Subgroups — C₁₃₁×#8149 #45694033

Order 33536.

554 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#431×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂²⋊C₈×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	C₄×C₂²⋊C₈×C₁₃₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#322×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#322×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#1273×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#1273×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
9	#431×C₁₃₁	—	2	2	no	—
10	#431×C₁₃₁	—	2	2	no	—
11	C₂×C₄⋊C₈×C₁₃₁	C₄	1	2	yes	—
12	C₂×C₂²⋊C₈×C₁₃₁	C₄	1	2	yes	—
13	C₂×C₂²⋊C₈×C₁₃₁	C₄	1	2	yes	—
14	C₂×C₂²⋊C₈×C₁₃₁	C₄	1	2	yes	—
15	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
21	#336×C₁₃₁	C₄	1	2	yes	—
22	#336×C₁₃₁	C₄	1	2	yes	—
23	#322×C₁₃₁	—	2	2	no	—
24	#322×C₁₃₁	—	2	2	no	—
25	C₂³×C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₈×C₁₃₁	C₂×C₄	1	2	yes	—
29	C₂²×C₈×C₁₃₁	C₂×C₄	1	2	yes	—
30	C₂²×C₈×C₁₃₁	C₂×C₄	1	2	yes	—
31	C₂²×C₈×C₁₃₁	C₂×C₄	1	2	yes	—
32	C₂²×C₈×C₁₃₁	C₂×C₄	1	2	yes	—
33	C₂²×C₈×C₁₃₁	C₂×C₄	1	2	yes	—
34	C₂×C₄²×C₁₃₁	—	2	1	no	—
35	C₂×C₄²×C₁₃₁	—	2	1	no	—
36	C₂×C₄²×C₁₃₁	—	2	1	no	—
37	C₂×C₄²×C₁₃₁	—	2	1	no	—
38	C₂×C₄²×C₁₃₁	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₃₁	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₃₁	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
42	C₄⋊C₈×C₁₃₁	—	2	4	no	—
43	C₂²⋊C₈×C₁₃₁	—	2	4	no	—
44	C₂²⋊C₈×C₁₃₁	—	2	4	no	—
45	C₂²⋊C₈×C₁₃₁	—	2	4	no	—
46	C₄×C₈×C₁₃₁	—	2	1	no	—
47	C₄×C₈×C₁₃₁	—	2	1	no	—
48	C₄×C₈×C₁₃₁	—	2	1	no	—
49	C₄×C₈×C₁₃₁	—	2	1	no	—
50	C₄×C₈×C₁₃₁	—	2	1	no	—
51	C₄×C₈×C₁₃₁	—	2	1	no	—
52	C₄×C₈×C₁₃₁	—	2	1	no	—
53	C₄×C₈×C₁₃₁	—	2	1	no	—
54	C₄×C₈×C₁₃₁	—	2	1	no	—
55	C₄×C₈×C₁₃₁	—	2	1	no	—
56	C₄×C₈×C₁₃₁	D₄	1	2	yes	—
57	C₄×C₈×C₁₃₁	D₄	1	2	yes	—
58	C₂⁴×C₁₃₁	C₄²	1	1	yes	characteristic
59	C₂²×C₄×C₁₃₁	—	2	1	no	—
60	C₂²×C₄×C₁₃₁	—	2	1	no	—
61	C₂²×C₄×C₁₃₁	—	2	2	no	—
62	C₂²×C₄×C₁₃₁	—	2	1	no	—
63	C₂²×C₄×C₁₃₁	—	2	1	no	—
64	C₂²×C₄×C₁₃₁	—	2	1	no	—
65	C₂²×C₄×C₁₃₁	—	2	1	no	—
66	C₂²×C₄×C₁₃₁	—	2	2	no	—
67	C₂²×C₄×C₁₃₁	—	2	2	no	—
68	C₂²×C₄×C₁₃₁	—	2	2	no	—
69	C₂²×C₄×C₁₃₁	—	2	2	no	—
70	C₂²×C₄×C₁₃₁	C₄²	1	1	yes	characteristic
71	C₂²×C₄×C₁₃₁	C₄²	1	1	yes	characteristic
72	C₂²×C₄×C₁₃₁	C₄²	1	1	yes	characteristic
73	C₂²×C₄×C₁₃₁	M₁₆	1	4	yes	—
