Subgroups — #44553387

Order 32128.

576 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22548693	C₂	1	1	yes	maximal, characteristic
2	C₂×#22548680	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#22548672	C₂	1	1	yes	maximal, characteristic
4	#30631591	C₂	1	1	yes	maximal, characteristic, complemented
5	#30631584	C₂	1	1	yes	maximal, characteristic, complemented
6	#30631579	C₂	1	1	yes	maximal, characteristic
7	#30631577	C₂	1	1	yes	maximal, characteristic
8	#30631576	C₂	1	1	yes	maximal, characteristic
9	#30631576	C₂	1	1	yes	maximal, characteristic
10	#30631569	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄⋊C₄×Dic₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×Dic₂₅₁⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	#30631538	C₂	1	1	yes	maximal, characteristic, complemented
14	#30631534	C₂	1	1	yes	maximal, characteristic
15	#387×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Dic₅₀₂	C₂²	1	1	yes	characteristic
17	C₂²×C₄×D₂₅₁	C₂²	1	1	yes	characteristic
18	#22548693	C₄	1	8	yes	complemented
19	#22548680	—	2	4	no	—
20	#22548672	—	2	4	no	—
21	C₂×C₄⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
22	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
35	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
36	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
37	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
38	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
40	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
41	C₂₅₁⋊#95	C₂²	1	1	yes	characteristic
42	C₂₅₁⋊#95	C₂²	1	1	yes	characteristic
43	C₂₅₁⋊#95	C₂²	1	1	yes	characteristic
44	C₂₅₁⋊#95	C₂²	1	1	yes	characteristic
45	C₂₅₁⋊#95	C₂²	1	1	yes	characteristic
46	C₂₅₁⋊#95	C₂²	1	1	yes	characteristic
47	C₂×C₄⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic
49	C₂×C₄²×C₂₅₁	C₂²	1	1	yes	characteristic
50	#95×C₂₅₁	C₂²	1	1	yes	characteristic
51	#95×C₂₅₁	C₂²	1	1	yes	characteristic
52	#95×C₂₅₁	C₂²	1	1	yes	characteristic
53	#95×C₂₅₁	C₂²	1	1	yes	characteristic
54	C₂³×D₂₅₁	C₂³	1	1	yes	characteristic
55	C₂×Dic₅₀₂	—	2	2	no	—
56	C₂×Dic₅₀₂	—	2	2	no	—
57	C₂×Dic₅₀₂	C₂×C₄	1	4	yes	—
58	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
59	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
60	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
