Subgroups — M₁₆×C₂²⋊D₂₅₁ #44559099

Order 32128.

544 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₂²⋊D₂₅₁	C₂	1	1	yes	maximal, characteristic
3	#30631763	C₂	1	2	yes	maximal, complemented
4	#30631758	C₂	1	2	yes	maximal, complemented
5	#30631756	C₂	1	2	yes	maximal, complemented
6	C₈×C₂²⋊D₂₅₁	C₂	1	2	yes	maximal, complemented
7	#30631710	C₂	1	1	yes	maximal, characteristic, complemented
8	#30631651	C₂	1	1	yes	maximal, characteristic, complemented
9	#30631650	C₂	1	1	yes	maximal, characteristic, complemented
10	M₁₆×Dic₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×M₁₆×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₂²⋊D₂₅₁	C₄	1	1	yes	characteristic
13	C₂²×C₄×D₂₅₁	C₂²	1	1	yes	characteristic
14	C₂×#16860794	C₂²	1	1	yes	characteristic
15	C₂×#16860794	C₂²	1	1	yes	characteristic
16	C₂×#16860793	C₂²	1	2	yes	complemented
17	M₁₆×D₂₅₁	—	2	4	no	—
18	C₂×C₈×D₂₅₁	C₂²	1	2	yes	complemented
19	C₄×C₂²⋊D₂₅₁	C₄	1	1	yes	characteristic
20	C₄×C₂²⋊D₂₅₁	C₄	1	1	yes	characteristic
21	C₄×C₂²⋊D₂₅₁	C₄	1	1	yes	characteristic
22	C₄×C₂²⋊D₂₅₁	C₄	1	1	yes	characteristic
23	C₄×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
24	C₄×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
25	C₄×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
26	C₄×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
27	C₂×Dic₂₅₁⋊C₄	C₄	1	1	yes	characteristic
28	C₂×C₂²⋊Dic₂₅₁	C₄	1	1	yes	characteristic
29	C₂×(C₂×D₂₅₁)⋊C₄	C₄	1	1	yes	characteristic
30	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
31	Dic₂₅₁⋊C₈	C₂²	1	2	yes	complemented
32	Dic₂₅₁⋊C₈	C₂²	1	2	yes	complemented
33	C₂²⋊(C₂₅₁⋊C₈)	C₂²	1	2	yes	complemented
34	C₂²⋊(C₂₅₁⋊C₈)	C₂²	1	2	yes	complemented
35	(C₂×D₂₅₁)⋊C₈	C₂²	1	2	yes	complemented
36	(C₂×D₂₅₁)⋊C₈	C₂²	1	2	yes	complemented
37	#22548625	C₂²	1	2	yes	complemented
38	C₈×Dic₂₅₁	C₂²	1	2	yes	complemented
39	C₂³×C₄×C₂₅₁	C₂²	1	1	yes	characteristic
40	C₂×M₁₆×C₂₅₁	—	2	4	no	—
41	C₂×M₁₆×C₂₅₁	C₂²	1	1	yes	characteristic
42	C₂×M₁₆×C₂₅₁	C₂²	1	1	yes	characteristic
43	C₂×M₁₆×C₂₅₁	C₂²	1	2	yes	complemented
44	C₂²×C₈×C₂₅₁	C₂²	1	2	yes	complemented
45	C₂³×D₂₅₁	C₂×C₄	1	1	yes	characteristic
46	C₂×C₂²⋊D₂₅₁	—	2	4	no	—
47	C₂×C₂²⋊D₂₅₁	C₂×C₄	1	1	yes	characteristic
