Finite Group Databasebeta

← D17×#2629 #17201385

Subgroups — D17×#2629 #17201385

Order 4352.

2614 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×D17C211yesmaximal, characteristic, complemented
2C2×#117×D17C211yesmaximal, characteristic
3#14534619C212yesmaximal, complemented
4#14534618C212yesmaximal, complemented
5#14534617C211yesmaximal, characteristic, complemented
6#14534616C214yesmaximal, complemented
7#14534615C211yesmaximal, characteristic, complemented
8#14534614C211yesmaximal, characteristic, complemented
9#14534613C214yesmaximal, complemented
10D17×#398C214yesmaximal, complemented
11D17×#396C214yesmaximal
12D17×#389C212yesmaximal, complemented
13D17×#384C211yesmaximal, characteristic, complemented
14D17×#380C212yesmaximal
15C17×#2629C211yesmaximal, characteristic, complemented
16C23×C4×D17C2211yescharacteristic
17C2×#10587556C2211yescharacteristic, complemented
18C2×#10587576C2212yescomplemented
19C2×#10587575C2214yescomplemented
20#125×D17—28no—
21C2×#10587612C2211yescharacteristic
22C2×#10587578C2212yes—
23C2×#10587558C2211yescharacteristic
24C2×#10587558C2211yescharacteristic
25C2×#10587563C2212yes—
26#117×D17—28no—
27C2×C4⋊C4×D17C2212yes—
28C2×C4⋊C4×D17C2212yes—
29C2×C4⋊C4×D17C2212yes—
30C2×C4⋊C4×D17C2214yes—
31C2×C4⋊C4×D17C2214yes—
32C2×C4⋊C4×D17C2214yes—
33C2×C22⋊C4×D17C2212yes—
34C2×C22⋊C4×D17C2214yes—
35C2×C42×D17C2211yescharacteristic
36C2×C42×D17C2211yescharacteristic
37#11762743C2214yescomplemented
38#11762743C2214yescomplemented
39#11762742C2214yescomplemented
40#11762742C2214yescomplemented
41#11762741C2214yescomplemented
42#11762740C2214yescomplemented
43#11762739C2214yescomplemented
44#11762733C2214yes—
45#11762732C2214yes—
46#11762732C2214yes—
47#11762732C2214yes—
48#11762731C2214yes—
49#11762731C2214yes—
50#11762731C2214yes—
51#11762708C2212yescomplemented
52#11762707C2212yescomplemented
53#11762706C2214yescomplemented
54#11762705C2212yescomplemented
55#11762704C2214yescomplemented
56#11762679C2211yescharacteristic, complemented
57#11762678C2214yescomplemented
58#11762678C2212yescomplemented
59#11762669C2212yes—
60#11762668C2214yes—
61#11762667C2214yes—
62#11762666C2212yes—
63#11762666C2212yes—
64#95×D17C2214yes—
65#95×D17C2214yes—
66C2×C17×#125C2211yescharacteristic, complemented
67C2×C17×#117C2211yescharacteristic
68C17×#398C2214yescomplemented
69C17×#396C2214yes—
70C17×#389C2212yescomplemented
71C17×#384C2211yescharacteristic, complemented
72C17×#380C2212yes—
73C24×D17C2311yescharacteristic
74C23×C4×C17C2311yescharacteristic
75C23×Dic17C2311yescharacteristic
76C22×C4×D17—24no—
77C22×C4×D17—24no—
78C22×C4×D17Q818yes—
79C22×C4×D17C2312yes—
80C22×C4×D17C2314yes—
81C22×C4×D17C2314yes—
82C22×C4×D17C2312yes—
