Subgroups — C₂×C₄×C₂²⋊C₈×C₁₃₁ #45706255

Order 33536.

2414 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄²×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂²⋊C₈×C₁₃₁	C₂	1	2	yes	maximal
3	C₂²×C₄×C₈×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	C₄×C₂²⋊C₈×C₁₃₁	C₂	1	8	yes	maximal, direct product factor
5	C₂×#336×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	C₂⁴×C₄×C₁₃₁	C₄	1	2	yes	—
7	C₂⁴×C₄×C₁₃₁	C₂²	1	1	yes	characteristic
8	C₂³×C₈×C₁₃₁	C₂²	1	4	yes	—
9	C₂²×C₄²×C₁₃₁	—	2	8	no	—
10	C₂²×C₄²×C₁₃₁	C₄	1	2	yes	—
11	C₂²×C₄²×C₁₃₁	C₄	1	4	yes	—
12	C₂²×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂²×C₄²×C₁₃₁	C₂²	1	4	yes	—
14	C₂²×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊C₈×C₁₃₁	C₄	1	16	yes	direct product factor
16	C₂×C₂²⋊C₈×C₁₃₁	C₂²	1	8	yes	—
17	C₂×C₄×C₈×C₁₃₁	—	2	8	no	—
18	C₂×C₄×C₈×C₁₃₁	C₂²	1	8	yes	complemented
19	#336×C₁₃₁	C₂²	1	8	yes	complemented
20	C₂⁵×C₁₃₁	C₂×C₄	1	1	yes	characteristic
21	C₂³×C₄×C₁₃₁	—	2	8	no	—
22	C₂³×C₄×C₁₃₁	—	2	8	no	—
23	C₂³×C₄×C₁₃₁	—	2	4	no	—
24	C₂³×C₄×C₁₃₁	—	2	4	no	—
25	C₂³×C₄×C₁₃₁	C₈	1	16	yes	complemented
26	C₂³×C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₃₁	C₂×C₄	1	2	yes	—
28	C₂³×C₄×C₁₃₁	C₂×C₄	1	8	yes	—
29	C₂³×C₄×C₁₃₁	C₂×C₄	1	2	yes	—
30	C₂³×C₄×C₁₃₁	C₂×C₄	1	8	yes	—
31	C₂³×C₄×C₁₃₁	C₂×C₄	1	2	yes	—
32	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
33	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
34	C₂²×C₈×C₁₃₁	—	2	8	no	—
35	C₂²×C₈×C₁₃₁	—	2	8	no	—
36	C₂²×C₈×C₁₃₁	C₂×C₄	1	16	yes	complemented
37	C₂²×C₈×C₁₃₁	C₂³	1	8	yes	—
38	C₂×C₄²×C₁₃₁	—	2	8	no	—
39	C₂×C₄²×C₁₃₁	—	2	4	no	—
40	C₂×C₄²×C₁₃₁	—	2	16	no	—
41	C₂×C₄²×C₁₃₁	—	2	16	no	—
42	C₂×C₄²×C₁₃₁	C₂×C₄	1	8	yes	—
43	C₂×C₄²×C₁₃₁	C₂×C₄	1	2	yes	—
44	C₂×C₄²×C₁₃₁	C₂×C₄	1	2	yes	—
45	C₂×C₄²×C₁₃₁	D₄	1	8	yes	—
46	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
47	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
48	C₂²⋊C₈×C₁₃₁	C₂×C₄	1	32	yes	direct product factor
49	C₄×C₈×C₁₃₁	—	2	16	no	—
50	C₂⁴×C₁₃₁	—	2	2	no	—
51	C₂⁴×C₁₃₁	—	2	2	no	—
52	C₂⁴×C₁₃₁	—	2	4	no	—
53	C₂⁴×C₁₃₁	C₄²	1	4	yes	—
54	C₂⁴×C₁₃₁	C₂×C₈	1	8	yes	—
55	C₂⁴×C₁₃₁	C₂²×C₄	1	2	yes	—
56	C₂⁴×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₃₁	—	2	2	no	—
