Finite Group Databasebeta

← C2×#13126124 #16735145

Subgroups — C2×#13126124 #16735145

Order 3328.

1742 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719434C211yesmaximal, characteristic, complemented
2C2×#11719287C211yesmaximal, characteristic
3#13126124C2116yesmaximal, direct product factor
4C2×#11718537C211yesmaximal, characteristic, complemented
5C2×#11718535C211yesmaximal, characteristic, complemented
6C2×#11718456C211yesmaximal, characteristic, complemented
7C2×#11718461C211yesmaximal, characteristic, complemented
8C2×#11718470C211yesmaximal, characteristic, complemented
9C2×#11718476C211yesmaximal, characteristic, complemented
10C2×#11718546C211yesmaximal, characteristic
11C2×#11718543C211yesmaximal, characteristic
12C2×#11718683C211yesmaximal, characteristic, complemented
13C2×#11718508C211yesmaximal, characteristic, complemented
14C2×#11718748C211yesmaximal, characteristic, complemented
15C2×#11718501C211yesmaximal, characteristic, complemented
16C2×C13×#477C211yesmaximal, characteristic, complemented
17C2×C13×C4⋊Q8C2211yescharacteristic
18C2×C4×Q8×C13C2211yescharacteristic
19C2×#88201C2211yescharacteristic
20C2×#88200—21no—
21C2×#88200C2211yescharacteristic
22C2×#88198—21no—
23#11719434—24no—
24#11719434C2218yescomplemented
25#11719287—24no—
26#11719287C2218yes—
27C2×#88150—21no—
28C2×#88150—21no—
29C2×#88149C2211yescharacteristic
30C2×#88148—21no—
31C2×#88146C2211yescharacteristic
32C2×C4⋊C4×D13C2211yescharacteristic
33C2×#88144C2211yescharacteristic
34C2×#88143—21no—
35C2×#88142C2211yescharacteristic
36C2×#88142C2211yescharacteristic
37C2×#88130—21no—
38C2×#88129—21no—
39C2×C4×D52C2211yescharacteristic
40C2×#88126C2211yescharacteristic
41C2×#88124C2211yescharacteristic
42C13×#477C2218yescomplemented
43C2×C13×#107C2211yescharacteristic
44C2×C13×#107C2211yescharacteristic
45C2×C13×C4⋊C8C2211yescharacteristic
46C2×C13×#103C2211yescharacteristic
47C2×C13×#103C2211yescharacteristic
48C2×#88075C2211yescharacteristic
49C2×#88075C2211yescharacteristic
50C2×#88061C2211yescharacteristic
51C2×#88061C2211yescharacteristic
52C2×#88060C2211yescharacteristic
53C2×#88060C2211yescharacteristic
54C2×#88058C2211yescharacteristic
55C2×#88057C2211yescharacteristic
56C2×#88055C2211yescharacteristic
57C2×C8×Dic13C2211yescharacteristic
58#11718748C2218yescomplemented
59#11718683C2218yescomplemented
60C2×#88049C2211yescharacteristic
61C2×#88049C2211yescharacteristic
62C2×#88048C2211yescharacteristic
63C2×#88047C2211yescharacteristic
64C2×#88047C2211yescharacteristic
65C2×#88047C2211yescharacteristic
66C2×C4⋊#1055C2211yescharacteristic
67#11718546C2218yes—
68#11718543C2218yes—
69#11718537C2218yescomplemented
70#11718535C2218yescomplemented