74	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
77	C₂×C₈×C₁₃₁	—	2	2	no	—
78	C₂×C₈×C₁₃₁	—	2	2	no	—
79	C₂×C₈×C₁₃₁	—	2	2	no	—
80	C₂×C₈×C₁₃₁	—	2	2	no	—
81	C₂×C₈×C₁₃₁	—	2	2	no	—
82	C₂×C₈×C₁₃₁	—	2	2	no	—
83	C₂×C₈×C₁₃₁	—	2	2	no	—
84	C₂×C₈×C₁₃₁	—	2	2	no	—
85	C₂×C₈×C₁₃₁	—	2	2	no	—
86	C₂×C₈×C₁₃₁	—	2	2	no	—
87	C₂×C₈×C₁₃₁	—	2	2	no	—
88	C₂×C₈×C₁₃₁	—	2	2	no	—
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	C₂²⋊C₄	1	4	yes	—
94	C₂×C₈×C₁₃₁	M₁₆	1	4	yes	—
95	C₄²×C₁₃₁	—	2	1	no	—
96	C₄²×C₁₃₁	—	2	1	no	—
97	C₄²×C₁₃₁	—	2	1	no	—
98	C₄²×C₁₃₁	—	2	1	no	—
99	C₄²×C₁₃₁	—	2	1	no	—
100	C₄²×C₁₃₁	—	2	1	no	—
101	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
102	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
103	C₄²×C₁₃₁	#41	1	1	yes	characteristic
104	C₄²×C₁₃₁	#41	1	1	yes	characteristic
105	C₂³×C₁₃₁	—	2	1	no	—
106	C₂³×C₁₃₁	—	2	1	no	—
107	C₂³×C₁₃₁	—	2	1	no	—
108	C₂³×C₁₃₁	—	2	1	no	—
109	C₂³×C₁₃₁	—	2	1	no	—
110	C₂³×C₁₃₁	—	2	1	no	—
111	C₂³×C₁₃₁	#97	1	2	yes	—
112	C₂³×C₁₃₁	C₂×C₄²	1	1	yes	characteristic
113	C₂×C₄×C₁₃₁	—	2	1	no	—
114	C₂×C₄×C₁₃₁	—	2	1	no	—
115	C₂×C₄×C₁₃₁	—	2	4	no	—
116	C₂×C₄×C₁₃₁	—	2	4	no	—
117	C₂×C₄×C₁₃₁	—	2	1	no	—
118	C₂×C₄×C₁₃₁	—	2	1	no	—
119	C₂×C₄×C₁₃₁	—	2	1	no	—
120	C₂×C₄×C₁₃₁	—	2	1	no	—
121	C₂×C₄×C₁₃₁	—	2	1	no	—
122	C₂×C₄×C₁₃₁	—	2	1	no	—
123	C₂×C₄×C₁₃₁	—	4	2	no	—
124	C₂×C₄×C₁₃₁	—	4	2	no	—
125	C₂×C₄×C₁₃₁	—	4	2	no	—
126	C₂×C₄×C₁₃₁	—	4	2	no	—
127	C₂×C₄×C₁₃₁	#97	1	2	yes	—
128	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
129	C₂×C₄×C₁₃₁	#117	1	1	yes	characteristic
130	C₂×C₄×C₁₃₁	C₄×D₄	1	1	yes	characteristic
131	C₂×C₄×C₁₃₁	C₄×D₄	1	1	yes	characteristic
132	C₂×C₄×C₁₃₁	C₄×D₄	1	1	yes	characteristic
133	C₂×C₄×C₁₃₁	C₄×D₄	1	1	yes	characteristic
134	C₂×C₄×C₁₃₁	C₂×M₁₆	1	2	yes	—
135	C₂×C₄×C₁₃₁	C₂×M₁₆	1	2	yes	—
136	C₂×C₄×C₁₃₁	#131	1	2	yes	—
137	C₂×C₄×C₁₃₁	#131	1	2	yes	—
138	C₂×C₄×C₁₃₁	#131	1	2	yes	—
139	C₂×C₄×C₁₃₁	#131	1	2	yes	—
140	C₈×C₁₃₁	—	2	4	no	—
141	C₈×C₁₃₁	—	2	4	no	—
142	C₈×C₁₃₁	—	4	2	no	—
143	C₈×C₁₃₁	—	4	2	no	—
144	C₈×C₁₃₁	—	4	2	no	—
145	C₈×C₁₃₁	—	4	2	no	—
146	C₂²×C₁₃₁	—	2	2	no	—
147	C₂²×C₁₃₁	—	2	2	no	—
148	C₂²×C₁₃₁	—	2	2	no	—
149	C₂²×C₁₃₁	—	4	1	no	—
150	C₂²×C₁₃₁	—	4	1	no	—
151	C₂²×C₁₃₁	—	4	1	no	—
152	C₂²×C₁₃₁	—	4	1	no	—
153	C₂²×C₁₃₁	C₄×C₂²⋊C₄	1	1	yes	characteristic
154	C₂²×C₁₃₁	C₂×#97	1	1	yes	characteristic
155	C₂²×C₁₃₁	C₄×M₁₆	1	1	yes	characteristic
