Finite Group Databasebeta

← C43×#19807 #24939824

Subgroups — C43×#19807 #24939824

Order 11008.

684 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3392C211yesmaximal, characteristic, complemented
2C43×#3381C211yesmaximal, characteristic, complemented
3C43×#3295C211yesmaximal, characteristic, complemented
4C43×#3274C211yesmaximal, characteristic
5C43×#1715C211yesmaximal, characteristic, complemented
6C43×#1691C211yesmaximal, characteristic, complemented
7C43×#1678C211yesmaximal, characteristic, complemented
8C43×#1668C211yesmaximal, characteristic, complemented
9C43×#1665C211yesmaximal, characteristic, complemented
10C43×#1639C211yesmaximal, characteristic, complemented
11C43×#1631C211yesmaximal, characteristic, complemented
12C43×#1626C211yesmaximal, characteristic, complemented
13C43×#1622C211yesmaximal, characteristic, complemented
14C43×#1583C211yesmaximal, characteristic, complemented
15C43×SD16⋊C8C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C43—21no—
17C43×#557C2211yescharacteristic, complemented
18C43×#554C2211yescharacteristic
19C43×#550C2211yescharacteristic
20D42×C43C2211yescharacteristic
21C43×#499—21no—
22C43×#498C2211yescharacteristic, complemented
23C43×#493C2211yescharacteristic
24C43×#492—21no—
25C43×#492C2211yescharacteristic, complemented
26C43×#492C2211yescharacteristic, complemented
27C43×#486C2211yescharacteristic
28C43×#486C2211yescharacteristic
29C43×#481—21no—
30C43×#479—21no—
31C43×#478—21no—
32C43×#477C2211yescharacteristic, complemented
33C43×#476C2211yescharacteristic
34C43×#474C2211yescharacteristic
35C43×#469—21no—
36C43×#465—21no—
37C43×#461—21no—
38C43×#461C2211yescharacteristic
39C43×#460—21no—
40C43×#460C2211yescharacteristic
41C43×#460C2211yescharacteristic
42C43×#460C2211yescharacteristic, complemented
43C43×#459C2211yescharacteristic
44C43×#450—21no—
45C43×#449—21no—
46C43×#447—21no—
47C8×Q8×C43C2211yescharacteristic, complemented
48C8×Q8×C43C2211yescharacteristic, complemented
49C4×SD16×C43—21no—
50C4×SD16×C43—21no—
51C4×SD16×C43C2211yescharacteristic
52C4×SD16×C43C2211yescharacteristic
53C43×#436C2211yescharacteristic
54C8×D4×C43C2211yescharacteristic
55C2×#102×C43—21no—
56C43×#335C2211yescharacteristic, complemented
57C43×#334C2211yescharacteristic, complemented
58C43×#333C2211yescharacteristic, complemented
59C43×#332C2211yescharacteristic, complemented
60C43×#331C2211yescharacteristic
61C43×#331C2211yescharacteristic, complemented
62C43×Q8⋊C8C2211yescharacteristic, complemented
63C43×Q8⋊C8C2211yescharacteristic, complemented
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic, complemented
67C2×#41×C43—21no—
68C22×D4×C43—21no—
69C22×D4×C43—21no—
70AGL(1,ℤ/8)×C43—44no—
71C2×SD16×C43—21no—
72C2×SD16×C43—21no—
73C2×SD16×C43—21no—
74C2×SD16×C43—21no—
75C2×SD16×C43—21no—
76C2×SD16×C43—21no—
77C2×SD16×C43—41no—
78C2×SD16×C43D411yescharacteristic
79C2×SD16×C43D411yescharacteristic
80C2×D8×C43—21no—
81C2×D8×C43—21no—
82C2×D8×C43—21no—
83C2×M16×C43—21no—
84C22×C8×C43—21no—
85C4⋊Q8×C43—21no—
86C4⋊Q8×C43C2311yescharacteristic
87C4⋊Q8×C43C2311yescharacteristic
88#127×C43—21no—
89#127×C43C2311yescharacteristic
