Subgroups — C₂×AGL(1,ℤ/8)×D₂₅₁ #44565095

Order 32128.

1720 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₄×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#22548743	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#22548742	C₂	1	2	yes	maximal, complemented
5	C₂×#22548741	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#22548740	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#22548739	C₂	1	2	yes	maximal, complemented
8	AGL(1,ℤ/8)×D₂₅₁	C₂	1	16	yes	maximal, direct product factor
9	C₂×SD₁₆×D₂₅₁	C₂	1	2	yes	maximal, complemented
10	C₂×D₈×D₂₅₁	C₂	1	2	yes	maximal, complemented
11	C₂×M₁₆×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁴×D₂₅₁	—	2	1	no	—
14	C₂×#16860811	C₂²	1	1	yes	characteristic, complemented
15	C₂×#16860810	—	2	1	no	—
16	C₂×#16860810	C₂²	1	1	yes	characteristic, complemented
17	C₂×#16860809	—	2	1	no	—
18	C₂×#16860809	C₂²	1	1	yes	characteristic, complemented
19	#41×D₂₅₁	—	2	4	no	—
20	#41×D₂₅₁	C₂²	1	8	yes	complemented
21	C₂×Q₈×D₂₅₁	C₂²	1	1	yes	characteristic, complemented
22	C₂²×D₁₀₀₄	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₂²⋊D₂₅₁	—	2	1	no	—
24	C₂×D₄×D₂₅₁	—	2	1	no	—
25	C₂×D₄×D₂₅₁	—	2	1	no	—
26	C₂×D₄×D₂₅₁	—	2	4	no	—
27	C₂×D₄×D₂₅₁	—	2	1	no	—
28	C₂×D₄×D₂₅₁	C₂²	1	2	yes	—
29	C₂×D₄×D₂₅₁	C₂²	1	2	yes	complemented
30	C₂×D₄×D₂₅₁	C₂²	1	8	yes	complemented
31	C₂×D₄×D₂₅₁	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₄×D₂₅₁	—	2	1	no	—
33	C₂²×C₄×D₂₅₁	C₂²	1	1	yes	characteristic
34	#22548743	C₂²	1	8	yes	complemented
35	#22548742	C₂²	1	16	yes	complemented
36	#22548741	C₂²	1	8	yes	complemented
37	#22548740	C₂²	1	8	yes	complemented
38	#22548739	C₂²	1	16	yes	complemented
39	C₂×#16860799	C₂²	1	2	yes	complemented
40	C₂×#16860798	C₂²	1	2	yes	complemented
41	C₂×#16860797	C₂²	1	2	yes	complemented
42	SD₁₆×D₂₅₁	C₂²	1	16	yes	complemented
43	C₂×D₂₀₀₈	C₂²	1	2	yes	complemented
44	C₂×#16860795	C₂²	1	2	yes	complemented
45	C₂×#16860795	C₂²	1	2	yes	complemented
46	D₈×D₂₅₁	C₂²	1	16	yes	complemented
47	C₂×#16860794	C₂²	1	1	yes	characteristic, complemented
48	C₂×#16860793	C₂²	1	2	yes	complemented
49	M₁₆×D₂₅₁	C₂²	1	8	yes	complemented
50	C₂×C₈×D₂₅₁	C₂²	1	2	yes	complemented
51	C₂×#41×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
