Finite Group Databasebeta

← #6519418

Subgroups — #6519418

Order 512.

2058 conjugacy classes of subgroups.

The subgroup lattice has 743 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2542C211yesmaximal, characteristic
2#34194C211yesmaximal, characteristic
3#26249C214yesmaximal, complemented
4#26247C214yesmaximal, complemented
5#26236C212yesmaximal, complemented
6#26234C212yesmaximal, complemented
7#26233C212yesmaximal, complemented
8#26231C212yesmaximal, complemented
9#24010C212yesmaximal, complemented
10#24010C212yesmaximal, complemented
11#24006C212yesmaximal, complemented
12#24003C212yesmaximal, complemented
13#21811C211yesmaximal, characteristic, complemented
14#21804C211yesmaximal, characteristic, complemented
15#21788C211yesmaximal, characteristic
16#21365C211yesmaximal, characteristic, complemented
17#21361C211yesmaximal, characteristic, complemented
18C22×C4⋊Q8C2211yescharacteristic
19C22×C22⋊Q8C2212yes—
20C22×C22⋊Q8C2212yes—
21C22×C4×D4C2211yescharacteristic
22C2×#484C2214yescomplemented
23C2×#485C2214yescomplemented
24C2×#485C2214yescomplemented
25C2×#483C2214yescomplemented
26C2×#432C2211yescharacteristic
27C2×#431C2211yescharacteristic
28#2542—22no—
29#2542—21no—
30#2542—21no—
31#2542C2212yes—
32#2542C2212yes—
33#2542C2214yes—
34C2×#399—22no—
35#2354C2211yescharacteristic
36#2354C2211yescharacteristic
37#2352C2212yes—
38#2352C2212yes—
39D4×C4⋊C4C2211yescharacteristic
40D4×C4⋊C4C2211yescharacteristic
41#2345—21no—
42#2342—22no—
43D4×C22⋊C4—21no—
44#2319—21no—
45#2318—22no—
46C2×#390—21no—
47#2285C2211yescharacteristic
48C2×#384—21no—
49#2283C2211yescharacteristic
50#2280C2212yes—
51C2×#380C2212yes—
52#2275—21no—
53C2×C4×C4⋊C4C2211yescharacteristic
54#2036C2214yescomplemented
55#2036C2214yescomplemented
56#2036C2214yescomplemented
57#2036C2214yescomplemented
58#2035C2214yescomplemented
59#2035C2214yescomplemented
60#2035C2214yescomplemented
61#2035C2214yescomplemented
62#1981C2214yescomplemented
63#1981C2212yescomplemented
64#1981C2212yescomplemented
65#1960C2212yescomplemented
66#1960C2212yescomplemented
67#1956C2212yescomplemented
68#1956C2212yescomplemented
69#1955C2214yes—
70#1954C2212yes—
71#1954C2212yes—
72#1949C2212yescomplemented
73#1949C2212yescomplemented
74#1948C2212yescomplemented
75#1947C2212yescomplemented
76#1873C2214yescomplemented
77#1873C2214yescomplemented
78#1872C2214yescomplemented
79#1872C2214yescomplemented
80#1853C2211yescharacteristic
81#1853C2211yescharacteristic
82#1853C2212yes—
83#1852C2211yescharacteristic
84#1852C2211yescharacteristic
85#1852C2212yes—
86#1787C2212yes—
87#1787C2212yes—
88#1787C2212yes—
89#1787C2212yes—
90#1779C2212yes—
91#1779C2212yes—
92#1776C2214yescomplemented
93C4×#107C2212yescomplemented
94C4×#106C2212yescomplemented
