Finite Group Databasebeta

← #7623497

Subgroups — #7623497

Order 512.

1331 conjugacy classes of subgroups.

The subgroup lattice has 765 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60673C211yesmaximal, characteristic, complemented
2C2×#3168C211yesmaximal, characteristic, complemented
3#33814C212yesmaximal, complemented
4#33813C212yesmaximal, complemented
5#33799C212yesmaximal, complemented
6#33798C212yesmaximal, complemented
7#33778C212yesmaximal, complemented
8#33777C212yesmaximal, complemented
9#33756C212yesmaximal, complemented
10#33754C212yesmaximal, complemented
11#33735C214yesmaximal, complemented
12#33664C211yesmaximal, characteristic, complemented
13#33663C211yesmaximal, characteristic, complemented
14#33662C214yesmaximal, complemented
15#33661C211yesmaximal, characteristic, complemented
16#33660C211yesmaximal, characteristic, complemented
17C2×#2162C211yesmaximal, characteristic, complemented
18#3444—21no—
19C2×#529—21no—
20#3170C2211yescharacteristic
21#3170C2211yescharacteristic, complemented
22#3169C2211yescharacteristic
23#3169C2211yescharacteristic, complemented
24#3168—21no—
25#3168—21no—
26#3168—21no—
27#3168—21no—
28#3168—21no—
29#3168—21no—
30#3168C2212yes—
31#3168C2212yes—
32#3168C2212yes—
33#3168C2212yes—
34#3168C2212yes—
35#3168C2212yescomplemented
36#3167—21no—
37#3167—21no—
38#3160C2211yescharacteristic, complemented
39C2×#499C2211yescharacteristic
40#3147C2211yescharacteristic, complemented
41C2×#495C2211yescharacteristic
42#3131—21no—
43C2×#488—21no—
44#3050—21no—
45#3050C2212yes—
46C2×#467C2211yescharacteristic
47C2×#466C2211yescharacteristic
48C2×#465—21no—
49C4×#135—21no—
50C4×#135C2212yescomplemented
51C2×C4×Q16C2211yescharacteristic
52C2×C4×SD16—21no—
53C2×C4×D8C2211yescharacteristic
54C22×C4×C8C2211yescharacteristic
55#2253C2214yescomplemented
56#2249C2214yescomplemented
57#2242C2214yescomplemented
58#2242C2214yescomplemented
59#2237C2214yescomplemented
60#2236C2212yes—
61#2235C2212yes—
62#2234C2214yes—
63#2233C2212yes—
64#2232C2212yes—
65#2229C2214yescomplemented
66#2228C2214yescomplemented
67#2227C2212yescomplemented
68#2226C2212yescomplemented
69#2225C2212yescomplemented
70#2224C2212yescomplemented
71#2217C2214yes—
72#2217C2214yescomplemented
73#2216C2214yescomplemented
74#2215C2214yes—
75#2211C2214yescomplemented
76#2210C2214yescomplemented
77#2209C2212yescomplemented
78#2208C2212yescomplemented
79#2207C2212yescomplemented
80#2206C2212yescomplemented
81#2189C2214yescomplemented
82#2188C2212yes—
83#2187C2212yes—
84#2186C2214yes—
85#2185C2212yes—
86#2184C2212yes—
87C4×Q32C2214yescomplemented
88C4×SD32C2214yescomplemented
89C4×SD32C2214yescomplemented
90C4×D16C2214yescomplemented
91#2162C2212yes—
92#2162C2211yescharacteristic
93#2162C2211yescharacteristic
94#2162C2212yescomplemented
95#2162C2212yescomplemented
96C2×C4⋊C16C2212yescomplemented
97C2×C22⋊C16C2212yes—
98C2×C4×C16C2212yescomplemented
99C2×#135—21no—
100C2×#135C2312yes—
101C22×Q16C2311yescharacteristic
102C22×SD16—21no—
103C22×D8C2311yescharacteristic
104C23×C8D411yescharacteristic
105C23×C8C2311yescharacteristic
106#533—21no—
107#533—21no—
108#533—21no—
109#532—21no—
110#532—21no—
