Finite Group Databasebeta

← SD16×#11924007 #33104381

Subgroups — SD16×#11924007 #33104381

Order 18688.

1030 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×Dic73C211yesmaximal, characteristic
2C2×SD16×Dic73C211yesmaximal, characteristic
3Q8×#11924007C211yesmaximal, characteristic, complemented
4D4×#11924007C211yesmaximal, characteristic
5#22610659C211yesmaximal, characteristic, complemented
6#22610657C211yesmaximal, characteristic, complemented
7#22610199C211yesmaximal, characteristic, complemented
8#22610197C211yesmaximal, characteristic, complemented
9#22610192C211yesmaximal, characteristic
10#22610190C211yesmaximal, characteristic
11#22610086C211yesmaximal, characteristic, complemented
12#22609934C211yesmaximal, characteristic, complemented
13#22609929C211yesmaximal, characteristic
14C8×#11924007C211yesmaximal, characteristic, complemented
15C2×C4×SD16×C73C211yesmaximal, characteristic
16C2×Q8×Dic73C2211yescharacteristic
17C2×Q8×Dic73C2211yescharacteristic
18C2×D4×Dic73C2211yescharacteristic
19C2×D4×Dic73C2211yescharacteristic
20C22×#11924007—21no—
21SD16×Dic73—24no—
22SD16×Dic73C418yescomplemented
23C2×#14556523C2211yescharacteristic
24C2×#14556523C2211yescharacteristic
25C2×#14556522C2211yescharacteristic
26C2×#14556522C2211yescharacteristic
27C2×#14556520C2211yescharacteristic
28C2×#14556515C2211yescharacteristic
29C2×#14556515C2211yescharacteristic
30C2×#14556512C2211yescharacteristic
31C2×#14556512C2211yescharacteristic
32C2×C8×Dic73C2211yescharacteristic
33C2×C8×Dic73C2211yescharacteristic
34#17988485—21no—
35#17988485C2211yescharacteristic
36#17988485C2211yescharacteristic
37#17988483—21no—
38#17988483C2211yescharacteristic
39#17988483C2211yescharacteristic
40#17988460—21no—
41#17988459—21no—
42#17988456—21no—
43#17988456C2211yescharacteristic
44#17988456C2211yescharacteristic
45#17988445—21no—
46C4×#11924007—21no—
47C4×#11924007C2211yescharacteristic
48#17988350C2211yescharacteristic
49#17988350C2211yescharacteristic
50#17988349C2211yescharacteristic
51#17988349C2211yescharacteristic
52#17988342C2211yescharacteristic
53#17988341C2211yescharacteristic
54C22×SD16×C73C2211yescharacteristic
55C2×C4×Q8×C73C2211yescharacteristic
56C2×C4×D4×C73C2211yescharacteristic
57C4×SD16×C73—24no—
58C2×#106×C73C2211yescharacteristic
59C2×#103×C73C2211yescharacteristic
60C2×#102×C73C2211yescharacteristic
61C2×C4×C8×C73C2211yescharacteristic
62C23×Dic73—21no—
63C23×Dic73—21no—
64C22×#10596831C2311yescharacteristic
65C22×#10596831C2311yescharacteristic
66Q8×Dic73—22no—
67Q8×Dic73—22no—
68Q8×Dic73—41no—
69Q8×Dic73C2×C414yescomplemented
70D4×Dic73—22no—
71D4×Dic73—22no—
72D4×Dic73—41no—
