Subgroups — #25253375

Order 11008.

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	#19147743	C₂	1	2	yes	maximal, complemented
2	#19146400	C₂	1	1	yes	maximal, characteristic, complemented
3	#19146395	C₂	1	1	yes	maximal, characteristic, complemented
4	#19136851	C₂	1	1	yes	maximal, characteristic, complemented
5	#19136725	C₂	1	2	yes	maximal, complemented
6	#19136677	C₂	1	1	yes	maximal, characteristic, complemented
7	#19136672	C₂	1	1	yes	maximal, characteristic, complemented
8	#19136568	C₂	1	2	yes	maximal, complemented
9	#19136561	C₂	1	2	yes	maximal, complemented
10	#19136477	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#2170	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583716	C₂²	1	2	yes	complemented
13	#14583713	—	2	1	no	—
14	#14583704	C₂²	1	2	yes	—
15	#14583701	—	2	1	no	—
16	#14583342	—	2	2	no	—
17	#14583342	C₂²	1	2	yes	—
18	#14583337	—	2	2	no	—
19	#14583337	C₂²	1	2	yes	complemented
20	#14583331	—	2	2	no	—
21	#14583331	C₂²	1	1	yes	characteristic
22	C₂×#13063270	—	2	2	no	—
23	C₂×#13063270	C₂²	1	2	yes	complemented
24	C₂×#13063270	C₂²	1	2	yes	complemented
25	#14583279	C₂²	1	1	yes	characteristic, complemented
26	#14583276	C₂²	1	1	yes	characteristic
27	#14583175	—	2	1	no	—
28	#14583174	C₂²	1	2	yes	complemented
29	#14583170	—	2	1	no	—
30	#14583169	C₂²	1	2	yes	—
31	#14583083	—	2	2	no	—
32	#14583068	—	2	2	no	—
33	#14583017	C₂²	1	1	yes	characteristic
34	#14583017	C₂²	1	1	yes	characteristic, complemented
35	#14582729	C₂²	1	1	yes	characteristic, complemented
36	#14582716	C₂²	1	2	yes	complemented
37	#14582713	C₂²	1	2	yes	complemented
38	#14582707	C₂²	1	1	yes	characteristic
39	#14582707	C₂²	1	1	yes	characteristic, complemented
40	C₄₃×#504	C₂²	1	2	yes	complemented
41	C₄₃×#443	C₂²	1	1	yes	characteristic
42	C₄₃×#364	C₂²	1	1	yes	characteristic, complemented
43	C₄₃×#350	C₂²	1	2	yes	complemented
44	C₄×C₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
45	#13063372	—	2	2	no	—
46	#13063371	—	2	2	no	—
47	#13063358	—	2	2	no	—
48	#13063358	—	4	2	no	—
49	#13063355	—	2	2	no	—
50	#13063354	—	4	2	no	—
51	#13063353	—	2	2	no	—
52	#13063353	—	4	2	no	—
53	#13063352	—	4	2	no	—
54	#13063350	—	2	2	no	—
55	#13063348	—	4	1	no	—
56	#13063347	—	2	2	no	—
57	#13063347	—	2	2	no	—