111#532—21no—
112#529—22no—
113#529—22no—
114#529—22no—
115#529—22no—
116#529—22no—
117#529—22no—
118#529—41no—
119#529—41no—
120#529—41no—
121#529—41no—
122#529—41no—
123#529—41no—
124#529—41no—
125#529—41no—
126C2×#126—41no—
127C2×#125—21no—
128C2×#124—21no—
129#525—22no—
130#525—41no—
131#525—41no—
132C2×#123—41no—
133C2×C22⋊Q8—21no—
134C2×#121—21no—
135C4×#41—22no—
136C4×#41—41no—
137C4×#41—41no—
138C2×C4×Q8—21no—
139C2×C4×D4—21no—
140C2×C4×D4—41no—
141C2×#117—41no—
142C22×C42D411yescharacteristic
143C2×Q32C2314yes—
144C2×SD32C2314yes—
145C2×SD32C2314yes—
146C2×D16C2314yes—
147C22×C16C2314yes—
148#500C2311yescharacteristic
149#500C2311yescharacteristic
150#499—21no—
151#499—21no—
152#499—21no—
153#499C2312yes—
154#499C2312yes—
155#499C2312yes—
156#498—21no—
157#495—21no—
158#495—21no—
159#495—21no—
160#495C2312yes—
161#495C2312yes—
162#495C2312yes—
163#494C2311yescharacteristic
164#493C2311yescharacteristic
165#492—21no—
166#488—22no—
167#488—22no—
168#488—22no—
169#488—22no—
170#488—22no—
171#488—22no—
172#487—21no—
173#487—21no—
174#486—21no—
175#486—21no—
176#467—21no—
177#467—21no—
178#467—21no—
179#467—21no—
180#467C2312yes—
181#467C2312yes—
182#467C2312yes—
183#467C2312yes—
184#466—21no—
185#466—21no—
186#466—21no—
187#466—21no—
188#466C2312yes—
189#466C2312yes—
190#466C2312yes—
191#466C2312yes—
192#465—22no—
193#465—22no—
194#465—22no—
195#465—22no—
196#465—22no—
197#465—22no—
198#465—22no—
199#465—22no—
200C4×Q16—21no—
201C4×Q16—21no—
202C4×Q16—21no—
203C4×Q16—21no—
204C4×Q16C2312yes—
205C4×Q16C2312yes—
206C4×Q16C2312yes—
207C4×Q16C2312yes—
208C4×SD16—22no—
209C4×SD16—22no—
210C4×SD16—22no—
211C4×SD16—22no—
212C4×SD16—22no—
213C4×SD16—22no—
214C4×SD16—22no—
215C4×SD16—22no—
216C4×D8—21no—
217C4×D8—21no—
218C4×D8—21no—
219C4×D8—21no—
220C4×D8C2312yes—
221C4×D8C2312yes—
222C4×D8C2312yes—
223C4×D8C2312yes—
224#427—21no—
225#427C2312yes—
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#106—21no—
229#416—22no—
230#416—22no—
231C2×#103—21no—
232C2×#103—21no—
233C2×#102—21no—
234C2×#102—21no—
235C2×C4×C8D411yescharacteristic
236C2×C4×C8D411yescharacteristic
237C2×C4×C8D411yescharacteristic
238C2×C4×C8D411yescharacteristic
239C2×C4×C8D411yescharacteristic
240C2×C4×C8D411yescharacteristic
241C2×C4×C8C2311yescharacteristic
242C2×C4×C8C2311yescharacteristic
243C2×C4×C8C2311yescharacteristic
244C2×C4×C8C2311yescharacteristic
245C2×C4×C8C2311yescharacteristic
246C2×C4×C8C2311yescharacteristic
247#367C2314yes—
248#367C2314yes—
249#366C2314yes—
250#366C2314yes—
251C4⋊C16C2312yes—
252C4⋊C16C2312yes—
253C4⋊C16C2314yes—
254#358C2314yes—
255#358C2314yes—
256#358C2314yes—
257#358C2314yes—
258#357C2314yes—
259#357C2314yes—
260#357C2314yes—
261#357C2314yes—
262C22⋊C16C2312yes—
263C22⋊C16C2312yes—
264C22⋊C16C2314yes—
265C4×C16C2312yes—
266C4×C16C2312yes—
267C4×C16C2314yes—
268C2×#41—22no—
269C2×#41—41no—
270C2×#41—41no—
271C22×Q8—21no—
272C22×D4—21no—
273C22×D4—41no—
274C23×C4—41no—
275C23×C4D811yescharacteristic
276C23×C4D811yescharacteristic
277C23×C4C2×D411yescharacteristic
278#135—44no—
279#135—44no—
280C2×Q16—21no—
281C2×Q16—21no—
282C2×Q16—42no—
283C2×Q16C2412yes—
284C2×Q16C2412yes—
285C2×SD16—22no—
