	2	yes	—
213	#488	—	2	1	no	—
214	#467	C₂²×C₁₃₁	1	1	yes	characteristic
215	#466	C₂²×C₁₃₁	1	1	yes	characteristic
216	#465	—	2	1	no	—
217	C₄×Q₁₆	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
218	C₄×SD₁₆	—	2	1	no	—
219	C₄×D₈	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
220	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
221	C₄⋊C₁₆	C₂²×C₁₃₁	1	2	yes	complemented
222	#357	C₂²×C₁₃₁	1	4	yes	complemented
223	#357	C₂²×C₁₃₁	1	4	yes	complemented
224	C₂²⋊C₁₆	C₂²×C₁₃₁	1	2	yes	—
225	#346	C₂²×C₁₃₁	1	2	yes	complemented
226	C₂²×D₄	—	2	2	no	—
227	C₂²×D₄	—	4	1	no	—
228	C₂²×D₄	—	4	1	no	—
229	C₂×Q₁₆	C₂³×C₁₃₁	1	1	yes	characteristic
230	C₂×SD₁₆	—	2	1	no	—
231	C₂×D₈	—	2	2	no	—
232	C₂×D₈	—	2	2	no	—
233	C₂×D₈	—	2	2	no	—
234	C₂×D₈	—	4	4	no	—
235	C₂×D₈	—	4	4	no	—
236	C₂×D₈	C₂³×C₁₃₁	1	4	yes	—
237	C₂×D₈	C₂³×C₁₃₁	1	1	yes	characteristic
238	C₂²×C₈	D₄×C₁₃₁	1	1	yes	characteristic
239	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
240	#127	—	2	2	no	—
241	#127	—	2	2	no	—
242	#127	—	4	1	no	—
243	#127	—	4	1	no	—
244	#126	—	4	1	no	—
245	#125	—	2	1	no	—
246	#124	—	2	1	no	—
247	#123	—	4	1	no	—
248	C₂²⋊Q₈	—	2	1	no	—
249	#121	—	2	1	no	—
250	C₄×Q₈	—	2	1	no	—
251	C₄×D₄	—	2	1	no	—
252	C₄×D₄	—	4	1	no	—
253	#117	—	4	1	no	—
254	C₂×C₄²	D₄×C₁₃₁	1	1	yes	characteristic
255	SD₃₂	—	4	4	no	—
256	D₁₆	—	4	4	no	—
257	C₂×C₁₆	C₂³×C₁₃₁	1	4	yes	—
258	#107	C₂³×C₁₃₁	1	1	yes	characteristic
259	#107	C₂³×C₁₃₁	1	1	yes	characteristic
260	#106	—	2	1	no	—
261	#103	—	2	1	no	—
262	#103	—	2	1	no	—
263	#102	—	2	1	no	—
264	#102	—	2	1	no	—
265	C₄×C₈	D₄×C₁₃₁	1	1	yes	characteristic
266	C₄×C₈	D₄×C₁₃₁	1	1	yes	characteristic
267	C₄×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
268	C₄×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
269	C₂⁴	—	4	2	no	—
270	C₂×Q₈	—	2	1	no	—
271	C₂×D₄	—	2	1	no	—
272	C₂×D₄	—	2	4	no	—
273	C₂×D₄	—	4	4	no	—
274	C₂×D₄	—	4	4	no	—
275	C₂×D₄	—	4	1	no	—
276	C₂×D₄	—	4	2	no	—
277	C₂×D₄	—	4	2	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	—	4	2	no	—
280	C₂×D₄	—	4	2	no	—
281	C₂×D₄	—	8	4	no	—
282	C₂×D₄	—	8	4	no	—
283	C₂²×C₄	—	4	1	no	—
284	C₂²×C₄	D₈×C₁₃₁	1	1	yes	characteristic
285	C₂²×C₄	D₈×C₁₃₁	1	1	yes	characteristic
286	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
287	Q₁₆	—	2	2	no	—
288	SD₁₆	—	4	2	no	—
289	D₈	—	2	2	no	—
290	D₈	—	2	4	no	—
291	D₈	—	2	4	no	—
292	D₈	—	4	4	no	—
293	D₈	—	4	4	no	—
294	D₈	—	4	4	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
298	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
299	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
300	C₂×C₈	C₂⁴×C₁₃₁	1	1	yes	characteristic
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	—	2	1	no	—
303	C₄⋊C₄	—	4	1	no	—
304	C₄⋊C₄	—	4	1	no	—
305	C₄⋊C₄	—	4	1	no	—
306	C₄⋊C₄	—	4	1	no	—
307	C₂²⋊C₄	—	4	1	no	—
308	C₂²⋊C₄	—	4	1	no	—
309	C₂²⋊C₄	—	4	1	no	—
310	C₂²⋊C₄	—	4	1	no	—
311	C₂²⋊C₄	—	4	1	no	—
312	C₄²	—	4	1	no	—
313	C₄²	D₈×C₁₃₁	1	1	yes	characteristic
314	C₄²	D₈×C₁₃₁	1	1	yes	characteristic
315	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
316	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
317	C₁₆	—	2	4	no	—
318	C₂³	—	4	1	no	—
319	C₂³	—	4	4	no	—
