Finite Group Databasebeta

← #6500820

Subgroups — #6500820

Order 512.

2032 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2414C211yesmaximal, characteristic
2#34185C211yesmaximal, characteristic, complemented
3#27617C212yesmaximal, complemented
4#27604C212yesmaximal, complemented
5#27588C212yesmaximal, complemented
6#26228C214yesmaximal, complemented
7#26224C214yesmaximal, complemented
8#26156C214yesmaximal, complemented
9#26152C214yesmaximal, complemented
10#24009C212yesmaximal, complemented
11#21764C211yesmaximal, characteristic, complemented
12#21764C211yesmaximal, characteristic, complemented
13#21742C211yesmaximal, characteristic, complemented
14#20846C211yesmaximal, characteristic, complemented
15#20846C211yesmaximal, characteristic, complemented
16C22×#121C2211yescharacteristic
17C22×#121C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C22×#117C2211yescharacteristic
20C2×#482C2214yescomplemented
21C2×#428C2212yescomplemented
22C2×#428C2212yescomplemented
23C2×#407C2211yescharacteristic
24C2×#407C2211yescharacteristic
25#2414—22no—
26#2414—22no—
27#2414C2214yes—
28#2414C2214yes—
29C2×#394—21no—
30C2×#392—21no—
31#2353—22no—
32#2353—22no—
33#2352C2212yescomplemented
34#2352C2212yescomplemented
35#2352C2212yescomplemented
36#2352C2212yescomplemented
37#2313—21no—
38#2312—21no—
39#2308—21no—
40C2×#390—21no—
41C2×#390C2211yescharacteristic
42C2×#389C2211yescharacteristic
43C2×#388—21no—
44#2283C2212yes—
45#2280C2212yes—
46C2×#380C2211yescharacteristic
47C2×#380C2211yescharacteristic
48C2×#380C2211yescharacteristic
49#2273—21no—
50#2101C2214yescomplemented
51#2092C2214yescomplemented
52#2085C2214yescomplemented
53#2077C2214yescomplemented
54#2075C2214yescomplemented
55#2073C2214yescomplemented
56#2034C2214yescomplemented
57#2033C2214yescomplemented
58#1926C2214yescomplemented
59#1925C2214yescomplemented
60#1919C2214yescomplemented
61#1918C2214yescomplemented
62#1895C2214yescomplemented
63#1895C2214yescomplemented
64#1875C2214yescomplemented
65#1874C2212yescomplemented
66#1874C2212yescomplemented
67#1874C2212yescomplemented
68#1874C2212yescomplemented
69#1870C2214yescomplemented
70#1870C2214yescomplemented
71#1854C2214yescomplemented
72#1854C2214yescomplemented
73#1854C2214yescomplemented
74#1853C2212yes—
75#1853C2212yes—
76#1852C2212yes—
77#1852C2212yes—
78#1825C2214yescomplemented
79#1824C2212yes—
80#1824C2212yes—
81#1817C2212yes—
82#1786C2212yes—
83#1786C2212yes—
84#1779C2212yes—
85#1736C2212yescomplemented
86#1736C2212yescomplemented
87C23×D4—21no—
88C23×D4—21no—
89C23×D4D411yescharacteristic
90C23×D4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C22×M16C2312yes—
94C22×M16C2312yes—
95C2×#121—21no—
96C2×#121—21no—
97C2×#121—22no—
98C2×#121—24no—
99C2×#121—24no—
100C2×#121—44no—
101C2×#121C2312yes—
102C2×#121C2312yes—
103C2×#121C2314yes—
104C2×C4×D4—24no—
105C2×C4×D4—24no—
106C2×C4×D4D412yes—
107C2×C4×D4D412yes—
108C2×C4×D4C2312yes—
109C2×C4×D4C2312yes—
110C2×#117—21no—
111C2×#117—21no—
112C2×#117—44no—
113C2×#117C2312yes—
114C2×#117C2312yes—
115C2×#117C2312yes—
116C2×#117C2312yes—
117C22×C4⋊C4—21no—
118C22×C4⋊C4D411yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C22⋊C4—21no—
127C22×C22⋊C4—21no—
128C22×C22⋊C4—21no—
129C22×C22⋊C4—21no—
130C22×C22⋊C4—21no—
131C22×C22⋊C4—21no—
132C22×C22⋊C4—21no—
133C22×C22⋊C4—21no—
134C22×C22⋊C4D411yescharacteristic