52	C₂²×D₄×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
53	AGL(1,ℤ/8)×C₂₅₁	C₂²	1	8	yes	complemented
54	C₂×SD₁₆×C₂₅₁	C₂²	1	2	yes	complemented
55	C₂×D₈×C₂₅₁	C₂²	1	2	yes	complemented
56	C₂×M₁₆×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
57	C₂³×D₂₅₁	—	2	1	no	—
58	C₂³×D₂₅₁	—	2	2	no	—
59	C₂³×D₂₅₁	—	2	2	no	—
60	C₂³×D₂₅₁	—	2	8	no	—
61	C₂³×D₂₅₁	—	2	1	no	—
62	C₂³×D₂₅₁	—	4	8	no	—
63	C₂³×D₂₅₁	D₄	1	1	yes	characteristic
64	#16860811	—	2	2	no	—
65	#16860811	C₂³	1	4	yes	complemented
66	#16860810	—	2	8	no	—
67	#16860810	—	2	2	no	—
68	#16860810	C₂³	1	4	yes	complemented
69	#16860809	—	2	8	no	—
70	#16860809	—	2	2	no	—
71	#16860809	C₂³	1	4	yes	complemented
72	C₂×Dic₅₀₂	—	2	1	no	—
73	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic, complemented
74	Q₈×D₂₅₁	—	2	2	no	—
75	Q₈×D₂₅₁	C₂³	1	4	yes	complemented
76	C₂×D₁₀₀₄	—	2	1	no	—
77	C₂×D₁₀₀₄	—	2	1	no	—
78	C₂×D₁₀₀₄	—	2	2	no	—
79	C₂×D₁₀₀₄	C₂³	1	2	yes	—
80	C₂×D₁₀₀₄	C₂³	1	4	yes	complemented
81	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic, complemented
82	C₂×C₂²⋊D₂₅₁	—	2	1	no	—
83	C₂×C₂²⋊D₂₅₁	—	2	2	no	—
84	C₂×C₂²⋊D₂₅₁	—	2	2	no	—
85	C₂×C₂²⋊D₂₅₁	—	2	8	no	—
86	C₂×C₂²⋊D₂₅₁	—	2	1	no	—
87	C₂×C₂²⋊D₂₅₁	—	2	1	no	—
88	D₄×D₂₅₁	—	2	8	no	—
89	D₄×D₂₅₁	—	2	4	no	—
90	D₄×D₂₅₁	—	2	4	no	—
91	D₄×D₂₅₁	—	2	8	no	—
92	D₄×D₂₅₁	—	2	8	no	—
93	D₄×D₂₅₁	—	2	2	no	—
94	D₄×D₂₅₁	C₂³	1	8	yes	—
95	D₄×D₂₅₁	C₂³	1	8	yes	complemented
96	D₄×D₂₅₁	C₂³	1	4	yes	complemented
97	C₂²×Dic₂₅₁	—	2	1	no	—
98	C₂²×Dic₂₅₁	D₄	1	1	yes	characteristic
99	C₂×C₄×D₂₅₁	—	2	1	no	—
100	C₂×C₄×D₂₅₁	—	2	1	no	—
101	C₂×C₄×D₂₅₁	—	2	8	no	—
102	C₂×C₄×D₂₅₁	—	2	1	no	—
103	C₂×C₄×D₂₅₁	D₄	1	1	yes	characteristic
104	C₂×C₄×D₂₅₁	D₄	1	4	yes	—
105	C₂×C₄×D₂₅₁	D₄	1	1	yes	characteristic
106	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
107	C₂×C₄×D₂₅₁	C₂³	1	4	yes	—
108	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
109	#16860799	C₂³	1	8	yes	complemented
110	#16860798	C₂³	1	8	yes	complemented
111	#16860797	C₂³	1	8	yes	complemented
112	D₂₀₀₈	C₂³	1	8	yes	complemented
113	#16860795	C₂³	1	8	yes	complemented
114	#16860795	C₂³	1	8	yes	complemented
115	#16860794	C₂³	1	4	yes	complemented
116	#16860793	C₂³	1	8	yes	complemented
117	C₂×C₂₅₁⋊C₈	C₂³	1	2	yes	complemented
118	C₈×D₂₅₁	C₂³	1	8	yes	complemented
119	C₂⁴×C₂₅₁	—	2	1	no	—
120	#41×C₂₅₁	—	2	2	no	—
