Finite Group Databasebeta

← #11876926

Subgroups — #11876926

Order 1152.

794 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595377C211yesmaximal, characteristic, complemented
2#10594427C211yesmaximal, characteristic, complemented
3#10592488C211yesmaximal, characteristic, complemented
4C3×#4812C211yesmaximal, characteristic, complemented
5C3×#4800C211yesmaximal, characteristic, complemented
6#10591606C211yesmaximal, characteristic, complemented
7#10591598C211yesmaximal, characteristic, complemented
8#10591572C211yesmaximal, characteristic, complemented
9#10590863C211yesmaximal, characteristic, complemented
10#10590828C211yesmaximal, characteristic, complemented
11#10590741C211yesmaximal, characteristic, complemented
12Dic3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
13#10590504C211yesmaximal, characteristic
14#10590461C211yesmaximal, characteristic, complemented
15#10590413C211yesmaximal, characteristic, complemented
16#81631—31nomaximal
17#80791—31nomaximal
18Q8×C3⋊Dic3C2211yescharacteristic
19C2×#3756C2211yescharacteristic
20#64096C2211yescharacteristic
21C3×#947C2211yescharacteristic
22C3×#946C2211yescharacteristic
23C2×C3×#215C2211yescharacteristic
24C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
25C3×#895C2211yescharacteristic
26C3×#890C2211yescharacteristic
27#63908C2211yescharacteristic
28#63902—21no—
29#63898—21no—
30#63898C2211yescharacteristic
31#63898C2211yescharacteristic
32#63891—21no—
33#63884—21no—
34#63878—21no—
35#63878—21no—
36C4×D3×Dic3C2211yescharacteristic
37#63869C2211yescharacteristic
38#63861—21no—
39#63860C2211yescharacteristic
40#63858—21no—
41#63857C2211yescharacteristic
42C2×#3716C2211yescharacteristic
43C2×#3713C2211yescharacteristic
44C2×#3711C2211yescharacteristic
45C32×#103C2211yescharacteristic
46#63643C2211yescharacteristic
47#63642C2211yescharacteristic
48#63635C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×C8×Dic3C2211yescharacteristic
53C3×#809C2211yescharacteristic
54C3×#807C2211yescharacteristic
55#63575C2211yescharacteristic
56#63574C2211yescharacteristic
57#63567C2211yescharacteristic
58#63563C2211yescharacteristic
59#63555C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5691—31no—
62#5680—31no—
63#5624—31no—
64#5600—31no—
65C3×#488—31no—
66C3×#468—31no—
67#5168—31no—
68#5164—31no—
69#5134—31no—
70Dic3×M16—31no—
71#5065—31no—
72#5059—31no—
73#5052—31no—
74#5039—31no—
75#4889—31no—
76#4878—31no—
77#4817—31no—
78#4816—31no—
79#4812D311yescharacteristic, complemented
80#4800D311yescharacteristic, complemented
81#4789—31no—
82#4789—31no—
83#4789—61no—
84#4785—31no—
85#4785—31no—
86#4782—31no—
87#4780—31no—
88#4768—31no—
89#4757—31no—
90#4697—31no—
91C4×ΓL(1,𝔽25)—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×#634C2311yescharacteristic
94C2×C3×D12—21no—
95C2×C3×D12C2311yescharacteristic
96C2×C3×D12C2311yescharacteristic
97C2×C3×C4×D3C2311yescharacteristic