286C2×SD16—22no—
287C2×SD16—22no—
288C2×SD16—22no—
289C2×SD16—44no—
290C2×D8—21no—
291C2×D8—21no—
292C2×D8—42no—
293C2×D8C2412yes—
294C2×D8C2412yes—
295C22×C8—42no—
296C22×C8—42no—
297C22×C8C2×D411yescharacteristic
298C22×C8C2×D411yescharacteristic
299C22×C8C2×D411yescharacteristic
300C22×C8C2×D411yescharacteristic
301C22×C8C2×D411yescharacteristic
302C22×C8C2×D411yescharacteristic
303C22×C8C2×D411yescharacteristic
304C22×C8C2×D411yescharacteristic
305C22×C8C2×D411yescharacteristic
306C22×C8C2411yescharacteristic
307C22×C8C2411yescharacteristic
308C22×C8C2411yescharacteristic
309C4⋊Q8—21no—
310C4⋊Q8—21no—
311C4⋊Q8—21no—
312#127—21no—
313#126—42no—
314#126—42no—
315#126—42no—
316#126—42no—
317#126—42no—
318#126—42no—
319#125—22no—
320#125—22no—
321#125—22no—
322#125—41no—
323#125—41no—
324#125—41no—
325#125—41no—
326#124—22no—
327#124—22no—
328#124—22no—
329#124—41no—
330#124—41no—
331#124—41no—
332#124—41no—
333#123—42no—
334#123—42no—
335#123—42no—
336#123—42no—
337#123—42no—
338#123—42no—
339#123—42no—
340C22⋊Q8—22no—
341C22⋊Q8—22no—
342C22⋊Q8—22no—
343C22⋊Q8—22no—
344C22⋊Q8—41no—
345C22⋊Q8—41no—
346C22⋊Q8—41no—
347C22⋊Q8—41no—
348C22⋊Q8—41no—
349C22⋊Q8—41no—
350#121—22no—
351#121—22no—
352#121—22no—
353#121—22no—
354#121—41no—
355#121—41no—
356#121—41no—
357#121—41no—
358#121—41no—
359#121—41no—
360#120—42no—
361C4×Q8—22no—
362C4×Q8—22no—
363C4×Q8—22no—
364C4×Q8—22no—
365C4×Q8—41no—
366C4×Q8—41no—
367C4×Q8—41no—
368C4×Q8—41no—
369C4×Q8—41no—
370C4×Q8—41no—
371C4×D4—22no—
372C4×D4—22no—
373C4×D4—22no—
374C4×D4—22no—
375C4×D4—42no—
376C4×D4—42no—
377C4×D4—42no—
378C4×D4—42no—
379C4×D4—42no—
380C4×D4—42no—
381C4×D4—42no—
382C4×D4—42no—
383C4×D4—42no—
384C4×D4—42no—
385C4×D4—41no—
386C4×D4—41no—
387C4×D4—41no—
388C4×D4—41no—
389C4×D4—41no—
390C4×D4—41no—
391#117—22no—
392#117—41no—
393#117—41no—
394#117—42no—
395#117—42no—
396#117—42no—
397#117—42no—
398#117—42no—
399#117—42no—
400#117—42no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—41no—
404C2×C4⋊C4—41no—
405C2×C4⋊C4—41no—
406C2×C4⋊C4—41no—
407C2×C22⋊C4—41no—
408C2×C22⋊C4—41no—
409C2×C22⋊C4—41no—
410C2×C22⋊C4—41no—
411C2×C22⋊C4—41no—
412C2×C42—41no—
413C2×C42—42no—
414C2×C42D811yescharacteristic
415C2×C42D811yescharacteristic
416C2×C42D811yescharacteristic
417C2×C42D811yescharacteristic
418C2×C42D811yescharacteristic
419C2×C42D811yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426Q32—44no—
427SD32—44no—
428SD32—44no—
429D16—44no—
430C2×C16—44no—
431C2×C16C2414yes—
432C2×C16C2414yes—
433#107—21no—
434#107—21no—
435#107—21no—
436#107—21no—
437#107C2412yes—
438#107C2412yes—
439#107C2412yes—
440#107C2412yes—
441#106—22no—
442#106—22no—
443#106—22no—
444#106—22no—
445#103—22no—
446#103—22no—
447#103—22no—
448#103—22no—
449#103—22no—
450#103—22no—
451#103—22no—
452#103—22no—
453#102—22no—
454#102—22no—
455#102—22no—
456#102—22no—
457#102—22no—
458#102—22no—
459#102—22no—
460#102—22no—
461C4×C8C2×D411yescharacteristic
462C4×C8C2×D411yescharacteristic
463C4×C8C2×D411yescharacteristic
464C4×C8C2×D411yescharacteristic
465C4×C8C2×D411yescharacteristic
466C4×C8C2×D411yescharacteristic
467C4×C8C2×D411yescharacteristic
