Subgroups — C₁₃₁×#22244 #45708128

Order 33536.

722 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#446×C₁₃₁	C₂	1	2	yes	maximal
2	C₄×C₄⋊Q₈×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#1985×C₁₃₁	C₂	1	2	yes	maximal
4	#1917×C₁₃₁	C₂	1	2	yes	maximal
5	#1917×C₁₃₁	C₂	1	2	yes	maximal
6	#1916×C₁₃₁	C₂	1	2	yes	maximal
7	#1916×C₁₃₁	C₂	1	2	yes	maximal
8	#1831×C₁₃₁	C₂	1	1	yes	maximal, characteristic
9	#1745×C₁₃₁	C₂	1	1	yes	maximal, characteristic
10	C₂×C₄⋊Q₈×C₁₃₁	C₄	1	1	yes	characteristic
11	C₂×C₄×Q₈×C₁₃₁	C₂²	1	2	yes	—
12	#446×C₁₃₁	—	2	8	no	—
13	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	2	yes	—
14	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	2	yes	—
15	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	2	yes	—
16	C₂×#97×C₁₃₁	C₂²	1	1	yes	characteristic
17	C₂×#97×C₁₃₁	C₂²	1	2	yes	—
18	C₂×#97×C₁₃₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₈×C₁₃₁	C₂²	1	2	yes	—
20	#391×C₁₃₁	C₄	1	2	yes	—
21	#389×C₁₃₁	C₄	1	2	yes	—
22	#389×C₁₃₁	C₄	1	1	yes	characteristic
23	#389×C₁₃₁	C₄	1	1	yes	characteristic
24	#384×C₁₃₁	C₄	1	1	yes	characteristic
25	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
26	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
27	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
28	C₄³×C₁₃₁	C₂²	1	1	yes	characteristic
29	#336×C₁₃₁	C₂²	1	2	yes	—
30	#336×C₁₃₁	C₂²	1	2	yes	—
31	#336×C₁₃₁	C₂²	1	2	yes	—
32	#336×C₁₃₁	C₂²	1	2	yes	—
33	#336×C₁₃₁	C₂²	1	2	yes	—
34	#336×C₁₃₁	C₂²	1	2	yes	—
35	#336×C₁₃₁	C₂²	1	1	yes	characteristic
36	#336×C₁₃₁	C₂²	1	2	yes	—
37	#336×C₁₃₁	C₂²	1	1	yes	characteristic
38	C₂²×Q₈×C₁₃₁	C₂×C₄	1	2	yes	—
39	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
40	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
41	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
42	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
43	C₄⋊Q₈×C₁₃₁	—	2	4	no	—
44	C₄×Q₈×C₁₃₁	—	2	4	no	—
45	C₄×Q₈×C₁₃₁	—	2	4	no	—
46	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	2	yes	—
47	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	2	yes	—
48	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	2	yes	—
50	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	2	yes	—
51	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	2	yes	—
52	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₁₃₁	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₁₃₁	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₁₃₁	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₁₃₁	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
60	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
61	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
64	C₄⋊C₈×C₁₃₁	—	2	4	no	—
65	C₄⋊C₈×C₁₃₁	—	2	4	no	—
66	C₄⋊C₈×C₁₃₁	—	2	4	no	—
67	#97×C₁₃₁	—	2	4	no	—
68	#97×C₁₃₁	—	2	2	no	—
69	#97×C₁₃₁	D₄	1	4	yes	—
70	C₄×C₈×C₁₃₁	—	2	4	no	—
71	#95×C₁₃₁	C₂×C₄	1	2	yes	—
72	#95×C₁₃₁	C₂×C₄	1	2	yes	—
73	#95×C₁₃₁	C₂×C₄	1	2	yes	—
74	#95×C₁₃₁	C₂×C₄	1	2	yes	—
75	C₂×Q₈×C₁₃₁	—	2	4	no	—
76	C₂×Q₈×C₁₃₁	—	2	4	no	—
77	C₂×Q₈×C₁₃₁	—	4	2	no	—
78	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
