Finite Group Databasebeta

← #30614174

Subgroups — #30614174

Order 15616.

1458 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840841C211yesmaximal, characteristic
2C2×#16840759C211yesmaximal, characteristic
3#21462384C211yesmaximal, characteristic, complemented
4C2×#16840725C211yesmaximal, characteristic, complemented
5#21461600C212yesmaximal, complemented
6#21461598C212yesmaximal, complemented
7#21461596C212yesmaximal, complemented
8#21461594C212yesmaximal, complemented
9C2×#16840638C211yesmaximal, characteristic, complemented
10#21461499C211yesmaximal, characteristic, complemented
11#416×D61C211yesmaximal, characteristic
12#16840841—24no—
13#16840841C418yescomplemented
14C2×#14519865C2212yes—
15C2×#14519864—22no—
16C2×#14519864C2212yes—
17C22×#11758213—21no—
18C22×#11758213C2211yescharacteristic
19C22×#11758213C2211yescharacteristic
20C2×D61⋊M16—21no—
21C2×D61⋊M16C2211yescharacteristic
22C2×#14519856C2211yescharacteristic
23#16840759C418yescomplemented
24C2×#14519842C2212yes—
25C2×#14519841C2212yes—
26#16840727C2212yescomplemented
27#16840727C2212yescomplemented
28#16840726—22no—
29#16840725—24no—
30C4×#11758213—21no—
31C4×#11758213—21no—
32C2×#14519831C2212yescomplemented
33C2×C8×#6923C2212yescomplemented
34#16840638C2212yescomplemented
35#16840638C2212yescomplemented
36#16840632C2212yescomplemented
37#16840632C2212yescomplemented
38C2×#41×D61C2211yescharacteristic
39C22×C8×D61C2211yescharacteristic
40#117×D61C2211yescharacteristic
41#16839759C411yescharacteristic, complemented
42#16839758C411yescharacteristic, complemented
43#16839757C2211yescharacteristic
44#16839757C2211yescharacteristic
45#16839756C411yescharacteristic, complemented
46#16839755C2211yescharacteristic
47#16839755C2211yescharacteristic
48#103×D61C411yescharacteristic, complemented
49#103×D61C411yescharacteristic, complemented
50#102×D61C411yescharacteristic, complemented
51#102×D61C411yescharacteristic, complemented
52C61×#416C411yescharacteristic, complemented
53#14519865—24no—
54#14519865C2×C418yescomplemented
55#14519864—216no—
56#14519864—24no—
57#14519864C2×C418yescomplemented
58C2×#11758213—21no—
59C2×#11758213—21no—
60C2×#11758213—22no—
61C2×#11758213—22no—
62C2×#11758213—22no—
63C2×#11758213—28no—
64C2×#11758213C2×C414yes—
65C2×#11758213C2×C414yes—
66C2×#11758213D411yescharacteristic
67C2×#11758213D411yescharacteristic
68C2×#11758213C2312yes—
69C2×#11758213C2312yes—
70D61⋊M16—28no—
71D61⋊M16C2×C414yes—
72D61⋊M16D414yes—
73C2×#11758217—22no—
74C2×#11758217D412yes—
75C2×D61⋊C8—22no—
76C2×D61⋊C8C2312yes—
77C22×#92420—21no—
78C22×#92420—21no—
79C22×#92420—22no—
80#14519856—22no—
81#14519856C2×C414yes—
82C2×C4⋊#6923—21no—
83C2×C22⋊#6923—21no—
84C2×C4×#6923C2312yes—
85#14519842C2×C418yescomplemented
86#14519841C2×C418yescomplemented
87#14519832—22no—
88#14519832—22no—
89#14519831—24no—
90C4×#92420—22no—
