Finite Group Databasebeta

← C151×#19807 #50324732

Subgroups — C151×#19807 #50324732

Order 38656.

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
1#3392×C151C211yesmaximal, characteristic, complemented
2#3381×C151C211yesmaximal, characteristic, complemented
3#3295×C151C211yesmaximal, characteristic, complemented
4#3274×C151C211yesmaximal, characteristic
5#1715×C151C211yesmaximal, characteristic, complemented
6#1691×C151C211yesmaximal, characteristic, complemented
7#1678×C151C211yesmaximal, characteristic, complemented
8#1668×C151C211yesmaximal, characteristic, complemented
9#1665×C151C211yesmaximal, characteristic, complemented
10#1639×C151C211yesmaximal, characteristic, complemented
11#1631×C151C211yesmaximal, characteristic, complemented
12#1626×C151C211yesmaximal, characteristic, complemented
13#1622×C151C211yesmaximal, characteristic, complemented
14#1583×C151C211yesmaximal, characteristic, complemented
15SD16⋊C8×C151C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C151—21no—
17#557×C151C2211yescharacteristic, complemented
18#554×C151C2211yescharacteristic
19#550×C151C2211yescharacteristic
20D42×C151C2211yescharacteristic
21#499×C151—21no—
22#498×C151C2211yescharacteristic, complemented
23#493×C151C2211yescharacteristic
24#492×C151—21no—
25#492×C151C2211yescharacteristic, complemented
26#492×C151C2211yescharacteristic, complemented
27#486×C151C2211yescharacteristic
28#486×C151C2211yescharacteristic
29#481×C151—21no—
30#479×C151—21no—
31#478×C151—21no—
32#477×C151C2211yescharacteristic, complemented
33#476×C151C2211yescharacteristic
34#474×C151C2211yescharacteristic
35#469×C151—21no—
36#465×C151—21no—
37#461×C151—21no—
38#461×C151C2211yescharacteristic
39#460×C151—21no—
40#460×C151C2211yescharacteristic
41#460×C151C2211yescharacteristic
42#460×C151C2211yescharacteristic, complemented
43#459×C151C2211yescharacteristic
44#450×C151—21no—
45#449×C151—21no—
46#447×C151—21no—
47C8×Q8×C151C2211yescharacteristic, complemented
48C8×Q8×C151C2211yescharacteristic, complemented
49C4×SD16×C151—21no—
50C4×SD16×C151—21no—
51C4×SD16×C151C2211yescharacteristic
52C4×SD16×C151C2211yescharacteristic
53#436×C151C2211yescharacteristic
54C8×D4×C151C2211yescharacteristic
55C2×#102×C151—21no—
56#335×C151C2211yescharacteristic, complemented
57#334×C151C2211yescharacteristic, complemented
58#333×C151C2211yescharacteristic, complemented
59#332×C151C2211yescharacteristic, complemented
60#331×C151C2211yescharacteristic
61#331×C151C2211yescharacteristic, complemented
62Q8⋊C8×C151C2211yescharacteristic, complemented
63Q8⋊C8×C151C2211yescharacteristic, complemented
64D4⋊C8×C151C2211yescharacteristic
65D4⋊C8×C151C2211yescharacteristic
66#322×C151C2211yescharacteristic, complemented
67C2×#41×C151—21no—
68C22×D4×C151—21no—
69C22×D4×C151—21no—
70AGL(1,ℤ/8)×C151—44no—
71C2×SD16×C151—21no—
72C2×SD16×C151—21no—
73C2×SD16×C151—21no—
74C2×SD16×C151—21no—
75C2×SD16×C151—21no—
76C2×SD16×C151—21no—
77C2×SD16×C151—41no—
78C2×SD16×C151D411yescharacteristic
79C2×SD16×C151D411yescharacteristic
80C2×D8×C151—21no—
81C2×D8×C151—21no—
82C2×D8×C151—21no—
83C2×M16×C151—21no—
84C22×C8×C151—21no—
85C4⋊Q8×C151—21no—
86C4⋊Q8×C151C2311yescharacteristic
87C4⋊Q8×C151C2311yescharacteristic