468C4×C8C2×D411yescharacteristic
469C4×C8C2×D411yescharacteristic
470C4×C8C2×D411yescharacteristic
471C4×C8C2×D411yescharacteristic
472C4×C8C2×D411yescharacteristic
473C4×C8C2411yescharacteristic
474C4×C8C2411yescharacteristic
475C4×C8C2411yescharacteristic
476C4×C8C2411yescharacteristic
477C24—41no—
478C24C2×D811yescharacteristic
479#41—44no—
480#41—44no—
481#41—84no—
482#41—84no—
483C2×Q8—22no—
484C2×Q8—22no—
485C2×Q8—42no—
486C2×Q8—42no—
487C2×Q8—41no—
488C2×Q8—41no—
489C2×Q8—41no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—41no—
500C2×D4—41no—
501C2×D4—41no—
502C2×D4—84no—
503C22×C4—24no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—42no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—84no—
516C22×C4C2×D811yescharacteristic
517C22×C4C2×D811yescharacteristic
518C22×C4C2×D811yescharacteristic
519C22×C4C2×D811yescharacteristic
520C22×C4C2×D811yescharacteristic
521C22×C4C2×D811yescharacteristic
522C22×C4C2×D811yescharacteristic
523C22×C4C2×D811yescharacteristic
524C22×C4C2×D811yescharacteristic
525C22×C4C2×D811yescharacteristic
526C22×C4C2×D811yescharacteristic
527C22×C4C2×D811yescharacteristic
528C22×C4C2×D811yescharacteristic
529C22×C4C2×D811yescharacteristic
530C22×C4C2×D811yescharacteristic
531C22×C4C22×D411yescharacteristic
532C22×C4C22×D411yescharacteristic
533C22×C4C22×D411yescharacteristic
534Q16—22no—
535Q16—24no—
536Q16—22no—
537Q16—42no—
538Q16—42no—
539SD16—44no—
540SD16—44no—
541SD16—44no—
542SD16—44no—
543D8—22no—
544D8—24no—
545D8—22no—
546D8—42no—
547D8—42no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—41no—
555C2×C8—41no—
556C2×C8—41no—
557C2×C8—41no—
558C2×C8—41no—
559C2×C8—41no—
560C2×C8C22×D411yescharacteristic
561C2×C8C22×D411yescharacteristic
562C2×C8C22×D411yescharacteristic
563C2×C8C22×D411yescharacteristic
564C2×C8C22×D411yescharacteristic
565C2×C8C22×D411yescharacteristic
566C2×C8C22×D411yescharacteristic
567C2×C8C2511yescharacteristic
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—41no—
573C4⋊C4—41no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—41no—
585C4⋊C4—41no—
586C4⋊C4—41no—
587C4⋊C4—41no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—42no—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—42no—
597C22⋊C4—42no—
598C22⋊C4—42no—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C42—42no—
612C42—42no—
613C42—42no—
614C42—42no—
615C42—42no—
616C42C2×D811yescharacteristic
617C42C2×D811yescharacteristic
618C42C2×D811yescharacteristic
619C42C2×D811yescharacteristic
620C42C2×D811yescharacteristic
621C42C2×D811yescharacteristic
622C42C2×D811yescharacteristic
623C42C2×D811yescharacteristic
624C42C2×D811yescharacteristic
625C42C2×D811yescharacteristic
626C42C2×D811yescharacteristic
627C42C2×D811yescharacteristic
628C42C22×D411yescharacteristic
629C42C22×D411yescharacteristic
630C42C22×D411yescharacteristic
631C42C22×D411yescharacteristic
632C16—24no—
633C16—24no—
634C23—22no—
635C23—22no—
636C23—41no—
637C23—42no—
638C23—42no—
639C23—82no—
640C23—82no—
641C23—82no—
642C23C22×D811yescharacteristic
643C23C22×D811yescharacteristic
644C23C22×D811yescharacteristic
645Q8—42no—
646Q8—42no—
647Q8—42no—
648Q8—42no—
649Q8—82no—