91C4×#92420—22no—
92C8×#6923—24no—
93C2×#11758226C2311yescharacteristic
94C2×#11758222—21no—
95C2×#11758222C2×C411yescharacteristic
96C2×#11758224—21no—
97C2×#11758224C2311yescharacteristic
98#41×D61—22no—
99#41×D61—22no—
100#41×D61C2×C414yes—
101#41×D61C2×C414yes—
102C2×Q8×D61C2×C411yescharacteristic
103C2×D4×D61—21no—
104C2×D4×D61C2×C411yescharacteristic
105C22×C4×D61—21no—
106C22×C4×D61C2311yescharacteristic
107C22×#92418C2×C411yescharacteristic
108C2×C8×D61—22no—
109C2×C8×D61—22no—
110C2×C8×D61C2×C411yescharacteristic
111C2×C8×D61C2×C411yescharacteristic
112C2×C8×D61C2311yescharacteristic
113C2×C8×D61C2311yescharacteristic
114#14519736C2×C411yescharacteristic
115#14519735C2311yescharacteristic
116#14519735C2311yescharacteristic
117#14519734—21no—
118#14519733—21no—
119C4⋊C4×D61C2×C411yescharacteristic
120C4⋊C4×D61C2×C411yescharacteristic
121C22⋊C4×D61—21no—
122C42×D61—21no—
123#14519702C2×C411yescharacteristic
124#14519702C2×C411yescharacteristic
125#14519701C2×C411yescharacteristic
126#14519701C2×C411yescharacteristic
127#14519700C2×C411yescharacteristic
128#14519700C2×C411yescharacteristic
129#14519699C2×C411yescharacteristic
130#14519699C2×C411yescharacteristic
131#14519698C2×C411yescharacteristic
132#14519698C2×C411yescharacteristic
133#14519697C2×C411yescharacteristic
134#14519697C2×C411yescharacteristic
135C2×#41×C61C2×C411yescharacteristic
136C22×C8×C61C2×C411yescharacteristic
137#117×C61C2×C411yescharacteristic
138#103×C61C2×C411yescharacteristic
139#103×C61C2×C411yescharacteristic
140#102×C61C2×C411yescharacteristic
141#102×C61C2×C411yescharacteristic
142C23×D61—21no—
143C23×D61#4111yescharacteristic
144C22×#6923—22no—
145#41×C61—22no—
146#41×C61C4214yes—
147C2×Q8×C61C22×C411yescharacteristic
148C2×D4×C61—21no—
149C2×D4×C61C22×C411yescharacteristic
150C22×C4×C61—21no—
151C22×C4×C61C22×C411yescharacteristic
152C2×C22⋊D61—21no—
153C2×C22⋊D61—21no—
154C2×C22⋊D61—21no—
155C22×Dic61—21no—
156C22×Dic61C2×D411yescharacteristic
157#11758226—21no—
158#11758226—21no—
159#11758226C22×C412yes—
160#11758226C22×C412yes—
161Q8×D61—22no—
162Q8×D61C4214yes—
163#11758224—24no—
164#11758224—24no—
165#11758224—21no—
166#11758224—21no—
167#11758224C22×C412yes—
168#11758224C22×C412yes—
169D4×D61—24no—
170D4×D61—24no—
171D4×D61—22no—
172D4×D61C4214yes—
173#11758222—22no—
174#11758222—24no—
175#11758222—24no—
176#11758222C4214yes—
177C2×D244—21no—
178C2×D244C22×C411yescharacteristic
179C2×C4×D61—21no—
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—24no—
183C2×C4×D61—24no—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61C22×C411yescharacteristic
187C2×C4×D61C22×C412yes—
188C2×C4×D61C22×C412yes—
189C2×C4×D61C2×D411yescharacteristic
190C2×C4×D61C2×D412yes—
191C2×C4×D61#4111yescharacteristic
192C2×C4×D61#4112yes—
193C2×C4×D61C2411yescharacteristic
194C2×Dic122—21no—