89	C₂×C₈×C₁₃₁	—	2	2	no	—
90	C₂×C₈×C₁₃₁	—	2	2	no	—
91	C₂×C₈×C₁₃₁	—	2	2	no	—
92	C₂×C₈×C₁₃₁	—	2	2	no	—
93	C₂×C₈×C₁₃₁	—	2	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	—	2	2	no	—
100	C₂×C₈×C₁₃₁	C₂×D₄	1	4	yes	—
101	C₄⋊C₄×C₁₃₁	—	2	4	no	—
102	C₄⋊C₄×C₁₃₁	—	2	4	no	—
103	C₄⋊C₄×C₁₃₁	—	2	4	no	—
104	C₄⋊C₄×C₁₃₁	—	2	4	no	—
105	C₄⋊C₄×C₁₃₁	—	2	2	no	—
106	C₄⋊C₄×C₁₃₁	—	2	4	no	—
107	C₄⋊C₄×C₁₃₁	—	4	1	no	—
108	C₄⋊C₄×C₁₃₁	—	4	1	no	—
109	C₄⋊C₄×C₁₃₁	M₁₆	1	4	yes	—
110	C₄²×C₁₃₁	—	2	2	no	—
111	C₄²×C₁₃₁	—	2	2	no	—
112	C₄²×C₁₃₁	—	2	2	no	—
113	C₄²×C₁₃₁	—	2	2	no	—
114	C₄²×C₁₃₁	—	2	2	no	—
115	C₄²×C₁₃₁	—	2	2	no	—
116	C₄²×C₁₃₁	—	2	2	no	—
117	C₄²×C₁₃₁	—	2	2	no	—
118	C₄²×C₁₃₁	—	4	1	no	—
119	C₄²×C₁₃₁	—	4	1	no	—
120	C₄²×C₁₃₁	C₂×D₄	1	2	yes	—
121	C₄²×C₁₃₁	#41	1	2	yes	—
122	C₂³×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
123	Q₈×C₁₃₁	—	4	8	no	—
124	C₂×C₄×C₁₃₁	—	2	2	no	—
125	C₂×C₄×C₁₃₁	—	2	1	no	—
126	C₂×C₄×C₁₃₁	—	2	1	no	—
127	C₂×C₄×C₁₃₁	—	2	1	no	—
128	C₂×C₄×C₁₃₁	—	2	1	no	—
129	C₂×C₄×C₁₃₁	—	2	1	no	—
130	C₂×C₄×C₁₃₁	—	2	1	no	—
131	C₂×C₄×C₁₃₁	—	2	1	no	—
132	C₂×C₄×C₁₃₁	—	2	1	no	—
133	C₂×C₄×C₁₃₁	—	2	2	no	—
134	C₂×C₄×C₁₃₁	—	2	2	no	—
135	C₂×C₄×C₁₃₁	—	2	2	no	—
136	C₂×C₄×C₁₃₁	—	2	2	no	—
137	C₂×C₄×C₁₃₁	—	2	1	no	—
138	C₂×C₄×C₁₃₁	—	2	1	no	—
139	C₂×C₄×C₁₃₁	—	2	2	no	—
140	C₂×C₄×C₁₃₁	—	2	1	no	—
141	C₂×C₄×C₁₃₁	—	2	2	no	—
142	C₂×C₄×C₁₃₁	—	2	2	no	—
143	C₂×C₄×C₁₃₁	—	2	1	no	—
144	C₂×C₄×C₁₃₁	—	2	1	no	—
145	C₂×C₄×C₁₃₁	—	2	1	no	—
146	C₂×C₄×C₁₃₁	—	2	2	no	—
147	C₂×C₄×C₁₃₁	—	2	2	no	—
148	C₂×C₄×C₁₃₁	—	2	2	no	—
149	C₂×C₄×C₁₃₁	C₄×D₄	1	2	yes	—
150	C₂×C₄×C₁₃₁	C₄×D₄	1	2	yes	—
151	C₂×C₄×C₁₃₁	C₂×M₁₆	1	2	yes	—
152	C₂×C₄×C₁₃₁	C₂×M₁₆	1	4	yes	—
153	C₂×C₄×C₁₃₁	#131	1	2	yes	—
154	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
156	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
157	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
158	C₈×C₁₃₁	—	2	4	no	—
159	C₈×C₁₃₁	—	4	2	no	—
160	C₈×C₁₃₁	—	4	2	no	—
161	C₈×C₁₃₁	—	4	2	no	—
162	C₂²×C₁₃₁	C₂×C₄×D₄	1	1	yes	characteristic
163	C₂²×C₁₃₁	#519	1	1	yes	characteristic
164	C₂²×C₁₃₁	#519	1	1	yes	characteristic
165	C₂²×C₁₃₁	C₂²×M₁₆	1	1	yes	characteristic
166	C₂²×C₁₃₁	C₂×#131	1	1	yes	characteristic
167	C₂²×C₁₃₁	#568	1	1	yes	characteristic
168	C₂²×C₁₃₁	#568	1	1	yes	characteristic
169	C₄×C₁₃₁	—	2	2	no	—
170	C₄×C₁₃₁	—	2	4	no	—
171	C₄×C₁₃₁	—	2	2	no	—
172	C₄×C₁₃₁	—	2	2	no	—
173	C₄×C₁₃₁	—	2	2	no	—
174	C₄×C₁₃₁	—	4	2	no	—
175	C₄×C₁₃₁	—	4	2	no	—
176	C₄×C₁₃₁	—	4	2	no	—
177	C₄×C₁₃₁	—	4	1	no	—
178	C₄×C₁₃₁	—	4	1	no	—
179	C₄×C₁₃₁	#536	1	2	yes	—
180	C₄×C₁₃₁	#541	1	2	yes	—
181	C₂×C₁₃₁	#2327	1	1	yes	characteristic
182	C₂×C₁₃₁	D₄×M₁₆	1	1	yes	characteristic
183	C₂×C₁₃₁	#2935	1	1	yes	characteristic
184	C₂×C₁₃₁	#2983	1	1	yes	characteristic
185	C₂×C₁₃₁	#2984	1	1	yes	characteristic
186	C₂×C₁₃₁	#2985	1	1	yes	characteristic
187	C₂×C₁₃₁	#2987	1	1	yes	characteristic
188	#22244	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₁₃₁	#22244	1	1	yes	characteristic, direct product factor, Sylow
190	C₂×#446	C₂×C₁₃₁	1	2	yes	—
191	C₄×C₄⋊Q₈	C₂×C₁₃₁	1	1	yes	characteristic