61	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
62	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
63	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
64	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
65	C₂×C₄×D₂₅₁	—	2	2	no	—
66	C₂×C₄×D₂₅₁	—	2	2	no	—
67	C₂×C₄×D₂₅₁	C₂×C₄	1	4	yes	—
68	C₄⋊Dic₂₅₁	—	2	2	no	—
69	Dic₂₅₁⋊C₄	—	2	2	no	—
70	Dic₂₅₁⋊C₄	—	2	2	no	—
71	Dic₂₅₁⋊C₄	—	2	2	no	—
72	Dic₂₅₁⋊C₄	C₂×C₄	1	4	yes	—
73	Dic₂₅₁⋊C₄	C₂×C₄	1	4	yes	—
74	Dic₂₅₁⋊C₄	D₄	1	4	yes	—
75	(C₂×D₂₅₁)⋊C₄	—	2	2	no	—
76	(C₂×D₂₅₁)⋊C₄	—	2	2	no	—
77	(C₂×D₂₅₁)⋊C₄	—	2	2	no	—
78	(C₂×D₂₅₁)⋊C₄	—	2	2	no	—
79	(C₂×D₂₅₁)⋊C₄	C₂×C₄	1	4	yes	—
80	(C₂×D₂₅₁)⋊C₄	C₂×C₄	1	4	yes	—
81	C₄×Dic₂₅₁	—	2	2	no	—
82	C₄×Dic₂₅₁	—	2	2	no	—
83	C₄×Dic₂₅₁	—	2	2	no	—
84	C₄×Dic₂₅₁	—	2	2	no	—
85	C₄×Dic₂₅₁	—	2	2	no	—
86	C₄×Dic₂₅₁	—	2	2	no	—
87	C₄×Dic₂₅₁	—	2	2	no	—
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	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
93	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
94	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
95	C₄⋊C₄×C₂₅₁	—	2	2	no	—
96	C₄⋊C₄×C₂₅₁	C₂×C₄	1	4	yes	—
97	C₄²×C₂₅₁	—	2	2	no	—
98	C₂²×D₂₅₁	—	2	1	no	—
99	C₂²×D₂₅₁	—	2	1	no	—
100	C₂²×D₂₅₁	—	2	1	no	—
101	C₂²×D₂₅₁	—	2	1	no	—
102	C₂²×D₂₅₁	—	2	1	no	—
103	C₂²×D₂₅₁	—	2	1	no	—
104	C₂²×D₂₅₁	C₂²×C₄	1	2	yes	—
105	Dic₅₀₂	—	2	8	no	—
106	C₂×Dic₂₅₁	—	2	1	no	—
107	C₂×Dic₂₅₁	—	2	1	no	—
108	C₂×Dic₂₅₁	—	2	1	no	—
109	C₂×Dic₂₅₁	—	2	1	no	—
110	C₂×Dic₂₅₁	—	2	1	no	—
111	C₂×Dic₂₅₁	—	2	1	no	—
112	C₂×Dic₂₅₁	—	2	1	no	—
113	C₂×Dic₂₅₁	—	2	1	no	—
114	C₂×Dic₂₅₁	—	2	1	no	—
115	C₂×Dic₂₅₁	—	2	1	no	—
116	C₂×Dic₂₅₁	—	2	1	no	—
117	C₂×Dic₂₅₁	—	2	1	no	—
118	C₂×Dic₂₅₁	—	2	1	no	—
119	C₂×Dic₂₅₁	C₂²×C₄	1	2	yes	—
120	C₂×Dic₂₅₁	C₂²×C₄	1	2	yes	—
121	C₂×Dic₂₅₁	C₂²×C₄	1	2	yes	—
122	C₂×Dic₂₅₁	C₂×D₄	1	2	yes	—
123	C₂×Dic₂₅₁	C₂×D₄	1	2	yes	—
124	C₂×Dic₂₅₁	#41	1	2	yes	—
125	C₂×Dic₂₅₁	#41	1	2	yes	—
126	C₂×Dic₂₅₁	#41	1	2	yes	—
127	C₄×D₂₅₁	—	2	8	no	—
128	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
129	C₂×C₄×C₂₅₁	—	2	1	no	—
130	C₂×C₄×C₂₅₁	—	2	1	no	—
131	C₂×C₄×C₂₅₁	—	2	1	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	—	2	1	no	—
137	C₂×C₄×C₂₅₁	—	2	1	no	—
138	C₂×C₄×C₂₅₁	—	2	1	no	—
139	C₂×C₄×C₂₅₁	—	2	1	no	—
140	C₂×C₄×C₂₅₁	—	2	1	no	—
141	C₂×C₄×C₂₅₁	—	2	1	no	—
142	C₂×C₄×C₂₅₁	—	2	1	no	—
143	C₂×C₄×C₂₅₁	—	2	1	no	—
144	C₂×C₄×C₂₅₁	—	2	1	no	—
145	C₂×C₄×C₂₅₁	—	2	1	no	—
