Subgroups — C₁₃₁×#33503 #45719387

Order 33536.

526 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#41×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#2183×C₁₃₁	C₂	1	2	yes	maximal, complemented
3	#2169×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#2168×C₁₃₁	C₂	1	4	yes	maximal, complemented
5	#2163×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2162×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#2150×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	C₂×C₄⋊C₁₆×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#41×C₁₃₁	C₄	1	1	yes	characteristic
10	C₂×M₃₂×C₁₃₁	C₂²	1	4	yes	—
11	C₂²×C₁₆×C₁₃₁	C₂²	1	2	yes	—
12	C₈×Q₈×C₁₃₁	C₄	1	1	yes	characteristic
13	C₈×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₈×D₄×C₁₃₁	C₄	1	1	yes	characteristic
15	C₈×D₄×C₁₃₁	C₄	1	2	yes	—
16	C₈×D₄×C₁₃₁	C₂²	1	2	yes	—
17	C₈×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
18	#431×C₁₃₁	C₄	1	2	yes	—
19	#431×C₁₃₁	C₄	1	1	yes	characteristic
20	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₁₃₁	C₂²	1	2	yes	—
22	C₄⋊C₁₆×C₁₃₁	C₂²	1	2	yes	—
23	C₄⋊C₁₆×C₁₃₁	C₂²	1	2	yes	—
24	C₄⋊C₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
25	C₄⋊C₁₆×C₁₃₁	C₂²	1	4	yes	—
26	C₄⋊C₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
27	C₂²⋊C₁₆×C₁₃₁	C₂²	1	2	yes	—
28	C₂²⋊C₁₆×C₁₃₁	C₂²	1	4	yes	—
29	#346×C₁₃₁	C₂²	1	4	yes	—
30	C₄×C₁₆×C₁₃₁	C₂²	1	2	yes	—
31	C₂×#41×C₁₃₁	C₈	1	1	yes	characteristic
32	C₂²×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₈×C₁₃₁	C₂×C₄	1	2	yes	—
34	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
35	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
36	C₄×Q₈×C₁₃₁	C₈	1	1	yes	characteristic
37	C₄×Q₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
38	C₄×D₄×C₁₃₁	C₈	1	2	yes	—
39	C₄×D₄×C₁₃₁	C₈	1	1	yes	characteristic
40	C₄×D₄×C₁₃₁	C₂×C₄	1	2	yes	—
41	C₄×D₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
42	#117×C₁₃₁	C₈	1	2	yes	—
43	#117×C₁₃₁	C₈	1	1	yes	characteristic
44	C₂×C₄²×C₁₃₁	C₂×C₄	1	2	yes	—
45	C₂×C₄²×C₁₃₁	C₂×C₄	1	1	yes	characteristic
46	M₃₂×C₁₃₁	—	4	4	no	—
47	C₂×C₁₆×C₁₃₁	—	4	2	no	—
48	C₂×C₁₆×C₁₃₁	C₂³	1	4	yes	—
49	C₂×C₁₆×C₁₃₁	C₂³	1	2	yes	—
50	C₂×C₁₆×C₁₃₁	C₂³	1	2	yes	—
51	C₄⋊C₈×C₁₃₁	C₂×C₄	1	2	yes	—
52	C₄⋊C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
53	C₄⋊C₈×C₁₃₁	C₂×C₄	1	2	yes	—
54	C₄⋊C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
55	C₂²⋊C₈×C₁₃₁	C₂×C₄	1	2	yes	—
56	C₂²⋊C₈×C₁₃₁	C₂×C₄	1	2	yes	—
57	C₂²⋊C₈×C₁₃₁	C₂×C₄	1	2	yes	—
58	C₄×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
59	C₄×C₈×C₁₃₁	C₂×C₄	1	2	yes	—