95C23×Q8C2312yes—
96C23×D4D411yescharacteristic
97C24×C4C2312yes—
98C2×C4⋊Q8—21no—
99C2×C4⋊Q8—21no—
100C2×C4⋊Q8—24no—
101C2×C4⋊Q8—24no—
102C2×C4⋊Q8C2312yes—
103C2×C4⋊Q8C2312yes—
104C2×C22⋊Q8—22no—
105C2×C22⋊Q8—22no—
106C2×C22⋊Q8—22no—
107C2×C22⋊Q8—22no—
108C2×C22⋊Q8—48no—
109C2×C22⋊Q8—48no—
110C2×C22⋊Q8C2314yes—
111C2×C22⋊Q8C2314yes—
112C2×C22⋊Q8C2314yes—
113C2×C22⋊Q8C2314yes—
114C2×C4×D4—21no—
115C2×C4×D4—21no—
116C2×C4×D4—24no—
117C2×C4×D4—24no—
118C2×C4×D4D412yes—
119C2×C4×D4D411yescharacteristic
120C2×C4×D4D411yescharacteristic
121C2×C4×D4C2311yescharacteristic
122C2×C4×D4C2312yes—
123C2×C4×D4C2311yescharacteristic
124C2×#117—21no—
125C2×#117C2312yes—
126C2×#117C2312yes—
127C22×C4⋊C4—21no—
128C22×C4⋊C4—22no—
129C22×C4⋊C4—22no—
130C22×C4⋊C4—21no—
131C22×C4⋊C4D411yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C22⋊C4—22no—
137C22×C22⋊C4—22no—
138C22×C22⋊C4—22no—
139C22×C22⋊C4D412yes—
140C22×C42—21no—
141C22×C42C2311yescharacteristic
142#485—48no—
143#485—48no—
144#484—48no—
145#483—48no—
146#432—24no—
147#431—24no—
148C2×#107C2312yes—
149C2×#107C2314yes—
150C2×#107C2312yes—
151C2×#106C2312yes—
152C2×#106C2314yes—
153C2×#106C2312yes—
154C2×C4⋊C8C2312yes—
155C2×C4⋊C8C2312yes—
156C2×#103C2314yes—
157C2×#103C2314yes—
158C2×#103C2314yes—
159C2×#103C2314yes—
160C2×#103C2314yes—
161C2×#103C2314yes—
162C2×#103C2314yes—
163C2×#103C2314yes—
164C2×C22⋊C8C2311yescharacteristic
165C2×C22⋊C8C2312yes—
166C2×C22⋊C8C2311yescharacteristic
167C2×C22⋊C8C2314yes—
168C2×C22⋊C8C2314yes—
169C2×C22⋊C8C2314yes—
170C2×C22⋊C8C2314yes—
171C2×#97C2312yes—
172C2×C4×C8C2312yes—
173#399—24no—
174#399—24no—
175#399—24no—
176#399—24no—
177#390—21no—
178#390—21no—
179#390—22no—
180#390—24no—
181#390—22no—
182#389—21no—
183#389—21no—
184#388—22no—
185#388—22no—
186#388—22no—
187#388—22no—
188#387—22no—
189#387—22no—
190#386—22no—
191#386—22no—
192#385—22no—
193#385—22no—
194#384—22no—
195#384—24no—
196#384—22no—
197#384C2311yescharacteristic
198#384C2311yescharacteristic
199#383—21no—
200#382—21no—
201#382C2311yescharacteristic
202#382C2311yescharacteristic
203#381—22no—
204#381—21no—
205#380—22no—
206#380—21no—
207#380—22no—
208#380C2312yes—
209#380C2312yes—
210#380C2312yes—
211#380C2312yes—
212#380C2311yescharacteristic
213#380C2312yes—
214#380C2311yescharacteristic
215#379—22no—
216C4×C4⋊C4—21no—
217C4×C4⋊C4—21no—
218C4×C4⋊C4—21no—
219C4×C4⋊C4—21no—
220C4×C4⋊C4—21no—
221C4×C4⋊C4C2311yescharacteristic
222C4×C4⋊C4C2311yescharacteristic
223C4×C4⋊C4C2312yes—
224C4×C4⋊C4C2312yes—
225C4×C4⋊C4C2312yes—
226C4×C22⋊C4—22no—
227C4×C22⋊C4—21no—
228C4×C22⋊C4—22no—
229C4×C22⋊C4—22no—
230C4×C22⋊C4—22no—
231#376—21no—
232C2×#95—22no—
233C2×#95—21no—
234#340C2312yes—
235#340C2314yes—
236#340C2312yes—
