Subgroups — C₂×#30631702 #44558905

Order 32128.

772 conjugacy classes of subgroups.

The subgroup lattice has 400 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
2	C₂×M₁₆×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#22548672	C₂	1	1	yes	maximal, characteristic, complemented
4	#30631702	C₂	1	8	yes	maximal, direct product factor
5	C₂×#22548643	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#22548642	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#22548641	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#104×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#16860811	C₄	1	1	yes	characteristic, complemented
10	C₂×#16860810	—	2	1	no	—
11	C₂×#16860810	C₂²	1	1	yes	characteristic
12	C₂×#16860809	—	2	1	no	—
13	C₂×#16860809	C₄	1	1	yes	characteristic, complemented
14	#41×D₂₅₁	—	2	2	no	—
15	#41×D₂₅₁	—	2	2	no	—
16	#41×D₂₅₁	C₄	1	4	yes	complemented
17	#41×D₂₅₁	C₂²	1	4	yes	—
18	C₂×Q₈×D₂₅₁	C₄	1	1	yes	characteristic, complemented
19	C₂×D₄×D₂₅₁	—	2	1	no	—
20	C₂×D₄×D₂₅₁	C₄	1	1	yes	characteristic, complemented
21	C₂²×C₄×D₂₅₁	—	2	1	no	—
22	C₂²×C₄×D₂₅₁	C₂²	1	1	yes	characteristic
23	C₂×#16860794	C₂²	1	1	yes	characteristic, complemented
24	C₂×#16860793	—	2	1	no	—
25	M₁₆×D₂₅₁	—	2	2	no	—
26	M₁₆×D₂₅₁	C₂²	1	4	yes	complemented
27	C₂×C₈×D₂₅₁	—	2	1	no	—
28	#22548672	—	2	2	no	—
29	#22548672	C₂²	1	4	yes	complemented
30	C₂×Dic₂₅₁⋊C₄	—	2	1	no	—
31	C₂×(C₂×D₂₅₁)⋊C₄	—	2	1	no	—
32	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
33	#22548643	C₂²	1	4	yes	complemented
34	#22548642	C₂²	1	4	yes	complemented
35	#22548641	C₂²	1	4	yes	complemented
36	C₂×#41×C₂₅₁	C₂²	1	1	yes	characteristic
37	C₂×M₁₆×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄²×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
39	#104×C₂₅₁	C₂²	1	4	yes	complemented
40	C₂³×D₂₅₁	—	2	1	no	—
41	C₂³×D₂₅₁	D₄	1	1	yes	characteristic
42	#16860811	—	2	2	no	—
43	#16860811	C₂×C₄	1	4	yes	complemented
44	#16860810	—	2	4	no	—
45	#16860810	—	2	4	no	—
46	#16860810	—	2	1	no	—
47	#16860810	—	2	1	no	—
48	#16860810	C₂×C₄	1	2	yes	—
49	#16860810	C₂³	1	2	yes	—
50	#16860809	—	2	4	no	—
51	#16860809	—	2	4	no	—
52	#16860809	—	2	2	no	—
53	#16860809	C₂×C₄	1	4	yes	complemented
54	C₂×Dic₅₀₂	—	2	1	no	—
55	C₂×Dic₅₀₂	C₂×C₄	1	1	yes	characteristic
56	Q₈×D₂₅₁	—	2	2	no	—
