Subgroups — #26373056

Order 12032.

652 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256536	C₂	1	2	yes	maximal, complemented
2	#20255193	C₂	1	1	yes	maximal, characteristic, complemented
3	#20255188	C₂	1	1	yes	maximal, characteristic, complemented
4	#20245644	C₂	1	1	yes	maximal, characteristic, complemented
5	#20245518	C₂	1	2	yes	maximal, complemented
6	#20245470	C₂	1	1	yes	maximal, characteristic, complemented
7	#20245465	C₂	1	1	yes	maximal, characteristic, complemented
8	#20245361	C₂	1	2	yes	maximal, complemented
9	#20245354	C₂	1	2	yes	maximal, complemented
10	#20245270	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#2170	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689940	C₂²	1	2	yes	complemented
13	#15689937	—	2	1	no	—
14	#15689928	C₂²	1	2	yes	—
15	#15689925	—	2	1	no	—
16	#15689566	—	2	2	no	—
17	#15689566	C₂²	1	2	yes	—
18	#15689561	—	2	2	no	—
19	#15689561	C₂²	1	2	yes	complemented
20	#15689555	—	2	2	no	—
21	#15689555	C₂²	1	1	yes	characteristic
22	C₂×#13093969	—	2	2	no	—
23	C₂×#13093969	C₂²	1	2	yes	complemented
24	C₂×#13093969	C₂²	1	2	yes	complemented
25	#15689503	C₂²	1	1	yes	characteristic, complemented
26	#15689500	C₂²	1	1	yes	characteristic
27	#15689399	—	2	1	no	—
28	#15689398	C₂²	1	2	yes	complemented
29	#15689394	—	2	1	no	—
30	#15689393	C₂²	1	2	yes	—
31	#15689307	—	2	2	no	—
32	#15689292	—	2	2	no	—
33	#15689241	C₂²	1	1	yes	characteristic
34	#15689241	C₂²	1	1	yes	characteristic, complemented
35	#15688953	C₂²	1	1	yes	characteristic, complemented
36	#15688940	C₂²	1	2	yes	complemented
37	#15688937	C₂²	1	2	yes	complemented
38	#15688931	C₂²	1	1	yes	characteristic
39	#15688931	C₂²	1	1	yes	characteristic, complemented
40	C₄₇×#504	C₂²	1	2	yes	complemented
41	C₄₇×#443	C₂²	1	1	yes	characteristic
42	C₄₇×#364	C₂²	1	1	yes	characteristic, complemented
43	C₄₇×#350	C₂²	1	2	yes	complemented
44	C₄×C₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
45	#13094071	—	2	2	no	—
46	#13094070	—	2	2	no	—
47	#13094057	—	2	2	no	—
48	#13094057	—	4	2	no	—
49	#13094054	—	2	2	no	—
50	#13094053	—	4	2	no	—
51	#13094052	—	2	2	no	—
52	#13094052	—	4	2	no	—
53	#13094051	—	4	2	no	—
54	#13094049	—	2	2	no	—
55	#13094047	—	4	1	no	—
56	#13094046	—	2	2	no	—
57	#13094046	—	2	2	no	—
58	#13094046	C₂³	1	1	yes	characteristic
