Subgroups — #26200201

Order 12032.

670 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689519	C₂	1	1	yes	maximal, characteristic, complemented
2	#20253197	C₂	1	1	yes	maximal, characteristic
3	#20252876	C₂	1	1	yes	maximal, characteristic
4	#20252344	C₂	1	1	yes	maximal, characteristic
5	#20242773	C₂	1	4	yes	maximal, complemented
6	#20242766	C₂	1	4	yes	maximal, complemented
7	#20242143	C₂	1	1	yes	maximal, characteristic, complemented
8	#20242059	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1548	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#13094057	—	2	1	no	—
11	C₂×#13094024	C₂²	1	1	yes	characteristic
12	C₄×#10625350	C₂²	1	1	yes	characteristic
13	#15689519	—	2	1	no	—
14	#15689519	—	2	1	no	—
15	#15689519	C₂²	1	4	yes	—
16	#15689415	C₂²	1	2	yes	—
17	#15689410	C₂²	1	2	yes	—
18	#15689405	—	2	1	no	—
19	#15689400	—	2	1	no	—
20	#15689334	—	2	1	no	—
21	#15689334	C₂²	1	2	yes	—
22	#15689329	—	2	1	no	—
23	#15689329	C₂²	1	2	yes	—
24	#15689247	C₂²	1	2	yes	—
25	#15689188	C₂²	1	2	yes	—
26	(C₂²⋊D₄₇)⋊C₈	—	2	2	no	—
27	#15689174	—	2	1	no	—
28	#15689163	—	2	1	no	—
29	C₂×#13093955	—	2	2	no	—
30	#15689147	C₂²	1	1	yes	characteristic
31	#15689133	—	2	1	no	—
32	#15689122	—	2	1	no	—
33	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₄₇	—	2	1	no	—
35	#15688873	C₂²	1	4	yes	—
36	#15688868	C₂²	1	4	yes	—
37	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₄₇×#431	C₂²	1	1	yes	characteristic
39	C₄₇×#423	C₂²	1	1	yes	characteristic
40	C₄₇×#333	C₂²	1	4	yes	—
41	C₂×#10625350	D₄	1	1	yes	characteristic
42	C₂²×Dic₉₄	—	2	1	no	—
43	#13094057	—	4	4	no	—
44	C₂×Dic₁₈₈	—	2	2	no	—
45	C₂×#10625325	—	2	2	no	—
46	C₂×#10625329	—	2	1	no	—
47	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
48	C₂×C₈×D₄₇	—	2	2	no	—
49	#13094024	—	2	1	no	—
50	#13094024	—	2	1	no	—
51	#13094024	—	2	1	no	—
52	#13094024	C₂³	1	2	yes	—
53	C₄×Dic₉₄	D₄	1	1	yes	characteristic
54	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
55	C₄×D₁₈₈	D₄	1	1	yes	characteristic
56	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
57	C₄×C₂²⋊D₄₇	—	2	1	no	—
58	C₄×C₂²⋊D₄₇	—	2	1	no	—
59	#13093983	D₄	1	1	yes	characteristic
60	#13093981	—	2	1	no	—
61	C₂×C₄⋊Dic₄₇	—	2	1	no	—
62	C₂×C₄⋊Dic₄₇	—	2	1	no	—
63	C₄²×D₄₇	—	2	1	no	—
64	#13093957	—	2	2	no	—
65	#13093955	—	2	2	no	—
66	#13093955	—	2	4	no	—
67	#13093955	—	2	4	no	—
68	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
69	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
70	Dic₄₇⋊C₈	—	2	2	no	—
71	#13093949	—	2	2	no	—
72	#13093949	—	2	2	no	—
