Finite Group Databasebeta

← #10816034

Subgroups — #10816034

Order 768.

1016 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2897C211yesmaximal, characteristic
2C2×#5242C211yesmaximal, characteristic
3#84099C211yesmaximal, characteristic
4#82571C211yesmaximal, characteristic, complemented
5#78821C211yesmaximal, characteristic, complemented
6#72019C211yesmaximal, characteristic, complemented
7#72008C211yesmaximal, characteristic, complemented
8#71665C211yesmaximal, characteristic, complemented
9#70325C211yesmaximal, characteristic, complemented
10#70318C211yesmaximal, characteristic, complemented
11#70304C211yesmaximal, characteristic, complemented
12#70298C211yesmaximal, characteristic, complemented
13#70289C211yesmaximal, characteristic, complemented
14#70195C211yesmaximal, characteristic, complemented
15#70158C211yesmaximal, characteristic, complemented
16#22896—31nomaximal, Sylow
17C2×C3×H(5,𝔽2)C2211yescharacteristic
18C2×C3×#131C2211yescharacteristic
19C3×#520C2211yescharacteristic
20#5827C2211yescharacteristic
21C2×#951C2211yescharacteristic
22C2×#951C2211yescharacteristic
23C2×#948C2211yescharacteristic
24C2×#936C2211yescharacteristic
25#5516C2211yescharacteristic, complemented
26C3×#418—21no—
27C3×#418C2211yescharacteristic
28C3×#417—21no—
29C3×#417C2211yescharacteristic
30C3×#416—21no—
31C3×#416C2211yescharacteristic
32C2×C3×#102—21no—
33C2×C3×#102C2211yescharacteristic
34#5242C418yescomplemented
35C2×#837C2211yescharacteristic
36C2×#837C2211yescharacteristic
37#5233—21no—
38#5233C2211yescharacteristic
39#5232—21no—
40#5232C2211yescharacteristic
41C2×#833C2211yescharacteristic
42#5215—21no—
43#5215C2211yescharacteristic
44C2×#832—21no—
45C2×#832C2211yescharacteristic
46C2×#824C2211yescharacteristic, complemented
47C2×#816C2211yescharacteristic, complemented
48#5101C2211yescharacteristic, complemented
49C2×C8×Dic3C2211yescharacteristic, complemented
50#5030—21no—
51C4×#216—21no—
52#5018—21no—
53C4×#214—21no—
54#4997C2211yescharacteristic, complemented
55#4995C2211yescharacteristic, complemented
56#4977C2211yescharacteristic, complemented
57C2×#810C2211yescharacteristic, complemented
58#4964C2211yescharacteristic, complemented
59#4790—21no—
60#4789—21no—
61#4758—21no—
62#4757—21no—
63#4558C2211yescharacteristic, complemented
64#4555C2211yescharacteristic, complemented
65#4554C2211yescharacteristic, complemented
66#4552C2211yescharacteristic, complemented
67#4532C2211yescharacteristic, complemented
68#4530C2211yescharacteristic, complemented
69C2×#455—31no—
70#2947—31no—
71#2947—31no—
72#2897—31no—
73#2897D311yescharacteristic
74#1958—31no—
75#1931—31no—
76#1931—31no—
77#1908—31no—
78#1908—31no—
79#1888—31no—
80#1860—31no—
