Subgroups — #44559827

Order 32128.

548 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22548742	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#22548739	C₂	1	1	yes	maximal, characteristic, complemented
3	#30632236	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₄×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#30631903	C₂	1	1	yes	maximal, characteristic, complemented
6	#30631902	C₂	1	1	yes	maximal, characteristic, complemented
7	#30631899	C₂	1	1	yes	maximal, characteristic, complemented
8	#30631891	C₂	1	1	yes	maximal, characteristic, complemented
9	#30631890	C₂	1	1	yes	maximal, characteristic, complemented
10	#30631881	C₂	1	1	yes	maximal, characteristic, complemented
11	#30631880	C₂	1	1	yes	maximal, characteristic, complemented
12	#30631709	C₂	1	1	yes	maximal, characteristic, complemented
13	#30631687	C₂	1	1	yes	maximal, characteristic, complemented
14	#30631685	C₂	1	1	yes	maximal, characteristic, complemented
15	#463×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#16860811	C₂²	1	1	yes	characteristic
17	C₂×#16860809	C₂²	1	1	yes	characteristic
18	C₂×D₄×D₂₅₁	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₂₅₁	—	2	1	no	—
20	#22548742	—	2	4	no	—
21	#22548739	—	2	4	no	—
22	C₂×#16860799	C₂²	1	1	yes	characteristic
23	C₂×#16860798	C₂²	1	1	yes	characteristic
24	C₂×#16860797	C₂²	1	1	yes	characteristic
25	C₂×D₂₀₀₈	C₂²	1	1	yes	characteristic
26	C₂×#16860795	C₂²	1	1	yes	characteristic
27	C₂×#16860795	C₂²	1	1	yes	characteristic
28	C₂×#16860793	C₂²	1	1	yes	characteristic
29	C₂×#16860793	C₂²	1	1	yes	characteristic
30	#22548713	C₂²	1	1	yes	characteristic, complemented
31	#22548711	C₂²	1	1	yes	characteristic, complemented
32	#22548703	C₂²	1	1	yes	characteristic, complemented
33	#22548688	—	2	1	no	—
34	#22548688	—	2	1	no	—
35	C₄×D₁₀₀₄	C₂²	1	1	yes	characteristic
36	D₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
37	#22548677	C₂²	1	1	yes	characteristic
38	C₄×C₂²⋊D₂₅₁	—	2	1	no	—
39	(C₂²⋊D₂₅₁)⋊C₄	—	2	1	no	—
40	(C₂²⋊D₂₅₁)⋊C₄	—	2	1	no	—
41	(C₂²⋊D₂₅₁)⋊C₄	—	2	1	no	—
42	C₄⋊C₄×D₂₅₁	C₂²	1	1	yes	characteristic
43	C₂²⋊C₄×D₂₅₁	—	2	1	no	—
44	C₄²×D₂₅₁	C₂²	1	1	yes	characteristic
45	C₄⋊(C₂₅₁⋊C₈)	C₂²	1	1	yes	characteristic, complemented
46	Dic₂₅₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
47	Dic₂₅₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
48	#22548640	C₂²	1	1	yes	characteristic, complemented
