Finite Group Databasebeta

← C2×#14536971 #17240543

Subgroups — C2×#14536971 #17240543

Order 4352.

2022 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14536971C2116yesmaximal, direct product factor
2C2×#11762751C211yesmaximal, characteristic, complemented
3C2×#11762751C211yesmaximal, characteristic, complemented
4C2×#11762750C211yesmaximal, characteristic, complemented
5C2×#11762749C211yesmaximal, characteristic, complemented
6C2×#11762748C211yesmaximal, characteristic, complemented
7C2×#11762738C211yesmaximal, characteristic
8C2×#11762736C211yesmaximal, characteristic
9C2×#11762735C211yesmaximal, characteristic
10C2×#11762730C211yesmaximal, characteristic, complemented
11C2×#11762729C211yesmaximal, characteristic, complemented
12C2×#11762722C211yesmaximal, characteristic
13C2×#11762683C211yesmaximal, characteristic
14C2×#11762683C211yesmaximal, characteristic
15C2×#11762680C211yesmaximal, characteristic
16C2×C17×#400C211yesmaximal, characteristic, complemented
17C23×Dic34C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C22×C4⋊Dic17C2211yescharacteristic
20C22×C4⋊Dic17C2211yescharacteristic
21C22×C4⋊Dic17C2211yescharacteristic
22C22×#63225C2211yescharacteristic
23C22×#63225C2211yescharacteristic
24C22×#63225C2211yescharacteristic
25C22×#63225C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32#11762751C2218yescomplemented
33#11762751C2218yescomplemented
34#11762750C2218yescomplemented
35#11762749C2218yescomplemented
36#11762748C2218yescomplemented
37#11762738C2218yes—
38#11762736C2218yes—
39#11762735C2218yes—
40#11762730C2218yescomplemented
41#11762729C2218yescomplemented
42#11762722C2218yes—
43#11762683C2218yes—
44#11762683C2218yes—
45#11762680C2218yes—
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C2×#10587502C2211yescharacteristic
52C2×#10587502C2211yescharacteristic
53C2×#10587502C2211yescharacteristic
54C2×#10587502C2211yescharacteristic
55C2×#10587502C2211yescharacteristic
56C2×#10587502C2211yescharacteristic
57C2×#10587502C2211yescharacteristic
58C2×#10587502C2211yescharacteristic
59C22×C4⋊C4×C17C2211yescharacteristic
60C22×C4⋊C4×C17C2211yescharacteristic
61C17×#400C2218yescomplemented
62C2×C17×#95C2211yescharacteristic
63C2×C17×#95C2211yescharacteristic
64C2×C17×#95C2211yescharacteristic
65C2×C17×#95C2211yescharacteristic
66C2×C17×#95C2211yescharacteristic
67C24×D17C2311yescharacteristic
68C23×C4×C17C2311yescharacteristic
69C23×C4×C17C2311yescharacteristic
70C23×C4×C17C2311yescharacteristic
71C23×C4×C17C2311yescharacteristic
72C23×C4×C17C2311yescharacteristic
73C23×C4×C17C2311yescharacteristic