58	#13063347	C₂³	1	1	yes	characteristic
59	#13063347	C₂³	1	1	yes	characteristic
60	#13063344	—	4	1	no	—
61	C₂×Dic₁₇₂	—	2	2	no	—
62	C₂×Dic₁₇₂	—	2	1	no	—
63	C₂×Dic₁₇₂	C₂³	1	2	yes	—
64	Q₁₆×D₄₃	—	4	1	no	—
65	C₂×D₃₄₄	—	2	2	no	—
66	C₂×D₃₄₄	—	2	1	no	—
67	C₂×D₃₄₄	C₂³	1	2	yes	—
68	D₈×D₄₃	—	4	1	no	—
69	#13063331	—	2	1	no	—
70	#13063331	—	2	1	no	—
71	#13063325	—	2	1	no	—
72	#13063322	—	2	1	no	—
73	Dic₃₄₄	—	2	2	no	—
74	Dic₃₄₄	D₄	1	1	yes	characteristic, complemented
75	#13063270	—	2	2	no	—
76	#13063270	—	2	2	no	—
77	#13063270	—	2	2	no	—
78	#13063270	—	2	2	no	—
79	#13063270	—	4	2	no	—
80	#13063270	D₄	1	1	yes	characteristic, complemented
81	#13063270	D₄	1	1	yes	characteristic, complemented
82	D₆₈₈	—	2	2	no	—
83	D₆₈₈	D₄	1	1	yes	characteristic, complemented
84	#13063261	C₂³	1	1	yes	characteristic
85	#13063261	C₂³	1	1	yes	characteristic
86	#13063253	—	2	1	no	—
87	#13063253	—	2	1	no	—
88	#13063243	—	2	2	no	—
89	#13063241	—	2	2	no	—
90	#135×C₄₃	D₄	1	1	yes	characteristic
91	#131×C₄₃	C₂³	1	2	yes	—
92	M₃₂×C₄₃	—	2	2	no	—
93	M₃₂×C₄₃	C₂³	1	2	yes	—
94	C₂×C₁₆×C₄₃	—	2	2	no	—
95	C₂×C₁₆×C₄₃	C₂³	1	1	yes	characteristic
96	C₂×C₁₆×C₄₃	C₂³	1	1	yes	characteristic
97	#108×C₄₃	D₄	1	1	yes	characteristic
98	#104×C₄₃	D₄	1	2	yes	—
99	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
100	#41×C₄₃	C₂×D₄	1	2	yes	—
101	#10621902	—	4	2	no	—
102	Q₈×D₄₃	—	4	2	no	—
103	#10621900	—	4	2	no	—
104	#10621900	—	8	2	no	—
105	D₄×D₄₃	—	4	2	no	—
106	D₄×D₄₃	—	8	2	no	—
107	#10621898	—	2	1	no	—
108	#10621898	—	2	1	no	—
109	#10621898	—	4	2	no	—
110	#10621898	—	4	2	no	—
111	C₂×D₁₇₂	—	2	2	no	—
112	C₂×D₁₇₂	—	4	2	no	—
113	C₂×D₁₇₂	—	8	1	no	—
114	C₂×Dic₈₆	—	2	2	no	—
115	C₂×Dic₈₆	—	4	2	no	—
116	Q₁₆×C₄₃	D₈	1	1	yes	characteristic
117	SD₁₆×C₄₃	D₈	1	2	yes	—
118	D₈×C₄₃	D₈	1	1	yes	characteristic
119	M₁₆×C₄₃	—	2	2	no	—
120	M₁₆×C₄₃	C₂×D₄	1	2	yes	—
121	C₂×C₈×C₄₃	—	2	2	no	—
122	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
124	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
125	#10621885	—	4	2	no	—
126	#10621884	—	4	2	no	—
127	#10621883	—	4	2	no	—
128	#10621882	—	4	2	no	—
129	C₄⋊Dic₄₃	—	8	1	no	—
130	#10621877	—	2	1	no	—
131	#10621877	—	2	1	no	—
132	Dic₁₇₂	—	2	2	no	—
133	Dic₁₇₂	—	2	2	no	—
134	Dic₁₇₂	—	4	2	no	—
135	Dic₁₇₂	—	4	1	no	—
136	Dic₁₇₂	—	4	1	no	—