48	C₂×C₂²⋊D₂₅₁	C₂×C₄	1	1	yes	characteristic
49	C₂×C₂²⋊D₂₅₁	C₂×C₄	1	1	yes	characteristic
50	C₂×C₂²⋊D₂₅₁	C₂×C₄	1	1	yes	characteristic
51	C₂²×Dic₂₅₁	C₂×C₄	1	1	yes	characteristic
52	C₂²×Dic₂₅₁	C₂×C₄	1	1	yes	characteristic
53	C₂²×Dic₂₅₁	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×D₂₅₁	—	2	2	no	—
55	C₂×C₄×D₂₅₁	—	2	2	no	—
56	C₂×C₄×D₂₅₁	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×D₂₅₁	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
59	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
60	#16860794	—	2	2	no	—
61	#16860794	—	2	2	no	—
62	#16860793	—	2	4	no	—
63	C₂×C₂₅₁⋊C₈	C₂³	1	2	yes	—
64	C₂×C₂₅₁⋊C₈	C₂³	1	2	yes	—
65	C₈×D₂₅₁	—	2	4	no	—
66	Dic₂₅₁⋊C₄	C₂×C₄	1	1	yes	characteristic
67	Dic₂₅₁⋊C₄	C₂×C₄	1	1	yes	characteristic
68	Dic₂₅₁⋊C₄	C₂×C₄	1	1	yes	characteristic
69	Dic₂₅₁⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₂²⋊Dic₂₅₁	C₂×C₄	1	1	yes	characteristic
71	C₂²⋊Dic₂₅₁	C₂×C₄	1	1	yes	characteristic
72	C₂²⋊Dic₂₅₁	C₂×C₄	1	1	yes	characteristic
73	C₂²⋊Dic₂₅₁	C₂×C₄	1	1	yes	characteristic
74	(C₂×D₂₅₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
75	(C₂×D₂₅₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
76	(C₂×D₂₅₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
77	(C₂×D₂₅₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₄×Dic₂₅₁	C₂×C₄	1	1	yes	characteristic
79	C₄×Dic₂₅₁	C₂×C₄	1	1	yes	characteristic
80	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
81	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
82	C₂⁴×C₂₅₁	C₂×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₂₅₁	—	2	2	no	—
84	C₂²×C₄×C₂₅₁	—	2	2	no	—
85	C₂²×C₄×C₂₅₁	C₂×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₂₅₁	C₂×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₂₅₁	C₂×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
91	M₁₆×C₂₅₁	—	2	2	no	—
92	M₁₆×C₂₅₁	—	2	4	no	—
93	M₁₆×C₂₅₁	D₄	1	4	yes	complemented
94	C₂×C₈×C₂₅₁	—	2	4	no	—
95	C₂×C₈×C₂₅₁	C₂³	1	2	yes	—
96	C₂×C₈×C₂₅₁	C₂³	1	2	yes	—
97	C₂²×D₂₅₁	—	2	2	no	—
98	C₂²×D₂₅₁	—	2	2	no	—
99	C₂²×D₂₅₁	—	4	1	no	—
100	C₂²×D₂₅₁	C₂²×C₄	1	1	yes	characteristic
101	C₂²×D₂₅₁	C₂²×C₄	1	1	yes	characteristic
102	C₂²⋊D₂₅₁	—	2	2	no	—
103	C₂²⋊D₂₅₁	—	2	2	no	—
104	C₂²⋊D₂₅₁	—	2	2	no	—
105	C₂²⋊D₂₅₁	M₁₆	1	4	yes	direct product factor