156	C₂²×C₁₃₁	#405	1	1	yes	characteristic
157	C₂²×C₁₃₁	#405	1	1	yes	characteristic
158	C₂²×C₁₃₁	#405	1	1	yes	characteristic
159	C₂²×C₁₃₁	#405	1	1	yes	characteristic
160	C₄×C₁₃₁	—	2	2	no	—
161	C₄×C₁₃₁	—	4	1	no	—
162	C₄×C₁₃₁	—	4	1	no	—
163	C₄×C₁₃₁	#408	1	2	yes	—
164	C₄×C₁₃₁	#433	1	2	yes	—
165	C₄×C₁₃₁	#435	1	2	yes	—
166	C₄×C₁₃₁	#435	1	2	yes	—
167	C₄×C₁₃₁	#435	1	2	yes	—
168	C₄×C₁₃₁	#436	1	2	yes	—
169	C₂×C₁₃₁	—	4	2	no	—
170	C₂×C₁₃₁	#1451	1	1	yes	characteristic
171	C₂×C₁₃₁	#1452	1	1	yes	characteristic
172	C₂×C₁₃₁	#1453	1	1	yes	characteristic
173	C₂×C₁₃₁	#1454	1	1	yes	characteristic
174	C₂×C₁₃₁	#1750	1	1	yes	characteristic
175	C₂×C₁₃₁	#1752	1	1	yes	characteristic
176	C₂×C₁₃₁	#1753	1	1	yes	characteristic
177	#8149	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₁₃₁	#8149	1	1	yes	characteristic, direct product factor, Sylow
179	C₂×#431	C₂×C₁₃₁	1	1	yes	characteristic
180	C₄×C₂²⋊C₈	C₂×C₁₃₁	1	1	yes	characteristic
181	C₄×C₂²⋊C₈	C₂×C₁₃₁	1	1	yes	characteristic
182	C₂×#322	C₂×C₁₃₁	1	1	yes	characteristic, complemented
183	C₂×#322	C₂×C₁₃₁	1	1	yes	characteristic, complemented
184	#1273	C₂×C₁₃₁	1	1	yes	characteristic, complemented
185	#1273	C₂×C₁₃₁	1	1	yes	characteristic, complemented
186	C₂²×C₄²	C₂²×C₁₃₁	1	1	yes	characteristic
187	#431	—	2	2	no	—
188	#431	—	2	2	no	—
189	C₂×C₄⋊C₈	C₄×C₁₃₁	1	2	yes	—
190	C₂×C₂²⋊C₈	C₄×C₁₃₁	1	2	yes	—
191	C₂×C₂²⋊C₈	C₄×C₁₃₁	1	2	yes	—
192	C₂×C₂²⋊C₈	C₄×C₁₃₁	1	2	yes	—
193	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
194	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
195	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
196	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
197	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
198	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
199	#336	C₄×C₁₃₁	1	2	yes	—
200	#336	C₄×C₁₃₁	1	2	yes	—
201	#322	—	2	2	no	—
202	#322	—	2	2	no	—
203	C₂³×C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
204	C₂³×C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
205	C₂³×C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
206	C₂²×C₈	C₂×C₄×C₁₃₁	1	2	yes	—
207	C₂²×C₈	C₂×C₄×C₁₃₁	1	2	yes	—
208	C₂²×C₈	C₂×C₄×C₁₃₁	1	2	yes	—
209	C₂²×C₈	C₂×C₄×C₁₃₁	1	2	yes	—
210	C₂²×C₈	C₂×C₄×C₁₃₁	1	2	yes	—
211	C₂²×C₈	C₂×C₄×C₁₃₁	1	2	yes	—
212	C₂×C₄²	—	2	1	no	—
213	C₂×C₄²	—	2	1	no	—
214	C₂×C₄²	—	2	1	no	—