58	C₂²×C₄×C₁₃₁	—	2	4	no	—
59	C₂²×C₄×C₁₃₁	—	2	2	no	—
60	C₂²×C₄×C₁₃₁	—	2	4	no	—
61	C₂²×C₄×C₁₃₁	—	2	64	no	—
62	C₂²×C₄×C₁₃₁	—	2	4	no	—
63	C₂²×C₄×C₁₃₁	—	2	16	no	—
64	C₂²×C₄×C₁₃₁	—	2	4	no	—
65	C₂²×C₄×C₁₃₁	—	2	32	no	—
66	C₂²×C₄×C₁₃₁	—	2	16	no	—
67	C₂²×C₄×C₁₃₁	—	2	4	no	—
68	C₂²×C₄×C₁₃₁	—	2	4	no	—
69	C₂²×C₄×C₁₃₁	C₄²	1	4	yes	—
70	C₂²×C₄×C₁₃₁	C₄²	1	8	yes	—
71	C₂²×C₄×C₁₃₁	C₂²⋊C₄	1	8	yes	—
72	C₂²×C₄×C₁₃₁	C₂×C₈	1	8	yes	—
73	C₂²×C₄×C₁₃₁	C₂×C₈	1	8	yes	—
74	C₂²×C₄×C₁₃₁	C₂×C₈	1	32	yes	complemented
75	C₂²×C₄×C₁₃₁	M₁₆	1	8	yes	—
76	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
77	C₂²×C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
78	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
79	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
81	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
82	C₂²×C₄×C₁₃₁	C₂×D₄	1	4	yes	—
83	C₂²×C₄×C₁₃₁	#41	1	4	yes	—
84	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
85	C₂×C₈×C₁₃₁	—	2	32	no	—
86	C₂×C₈×C₁₃₁	—	2	8	no	—
87	C₂×C₈×C₁₃₁	—	2	8	no	—
88	C₂×C₈×C₁₃₁	C₂²×C₄	1	16	yes	complemented
89	C₄²×C₁₃₁	—	2	4	no	—
90	C₄²×C₁₃₁	—	2	16	no	—
91	C₄²×C₁₃₁	—	2	4	no	—
92	C₄²×C₁₃₁	C₂²⋊C₄	1	8	yes	—
93	C₄²×C₁₃₁	C₂×D₄	1	8	yes	—
94	C₂³×C₁₃₁	—	2	2	no	—
95	C₂³×C₁₃₁	—	2	2	no	—
96	C₂³×C₁₃₁	—	2	4	no	—
97	C₂³×C₁₃₁	—	2	8	no	—
98	C₂³×C₁₃₁	—	2	8	no	—
99	C₂³×C₁₃₁	—	2	16	no	—
100	C₂³×C₁₃₁	—	2	16	no	—
101	C₂³×C₁₃₁	C₄×C₈	1	16	yes	complemented
102	C₂³×C₁₃₁	C₂×C₄²	1	4	yes	—
103	C₂³×C₁₃₁	C₂×C₄²	1	2	yes	—
104	C₂³×C₁₃₁	C₂×C₂²⋊C₄	1	2	yes	—
105	C₂³×C₁₃₁	#117	1	2	yes	—
106	C₂³×C₁₃₁	C₂²×C₈	1	8	yes	—
107	C₂³×C₁₃₁	C₂²×C₈	1	4	yes	—
108	C₂³×C₁₃₁	C₂×M₁₆	1	4	yes	—
109	C₂³×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
110	C₂×C₄×C₁₃₁	—	2	4	no	—
111	C₂×C₄×C₁₃₁	—	2	2	no	—
112	C₂×C₄×C₁₃₁	—	2	2	no	—
113	C₂×C₄×C₁₃₁	—	2	4	no	—
114	C₂×C₄×C₁₃₁	—	2	8	no	—
115	C₂×C₄×C₁₃₁	—	2	16	no	—
116	C₂×C₄×C₁₃₁	—	2	16	no	—
117	C₂×C₄×C₁₃₁	—	2	16	no	—
118	C₂×C₄×C₁₃₁	—	2	64	no	—
119	C₂×C₄×C₁₃₁	C₂²⋊C₈	1	32	yes	direct product factor
120	C₂×C₄×C₁₃₁	C₂×C₄²	1	4	yes	—
121	C₂×C₄×C₁₃₁	C₂×C₄²	1	2	yes	—
122	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	2	yes	—