71#11718508C2218yescomplemented
72#11718501C2218yescomplemented
73#11718476C2218yescomplemented
74#11718470C2218yescomplemented
75#11718461C2218yescomplemented
76#11718456C2218yescomplemented
77C22×Q8×C13—21no—
78C22×Q8×C13C2311yescharacteristic
79C22×D52—21no—
80C22×D52C2311yescharacteristic
81C22×C4×D13—21no—
82C22×C4×D13—21no—
83C22×C4×D13C2311yescharacteristic
84C22×Dic26—21no—
85C22×Dic26—21no—
86C22×C8×C13C2311yescharacteristic
87C22×C8×C13C2311yescharacteristic
88C13×C4⋊Q8—22no—
89C13×C4⋊Q8C2314yes—
90C4×Q8×C13—22no—
91C4×Q8×C13C2314yes—
92C2×C13×C4⋊C4—21no—
93C2×C13×C4⋊C4—21no—
94C2×C13×C4⋊C4C2311yescharacteristic
95C2×C13×C4⋊C4C2311yescharacteristic
96C2×C13×C4⋊C4C2311yescharacteristic
97C2×C42×C13—21no—
98C2×C42×C13C2311yescharacteristic
99#88201—22no—
100#88201C2314yes—
101#88200—22no—
102#88200—28no—
103#88200C2314yes—
104#88198—28no—
105C2×#6103—21no—
106C2×#6103—21no—
107C2×#6103—21no—
108C2×#6103—21no—
109C2×#6103—21no—
110C2×#6103—21no—
111C2×#6103D411yescharacteristic
112C2×#6103D411yescharacteristic
113C2×C4⋊Dic13—21no—
114C2×C4⋊Dic13C2311yescharacteristic
115C2×C4⋊Dic13C2311yescharacteristic
116C2×C4⋊Dic13C2311yescharacteristic
117C2×#6101—21no—
118C2×#6101—21no—
119C2×#6101—21no—
120C2×#6101—21no—
121C2×#6101—21no—
122C2×#6101—21no—
123C2×#6101—21no—
124C2×#6101D411yescharacteristic
125C2×#6101D411yescharacteristic
126C2×C4×Dic13—21no—
127C2×C4×Dic13C2311yescharacteristic
128C22×#1055C2311yescharacteristic
129C22×#1055C2311yescharacteristic
130#88150—28no—
131#88150—28no—
132#88149—22no—
133#88149C2314yes—
134#88148—28no—
135#88146—22no—
136#88146C2314yes—
137C4⋊C4×D13—22no—
138C4⋊C4×D13C2314yes—
139#88144—22no—
140#88144C2314yes—
141#88143—28no—
142#88142—22no—
143#88142—22no—
144#88142C2314yes—
145#88142C2314yes—
146#88130—28no—
147#88129—28no—
148C4×D52—22no—
149C4×D52C2314yes—
150#88126D414yes—
151#88126C2314yes—
152#88124—22no—
153#88124C2314yes—
154C13×#107C2314yes—
155C13×#107C2314yes—
156C13×C4⋊C8C2314yes—
157C13×#103C2314yes—
158C13×#103C2314yes—
159#88075C2314yes—
160#88075C2314yes—
161#88061C2314yes—
162#88061C2314yes—
163#88060C2314yes—
164#88060C2314yes—
165#88058C2314yes—
166#88057C2314yes—
167#88055C2314yes—
168C8×Dic13C2314yes—
169#88049C2314yes—
170#88049C2314yes—
171#88048C2314yes—
172#88047C2314yes—
173#88047C2314yes—
174#88047C2314yes—
175C4⋊#1055C2314yes—
176C2×#3243—131nomaximal, Sylow
177C23×D13—21no—
178C23×D13C2×D411yescharacteristic
179C2×Q8×C13—21no—
180C2×Q8×C13—24no—
181C2×Q8×C13—22no—
182C2×Q8×C13—22no—
183C2×Q8×C13—82no—
184C2×Q8×C13C2412yes—
185C22×C4×C13—21no—
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13C2×D411yescharacteristic
190C22×C4×C13C2×D411yescharacteristic