57	Q₈×D₂₅₁	C₂×C₄	1	4	yes	complemented
58	C₂×D₁₀₀₄	—	2	1	no	—
59	C₂×D₁₀₀₄	C₂×C₄	1	1	yes	characteristic
60	C₂×C₂²⋊D₂₅₁	—	2	1	no	—
61	C₂×C₂²⋊D₂₅₁	—	2	1	no	—
62	C₂×C₂²⋊D₂₅₁	—	2	1	no	—
63	D₄×D₂₅₁	—	2	4	no	—
64	D₄×D₂₅₁	—	2	4	no	—
65	D₄×D₂₅₁	—	2	2	no	—
66	D₄×D₂₅₁	C₂×C₄	1	4	yes	complemented
67	C₂²×Dic₂₅₁	—	2	1	no	—
68	C₂²×Dic₂₅₁	—	2	1	no	—
69	C₂²×Dic₂₅₁	D₄	1	1	yes	characteristic
70	C₂×C₄×D₂₅₁	—	2	1	no	—
71	C₂×C₄×D₂₅₁	—	2	1	no	—
72	C₂×C₄×D₂₅₁	—	2	4	no	—
73	C₂×C₄×D₂₅₁	—	2	4	no	—
74	C₂×C₄×D₂₅₁	—	2	1	no	—
75	C₂×C₄×D₂₅₁	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄×D₂₅₁	C₂×C₄	1	2	yes	—
77	C₂×C₄×D₂₅₁	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄×D₂₅₁	D₄	1	2	yes	—
79	C₂×C₄×D₂₅₁	D₄	1	1	yes	characteristic
80	C₂×C₄×D₂₅₁	D₄	1	2	yes	—
81	C₂×C₄×D₂₅₁	D₄	1	1	yes	characteristic
82	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
83	#16860794	—	2	1	no	—
84	#16860794	C₂³	1	2	yes	complemented
85	#16860793	—	2	4	no	—
86	C₂×C₂₅₁⋊C₈	—	2	1	no	—
87	C₈×D₂₅₁	—	2	4	no	—
88	Dic₂₅₁⋊C₄	—	2	4	no	—
89	(C₂×D₂₅₁)⋊C₄	—	2	4	no	—
90	C₄×Dic₂₅₁	—	2	1	no	—
91	C₄×Dic₂₅₁	C₂³	1	2	yes	complemented
92	#41×C₂₅₁	—	2	1	no	—
93	#41×C₂₅₁	—	2	1	no	—
94	#41×C₂₅₁	C₂×C₄	1	2	yes	—
95	#41×C₂₅₁	C₂³	1	2	yes	—
96	C₂×Q₈×C₂₅₁	C₂×C₄	1	1	yes	characteristic
97	C₂×D₄×C₂₅₁	—	2	1	no	—
98	C₂×D₄×C₂₅₁	C₂×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₂₅₁	—	2	1	no	—
100	C₂²×C₄×C₂₅₁	—	2	1	no	—
101	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
102	M₁₆×C₂₅₁	—	2	1	no	—
103	M₁₆×C₂₅₁	C₂³	1	2	yes	complemented
104	C₂×C₈×C₂₅₁	—	2	1	no	—
105	C₄²×C₂₅₁	—	2	1	no	—
106	C₄²×C₂₅₁	C₂³	1	2	yes	complemented
107	C₂²×D₂₅₁	—	2	1	no	—
108	C₂²×D₂₅₁	—	2	4	no	—
109	C₂²×D₂₅₁	—	4	2	no	—
110	C₂²×D₂₅₁	—	4	4	no	—
111	C₂²×D₂₅₁	C₂²⋊C₄	1	1	yes	characteristic
112	C₂²×D₂₅₁	C₂²⋊C₄	1	1	yes	characteristic
113	C₂²×D₂₅₁	C₂²⋊C₄	1	2	yes	—
114	C₂²×D₂₅₁	C₂×D₄	1	2	yes	—
115	Dic₅₀₂	—	2	1	no	—
116	Dic₅₀₂	—	2	4	no	—
117	Dic₅₀₂	C₂²×C₄	1	2	yes	—
118	D₁₀₀₄	—	2	4	no	—
119	D₁₀₀₄	—	2	1	no	—
120	D₁₀₀₄	C₂²×C₄	1	2	yes	—
121	C₂²⋊D₂₅₁	—	2	2	no	—
122	C₂²⋊D₂₅₁	—	2	2	no	—
123	C₂²⋊D₂₅₁	—	2	4	no	—
124	C₂²⋊D₂₅₁	—	2	4	no	—
125	C₂×Dic₂₅₁	—	2	1	no	—
126	C₂×Dic₂₅₁	—	2	4	no	—
127	C₂×Dic₂₅₁	—	2	2	no	—
128	C₂×Dic₂₅₁	—	4	2	no	—
129	C₂×Dic₂₅₁	C₂²⋊C₄	1	1	yes	characteristic
130	C₂×Dic₂₅₁	C₂²⋊C₄	1	1	yes	characteristic
