Finite Group Databasebeta

← #7506772

Subgroups — #7506772

Order 512.

1936 conjugacy classes of subgroups.

The subgroup lattice has 777 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2503C211yesmaximal, characteristic, complemented
2#34742C211yesmaximal, characteristic
3#31953C214yesmaximal, complemented
4#31951C214yesmaximal, complemented
5#31941C214yesmaximal, complemented
6#31939C214yesmaximal, complemented
7#23733C211yesmaximal, characteristic, complemented
8#23659C211yesmaximal, characteristic, complemented
9#23629C211yesmaximal, characteristic, complemented
10#23619C211yesmaximal, characteristic, complemented
11#23481C211yesmaximal, characteristic, complemented
12#23392C211yesmaximal, characteristic
13#21237C211yesmaximal, characteristic, complemented
14#21049C211yesmaximal, characteristic, complemented
15#20927C211yesmaximal, characteristic, complemented
16#20909C211yesmaximal, characteristic
17#20844C211yesmaximal, characteristic, complemented
18#20765C211yesmaximal, characteristic, complemented
19#20649C211yesmaximal, characteristic, complemented
20C22×#137C2211yescharacteristic
21C2×#525C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C2×C4×#41C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C2×#428C2211yescharacteristic
26C2×#428C2211yescharacteristic
27C2×#428C2211yescharacteristic
28C2×#423C2211yescharacteristic
29C2×#417C2211yescharacteristic
30C2×#417C2211yescharacteristic
31C2×#417C2211yescharacteristic
32C2×#419C2211yescharacteristic
33C2×#419C2211yescharacteristic
34C2×#419C2211yescharacteristic
35C2×#407C2211yescharacteristic
36C2×#407C2211yescharacteristic
37C2×C4×M16C2211yescharacteristic
38#2503—22no—
39#2503—22no—
40#2503C2214yes—
41#2503C2214yes—
42#2423C2212yes—
43#2422C2212yes—
44#2421C2212yes—
45#2420C2212yes—
46#2419—22no—
47#2418—22no—
48#2395—22no—
49C2×#400—22no—
50C4×#123—22no—
51#2297C2211yescharacteristic
52#2296C2211yescharacteristic
53C2×#391C2211yescharacteristic
54C2×#391C2211yescharacteristic
55#2285C2211yescharacteristic
56C2×#382C2211yescharacteristic
57C2×#382C2211yescharacteristic
58#2280C2211yescharacteristic
59C2×#381—22no—
60C2×C4×C22⋊C4C2211yescharacteristic
61#2097C2212yescomplemented
62#2097C2212yescomplemented
63#2092C2212yescomplemented
64#2092C2212yescomplemented
65#2085C2214yescomplemented
66#2085C2214yescomplemented
67#2074C2214yescomplemented
68#2072C2214yescomplemented
69#2068C2214yescomplemented
70#2066C2214yescomplemented
71#2036C2214yes—
72#2035C2214yes—
73#2001C2214yes—
74#2000C2214yes—
75#1973C2212yescomplemented
76#1971C2212yescomplemented
77#1969C2212yescomplemented
78#1968C2212yescomplemented
79#1924C2214yes—
80#1923C2214yes—
81#1878C2214yescomplemented
82#1877C2214yescomplemented
83#1874C2214yes—
84#1872C2214yes—
85#1853C2214yes—
86#1852C2214yes—
87#1836C2214yescomplemented
88#1835C2214yescomplemented
89#1805C2214yescomplemented
90#1804C2214yescomplemented
91#1736C2211yescharacteristic
92#1736C2211yescharacteristic
93#1736C2211yescharacteristic
94#1736C2211yescharacteristic
95#1736C2211yescharacteristic
96#1736C2211yescharacteristic
97#1728C2211yescharacteristic
98#1728C2211yescharacteristic
99C22×#41C2311yescharacteristic
100C23×Q8C2311yescharacteristic
101C24×C4—21no—
102C24×C4C2311yescharacteristic
103C2×#137—24no—
104C2×#137—24no—
105C2×#137—42no—
106C22×Q16C2312yes—
107C22×SD16C2312yes—
108C22×M16C2311yescharacteristic
109C22×M16C2311yescharacteristic
