Subgroups — #44560371

Order 32128.

448 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632241	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×D₄×D₂₅₁	C₂	1	1	yes	maximal, characteristic
3	#30632019	C₂	1	1	yes	maximal, characteristic, complemented
4	#30632016	C₂	1	1	yes	maximal, characteristic, complemented
5	#30631976	C₂	1	1	yes	maximal, characteristic, complemented
6	#30631975	C₂	1	1	yes	maximal, characteristic, complemented
7	#30631891	C₂	1	1	yes	maximal, characteristic, complemented
8	#30631890	C₂	1	1	yes	maximal, characteristic, complemented
9	#30631839	C₂	1	1	yes	maximal, characteristic
10	#30631836	C₂	1	1	yes	maximal, characteristic
11	C₄×#16860799	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#16860797	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×#16860798	C₂	1	1	yes	maximal, characteristic, complemented
14	#30631738	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×SD₁₆×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₄×D₂₅₁	C₂²	1	1	yes	characteristic
17	C₂²×C₄×D₂₅₁	—	2	1	no	—
18	C₂×#16860799	C₂²	1	1	yes	characteristic
19	C₂×#16860798	C₂²	1	1	yes	characteristic
20	C₂×#16860797	C₂²	1	1	yes	characteristic
21	#22548714	C₂²	1	1	yes	characteristic, complemented
22	#22548713	C₂²	1	1	yes	characteristic, complemented
23	#22548705	—	2	1	no	—
24	#22548695	C₂²	1	1	yes	characteristic
25	#22548693	—	2	1	no	—
26	#22548691	C₂²	1	1	yes	characteristic
27	C₄×Dic₅₀₂	—	2	1	no	—
28	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic, complemented
29	C₄×D₁₀₀₄	C₂²	1	1	yes	characteristic
30	D₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
31	#22548677	C₂²	1	1	yes	characteristic
32	C₄×C₂²⋊D₂₅₁	—	2	1	no	—
33	(C₂²⋊D₂₅₁)⋊C₄	—	2	1	no	—
34	#22548672	—	2	1	no	—
35	C₄⋊C₄×D₂₅₁	C₂²	1	1	yes	characteristic
36	C₂²⋊C₄×D₂₅₁	—	2	1	no	—
37	C₄²×D₂₅₁	C₂²	1	1	yes	characteristic
38	#22548647	C₂²	1	1	yes	characteristic, complemented
39	#22548646	C₂²	1	1	yes	characteristic, complemented
40	#22548646	C₂²	1	1	yes	characteristic, complemented
41	Dic₂₅₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
42	Dic₂₅₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
43	#22548640	C₂²	1	1	yes	characteristic, complemented
44	#22548639	C₂²	1	1	yes	characteristic, complemented
45	#22548638	C₂²	1	1	yes	characteristic, complemented
46	#22548637	C₂²	1	1	yes	characteristic
47	#22548636	C₂²	1	1	yes	characteristic
48	#22548635	C₂²	1	1	yes	characteristic
49	(C₂×D₂₅₁)⋊C₈	C₂²	1	1	yes	characteristic
50	(C₂×D₂₅₁)⋊C₈	C₂²	1	1	yes	characteristic
51	C₄×C₂₅₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