60	C₄×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
61	C₄×C₈×C₁₃₁	C₂×C₄	1	2	yes	—
62	C₄×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
63	C₄×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
64	C₄×C₈×C₁₃₁	C₂³	1	2	yes	—
65	#41×C₁₃₁	—	2	4	no	—
66	C₂×Q₈×C₁₃₁	C₂×C₈	1	1	yes	characteristic
67	C₂×D₄×C₁₃₁	C₂×C₈	1	2	yes	—
68	C₂×D₄×C₁₃₁	C₂×C₈	1	1	yes	characteristic
69	C₂²×C₄×C₁₃₁	C₂×C₈	1	2	yes	—
70	C₂²×C₄×C₁₃₁	C₂×C₈	1	2	yes	—
71	C₂²×C₄×C₁₃₁	C₂×C₈	1	1	yes	characteristic
72	C₂²×C₄×C₁₃₁	C₂×C₈	1	1	yes	characteristic
73	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
74	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
75	C₂×C₈×C₁₃₁	—	2	1	no	—
76	C₂×C₈×C₁₃₁	—	2	2	no	—
77	C₂×C₈×C₁₃₁	—	2	1	no	—
78	C₂×C₈×C₁₃₁	—	2	2	no	—
79	C₂×C₈×C₁₃₁	—	4	1	no	—
80	C₂×C₈×C₁₃₁	—	4	2	no	—
81	C₂×C₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
82	C₂×C₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
83	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
84	C₂×C₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
85	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
86	C₂×C₈×C₁₃₁	C₂⁴	1	1	yes	characteristic
87	C₄⋊C₄×C₁₃₁	C₂×C₈	1	2	yes	—
88	C₄⋊C₄×C₁₃₁	C₂×C₈	1	1	yes	characteristic
89	C₄⋊C₄×C₁₃₁	C₂×C₈	1	2	yes	—
90	C₄⋊C₄×C₁₃₁	C₂×C₈	1	1	yes	characteristic
91	C₂²⋊C₄×C₁₃₁	C₂×C₈	1	2	yes	—
92	C₂²⋊C₄×C₁₃₁	C₂×C₈	1	2	yes	—
93	C₂²⋊C₄×C₁₃₁	C₂×C₈	1	2	yes	—
94	C₄²×C₁₃₁	C₂×C₈	1	2	yes	—
95	C₄²×C₁₃₁	C₂×C₈	1	1	yes	characteristic
96	C₄²×C₁₃₁	C₂×C₈	1	2	yes	—
97	C₄²×C₁₃₁	C₂×C₈	1	1	yes	characteristic
98	C₄²×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
99	C₄²×C₁₃₁	C₂²×C₄	1	2	yes	—
100	C₄²×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
101	C₁₆×C₁₃₁	—	2	4	no	—
102	C₁₆×C₁₃₁	—	2	2	no	—
103	C₁₆×C₁₃₁	—	2	2	no	—
104	C₂³×C₁₃₁	C₂²×C₈	1	2	yes	—
105	C₂³×C₁₃₁	C₂²×C₈	1	1	yes	characteristic
106	Q₈×C₁₃₁	—	2	2	no	—
107	D₄×C₁₃₁	—	2	4	no	—
108	D₄×C₁₃₁	—	2	2	no	—
109	C₂×C₄×C₁₃₁	—	2	1	no	—
110	C₂×C₄×C₁₃₁	—	2	2	no	—
111	C₂×C₄×C₁₃₁	—	2	1	no	—
112	C₂×C₄×C₁₃₁	—	2	2	no	—
113	C₂×C₄×C₁₃₁	—	2	4	no	—
114	C₂×C₄×C₁₃₁	—	4	1	no	—
115	C₂×C₄×C₁₃₁	—	4	2	no	—
116	C₂×C₄×C₁₃₁	M₃₂	1	4	yes	complemented
117	C₂×C₄×C₁₃₁	C₂²×C₈	1	1	yes	characteristic
118	C₂×C₄×C₁₃₁	C₂²×C₈	1	2	yes	—
119	C₂×C₄×C₁₃₁	C₂²×C₈	1	1	yes	characteristic
120	C₂×C₄×C₁₃₁	C₂²×C₈	1	2	yes	—
121	C₂×C₄×C₁₃₁	C₂²×C₈	1	1	yes	characteristic
122	C₂×C₄×C₁₃₁	C₂²×C₈	1	2	yes	—
123	C₂×C₄×C₁₃₁	C₂²×C₈	1	1	yes	characteristic
124	C₂×C₄×C₁₃₁	C₂²×C₈	1	1	yes	characteristic
125	C₂×C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
126	C₈×C₁₃₁	—	2	1	no	—
127	C₈×C₁₃₁	—	2	2	no	—