73D4×Dic73C2×C414yes—
74C2×C4⋊Dic73—21no—
75C2×C4⋊Dic73—21no—
76C2×C4⋊Dic73C2311yescharacteristic
77C2×C4⋊Dic73C2311yescharacteristic
78C2×C4⋊Dic73C2311yescharacteristic
79C2×C4⋊Dic73C2311yescharacteristic
80C2×#11924007—21no—
81C2×#11924007—21no—
82C2×#11924007—21no—
83C2×#11924007—21no—
84C2×#11924007—21no—
85C2×#11924007—21no—
86C2×#11924007—21no—
87C2×#11924007—21no—
88C2×#11924007—44no—
89C2×#11924007D411yescharacteristic
90C2×#11924007D411yescharacteristic
91C2×C22⋊Dic73—21no—
92C2×C22⋊Dic73—21no—
93C2×C4×Dic73—21no—
94C2×C4×Dic73—21no—
95C2×C4×Dic73C2311yescharacteristic
96C2×C4×Dic73C2311yescharacteristic
97#14556523—22no—
98#14556523C2×C414yescomplemented
99#14556522—41no—
100#14556522—41no—
101#14556520—22no—
102#14556515—22no—
103#14556515C2×C414yescomplemented
104#14556512—22no—
105#14556512C2×C414yes—
106C8×Dic73—22no—
107C8×Dic73C2×C414yescomplemented
108#14556498—21no—
109#14556498—21no—
110#14556498—21no—
111#14556498—21no—
112#14556498D411yescharacteristic
113#14556498D411yescharacteristic
114C22×Q8×C73C2311yescharacteristic
115C22×D4×C73C2311yescharacteristic
116C23×C4×C73—21no—
117C2×SD16×C73C2×C414yes—
118C2×SD16×C73D414yes—
119C2×SD16×C73Q814yes—
120C22×C8×C73C2311yescharacteristic
121C22×C8×C73C2311yescharacteristic
122C4×Q8×C73—22no—
123C4×Q8×C73—41no—
124C4×D4×C73—22no—
125C4×D4×C73—41no—
126C2×C4⋊C4×C73—21no—
127C2×C4⋊C4×C73C2311yescharacteristic
128C2×C4⋊C4×C73C2311yescharacteristic
129C2×C22⋊C4×C73—21no—
130C2×C42×C73—21no—
131C2×C42×C73C2311yescharacteristic
132#106×C73—22no—
133#103×C73—22no—
134#102×C73—22no—
135C4×C8×C73—22no—
136C22×Dic73—21no—
137C22×Dic73—21no—
138C22×Dic73—24no—
139C22×Dic73—21no—
140C22×Dic73—21no—
141C22×Dic73—42no—
142C22×Dic73—42no—
143C22×Dic73—42no—
144C22×Dic73—42no—
145C22×Dic73—81no—
146C22×Dic73C2×D411yescharacteristic
147C22×Dic73C2×D411yescharacteristic
148C22×Dic73C2×D411yescharacteristic
149C22×Dic73C2×D411yescharacteristic
150C2×#10596831—21no—
151C2×#10596831—21no—
152C2×#10596831—21no—
153C2×#10596831—21no—
154C2×#10596831—21no—
155C2×#10596831C22×C412yes—
156C4⋊Dic73—21no—
157C4⋊Dic73—21no—
158C4⋊Dic73—24no—
159C4⋊Dic73—21no—
160C4⋊Dic73—21no—
161C4⋊Dic73—21no—
162C4⋊Dic73—21no—
163C4⋊Dic73—42no—
164C4⋊Dic73C22×C412yes—
165C4⋊Dic73C22×C412yes—
166#11924007—22no—
167#11924007—42no—
168#11924007—42no—
169#11924007—42no—
170#11924007—42no—
171#11924007—81no—
172#11924007—81no—
173#11924007—81no—
174#11924007—81no—
175#11924007SD1614yesdirect product factor
176C22⋊Dic73—24no—
177C22⋊Dic73—42no—
178C4×Dic73—21no—
179C4×Dic73—21no—
180C4×Dic73—24no—
181C4×Dic73—42no—
182C4×Dic73C22×C412yes—
183C4×Dic73#4112yes—
184C24×C73—21no—
