Finite Group Databasebeta

← #29689825

Subgroups — #29689825

Order 15616.

1158 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840298C211yesmaximal, characteristic
2#21448221C211yesmaximal, characteristic, complemented
3#21448213C211yesmaximal, characteristic, complemented
4#21446805C211yesmaximal, characteristic, complemented
5#21446655C211yesmaximal, characteristic
6#21446654C211yesmaximal, characteristic
7#21446276C214yesmaximal, complemented
8#21445806C214yesmaximal, complemented
9C61×#1996C211yesmaximal, characteristic, complemented
10#16840298—21no—
11#16840298—21no—
12#16840298—21no—
13#16840298—21no—
14#16840298—21no—
15#16840298—21no—
16#16840298—21no—
17#16840298—21no—
18C2×#14519772C412yescomplemented
19C2×#14519768C411yescharacteristic, complemented
20C2×#14519766C411yescharacteristic, complemented
21C2×#14519761C2212yes—
22C2×#14519751C2211yescharacteristic
23C2×Q8×Dic61C411yescharacteristic, complemented
24C2×#14519739C411yescharacteristic, complemented
25C2×#14519737C2212yes—
26C2×#14519735C412yescomplemented
27C2×#14519733C2212yes—
28C22×C4×Dic61C2211yescharacteristic
29C2×#14519691C2214yes—
30C2×#14519691C2214yes—
31#16839631—21no—
32#16839629—21no—
33#16839626—21no—
34#16839626—21no—
35#16839623C2212yes—
36#16839622C2211yescharacteristic
37#16839620C2212yes—
38#16839620C2212yes—
39C4⋊C4×Dic61—21no—
40C4×#11758196—21no—
41#16839613—21no—
42C4×C22⋊Dic61C2211yescharacteristic
43#16839608—21no—
44#16839529C2214yes—
45C2×C22⋊Q8×C61C2211yescharacteristic
46C61×#380C2211yescharacteristic
47C4×C22⋊C4×C61C2211yescharacteristic
48C61×#342C2214yes—
49C22×D244C2×C411yescharacteristic
50C22×C22⋊D61C2312yes—
51C23×Dic61C2311yescharacteristic
52C23×Dic61C2311yescharacteristic
53C22×C4×D61C2×C412yes—
54#14519772—22no—
55#14519772—22no—
56#14519772—22no—
57#14519772—22no—
58#14519768—21no—
59#14519768—21no—
60#14519768—21no—
61#14519768—21no—
62#14519766—21no—
63#14519766—21no—
64#14519766—21no—
65#14519766—21no—
66#14519761—22no—
67#14519761—22no—
68#14519761—22no—
69#14519761—22no—
70#14519751—21no—
71#14519751—21no—
72#14519751—21no—
73#14519751—21no—
74Q8×Dic61—21no—
75Q8×Dic61—21no—
76Q8×Dic61—21no—
77Q8×Dic61—21no—
78#14519739—21no—
79#14519739—21no—
80#14519739—21no—
81#14519739—21no—
82#14519737—22no—
83#14519737—22no—
84#14519737—22no—
85#14519737—22no—
86#14519735—22no—
87#14519735—22no—
88#14519735—22no—
89#14519735—22no—
90#14519733—44no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61C2×C412yes—
93C2×C4⋊Dic61C2×C411yescharacteristic
94C2×C4⋊Dic61C2×C412yes—
95C2×#11758196—22no—
96C2×#11758196—22no—
97C2×#11758196—22no—
98C2×#11758196C2×C412yes—