128	C₈×C₁₃₁	—	2	1	no	—
129	C₈×C₁₃₁	—	2	1	no	—
130	C₈×C₁₃₁	—	2	2	no	—
131	C₈×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
132	C₈×C₁₃₁	2₋¹⁺⁴	1	1	yes	characteristic
133	C₂²×C₁₃₁	—	2	1	no	—
134	C₂²×C₁₃₁	—	2	1	no	—
135	C₂²×C₁₃₁	—	2	2	no	—
136	C₂²×C₁₃₁	—	2	2	no	—
137	C₂²×C₁₃₁	—	2	2	no	—
138	C₂²×C₁₃₁	C₂×M₃₂	1	2	yes	—
139	C₂²×C₁₃₁	C₂³×C₈	1	1	yes	characteristic
140	C₄×C₁₃₁	—	2	2	no	—
141	C₄×C₁₃₁	—	2	1	no	—
142	C₄×C₁₃₁	—	2	1	no	—
143	C₄×C₁₃₁	—	2	2	no	—
144	C₄×C₁₃₁	—	2	1	no	—
145	C₄×C₁₃₁	—	2	2	no	—
146	C₄×C₁₃₁	C₂×M₃₂	1	2	yes	—
147	C₄×C₁₃₁	C₂×M₃₂	1	2	yes	—
148	C₄×C₁₃₁	#520	1	1	yes	characteristic
149	C₄×C₁₃₁	#568	1	1	yes	characteristic
150	C₂×C₁₃₁	—	2	2	no	—
151	C₂×C₁₃₁	—	4	2	no	—
152	C₂×C₁₃₁	#2988	1	1	yes	characteristic
153	C₂×C₁₃₁	C₂²×M₃₂	1	1	yes	characteristic
154	C₂×C₁₃₁	#3407	1	1	yes	characteristic
155	#33503	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
156	C₁₃₁	#33503	1	1	yes	characteristic, direct product factor, Sylow
157	C₈×#41	C₂×C₁₃₁	1	1	yes	characteristic
158	#2183	C₂×C₁₃₁	1	2	yes	complemented
159	#2169	C₂×C₁₃₁	1	2	yes	complemented
160	#2168	C₂×C₁₃₁	1	4	yes	complemented
161	#2163	C₂×C₁₃₁	1	2	yes	complemented
162	#2162	C₂×C₁₃₁	1	1	yes	characteristic, complemented
163	#2150	C₂×C₁₃₁	1	2	yes	complemented
164	C₂×C₄⋊C₁₆	C₂×C₁₃₁	1	1	yes	characteristic, complemented
165	C₄×#41	C₄×C₁₃₁	1	1	yes	characteristic
166	C₂×M₃₂	C₂²×C₁₃₁	1	4	yes	—
167	C₂²×C₁₆	C₂²×C₁₃₁	1	2	yes	—
168	C₈×Q₈	C₄×C₁₃₁	1	1	yes	characteristic
169	C₈×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
170	C₈×D₄	C₄×C₁₃₁	1	1	yes	characteristic
171	C₈×D₄	C₄×C₁₃₁	1	2	yes	—
172	C₈×D₄	C₂²×C₁₃₁	1	2	yes	—
173	C₈×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
174	#431	C₄×C₁₃₁	1	2	yes	—
175	#431	C₄×C₁₃₁	1	1	yes	characteristic
176	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
177	C₂×C₄×C₈	C₂²×C₁₃₁	1	2	yes	—
178	C₄⋊C₁₆	C₂²×C₁₃₁	1	2	yes	—
179	C₄⋊C₁₆	C₂²×C₁₃₁	1	2	yes	—
180	C₄⋊C₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
181	C₄⋊C₁₆	C₂²×C₁₃₁	1	4	yes	—
182	C₄⋊C₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
183	C₂²⋊C₁₆	C₂²×C₁₃₁	1	2	yes	—
184	C₂²⋊C₁₆	C₂²×C₁₃₁	1	4	yes	—
185	#346	C₂²×C₁₃₁	1	4	yes	—
186	C₄×C₁₆	C₂²×C₁₃₁	1	2	yes	—
187	C₂×#41	C₈×C₁₃₁	1	1	yes	characteristic
188	C₂²×C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
189	C₂²×C₈	C₂×C₄×C₁₃₁	1	2	yes	—
190	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
191	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
192	C₄×Q₈	C₈×C₁₃₁	1	1	yes	characteristic
193	C₄×Q₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
