Finite Group Databasebeta

← #11895370

Subgroups — #11895370

Order 1152.

786 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595388C211yesmaximal, characteristic, complemented
2#10594470C211yesmaximal, characteristic, complemented
3#10592518C211yesmaximal, characteristic, complemented
4C3×#4800C211yesmaximal, characteristic, complemented
5C3×#4793C211yesmaximal, characteristic, complemented
6#10591568C211yesmaximal, characteristic, complemented
7#10591539C211yesmaximal, characteristic, complemented
8#10591536C211yesmaximal, characteristic, complemented
9#10590780C211yesmaximal, characteristic, complemented
10#10590765C211yesmaximal, characteristic
11#10590763C211yesmaximal, characteristic, complemented
12#10590644C211yesmaximal, characteristic, complemented
13#10590548C211yesmaximal, characteristic, complemented
14#10590468C211yesmaximal, characteristic, complemented
15#10590459C211yesmaximal, characteristic, complemented
16#81633—31nomaximal
17#81134—31nomaximal
18#64156C2211yescharacteristic
19C2×#3755C2211yescharacteristic
20C2×#3745C2211yescharacteristic
21#64102C2211yescharacteristic
22C3×#947C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C3×#890C2211yescharacteristic
25C3×#888C2211yescharacteristic
26C4×#627C2211yescharacteristic
27#63911C2211yescharacteristic
28#63898C2211yescharacteristic
29#63895—21no—
30#63894C2211yescharacteristic
31#63894C2211yescharacteristic
32#63894C2211yescharacteristic
33#63890—21no—
34#63888—21no—
35#63883—21no—
36#63880—21no—
37#63872C2211yescharacteristic
38#63871—21no—
39#63854—21no—
40#63852—21no—
41C2×#3714C2211yescharacteristic
42C32×#103C2211yescharacteristic
43#63641C2211yescharacteristic
44#63636C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#821C2211yescharacteristic
48C3×#818C2211yescharacteristic
49C3×Dic3⋊C8C2211yescharacteristic
50C3×C8×Dic3C2211yescharacteristic
51C3×#809C2211yescharacteristic
52C3×#807C2211yescharacteristic
53#63574C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63562C2211yescharacteristic
59#63553C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5730—31no—
62#5690—31no—
63#5681—31no—
64#5585—31no—
65C3×#488—31no—
66C3×#477—31no—
67#5088—31no—
68#5066—31no—
69#5057—31no—
70C4×#215—31no—
71#4891—31no—
72#4891—31no—
73#4872—31no—
74#4872—31no—
75#4843—31no—
76#4830—31no—
77#4819—31no—
78#4819—31no—
79#4819—31no—
80#4819—61no—
81#4800—31no—
82#4800—31no—
83#4800D311yescharacteristic, complemented
84#4793D311yescharacteristic, complemented
85#4788—31no—
86#4786—31no—
87#4766—31no—
88#4760—31no—
89#4756—31no—
90C4×D24—31no—
91C8×Dic6—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C3×D12C2311yescharacteristic
97C2×C3×Dic6—21no—
98C2×#627D411yescharacteristic
99C2×#626—21no—
100C2×#626—21no—
101C2×#624—21no—
102C2×#624—21no—
103C2×#624—21no—
104C2×D3×Dic3—21no—
105C2×C32×C8C2311yescharacteristic
106C32×C4⋊C4C2311yescharacteristic
107#3755—22no—
108#3752—21no—
109#3752—21no—
110#3752—21no—
111C4×C3⋊Dic3C2311yescharacteristic
112C2×C3⋊(C3⋊C8)C2311yescharacteristic
113#3745—22no—
