Finite Group Databasebeta

← #11876940

Subgroups — #11876940

Order 1152.

795 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595382C211yesmaximal, characteristic, complemented
2#10594447C211yesmaximal, characteristic, complemented
3#10592515C211yesmaximal, characteristic, complemented
4C3×#4817C211yesmaximal, characteristic, complemented
5C3×#4800C211yesmaximal, characteristic, complemented
6#10591606C211yesmaximal, characteristic, complemented
7#10591590C211yesmaximal, characteristic, complemented
8#10591541C211yesmaximal, characteristic, complemented
9#10590863C211yesmaximal, characteristic, complemented
10#10590840C211yesmaximal, characteristic
11#10590747C211yesmaximal, characteristic, complemented
12#10590664C211yesmaximal, characteristic, complemented
13#10590506C211yesmaximal, characteristic, complemented
14#10590455C211yesmaximal, characteristic, complemented
15#10590413C211yesmaximal, characteristic, complemented
16#81631—31nomaximal
17#79793—31nomaximal
18#64155C2211yescharacteristic
19C2×#3756C2211yescharacteristic
20C2×#3743C2211yescharacteristic
21#64106C2211yescharacteristic
22C3×#947C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#215C2211yescharacteristic
25C3×#893C2211yescharacteristic
26C3×#890C2211yescharacteristic
27#63916C2211yescharacteristic
28#63916C2211yescharacteristic
29#63904—21no—
30Dic3×D12C2211yescharacteristic
31C4×#624C2211yescharacteristic
32#63880—21no—
33#63877—21no—
34#63869C2211yescharacteristic
35#63861—21no—
36#63860C2211yescharacteristic
37#63858—21no—
38#63854—21no—
39#63854—21no—
40#63844C2211yescharacteristic
41#63841—21no—
42C2×#3716C2211yescharacteristic
43C2×#3713C2211yescharacteristic
44C2×#3712C2211yescharacteristic
45C32×#103C2211yescharacteristic
46#63643C2211yescharacteristic
47#63635C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#815C2211yescharacteristic
52C3×C8×Dic3C2211yescharacteristic
53C3×#809C2211yescharacteristic
54C3×#807C2211yescharacteristic
55#63575C2211yescharacteristic
56#63574C2211yescharacteristic
57#63567C2211yescharacteristic
58#63563C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5691—31no—
62#5680—31no—
63#5580—31no—
64#5557—31no—
65C3×#488—31no—
66C3×#440—31no—
67#5174—31no—
68#5168—31no—
69#5065—31no—
70#5059—31no—
71#5030—31no—
72#5014—31no—
73#4886—31no—
74#4878—31no—
75#4817D311yescharacteristic, complemented
76#4816—31no—
77#4816—31no—
78#4816—61no—
79#4812—31no—
80#4800D311yescharacteristic, complemented
81#4789—31no—
82#4785—31no—
83#4782—31no—
84#4782—31no—
85#4780—31no—
86#4768—31no—
87#4757—31no—
88#4710—31no—
89#4707—31no—
90#4697—31no—
91C4×ΓL(1,𝔽25)—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C4×C3⋊D3C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×D12C2311yescharacteristic
96C2×C3×D12C2311yescharacteristic
97C2×C3×C4×D3—21no—
98C2×#626—21no—
99C2×#626—21no—
100C2×#624D411yescharacteristic
101C2×#624D411yescharacteristic
102C2×D3×Dic3—21no—
103C2×C32×C8C2311yescharacteristic
104C32×C4⋊C4C2311yescharacteristic
105#3756—22no—
106#3752—21no—
107#3752—21no—