131	C₂×Dic₂₅₁	C₂²⋊C₄	1	2	yes	—
132	C₂×Dic₂₅₁	C₂×D₄	1	2	yes	—
133	C₄×D₂₅₁	—	2	4	no	—
134	C₄×D₂₅₁	—	2	2	no	—
135	C₄×D₂₅₁	—	2	2	no	—
136	C₄×D₂₅₁	—	2	4	no	—
137	C₄×D₂₅₁	C₂²⋊C₄	1	2	yes	—
138	C₄×D₂₅₁	C₂²⋊C₄	1	2	yes	—
139	C₄×D₂₅₁	C₂²⋊C₄	1	2	yes	—
140	C₄×D₂₅₁	C₂²⋊C₄	1	2	yes	—
141	C₄×D₂₅₁	C₂²×C₄	1	2	yes	—
142	C₄×D₂₅₁	C₂²×C₄	1	2	yes	—
143	C₄×D₂₅₁	C₂×D₄	1	2	yes	—
144	C₄×D₂₅₁	C₂×D₄	1	2	yes	—
145	C₂₅₁⋊C₈	—	2	2	no	—
146	C₂³×C₂₅₁	—	2	1	no	—
147	C₂³×C₂₅₁	C₂×D₄	1	1	yes	characteristic
148	Q₈×C₂₅₁	—	2	1	no	—
149	Q₈×C₂₅₁	C₂²×C₄	1	2	yes	—
150	D₄×C₂₅₁	—	2	2	no	—
151	D₄×C₂₅₁	—	2	2	no	—
152	D₄×C₂₅₁	—	2	1	no	—
153	D₄×C₂₅₁	C₂²×C₄	1	2	yes	—
154	C₂×C₄×C₂₅₁	—	2	1	no	—
155	C₂×C₄×C₂₅₁	—	2	2	no	—
156	C₂×C₄×C₂₅₁	—	2	2	no	—
157	C₂×C₄×C₂₅₁	—	2	2	no	—
158	C₂×C₄×C₂₅₁	—	4	2	no	—
159	C₂×C₄×C₂₅₁	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₄×C₂₅₁	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
162	C₂×C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
163	C₂×C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
164	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
165	C₈×C₂₅₁	—	2	2	no	—
166	C₂²×C₂₅₁	—	2	2	no	—
167	C₂²×C₂₅₁	—	2	2	no	—
168	C₂²×C₂₅₁	—	4	2	no	—
169	C₂²×C₂₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
170	C₂²×C₂₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₂²×C₂₅₁	C₂²×D₄	1	1	yes	characteristic
172	C₂×D₂₅₁	—	2	2	no	—
173	C₂×D₂₅₁	—	2	2	no	—
174	C₂×D₂₅₁	—	2	2	no	—
175	C₂×D₂₅₁	—	4	2	no	—
176	C₂×D₂₅₁	—	4	2	no	—
177	C₂×D₂₅₁	—	4	8	no	—
178	C₂×D₂₅₁	—	4	2	no	—
179	C₂×D₂₅₁	C₂×C₂²⋊C₄	1	2	yes	—
180	C₂×D₂₅₁	C₂×C₂²⋊C₄	1	2	yes	—
181	C₄×C₂₅₁	—	2	2	no	—
182	C₄×C₂₅₁	—	4	2	no	—
183	C₄×C₂₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₄×C₂₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₄×C₂₅₁	C₂³×C₄	1	1	yes	characteristic
186	C₄×C₂₅₁	C₂²×D₄	1	1	yes	characteristic
187	Dic₂₅₁	—	2	2	no	—
188	Dic₂₅₁	—	4	2	no	—
189	Dic₂₅₁	C₂×C₂²⋊C₄	1	2	yes	—
190	Dic₂₅₁	C₂×C₂²⋊C₄	1	2	yes	—
191	C₂×C₂₅₁	—	2	1	no	—
192	C₂×C₂₅₁	—	2	1	no	—
193	C₂×C₂₅₁	—	4	2	no	—
194	C₂×C₂₅₁	#421	1	2	yes	complemented
195	C₂×C₂₅₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
196	D₂₅₁	—	2	2	no	—
197	D₂₅₁	—	2	2	no	—
198	D₂₅₁	—	4	2	no	—
199	C₂₅₁	C₂×#421	1	1	yes	characteristic, complemented, Sylow
200	C₂×#421	—	251	1	no	maximal, Sylow
