Finite Group Databasebeta

← #25062741

Subgroups — #25062741

Order 11008.

1048 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583488C211yesmaximal, characteristic
2#19143635C211yesmaximal, characteristic, complemented
3#19143623C211yesmaximal, characteristic, complemented
4#19132964C211yesmaximal, characteristic, complemented
5#19132953C212yesmaximal, complemented
6#19132948C211yesmaximal, characteristic, complemented
7#19132946C211yesmaximal, characteristic, complemented
8#19132942C212yesmaximal, complemented
9#19132932C212yesmaximal, complemented
10#19132920C212yesmaximal, complemented
11C43×#1473C211yesmaximal, characteristic, complemented
12#14583488—22no—
13#14583488—22no—
14#14583488—22no—
15#14583488—22no—
16C2×#13063320C411yescharacteristic
17C2×#13063313C2211yescharacteristic
18C2×#13063311C411yescharacteristic
19C2×#13063310C2211yescharacteristic
20C2×#13063307C411yescharacteristic
21C2×#13063303C411yescharacteristic
22C2×#13063300C411yescharacteristic
23C2×#13063300C411yescharacteristic
24C2×#13063298C2211yescharacteristic
25C2×#13063295C411yescharacteristic
26C2×#13063295C411yescharacteristic
27C2×C4×D172C2211yescharacteristic
28C2×#13063287C2211yescharacteristic
29C2×C22⋊C4×D43C2211yescharacteristic
30#14582978—22no—
31#14582976—22no—
32#14582972—22no—
33#14582969—22no—
34#14582956C2211yescharacteristic, complemented
35#14582952C2211yescharacteristic, complemented
36#14582861C2212yes—
37#14582861C2212yes—
38#14582861C2212yescomplemented
39C22⋊C8×D43C2212yescomplemented
40#14582625C2212yescomplemented
41#14582623C2212yes—
42#14582622C2212yes—
43#14582622C2212yes—
44#14582622C2212yescomplemented
45#14582622C2212yescomplemented
46C2×#126×C43C2211yescharacteristic
47C43×#432C2211yescharacteristic, complemented
48C43×#431C2211yescharacteristic, complemented
49C43×#324C2212yescomplemented
50C43×#323C2212yes—
51C24×D43C2×C411yescharacteristic
52C22×Dic86C2×C411yescharacteristic
53C22×D172C2×C411yescharacteristic
54C22×D172C2×C411yescharacteristic
55C22×D172C2×C411yescharacteristic
56C22×D172C2×C411yescharacteristic
57C22×D172C2×C411yescharacteristic
58C22×C22⋊D43C2×C411yescharacteristic
59C22×C22⋊D43C2×C411yescharacteristic
60C22×C4×D43C2×C411yescharacteristic
61C22×C4×D43C2×C411yescharacteristic
62C22×C4×D43C2311yescharacteristic
63C22×C4×D43C2311yescharacteristic
64C2×#10621872—22no—
65C2×#10621872—22no—
66C2×#10621872—22no—
67C2×C8×D43—22no—
68#13063320—22no—
69#13063320—22no—
70#13063313—21no—
71#13063313—21no—
72#13063313—21no—
73#13063313—21no—
74#13063311—22no—
75#13063311—22no—
76#13063310—22no—
77#13063310—22no—
78#13063307—22no—
79#13063307—22no—
80#13063303—22no—
81#13063303—22no—