90#127×C43C2311yescharacteristic
91#125×C43—21no—
92#125×C43—21no—
93#125×C43—41no—
94C22⋊Q8×C43—21no—
95C22⋊Q8×C43—41no—
96#121×C43—21no—
97#121×C43—21no—
98#121×C43—21no—
99#121×C43—41no—
100#120×C43—41no—
101C4×Q8×C43—21no—
102C4×Q8×C43—21no—
103C4×Q8×C43C2311yescharacteristic
104C4×Q8×C43C2311yescharacteristic
105C4×D4×C43—21no—
106C4×D4×C43—21no—
107C4×D4×C43C2311yescharacteristic
108C4×D4×C43C2311yescharacteristic
109C2×C4⋊C4×C43—21no—
110#107×C43—21no—
111#107×C43—21no—
112#106×C43—21no—
113#106×C43—21no—
114#106×C43—21no—
115#106×C43D411yescharacteristic
116#106×C43D411yescharacteristic
117C4⋊C8×C43—21no—
118C4⋊C8×C43—21no—
119C4⋊C8×C43C2311yescharacteristic
120C4⋊C8×C43C2311yescharacteristic
121C4⋊C8×C43C2311yescharacteristic
122C4⋊C8×C43C2311yescharacteristic
123#103×C43—21no—
124#103×C43—21no—
125#103×C43D411yescharacteristic
126#103×C43D411yescharacteristic
127#102×C43—21no—
128#102×C43—21no—
129#102×C43—21no—
130#102×C43—21no—
131#102×C43—21no—
132#102×C43—21no—
133#102×C43—21no—
134#102×C43—21no—
135#102×C43—41no—
136#102×C43D411yescharacteristic
137#102×C43D411yescharacteristic
138C22⋊C8×C43—21no—
139C22⋊C8×C43—21no—
140C4×C8×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C24×C43—41no—
146#41×C43—42no—
147#41×C43—81no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43C2×D411yescharacteristic
151C2×Q8×C43C2×D411yescharacteristic
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—41no—
159C2×D4×C43—41no—
160C2×D4×C43—41no—
161C2×D4×C43—41no—
162C2×D4×C43—42no—
163C2×D4×C43—42no—
164C2×D4×C43—81no—
165C2×D4×C43—81no—
166C2×D4×C43C2×D411yescharacteristic
167C2×D4×C43C2×D411yescharacteristic
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—41no—
171C22×C4×C43—41no—
172SD16×C43—41no—
173SD16×C43—42no—
174SD16×C43—42no—
175SD16×C43—81no—
176SD16×C43—81no—
177SD16×C43—81no—
178SD16×C43—81no—
179SD16×C43—82no—
180SD16×C43SD1614yescomplemented
181D8×C43—42no—
182D8×C43—42no—
183D8×C43—81no—
184M16×C43—42no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—81no—
191C2×C8×C43C2×D411yescharacteristic
192C2×C8×C43C2×D411yescharacteristic
193C2×C8×C43C2×D411yescharacteristic
194C2×C8×C43C2×D411yescharacteristic
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—41no—
202C4⋊C4×C43—41no—
203C4⋊C4×C43—41no—
204C4⋊C4×C43—41no—
205C4⋊C4×C43—41no—
206C4⋊C4×C43C2×D411yescharacteristic
207C4⋊C4×C43C2×D411yescharacteristic
208C4⋊C4×C43C2×D411yescharacteristic
209C4⋊C4×C43C2×D411yescharacteristic
210C22⋊C4×C43—21no—
211C22⋊C4×C43—21no—
212C22⋊C4×C43—41no—
213C22⋊C4×C43—41no—
214C22⋊C4×C43—41no—
215C42×C43—21no—
216C42×C43—21no—
217C42×C43—41no—
218C42×C43C2411yescharacteristic
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—82no—
224C23×C43—82no—
225C23×C43—161no—
226Q8×C43—21no—
227Q8×C43—21no—
228Q8×C43—21no—
229Q8×C43—41no—
230Q8×C43—41no—
231Q8×C43—81no—
232Q8×C43C2×SD1612yes—
233D4×C43—21no—
234D4×C43—21no—
235D4×C43—21no—
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—41no—
241D4×C43—41no—
242D4×C43—41no—
243D4×C43—41no—
244D4×C43—82no—
245D4×C43—81no—
246D4×C43—81no—
247D4×C43—82no—
248D4×C43—82no—
249D4×C43—161no—