191C22×C4×C13C2411yescharacteristic
192C22×Dic13—21no—
193C22×Dic13—21no—
194C22×Dic13—21no—
195C22×Dic13C2×D411yescharacteristic
196C22×Dic13C2×D411yescharacteristic
197C22×Dic13C2×D411yescharacteristic
198C2×D52—22no—
199C2×D52—22no—
200C2×D52—21no—
201C2×D52—24no—
202C2×D52—82no—
203C2×D52C2412yes—
204C2×C4×D13—22no—
205C2×C4×D13—22no—
206C2×C4×D13—24no—
207C2×C4×D13—24no—
208C2×C4×D13—82no—
209C2×C4×D13—82no—
210C2×C4×D13C2×D412yes—
211C2×C4×D13C2412yes—
212C2×Dic26—24no—
213C2×Dic26—24no—
214C2×Dic26—82no—
215C2×Dic26—82no—
216C2×C8×C13—22no—
217C2×C8×C13—22no—
218C2×C8×C13C2412yes—
219C2×C8×C13C2412yes—
220C13×C4⋊C4—21no—
221C13×C4⋊C4—21no—
222C13×C4⋊C4—24no—
223C13×C4⋊C4—21no—
224C13×C4⋊C4—24no—
225C13×C4⋊C4C2412yes—
226C13×C4⋊C4C2412yes—
227C13×C4⋊C4C2412yes—
228C42×C13—24no—
229C42×C13C2×D412yes—
230C42×C13C2412yes—
231#6103—24no—
232#6103—24no—
233#6103—24no—
234#6103—24no—
235#6103—24no—
236#6103—24no—
237#6103C2×D414yes—
238#6103C2×D414yes—
239C4⋊Dic13—21no—
240C4⋊Dic13—21no—
241C4⋊Dic13—21no—
242C4⋊Dic13—24no—
243C4⋊Dic13C2412yes—
244C4⋊Dic13C2412yes—
245C4⋊Dic13C2412yes—
246#6101—24no—
247#6101—24no—
248#6101—24no—
249#6101—24no—
250#6101—24no—
251#6101—24no—
252#6101—24no—
253#6101C2×D414yes—
254#6101C2×D414yes—
255C4×Dic13—24no—
256C4×Dic13C2×D412yes—
257C4×Dic13C2412yes—
258C2×#1055—22no—
259C2×#1055—22no—
260C2×#1055C2412yes—
261C2×#1055C2412yes—
262C2×#544—131no—
263C2×#542—131no—
264#3243—1316no—
265C2×#501—131no—
266C2×#500—131no—
267C2×#489—131no—
268C2×#488—131no—
269C2×#484—131no—
270C2×#485—131no—
271C2×#482—131no—
272C2×#480—131no—
273C2×#479—131no—
274C2×#477D1311yescharacteristic, complemented
275C2×#478—131no—
276C2×#474—131no—
277C2×#433—131no—
278C23×C13C22×D411yescharacteristic
279C22×D13—22no—
280C22×D13—22no—
281C22×D13—22no—
282C22×D13—22no—
283C22×D13—42no—
284C22×D13—42no—
285C22×D13—42no—
286C22×D13C22×D412yes—
287Q8×C13—22no—
288Q8×C13—22no—
289Q8×C13—42no—
290Q8×C13—84no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—22no—
294C2×C4×C13—22no—
295C2×C4×C13—22no—
296C2×C4×C13—22no—
297C2×C4×C13—42no—
298C2×C4×C13—42no—
299C2×C4×C13—42no—
300C2×C4×C13—42no—
301C2×C4×C13C22×D412yes—
302C2×C4×C13C22×D412yes—
303C2×C4×C13C22×D411yescharacteristic
304C2×C4×C132−1+412yes—
305C2×C4×C132−1+412yes—
306C2×C4×C13C2511yescharacteristic
307C2×Dic13—22no—
308C2×Dic13—22no—
309C2×Dic13—22no—
310C2×Dic13—22no—
311C2×Dic13—22no—
312C2×Dic13—22no—
313C2×Dic13—42no—
314C2×Dic13—42no—
315C2×Dic13—42no—
316C2×Dic13C22×D412yes—
317C2×Dic13C22×D412yes—
318C2×Dic13C22×D412yes—
319D52—22no—
320D52—22no—
321D52—42no—
322D52—84no—
323C4×D13—24no—
324C4×D13—22no—
325C4×D13—22no—
326C4×D13—84no—
327C4×D13—84no—