146	C₂×C₄×C₂₅₁	C₂²×C₄	1	2	yes	—
147	C₂×C₄×C₂₅₁	C₂²×C₄	1	2	yes	—
148	C₂×C₄×C₂₅₁	C₂²×C₄	1	2	yes	—
149	C₂×C₄×C₂₅₁	C₂×D₄	1	2	yes	—
150	C₂²×C₂₅₁	C₂³×C₄	1	1	yes	characteristic
151	C₂²×C₂₅₁	C₂²×D₄	1	1	yes	characteristic
152	C₂²×C₂₅₁	C₂×#41	1	1	yes	characteristic
153	C₂²×C₂₅₁	C₂×#41	1	1	yes	characteristic
154	C₂²×C₂₅₁	C₂×#41	1	1	yes	characteristic
155	C₂²×C₂₅₁	2₋¹⁺⁴	1	1	yes	characteristic
156	C₂²×C₂₅₁	2₋¹⁺⁴	1	1	yes	characteristic
157	C₂×D₂₅₁	—	2	2	no	—
158	C₂×D₂₅₁	—	2	2	no	—
159	C₂×D₂₅₁	—	2	2	no	—
160	C₂×D₂₅₁	—	4	1	no	—
161	C₂×D₂₅₁	—	4	1	no	—
162	C₂×D₂₅₁	—	4	1	no	—
163	C₂×D₂₅₁	—	4	1	no	—
164	C₄×C₂₅₁	—	2	2	no	—
165	C₄×C₂₅₁	—	2	2	no	—
166	C₄×C₂₅₁	—	2	2	no	—
167	C₄×C₂₅₁	—	2	2	no	—
168	C₄×C₂₅₁	—	4	1	no	—
169	C₄×C₂₅₁	—	4	1	no	—
170	C₄×C₂₅₁	—	4	1	no	—
171	Dic₂₅₁	—	2	2	no	—
172	Dic₂₅₁	—	2	2	no	—
173	Dic₂₅₁	—	2	2	no	—
174	Dic₂₅₁	—	2	2	no	—
175	Dic₂₅₁	—	2	2	no	—
176	Dic₂₅₁	—	4	1	no	—
177	Dic₂₅₁	C₄×D₄	1	4	yes	—
178	C₂×C₂₅₁	C₂×C₄×D₄	1	1	yes	characteristic
179	C₂×C₂₅₁	C₄×#41	1	1	yes	characteristic
180	C₂×C₂₅₁	#519	1	1	yes	characteristic
181	C₂×C₂₅₁	#547	1	1	yes	characteristic
182	C₂×C₂₅₁	#548	1	1	yes	characteristic
183	C₂×C₂₅₁	#552	1	1	yes	characteristic
184	C₂×C₂₅₁	#556	1	1	yes	characteristic
185	D₂₅₁	—	4	2	no	—
186	C₂₅₁	#2362	1	1	yes	characteristic, complemented, Sylow
187	#2362	—	251	1	no	maximal, Sylow
188	C₂×C₂²⋊Q₈	—	251	1	no	—
189	C₂×C₄×Q₈	—	251	1	no	—
190	C₂×#117	—	251	1	no	—
191	#391	—	251	1	no	—
192	#389	—	251	1	no	—
193	#388	—	251	1	no	—
194	#388	—	251	1	no	—
195	#388	—	251	1	no	—
196	#388	—	251	1	no	—
197	#387	—	251	1	no	—
198	#387	D₂₅₁	1	1	yes	characteristic, complemented
199	C₄×C₄⋊C₄	—	251	1	no	—
200	C₄×C₄⋊C₄	—	251	1	no	—
201	C₄×C₄⋊C₄	—	251	1	no	—
202	C₄×C₂²⋊C₄	—	251	1	no	—
203	C₂²×Q₈	—	251	1	no	—
204	C₂³×C₄	—	251	1	no	—
205	C₂²⋊Q₈	—	251	8	no	—
206	C₄×Q₈	—	502	4	no	—
207	#117	—	502	4	no	—
208	C₂×C₄⋊C₄	—	251	1	no	—
209	C₂×C₄⋊C₄	—	251	1	no	—
210	C₂×C₄⋊C₄	—	251	1	no	—
211	C₂×C₄⋊C₄	—	251	1	no	—
212	C₂×C₄⋊C₄	—	251	1	no	—
213	C₂×C₄⋊C₄	—	251	1	no	—
214	C₂×C₄⋊C₄	—	251	1	no	—
215	C₂×C₄⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic
216	C₂×C₄⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic
217	C₂×C₂²⋊C₄	—	251	1	no	—
218	C₂×C₂²⋊C₄	—	251	1	no	—
219	C₂×C₂²⋊C₄	—	251	1	no	—
220	C₂×C₂²⋊C₄	—	251	1	no	—
221	C₂×C₂²⋊C₄	—	251	1	no	—
222	C₂×C₂²⋊C₄	—	251	1	no	—