88#127×C151—21no—
89#127×C151C2311yescharacteristic
90#127×C151C2311yescharacteristic
91#125×C151—21no—
92#125×C151—21no—
93#125×C151—41no—
94C22⋊Q8×C151—21no—
95C22⋊Q8×C151—41no—
96#121×C151—21no—
97#121×C151—21no—
98#121×C151—21no—
99#121×C151—41no—
100#120×C151—41no—
101C4×Q8×C151—21no—
102C4×Q8×C151—21no—
103C4×Q8×C151C2311yescharacteristic
104C4×Q8×C151C2311yescharacteristic
105C4×D4×C151—21no—
106C4×D4×C151—21no—
107C4×D4×C151C2311yescharacteristic
108C4×D4×C151C2311yescharacteristic
109C2×C4⋊C4×C151—21no—
110#107×C151—21no—
111#107×C151—21no—
112#106×C151—21no—
113#106×C151—21no—
114#106×C151—21no—
115#106×C151D411yescharacteristic
116#106×C151D411yescharacteristic
117C4⋊C8×C151—21no—
118C4⋊C8×C151—21no—
119C4⋊C8×C151C2311yescharacteristic
120C4⋊C8×C151C2311yescharacteristic
121C4⋊C8×C151C2311yescharacteristic
122C4⋊C8×C151C2311yescharacteristic
123#103×C151—21no—
124#103×C151—21no—
125#103×C151D411yescharacteristic
126#103×C151D411yescharacteristic
127#102×C151—21no—
128#102×C151—21no—
129#102×C151—21no—
130#102×C151—21no—
131#102×C151—21no—
132#102×C151—21no—
133#102×C151—21no—
134#102×C151—21no—
135#102×C151—41no—
136#102×C151D411yescharacteristic
137#102×C151D411yescharacteristic
138C22⋊C8×C151—21no—
139C22⋊C8×C151—21no—
140C4×C8×C151—21no—
141C4×C8×C151—21no—
142C4×C8×C151C2311yescharacteristic
143C4×C8×C151C2311yescharacteristic
144C4×C8×C151C2311yescharacteristic
145C24×C151—41no—
146#41×C151—42no—
147#41×C151—81no—
148C2×Q8×C151—21no—
149C2×Q8×C151—21no—
150C2×Q8×C151C2×D411yescharacteristic
151C2×Q8×C151C2×D411yescharacteristic
152C2×D4×C151—21no—
153C2×D4×C151—21no—
154C2×D4×C151—21no—
155C2×D4×C151—21no—
156C2×D4×C151—21no—
157C2×D4×C151—21no—
158C2×D4×C151—41no—
159C2×D4×C151—41no—
160C2×D4×C151—41no—
161C2×D4×C151—41no—
162C2×D4×C151—42no—
163C2×D4×C151—42no—
164C2×D4×C151—81no—
165C2×D4×C151—81no—
166C2×D4×C151C2×D411yescharacteristic
167C2×D4×C151C2×D411yescharacteristic
168C22×C4×C151—21no—
169C22×C4×C151—21no—
170C22×C4×C151—41no—
171C22×C4×C151—41no—
172SD16×C151—41no—
173SD16×C151—42no—
174SD16×C151—42no—
175SD16×C151—81no—
176SD16×C151—81no—
177SD16×C151—81no—
178SD16×C151—81no—
179SD16×C151—82no—
180SD16×C151SD1614yescomplemented
181D8×C151—42no—
182D8×C151—42no—
183D8×C151—81no—
184M16×C151—42no—
185C2×C8×C151—21no—
186C2×C8×C151—21no—
187C2×C8×C151—21no—
188C2×C8×C151—21no—
189C2×C8×C151—21no—
190C2×C8×C151—81no—
191C2×C8×C151C2×D411yescharacteristic
192C2×C8×C151C2×D411yescharacteristic
193C2×C8×C151C2×D411yescharacteristic
194C2×C8×C151C2×D411yescharacteristic
195C4⋊C4×C151—21no—
196C4⋊C4×C151—21no—
197C4⋊C4×C151—21no—
198C4⋊C4×C151—21no—
199C4⋊C4×C151—21no—
200C4⋊C4×C151—21no—
201C4⋊C4×C151—41no—
202C4⋊C4×C151—41no—
203C4⋊C4×C151—41no—
204C4⋊C4×C151—41no—
205C4⋊C4×C151—41no—
206C4⋊C4×C151C2×D411yescharacteristic
207C4⋊C4×C151C2×D411yescharacteristic
208C4⋊C4×C151C2×D411yescharacteristic
209C4⋊C4×C151C2×D411yescharacteristic
210C22⋊C4×C151—21no—
211C22⋊C4×C151—21no—
212C22⋊C4×C151—41no—
213C22⋊C4×C151—41no—
214C22⋊C4×C151—41no—
215C42×C151—21no—
216C42×C151—21no—
217C42×C151—41no—
218C42×C151C2411yescharacteristic
219C23×C151—21no—
220C23×C151—21no—
221C23×C151—41no—
222C23×C151—41no—