73	#13093947	—	2	2	no	—
74	#13093944	—	2	2	no	—
75	(C₂×D₄₇)⋊C₈	—	2	2	no	—
76	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
77	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
78	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
79	C₈×Dic₄₇	—	2	2	no	—
80	C₂²×Q₈×C₄₇	—	2	1	no	—
81	C₂×M₁₆×C₄₇	—	2	1	no	—
82	C₄⋊Q₈×C₄₇	—	2	1	no	—
83	C₄⋊Q₈×C₄₇	—	2	1	no	—
84	C₄⋊Q₈×C₄₇	—	2	1	no	—
85	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
87	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
88	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
89	C₄⋊C₈×C₄₇	—	2	1	no	—
90	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
91	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
92	C₂²⋊C₈×C₄₇	—	2	1	no	—
93	C₄×C₈×C₄₇	—	2	1	no	—
94	C₂×Q₈×C₄₇	—	2	2	no	—
95	C₂×Q₈×C₄₇	—	4	1	no	—
96	C₂×Q₈×C₄₇	—	8	2	no	—
97	C₂²×C₄×C₄₇	—	4	1	no	—
98	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
101	C₂×C₂²⋊D₄₇	—	2	1	no	—
102	C₂²×Dic₄₇	—	4	1	no	—
103	#10625350	—	2	2	no	—
104	#10625350	SD₁₆	1	4	yes	—
105	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
106	C₂×C₄×D₄₇	—	2	1	no	—
107	C₂×C₄×D₄₇	—	2	1	no	—
108	C₂×C₄×D₄₇	—	2	1	no	—
109	C₂×Dic₉₄	—	2	2	no	—
110	C₂×Dic₉₄	—	4	2	no	—
111	C₂×Dic₉₄	—	4	2	no	—
112	C₂×Dic₉₄	—	4	1	no	—
113	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
114	M₁₆×C₄₇	—	4	2	no	—
115	C₂×C₈×C₄₇	—	2	2	no	—
116	C₂×C₈×C₄₇	—	2	2	no	—
117	C₄⋊C₄×C₄₇	—	2	2	no	—
118	C₄⋊C₄×C₄₇	—	2	2	no	—
119	C₄⋊C₄×C₄₇	—	4	1	no	—
120	C₄⋊C₄×C₄₇	—	4	1	no	—
121	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₄₇	#41	1	1	yes	characteristic
124	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
125	C₂²⋊Dic₄₇	—	2	1	no	—
126	(C₂×D₄₇)⋊C₄	—	2	1	no	—
127	(C₂×D₄₇)⋊C₄	—	2	1	no	—
128	C₄⋊Dic₄₇	—	2	2	no	—
129	C₄⋊Dic₄₇	—	2	2	no	—
130	C₄⋊Dic₄₇	—	4	1	no	—
131	C₄⋊Dic₄₇	—	4	1	no	—
132	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
133	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
134	Dic₄₇⋊C₄	—	2	1	no	—
135	Dic₄₇⋊C₄	—	2	1	no	—
136	C₄×Dic₄₇	—	2	1	no	—
137	C₄×Dic₄₇	—	2	1	no	—
138	C₄×Dic₄₇	—	2	1	no	—
139	#10625329	—	4	2	no	—
140	C₂×C₄₇⋊C₈	—	2	4	no	—
141	C₂×C₄₇⋊C₈	—	2	2	no	—
142	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
143	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
144	Dic₁₈₈	—	4	4	no	—
145	#10625325	—	4	4	no	—
146	C₈×D₄₇	—	4	4	no	—
147	C₂³×C₄₇	#121	1	1	yes	characteristic
148	C₂²×D₄₇	—	2	1	no	—
149	Q₈×C₄₇	—	8	2	no	—
150	Q₈×C₄₇	—	8	2	no	—
151	C₂×C₄×C₄₇	—	2	2	no	—
152	C₂×C₄×C₄₇	—	2	2	no	—
153	C₂×C₄×C₄₇	—	4	2	no	—
154	C₂×C₄×C₄₇	—	8	2	no	—