250D4×C43C2×SD1612yes—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—82no—
264C2×C4×C43—161no—
265C2×C4×C43C22×D411yescharacteristic
266C2×C4×C43C22×D411yescharacteristic
267C2×C4×C43H(5,𝔽2)11yescharacteristic
268C8×C43—21no—
269C8×C43—21no—
270C8×C43—21no—
271C8×C43—41no—
272C8×C43—41no—
273C8×C43—41no—
274C8×C43—41no—
275C8×C43—41no—
276C8×C43C2×SD1612yes—
277#19807C4311yesmaximal, characteristic, direct product factor, Sylow
278C22×C43—22no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43—81no—
290C22×C43—164no—
291C22×C43D4211yescharacteristic
292C4×C43—22no—
293C4×C43—21no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43—41no—
297C4×C43—41no—
298C4×C43—41no—
299C4×C43—81no—
300C4×C43—81no—
301C4×C43C22×SD1611yescharacteristic
302C4×C43#57511yescharacteristic
303C4×C43#57611yescharacteristic
304C4×C43#57711yescharacteristic
305#3392C2×C4311yescharacteristic, complemented
306#3381C2×C4311yescharacteristic, complemented
307#3295C2×C4311yescharacteristic, complemented
308#3274C2×C4311yescharacteristic
309#1715C2×C4311yescharacteristic, complemented
310#1691C2×C4311yescharacteristic, complemented
311#1678C2×C4311yescharacteristic, complemented
312#1668C2×C4311yescharacteristic, complemented
313#1665C2×C4311yescharacteristic, complemented
314#1639C2×C4311yescharacteristic, complemented
315#1631C2×C4311yescharacteristic, complemented
316#1626C2×C4311yescharacteristic, complemented
317#1622C2×C4311yescharacteristic, complemented
318#1583C2×C4311yescharacteristic, complemented
319SD16⋊C8C2×C4311yescharacteristic, complemented
320C2×C43—42no—
321C2×C43—81no—
322C2×C43—161no—
323C2×C43—161no—
324C2×C43#326811yescharacteristic
325C2×C43D4×SD1611yescharacteristic
326C2×C43#328811yescharacteristic
327C2×AGL(1,ℤ/8)—21no—
328#557C22×C4311yescharacteristic, complemented
329#554C22×C4311yescharacteristic
330#550C22×C4311yescharacteristic
331D42C22×C4311yescharacteristic
332#499—21no—
333#498C22×C4311yescharacteristic, complemented
334#493C22×C4311yescharacteristic
335#492—21no—
336#492C22×C4311yescharacteristic, complemented
337#492C22×C4311yescharacteristic, complemented
338#486C22×C4311yescharacteristic
339#486C22×C4311yescharacteristic
340#481—21no—
341#479—21no—
342#478—21no—
343#477C22×C4311yescharacteristic, complemented
344#476C22×C4311yescharacteristic
345#474C22×C4311yescharacteristic
346#469—21no—
347#465—21no—
348#461—21no—
349#461C22×C4311yescharacteristic
350#460—21no—
351#460C22×C4311yescharacteristic
352#460C22×C4311yescharacteristic
353#460C22×C4311yescharacteristic, complemented
354#459C22×C4311yescharacteristic
355#450—21no—
356#449—21no—
357#447—21no—
358C8×Q8C22×C4311yescharacteristic, complemented
359C8×Q8C22×C4311yescharacteristic, complemented
360C4×SD16—21no—
361C4×SD16—21no—
362C4×SD16C22×C4311yescharacteristic
363C4×SD16C22×C4311yescharacteristic
364#436C22×C4311yescharacteristic
365C8×D4C22×C4311yescharacteristic
366C2×#102—21no—
367#335C22×C4311yescharacteristic, complemented
368#334C22×C4311yescharacteristic, complemented
369#333C22×C4311yescharacteristic, complemented
370#332C22×C4311yescharacteristic, complemented
371#331C22×C4311yescharacteristic