110C22×M16C2311yescharacteristic
111C22×M16C2311yescharacteristic
112#525—24no—
113#525—42no—
114C2×#123—21no—
115C2×#123—22no—
116C2×C22⋊Q8—22no—
117C2×C22⋊Q8—42no—
118C2×C22⋊Q8—42no—
119C2×C22⋊Q8C2312yes—
120C2×C22⋊Q8C2314yes—
121C2×#121C2312yes—
122C2×#120—21no—
123C4×#41—24no—
124C4×#41—42no—
125C2×C4×Q8C2312yes—
126C2×C4×D4—22no—
127C2×C4×D4—22no—
128C2×C4×D4C2312yes—
129C2×#117—21no—
130C2×#117C2311yescharacteristic
131C2×#117C2311yescharacteristic
132C2×#117C2311yescharacteristic
133C22×C4⋊C4—21no—
134C22×C4⋊C4—21no—
135C22×C4⋊C4—22no—
136C22×C4⋊C4—42no—
137C22×C4⋊C4—42no—
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2314yes—
142C22×C22⋊C4—21no—
143C22×C22⋊C4D412yes—
144C22×C42—21no—
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147#428—42no—
148#428—42no—
149#428—42no—
150C2×#107C2312yes—
151C2×#107C2312yes—
152C2×#107C2312yes—
153C2×#106C2312yes—
154C2×#106C2312yes—
155C2×#106C2312yes—
156#423—42no—
157C2×C4⋊C8C2314yes—
158#419—42no—
159#419—42no—
160#419—42no—
161#417—42no—
162#417—42no—
163#417—42no—
164C2×#103C2312yes—
165C2×#103C2312yes—
166C2×#103C2312yes—
167C2×#103C2314yes—
168C2×#103C2312yes—
169C2×#103C2314yes—
170C2×#103C2312yes—
171C2×#102C2312yes—
172C2×#102C2312yes—
173C2×#102C2312yes—
174#407—24no—
175#407—42no—
176C2×C22⋊C8C2314yes—
177C2×C22⋊C8C2314yes—
178C4×M16—24no—
179C2×#97C2312yes—
180C2×C4×C8C2312yes—
181#400—24no—
182#400—24no—
183#400—24no—
184#400—24no—
185#400—22no—
186#399—22no—
187#398—22no—
188#397—22no—
189#397—22no—
190#397—22no—
191#394—22no—
192#394—22no—
193#391—21no—
194#391—22no—
195#391—21no—
196#391C2314yes—
197#391C2312yes—
198#391C2312yes—
199#391C2311yescharacteristic
200#391C2311yescharacteristic
201#390C2311yescharacteristic
202#390C2311yescharacteristic
203#389C2312yes—
204#389C2312yes—
205#388—22no—
206#388—22no—
207#387—22no—
208#387—22no—
209#386—22no—
210#386—22no—
211#385—22no—
212#385—22no—
213#384C2312yes—
214#382—21no—
215#382—22no—
216#382—21no—
217#382C2314yes—
218#382C2312yes—
219#382C2312yes—
220#382C2312yes—
221#381—21no—
222#381—24no—
223#381—24no—
224#381—24no—
225#381—24no—
226#381—22no—
227#380—22no—
228#380C2312yes—
229#380C2312yes—
230#379—21no—
231C4×C4⋊C4—21no—
232C4×C4⋊C4—22no—
233C4×C4⋊C4—21no—
234C4×C22⋊C4—22no—
235C4×C22⋊C4—22no—
236C4×C22⋊C4D412yes—
237C4×C22⋊C4D412yes—
238C4×C22⋊C4C2312yes—
239C4×C22⋊C4C2312yes—
240C2×#95—22no—
241C2×#95—22no—
242C2×#95—22no—
243C2×#95—22no—
244C2×#95D412yes—
245#340C2314yes—
246#340C2314yes—
247#340C2314yes—
248#340C2314yes—
249#340C2314yes—
250#340C2314yes—
251#336C2312yes—
252#336C2312yes—
253#336C2314yes—
254C25C2×D411yescharacteristic
255C2×#41—22no—
256C2×#41—22no—
257C2×#41—22no—
258C2×#41—22no—
259C2×#41—22no—
260C2×#41#4114yes—
261C22×Q8—21no—
262C22×Q8—22no—
263C22×Q8—22no—
264C22×Q8—22no—
265C22×Q8—22no—
266C22×Q8—22no—
267C22×Q8—22no—
268C22×Q8C2412yes—
269C22×Q8C2411yescharacteristic
270C22×D4—21no—
271C22×D4—22no—
272C22×D4C2411yescharacteristic
273C23×C4—21no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—24no—
285C23×C4—22no—
286C23×C4—44no—
287C23×C4—48no—
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D412yes—
290C23×C4C2×D412yes—
291C23×C4C2×D412yes—
292C23×C4C2412yes—
293C23×C4C2411yescharacteristic
294#137—416no—
295C2×Q16—24no—
296C2×Q16—24no—
297C2×Q16—42no—
298C2×SD16—24no—
299C2×SD16—24no—
300C2×SD16—42no—
301C2×M16—22no—
302C2×M16—22no—
303C2×M16—22no—
304C2×M16—22no—
305C2×M16—22no—