106	C₂×Dic₂₅₁	—	2	2	no	—
107	C₂×Dic₂₅₁	—	2	2	no	—
108	C₂×Dic₂₅₁	—	4	1	no	—
109	C₂×Dic₂₅₁	C₂²×C₄	1	1	yes	characteristic
110	C₂×Dic₂₅₁	C₂²×C₄	1	1	yes	characteristic
111	C₂×Dic₂₅₁	C₂²×C₄	1	1	yes	characteristic
112	C₂×Dic₂₅₁	C₂²×C₄	1	1	yes	characteristic
113	C₂×Dic₂₅₁	C₂²×C₄	1	1	yes	characteristic
114	C₂×Dic₂₅₁	C₂²×C₄	1	1	yes	characteristic
115	C₄×D₂₅₁	—	2	2	no	—
116	C₄×D₂₅₁	—	2	2	no	—
117	C₄×D₂₅₁	—	2	1	no	—
118	C₄×D₂₅₁	—	2	1	no	—
119	C₄×D₂₅₁	—	2	1	no	—
120	C₄×D₂₅₁	—	2	1	no	—
121	C₂₅₁⋊C₈	—	2	2	no	—
122	C₂₅₁⋊C₈	—	2	2	no	—
123	C₂³×C₂₅₁	—	2	2	no	—
124	C₂³×C₂₅₁	—	2	2	no	—
125	C₂³×C₂₅₁	—	4	1	no	—
126	C₂³×C₂₅₁	C₂²×C₄	1	1	yes	characteristic
127	C₂³×C₂₅₁	C₂²×C₄	1	1	yes	characteristic
128	C₂³×C₂₅₁	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₄×C₂₅₁	—	2	2	no	—
130	C₂×C₄×C₂₅₁	—	2	2	no	—
131	C₂×C₄×C₂₅₁	—	2	2	no	—
132	C₂×C₄×C₂₅₁	—	2	1	no	—
133	C₂×C₄×C₂₅₁	—	2	1	no	—
134	C₂×C₄×C₂₅₁	—	2	1	no	—
135	C₂×C₄×C₂₅₁	—	2	1	no	—
136	C₂×C₄×C₂₅₁	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₄×C₂₅₁	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₄×C₂₅₁	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₄×C₂₅₁	C₂×D₄	1	2	yes	—
140	C₂×C₄×C₂₅₁	#41	1	2	yes	—
141	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
142	C₈×C₂₅₁	—	2	2	no	—
143	C₈×C₂₅₁	C₂×D₄	1	4	yes	complemented
144	C₂²×C₂₅₁	—	2	1	no	—
145	C₂²×C₂₅₁	—	2	1	no	—
146	C₂²×C₂₅₁	—	2	1	no	—
147	C₂²×C₂₅₁	—	2	1	no	—
148	C₂²×C₂₅₁	—	2	1	no	—
149	C₂²×C₂₅₁	—	2	1	no	—
150	C₂²×C₂₅₁	—	2	1	no	—
151	C₂²×C₂₅₁	—	4	4	no	—
152	C₂²×C₂₅₁	C₄×D₄	1	2	yes	—
153	C₂²×C₂₅₁	C₂×M₁₆	1	2	yes	complemented
154	C₂²×C₂₅₁	C₂³×C₄	1	1	yes	characteristic
155	C₂×D₂₅₁	—	2	1	no	—
156	C₂×D₂₅₁	—	2	1	no	—
157	C₂×D₂₅₁	—	2	1	no	—
158	C₂×D₂₅₁	—	2	1	no	—
159	C₂×D₂₅₁	—	2	1	no	—
160	C₂×D₂₅₁	—	4	4	no	—
161	C₂×D₂₅₁	C₂×M₁₆	1	2	yes	complemented
162	C₄×C₂₅₁	—	2	1	no	—
163	C₄×C₂₅₁	—	2	1	no	—
164	C₄×C₂₅₁	C₄×D₄	1	2	yes	—
165	C₄×C₂₅₁	C₂²×D₄	1	1	yes	characteristic
166	C₄×C₂₅₁	C₂×#41	1	1	yes	characteristic
167	Dic₂₅₁	—	2	1	no	—
168	Dic₂₅₁	—	2	1	no	—
169	Dic₂₅₁	—	2	1	no	—
170	Dic₂₅₁	—	2	1	no	—
171	Dic₂₅₁	—	2	1	no	—
172	Dic₂₅₁	C₂×M₁₆	1	2	yes	complemented
173	C₂×C₂₅₁	—	2	2	no	—
174	C₂×C₂₅₁	—	2	2	no	—
175	C₂×C₂₅₁	—	4	1	no	—