81#1860—31no—
82#1764—31no—
83#1764—31no—
84C3×H(5,𝔽2)—22no—
85C3×H(5,𝔽2)—22no—
86C3×H(5,𝔽2)—41no—
87C3×H(5,𝔽2)C2×C414yes—
88C2×C3×#41—21no—
89C2×C3×#41—21no—
90C2×C3×#41C2311yescharacteristic
91C2×C3×#41C2311yescharacteristic
92C22×C3×D4—21no—
93C22×C3×D4—21no—
94C22×C3×D4—41no—
95C22×C3×D4C2311yescharacteristic
96C22×Dic6C2311yescharacteristic
97C3×#131—22no—
98C3×#131—41no—
99C2×C3×M16—21no—
100C2×C3×M16C2311yescharacteristic
101C22×C3×C8—21no—
102C22×C3×C8C2311yescharacteristic
103C3×C4×Q8—21no—
104C3×C4×D4—21no—
105C3×C4×D4—41no—
106C3×#117—21no—
107C3×#117C2311yescharacteristic
108C2×C3×C4⋊C4—21no—
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×#217—41no—
111#951—22no—
112#951—22no—
113#951C2×C414yescomplemented
114#951C2×C414yescomplemented
115#948—22no—
116#948—41no—
117Q8×Dic3—21no—
118C2×#216—21no—
119C2×#216—21no—
120#936—41no—
121#936C2×C414yescomplemented
122D4×Dic3—21no—
123D4×Dic3—41no—
124C2×#214—21no—
125C2×#214—21no—
126#926—21no—
127#926C2311yescharacteristic
128C2×C4⋊Dic3—21no—
129C2×C4⋊Dic3C2311yescharacteristic
130C2×C4×Dic3C2311yescharacteristic
131C2×#208—21no—
132C2×#208C2311yescharacteristic
133C2×#208C2311yescharacteristic
134C2×#208C2311yescharacteristic
135C22×C3⋊C8—21no—
136C22×C3⋊C8C2311yescharacteristic
137#887—21no—
138#887—21no—
139#877—41no—
140C4×Dic6—21no—
141C4×Dic6—21no—
142C3×#103—21no—
143C3×#103D411yescharacteristic
144C3×#103D411yescharacteristic
145C3×#102—21no—
146C3×#102—21no—
147C3×#102—21no—
148C3×#102—21no—
149C3×#102—21no—
150C3×#102D411yescharacteristic
151C3×#102D411yescharacteristic
152#837C2×C414yescomplemented
153#837C2×C414yescomplemented
154#835—21no—
155#835D411yescharacteristic
156#835D411yescharacteristic
157#833C2×C414yescomplemented
158#832—21no—
159#832—21no—
160#832—21no—
161#832—21no—
162#832—21no—
163#832D411yescharacteristic
164#832D411yescharacteristic
165C3⋊#95—41no—
166#824—41no—
167#816—21no—
168#816—21no—
169#815—21no—
170C8×Dic3—21no—
171C8×Dic3—41no—
172#810—21no—
173#810—21no—
174#808—21no—
175#808—21no—
176#807—21no—
177#807—21no—
178#803—21no—
179C4×C3⋊C8—21no—
180C2×H(5,𝔽2)C2×D311yescharacteristic
181C2×#137—31no—
182C2×#137—31no—
183C2×#131—31no—
184C2×#131C2×D311yescharacteristic
185C2×#124—31no—
186#520—31no—
187#520C2×D311yescharacteristic
188#519—31no—
189#455—38no—
190#441—61no—
191#441—61no—
192#440—61no—
193#440—61no—
194C4×Q16—61no—
195C4×Q16—61no—
196C4×SD16—61no—
197C4×SD16—61no—
198#428—31no—
199#428—31no—
200C2×#104—31no—
201C2×#104—31no—
202#418—21no—
203#418—31no—
204#418—61no—
205#418C2×D311yescharacteristic
206#417—21no—
207#417—31no—
208#417—61no—
209#417C2×D311yescharacteristic
210#416—21no—
211#416—31no—
212#416—61no—
213#416C2×D311yescharacteristic