74C23×C4×C17C2311yescharacteristic
75C23×Dic17C2311yescharacteristic
76C23×Dic17C2311yescharacteristic
77C23×Dic17C2311yescharacteristic
78C23×Dic17C2311yescharacteristic
79C23×Dic17C2311yescharacteristic
80C23×Dic17C2311yescharacteristic
81C23×Dic17C2311yescharacteristic
82C22×C4×D17—42no—
83C22×C4×D17—42no—
84C22×C4×D17—42no—
85C22×C4×D17C2314yes—
86C22×Dic34—42no—
87C22×Dic34—42no—
88C22×Dic34—42no—
89C22×Dic34C2314yes—
90C2×C4⋊C4×C17—42no—
91C2×C4⋊C4×C17—42no—
92C2×C4⋊C4×C17C2314yes—
93C2×C4⋊C4×C17C2314yes—
94C2×#63227—24no—
95C2×#63227—24no—
96C2×#63227—24no—
97C2×#63227—42no—
98C2×#63227—42no—
99C2×#63227—42no—
100C2×#63227C2314yes—
101C2×#63227C2314yes—
102C2×#63227C2314yes—
103C2×#63227C2314yes—
104C2×#63227C2314yes—
105C2×#63227C2314yes—
106C2×C4⋊Dic17—42no—
107C2×C4⋊Dic17—42no—
108C2×C4⋊Dic17—42no—
109C2×C4⋊Dic17C2314yes—
110C2×C4⋊Dic17C2314yes—
111C2×C4⋊Dic17C2314yes—
112C2×#63225—42no—
113C2×#63225—42no—
114C2×#63225—42no—
115C2×#63225—42no—
116C2×#63225C2314yes—
117C2×#63225C2314yes—
118C2×#63225C2314yes—
119C2×#63225C2314yes—
120C17×#95C2314yes—
121C17×#95C2314yes—
122C17×#95C2314yes—
123C17×#95C2314yes—
124C17×#95C2314yes—
125#10587502C2314yes—
126#10587502C2314yes—
127#10587502C2314yes—
128#10587502C2314yes—
129#10587502C2314yes—
130#10587502C2314yes—
131#10587502C2314yes—
132#10587502C2314yes—
133#10587502C2314yes—
134#10587502C2314yes—
135#10587502C2314yes—
136#10587502C2314yes—
137#10587502C2314yes—
138C24×C17C2411yescharacteristic
139C23×D17—22no—
140C23×D17—22no—
141C23×D17—22no—
142C23×D17—22no—
143C23×D17—22no—
144C23×D17—22no—
145C23×D17#4114yes—
146C23×D17C2412yes—
147C22×C4×C17—22no—
148C22×C4×C17—22no—
149C22×C4×C17—22no—
150C22×C4×C17—22no—
151C22×C4×C17—22no—
152C22×C4×C17—22no—
153C22×C4×C17—22no—
154C22×C4×C17—22no—
155C22×C4×C17—22no—
156C22×C4×C17—22no—
157C22×C4×C17—22no—
158C22×C4×C17—22no—
159C22×C4×C17—22no—
160C22×C4×C17—22no—
161C22×C4×C17—22no—
162C22×C4×C17—22no—
163C22×C4×C17—22no—
164C22×C4×C17—22no—
165C22×C4×C17—22no—
166C22×C4×C17—22no—
167C22×C4×C17—22no—
168C22×C4×C17C2412yes—
169C22×C4×C17C2412yes—
170C22×C4×C17C2412yes—
171C22×C4×C17C2412yes—
172C22×C4×C17C2412yes—
173C22×C4×C17C2412yes—
174C22×C4×C17C2412yes—
175C22×Dic17—22no—
176C22×Dic17—22no—
177C22×Dic17—22no—
178C22×Dic17—22no—
179C22×Dic17—22no—
180C22×Dic17—22no—
181C22×Dic17—22no—
182C22×Dic17—22no—
183C22×Dic17—22no—
184C22×Dic17—22no—
185C22×Dic17—22no—
186C22×Dic17—22no—
187C22×Dic17—22no—
188C22×Dic17—22no—
189C22×Dic17—22no—
190C22×Dic17—22no—
191C22×Dic17—22no—
192C22×Dic17—22no—
193C22×Dic17—22no—
194C22×Dic17—22no—