194	C₄×D₄	C₈×C₁₃₁	1	2	yes	—
195	C₄×D₄	C₈×C₁₃₁	1	1	yes	characteristic
196	C₄×D₄	C₂×C₄×C₁₃₁	1	2	yes	—
197	C₄×D₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
198	#117	C₈×C₁₃₁	1	2	yes	—
199	#117	C₈×C₁₃₁	1	1	yes	characteristic
200	C₂×C₄²	C₂×C₄×C₁₃₁	1	2	yes	—
201	C₂×C₄²	C₂×C₄×C₁₃₁	1	1	yes	characteristic
202	M₃₂	—	4	4	no	—
203	C₂×C₁₆	—	4	2	no	—
204	C₂×C₁₆	C₂³×C₁₃₁	1	2	yes	—
205	C₂×C₁₆	C₂³×C₁₃₁	1	2	yes	—
206	C₂×C₁₆	C₂³×C₁₃₁	1	4	yes	—
207	C₄⋊C₈	C₂×C₄×C₁₃₁	1	2	yes	—
208	C₄⋊C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
209	C₄⋊C₈	C₂×C₄×C₁₃₁	1	2	yes	—
210	C₄⋊C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
211	C₂²⋊C₈	C₂×C₄×C₁₃₁	1	2	yes	—
212	C₂²⋊C₈	C₂×C₄×C₁₃₁	1	2	yes	—
213	C₂²⋊C₈	C₂×C₄×C₁₃₁	1	2	yes	—
214	C₄×C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
215	C₄×C₈	C₂×C₄×C₁₃₁	1	2	yes	—
216	C₄×C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
217	C₄×C₈	C₂×C₄×C₁₃₁	1	2	yes	—
218	C₄×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
219	C₄×C₈	C₂³×C₁₃₁	1	2	yes	—
220	C₄×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
221	#41	—	2	4	no	—
222	C₂×Q₈	C₂×C₈×C₁₃₁	1	1	yes	characteristic
223	C₂×D₄	C₂×C₈×C₁₃₁	1	2	yes	—
224	C₂×D₄	C₂×C₈×C₁₃₁	1	1	yes	characteristic
225	C₂²×C₄	C₂×C₈×C₁₃₁	1	2	yes	—
226	C₂²×C₄	C₂×C₈×C₁₃₁	1	2	yes	—
227	C₂²×C₄	C₂×C₈×C₁₃₁	1	1	yes	characteristic
228	C₂²×C₄	C₂×C₈×C₁₃₁	1	1	yes	characteristic
229	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
230	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
231	C₂×C₈	—	2	1	no	—
232	C₂×C₈	—	2	2	no	—
233	C₂×C₈	—	2	1	no	—
234	C₂×C₈	—	2	2	no	—
235	C₂×C₈	—	4	1	no	—
236	C₂×C₈	—	4	2	no	—
237	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
238	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
239	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
240	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
241	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
242	C₂×C₈	C₂⁴×C₁₃₁	1	1	yes	characteristic
243	C₄⋊C₄	C₂×C₈×C₁₃₁	1	2	yes	—
244	C₄⋊C₄	C₂×C₈×C₁₃₁	1	1	yes	characteristic
245	C₄⋊C₄	C₂×C₈×C₁₃₁	1	2	yes	—
246	C₄⋊C₄	C₂×C₈×C₁₃₁	1	1	yes	characteristic
247	C₂²⋊C₄	C₂×C₈×C₁₃₁	1	2	yes	—
248	C₂²⋊C₄	C₂×C₈×C₁₃₁	1	2	yes	—
249	C₂²⋊C₄	C₂×C₈×C₁₃₁	1	2	yes	—
250	C₄²	C₂×C₈×C₁₃₁	1	2	yes	—
251	C₄²	C₂×C₈×C₁₃₁	1	1	yes	characteristic
252	C₄²	C₂×C₈×C₁₃₁	1	2	yes	—
253	C₄²	C₂×C₈×C₁₃₁	1	1	yes	characteristic
254	C₄²	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
255	C₄²	C₂²×C₄×C₁₃₁	1	2	yes	—
256	C₄²	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
257	C₁₆	—	2	4	no	—
258	C₁₆	—	2	2	no	—