52	C₂×SD₁₆×C₂₅₁	C₂²	1	1	yes	characteristic
53	C₄×Q₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
54	C₄×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
55	#106×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
56	#103×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
57	#102×C₂₅₁	C₂²	1	1	yes	characteristic
58	C₄×C₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
59	C₂³×D₂₅₁	—	2	1	no	—
60	C₂×Dic₅₀₂	—	2	1	no	—
61	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
62	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
63	C₂×C₂²⋊D₂₅₁	—	2	1	no	—
64	D₄×D₂₅₁	—	2	2	no	—
65	D₄×D₂₅₁	—	2	2	no	—
66	C₂²×Dic₂₅₁	—	2	1	no	—
67	C₂×C₄×D₂₅₁	—	2	1	no	—
68	C₂×C₄×D₂₅₁	—	2	1	no	—
69	C₂×C₄×D₂₅₁	—	2	1	no	—
70	C₂×C₄×D₂₅₁	—	4	4	no	—
71	C₂×C₄×D₂₅₁	D₄	1	1	yes	characteristic
72	C₂×C₄×D₂₅₁	D₄	1	1	yes	characteristic
73	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
74	#16860799	—	2	2	no	—
75	#16860798	—	2	2	no	—
76	#16860797	—	2	2	no	—
77	C₂×C₂₅₁⋊C₈	C₂³	1	1	yes	characteristic
78	C₂×C₂₅₁⋊C₈	C₂³	1	1	yes	characteristic
79	C₄⋊Dic₂₅₁	—	2	1	no	—
80	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
81	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
82	Dic₂₅₁⋊C₄	—	2	1	no	—
83	Dic₂₅₁⋊C₄	—	2	1	no	—
84	Dic₂₅₁⋊C₄	—	2	1	no	—
85	Dic₂₅₁⋊C₄	—	2	1	no	—
86	Dic₂₅₁⋊C₄	—	2	1	no	—
87	Dic₂₅₁⋊C₄	—	2	1	no	—
88	C₂²⋊Dic₂₅₁	—	2	1	no	—
89	(C₂×D₂₅₁)⋊C₄	—	2	1	no	—
90	(C₂×D₂₅₁)⋊C₄	—	2	1	no	—
91	(C₂×D₂₅₁)⋊C₄	—	2	1	no	—
92	(C₂×D₂₅₁)⋊C₄	—	2	1	no	—
93	C₄×Dic₂₅₁	—	2	1	no	—
94	C₄×Dic₂₅₁	D₄	1	1	yes	characteristic
95	C₄×Dic₂₅₁	D₄	1	1	yes	characteristic
96	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
97	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
98	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
99	C₂²×C₄×C₂₅₁	—	2	1	no	—
100	SD₁₆×C₂₅₁	—	2	2	no	—
101	C₂×C₈×C₂₅₁	C₂³	1	1	yes	characteristic
102	C₂×C₈×C₂₅₁	C₂³	1	1	yes	characteristic
103	C₄⋊C₄×C₂₅₁	—	2	1	no	—
104	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
105	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
106	C₂²⋊C₄×C₂₅₁	—	2	1	no	—
107	C₄²×C₂₅₁	—	2	1	no	—
108	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
109	C₂²×D₂₅₁	—	2	4	no	—
110	C₂²×D₂₅₁	—	2	1	no	—
111	C₂²×D₂₅₁	—	4	2	no	—
112	C₂²×D₂₅₁	—	4	2	no	—
113	C₂²×D₂₅₁	C₂×D₄	1	1	yes	characteristic
114	Dic₅₀₂	—	2	1	no	—
115	Dic₅₀₂	—	2	1	no	—
116	Dic₅₀₂	—	4	2	no	—
117	D₁₀₀₄	—	2	1	no	—
118	D₁₀₀₄	#41	1	2	yes	—
119	C₂²⋊D₂₅₁	—	2	4	no	—
120	C₂×Dic₂₅₁	—	2	1	no	—
121	C₂×Dic₂₅₁	—	2	1	no	—
122	C₂×Dic₂₅₁	—	2	1	no	—
123	C₂×Dic₂₅₁	—	4	2	no	—
124	C₂×Dic₂₅₁	C₂×D₄	1	1	yes	characteristic
125	C₂×Dic₂₅₁	C₂×D₄	1	1	yes	characteristic