59	#13094046	C₂³	1	1	yes	characteristic
60	#13094043	—	4	1	no	—
61	C₂×Dic₁₈₈	—	2	2	no	—
62	C₂×Dic₁₈₈	—	2	1	no	—
63	C₂×Dic₁₈₈	C₂³	1	2	yes	—
64	Q₁₆×D₄₇	—	4	1	no	—
65	C₂×D₃₇₆	—	2	2	no	—
66	C₂×D₃₇₆	—	2	1	no	—
67	C₂×D₃₇₆	C₂³	1	2	yes	—
68	D₈×D₄₇	—	4	1	no	—
69	#13094030	—	2	1	no	—
70	#13094030	—	2	1	no	—
71	#13094024	—	2	1	no	—
72	#13094021	—	2	1	no	—
73	Dic₃₇₆	—	2	2	no	—
74	Dic₃₇₆	D₄	1	1	yes	characteristic, complemented
75	#13093969	—	2	2	no	—
76	#13093969	—	2	2	no	—
77	#13093969	—	2	2	no	—
78	#13093969	—	2	2	no	—
79	#13093969	—	4	2	no	—
80	#13093969	D₄	1	1	yes	characteristic, complemented
81	#13093969	D₄	1	1	yes	characteristic, complemented
82	D₇₅₂	—	2	2	no	—
83	D₇₅₂	D₄	1	1	yes	characteristic, complemented
84	#13093960	C₂³	1	1	yes	characteristic
85	#13093960	C₂³	1	1	yes	characteristic
86	#13093952	—	2	1	no	—
87	#13093952	—	2	1	no	—
88	#13093942	—	2	2	no	—
89	#13093940	—	2	2	no	—
90	#135×C₄₇	D₄	1	1	yes	characteristic
91	#131×C₄₇	C₂³	1	2	yes	—
92	M₃₂×C₄₇	—	2	2	no	—
93	M₃₂×C₄₇	C₂³	1	2	yes	—
94	C₂×C₁₆×C₄₇	—	2	2	no	—
95	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
96	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
97	#108×C₄₇	D₄	1	1	yes	characteristic
98	#104×C₄₇	D₄	1	2	yes	—
99	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
100	#41×C₄₇	C₂×D₄	1	2	yes	—
101	#10625354	—	4	2	no	—
102	Q₈×D₄₇	—	4	2	no	—
103	#10625352	—	4	2	no	—
104	#10625352	—	8	2	no	—
105	D₄×D₄₇	—	4	2	no	—
106	D₄×D₄₇	—	8	2	no	—
107	#10625350	—	2	1	no	—
108	#10625350	—	2	1	no	—
109	#10625350	—	4	2	no	—
110	#10625350	—	4	2	no	—
111	C₂×D₁₈₈	—	2	2	no	—
112	C₂×D₁₈₈	—	4	2	no	—
113	C₂×D₁₈₈	—	8	1	no	—
114	C₂×Dic₉₄	—	2	2	no	—
115	C₂×Dic₉₄	—	4	2	no	—
116	Q₁₆×C₄₇	D₈	1	1	yes	characteristic
117	SD₁₆×C₄₇	D₈	1	2	yes	—
118	D₈×C₄₇	D₈	1	1	yes	characteristic
119	M₁₆×C₄₇	—	2	2	no	—
120	M₁₆×C₄₇	C₂×D₄	1	2	yes	—
121	C₂×C₈×C₄₇	—	2	2	no	—
122	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
124	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
125	#10625337	—	4	2	no	—
126	#10625336	—	4	2	no	—
127	#10625335	—	4	2	no	—
128	#10625334	—	4	2	no	—
129	C₄⋊Dic₄₇	—	8	1	no	—
130	#10625329	—	2	1	no	—
131	#10625329	—	2	1	no	—
132	Dic₁₈₈	—	2	2	no	—
133	Dic₁₈₈	—	2	2	no	—
134	Dic₁₈₈	—	4	2	no	—
135	Dic₁₈₈	—	4	1	no	—
136	Dic₁₈₈	—	4	1	no	—