195C22×Dic17—22no—
196C22×Dic17C2412yes—
197C22×Dic17C2412yes—
198C22×Dic17C2412yes—
199C22×Dic17C2412yes—
200C22×Dic17C2412yes—
201C22×Dic17C2412yes—
202C22×Dic17C2412yes—
203C2×C4×D17—44no—
204C2×C4×D17—44no—
205C2×C4×D17—44no—
206C2×C4×D17—416no—
207C2×Dic34—44no—
208C2×Dic34—44no—
209C2×Dic34—44no—
210C2×Dic34—416no—
211C4⋊C4×C17—44no—
212C4⋊C4×C17—44no—
213#63227—28no—
214#63227—28no—
215#63227—28no—
216#63227—44no—
217#63227—44no—
218#63227—44no—
219C4⋊Dic17—44no—
220C4⋊Dic17—44no—
221C4⋊Dic17—44no—
222#63225—44no—
223#63225—44no—
224#63225—44no—
225#63225—44no—
226C2×#2835—171nomaximal, Sylow
227C23×C17C2×#4112yes—
228C23×C17H(5,𝔽2)12yes—
229C23×C17H(5,𝔽2)12yes—
230C23×C17H(5,𝔽2)12yes—
231C23×C172−1+412yes—
232C23×C172−1+412yes—
233C23×C172−1+412yes—
234C23×C17C2511yescharacteristic
235C22×D17—28no—
236C22×D17—28no—
237C22×D17—28no—
238C22×D17—22no—
239C22×D17—22no—
240C22×D17—22no—
241C22×D17—22no—
242C22×D17—22no—
243C22×D17—22no—
244C22×D17—44no—
245C22×D17—44no—
246C22×D17—44no—
247C22×D17—44no—
248C22×D17C2×#4114yes—
249C2×C4×C17—22no—
250C2×C4×C17—22no—
251C2×C4×C17—22no—
252C2×C4×C17—22no—
253C2×C4×C17—22no—
254C2×C4×C17—22no—
255C2×C4×C17—22no—
256C2×C4×C17—22no—
257C2×C4×C17—22no—
258C2×C4×C17—22no—
259C2×C4×C17—22no—
260C2×C4×C17—22no—
261C2×C4×C17—22no—
262C2×C4×C17—22no—
263C2×C4×C17—22no—
264C2×C4×C17—22no—
265C2×C4×C17—22no—
266C2×C4×C17—22no—
267C2×C4×C17—22no—
268C2×C4×C17—22no—
269C2×C4×C17—22no—
270C2×C4×C17—44no—
271C2×C4×C17—44no—
272C2×C4×C17—44no—
273C2×C4×C17—44no—
274C2×C4×C17—44no—
275C2×C4×C17—44no—
276C2×C4×C17—44no—
277C2×Dic17—22no—
278C2×Dic17—22no—
279C2×Dic17—22no—
280C2×Dic17—22no—
281C2×Dic17—22no—
282C2×Dic17—22no—
283C2×Dic17—22no—
284C2×Dic17—22no—
285C2×Dic17—22no—
286C2×Dic17—22no—
287C2×Dic17—22no—
288C2×Dic17—22no—
289C2×Dic17—22no—
290C2×Dic17—22no—
291C2×Dic17—22no—
292C2×Dic17—22no—
293C2×Dic17—22no—
294C2×Dic17—22no—
295C2×Dic17—22no—
296C2×Dic17—22no—
297C2×Dic17—22no—
298C2×Dic17—44no—
299C2×Dic17—44no—
300C2×Dic17—44no—
301C2×Dic17—44no—
302C2×Dic17—44no—
303C2×Dic17—44no—
304C2×Dic17—44no—
305C4×D17—416no—
306Dic34—416no—
307#2835—1716no—
308C2×#400—171no—
309C2×#400—171no—
310C2×#400—171no—
311C2×#400—171no—
312C2×#400—171no—
313C2×#400D1711yescharacteristic, complemented
314C2×#397—171no—
315C2×#397—171no—
316C2×#397—171no—
317C2×#395—171no—
318C2×#395—171no—
319C2×#393—171no—
320C2×#385—171no—
321C2×#385—171no—
322C2×#385—171no—
323C22×C17#53914yes—
324C22×C17#53914yes—
325C22×C17#53914yes—
326C22×C17H(3,𝔽4)14yes—
327C22×C17#56314yes—
328C22×C17#56314yes—
329C22×C17#56314yes—