259	C₁₆	—	2	2	no	—
260	C₂³	C₂²×C₈×C₁₃₁	1	2	yes	—
261	C₂³	C₂²×C₈×C₁₃₁	1	1	yes	characteristic
262	Q₈	—	2	2	no	—
263	D₄	—	2	4	no	—
264	D₄	—	2	2	no	—
265	C₂×C₄	—	2	4	no	—
266	C₂×C₄	—	2	1	no	—
267	C₂×C₄	—	2	2	no	—
268	C₂×C₄	—	2	1	no	—
269	C₂×C₄	—	2	2	no	—
270	C₂×C₄	—	4	1	no	—
271	C₂×C₄	—	4	2	no	—
272	C₂×C₄	M₃₂×C₁₃₁	1	4	yes	complemented
273	C₂×C₄	C₂²×C₈×C₁₃₁	1	1	yes	characteristic
274	C₂×C₄	C₂²×C₈×C₁₃₁	1	2	yes	—
275	C₂×C₄	C₂²×C₈×C₁₃₁	1	1	yes	characteristic
276	C₂×C₄	C₂²×C₈×C₁₃₁	1	2	yes	—
277	C₂×C₄	C₂²×C₈×C₁₃₁	1	1	yes	characteristic
278	C₂×C₄	C₂²×C₈×C₁₃₁	1	2	yes	—
279	C₂×C₄	C₂²×C₈×C₁₃₁	1	1	yes	characteristic
280	C₂×C₄	C₂²×C₈×C₁₃₁	1	1	yes	characteristic
281	C₂×C₄	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
282	C₈	—	2	1	no	—
283	C₈	—	2	2	no	—
284	C₈	—	2	1	no	—
285	C₈	—	2	1	no	—
286	C₈	—	2	2	no	—
287	C₈	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
288	C₈	2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
289	C₂²	—	2	1	no	—
290	C₂²	—	2	1	no	—
291	C₂²	—	2	2	no	—
292	C₂²	—	2	2	no	—
293	C₂²	—	2	2	no	—
294	C₂²	C₂×M₃₂×C₁₃₁	1	2	yes	—
295	C₂²	C₂³×C₈×C₁₃₁	1	1	yes	characteristic
296	C₄	—	2	1	no	—
297	C₄	—	2	2	no	—
298	C₄	—	2	2	no	—
299	C₄	—	2	1	no	—
300	C₄	—	2	1	no	—
301	C₄	—	2	2	no	—
302	C₄	C₂×M₃₂×C₁₃₁	1	2	yes	—
303	C₄	C₂×M₃₂×C₁₃₁	1	2	yes	—
304	C₄	#520×C₁₃₁	1	1	yes	characteristic
305	C₄	#568×C₁₃₁	1	1	yes	characteristic
306	C₂	—	2	2	no	—
307	C₂	—	4	2	no	—
308	C₂	#2988×C₁₃₁	1	1	yes	characteristic
309	C₂	C₂²×M₃₂×C₁₃₁	1	1	yes	characteristic
310	C₂	#3407×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₁₃₁	C₂⁴
commutator	C₂²	C₂³×C₈×C₁₃₁
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃₁
socle	C₂²×C₁₃₁	C₂³×C₈
prime radical	C₂×#41×C₁₃₁	C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2183×C₁₃₁	C₂	semidirect
3. #2169×C₁₃₁	C₂	semidirect
4. #2168×C₁₃₁	C₂	semidirect
5. #2163×C₁₃₁	C₂	semidirect
6. #2162×C₁₃₁	C₂	semidirect
7. #2150×C₁₃₁	C₂	semidirect
8. C₂×C₄⋊C₁₆×C₁₃₁	C₂	semidirect
116. C₂×C₄×C₁₃₁	M₃₂	semidirect
155. #33503	C₁₃₁	direct (N × H)
156. C₁₃₁	#33503	direct (N × H)
158. #2183	C₂×C₁₃₁	semidirect
159. #2169	C₂×C₁₃₁	semidirect
160. #2168	C₂×C₁₃₁	semidirect
161. #2163	C₂×C₁₃₁	semidirect
162. #2162	C₂×C₁₃₁	semidirect
163. #2150	C₂×C₁₃₁	semidirect
164. C₂×C₄⋊C₁₆	C₂×C₁₃₁	semidirect
272. C₂×C₄	M₃₂×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₈×#41×C₁₃₁	2
#2183×C₁₃₁	2
#2169×C₁₃₁	2
#2168×C₁₃₁	2
#2163×C₁₃₁	2
#2162×C₁₃₁	2
#2150×C₁₃₁	2
C₂×C₄⋊C₁₆×C₁₃₁	2
#33503	131

Subgroups — C131×#33503 #45719387

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#33503 #45719387