108C4⋊(C3⋊Dic3)—21no—
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110#3750—21no—
111C2×C3⋊(C3⋊C8)C2311yescharacteristic
112#3743—22no—
113C3×#215—22no—
114C3×(C2×D3)⋊C4—21no—
115C3×(C2×D3)⋊C4—21no—
116C3×(C2×D3)⋊C4—21no—
117C3×C4⋊Dic3—21no—
118C3×C4⋊Dic3—21no—
119C3×C4⋊Dic3C2311yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×Dic3⋊C4—21no—
122C3×C4×Dic3—21no—
123C3×C4×Dic3C2311yescharacteristic
124C3×C4×Dic3C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127#3724—21no—
128#3724—21no—
129Dic3⋊Dic3—21no—
130(C2×D3)⋊Dic3—21no—
131(C2×D3)⋊Dic3—21no—
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135Dic32—21no—
136Dic32D411yescharacteristic
137Dic32D411yescharacteristic
138#3716—22no—
139#3713—22no—
140#3712—22no—
141#3183—91noSylow
142C2×C3×SD16—31no—
143C3×#125—31no—
144C3×#124—31no—
145C3×C4×Q8—31no—
146C3×C4×D4—31no—
147#947C2×D311yescharacteristic
148#946—31no—
149#946—31no—
150#946—61no—
151Q8×Dic3C2×D311yescharacteristic
152C2×#216—31no—
153C2×#216—31no—
154C2×#216—61no—
155C2×#215C2×D311yescharacteristic
156#938—31no—
157#938—31no—
158#936—31no—
159D4×Dic3—31no—
160C2×#214—31no—
161C2×#213—31no—
162C2×#213—31no—
163C4×#67—61no—
164#926—61no—
165C2×#204—31no—
166C2×ΓL(1,𝔽25)—31no—
167C2×ΓL(1,𝔽25)—31no—
168C2×ΓL(1,𝔽25)—31no—
169C2×ΓL(1,𝔽25)—31no—
170C2×ΓL(1,𝔽25)—61no—
171#898—61no—
172#898—61no—
173#897—31no—
174#897—31no—
175#897—61no—
176#895—31no—
177#895—31no—
178#894—61no—
179#894—61no—
180#893—61no—
181#893C2×D311yescharacteristic
182#892—61no—
183#890—31no—
184#890C2×D311yescharacteristic
185#887—31no—
186#883—61no—
187#883—61no—
188#67⋊C4—61no—
189#879—61no—
190#879—61no—
191#877—61no—
192#875—31no—
193C4×D12—31no—
194C4×D12—61no—
195#872—61no—
196C42×D3—31no—
197C42×D3—31no—
198#870—31no—
199C4×Dic6—31no—
200C3×#107—31no—
201C3×#103—21no—
202C3×#103—31no—
203C3×#103C2×D311yescharacteristic
204C3×#103C2×D311yescharacteristic
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#97—31no—
209C3×C4×C8—31no—
210#835C2×D311yescharacteristic
211#832—31no—
212#821—31no—
213#821C2×D311yescharacteristic
214#821C2×D311yescharacteristic
215#818—31no—
216#816—31no—
217#816—31no—
218#816—31no—
219#816—61no—
220#815—31no—
221#815C2×D311yescharacteristic
222C8×Dic3—31no—
223C8×Dic3C2×D311yescharacteristic
224#810—31no—
225#809C2×D311yescharacteristic
226#808—31no—
227#808—31no—
228#808—31no—
229#808—31no—
230#808—61no—
231#807—31no—
232#807C2×D311yescharacteristic
233#803—31no—
234C4×C3⋊C8—31no—
235C22×C3⋊D3C2×D411yescharacteristic
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C32×Q8—21no—
239C32×Q8—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4C2411yescharacteristic
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3C2×D411yescharacteristic
246C4×C3⋊D3—21no—
247C4×C3⋊D3—21no—
248#634—21no—
249#634—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C3×D12—21no—
257C3×D12—21no—
258C3×D12—21no—
259C3×D12—21no—
260C3×C4×D3—42no—
261#626—42no—
262#626—42no—
263#624—41no—
264#624—41no—
265D3×Dic3—42no—
266C32×C8—21no—
267C3⋊(C3⋊C8)#4112yes—