82#13063300—22no—
83#13063300—22no—
84#13063300—22no—
85#13063300—22no—
86#13063298—22no—
87#13063298—22no—
88#13063295—22no—
89#13063295—22no—
90#13063295—22no—
91#13063295—22no—
92C4×D172D412yes—
93C4×D172D412yes—
94C4×D172D412yes—
95C4×D172D412yes—
96#13063287—22no—
97#13063287—22no—
98C2×C4⋊Dic43C2×C411yescharacteristic
99C2×Dic43⋊C4C2×C411yescharacteristic
100C2×Dic43⋊C4C2×C411yescharacteristic
101C2×C22⋊Dic43C2×C411yescharacteristic
102C2×(C2×D43)⋊C4C2×C411yescharacteristic
103C2×(C2×D43)⋊C4C2×C411yescharacteristic
104C2×(C2×D43)⋊C4C2×C411yescharacteristic
105C2×(C2×D43)⋊C4C2×C411yescharacteristic
106C2×(C2×D43)⋊C4C2×C411yescharacteristic
107C2×(C2×D43)⋊C4C2×C411yescharacteristic
108C2×(C2×D43)⋊C4C2×C411yescharacteristic
109C2×(C2×D43)⋊C4C2×C411yescharacteristic
110C2×(C2×D43)⋊C4C2311yescharacteristic
111C2×(C2×D43)⋊C4C2311yescharacteristic
112C22⋊C4×D43—22no—
113C22⋊C4×D43—22no—
114C2×C4×Dic43C2×C411yescharacteristic
115C4⋊(C43⋊C8)—21no—
116C4⋊(C43⋊C8)—21no—
117C22⋊(C43⋊C8)C2312yes—
118C22⋊(C43⋊C8)C2312yes—
119(C2×D43)⋊C8—22no—
120(C2×D43)⋊C8—22no—
121(C2×D43)⋊C8—22no—
122(C2×D43)⋊C8—22no—
123#13063236—21no—
124C4×C43⋊C8—21no—
125#126×C43—21no—
126#126×C43—21no—
127#126×C43—21no—
128#126×C43—21no—
129C2×C4⋊C4×C43C2×C411yescharacteristic
130C2×C4⋊C4×C43C2×C411yescharacteristic
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C22⋊C4×C43C2×C411yescharacteristic
133C2×C22⋊C4×C43C2×C411yescharacteristic
134C2×C22⋊C4×C43C2311yescharacteristic
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43—21no—
138C22⋊C8×C43C2312yes—
139C22⋊C8×C43C2312yes—
140#97×C43—21no—
141C4×C8×C43—21no—
142C24×C43C22×C411yescharacteristic
143C23×D43—22no—
144C23×D43—42no—
145C23×D43—81no—
146C23×D43—81no—
147C23×D43C22×C411yescharacteristic
148C23×D43C22×C411yescharacteristic
149C23×D43C22×C411yescharacteristic
150C23×D43C22×C411yescharacteristic
151C22×C4×C43C22×C411yescharacteristic
152C22×C4×C43C22×C411yescharacteristic
153C22×C4×C43C22×C411yescharacteristic
154C22×C4×C43C22×C411yescharacteristic
155C22×C4×C43C22×C411yescharacteristic
156C22×C4×C43C2411yescharacteristic
157C2×C22⋊D43—22no—
158C2×C22⋊D43—22no—
159C2×C22⋊D43—81no—
160C2×C22⋊D43—81no—
161C22×Dic43C22×C411yescharacteristic
162C22×Dic43C22×C411yescharacteristic
163C22×Dic43C22×C411yescharacteristic
164C22×Dic43C22×C411yescharacteristic
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—22no—
168C2×D172—22no—
169C2×D172—22no—
170C2×D172—42no—
171C2×D172—42no—
172C2×D172—81no—
173C2×D172—81no—
174C2×D172—81no—
175C2×D172C22⋊C412yes—
176C2×D172C22⋊C412yes—
177C2×C4×D43—22no—
178C2×C4×D43—22no—
179C2×C4×D43—81no—
180C2×C4×D43—81no—
181C2×C4×D43—81no—
182C2×C4×D43—81no—
