Finite Group Databasebeta

← #26376559

Subgroups — #26376559

Order 12032.

3534 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689635C211yesmaximal, characteristic
2C2×#15689603C211yesmaximal, characteristic, complemented
3C22×C4⋊C4×D47C211yesmaximal, characteristic, complemented
4#20246403C214yesmaximal, complemented
5#20246392C214yesmaximal, complemented
6#20246314C214yesmaximal, complemented
7#20246288C214yesmaximal, complemented
8#20246056C214yesmaximal, complemented
9#20245981C211yesmaximal, characteristic, complemented
10#20245889C214yesmaximal, complemented
11#20245767C211yesmaximal, characteristic, complemented
12#20245744C211yesmaximal, characteristic, complemented
13C47×#2317C211yesmaximal, characteristic, complemented
14C22×#10625350C2211yescharacteristic
15C23×C4×D47C2211yescharacteristic
16C23×C4×D47C2212yes—
17#15689635C4116yescomplemented
18C2×#13094008C2212yes—
19C2×#13094004C2212yes—
20C2×#13093999C2212yes—
21C2×#13093994C2212yes—
22#15689603—28no—
23C2×C4×Dic94C2212yescomplemented
24C2×C4×D188C2214yes—
25C2×C4×D188C2212yescomplemented
26C2×#13093986C2218yes—
27C2×(C22⋊D47)⋊C4C2214yes—
28C2×#13093983C2211yescharacteristic
29C2×#13093982C2212yescomplemented
30C22×C4⋊Dic47C2211yescharacteristic
31C22×Dic47⋊C4C2212yes—
32C2×C4⋊C4×D47—28no—
33C2×C4⋊C4×D47C2214yes—
34C2×C4⋊C4×D47C2214yes—
35C2×C4⋊C4×D47C2212yescomplemented
36#15689028C2212yescomplemented
37#15689024C2212yescomplemented
38#15689019C2218yescomplemented
39#15689012C2218yescomplemented
40#15689006C2218yescomplemented
41#15689002C2214yes—
42#15689001C2218yes—
43#15688994C2218yes—
44#15688994C2218yescomplemented
45#15688984C2212yes—
46#15688980C2212yes—
47#15688980C2212yes—
48#15688980C2214yescomplemented
49#15688978C2212yes—
50C4⋊C4×Dic47C2214yescomplemented
51C4×C4⋊Dic47C2214yescomplemented
52C22⋊C4×Dic47C2214yes—
53C4×(C2×D47)⋊C4C2214yes—
54#15688970C2218yes—
55C2×#117×C47C2211yescharacteristic
56C2×#117×C47C2211yescharacteristic
57C22×C4⋊C4×C47C2211yescharacteristic
58C47×#389C2214yescomplemented
59C47×#385C2214yes—
60C47×#384C2212yescomplemented
61C47×#382C2212yescomplemented
62C24×D47C2311yescharacteristic
63C2×#10625350—24no—
64C2×#10625350—24no—
65C2×#10625350C2×C418yescomplemented
66C22×Dic94C2311yescharacteristic
67C22×D188C2314yes—
68C22×D188C2311yescharacteristic
69C22×C22⋊D47C2312yes—
70C23×Dic47C2311yescharacteristic
71C23×Dic47C2312yes—
72C22×C4×D47—24no—
73C22×C4×D47—24no—
74C22×C4×D47—28no—
75C22×C4×D47—48no—
76C22×C4×D47C2×C418yescomplemented
77C22×C4×D47C2318yes—
78C22×C4×D47C2312yes—
79C22×C4×D47C2312yes—
80C22×C4×D47C2312yes—
81C22×C4×D47C2314yes—
82#13094008C2×C4116yescomplemented