214C2×#103—31no—
215C2×#103—31no—
216C2×#102—21no—
217C2×#102—31no—
218C2×#102—61no—
219C2×#102C2×D311yescharacteristic
220C2×#101—31no—
221C2×#100—31no—
222#405—31no—
223#405—31no—
224C2×C4×C8—31no—
225#382—31no—
226#343—31no—
227#343—31no—
228#341—31no—
229#341—31no—
230#339—31no—
231#339—31no—
232C24×C3—21no—
233C24×C3—41no—
234C3×#41—21no—
235C3×#41—21no—
236C3×#41—21no—
237C3×#41—21no—
238C3×#41—24no—
239C3×#41—24no—
240C3×#41—42no—
241C3×#41—42no—
242C3×#41C22×C412yes—
243C3×#41C22×C412yes—
244C3×#41#4112yes—
245C3×#41#4112yes—
246C2×C3×Q8C2×D411yescharacteristic
247C2×C3×Q8C2×D411yescharacteristic
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4—24no—
251C2×C3×D4—24no—
252C2×C3×D4—21no—
253C2×C3×D4—21no—
254C2×C3×D4—21no—
255C2×C3×D4—21no—
256C2×C3×D4—21no—
257C2×C3×D4—42no—
258C2×C3×D4—42no—
259C2×C3×D4—41no—
260C2×C3×D4—41no—
261C2×C3×D4—44no—
262C2×C3×D4—44no—
263C2×C3×D4C22×C412yes—
264C2×C3×D4C2×D411yescharacteristic
265C2×C3×D4C2×D411yescharacteristic
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—41no—
270C22×C3×C4—41no—
271C22×C3×C4C2411yescharacteristic
272C22×Dic3—21no—
273C22×Dic3—21no—
274C22×Dic3—21no—
275C22×Dic3—41no—
276C2×Dic6—21no—
277C2×Dic6—21no—
278C2×Dic6—21no—
279C2×Dic6—21no—
280C2×Dic6—21no—
281C2×Dic6C22×C412yes—
282C3×M16—21no—
283C3×M16—21no—
284C3×M16—42no—
285C2×C3×C8—21no—
286C2×C3×C8—21no—
287C2×C3×C8—21no—
288C2×C3×C8—42no—
289C2×C3×C8C2×D411yescharacteristic
290C2×C3×C8C2×D411yescharacteristic
291C3×C4⋊C4—21no—
292C3×C4⋊C4—21no—
293C3×C4⋊C4—41no—
294C3×C4⋊C4C2×D411yescharacteristic
295C3×C4⋊C4C2×D411yescharacteristic
296C3×C22⋊C4—21no—
297C3×C22⋊C4—41no—
298C3×C42—21no—
299C3×C42—41no—
300#217—21no—
301#217—44no—
302#217—41no—
303#216—24no—
304#216—24no—
305#214—24no—
306#214—24no—
307C4⋊Dic3—21no—
308C4⋊Dic3—21no—
309C4⋊Dic3—41no—
310C4⋊Dic3C2×D411yescharacteristic
311C4⋊Dic3C2×D411yescharacteristic
312Dic3⋊C4—41no—
313Dic3⋊C4—41no—
314C4×Dic3—21no—
315C4×Dic3—21no—
316C4×Dic3—41no—
317C4×Dic3—41no—
318C4×Dic3—41no—
319C4×Dic3C22×C412yes—
320#208—21no—
321#208—21no—
322#208—21no—
323#208—21no—
324#208—42no—
325#208C22×C412yes—
326#208C22×C412yes—
327C2×C3⋊C8—21no—
328C2×C3⋊C8—21no—
329C2×C3⋊C8—21no—
330C2×C3⋊C8—21no—
331C2×C3⋊C8—21no—
332C2×C3⋊C8—42no—
333C2×C3⋊C8C2×D411yescharacteristic
334C2×C3⋊C8C2×D411yescharacteristic
335H(5,𝔽2)—22no—
336H(5,𝔽2)—22no—
337H(5,𝔽2)—41no—
338H(5,𝔽2)C4×D314yes—
339C2×#41—21no—
340C2×#41—21no—
341C2×#41C22×D311yescharacteristic
342C2×#41C22×D311yescharacteristic
343C22×Q8—31no—
344C22×D4—21no—
345C22×D4—21no—
346C22×D4—41no—
347C22×D4C22×D311yescharacteristic
348#137—34no—
349#137—34no—
350#137—62no—
351#137—62no—
352C2×Q16—61no—