306C2×M16—22no—
307C2×M16—22no—
308C2×M16—22no—
309C2×M16—22no—
310C2×M16—22no—
311C2×M16—22no—
312C2×M16#4114yes—
313C22×C8C2412yes—
314C22×C8C2412yes—
315C22×C8C2412yes—
316C22×C8C2412yes—
317#123—48no—
318#123—44no—
319C22⋊Q8—24no—
320C22⋊Q8—44no—
321C22⋊Q8—44no—
322C22⋊Q8—42no—
323C22⋊Q8—48no—
324#121—24no—
325#121—42no—
326#120—44no—
327C4×Q8—24no—
328C4×Q8—42no—
329C4×D4—24no—
330C4×D4—42no—
331C4×D4—48no—
332C4×D4—48no—
333#117—22no—
334#117—22no—
335#117—22no—
336#117—22no—
337#117—22no—
338#117—22no—
339#117—44no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4—48no—
361C2×C4⋊C4—44no—
362C2×C4⋊C4C2412yes—
363C2×C4⋊C4C2412yes—
364C2×C4⋊C4C2412yes—
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2412yes—
367C2×C4⋊C4C2411yescharacteristic
368C2×C4⋊C4C2411yescharacteristic
369C2×C22⋊C4—24no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4C2×D412yes—
383C2×C22⋊C4C2×D412yes—
384C2×C22⋊C4C2×D412yes—
385C2×C22⋊C4C2×D412yes—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—22no—
394C2×C42—44no—
395C2×C42C2×D411yescharacteristic
396C2×C42C2×D412yes—
397C2×C42C2×D411yescharacteristic
398C2×C42C2412yes—
399C2×C42C2411yescharacteristic
400C2×C42C2411yescharacteristic
401#107—42no—
402#107—42no—
403#107—42no—
404#106—42no—
405#106—42no—
406#106—42no—
407C4⋊C8—44no—
408#103—42no—
409#103—42no—
410#103—42no—
411#103—42no—
412#103—42no—
413#103—44no—
414#103—44no—
415#102—42no—
416#102—42no—
417#102—42no—
418C22⋊C8—28no—
419C22⋊C8—44no—
420#97—24no—
421C4×C8—24no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—24no—
430#95—22no—
431#95—22no—
432#95—22no—
433#95—22no—
434#95—22no—
435#95—22no—
436#95—22no—
437#95—22no—
438#95C2×D412yes—
439#95C2×D412yes—
440#95C2×D412yes—
441#95C2×D412yes—
442C24—22no—
443C24—24no—
444C24—22no—
445C24—22no—
446C24—21no—
447C24—42no—
448C24C22×D412yes—
449C24C22×D411yescharacteristic
450#41—28no—
451#41—28no—
452#41—44no—
453#41—44no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8—22no—
463C2×Q8—21no—
464C2×Q8—22no—
465C2×Q8—42no—
466C2×Q8—42no—
467C2×Q8—42no—
468C2×Q8—44no—
469C2×Q8—44no—
470C2×Q8—44no—
471C2×Q8—44no—
472C2×Q8C2×#4112yes—
473C2×D4—24no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—82no—
484C2×D4C2×#4112yes—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—42no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4—42no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—48no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—48no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—48no—
533C22×C4—82no—
534C22×C4—816no—
535C22×C4C22×D412yes—
536C22×C4C22×D412yes—
537C22×C4C22×D412yes—
538C22×C4C22×D412yes—
539C22×C4C22×D412yes—
540C22×C4C22×D411yescharacteristic
541C22×C4C2×#4112yes—
542C22×C4C2×#4112yes—
543C22×C4H(5,𝔽2)12yes—
544C22×C4H(5,𝔽2)12yes—
545C22×C4H(5,𝔽2)12yes—
546C22×C42−1+412yes—
547C22×C4C2511yescharacteristic
548Q16—48no—
549SD16—48no—
550M16—28no—
551M16—44no—
552M16—44no—
553M16—44no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8C2×#4114yes—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—44no—
581C4⋊C4—44no—
582C4⋊C4—48no—
583C4⋊C4—48no—
584C4⋊C4—44no—
585C4⋊C4—44no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—82no—
590C4⋊C4—82no—
591C22⋊C4—24no—
592C22⋊C4—24no—
593C22⋊C4—42no—
594C22⋊C4—42no—
595C22⋊C4—44no—
596C22⋊C4—44no—
597C22⋊C4—44no—
598C22⋊C4—44no—
599C22⋊C4—48no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—44no—