83C22×C4×D17C2311yescharacteristic
84C22×C4×D17C2311yescharacteristic
85C22×C4×D17C2311yescharacteristic
86C22×C4×D17C2311yescharacteristic
87C17×#125—24no—
88C17×#117—24no—
89C2×C4⋊C4×C17C2312yes—
90C2×C4⋊C4×C17C2312yes—
91C2×C4⋊C4×C17C2312yes—
92C2×C4⋊C4×C17C2314yes—
93C2×C4⋊C4×C17C2314yes—
94C2×C4⋊C4×C17C2314yes—
95C2×C22⋊C4×C17C2312yes—
96C2×C22⋊C4×C17C2314yes—
97C2×C42×C17C2311yescharacteristic
98C2×C42×C17C2311yescharacteristic
99C2×C22⋊Dic17C2312yes—
100C2×C22⋊Dic17C2314yes—
101C2×#63227C2312yes—
102C2×#63227C2312yes—
103C2×#63227C2314yes—
104C2×#63227C2314yes—
105#10587612—24no—
106C2×C4⋊Dic17C2312yes—
107C2×C4⋊Dic17C2312yes—
108C2×C4⋊Dic17C2314yes—
109C2×C4⋊Dic17C2312yes—
110C2×C4⋊Dic17C2314yes—
111C2×C4⋊Dic17C2314yes—
112C2×#63225C2314yes—
113C2×#63225C2314yes—
114C2×#63225C2314yes—
115C2×#63225C2314yes—
116C2×#63225C2312yes—
117C2×#63225C2312yes—
118C2×#63225C2314yes—
119C2×#63225C2314yes—
120C2×#63225C2314yes—
121C2×#63225C2314yes—
122C2×C4×Dic17C2312yes—
123C2×C4×Dic17C2311yescharacteristic
124C2×C4×Dic17C2312yes—
125C2×C4×Dic17C2311yescharacteristic
126#10587578—28no—
127C4⋊C4×D17—28no—
128C4⋊C4×D17—216no—
129C4⋊C4×D17—28no—
130C4⋊C4×D17—28no—
131C4⋊C4×D17—48no—
132C4⋊C4×D17—48no—
133#10587576—28no—
134#10587575—216no—
135C22⋊C4×D17—28no—
136C22⋊C4×D17—48no—
137#10587563—28no—
138#10587558—24no—
139#10587558—24no—
140C42×D17—24no—
141C42×D17D418yes—
142#10587556—24no—
143C17×#95C2314yes—
144C17×#95C2314yes—
145#10587502C2314yes—
146#10587502C2314yes—
147#10587502C2314yes—
148#10587502C2314yes—
149#10587502C2314yes—
150#10587502C2314yes—
151C24×C17C2411yescharacteristic
152C23×D17—22no—
153C23×D17—22no—
154C23×D17—24no—
155C23×D17—24no—
156C23×D17C2×Q814yes—
157C23×D17C2411yescharacteristic
158C23×D17C2411yescharacteristic
159C22×C4×C17—22no—
160C22×C4×C17—22no—
161C22×C4×C17C2×Q814yes—
162C22×C4×C17C2412yes—
163C22×C4×C17C2414yes—
164C22×C4×C17C2414yes—
165C22×C4×C17C2412yes—
166C22×C4×C17C2411yescharacteristic
167C22×C4×C17C2411yescharacteristic
168C22×Dic17—22no—
169C22×Dic17—22no—
170C22×Dic17C2×Q814yes—
171C22×Dic17C2412yes—
172C22×Dic17C2414yes—
173C22×Dic17C2414yes—
174C22×Dic17C2412yes—
175C22×Dic17C2411yescharacteristic
176C22×Dic17C2411yescharacteristic
177C2×C4×D17—22no—
178C2×C4×D17—22no—
179C2×C4×D17—24no—
180C2×C4×D17—24no—
181C2×C4×D17—22no—
182C2×C4×D17—22no—
183C2×C4×D17—22no—
184C2×C4×D17—22no—
185C2×C4×D17—232no—
186C2×C4×D17—24no—
187C2×C4×D17—28no—
188C2×C4×D17—28no—
189C2×C4×D17—28no—
190C2×C4×D17—28no—
191C2×C4×D17—24no—
192C2×C4×D17—28no—
193C2×C4×D17—24no—
194C2×C4×D17—28no—
195C2×C4×D17C2×D418yes—
196C2×C4×D17C2×D414yes—
197C2×C4×D17C2×Q814yes—
198C2×C4×D17C2×Q814yes—
199C2×C4×D17C2×Q814yes—