121	#41×C₂₅₁	C₂³	1	4	yes	complemented
122	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic, complemented
123	C₂×D₄×C₂₅₁	—	2	1	no	—
124	C₂×D₄×C₂₅₁	—	2	1	no	—
125	C₂×D₄×C₂₅₁	—	2	2	no	—
126	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
127	C₂×D₄×C₂₅₁	C₂³	1	4	yes	complemented
128	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic, complemented
129	C₂²×C₄×C₂₅₁	—	2	1	no	—
130	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
131	SD₁₆×C₂₅₁	C₂³	1	8	yes	complemented
132	D₈×C₂₅₁	C₂³	1	8	yes	complemented
133	M₁₆×C₂₅₁	C₂³	1	4	yes	complemented
134	C₂×C₈×C₂₅₁	C₂³	1	2	yes	complemented
135	C₂²×D₂₅₁	—	2	4	no	—
136	C₂²×D₂₅₁	—	2	1	no	—
137	C₂²×D₂₅₁	—	2	2	no	—
138	C₂²×D₂₅₁	—	2	4	no	—
139	C₂²×D₂₅₁	—	2	4	no	—
140	C₂²×D₂₅₁	—	2	8	no	—
141	C₂²×D₂₅₁	—	2	8	no	—
142	C₂²×D₂₅₁	—	4	8	no	—
143	C₂²×D₂₅₁	—	4	32	no	—
144	C₂²×D₂₅₁	—	4	4	no	—
145	C₂²×D₂₅₁	—	4	4	no	—
146	C₂²×D₂₅₁	—	4	8	no	—
147	C₂²×D₂₅₁	C₂×D₄	1	4	yes	—
148	C₂²×D₂₅₁	C₂×D₄	1	1	yes	characteristic
149	C₂²×D₂₅₁	C₂×D₄	1	1	yes	characteristic
150	Dic₅₀₂	—	2	1	no	—
151	Dic₅₀₂	—	2	4	no	—
152	Dic₅₀₂	C₂⁴	1	2	yes	complemented
153	D₁₀₀₄	—	2	4	no	—
154	D₁₀₀₄	—	2	2	no	—
155	D₁₀₀₄	—	2	4	no	—
156	D₁₀₀₄	—	2	1	no	—
157	D₁₀₀₄	C₂⁴	1	4	yes	—
158	D₁₀₀₄	C₂⁴	1	2	yes	complemented
159	C₂²⋊D₂₅₁	—	2	4	no	—
160	C₂²⋊D₂₅₁	—	2	4	no	—
161	C₂²⋊D₂₅₁	—	2	8	no	—
162	C₂²⋊D₂₅₁	—	2	8	no	—
163	C₂²⋊D₂₅₁	—	2	4	no	—
164	C₂×Dic₂₅₁	—	2	1	no	—
165	C₂×Dic₂₅₁	—	2	4	no	—
166	C₂×Dic₂₅₁	C₂×D₄	1	1	yes	characteristic
167	C₂×Dic₂₅₁	C₂×D₄	1	1	yes	characteristic
168	C₂×Dic₂₅₁	C₂×D₄	1	4	yes	—
169	C₄×D₂₅₁	—	2	4	no	—
170	C₄×D₂₅₁	—	2	4	no	—
171	C₄×D₂₅₁	—	2	4	no	—
172	C₄×D₂₅₁	C₂×D₄	1	4	yes	—
173	C₄×D₂₅₁	C₂×D₄	1	2	yes	—
174	C₄×D₂₅₁	C₂×D₄	1	2	yes	—
175	C₄×D₂₅₁	C₂×D₄	1	4	yes	—
176	C₄×D₂₅₁	C₂⁴	1	2	yes	—
177	C₄×D₂₅₁	C₂⁴	1	2	yes	—
178	C₂₅₁⋊C₈	C₂⁴	1	4	yes	complemented
179	C₂³×C₂₅₁	—	2	1	no	—
180	C₂³×C₂₅₁	—	2	2	no	—
181	C₂³×C₂₅₁	—	2	4	no	—
182	C₂³×C₂₅₁	—	4	4	no	—
183	C₂³×C₂₅₁	C₂×D₄	1	1	yes	characteristic
184	Q₈×C₂₅₁	—	2	1	no	—
185	Q₈×C₂₅₁	C₂⁴	1	2	yes	complemented
186	D₄×C₂₅₁	—	2	4	no	—
187	D₄×C₂₅₁	—	2	2	no	—
188	D₄×C₂₅₁	—	2	4	no	—
189	D₄×C₂₅₁	—	2	1	no	—
190	D₄×C₂₅₁	C₂⁴	1	4	yes	—
191	D₄×C₂₅₁	C₂⁴	1	2	yes	complemented
192	C₂×C₄×C₂₅₁	—	2	1	no	—
193	C₂×C₄×C₂₅₁	—	2	4	no	—