237#340C2312yes—
238#340C2314yes—
239#340C2312yes—
240C25C2×D412yes—
241C22×Q8—22no—
242C22×Q8—24no—
243C22×Q8—24no—
244C22×Q8—44no—
245C22×Q8—44no—
246C22×Q8C2414yes—
247C22×D4—24no—
248C22×D4—24no—
249C22×D4—42no—
250C22×D4C2×D411yescharacteristic
251C22×D4C2×D412yes—
252C22×D4C2×D411yescharacteristic
253C23×C4—21no—
254C23×C4—21no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—44no—
261C23×C4—44no—
262C23×C4C2×D411yescharacteristic
263C23×C4C2×D411yescharacteristic
264C23×C4C2×D412yes—
265C23×C4C2×D412yes—
266C23×C4C2×D412yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2411yescharacteristic
270C22×C8C2412yes—
271C22×C8C2412yes—
272C22×C8C2414yes—
273C4⋊Q8—24no—
274C4⋊Q8—24no—
275C4⋊Q8—24no—
276C4⋊Q8—24no—
277C4⋊Q8—44no—
278C4⋊Q8—44no—
279C22⋊Q8—28no—
280C22⋊Q8—28no—
281C22⋊Q8—28no—
282C22⋊Q8—28no—
283C22⋊Q8—44no—
284C22⋊Q8—44no—
285C22⋊Q8—44no—
286C22⋊Q8—44no—
287C22⋊Q8—48no—
288C22⋊Q8—48no—
289C22⋊Q8—48no—
290C22⋊Q8—48no—
291C4×D4—24no—
292C4×D4—28no—
293C4×D4—24no—
294C4×D4—22no—
295C4×D4—22no—
296C4×D4—24no—
297C4×D4—22no—
298C4×D4—24no—
299C4×D4—22no—
300C4×D4—44no—
301C4×D4—44no—
302#117—44no—
303#117—44no—
304#117—82no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4—44no—
326C2×C4⋊C4—48no—
327C2×C4⋊C4—48no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4C2×D411yescharacteristic
331C2×C4⋊C4C2×D412yes—
332C2×C4⋊C4C2×D411yescharacteristic
333C2×C4⋊C4C2411yescharacteristic
334C2×C4⋊C4C2411yescharacteristic
335C2×C4⋊C4C2412yes—
336C2×C4⋊C4C2412yes—
337C2×C4⋊C4C2411yescharacteristic
338C2×C4⋊C4C2411yescharacteristic
339C2×C4⋊C4C2412yes—
340C2×C4⋊C4C2412yes—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—48no—
356C2×C22⋊C4—48no—
357C2×C22⋊C4—84no—
358C2×C22⋊C4C2×D412yes—
359C2×C22⋊C4C2×D412yes—
360C2×C22⋊C4C2×D412yes—
361C2×C22⋊C4C2×D412yes—
362C2×C42—21no—
363C2×C42—21no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—44no—
370C2×C42C2×D411yescharacteristic
371C2×C42C2×D411yescharacteristic
372C2×C42#4114yes—
373C2×C42#4114yes—
374C2×C42C2411yescharacteristic
375C2×C42C2411yescharacteristic
376#107—24no—
377#107—28no—
378#107—24no—
379#106—24no—
380#106—28no—
381#106—24no—
382C4⋊C8—24no—
383C4⋊C8—24no—
384#103—44no—
385#103—44no—
386#103—44no—
387#103—44no—
388#103—44no—
389#103—44no—
390#103—44no—
391#103—44no—
392C22⋊C8—22no—
393C22⋊C8—22no—
394C22⋊C8—24no—
395C22⋊C8—44no—
396C22⋊C8—44no—
397C22⋊C8—44no—
398C22⋊C8—44no—
399#97—24no—
400C4×C8—24no—
401#95—21no—
402#95—22no—
403#95—22no—
404#95—22no—
405#95—22no—
406#95—22no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—22no—
411#95—22no—
412#95—21no—
413#95—21no—
414#95—22no—
415#95—21no—
416#95—21no—
417C24—24no—
418C24—24no—
419C24—24no—
420C24—24no—
421C24—42no—
422C24—42no—