99C2×C22⋊Dic61C2312yes—
100C2×C22⋊Dic61C2312yes—
101C2×#11758198C2×C412yes—
102C2×#11758198C2×C412yes—
103C2×#11758198C2×C412yes—
104C2×#11758198C2×C412yes—
105C2×C4×Dic61—21no—
106C2×C4×Dic61—22no—
107C2×C4×Dic61C2×C412yes—
108C2×C4×Dic61C2×C411yescharacteristic
109C2×C4×Dic61C2×C411yescharacteristic
110C2×C4×Dic61C2×C411yescharacteristic
111C2×C4×Dic61C2×C411yescharacteristic
112C2×C4×Dic61D411yescharacteristic
113C2×C4×Dic61D411yescharacteristic
114C2×C4×Dic61D411yescharacteristic
115C2×C4×Dic61D411yescharacteristic
116C2×C4×Dic61D411yescharacteristic
117C2×C4×Dic61D411yescharacteristic
118C2×C4×Dic61D411yescharacteristic
119C2×C4×Dic61D411yescharacteristic
120#14519691—44no—
121#14519691—44no—
122#14519684—21no—
123#14519684—21no—
124#14519684—22no—
125#14519684—22no—
126#14519684—22no—
127#14519684—22no—
128C22×Q8×C61C2×C411yescharacteristic
129C23×C4×C61C2311yescharacteristic
130C22⋊Q8×C61—21no—
131C22⋊Q8×C61—21no—
132C22⋊Q8×C61—21no—
133C22⋊Q8×C61—21no—
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61C2×C412yes—
136C2×C4⋊C4×C61C2×C411yescharacteristic
137C2×C22⋊C4×C61C2312yes—
138C2×C22⋊C4×C61C2312yes—
139C2×C22⋊C4×C61C2312yes—
140C2×C42×C61—21no—
141#95×C61—21no—
142#95×C61—21no—
143C24×C61C2411yescharacteristic
144C23×D61C22×C412yes—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—42no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—42no—
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C412yes—
153C22×C4×C61C22×C412yes—
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2×D411yescharacteristic
159C2×C22⋊D61—22no—
160C2×C22⋊D61—22no—
161C2×C22⋊D61—24no—
162C2×C22⋊D61—24no—
163C22×Dic61—22no—
164C22×Dic61—22no—
165C22×Dic61—22no—
166C22×Dic61—22no—
167C22×Dic61—42no—
168C22×Dic61C22×C412yes—
169C22×Dic61C22×C411yescharacteristic
170C22×Dic61C22×C411yescharacteristic
171C22×Dic61C22×C411yescharacteristic
172C22×Dic61C22×C411yescharacteristic
173C22×Dic61C2×D411yescharacteristic
174C22×Dic61C2×D411yescharacteristic
175C22×Dic61C2×D411yescharacteristic
176C22×Dic61C2×D411yescharacteristic
177C22×Dic61C2×D411yescharacteristic
178C22×Dic61C2×D411yescharacteristic
179C22×Dic61C2×D411yescharacteristic
180C22×Dic61C2×D411yescharacteristic
181C2×D244—21no—
182C2×D244—21no—
183C2×D244—42no—
184C2×C4×D61—22no—
185C2×C4×D61—22no—
186C2×C4×D61—44no—
187C4⋊C4×C61—22no—
188C4⋊C4×C61—22no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61—42no—
192C22⋊C4×C61—22no—
193C22⋊C4×C61—22no—
194C22⋊C4×C61—22no—
195C22⋊C4×C61—24no—
196C22⋊C4×C61—22no—
197C42×C61—42no—
198C22⋊Dic61—22no—
199C22⋊Dic61—24no—
200C22⋊Dic61—22no—
201#11758198—22no—
202#11758198—22no—