155	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
156	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
157	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
159	C₂×C₄×C₄₇	#135	1	2	yes	—
160	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
163	C₂²⋊D₄₇	—	2	4	no	—
164	C₂×Dic₄₇	—	2	1	no	—
165	C₂×Dic₄₇	—	2	1	no	—
166	C₂×Dic₄₇	—	2	1	no	—
167	C₂×Dic₄₇	—	4	2	no	—
168	C₂×Dic₄₇	—	8	2	no	—
169	D₁₈₈	—	2	1	no	—
170	D₁₈₈	C₂×SD₁₆	1	2	yes	—
171	C₄×D₄₇	—	2	4	no	—
172	C₄×D₄₇	—	4	2	no	—
173	C₄×D₄₇	—	4	2	no	—
174	Dic₉₄	—	2	1	no	—
175	Dic₉₄	—	4	2	no	—
176	Dic₉₄	—	4	2	no	—
177	Dic₉₄	—	8	2	no	—
178	Dic₉₄	C₂×SD₁₆	1	2	yes	—
179	C₈×C₄₇	—	4	2	no	—
180	C₈×C₄₇	—	4	2	no	—
181	C₄₇⋊C₈	—	2	2	no	—
182	C₄₇⋊C₈	—	4	2	no	—
183	C₄₇⋊C₈	#137	1	4	yes	complemented
184	#19270	—	47	1	no	maximal, Sylow
185	C₂²×C₄₇	—	2	1	no	—
186	C₂²×C₄₇	—	2	1	no	—
187	C₂²×C₄₇	#465	1	2	yes	—
188	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
189	C₂×D₄₇	—	2	2	no	—
190	C₂×D₄₇	—	4	1	no	—
191	C₂×D₄₇	—	4	1	no	—
192	C₄×C₄₇	—	2	1	no	—
193	C₄×C₄₇	—	2	1	no	—
194	C₄×C₄₇	—	8	2	no	—
195	C₄×C₄₇	#465	1	2	yes	—
196	C₄×C₄₇	#471	1	2	yes	—
197	C₄×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
198	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
199	C₄×C₄₇	C₂×#137	1	2	yes	—
200	Dic₄₇	—	2	2	no	—
201	Dic₄₇	—	4	1	no	—
202	Dic₄₇	—	4	1	no	—
203	Dic₄₇	—	8	2	no	—
204	C₂×#498	—	47	1	no	—
205	#3079	—	47	1	no	—
206	#3039	—	47	1	no	—
207	C₈×#41	—	47	1	no	—
208	#1672	—	47	4	no	—
209	#1671	—	47	4	no	—
210	#1566	—	47	1	no	—
211	#1548	D₄₇	1	1	yes	characteristic, complemented
212	#1546	—	47	1	no	—
213	C₂×C₄₇	—	2	2	no	—
214	C₂×C₄₇	#3039	1	1	yes	characteristic
215	C₂×C₄₇	C₂×#465	1	1	yes	characteristic
216	C₂×C₄₇	C₂×#471	1	1	yes	characteristic
217	D₄₇	—	4	2	no	—
218	C₂×#137	—	94	1	no	—
219	C₂×C₄⋊Q₈	—	47	1	no	—
220	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
221	C₄×#41	—	47	1	no	—
222	#498	—	47	4	no	—
223	#498	—	94	1	no	—
224	#498	—	94	1	no	—
225	#477	—	47	2	no	—
226	#476	—	47	2	no	—
227	#475	—	94	1	no	—
228	#474	—	94	1	no	—
229	#462	—	47	2	no	—
230	#462	—	94	1	no	—
231	#461	—	47	2	no	—
232	#461	—	94	1	no	—
233	C₈×Q₈	—	47	2	no	—
234	C₈×D₄	—	47	2	no	—
235	C₈×D₄	—	94	2	no	—
236	#431	—	94	1	no	—
237	#431	C₂×D₄₇	1	1	yes	characteristic
238	#428	—	94	1	no	—
239	C₂×#106	—	94	2	no	—
240	#423	—	47	1	no	—
241	#423	C₂×D₄₇	1	1	yes	characteristic
242	#419	—	94	1	no	—
243	#417	—	94	1	no	—
244	C₂×C₄×C₈	—	47	1	no	—
245	C₂×C₄×C₈	—	94	1	no	—
246	#334	—	47	4	no	—
247	#333	C₂×D₄₇	1	4	yes	—
248	#332	—	47	4	no	—