268C3×C3⋊C8—21no—
269C3×C3⋊C8#4112yes—
270#529—91no—
271#529—91no—
272#499—91no—
273#495—91no—
274#488—31no—
275#488—91no—
276#470—91no—
277#469—91no—
278#468—91no—
279#468—91no—
280#442—91no—
281#441—91no—
282#440—31no—
283#440—91no—
284C4×M16—91no—
285C2×C3×Q8—21no—
286C2×C3×Q8C22×D311yescharacteristic
287C2×C3×Q8C22×D311yescharacteristic
288C2×C3×D4—31no—
289C2×C3×D4—31no—
290C22×C3×C4—61no—
291C2×#67—61no—
292C2×#67—61no—
293C22×Dic3—61no—
294C2×D12—61no—
295C2×D12—61no—
296C2×D12C22×D311yescharacteristic
297C2×D12C22×D311yescharacteristic
298C2×C4×D3—21no—
299C2×C4×D3—31no—
300C2×C4×D3—31no—
301C2×C4×D3—31no—
302C2×C4×D3—31no—
303C2×C4×D3—31no—
304C2×C4×D3—31no—
305C2×C4×D3—61no—
306C2×C4×D3—61no—
307C2×Dic6—31no—
308C2×Dic6—31no—
309C2×Dic6—61no—
310C3×SD16—62no—
311C2×C3×C8—21no—
312C2×C3×C8—31no—
313C2×C3×C8—31no—
314C2×C3×C8C22×D311yescharacteristic
315C2×C3×C8C22×D311yescharacteristic
316C3×C4⋊C4—21no—
317C3×C4⋊C4—31no—
318C3×C4⋊C4—31no—
319C3×C4⋊C4—61no—
320C3×C4⋊C4—61no—
321C3×C4⋊C4—61no—
322C3×C4⋊C4C22×D311yescharacteristic
323C3×C4⋊C4C22×D311yescharacteristic
324C3×C22⋊C4—61no—
325C3×C22⋊C4—61no—
326C3×C22⋊C4—61no—
327C3×C42—31no—
328C3×C42—31no—
329C3×C42—61no—
330#217—61no—
331#217—61no—
332#217—61no—
333#217—61no—
334#217—61no—
335#216—62no—
336#216—62no—
337#216—122no—
338#215—22no—
339#214—62no—
340#213—62no—
341#213—62no—
342(C2×D3)⋊C4—21no—
343(C2×D3)⋊C4—21no—
344(C2×D3)⋊C4—21no—
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—61no—
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⋊Dic3—61no—
363C4⋊Dic3—61no—
364C4⋊Dic3—121no—
365C4⋊Dic3C22×D311yescharacteristic
366C4⋊Dic3C22×D311yescharacteristic
367Dic3⋊C4—21no—
368Dic3⋊C4—61no—
369Dic3⋊C4—61no—
370Dic3⋊C4—61no—
371Dic3⋊C4—61no—
372Dic3⋊C4—61no—
373Dic3⋊C4—61no—
374Dic3⋊C4—61no—
375Dic3⋊C4—121no—
376C4×Dic3—21no—
377C4×Dic3—31no—
378C4×Dic3—31no—
379C4×Dic3—31no—
380C4×Dic3—31no—
381C4×Dic3—61no—
382C4×Dic3—61no—
383C4×Dic3C22×D311yescharacteristic
384C4×Dic3C22×D311yescharacteristic
385C2×C3⋊C8—31no—
386C2×C3⋊C8—31no—
387C2×C3⋊C8—61no—
388C2×C3⋊C8C22×D311yescharacteristic
389C2×C3⋊C8C22×D311yescharacteristic
390#204—62no—
391ΓL(1,𝔽25)—62no—
392ΓL(1,𝔽25)—62no—
393ΓL(1,𝔽25)—62no—
394ΓL(1,𝔽25)—62no—
395ΓL(1,𝔽25)—122no—
396C22×C32C22×D411yescharacteristic
397C2×C3⋊D3—21no—
398C2×C3⋊D3—21no—
399C2×C3⋊D3—21no—
400C2×C3×D3—41no—
401C2×C3×D3—41no—
402C2×C3×D3—41no—
403C2×C3×D3—41no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
406C32×C4—41no—
407C32×C4—41no—
408C32×C4C2×#4111yescharacteristic
409C32×C4C2×#4111yescharacteristic
410C3⋊Dic3—21no—
411C3⋊Dic3—41no—
412C3⋊Dic3—41no—
413C3×Dic3—21no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—41no—
418C3×Dic3—41no—
419C2×Q16—91no—
420C2×SD16—31no—
421C2×SD16—91no—
422C2×D8—91no—
423C2×M16—91no—
424C2×M16—91no—
425#126—181no—
426#126—181no—
427#125—31no—
428#125—91no—
429#124—31no—
430#124—91no—
431#123—181no—
432#123—181no—
433C22⋊Q8—91no—
434C22⋊Q8—91no—
435#121—91no—
436#121—91no—
437C4×Q8—31no—
438C4×Q8—91no—
439C4×D4—31no—
440C4×D4—91no—