137	Dic₁₈₈	C₂×D₄	1	1	yes	characteristic
138	Dic₁₈₈	C₂×D₄	1	1	yes	characteristic
139	D₃₇₆	—	2	2	no	—
140	D₃₇₆	—	2	2	no	—
141	D₃₇₆	—	4	2	no	—
142	D₃₇₆	—	4	1	no	—
143	D₃₇₆	—	4	1	no	—
144	D₃₇₆	C₂×D₄	1	1	yes	characteristic
145	D₃₇₆	C₂×D₄	1	1	yes	characteristic
146	#10625325	—	2	1	no	—
147	#10625325	—	2	1	no	—
148	#10625325	—	4	2	no	—
149	#10625325	—	4	2	no	—
150	#10625324	—	4	1	no	—
151	#10625324	—	4	1	no	—
152	C₈×D₄₇	—	4	1	no	—
153	C₈×D₄₇	—	4	1	no	—
154	C₁₆×C₄₇	—	2	2	no	—
155	C₁₆×C₄₇	—	2	1	no	—
156	C₁₆×C₄₇	C₂×D₄	1	1	yes	characteristic
157	C₁₆×C₄₇	C₂×D₄	1	1	yes	characteristic
158	C₂²×D₄₇	—	4	2	no	—
159	C₂²×D₄₇	—	8	2	no	—
160	Q₈×C₄₇	C₂×D₈	1	2	yes	—
161	D₄×C₄₇	—	2	2	no	—
162	D₄×C₄₇	C₂×D₈	1	2	yes	—
163	C₂×C₄×C₄₇	—	2	1	no	—
164	C₂×C₄×C₄₇	—	2	2	no	—
165	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
166	C₂²⋊D₄₇	—	4	1	no	—
167	C₂²⋊D₄₇	—	4	1	no	—
168	C₂²⋊D₄₇	—	8	2	no	—
169	C₂²⋊D₄₇	—	8	2	no	—
170	C₂×Dic₄₇	—	4	2	no	—
171	C₂×Dic₄₇	—	8	2	no	—
172	D₁₈₈	—	2	1	no	—
173	D₁₈₈	—	2	1	no	—
174	D₁₈₈	—	4	2	no	—
175	D₁₈₈	—	4	2	no	—
176	D₁₈₈	—	8	2	no	—
177	D₁₈₈	—	16	2	no	—
178	C₄×D₄₇	—	4	1	no	—
179	C₄×D₄₇	—	4	1	no	—
180	C₄×D₄₇	—	8	2	no	—
181	C₄×D₄₇	—	8	2	no	—
182	Dic₉₄	—	2	1	no	—
183	Dic₉₄	—	2	1	no	—
184	Dic₉₄	—	4	2	no	—
185	Dic₉₄	—	4	2	no	—
186	Dic₉₄	—	8	2	no	—
187	C₈×C₄₇	—	2	2	no	—
188	C₈×C₄₇	C₂×D₈	1	1	yes	characteristic
189	C₈×C₄₇	C₂×D₈	1	1	yes	characteristic
190	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
191	C₈×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
192	C₄₇⋊C₈	—	4	1	no	—
193	C₄₇⋊C₈	—	4	1	no	—
194	#33856	—	47	1	no	maximal, Sylow
195	C₂²×C₄₇	—	2	2	no	—
196	C₂²×C₄₇	#576	1	1	yes	characteristic
197	C₂×D₄₇	—	4	1	no	—
198	C₂×D₄₇	—	4	1	no	—
199	C₂×D₄₇	—	8	2	no	—
200	C₂×D₄₇	—	16	2	no	—
201	C₂×D₄₇	—	32	2	no	—
202	C₄×C₄₇	—	2	2	no	—
203	C₄×C₄₇	—	2	2	no	—
204	C₄×C₄₇	D₄²	1	1	yes	characteristic
205	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
206	Dic₄₇	—	4	1	no	—
207	Dic₄₇	—	4	1	no	—
208	Dic₄₇	—	8	2	no	—
209	#3416	—	47	2	no	—
210	#3293	—	47	1	no	—
211	#3292	—	47	1	no	—
212	#2248	—	47	1	no	—
213	#2223	—	47	2	no	—
214	#2214	—	47	1	no	—
215	#2213	—	47	1	no	—
216	#2194	—	47	2	no	—
217	#2193	—	47	2	no	—
218	#2178	—	47	1	no	—
219	#2170	D₄₇	1	1	yes	characteristic, complemented
220	C₂×C₄₇	—	2	1	no	—