328Dic26—84no—
329Dic26—84no—
330C8×C13—22no—
331C8×C13—22no—
332#1055—22no—
333#1055—22no—
334#544—138no—
335#544—264no—
336#542—138no—
337#542—264no—
338C2×C4⋊Q8—131no—
339C2×C4⋊Q8—131no—
340C2×C4⋊Q8—261no—
341C2×C4⋊Q8C2×D1311yescharacteristic
342C2×#126—261no—
343C2×#125—131no—
344C2×#125—131no—
345C2×#125—261no—
346C2×#124—131no—
347C2×#124—261no—
348C2×#123—261no—
349C2×C22⋊Q8—131no—
350C2×C22⋊Q8—261no—
351C2×C22⋊Q8—261no—
352C2×C22⋊Q8—261no—
353C2×#121—131no—
354C2×C4×Q8C2×D1311yescharacteristic
355C2×C4×D4—131no—
356C2×#117—131no—
357C2×#117—131no—
358C22×C4⋊C4—131no—
359#501—138no—
360#500—138no—
361#489—138no—
362#488—138no—
363#485—138no—
364#484—138no—
365#482—138no—
366#480—138no—
367#479—138no—
368#478—138no—
369#477C2×D1318yescomplemented
370#474—138no—
371#433—138no—
372C2×#107—131no—
373C2×#107—131no—
374C2×#107—131no—
375C2×#107—131no—
376C2×#107C2×D1311yescharacteristic
377C2×#107C2×D1311yescharacteristic
378C2×#106—131no—
379C2×#106—131no—
380C2×C4⋊C8—131no—
381C2×C4⋊C8C2×D1311yescharacteristic
382C2×#103—131no—
383C2×#103—131no—
384C2×#103C2×D1311yescharacteristic
385C2×#103C2×D1311yescharacteristic
386C2×#102—131no—
387C2×#102—131no—
388C2×#102—131no—
389C2×#102—131no—
390C2×C22⋊C8—131no—
391C2×C22⋊C8—131no—
392C2×#97—131no—
393C2×C4×C8—131no—
394C22×C13#53612yes—
395C22×C13#57612yes—
396C22×C13#57812yes—
397C22×C13C23×D411yescharacteristic
398C2×D13—22no—
399C2×D13—22no—
400C2×D13—22no—
401C2×D13—44no—
402C2×D13—42no—
403C2×D13—42no—
404C2×D13—42no—
405C2×D13—84no—
406C4×C13—22no—
407C4×C13—22no—
408C4×C13—42no—
409C4×C13—42no—
410C4×C13—42no—
411C4×C13—42no—
412C4×C13#53612yes—
413C4×C13C2×2−1+411yescharacteristic
414C4×C13C2×2−1+411yescharacteristic
415Dic13—22no—
416Dic13—22no—
417Dic13—22no—
418Dic13—42no—
419Dic13—42no—
420Dic13—42no—
421C22×Q8—21no—
422C22×Q8—261no—
423C22×Q8—261no—
424C22×Q8C22×D1311yescharacteristic
425C22×D4—131no—
426C22×D4—261no—
427C23×C4—131no—
428C23×C4—261no—
429C23×C4—261no—
430C22×C8—131no—
431C22×C8—131no—
432C22×C8C22×D1311yescharacteristic
433C22×C8C22×D1311yescharacteristic
434C4⋊Q8—22no—
435C4⋊Q8—134no—
436C4⋊Q8—134no—
437C4⋊Q8—262no—
438C4⋊Q8—262no—
439C4⋊Q8—268no—
440C4⋊Q8C22×D1314yes—
441#126—268no—
442#125—134no—
443#125—134no—
444#125—262no—
445#125—268no—
446#125—262no—
447#124—134no—
448#124—268no—
449#124—262no—
450#123—268no—
451C22⋊Q8—134no—
452C22⋊Q8—268no—
453C22⋊Q8—268no—
454C22⋊Q8—268no—
455C22⋊Q8—262no—
456#121—134no—
457#121—262no—
458C4×Q8—22no—
459C4×Q8C22×D1314yes—
460C4×D4—134no—
461C4×D4—262no—
462#117—134no—
463#117—134no—
464#117—134no—
465#117—262no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—131no—
469C2×C4⋊C4—131no—
470C2×C4⋊C4—131no—