83#13094004C2×C4116yescomplemented
84#13093999C2×C4116yescomplemented
85#13093994C2×C4116yescomplemented
86C4×Dic94—28no—
87C4×D188—28no—
88C4×D188C2×C4132yescomplemented
89#13093986—416no—
90(C22⋊D47)⋊C4—216no—
91#13093983—24no—
92#13093982—28no—
93C2×C4⋊Dic47D418yescomplemented
94C2×C4⋊Dic47C2312yes—
95C2×C4⋊Dic47C2314yes—
96C2×C4⋊Dic47C2312yes—
97C2×C4⋊Dic47C2312yes—
98C2×Dic47⋊C4—28no—
99C2×Dic47⋊C4C2314yes—
100C2×Dic47⋊C4C2318yes—
101C4⋊C4×D47—216no—
102C4⋊C4×D47—216no—
103C4⋊C4×D47—28no—
104C2×C22⋊Dic47C2312yes—
105C2×(C2×D47)⋊C4C2314yes—
106C2×(C2×D47)⋊C4C2314yes—
107C2×(C2×D47)⋊C4C2314yes—
108C2×(C2×D47)⋊C4C2318yes—
109C2×(C2×D47)⋊C4C2314yes—
110C2×(C2×D47)⋊C4C2314yes—
111C2×C4×Dic47C2314yes—
112C2×C4×Dic47C2312yes—
113C2×C4×Dic47C2318yes—
114C47⋊#95C2318yes—
115C47⋊#95C2314yes—
116C47⋊#95C2314yes—
117C47⋊#95C2318yes—
118C23×C4×C47C2312yes—
119C23×C4×C47C2311yescharacteristic
120#117×C47—24no—
121#117×C47C2×C418yescomplemented
122C2×C4⋊C4×C47—24no—
123C2×C4⋊C4×C47C2311yescharacteristic
124C2×C4⋊C4×C47C2311yescharacteristic
125C2×C4⋊C4×C47C2312yes—
126C2×C4⋊C4×C47C2312yes—
127C2×C4⋊C4×C47C2318yes—
128C2×C4⋊C4×C47C2312yes—
129C2×C22⋊C4×C47C2312yes—
130C2×C22⋊C4×C47C2312yes—
131C2×C42×C47C2312yes—
132C2×C42×C47C2312yes—
133#95×C47C2318yes—
134C24×C47C2411yescharacteristic
135C23×D47—22no—
136C23×D47—22no—
137C23×D47—24no—
138C23×D47—24no—
139C23×D47C22×C414yes—
140C23×D47C2412yes—
141C23×D47C2412yes—
142C22×C4×C47—24no—
143C22×C4×C47—44no—
144C22×C4×C47C22×C414yes—
145C22×C4×C47C2×D414yes—
146C22×C4×C47#4114yes—
147C22×C4×C47C2412yes—
148C22×C4×C47C2412yes—
149C22×C4×C47C2414yes—
150C22×C4×C47C2414yes—
151C22×C4×C47C2411yescharacteristic
152C22×C4×C47C2411yescharacteristic
153C2×C22⋊D47—24no—
154C2×C22⋊D47—24no—
155C2×C22⋊D47C22×C418yes—
156C22×Dic47—22no—
157C22×Dic47—22no—
158C22×Dic47—44no—
159C22×Dic47C22×C414yes—
160C22×Dic47C2×D418yes—
161C22×Dic47C2414yes—
162C22×Dic47C2412yes—
163C22×Dic47C2412yes—
164C22×Dic47C2414yes—
165#10625350—232no—
166C2×D188—28no—
167C2×D188—28no—
168C2×D188—22no—
169C2×D188—22no—
170C2×D188C22×C4116yes—
171C2×D188C22×C414yescomplemented
172C2×C4×D47—232no—
173C2×C4×D47—24no—
174C2×C4×D47—24no—
175C2×C4×D47—24no—
176C2×C4×D47—24no—
177C2×C4×D47—24no—
178C2×C4×D47—24no—
179C2×C4×D47—216no—
180C2×C4×D47—216no—
181C2×C4×D47—28no—
182C2×C4×D47—48no—
183C2×C4×D47—432no—
184C2×C4×D47—48no—
185C2×C4×D47C22×C418yes—
186C2×C4×D47C22×C418yes—
187C2×C4×D47C22×C418yescomplemented
188C2×Dic94—22no—
189C2×Dic94—22no—
190C2×Dic94C22×C414yescomplemented
191C4⋊C4×C47—24no—
192C4⋊C4×C47—24no—
193C4⋊C4×C47—22no—
194C4⋊C4×C47—22no—
195C4⋊C4×C47—48no—
196C4⋊C4×C47C22×C418yescomplemented