221	C₂×C₄₇	—	4	2	no	—
222	C₂×C₄₇	D₄×D₈	1	1	yes	characteristic
223	D₄₇	—	8	1	no	—
224	D₄₇	—	8	1	no	—
225	D₄₇	—	16	2	no	—
226	#578	—	47	2	no	—
227	#578	—	94	1	no	—
228	#576	—	47	2	no	—
229	#576	—	94	1	no	—
230	#510	—	47	2	no	—
231	#510	—	94	2	no	—
232	#509	—	47	2	no	—
233	#509	—	94	2	no	—
234	#508	—	47	1	no	—
235	#508	—	94	2	no	—
236	C₂×SD₃₂	—	47	2	no	—
237	C₂×SD₃₂	—	47	2	no	—
238	C₂×SD₃₂	—	94	2	no	—
239	#504	C₂×D₄₇	1	2	yes	complemented
240	#494	—	47	1	no	—
241	#493	—	47	1	no	—
242	#473	—	47	2	no	—
243	#473	—	94	1	no	—
244	#472	—	47	2	no	—
245	#472	—	94	1	no	—
246	#456	—	94	2	no	—
247	#453	—	94	2	no	—
248	#443	—	47	1	no	—
249	#443	—	47	1	no	—
250	#443	C₂×D₄₇	1	1	yes	characteristic
251	#368	—	47	1	no	—
252	#364	C₂×D₄₇	1	1	yes	characteristic, complemented
253	#362	—	47	2	no	—
254	#361	—	47	2	no	—
255	#359	—	47	1	no	—
256	#359	—	47	1	no	—
257	#350	C₂×D₄₇	1	2	yes	complemented
258	C₄×C₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
259	C₄₇	#33856	1	1	yes	characteristic, complemented, Sylow
260	2₋¹⁺⁴	—	94	2	no	—
261	H(5,𝔽₂)	—	94	2	no	—
262	#137	—	94	2	no	—
263	#137	—	94	2	no	—
264	#137	—	188	2	no	—
265	#137	—	188	2	no	—
266	AGL(1,ℤ/8)	—	94	2	no	—
267	AGL(1,ℤ/8)	—	94	2	no	—
268	AGL(1,ℤ/8)	—	188	2	no	—
269	AGL(1,ℤ/8)	—	188	2	no	—
270	#135	—	47	1	no	—
271	#135	—	47	1	no	—
272	#135	—	94	2	no	—
273	#135	—	94	2	no	—
274	#135	—	188	1	no	—
275	#135	—	188	1	no	—
276	#135	D₁₈₈	1	1	yes	characteristic
277	C₂×Q₁₆	—	47	2	no	—
278	C₂×Q₁₆	—	94	2	no	—
279	C₂×Q₁₆	—	94	1	no	—
280	C₂×Q₁₆	—	188	1	no	—
281	C₂×D₈	—	47	2	no	—
282	C₂×D₈	—	94	2	no	—
283	C₂×D₈	—	94	1	no	—
284	C₂×D₈	—	188	1	no	—
285	#131	—	94	1	no	—
286	#131	—	94	1	no	—
287	#131	C₂²×D₄₇	1	2	yes	—
288	C₄⋊Q₈	—	94	1	no	—
289	#127	—	94	1	no	—
290	Q₃₂	—	47	1	no	—
291	Q₃₂	—	94	2	no	—
292	SD₃₂	—	47	1	no	—
293	SD₃₂	—	47	1	no	—
294	SD₃₂	—	94	2	no	—
295	SD₃₂	—	94	2	no	—
296	SD₃₂	—	94	2	no	—
297	SD₃₂	—	94	2	no	—
298	SD₃₂	—	188	2	no	—
299	D₁₆	—	47	1	no	—
300	D₁₆	—	94	2	no	—
301	M₃₂	—	2	2	no	—
302	M₃₂	C₂²×D₄₇	1	2	yes	—
303	C₂×C₁₆	—	2	2	no	—
304	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
305	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
306	#108	—	47	1	no	—
307	#108	—	47	1	no	—
308	#108	D₁₈₈	1	1	yes	characteristic
309	#104	—	94	1	no	—