223	C₂×C₄²	—	251	1	no	—
224	C₂×C₄²	—	251	1	no	—
225	C₂×C₄²	—	251	1	no	—
226	C₂×C₄²	—	251	1	no	—
227	C₂×C₄²	—	251	1	no	—
228	C₂×C₄²	—	251	1	no	—
229	C₂×C₄²	—	251	1	no	—
230	C₂×C₄²	C₂×D₂₅₁	1	1	yes	characteristic
231	#95	—	251	1	no	—
232	#95	—	251	1	no	—
233	#95	—	251	1	no	—
234	#95	—	251	1	no	—
235	#95	—	251	1	no	—
236	#95	—	251	1	no	—
237	#95	C₂×D₂₅₁	1	1	yes	characteristic
238	#95	C₂×D₂₅₁	1	1	yes	characteristic
239	#95	C₂×D₂₅₁	1	1	yes	characteristic
240	#95	C₂×D₂₅₁	1	1	yes	characteristic
241	C₂⁴	—	251	1	no	—
242	C₂×Q₈	—	502	2	no	—
243	C₂×Q₈	—	502	2	no	—
244	C₂×Q₈	—	251	4	no	—
245	C₂²×C₄	—	502	2	no	—
246	C₂²×C₄	—	502	2	no	—
247	C₂²×C₄	—	251	1	no	—
248	C₂²×C₄	—	251	1	no	—
249	C₂²×C₄	—	251	1	no	—
250	C₂²×C₄	—	251	1	no	—
251	C₂²×C₄	—	251	1	no	—
252	C₂²×C₄	—	251	1	no	—
253	C₂²×C₄	—	251	4	no	—
254	C₂²×C₄	—	251	1	no	—
255	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
256	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
257	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
258	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
259	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
260	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
261	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
262	C₄⋊C₄	—	2	2	no	—
263	C₄⋊C₄	—	502	2	no	—
264	C₄⋊C₄	—	502	2	no	—
265	C₄⋊C₄	—	502	2	no	—
266	C₄⋊C₄	—	502	2	no	—
267	C₄⋊C₄	—	251	4	no	—
268	C₄⋊C₄	—	251	4	no	—
269	C₄⋊C₄	—	251	4	no	—
270	C₄⋊C₄	C₄×D₂₅₁	1	4	yes	—
271	C₂²⋊C₄	—	502	2	no	—
272	C₂²⋊C₄	—	502	2	no	—
273	C₂²⋊C₄	—	502	2	no	—
274	C₂²⋊C₄	—	502	2	no	—
275	C₂²⋊C₄	—	251	4	no	—
276	C₂²⋊C₄	—	251	4	no	—
277	C₄²	—	2	2	no	—
278	C₄²	—	502	2	no	—
279	C₄²	—	502	2	no	—
280	C₄²	—	502	2	no	—
281	C₄²	—	502	2	no	—
282	C₄²	—	502	2	no	—
283	C₄²	—	502	2	no	—
284	C₄²	—	502	2	no	—
285	C₂³	—	502	1	no	—
286	C₂³	—	502	1	no	—
287	C₂³	—	502	1	no	—
288	C₂³	—	502	1	no	—
289	C₂³	—	502	1	no	—
290	C₂³	—	502	1	no	—
291	C₂³	—	251	2	no	—
292	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
293	Q₈	—	502	8	no	—
294	C₂×C₄	—	2	1	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	1	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	502	8	no	—
312	C₂×C₄	—	502	1	no	—
313	C₂×C₄	—	502	1	no	—
314	C₂×C₄	—	502	1	no	—
315	C₂×C₄	—	502	1	no	—
316	C₂×C₄	—	502	1	no	—
317	C₂×C₄	—	502	1	no	—
318	C₂×C₄	—	502	1	no	—
319	C₂×C₄	—	502	1	no	—