203#11758198—22no—
204#11758198—22no—
205#11758198—22no—
206#11758198—22no—
207#11758198—22no—
208#11758198—22no—
209C4⋊Dic61—21no—
210C4⋊Dic61—21no—
211C4⋊Dic61—22no—
212C4⋊Dic61—22no—
213C4⋊Dic61—22no—
214C4⋊Dic61—22no—
215C4⋊Dic61—42no—
216#11758196—22no—
217#11758196—22no—
218#11758196—44no—
219#11758196—44no—
220#11758196—44no—
221C4×Dic61—22no—
222C4×Dic61—22no—
223C4×Dic61—44no—
224C4×Dic61—42no—
225C4×Dic61C22⋊C411yescharacteristic
226C4×Dic61C22⋊C411yescharacteristic
227C4×Dic61C22⋊C411yescharacteristic
228C4×Dic61C22⋊C411yescharacteristic
229C4×Dic61C22⋊C411yescharacteristic
230C4×Dic61C22⋊C411yescharacteristic
231C4×Dic61C22⋊C411yescharacteristic
232C4×Dic61C22⋊C411yescharacteristic
233C4×Dic61C22⋊C411yescharacteristic
234C4×Dic61C22⋊C411yescharacteristic
235C4×Dic61C22⋊C411yescharacteristic
236C4×Dic61C22⋊C411yescharacteristic
237C4×Dic61C22⋊C411yescharacteristic
238C4×Dic61C22⋊C411yescharacteristic
239C4×Dic61C22⋊C411yescharacteristic
240C4×Dic61C22⋊C411yescharacteristic
241C23×C61—41no—
242C23×C61—41no—
243C23×C61C23×C411yescharacteristic
244C23×C61C22×D411yescharacteristic
245C23×C61C22×D411yescharacteristic
246C23×C61H(5,𝔽2)12yes—
247C23×C612−1+412yes—
248C22×D61—22no—
249C22×D61—24no—
250C22×D61—42no—
251C22×D61—42no—
252Q8×C61—42no—
253Q8×C61—42no—
254C2×C4×C61—22no—
255C2×C4×C61—22no—
256C2×C4×C61—22no—
257C2×C4×C61—22no—
258C2×C4×C61—22no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
261C2×C4×C61—41no—
262C2×C4×C61—42no—
263C2×C4×C61—42no—
264C2×C4×C61—42no—
265C2×C4×C61—42no—
266C2×C4×C61—42no—
267C2×C4×C61—42no—
268C2×C4×C61—42no—
269C2×C4×C61—42no—
270C2×C4×C61C2×C22⋊C411yescharacteristic
271C2×C4×C61C2×C22⋊C411yescharacteristic
272C2×C4×C61C2×C22⋊C411yescharacteristic
273C2×C4×C61C2×C22⋊C411yescharacteristic
274C22⋊D61—42no—
275C22⋊D61—42no—
276C22⋊D61—44no—
277C2×Dic61—22no—
278C2×Dic61—22no—
279C2×Dic61—21no—
280C2×Dic61—21no—
281C2×Dic61—21no—
282C2×Dic61—21no—
283C2×Dic61—22no—
284C2×Dic61—22no—
285C2×Dic61—22no—
286C2×Dic61—22no—
287C2×Dic61—22no—
288C2×Dic61—22no—
289C2×Dic61—24no—
290C2×Dic61—41no—
291C2×Dic61—41no—
292C2×Dic61—41no—
293C2×Dic61—42no—
294C2×Dic61—42no—
295C2×Dic61—42no—
296C2×Dic61—42no—
297C2×Dic61—42no—
298C2×Dic61—42no—
299C2×Dic61C2×C22⋊C411yescharacteristic
300C2×Dic61C2×C22⋊C411yescharacteristic
301C2×Dic61C2×C22⋊C411yescharacteristic
302C2×Dic61C2×C22⋊C411yescharacteristic
303C2×Dic61C2×C22⋊C411yescharacteristic
304C2×Dic61C2×C22⋊C411yescharacteristic
305C2×Dic61C2×C22⋊C411yescharacteristic
306C2×Dic61C2×C22⋊C411yescharacteristic
307D244—42no—
308D244—42no—
309C4×D61—44no—
310C4×D61—44no—
311#21875—611nomaximal, Sylow