98C2×#625—21no—
99C2×D3×Dic3—21no—
100C2×D3×Dic3—21no—
101C2×D3×Dic3D411yescharacteristic
102C2×D3×Dic3D411yescharacteristic
103C2×C32×C8C2311yescharacteristic
104C32×C4⋊C4C2311yescharacteristic
105#3756—22no—
106C4⋊(C3⋊Dic3)—21no—
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108#3750—21no—
109C4×C3⋊Dic3—21no—
110C4×C3⋊Dic3—21no—
111C4×C3⋊Dic3C2311yescharacteristic
112C2×C3⋊(C3⋊C8)C2311yescharacteristic
113C3×#215—22no—
114C3×(C2×D3)⋊C4—21no—
115C3×(C2×D3)⋊C4—21no—
116C3×(C2×D3)⋊C4—21no—
117C3×(C2×D3)⋊C4—21no—
118C3×C4⋊Dic3—21no—
119C3×C4⋊Dic3C2311yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×Dic3⋊C4—21no—
122C3×Dic3⋊C4—21no—
123C3×C4×Dic3C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C3×ΓL(1,𝔽25)—22no—
127#3724—21no—
128Dic3⋊Dic3—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—
135(C2×D3)⋊Dic3—21no—
136Dic32D411yescharacteristic
137Dic32D411yescharacteristic
138#3716—22no—
139#3713—22no—
140#3711—22no—
141#3183—91noSylow
142C2×C3×SD16—31no—
143C2×C3×M16—31no—
144C3×#125—31no—
145C3×#124—31no—
146C3×C22⋊Q8—31no—
147C3×#121—31no—
148#947C2×D311yescharacteristic
149#946C2×D311yescharacteristic
150Q8×Dic3—31no—
151Q8×Dic3—31no—
152Q8×Dic3—61no—
153C2×#216—31no—
154C2×#216—31no—
155C2×#216—61no—
156C2×#215C2×D311yescharacteristic
157#938—31no—
158#936—31no—
159#935—61no—
160D4×Dic3—31no—
161D4×Dic3—31no—
162D4×Dic3—61no—
163C2×#214—31no—
164C2×#213—31no—
165C2×#213—31no—
166#930—31no—
167#924—31no—
168C2×C4×Dic3—31no—
169C2×#208—31no—
170C2×#204—31no—
171C2×ΓL(1,𝔽25)—31no—
172C2×ΓL(1,𝔽25)C2×D311yescharacteristic
173#898—61no—
174#898—61no—
175#897—31no—
176#895C2×D311yescharacteristic
177#894—61no—
178#893—31no—
179#893—31no—
180#893—61no—
181#892—61no—
182#892—61no—
183#890—31no—
184#890C2×D311yescharacteristic
185#887—31no—
186#887—31no—
187#887—61no—
188#886—61no—
189#883—61no—
190#67⋊C4—61no—
191#67⋊C4—61no—
192#879—61no—
193#879—61no—
194#877—61no—
195#877—61no—
196#875—31no—
197C42×D3—31no—
198#870—31no—
199C3×#107—31no—
200C3×#103—21no—
201C3×#103—31no—
202C3×#103C2×D311yescharacteristic
203C3×#103C2×D311yescharacteristic
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×C4×C8—31no—
208#835C2×D311yescharacteristic
209#832—31no—
210#821—31no—
211#821C2×D311yescharacteristic
212#821C2×D311yescharacteristic
213#818—31no—
214#816—31no—
215#816—31no—
216#816—31no—
217#816—61no—
218#815—31no—
219#815—31no—
220#815—31no—
221#815—31no—
222#815—61no—
223C8×Dic3—31no—
224C8×Dic3C2×D311yescharacteristic
225#810—31no—
226#809C2×D311yescharacteristic
227#808—31no—
228#808—31no—
229#808—31no—
230#808—31no—
231#808—61no—
232#807—31no—
233#807C2×D311yescharacteristic
234C4×C3⋊C8—31no—
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3C2×D411yescharacteristic
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
246C2×C3⋊Dic3C2×D411yescharacteristic
247#634—21no—