114C3×(C2×D3)⋊C4—21no—
115C3×(C2×D3)⋊C4—21no—
116C3×C4⋊Dic3—21no—
117C3×C4⋊Dic3—21no—
118C3×C4⋊Dic3C2311yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×Dic3⋊C4—21no—
122C3×Dic3⋊C4—21no—
123C3×C4×Dic3—21no—
124C3×C4×Dic3C2311yescharacteristic
125C3×C4×Dic3C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128#3724D411yescharacteristic
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3D411yescharacteristic
132Dic3⋊Dic3D411yescharacteristic
133#3722—21no—
134#3722—21no—
135#3722—21no—
136(C2×D3)⋊Dic3—21no—
137#3714—22no—
138#3361—91noSylow
139C3×C4⋊Q8—31no—
140C3×#125—31no—
141C3×#124—31no—
142C3×C4×Q8—31no—
143#947—31no—
144#947—31no—
145#947—61no—
146#947C2×D311yescharacteristic
147#946—61no—
148#946—61no—
149Q8×Dic3C2×D311yescharacteristic
150C2×#215—31no—
151C2×#215—31no—
152C2×#215—61no—
153#940—31no—
154D4×Dic3—31no—
155C2×#213—31no—
156C2×D24—31no—
157C2×D24—31no—
158C2×D24—31no—
159C2×D24—61no—
160#897—61no—
161#897—61no—
162#896—61no—
163#896—61no—
164#894—61no—
165#894—61no—
166#893—31no—
167#893—31no—
168#893—31no—
169#893—31no—
170#893—31no—
171#893—31no—
172#893—61no—
173D3×C4⋊C4—61no—
174D3×C4⋊C4—61no—
175#890—31no—
176#890—31no—
177#890C2×D311yescharacteristic
178#888C2×D311yescharacteristic
179#886—61no—
180#885—61no—
181#883—61no—
182#67⋊C4—61no—
183#875—61no—
184#874—31no—
185C4×D12—31no—
186C4×D12—31no—
187C4×D12—31no—
188C4×D12—61no—
189C4×Dic6—31no—
190C4×Dic6—31no—
191C3×#107—31no—
192C3×#107—31no—
193C3×C4⋊C8—31no—
194C3×#103—21no—
195C3×#103—31no—
196C3×#103—31no—
197C3×#103C2×D311yescharacteristic
198C3×#103C2×D311yescharacteristic
199C3×#102—31no—
200C3×#102—31no—
201C3×C4×C8—31no—
202#835C2×D311yescharacteristic
203#835C2×D311yescharacteristic
204#832—31no—
205#821—31no—
206#821—31no—
207#821—31no—
208#821C2×D311yescharacteristic
209#818C2×D311yescharacteristic
210Dic3⋊C8—31no—
211Dic3⋊C8—31no—
212Dic3⋊C8—31no—
213Dic3⋊C8—61no—
214Dic3⋊C8C2×D311yescharacteristic
215C8×Dic3—31no—
216C8×Dic3—31no—
217C8×Dic3—31no—
218C8×Dic3C2×D311yescharacteristic
219#809—31no—
220#809—31no—
221#809—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—61no—
226#809C2×D311yescharacteristic
227#808—31no—
228#808—31no—
229#807C2×D311yescharacteristic
230C4⋊(C3⋊C8)—31no—
231C4×C3⋊C8—31no—
232C22×C3⋊D3—21no—
233C22×C3⋊D3—21no—
234C22×C3×D3—21no—
235C32×Q8—21no—
236C32×Q8—21no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4C2411yescharacteristic
240C2×C3⋊Dic3C2×D411yescharacteristic
241C2×C3⋊Dic3C2×D411yescharacteristic
242C4⋊(C3⋊D3)—21no—
243C4⋊(C3⋊D3)—21no—
244C4⋊(C3⋊D3)—21no—
245C4⋊(C3⋊D3)#4112yes—
246C4×C3⋊D3—81no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C3×D12—21no—
255C3×D12—21no—
256C3×Dic6—81no—
257#627—22no—
258#626—42no—
259#626—81no—
260#624—42no—
261#624—81no—
262#624—81no—
263D3×Dic3—81no—
264C32×C8—21no—
265C3⋊(C3⋊C8)—21no—
266C3×C3⋊C8—21no—
267C3×C3⋊C8—21no—
268#559—91no—
269#554—91no—
270#488—31no—
271#488—91no—
272#486—91no—
273#478—91no—
274#478—91no—
275#477—31no—
276#463—91no—
277#463—91no—
278#459—91no—
279C8×Q8—91no—