200C2×C4×D17C2×Q814yes—
201C2×C4×D17#4114yes—
202C4⋊C4×C17—28no—
203C4⋊C4×C17—24no—
204C4⋊C4×C17—24no—
205C4⋊C4×C17—24no—
206C4⋊C4×C17—44no—
207C4⋊C4×C17—44no—
208C22⋊C4×C17—24no—
209C22⋊C4×C17—44no—
210C42×C17—22no—
211C42×C17C2×D414yes—
212C22⋊Dic17—24no—
213C22⋊Dic17—44no—
214#63227—24no—
215#63227—24no—
216#63227—44no—
217#63227—44no—
218C4⋊Dic17—24no—
219C4⋊Dic17—24no—
220C4⋊Dic17—28no—
221C4⋊Dic17—24no—
222C4⋊Dic17—44no—
223C4⋊Dic17—44no—
224#63225—28no—
225#63225—24no—
226#63225—24no—
227#63225—28no—
228#63225—28no—
229#63225—28no—
230#63225—44no—
231#63225—44no—
232#63225—44no—
233#63225—44no—
234C4×Dic17—22no—
235C4×Dic17—24no—
236C4×Dic17C2×D414yes—
237C4×Dic17C2×D418yes—
238C2×#2629—171nomaximal, Sylow
239C23×C17—21no—
240C23×C17—21no—
241C23×C17—22no—
242C23×C17—22no—
243C23×C17C22×Q812yes—
244C23×C17C2511yescharacteristic
245C22×D17—21no—
246C22×D17—21no—
247C22×D17—22no—
248C22×D17—22no—
249C22×D17—28no—
250C22×D17—216no—
251C22×D17—48no—
252C22×D17—44no—
253C22×D17—44no—
254C22×D17C22×D412yes—
255C22×D17C22×Q812yes—
256C22×D17C22×Q812yes—
257C22×D17C2×#4112yes—
258C22×D17H(5,𝔽2)14yes—
259C22×D172−1+414yes—
260C2×C4×C17—21no—
261C2×C4×C17—21no—
262C2×C4×C17—22no—
263C2×C4×C17—22no—
264C2×C4×C17—28no—
265C2×C4×C17—22no—
266C2×C4×C17—24no—
267C2×C4×C17—24no—
268C2×C4×C17—24no—
269C2×C4×C17—24no—
270C2×C4×C17—22no—
271C2×C4×C17—24no—
272C2×C4×C17—22no—
273C2×C4×C17—24no—
274C2×C4×C17C22×D414yes—
275C2×C4×C17C22×D412yes—
276C2×C4×C17C22×Q812yes—
277C2×C4×C17C22×Q812yes—
278C2×C4×C17C2×#4112yes—
279C2×Dic17—21no—
280C2×Dic17—21no—
281C2×Dic17—22no—
282C2×Dic17—22no—
283C2×Dic17—28no—
284C2×Dic17—22no—
285C2×Dic17—24no—
286C2×Dic17—24no—
287C2×Dic17—24no—
288C2×Dic17—24no—
289C2×Dic17—24no—
290C2×Dic17—22no—
291C2×Dic17—22no—
292C2×Dic17—24no—
293C2×Dic17C22×D414yes—
294C2×Dic17C22×D412yes—
295C2×Dic17C22×Q812yes—
296C2×Dic17C22×Q812yes—
297C2×Dic17C2×#4112yes—
298C4×D17—28no—
299C4×D17—216no—
300C4×D17—28no—
301C4×D17—28no—
302C4×D17—48no—
303C4×D17—416no—
304C4×D17—416no—
305C4×D17C22⋊Q8116yes—
306C22×#125—171no—
307C22×#117—171no—
308#2629—174no—
309#2629—174no—
310#2629—172no—
311#2629—171no—
312#2629—172no—
313#2629—171no—
314#2629—171no—
315#2629D1711yescharacteristic, direct product factor
316C2×#398—174no—
317C2×#396—174no—
318C2×#389—172no—
319C2×#384—171no—
320C2×#380—172no—
321C22×C17—22no—
322C22×C17—24no—
323C22×C17—42no—
324C22×C17—41no—
325C22×C17—41no—
326C22×C17C23×D411yescharacteristic
327C22×C17C23×Q811yescharacteristic
328C22×C17C22×#4111yescharacteristic
329C22×C17C2×H(5,𝔽2)12yes—
330C22×C17C2×2−1+412yes—
331C2×D17—22no—
332C2×D17—24no—
333C2×D17—42no—
334C2×D17—41no—
335C2×D17—41no—
336C2×D17—416no—