223C23×C151—82no—
224C23×C151—82no—
225C23×C151—161no—
226Q8×C151—21no—
227Q8×C151—21no—
228Q8×C151—21no—
229Q8×C151—41no—
230Q8×C151—41no—
231Q8×C151—81no—
232Q8×C151C2×SD1612yes—
233D4×C151—21no—
234D4×C151—21no—
235D4×C151—21no—
236D4×C151—41no—
237D4×C151—41no—
238D4×C151—41no—
239D4×C151—41no—
240D4×C151—41no—
241D4×C151—41no—
242D4×C151—41no—
243D4×C151—41no—
244D4×C151—82no—
245D4×C151—81no—
246D4×C151—81no—
247D4×C151—82no—
248D4×C151—82no—
249D4×C151—161no—
250D4×C151C2×SD1612yes—
251C2×C4×C151—21no—
252C2×C4×C151—21no—
253C2×C4×C151—21no—
254C2×C4×C151—21no—
255C2×C4×C151—21no—
256C2×C4×C151—21no—
257C2×C4×C151—41no—
258C2×C4×C151—41no—
259C2×C4×C151—41no—
260C2×C4×C151—41no—
261C2×C4×C151—41no—
262C2×C4×C151—41no—
263C2×C4×C151—82no—
264C2×C4×C151—161no—
265C2×C4×C151C22×D411yescharacteristic
266C2×C4×C151C22×D411yescharacteristic
267C2×C4×C151H(5,𝔽2)11yescharacteristic
268C8×C151—21no—
269C8×C151—21no—
270C8×C151—21no—
271C8×C151—41no—
272C8×C151—41no—
273C8×C151—41no—
274C8×C151—41no—
275C8×C151—41no—
276C8×C151C2×SD1612yes—
277C22×C151—22no—
278C22×C151—41no—
279C22×C151—41no—
280C22×C151—41no—
281C22×C151—41no—
282C22×C151—41no—
283C22×C151—81no—
284C22×C151—81no—
285C22×C151—81no—
286C22×C151—81no—
287C22×C151—81no—
288C22×C151—81no—
289C22×C151—164no—
290C22×C151D4211yescharacteristic
291C4×C151—22no—
292C4×C151—21no—
293C4×C151—41no—
294C4×C151—41no—
295C4×C151—41no—
296C4×C151—41no—
297C4×C151—41no—
298C4×C151—81no—
299C4×C151—81no—
300C4×C151C22×SD1611yescharacteristic
301C4×C151#57511yescharacteristic
302C4×C151#57611yescharacteristic
303C4×C151#57711yescharacteristic
304C2×C151—42no—
305C2×C151—81no—
306C2×C151—161no—
307C2×C151—161no—
308C2×C151#326811yescharacteristic
309C2×C151D4×SD1611yescharacteristic
310C2×C151#328811yescharacteristic
311#19807C15111yesmaximal, characteristic, direct product factor, Sylow
312C151#1980711yescharacteristic, direct product factor, Sylow
313#3392C2×C15111yescharacteristic, complemented
314#3381C2×C15111yescharacteristic, complemented
315#3295C2×C15111yescharacteristic, complemented
316#3274C2×C15111yescharacteristic
317#1715C2×C15111yescharacteristic, complemented
318#1691C2×C15111yescharacteristic, complemented
319#1678C2×C15111yescharacteristic, complemented
320#1668C2×C15111yescharacteristic, complemented
321#1665C2×C15111yescharacteristic, complemented
322#1639C2×C15111yescharacteristic, complemented
323#1631C2×C15111yescharacteristic, complemented
324#1626C2×C15111yescharacteristic, complemented
325#1622C2×C15111yescharacteristic, complemented
326#1583C2×C15111yescharacteristic, complemented
327SD16⋊C8C2×C15111yescharacteristic, complemented
328C2×AGL(1,ℤ/8)—21no—
329#557C22×C15111yescharacteristic, complemented
330#554C22×C15111yescharacteristic
331#550C22×C15111yescharacteristic
332D42C22×C15111yescharacteristic
333#499—21no—
334#498C22×C15111yescharacteristic, complemented
335#493C22×C15111yescharacteristic
336#492—21no—
337#492C22×C15111yescharacteristic, complemented
338#492C22×C15111yescharacteristic, complemented
339#486C22×C15111yescharacteristic
340#486C22×C15111yescharacteristic
341#481—21no—
342#479—21no—
343#478—21no—
344#477C22×C15111yescharacteristic, complemented