194	C₂×C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
195	C₂×C₄×C₂₅₁	C₂×D₄	1	2	yes	—
196	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
197	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
198	C₈×C₂₅₁	C₂⁴	1	4	yes	complemented
199	C₂²×C₂₅₁	—	2	2	no	—
200	C₂²×C₂₅₁	—	2	2	no	—
201	C₂²×C₂₅₁	—	2	4	no	—
202	C₂²×C₂₅₁	—	4	8	no	—
203	C₂²×C₂₅₁	—	4	4	no	—
204	C₂²×C₂₅₁	—	4	2	no	—
205	C₂²×C₂₅₁	C₂²×D₄	1	2	yes	—
206	C₂²×C₂₅₁	C₂²×D₄	1	1	yes	characteristic
207	C₂×D₂₅₁	—	2	2	no	—
208	C₂×D₂₅₁	—	2	8	no	—
209	C₂×D₂₅₁	—	2	2	no	—
210	C₂×D₂₅₁	—	2	4	no	—
211	C₂×D₂₅₁	—	4	16	no	—
212	C₂×D₂₅₁	—	4	8	no	—
213	C₂×D₂₅₁	—	4	2	no	—
214	C₂×D₂₅₁	—	4	4	no	—
215	C₂×D₂₅₁	—	4	8	no	—
216	C₂×D₂₅₁	—	4	16	no	—
217	C₂×D₂₅₁	AGL(1,ℤ/8)	1	4	yes	direct product factor
218	C₂×D₂₅₁	C₂²×D₄	1	2	yes	—
219	C₂×D₂₅₁	C₂²×D₄	1	2	yes	—
220	C₄×C₂₅₁	—	2	2	no	—
221	C₄×C₂₅₁	C₂²×D₄	1	2	yes	—
222	C₄×C₂₅₁	C₂²×D₄	1	1	yes	characteristic
223	C₄×C₂₅₁	C₂⁵	1	1	yes	characteristic
224	Dic₂₅₁	—	2	2	no	—
225	Dic₂₅₁	C₂²×D₄	1	2	yes	—
226	Dic₂₅₁	C₂²×D₄	1	2	yes	—
227	C₂×C₂₅₁	—	2	2	no	—
228	C₂×C₂₅₁	—	4	4	no	—
229	C₂×C₂₅₁	—	4	2	no	—
230	C₂×C₂₅₁	C₂×AGL(1,ℤ/8)	1	2	yes	complemented
231	C₂×C₂₅₁	C₂³×D₄	1	1	yes	characteristic
232	D₂₅₁	—	2	2	no	—
233	D₂₅₁	—	4	2	no	—
234	D₂₅₁	—	4	4	no	—
235	D₂₅₁	C₂×AGL(1,ℤ/8)	1	4	yes	direct product factor
236	C₂₅₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
237	C₂²×AGL(1,ℤ/8)	—	251	1	no	maximal, Sylow
238	C₂²×#41	—	251	1	no	—
239	C₂³×D₄	—	251	1	no	—
240	C₂×AGL(1,ℤ/8)	—	251	1	no	—
241	C₂×AGL(1,ℤ/8)	—	251	1	no	—
242	C₂×AGL(1,ℤ/8)	—	251	16	no	—
243	C₂×AGL(1,ℤ/8)	—	251	2	no	—
244	C₂×AGL(1,ℤ/8)	—	251	2	no	—
245	C₂×AGL(1,ℤ/8)	—	251	1	no	—
246	C₂×AGL(1,ℤ/8)	D₂₅₁	1	1	yes	characteristic, direct product factor
247	C₂²×SD₁₆	—	251	2	no	—
248	C₂²×D₈	—	251	2	no	—
249	C₂²×M₁₆	—	251	1	no	—
250	C₂⁵	—	502	1	no	—
251	C₂×#41	—	502	1	no	—
252	C₂×#41	—	502	1	no	—
253	C₂×#41	—	502	4	no	—
254	C₂×#41	—	251	8	no	—
255	C₂×#41	—	251	1	no	—
256	C₂×#41	—	251	1	no	—
257	C₂×#41	—	251	1	no	—
258	C₂×#41	C₂×D₂₅₁	1	1	yes	characteristic, complemented
259	C₂²×Q₈	—	251	1	no	—
260	C₂²×D₄	—	502	1	no	—
261	C₂²×D₄	—	502	1	no	—
262	C₂²×D₄	—	502	4	no	—
263	C₂²×D₄	—	502	1	no	—
264	C₂²×D₄	—	502	1	no	—
265	C₂²×D₄	—	251	2	no	—
266	C₂²×D₄	—	251	2	no	—
267	C₂²×D₄	—	251	1	no	—
268	C₂²×D₄	—	251	8	no	—