123	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	8	yes	—
124	C₂×C₄×C₁₃₁	#117	1	2	yes	—
125	C₂×C₄×C₁₃₁	C₄×D₄	1	16	yes	—
126	C₂×C₄×C₁₃₁	C₂²×C₈	1	8	yes	—
127	C₂×C₄×C₁₃₁	C₂²×C₈	1	8	yes	—
128	C₂×C₄×C₁₃₁	C₂×M₁₆	1	8	yes	—
129	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
130	C₂×C₄×C₁₃₁	C₂²×D₄	1	2	yes	—
131	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
132	C₈×C₁₃₁	—	2	16	no	—
133	C₂²×C₁₃₁	—	2	4	no	—
134	C₂²×C₁₃₁	—	2	8	no	—
135	C₂²×C₁₃₁	—	2	8	no	—
136	C₂²×C₁₃₁	—	2	32	no	—
137	C₂²×C₁₃₁	—	2	4	no	—
138	C₂²×C₁₃₁	C₄×C₂²⋊C₄	1	4	yes	—
139	C₂²×C₁₃₁	C₂×C₄×C₈	1	4	yes	—
140	C₂²×C₁₃₁	C₂×C₄×C₈	1	8	yes	complemented
141	C₂²×C₁₃₁	C₄×M₁₆	1	4	yes	—
142	C₂²×C₁₃₁	C₂×C₂²⋊C₈	1	8	yes	—
143	C₂²×C₁₃₁	#431	1	8	yes	—
144	C₂²×C₁₃₁	C₂²×C₄²	1	1	yes	characteristic
145	C₂²×C₁₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
146	C₂²×C₁₃₁	C₂×#117	1	1	yes	characteristic
147	C₂²×C₁₃₁	C₂³×C₈	1	2	yes	—
148	C₂²×C₁₃₁	C₂²×M₁₆	1	2	yes	—
149	C₄×C₁₃₁	—	2	8	no	—
150	C₄×C₁₃₁	—	2	4	no	—
151	C₄×C₁₃₁	C₄×C₂²⋊C₄	1	4	yes	—
152	C₄×C₁₃₁	C₂×C₂²⋊C₈	1	16	yes	direct product factor
153	C₄×C₁₃₁	C₂×C₄×D₄	1	4	yes	—
154	C₂×C₁₃₁	—	2	8	no	—
155	C₂×C₁₃₁	C₄×C₂²⋊C₈	1	8	yes	direct product factor
156	C₂×C₁₃₁	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
157	C₂×C₁₃₁	C₂²×C₄×C₈	1	1	yes	characteristic
158	C₂×C₁₃₁	C₂×C₄×M₁₆	1	1	yes	characteristic
159	C₂×C₁₃₁	C₂²×C₂²⋊C₈	1	2	yes	—
160	C₂×C₁₃₁	C₂×#431	1	2	yes	—
161	C₂×C₄×C₂²⋊C₈	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
162	C₁₃₁	C₂×C₄×C₂²⋊C₈	1	1	yes	characteristic, direct product factor, Sylow
163	C₂³×C₄²	C₂×C₁₃₁	1	1	yes	characteristic
164	C₂²×C₂²⋊C₈	C₂×C₁₃₁	1	2	yes	—
165	C₂²×C₄×C₈	C₂×C₁₃₁	1	2	yes	complemented
166	C₄×C₂²⋊C₈	C₂×C₁₃₁	1	8	yes	direct product factor
167	C₂×#336	C₂×C₁₃₁	1	2	yes	complemented
168	C₂⁴×C₄	C₄×C₁₃₁	1	2	yes	—
169	C₂⁴×C₄	C₂²×C₁₃₁	1	1	yes	characteristic
170	C₂³×C₈	C₂²×C₁₃₁	1	4	yes	—
171	C₂²×C₄²	—	2	8	no	—
172	C₂²×C₄²	C₄×C₁₃₁	1	2	yes	—
173	C₂²×C₄²	C₄×C₁₃₁	1	4	yes	—
174	C₂²×C₄²	C₂²×C₁₃₁	1	1	yes	characteristic
175	C₂²×C₄²	C₂²×C₁₃₁	1	4	yes	—
176	C₂²×C₄²	C₂²×C₁₃₁	1	1	yes	characteristic
177	C₂×C₂²⋊C₈	C₄×C₁₃₁	1	16	yes	direct product factor
178	C₂×C₂²⋊C₈	C₂²×C₁₃₁	1	8	yes	—
179	C₂×C₄×C₈	—	2	8	no	—