345#476C22×C15111yescharacteristic
346#474C22×C15111yescharacteristic
347#469—21no—
348#465—21no—
349#461—21no—
350#461C22×C15111yescharacteristic
351#460—21no—
352#460C22×C15111yescharacteristic
353#460C22×C15111yescharacteristic
354#460C22×C15111yescharacteristic, complemented
355#459C22×C15111yescharacteristic
356#450—21no—
357#449—21no—
358#447—21no—
359C8×Q8C22×C15111yescharacteristic, complemented
360C8×Q8C22×C15111yescharacteristic, complemented
361C4×SD16—21no—
362C4×SD16—21no—
363C4×SD16C22×C15111yescharacteristic
364C4×SD16C22×C15111yescharacteristic
365#436C22×C15111yescharacteristic
366C8×D4C22×C15111yescharacteristic
367C2×#102—21no—
368#335C22×C15111yescharacteristic, complemented
369#334C22×C15111yescharacteristic, complemented
370#333C22×C15111yescharacteristic, complemented
371#332C22×C15111yescharacteristic, complemented
372#331C22×C15111yescharacteristic
373#331C22×C15111yescharacteristic, complemented
374Q8⋊C8C22×C15111yescharacteristic, complemented
375Q8⋊C8C22×C15111yescharacteristic, complemented
376D4⋊C8C22×C15111yescharacteristic
377D4⋊C8C22×C15111yescharacteristic
378#322C22×C15111yescharacteristic, complemented
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×C15111yescharacteristic
391C2×SD16D4×C15111yescharacteristic
392C2×D8—21no—
393C2×D8—21no—
394C2×D8—21no—
395C2×M16—21no—
396C22×C8—21no—
397C4⋊Q8—21no—
398C4⋊Q8C23×C15111yescharacteristic
399C4⋊Q8C23×C15111yescharacteristic
400#127—21no—
401#127C23×C15111yescharacteristic
402#127C23×C15111yescharacteristic
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×C15111yescharacteristic
416C4×Q8C23×C15111yescharacteristic
417C4×D4—21no—
418C4×D4—21no—
419C4×D4C23×C15111yescharacteristic
420C4×D4C23×C15111yescharacteristic
421C2×C4⋊C4—21no—
422#107—21no—
423#107—21no—
424#106—21no—
425#106—21no—
426#106—21no—
427#106D4×C15111yescharacteristic
428#106D4×C15111yescharacteristic
429C4⋊C8—21no—
430C4⋊C8—21no—
431C4⋊C8C23×C15111yescharacteristic
432C4⋊C8C23×C15111yescharacteristic
433C4⋊C8C23×C15111yescharacteristic
434C4⋊C8C23×C15111yescharacteristic
435#103—21no—
436#103—21no—
437#103D4×C15111yescharacteristic
438#103D4×C15111yescharacteristic
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×C15111yescharacteristic
449#102D4×C15111yescharacteristic
450C22⋊C8—21no—
451C22⋊C8—21no—
452C4×C8—21no—
453C4×C8—21no—
454C4×C8C23×C15111yescharacteristic
455C4×C8C23×C15111yescharacteristic
456C4×C8C23×C15111yescharacteristic
457C24—41no—
458#41—42no—
459#41—81no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8C2×D4×C15111yescharacteristic
463C2×Q8C2×D4×C15111yescharacteristic
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×C15111yescharacteristic
479C2×D4C2×D4×C15111yescharacteristic
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×C15114yescomplemented
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×C15111yescharacteristic
504C2×C8C2×D4×C15111yescharacteristic
505C2×C8C2×D4×C15111yescharacteristic
506C2×C8C2×D4×C15111yescharacteristic
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×C15111yescharacteristic
519C4⋊C4C2×D4×C15111yescharacteristic
520C4⋊C4C2×D4×C15111yescharacteristic
521C4⋊C4C2×D4×C15111yescharacteristic