330C22×C17C22×#4111yescharacteristic
331C22×C17C2×H(5,𝔽2)11yescharacteristic
332C22×C17C2×H(5,𝔽2)11yescharacteristic
333C22×C17C2×H(5,𝔽2)11yescharacteristic
334C22×C17C2×2−1+411yescharacteristic
335C22×C17C2×2−1+411yescharacteristic
336C22×C17C2×2−1+411yescharacteristic
337C2×D17—24no—
338C2×D17—24no—
339C2×D17—24no—
340C2×D17—416no—
341C2×D17—42no—
342C2×D17—42no—
343C2×D17—42no—
344C2×D17—42no—
345C4×C17—42no—
346C4×C17—42no—
347C4×C17—42no—
348C4×C17—42no—
349C4×C17—42no—
350C4×C17—42no—
351C4×C17—42no—
352Dic17—42no—
353Dic17—42no—
354Dic17—42no—
355Dic17—42no—
356Dic17—42no—
357Dic17—42no—
358Dic17—42no—
359C23×Q8—171no—
360C24×C4—171no—
361C22×C4⋊C4—171no—
362C22×C4⋊C4—171no—
363C22×C4⋊C4—171no—
364C22×C4⋊C4—171no—
365C22×C4⋊C4—171no—
366C22×C4⋊C4—171no—
367C22×C4⋊C4—171no—
368C22×C4⋊C4C2×D1711yescharacteristic
369C22×C4⋊C4C2×D1711yescharacteristic
370C22×C22⋊C4—171no—
371C22×C22⋊C4—171no—
372C22×C22⋊C4—171no—
373C22×C22⋊C4—171no—
374C22×C22⋊C4—171no—
375C22×C22⋊C4—171no—
376#400—178no—
377#400—178no—
378#400—178no—
379#400—178no—
380#400—178no—
381#400C2×D1718yescomplemented
382#397—178no—
383#397—178no—
384#397—178no—
385#395—178no—
386#395—178no—
387#393—178no—
388#385—178no—
389#385—178no—
390#385—178no—
391C2×#95—171no—
392C2×#95—171no—
393C2×#95—171no—
394C2×#95—171no—
395C2×#95—171no—
396C2×#95—171no—
397C2×#95—171no—
398C2×#95—171no—
399C2×#95—171no—
400C2×#95—171no—
401C2×#95—171no—
402C2×#95—171no—
403C2×#95—171no—
404C2×#95C2×D1711yescharacteristic
405C2×#95C2×D1711yescharacteristic
406C2×#95C2×D1711yescharacteristic
407C2×#95C2×D1711yescharacteristic
408C2×#95C2×D1711yescharacteristic
409C2×C17#283518yescomplemented
410C2×C17C2×#53911yescharacteristic
411C2×C17C2×#53911yescharacteristic
412C2×C17C2×#53911yescharacteristic
413C2×C17C2×H(3,𝔽4)11yescharacteristic
414C2×C17C2×#56311yescharacteristic
415C2×C17C2×#56311yescharacteristic
416C2×C17C2×#56311yescharacteristic
417D17—44no—
418C25—171no—
419C22×Q8—174no—
420C22×Q8—682no—
421C22×Q8—682no—
422C22×Q8—682no—
423C23×C4—171no—
424C23×C4—171no—
425C23×C4—171no—
426C23×C4—171no—
427C23×C4—171no—
428C23×C4—171no—
429C23×C4—171no—
430C23×C4—174no—
431C23×C4—682no—
432C23×C4—682no—
433C23×C4—682no—
434C23×C4C22×D1711yescharacteristic
435C23×C4C22×D1711yescharacteristic
436C23×C4C22×D1711yescharacteristic
437C23×C4C22×D1711yescharacteristic
438C23×C4C22×D1711yescharacteristic
439C23×C4C22×D1711yescharacteristic
440C23×C4C22×D1711yescharacteristic
441C2×C4⋊C4—42no—
442C2×C4⋊C4—42no—
443C2×C4⋊C4—174no—
444C2×C4⋊C4—174no—
445C2×C4⋊C4—174no—
446C2×C4⋊C4—174no—