353C2×Q16—61no—
354C2×SD16—61no—
355C2×SD16—61no—
356#131—22no—
357#131—41no—
358#131—62no—
359#131—121no—
360C2×M16—21no—
361C2×M16—31no—
362C2×M16—31no—
363C2×M16—31no—
364C2×M16—61no—
365C2×M16C22×D311yescharacteristic
366C22×C8—21no—
367C22×C8—31no—
368C22×C8—61no—
369C22×C8C22×D311yescharacteristic
370#124—34no—
371#124—121no—
372C4×Q8—21no—
373C4×Q8—61no—
374C4×Q8—61no—
375C4×Q8—61no—
376C4×Q8—61no—
377C4×Q8—61no—
378C4×D4—21no—
379C4×D4—41no—
380C4×D4—61no—
381C4×D4—121no—
382#117—21no—
383#117—31no—
384#117—61no—
385#117—121no—
386#117C22×D311yescharacteristic
387C2×C4⋊C4—21no—
388C2×C4⋊C4—31no—
389C2×C4⋊C4—61no—
390C2×C4⋊C4C22×D311yescharacteristic
391C2×C22⋊C4—121no—
392C2×C42—31no—
393#107—61no—
394#107—61no—
395#106—61no—
396#106—61no—
397#104—34no—
398#104—34no—
399#103—21no—
400#103—31no—
401#103—31no—
402#103—61no—
403#103—61no—
404#103—61no—
405#103—61no—
406#103—61no—
407#103#6711yescharacteristic
408#103#6711yescharacteristic
409#102—21no—
410#102—21no—
411#102—21no—
412#102—21no—
413#102—21no—
414#102—31no—
415#102—31no—
416#102—61no—
417#102—61no—
418#102—61no—
419#102—61no—
420#102—61no—
421#102#6711yescharacteristic
422#102#6711yescharacteristic
423#101—121no—
424#100—34no—
425#97—61no—
426#97—61no—
427C4×C8—61no—
428C4×C8—61no—
429C4×C8—121no—
430#95—121no—
431C23×C3—21no—
432C23×C3—21no—
433C23×C3—22no—
434C23×C3—44no—
435C23×C3—41no—
436C23×C3—41no—
437C23×C3—81no—
438C23×C3—81no—
439C23×C3—161no—
440C23×C3—161no—
441C23×C3H(5,𝔽2)11yescharacteristic
442C3×Q8—21no—
443C3×Q8—21no—
444C3×Q8C4×D412yes—
445C3×Q8C4×D412yes—
446C3×D4—22no—
447C3×D4—22no—
448C3×D4—22no—
449C3×D4—22no—
450C3×D4—22no—
451C3×D4—22no—
452C3×D4—21no—
453C3×D4—21no—
454C3×D4—44no—
455C3×D4—44no—
456C3×D4—41no—
457C3×D4—41no—
458C3×D4C4×D412yes—
459C3×D4C4×D412yes—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—44no—
469C2×C3×C4—41no—
470C2×C3×C4—81no—
471C2×C3×C4—161no—
472C2×C3×C4C23×C411yescharacteristic
473C2×C3×C4C22×D411yescharacteristic
474C2×C3×C4C22×D411yescharacteristic
475C2×C3×C4C2×#4111yescharacteristic
476C2×C3×C4C2×#4111yescharacteristic
477C2×C3×C4H(5,𝔽2)11yescharacteristic
478C2×Dic3—22no—
479C2×Dic3—22no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—41no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—81no—
488C2×Dic3—161no—
489Dic6—22no—
490Dic6—22no—
491Dic6—41no—
492Dic6—41no—
493C3×C8—21no—
494C3×C8—21no—
495C3×C8—41no—
496C3⋊C8—22no—
497C3⋊C8—22no—
498C3⋊C8—21no—
499C3⋊C8—21no—
500C3⋊C8—41no—
501C24—21no—
502C24—41no—
503#41—21no—
504#41—21no—
505#41—21no—
506#41—21no—
507#41—24no—
508#41—24no—
509#41—42no—
510#41—42no—
511#41C2×C4×D312yes—
512#41C2×C4×D312yes—
513#41#23512yes—
514#41#23712yes—
515C2×Q8—32no—