180	C₂×C₄×C₈	C₂²×C₁₃₁	1	8	yes	complemented
181	#336	C₂²×C₁₃₁	1	8	yes	complemented
182	C₂⁵	C₂×C₄×C₁₃₁	1	1	yes	characteristic
183	C₂³×C₄	—	2	8	no	—
184	C₂³×C₄	—	2	8	no	—
185	C₂³×C₄	—	2	4	no	—
186	C₂³×C₄	—	2	4	no	—
187	C₂³×C₄	C₈×C₁₃₁	1	16	yes	complemented
188	C₂³×C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
189	C₂³×C₄	C₂×C₄×C₁₃₁	1	2	yes	—
190	C₂³×C₄	C₂×C₄×C₁₃₁	1	8	yes	—
191	C₂³×C₄	C₂×C₄×C₁₃₁	1	2	yes	—
192	C₂³×C₄	C₂×C₄×C₁₃₁	1	8	yes	—
193	C₂³×C₄	C₂×C₄×C₁₃₁	1	2	yes	—
194	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
195	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
196	C₂²×C₈	—	2	8	no	—
197	C₂²×C₈	—	2	8	no	—
198	C₂²×C₈	C₂×C₄×C₁₃₁	1	16	yes	complemented
199	C₂²×C₈	C₂³×C₁₃₁	1	8	yes	—
200	C₂×C₄²	—	2	8	no	—
201	C₂×C₄²	—	2	4	no	—
202	C₂×C₄²	—	2	16	no	—
203	C₂×C₄²	—	2	16	no	—
204	C₂×C₄²	C₂×C₄×C₁₃₁	1	8	yes	—
205	C₂×C₄²	C₂×C₄×C₁₃₁	1	2	yes	—
206	C₂×C₄²	C₂×C₄×C₁₃₁	1	2	yes	—
207	C₂×C₄²	D₄×C₁₃₁	1	8	yes	—
208	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
209	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
210	C₂²⋊C₈	C₂×C₄×C₁₃₁	1	32	yes	direct product factor
211	C₄×C₈	—	2	16	no	—
212	C₂⁴	—	2	2	no	—
213	C₂⁴	—	2	2	no	—
214	C₂⁴	—	2	4	no	—
215	C₂⁴	C₄²×C₁₃₁	1	4	yes	—
216	C₂⁴	C₂×C₈×C₁₃₁	1	8	yes	—
217	C₂⁴	C₂²×C₄×C₁₃₁	1	2	yes	—
218	C₂⁴	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
219	C₂²×C₄	—	2	4	no	—
220	C₂²×C₄	—	2	2	no	—
221	C₂²×C₄	—	2	2	no	—
222	C₂²×C₄	—	2	4	no	—
223	C₂²×C₄	—	2	64	no	—
224	C₂²×C₄	—	2	16	no	—
225	C₂²×C₄	—	2	4	no	—
226	C₂²×C₄	—	2	4	no	—
227	C₂²×C₄	—	2	32	no	—
228	C₂²×C₄	—	2	16	no	—
229	C₂²×C₄	—	2	4	no	—
230	C₂²×C₄	—	2	4	no	—
231	C₂²×C₄	C₄²×C₁₃₁	1	4	yes	—
232	C₂²×C₄	C₄²×C₁₃₁	1	8	yes	—
233	C₂²×C₄	C₂²⋊C₄×C₁₃₁	1	8	yes	—
234	C₂²×C₄	C₂×C₈×C₁₃₁	1	8	yes	—
235	C₂²×C₄	C₂×C₈×C₁₃₁	1	8	yes	—
236	C₂²×C₄	C₂×C₈×C₁₃₁	1	32	yes	complemented
237	C₂²×C₄	M₁₆×C₁₃₁	1	8	yes	—
238	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
239	C₂²×C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
240	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
241	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
242	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