49	#22548639	C₂²	1	1	yes	characteristic, complemented
50	#22548638	C₂²	1	1	yes	characteristic, complemented
51	#22548637	C₂²	1	1	yes	characteristic, complemented
52	#22548636	C₂²	1	1	yes	characteristic, complemented
53	#22548635	C₂²	1	1	yes	characteristic, complemented
54	C₂×SD₁₆×C₂₅₁	C₂²	1	1	yes	characteristic
55	C₂×D₈×C₂₅₁	C₂²	1	1	yes	characteristic
56	#124×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
57	C₄×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
58	C₄⋊C₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
59	#103×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
60	#102×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₂₅₁	—	2	1	no	—
62	#16860811	—	2	2	no	—
63	#16860811	—	2	2	no	—
64	#16860809	—	2	2	no	—
65	#16860809	—	2	2	no	—
66	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
67	C₂×D₁₀₀₄	—	2	1	no	—
68	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
69	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
70	C₂×C₂²⋊D₂₅₁	—	2	1	no	—
71	C₂×C₂²⋊D₂₅₁	—	2	1	no	—
72	C₂×C₂²⋊D₂₅₁	—	2	1	no	—
73	C₂×C₂²⋊D₂₅₁	—	2	1	no	—
74	D₄×D₂₅₁	—	2	2	no	—
75	D₄×D₂₅₁	D₄	1	4	yes	complemented
76	C₂²×Dic₂₅₁	—	2	1	no	—
77	C₂²×Dic₂₅₁	—	2	1	no	—
78	C₂×C₄×D₂₅₁	—	2	1	no	—
79	C₂×C₄×D₂₅₁	—	2	1	no	—
80	C₂×C₄×D₂₅₁	—	2	1	no	—
81	C₂×C₄×D₂₅₁	—	2	1	no	—
82	C₂×C₄×D₂₅₁	—	4	4	no	—
83	C₂×C₄×D₂₅₁	D₄	1	1	yes	characteristic
84	C₂×C₄×D₂₅₁	D₄	1	1	yes	characteristic
85	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
86	#16860799	—	2	2	no	—
87	#16860798	—	2	2	no	—
88	#16860797	—	2	2	no	—
89	D₂₀₀₈	—	2	2	no	—
90	#16860795	—	2	2	no	—
91	#16860795	—	2	2	no	—
92	#16860793	—	2	2	no	—
93	#16860793	—	2	2	no	—
94	C₂×C₂₅₁⋊C₈	C₂³	1	1	yes	characteristic
95	C₂×C₂₅₁⋊C₈	C₂³	1	1	yes	characteristic
96	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
97	Dic₂₅₁⋊C₄	—	2	1	no	—
98	Dic₂₅₁⋊C₄	—	2	1	no	—
99	Dic₂₅₁⋊C₄	—	2	1	no	—
100	C₂²⋊Dic₂₅₁	—	2	1	no	—
101	(C₂×D₂₅₁)⋊C₄	—	2	1	no	—
102	(C₂×D₂₅₁)⋊C₄	—	2	1	no	—
103	(C₂×D₂₅₁)⋊C₄	—	2	1	no	—
104	(C₂×D₂₅₁)⋊C₄	—	2	1	no	—
105	C₄×Dic₂₅₁	D₄	1	1	yes	characteristic
106	C₄×Dic₂₅₁	D₄	1	1	yes	characteristic
107	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
108	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
109	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
110	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
111	C₂²×C₄×C₂₅₁	—	2	1	no	—
112	SD₁₆×C₂₅₁	—	2	2	no	—
113	D₈×C₂₅₁	—	2	2	no	—
114	C₂×C₈×C₂₅₁	C₂³	1	1	yes	characteristic