176	C₂×C₂₅₁	C₂×C₄×D₄	1	1	yes	characteristic
177	C₂×C₂₅₁	C₂²×M₁₆	1	1	yes	characteristic
178	C₂×C₂₅₁	#568	1	1	yes	characteristic
179	D₂₅₁	—	2	2	no	—
180	D₂₅₁	—	4	1	no	—
181	C₂₅₁	D₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
182	D₄×M₁₆	—	251	1	no	maximal, Sylow
183	C₂²×M₁₆	—	251	1	no	—
184	C₂²×M₁₆	D₂₅₁	1	1	yes	characteristic, complemented
185	C₂×C₄×D₄	—	251	1	no	—
186	#436	—	251	2	no	—
187	#435	—	251	2	no	—
188	#435	—	251	2	no	—
189	C₈×D₄	—	251	2	no	—
190	#423	—	251	1	no	—
191	#407	—	251	1	no	—
192	#407	—	251	1	no	—
193	C₄×M₁₆	—	251	1	no	—
194	C₂²×D₄	—	251	1	no	—
195	C₂³×C₄	—	251	1	no	—
196	C₂³×C₄	C₂×D₂₅₁	1	1	yes	characteristic
197	C₂×M₁₆	—	2	4	no	—
198	C₂×M₁₆	—	502	4	no	—
199	C₂×M₁₆	—	251	1	no	—
200	C₂×M₁₆	—	251	1	no	—
201	C₂×M₁₆	—	251	2	no	—
202	C₂×M₁₆	C₂×D₂₅₁	1	1	yes	characteristic
203	C₂×M₁₆	C₂×D₂₅₁	1	1	yes	characteristic
204	C₂×M₁₆	C₂×D₂₅₁	1	2	yes	complemented
205	C₂²×C₈	—	251	2	no	—
206	C₂²×C₈	C₂×D₂₅₁	1	2	yes	complemented
207	C₄×D₄	—	251	1	no	—
208	C₄×D₄	—	251	1	no	—
209	C₄×D₄	—	251	1	no	—
210	C₄×D₄	—	251	1	no	—
211	C₄×D₄	—	251	1	no	—
212	C₄×D₄	—	251	1	no	—
213	C₄×D₄	—	251	1	no	—
214	C₄×D₄	—	251	1	no	—
215	C₂×C₄⋊C₄	—	251	1	no	—
216	C₂×C₂²⋊C₄	—	251	1	no	—
217	C₂×C₂²⋊C₄	—	251	1	no	—
218	C₂×C₄²	—	251	1	no	—
219	C₄⋊C₈	—	251	2	no	—
220	C₄⋊C₈	—	251	2	no	—
221	C₂²⋊C₈	—	251	2	no	—
222	C₂²⋊C₈	—	251	2	no	—
223	C₂²⋊C₈	—	251	2	no	—
224	C₂²⋊C₈	—	251	2	no	—
225	#97	—	251	2	no	—
226	C₄×C₈	—	251	2	no	—
227	C₂⁴	—	251	1	no	—
228	C₂⁴	C₄×D₂₅₁	1	1	yes	characteristic
229	C₂×D₄	—	502	4	no	—
230	C₂×D₄	—	251	1	no	—
231	C₂×D₄	—	251	1	no	—
232	C₂×D₄	—	251	1	no	—
233	C₂×D₄	—	251	1	no	—
234	C₂²×C₄	—	2	2	no	—
235	C₂²×C₄	—	2	2	no	—
236	C₂²×C₄	—	502	2	no	—
237	C₂²×C₄	—	502	2	no	—
238	C₂²×C₄	—	251	1	no	—
239	C₂²×C₄	—	251	1	no	—
240	C₂²×C₄	—	251	1	no	—
241	C₂²×C₄	—	251	1	no	—
242	C₂²×C₄	—	251	1	no	—
243	C₂²×C₄	—	251	1	no	—
244	C₂²×C₄	—	251	1	no	—
245	C₂²×C₄	C₄×D₂₅₁	1	1	yes	characteristic
246	C₂²×C₄	C₄×D₂₅₁	1	1	yes	characteristic
247	C₂²×C₄	C₄×D₂₅₁	1	1	yes	characteristic
248	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
249	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
250	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
251	M₁₆	—	2	2	no	—