269	C₂²×D₄	—	251	1	no	—
270	C₂²×D₄	C₂×D₂₅₁	1	1	yes	characteristic, complemented
271	C₂³×C₄	—	502	1	no	—
272	C₂³×C₄	—	251	1	no	—
273	AGL(1,ℤ/8)	—	251	8	no	—
274	AGL(1,ℤ/8)	—	251	8	no	—
275	AGL(1,ℤ/8)	—	251	16	no	—
276	AGL(1,ℤ/8)	—	251	16	no	—
277	AGL(1,ℤ/8)	—	251	8	no	—
278	AGL(1,ℤ/8)	C₂×D₂₅₁	1	8	yes	direct product factor
279	C₂×SD₁₆	—	251	2	no	—
280	C₂×SD₁₆	—	251	2	no	—
281	C₂×SD₁₆	—	251	16	no	—
282	C₂×SD₁₆	—	251	2	no	—
283	C₂×SD₁₆	C₂×D₂₅₁	1	2	yes	complemented
284	C₂×D₈	—	251	2	no	—
285	C₂×D₈	—	251	2	no	—
286	C₂×D₈	—	251	16	no	—
287	C₂×D₈	—	251	2	no	—
288	C₂×D₈	C₂×D₂₅₁	1	2	yes	complemented
289	C₂×M₁₆	—	251	1	no	—
290	C₂×M₁₆	—	251	8	no	—
291	C₂×M₁₆	—	251	2	no	—
292	C₂×M₁₆	C₂×D₂₅₁	1	1	yes	characteristic, complemented
293	C₂²×C₈	—	251	2	no	—
294	C₂⁴	—	2	1	no	—
295	C₂⁴	—	1004	8	no	—
296	C₂⁴	—	502	1	no	—
297	C₂⁴	—	502	8	no	—
298	C₂⁴	—	502	2	no	—
299	C₂⁴	—	502	2	no	—
300	C₂⁴	—	502	1	no	—
301	C₂⁴	—	251	1	no	—
302	#41	—	2	2	no	—
303	#41	—	502	8	no	—
304	#41	—	502	8	no	—
305	#41	—	502	2	no	—
306	#41	—	502	2	no	—
307	#41	—	502	2	no	—
308	#41	—	251	4	no	—
309	#41	—	251	4	no	—
310	#41	—	251	4	no	—
311	#41	C₂²×D₂₅₁	1	4	yes	complemented
312	C₂×Q₈	—	502	1	no	—
313	C₂×Q₈	—	502	2	no	—
314	C₂×Q₈	—	251	4	no	—
315	C₂×Q₈	—	251	1	no	—
316	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic, complemented
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	502	1	no	—
321	C₂×D₄	—	502	8	no	—
322	C₂×D₄	—	502	1	no	—
323	C₂×D₄	—	502	1	no	—
324	C₂×D₄	—	502	8	no	—
325	C₂×D₄	—	502	4	no	—
326	C₂×D₄	—	502	4	no	—
327	C₂×D₄	—	502	8	no	—
328	C₂×D₄	—	502	2	no	—
329	C₂×D₄	—	502	8	no	—
330	C₂×D₄	—	502	2	no	—
331	C₂×D₄	—	502	2	no	—
332	C₂×D₄	—	502	1	no	—
333	C₂×D₄	—	502	2	no	—
334	C₂×D₄	—	502	1	no	—
335	C₂×D₄	—	251	8	no	—
336	C₂×D₄	—	251	8	no	—
337	C₂×D₄	—	251	4	no	—
338	C₂×D₄	—	251	1	no	—
339	C₂×D₄	—	251	2	no	—
340	C₂×D₄	—	251	4	no	—
341	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
342	C₂×D₄	C₂²×D₂₅₁	1	4	yes	complemented
343	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic, complemented
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	502	1	no	—
346	C₂²×C₄	—	502	1	no	—
347	C₂²×C₄	—	502	8	no	—
348	C₂²×C₄	—	502	1	no	—
349	C₂²×C₄	—	502	1	no	—
350	C₂²×C₄	—	251	1	no	—
351	C₂²×C₄	—	251	1	no	—