650Q8—82no—
651Q8—82no—
652D4—42no—
653D4—42no—
654D4—42no—
655D4—42no—
656D4—82no—
657D4—82no—
658D4—84no—
659D4—84no—
660D4—84no—
661D4—84no—
662D4—84no—
663D4—82no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—84no—
691C2×C4—84no—
692C2×C4—82no—
693C2×C4—82no—
694C2×C4—82no—
695C2×C4—84no—
696C2×C4—84no—
697C2×C4—84no—
698C2×C4#50814yes—
699C2×C4C22×D811yescharacteristic
700C2×C4C22×D811yescharacteristic
701C2×C4C22×D811yescharacteristic
702C2×C4C22×D811yescharacteristic
703C2×C4C22×D811yescharacteristic
704C2×C4C22×D811yescharacteristic
705C2×C4C22×D811yescharacteristic
706C2×C4C22×D811yescharacteristic
707C2×C4C22×D811yescharacteristic
708C2×C4C22×D811yescharacteristic
709C2×C4C22×D811yescharacteristic
710C2×C4C23×D411yescharacteristic
711C8—21no—
712C8—21no—
713C8—21no—
714C8—21no—
715C8—21no—
716C8—21no—
717C8#57512yes—
718C8#58512yes—
719C22—21no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—44no—
727C22—82no—
728C22—82no—
729C22—82no—
730C22—82no—
731C22—82no—
732C22—82no—
733C22—164no—
734C22C2×#50812yes—
735C22#341412yes—
736C22C23×D811yescharacteristic
737C4—21no—
738C4—21no—
739C4—21no—
740C4—21no—
741C4—21no—
742C4—21no—
743C4—21no—
744C4—21no—
745C4—21no—
746C4—82no—
747C4—82no—
748C4—82no—
749C4—82no—
750C4—82no—
751C4—82no—
752C4C2×#50812yes—
753C4C2×#50812yes—
754C4#344911yescharacteristic
755C4C2×#57511yescharacteristic
756C2—22no—
757C2—22no—
758C2—41no—
759C2—162no—
760C2—162no—
761C2#6094011yescharacteristic
762C2C22×#50811yescharacteristic
763C2C2×#341411yescharacteristic
subgroupG/H
centerC2×C4C22×D8
commutator, Frattini, cosocleC2×C8C25
socleC22C23×D8
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C22×C4×C8 ◁ G
LECSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #60673C2semidirect
2. C2×#3168C2semidirect
3. #33814C2semidirect
4. #33813C2semidirect
5. #33799C2semidirect
6. #33798C2semidirect
7. #33778C2semidirect
8. #33777C2semidirect
9. #33756C2semidirect
10. #33754C2semidirect
11. #33735C2semidirect
12. #33664C2semidirect
13. #33663C2semidirect
14. #33662C2semidirect
15. #33661C2semidirect
16. #33660C2semidirect
17. C2×#2162C2semidirect
21. #3170C22semidirect
23. #3169C22semidirect
35. #3168C22semidirect
38. #3160C22semidirect
40. #3147C22semidirect
50. C4×#135C22semidirect
55. #2253C22semidirect
56. #2249C22semidirect
57. #2242C22semidirect
58. #2242C22semidirect
59. #2237C22semidirect
65. #2229C22semidirect
66. #2228C22semidirect
67. #2227C22semidirect
68. #2226C22semidirect
69. #2225C22semidirect
70. #2224C22semidirect
72. #2217C22semidirect
73. #2216C22semidirect
75. #2211C22semidirect
76. #2210C22semidirect
77. #2209C22semidirect
78. #2208C22semidirect
79. #2207C22semidirect
80. #2206C22semidirect
81. #2189C22semidirect
87. C4×Q32C22semidirect
88. C4×SD32C22semidirect
89. C4×SD32C22semidirect
90. C4×D16C22semidirect
94. #2162C22semidirect
95. #2162C22semidirect
96. C2×C4⋊C16C22semidirect
98. C2×C4×C16C22semidirect

Maximal subgroups

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

subgroupindex
#606732
C2×#31682
#338142
#338132
#337992
#337982
#337782
#337772
#337562
#337542
#337352
#336642
#336632
#336622
#336612
#336602
C2×#21622