516C2×Q8—61no—
517C2×Q8—61no—
518C2×Q8—61no—
519C2×Q8—61no—
520C2×Q8—61no—
521C2×Q8D3×D411yescharacteristic
522C2×Q8C2×#6711yescharacteristic
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—24no—
526C2×D4—24no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—41no—
535C2×D4—41no—
536C2×D4—44no—
537C2×D4—44no—
538C2×D4C2×C4×D312yes—
539C2×D4D3×D411yescharacteristic
540C2×D4C2×#6711yescharacteristic
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—61no—
547C22×C4—61no—
548C22×C4—61no—
549C22×C4—121no—
550C22×C4C23×D311yescharacteristic
551Q16—64no—
552Q16—64no—
553SD16—64no—
554SD16—64no—
555M16—21no—
556M16—21no—
557M16—32no—
558M16—32no—
559M16—42no—
560M16—61no—
561M16—61no—
562M16—61no—
563M16—61no—
564M16—122no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—31no—
569C2×C8—31no—
570C2×C8—42no—
571C2×C8—61no—
572C2×C8—61no—
573C2×C8—61no—
574C2×C8—61no—
575C2×C8—61no—
576C2×C8—122no—
577C2×C8C2×#6711yescharacteristic
578C2×C8C2×#6711yescharacteristic
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—31no—
582C4⋊C4—31no—
583C4⋊C4—41no—
584C4⋊C4—61no—
585C4⋊C4—61no—
586C4⋊C4—121no—
587C4⋊C4—121no—
588C4⋊C4—121no—
589C4⋊C4C2×#6711yescharacteristic
590C4⋊C4C2×#6711yescharacteristic
591C22⋊C4—21no—
592C22⋊C4—41no—
593C22⋊C4—61no—
594C22⋊C4—124no—
595C22⋊C4—121no—
596C42—21no—
597C42—32no—
598C42—41no—
599C42—61no—
600C42—61no—
601C42—121no—
602C42—121no—
603C42—121no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—22no—
607C22×C3—22no—
608C22×C3—41no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—42no—
613C22×C3—82no—
614C22×C3—81no—
615C22×C3—81no—
616C22×C3—161no—
617C22×C3—164no—
618C22×C3#51811yescharacteristic
619C22×C3D4211yescharacteristic
620C22×C3#55111yescharacteristic
621C3×C4—22no—
622C3×C4—22no—
623C3×C4—41no—
624C3×C4—41no—
625C3×C4—81no—
626C3×C4C2×C4×D411yescharacteristic
627C3×C4C2×C4×D411yescharacteristic
628C3×C4#54611yescharacteristic
629C3×C4#54611yescharacteristic
630Dic3—42no—
631Dic3—42no—
632Dic3—41no—
633Dic3—41no—
634Dic3—81no—
635C23—21no—
636C23—21no—
637C23—22no—
638C23—44no—
639C23—41no—
640C23—41no—
641C23—81no—
642C23—81no—
643C23—161no—
644C23—161no—
645C23#100411yescharacteristic
646Q8—21no—
647Q8—21no—
648Q8—62no—
649Q8—62no—
650Q8—121no—
651Q8—121no—
652Q8#67⋊C412yes—
653Q8C4×#6712yes—
654D4—22no—
655D4—22no—
656D4—22no—
657D4—22no—
658D4—22no—
659D4—21no—
660D4—22no—
661D4—21no—
662D4—44no—
663D4—44no—
664D4—41no—
665D4—41no—
666D4#67⋊C412yes—
667D4C4×#6712yes—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—44no—
677C2×C4—41no—
678C2×C4—62no—
679C2×C4—62no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—81no—
683C2×C4—121no—
684C2×C4—121no—
685C2×C4—121no—