243	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
244	C₂²×C₄	C₂×D₄×C₁₃₁	1	4	yes	—
245	C₂²×C₄	#41×C₁₃₁	1	4	yes	—
246	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
247	C₂×C₈	—	2	32	no	—
248	C₂×C₈	—	2	8	no	—
249	C₂×C₈	—	2	8	no	—
250	C₂×C₈	C₂²×C₄×C₁₃₁	1	16	yes	complemented
251	C₄²	—	2	16	no	—
252	C₄²	—	2	4	no	—
253	C₄²	—	2	4	no	—
254	C₄²	C₂²⋊C₄×C₁₃₁	1	8	yes	—
255	C₄²	C₂×D₄×C₁₃₁	1	8	yes	—
256	C₂³	—	2	8	no	—
257	C₂³	—	2	16	no	—
258	C₂³	—	2	16	no	—
259	C₂³	—	2	2	no	—
260	C₂³	—	2	2	no	—
261	C₂³	—	2	4	no	—
262	C₂³	—	2	8	no	—
263	C₂³	C₄×C₈×C₁₃₁	1	16	yes	complemented
264	C₂³	C₂×C₄²×C₁₃₁	1	4	yes	—
265	C₂³	C₂×C₄²×C₁₃₁	1	2	yes	—
266	C₂³	C₂×C₂²⋊C₄×C₁₃₁	1	2	yes	—
267	C₂³	#117×C₁₃₁	1	2	yes	—
268	C₂³	C₂²×C₈×C₁₃₁	1	8	yes	—
269	C₂³	C₂²×C₈×C₁₃₁	1	4	yes	—
270	C₂³	C₂×M₁₆×C₁₃₁	1	4	yes	—
271	C₂³	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
272	C₂×C₄	—	2	16	no	—
273	C₂×C₄	—	2	2	no	—
274	C₂×C₄	—	2	4	no	—
275	C₂×C₄	—	2	2	no	—
276	C₂×C₄	—	2	4	no	—
277	C₂×C₄	—	2	8	no	—
278	C₂×C₄	—	2	64	no	—
279	C₂×C₄	—	2	16	no	—
280	C₂×C₄	—	2	16	no	—
281	C₂×C₄	C₂²⋊C₈×C₁₃₁	1	32	yes	direct product factor
282	C₂×C₄	C₂×C₄²×C₁₃₁	1	4	yes	—
283	C₂×C₄	C₂×C₄²×C₁₃₁	1	2	yes	—
284	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	8	yes	—
285	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	2	yes	—
286	C₂×C₄	#117×C₁₃₁	1	2	yes	—
287	C₂×C₄	C₄×D₄×C₁₃₁	1	16	yes	—
288	C₂×C₄	C₂²×C₈×C₁₃₁	1	8	yes	—
289	C₂×C₄	C₂²×C₈×C₁₃₁	1	8	yes	—
290	C₂×C₄	C₂×M₁₆×C₁₃₁	1	8	yes	—
291	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
292	C₂×C₄	C₂²×D₄×C₁₃₁	1	2	yes	—
293	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
294	C₈	—	2	16	no	—
295	C₂²	—	2	32	no	—
296	C₂²	—	2	4	no	—
297	C₂²	—	2	4	no	—
298	C₂²	—	2	8	no	—
299	C₂²	—	2	8	no	—
300	C₂²	C₄×C₂²⋊C₄×C₁₃₁	1	4	yes	—
301	C₂²	C₂×C₄×C₈×C₁₃₁	1	4	yes	—
302	C₂²	C₂×C₄×C₈×C₁₃₁	1	8	yes	complemented
303	C₂²	C₄×M₁₆×C₁₃₁	1	4	yes	—
304	C₂²	C₂×C₂²⋊C₈×C₁₃₁	1	8	yes	—
305	C₂²	#431×C₁₃₁	1	8	yes	—
306	C₂²	C₂²×C₄²×C₁₃₁	1	1	yes	characteristic
307	C₂²	C₂²×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
308	C₂²	C₂×#117×C₁₃₁	1	1	yes	characteristic
309	C₂²	C₂³×C₈×C₁₃₁	1	2	yes	—
310	C₂²	C₂²×M₁₆×C₁₃₁	1	2	yes	—
311	C₄	—	2	4	no	—