135C22×C22⋊C4D411yescharacteristic
136C22×C42—21no—
137C22×C42C2311yescharacteristic
138#482—48no—
139#428—44no—
140#428—44no—
141C2×#107C2314yes—
142C2×#107C2314yes—
143C2×#106C2314yes—
144C2×#106C2314yes—
145C2×#102C2314yes—
146C2×#102C2314yes—
147C2×#102C2314yes—
148C2×#102C2314yes—
149#407—24no—
150#407—24no—
151C2×C22⋊C8C2312yes—
152C2×C22⋊C8C2312yes—
153C2×C22⋊C8C2312yes—
154C2×C22⋊C8C2312yes—
155C2×C22⋊C8C2314yes—
156C2×C22⋊C8C2314yes—
157#394—24no—
158#394—24no—
159#392—24no—
160#392—24no—
161#390—24no—
162#390—24no—
163#390—22no—
164#390C2314yes—
165#389—22no—
166#389C2314yes—
167#388—24no—
168#388—24no—
169#388—22no—
170#388—22no—
171#388—22no—
172#388—22no—
173#387—22no—
174#387—22no—
175#387—22no—
176#387—22no—
177#386—22no—
178#386—22no—
179#386—22no—
180#386—22no—
181#383—22no—
182#382C2312yes—
183#382C2312yes—
184#381—22no—
185#381—22no—
186#380—21no—
187#380—21no—
188#380—21no—
189#380—21no—
190#380—22no—
191#380C2312yes—
192#380C2314yes—
193#380C2312yes—
194#380C2312yes—
195#380C2312yes—
196#380C2312yes—
197#380C2312yes—
198#379—22no—
199C4×C4⋊C4C2312yes—
200C4×C4⋊C4C2312yes—
201C4×C22⋊C4—22no—
202C4×C22⋊C4—22no—
203C4×C22⋊C4—22no—
204C4×C22⋊C4—22no—
205C4×C22⋊C4—22no—
206C4×C22⋊C4—22no—
207C4×C22⋊C4—22no—
208#376—22no—
209C2×#95—21no—
210C2×#95—21no—
211C2×#95—21no—
212C2×#95—21no—
213#340C2314yes—
214#340C2314yes—
215#340C2314yes—
216#340C2314yes—
217#340C2314yes—
218#340C2314yes—
219#340C2314yes—
220#340C2314yes—
221#336C2314yes—
222#336C2314yes—
223C25—21no—
224C25C2×D411yescharacteristic
225C25C2×D411yescharacteristic
226C22×D4—24no—
227C22×D4—24no—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—21no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—42no—
234C22×D4—42no—
235C22×D4—42no—
236C22×D4—42no—
237C22×D4—44no—
238C22×D4—44no—
239C22×D4—44no—
240C22×D4—82no—
241C22×D4—82no—
242C22×D4—82no—
243C22×D4C2×D412yes—
244C22×D4C2×D412yes—
245C22×D4C2412yes—
246C23×C4—21no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—21no—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4—21no—
253C23×C4—21no—
254C23×C4—21no—
255C23×C4—42no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4C2×D411yescharacteristic
260C23×C4C2×D411yescharacteristic
261C23×C4C2×D411yescharacteristic
262C23×C4C2×D412yes—
263C23×C4C2×D411yescharacteristic
264C23×C4C2×D411yescharacteristic
265C23×C4C2×D411yescharacteristic
266C23×C4#4114yes—
267C23×C4#4114yes—
268C23×C4C2412yes—
269C23×C4C2411yescharacteristic
270C23×C4C2411yescharacteristic
271C23×C4C2411yescharacteristic
272C2×M16—24no—
273C2×M16—24no—
274C2×M16—42no—
275C2×M16—42no—
276C2×M16—42no—
277C2×M16—42no—
278C22×C8C2414yes—
279C22×C8C2414yes—
280#121—24no—
281#121—24no—
282#121—24no—
283#121—24no—
284#121—28no—
285#121—44no—
286#121—48no—
287#121—44no—
288#121—44no—
289C4×D4—28no—
290C4×D4—28no—
291C4×D4—24no—
292C4×D4—24no—
293C4×D4—24no—
294C4×D4—24no—
295#117—24no—
296#117—24no—
297#117—42no—
298#117—42no—
299#117—44no—
300#117—44no—
301#117—44no—
302#117—44no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—82no—
321C2×C4⋊C4C2×D412yes—
322C2×C4⋊C4C2×D412yes—
323C2×C4⋊C4C2412yes—
324C2×C4⋊C4C2412yes—
325C2×C4⋊C4C2412yes—
326C2×C4⋊C4C2412yes—
327C2×C4⋊C4C2412yes—
328C2×C4⋊C4C2412yes—
329C2×C4⋊C4C2412yes—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4—44no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—82no—