447C2×C4⋊C4—174no—
448C2×C4⋊C4—174no—
449C2×C4⋊C4—174no—
450C2×C4⋊C4—682no—
451C2×C4⋊C4—682no—
452C2×C4⋊C4—682no—
453C2×C4⋊C4—682no—
454C2×C4⋊C4—682no—
455C2×C4⋊C4—682no—
456C2×C4⋊C4—682no—
457C2×C4⋊C4C22×D1714yes—
458C2×C4⋊C4C22×D1714yes—
459C2×C22⋊C4—174no—
460C2×C22⋊C4—174no—
461C2×C22⋊C4—174no—
462C2×C22⋊C4—174no—
463C2×C22⋊C4—174no—
464C2×C22⋊C4—174no—
465C2×C22⋊C4—344no—
466C2×C22⋊C4—344no—
467C2×C22⋊C4—344no—
468C2×C22⋊C4—682no—
469C2×C22⋊C4—682no—
470C2×C22⋊C4—682no—
471#95—174no—
472#95—174no—
473#95—174no—
474#95—174no—
475#95—174no—
476#95—174no—
477#95—174no—
478#95—174no—
479#95—174no—
480#95—174no—
481#95—174no—
482#95—174no—
483#95—174no—
484#95C22×D1714yes—
485#95C22×D1714yes—
486#95C22×D1714yes—
487#95C22×D1714yes—
488#95C22×D1714yes—
489C17C2×#283511yescharacteristic, complemented, Sylow
490C24—174no—
491C24—172no—
492C24—342no—
493C24—342no—
494C24—342no—
495C24—342no—
496C24—342no—
497C24—342no—
498C24C23×D1711yescharacteristic
499C2×Q8—684no—
500C2×Q8—684no—
501C2×Q8—684no—
502C2×Q8—6816no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—172no—
525C22×C4—172no—
526C22×C4—172no—
527C22×C4—172no—
528C22×C4—172no—
529C22×C4—172no—
530C22×C4—172no—
531C22×C4—342no—
532C22×C4—342no—
533C22×C4—342no—
534C22×C4—342no—
535C22×C4—342no—
536C22×C4—342no—
537C22×C4—342no—
538C22×C4—342no—
539C22×C4—342no—
540C22×C4—342no—
541C22×C4—342no—
542C22×C4—342no—
543C22×C4—342no—
544C22×C4—342no—
545C22×C4—342no—
546C22×C4—342no—
547C22×C4—342no—
548C22×C4—342no—
549C22×C4—342no—
550C22×C4—342no—
551C22×C4—342no—
552C22×C4—684no—
553C22×C4—684no—
554C22×C4—684no—
555C22×C4—6816no—
556C22×C4C23×D1712yes—
557C22×C4C23×D1712yes—
558C22×C4C23×D1712yes—
559C22×C4C23×D1712yes—
560C22×C4C23×D1712yes—
561C22×C4C23×D1712yes—
562C22×C4C23×D1712yes—
563C4⋊C4—44no—
564C4⋊C4—44no—
565C4⋊C4—684no—
566C4⋊C4—684no—
567C4⋊C4—684no—
568C4⋊C4—684no—
569C4⋊C4—684no—
570C4⋊C4—684no—
571C4⋊C4—684no—
572C22⋊C4—348no—
573C22⋊C4—348no—
574C22⋊C4—348no—
575C22⋊C4—684no—
576C22⋊C4—684no—
577C22⋊C4—684no—
578C23—174no—
579C23—342no—
580C23—342no—
581C23—342no—
582C23—342no—
583C23—342no—
584C23—342no—
585C23—348no—
586C23—348no—
587C23—348no—
588C23—684no—
589C23—684no—
590C23—684no—
591C23—684no—
592C23#1058769112yes—
593C23#1058769412yes—
594C23#41×D1712yes—
595C23#1058769612yes—
596C23#1058769612yes—
597C23#1058769712yes—
598C23#1058769712yes—
599C23C24×D1711yescharacteristic
600Q8—6816no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—44no—
623C2×C4—44no—
624C2×C4—44no—
625C2×C4—44no—
626C2×C4—44no—
627C2×C4—44no—
628C2×C4—44no—
629C2×C4—342no—