320	C₂×C₄	—	502	1	no	—
321	C₂×C₄	—	502	1	no	—
322	C₂×C₄	—	502	1	no	—
323	C₂×C₄	—	502	1	no	—
324	C₂×C₄	—	502	1	no	—
325	C₂×C₄	—	251	2	no	—
326	C₂×C₄	—	251	2	no	—
327	C₂×C₄	—	251	2	no	—
328	C₂×C₄	—	251	2	no	—
329	C₂×C₄	—	251	2	no	—
330	C₂×C₄	—	251	2	no	—
331	C₂×C₄	—	251	2	no	—
332	C₂×C₄	—	251	2	no	—
333	C₂×C₄	C₂×C₄×D₂₅₁	1	2	yes	—
334	C₂×C₄	C₂×C₄×D₂₅₁	1	2	yes	—
335	C₂×C₄	C₂×C₄×D₂₅₁	1	2	yes	—
336	C₂×C₄	D₄×D₂₅₁	1	2	yes	—
337	C₂²	—	1004	1	no	—
338	C₂²	—	1004	1	no	—
339	C₂²	—	1004	1	no	—
340	C₂²	—	1004	1	no	—
341	C₂²	—	502	2	no	—
342	C₂²	—	502	2	no	—
343	C₂²	—	502	2	no	—
344	C₂²	C₂²×C₄×D₂₅₁	1	1	yes	characteristic
345	C₂²	C₂×D₄×D₂₅₁	1	1	yes	characteristic
346	C₂²	#41×D₂₅₁	1	1	yes	characteristic
347	C₂²	#41×D₂₅₁	1	1	yes	characteristic
348	C₂²	#41×D₂₅₁	1	1	yes	characteristic
349	C₂²	#22548762	1	1	yes	characteristic
350	C₂²	#22548763	1	1	yes	characteristic
351	C₄	—	2	2	no	—
352	C₄	—	2	2	no	—
353	C₄	—	2	2	no	—
354	C₄	—	2	2	no	—
355	C₄	—	4	1	no	—
356	C₄	—	4	1	no	—
357	C₄	—	4	1	no	—
358	C₄	—	1004	1	no	—
359	C₄	—	502	2	no	—
360	C₄	—	502	2	no	—
361	C₄	—	502	2	no	—
362	C₄	—	502	2	no	—
363	C₄	—	502	2	no	—
364	C₄	—	251	4	no	—
365	C₂	—	1004	2	no	—
366	C₂	C₄×D₄×D₂₅₁	1	1	yes	characteristic
367	C₂	#30632155	1	1	yes	characteristic
368	C₂	#30632163	1	1	yes	characteristic
369	C₂	#30632335	1	1	yes	characteristic
370	C₂	#30632347	1	1	yes	characteristic
371	C₂	#30632369	1	1	yes	characteristic
372	C₂	#30632404	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₂₅₁
commutator	C₂²×C₂₅₁	C₂³×C₄
Fitting	#387×C₂₅₁	C₂
socle, cosocle	C₂³×C₂₅₁	C₂⁴
prime radical	C₂³×D₂₅₁	C₂³
hypercenter	#387	D₂₅₁
hypocenter	C₂₅₁	#2362
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂³ ◁ #387

Complements

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

N	H ≅ G/N	type
2. C₂×#22548680	C₂	semidirect
4. #30631591	C₂	semidirect
5. #30631584	C₂	semidirect
10. #30631569	C₂	semidirect
11. C₄⋊C₄×Dic₂₅₁	C₂	semidirect
12. C₄×Dic₂₅₁⋊C₄	C₂	semidirect
13. #30631538	C₂	semidirect
15. #387×C₂₅₁	C₂	semidirect
18. #22548693	C₄	semidirect
186. C₂₅₁	#2362	semidirect
198. #387	D₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#22548693	2
C₂×#22548680	2
C₂×#22548672	2
#30631591	2
#30631584	2
#30631579	2
#30631577	2
#30631576	2
#30631569	2
C₄⋊C₄×Dic₂₅₁	2
C₄×Dic₂₅₁⋊C₄	2
#30631538	2
#30631534	2
#387×C₂₅₁	2
#2362	251