201	C₂²×#41	—	251	1	no	—
202	C₂²×M₁₆	—	251	1	no	—
203	C₂×#117	—	251	1	no	—
204	#421	—	251	8	no	—
205	C₂×#104	—	251	1	no	—
206	C₂×#104	—	251	1	no	—
207	C₂×#104	—	251	1	no	—
208	C₂×#104	D₂₅₁	1	1	yes	characteristic, complemented
209	C₂×#41	—	502	1	no	—
210	C₂×#41	—	502	1	no	—
211	C₂×#41	—	502	2	no	—
212	C₂×#41	—	502	2	no	—
213	C₂×#41	—	251	4	no	—
214	C₂×#41	—	251	4	no	—
215	C₂×#41	—	251	1	no	—
216	C₂×#41	—	251	1	no	—
217	C₂×#41	—	251	1	no	—
218	C₂×#41	C₂×D₂₅₁	1	1	yes	characteristic
219	C₂²×Q₈	—	251	1	no	—
220	C₂²×D₄	—	502	1	no	—
221	C₂²×D₄	—	251	1	no	—
222	C₂³×C₄	—	502	1	no	—
223	C₂³×C₄	—	251	1	no	—
224	C₂×M₁₆	—	502	1	no	—
225	C₂×M₁₆	—	502	2	no	—
226	C₂×M₁₆	—	251	1	no	—
227	C₂×M₁₆	—	251	4	no	—
228	C₂×M₁₆	C₂×D₂₅₁	1	1	yes	characteristic, complemented
229	C₂²×C₈	—	502	1	no	—
230	#117	—	502	2	no	—
231	#117	—	251	4	no	—
232	C₂×C₄⋊C₄	—	502	1	no	—
233	C₂×C₂²⋊C₄	—	502	1	no	—
234	C₂×C₄²	—	251	1	no	—
235	C₂×C₄²	C₂×D₂₅₁	1	1	yes	characteristic, complemented
236	#104	—	251	4	no	—
237	#104	—	251	4	no	—
238	#104	—	251	4	no	—
239	#104	C₂×D₂₅₁	1	4	yes	complemented
240	C₂⁴	—	502	1	no	—
241	C₂⁴	—	251	1	no	—
242	#41	—	2	1	no	—
243	#41	—	2	1	no	—
244	#41	—	502	4	no	—
245	#41	—	502	4	no	—
246	#41	—	502	4	no	—
247	#41	—	502	4	no	—
248	#41	—	502	2	no	—
249	#41	—	502	2	no	—
250	#41	—	502	1	no	—
251	#41	—	502	1	no	—
252	#41	—	251	4	no	—
253	#41	—	251	4	no	—
254	#41	—	251	2	no	—
255	#41	—	251	2	no	—
256	#41	C₄×D₂₅₁	1	2	yes	—
257	#41	C₂²×D₂₅₁	1	2	yes	—
258	C₂×Q₈	—	502	1	no	—
259	C₂×Q₈	—	502	2	no	—
260	C₂×Q₈	—	251	4	no	—
261	C₂×Q₈	—	251	1	no	—
262	C₂×Q₈	C₄×D₂₅₁	1	1	yes	characteristic
263	C₂×D₄	—	2	1	no	—
264	C₂×D₄	—	502	1	no	—
265	C₂×D₄	—	502	4	no	—
266	C₂×D₄	—	502	4	no	—
267	C₂×D₄	—	502	1	no	—
268	C₂×D₄	—	502	1	no	—
269	C₂×D₄	—	502	2	no	—
270	C₂×D₄	—	502	1	no	—
271	C₂×D₄	—	251	4	no	—
272	C₂×D₄	—	251	1	no	—
273	C₂×D₄	C₄×D₂₅₁	1	1	yes	characteristic
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	502	1	no	—
277	C₂²×C₄	—	502	1	no	—
278	C₂²×C₄	—	502	4	no	—
279	C₂²×C₄	—	502	4	no	—
280	C₂²×C₄	—	502	1	no	—
281	C₂²×C₄	—	502	1	no	—
282	C₂²×C₄	—	502	1	no	—
283	C₂²×C₄	—	251	1	no	—
284	C₂²×C₄	—	251	1	no	—
285	C₂²×C₄	—	251	1	no	—
286	C₂²×C₄	—	251	2	no	—
287	C₂²×C₄	—	251	2	no	—
288	C₂²×C₄	—	251	2	no	—
289	C₂²×C₄	—	251	1	no	—
290	C₂²×C₄	—	251	1	no	—