183C2×C4×D43C2×D412yes—
184C2×C4×D43C2×D412yes—
185C2×C4×D43C2×D412yes—
186C2×C4×D43C2×D412yes—
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86—81no—
190C2×C8×C43—22no—
191C2×C8×C43—22no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C22⋊C4×C43—21no—
199C22⋊C4×C43—21no—
200C22⋊C4×C43—21no—
201C22⋊C4×C43—21no—
202C22⋊C4×C43—21no—
203C22⋊C4×C43—21no—
204C42×C43C2×D411yescharacteristic
205C42×C43C2×D411yescharacteristic
206C42×C43C2×D411yescharacteristic
207C42×C43C2×D411yescharacteristic
208C22⋊Dic43—22no—
209(C2×D43)⋊C4—21no—
210(C2×D43)⋊C4—21no—
211(C2×D43)⋊C4—21no—
212(C2×D43)⋊C4—21no—
213(C2×D43)⋊C4—21no—
214(C2×D43)⋊C4—21no—
215(C2×D43)⋊C4—21no—
216(C2×D43)⋊C4—21no—
217(C2×D43)⋊C4—22no—
218(C2×D43)⋊C4—22no—
219(C2×D43)⋊C4—22no—
220(C2×D43)⋊C4—22no—
221(C2×D43)⋊C4C22⋊C412yes—
222(C2×D43)⋊C4C22⋊C412yes—
223(C2×D43)⋊C4C22⋊C412yes—
224(C2×D43)⋊C4C22⋊C412yes—
225C4⋊Dic43C22⋊C412yes—
226C4⋊Dic43C22⋊C412yes—
227Dic43⋊C4—22no—
228Dic43⋊C4—22no—
229C4×Dic43—22no—
230C2×C43⋊C8—22no—
231C2×C43⋊C8—22no—
232#10621872—82no—
233#10621872—82no—
234#10621872—82no—
235C8×D43—82no—
236C23×C43—21no—
237C23×C43—22no—
238C23×C43—41no—
239C23×C43—41no—
240C23×C43C23×C411yescharacteristic
241C22×D43—22no—
242C22×D43—22no—
243C22×D43—21no—
244C22×D43—21no—
245C22×D43—22no—
246C22×D43—22no—
247C22×D43—41no—
248C22×D43—41no—
249C22×D43—41no—
250C22×D43—41no—
251C22×D43—44no—
252C22×D43—41no—
253C22×D43—41no—
254C22×D43—41no—
255C22×D43—41no—
256C22×D43—82no—
257C22×D43—82no—
258C22×D43—88no—
259C22×D43C2×C22⋊C412yes—
260C22×D43C2×C22⋊C412yes—
261C2×C4×C43—22no—
262C2×C4×C43—21no—
263C2×C4×C43—21no—
264C2×C4×C43—21no—
265C2×C4×C43—22no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
269C2×C4×C43—41no—
270C2×C4×C43C2×C22⋊C411yescharacteristic
271C2×C4×C43C2×C22⋊C411yescharacteristic
272C2×C4×C43C2×C22⋊C411yescharacteristic
273C2×C4×C43C2×C22⋊C411yescharacteristic
274C2×C4×C43C22×D411yescharacteristic
275C2×C4×C43C22×D411yescharacteristic
276C22⋊D43—82no—
277C22⋊D43—82no—
278C2×Dic43—21no—
279C2×Dic43—21no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43C2×C22⋊C412yes—
285C2×Dic43C2×C22⋊C412yes—
286D172—42no—
287D172—42no—
288D172—44no—
289D172—81no—
290D172—81no—
291D172—82no—
292D172—82no—
293C4×D43—42no—
294C4×D43—42no—
295C4×D43—42no—
296C4×D43—42no—
297C4×D43—82no—
298C4×D43—82no—
299Dic86—81no—
300Dic86—81no—
301C8×C43—42no—
302C8×C43—42no—
303C43⋊C8—42no—
304C43⋊C8—42no—
305#17405—431nomaximal, Sylow
306C22×C43—21no—
307C22×C43—21no—
308C22×C43—41no—
309C22×C43—41no—
310C22×C43—41no—
311C22×C43—82no—
312C22×C43C22×C22⋊C411yescharacteristic
313C22×C43#56812yes—
314C2×D43—22no—
315C2×D43—22no—
316C2×D43—22no—