686C2×C4—121no—
687C2×C4—121no—
688C2×C4—161no—
689C2×C4—241no—
690C2×C4—481no—
691C2×C4C22×C4×D311yescharacteristic
692C2×C4C2×#23511yescharacteristic
693C2×C4C2×D3×D411yescharacteristic
694C2×C4C2×#23711yescharacteristic
695C2×C4#100411yescharacteristic
696C2×C4C22×#6711yescharacteristic
697C8—21no—
698C8—21no—
699C8—41no—
700C8—62no—
701C8—61no—
702C8—61no—
703C8—62no—
704C8—121no—
705C2×C3—21no—
706C2×C3—21no—
707C2×C3—42no—
708C2×C3—42no—
709C2×C3—82no—
710C2×C3#235811yescharacteristic
711C2×C3#329011yescharacteristic
712C2×C3#329011yescharacteristic
713C22—21no—
714C22—21no—
715C22—22no—
716C22—22no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—42no—
722C22—82no—
723C22—81no—
724C22—81no—
725C22—161no—
726C22—164no—
727C22#548611yescharacteristic
728C22#549511yescharacteristic
729C22D4×#6711yescharacteristic
730C4—22no—
731C4—22no—
732C4—41no—
733C4—41no—
734C4—81no—
735C4—122no—
736C4—121no—
737C4—121no—
738C4—122no—
739C4—241no—
740C4C2×#67⋊C411yescharacteristic
741C4#549011yescharacteristic
742C4C2×C4×#6711yescharacteristic
743C4#580611yescharacteristic
744C3#2289611yescharacteristic, complemented, Sylow
745C2—21no—
746C2—21no—
747C2—42no—
748C2—42no—
749C2—82no—
750C2#8209911yescharacteristic
751C2#8401111yescharacteristic
752C2#8401211yescharacteristic
subgroupG/H
centerC22D4×#67
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#2897C2
socleC22×C3D42
prime radicalC2×C3×H(5,𝔽2)C22
cosocleC22×C3×C4C24
hypercenter#2897D3
hypocenterC3#22896
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2897

Complements

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

NH ≅ G/Ntype
4. #82571C2semidirect
5. #78821C2semidirect
6. #72019C2semidirect
7. #72008C2semidirect
8. #71665C2semidirect
9. #70325C2semidirect
10. #70318C2semidirect
11. #70304C2semidirect
12. #70298C2semidirect
13. #70289C2semidirect
14. #70195C2semidirect
15. #70158C2semidirect
25. #5516C22semidirect
34. #5242C4semidirect
46. C2×#824C22semidirect
47. C2×#816C22semidirect
48. #5101C22semidirect
49. C2×C8×Dic3C22semidirect
54. #4997C22semidirect
55. #4995C22semidirect
56. #4977C22semidirect
57. C2×#810C22semidirect
58. #4964C22semidirect
63. #4558C22semidirect
64. #4555C22semidirect
65. #4554C22semidirect
66. #4552C22semidirect
67. #4532C22semidirect
68. #4530C22semidirect
113. #951C2×C4semidirect
114. #951C2×C4semidirect
121. #936C2×C4semidirect
152. #837C2×C4semidirect
153. #837C2×C4semidirect
157. #833C2×C4semidirect
744. C3#22896semidirect

Maximal subgroups

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

subgroupindex
C3×#28972
C2×#52422
#840992
#825712
#788212
#720192
#720082
#716652
#703252
#703182
#703042
#702982
#702892
#701952
#701582
#228963