195C2×Dic122C22×C411yescharacteristic
196C22⋊#6923—24no—
197#11758217—28no—
198#11758217C22⋊C418yes—
199C2×#92420—24no—
200C2×#92420—24no—
201C2×#92420—22no—
202C2×#92420—22no—
203C2×#92420—28no—
204C2×#92420C2×D412yes—
205C2×#92420C2×D412yes—
206C4⋊#6923—24no—
207C4×#6923—22no—
208C4×#6923C22×C414yes—
209#11758213—24no—
210#11758213—24no—
211#11758213—22no—
212#11758213—22no—
213#11758213—28no—
214#11758213C22⋊C414yes—
215#11758213C22⋊C414yes—
216#11758213C22×C414yes—
217#11758213C22×C414yes—
218D61⋊C8—28no—
219D61⋊C8C22×C414yes—
220D61⋊C8C2×D414yes—
221C2×C8×C61—22no—
222C2×C8×C61C22×C411yescharacteristic
223C2×C8×C61C22×C411yescharacteristic
224C4⋊C4×C61C22×C411yescharacteristic
225C4⋊C4×C61C22×C411yescharacteristic
226C22⋊C4×C61—21no—
227C42×C61—21no—
228C22⋊Dic61—21no—
229#11758198—21no—
230#11758198—21no—
231C4⋊Dic61C22×C411yescharacteristic
232C4⋊Dic61C22×C411yescharacteristic
233#11758196—21no—
234#11758196—21no—
235C4×Dic61—21no—
236C4×Dic61—21no—
237C4×Dic61—21no—
238C2×#92418—22no—
239C2×#92418C22×C411yescharacteristic
240C2×#92418C22×C411yescharacteristic
241C8×D61—22no—
242C8×D61—22no—
243C8×D61—21no—
244C8×D61—21no—
245C8×D61—21no—
246C8×D61—21no—
247C23×C61—21no—
248C23×C61C4×D411yescharacteristic
249C22×D61—21no—
250C22×D61—24no—
251C22×D61—41no—
252C22×D61—41no—
253C22×D61—81no—
254C22×D61—81no—
255C22×D61#11712yes—
256C22×D61C4×D411yescharacteristic
257C22×D61C4×D412yes—
258C22×D61C2×#4111yescharacteristic
259C2×#6923—24no—
260C2×#6923—42no—
261C2×#6923—42no—
262Q8×C61—21no—
263Q8×C61C2×C4212yes—
264D4×C61—24no—
265D4×C61—21no—
266D4×C61C2×C4212yes—
267C2×C4×C61—21no—
268C2×C4×C61—24no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61C2×C4212yes—
272C2×C4×C61C4×D412yes—
273C2×C4×C61C4×D411yescharacteristic
274C2×C4×C61C23×C411yescharacteristic
275C22⋊D61—24no—
276C22⋊D61—22no—
277C22⋊D61—22no—
278C22⋊D61—24no—
279C2×Dic61—21no—
280C2×Dic61—22no—
281C2×Dic61—22no—
282C2×Dic61—21no—
283C2×Dic61—21no—
284C2×Dic61C2×C22⋊C412yes—
285C2×Dic61C4×D412yes—
286C2×Dic61C4×D411yescharacteristic
287C2×Dic61C22×D411yescharacteristic
288D244—22no—
289D244—22no—
290D244—21no—
291D244C2×C4212yes—
292C4×D61—24no—
293C4×D61—24no—
294C4×D61—22no—
295C4×D61—22no—
296C4×D61—81no—
297C4×D61—81no—
298C4×D61C2×C4212yes—
299C4×D61C2×C22⋊C412yes—
300C4×D61#11712yes—
301C4×D61C4×D412yes—
302C4×D61C4×D412yes—
303C4×D61C4×D412yes—
304C4×D61C23×C411yescharacteristic
305C4×D61C23×C411yescharacteristic
306C4×D61C22×D411yescharacteristic
307C4×D61C2×#4111yescharacteristic
308Dic122—21no—
309Dic122—24no—
310Dic122C2×C4212yes—
311#92420—24no—
312#92420—24no—
313#92420C2×C22⋊C414yes—
314#92420C2×C22⋊C414yes—
315C8×C61—21no—
316C8×C61—21no—
317#92418—21no—
318#92418—21no—
319#20422—611nomaximal, Sylow
320C22×C61—21no—
321C22×C61—21no—
322C22×C61—22no—
323C22×C61—41no—
324C22×C61—41no—