352	C₂²×C₄	—	251	4	no	—
353	C₂²×C₄	—	251	1	no	—
354	C₂²×C₄	—	251	1	no	—
355	C₂²×C₄	—	251	4	no	—
356	C₂²×C₄	—	251	1	no	—
357	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
358	SD₁₆	—	251	8	no	—
359	SD₁₆	—	251	8	no	—
360	SD₁₆	—	251	8	no	—
361	SD₁₆	C₂²×D₂₅₁	1	8	yes	complemented
362	D₈	—	251	8	no	—
363	D₈	—	251	8	no	—
364	D₈	—	251	8	no	—
365	D₈	C₂²×D₂₅₁	1	8	yes	complemented
366	M₁₆	—	251	4	no	—
367	M₁₆	—	251	8	no	—
368	M₁₆	C₂²×D₂₅₁	1	4	yes	complemented
369	C₂×C₈	—	251	2	no	—
370	C₂×C₈	—	251	8	no	—
371	C₂×C₈	C₂²×D₂₅₁	1	2	yes	complemented
372	C₂³	—	2	4	no	—
373	C₂³	—	2	1	no	—
374	C₂³	—	2	2	no	—
375	C₂³	—	4	4	no	—
376	C₂³	—	1004	4	no	—
377	C₂³	—	1004	32	no	—
378	C₂³	—	1004	8	no	—
379	C₂³	—	1004	8	no	—
380	C₂³	—	1004	4	no	—
381	C₂³	—	502	4	no	—
382	C₂³	—	502	8	no	—
383	C₂³	—	502	8	no	—
384	C₂³	—	502	4	no	—
385	C₂³	—	502	4	no	—
386	C₂³	—	502	1	no	—
387	C₂³	—	502	2	no	—
388	C₂³	—	251	4	no	—
389	C₂³	—	251	1	no	—
390	C₂³	—	251	1	no	—
391	C₂³	D₄×D₂₅₁	1	1	yes	characteristic
392	Q₈	—	2	1	no	—
393	Q₈	—	502	4	no	—
394	Q₈	—	502	1	no	—
395	Q₈	—	251	2	no	—
396	Q₈	C₂³×D₂₅₁	1	2	yes	complemented
397	D₄	—	2	4	no	—
398	D₄	—	2	2	no	—
399	D₄	—	2	4	no	—
400	D₄	—	2	1	no	—
401	D₄	—	502	4	no	—
402	D₄	—	502	4	no	—
403	D₄	—	502	4	no	—
404	D₄	—	502	8	no	—
405	D₄	—	502	8	no	—
406	D₄	—	502	4	no	—
407	D₄	—	502	4	no	—
408	D₄	—	502	2	no	—
409	D₄	—	502	1	no	—
410	D₄	—	251	2	no	—
411	D₄	—	251	4	no	—
412	D₄	C₂³×D₂₅₁	1	4	yes	—
413	D₄	C₂³×D₂₅₁	1	2	yes	complemented
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	502	4	no	—
417	C₂×C₄	—	502	4	no	—
418	C₂×C₄	—	502	1	no	—
419	C₂×C₄	—	502	4	no	—
420	C₂×C₄	—	502	4	no	—
421	C₂×C₄	—	251	4	no	—
422	C₂×C₄	—	251	1	no	—
423	C₂×C₄	—	251	1	no	—
424	C₂×C₄	—	251	4	no	—
425	C₂×C₄	—	251	2	no	—
426	C₂×C₄	—	251	2	no	—
427	C₂×C₄	—	251	4	no	—
428	C₂×C₄	—	251	2	no	—
429	C₂×C₄	—	251	2	no	—
430	C₂×C₄	D₄×D₂₅₁	1	2	yes	—
431	C₂×C₄	D₄×D₂₅₁	1	1	yes	characteristic
432	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
433	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
434	C₈	—	251	4	no	—
435	C₈	C₂³×D₂₅₁	1	4	yes	complemented
436	C₂²	—	2	2	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	2	4	no	—
439	C₂²	—	4	8	no	—
440	C₂²	—	4	4	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	1004	8	no	—
