Finite Group Databasebeta

← C3×#78928 #11864260

Subgroups — C3×#78928 #11864260

Order 1152.

1663 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1004C211yesmaximal, characteristic, complemented
2C22×C3×#213C211yesmaximal, characteristic, complemented
3C2×C3×#908C211yesmaximal, characteristic, complemented
4C3×#5525C211yesmaximal, characteristic, complemented
5C32×#418C211yesmaximal, characteristic, complemented
6C3×#5129C211yesmaximal, characteristic, complemented
7C3×#5002C211yesmaximal, characteristic, complemented
8C3×#4781C214yesmaximal, complemented
9C3×#4773C214yesmaximal, complemented
10C3×#3008—31nomaximal
11#78928C311yesmaximal, characteristic, direct product factor
12C22×C32×D4C2211yescharacteristic
13C22×C3×#67—22no—
14C3×#1004—24no—
15C3×#1004—24no—
16C2×C3×#237—21no—
17C2×C3×#237C2212yescomplemented
18C2×C3×D3×D4—21no—
19C2×C3×D3×D4C2212yescomplemented
20C2×C3×#235C2211yescharacteristic
21C2×C3×#235C2211yescharacteristic
22C22×C3×D12C2211yescharacteristic, complemented
23C2×C32×M16C2211yescharacteristic, complemented
24C32×#117C2211yescharacteristic, complemented
25C2×C3×#213—24no—
26C2×C3×#213C2214yescomplemented
27C22×C3×C3⋊C8C2211yescharacteristic, complemented
28C3×#908—24no—
29C2×C3×D24C2212yescomplemented
30C2×C3×#204C2212yescomplemented
31C3×#895C2214yescomplemented
32C3×#882—22no—
33C3×#875—21no—
34C3×#874—21no—
35C32×#102C2214yescomplemented
36C3×(C2×D3)⋊C8C2214yescomplemented
37C3×#810C2212yescomplemented
38C3×#809C2212yescomplemented
39C2×C3×H(5,𝔽2)—31no—
40C2×#1004C2×C311yescharacteristic, complemented
41C2×C3×AGL(1,ℤ/8)—31no—
42C22×C3×D8—31no—
43C3×#535—31no—
44C22×#213C2×C311yescharacteristic, complemented
45C2×#908C2×C311yescharacteristic, complemented
46#5525C2×C311yescharacteristic, complemented
47C3×#449—34no—
48C3×#447—34no—
49C3×#418—21no—
50C3×#418D311yescharacteristic, complemented
51C3×#418C2×C311yescharacteristic, complemented
52C3×#416—31no—
53C3×#408—31no—
54#5129C2×C311yescharacteristic, complemented
55#5002C2×C311yescharacteristic, complemented
56#4781C2×C314yescomplemented
57#4773C2×C314yescomplemented
58C24×C32—21no—
59C23×C3×D3—22no—
60C23×C3×D3—21no—
61C2×C32×D4—21no—
62C2×C32×D4—22no—
63C2×C32×D4D414yescomplemented
64C2×C32×D4C2312yes—
65C22×C32×C4C2311yescharacteristic
66C2×C3×#67—216no—
67C2×C3×#67—21no—
68C2×C3×#67—22no—
69C2×C3×#67—22no—
70C2×C3×#67D412yes—
71C22×C3×Dic3—22no—
72C3×#237—28no—
73C3×#237—24no—
74C3×#237—24no—
75C3×D3×D4—28no—
76C3×D3×D4—24no—
77C3×D3×D4—24no—
78C3×#235—22no—
79C3×#235—22no—
80C3×#235—22no—
81C3×#235D414yescomplemented
82C2×C3×D12—22no—
83C2×C3×D12—22no—