325C22×C61C4×C22⋊C412yes—
326C22×C61C2×C4×D411yescharacteristic
327C2×D61—21no—
328C2×D61—21no—
329C2×D61—21no—
330C2×D61—21no—
331C2×D61—22no—
332C2×D61—42no—
333C2×D61—42no—
334C2×D61—41no—
335C2×D61—41no—
336C2×D61—84no—
337C2×D61C4×C22⋊C412yes—
338C2×D61C2×#11711yescharacteristic
339C2×D61C2×C4×D411yescharacteristic
340#6923—44no—
341C4×C61—22no—
342C4×C61—41no—
343C4×C61—41no—
344C4×C61C4×C22⋊C412yes—
345C4×C61C22×C4211yescharacteristic
346C4×C61C2×C4×D411yescharacteristic
347Dic61—22no—
348Dic61—41no—
349Dic61—41no—
350Dic61C4×C22⋊C412yes—
351Dic61C22×C22⋊C411yescharacteristic
352Dic61C2×C4×D411yescharacteristic
353C2×#568—611no—
354C2×#421—611no—
355C2×#416—611no—
356#2873—611no—
357C2×#405—611no—
358#1765—612no—
359#1765—612no—
360#1764—612no—
361#1764—612no—
362C2×#341—611no—
363#1733—611no—
364C2×C61—22no—
365C2×C61—42no—
366C2×C61C2×C4×C22⋊C411yescharacteristic
367C2×C61#295711yescharacteristic
368C2×C61#295711yescharacteristic
369D61—21no—
370D61—22no—
371D61—21no—
372D61—42no—
373C22×#41—611no—
374#568—618no—
375#568—1224no—
376C2×#131—612no—
377C2×#131—612no—
378C2×#131—1222no—
379C22×M16—611no—
380C22×M16—611no—
381C22×M16—611no—
382C22×M16—1221no—
383C22×M16—1221no—
384C23×C8—611no—
385C2×#117—611no—
386C2×#117—611no—
387#421—618no—
388C2×#104—612no—
389C2×#104—612no—
390#416—611no—
391#416—611no—
392#416—611no—
393#416—611no—
394#416—611no—
395#416—611no—
396#416—611no—
397#416#692311yescharacteristic, complemented
398C2×#103—611no—
399C2×#103—611no—
400C2×#102—611no—
401C2×#102—611no—
402#405—612no—
403#405—612no—
404#405—1224no—
405#405—1222no—
406C4×M16—1221no—
407C4×M16—1221no—
408C2×#97—612no—
409C2×C4×C8—612no—
410#341—612no—
411#341—612no—
412#339—612no—
413#339—612no—
414C61#2042211yescharacteristic, complemented, Sylow
415C2×#41—614no—
416C2×#41—614no—
417C2×#41—611no—
418C2×#41—611no—
419C2×#41—611no—
420C2×#41—1221no—
421C2×#41—1221no—
422C2×#41—1222no—
423C2×#41—1222no—
424C2×#41C2×#692311yescharacteristic
425C22×Q8—611no—
426C22×D4—611no—
427C22×D4—1221no—
428C23×C4—611no—
429C23×C4—1221no—
430#131—618no—
431#131—618no—
432#131—1224no—
433#131—1224no—
434#131—12216no—
435C2×M16—612no—
436C2×M16—611no—
437C2×M16—611no—
438C2×M16—614no—
439C2×M16—614no—
440C2×M16—612no—
441C2×M16—614no—
442C2×M16—614no—
443C2×M16—612no—
444C2×M16—1222no—
445C2×M16—1222no—
446C2×M16—1228no—
447C2×M16—1228no—
448C2×M16—1221no—
449C2×M16—1222no—
450C2×M16—1222no—
451C2×M16—1221no—
452C22×C8—612no—
453C22×C8—611no—
454C22×C8—611no—
455C22×C8—611no—
456C22×C8—611no—
457C22×C8—611no—
458C22×C8—1222no—
459C22×C8—1222no—
460C22×C8—1222no—
461C22×C8—1222no—
462C22×C8—1221no—
463C22×C8—1221no—
464C22×C8C2×#692311yescharacteristic
465#117—614no—
466#117—611no—
467#117—611no—
468#117—611no—
469#117—1221no—
470#117—1221no—
471#117—1222no—
472#117C2×#692311yescharacteristic