355C2×C22⋊C4—82no—
356C2×C22⋊C4C2×D412yes—
357C2×C22⋊C4C2×D412yes—
358C2×C22⋊C4C2×D412yes—
359C2×C22⋊C4C2×D412yes—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—44no—
369C2×C42C2×D412yes—
370C2×C42C2412yes—
371#107—28no—
372#107—44no—
373#106—28no—
374#106—44no—
375#102—44no—
376#102—44no—
377#102—44no—
378#102—44no—
379C22⋊C8—24no—
380C22⋊C8—24no—
381C22⋊C8—24no—
382C22⋊C8—24no—
383C22⋊C8—44no—
384C22⋊C8—44no—
385#95—22no—
386#95—22no—
387#95—22no—
388#95—22no—
389#95—24no—
390#95—24no—
391#95—22no—
392#95—22no—
393#95—22no—
394#95—22no—
395#95—22no—
396#95—22no—
397#95—22no—
398#95—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—41no—
406C24—41no—
407C24—41no—
408C24—41no—
409C24—41no—
410C24—41no—
411C24—41no—
412C24—41no—
413C24—42no—
414C24—42no—
415C24—42no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24—42no—
420C24#12314yes—
421C24C22×D412yes—
422C24C22×D411yescharacteristic
423C24C22×D411yescharacteristic
424C24C22×D411yescharacteristic
425C2×D4—24no—
426C2×D4—24no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—24no—
430C2×D4—24no—
431C2×D4—42no—
432C2×D4—42no—
433C2×D4—42no—
434C2×D4—42no—
435C2×D4—48no—
436C2×D4—42no—
437C2×D4—42no—
438C2×D4—416no—
439C2×D4—48no—
440C2×D4—44no—
441C2×D4—44no—
442C2×D4—42no—
443C2×D4—84no—
444C2×D4—84no—
445C2×D4—84no—
446C2×D4—82no—
447C2×D4—82no—
448C2×D4—82no—
449C2×D4—82no—
450C2×D4—816no—
451C2×D4—816no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—24no—
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—24no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—48no—
477C22×C4—48no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—41no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—84no—
503C22×C4—84no—
504C22×C4—81no—
505C22×C4—81no—
506C22×C4—81no—
507C22×C4—81no—
508C22×C4—81no—
509C22×C4—81no—
510C22×C4—81no—
511C22×C4—81no—
512C22×C4#12314yes—
513C22×C4#12314yes—
514C22×C4#12314yes—
515C22×C4C22×D412yes—
516C22×C4C22×D412yes—
517C22×C4C22×D412yes—
518C22×C4C22×D411yescharacteristic
519C22×C4C22×D411yescharacteristic
520C22×C4C22×D411yescharacteristic
521C22×C4C2×#4112yes—
522C22×C4C2×#4112yes—
523C22×C4C2×#4112yes—
524C22×C4C2×#4112yes—
525C22×C4C2×#4112yes—
526C22×C4C2×#4112yes—
527C22×C4C2511yescharacteristic
528M16—48no—
529M16—48no—
530C2×C8—24no—
531C2×C8—24no—
532C2×C8—24no—
533C2×C8—24no—
534C2×C8—24no—
535C2×C8—24no—
536C4⋊C4—24no—
537C4⋊C4—24no—
538C4⋊C4—24no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—24no—
543C4⋊C4—24no—
544C4⋊C4—22no—
545C4⋊C4—22no—
546C4⋊C4—24no—
547C4⋊C4—24no—
548C4⋊C4—42no—
549C4⋊C4—42no—
550C4⋊C4—81no—
551C4⋊C4—81no—
552C4⋊C4—81no—
553C4⋊C4—81no—
554C4⋊C4—84no—
555C4⋊C4H(5,𝔽2)14yes—
556C22⋊C4—24no—
557C22⋊C4—24no—
558C22⋊C4—24no—
559C22⋊C4—24no—
560C22⋊C4—48no—
561C22⋊C4—44no—
562C22⋊C4—44no—
563C22⋊C4—48no—
564C22⋊C4—44no—
565C22⋊C4—44no—
566C22⋊C4—44no—
567C22⋊C4—44no—
568C22⋊C4—44no—
569C22⋊C4—44no—
570C22⋊C4—84no—
571C22⋊C4—82no—
572C22⋊C4—82no—
573C22⋊C4—84no—
574C22⋊C4—82no—
575C22⋊C4—82no—
576C42—24no—
577C42—22no—
578C42—22no—
579C42—44no—
580C42—44no—
581C42—82no—
582C42—82no—
583C42—82no—
584C42—82no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—28no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—44no—
610C23—44no—
611C23—44no—
612C23—44no—
613C23—44no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—82no—