441C4×D4—181no—
442C4×D4—181no—
443#117—181no—
444#117—181no—
445C2×C42—91no—
446#107—31no—
447#107—91no—
448#106—91no—
449#106—91no—
450#103—31no—
451#103—91no—
452#103—91no—
453#103D3211yescharacteristic
454#102—31no—
455#102—31no—
456#102—31no—
457#102—91no—
458#97—31no—
459#97—91no—
460C4×C8—31no—
461C4×C8—91no—
462C23×C3—61no—
463C23×C3—61no—
464C22×D3—21no—
465C22×D3—21no—
466C22×D3—31no—
467C22×D3—31no—
468C22×D3—61no—
469C3×Q8—21no—
470C3×Q8—21no—
471C3×Q8—21no—
472C3×Q8—21no—
473C3×Q8—41no—
474C3×Q8—41no—
475C3×D4—61no—
476C3×D4—61no—
477C3×D4—61no—
478C3×D4—61no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—31no—
485C2×C3×C4—31no—
486C2×C3×C4—31no—
487C2×C3×C4—31no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—61no—
491C2×C3×C4—61no—
492C2×C3×C4—122no—
493C2×C3×C4C23×D311yescharacteristic
494C2×C3×C4C23×D311yescharacteristic
495#67—122no—
496#67—122no—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—31no—
500C2×Dic3—31no—
501C2×Dic3—61no—
502C2×Dic3—61no—
503C2×Dic3—61no—
504C2×Dic3—61no—
505C2×Dic3—61no—
506C2×Dic3—121no—
507C2×Dic3—121no—
508C2×Dic3—122no—
509C2×Dic3D3×D411yescharacteristic
510C2×Dic3D3×D411yescharacteristic
511C2×Dic3D3×D411yescharacteristic
512C2×Dic3D3×D411yescharacteristic
513D12—21no—
514D12—21no—
515D12—21no—
516D12—21no—
517D12—122no—
518D12—122no—
519C4×D3—42no—
520C4×D3—61no—
521C4×D3—61no—
522C4×D3—61no—
523C4×D3—61no—
524C4×D3—121no—
525C4×D3—121no—
526C4×D3—121no—
527C4×D3—121no—
528C4×D3—121no—
529C4×D3—121no—
530C4×D3—122no—
531Dic6—61no—
532Dic6—61no—
533Dic6—61no—
534Dic6—61no—
535Dic6—121no—
536Dic6—121no—
537C3×C8—21no—
538C3×C8—21no—
539C3×C8—32no—
540C3×C8—41no—
541C3×C8—61no—
542C3⋊C8—21no—
543C3⋊C8—32no—
544C3⋊C8—32no—
545C3⋊C8—62no—
546C3⋊C8#23512yes—
547C2×C32#53211yescharacteristic
548C2×C32#57511yescharacteristic
549C2×C32#57511yescharacteristic
550C3⋊D3—41no—
551C3×D3—81no—
552C3×D3—81no—
553C2×Q8—91no—
554C2×Q8C2×D3211yescharacteristic
555C2×D4—31no—
556C2×D4—31no—
557C2×D4—181no—
558C2×D4—181no—
559C22×C4—61no—
560C22×C4—91no—
561C22×C4—91no—
562C22×C4—91no—
563C22×C4—181no—
564Q16—182no—
565SD16—62no—
566SD16—182no—
567D8—182no—
568M16—182no—
569M16—182no—
570C2×C8—31no—
571C2×C8—31no—
572C2×C8—91no—
573C2×C8C2×D3211yescharacteristic
574C4⋊C4—31no—
575C4⋊C4—31no—
576C4⋊C4—61no—
577C4⋊C4—61no—
578C4⋊C4—61no—
579C4⋊C4—91no—
580C4⋊C4—181no—
581C4⋊C4—181no—
582C4⋊C4—181no—
583C4⋊C4—181no—
584C4⋊C4—181no—
585C4⋊C4C2×D3211yescharacteristic
586C22⋊C4—61no—
587C22⋊C4—61no—
588C22⋊C4—61no—
589C22⋊C4—181no—
590C22⋊C4—181no—
591C22⋊C4—181no—
592C22⋊C4—181no—
593C22⋊C4—181no—
594C22⋊C4—181no—
595C22⋊C4—181no—
596C42—31no—
597C42—31no—
598C42—61no—
599C42—91no—
600C42—91no—
601C42—181no—
602C22×C3—21no—
603C22×C3—121no—
604C22×C3—121no—
605C22×C3—121no—
606C22×C3—121no—
607C22×C3—121no—
608C22×C3—121no—
609C22×C3C2×D3×D411yescharacteristic
610C22×C3C2×D3×D411yescharacteristic
611C2×D3—41no—
612C2×D3—41no—
613C2×D3—41no—
614C2×D3—41no—
615C2×D3—41no—
616C2×D3—41no—
617C2×D3—61no—
618C2×D3—61no—
619C2×D3—61no—
620C2×D3—61no—
