Finite Group Databasebeta

← #6491693

Subgroups — #6491693

Order 512.

2246 conjugacy classes of subgroups.

The subgroup lattice has 769 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3209C211yesmaximal, characteristic, complemented
2C2×#2920C211yesmaximal, characteristic
3#36625C211yesmaximal, characteristic
4C2×#2857C211yesmaximal, characteristic
5#33176C212yesmaximal, complemented
6#33049C212yesmaximal, complemented
7#29845C212yesmaximal, complemented
8#29808C212yesmaximal, complemented
9#24760C214yesmaximal, complemented
10#24660C214yesmaximal, complemented
11#24508C214yesmaximal, complemented
12#24386C214yesmaximal
13#21981C211yesmaximal, characteristic, complemented
14#21860C211yesmaximal, characteristic, complemented
15#21804C211yesmaximal, characteristic, complemented
16C2×#533C2211yescharacteristic
17C22×C4⋊Q8C2211yescharacteristic
18C22×C22⋊Q8C2212yes—
19C23×C42C2211yescharacteristic
20#3209—28no—
21C2×#494C2212yescomplemented
22C2×#487C2212yescomplemented
23C2×#470C2218yes—
24C2×#462C2214yescomplemented
25C2×#451C2214yes—
26#2920—28no—
27C2×#432C2212yes—
28C2×#432C2212yes—
29C2×#431C2211yescharacteristic
30C2×#431C2212yes—
31C2×#431C2211yescharacteristic
32C2×#423C2212yes—
33C2×#407C2212yes—
34C2×C4×M16C2212yes—
35#2857—21no—
36#2857—21no—
37#2857—21no—
38#2857—21no—
39#2857C2211yescharacteristic
40#2857C2211yescharacteristic
41#2857C2212yes—
42#2857C2212yes—
43#2857C2212yes—
44#2857C2212yes—
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2855—21no—
48#2855C2212yes—
49#2851—21no—
50#2851—21no—
51#2848—21no—
52#2848C2212yes—
53C4×C22⋊Q8—21no—
54C4×C22⋊Q8—21no—
55C4×C22⋊Q8C2212yes—
56C4×C22⋊Q8C2212yes—
57#2296—21no—
58C2×#391C2212yes—
59C2×#389—21no—
60C2×#389—21no—
61#2285C2211yescharacteristic
62C2×#384C2211yescharacteristic
63#2280—21no—
64C2×#380—21no—
65C2×#380—21no—
66#2066C2218yescomplemented
67#2056C2218yescomplemented
68#2035C2218yes—
69#2001C2218yes—
70#1990C2212yescomplemented
71#1981C2214yescomplemented
72#1971C2218yescomplemented
73#1956C2212yescomplemented
74#1956C2212yescomplemented
75#1956C2212yescomplemented
76#1948C2214yescomplemented
77#1935C2218yescomplemented
78#1894C2218yes—
79#1872C2214yes—
80#1853C2214yes—
81#1844C2212yescomplemented
82#1834C2212yescomplemented
83#1803C2214yescomplemented
84#1787C2214yes—
85C23×Q8C2312yes—
86C24×C4D411yescharacteristic
87C24×C4D411yescharacteristic
88C24×C4C2311yescharacteristic
89C22×Q16C2318yes—
90C22×M16C2314yes—
91#533—24no—
92#533—24no—
93C2×C4⋊Q8—21no—
94C2×C4⋊Q8—21no—
95C2×C4⋊Q8—24no—
96C2×C4⋊Q8—24no—
97C2×C4⋊Q8C2312yes—
98C2×C4⋊Q8C2311yescharacteristic
99C2×C4⋊Q8C2312yes—
100C2×C4⋊Q8C2311yescharacteristic
101C2×#125—21no—
102C2×C22⋊Q8—21no—
103C2×C22⋊Q8—21no—
104C2×C22⋊Q8—21no—
105C2×C22⋊Q8—22no—
106C2×C22⋊Q8—22no—
107C2×C22⋊Q8—48no—
108C2×C22⋊Q8C2312yes—
109C2×C22⋊Q8C2312yes—
110C2×C22⋊Q8C2314yes—
111C2×C22⋊Q8C2312yes—
112C2×C22⋊Q8C2314yes—
113C2×C4×Q8—21no—
114C2×C4×Q8C2312yes—
115C2×#117—21no—
116C2×#117—21no—
117C22×C4⋊C4—22no—
118C22×C4⋊C4—21no—
119C22×C4⋊C4—21no—
120C22×C4⋊C4—21no—
121C22×C4⋊C4—21no—
122C22×C4⋊C4C2312yes—
123C22×C22⋊C4—22no—
124C22×C42—24no—
125C22×C42—24no—
126C22×C42D411yescharacteristic
127C22×C42D411yescharacteristic
128C22×C42D411yescharacteristic
129C22×C42D411yescharacteristic
130C22×C42D411yescharacteristic
131C22×C42D411yescharacteristic
132C22×C42C2311yescharacteristic