312C22×C61—21no—
313C22×C61—21no—
314C22×C61—21no—
315C22×C61—21no—
316C22×C61—21no—
317C22×C61—21no—
318C22×C61—42no—
319C22×C61—42no—
320C22×C61C22×C22⋊C411yescharacteristic
321C22×C61#52012yes—
322C22×C61#53511yescharacteristic
323C22×C61#53611yescharacteristic
324C22×C61#53712yes—
325C2×D61—42no—
326C2×D61—42no—
327C2×D61—42no—
328C2×D61—84no—
329C4×C61—21no—
330C4×C61—21no—
331C4×C61—21no—
332C4×C61—42no—
333C4×C61—42no—
334C4×C61—82no—
335C4×C61—82no—
336C4×C61#41012yes—
337Dic61—21no—
338Dic61—21no—
339Dic61—21no—
340Dic61—21no—
341Dic61—21no—
342Dic61—21no—
343Dic61—21no—
344Dic61—42no—
345Dic61—82no—
346Dic61—82no—
347Dic61#41012yes—
348C2×#529—611no—
349#2285—611no—
350#2283—611no—
351#1996—611no—
352#1996D6111yescharacteristic, complemented
353#1964—611no—
354#1964—611no—
355#1899—614no—
356#1799—614no—
357C2×C61—21no—
358C2×C61—22no—
359C2×C61—22no—
360C2×C61—21no—
361C2×C61#231111yescharacteristic
362C2×C61C2×#41011yescharacteristic
363C2×C61C2×#41011yescharacteristic
364D61—82no—
365#529—1221no—
366#529—1221no—
367#529—1221no—
368#529—1221no—
369#529—1221no—
370#529—1221no—
371#529—1221no—
372#529—1221no—
373C2×#126—612no—
374C2×#125—611no—
375C2×#124—611no—
376C2×#123—612no—
377C2×C22⋊Q8C2×D6111yescharacteristic
378C2×#121—611no—
379C2×C4×Q8—611no—
380C2×C4×D4—611no—
381C2×C4×D4—612no—
382C2×#117—612no—
383C2×#117—612no—
384C22×C42—611no—
385C2×#99—614no—
386C2×#99—614no—
387#384—1221no—
388#383—1221no—
389#382—1221no—
390#382—1221no—
391#381—612no—
392#380—611no—
393#380—612no—
394#380—612no—
395#380C2×D6111yescharacteristic
396C4×C4⋊C4—1221no—
397C4×C4⋊C4—1221no—
398C4×C4⋊C4—1221no—
399C4×C22⋊C4—611no—
400C4×C22⋊C4C2×D6111yescharacteristic
401#376—1221no—
402#342—614no—
403#342C2×D6114yes—
404C61#2187511yescharacteristic, complemented, Sylow
405C22×Q8C4×D6111yescharacteristic
406C22×D4—612no—
407C22×D4—611no—
408C23×C4—611no—
409C23×C4—611no—
410C23×C4—612no—
411C23×C4C22×D6111yescharacteristic
412#126—1222no—
413#126—1222no—
414#126—1222no—
415#126—1222no—
416#125—1221no—
417#125—1221no—
418#125—1221no—
419#125—1221no—
420#124—1221no—
421#124—1221no—
422#124—1221no—
423#124—1221no—
424#123—1222no—
425#123—1222no—
426#123—1222no—
427#123—1222no—
428C22⋊Q8—21no—
429C22⋊Q8—21no—
430C22⋊Q8—21no—
431C22⋊Q8—21no—
432#121—1221no—
433#121—1221no—
434#121—1221no—
435#121—1221no—
436C4×Q8—1221no—
437C4×Q8—1221no—
438C4×Q8—1221no—
439C4×Q8—1221no—
440C4×D4—1221no—
441C4×D4—1221no—
442C4×D4—1221no—
443C4×D4—1221no—
444C4×D4—1222no—
445C4×D4—1222no—
446C4×D4—1222no—
447C4×D4—1222no—
448#117—1222no—
449#117—1222no—
450#117—1222no—
451#117—1222no—