126	C₂×Dic₂₅₁	C₂×D₄	1	1	yes	characteristic
127	C₄×D₂₅₁	—	2	1	no	—
128	C₄×D₂₅₁	—	2	1	no	—
129	C₄×D₂₅₁	—	4	1	no	—
130	C₄×D₂₅₁	—	4	2	no	—
131	C₄×D₂₅₁	—	4	2	no	—
132	C₄×D₂₅₁	—	4	2	no	—
133	C₄×D₂₅₁	SD₁₆	1	4	yes	complemented
134	C₂₅₁⋊C₈	—	2	1	no	—
135	C₂₅₁⋊C₈	—	2	1	no	—
136	C₂³×C₂₅₁	—	2	1	no	—
137	Q₈×C₂₅₁	—	2	1	no	—
138	Q₈×C₂₅₁	—	2	1	no	—
139	D₄×C₂₅₁	—	2	1	no	—
140	D₄×C₂₅₁	#41	1	2	yes	—
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	—	4	2	no	—
145	C₂×C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
146	C₂×C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
147	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
148	C₈×C₂₅₁	—	2	1	no	—
149	C₈×C₂₅₁	—	2	1	no	—
150	C₂²×C₂₅₁	—	2	2	no	—
151	C₂²×C₂₅₁	—	4	1	no	—
152	C₂²×C₂₅₁	—	4	1	no	—
153	C₂²×C₂₅₁	C₂²×D₄	1	1	yes	characteristic
154	C₂×D₂₅₁	—	2	1	no	—
155	C₂×D₂₅₁	—	2	1	no	—
156	C₂×D₂₅₁	—	2	2	no	—
157	C₂×D₂₅₁	—	4	8	no	—
158	C₂×D₂₅₁	—	4	1	no	—
159	C₂×D₂₅₁	—	4	1	no	—
160	C₂×D₂₅₁	C₂×SD₁₆	1	2	yes	—
161	C₄×C₂₅₁	—	2	1	no	—
162	C₄×C₂₅₁	—	4	1	no	—
163	C₄×C₂₅₁	—	4	1	no	—
164	C₄×C₂₅₁	—	4	1	no	—
165	C₄×C₂₅₁	C₂×SD₁₆	1	2	yes	—
166	C₄×C₂₅₁	C₂×#41	1	1	yes	characteristic
167	C₄×C₂₅₁	C₂×#41	1	1	yes	characteristic
168	Dic₂₅₁	—	2	1	no	—
169	Dic₂₅₁	—	2	1	no	—
170	Dic₂₅₁	—	4	1	no	—
171	Dic₂₅₁	—	4	1	no	—
172	Dic₂₅₁	—	4	1	no	—
173	Dic₂₅₁	C₂×SD₁₆	1	2	yes	—
174	C₂×C₂₅₁	—	4	2	no	—
175	C₂×C₂₅₁	#525	1	1	yes	characteristic
176	C₂×C₂₅₁	C₂²×SD₁₆	1	1	yes	characteristic
177	C₂×C₂₅₁	#575	1	1	yes	characteristic
178	D₂₅₁	—	2	2	no	—
179	D₂₅₁	—	4	2	no	—
180	C₂₅₁	#3101	1	1	yes	characteristic, complemented, Sylow
181	#3101	—	251	1	no	maximal, Sylow
182	#533	—	251	1	no	—
183	C₂×C₄×D₄	—	251	1	no	—
184	#483	—	251	1	no	—
185	#483	—	251	1	no	—
186	#476	—	251	1	no	—
187	#476	—	251	1	no	—
188	#461	—	251	1	no	—
189	#461	—	251	1	no	—
190	#450	—	251	1	no	—
191	#450	—	251	1	no	—
192	C₄×SD₁₆	—	251	1	no	—
193	C₄×SD₁₆	—	251	1	no	—
194	C₄×SD₁₆	—	251	1	no	—
195	C₄×SD₁₆	D₂₅₁	1	1	yes	characteristic, complemented
196	#431	—	251	1	no	—
197	C₂²×D₄	—	251	1	no	—
198	C₂³×C₄	—	502	1	no	—
199	C₂×SD₁₆	—	251	1	no	—
200	C₂×SD₁₆	—	251	1	no	—
201	C₂×SD₁₆	—	251	1	no	—
202	C₂×SD₁₆	C₂×D₂₅₁	1	1	yes	characteristic
203	C₄⋊Q₈	—	251	1	no	—
204	C₄⋊Q₈	—	251	1	no	—
205	#125	—	502	1	no	—
206	C₂²⋊Q₈	—	502	1	no	—
207	C₂²⋊Q₈	—	251	1	no	—
208	C₂²⋊Q₈	—	251	1	no	—
209	C₄×Q₈	—	502	1	no	—
210	C₄×Q₈	—	251	1	no	—
211	C₄×Q₈	C₂×D₂₅₁	1	1	yes	characteristic, complemented
212	C₄×D₄	—	502	1	no	—
213	C₄×D₄	—	502	1	no	—
214	C₄×D₄	—	251	1	no	—
215	C₄×D₄	—	251	1	no	—
216	C₄×D₄	—	251	1	no	—
217	C₄×D₄	C₂×D₂₅₁	1	1	yes	characteristic