197C22⋊C4×C47—24no—
198C22⋊C4×C47C22×C418yes—
199C42×C47—24no—
200C42×C47C22×C418yescomplemented
201C22⋊Dic47—24no—
202(C2×D47)⋊C4—28no—
203(C2×D47)⋊C4—28no—
204(C2×D47)⋊C4—28no—
205(C2×D47)⋊C4—48no—
206(C2×D47)⋊C4C22×C4116yes—
207(C2×D47)⋊C4C22×C4116yescomplemented
208C4⋊Dic47—24no—
209C4⋊Dic47C22×C4116yescomplemented
210C4⋊Dic47C2×D418yes—
211C4⋊Dic47C2×D418yes—
212Dic47⋊C4—216no—
213Dic47⋊C4—28no—
214C4×Dic47—24no—
215C4×Dic47—28no—
216C4×Dic47—48no—
217C23×C47—22no—
218C23×C47—22no—
219C23×C47C23×C412yes—
220C23×C47C22×D412yes—
221C23×C47C2×#4112yes—
222C23×C47C2511yescharacteristic
223C22×D47—28no—
224C22×D47—28no—
225C22×D47—216no—
226C22×D47—28no—
227C22×D47—22no—
228C22×D47—22no—
229C22×D47—22no—
230C22×D47—22no—
231C22×D47—216no—
232C22×D47—22no—
233C22×D47—22no—
234C22×D47—24no—
235C22×D47—24no—
236C22×D47C23×C414yes—
237C22×D47C23×C414yes—
238C22×D47H(5,𝔽2)14yes—
239C22×D472−1+414yes—
240C2×C4×C47—24no—
241C2×C4×C47—24no—
242C2×C4×C47—22no—
243C2×C4×C47—22no—
244C2×C4×C47—24no—
245C2×C4×C47—24no—
246C2×C4×C47—28no—
247C2×C4×C47—24no—
248C2×C4×C47—48no—
249C2×C4×C47C4×D4116yescomplemented
250C2×C4×C47C23×C418yes—
251C2×C4×C47C23×C412yes—
252C2×C4×C47C23×C412yes—
253C2×C4×C47C22×D412yes—
254C2×C4×C47C22×D412yes—
255C2×C4×C47C2×#4112yes—
256C2×C4×C47C2×#4112yes—
257C22⋊D47—216no—
258C2×Dic47—28no—
259C2×Dic47—22no—
260C2×Dic47—22no—
261C2×Dic47—22no—
262C2×Dic47—22no—
263C2×Dic47—28no—
264C2×Dic47—24no—
265C2×Dic47—24no—
266C2×Dic47—24no—
267C2×Dic47—48no—
268C2×Dic47C23×C414yes—
269C2×Dic47C23×C414yes—
270C2×Dic47C22×D418yes—
271D188—232no—
272D188—28no—
273C4×D47—216no—
274C4×D47—216no—
275C4×D47—216no—
276C4×D47—432no—
277C4×D47—88no—
278Dic94—28no—
279#34200—471nomaximal, Sylow
280C22×C47—24no—
281C22×C47—22no—
282C22×C47—22no—
283C22×C47—24no—
284C22×C47C2×C4×D414yes—
285C22×C47C24×C411yescharacteristic
286C22×C47C23×D411yescharacteristic
287C22×C47C22×#4111yescharacteristic
288C22×C47C2×H(5,𝔽2)12yes—
289C22×C47C2×2−1+412yes—
290C2×D47—232no—
291C2×D47—24no—
292C2×D47—24no—
293C2×D47—24no—
294C2×D47—24no—
295C2×D47—24no—
296C2×D47—24no—
297C2×D47—24no—
298C2×D47—28no—
299C2×D47—42no—
300C2×D47—42no—
301C2×D47—44no—
302C2×D47#52018yescomplemented
303C4×C47—28no—
304C4×C47—44no—
305C4×C47—42no—
306C4×C47—42no—
307C4×C47C2×C4×D414yes—
308C4×C47C2×C4×D414yes—
309Dic47—24no—
310Dic47—24no—
311Dic47—28no—
312Dic47—44no—
313C2×#525—471no—
314C2×#520—471no—
315C23×C4⋊C4—471no—
316#2361—474no—
317#2360—474no—
318#2352—474no—
319D4×C4⋊C4—474no—
320#2322—474no—
321#2317D4711yescharacteristic, complemented
322#2311—471no—
323C4×#120—474no—
324#2280—471no—
325#2274—471no—
326C2×C47—24no—