310	#104	—	94	1	no	—
311	#104	D₁₈₈	1	2	yes	—
312	#101	—	94	2	no	—
313	#100	—	94	2	no	—
314	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
315	#41	—	94	1	no	—
316	#41	—	94	1	no	—
317	#41	—	376	2	no	—
318	#41	—	188	2	no	—
319	#41	—	188	2	no	—
320	#41	—	188	2	no	—
321	#41	—	188	2	no	—
322	#41	C₂×D₁₈₈	1	2	yes	—
323	C₂×Q₈	—	94	2	no	—
324	C₂×Q₈	—	188	2	no	—
325	C₂×Q₈	—	188	2	no	—
326	C₂×D₄	—	94	2	no	—
327	C₂×D₄	—	376	1	no	—
328	C₂×D₄	—	376	2	no	—
329	C₂×D₄	—	188	2	no	—
330	C₂×D₄	—	188	2	no	—
331	Q₁₆	—	47	1	no	—
332	Q₁₆	—	47	1	no	—
333	Q₁₆	—	94	2	no	—
334	Q₁₆	—	94	2	no	—
335	Q₁₆	—	188	2	no	—
336	Q₁₆	—	188	2	no	—
337	Q₁₆	—	188	1	no	—
338	Q₁₆	—	188	1	no	—
339	Q₁₆	D₃₇₆	1	1	yes	characteristic
340	SD₁₆	—	94	1	no	—
341	SD₁₆	—	94	1	no	—
342	SD₁₆	—	188	2	no	—
343	SD₁₆	—	188	2	no	—
344	SD₁₆	—	188	2	no	—
345	SD₁₆	—	188	2	no	—
346	SD₁₆	D₃₇₆	1	2	yes	—
347	D₈	—	47	1	no	—
348	D₈	—	47	1	no	—
349	D₈	—	94	2	no	—
350	D₈	—	94	2	no	—
351	D₈	—	188	2	no	—
352	D₈	—	188	2	no	—
353	D₈	—	188	1	no	—
354	D₈	—	188	1	no	—
355	D₈	D₃₇₆	1	1	yes	characteristic
356	M₁₆	—	2	2	no	—
357	M₁₆	—	94	1	no	—
358	M₁₆	—	94	1	no	—
359	M₁₆	—	188	1	no	—
360	M₁₆	—	188	1	no	—
361	M₁₆	C₂×D₁₈₈	1	2	yes	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	188	1	no	—
364	C₂×C₈	—	188	1	no	—
365	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
366	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
367	C₄⋊C₄	—	376	1	no	—
368	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
369	C₁₆	—	2	2	no	—
370	C₁₆	—	2	1	no	—
371	C₁₆	D₄×D₄₇	1	1	yes	characteristic
372	C₁₆	D₄×D₄₇	1	1	yes	characteristic
373	C₂³	—	376	2	no	—
374	C₂³	—	188	2	no	—
375	Q₈	—	94	1	no	—
376	Q₈	—	94	1	no	—
377	Q₈	—	376	2	no	—
378	Q₈	—	188	2	no	—
379	Q₈	—	188	2	no	—
380	Q₈	C₂×D₃₇₆	1	2	yes	—
381	D₄	—	2	2	no	—
382	D₄	—	94	1	no	—
383	D₄	—	94	1	no	—
384	D₄	—	376	2	no	—
385	D₄	—	376	2	no	—
386	D₄	—	376	2	no	—
387	D₄	—	188	1	no	—
388	D₄	—	188	1	no	—
389	D₄	—	188	2	no	—
390	D₄	—	188	2	no	—
391	D₄	—	752	2	no	—
392	D₄	C₂×D₃₇₆	1	2	yes	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	376	2	no	—
396	C₂×C₄	—	376	2	no	—
397	C₂×C₄	—	376	2	no	—
398	C₂×C₄	—	188	2	no	—
399	C₂×C₄	—	188	1	no	—
400	C₂×C₄	—	188	1	no	—
401	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
402	C₈	—	2	2	no	—