115	C₂×C₈×C₂₅₁	C₂³	1	1	yes	characteristic
116	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
117	C₂²⋊C₄×C₂₅₁	—	2	1	no	—
118	C₂²⋊C₄×C₂₅₁	—	2	1	no	—
119	C₂²⋊C₄×C₂₅₁	—	2	1	no	—
120	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
121	C₂²×D₂₅₁	—	2	1	no	—
122	C₂²×D₂₅₁	—	2	4	no	—
123	C₂²×D₂₅₁	—	2	1	no	—
124	C₂²×D₂₅₁	—	4	2	no	—
125	C₂²×D₂₅₁	—	4	2	no	—
126	C₂²×D₂₅₁	C₂×D₄	1	1	yes	characteristic
127	Dic₅₀₂	—	2	1	no	—
128	Dic₅₀₂	—	2	1	no	—
129	D₁₀₀₄	—	2	1	no	—
130	D₁₀₀₄	—	2	1	no	—
131	D₁₀₀₄	—	2	1	no	—
132	D₁₀₀₄	—	4	2	no	—
133	D₁₀₀₄	C₂×D₄	1	2	yes	—
134	C₂²⋊D₂₅₁	—	2	4	no	—
135	C₂²⋊D₂₅₁	—	4	2	no	—
136	C₂²⋊D₂₅₁	—	4	2	no	—
137	C₂²⋊D₂₅₁	—	4	2	no	—
138	C₂×Dic₂₅₁	—	2	1	no	—
139	C₂×Dic₂₅₁	—	2	1	no	—
140	C₂×Dic₂₅₁	—	4	2	no	—
141	C₂×Dic₂₅₁	—	4	2	no	—
142	C₂×Dic₂₅₁	C₂×D₄	1	1	yes	characteristic
143	C₂×Dic₂₅₁	C₂×D₄	1	1	yes	characteristic
144	C₂×Dic₂₅₁	C₂×D₄	1	1	yes	characteristic
145	C₄×D₂₅₁	—	2	2	no	—
146	C₄×D₂₅₁	—	4	1	no	—
147	C₄×D₂₅₁	—	4	2	no	—
148	C₄×D₂₅₁	—	4	2	no	—
149	C₄×D₂₅₁	—	4	2	no	—
150	C₄×D₂₅₁	—	4	2	no	—
151	C₄×D₂₅₁	C₂×D₄	1	2	yes	—
152	C₄×D₂₅₁	#41	1	2	yes	—
153	C₂₅₁⋊C₈	—	2	1	no	—
154	C₂₅₁⋊C₈	—	2	1	no	—
155	C₂³×C₂₅₁	—	2	1	no	—
156	C₂³×C₂₅₁	—	2	1	no	—
157	Q₈×C₂₅₁	—	2	1	no	—
158	Q₈×C₂₅₁	—	2	1	no	—
159	D₄×C₂₅₁	—	2	1	no	—
160	D₄×C₂₅₁	—	2	1	no	—
161	D₄×C₂₅₁	—	2	1	no	—
162	D₄×C₂₅₁	C₂×D₄	1	2	yes	—
163	C₂×C₄×C₂₅₁	—	2	1	no	—
164	C₂×C₄×C₂₅₁	—	2	1	no	—
165	C₂×C₄×C₂₅₁	—	4	2	no	—
166	C₂×C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
167	C₂×C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
168	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
169	C₈×C₂₅₁	—	2	1	no	—
170	C₈×C₂₅₁	—	2	1	no	—
171	C₂²×C₂₅₁	—	2	2	no	—
172	C₂²×C₂₅₁	—	4	1	no	—
173	C₂²×C₂₅₁	—	4	1	no	—
174	C₂²×C₂₅₁	—	4	1	no	—
175	C₂²×C₂₅₁	—	4	1	no	—
176	C₂²×C₂₅₁	—	4	1	no	—
177	C₂²×C₂₅₁	C₂²×D₄	1	1	yes	characteristic
178	C₂×D₂₅₁	—	2	1	no	—
179	C₂×D₂₅₁	—	2	1	no	—
180	C₂×D₂₅₁	—	2	2	no	—
181	C₂×D₂₅₁	—	4	8	no	—
182	C₂×D₂₅₁	—	4	1	no	—
183	C₂×D₂₅₁	—	4	1	no	—
184	C₂×D₂₅₁	—	4	1	no	—
185	C₂×D₂₅₁	—	4	1	no	—
186	C₂×D₂₅₁	—	4	1	no	—
187	C₂×D₂₅₁	#121	1	2	yes	—
188	C₄×C₂₅₁	—	2	1	no	—
189	C₄×C₂₅₁	—	2	1	no	—
190	C₄×C₂₅₁	—	4	1	no	—
191	C₄×C₂₅₁	—	4	1	no	—
192	C₄×C₂₅₁	C₂²×D₄	1	1	yes	characteristic
193	C₄×C₂₅₁	C₂×#41	1	1	yes	characteristic
194	Dic₂₅₁	—	2	1	no	—
195	Dic₂₅₁	—	4	1	no	—
196	Dic₂₅₁	—	4	1	no	—
197	Dic₂₅₁	#121	1	2	yes	—
198	Dic₂₅₁	AGL(1,ℤ/8)	1	2	yes	complemented
199	C₂×C₂₅₁	—	4	2	no	—