320	C₂³	—	8	4	no	—
321	C₂³	—	8	4	no	—
322	C₂³	—	8	4	no	—
323	C₂³	C₂×D₈×C₁₃₁	1	1	yes	characteristic
324	Q₈	—	4	1	no	—
325	Q₈	—	4	1	no	—
326	D₄	—	4	4	no	—
327	D₄	—	4	1	no	—
328	D₄	—	4	4	no	—
329	D₄	—	4	1	no	—
330	D₄	—	8	4	no	—
331	D₄	—	8	4	no	—
332	D₄	—	8	4	no	—
333	D₄	—	8	4	no	—
334	D₄	—	8	2	no	—
335	D₄	—	8	4	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	8	2	no	—
344	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
345	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
346	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
347	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
348	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
349	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
350	C₈	—	2	1	no	—
351	C₈	—	2	1	no	—
352	C₈	AGL(1,ℤ/8)×C₁₃₁	1	2	yes	—
353	C₈	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	8	1	no	—
357	C₂²	—	8	4	no	—
358	C₂²	—	8	4	no	—
359	C₂²	—	8	1	no	—
360	C₂²	—	8	4	no	—
361	C₂²	—	8	1	no	—
362	C₂²	—	16	8	no	—
363	C₂²	#509×C₁₃₁	1	2	yes	—
364	C₂²	C₂²×D₈×C₁₃₁	1	1	yes	characteristic
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	8	1	no	—
370	C₄	—	8	1	no	—
371	C₄	—	8	1	no	—
372	C₄	#509×C₁₃₁	1	2	yes	—
373	C₄	#535×C₁₃₁	1	1	yes	characteristic
374	C₄	C₂×AGL(1,ℤ/8)×C₁₃₁	1	1	yes	characteristic
375	C₂	—	2	2	no	—
376	C₂	—	16	4	no	—
377	C₂	—	16	1	no	—
378	C₂	#3205×C₁₃₁	1	1	yes	characteristic
379	C₂	C₂×#509×C₁₃₁	1	1	yes	characteristic
380	C₂	C₂×#509×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃₁
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₁ ◁ C₂×C₄²×C₁₃₁ ◁ C₂×C₄×C₈×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3168×C₁₃₁	C₂	semidirect
2. C₂×#493×C₁₃₁	C₂	semidirect
3. #2250×C₁₃₁	C₂	semidirect
4. #2244×C₁₃₁	C₂	semidirect
5. #2207×C₁₃₁	C₂	semidirect
6. #2206×C₁₃₁	C₂	semidirect
7. #2187×C₁₃₁	C₂	semidirect
8. #2184×C₁₃₁	C₂	semidirect
9. #2163×C₁₃₁	C₂	semidirect
14. C₂×SD₃₂×C₁₃₁	C₂²	semidirect
15. C₂×D₁₆×C₁₃₁	C₂²	semidirect
16. #499×C₁₃₁	C₂²	semidirect
17. #495×C₁₃₁	C₂²	semidirect
26. C₄×Q₁₆×C₁₃₁	C₂²	semidirect
28. C₄×D₈×C₁₃₁	C₂²	semidirect
30. C₄⋊C₁₆×C₁₃₁	C₂²	semidirect
31. #357×C₁₃₁	C₂²	semidirect
32. #357×C₁₃₁	C₂²	semidirect
34. #346×C₁₃₁	C₂²	semidirect
190. #33783	C₁₃₁	direct (N × H)
191. C₁₃₁	#33783	direct (N × H)
192. #3168	C₂×C₁₃₁	semidirect
193. C₂×#493	C₂×C₁₃₁	semidirect
194. #2250	C₂×C₁₃₁	semidirect
195. #2244	C₂×C₁₃₁	semidirect
196. #2207	C₂×C₁₃₁	semidirect
197. #2206	C₂×C₁₃₁	semidirect
198. #2187	C₂×C₁₃₁	semidirect
199. #2184	C₂×C₁₃₁	semidirect
200. #2163	C₂×C₁₃₁	semidirect
205. C₂×SD₃₂	C₂²×C₁₃₁	semidirect
206. C₂×D₁₆	C₂²×C₁₃₁	semidirect
207. #499	C₂²×C₁₃₁	semidirect
208. #495	C₂²×C₁₃₁	semidirect
217. C₄×Q₁₆	C₂²×C₁₃₁	semidirect
219. C₄×D₈	C₂²×C₁₃₁	semidirect
221. C₄⋊C₁₆	C₂²×C₁₃₁	semidirect
222. #357	C₂²×C₁₃₁	semidirect
223. #357	C₂²×C₁₃₁	semidirect
225. #346	C₂²×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#3168×C₁₃₁	2
C₂×#493×C₁₃₁	2
#2250×C₁₃₁	2
#2244×C₁₃₁	2
#2207×C₁₃₁	2
#2206×C₁₃₁	2
#2187×C₁₃₁	2
#2184×C₁₃₁	2
#2163×C₁₃₁	2
#33783	131

Subgroups — C131×#33783 #45719667

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#33783 #45719667