137	Dic₁₇₂	C₂×D₄	1	1	yes	characteristic
138	Dic₁₇₂	C₂×D₄	1	1	yes	characteristic
139	D₃₄₄	—	2	2	no	—
140	D₃₄₄	—	2	2	no	—
141	D₃₄₄	—	4	2	no	—
142	D₃₄₄	—	4	1	no	—
143	D₃₄₄	—	4	1	no	—
144	D₃₄₄	C₂×D₄	1	1	yes	characteristic
145	D₃₄₄	C₂×D₄	1	1	yes	characteristic
146	#10621873	—	2	1	no	—
147	#10621873	—	2	1	no	—
148	#10621873	—	4	2	no	—
149	#10621873	—	4	2	no	—
150	#10621872	—	4	1	no	—
151	#10621872	—	4	1	no	—
152	C₈×D₄₃	—	4	1	no	—
153	C₈×D₄₃	—	4	1	no	—
154	C₁₆×C₄₃	—	2	2	no	—
155	C₁₆×C₄₃	—	2	1	no	—
156	C₁₆×C₄₃	C₂×D₄	1	1	yes	characteristic
157	C₁₆×C₄₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×D₄₃	—	4	2	no	—
159	C₂²×D₄₃	—	8	2	no	—
160	Q₈×C₄₃	C₂×D₈	1	2	yes	—
161	D₄×C₄₃	—	2	2	no	—
162	D₄×C₄₃	C₂×D₈	1	2	yes	—
163	C₂×C₄×C₄₃	—	2	1	no	—
164	C₂×C₄×C₄₃	—	2	2	no	—
165	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
166	C₂²⋊D₄₃	—	4	1	no	—
167	C₂²⋊D₄₃	—	4	1	no	—
168	C₂²⋊D₄₃	—	8	2	no	—
169	C₂²⋊D₄₃	—	8	2	no	—
170	C₂×Dic₄₃	—	4	2	no	—
171	C₂×Dic₄₃	—	8	2	no	—
172	D₁₇₂	—	2	1	no	—
173	D₁₇₂	—	2	1	no	—
174	D₁₇₂	—	4	2	no	—
175	D₁₇₂	—	4	2	no	—
176	D₁₇₂	—	8	2	no	—
177	D₁₇₂	—	16	2	no	—
178	C₄×D₄₃	—	4	1	no	—
179	C₄×D₄₃	—	4	1	no	—
180	C₄×D₄₃	—	8	2	no	—
181	C₄×D₄₃	—	8	2	no	—
182	Dic₈₆	—	2	1	no	—
183	Dic₈₆	—	2	1	no	—
184	Dic₈₆	—	4	2	no	—
185	Dic₈₆	—	4	2	no	—
186	Dic₈₆	—	8	2	no	—
187	C₈×C₄₃	—	2	2	no	—
188	C₈×C₄₃	C₂×D₈	1	1	yes	characteristic
189	C₈×C₄₃	C₂×D₈	1	1	yes	characteristic
190	C₈×C₄₃	C₂²×D₄	1	1	yes	characteristic
191	C₈×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
192	C₄₃⋊C₈	—	4	1	no	—
193	C₄₃⋊C₈	—	4	1	no	—
194	#33856	—	43	1	no	maximal, Sylow
195	C₂²×C₄₃	—	2	2	no	—
196	C₂²×C₄₃	#576	1	1	yes	characteristic
197	C₂×D₄₃	—	4	1	no	—
198	C₂×D₄₃	—	4	1	no	—
199	C₂×D₄₃	—	8	2	no	—
200	C₂×D₄₃	—	16	2	no	—
201	C₂×D₄₃	—	32	2	no	—
202	C₄×C₄₃	—	2	2	no	—
203	C₄×C₄₃	—	2	2	no	—
204	C₄×C₄₃	D₄²	1	1	yes	characteristic
205	C₄×C₄₃	C₂²×D₈	1	1	yes	characteristic
206	Dic₄₃	—	4	1	no	—
207	Dic₄₃	—	4	1	no	—
208	Dic₄₃	—	8	2	no	—
209	#3416	—	43	2	no	—
210	#3293	—	43	1	no	—
211	#3292	—	43	1	no	—
212	#2248	—	43	1	no	—
213	#2223	—	43	2	no	—
214	#2214	—	43	1	no	—
215	#2213	—	43	1	no	—
216	#2194	—	43	2	no	—
217	#2193	—	43	2	no	—
218	#2178	—	43	1	no	—
219	#2170	D₄₃	1	1	yes	characteristic, complemented
220	C₂×C₄₃	—	2	1	no	—
221	C₂×C₄₃	—	4	2	no	—