312	C₄	—	2	8	no	—
313	C₄	C₄×C₂²⋊C₄×C₁₃₁	1	4	yes	—
314	C₄	C₂×C₂²⋊C₈×C₁₃₁	1	16	yes	direct product factor
315	C₄	C₂×C₄×D₄×C₁₃₁	1	4	yes	—
316	C₂	—	2	8	no	—
317	C₂	C₄×C₂²⋊C₈×C₁₃₁	1	8	yes	direct product factor
318	C₂	C₂×C₄×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
319	C₂	C₂²×C₄×C₈×C₁₃₁	1	1	yes	characteristic
320	C₂	C₂×C₄×M₁₆×C₁₃₁	1	1	yes	characteristic
321	C₂	C₂²×C₂²⋊C₈×C₁₃₁	1	2	yes	—
322	C₂	C₂×#431×C₁₃₁	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄²×C₁₃₁	C₂²
commutator	C₂	C₂²×C₄×C₈×C₁₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
socle	C₂⁴×C₁₃₁	C₂²×C₄
prime radical	C₂⁵×C₁₃₁	C₂×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄²×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂²×C₄×C₈×C₁₃₁	C₂	semidirect
4. C₄×C₂²⋊C₈×C₁₃₁	C₂	direct (N × H)
5. C₂×#336×C₁₃₁	C₂	semidirect
15. C₂×C₂²⋊C₈×C₁₃₁	C₄	direct (N × H)
18. C₂×C₄×C₈×C₁₃₁	C₂²	semidirect
19. #336×C₁₃₁	C₂²	semidirect
25. C₂³×C₄×C₁₃₁	C₈	semidirect
36. C₂²×C₈×C₁₃₁	C₂×C₄	semidirect
48. C₂²⋊C₈×C₁₃₁	C₂×C₄	direct (N × H)
74. C₂²×C₄×C₁₃₁	C₂×C₈	semidirect
88. C₂×C₈×C₁₃₁	C₂²×C₄	semidirect
101. C₂³×C₁₃₁	C₄×C₈	semidirect
119. C₂×C₄×C₁₃₁	C₂²⋊C₈	direct (N × H)
140. C₂²×C₁₃₁	C₂×C₄×C₈	semidirect
152. C₄×C₁₃₁	C₂×C₂²⋊C₈	direct (N × H)
155. C₂×C₁₃₁	C₄×C₂²⋊C₈	direct (N × H)
161. C₂×C₄×C₂²⋊C₈	C₁₃₁	direct (N × H)
162. C₁₃₁	C₂×C₄×C₂²⋊C₈	direct (N × H)
165. C₂²×C₄×C₈	C₂×C₁₃₁	semidirect
166. C₄×C₂²⋊C₈	C₂×C₁₃₁	direct (N × H)
167. C₂×#336	C₂×C₁₃₁	semidirect
177. C₂×C₂²⋊C₈	C₄×C₁₃₁	direct (N × H)
180. C₂×C₄×C₈	C₂²×C₁₃₁	semidirect
181. #336	C₂²×C₁₃₁	semidirect
187. C₂³×C₄	C₈×C₁₃₁	semidirect
198. C₂²×C₈	C₂×C₄×C₁₃₁	semidirect
210. C₂²⋊C₈	C₂×C₄×C₁₃₁	direct (N × H)
236. C₂²×C₄	C₂×C₈×C₁₃₁	semidirect
250. C₂×C₈	C₂²×C₄×C₁₃₁	semidirect
263. C₂³	C₄×C₈×C₁₃₁	semidirect
281. C₂×C₄	C₂²⋊C₈×C₁₃₁	direct (N × H)
302. C₂²	C₂×C₄×C₈×C₁₃₁	semidirect
314. C₄	C₂×C₂²⋊C₈×C₁₃₁	direct (N × H)
317. C₂	C₄×C₂²⋊C₈×C₁₃₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄²×C₁₃₁	2
C₂²×C₂²⋊C₈×C₁₃₁	2
C₂²×C₄×C₈×C₁₃₁	2
C₄×C₂²⋊C₈×C₁₃₁	2
C₂×#336×C₁₃₁	2
C₂×C₄×C₂²⋊C₈	131

Subgroups — C2×C4×C22⋊C8×C131 #45706255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₂²⋊C₈×C₁₃₁ #45706255