249	C₄₇	#19270	1	1	yes	characteristic, complemented, Sylow
250	C₂×#41	—	47	1	no	—
251	C₂²×Q₈	—	2	1	no	—
252	C₂²×Q₈	—	94	1	no	—
253	#137	—	188	4	no	—
254	C₂×Q₁₆	—	94	2	no	—
255	C₂×SD₁₆	—	94	2	no	—
256	C₂×M₁₆	—	2	1	no	—
257	C₂×M₁₆	—	94	1	no	—
258	C₂²×C₈	—	47	2	no	—
259	C₂²×C₈	—	94	2	no	—
260	C₄⋊Q₈	—	2	1	no	—
261	C₄⋊Q₈	—	2	1	no	—
262	C₄⋊Q₈	—	2	1	no	—
263	C₄⋊Q₈	—	47	2	no	—
264	C₄⋊Q₈	—	94	1	no	—
265	C₄⋊Q₈	—	94	1	no	—
266	C₄⋊Q₈	—	94	1	no	—
267	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
268	C₄×Q₈	—	47	1	no	—
269	C₄×Q₈	—	47	1	no	—
270	C₄×D₄	—	47	1	no	—
271	C₄×D₄	—	47	1	no	—
272	C₄×D₄	—	94	1	no	—
273	C₄×D₄	—	94	1	no	—
274	#117	—	47	1	no	—
275	#117	—	94	1	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	94	1	no	—
279	C₂×C₄⋊C₄	—	94	1	no	—
280	C₂×C₄²	—	94	1	no	—
281	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
282	#107	—	94	2	no	—
283	#106	—	94	2	no	—
284	#106	—	94	4	no	—
285	#106	—	94	4	no	—
286	C₄⋊C₈	—	2	1	no	—
287	C₄⋊C₈	—	47	2	no	—
288	C₄⋊C₈	—	94	2	no	—
289	C₄⋊C₈	—	94	1	no	—
290	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
291	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
292	#103	—	94	2	no	—
293	#103	—	94	2	no	—
294	#103	—	94	2	no	—
295	#102	—	94	2	no	—
296	C₂²⋊C₈	—	2	1	no	—
297	C₂²⋊C₈	—	94	2	no	—
298	C₄×C₈	—	2	1	no	—
299	C₄×C₈	—	47	1	no	—
300	C₄×C₈	—	47	1	no	—
301	C₄×C₈	—	47	2	no	—
302	C₄×C₈	—	94	2	no	—
303	#41	—	47	4	no	—
304	#41	—	94	2	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	4	1	no	—
307	C₂×Q₈	—	8	2	no	—
308	C₂×Q₈	—	47	1	no	—
309	C₂×Q₈	—	94	2	no	—
310	C₂×Q₈	—	188	2	no	—
311	C₂×Q₈	—	188	2	no	—
312	C₂×Q₈	—	188	1	no	—
313	C₂×D₄	—	47	1	no	—
314	C₂×D₄	—	94	1	no	—
315	C₂²×C₄	—	4	1	no	—
316	C₂²×C₄	—	94	1	no	—
317	C₂²×C₄	—	94	1	no	—
318	C₂²×C₄	—	94	1	no	—
319	C₂²×C₄	—	188	1	no	—
320	C₂²×C₄	#10625350	1	1	yes	characteristic
321	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
322	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
323	Q₁₆	—	188	4	no	—
324	SD₁₆	—	188	4	no	—
325	M₁₆	—	4	2	no	—
326	M₁₆	—	188	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	47	2	no	—
330	C₂×C₈	—	47	2	no	—
331	C₂×C₈	—	94	4	no	—
332	C₂×C₈	—	94	2	no	—
333	C₂×C₈	—	188	4	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	4	1	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	47	1	no	—
339	C₄⋊C₄	—	47	1	no	—
340	C₄⋊C₄	—	94	1	no	—
341	C₄⋊C₄	—	94	1	no	—
342	C₄⋊C₄	—	94	2	no	—
343	C₄⋊C₄	—	94	2	no	—
344	C₄⋊C₄	—	188	1	no	—
345	C₄⋊C₄	—	188	1	no	—
346	C₂²⋊C₄	—	94	1	no	—
347	C₂²⋊C₄	—	94	1	no	—
348	C₂²⋊C₄	—	94	1	no	—
349	C₄²	—	94	1	no	—