222	C₂×C₄₃	D₄×D₈	1	1	yes	characteristic
223	D₄₃	—	8	1	no	—
224	D₄₃	—	8	1	no	—
225	D₄₃	—	16	2	no	—
226	#578	—	43	2	no	—
227	#578	—	86	1	no	—
228	#576	—	43	2	no	—
229	#576	—	86	1	no	—
230	#510	—	43	2	no	—
231	#510	—	86	2	no	—
232	#509	—	43	2	no	—
233	#509	—	86	2	no	—
234	#508	—	43	1	no	—
235	#508	—	86	2	no	—
236	C₂×SD₃₂	—	43	2	no	—
237	C₂×SD₃₂	—	43	2	no	—
238	C₂×SD₃₂	—	86	2	no	—
239	#504	C₂×D₄₃	1	2	yes	complemented
240	#494	—	43	1	no	—
241	#493	—	43	1	no	—
242	#473	—	43	2	no	—
243	#473	—	86	1	no	—
244	#472	—	43	2	no	—
245	#472	—	86	1	no	—
246	#456	—	86	2	no	—
247	#453	—	86	2	no	—
248	#443	—	43	1	no	—
249	#443	—	43	1	no	—
250	#443	C₂×D₄₃	1	1	yes	characteristic
251	#368	—	43	1	no	—
252	#364	C₂×D₄₃	1	1	yes	characteristic, complemented
253	#362	—	43	2	no	—
254	#361	—	43	2	no	—
255	#359	—	43	1	no	—
256	#359	—	43	1	no	—
257	#350	C₂×D₄₃	1	2	yes	complemented
258	C₄×C₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
259	C₄₃	#33856	1	1	yes	characteristic, complemented, Sylow
260	2₋¹⁺⁴	—	86	2	no	—
261	H(5,𝔽₂)	—	86	2	no	—
262	#137	—	86	2	no	—
263	#137	—	86	2	no	—
264	#137	—	172	2	no	—
265	#137	—	172	2	no	—
266	AGL(1,ℤ/8)	—	86	2	no	—
267	AGL(1,ℤ/8)	—	86	2	no	—
268	AGL(1,ℤ/8)	—	172	2	no	—
269	AGL(1,ℤ/8)	—	172	2	no	—
270	#135	—	43	1	no	—
271	#135	—	43	1	no	—
272	#135	—	86	2	no	—
273	#135	—	86	2	no	—
274	#135	—	172	1	no	—
275	#135	—	172	1	no	—
276	#135	D₁₇₂	1	1	yes	characteristic
277	C₂×Q₁₆	—	43	2	no	—
278	C₂×Q₁₆	—	86	2	no	—
279	C₂×Q₁₆	—	86	1	no	—
280	C₂×Q₁₆	—	172	1	no	—
281	C₂×D₈	—	43	2	no	—
282	C₂×D₈	—	86	2	no	—
283	C₂×D₈	—	86	1	no	—
284	C₂×D₈	—	172	1	no	—
285	#131	—	86	1	no	—
286	#131	—	86	1	no	—
287	#131	C₂²×D₄₃	1	2	yes	—
288	C₄⋊Q₈	—	86	1	no	—
289	#127	—	86	1	no	—
290	Q₃₂	—	43	1	no	—
291	Q₃₂	—	86	2	no	—
292	SD₃₂	—	43	1	no	—
293	SD₃₂	—	43	1	no	—
294	SD₃₂	—	86	2	no	—
295	SD₃₂	—	86	2	no	—
296	SD₃₂	—	86	2	no	—
297	SD₃₂	—	86	2	no	—
298	SD₃₂	—	172	2	no	—
299	D₁₆	—	43	1	no	—
300	D₁₆	—	86	2	no	—
301	M₃₂	—	2	2	no	—
302	M₃₂	C₂²×D₄₃	1	2	yes	—
303	C₂×C₁₆	—	2	2	no	—
304	C₂×C₁₆	C₂²×D₄₃	1	1	yes	characteristic
305	C₂×C₁₆	C₂²×D₄₃	1	1	yes	characteristic
306	#108	—	43	1	no	—
307	#108	—	43	1	no	—
308	#108	D₁₇₂	1	1	yes	characteristic
309	#104	—	86	1	no	—
310	#104	—	86	1	no	—
311	#104	D₁₇₂	1	2	yes	—