280C4×SD16—91no—
281C4×D8—91no—
282C4×D8—91no—
283C2×C3×Q8—21no—
284C2×C3×Q8—61no—
285C2×C3×Q8C22×D311yescharacteristic
286C2×C3×Q8C22×D311yescharacteristic
287C2×C3×D4—31no—
288C2×#67—61no—
289C2×#67—61no—
290C22×Dic3—61no—
291C2×D12—31no—
292C2×D12—31no—
293C2×D12—31no—
294C2×D12—31no—
295C2×D12—61no—
296C2×D12—61no—
297C2×D12—61no—
298C2×D12—61no—
299C2×D12C22×D311yescharacteristic
300C2×C4×D3—61no—
301C2×C4×D3—61no—
302C2×C4×D3—61no—
303C2×C4×D3—61no—
304C2×C4×D3—61no—
305C2×C4×D3—61no—
306C2×C4×D3—61no—
307C2×C4×D3—61no—
308C2×C4×D3—61no—
309C2×C4×D3—121no—
310C2×Dic6—21no—
311C2×Dic6—31no—
312C2×Dic6—31no—
313C2×C3×C8—21no—
314C2×C3×C8—31no—
315C2×C3×C8—31no—
316C2×C3×C8C22×D311yescharacteristic
317C2×C3×C8C22×D311yescharacteristic
318C3×C4⋊C4—21no—
319C3×C4⋊C4—31no—
320C3×C4⋊C4—31no—
321C3×C4⋊C4—31no—
322C3×C4⋊C4—61no—
323C3×C4⋊C4—61no—
324C3×C4⋊C4—61no—
325C3×C4⋊C4—61no—
326C3×C4⋊C4C22×D311yescharacteristic
327C3×C4⋊C4C22×D311yescharacteristic
328C3×C22⋊C4—61no—
329C3×C22⋊C4—61no—
330C3×C42—31no—
331C3×C42—31no—
332C3×C42—61no—
333#217—61no—
334#215—62no—
335#215—62no—
336#215—122no—
337#213—62no—
338(C2×D3)⋊C4—21no—
339(C2×D3)⋊C4—21no—
340(C2×D3)⋊C4—61no—
341(C2×D3)⋊C4—61no—
342(C2×D3)⋊C4—61no—
343(C2×D3)⋊C4—61no—
344(C2×D3)⋊C4—61no—
345(C2×D3)⋊C4—61no—
346(C2×D3)⋊C4—61no—
347(C2×D3)⋊C4—61no—
348(C2×D3)⋊C4—61no—
349(C2×D3)⋊C4—61no—
350(C2×D3)⋊C4—61no—
351(C2×D3)⋊C4—61no—
352(C2×D3)⋊C4—61no—
353(C2×D3)⋊C4—121no—
354(C2×D3)⋊C4—121no—
355(C2×D3)⋊C4—121no—
356C4⋊Dic3—21no—
357C4⋊Dic3—21no—
358C4⋊Dic3—31no—
359C4⋊Dic3—31no—
360C4⋊Dic3—61no—
361C4⋊Dic3—61no—
362C4⋊Dic3C22×D311yescharacteristic
363C4⋊Dic3C22×D311yescharacteristic
364C4⋊Dic3C22×D311yescharacteristic
365Dic3⋊C4—21no—
366Dic3⋊C4—21no—
367Dic3⋊C4—31no—
368Dic3⋊C4—31no—
369Dic3⋊C4—31no—
370Dic3⋊C4—31no—
371Dic3⋊C4—61no—
372Dic3⋊C4—61no—
373C4×Dic3—21no—
374C4×Dic3—31no—
375C4×Dic3—31no—
376C4×Dic3—61no—
377C4×Dic3C22×D311yescharacteristic
378C4×Dic3C22×D311yescharacteristic
379C2×C3⋊C8—31no—
380C2×C3⋊C8—31no—
381C2×C3⋊C8—61no—
382C2×C3⋊C8C22×D311yescharacteristic
383C2×C3⋊C8C22×D311yescharacteristic
384D24—62no—
385D24—62no—
386D24—62no—
387D24—122no—
388C22×C32C22×D411yescharacteristic
389C2×C3⋊D3—22no—
390C2×C3⋊D3—41no—
391C2×C3⋊D3—41no—
392C2×C3⋊D3—41no—
393C2×C3⋊D3—41no—
394C2×C3⋊D3—41no—
395C2×C3×D3—41no—
396C2×C3×D3—41no—
397C2×C3×D3—41no—
398C32×C4—41no—
399C32×C4—41no—
400C32×C4C2×#4111yescharacteristic
401C32×C42−1+411yescharacteristic
402C3⋊Dic3—21no—
403C3⋊Dic3—21no—
404C3×Dic3—21no—
405C3×Dic3—21no—
406C3×Dic3—21no—
407C3×Dic3—41no—
408C3×Dic3—41no—
409C3×Dic3—41no—
410C3×Dic3#13512yes—
411C2×SD16—91no—
412C2×D8—91no—
413C2×D8—91no—
414C4⋊Q8—31no—
415#127—91no—
416#125—31no—
417#125—91no—
418#124—31no—
419#124—91no—
420#124—181no—
421#123—181no—
422#123—181no—
423C22⋊Q8—181no—
424C22⋊Q8—181no—
425C22⋊Q8—181no—
426C4×Q8—31no—
427C4×Q8—91no—
428C4×D4—91no—
429C4×D4—91no—
430C4×D4—91no—
431C4×D4—91no—
432C4×D4—91no—
433C4×D4—181no—
434C2×C4⋊C4—181no—
435#107—31no—
436#107—31no—
437#106—91no—
438C4⋊C8—31no—