473C2×C4⋊C4—611no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4—1221no—
476C2×C22⋊C4—1221no—
477C2×C22⋊C4—1221no—
478C2×C42—612no—
479C2×C42—1221no—
480#104—618no—
481#104—618no—
482#103—611no—
483#103—611no—
484#103—611no—
485#103—611no—
486#103—611no—
487#103—611no—
488#103C2×#692311yescharacteristic
489#103C2×#692311yescharacteristic
490#102—611no—
491#102—611no—
492#102—611no—
493#102—611no—
494#102—611no—
495#102—611no—
496#102C2×#692311yescharacteristic
497#102C2×#692311yescharacteristic
498#97—1224no—
499#97—1222no—
500#97—1222no—
501C4×C8—1224no—
502C4×C8—1222no—
503C4×C8—1222no—
504C24—611no—
505C24—1221no—
506#41—22no—
507#41—612no—
508#41—612no—
509#41—612no—
510#41—612no—
511#41—614no—
512#41—1224no—
513#41—1224no—
514#41—1224no—
515#41—1221no—
516#41—1224no—
517#41—1221no—
518#41—1221no—
519#41—1221no—
520#41—1222no—
521#41C4×#692314yes—
522C2×Q8—614no—
523C2×Q8—611no—
524C2×Q8—1221no—
525C2×Q8—1222no—
526C2×Q8C22×#692311yescharacteristic
527C2×D4—21no—
528C2×D4—614no—
529C2×D4—611no—
530C2×D4—1221no—
531C2×D4—1222no—
532C2×D4—1221no—
533C2×D4—1224no—
534C2×D4—1224no—
535C2×D4—1221no—
536C2×D4—1221no—
537C2×D4C22×#692311yescharacteristic
538C22×C4—21no—
539C22×C4—611no—
540C22×C4—612no—
541C22×C4—612no—
542C22×C4—611no—
543C22×C4—611no—
544C22×C4—612no—
545C22×C4—612no—
546C22×C4—611no—
547C22×C4—611no—
548C22×C4—1221no—
549C22×C4—1224no—
550C22×C4—1224no—
551C22×C4—1221no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—1222no—
557C22×C4C22×#692311yescharacteristic
558M16—614no—
559M16—614no—
560M16—618no—
561M16—614no—
562M16—614no—
563M16—1228no—
564M16—1228no—
565M16—1224no—
566M16—1222no—
567M16—1222no—
568M16—1224no—
569C2×C8—22no—
570C2×C8—612no—
571C2×C8—612no—
572C2×C8—614no—
573C2×C8—614no—
574C2×C8—611no—
575C2×C8—611no—
576C2×C8—1221no—
577C2×C8—1221no—
578C2×C8—1222no—
579C2×C8—1222no—
580C2×C8—1221no—
581C2×C8—1221no—
582C2×C8—1228no—
583C2×C8—1228no—
584C2×C8—1222no—
585C2×C8—1222no—
586C2×C8—1224no—
587C2×C8—1224no—
588C2×C8—1222no—
589C2×C8C22×#692311yescharacteristic
590C2×C8C22×#692311yescharacteristic
591C4⋊C4—611no—
592C4⋊C4—611no—
593C4⋊C4—1221no—
594C4⋊C4—1221no—
595C4⋊C4—1224no—
596C4⋊C4C22×#692311yescharacteristic
597C4⋊C4C22×#692311yescharacteristic
598C22⋊C4—21no—
599C22⋊C4—1221no—
600C22⋊C4—1221no—
601C22⋊C4—1224no—
602C22⋊C4—1221no—
603C42—21no—
604C42—614no—
605C42—1221no—
606C42—1221no—
607C42—1222no—
608C42—1221no—
609C23—21no—
610C23—611no—
611C23—611no—
612C23—612no—
613C23—612no—
614C23—1224no—
615C23—1221no—
616C23—4881no—
617C23—4881no—
618C23—2441no—
619C23—2441no—
620C23D4×#692311yescharacteristic
621Q8—21no—
622Q8—612no—
623Q8—1224no—
624Q8—1221no—
625Q8C2×C4×#692312yes—
626D4—24no—
627D4—21no—
628D4—612no—
629D4—1222no—
630D4—1222no—
631D4—1224no—
632D4—1222no—
633D4—1222no—
634D4—1224no—
635D4—1221no—
636D4C2×C4×#692312yes—