317C2×D43—22no—
318C2×D43—22no—
319C2×D43—22no—
320C2×D43—44no—
321C2×D43—41no—
322C2×D43—41no—
323C2×D43—41no—
324C2×D43—41no—
325C2×D43—41no—
326C2×D43—41no—
327C2×D43—82no—
328C2×D43—88no—
329C2×D43—82no—
330C2×D43—82no—
331C4×C43—21no—
332C4×C43—21no—
333C4×C43—21no—
334C4×C43—21no—
335C4×C43—21no—
336C4×C43—21no—
337C4×C43—41no—
338C4×C43—41no—
339C4×C43—41no—
340Dic43—22no—
341Dic43—22no—
342Dic43—41no—
343Dic43—41no—
344C2×#538—431no—
345#2975—431no—
346#2973—431no—
347#1473—431no—
348#1473D4311yescharacteristic, complemented
349#1471—432no—
350#1469—431no—
351#1469—431no—
352#1468—432no—
353#1465—432no—
354#1462—432no—
355C2×C43—22no—
356C2×C43—81no—
357C2×C43#287911yescharacteristic
358C2×C43#288311yescharacteristic
359C2×C43#288811yescharacteristic
360D43—42no—
361D43—42no—
362D43—81no—
363D43—81no—
364#538—862no—
365#538—862no—
366#538—862no—
367#538—862no—
368C2×#126—431no—
369C2×#126C2×D4311yescharacteristic
370C2×#124—431no—
371C2×#124—431no—
372C2×#123—431no—
373C2×#123—431no—
374C2×C22⋊Q8—431no—
375C2×#121—431no—
376C2×#121—431no—
377C2×#121—431no—
378C2×#120—431no—
379C2×#120—431no—
380C2×C4×D4—431no—
381C2×C4×D4—431no—
382C22×C22⋊C4—431no—
383#436—862no—
384#436—862no—
385#435—862no—
386#435—862no—
387#432—431no—
388#432C2×D4311yescharacteristic, complemented
389#431—431no—
390#431C2×D4311yescharacteristic, complemented
391#407—432no—
392#407—432no—
393#407—432no—
394C2×C22⋊C8—432no—
395#324—432no—
396#324C2×D4312yescomplemented
397#323—432no—
398#323—432no—
399#323—432no—
400#323—432no—
401#323—432no—
402#323C2×D4312yes—
403C43#1740511yescharacteristic, complemented, Sylow
404C25—431no—
405C22×Q8—431no—
406C22×D4—431no—
407C22×D4—431no—
408C22×D4—431no—
409C22×D4—431no—
410C22×D4—431no—
411C22×D4—431no—
412C22×D4—431no—
413C23×C4—431no—
414C23×C4—431no—
415C23×C4—431no—
416C23×C4—431no—
417C2×M16—862no—
418C2×M16—862no—
419C2×M16—862no—
420C22×C8—862no—
421#126—21no—
422#126—21no—
423#126—21no—
424#126—21no—
425#126—862no—
426#126—862no—
427#124—862no—
428#124—862no—
429#124—861no—
430#124—861no—
431#124—861no—
432#124—861no—
433#123—862no—
434#123—862no—
435#123—862no—
436#123—862no—
437C22⋊Q8—862no—
438C22⋊Q8—862no—
439#121—862no—
440#121—862no—
441#121—862no—
442#121—862no—
443#121—862no—
444#121—862no—
445#120—862no—
446#120—862no—
447#120—862no—
448#120—862no—
449C4×D4—432no—
450C4×D4—432no—
451C4×D4—432no—
452C4×D4—432no—
453C4×D4—862no—
454C4×D4—862no—
455C2×C4⋊C4—431no—
456C2×C4⋊C4—431no—
457C2×C4⋊C4—431no—
458C2×C4⋊C4C4×D4311yescharacteristic
459C2×C4⋊C4C4×D4311yescharacteristic
460C2×C4⋊C4C22×D4311yescharacteristic
461C2×C22⋊C4—431no—
462C2×C22⋊C4—431no—
463C2×C22⋊C4—431no—
464C2×C22⋊C4—431no—