439C4⋊C8—91no—
440C4⋊C8—91no—
441#103—31no—
442#103—31no—
443#103D3211yescharacteristic
444#102—31no—
445#102—31no—
446#102—91no—
447#102—91no—
448#102—91no—
449#102—91no—
450#102—91no—
451C4×C8—31no—
452C4×C8—91no—
453C4×C8—91no—
454C23×C3—61no—
455C22×D3—21no—
456C22×D3—61no—
457C22×D3—61no—
458C22×D3—61no—
459C22×D3—61no—
460C22×D3—121no—
461C22×D3—121no—
462C3×Q8—21no—
463C3×Q8—21no—
464C3×Q8—21no—
465C3×Q8—21no—
466C3×Q8—41no—
467C3×Q8—41no—
468C3×Q8—241no—
469C3×D4—61no—
470C3×D4—61no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—31no—
477C2×C3×C4—31no—
478C2×C3×C4—31no—
479C2×C3×C4—31no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—61no—
483C2×C3×C4—61no—
484C2×C3×C4—61no—
485C2×C3×C4C23×D311yescharacteristic
486C2×C3×C4C23×D311yescharacteristic
487#67—122no—
488#67—241no—
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—21no—
492C2×Dic3—31no—
493C2×Dic3—31no—
494C2×Dic3—31no—
495C2×Dic3—31no—
496C2×Dic3—61no—
497C2×Dic3—61no—
498C2×Dic3—241no—
499C2×Dic3D3×D411yescharacteristic
500C2×Dic3D3×D411yescharacteristic
501C2×Dic3D3×D411yescharacteristic
502C2×Dic3D3×D411yescharacteristic
503D12—21no—
504D12—21no—
505D12—32no—
506D12—32no—
507D12—62no—
508D12—61no—
509D12—61no—
510D12—61no—
511D12—61no—
512D12—61no—
513D12—61no—
514D12—121no—
515D12—121no—
516D12—121no—
517D12—122no—
518D12—241no—
519C4×D3—122no—
520C4×D3—122no—
521C4×D3—241no—
522C4×D3—241no—
523C4×D3—241no—
524C4×D3—241no—
525C4×D3—241no—
526C4×D3—241no—
527C4×D3—241no—
528C4×D3—242no—
529Dic6—62no—
530Dic6—62no—
531Dic6—81no—
532C3×C8—21no—
533C3×C8—21no—
534C3×C8—41no—
535C3×C8—61no—
536C3×C8—61no—
537C3⋊C8—21no—
538C3⋊C8—21no—
539C3⋊C8—61no—
540C3⋊C8—61no—
541C3⋊C8—121no—
542C2×C32#54811yescharacteristic
543C2×C32C2×#13511yescharacteristic
544C2×C32#57611yescharacteristic
545C3⋊D3—42no—
546C3⋊D3—81no—
547C3×D3—81no—
548C2×Q8—61no—
549C2×Q8—91no—
550C2×Q8C2×D3211yescharacteristic
551C2×D4—31no—
552C2×D4—91no—
553C2×D4—91no—
554C2×D4—181no—
555C2×D4—181no—
556C22×C4—181no—
557C22×C4—181no—
558C22×C4—181no—
559C22×C4—181no—
560C22×C4—181no—
561SD16—182no—
562D8—182no—
563D8—182no—
564C2×C8—31no—
565C2×C8—31no—
566C2×C8—91no—
567C2×C8C2×D3211yescharacteristic
568C4⋊C4—31no—
569C4⋊C4—31no—
570C4⋊C4—31no—
571C4⋊C4—61no—
572C4⋊C4—61no—
573C4⋊C4—61no—
574C4⋊C4—61no—
575C4⋊C4—91no—
576C4⋊C4—91no—
577C4⋊C4—91no—
578C4⋊C4—181no—
579C4⋊C4—181no—
580C4⋊C4C2×D3211yescharacteristic
581C22⋊C4—61no—
582C22⋊C4—61no—
583C22⋊C4—181no—
584C22⋊C4—181no—
585C22⋊C4—181no—
586C22⋊C4—181no—
587C22⋊C4—181no—
588C22⋊C4—181no—
589C22⋊C4—181no—
590C42—31no—
591C42—31no—
592C42—61no—
593C42—91no—
594C22×C3—21no—
595C22×C3—121no—
596C22×C3—121no—
597C22×C3—121no—
598C22×C3C2×D3×D411yescharacteristic
599C22×C3C2×D3×D411yescharacteristic
600C2×D3—41no—
601C2×D3—41no—
602C2×D3—41no—
603C2×D3—62no—
604C2×D3—62no—
605C2×D3—122no—
606C2×D3—121no—
607C2×D3—121no—
608C2×D3—121no—
609C2×D3—121no—
610C2×D3—121no—
611C2×D3—121no—
612C2×D3—121no—
613C2×D3—121no—
614C2×D3—121no—
615C2×D3—121no—
616C2×D3—241no—
617C2×D3—241no—