248#634—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C3×D12—21no—
255C3×D12—21no—
256C3×D12—21no—
257C3×D12—21no—
258C3×D12—42no—
259C3×C4×D3—21no—
260C3×C4×D3—21no—
261#625—42no—
262D3×Dic3—41no—
263D3×Dic3—41no—
264D3×Dic3—42no—
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—31no—
279#468—91no—
280#442—91no—
281#441—91no—
282#440—91no—
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—
290C2×C3×D4—61no—
291C22×C3×C4—31no—
292C2×#67—61no—
293C2×#67—61no—
294C22×Dic3—31no—
295C22×Dic3—31no—
296C22×Dic3—61no—
297C22×Dic3—61no—
298C2×D12—21no—
299C2×D12C22×D311yescharacteristic
300C2×D12C22×D311yescharacteristic
301C2×C4×D3—31no—
302C2×C4×D3—31no—
303C2×C4×D3—61no—
304C2×C4×D3—61no—
305C2×C4×D3C22×D311yescharacteristic
306C2×Dic6—31no—
307C2×Dic6—31no—
308C2×Dic6—61no—
309C3×SD16—62no—
310C3×M16—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×C22⋊C4—61no—
328C3×C42—31no—
329#217—61no—
330#217—61no—
331#217—61no—
332#217—61no—
333#217—61no—
334#217—61no—
335#216—62no—
336#216—62no—
337#216—64no—
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—21no—
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—
352C4⋊Dic3—21no—
353C4⋊Dic3—31no—
354C4⋊Dic3—31no—
355C4⋊Dic3—61no—
356C4⋊Dic3—61no—
357C4⋊Dic3—61no—
358C4⋊Dic3—61no—
359C4⋊Dic3—61no—
360C4⋊Dic3—121no—
361C4⋊Dic3C22×D311yescharacteristic
362C4⋊Dic3C22×D311yescharacteristic
363Dic3⋊C4—21no—
364Dic3⋊C4—21no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367Dic3⋊C4—61no—
368Dic3⋊C4—61no—
369Dic3⋊C4—61no—
370Dic3⋊C4—61no—
371Dic3⋊C4—121no—
372C4×Dic3—31no—
373C4×Dic3—31no—
374C4×Dic3—31no—
375C4×Dic3—31no—
376C4×Dic3—31no—
377C4×Dic3—31no—
378C4×Dic3—61no—
379C4×Dic3—61no—
380C4×Dic3—61no—
381C4×Dic3—61no—
382C4×Dic3—61no—
383C4×Dic3—121no—
384C4×Dic3—121no—
385C4×Dic3C22×D311yescharacteristic
386#208—62no—
387C2×C3⋊C8—31no—
388C2×C3⋊C8—31no—
389C2×C3⋊C8—61no—
390C2×C3⋊C8C22×D311yescharacteristic
391C2×C3⋊C8C22×D311yescharacteristic
392#204—62no—
393ΓL(1,𝔽25)—22no—
394ΓL(1,𝔽25)—62no—
395C22×C32C22×D411yescharacteristic
396C2×C3×D3—21no—
397C2×C3×D3—21no—
398C2×C3×D3—21no—
399C2×C3×D3—41no—
400C2×C3×D3—41no—
401C2×C3×D3—41no—
402C2×C3×D3—41no—
403C2×C3×D3—41no—
404C2×C3×D3—41no—
405C32×C4—41no—
406C32×C4—41no—
407C32×C4C2×#4111yescharacteristic
408C32×C4C2×#4111yescharacteristic
409C3⋊Dic3—21no—
410C3⋊Dic3—21no—
411C3⋊Dic3—41no—
412C3⋊Dic3—41no—
413C3×Dic3—21no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—41no—
417C3×Dic3—41no—
418C2×Q16—91no—
419C2×SD16—31no—
420C2×SD16—91no—
421C2×D8—91no—
422C2×M16—31no—
423C2×M16—91no—
424#126—181no—
425#126—181no—
426#125—31no—
427#125—91no—
428#124—31no—
429#124—91no—
430#123—181no—
431#123—181no—
432C22⋊Q8—31no—
433C22⋊Q8—91no—
434#121—31no—
435#121—91no—
436C4×Q8—91no—
437C4×Q8—91no—
438C4×D4—91no—
439C4×D4—91no—
440C4×D4—181no—
441C4×D4—181no—
442#117—181no—
443#117—181no—
444C2×C42—91no—
445#107—31no—
446#107—91no—