312	#101	—	86	2	no	—
313	#100	—	86	2	no	—
314	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
315	#41	—	86	1	no	—
316	#41	—	86	1	no	—
317	#41	—	344	2	no	—
318	#41	—	172	2	no	—
319	#41	—	172	2	no	—
320	#41	—	172	2	no	—
321	#41	—	172	2	no	—
322	#41	C₂×D₁₇₂	1	2	yes	—
323	C₂×Q₈	—	86	2	no	—
324	C₂×Q₈	—	172	2	no	—
325	C₂×Q₈	—	172	2	no	—
326	C₂×D₄	—	86	2	no	—
327	C₂×D₄	—	344	1	no	—
328	C₂×D₄	—	344	2	no	—
329	C₂×D₄	—	172	2	no	—
330	C₂×D₄	—	172	2	no	—
331	Q₁₆	—	43	1	no	—
332	Q₁₆	—	43	1	no	—
333	Q₁₆	—	86	2	no	—
334	Q₁₆	—	86	2	no	—
335	Q₁₆	—	172	2	no	—
336	Q₁₆	—	172	2	no	—
337	Q₁₆	—	172	1	no	—
338	Q₁₆	—	172	1	no	—
339	Q₁₆	D₃₄₄	1	1	yes	characteristic
340	SD₁₆	—	86	1	no	—
341	SD₁₆	—	86	1	no	—
342	SD₁₆	—	172	2	no	—
343	SD₁₆	—	172	2	no	—
344	SD₁₆	—	172	2	no	—
345	SD₁₆	—	172	2	no	—
346	SD₁₆	D₃₄₄	1	2	yes	—
347	D₈	—	43	1	no	—
348	D₈	—	43	1	no	—
349	D₈	—	86	2	no	—
350	D₈	—	86	2	no	—
351	D₈	—	172	2	no	—
352	D₈	—	172	2	no	—
353	D₈	—	172	1	no	—
354	D₈	—	172	1	no	—
355	D₈	D₃₄₄	1	1	yes	characteristic
356	M₁₆	—	2	2	no	—
357	M₁₆	—	86	1	no	—
358	M₁₆	—	86	1	no	—
359	M₁₆	—	172	1	no	—
360	M₁₆	—	172	1	no	—
361	M₁₆	C₂×D₁₇₂	1	2	yes	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	172	1	no	—
364	C₂×C₈	—	172	1	no	—
365	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
366	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
367	C₄⋊C₄	—	344	1	no	—
368	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
369	C₁₆	—	2	2	no	—
370	C₁₆	—	2	1	no	—
371	C₁₆	D₄×D₄₃	1	1	yes	characteristic
372	C₁₆	D₄×D₄₃	1	1	yes	characteristic
373	C₂³	—	344	2	no	—
374	C₂³	—	172	2	no	—
375	Q₈	—	86	1	no	—
376	Q₈	—	86	1	no	—
377	Q₈	—	344	2	no	—
378	Q₈	—	172	2	no	—
379	Q₈	—	172	2	no	—
380	Q₈	C₂×D₃₄₄	1	2	yes	—
381	D₄	—	2	2	no	—
382	D₄	—	86	1	no	—
383	D₄	—	86	1	no	—
384	D₄	—	344	2	no	—
385	D₄	—	344	2	no	—
386	D₄	—	344	2	no	—
387	D₄	—	172	1	no	—
388	D₄	—	172	1	no	—
389	D₄	—	172	2	no	—
390	D₄	—	172	2	no	—
391	D₄	—	688	2	no	—
392	D₄	C₂×D₃₄₄	1	2	yes	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	344	2	no	—
396	C₂×C₄	—	344	2	no	—
397	C₂×C₄	—	344	2	no	—
398	C₂×C₄	—	172	2	no	—
399	C₂×C₄	—	172	1	no	—
400	C₂×C₄	—	172	1	no	—
401	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
402	C₈	—	2	2	no	—
403	C₈	—	172	1	no	—
404	C₈	—	172	1	no	—