218	#117	—	502	1	no	—
219	C₂×C₄⋊C₄	—	251	1	no	—
220	C₂×C₂²⋊C₄	—	502	1	no	—
221	C₂×C₄²	—	251	1	no	—
222	#106	—	251	1	no	—
223	#106	—	251	1	no	—
224	#106	—	251	1	no	—
225	#106	C₂×D₂₅₁	1	1	yes	characteristic, complemented
226	C₄⋊C₈	—	251	1	no	—
227	C₄⋊C₈	—	251	1	no	—
228	#103	—	251	1	no	—
229	#103	—	251	1	no	—
230	#103	—	251	1	no	—
231	#103	C₂×D₂₅₁	1	1	yes	characteristic, complemented
232	#102	—	251	1	no	—
233	#102	—	251	1	no	—
234	#102	—	251	1	no	—
235	#102	C₂×D₂₅₁	1	1	yes	characteristic
236	C₂²⋊C₈	—	251	1	no	—
237	C₂²⋊C₈	—	251	1	no	—
238	C₄×C₈	—	251	1	no	—
239	C₄×C₈	C₂×D₂₅₁	1	1	yes	characteristic, complemented
240	C₂⁴	—	502	1	no	—
241	C₂×Q₈	—	502	1	no	—
242	C₂×Q₈	—	251	1	no	—
243	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
244	C₂×D₄	—	502	2	no	—
245	C₂×D₄	—	502	2	no	—
246	C₂×D₄	—	502	1	no	—
247	C₂×D₄	—	251	1	no	—
248	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
249	C₂²×C₄	—	2	1	no	—
250	C₂²×C₄	—	1004	4	no	—
251	C₂²×C₄	—	502	1	no	—
252	C₂²×C₄	—	502	1	no	—
253	C₂²×C₄	—	502	1	no	—
254	C₂²×C₄	—	502	1	no	—
255	C₂²×C₄	—	251	1	no	—
256	C₂²×C₄	—	251	1	no	—
257	C₂²×C₄	—	251	1	no	—
258	SD₁₆	—	2	2	no	—
259	SD₁₆	—	502	2	no	—
260	SD₁₆	—	502	2	no	—
261	SD₁₆	—	502	2	no	—
262	C₂×C₈	—	251	1	no	—
263	C₂×C₈	—	251	1	no	—
264	C₂×C₈	C₂²×D₂₅₁	1	1	yes	characteristic
265	C₂×C₈	C₂²×D₂₅₁	1	1	yes	characteristic
266	C₄⋊C₄	—	2	1	no	—
267	C₄⋊C₄	—	502	1	no	—
268	C₄⋊C₄	—	502	1	no	—
269	C₄⋊C₄	—	502	1	no	—
270	C₄⋊C₄	—	502	1	no	—
271	C₄⋊C₄	—	502	1	no	—
272	C₄⋊C₄	—	502	1	no	—
273	C₄⋊C₄	—	502	1	no	—
274	C₄⋊C₄	—	251	1	no	—
275	C₄⋊C₄	—	251	1	no	—
276	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
277	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
278	C₂²⋊C₄	—	2	1	no	—
279	C₂²⋊C₄	—	502	1	no	—
280	C₂²⋊C₄	—	502	1	no	—
281	C₂²⋊C₄	—	502	1	no	—
282	C₂²⋊C₄	—	502	1	no	—
283	C₂²⋊C₄	—	502	1	no	—
284	C₄²	—	2	1	no	—
285	C₄²	—	502	1	no	—
286	C₄²	—	251	1	no	—
287	C₄²	—	251	1	no	—
288	C₄²	—	251	1	no	—
289	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
290	C₂³	—	2	1	no	—
291	C₂³	—	1004	2	no	—
292	C₂³	—	1004	2	no	—
293	C₂³	—	502	4	no	—
294	C₂³	—	502	1	no	—
295	C₂³	—	251	1	no	—
296	Q₈	—	2	1	no	—
297	Q₈	—	2	1	no	—
298	Q₈	—	1004	2	no	—
299	Q₈	—	502	1	no	—
300	Q₈	—	502	1	no	—
301	D₄	—	2	1	no	—
302	D₄	—	502	4	no	—
303	D₄	—	502	1	no	—
304	D₄	—	251	2	no	—
305	D₄	#16860810	1	2	yes	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	4	2	no	—
310	C₂×C₄	—	1004	1	no	—
311	C₂×C₄	—	1004	2	no	—
312	C₂×C₄	—	1004	2	no	—
313	C₂×C₄	—	1004	2	no	—
314	C₂×C₄	—	1004	2	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	—	251	1	no	—
321	C₂×C₄	—	251	1	no	—