372#331C22×C4311yescharacteristic, complemented
373Q8⋊C8C22×C4311yescharacteristic, complemented
374Q8⋊C8C22×C4311yescharacteristic, complemented
375D4⋊C8C22×C4311yescharacteristic
376D4⋊C8C22×C4311yescharacteristic
377#322C22×C4311yescharacteristic, complemented
378C43#1980711yescharacteristic, direct product factor, Sylow
379C2×#41—21no—
380C22×D4—21no—
381C22×D4—21no—
382AGL(1,ℤ/8)—44no—
383C2×SD16—21no—
384C2×SD16—21no—
385C2×SD16—21no—
386C2×SD16—21no—
387C2×SD16—21no—
388C2×SD16—21no—
389C2×SD16—41no—
390C2×SD16D4×C4311yescharacteristic
391C2×SD16D4×C4311yescharacteristic
392C2×D8—21no—
393C2×D8—21no—
394C2×D8—21no—
395C2×M16—21no—
396C22×C8—21no—
397C4⋊Q8—21no—
398C4⋊Q8C23×C4311yescharacteristic
399C4⋊Q8C23×C4311yescharacteristic
400#127—21no—
401#127C23×C4311yescharacteristic
402#127C23×C4311yescharacteristic
403#125—21no—
404#125—21no—
405#125—41no—
406C22⋊Q8—21no—
407C22⋊Q8—41no—
408#121—21no—
409#121—21no—
410#121—21no—
411#121—41no—
412#120—41no—
413C4×Q8—21no—
414C4×Q8—21no—
415C4×Q8C23×C4311yescharacteristic
416C4×Q8C23×C4311yescharacteristic
417C4×D4—21no—
418C4×D4—21no—
419C4×D4C23×C4311yescharacteristic
420C4×D4C23×C4311yescharacteristic
421C2×C4⋊C4—21no—
422#107—21no—
423#107—21no—
424#106—21no—
425#106—21no—
426#106—21no—
427#106D4×C4311yescharacteristic
428#106D4×C4311yescharacteristic
429C4⋊C8—21no—
430C4⋊C8—21no—
431C4⋊C8C23×C4311yescharacteristic
432C4⋊C8C23×C4311yescharacteristic
433C4⋊C8C23×C4311yescharacteristic
434C4⋊C8C23×C4311yescharacteristic
435#103—21no—
436#103—21no—
437#103D4×C4311yescharacteristic
438#103D4×C4311yescharacteristic
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—21no—
444#102—21no—
445#102—21no—
446#102—21no—
447#102—41no—
448#102D4×C4311yescharacteristic
449#102D4×C4311yescharacteristic
450C22⋊C8—21no—
451C22⋊C8—21no—
452C4×C8—21no—
453C4×C8—21no—
454C4×C8C23×C4311yescharacteristic
455C4×C8C23×C4311yescharacteristic
456C4×C8C23×C4311yescharacteristic
457C24—41no—
458#41—42no—
459#41—81no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8C2×D4×C4311yescharacteristic
463C2×Q8C2×D4×C4311yescharacteristic
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—41no—
474C2×D4—42no—
475C2×D4—42no—
476C2×D4—81no—
477C2×D4—81no—
478C2×D4C2×D4×C4311yescharacteristic
479C2×D4C2×D4×C4311yescharacteristic
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—41no—
483C22×C4—41no—
484SD16—41no—
485SD16—42no—
486SD16—42no—
487SD16—81no—
488SD16—81no—
489SD16—81no—
490SD16—81no—
491SD16—82no—
492SD16SD16×C4314yescomplemented
493D8—42no—
494D8—42no—
495D8—81no—
496M16—42no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—81no—
503C2×C8C2×D4×C4311yescharacteristic
504C2×C8C2×D4×C4311yescharacteristic
505C2×C8C2×D4×C4311yescharacteristic
506C2×C8C2×D4×C4311yescharacteristic
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C4⋊C4C2×D4×C4311yescharacteristic
519C4⋊C4C2×D4×C4311yescharacteristic
520C4⋊C4C2×D4×C4311yescharacteristic
521C4⋊C4C2×D4×C4311yescharacteristic
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C42—21no—
528C42—21no—
529C42—41no—
530C42C24×C4311yescharacteristic
531C23—21no—
532C23—21no—
533C23—41no—
534C23—41no—
535C23—82no—