423C24—42no—
424C24C22×D412yes—
425C24C22×D412yes—
426C24C22×D411yescharacteristic
427C2×Q8—24no—
428C2×Q8—24no—
429C2×Q8—24no—
430C2×Q8—24no—
431C2×Q8—24no—
432C2×Q8—24no—
433C2×Q8—44no—
434C2×Q8—44no—
435C2×Q8—44no—
436C2×Q8—88no—
437C2×Q8—88no—
438C2×D4—24no—
439C2×D4—22no—
440C2×D4—24no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—416no—
446C2×D4—42no—
447C2×D4#13714yes—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—24no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—24no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—44no—
487C22×C4—44no—
488C22×C4—44no—
489C22×C4—44no—
490C22×C4—44no—
491C22×C4—88no—
492C22×C4—88no—
493C22×C4—82no—
494C22×C4—82no—
495C22×C4—82no—
496C22×C4—82no—
497C22×C4#12314yes—
498C22×C4#12314yes—
499C22×C4C22×D412yes—
500C22×C4C22×D412yes—
501C22×C4C22×D411yescharacteristic
502C22×C4C22×D411yescharacteristic
503C22×C4C22×D411yescharacteristic
504C22×C4C22×D411yescharacteristic
505C22×C4C22×D411yescharacteristic
506C22×C4C2×#4112yes—
507C22×C4C2×#4112yes—
508C22×C4C2511yescharacteristic
509C2×C8—22no—
510C2×C8—22no—
511C2×C8—24no—
512C2×C8—22no—
513C2×C8—24no—
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—24no—
517C2×C8—22no—
518C4⋊C4—24no—
519C4⋊C4—24no—
520C4⋊C4—24no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—24no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—24no—
530C4⋊C4—22no—
531C4⋊C4—48no—
532C4⋊C4—48no—
533C4⋊C4—48no—
534C4⋊C4—48no—
535C4⋊C4—44no—
536C4⋊C4—44no—
537C4⋊C4—44no—
538C4⋊C4—44no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4—82no—
542C4⋊C4—82no—
543C4⋊C4—81no—
544C4⋊C4—81no—
545C4⋊C4H(5,𝔽2)14yes—
546C4⋊C4H(5,𝔽2)14yes—
547C22⋊C4—24no—
548C22⋊C4—24no—
549C22⋊C4—24no—
550C22⋊C4—24no—
551C22⋊C4—48no—
552C22⋊C4—48no—
553C22⋊C4—48no—
554C22⋊C4—48no—
555C22⋊C4—44no—
556C22⋊C4—44no—
557C22⋊C4—42no—
558C22⋊C4—44no—
559C22⋊C4—42no—
560C22⋊C4—82no—
561C22⋊C4—82no—
562C22⋊C4—82no—
563C22⋊C4—82no—
564C42—44no—
565C42—42no—
566C42—44no—
567C42—42no—
568C42—82no—
569C42—82no—
570C42—82no—
571C42#12314yes—
572C42#12314yes—
573C42C2×#4112yes—
574C42C2×#4112yes—
575C42C2×#4112yes—
576C42C2×#4112yes—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—22no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—48no—
595C23—48no—
596C23—48no—
597C23—48no—
598C23—84no—
599C23—84no—
600C23—84no—
601C23C2×#12312yes—
602C23C2×#13714yes—
603C23#57712yes—
604C23#57812yes—
605C23C23×D411yescharacteristic
606Q8—44no—
607Q8—44no—
608Q8—44no—
609Q8—44no—
610Q8—88no—
611D4—28no—
612D4—48no—
613D4—44no—
614C2×C4—28no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—28no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—48no—
635C2×C4—48no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—44no—