452#117—2444no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—612no—
455C2×C4⋊C4—612no—
456C2×C4⋊C4—611no—
457C2×C4⋊C4—612no—
458C2×C4⋊C4—1222no—
459C2×C4⋊C4—1222no—
460C2×C4⋊C4—1222no—
461C2×C4⋊C4—1221no—
462C2×C4⋊C4C4×D6112yes—
463C2×C4⋊C4C4×D6111yescharacteristic
464C2×C22⋊C4—612no—
465C2×C22⋊C4—612no—
466C2×C22⋊C4—612no—
467C2×C22⋊C4—612no—
468C2×C22⋊C4—612no—
469C2×C22⋊C4—612no—
470C2×C22⋊C4C22×D6112yes—
471C2×C22⋊C4C22×D6112yes—
472C2×C22⋊C4C22×D6112yes—
473C2×C42—21no—
474C2×C42—611no—
475C2×C42—611no—
476C2×C42—611no—
477C2×C42—611no—
478C2×C42—611no—
479C2×C42—611no—
480C2×C42—611no—
481C2×C42—611no—
482C2×C42—611no—
483C2×C42—611no—
484C2×C42—611no—
485C2×C42—611no—
486C2×C42—612no—
487C2×C42—1222no—
488C2×C42—1221no—
489#99—2444no—
490#99—2444no—
491#95—21no—
492#95—21no—
493#95—1222no—
494#95—1222no—
495#95—1222no—
496#95—1222no—
497#95—1221no—
498#95—1221no—
499C24—612no—
500C24C23×D6111yescharacteristic
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—42no—
504C2×D4—1222no—
505C2×D4—1222no—
506C2×D4—1224no—
507C2×D4—1224no—
508C2×D4—1221no—
509C2×D4—1221no—
510C2×D4—2442no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—42no—
514C22×C4—611no—
515C22×C4—611no—
516C22×C4—611no—
517C22×C4—611no—
518C22×C4—611no—
519C22×C4—611no—
520C22×C4—611no—
521C22×C4—611no—
522C22×C4—611no—
523C22×C4—611no—
524C22×C4—611no—
525C22×C4—611no—
526C22×C4—612no—
527C22×C4—1222no—
528C22×C4—1222no—
529C22×C4—1222no—
530C22×C4—1222no—
531C22×C4—1222no—
532C22×C4—1222no—
533C22×C4—2444no—
534C22×C4—2442no—
535C22×C4C2×C4×D6111yescharacteristic
536C22×C4C2×C4×D6112yes—
537C22×C4C2×C4×D6112yes—
538C22×C4C2×C4×D6111yescharacteristic
539C22×C4D4×D6111yescharacteristic
540C22×C4D4×D6111yescharacteristic
541C22×C4D4×D6111yescharacteristic
542C22×C4D4×D6111yescharacteristic
543C4⋊C4—22no—
544C4⋊C4—22no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—42no—
548C4⋊C4—1222no—
549C4⋊C4—1222no—
550C4⋊C4—1222no—
551C4⋊C4—1222no—
552C4⋊C4—1222no—
553C4⋊C4—1222no—
554C4⋊C4—1221no—
555C4⋊C4—1221no—
556C4⋊C4—2442no—
557C4⋊C4—2444no—
558C4⋊C4—2444no—
559C4⋊C4—2444no—
560C22⋊C4—22no—
561C22⋊C4—22no—
562C22⋊C4—22no—
563C22⋊C4—24no—
564C22⋊C4—22no—
565C22⋊C4—1222no—
566C22⋊C4—1222no—
567C22⋊C4—1222no—
568C22⋊C4—1222no—
569C22⋊C4—1222no—
570C22⋊C4—1222no—
571C22⋊C4—1222no—
572C22⋊C4—1222no—
573C22⋊C4—1222no—
574C22⋊C4—1224no—
575C22⋊C4—1222no—
576C42—42no—
577C42—611no—
578C42—611no—
579C42—611no—
580C42—611no—
581C42—611no—
582C42—611no—
583C42—611no—
584C42—611no—
585C42—611no—
586C42—611no—
587C42—611no—
588C42—611no—
589C42—611no—
590C42—611no—
591C42—611no—
592C42—611no—
593C42—1222no—
594C42—1222no—