622C23—82no—
623C23—82no—
624C23—82no—
625C23—82no—
626C23—82no—
627C23—82no—
628C23—82no—
629C23—84no—
630C23—84no—
631C23—84no—
632C23—84no—
633C23—84no—
634C23—84no—
635C23—84no—
636C23C2×#12312yes—
637C23C2×#12312yes—
638C23C2×#12312yes—
639C23#57512yes—
640C23#57512yes—
641C23C23×D411yescharacteristic
642D4—48no—
643D4—48no—
644D4—44no—
645D4—44no—
646D4—84no—
647D4—816no—
648D4—88no—
649D4—88no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—44no—
673C2×C4—44no—
674C2×C4—44no—
675C2×C4—48no—
676C2×C4—42no—
677C2×C4—44no—
678C2×C4—42no—
679C2×C4—44no—
680C2×C4—44no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
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—84no—
700C2×C4—82no—
701C2×C4—82no—
702C2×C4—84no—
703C2×C4—84no—
704C2×C4—162no—
705C2×C4—162no—
706C2×C4—162no—
707C2×C4—162no—
708C2×C4C2×#12312yes—
709C2×C4C2×#12312yes—
710C2×C4C2×#12312yes—
711C2×C4C22×#4111yescharacteristic
712C2×C4C22×#4111yescharacteristic
713C2×C4C2×H(5,𝔽2)12yes—
714C2×C4#58512yes—
715C8—44no—
716C8—44no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—88no—
745C22—88no—
746C22—82no—
747C22—82no—
748C22—82no—
749C22—82no—
750C22—82no—
751C22—82no—
752C22—82no—
753C22—168no—
754C22#309314yes—
755C22C22×#12311yescharacteristic
756C22#348411yescharacteristic
757C22#348511yescharacteristic
758C22C2×#57511yescharacteristic
759C22C2×#57511yescharacteristic
760C22#358511yescharacteristic
761C22#358511yescharacteristic
762C4—22no—
763C4—22no—
764C4—22no—
765C4—42no—
766C4—42no—
767C4—42no—
768C4—44no—
769C4—82no—
770C4—82no—
771C4—82no—
772C4—82no—
773C4—82no—
774C4—82no—
775C4#350512yes—
776C4#350512yes—
777C2—24no—
778C2—42no—
779C2—42no—
780C2—82no—
781C2—162no—
782C2#3535111yescharacteristic
783C2C2×#309311yescharacteristic
784C2#6051811yescharacteristic
785C2#6157711yescharacteristic
786C2#6158111yescharacteristic
787C2#6171011yescharacteristic
788C2#6171811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#2414C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34185C2semidirect
3. #27617C2semidirect
4. #27604C2semidirect
5. #27588C2semidirect
6. #26228C2semidirect
7. #26224C2semidirect
8. #26156C2semidirect
9. #26152C2semidirect
10. #24009C2semidirect
11. #21764C2semidirect
12. #21764C2semidirect
13. #21742C2semidirect
14. #20846C2semidirect
15. #20846C2semidirect
20. C2×#482C22semidirect
21. C2×#428C22semidirect
22. C2×#428C22semidirect
33. #2352C22semidirect
34. #2352C22semidirect
35. #2352C22semidirect
36. #2352C22semidirect
50. #2101C22semidirect
51. #2092C22semidirect
52. #2085C22semidirect
53. #2077C22semidirect
54. #2075C22semidirect
55. #2073C22semidirect
56. #2034C22semidirect
57. #2033C22semidirect
58. #1926C22semidirect
59. #1925C22semidirect
60. #1919C22semidirect
61. #1918C22semidirect
62. #1895C22semidirect
63. #1895C22semidirect
64. #1875C22semidirect
65. #1874C22semidirect
66. #1874C22semidirect
67. #1874C22semidirect
68. #1874C22semidirect
69. #1870C22semidirect
70. #1870C22semidirect
71. #1854C22semidirect
72. #1854C22semidirect
73. #1854C22semidirect
78. #1825C22semidirect
85. #1736C22semidirect
86. #1736C22semidirect

Maximal subgroups

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

subgroupindex
C2×#24142
#341852
#276172
#276042
#275882
#262282
#262242
#261562
#261522
#240092
#217642
#217422
#208462