471C2×C4⋊C4—131no—
472C2×C4⋊C4—131no—
473C2×C4⋊C4—134no—
474C2×C4⋊C4—262no—
475C2×C4⋊C4—261no—
476C2×C4⋊C4—261no—
477C2×C4⋊C4—261no—
478C2×C4⋊C4—261no—
479C2×C4⋊C4—261no—
480C2×C4⋊C4—261no—
481C2×C4⋊C4—261no—
482C2×C4⋊C4—261no—
483C2×C4⋊C4C22×D1311yescharacteristic
484C2×C4⋊C4C22×D1311yescharacteristic
485C2×C4⋊C4C22×D1311yescharacteristic
486C2×C22⋊C4—131no—
487C2×C22⋊C4—131no—
488C2×C22⋊C4—261no—
489C2×C22⋊C4—261no—
490C2×C22⋊C4—261no—
491C2×C22⋊C4—261no—
492C2×C22⋊C4—261no—
493C2×C22⋊C4—261no—
494C2×C42—21no—
495C2×C42—131no—
496C2×C42—261no—
497C2×C42C22×D1311yescharacteristic
498#107—134no—
499#107—134no—
500#107—134no—
501#107—134no—
502#107C22×D1314yes—
503#107C22×D1314yes—
504#106—134no—
505#106—134no—
506C4⋊C8—134no—
507C4⋊C8C22×D1314yes—
508#103—134no—
509#103—134no—
510#103C22×D1314yes—
511#103C22×D1314yes—
512#102—134no—
513#102—134no—
514#102—134no—
515#102—134no—
516C22⋊C8—134no—
517C22⋊C8—134no—
518#97—134no—
519C4×C8—134no—
520C2×C13#324314yescomplemented
521C2×C13C2×#53611yescharacteristic
522C2×C13C2×#57611yescharacteristic
523C2×C13C2×#57811yescharacteristic
524D13—42no—
525D13—82no—
526C24—131no—
527C24—261no—
528C2×Q8—21no—
529C2×Q8—24no—
530C2×Q8—22no—
531C2×Q8—22no—
532C2×Q8—82no—
533C2×Q8—264no—
534C2×Q8—264no—
535C2×Q8—1042no—
536C2×Q8—1042no—
537C2×Q8C23×D1312yes—
538C2×D4—132no—
539C2×D4—264no—
540C2×D4—261no—
541C2×D4—262no—
542C2×D4—262no—
543C2×D4—1042no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—131no—
549C22×C4—131no—
550C22×C4—131no—
551C22×C4—132no—
552C22×C4—132no—
553C22×C4—264no—
554C22×C4—262no—
555C22×C4—262no—
556C22×C4—261no—
557C22×C4—261no—
558C22×C4—261no—
559C22×C4—264no—
560C22×C4—1042no—
561C22×C4—1042no—
562C22×C4D4×D1311yescharacteristic
563C22×C4D4×D1311yescharacteristic
564C22×C4C23×D1311yescharacteristic
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—132no—
568C2×C8—132no—
569C2×C8—262no—
570C2×C8—262no—
571C2×C8C23×D1312yes—
572C2×C8C23×D1312yes—
573C4⋊C4—24no—
574C4⋊C4—24no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—134no—
579C4⋊C4—134no—
580C4⋊C4—132no—
581C4⋊C4—132no—
582C4⋊C4—132no—
583C4⋊C4—264no—
584C4⋊C4—264no—
585C4⋊C4—264no—
586C4⋊C4—264no—
587C4⋊C4—264no—
588C4⋊C4—264no—
589C4⋊C4—261no—
590C4⋊C4—261no—
591C4⋊C4—261no—
592C4⋊C4—264no—
593C4⋊C4—264no—
594C4⋊C4C23×D1312yes—
595C4⋊C4C23×D1312yes—
596C4⋊C4C23×D1312yes—
597C22⋊C4—134no—
598C22⋊C4—134no—
599C22⋊C4—264no—
600C22⋊C4—264no—
601C22⋊C4—264no—
602C22⋊C4—264no—
603C22⋊C4—264no—
604C22⋊C4—264no—
605C42—24no—
606C42—132no—
607C42—132no—
608C42—264no—
609C42D4×D1312yes—
610C42C23×D1312yes—
611C13C2×#324311yescharacteristic, complemented, Sylow
612C23—132no—
613C23—262no—
614C23—262no—