133C22×C42C2311yescharacteristic
134C22×C42C2311yescharacteristic
135C22×C42C2311yescharacteristic
136C22×C42C2311yescharacteristic
137C22×C42C2311yescharacteristic
138#494—28no—
139#487—28no—
140#470—416no—
141#462—216no—
142#451—216no—
143#432—28no—
144#432—28no—
145#431—24no—
146#431—28no—
147#431D418yes—
148C2×#106C2318yes—
149#423—28no—
150C2×C4⋊C8C2314yes—
151C2×C4⋊C8C2312yes—
152C2×C4⋊C8C2312yes—
153C2×#103C2318yes—
154C2×#103C2318yes—
155C2×#103C2318yes—
156C2×#103C2318yes—
157#407—28no—
158C2×C22⋊C8C2312yes—
159C2×C22⋊C8C2314yes—
160C2×C22⋊C8C2312yes—
161C4×M16—28no—
162C2×#97C2314yes—
163C2×C4×C8C2312yes—
164C2×C4×C8C2312yes—
165#391—21no—
166#391—21no—
167#391—22no—
168#391—22no—
169#391C2312yes—
170#391C2314yes—
171#391C2312yes—
172#391C2314yes—
173#389—21no—
174#389—21no—
175#389—21no—
176#389—21no—
177#389—21no—
178#389—21no—
179#389—22no—
180#389—22no—
181#389—22no—
182#389—22no—
183#389—22no—
184#389—22no—
185#389—22no—
186#389—22no—
187#389C2312yes—
188#389C2312yes—
189#387—22no—
190#387—22no—
191#387—22no—
192#387—22no—
193#385—22no—
194#385—22no—
195#385—22no—
196#385—22no—
197#385—22no—
198#385—22no—
199#384—21no—
200#384—21no—
201#384C2312yes—
202#384C2311yescharacteristic
203#384C2312yes—
204#384C2311yescharacteristic
205#382—21no—
206#381—22no—
207#380—21no—
208#380—21no—
209#380—21no—
210#380—21no—
211#380—21no—
212#380—21no—
213#380—21no—
214#380—22no—
215#380—22no—
216#380—22no—
217#380—22no—
218#380—22no—
219#380—22no—
220#380—22no—
221#380—22no—
222#380C2312yes—
223#380C2312yes—
224#380C2312yes—
225#379—22no—
226C4×C4⋊C4—21no—
227C4×C4⋊C4—22no—
228C4×C4⋊C4—22no—
229C4×C4⋊C4C2312yes—
230C4×C22⋊C4—22no—
231C4×C22⋊C4—22no—
232C2×#95—22no—
233C2×#95—22no—
234#340C2318yes—
235#340C2318yes—
236C25C2×D411yescharacteristic
237C22×Q8—21no—
238C22×Q8—22no—
239C22×Q8—24no—
240C22×Q8—24no—
241C22×Q8—44no—
242C22×Q8—44no—
243C22×Q8C2412yes—
244C22×Q8C2414yes—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—24no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—42no—
256C23×C4—42no—
257C23×C4C2×D411yescharacteristic
258C23×C4C2×D411yescharacteristic
259C23×C4C2×D411yescharacteristic
260C23×C4C2×D411yescharacteristic
261C23×C4C2×D411yescharacteristic
262C23×C4C2×D411yescharacteristic
263C23×C4C2×D411yescharacteristic
264C23×C4C2×D411yescharacteristic
265C23×C4C2×D411yescharacteristic
266C23×C4C2×D411yescharacteristic
267C23×C4C2×D411yescharacteristic
268C23×C4C2×D411yescharacteristic
269C23×C4C2×D411yescharacteristic
270C23×C4C2×D411yescharacteristic
271C23×C4C2×D411yescharacteristic
272C23×C4C2411yescharacteristic
273C23×C4C2411yescharacteristic
274C23×C4C2411yescharacteristic
275C2×Q16—216no—
276C2×Q16—48no—
277C2×Q16—48no—
278C2×M16—28no—
279C2×M16—28no—
280C2×M16—44no—
281C22×C8C2414yes—
282C22×C8C2414yes—
283C4⋊Q8—22no—
284C4⋊Q8—24no—
285C4⋊Q8—24no—
286C4⋊Q8—22no—
287C4⋊Q8—22no—
288C4⋊Q8—24no—
289C4⋊Q8—24no—
290C4⋊Q8—22no—
291C4⋊Q8—44no—
292C4⋊Q8—44no—
293#125—44no—
294C22⋊Q8—24no—
295C22⋊Q8—24no—
296C22⋊Q8—216no—
297C22⋊Q8—28no—
298C22⋊Q8—48no—
299C22⋊Q8—44no—
300C22⋊Q8—44no—
301C22⋊Q8—48no—
302C22⋊Q8—48no—
303C22⋊Q8—44no—
304C22⋊Q8—44no—
305C4×Q8—24no—
306C4×Q8—24no—
307C4×Q8—44no—
308#117—44no—
309#117—44no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—48no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—44no—
340C2×C4⋊C4C2414yes—
341C2×C4⋊C4C2412yes—