650C2×C4—44no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—42no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—84no—
666C2×C4—84no—
667C2×C4—84no—
668C2×C4—88no—
669C2×C4—164no—
670C2×C4—164no—
671C2×C4C2×#12312yes—
672C2×C4C2×#12312yes—
673C2×C4C2×#12312yes—
674C2×C4C2×#12312yes—
675C2×C4C2×#12312yes—
676C2×C4C2×#13712yes—
677C2×C4#57512yes—
678C2×C4C22×#4111yescharacteristic
679C2×C4C22×#4111yescharacteristic
680C2×C4C2×H(5,𝔽2)12yes—
681C2×C4C2×H(5,𝔽2)12yes—
682C8—42no—
683C8—42no—
684C8—44no—
685C22—22no—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—24no—
692C22—24no—
693C22—24no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—816no—
706C22#309714yes—
707C22C22×#12311yescharacteristic
708C22#348411yescharacteristic
709C22#348411yescharacteristic
710C22C22×#13711yescharacteristic
711C22C2×#57511yescharacteristic
712C22C2×#57711yescharacteristic
713C22C2×#57811yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—44no—
719C4—44no—
720C4—42no—
721C4—42no—
722C4—82no—
723C4—81no—
724C4—81no—
725C4—81no—
726C4—82no—
727C4—81no—
728C4—84no—
729C4#309514yes—
730C4#350812yes—
731C4#350812yes—
732C2—24no—
733C2—44no—
734C2—82no—
735C2#3555411yescharacteristic
736C2C2×#309511yescharacteristic
737C2C2×#309711yescharacteristic
738C2#6159311yescharacteristic
739C2#6159511yescharacteristic
740C2#6160211yescharacteristic
741C2#6160411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4D4
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
3. #26249C2semidirect
4. #26247C2semidirect
5. #26236C2semidirect
6. #26234C2semidirect
7. #26233C2semidirect
8. #26231C2semidirect
9. #24010C2semidirect
10. #24010C2semidirect
11. #24006C2semidirect
12. #24003C2semidirect
13. #21811C2semidirect
14. #21804C2semidirect
16. #21365C2semidirect
17. #21361C2semidirect
22. C2×#484C22semidirect
23. C2×#485C22semidirect
24. C2×#485C22semidirect
25. C2×#483C22semidirect
54. #2036C22semidirect
55. #2036C22semidirect
56. #2036C22semidirect
57. #2036C22semidirect
58. #2035C22semidirect
59. #2035C22semidirect
60. #2035C22semidirect
61. #2035C22semidirect
62. #1981C22semidirect
63. #1981C22semidirect
64. #1981C22semidirect
65. #1960C22semidirect
66. #1960C22semidirect
67. #1956C22semidirect
68. #1956C22semidirect
72. #1949C22semidirect
73. #1949C22semidirect
74. #1948C22semidirect
75. #1947C22semidirect
76. #1873C22semidirect
77. #1873C22semidirect
78. #1872C22semidirect
79. #1872C22semidirect
92. #1776C22semidirect
93. C4×#107C22semidirect
94. C4×#106C22semidirect

Maximal subgroups

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

subgroupindex
C2×#25422
#341942
#262492
#262472
#262362
#262342
#262332
#262312
#240102
#240062
#240032
#218112
#218042
#217882
#213652
#213612