465C2×C22⋊C4—431no—
466C2×C22⋊C4—431no—
467C2×C22⋊C4—431no—
468C2×C22⋊C4—431no—
469C2×C22⋊C4—431no—
470C2×C22⋊C4—431no—
471C2×C22⋊C4—431no—
472C2×C22⋊C4—862no—
473C2×C22⋊C4—862no—
474C2×C22⋊C4C4×D4311yescharacteristic
475C2×C22⋊C4C4×D4311yescharacteristic
476C2×C22⋊C4C22×D4311yescharacteristic
477C2×C42—431no—
478C2×C42C22×D4311yescharacteristic
479C4⋊C8—21no—
480C4⋊C8—21no—
481C4⋊C8—861no—
482C4⋊C8—861no—
483C22⋊C8—432no—
484C22⋊C8—432no—
485C22⋊C8—862no—
486C22⋊C8—862no—
487C22⋊C8—862no—
488C22⋊C8—862no—
489C22⋊C8C22×D4312yes—
490C22⋊C8C22×D4312yes—
491#97—21no—
492#97—861no—
493C4×C8—21no—
494C4×C8—861no—
495C24—431no—
496C24—431no—
497C24—431no—
498C24—431no—
499C24—862no—
500C24—3441no—
501C24—3441no—
502C24—1722no—
503C24C2×C4×D4311yescharacteristic
504C2×Q8—861no—
505C2×Q8—861no—
506C2×Q8—3441no—
507C2×D4—432no—
508C2×D4—432no—
509C2×D4—862no—
510C2×D4—862no—
511C2×D4—862no—
512C2×D4—862no—
513C2×D4—862no—
514C2×D4—861no—
515C2×D4—861no—
516C2×D4—3441no—
517C2×D4—3441no—
518C2×D4—3441no—
519C2×D4—3441no—
520C2×D4—3441no—
521C2×D4—1722no—
522C2×D4—1722no—
523C22×C4—431no—
524C22×C4—431no—
525C22×C4—432no—
526C22×C4—432no—
527C22×C4—432no—
528C22×C4—432no—
529C22×C4—431no—
530C22×C4—431no—
531C22×C4—862no—
532C22×C4—862no—
533C22×C4—3441no—
534C22×C4—3441no—
535C22×C4—3441no—
536C22×C4—3441no—
537C22×C4C2×C4×D4311yescharacteristic
538C22×C4C2×C4×D4311yescharacteristic
539C22×C4C2×C4×D4311yescharacteristic
540C22×C4C2×C4×D4311yescharacteristic
541C22×C4C2×C4×D4311yescharacteristic
542C22×C4C23×D4311yescharacteristic
543M16—3442no—
544M16—3442no—
545M16—3442no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—862no—
549C2×C8—862no—
550C2×C8—3442no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—432no—
558C4⋊C4—432no—
559C4⋊C4—862no—
560C4⋊C4—862no—
561C22⋊C4—21no—
562C22⋊C4—21no—
563C22⋊C4—21no—
564C22⋊C4—21no—
565C22⋊C4—21no—
566C22⋊C4—21no—
567C22⋊C4—432no—
568C22⋊C4—432no—
569C22⋊C4—432no—
570C22⋊C4—432no—
571C22⋊C4—862no—
572C22⋊C4—862no—
573C22⋊C4—862no—
574C22⋊C4—862no—
575C22⋊C4—862no—
576C22⋊C4—861no—
577C22⋊C4—861no—
578C22⋊C4—861no—
579C22⋊C4—861no—
580C22⋊C4—861no—
581C22⋊C4—861no—
582C22⋊C4—861no—
583C22⋊C4—861no—
584C42—862no—
585C42D4×D4311yescharacteristic
586C42D4×D4311yescharacteristic
587C42D4×D4311yescharacteristic
588C42D4×D4311yescharacteristic
589C23—21no—
590C23—22no—
591C23—41no—
592C23—41no—
593C23—432no—
594C23—432no—
595C23—862no—
596C23—862no—
597C23—862no—
598C23—862no—
599C23—861no—
600C23—861no—
601C23—3442no—
602C23—3442no—
603C23—3448no—
604C23—1721no—
605C23—1721no—
606C23—1721no—
607C23—1721no—
608C23—1721no—
609C23—1721no—
610C23—1721no—
611C23—1721no—
612C23—1724no—