327C2×C47C22×C4×D411yescharacteristic
328C2×C47C2×#52012yes—
329C2×C47#348411yescharacteristic
330C2×C47#348611yescharacteristic
331C2×C47#349212yes—
332D47—28no—
333D47—44no—
334C22×#41—471no—
335C24×C4—471no—
336C24×C4—472no—
337#525—4716no—
338C2×#123—472no—
339C2×C22⋊Q8—472no—
340C2×#121—472no—
341C2×#120—472no—
342#520—948no—
343C2×C4×Q8—472no—
344C2×C4×D4—478no—
345C2×C4×D4—474no—
346C2×C4×D4—474no—
347C2×C4×D4—472no—
348C2×#117—471no—
349C2×#117—472no—
350C2×#117C2×D4711yescharacteristic
351C2×#117C2×D4711yescharacteristic
352C22×C4⋊C4—471no—
353C22×C4⋊C4—472no—
354C22×C4⋊C4—472no—
355C22×C4⋊C4—474no—
356C22×C4⋊C4—474no—
357C22×C4⋊C4—948no—
358C22×C4⋊C4C2×D4711yescharacteristic
359#391—472no—
360#390—472no—
361#389—478no—
362#389C2×D4714yescomplemented
363#388—478no—
364#387—478no—
365#386—474no—
366#386—478no—
367#385—478no—
368#385—478no—
369#385C2×D4714yes—
370#384C2×D4712yescomplemented
371#382C2×D4712yescomplemented
372#381—472no—
373#380—474no—
374#380—472no—
375#380—472no—
376#379—472no—
377C4×C4⋊C4—474no—
378C4×C4⋊C4—474no—
379C4×C22⋊C4—474no—
380C4×C22⋊C4—474no—
381C4×C22⋊C4—478no—
382C47#3420011yescharacteristic, complemented, Sylow
383C25—471no—
384C2×#41—478no—
385C2×#41—944no—
386C2×#41—944no—
387C22×Q8—471no—
388C22×D4—472no—
389C22×D4—474no—
390C22×D4—471no—
391C23×C4—471no—
392C23×C4—472no—
393C23×C4—478no—
394C23×C4—472no—
395C23×C4—472no—
396C23×C4—472no—
397C23×C4—478no—
398C23×C4—474no—
399C23×C4—948no—
400C23×C4—944no—
401C23×C4—944no—
402C23×C4—1888no—
403C23×C4C22×D4712yes—
404C23×C4C22×D4711yescharacteristic
405#123—4716no—
406C22⋊Q8—4716no—
407#121—4716no—
408#120—4716no—
409C4×Q8—948no—
410C4×D4—4732no—
411C4×D4—948no—
412C4×D4—9416no—
413C4×D4—18816no—
414#117—24no—
415#117—948no—
416#117—944no—
417#117C4×D4718yescomplemented
418C2×C4⋊C4—24no—
419C2×C4⋊C4—478no—
420C2×C4⋊C4—472no—
421C2×C4⋊C4—472no—
422C2×C4⋊C4—474no—
423C2×C4⋊C4—478no—
424C2×C4⋊C4—474no—
425C2×C4⋊C4—472no—
426C2×C4⋊C4—9416no—
427C2×C4⋊C4—9416no—
428C2×C4⋊C4—948no—
429C2×C4⋊C4—948no—
430C2×C4⋊C4C22×D4712yes—
431C2×C4⋊C4C22×D4712yes—
432C2×C4⋊C4C22×D4711yescharacteristic
433C2×C4⋊C4C22×D4711yescharacteristic
434C2×C4⋊C4C22×D4718yes—
435C2×C4⋊C4C22×D4712yes—
436C2×C22⋊C4—474no—
437C2×C22⋊C4—474no—
438C2×C22⋊C4—472no—
439C2×C22⋊C4—474no—
440C2×C22⋊C4—474no—
441C2×C22⋊C4—474no—
442C2×C22⋊C4—478no—
443C2×C22⋊C4C22×D4712yes—
444C2×C22⋊C4C22×D4712yes—
445C2×C42—474no—
446C2×C42—472no—
447C2×C42—478no—
448C2×C42C22×D4712yes—
449C2×C42C22×D4712yes—
450#95—478no—
451#95—474no—
452#95—474no—
453#95—478no—
454#95C22×D4718yes—
455C24—472no—
456C24—474no—
457C24—472no—
458C24—944no—
459C24—944no—
460C24—942no—
461C24—942no—