200	C₂×C₂₅₁	—	8	1	no	—
201	C₂×C₂₅₁	C₂×#121	1	1	yes	characteristic
202	C₂×C₂₅₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
203	C₂×C₂₅₁	#575	1	1	yes	characteristic
204	D₂₅₁	—	2	2	no	—
205	D₂₅₁	—	4	2	no	—
206	D₂₅₁	—	8	1	no	—
207	C₂₅₁	#3036	1	1	yes	characteristic, complemented, Sylow
208	#3036	—	251	1	no	maximal, Sylow
209	C₂×AGL(1,ℤ/8)	—	251	1	no	—
210	C₂×AGL(1,ℤ/8)	—	251	1	no	—
211	#532	—	251	1	no	—
212	C₂×C₄×D₄	—	251	1	no	—
213	#463	—	251	1	no	—
214	#463	—	251	1	no	—
215	#463	—	251	1	no	—
216	#463	D₂₅₁	1	1	yes	characteristic, complemented
217	#461	—	251	1	no	—
218	#461	—	251	1	no	—
219	#459	—	251	1	no	—
220	#459	—	251	1	no	—
221	#423	—	251	1	no	—
222	#417	—	251	1	no	—
223	#417	—	251	1	no	—
224	C₂×#41	—	251	1	no	—
225	C₂×#41	—	251	1	no	—
226	C₂²×D₄	—	251	1	no	—
227	C₂³×C₄	—	502	1	no	—
228	AGL(1,ℤ/8)	—	502	4	no	—
229	AGL(1,ℤ/8)	—	502	4	no	—
230	C₂×SD₁₆	—	251	1	no	—
231	C₂×SD₁₆	—	251	1	no	—
232	C₂×SD₁₆	—	251	1	no	—
233	C₂×SD₁₆	C₂×D₂₅₁	1	1	yes	characteristic
234	C₂×D₈	—	251	1	no	—
235	C₂×D₈	—	251	1	no	—
236	C₂×D₈	—	251	1	no	—
237	C₂×D₈	C₂×D₂₅₁	1	1	yes	characteristic
238	C₂×M₁₆	—	251	1	no	—
239	C₂×M₁₆	—	251	1	no	—
240	C₄⋊Q₈	—	251	1	no	—
241	#127	—	251	1	no	—
242	#124	—	251	1	no	—
243	#124	C₂×D₂₅₁	1	1	yes	characteristic, complemented
244	#121	—	502	1	no	—
245	#121	—	502	1	no	—
246	C₄×D₄	—	502	1	no	—
247	C₄×D₄	—	502	1	no	—
248	C₄×D₄	—	502	1	no	—
249	C₄×D₄	—	502	1	no	—
250	C₄×D₄	—	251	1	no	—
251	C₄×D₄	—	251	1	no	—
252	C₄×D₄	—	251	1	no	—
253	C₄×D₄	C₂×D₂₅₁	1	1	yes	characteristic
254	C₂×C₄⋊C₄	—	251	1	no	—
255	C₂×C₂²⋊C₄	—	502	1	no	—
256	C₂×C₄²	—	251	1	no	—
257	C₄⋊C₈	—	251	1	no	—
258	C₄⋊C₈	—	251	1	no	—
259	C₄⋊C₈	—	251	1	no	—
260	C₄⋊C₈	C₂×D₂₅₁	1	1	yes	characteristic, complemented
261	#103	—	251	1	no	—
262	#103	—	251	1	no	—
263	#103	—	251	1	no	—
264	#103	C₂×D₂₅₁	1	1	yes	characteristic, complemented
265	#102	—	251	1	no	—
266	#102	—	251	1	no	—
267	#102	—	251	1	no	—
268	#102	C₂×D₂₅₁	1	1	yes	characteristic, complemented
269	C₂⁴	—	502	1	no	—
270	#41	—	502	2	no	—
271	#41	—	502	2	no	—
272	#41	—	502	2	no	—
273	#41	—	502	2	no	—
274	C₂×Q₈	—	251	1	no	—
275	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
276	C₂×D₄	—	502	1	no	—
277	C₂×D₄	—	502	1	no	—
278	C₂×D₄	—	502	2	no	—
279	C₂×D₄	—	502	1	no	—
280	C₂×D₄	—	502	1	no	—
281	C₂×D₄	—	502	1	no	—
282	C₂×D₄	—	251	4	no	—
283	C₂×D₄	—	251	1	no	—
284	C₂×D₄	—	251	1	no	—
285	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