447#106—91no—
448#106—91no—
449#103—31no—
450#103—91no—
451#103—91no—
452#103D3211yescharacteristic
453#102—31no—
454#102—31no—
455#102—31no—
456#102—91no—
457#97—91no—
458#97—91no—
459C4×C8—31no—
460C4×C8—91no—
461C23×C3—31no—
462C23×C3—61no—
463C23×C3—61no—
464C22×D3—21no—
465C22×D3—21no—
466C22×D3D3×D411yescharacteristic
467C3×Q8—22no—
468C3×Q8—21no—
469C3×Q8—21no—
470C3×Q8—21no—
471C3×Q8—21no—
472C3×Q8—41no—
473C3×D4—61no—
474C3×D4—61no—
475C3×D4—61no—
476C3×D4—61no—
477C3×D4—122no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—31no—
484C2×C3×C4—31no—
485C2×C3×C4—31no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—61no—
489C2×C3×C4—61no—
490C2×C3×C4—61no—
491C2×C3×C4—61no—
492C2×C3×C4C23×D311yescharacteristic
493C2×C3×C4C23×D311yescharacteristic
494#67—122no—
495#67—122no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—31no—
499C2×Dic3—31no—
500C2×Dic3—31no—
501C2×Dic3—31no—
502C2×Dic3—61no—
503C2×Dic3—61no—
504C2×Dic3—61no—
505C2×Dic3—61no—
506C2×Dic3—61no—
507C2×Dic3—61no—
508C2×Dic3—121no—
509C2×Dic3—121no—
510C2×Dic3—121no—
511C2×Dic3—121no—
512C2×Dic3—122no—
513C2×Dic3—122no—
514C2×Dic3D3×D411yescharacteristic
515C2×Dic3D3×D411yescharacteristic
516C2×Dic3D3×D411yescharacteristic
517D12—21no—
518D12—21no—
519D12—21no—
520D12—21no—
521D12—42no—
522C4×D3—21no—
523C4×D3—21no—
524C4×D3—121no—
525C4×D3—121no—
526C4×D3—122no—
527C4×D3—122no—
528Dic6—62no—
529Dic6—61no—
530Dic6—61no—
531Dic6—61no—
532Dic6—61no—
533Dic6—121no—
534C3×C8—21no—
535C3×C8—21no—
536C3×C8—32no—
537C3×C8—41no—
538C3×C8—61no—
539C3⋊C8—21no—
540C3⋊C8—32no—
541C3⋊C8—32no—
542C3⋊C8—62no—
543C3⋊C8#23712yes—
544C2×C32#53211yescharacteristic
545C2×C32#57511yescharacteristic
546C2×C32#57511yescharacteristic
547C3×D3—41no—
548C3×D3—81no—
549C3×D3—81no—
550C2×Q8—91no—
551C2×Q8C2×D3211yescharacteristic
552C2×D4—31no—
553C2×D4—31no—
554C2×D4—61no—
555C2×D4—181no—
556C22×C4—31no—
557C22×C4—91no—
558C22×C4—91no—
559C22×C4—181no—
560C22×C4—181no—
561Q16—182no—
562SD16—62no—
563SD16—182no—
564D8—182no—
565M16—62no—
566M16—182no—
567C2×C8—31no—
568C2×C8—31no—
569C2×C8—91no—
570C2×C8C2×D3211yescharacteristic
571C4⋊C4—31no—
572C4⋊C4—31no—
573C4⋊C4—61no—
574C4⋊C4—61no—
575C4⋊C4—61no—
576C4⋊C4—91no—
577C4⋊C4—181no—
578C4⋊C4—181no—
579C4⋊C4—181no—
580C4⋊C4—181no—
581C4⋊C4—181no—
582C4⋊C4C2×D3211yescharacteristic
583C22⋊C4—61no—
584C22⋊C4—61no—
585C22⋊C4—61no—
586C22⋊C4—61no—
587C22⋊C4—181no—
588C22⋊C4—181no—
589C22⋊C4—181no—
590C22⋊C4—181no—
591C22⋊C4—181no—
592C22⋊C4—181no—
593C42—31no—
594C42—91no—
595C42—91no—
596C42—91no—
597C42—181no—
598C42—181no—
599C22×C3—21no—
600C22×C3—61no—
601C22×C3—61no—
602C22×C3—61no—
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—21no—
612C2×D3—21no—
613C2×D3—21no—
614C2×D3—41no—
615C2×D3—41no—
616C2×D3—41no—
617C2×D3—41no—
618C2×D3—41no—
619C2×D3—41no—
620C3×C4—21no—
621C3×C4—21no—
622C3×C4—42no—
623C3×C4—41no—