462C24C23×D4711yescharacteristic
463#41—9432no—
464C2×Q8—474no—
465C2×Q8—942no—
466C2×Q8—942no—
467C2×D4—478no—
468C2×D4—4716no—
469C2×D4—474no—
470C2×D4—948no—
471C2×D4—948no—
472C2×D4—944no—
473C2×D4—944no—
474C2×D4—942no—
475C2×D4—942no—
476C22×C4—24no—
477C22×C4—44no—
478C22×C4—474no—
479C22×C4—472no—
480C22×C4—472no—
481C22×C4—474no—
482C22×C4—478no—
483C22×C4—478no—
484C22×C4—478no—
485C22×C4—478no—
486C22×C4—474no—
487C22×C4—948no—
488C22×C4—9416no—
489C22×C4—9416no—
490C22×C4—942no—
491C22×C4—942no—
492C22×C4—9432no—
493C22×C4—944no—
494C22×C4—944no—
495C22×C4—944no—
496C22×C4—944no—
497C22×C4—944no—
498C22×C4—944no—
499C22×C4—1888no—
500C22×C4—1888no—
501C22×C4—18832no—
502C22×C4—1884no—
503C22×C4C2×C4×D4714yes—
504C22×C4D4×D4714yes—
505C22×C4#1062535414yes—
506C22×C4C23×D4712yes—
507C22×C4C23×D4714yes—
508C22×C4C23×D4712yes—
509C22×C4C23×D4714yes—
510C22×C4C23×D4711yescharacteristic
511C22×C4C23×D4711yescharacteristic
512C4⋊C4—24no—
513C4⋊C4—24no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—48no—
517C4⋊C4—4716no—
518C4⋊C4—478no—
519C4⋊C4—478no—
520C4⋊C4—9416no—
521C4⋊C4—948no—
522C4⋊C4—944no—
523C4⋊C4C2×C4×D4718yescomplemented
524C22⋊C4—24no—
525C22⋊C4—4716no—
526C22⋊C4—4716no—
527C22⋊C4—948no—
528C22⋊C4—948no—
529C22⋊C4—948no—
530C22⋊C4—944no—
531C22⋊C4—1888no—
532C22⋊C4C2×C4×D4718yes—
533C42—24no—
534C42—948no—
535C42—944no—
536C42—1888no—
537C42C2×C4×D4718yescomplemented
538C23—22no—
539C23—22no—
540C23—474no—
541C23—474no—
542C23—474no—
543C23—474no—
544C23—9416no—
545C23—948no—
546C23—948no—
547C23—9416no—
548C23—948no—
549C23—942no—
550C23—942no—
551C23—942no—
552C23—942no—
553C23—942no—
554C23—942no—
555C23—944no—
556C23—944no—
557C23C22×C4×D4712yes—
558C23C2×D4×D4712yes—
559C23C2×#1062535412yes—
560C23C24×D4711yescharacteristic
561Q8—948no—
562D4—9432no—
563D4—9416no—
564D4—948no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—28no—
572C2×C4—24no—
573C2×C4—48no—
574C2×C4—474no—
575C2×C4—474no—
576C2×C4—478no—
577C2×C4—948no—
578C2×C4—942no—
579C2×C4—942no—
580C2×C4—942no—
581C2×C4—942no—
582C2×C4—948no—
583C2×C4—9416no—
584C2×C4—9416no—
585C2×C4—9416no—
586C2×C4—944no—
587C2×C4—944no—
588C2×C4—944no—
589C2×C4—3768no—
590C2×C4—18832no—
591C2×C4—1888no—
592C2×C4#13093986116yescomplemented
593C2×C4C22×C4×D4718yes—
594C2×C4C22×C4×D4712yes—
595C2×C4C22×C4×D4712yes—
596C2×C4C2×D4×D4712yes—
597C2×C4C2×D4×D4712yes—
598C2×C4C2×#1062535412yes—
599C2×C4C2×#1062535412yes—
600C22—22no—
601C22—24no—
602C22—24no—
603C22—22no—
604C22—478no—
605C22—9432no—
606C22—944no—
607C22—944no—
608C22—944no—
609C22—944no—
610C22—944no—
611C22—944no—
612C22—944no—
613C22—948no—
614C22—1882no—