185C2×Q8×C73—21no—
186C2×Q8×C73—21no—
187C2×Q8×C73—21no—
188C2×Q8×C73C22×C412yes—
189C2×Q8×C73C2×D412yes—
190C2×Q8×C73C2×Q812yes—
191C2×D4×C73—21no—
192C2×D4×C73—21no—
193C2×D4×C73—21no—
194C2×D4×C73C22×C412yes—
195C2×D4×C73C2×D412yes—
196C2×D4×C73C2×Q812yes—
197C22×C4×C73—21no—
198C22×C4×C73—21no—
199C22×C4×C73—21no—
200C22×C4×C73—42no—
201C22×C4×C73—42no—
202C22×C4×C73—81no—
203C22×C4×C73C2×D411yescharacteristic
204C22×C4×C73C2×D411yescharacteristic
205C22×C4×C73C2411yescharacteristic
206SD16×C73C4⋊C4116yescomplemented
207C2×C8×C73—21no—
208C2×C8×C73—21no—
209C2×C8×C73—21no—
210C2×C8×C73C22×C412yes—
211C2×C8×C73C2×D412yes—
212C2×C8×C73C2×Q812yes—
213C4⋊C4×C73—21no—
214C4⋊C4×C73—21no—
215C4⋊C4×C73—21no—
216C4⋊C4×C73—21no—
217C4⋊C4×C73—42no—
218C22⋊C4×C73—42no—
219C42×C73—21no—
220C42×C73—21no—
221C42×C73—42no—
222C23×C73—22no—
223C23×C73—22no—
224C23×C73—22no—
225C23×C73—41no—
226C23×C73—41no—
227C23×C73—41no—
228C23×C73—41no—
229C23×C73C22×D411yescharacteristic
230Q8×C73—22no—
231Q8×C73—22no—
232Q8×C73—22no—
233Q8×C73C2×C4⋊C414yescomplemented
234D4×C73—22no—
235D4×C73—22no—
236D4×C73—22no—
237D4×C73C2×C4⋊C414yes—
238C2×C4×C73—22no—
239C2×C4×C73—21no—
240C2×C4×C73—22no—
241C2×C4×C73—22no—
242C2×C4×C73—21no—
243C2×C4×C73—21no—
244C2×C4×C73—21no—
245C2×C4×C73—21no—
246C2×C4×C73—41no—
247C2×C4×C73—41no—
248C2×C4×C73—41no—
249C2×C4×C73—41no—
250C2×C4×C73—41no—
251C2×C4×C73—41no—
252C2×C4×C73—84no—
253C2×C4×C73C2×SD1612yes—
254C2×C4×C73C23×C411yescharacteristic
255C2×C4×C73C22×D411yescharacteristic
256C2×C4×C73C22×Q811yescharacteristic
257C2×C4×C73C2×#4111yescharacteristic
258C2×C4×C73H(5,𝔽2)11yescharacteristic
259C2×C4×C732−1+411yescharacteristic
260C2×Dic73—21no—
261C2×Dic73—21no—
262C2×Dic73—21no—
263C2×Dic73—21no—
264C2×Dic73—22no—
265C2×Dic73—22no—
266C2×Dic73—21no—
267C2×Dic73—21no—
268C2×Dic73—21no—
269C2×Dic73—41no—
270C2×Dic73—41no—
271C2×Dic73—41no—
272C2×Dic73—41no—
273C2×Dic73—48no—
274C2×Dic73—41no—
275C2×Dic73—41no—
276C2×Dic73—41no—
277C2×Dic73—41no—
278C2×Dic73—41no—
279C2×Dic73—41no—
280C2×Dic73—84no—
281C2×Dic73C4×D412yes—
282C2×Dic73C4×D412yes—
283C2×Dic73C2×SD1612yes—
284C2×Dic73C2×SD1612yes—
285C2×Dic73#13512yes—
286C8×C73—41no—
287C8×C73C2×C4⋊C414yescomplemented
288#10596831—22no—
289#10596831—41no—
290C22×C73—24no—
291C22×C73—42no—
292C22×C73—42no—
293C22×C73—42no—
294C22×C73—42no—
295C22×C73—42no—
296C22×C73—42no—
297C22×C73C2×C4×D411yescharacteristic
298C22×C73D4211yescharacteristic
299C22×C73D4×Q811yescharacteristic
300C22×C73C22×SD1611yescharacteristic
301C22×C73C2×#13511yescharacteristic
302C22×C73#57711yescharacteristic
303C22×C73#57711yescharacteristic