630C2×C4—342no—
631C2×C4—342no—
632C2×C4—342no—
633C2×C4—342no—
634C2×C4—342no—
635C2×C4—342no—
636C2×C4—342no—
637C2×C4—342no—
638C2×C4—342no—
639C2×C4—342no—
640C2×C4—342no—
641C2×C4—342no—
642C2×C4—342no—
643C2×C4—342no—
644C2×C4—342no—
645C2×C4—342no—
646C2×C4—342no—
647C2×C4—342no—
648C2×C4—342no—
649C2×C4—342no—
650C2×C4—6816no—
651C2×C4—684no—
652C2×C4—684no—
653C2×C4—684no—
654C2×C4—684no—
655C2×C4—684no—
656C2×C4—684no—
657C2×C4—684no—
658C22—344no—
659C22—344no—
660C22—344no—
661C22—6816no—
662C22—682no—
663C22—682no—
664C22—682no—
665C22—682no—
666C22#1176340014yes—
667C22#1176340214yes—
668C22#1176340714yes—
669C22#1176355114yes—
670C22#1176356014yes—
671C22#1176356114yes—
672C22#1176356314yes—
673C22C2×#41×D1711yescharacteristic
674C22C2×#1058769111yescharacteristic
675C22C2×#1058769611yescharacteristic
676C22C2×#1058769611yescharacteristic
677C22C2×#1058769711yescharacteristic
678C22C2×#1058769711yescharacteristic
679C22C2×#1058769411yescharacteristic
680C4—42no—
681C4—42no—
682C4—42no—
683C4—42no—
684C4—42no—
685C4—42no—
686C4—42no—
687C4—682no—
688C4—682no—
689C4—682no—
690C4—682no—
691C4—682no—
692C4—682no—
693C4—682no—
694C2—684no—
695C2#1453697118yesdirect product factor
696C2C2×#1176340011yescharacteristic
697C2C2×#1176340211yescharacteristic
698C2C2×#1176340711yescharacteristic
699C2C2×#1176355111yescharacteristic
700C2C2×#1176356011yescharacteristic
701C2C2×#1176356111yescharacteristic
702C2C2×#1176356311yescharacteristic
subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC2×C17×#400C2
socleC24×C17C24
prime radicalC24×D17C23
hypercenterC2×#400D17
hypocenterC17C2×#2835
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. #14536971C2direct (N × H)
2. C2×#11762751C2semidirect
3. C2×#11762751C2semidirect
4. C2×#11762750C2semidirect
5. C2×#11762749C2semidirect
6. C2×#11762748C2semidirect
10. C2×#11762730C2semidirect
11. C2×#11762729C2semidirect
16. C2×C17×#400C2semidirect
32. #11762751C22semidirect
33. #11762751C22semidirect
34. #11762750C22semidirect
35. #11762749C22semidirect
36. #11762748C22semidirect
40. #11762730C22semidirect
41. #11762729C22semidirect
61. C17×#400C22semidirect
313. C2×#400D17semidirect
381. #400C2×D17semidirect
409. C2×C17#2835semidirect
489. C17C2×#2835semidirect
695. C2#14536971direct (N × H)

Maximal subgroups

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

subgroupindex
#145369712
C2×#117627512
C2×#117627502
C2×#117627492
C2×#117627482
C2×#117627382
C2×#117627362
C2×#117627352
C2×#117627302
C2×#117627292
C2×#117627222
C2×#117626832
C2×#117626802
C2×C17×#4002
C2×#283517