291	C₂²×C₄	—	251	2	no	—
292	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
293	M₁₆	—	2	1	no	—
294	M₁₆	—	502	4	no	—
295	M₁₆	—	502	1	no	—
296	M₁₆	—	251	2	no	—
297	M₁₆	C₂²×D₂₅₁	1	2	yes	complemented
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	502	4	no	—
300	C₂×C₈	—	502	1	no	—
301	C₄⋊C₄	—	502	4	no	—
302	C₂²⋊C₄	—	502	4	no	—
303	C₄²	—	2	1	no	—
304	C₄²	—	502	1	no	—
305	C₄²	—	251	2	no	—
306	C₄²	C₂²×D₂₅₁	1	2	yes	complemented
307	C₂³	—	2	1	no	—
308	C₂³	—	1004	2	no	—
309	C₂³	—	1004	4	no	—
310	C₂³	—	502	4	no	—
311	C₂³	—	502	1	no	—
312	C₂³	—	251	2	no	—
313	C₂³	—	251	2	no	—
314	C₂³	—	251	1	no	—
315	C₂³	—	251	1	no	—
316	C₂³	D₄×D₂₅₁	1	1	yes	characteristic
317	Q₈	—	2	1	no	—
318	Q₈	—	502	4	no	—
319	Q₈	—	502	1	no	—
320	Q₈	—	251	2	no	—
321	Q₈	C₂×C₄×D₂₅₁	1	2	yes	—
322	D₄	—	2	2	no	—
323	D₄	—	2	2	no	—
324	D₄	—	2	1	no	—
325	D₄	—	502	4	no	—
326	D₄	—	502	4	no	—
327	D₄	—	502	2	no	—
328	D₄	—	502	2	no	—
329	D₄	—	502	4	no	—
330	D₄	—	502	1	no	—
331	D₄	—	251	2	no	—
332	D₄	C₂×C₄×D₂₅₁	1	2	yes	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	1004	2	no	—
339	C₂×C₄	—	502	4	no	—
340	C₂×C₄	—	502	4	no	—
341	C₂×C₄	—	502	2	no	—
342	C₂×C₄	—	502	1	no	—
343	C₂×C₄	—	502	4	no	—
344	C₂×C₄	—	502	2	no	—
345	C₂×C₄	—	502	2	no	—
346	C₂×C₄	—	251	2	no	—
347	C₂×C₄	—	251	1	no	—
348	C₂×C₄	—	251	1	no	—
349	C₂×C₄	—	251	2	no	—
350	C₂×C₄	—	251	2	no	—
351	C₂×C₄	—	251	2	no	—
352	C₂×C₄	—	251	2	no	—
353	C₂×C₄	—	251	2	no	—
354	C₂×C₄	—	251	2	no	—
355	C₂×C₄	—	251	2	no	—
356	C₂×C₄	—	251	2	no	—
357	C₂×C₄	—	251	2	no	—
358	C₂×C₄	C₂×C₄×D₂₅₁	1	1	yes	characteristic
359	C₂×C₄	C₂×C₄×D₂₅₁	1	1	yes	characteristic
360	C₂×C₄	D₄×D₂₅₁	1	1	yes	characteristic
361	C₂×C₄	D₄×D₂₅₁	1	1	yes	characteristic
362	C₂×C₄	D₄×D₂₅₁	1	1	yes	characteristic
363	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
364	C₈	—	2	2	no	—
365	C₈	—	502	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	1004	2	no	—
370	C₂²	—	1004	2	no	—
371	C₂²	—	1004	8	no	—
372	C₂²	—	1004	2	no	—
373	C₂²	—	502	2	no	—
374	C₂²	—	502	2	no	—
375	C₂²	—	502	2	no	—
376	C₂²	—	251	2	no	—
377	C₂²	—	251	2	no	—
378	C₂²	C₂²⋊C₄×D₂₅₁	1	1	yes	characteristic
379	C₂²	C₂²⋊C₄×D₂₅₁	1	1	yes	characteristic
380	C₂²	C₂×D₄×D₂₅₁	1	1	yes	characteristic
381	C₄	—	2	2	no	—
382	C₄	—	4	2	no	—
383	C₄	—	1004	2	no	—
384	C₄	—	502	2	no	—
385	C₄	—	251	2	no	—