350	C₄²	—	94	1	no	—
351	C₄²	—	94	1	no	—
352	C₄²	#10625350	1	1	yes	characteristic
353	C₄²	D₄×D₄₇	1	1	yes	characteristic
354	C₄²	D₄×D₄₇	1	1	yes	characteristic
355	C₄²	C₂³×D₄₇	1	1	yes	characteristic
356	C₂³	—	94	1	no	—
357	C₂³	#13093997	1	1	yes	characteristic
358	Q₈	—	8	2	no	—
359	Q₈	—	8	2	no	—
360	Q₈	—	47	2	no	—
361	Q₈	—	94	1	no	—
362	Q₈	—	376	2	no	—
363	Q₈	—	188	2	no	—
364	Q₈	—	188	2	no	—
365	D₄	—	47	2	no	—
366	D₄	—	94	4	no	—
367	D₄	—	94	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	8	2	no	—
372	C₂×C₄	—	94	1	no	—
373	C₂×C₄	—	94	4	no	—
374	C₂×C₄	—	94	1	no	—
375	C₂×C₄	—	94	1	no	—
376	C₂×C₄	—	376	2	no	—
377	C₂×C₄	—	188	2	no	—
378	C₂×C₄	—	188	2	no	—
379	C₂×C₄	—	188	2	no	—
380	C₂×C₄	#13093997	1	1	yes	characteristic
381	C₂×C₄	#13093997	1	1	yes	characteristic
382	C₂×C₄	#13093997	1	1	yes	characteristic
383	C₂×C₄	SD₁₆×D₄₇	1	2	yes	—
384	C₂×C₄	#13094047	1	2	yes	—
385	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
386	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
387	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
388	C₈	—	4	2	no	—
389	C₈	—	4	2	no	—
390	C₈	—	47	4	no	—
391	C₈	—	94	2	no	—
392	C₈	—	188	2	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	94	2	no	—
396	C₂²	—	188	1	no	—
397	C₂²	—	188	1	no	—
398	C₂²	#15689355	1	2	yes	—
399	C₂²	C₂×#13093997	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	8	2	no	—
403	C₄	—	94	2	no	—
404	C₄	—	376	2	no	—
405	C₄	—	188	1	no	—
406	C₄	—	188	1	no	—
407	C₄	#15689355	1	2	yes	—
408	C₄	#15689385	1	2	yes	—
409	C₄	C₂×SD₁₆×D₄₇	1	1	yes	characteristic
410	C₄	C₂×#13094047	1	1	yes	characteristic
411	C₄	#137×D₄₇	1	2	yes	—
412	C₂	—	2	2	no	—
413	C₂	—	188	2	no	—
414	C₂	#20252874	1	1	yes	characteristic
415	C₂	C₂×#15689355	1	1	yes	characteristic
416	C₂	C₂×#15689385	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13093997
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1548	C₂
socle	C₂²×C₄₇	C₂×#121
prime radical	C₂×#10625350	D₄
hypercenter	#1548	D₄₇
hypocenter	C₄₇	#19270
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1548

Complements

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

N	H ≅ G/N	type
1. C₂×#15689519	C₂	semidirect
5. #20242773	C₂	semidirect
6. #20242766	C₂	semidirect
7. #20242143	C₂	semidirect
8. #20242059	C₂	semidirect
9. C₄₇×#1548	C₂	semidirect
183. C₄₇⋊C₈	#137	semidirect
211. #1548	D₄₇	semidirect
249. C₄₇	#19270	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689519	2
#20253197	2
#20252876	2
#20252344	2
#20242773	2
#20242766	2
#20242143	2
#20242059	2
C₄₇×#1548	2
#19270	47