Subgroups — C₁₃₁×#33648 #45719532

Order 33536.

632 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#466×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#427×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#2234×C₁₃₁	C₂	1	4	yes	maximal, complemented
4	#2233×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#2232×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2159×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#2140×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#2112×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×D₈×C₁₃₁	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
11	C₂×#121×C₁₃₁	—	2	1	no	—
12	C₂×#117×C₁₃₁	—	2	1	no	—
13	C₂×M₃₂×C₁₃₁	C₂²	1	2	yes	—
14	#466×C₁₃₁	—	2	1	no	—
15	#466×C₁₃₁	—	2	1	no	—
16	#466×C₁₃₁	C₂²	1	2	yes	—
17	#466×C₁₃₁	C₂²	1	2	yes	—
18	#427×C₁₃₁	—	2	1	no	—
19	#427×C₁₃₁	—	2	1	no	—
20	#427×C₁₃₁	C₂²	1	2	yes	—
21	#427×C₁₃₁	C₂²	1	2	yes	complemented
22	C₂×#107×C₁₃₁	C₂²	1	1	yes	characteristic
23	C₂×#107×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
24	C₂×#107×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
25	C₂×#106×C₁₃₁	—	2	1	no	—
26	C₂×#102×C₁₃₁	—	2	1	no	—
27	#367×C₁₃₁	C₂²	1	4	yes	complemented
28	#366×C₁₃₁	C₂²	1	4	yes	complemented
29	#357×C₁₃₁	C₂²	1	4	yes	complemented
30	#357×C₁₃₁	C₂²	1	4	yes	complemented
31	C₂²⋊C₁₆×C₁₃₁	C₂²	1	2	yes	complemented
32	C₂²⋊C₁₆×C₁₃₁	C₂²	1	2	yes	complemented
33	C₂²×D₄×C₁₃₁	—	2	1	no	—
34	C₂²×D₄×C₁₃₁	—	4	1	no	—
35	C₂³×C₄×C₁₃₁	D₄	1	1	yes	characteristic
36	C₂×D₈×C₁₃₁	—	2	1	no	—
37	C₂×D₈×C₁₃₁	—	2	4	no	—
38	C₂×D₈×C₁₃₁	C₂³	1	2	yes	—
39	C₂²×C₈×C₁₃₁	—	2	4	no	—
40	C₂²×C₈×C₁₃₁	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₁₃₁	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₁₃₁	D₄	1	1	yes	characteristic
43	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
46	#121×C₁₃₁	—	2	2	no	—
47	#121×C₁₃₁	—	2	2	no	—
48	#121×C₁₃₁	—	4	1	no	—
49	#121×C₁₃₁	—	4	1	no	—
50	#117×C₁₃₁	—	2	2	no	—
51	#117×C₁₃₁	—	2	2	no	—
52	#117×C₁₃₁	—	4	1	no	—
53	#117×C₁₃₁	—	4	1	no	—
54	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
57	C₂×C₂²⋊C₄×C₁₃₁	—	4	1	no	—
58	C₂×C₂²⋊C₄×C₁₃₁	—	4	1	no	—
59	C₂×C₄²×C₁₃₁	—	4	1	no	—
60	M₃₂×C₁₃₁	—	2	4	no	—
61	C₂×C₁₆×C₁₃₁	C₂³	1	4	yes	—
62	#107×C₁₃₁	—	2	1	no	—
63	#107×C₁₃₁	—	2	1	no	—
64	#107×C₁₃₁	—	2	1	no	—
65	#107×C₁₃₁	C₂³	1	2	yes	—
66	#107×C₁₃₁	C₂³	1	2	yes	—
67	#107×C₁₃₁	C₂³	1	2	yes	—
68	#106×C₁₃₁	—	2	2	no	—
69	#106×C₁₃₁	—	2	2	no	—
70	#102×C₁₃₁	—	2	2	no	—
71	#102×C₁₃₁	—	2	2	no	—
72	C₂⁴×C₁₃₁	—	4	1	no	—