304C4×C73—24no—
305C4×C73—22no—
306C4×C73—41no—
307C4×C73—81no—
308C4×C73—81no—
309C4×C73C22×C4⋊C411yescharacteristic
310C4×C73#52011yescharacteristic
311C4×C73#54711yescharacteristic
312C4×C73#55411yescharacteristic
313Dic73—22no—
314Dic73—22no—
315Dic73—42no—
316Dic73—42no—
317Dic73—41no—
318Dic73—81no—
319Dic73—81no—
320Dic73C4×SD1614yescomplemented
321C4⋊C4×SD16—731nomaximal, Sylow
322C2×C73—44no—
323C2×C73D4×C4⋊C411yescharacteristic
324C2×C73C2×C4×SD1611yescharacteristic
325C2×C73#295211yescharacteristic
326C2×C73D4×SD1611yescharacteristic
327C2×C73#328411yescharacteristic
328C2×C73Q8×SD1611yescharacteristic
329C2×C73#338111yescharacteristic
330C2×C4×SD16—731no—
331C2×C4×SD16—731no—
332C2×C4×SD16D7311yescharacteristic
333Q8×C4⋊C4—731no—
334D4×C4⋊C4—731no—
335#1941—731no—
336#1941—731no—
337#1865—731no—
338#1865—731no—
339#1864—731no—
340#1864—731no—
341#1844—731no—
342#1803—731no—
343#1802—731no—
344C8×C4⋊C4—731no—
345C73C4⋊C4×SD1611yescharacteristic, complemented, Sylow
346C22×SD16C2×D7311yescharacteristic
347C2×C4×Q8—731no—
348C2×C4×Q8—731no—
349C2×C4×Q8C2×D7311yescharacteristic
350C2×C4×D4—731no—
351C2×C4×D4—731no—
352C2×C4×D4C2×D7311yescharacteristic
353C22×C4⋊C4—1461no—
354C4×SD16—24no—
355C4×SD16—738no—
356C4×SD16—1464no—
357C2×#106—731no—
358C2×#106—731no—
359C2×#106—731no—
360C2×#106—731no—
361C2×#106C2×D7311yescharacteristic
362C2×C4⋊C8—731no—
363C2×#103—731no—
364C2×#103—731no—
365C2×#103C2×D7311yescharacteristic
366C2×#102—731no—
367C2×#102—731no—
368C2×#102C2×D7311yescharacteristic
369C2×C4×C8—731no—
370C2×C4×C8—731no—
371C2×C4×C8C2×D7311yescharacteristic
372#389—731no—
373#389—731no—
374#389—731no—
375#389—731no—
376#389—1461no—
377#389—1461no—
378#385—1461no—
379#385—1461no—
380#384—731no—
381#384—731no—
382#384—1461no—
383#380—1461no—
384C4×C4⋊C4—731no—
385C4×C4⋊C4—1461no—
386#340—731no—
387#340—731no—
388#340—731no—
389#340—731no—
390#336—731no—
391#336—731no—
392C22×Q8C22×D7311yescharacteristic
393C22×D4C22×D7311yescharacteristic
394C23×C4—21no—
395C23×C4—1461no—
396C23×C4—1461no—
397C2×SD16Dic14614yes—
398C2×SD16C4×D7314yes—
399C2×SD16C22⋊D7314yes—
400C22×C8—731no—
401C22×C8—731no—
402C22×C8C22×D7311yescharacteristic
403C22×C8C22×D7311yescharacteristic
404C4×Q8—22no—
405C4×Q8—41no—
406C4×Q8—2921no—
407C4×Q8—734no—
408C4×Q8—1462no—
409C4×Q8—1462no—
410C4×D4—22no—
411C4×D4—41no—
412C4×D4—2921no—
413C4×D4—734no—
414C4×D4—1462no—
415C4×D4—1462no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—2924no—
418C2×C4⋊C4—731no—
419C2×C4⋊C4—731no—
420C2×C4⋊C4—731no—
421C2×C4⋊C4—731no—
422C2×C4⋊C4—731no—
423C2×C4⋊C4—731no—
424C2×C4⋊C4—1461no—
425C2×C4⋊C4—1461no—
426C2×C4⋊C4—1461no—