322	C₂×C₄	—	251	1	no	—
323	C₂×C₄	—	251	4	no	—
324	C₂×C₄	D₄×D₂₅₁	1	1	yes	characteristic
325	C₂×C₄	D₄×D₂₅₁	1	1	yes	characteristic
326	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
327	C₈	—	2	1	no	—
328	C₈	—	2	1	no	—
329	C₈	—	502	1	no	—
330	C₈	—	502	1	no	—
331	C₂²	—	2	2	no	—
332	C₂²	—	4	1	no	—
333	C₂²	—	4	1	no	—
334	C₂²	—	1004	8	no	—
335	C₂²	—	1004	1	no	—
336	C₂²	—	1004	1	no	—
337	C₂²	—	502	2	no	—
338	C₂²	—	502	1	no	—
339	C₂²	—	502	1	no	—
340	C₂²	—	251	2	no	—
341	C₂²	C₂×D₄×D₂₅₁	1	1	yes	characteristic
342	C₄	—	2	1	no	—
343	C₄	—	4	1	no	—
344	C₄	—	4	1	no	—
345	C₄	—	4	1	no	—
346	C₄	—	1004	1	no	—
347	C₄	—	1004	1	no	—
348	C₄	—	1004	1	no	—
349	C₄	—	502	1	no	—
350	C₄	—	502	1	no	—
351	C₄	—	251	2	no	—
352	C₄	SD₁₆×D₂₅₁	1	2	yes	—
353	C₄	#41×D₂₅₁	1	1	yes	characteristic
354	C₄	C₂×#16860810	1	1	yes	characteristic
355	C₂	—	4	2	no	—
356	C₂	—	1004	2	no	—
357	C₂	—	502	2	no	—
358	C₂	#30632196	1	1	yes	characteristic
359	C₂	C₂×SD₁₆×D₂₅₁	1	1	yes	characteristic
360	C₂	#30632484	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₂₅₁
commutator, cosocle	C₂×C₄×C₂₅₁	C₂⁴
Frattini	C₂×C₄	C₂³×D₂₅₁
Fitting	C₄×SD₁₆×C₂₅₁	C₂
socle	C₂²×C₂₅₁	C₂²×D₄
prime radical	C₂×D₄×D₂₅₁	C₂²
hypercenter	C₄×SD₁₆	D₂₅₁
hypocenter	C₂₅₁	#3101
LCS	G ▷ C₂×C₄×C₂₅₁ ▷ C₂×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
1. #30632241	C₂	semidirect
3. #30632019	C₂	semidirect
4. #30632016	C₂	semidirect
5. #30631976	C₂	semidirect
6. #30631975	C₂	semidirect
7. #30631891	C₂	semidirect
8. #30631890	C₂	semidirect
11. C₄×#16860799	C₂	semidirect
12. C₄×#16860797	C₂	semidirect
13. C₄×#16860798	C₂	semidirect
14. #30631738	C₂	semidirect
15. C₄×SD₁₆×C₂₅₁	C₂	semidirect
21. #22548714	C₂²	semidirect
22. #22548713	C₂²	semidirect
28. C₄×Dic₅₀₂	C₂²	semidirect
38. #22548647	C₂²	semidirect
39. #22548646	C₂²	semidirect
40. #22548646	C₂²	semidirect
41. Dic₂₅₁⋊C₈	C₂²	semidirect
42. Dic₂₅₁⋊C₈	C₂²	semidirect
43. #22548640	C₂²	semidirect
44. #22548639	C₂²	semidirect
45. #22548638	C₂²	semidirect
51. C₄×C₂₅₁⋊C₈	C₂²	semidirect
53. C₄×Q₈×C₂₅₁	C₂²	semidirect
55. #106×C₂₅₁	C₂²	semidirect
56. #103×C₂₅₁	C₂²	semidirect
58. C₄×C₈×C₂₅₁	C₂²	semidirect
133. C₄×D₂₅₁	SD₁₆	semidirect
180. C₂₅₁	#3101	semidirect
195. C₄×SD₁₆	D₂₅₁	semidirect
211. C₄×Q₈	C₂×D₂₅₁	semidirect
225. #106	C₂×D₂₅₁	semidirect
231. #103	C₂×D₂₅₁	semidirect
239. C₄×C₈	C₂×D₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
#30632241	2
C₄×D₄×D₂₅₁	2
#30632019	2
#30632016	2
#30631976	2
#30631975	2
#30631891	2
#30631890	2
#30631839	2
#30631836	2
C₄×#16860799	2
C₄×#16860797	2
C₄×#16860798	2
#30631738	2
C₄×SD₁₆×C₂₅₁	2
#3101	251