73	C₂⁴×C₁₃₁	D₈	1	1	yes	characteristic
74	C₂×D₄×C₁₃₁	—	2	2	no	—
75	C₂×D₄×C₁₃₁	—	4	2	no	—
76	C₂×D₄×C₁₃₁	—	4	2	no	—
77	C₂×D₄×C₁₃₁	—	4	2	no	—
78	C₂×D₄×C₁₃₁	—	4	1	no	—
79	C₂×D₄×C₁₃₁	—	4	2	no	—
80	C₂×D₄×C₁₃₁	—	8	4	no	—
81	C₂²×C₄×C₁₃₁	—	2	2	no	—
82	C₂²×C₄×C₁₃₁	—	2	2	no	—
83	C₂²×C₄×C₁₃₁	—	4	1	no	—
84	C₂²×C₄×C₁₃₁	—	4	1	no	—
85	C₂²×C₄×C₁₃₁	—	4	1	no	—
86	C₂²×C₄×C₁₃₁	D₈	1	1	yes	characteristic
87	C₂²×C₄×C₁₃₁	D₈	1	1	yes	characteristic
88	C₂²×C₄×C₁₃₁	D₈	1	1	yes	characteristic
89	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
92	D₈×C₁₃₁	—	2	4	no	—
93	D₈×C₁₃₁	—	4	2	no	—
94	C₂×C₈×C₁₃₁	—	2	2	no	—
95	C₂×C₈×C₁₃₁	—	2	2	no	—
96	C₂×C₈×C₁₃₁	—	2	2	no	—
97	C₂×C₈×C₁₃₁	—	2	2	no	—
98	C₂×C₈×C₁₃₁	—	2	2	no	—
99	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
100	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
101	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
102	C₂×C₈×C₁₃₁	#41	1	4	yes	—
103	C₂×C₈×C₁₃₁	C₂⁴	1	1	yes	characteristic
104	C₄⋊C₄×C₁₃₁	—	2	2	no	—
105	C₄⋊C₄×C₁₃₁	—	2	2	no	—
106	C₄⋊C₄×C₁₃₁	—	2	2	no	—
107	C₄⋊C₄×C₁₃₁	—	4	1	no	—
108	C₄⋊C₄×C₁₃₁	—	4	1	no	—
109	C₄⋊C₄×C₁₃₁	—	4	1	no	—
110	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
111	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
112	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
113	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
114	C₄²×C₁₃₁	—	4	2	no	—
115	C₄²×C₁₃₁	—	4	2	no	—
116	C₁₆×C₁₃₁	—	2	4	no	—
117	C₂³×C₁₃₁	—	2	2	no	—
118	C₂³×C₁₃₁	—	2	2	no	—
119	C₂³×C₁₃₁	—	4	1	no	—
120	C₂³×C₁₃₁	—	4	2	no	—
121	C₂³×C₁₃₁	—	8	2	no	—
122	C₂³×C₁₃₁	—	8	2	no	—
123	C₂³×C₁₃₁	—	8	2	no	—
124	C₂³×C₁₃₁	C₂×D₈	1	1	yes	characteristic
125	C₂³×C₁₃₁	C₂×D₈	1	1	yes	characteristic
126	C₂³×C₁₃₁	C₂×D₈	1	1	yes	characteristic
127	D₄×C₁₃₁	—	4	2	no	—
128	D₄×C₁₃₁	—	4	2	no	—
129	D₄×C₁₃₁	—	8	4	no	—
130	D₄×C₁₃₁	—	8	4	no	—
131	D₄×C₁₃₁	—	8	2	no	—
132	C₂×C₄×C₁₃₁	—	2	2	no	—
133	C₂×C₄×C₁₃₁	—	2	1	no	—
134	C₂×C₄×C₁₃₁	—	2	1	no	—
135	C₂×C₄×C₁₃₁	—	2	1	no	—
136	C₂×C₄×C₁₃₁	—	2	1	no	—
137	C₂×C₄×C₁₃₁	—	2	2	no	—
138	C₂×C₄×C₁₃₁	—	2	2	no	—
139	C₂×C₄×C₁₃₁	—	4	2	no	—
140	C₂×C₄×C₁₃₁	—	4	2	no	—
141	C₂×C₄×C₁₃₁	—	4	2	no	—
142	C₂×C₄×C₁₃₁	—	8	2	no	—
143	C₂×C₄×C₁₃₁	—	8	2	no	—
144	C₂×C₄×C₁₃₁	—	8	2	no	—
145	C₂×C₄×C₁₃₁	#123	1	2	yes	—
146	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
147	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
148	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
149	C₂×C₄×C₁₃₁	#137	1	2	yes	—
150	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