443	C₂²	—	1004	16	no	—
444	C₂²	—	1004	16	no	—
445	C₂²	—	1004	8	no	—
446	C₂²	—	1004	4	no	—
447	C₂²	—	1004	2	no	—
448	C₂²	—	502	8	no	—
449	C₂²	—	502	2	no	—
450	C₂²	—	502	4	no	—
451	C₂²	—	502	2	no	—
452	C₂²	—	251	2	no	—
453	C₂²	—	251	4	no	—
454	C₂²	—	251	2	no	—
455	C₂²	C₂×D₄×D₂₅₁	1	2	yes	—
456	C₂²	C₂×D₄×D₂₅₁	1	1	yes	characteristic
457	C₄	—	2	2	no	—
458	C₄	—	502	2	no	—
459	C₄	—	251	2	no	—
460	C₄	—	251	2	no	—
461	C₄	C₂×D₄×D₂₅₁	1	2	yes	—
462	C₄	C₂×D₄×D₂₅₁	1	1	yes	characteristic
463	C₄	C₂⁴×D₂₅₁	1	1	yes	characteristic
464	C₂	—	2	2	no	—
465	C₂	—	4	4	no	—
466	C₂	—	4	2	no	—
467	C₂	—	1004	4	no	—
468	C₂	—	1004	2	no	—
469	C₂	—	502	2	no	—
470	C₂	—	251	4	no	—
471	C₂	AGL(1,ℤ/8)×D₂₅₁	1	2	yes	direct product factor
472	C₂	C₂²×D₄×D₂₅₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₂₅₁
commutator, cosocle	C₄×C₂₅₁	C₂⁵
Frattini	C₄	C₂⁴×D₂₅₁
Fitting	C₂×AGL(1,ℤ/8)×C₂₅₁	C₂
socle	C₂²×C₂₅₁	C₂²×D₄
hypercenter	C₂×AGL(1,ℤ/8)	D₂₅₁
hypocenter	C₂₅₁	C₂²×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₂₅₁ ▷ C₂×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₂₅₁	C₂	semidirect
2. C₂²×D₄×D₂₅₁	C₂	semidirect
3. C₂×#22548743	C₂	semidirect
4. C₂×#22548742	C₂	semidirect
5. C₂×#22548741	C₂	semidirect
6. C₂×#22548740	C₂	semidirect
7. C₂×#22548739	C₂	semidirect
8. AGL(1,ℤ/8)×D₂₅₁	C₂	direct (N × H)
9. C₂×SD₁₆×D₂₅₁	C₂	semidirect
10. C₂×D₈×D₂₅₁	C₂	semidirect
11. C₂×M₁₆×D₂₅₁	C₂	semidirect
12. C₂×AGL(1,ℤ/8)×C₂₅₁	C₂	semidirect
14. C₂×#16860811	C₂²	semidirect
16. C₂×#16860810	C₂²	semidirect
18. C₂×#16860809	C₂²	semidirect
20. #41×D₂₅₁	C₂²	semidirect
21. C₂×Q₈×D₂₅₁	C₂²	semidirect
22. C₂²×D₁₀₀₄	C₂²	semidirect
29. C₂×D₄×D₂₅₁	C₂²	semidirect
30. C₂×D₄×D₂₅₁	C₂²	semidirect
31. C₂×D₄×D₂₅₁	C₂²	semidirect
34. #22548743	C₂²	semidirect
35. #22548742	C₂²	semidirect
36. #22548741	C₂²	semidirect
37. #22548740	C₂²	semidirect
38. #22548739	C₂²	semidirect
39. C₂×#16860799	C₂²	semidirect
40. C₂×#16860798	C₂²	semidirect
41. C₂×#16860797	C₂²	semidirect
42. SD₁₆×D₂₅₁	C₂²	semidirect
43. C₂×D₂₀₀₈	C₂²	semidirect
44. C₂×#16860795	C₂²	semidirect
45. C₂×#16860795	C₂²	semidirect
46. D₈×D₂₅₁	C₂²	semidirect
47. C₂×#16860794	C₂²	semidirect
48. C₂×#16860793	C₂²	semidirect
49. M₁₆×D₂₅₁	C₂²	semidirect
50. C₂×C₈×D₂₅₁	C₂²	semidirect
51. C₂×#41×C₂₅₁	C₂²	semidirect