252	M₁₆	—	2	4	no	—
253	M₁₆	—	502	2	no	—
254	M₁₆	—	502	2	no	—
255	M₁₆	—	502	4	no	—
256	M₁₆	C₂²⋊D₂₅₁	1	4	yes	direct product factor
257	C₂×C₈	—	2	4	no	—
258	C₂×C₈	—	502	4	no	—
259	C₂×C₈	—	251	2	no	—
260	C₂×C₈	—	251	2	no	—
261	C₂×C₈	C₂²×D₂₅₁	1	2	yes	—
262	C₂×C₈	C₂²×D₂₅₁	1	2	yes	—
263	C₄⋊C₄	—	251	1	no	—
264	C₄⋊C₄	—	251	1	no	—
265	C₄⋊C₄	—	251	1	no	—
266	C₄⋊C₄	—	251	1	no	—
267	C₂²⋊C₄	—	251	1	no	—
268	C₂²⋊C₄	—	251	1	no	—
269	C₂²⋊C₄	—	251	1	no	—
270	C₂²⋊C₄	—	251	1	no	—
271	C₂²⋊C₄	—	251	1	no	—
272	C₂²⋊C₄	—	251	1	no	—
273	C₂²⋊C₄	—	251	1	no	—
274	C₂²⋊C₄	—	251	1	no	—
275	C₄²	—	251	1	no	—
276	C₄²	—	251	1	no	—
277	C₄²	—	251	1	no	—
278	C₄²	—	251	1	no	—
279	C₂³	—	2	2	no	—
280	C₂³	—	2	2	no	—
281	C₂³	—	4	1	no	—
282	C₂³	—	1004	1	no	—
283	C₂³	—	502	2	no	—
284	C₂³	—	502	2	no	—
285	C₂³	—	251	1	no	—
286	C₂³	—	251	1	no	—
287	C₂³	C₂×C₄×D₂₅₁	1	1	yes	characteristic
288	C₂³	C₂×C₄×D₂₅₁	1	1	yes	characteristic
289	C₂³	C₂×C₄×D₂₅₁	1	1	yes	characteristic
290	D₄	—	502	2	no	—
291	D₄	—	502	2	no	—
292	D₄	—	502	2	no	—
293	D₄	—	251	4	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	1	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	1004	1	no	—
302	C₂×C₄	—	502	2	no	—
303	C₂×C₄	—	502	2	no	—
304	C₂×C₄	—	502	1	no	—
305	C₂×C₄	—	502	1	no	—
306	C₂×C₄	—	502	1	no	—
307	C₂×C₄	—	502	1	no	—
308	C₂×C₄	—	502	2	no	—
309	C₂×C₄	—	502	2	no	—
310	C₂×C₄	—	251	1	no	—
311	C₂×C₄	—	251	1	no	—
312	C₂×C₄	—	251	1	no	—
313	C₂×C₄	—	251	1	no	—
314	C₂×C₄	—	251	1	no	—
315	C₂×C₄	—	251	1	no	—
316	C₂×C₄	C₂×C₄×D₂₅₁	1	1	yes	characteristic
317	C₂×C₄	C₂×C₄×D₂₅₁	1	1	yes	characteristic
318	C₂×C₄	C₂×C₄×D₂₅₁	1	1	yes	characteristic
319	C₂×C₄	C₂×C₂²⋊D₂₅₁	1	2	yes	—
320	C₂×C₄	#16860810	1	2	yes	—
321	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
322	C₈	—	2	2	no	—
323	C₈	—	502	2	no	—
324	C₈	—	502	2	no	—
325	C₈	C₂×C₂²⋊D₂₅₁	1	4	yes	complemented
326	C₂²	—	2	1	no	—
327	C₂²	—	2	1	no	—
328	C₂²	—	2	1	no	—
329	C₂²	—	2	1	no	—
330	C₂²	—	2	1	no	—
331	C₂²	—	2	1	no	—
332	C₂²	—	2	1	no	—
333	C₂²	—	4	4	no	—
334	C₂²	—	1004	4	no	—
335	C₂²	—	502	1	no	—
336	C₂²	—	502	1	no	—
337	C₂²	—	502	1	no	—
338	C₂²	—	502	1	no	—
339	C₂²	—	502	1	no	—
340	C₂²	—	251	2	no	—
341	C₂²	C₄×C₂²⋊D₂₅₁	1	2	yes	—
342	C₂²	M₁₆×D₂₅₁	1	2	yes	complemented