151	C₈×C₁₃₁	—	2	1	no	—
152	C₈×C₁₃₁	—	2	1	no	—
153	C₈×C₁₃₁	#123	1	2	yes	—
154	C₈×C₁₃₁	C₂×#41	1	2	yes	—
155	C₂²×C₁₃₁	—	2	1	no	—
156	C₂²×C₁₃₁	—	2	1	no	—
157	C₂²×C₁₃₁	—	2	1	no	—
158	C₂²×C₁₃₁	—	2	1	no	—
159	C₂²×C₁₃₁	—	2	1	no	—
160	C₂²×C₁₃₁	—	2	1	no	—
161	C₂²×C₁₃₁	—	2	1	no	—
162	C₂²×C₁₃₁	—	4	4	no	—
163	C₂²×C₁₃₁	—	8	2	no	—
164	C₂²×C₁₃₁	—	8	2	no	—
165	C₂²×C₁₃₁	—	8	2	no	—
166	C₂²×C₁₃₁	—	16	4	no	—
167	C₂²×C₁₃₁	#480	1	2	yes	—
168	C₂²×C₁₃₁	#509	1	2	yes	—
169	C₂²×C₁₃₁	C₂²×D₈	1	1	yes	characteristic
170	C₄×C₁₃₁	—	2	1	no	—
171	C₄×C₁₃₁	—	2	1	no	—
172	C₄×C₁₃₁	—	8	2	no	—
173	C₄×C₁₃₁	—	8	2	no	—
174	C₄×C₁₃₁	—	8	2	no	—
175	C₄×C₁₃₁	#480	1	2	yes	—
176	C₄×C₁₃₁	C₂×#123	1	1	yes	characteristic
177	C₄×C₁₃₁	C₂×#137	1	1	yes	characteristic
178	C₂×C₁₃₁	—	2	2	no	—
179	C₂×C₁₃₁	—	2	2	no	—
180	C₂×C₁₃₁	—	4	1	no	—
181	C₂×C₁₃₁	—	16	2	no	—
182	C₂×C₁₃₁	C₂×#480	1	1	yes	characteristic
183	C₂×C₁₃₁	C₂×#509	1	1	yes	characteristic
184	C₂×C₁₃₁	#3414	1	1	yes	characteristic
185	#33648	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₁₃₁	#33648	1	1	yes	characteristic, direct product factor, Sylow
187	C₂×#466	C₂×C₁₃₁	1	1	yes	characteristic
188	C₂×#427	C₂×C₁₃₁	1	1	yes	characteristic, complemented
189	#2234	C₂×C₁₃₁	1	4	yes	complemented
190	#2233	C₂×C₁₃₁	1	2	yes	complemented
191	#2232	C₂×C₁₃₁	1	2	yes	complemented
192	#2159	C₂×C₁₃₁	1	2	yes	complemented
193	#2140	C₂×C₁₃₁	1	2	yes	complemented
194	#2112	C₂×C₁₃₁	1	1	yes	characteristic, complemented
195	C₂²×D₈	C₂²×C₁₃₁	1	1	yes	characteristic
196	C₂³×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
197	C₂×#121	—	2	1	no	—
198	C₂×#117	—	2	1	no	—
199	C₂×M₃₂	C₂²×C₁₃₁	1	2	yes	—
200	#466	—	2	1	no	—
201	#466	—	2	1	no	—
202	#466	C₂²×C₁₃₁	1	2	yes	—
203	#466	C₂²×C₁₃₁	1	2	yes	—
204	#427	—	2	1	no	—
205	#427	—	2	1	no	—
206	#427	C₂²×C₁₃₁	1	2	yes	—
207	#427	C₂²×C₁₃₁	1	2	yes	complemented
208	C₂×#107	C₂²×C₁₃₁	1	1	yes	characteristic
209	C₂×#107	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
210	C₂×#107	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
211	C₂×#106	—	2	1	no	—
212	C₂×#102	—	2	1	no	—
213	#367	C₂²×C₁₃₁	1	4	yes	complemented
214	#366	C₂²×C₁₃₁	1	4	yes	complemented
215	#357	C₂²×C₁₃₁	1	4	yes	complemented
216	#357	C₂²×C₁₃₁	1	4	yes	complemented
217	C₂²⋊C₁₆	C₂²×C₁₃₁	1	2	yes	complemented
218	C₂²⋊C₁₆	C₂²×C₁₃₁	1	2	yes	complemented
219	C₂²×D₄	—	2	1	no	—
220	C₂²×D₄	—	4	1	no	—
221	C₂³×C₄	D₄×C₁₃₁	1	1	yes	characteristic
222	C₂×D₈	—	2	1	no	—
223	C₂×D₈	—	2	4	no	—
224	C₂×D₈	C₂³×C₁₃₁	1	2	yes	—
225	C₂²×C₈	—	2	4	no	—