342C2×C4⋊C4C2412yes—
343C2×C4⋊C4C2412yes—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—48no—
353C2×C42—24no—
354C2×C42—24no—
355C2×C42—22no—
356C2×C42—22no—
357C2×C42—24no—
358C2×C42—24no—
359C2×C42—24no—
360C2×C42—24no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42C2×D411yescharacteristic
372C2×C42C2×D411yescharacteristic
373C2×C42C2×D411yescharacteristic
374C2×C42C2×D411yescharacteristic
375C2×C42C2×D411yescharacteristic
376C2×C42C2×D411yescharacteristic
377C2×C42C2×D411yescharacteristic
378C2×C42C2×D411yescharacteristic
379C2×C42C2×D411yescharacteristic
380C2×C42C2×D411yescharacteristic
381C2×C42C2×D411yescharacteristic
382C2×C42C2×D411yescharacteristic
383C2×C42C2×D414yes—
384C2×C42#4114yes—
385C2×C42C2411yescharacteristic
386C2×C42C2411yescharacteristic
387C2×C42C2411yescharacteristic
388C2×C42C2411yescharacteristic
389#106—48no—
390C4⋊C8—28no—
391C4⋊C8—24no—
392C4⋊C8C2×D418yes—
393#103—216no—
394#103—48no—
395#103—48no—
396#103—48no—
397C22⋊C8—24no—
398C22⋊C8—28no—
399C22⋊C8C2×D418yes—
400#97—28no—
401C4×C8—24no—
402C4×C8C2×D418yes—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—22no—
408#95—22no—
409#95—22no—
410#95—22no—
411#95—22no—
412#95—22no—
413#95—22no—
414#95—22no—
415#95—22no—
416#95—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—41no—
423C24—41no—
424C24C22×D411yescharacteristic
425C24C22×D411yescharacteristic
426C24C22×D411yescharacteristic
427C2×Q8—24no—
428C2×Q8—22no—
429C2×Q8—22no—
430C2×Q8—24no—
431C2×Q8—24no—
432C2×Q8—28no—
433C2×Q8—28no—
434C2×Q8—24no—
435C2×Q8—44no—
436C2×Q8—44no—
437C2×Q8—42no—
438C2×Q8—44no—
439C2×Q8—42no—
440C2×Q8—42no—
441C2×Q8—88no—
442C2×Q8—88no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—48no—
499C22×C4—48no—
500C22×C4—416no—
501C22×C4—416no—
502C22×C4—44no—
503C22×C4—44no—
504C22×C4—44no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4#12114yes—
509C22×C4#12114yes—
510C22×C4#13714yes—
511C22×C4#13714yes—
512C22×C4#13714yes—
513C22×C4C22×D411yescharacteristic
514C22×C4C22×D411yescharacteristic
515C22×C4C22×D411yescharacteristic
516C22×C4C22×D411yescharacteristic
517C22×C4C22×D411yescharacteristic
518C22×C4C22×D411yescharacteristic
519C22×C4C22×D412yes—
520C22×C4C22×D411yescharacteristic
521C22×C4C22×D411yescharacteristic
522C22×C4C22×D411yescharacteristic
523C22×C4C22×D411yescharacteristic
524C22×C4C22×D411yescharacteristic
525C22×C4C2×#4112yes—
526C22×C4H(5,𝔽2)14yes—
527C22×C4C2511yescharacteristic
528Q16—816no—
529M16—416no—
530C2×C8—24no—
531C2×C8—24no—
532C2×C8—24no—
533C2×C8—24no—
534C2×C8—24no—
535C2×C8C22×D418yes—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—24no—
539C4⋊C4—28no—
540C4⋊C4—24no—
541C4⋊C4—44no—
542C4⋊C4—44no—
543C4⋊C4—48no—
544C4⋊C4—44no—
545C4⋊C4—44no—
546C4⋊C4—44no—
547C4⋊C4—44no—
548C4⋊C4—44no—
549C4⋊C4—44no—
550C4⋊C4—42no—
551C4⋊C4—42no—
552C4⋊C4—44no—
553C4⋊C4—44no—
554C4⋊C4—42no—
555C4⋊C4—48no—
556C4⋊C4—44no—
557C4⋊C4—44no—
558C4⋊C4—44no—
559C4⋊C4—42no—
560C4⋊C4—42no—
561C4⋊C4—42no—
562C4⋊C4—44no—
563C4⋊C4—44no—
564C4⋊C4—42no—
565C22⋊C4—48no—
566C22⋊C4—44no—
567C22⋊C4—44no—
568C22⋊C4—44no—
569C22⋊C4—48no—
570C22⋊C4—44no—
571C22⋊C4—44no—
572C22⋊C4—44no—
573C42—22no—
574C42—22no—
575C42—22no—
576C42—22no—
577C42—22no—
578C42—22no—
579C42—22no—
580C42—22no—
581C42—22no—
582C42—22no—
583C42—21no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—44no—
588C42—44no—