192	#1985	C₂×C₁₃₁	1	2	yes	—
193	#1917	C₂×C₁₃₁	1	2	yes	—
194	#1917	C₂×C₁₃₁	1	2	yes	—
195	#1916	C₂×C₁₃₁	1	2	yes	—
196	#1916	C₂×C₁₃₁	1	2	yes	—
197	#1831	C₂×C₁₃₁	1	1	yes	characteristic
198	#1745	C₂×C₁₃₁	1	1	yes	characteristic
199	C₂×C₄⋊Q₈	C₄×C₁₃₁	1	1	yes	characteristic
200	C₂×C₄×Q₈	C₂²×C₁₃₁	1	2	yes	—
201	#446	—	2	8	no	—
202	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	2	yes	—
203	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	2	yes	—
204	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	2	yes	—
205	C₂×#97	C₂²×C₁₃₁	1	2	yes	—
206	C₂×#97	C₂²×C₁₃₁	1	1	yes	characteristic
207	C₂×#97	C₂²×C₁₃₁	1	1	yes	characteristic
208	C₂×C₄×C₈	C₂²×C₁₃₁	1	2	yes	—
209	#391	C₄×C₁₃₁	1	2	yes	—
210	#389	C₄×C₁₃₁	1	2	yes	—
211	#389	C₄×C₁₃₁	1	1	yes	characteristic
212	#389	C₄×C₁₃₁	1	1	yes	characteristic
213	#384	C₄×C₁₃₁	1	1	yes	characteristic
214	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
215	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
216	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
217	C₄³	C₂²×C₁₃₁	1	1	yes	characteristic
218	#336	C₂²×C₁₃₁	1	1	yes	characteristic
219	#336	C₂²×C₁₃₁	1	2	yes	—
220	#336	C₂²×C₁₃₁	1	1	yes	characteristic
221	#336	C₂²×C₁₃₁	1	2	yes	—
222	#336	C₂²×C₁₃₁	1	2	yes	—
223	#336	C₂²×C₁₃₁	1	2	yes	—
224	#336	C₂²×C₁₃₁	1	2	yes	—
225	#336	C₂²×C₁₃₁	1	2	yes	—
226	#336	C₂²×C₁₃₁	1	2	yes	—
227	C₂²×Q₈	C₂×C₄×C₁₃₁	1	2	yes	—
228	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
229	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
230	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
231	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
232	C₄⋊Q₈	—	2	4	no	—
233	C₄×Q₈	—	2	4	no	—
234	C₄×Q₈	—	2	4	no	—
235	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	2	yes	—
236	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	2	yes	—
237	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	2	yes	—
238	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
239	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	2	yes	—
240	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	2	yes	—
241	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
242	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
243	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
244	C₂×C₄²	C₂×C₄×C₁₃₁	1	1	yes	characteristic
245	C₂×C₄²	C₂×C₄×C₁₃₁	1	1	yes	characteristic
246	C₂×C₄²	C₂×C₄×C₁₃₁	1	1	yes	characteristic
247	C₂×C₄²	C₂×C₄×C₁₃₁	1	1	yes	characteristic
248	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
249	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
250	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
251	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
252	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
253	C₄⋊C₈	—	2	4	no	—
254	C₄⋊C₈	—	2	4	no	—
255	C₄⋊C₈	—	2	4	no	—
256	#97	—	2	4	no	—
257	#97	—	2	2	no	—
258	#97	D₄×C₁₃₁	1	4	yes	—
259	C₄×C₈	—	2	4	no	—
260	#95	C₂×C₄×C₁₃₁	1	2	yes	—
261	#95	C₂×C₄×C₁₃₁	1	2	yes	—
262	#95	C₂×C₄×C₁₃₁	1	2	yes	—
263	#95	C₂×C₄×C₁₃₁	1	2	yes	—
264	C₂×Q₈	—	2	4	no	—
265	C₂×Q₈	—	2	4	no	—