226	C₂²×C₈	D₄×C₁₃₁	1	1	yes	characteristic
227	C₂²×C₈	D₄×C₁₃₁	1	1	yes	characteristic
228	C₂²×C₈	D₄×C₁₃₁	1	1	yes	characteristic
229	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
230	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
231	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
232	#121	—	2	2	no	—
233	#121	—	2	2	no	—
234	#121	—	4	1	no	—
235	#121	—	4	1	no	—
236	#117	—	2	2	no	—
237	#117	—	2	2	no	—
238	#117	—	4	1	no	—
239	#117	—	4	1	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	—	2	1	no	—
243	C₂×C₂²⋊C₄	—	4	1	no	—
244	C₂×C₂²⋊C₄	—	4	1	no	—
245	C₂×C₄²	—	4	1	no	—
246	M₃₂	—	2	4	no	—
247	C₂×C₁₆	C₂³×C₁₃₁	1	4	yes	—
248	#107	—	2	1	no	—
249	#107	—	2	1	no	—
250	#107	—	2	1	no	—
251	#107	C₂³×C₁₃₁	1	2	yes	—
252	#107	C₂³×C₁₃₁	1	2	yes	—
253	#107	C₂³×C₁₃₁	1	2	yes	—
254	#106	—	2	2	no	—
255	#106	—	2	2	no	—
256	#102	—	2	2	no	—
257	#102	—	2	2	no	—
258	C₂⁴	—	4	1	no	—
259	C₂⁴	D₈×C₁₃₁	1	1	yes	characteristic
260	C₂×D₄	—	2	2	no	—
261	C₂×D₄	—	4	2	no	—
262	C₂×D₄	—	4	2	no	—
263	C₂×D₄	—	4	2	no	—
264	C₂×D₄	—	4	1	no	—
265	C₂×D₄	—	4	2	no	—
266	C₂×D₄	—	8	4	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	4	1	no	—
270	C₂²×C₄	—	4	1	no	—
271	C₂²×C₄	—	4	1	no	—
272	C₂²×C₄	D₈×C₁₃₁	1	1	yes	characteristic
273	C₂²×C₄	D₈×C₁₃₁	1	1	yes	characteristic
274	C₂²×C₄	D₈×C₁₃₁	1	1	yes	characteristic
275	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
277	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
278	D₈	—	2	4	no	—
279	D₈	—	4	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
286	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
287	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
288	C₂×C₈	#41×C₁₃₁	1	4	yes	—
289	C₂×C₈	C₂⁴×C₁₃₁	1	1	yes	characteristic
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	4	1	no	—
294	C₄⋊C₄	—	4	1	no	—
295	C₄⋊C₄	—	4	1	no	—
296	C₂²⋊C₄	—	4	2	no	—
297	C₂²⋊C₄	—	4	2	no	—
298	C₂²⋊C₄	—	4	2	no	—
299	C₂²⋊C₄	—	4	2	no	—
300	C₄²	—	4	2	no	—
301	C₄²	—	4	2	no	—
302	C₁₆	—	2	4	no	—
303	C₂³	—	2	2	no	—
304	C₂³	—	2	2	no	—
305	C₂³	—	4	1	no	—
306	C₂³	—	4	2	no	—
307	C₂³	—	8	2	no	—
308	C₂³	—	8	2	no	—
309	C₂³	—	8	2	no	—
310	C₂³	C₂×D₈×C₁₃₁	1	1	yes	characteristic
311	C₂³	C₂×D₈×C₁₃₁	1	1	yes	characteristic
312	C₂³	C₂×D₈×C₁₃₁	1	1	yes	characteristic
313	D₄	—	4	2	no	—
314	D₄	—	4	2	no	—
315	D₄	—	8	4	no	—
316	D₄	—	8	4	no	—
317	D₄	—	8	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	8	2	no	—
329	C₂×C₄	—	8	2	no	—
330	C₂×C₄	—	8	2	no	—
331	C₂×C₄	#123×C₁₃₁	1	2	yes	—