613C23C22×C4×D4311yescharacteristic
614Q8—3441no—
615Q8—3441no—
616D4—3441no—
617D4—3441no—
618D4—3442no—
619D4—3442no—
620D4—3442no—
621D4—3442no—
622D4—1722no—
623D4—1722no—
624D4—1724no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—432no—
635C2×C4—432no—
636C2×C4—861no—
637C2×C4—861no—
638C2×C4—3442no—
639C2×C4—3442no—
640C2×C4—1722no—
641C2×C4—1722no—
642C2×C4—1722no—
643C2×C4—1722no—
644C2×C4—1721no—
645C2×C4—1721no—
646C2×C4—1721no—
647C2×C4—1721no—
648C2×C4C22⋊C4×D4311yescharacteristic
649C2×C4C22⋊C4×D4311yescharacteristic
650C2×C4C22⋊C4×D4311yescharacteristic
651C2×C4C22⋊C4×D4311yescharacteristic
652C2×C4C2×D4×D4311yescharacteristic
653C2×C4C2×D4×D4311yescharacteristic
654C8—42no—
655C8—42no—
656C8—1722no—
657C8—1722no—
658C22—21no—
659C22—21no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—82no—
664C22—862no—
665C22—862no—
666C22—862no—
667C22—862no—
668C22—862no—
669C22—862no—
670C22—3442no—
671C22—3442no—
672C22—3442no—
673C22—3448no—
674C22—1724no—
675C22—1721no—
676C22—1721no—
677C22—1721no—
678C22—1721no—
679C22—1721no—
680C22—1721no—
681C22C2×C22⋊C4×D4311yescharacteristic
682C22#1458366412yes—
683C4—21no—
684C4—21no—
685C4—21no—
686C4—21no—
687C4—21no—
688C4—21no—
689C4—41no—
690C4—41no—
691C4—41no—
692C4—862no—
693C4—862no—
694C4—1721no—
695C4—1721no—
696C2—22no—
697C2—81no—
698C2—3441no—
699C2—3441no—
700C2—1722no—
701C2—1722no—
702C2#1914303711yescharacteristic
703C2#1914305411yescharacteristic
704C2#1914307211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1473C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583488C2
cosocleC22×C4×C43C24
hypercenter#1473D43
hypocenterC43#17405
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1473

Complements

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

NH ≅ G/Ntype
2. #19143635C2semidirect
3. #19143623C2semidirect
4. #19132964C2semidirect
5. #19132953C2semidirect
6. #19132948C2semidirect
7. #19132946C2semidirect
8. #19132942C2semidirect
9. #19132932C2semidirect
10. #19132920C2semidirect
11. C43×#1473C2semidirect
34. #14582956C22semidirect
35. #14582952C22semidirect
38. #14582861C22semidirect
39. C22⋊C8×D43C22semidirect
40. #14582625C22semidirect
44. #14582622C22semidirect
45. #14582622C22semidirect
47. C43×#432C22semidirect
48. C43×#431C22semidirect
49. C43×#324C22semidirect
348. #1473D43semidirect
388. #432C2×D43semidirect
390. #431C2×D43semidirect
396. #324C2×D43semidirect
403. C43#17405semidirect

Maximal subgroups

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

subgroupindex
C2×#145834882
#191436352
#191436232
#191329642
#191329532
#191329482
#191329462
#191329422
#191329322
#191329202
C43×#14732
#1740543