337C2×D17C2×C22⋊Q814yes—
338C2×D17#53718yes—
339C2×D17#54014yes—
340C2×D17#54114yes—
341C2×D17#54418yes—
342C4×C17—22no—
343C4×C17—24no—
344C4×C17—42no—
345C4×C17—44no—
346C4×C17—44no—
347C4×C17C2×C22⋊Q814yes—
348Dic17—22no—
349Dic17—24no—
350Dic17—42no—
351Dic17—44no—
352Dic17—44no—
353Dic17C2×C22⋊Q814yes—
354C24×C4—171no—
355C2×#125—174no—
356C2×#125—172no—
357C2×#125—171no—
358C2×#125—348no—
359C2×#125C2×D1711yescharacteristic, complemented
360C2×#117—171no—
361C2×#117—172no—
362C2×#117—172no—
363C2×#117—171no—
364C2×#117—171no—
365C2×#117—348no—
366C2×#117C2×D1711yescharacteristic
367C22×C4⋊C4—174no—
368C22×C4⋊C4—172no—
369C22×C4⋊C4—172no—
370C22×C4⋊C4—172no—
371C22×C4⋊C4—174no—
372C22×C4⋊C4—174no—
373C22×C22⋊C4—172no—
374C22×C22⋊C4—174no—
375C22×C42—171no—
376C22×C42—171no—
377#398—174no—
378#398—174no—
379#398—174no—
380#398—174no—
381#398—174no—
382#398—174no—
383#398—174no—
384#398C2×D1714yescomplemented
385#396—174no—
386#396—174no—
387#396—174no—
388#396—174no—
389#396—174no—
390#396—174no—
391#396—174no—
392#396C2×D1714yes—
393#389—174no—
394#389—172no—
395#389—172no—
396#389—172no—
397#389—174no—
398#389C2×D1712yescomplemented
399#384—174no—
400#384—172no—
401#384—171no—
402#384C2×D1711yescharacteristic, complemented
403#380—172no—
404#380—172no—
405#380—172no—
406#380—174no—
407#380—174no—
408#380C2×D1712yes—
409C2×#95—174no—
410C2×#95—174no—
411C2×C17—42no—
412C2×C17C22×C22⋊Q811yescharacteristic
413C2×C17C2×#53712yes—
414C2×C17C2×#54011yescharacteristic
415C2×C17C2×#54111yescharacteristic
416C2×C17C2×#54412yes—
417D17—42no—
418D17#262918yesdirect product factor
419C25—171no—
420C23×C4—171no—
421C23×C4—171no—
422C23×C4—178no—
423C23×C4—172no—
424C23×C4—171no—
425C23×C4—171no—
426C23×C4—171no—
427C23×C4—174no—
428C23×C4—174no—
429C23×C4—172no—
430C23×C4—344no—
431C23×C4—344no—
432C23×C4C22×D1711yescharacteristic
433#125—24no—
434#125—3416no—
435#125—348no—
436#125—344no—
437#117—24no—
438#117—344no—
439#117—348no—
440#117—348no—
441#117—344no—
442#117—344no—
443C2×C4⋊C4—172no—
444C2×C4⋊C4—172no—
445C2×C4⋊C4—172no—
446C2×C4⋊C4—174no—
447C2×C4⋊C4—172no—
448C2×C4⋊C4—174no—
449C2×C4⋊C4—174no—
450C2×C4⋊C4—174no—
451C2×C4⋊C4—174no—
452C2×C4⋊C4—172no—
453C2×C4⋊C4—174no—
454C2×C4⋊C4—174no—
455C2×C4⋊C4—174no—
456C2×C4⋊C4—174no—
457C2×C4⋊C4—174no—
458C2×C4⋊C4—174no—
459C2×C4⋊C4—348no—
460C2×C4⋊C4—348no—
461C2×C4⋊C4—3416no—
462C2×C4⋊C4—348no—
463C2×C4⋊C4—688no—
464C2×C4⋊C4—688no—
465C2×C4⋊C4C22×D1712yes—
466C2×C4⋊C4C22×D1712yes—
467C2×C4⋊C4C22×D1714yes—
468C2×C4⋊C4C22×D1712yes—
469C2×C4⋊C4C22×D1714yes—
470C2×C4⋊C4C22×D1714yes—
471C2×C22⋊C4—172no—
472C2×C22⋊C4—172no—
473C2×C22⋊C4—172no—
474C2×C22⋊C4—174no—
475C2×C22⋊C4—174no—
476C2×C22⋊C4—174no—