332	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
333	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
334	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
335	C₂×C₄	#137×C₁₃₁	1	2	yes	—
336	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
337	C₈	—	2	1	no	—
338	C₈	—	2	1	no	—
339	C₈	#123×C₁₃₁	1	2	yes	—
340	C₈	C₂×#41×C₁₃₁	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	—	4	4	no	—
349	C₂²	—	8	2	no	—
350	C₂²	—	8	2	no	—
351	C₂²	—	8	2	no	—
352	C₂²	—	16	4	no	—
353	C₂²	#480×C₁₃₁	1	2	yes	—
354	C₂²	#509×C₁₃₁	1	2	yes	—
355	C₂²	C₂²×D₈×C₁₃₁	1	1	yes	characteristic
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	—	8	2	no	—
359	C₄	—	8	2	no	—
360	C₄	—	8	2	no	—
361	C₄	#480×C₁₃₁	1	2	yes	—
362	C₄	C₂×#123×C₁₃₁	1	1	yes	characteristic
363	C₄	C₂×#137×C₁₃₁	1	1	yes	characteristic
364	C₂	—	2	2	no	—
365	C₂	—	2	2	no	—
366	C₂	—	4	1	no	—
367	C₂	—	16	2	no	—
368	C₂	C₂×#480×C₁₃₁	1	1	yes	characteristic
369	C₂	C₂×#509×C₁₃₁	1	1	yes	characteristic
370	C₂	#3414×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃₁
prime radical	C₂×#466×C₁₃₁	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₁ ◁ C₂³×C₄×C₁₃₁ ◁ C₂³×C₈×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#427×C₁₃₁	C₂	semidirect
3. #2234×C₁₃₁	C₂	semidirect
4. #2233×C₁₃₁	C₂	semidirect
5. #2232×C₁₃₁	C₂	semidirect
6. #2159×C₁₃₁	C₂	semidirect
7. #2140×C₁₃₁	C₂	semidirect
8. #2112×C₁₃₁	C₂	semidirect
21. #427×C₁₃₁	C₂²	semidirect
23. C₂×#107×C₁₃₁	C₂²	semidirect
24. C₂×#107×C₁₃₁	C₂²	semidirect
27. #367×C₁₃₁	C₂²	semidirect
28. #366×C₁₃₁	C₂²	semidirect
29. #357×C₁₃₁	C₂²	semidirect
30. #357×C₁₃₁	C₂²	semidirect
31. C₂²⋊C₁₆×C₁₃₁	C₂²	semidirect
32. C₂²⋊C₁₆×C₁₃₁	C₂²	semidirect
185. #33648	C₁₃₁	direct (N × H)
186. C₁₃₁	#33648	direct (N × H)
188. C₂×#427	C₂×C₁₃₁	semidirect
189. #2234	C₂×C₁₃₁	semidirect
190. #2233	C₂×C₁₃₁	semidirect
191. #2232	C₂×C₁₃₁	semidirect
192. #2159	C₂×C₁₃₁	semidirect
193. #2140	C₂×C₁₃₁	semidirect
194. #2112	C₂×C₁₃₁	semidirect
207. #427	C₂²×C₁₃₁	semidirect
209. C₂×#107	C₂²×C₁₃₁	semidirect
210. C₂×#107	C₂²×C₁₃₁	semidirect
213. #367	C₂²×C₁₃₁	semidirect
214. #366	C₂²×C₁₃₁	semidirect
215. #357	C₂²×C₁₃₁	semidirect
216. #357	C₂²×C₁₃₁	semidirect
217. C₂²⋊C₁₆	C₂²×C₁₃₁	semidirect
218. C₂²⋊C₁₆	C₂²×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#466×C₁₃₁	2
C₂×#427×C₁₃₁	2
#2234×C₁₃₁	2
#2233×C₁₃₁	2
#2232×C₁₃₁	2
#2159×C₁₃₁	2
#2140×C₁₃₁	2
#2112×C₁₃₁	2
#33648	131

Subgroups — C131×#33648 #45719532

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#33648 #45719532