427C2×C4⋊C4—1461no—
428C2×C4⋊C4—1461no—
429C2×C4⋊C4—1461no—
430C2×C4⋊C4—1461no—
431C2×C4⋊C4—1461no—
432C2×C4⋊C4—1461no—
433C2×C4⋊C4—1461no—
434C2×C4⋊C4C22×D7311yescharacteristic
435C2×C4⋊C4C22×D7311yescharacteristic
436C2×C22⋊C4—21no—
437C2×C22⋊C4—1461no—
438C2×C22⋊C4—1461no—
439C2×C42—21no—
440C2×C42—731no—
441C2×C42—731no—
442C2×C42—1461no—
443C2×C42—1461no—
444C2×C42C22×D7311yescharacteristic
445#106—22no—
446#106—2921no—
447#106—2921no—
448#106—734no—
449#106—1462no—
450C4⋊C8—1462no—
451#103—22no—
452#103—734no—
453#103—1462no—
454#102—22no—
455#102—734no—
456#102—1462no—
457C4×C8—22no—
458C4×C8—734no—
459C4×C8—1462no—
460#95—731no—
461#95—731no—
462#95—1461no—
463#95—1461no—
464#95—1461no—
465#95—1461no—
466C24—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8C2×C4×D7312yes—
471C2×Q8C2×C22⋊D7312yes—
472C2×Q8C2×Dic14612yes—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4C2×C4×D7312yes—
477C2×D4C2×C22⋊D7312yes—
478C2×D4C2×Dic14612yes—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—81no—
485C22×C4—2922no—
486C22×C4—2922no—
487C22×C4—2922no—
488C22×C4—2922no—
489C22×C4—5841no—
490C22×C4—731no—
491C22×C4—731no—
492C22×C4—731no—
493C22×C4—731no—
494C22×C4—1461no—
495C22×C4—1461no—
496C22×C4—1464no—
497C22×C4—1461no—
498C22×C4—1461no—
499C22×C4D4×D7311yescharacteristic
500C22×C4D4×D7311yescharacteristic
501C22×C4C23×D7311yescharacteristic
502SD16#11924007116yesdirect product factor
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—732no—
507C2×C8—1461no—
508C2×C8—1461no—
509C2×C8—1461no—
510C2×C8—1461no—
511C2×C8—1461no—
512C2×C8C2×C4×D7312yes—
513C2×C8C2×C22⋊D7312yes—
514C2×C8C2×Dic14612yes—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—42no—
520C4⋊C4—2922no—
521C4⋊C4—2922no—
522C4⋊C4—2922no—
523C4⋊C4—2922no—
524C4⋊C4—2922no—
525C4⋊C4—5841no—
526C4⋊C4—5841no—
527C4⋊C4—5841no—
528C4⋊C4—5841no—
529C4⋊C4—734no—
530C4⋊C4—732no—
531C4⋊C4—732no—
532C4⋊C4—1462no—
533C4⋊C4—1464no—
534C4⋊C4—1461no—
535C4⋊C4—1461no—
536C4⋊C4—1461no—
537C4⋊C4—1461no—
538C4⋊C4—1461no—
539C4⋊C4—1461no—
540C22⋊C4—42no—
541C22⋊C4—2922no—
542C22⋊C4—1464no—
543C42—21no—
544C42—21no—
545C42—42no—
546C42—2922no—
547C42—732no—
548C42—732no—
549C42—1464no—
550C42—1461no—
551C42—1461no—
552C23—22no—
553C23—22no—
554C23—22no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23C2×D4×D7311yescharacteristic
560Q8—22no—
561Q8—22no—
562Q8—22no—
563Q8C2×#1192400714yescomplemented
564D4—22no—
565D4—22no—
566D4—22no—
567D4C2×#1192400714yes—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—84no—
583C2×C4—2921no—
584C2×C4—2921no—
585C2×C4—2921no—
586C2×C4—2921no—
587C2×C4—2928no—
588C2×C4—2921no—