215	C₂×C₄²	—	2	1	no	—
216	C₂×C₄²	C₂×C₄×C₁₃₁	1	1	yes	characteristic
217	C₂×C₄²	C₂×C₄×C₁₃₁	1	1	yes	characteristic
218	C₂×C₄²	C₂×C₄×C₁₃₁	1	1	yes	characteristic
219	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
220	C₄⋊C₈	—	2	4	no	—
221	C₂²⋊C₈	—	2	4	no	—
222	C₂²⋊C₈	—	2	4	no	—
223	C₂²⋊C₈	—	2	4	no	—
224	C₄×C₈	—	2	1	no	—
225	C₄×C₈	—	2	1	no	—
226	C₄×C₈	—	2	1	no	—
227	C₄×C₈	—	2	1	no	—
228	C₄×C₈	—	2	1	no	—
229	C₄×C₈	—	2	1	no	—
230	C₄×C₈	—	2	1	no	—
231	C₄×C₈	—	2	1	no	—
232	C₄×C₈	—	2	1	no	—
233	C₄×C₈	—	2	1	no	—
234	C₄×C₈	D₄×C₁₃₁	1	2	yes	—
235	C₄×C₈	D₄×C₁₃₁	1	2	yes	—
236	C₂⁴	C₄²×C₁₃₁	1	1	yes	characteristic
237	C₂²×C₄	—	2	1	no	—
238	C₂²×C₄	—	2	1	no	—
239	C₂²×C₄	—	2	2	no	—
240	C₂²×C₄	—	2	1	no	—
241	C₂²×C₄	—	2	1	no	—
242	C₂²×C₄	—	2	1	no	—
243	C₂²×C₄	—	2	1	no	—
244	C₂²×C₄	—	2	2	no	—
245	C₂²×C₄	—	2	2	no	—
246	C₂²×C₄	—	2	2	no	—
247	C₂²×C₄	—	2	2	no	—
248	C₂²×C₄	C₄²×C₁₃₁	1	1	yes	characteristic
249	C₂²×C₄	C₄²×C₁₃₁	1	1	yes	characteristic
250	C₂²×C₄	C₄²×C₁₃₁	1	1	yes	characteristic
251	C₂²×C₄	M₁₆×C₁₃₁	1	4	yes	—
252	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
253	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
254	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
255	C₂×C₈	—	2	2	no	—
256	C₂×C₈	—	2	2	no	—
257	C₂×C₈	—	2	2	no	—
258	C₂×C₈	—	2	2	no	—
259	C₂×C₈	—	2	2	no	—
260	C₂×C₈	—	2	2	no	—
261	C₂×C₈	—	2	2	no	—
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	—	2	2	no	—
264	C₂×C₈	—	2	2	no	—
265	C₂×C₈	—	2	2	no	—
266	C₂×C₈	—	2	2	no	—
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	C₂²⋊C₄×C₁₃₁	1	4	yes	—
272	C₂×C₈	M₁₆×C₁₃₁	1	4	yes	—
273	C₄²	—	2	1	no	—
274	C₄²	—	2	1	no	—
275	C₄²	—	2	1	no	—
276	C₄²	—	2	1	no	—
277	C₄²	—	2	1	no	—
278	C₄²	—	2	1	no	—
279	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
280	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
281	C₄²	#41×C₁₃₁	1	1	yes	characteristic
282	C₄²	#41×C₁₃₁	1	1	yes	characteristic
283	C₂³	—	2	1	no	—
284	C₂³	—	2	1	no	—
285	C₂³	—	2	1	no	—
286	C₂³	—	2	1	no	—
287	C₂³	—	2	1	no	—
288	C₂³	—	2	1	no	—
289	C₂³	#97×C₁₃₁	1	2	yes	—
290	C₂³	C₂×C₄²×C₁₃₁	1	1	yes	characteristic
291	C₂×C₄	—	2	1	no	—
292	C₂×C₄	—	2	1	no	—
293	C₂×C₄	—	2	4	no	—
294	C₂×C₄	—	2	4	no	—
295	C₂×C₄	—	2	1	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	4	2	no	—
302	C₂×C₄	—	4	2	no	—
303	C₂×C₄	—	4	2	no	—
304	C₂×C₄	—	4	2	no	—