615C22—1884no—
616C22—1882no—
617C22C2×#1309398614yes—
618C22C23×C4×D4711yescharacteristic
619C22C22×D4×D4711yescharacteristic
620C22C22×#1062535411yescharacteristic
621C22H(5,𝔽2)×D4712yes—
622C222−1+4×D4712yes—
623C4—28no—
624C4—42no—
625C4—44no—
626C4—42no—
627C4—944no—
628C4—944no—
629C4—948no—
630C4—1884no—
631C4C2×#1309398614yes—
632C4C2×#1309398614yes—
633C2—24no—
634C2—948no—
635C2—1884no—
636C2C22×#1309398611yescharacteristic
637C2#520×D4712yes—
638C2#2025702211yescharacteristic
639C2#2025703711yescharacteristic
640C2#2025709812yes—
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2317C2
socle, cosocleC23×C47C25
prime radicalC2×#15689635C2
hypercenter#2317D47
hypocenterC47#34200
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2317

Complements

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

NH ≅ G/Ntype
2. C2×#15689603C2semidirect
3. C22×C4⋊C4×D47C2semidirect
4. #20246403C2semidirect
5. #20246392C2semidirect
6. #20246314C2semidirect
7. #20246288C2semidirect
8. #20246056C2semidirect
9. #20245981C2semidirect
10. #20245889C2semidirect
11. #20245767C2semidirect
12. #20245744C2semidirect
13. C47×#2317C2semidirect
17. #15689635C4semidirect
23. C2×C4×Dic94C22semidirect
25. C2×C4×D188C22semidirect
29. C2×#13093982C22semidirect
35. C2×C4⋊C4×D47C22semidirect
36. #15689028C22semidirect
37. #15689024C22semidirect
38. #15689019C22semidirect
39. #15689012C22semidirect
40. #15689006C22semidirect
44. #15688994C22semidirect
48. #15688980C22semidirect
50. C4⋊C4×Dic47C22semidirect
51. C4×C4⋊Dic47C22semidirect
58. C47×#389C22semidirect
60. C47×#384C22semidirect
61. C47×#382C22semidirect
65. C2×#10625350C2×C4semidirect
76. C22×C4×D47C2×C4semidirect
82. #13094008C2×C4semidirect
83. #13094004C2×C4semidirect
84. #13093999C2×C4semidirect
85. #13093994C2×C4semidirect
88. C4×D188C2×C4semidirect
93. C2×C4⋊Dic47D4semidirect
121. #117×C47C2×C4semidirect
171. C2×D188C22×C4semidirect
187. C2×C4×D47C22×C4semidirect
190. C2×Dic94C22×C4semidirect
196. C4⋊C4×C47C22×C4semidirect
200. C42×C47C22×C4semidirect
207. (C2×D47)⋊C4C22×C4semidirect
209. C4⋊Dic47C22×C4semidirect
249. C2×C4×C47C4×D4semidirect
302. C2×D47#520semidirect
321. #2317D47semidirect
362. #389C2×D47semidirect
370. #384C2×D47semidirect
371. #382C2×D47semidirect
382. C47#34200semidirect
417. #117C4×D47semidirect
523. C4⋊C4C2×C4×D47semidirect
537. C42C2×C4×D47semidirect
592. C2×C4#13093986semidirect

Maximal subgroups

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

subgroupindex
C2×#156896352
C2×#156896032
C22×C4⋊C4×D472
#202464032
#202463922
#202463142
#202462882
#202460562
#202459812
#202458892
#202457672
#202457442
C47×#23172
#3420047