477C2×C22⋊C4—348no—
478C2×C22⋊C4—688no—
479C2×C22⋊C4C22×D1712yes—
480C2×C22⋊C4C22×D1714yes—
481C2×C42—172no—
482C2×C42—171no—
483C2×C42—178no—
484C2×C42—172no—
485C2×C42—171no—
486C2×C42—344no—
487C2×C42C22×D1711yescharacteristic
488C2×C42C22×D1711yescharacteristic
489#95—174no—
490#95—174no—
491#95—174no—
492#95—174no—
493#95—174no—
494#95—174no—
495#95C22×D1714yes—
496#95C22×D1714yes—
497C17C2×#262911yescharacteristic, complemented, Sylow
498C24—171no—
499C24—174no—
500C24—171no—
501C24—342no—
502C24—344no—
503C24—342no—
504C24—344no—
505C24C23×D1711yescharacteristic
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—171no—
509C22×C4—174no—
510C22×C4—174no—
511C22×C4—174no—
512C22×C4—174no—
513C22×C4—171no—
514C22×C4—172no—
515C22×C4—178no—
516C22×C4—174no—
517C22×C4—174no—
518C22×C4—174no—
519C22×C4—172no—
520C22×C4—174no—
521C22×C4—174no—
522C22×C4—342no—
523C22×C4—342no—
524C22×C4—3432no—
525C22×C4—342no—
526C22×C4—344no—
527C22×C4—344no—
528C22×C4—342no—
529C22×C4—344no—
530C22×C4—348no—
531C22×C4—348no—
532C22×C4—348no—
533C22×C4—348no—
534C22×C4—348no—
535C22×C4—344no—
536C22×C4—348no—
537C22×C4—344no—
538C22×C4—342no—
539C22×C4—342no—
540C22×C4—342no—
541C22×C4—342no—
542C22×C4Q8×D1714yes—
543C22×C4C23×D1712yes—
544C22×C4C23×D1714yes—
545C22×C4C23×D1714yes—
546C22×C4C23×D1712yes—
547C22×C4C23×D1711yescharacteristic
548C22×C4C23×D1711yescharacteristic
549C4⋊C4—24no—
550C4⋊C4—28no—
551C4⋊C4—24no—
552C4⋊C4—24no—
553C4⋊C4—44no—
554C4⋊C4—44no—
555C4⋊C4—344no—
556C4⋊C4—344no—
557C4⋊C4—348no—
558C4⋊C4—348no—
559C4⋊C4—348no—
560C4⋊C4—348no—
561C4⋊C4—344no—
562C4⋊C4—348no—
563C4⋊C4—344no—
564C4⋊C4—344no—
565C4⋊C4—684no—
566C4⋊C4—684no—
567C4⋊C4—684no—
568C4⋊C4—684no—
569C4⋊C4—684no—
570C4⋊C4—684no—
571C22⋊C4—24no—
572C22⋊C4—44no—
573C22⋊C4—344no—
574C22⋊C4—344no—
575C22⋊C4—344no—
576C22⋊C4—684no—
577C22⋊C4—684no—
578C22⋊C4—684no—
579C42—22no—
580C42—178no—
581C42—174no—
582C42—344no—
583C42—342no—
584C42D4×D1714yes—
585C23—21no—
586C23—21no—
587C23—22no—
588C23—22no—
589C23—172no—
590C23—172no—
591C23—172no—
592C23—174no—
593C23—174no—
594C23—172no—
595C23—348no—
596C23—3416no—
597C23—341no—
598C23—341no—
599C23—342no—
600C23—342no—
601C23—688no—
602C23—684no—
603C23—684no—
604C23C2×Q8×D1712yes—
605C23C24×D1711yescharacteristic
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—28no—
611C2×C4—22no—
612C2×C4—24no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—22no—
617C2×C4—24no—
618C2×C4—22no—
619C2×C4—24no—
620C2×C4—172no—
621C2×C4—172no—
622C2×C4—172no—
623C2×C4—1716no—
624C2×C4—174no—
625C2×C4—172no—
626C2×C4—348no—
627C2×C4—348no—
628C2×C4—3416no—
629C2×C4—348no—
630C2×C4—341no—
631C2×C4—341no—
632C2×C4—342no—