286	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	1004	4	no	—
289	C₂²×C₄	—	502	1	no	—
290	C₂²×C₄	—	502	1	no	—
291	C₂²×C₄	—	502	1	no	—
292	C₂²×C₄	—	502	1	no	—
293	C₂²×C₄	—	502	1	no	—
294	C₂²×C₄	—	502	1	no	—
295	C₂²×C₄	—	251	1	no	—
296	C₂²×C₄	—	251	1	no	—
297	C₂²×C₄	—	251	1	no	—
298	SD₁₆	—	2	2	no	—
299	SD₁₆	—	502	2	no	—
300	SD₁₆	—	502	2	no	—
301	SD₁₆	—	502	2	no	—
302	D₈	—	2	2	no	—
303	D₈	—	502	2	no	—
304	D₈	—	502	2	no	—
305	D₈	—	502	2	no	—
306	M₁₆	—	502	2	no	—
307	M₁₆	—	502	2	no	—
308	C₂×C₈	—	251	1	no	—
309	C₂×C₈	—	251	1	no	—
310	C₂×C₈	C₂²×D₂₅₁	1	1	yes	characteristic
311	C₂×C₈	C₂²×D₂₅₁	1	1	yes	characteristic
312	C₄⋊C₄	—	502	1	no	—
313	C₄⋊C₄	—	502	1	no	—
314	C₄⋊C₄	—	502	1	no	—
315	C₄⋊C₄	—	251	1	no	—
316	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
317	C₂²⋊C₄	—	2	1	no	—
318	C₂²⋊C₄	—	2	1	no	—
319	C₂²⋊C₄	—	2	1	no	—
320	C₂²⋊C₄	—	502	1	no	—
321	C₂²⋊C₄	—	502	1	no	—
322	C₂²⋊C₄	—	502	1	no	—
323	C₂²⋊C₄	—	502	1	no	—
324	C₂²⋊C₄	—	502	1	no	—
325	C₄²	—	251	1	no	—
326	C₄²	—	251	1	no	—
327	C₄²	—	251	1	no	—
328	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
329	C₂³	—	2	1	no	—
330	C₂³	—	2	1	no	—
331	C₂³	—	1004	2	no	—
332	C₂³	—	1004	2	no	—
333	C₂³	—	502	4	no	—
334	C₂³	—	502	1	no	—
335	C₂³	—	502	1	no	—
336	C₂³	—	251	1	no	—
337	Q₈	—	2	1	no	—
338	Q₈	—	2	1	no	—
339	Q₈	—	502	1	no	—
340	Q₈	—	502	1	no	—
341	D₄	—	2	1	no	—
342	D₄	—	2	1	no	—
343	D₄	—	2	1	no	—
344	D₄	—	1004	2	no	—
345	D₄	—	1004	2	no	—
346	D₄	—	1004	2	no	—
347	D₄	—	1004	2	no	—
348	D₄	—	502	4	no	—
349	D₄	—	502	1	no	—
350	D₄	—	502	1	no	—
351	D₄	—	502	1	no	—
352	D₄	—	251	2	no	—
353	D₄	D₄×D₂₅₁	1	2	yes	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	1004	2	no	—
358	C₂×C₄	—	1004	1	no	—
359	C₂×C₄	—	1004	2	no	—
360	C₂×C₄	—	1004	2	no	—
361	C₂×C₄	—	1004	2	no	—
362	C₂×C₄	—	1004	2	no	—
363	C₂×C₄	—	1004	2	no	—
364	C₂×C₄	—	502	2	no	—
365	C₂×C₄	—	502	1	no	—
366	C₂×C₄	—	502	1	no	—
367	C₂×C₄	—	251	1	no	—
368	C₂×C₄	—	251	1	no	—
369	C₂×C₄	—	251	1	no	—
370	C₂×C₄	—	251	2	no	—
371	C₂×C₄	—	251	2	no	—
372	C₂×C₄	D₄×D₂₅₁	1	1	yes	characteristic
373	C₂×C₄	D₄×D₂₅₁	1	1	yes	characteristic
374	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	—	502	1	no	—
378	C₈	—	502	1	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	4	1	no	—
381	C₂²	—	4	1	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	4	1	no	—
384	C₂²	—	4	1	no	—
385	C₂²	—	1004	8	no	—
386	C₂²	—	1004	1	no	—
387	C₂²	—	1004	1	no	—