589C2×C4—2921no—
590C2×C4—2921no—
591C2×C4—2921no—
592C2×C4—2921no—
593C2×C4—2921no—
594C2×C4—5844no—
595C2×C4—732no—
596C2×C4—732no—
597C2×C4—732no—
598C2×C4—732no—
599C2×C4—732no—
600C2×C4—1461no—
601C2×C4—1461no—
602C2×C4—1462no—
603C2×C4—1462no—
604C2×C4—1461no—
605C2×C4—1461no—
606C2×C4—1461no—
607C2×C4—1461no—
608C2×C4—1461no—
609C2×C4SD16×D7312yes—
610C2×C4C22×C4×D7311yescharacteristic
611C2×C4C22×C22⋊D7311yescharacteristic
612C2×C4C22×Dic14611yescharacteristic
613C2×C4#41×D7311yescharacteristic
614C2×C4#1455663611yescharacteristic
615C2×C4#1455663811yescharacteristic
616C8—41no—
617C8—2921no—
618C8—1462no—
619C8C2×#1192400714yescomplemented
620C22—24no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—42no—
625C22—42no—
626C22—42no—
627C22C4×D4×D7311yescharacteristic
628C22D4×C22⋊D7311yescharacteristic
629C22D4×Dic14611yescharacteristic
630C22C2×SD16×D7311yescharacteristic
631C22#135×D7311yescharacteristic
632C22#1798939311yescharacteristic
633C22#1798939411yescharacteristic
634C4—24no—
635C4—22no—
636C4—41no—
637C4—81no—
638C4—81no—
639C4—2922no—
640C4—2922no—
641C4—2921no—
642C4—5841no—
643C4—5841no—
644C4—734no—
645C4—1462no—
646C4—1462no—
647C4C22×#1192400711yescharacteristic
648C4#1798906611yescharacteristic
649C4#1798923611yescharacteristic
650C4#1798929611yescharacteristic
651C2—44no—
652C2D4×#1192400711yescharacteristic
653C2C4×SD16×D7311yescharacteristic
654C2#2261880911yescharacteristic
655C2SD16×C22⋊D7311yescharacteristic
656C2#2262165511yescharacteristic
657C2SD16×Dic14611yescharacteristic
658C2#2262280711yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×C4×SD16×C73C2
socleC23×C73C22×D4
prime radicalC22×D4×C73C23
cosocleC22×C4×C73C24
hypercenterC2×C4×SD16D73
hypocenterC73C4⋊C4×SD16
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
3. Q8×#11924007C2semidirect
5. #22610659C2semidirect
6. #22610657C2semidirect
7. #22610199C2semidirect
8. #22610197C2semidirect
11. #22610086C2semidirect
12. #22609934C2semidirect
14. C8×#11924007C2semidirect
22. SD16×Dic73C4semidirect
69. Q8×Dic73C2×C4semidirect
98. #14556523C2×C4semidirect
103. #14556515C2×C4semidirect
107. C8×Dic73C2×C4semidirect
175. #11924007SD16direct (N × H)
206. SD16×C73C4⋊C4semidirect
233. Q8×C73C2×C4⋊C4semidirect
287. C8×C73C2×C4⋊C4semidirect
320. Dic73C4×SD16semidirect
345. C73C4⋊C4×SD16semidirect
502. SD16#11924007direct (N × H)
563. Q8C2×#11924007semidirect
619. C8C2×#11924007semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×Dic732
Q8×#119240072
D4×#119240072
#226106592
#226106572
#226101992
#226101972
#226101922
#226101902
#226100862
#226099342
#226099292
C8×#119240072
C2×C4×SD16×C732
C4⋊C4×SD1673