618C2×D3—241no—
619C2×D3—241no—
620C2×D3—241no—
621C3×C4—21no—
622C3×C4—21no—
623C3×C4—32no—
624C3×C4—41no—
625C3×C4—41no—
626C3×C4—41no—
627C3×C4—41no—
628C3×C4—61no—
629C3×C4—61no—
630C3×C4—61no—
631C3×C4—81no—
632C3×C4—81no—
633C3×C4—121no—
634C3×C4—121no—
635C3×C4—121no—
636C3×C4#100711yescharacteristic
637C3×C4D3×#4111yescharacteristic
638C3×C4D3×#4111yescharacteristic
639C3×C4#101011yescharacteristic
640Dic3—21no—
641Dic3—21no—
642Dic3—21no—
643Dic3—41no—
644Dic3—41no—
645Dic3—41no—
646Dic3—61no—
647Dic3—61no—
648Dic3—61no—
649Dic3—61no—
650Dic3—121no—
651Dic3—121no—
652Dic3#91912yes—
653C32#336111yescharacteristic, complemented, Sylow
654C23—61no—
655C23—181no—
656C23—181no—
657Q8—21no—
658Q8—21no—
659Q8—182no—
660Q8—241no—
661D4—61no—
662D4—61no—
663D4—92no—
664D4—181no—
665D4—181no—
666D4—181no—
667D4—362no—
668D4—721no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—31no—
672C2×C4—31no—
673C2×C4—31no—
674C2×C4—31no—
675C2×C4—61no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—91no—
679C2×C4—91no—
680C2×C4—362no—
681C2×C4—721no—
682C2×C4—721no—
683C2×C4—721no—
684C2×C4—721no—
685C2×C4C22×D3211yescharacteristic
686C8—21no—
687C8—61no—
688C8—61no—
689C8—181no—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—21no—
693C2×C3—241no—
694C2×C3#563311yescharacteristic
695C2×C3#567711yescharacteristic
696C2×C3C2×#91911yescharacteristic
697C2×C3D3×#13511yescharacteristic
698C2×C3#576911yescharacteristic
699C2×C3#577411yescharacteristic
700D3—81no—
701D3—122no—
702D3—122no—
703D3—242no—
704D3—241no—
705D3—241no—
706D3—481no—
707C22—121no—
708C22—121no—
709C22—121no—
710C22—182no—
711C22—361no—
712C22—361no—
713C22—361no—
714C22—361no—
715C22—361no—
716C22D32×D411yescharacteristic
717C4—32no—
718C4—41no—
719C4—41no—
720C4—61no—
721C4—61no—
722C4—61no—
723C4—121no—
724C4—121no—
725C4—121no—
726C4—181no—
727C4—181no—
728C4#6429711yescharacteristic
729C4#6431211yescharacteristic
730C3—21no—
731C3#8113411yescharacteristic, complemented
732C3#8163311yescharacteristic, complemented
733C2—241no—
734C2—362no—
735C2—721no—
736C2#1059407511yescharacteristic
737C2#1059475511yescharacteristic
738C2D3×#91911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10590765C2
hypercenter#103D32
hypocenterC32#3361
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #10595388C2semidirect
2. #10594470C2semidirect
3. #10592518C2semidirect
4. C3×#4800C2semidirect
5. C3×#4793C2semidirect
6. #10591568C2semidirect
7. #10591539C2semidirect
8. #10591536C2semidirect
9. #10590780C2semidirect
11. #10590763C2semidirect
12. #10590644C2semidirect
13. #10590548C2semidirect
14. #10590468C2semidirect
15. #10590459C2semidirect
83. #4800D3semidirect
84. #4793D3semidirect
653. C32#3361semidirect
731. C3#81134semidirect
732. C3#81633semidirect

Maximal subgroups

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

subgroupindex
#105953882
#105944702
#105925182
C3×#48002
C3×#47932
#105915682
#105915392
#105915362
#105907802
#105907652
#105907632
#105906442
#105905482
#105904682
#105904592
#816333
#811343