604C22⋊C4—82no—
605C22⋊C4—82no—
606C42—22no—
607C42—22no—
608C42—24no—
609C42—21no—
610C42—21no—
611C42—22no—
612C42—22no—
613C42—21no—
614C42—21no—
615C42—44no—
616C42—42no—
617C42—42no—
618C42—42no—
619C23—22no—
620C23—22no—
621C23—28no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—48no—
630C23—48no—
631C23—44no—
632C23—44no—
633C23—42no—
634C23—41no—
635C23—41no—
636C23—42no—
637C23#53512yes—
638C23#54612yes—
639C23#54712yes—
640C23#57514yes—
641C23C23×D411yescharacteristic
642Q8—22no—
643Q8—22no—
644Q8—41no—
645Q8—41no—
646Q8—42no—
647Q8—42no—
648Q8—42no—
649Q8—42no—
650Q8—84no—
651D4—22no—
652D4—22no—
653D4—48no—
654D4—41no—
655D4—41no—
656D4—88no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—44no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—48no—
680C2×C4—48no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—44no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—84no—
702C2×C4—84no—
703C2×C4—88no—
704C2×C4—84no—
705C2×C4—84no—
706C2×C4—84no—
707C2×C4—816no—
708C2×C4—84no—
709C2×C4#53512yes—
710C2×C4#53914yes—
711C2×C4#54014yes—
712C2×C4#54612yes—
713C2×C4#54712yes—
714C2×C4#55114yes—
715C2×C4#56214yes—
716C2×C4C22×#4111yescharacteristic
717C2×C4C22×#4111yescharacteristic
718C2×C4C2×H(5,𝔽2)11yescharacteristic
719C2×C4C2×H(5,𝔽2)11yescharacteristic
720C2×C4C2×H(5,𝔽2)11yescharacteristic
721C2×C4C2×2−1+411yescharacteristic
722C8—24no—
723C8—42no—
724C8—42no—
725C8—42no—
726C22—24no—
727C22—22no—
728C22—22no—
729C22—24no—
730C22—24no—
731C22—24no—
732C22—24no—
733C22—416no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—44no—
740C22—82no—
741C22—81no—
742C22—81no—
743C22#270614yes—
744C22C2×#53511yescharacteristic
745C22C2×#54611yescharacteristic
746C22C2×#54711yescharacteristic
747C22C2×#57512yes—
748C22#358612yes—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—81no—
756C4—82no—
757C4—82no—
758C4—81no—
759C4—82no—
760C4—82no—
761C4—82no—
762C4—82no—
763C4#270614yes—
764C4C2×#53911yescharacteristic
765C4C2×#54011yescharacteristic
766C4C2×#55111yescharacteristic
767C4C2×#56211yescharacteristic
768C2—24no—
769C2—44no—
770C2—82no—
771C2C2×#270611yescharacteristic
772C2#6079911yescharacteristic
773C2#6080711yescharacteristic
774C2#6116312yes—
775C2#6125312yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#525C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2503C2semidirect
3. #31953C2semidirect
4. #31951C2semidirect
5. #31941C2semidirect
6. #31939C2semidirect
7. #23733C2semidirect
8. #23659C2semidirect
9. #23629C2semidirect
10. #23619C2semidirect
11. #23481C2semidirect
13. #21237C2semidirect
14. #21049C2semidirect
15. #20927C2semidirect
17. #20844C2semidirect
18. #20765C2semidirect
19. #20649C2semidirect
61. #2097C22semidirect
62. #2097C22semidirect
63. #2092C22semidirect
64. #2092C22semidirect
65. #2085C22semidirect
66. #2085C22semidirect
67. #2074C22semidirect
68. #2072C22semidirect
69. #2068C22semidirect
70. #2066C22semidirect
75. #1973C22semidirect
76. #1971C22semidirect
77. #1969C22semidirect
78. #1968C22semidirect
81. #1878C22semidirect
82. #1877C22semidirect
87. #1836C22semidirect
88. #1835C22semidirect
89. #1805C22semidirect
90. #1804C22semidirect

Maximal subgroups

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

subgroupindex
C2×#25032
#347422
#319532
#319512
#319412
#319392
#237332
#236592
#236292
#236192
#234812
#233922
#212372
#210492
#209272
#209092
#208442
#207652
#206492