637C2×C4—21no—
638C2×C4—24no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—611no—
642C2×C4—611no—
643C2×C4—612no—
644C2×C4—612no—
645C2×C4—612no—
646C2×C4—611no—
647C2×C4—611no—
648C2×C4—612no—
649C2×C4—611no—
650C2×C4—611no—
651C2×C4—612no—
652C2×C4—612no—
653C2×C4—612no—
654C2×C4—612no—
655C2×C4—1222no—
656C2×C4—1222no—
657C2×C4—1224no—
658C2×C4—1222no—
659C2×C4—1222no—
660C2×C4—1221no—
661C2×C4—1224no—
662C2×C4—1224no—
663C2×C4—1221no—
664C2×C4—1221no—
665C2×C4—4881no—
666C2×C4—4881no—
667C2×C4—2442no—
668C2×C4—2442no—
669C2×C4C2×C4×#692312yes—
670C2×C4D4×#692312yes—
671C2×C4D4×#692311yescharacteristic
672C2×C4C23×#692311yescharacteristic
673C8—21no—
674C8—21no—
675C8—614no—
676C8—614no—
677C8—1224no—
678C8—1224no—
679C8—1221no—
680C8—1221no—
681C22—21no—
682C22—21no—
683C22—22no—
684C22—41no—
685C22—41no—
686C22—611no—
687C22—612no—
688C22—611no—
689C22—1221no—
690C22—1221no—
691C22—1221no—
692C22—1221no—
693C22—1222no—
694C22—4884no—
695C22—2442no—
696C22—2442no—
697C22—2441no—
698C22—2441no—
699C22C22⋊C4×#692312yes—
700C22C2×D4×#692311yescharacteristic
701C4—22no—
702C4—41no—
703C4—41no—
704C4—611no—
705C4—611no—
706C4—612no—
707C4—1222no—
708C4—2444no—
709C4—2441no—
710C4—2441no—
711C4C22⋊C4×#692312yes—
712C4C22×C4×#692311yescharacteristic
713C4C2×D4×#692311yescharacteristic
714C2—22no—
715C2—42no—
716C2—1221no—
717C2—1222no—
718C2—1221no—
719C2—2442no—
720C2C2×C22⋊C4×#692311yescharacteristic
721C2#2146259611yescharacteristic
722C2#2146259811yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC4×C61C22×C42
FrattiniC2×C4C23×#6923
FittingC61×#416C4
socleC22×C61C2×C4×D4
prime radicalC2×#41×D61C22
cosocleC2×C4×D61C24
hypercenter#416#6923
hypocenterC61#20422
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
3. #21462384C2semidirect
4. C2×#16840725C2semidirect
5. #21461600C2semidirect
6. #21461598C2semidirect
7. #21461596C2semidirect
8. #21461594C2semidirect
9. C2×#16840638C2semidirect
10. #21461499C2semidirect
13. #16840841C4semidirect
23. #16840759C4semidirect
26. #16840727C22semidirect
27. #16840727C22semidirect
32. C2×#14519831C22semidirect
33. C2×C8×#6923C22semidirect
34. #16840638C22semidirect
35. #16840638C22semidirect
36. #16840632C22semidirect
37. #16840632C22semidirect
41. #16839759C4semidirect
42. #16839758C4semidirect
45. #16839756C4semidirect
48. #103×D61C4semidirect
49. #103×D61C4semidirect
50. #102×D61C4semidirect
51. #102×D61C4semidirect
52. C61×#416C4semidirect
54. #14519865C2×C4semidirect
57. #14519864C2×C4semidirect
85. #14519842C2×C4semidirect
86. #14519841C2×C4semidirect
397. #416#6923semidirect
414. C61#20422semidirect

Maximal subgroups

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

subgroupindex
C2×#168408412
C2×#168407592
#214623842
C2×#168407252
#214616002
#214615982
#214615962
#214615942
C2×#168406382
#214614992
#416×D612
#2042261