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C42—21no—
528C42—21no—
529C42—41no—
530C42C24×C15111yescharacteristic
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×C15112yes—
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×C15112yes—
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×C15111yescharacteristic
578C2×C4C22×D4×C15111yescharacteristic
579C2×C4H(5,𝔽2)×C15111yescharacteristic
580C8—21no—
581C8—21no—
582C8—21no—
583C8—41no—
584C8—41no—
585C8—41no—
586C8—41no—
587C8—41no—
588C8C2×SD16×C15112yes—
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×C15111yescharacteristic
603C4—22no—
604C4—21no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—81no—
611C4—81no—
612C4C22×SD16×C15111yescharacteristic
613C4#575×C15111yescharacteristic
614C4#576×C15111yescharacteristic
615C4#577×C15111yescharacteristic
616C2—42no—
617C2—81no—
618C2—161no—
619C2—161no—
620C2#3268×C15111yescharacteristic
621C2D4×SD16×C15111yescharacteristic
622C2#3288×C15111yescharacteristic
subgroupG/H
center, socleC22×C151D42
commutator, Frattini, cosocleC42C24×C151
prime radical#3274×C151C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3392×C151C2semidirect
2. #3381×C151C2semidirect
3. #3295×C151C2semidirect
5. #1715×C151C2semidirect
6. #1691×C151C2semidirect
7. #1678×C151C2semidirect
8. #1668×C151C2semidirect
9. #1665×C151C2semidirect
10. #1639×C151C2semidirect
11. #1631×C151C2semidirect
12. #1626×C151C2semidirect
13. #1622×C151C2semidirect
14. #1583×C151C2semidirect
15. SD16⋊C8×C151C2semidirect
17. #557×C151C22semidirect
22. #498×C151C22semidirect
25. #492×C151C22semidirect
26. #492×C151C22semidirect
32. #477×C151C22semidirect
42. #460×C151C22semidirect
47. C8×Q8×C151C22semidirect
48. C8×Q8×C151C22semidirect
56. #335×C151C22semidirect
57. #334×C151C22semidirect
58. #333×C151C22semidirect
59. #332×C151C22semidirect
61. #331×C151C22semidirect
62. Q8⋊C8×C151C22semidirect
63. Q8⋊C8×C151C22semidirect
66. #322×C151C22semidirect
180. SD16×C151SD16semidirect
311. #19807C151direct (N × H)
312. C151#19807direct (N × H)
313. #3392C2×C151semidirect
314. #3381C2×C151semidirect
315. #3295C2×C151semidirect
317. #1715C2×C151semidirect
318. #1691C2×C151semidirect
319. #1678C2×C151semidirect
320. #1668C2×C151semidirect
321. #1665C2×C151semidirect
322. #1639C2×C151semidirect
323. #1631C2×C151semidirect
324. #1626C2×C151semidirect
325. #1622C2×C151semidirect
326. #1583C2×C151semidirect
327. SD16⋊C8C2×C151semidirect
329. #557C22×C151semidirect
334. #498C22×C151semidirect
337. #492C22×C151semidirect
338. #492C22×C151semidirect
344. #477C22×C151semidirect
354. #460C22×C151semidirect
359. C8×Q8C22×C151semidirect
360. C8×Q8C22×C151semidirect
368. #335C22×C151semidirect
369. #334C22×C151semidirect
370. #333C22×C151semidirect
371. #332C22×C151semidirect
373. #331C22×C151semidirect
374. Q8⋊C8C22×C151semidirect
375. Q8⋊C8C22×C151semidirect
378. #322C22×C151semidirect
492. SD16SD16×C151semidirect

Maximal subgroups

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

subgroupindex
#3392×C1512
#3381×C1512
#3295×C1512
#3274×C1512
#1715×C1512
#1691×C1512
#1678×C1512
#1668×C1512
#1665×C1512
#1639×C1512
#1631×C1512
#1626×C1512
#1622×C1512
#1583×C1512
SD16⋊C8×C1512
#19807151