305	C₂×C₄	#97×C₁₃₁	1	2	yes	—
306	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
307	C₂×C₄	#117×C₁₃₁	1	1	yes	characteristic
308	C₂×C₄	C₄×D₄×C₁₃₁	1	1	yes	characteristic
309	C₂×C₄	C₄×D₄×C₁₃₁	1	1	yes	characteristic
310	C₂×C₄	C₄×D₄×C₁₃₁	1	1	yes	characteristic
311	C₂×C₄	C₄×D₄×C₁₃₁	1	1	yes	characteristic
312	C₂×C₄	C₂×M₁₆×C₁₃₁	1	2	yes	—
313	C₂×C₄	C₂×M₁₆×C₁₃₁	1	2	yes	—
314	C₂×C₄	#131×C₁₃₁	1	2	yes	—
315	C₂×C₄	#131×C₁₃₁	1	2	yes	—
316	C₂×C₄	#131×C₁₃₁	1	2	yes	—
317	C₂×C₄	#131×C₁₃₁	1	2	yes	—
318	C₈	—	2	4	no	—
319	C₈	—	2	4	no	—
320	C₈	—	4	2	no	—
321	C₈	—	4	2	no	—
322	C₈	—	4	2	no	—
323	C₈	—	4	2	no	—
324	C₂²	—	2	2	no	—
325	C₂²	—	2	2	no	—
326	C₂²	—	2	2	no	—
327	C₂²	—	4	1	no	—
328	C₂²	—	4	1	no	—
329	C₂²	—	4	1	no	—
330	C₂²	—	4	1	no	—
331	C₂²	C₄×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
332	C₂²	C₂×#97×C₁₃₁	1	1	yes	characteristic
333	C₂²	C₄×M₁₆×C₁₃₁	1	1	yes	characteristic
334	C₂²	#405×C₁₃₁	1	1	yes	characteristic
335	C₂²	#405×C₁₃₁	1	1	yes	characteristic
336	C₂²	#405×C₁₃₁	1	1	yes	characteristic
337	C₂²	#405×C₁₃₁	1	1	yes	characteristic
338	C₄	—	2	2	no	—
339	C₄	—	4	1	no	—
340	C₄	—	4	1	no	—
341	C₄	#408×C₁₃₁	1	2	yes	—
342	C₄	#433×C₁₃₁	1	2	yes	—
343	C₄	#435×C₁₃₁	1	2	yes	—
344	C₄	#435×C₁₃₁	1	2	yes	—
345	C₄	#435×C₁₃₁	1	2	yes	—
346	C₄	#436×C₁₃₁	1	2	yes	—
347	C₂	—	4	2	no	—
348	C₂	#1451×C₁₃₁	1	1	yes	characteristic
349	C₂	#1452×C₁₃₁	1	1	yes	characteristic
350	C₂	#1453×C₁₃₁	1	1	yes	characteristic
351	C₂	#1454×C₁₃₁	1	1	yes	characteristic
352	C₂	#1750×C₁₃₁	1	1	yes	characteristic
353	C₂	#1752×C₁₃₁	1	1	yes	characteristic
354	C₂	#1753×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄²×C₁₃₁	C₂³
commutator	C₂³	C₂×C₄²×C₁₃₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃₁
socle	C₂³×C₁₃₁	C₂×C₄²
prime radical	C₂⁴×C₁₃₁	C₄²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×#322×C₁₃₁	C₂	semidirect
5. C₂×#322×C₁₃₁	C₂	semidirect
6. #1273×C₁₃₁	C₂	semidirect
7. #1273×C₁₃₁	C₂	semidirect
177. #8149	C₁₃₁	direct (N × H)
178. C₁₃₁	#8149	direct (N × H)
182. C₂×#322	C₂×C₁₃₁	semidirect
183. C₂×#322	C₂×C₁₃₁	semidirect
184. #1273	C₂×C₁₃₁	semidirect
185. #1273	C₂×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#431×C₁₃₁	2
C₄×C₂²⋊C₈×C₁₃₁	2
C₂×#322×C₁₃₁	2
#1273×C₁₃₁	2
#8149	131

Subgroups — C131×#8149 #45694033

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#8149 #45694033