621C2×D3—61no—
622C2×D3—61no—
623C2×D3—121no—
624C2×D3—121no—
625C2×D3—121no—
626C3×C4—21no—
627C3×C4—21no—
628C3×C4—41no—
629C3×C4—41no—
630C3×C4—41no—
631C3×C4—41no—
632C3×C4—61no—
633C3×C4—61no—
634C3×C4—61no—
635C3×C4—61no—
636C3×C4—81no—
637C3×C4—81no—
638C3×C4—121no—
639C3×C4—121no—
640C3×C4C2×#23511yescharacteristic
641C3×C4D3×#4111yescharacteristic
642C3×C4D3×#4111yescharacteristic
643C3×C4D3×#4111yescharacteristic
644Dic3—21no—
645Dic3—21no—
646Dic3—21no—
647Dic3—21no—
648Dic3—41no—
649Dic3—41no—
650Dic3—61no—
651Dic3—61no—
652Dic3—121no—
653Dic3—121no—
654Dic3—121no—
655Dic3—121no—
656Dic3—121no—
657Dic3—241no—
658Dic3—241no—
659C32#318311yescharacteristic, complemented, Sylow
660C23—61no—
661C23—61no—
662C23—91no—
663Q8—21no—
664Q8—21no—
665Q8—181no—
666Q8—181no—
667D4—61no—
668D4—61no—
669D4—61no—
670D4—61no—
671D4—362no—
672D4—362no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—31no—
676C2×C4—31no—
677C2×C4—31no—
678C2×C4—31no—
679C2×C4—61no—
680C2×C4—61no—
681C2×C4—91no—
682C2×C4—122no—
683C2×C4—181no—
684C2×C4—181no—
685C2×C4—181no—
686C2×C4—181no—
687C2×C4—361no—
688C2×C4—361no—
689C2×C4—362no—
690C2×C4C22×D3211yescharacteristic
691C8—21no—
692C8—32no—
693C8—61no—
694C8—92no—
695C2×C3—21no—
696C2×C3—21no—
697C2×C3—21no—
698C2×C3—241no—
699C2×C3—241no—
700C2×C3#554811yescharacteristic
701C2×C3#566811yescharacteristic
702C2×C3#576811yescharacteristic
703C2×C3#576811yescharacteristic
704C2×C3#577311yescharacteristic
705C2×C3#577711yescharacteristic
706D3—81no—
707D3—81no—
708D3—121no—
709D3—121no—
710D3—241no—
711C22—121no—
712C22—121no—
713C22—121no—
714C22—121no—
715C22—121no—
716C22—121no—
717C22—181no—
718C22—181no—
719C22—181no—
720C22D32×D411yescharacteristic
721C4—41no—
722C4—41no—
723C4—61no—
724C4—61no—
725C4—61no—
726C4—61no—
727C4—121no—
728C4—121no—
729C4—181no—
730C4—361no—
731C4—361no—
732C4D3×#23511yescharacteristic
733C4#6431211yescharacteristic
734C3—21no—
735C3#7979311yescharacteristic, complemented
736C3#8163111yescharacteristic, complemented
737C2—241no—
738C2—241no—
739C2—361no—
740C2#1059406811yescharacteristic
741C2#1059474511yescharacteristic
742C2#1059476311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10590840C2
hypercenter#103D32
hypocenterC32#3183
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. #10595382C2semidirect
2. #10594447C2semidirect
3. #10592515C2semidirect
4. C3×#4817C2semidirect
5. C3×#4800C2semidirect
6. #10591606C2semidirect
7. #10591590C2semidirect
8. #10591541C2semidirect
9. #10590863C2semidirect
11. #10590747C2semidirect
12. #10590664C2semidirect
13. #10590506C2semidirect
14. #10590455C2semidirect
15. #10590413C2semidirect
75. #4817D3semidirect
80. #4800D3semidirect
659. C32#3183semidirect
735. C3#79793semidirect
736. C3#81631semidirect

Maximal subgroups

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

subgroupindex
#105953822
#105944472
#105925152
C3×#48172
C3×#48002
#105916062
#105915902
#105915412
#105908632
#105908402
#105907472
#105906642
#105905062
#105904552
#105904132
#816313
#797933