633C2×C4—342no—
634C2×C4—348no—
635C2×C4—342no—
636C2×C4—344no—
637C2×C4—344no—
638C2×C4—344no—
639C2×C4—344no—
640C2×C4—342no—
641C2×C4—344no—
642C2×C4—342no—
643C2×C4—344no—
644C2×C4—688no—
645C2×C4—6816no—
646C2×C4—6816no—
647C2×C4C2×D4×D1714yes—
648C2×C4C2×D4×D1712yes—
649C2×C4C2×Q8×D1712yes—
650C2×C4C2×Q8×D1712yes—
651C2×C4#41×D1712yes—
652C22—24no—
653C22—22no—
654C22—42no—
655C22—41no—
656C22—41no—
657C22—178no—
658C22—174no—
659C22—174no—
660C22—178no—
661C22—174no—
662C22—344no—
663C22—342no—
664C22—6816no—
665C22—682no—
666C22—681no—
667C22—681no—
668C22C22×D4×D1711yescharacteristic
669C22C22×Q8×D1711yescharacteristic
670C22C2×#41×D1711yescharacteristic
671C22H(5,𝔽2)×D1712yes—
672C222−1+4×D1712yes—
673C4—24no—
674C4—22no—
675C4—42no—
676C4—44no—
677C4—44no—
678C4—174no—
679C4—344no—
680C4—342no—
681C4—682no—
682C4—684no—
683C4—684no—
684C4C22⋊Q8×D1714yes—
685C2—42no—
686C2—178no—
687C2—682no—
688C2C2×C22⋊Q8×D1711yescharacteristic
689C2D17×#53712yes—
690C2D17×#54011yescharacteristic
691C2D17×#54111yescharacteristic
692C2D17×#54412yes—
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2629C2
prime radicalC24×D17C23
hypercenter#2629D17
hypocenterC17C2×#2629
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2629

Complements

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

NH ≅ G/Ntype
1. C2×#125×D17C2semidirect
3. #14534619C2semidirect
4. #14534618C2semidirect
5. #14534617C2semidirect
6. #14534616C2semidirect
7. #14534615C2semidirect
8. #14534614C2semidirect
9. #14534613C2semidirect
10. D17×#398C2semidirect
12. D17×#389C2semidirect
13. D17×#384C2semidirect
15. C17×#2629C2semidirect
17. C2×#10587556C22semidirect
18. C2×#10587576C22semidirect
19. C2×#10587575C22semidirect
37. #11762743C22semidirect
38. #11762743C22semidirect
39. #11762742C22semidirect
40. #11762742C22semidirect
41. #11762741C22semidirect
42. #11762740C22semidirect
43. #11762739C22semidirect
51. #11762708C22semidirect
52. #11762707C22semidirect
53. #11762706C22semidirect
54. #11762705C22semidirect
55. #11762704C22semidirect
56. #11762679C22semidirect
57. #11762678C22semidirect
58. #11762678C22semidirect
66. C2×C17×#125C22semidirect
68. C17×#398C22semidirect
70. C17×#389C22semidirect
71. C17×#384C22semidirect
315. #2629D17direct (N × H)
359. C2×#125C2×D17semidirect
384. #398C2×D17semidirect
398. #389C2×D17semidirect
402. #384C2×D17semidirect
418. D17#2629direct (N × H)
497. C17C2×#2629semidirect

Maximal subgroups

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

subgroupindex
C2×#125×D172
C2×#117×D172
#145346192
#145346182
#145346172
#145346162
#145346152
#145346142
#145346132
D17×#3982
D17×#3962
D17×#3892
D17×#3842
D17×#3802
C17×#26292
C2×#262917