536C23—82no—
537C23—161no—
538Q8—21no—
539Q8—21no—
540Q8—21no—
541Q8—41no—
542Q8—41no—
543Q8—81no—
544Q8C2×SD16×C4312yes—
545D4—21no—
546D4—21no—
547D4—21no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—41no—
555D4—41no—
556D4—82no—
557D4—81no—
558D4—81no—
559D4—82no—
560D4—82no—
561D4—161no—
562D4C2×SD16×C4312yes—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—82no—
576C2×C4—161no—
577C2×C4C22×D4×C4311yescharacteristic
578C2×C4C22×D4×C4311yescharacteristic
579C2×C4H(5,𝔽2)×C4311yescharacteristic
580C8—21no—
581C8—21no—
582C8—21no—
583C8—41no—
584C8—41no—
585C8—41no—
586C8—41no—
587C8—41no—
588C8C2×SD16×C4312yes—
589C22—22no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—164no—
602C22D42×C4311yescharacteristic
603C4—22no—
604C4—21no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—81no—
611C4—81no—
612C4C22×SD16×C4311yescharacteristic
613C4C43×#57511yescharacteristic
614C4C43×#57611yescharacteristic
615C4C43×#57711yescharacteristic
616C2—42no—
617C2—81no—
618C2—161no—
619C2—161no—
620C2C43×#326811yescharacteristic
621C2D4×SD16×C4311yescharacteristic
622C2C43×#328811yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#3274C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3392C2semidirect
2. C43×#3381C2semidirect
3. C43×#3295C2semidirect
5. C43×#1715C2semidirect
6. C43×#1691C2semidirect
7. C43×#1678C2semidirect
8. C43×#1668C2semidirect
9. C43×#1665C2semidirect
10. C43×#1639C2semidirect
11. C43×#1631C2semidirect
12. C43×#1626C2semidirect
13. C43×#1622C2semidirect
14. C43×#1583C2semidirect
15. C43×SD16⋊C8C2semidirect
17. C43×#557C22semidirect
22. C43×#498C22semidirect
25. C43×#492C22semidirect
26. C43×#492C22semidirect
32. C43×#477C22semidirect
42. C43×#460C22semidirect
47. C8×Q8×C43C22semidirect
48. C8×Q8×C43C22semidirect
56. C43×#335C22semidirect
57. C43×#334C22semidirect
58. C43×#333C22semidirect
59. C43×#332C22semidirect
61. C43×#331C22semidirect
62. C43×Q8⋊C8C22semidirect
63. C43×Q8⋊C8C22semidirect
66. C43×#322C22semidirect
180. SD16×C43SD16semidirect
277. #19807C43direct (N × H)
305. #3392C2×C43semidirect
306. #3381C2×C43semidirect
307. #3295C2×C43semidirect
309. #1715C2×C43semidirect
310. #1691C2×C43semidirect
311. #1678C2×C43semidirect
312. #1668C2×C43semidirect
313. #1665C2×C43semidirect
314. #1639C2×C43semidirect
315. #1631C2×C43semidirect
316. #1626C2×C43semidirect
317. #1622C2×C43semidirect
318. #1583C2×C43semidirect
319. SD16⋊C8C2×C43semidirect
328. #557C22×C43semidirect
333. #498C22×C43semidirect
336. #492C22×C43semidirect
337. #492C22×C43semidirect
343. #477C22×C43semidirect
353. #460C22×C43semidirect
358. C8×Q8C22×C43semidirect
359. C8×Q8C22×C43semidirect
367. #335C22×C43semidirect
368. #334C22×C43semidirect
369. #333C22×C43semidirect
370. #332C22×C43semidirect
372. #331C22×C43semidirect
373. Q8⋊C8C22×C43semidirect
374. Q8⋊C8C22×C43semidirect
377. #322C22×C43semidirect
378. C43#19807direct (N × H)
492. SD16SD16×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#33922
C43×#33812
C43×#32952
C43×#32742
C43×#17152
C43×#16912
C43×#16782
C43×#16682
C43×#16652
C43×#16392
C43×#16312
C43×#16262
C43×#16222
C43×#15832
C43×SD16⋊C82
#1980743