589C42#12114yes—
590C42#12114yes—
591C42C22×D412yes—
592C42C22×D412yes—
593C42C2×#4112yes—
594C42C2×#4112yes—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—28no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—44no—
613C23—44no—
614C23—44no—
615C23—44no—
616C23—44no—
617C23—44no—
618C23C2×#12112yes—
619C23#53512yes—
620C23C2×#13712yes—
621C23C2×#13712yes—
622C23C2×#13712yes—
623C23C23×D411yescharacteristic
624Q8—44no—
625Q8—48no—
626Q8—44no—
627Q8—48no—
628Q8—88no—
629Q8—84no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—28no—
643C2×C4—28no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—44no—
657C2×C4—44no—
658C2×C4—44no—
659C2×C4—44no—
660C2×C4—44no—
661C2×C4—44no—
662C2×C4—44no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—44no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—44no—
669C2×C4—44no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—44no—
673C2×C4—44no—
674C2×C4—44no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—44no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—44no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—44no—
688C2×C4—88no—
689C2×C4—88no—
690C2×C4#470116yescomplemented
691C2×C4C2×#12112yes—
692C2×C4C2×#12112yes—
693C2×C4C2×#12112yes—
694C2×C4C2×#12112yes—
695C2×C4C2×#12112yes—
696C2×C4#53512yes—
697C2×C4C2×#13712yes—
698C2×C4C2×#13712yes—
699C2×C4C2×#13712yes—
700C2×C4C2×#13712yes—
701C2×C4C2×#13712yes—
702C2×C4C2×#13712yes—
703C2×C4#57512yes—
704C2×C4C23×D411yescharacteristic
705C2×C4C22×#4111yescharacteristic
706C2×C4C2×H(5,𝔽2)12yes—
707C2×C4#58512yes—
708C8—28no—
709C8—44no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—416no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22C2×#47014yes—
732C22C22×#12111yescharacteristic
733C22C2×#53511yescharacteristic
734C22#344911yescharacteristic
735C22C22×#13711yescharacteristic
736C22C22×#13711yescharacteristic
737C22C22×#13711yescharacteristic
738C22C2×#57511yescharacteristic
739C4—22no—
740C4—22no—
741C4—22no—
742C4—22no—
743C4—41no—
744C4—41no—
745C4—41no—
746C4—41no—
747C4—82no—
748C4—82no—
749C4—82no—
750C4—84no—
751C4—84no—
752C4—82no—
753C4C2×#47014yes—
754C4C2×#47014yes—
755C4#305614yes—
756C4#348812yes—
757C4#349412yes—
758C2—24no—
759C2—42no—
760C2—42no—
761C2#3525211yescharacteristic
762C2C22×#47011yescharacteristic
763C2C2×#305611yescharacteristic
764C2#6080011yescharacteristic
765C2#6080411yescharacteristic
766C2#6096611yescharacteristic
767C2#6097111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3209C2semidirect
5. #33176C2semidirect
6. #33049C2semidirect
7. #29845C2semidirect
8. #29808C2semidirect
9. #24760C2semidirect
10. #24660C2semidirect
11. #24508C2semidirect
13. #21981C2semidirect
14. #21860C2semidirect
15. #21804C2semidirect
21. C2×#494C22semidirect
22. C2×#487C22semidirect
24. C2×#462C22semidirect
66. #2066C22semidirect
67. #2056C22semidirect
70. #1990C22semidirect
71. #1981C22semidirect
72. #1971C22semidirect
73. #1956C22semidirect
74. #1956C22semidirect
75. #1956C22semidirect
76. #1948C22semidirect
77. #1935C22semidirect
81. #1844C22semidirect
82. #1834C22semidirect
83. #1803C22semidirect
690. C2×C4#470semidirect

Maximal subgroups

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

subgroupindex
C2×#32092
C2×#29202
#366252
C2×#28572
#331762
#330492
#298452
#298082
#247602
#246602
#245082
#243862
#219812
#218602
#218042