386	C₄	—	251	2	no	—
387	C₄	C₂²⋊C₄×D₂₅₁	1	1	yes	characteristic
388	C₄	C₂²⋊C₄×D₂₅₁	1	1	yes	characteristic
389	C₄	C₂²×C₄×D₂₅₁	1	1	yes	characteristic
390	C₄	C₂×D₄×D₂₅₁	1	1	yes	characteristic
391	C₂	—	2	1	no	—
392	C₂	—	2	1	no	—
393	C₂	—	4	2	no	—
394	C₂	—	1004	2	no	—
395	C₂	—	502	2	no	—
396	C₂	—	502	2	no	—
397	C₂	#30631702	1	2	yes	direct product factor
398	C₂	C₂×C₂²⋊C₄×D₂₅₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₂₅₁
commutator	C₄×C₂₅₁	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₂₅₁
Fitting	C₂×#104×C₂₅₁	C₂
socle	C₂²×C₂₅₁	C₂×C₂²⋊C₄
prime radical	C₂×#41×D₂₅₁	C₂
cosocle	C₂×C₄×C₂₅₁	C₂⁴
hypercenter	C₂×#104	D₂₅₁
hypocenter	C₂₅₁	C₂×#421
LCS	G ▷ C₄×C₂₅₁ ▷ C₂×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#104

Complements

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

N	H ≅ G/N	type
2. C₂×M₁₆×D₂₅₁	C₂	semidirect
3. C₂×#22548672	C₂	semidirect
4. #30631702	C₂	direct (N × H)
5. C₂×#22548643	C₂	semidirect
6. C₂×#22548642	C₂	semidirect
7. C₂×#22548641	C₂	semidirect
8. C₂×#104×C₂₅₁	C₂	semidirect
9. C₂×#16860811	C₄	semidirect
13. C₂×#16860809	C₄	semidirect
16. #41×D₂₅₁	C₄	semidirect
18. C₂×Q₈×D₂₅₁	C₄	semidirect
20. C₂×D₄×D₂₅₁	C₄	semidirect
23. C₂×#16860794	C₂²	semidirect
26. M₁₆×D₂₅₁	C₂²	semidirect
29. #22548672	C₂²	semidirect
32. C₂×C₄×Dic₂₅₁	C₂²	semidirect
33. #22548643	C₂²	semidirect
34. #22548642	C₂²	semidirect
35. #22548641	C₂²	semidirect
37. C₂×M₁₆×C₂₅₁	C₂²	semidirect
38. C₂×C₄²×C₂₅₁	C₂²	semidirect
39. #104×C₂₅₁	C₂²	semidirect
43. #16860811	C₂×C₄	semidirect
53. #16860809	C₂×C₄	semidirect
57. Q₈×D₂₅₁	C₂×C₄	semidirect
66. D₄×D₂₅₁	C₂×C₄	semidirect
84. #16860794	C₂³	semidirect
91. C₄×Dic₂₅₁	C₂³	semidirect
103. M₁₆×C₂₅₁	C₂³	semidirect
106. C₄²×C₂₅₁	C₂³	semidirect
194. C₂×C₂₅₁	#421	semidirect
199. C₂₅₁	C₂×#421	semidirect
208. C₂×#104	D₂₅₁	semidirect
228. C₂×M₁₆	C₂×D₂₅₁	semidirect
235. C₂×C₄²	C₂×D₂₅₁	semidirect
239. #104	C₂×D₂₅₁	semidirect
297. M₁₆	C₂²×D₂₅₁	semidirect
306. C₄²	C₂²×D₂₅₁	semidirect
397. C₂	#30631702	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
C₂×M₁₆×D₂₅₁	2
C₂×#22548672	2
#30631702	2
C₂×#22548643	2
C₂×#22548642	2
C₂×#22548641	2
C₂×#104×C₂₅₁	2
C₂×#421	251

Subgroups — C2×#30631702 #44558905

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#30631702 #44558905