52. C₂²×D₄×C₂₅₁	C₂²	semidirect
53. AGL(1,ℤ/8)×C₂₅₁	C₂²	semidirect
54. C₂×SD₁₆×C₂₅₁	C₂²	semidirect
55. C₂×D₈×C₂₅₁	C₂²	semidirect
56. C₂×M₁₆×C₂₅₁	C₂²	semidirect
65. #16860811	C₂³	semidirect
68. #16860810	C₂³	semidirect
71. #16860809	C₂³	semidirect
73. C₂×Dic₅₀₂	C₂³	semidirect
75. Q₈×D₂₅₁	C₂³	semidirect
80. C₂×D₁₀₀₄	C₂³	semidirect
81. C₂×D₁₀₀₄	C₂³	semidirect
95. D₄×D₂₅₁	C₂³	semidirect
96. D₄×D₂₅₁	C₂³	semidirect
109. #16860799	C₂³	semidirect
110. #16860798	C₂³	semidirect
111. #16860797	C₂³	semidirect
112. D₂₀₀₈	C₂³	semidirect
113. #16860795	C₂³	semidirect
114. #16860795	C₂³	semidirect
115. #16860794	C₂³	semidirect
116. #16860793	C₂³	semidirect
117. C₂×C₂₅₁⋊C₈	C₂³	semidirect
118. C₈×D₂₅₁	C₂³	semidirect
121. #41×C₂₅₁	C₂³	semidirect
122. C₂×Q₈×C₂₅₁	C₂³	semidirect
127. C₂×D₄×C₂₅₁	C₂³	semidirect
128. C₂×D₄×C₂₅₁	C₂³	semidirect
131. SD₁₆×C₂₅₁	C₂³	semidirect
132. D₈×C₂₅₁	C₂³	semidirect
133. M₁₆×C₂₅₁	C₂³	semidirect
134. C₂×C₈×C₂₅₁	C₂³	semidirect
152. Dic₅₀₂	C₂⁴	semidirect
158. D₁₀₀₄	C₂⁴	semidirect
178. C₂₅₁⋊C₈	C₂⁴	semidirect
185. Q₈×C₂₅₁	C₂⁴	semidirect
191. D₄×C₂₅₁	C₂⁴	semidirect
198. C₈×C₂₅₁	C₂⁴	semidirect
217. C₂×D₂₅₁	AGL(1,ℤ/8)	direct (N × H)
230. C₂×C₂₅₁	C₂×AGL(1,ℤ/8)	semidirect
235. D₂₅₁	C₂×AGL(1,ℤ/8)	direct (N × H)
236. C₂₅₁	C₂²×AGL(1,ℤ/8)	semidirect
246. C₂×AGL(1,ℤ/8)	D₂₅₁	direct (N × H)
258. C₂×#41	C₂×D₂₅₁	semidirect
270. C₂²×D₄	C₂×D₂₅₁	semidirect
278. AGL(1,ℤ/8)	C₂×D₂₅₁	direct (N × H)
283. C₂×SD₁₆	C₂×D₂₅₁	semidirect
288. C₂×D₈	C₂×D₂₅₁	semidirect
292. C₂×M₁₆	C₂×D₂₅₁	semidirect
311. #41	C₂²×D₂₅₁	semidirect
316. C₂×Q₈	C₂²×D₂₅₁	semidirect
342. C₂×D₄	C₂²×D₂₅₁	semidirect
343. C₂×D₄	C₂²×D₂₅₁	semidirect
361. SD₁₆	C₂²×D₂₅₁	semidirect
365. D₈	C₂²×D₂₅₁	semidirect
368. M₁₆	C₂²×D₂₅₁	semidirect
371. C₂×C₈	C₂²×D₂₅₁	semidirect
396. Q₈	C₂³×D₂₅₁	semidirect
413. D₄	C₂³×D₂₅₁	semidirect
435. C₈	C₂³×D₂₅₁	semidirect
471. C₂	AGL(1,ℤ/8)×D₂₅₁	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×#41×D₂₅₁	2
C₂²×D₄×D₂₅₁	2
C₂×#22548743	2
C₂×#22548742	2
C₂×#22548741	2
C₂×#22548740	2
C₂×#22548739	2
AGL(1,ℤ/8)×D₂₅₁	2
C₂×SD₁₆×D₂₅₁	2
C₂×D₈×D₂₅₁	2
C₂×M₁₆×D₂₅₁	2
C₂×AGL(1,ℤ/8)×C₂₅₁	2
C₂²×AGL(1,ℤ/8)	251

Subgroups — C2×AGL(1,ℤ/8)×D251 #44565095

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×AGL(1,ℤ/8)×D₂₅₁ #44565095