266	C₂×Q₈	—	4	2	no	—
267	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
268	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
269	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
270	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
271	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
272	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
273	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
274	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
275	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
276	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
277	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	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	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	C₂×D₄×C₁₃₁	1	4	yes	—
290	C₄⋊C₄	—	2	4	no	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄⋊C₄	—	2	4	no	—
293	C₄⋊C₄	—	2	4	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	4	no	—
296	C₄⋊C₄	—	4	1	no	—
297	C₄⋊C₄	—	4	1	no	—
298	C₄⋊C₄	M₁₆×C₁₃₁	1	4	yes	—
299	C₄²	—	2	2	no	—
300	C₄²	—	2	2	no	—
301	C₄²	—	2	2	no	—
302	C₄²	—	2	2	no	—
303	C₄²	—	2	2	no	—
304	C₄²	—	2	2	no	—
305	C₄²	—	2	2	no	—
306	C₄²	—	2	2	no	—
307	C₄²	—	4	1	no	—
308	C₄²	—	4	1	no	—
309	C₄²	C₂×D₄×C₁₃₁	1	2	yes	—
310	C₄²	#41×C₁₃₁	1	2	yes	—
311	C₂³	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
312	Q₈	—	4	8	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	C₄×D₄×C₁₃₁	1	2	yes	—
339	C₂×C₄	C₄×D₄×C₁₃₁	1	2	yes	—
340	C₂×C₄	C₂×M₁₆×C₁₃₁	1	2	yes	—
341	C₂×C₄	C₂×M₁₆×C₁₃₁	1	4	yes	—
342	C₂×C₄	#131×C₁₃₁	1	2	yes	—
343	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
344	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
345	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
346	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
347	C₈	—	2	4	no	—
348	C₈	—	4	2	no	—
349	C₈	—	4	2	no	—
350	C₈	—	4	2	no	—
351	C₂²	C₂×C₄×D₄×C₁₃₁	1	1	yes	characteristic
352	C₂²	#519×C₁₃₁	1	1	yes	characteristic
353	C₂²	#519×C₁₃₁	1	1	yes	characteristic
354	C₂²	C₂²×M₁₆×C₁₃₁	1	1	yes	characteristic
355	C₂²	C₂×#131×C₁₃₁	1	1	yes	characteristic
356	C₂²	#568×C₁₃₁	1	1	yes	characteristic
357	C₂²	#568×C₁₃₁	1	1	yes	characteristic
358	C₄	—	2	2	no	—
359	C₄	—	2	4	no	—
360	C₄	—	2	2	no	—
361	C₄	—	2	2	no	—
362	C₄	—	2	2	no	—
363	C₄	—	4	1	no	—
364	C₄	—	4	1	no	—
365	C₄	—	4	2	no	—
366	C₄	—	4	2	no	—
367	C₄	—	4	2	no	—
368	C₄	#536×C₁₃₁	1	2	yes	—
369	C₄	#541×C₁₃₁	1	2	yes	—
370	C₂	#2327×C₁₃₁	1	1	yes	characteristic
371	C₂	D₄×M₁₆×C₁₃₁	1	1	yes	characteristic
372	C₂	#2935×C₁₃₁	1	1	yes	characteristic
373	C₂	#2983×C₁₃₁	1	1	yes	characteristic
374	C₂	#2984×C₁₃₁	1	1	yes	characteristic
375	C₂	#2985×C₁₃₁	1	1	yes	characteristic
376	C₂	#2987×C₁₃₁	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
188. #22244	C₁₃₁	direct (N × H)
189. C₁₃₁	#22244	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#446×C₁₃₁	2
C₄×C₄⋊Q₈×C₁₃₁	2
#1985×C₁₃₁	2
#1917×C₁₃₁	2
#1916×C₁₃₁	2
#1831×C₁₃₁	2
#1745×C₁₃₁	2
#22244	131

Subgroups — C131×#22244 #45708128

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#22244 #45708128