388	C₂²	—	1004	1	no	—
389	C₂²	—	1004	1	no	—
390	C₂²	—	1004	1	no	—
391	C₂²	—	502	2	no	—
392	C₂²	—	502	1	no	—
393	C₂²	—	502	1	no	—
394	C₂²	—	251	2	no	—
395	C₂²	C₂×D₄×D₂₅₁	1	1	yes	characteristic
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	4	1	no	—
399	C₄	—	4	1	no	—
400	C₄	—	1004	1	no	—
401	C₄	—	1004	1	no	—
402	C₄	—	502	1	no	—
403	C₄	—	251	2	no	—
404	C₄	—	251	2	no	—
405	C₄	C₂×D₄×D₂₅₁	1	1	yes	characteristic
406	C₄	#41×D₂₅₁	1	1	yes	characteristic
407	C₂	—	4	2	no	—
408	C₂	—	8	1	no	—
409	C₂	—	2008	1	no	—
410	C₂	—	1004	2	no	—
411	C₂	—	502	2	no	—
412	C₂	#121×D₂₅₁	1	1	yes	characteristic
413	C₂	AGL(1,ℤ/8)×D₂₅₁	1	1	yes	characteristic
414	C₂	#30632484	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₂₅₁
commutator, cosocle	C₂×C₄×C₂₅₁	C₂⁴
Frattini	C₂×C₄	C₂³×D₂₅₁
Fitting	#463×C₂₅₁	C₂
socle	C₂²×C₂₅₁	C₂²×D₄
hypercenter	#463	D₂₅₁
hypocenter	C₂₅₁	#3036
LCS	G ▷ C₂×C₄×C₂₅₁ ▷ C₂×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #463

Complements

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

N	H ≅ G/N	type
1. C₂×#22548742	C₂	semidirect
2. C₂×#22548739	C₂	semidirect
3. #30632236	C₂	semidirect
4. C₄×D₄×D₂₅₁	C₂	semidirect
5. #30631903	C₂	semidirect
6. #30631902	C₂	semidirect
7. #30631899	C₂	semidirect
8. #30631891	C₂	semidirect
9. #30631890	C₂	semidirect
10. #30631881	C₂	semidirect
11. #30631880	C₂	semidirect
12. #30631709	C₂	semidirect
13. #30631687	C₂	semidirect
14. #30631685	C₂	semidirect
15. #463×C₂₅₁	C₂	semidirect
30. #22548713	C₂²	semidirect
31. #22548711	C₂²	semidirect
32. #22548703	C₂²	semidirect
45. C₄⋊(C₂₅₁⋊C₈)	C₂²	semidirect
46. Dic₂₅₁⋊C₈	C₂²	semidirect
47. Dic₂₅₁⋊C₈	C₂²	semidirect
48. #22548640	C₂²	semidirect
49. #22548639	C₂²	semidirect
50. #22548638	C₂²	semidirect
51. #22548637	C₂²	semidirect
52. #22548636	C₂²	semidirect
53. #22548635	C₂²	semidirect
56. #124×C₂₅₁	C₂²	semidirect
58. C₄⋊C₈×C₂₅₁	C₂²	semidirect
59. #103×C₂₅₁	C₂²	semidirect
60. #102×C₂₅₁	C₂²	semidirect
75. D₄×D₂₅₁	D₄	semidirect
198. Dic₂₅₁	AGL(1,ℤ/8)	semidirect
207. C₂₅₁	#3036	semidirect
216. #463	D₂₅₁	semidirect
243. #124	C₂×D₂₅₁	semidirect
260. C₄⋊C₈	C₂×D₂₅₁	semidirect
264. #103	C₂×D₂₅₁	semidirect
268. #102	C₂×D₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#22548742	2
C₂×#22548739	2
#30632236	2
C₄×D₄×D₂₅₁	2
#30631903	2
#30631902	2
#30631899	2
#30631891	2
#30631890	2
#30631881	2
#30631880	2
#30631709	2
#30631687	2
#30631685	2
#463×C₂₅₁	2
#3036	251