595C42—2442no—
596C42—2444no—
597C23—41no—
598C23—41no—
599C23—1224no—
600C23—1222no—
601C23—2442no—
602C23—2442no—
603C23C22×C4×D6111yescharacteristic
604C23C2×D4×D6111yescharacteristic
605C23C2×D4×D6111yescharacteristic
606C23#1451982312yes—
607C23#1451982512yes—
608Q8—42no—
609Q8—42no—
610D4—2442no—
611D4—2442no—
612D4—2442no—
613D4—2444no—
614D4—2442no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—611no—
632C2×C4—611no—
633C2×C4—611no—
634C2×C4—611no—
635C2×C4—611no—
636C2×C4—611no—
637C2×C4—611no—
638C2×C4—611no—
639C2×C4—1222no—
640C2×C4—1222no—
641C2×C4—1222no—
642C2×C4—1222no—
643C2×C4—1222no—
644C2×C4—1221no—
645C2×C4—1221no—
646C2×C4—1221no—
647C2×C4—1221no—
648C2×C4—1222no—
649C2×C4—1222no—
650C2×C4—1222no—
651C2×C4—1224no—
652C2×C4—2444no—
653C2×C4—2444no—
654C2×C4—2441no—
655C2×C4—2441no—
656C2×C4—2441no—
657C2×C4—2442no—
658C2×C4—2442no—
659C2×C4—2442no—
660C2×C4—2442no—
661C2×C4—2442no—
662C2×C4—2442no—
663C2×C4C22⋊C4×D6111yescharacteristic
664C2×C4C22⋊C4×D6111yescharacteristic
665C2×C4C22⋊C4×D6111yescharacteristic
666C2×C4C22⋊C4×D6111yescharacteristic
667C22—21no—
668C22—21no—
669C22—21no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—42no—
674C22—42no—
675C22—4884no—
676C22—2442no—
677C22—2442no—
678C22—2442no—
679C22C2×C22⋊C4×D6111yescharacteristic
680C22#1684024412yes—
681C22#1684033011yescharacteristic
682C22#1684033711yescharacteristic
683C22#1684034212yes—
684C4—21no—
685C4—21no—
686C4—21no—
687C4—42no—
688C4—42no—
689C4—82no—
690C4—82no—
691C4—612no—
692C4—1221no—
693C4—1221no—
694C4—1221no—
695C4—1221no—
696C4—1221no—
697C4—1221no—
698C4—1221no—
699C4—4882no—
700C4—4882no—
701C4—2442no—
702C4#1683973412yes—
703C2—21no—
704C2—22no—
705C2—22no—
706C2—21no—
707C2—4882no—
708C2#2144841011yescharacteristic
709C2#410×D6111yescharacteristic
710C2C2×#1683973411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1996C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519751C22
cosocleC24×C61C24
hypercenter#1996D61
hypocenterC61#21875
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
2. #21448221C2semidirect
3. #21448213C2semidirect
4. #21446805C2semidirect
7. #21446276C2semidirect
8. #21445806C2semidirect
9. C61×#1996C2semidirect
18. C2×#14519772C4semidirect
19. C2×#14519768C4semidirect
20. C2×#14519766C4semidirect
23. C2×Q8×Dic61C4semidirect
24. C2×#14519739C4semidirect
26. C2×#14519735C4semidirect
352. #1996D61semidirect
404. C61#21875semidirect

Maximal subgroups

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

subgroupindex
C2×#168402982
#214482212
#214482132
#214468052
#214466552
#214466542
#214462762
#214458062
C61×#19962
#2187561