615C23—262no—
616C23—262no—
617C23—522no—
618C23—522no—
619C23—522no—
620C23C2×D4×D1311yescharacteristic
621Q8—22no—
622Q8—22no—
623Q8—42no—
624Q8—84no—
625Q8—1044no—
626Q8—1044no—
627D4—262no—
628D4—262no—
629D4—522no—
630D4—1044no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—132no—
642C2×C4—132no—
643C2×C4—132no—
644C2×C4—262no—
645C2×C4—262no—
646C2×C4—262no—
647C2×C4—264no—
648C2×C4—262no—
649C2×C4—262no—
650C2×C4—262no—
651C2×C4—262no—
652C2×C4—262no—
653C2×C4—522no—
654C2×C4—522no—
655C2×C4—522no—
656C2×C4—1044no—
657C2×C4—1044no—
658C2×C4C2×D4×D1312yes—
659C2×C4C2×D4×D1312yes—
660C2×C4C2×D4×D1311yescharacteristic
661C2×C4#8825412yes—
662C2×C4#8825712yes—
663C2×C4C24×D1311yescharacteristic
664C8—22no—
665C8—22no—
666C8—262no—
667C8—262no—
668C22—262no—
669C22—262no—
670C22—262no—
671C22—524no—
672C22—522no—
673C22—522no—
674C22—522no—
675C22—1044no—
676C22#1171933312yes—
677C22#1171947112yes—
678C22#1171947912yes—
679C22C22×D4×D1311yescharacteristic
680C4—22no—
681C4—22no—
682C4—42no—
683C4—42no—
684C4—42no—
685C4—42no—
686C4—262no—
687C4—262no—
688C4—262no—
689C4—522no—
690C4—522no—
691C4—522no—
692C4#1171933312yes—
693C4C2×#8825411yescharacteristic
694C4C2×#8825711yescharacteristic
695C2—522no—
696C2—1042no—
697C2#1312612414yesdirect product factor
698C2C2×#1171933311yescharacteristic
699C2C2×#1171947911yescharacteristic
700C2C2×#1171947111yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#477C2
socleC23×C13C22×D4
prime radicalC2×#88149C22
hypercenterC2×#477D13
hypocenterC13C2×#3243
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
1. C2×#11719434C2semidirect
3. #13126124C2direct (N × H)
4. C2×#11718537C2semidirect
5. C2×#11718535C2semidirect
6. C2×#11718456C2semidirect
7. C2×#11718461C2semidirect
8. C2×#11718470C2semidirect
9. C2×#11718476C2semidirect
12. C2×#11718683C2semidirect
13. C2×#11718508C2semidirect
14. C2×#11718748C2semidirect
15. C2×#11718501C2semidirect
16. C2×C13×#477C2semidirect
24. #11719434C22semidirect
42. C13×#477C22semidirect
58. #11718748C22semidirect
59. #11718683C22semidirect
69. #11718537C22semidirect
70. #11718535C22semidirect
71. #11718508C22semidirect
72. #11718501C22semidirect
73. #11718476C22semidirect
74. #11718470C22semidirect
75. #11718461C22semidirect
76. #11718456C22semidirect
274. C2×#477D13semidirect
369. #477C2×D13semidirect
520. C2×C13#3243semidirect
611. C13C2×#3243semidirect
697. C2#13126124direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117194342
C2×#117192872
#131261242
C2×#117185372
C2×#117185352
C2×#117184562
C2×#117184612
C2×#117184702
C2×#117184762
C2×#117185462
C2×#117185432
C2×#117186832
C2×#117185082
C2×#117187482
C2×#117185012
C2×C13×#4772
C2×#324313