405	C₈	C₂×D₃₄₄	1	1	yes	characteristic
406	C₈	C₂×D₃₄₄	1	1	yes	characteristic
407	C₈	C₂×D₄×D₄₃	1	1	yes	characteristic
408	C₈	#13063371	1	1	yes	characteristic
409	C₂²	—	2	2	no	—
410	C₂²	—	344	2	no	—
411	C₂²	—	1376	2	no	—
412	C₂²	—	172	1	no	—
413	C₂²	—	172	1	no	—
414	C₂²	—	688	2	no	—
415	C₂²	#14583704	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	2	2	no	—
418	C₄	—	344	2	no	—
419	C₄	—	172	1	no	—
420	C₄	—	172	1	no	—
421	C₄	D₄×D₁₇₂	1	1	yes	characteristic
422	C₄	C₂²×D₃₄₄	1	1	yes	characteristic
423	C₂	—	2	1	no	—
424	C₂	—	4	2	no	—
425	C₂	—	344	1	no	—
426	C₂	—	344	1	no	—
427	C₂	—	688	2	no	—
428	C₂	D₄×D₃₄₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₃₄₄
commutator, cosocle	C₂×C₈×C₄₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₄₃
Fitting	C₄₃×#2170	C₂
socle	C₂×C₄₃	D₄×D₈
hypercenter	#2170	D₄₃
hypocenter	C₄₃	#33856
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #443 ◁ #2170

Complements

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

N	H ≅ G/N	type
1. #19147743	C₂	semidirect
2. #19146400	C₂	semidirect
3. #19146395	C₂	semidirect
4. #19136851	C₂	semidirect
5. #19136725	C₂	semidirect
6. #19136677	C₂	semidirect
7. #19136672	C₂	semidirect
8. #19136568	C₂	semidirect
9. #19136561	C₂	semidirect
10. #19136477	C₂	semidirect
11. C₄₃×#2170	C₂	semidirect
12. #14583716	C₂²	semidirect
19. #14583337	C₂²	semidirect
23. C₂×#13063270	C₂²	semidirect
24. C₂×#13063270	C₂²	semidirect
25. #14583279	C₂²	semidirect
28. #14583174	C₂²	semidirect
34. #14583017	C₂²	semidirect
35. #14582729	C₂²	semidirect
36. #14582716	C₂²	semidirect
37. #14582713	C₂²	semidirect
39. #14582707	C₂²	semidirect
40. C₄₃×#504	C₂²	semidirect
42. C₄₃×#364	C₂²	semidirect
43. C₄₃×#350	C₂²	semidirect
44. C₄×C₁₆×C₄₃	C₂²	semidirect
74. Dic₃₄₄	D₄	semidirect
80. #13063270	D₄	semidirect
81. #13063270	D₄	semidirect
83. D₆₈₈	D₄	semidirect
219. #2170	D₄₃	semidirect
239. #504	C₂×D₄₃	semidirect
252. #364	C₂×D₄₃	semidirect
257. #350	C₂×D₄₃	semidirect
258. C₄×C₁₆	C₂×D₄₃	semidirect
259. C₄₃	#33856	semidirect

Maximal subgroups

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

subgroup	index
#19147743	2
#19146400	2
#19146395	2
#19136851	2
#19136725	2
#19136677	2
#19136672	2
#19136568	2
#19136561	2
#19136477	2
C₄₃×#2170	2
#33856	43