624C3×C4—41no—
625C3×C4—41no—
626C3×C4—41no—
627C3×C4—61no—
628C3×C4—61no—
629C3×C4—61no—
630C3×C4—81no—
631C3×C4—121no—
632C3×C4—121no—
633C3×C4C2×#23711yescharacteristic
634C3×C4D3×#4111yescharacteristic
635C3×C4D3×#4111yescharacteristic
636C3×C4D3×#4111yescharacteristic
637Dic3—21no—
638Dic3—21no—
639Dic3—21no—
640Dic3—41no—
641Dic3—41no—
642Dic3—61no—
643Dic3—61no—
644Dic3—61no—
645Dic3—61no—
646Dic3—121no—
647Dic3—121no—
648Dic3—122no—
649Dic3—121no—
650Dic3—121no—
651Dic3—121no—
652Dic3—121no—
653Dic3—241no—
654C32#318311yescharacteristic, complemented, Sylow
655C23—31no—
656C23—61no—
657C23—61no—
658Q8—21no—
659Q8—21no—
660Q8—181no—
661Q8—181no—
662D4—61no—
663D4—61no—
664D4—61no—
665D4—61no—
666D4—122no—
667D4—362no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—31no—
671C2×C4—31no—
672C2×C4—31no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—61no—
677C2×C4—91no—
678C2×C4—91no—
679C2×C4—181no—
680C2×C4—181no—
681C2×C4—361no—
682C2×C4—361no—
683C2×C4—362no—
684C2×C4—362no—
685C2×C4C22×D3211yescharacteristic
686C8—21no—
687C8—32no—
688C8—61no—
689C8—92no—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—21no—
693C2×C3—121no—
694C2×C3—241no—
695C2×C3—241no—
696C2×C3#559611yescharacteristic
697C2×C3#566811yescharacteristic
698C2×C3#576811yescharacteristic
699C2×C3#576811yescharacteristic
700C2×C3#577311yescharacteristic
701C2×C3#577711yescharacteristic
702D3—41no—
703D3—81no—
704D3—81no—
705C22—61no—
706C22—61no—
707C22—61no—
708C22—121no—
709C22—121no—
710C22—121no—
711C22—121no—
712C22—121no—
713C22—121no—
714C22D32×D411yescharacteristic
715C4—41no—
716C4—41no—
717C4—61no—
718C4—61no—
719C4—61no—
720C4—121no—
721C4—121no—
722C4—181no—
723C4—181no—
724C4—361no—
725C4—361no—
726C4#6430611yescharacteristic
727C4D3×#23711yescharacteristic
728C3—21no—
729C3#8079111yescharacteristic, complemented
730C3#8163111yescharacteristic, complemented
731C2—121no—
732C2—241no—
733C2—241no—
734C2#1059406111yescharacteristic
735C2#1059474511yescharacteristic
736C2#1059476311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10590504C2
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. #10595377C2semidirect
2. #10594427C2semidirect
3. #10592488C2semidirect
4. C3×#4812C2semidirect
5. C3×#4800C2semidirect
6. #10591606C2semidirect
7. #10591598C2semidirect
8. #10591572C2semidirect
9. #10590863C2semidirect
10. #10590828C2semidirect
11. #10590741C2semidirect
12. Dic3×ΓL(1,𝔽25)C2semidirect
14. #10590461C2semidirect
15. #10590413C2semidirect
79. #4812D3semidirect
80. #4800D3semidirect
654. C32#3183semidirect
729. C3#80791semidirect
730. C3#81631semidirect

Maximal subgroups

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

subgroupindex
#105953772
#105944272
#105924882
C3×#48122
C3×#48002
#105916062
#105915982
#105915722
#105908632
#105908282
#105907412
Dic3×ΓL(1,𝔽25)2
#105905042
#105904612
#105904132
#816313
#807913