343	C₂²	C₂²×C₄×D₂₅₁	1	1	yes	characteristic
344	C₄	—	2	1	no	—
345	C₄	—	2	1	no	—
346	C₄	—	502	1	no	—
347	C₄	—	502	1	no	—
348	C₄	—	502	1	no	—
349	C₄	—	502	1	no	—
350	C₄	—	502	1	no	—
351	C₄	—	251	2	no	—
352	C₄	C₄×C₂²⋊D₂₅₁	1	2	yes	—
353	C₄	C₂²×C₂²⋊D₂₅₁	1	1	yes	characteristic
354	C₄	C₂×#16860810	1	1	yes	characteristic
355	C₂	—	2	2	no	—
356	C₂	—	2	2	no	—
357	C₂	—	4	1	no	—
358	C₂	—	1004	1	no	—
359	C₂	—	502	2	no	—
360	C₂	C₂×C₄×C₂²⋊D₂₅₁	1	1	yes	characteristic
361	C₂	C₂×M₁₆×D₂₅₁	1	1	yes	characteristic
362	C₂	#30632453	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₂₅₁
commutator, socle	C₂²×C₂₅₁	C₂³×C₄
Fitting	C₂²×M₁₆×C₂₅₁	C₂
prime radical	C₂²×C₂²⋊D₂₅₁	C₄
cosocle	C₂×C₄×C₂₅₁	C₂⁴
hypercenter	C₂²×M₁₆	D₂₅₁
hypocenter	C₂₅₁	D₄×M₁₆
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×M₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×M₁₆×D₂₅₁	C₂	semidirect
3. #30631763	C₂	semidirect
4. #30631758	C₂	semidirect
5. #30631756	C₂	semidirect
6. C₈×C₂²⋊D₂₅₁	C₂	semidirect
7. #30631710	C₂	semidirect
8. #30631651	C₂	semidirect
9. #30631650	C₂	semidirect
10. M₁₆×Dic₂₅₁	C₂	semidirect
11. C₂²×M₁₆×C₂₅₁	C₂	semidirect
16. C₂×#16860793	C₂²	semidirect
18. C₂×C₈×D₂₅₁	C₂²	semidirect
31. Dic₂₅₁⋊C₈	C₂²	semidirect
32. Dic₂₅₁⋊C₈	C₂²	semidirect
33. C₂²⋊(C₂₅₁⋊C₈)	C₂²	semidirect
34. C₂²⋊(C₂₅₁⋊C₈)	C₂²	semidirect
35. (C₂×D₂₅₁)⋊C₈	C₂²	semidirect
36. (C₂×D₂₅₁)⋊C₈	C₂²	semidirect
37. #22548625	C₂²	semidirect
38. C₈×Dic₂₅₁	C₂²	semidirect
43. C₂×M₁₆×C₂₅₁	C₂²	semidirect
44. C₂²×C₈×C₂₅₁	C₂²	semidirect
93. M₁₆×C₂₅₁	D₄	semidirect
105. C₂²⋊D₂₅₁	M₁₆	direct (N × H)
143. C₈×C₂₅₁	C₂×D₄	semidirect
153. C₂²×C₂₅₁	C₂×M₁₆	semidirect
161. C₂×D₂₅₁	C₂×M₁₆	semidirect
172. Dic₂₅₁	C₂×M₁₆	semidirect
181. C₂₅₁	D₄×M₁₆	semidirect
184. C₂²×M₁₆	D₂₅₁	semidirect
204. C₂×M₁₆	C₂×D₂₅₁	semidirect
206. C₂²×C₈	C₂×D₂₅₁	semidirect
256. M₁₆	C₂²⋊D₂₅₁	direct (N × H)
325. C₈	C₂×C₂²⋊D₂₅₁	semidirect
342. C₂²	M₁₆×D₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₁₆×D₂₅₁	2
C₂×C₄×C₂²⋊D₂₅₁	2
#30631763	2
#30631758	2
#30631756	2
C₈×C₂²⋊D₂₅₁	2
#30631710	2
#30631651	2
#30631650	2
M₁₆×Dic₂₅₁	2
C₂²×M₁₆×C₂₅₁	2
D₄×M₁₆	251

Subgroups — M16×C22⋊D251 #44559099

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — M₁₆×C₂²⋊D₂₅₁ #44559099