403	C₈	—	188	1	no	—
404	C₈	—	188	1	no	—
405	C₈	C₂×D₃₇₆	1	1	yes	characteristic
406	C₈	C₂×D₃₇₆	1	1	yes	characteristic
407	C₈	C₂×D₄×D₄₇	1	1	yes	characteristic
408	C₈	#13094070	1	1	yes	characteristic
409	C₂²	—	2	2	no	—
410	C₂²	—	376	2	no	—
411	C₂²	—	188	1	no	—
412	C₂²	—	188	1	no	—
413	C₂²	—	1504	2	no	—
414	C₂²	—	752	2	no	—
415	C₂²	#15689928	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	2	2	no	—
418	C₄	—	376	2	no	—
419	C₄	—	188	1	no	—
420	C₄	—	188	1	no	—
421	C₄	D₄×D₁₈₈	1	1	yes	characteristic
422	C₄	C₂²×D₃₇₆	1	1	yes	characteristic
423	C₂	—	2	1	no	—
424	C₂	—	4	2	no	—
425	C₂	—	376	1	no	—
426	C₂	—	376	1	no	—
427	C₂	—	752	2	no	—
428	C₂	D₄×D₃₇₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₃₇₆
commutator, cosocle	C₂×C₈×C₄₇	C₂⁴
Frattini	C₂×C₈	C₂³×D₄₇
Fitting	C₄₇×#2170	C₂
socle	C₂×C₄₇	D₄×D₈
hypercenter	#2170	D₄₇
hypocenter	C₄₇	#33856
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #443 ◁ #2170

Complements

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

N	H ≅ G/N	type
1. #20256536	C₂	semidirect
2. #20255193	C₂	semidirect
3. #20255188	C₂	semidirect
4. #20245644	C₂	semidirect
5. #20245518	C₂	semidirect
6. #20245470	C₂	semidirect
7. #20245465	C₂	semidirect
8. #20245361	C₂	semidirect
9. #20245354	C₂	semidirect
10. #20245270	C₂	semidirect
11. C₄₇×#2170	C₂	semidirect
12. #15689940	C₂²	semidirect
19. #15689561	C₂²	semidirect
23. C₂×#13093969	C₂²	semidirect
24. C₂×#13093969	C₂²	semidirect
25. #15689503	C₂²	semidirect
28. #15689398	C₂²	semidirect
34. #15689241	C₂²	semidirect
35. #15688953	C₂²	semidirect
36. #15688940	C₂²	semidirect
37. #15688937	C₂²	semidirect
39. #15688931	C₂²	semidirect
40. C₄₇×#504	C₂²	semidirect
42. C₄₇×#364	C₂²	semidirect
43. C₄₇×#350	C₂²	semidirect
44. C₄×C₁₆×C₄₇	C₂²	semidirect
74. Dic₃₇₆	D₄	semidirect
80. #13093969	D₄	semidirect
81. #13093969	D₄	semidirect
83. D₇₅₂	D₄	semidirect
219. #2170	D₄₇	semidirect
239. #504	C₂×D₄₇	semidirect
252. #364	C₂×D₄₇	semidirect
257. #350	C₂×D₄₇	semidirect
258. C₄×C₁₆	C₂×D₄₇	semidirect
259. C₄₇	#33856	semidirect

Maximal subgroups

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

subgroup	index
#20256536	2
#20255193	2
#20255188	2
#20245644	2
#20245518	2
#20245470	2
#20245465	2
#20245361	2
#20245354	2
#20245270	2
C₄₇×#2170	2
#33856	47