84C2×C3×D12—21no—
85C2×C3×D12—24no—
86C2×C3×D12D411yescharacteristic
87C2×C3×D12C2312yes—
88C2×C3×D12C2311yescharacteristic
89C2×C3×C4×D3—21no—
90C2×C3×C4×D3C2312yes—
91C2×C3×Dic6D411yescharacteristic
92C2×C3×Dic6C2311yescharacteristic
93C32×M16—22no—
94C2×C32×C8C2312yes—
95C32×C4⋊C4C2312yes—
96C32×C22⋊C4—21no—
97C32×C42—21no—
98C3×#213—28no—
99C3×(C2×D3)⋊C4—24no—
100C2×C3×C3⋊C8—22no—
101C2×C3×C3⋊C8C2312yes—
102C3×D24—24no—
103C3×#204—24no—
104#3008—31noSylow
105C3×H(5,𝔽2)—64no—
106C3×H(5,𝔽2)—64no—
107C2×C3×#41—31no—
108C2×C3×#41—32no—
109C2×C3×#41—31no—
110C2×C3×#41—61no—
111C22×C3×D4—21no—
112C22×C3×D4—32no—
113C22×C3×D4—31no—
114C22×C3×D4—61no—
115C22×C3×D4—62no—
116C22×C3×D4C2×D311yescharacteristic
117C22×C3×D4C22×C311yescharacteristic
118C22×#67—22no—
119#1004—24no—
120#1004—24no—
121C2×#237—21no—
122C2×#237C22×C312yescomplemented
123C2×D3×D4—21no—
124C2×D3×D4C22×C312yescomplemented
125C2×#235C22×C311yescharacteristic
126C2×#235C22×C311yescharacteristic
127C22×D12C22×C311yescharacteristic, complemented
128C3×AGL(1,ℤ/8)—64no—
129C2×C3×SD16—32no—
130C2×C3×D8—34no—
131C2×C3×D8—32no—
132C2×C3×D8—64no—
133C2×C3×M16—21no—
134C2×C3×M16C2×D311yescharacteristic, complemented
135C2×C3×M16C22×C311yescharacteristic, complemented
136C22×C3×C8—31no—
137C3×#127—61no—
138C3×#124—61no—
139C3×#121—34no—
140C3×#120—62no—
141C3×#117—21no—
142C3×#117C2×D311yescharacteristic, complemented
143C3×#117C22×C311yescharacteristic, complemented
144C2×#213—24no—
145C2×#213C22×C314yescomplemented
146C22×C3⋊C8C22×C311yescharacteristic, complemented
147#908—24no—
148C2×D24C22×C312yescomplemented
149C2×#204C22×C312yescomplemented
150#895C22×C314yescomplemented
151#882—22no—
152#875—21no—
153#874—21no—
154C3×#103—32no—
155C3×#102—24no—
156C3×#102—32no—
157C3×#102C2×D314yescomplemented
158C3×#102C22×C314yescomplemented
159C3×C22⋊C8—34no—
160(C2×D3)⋊C8C22×C314yescomplemented
161#810C22×C312yescomplemented
162#809C22×C312yescomplemented
163C23×C32—22no—
164C23×C32—24no—
165C23×C32—82no—
166C23×C32C2×D411yescharacteristic
167C22×C3×D3—21no—
168C22×C3×D3—28no—
169C22×C3×D3—22no—
170C22×C3×D3—42no—
171C22×C3×D3—84no—
172C22×C3×D3—82no—
173C22×C3×D3C2×D412yes—
174C32×D4—24no—
175C32×D4—22no—
176C32×D4C2×D414yes—
177C2×C32×C4—22no—
178C2×C32×C4C2×D412yes—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2×D412yes—
181C2×C32×C4C2411yescharacteristic
182C3×#67—28no—
183C3×#67—28no—
184C3×#67—24no—
185C3×#67—24no—
186C2×C3×Dic3—28no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3C2×D412yes—
189C3×D12—22no—
190C3×D12—21no—
191C3×D12—22no—
192C3×D12—22no—
193C3×D12—42no—
194C3×D12—84no—
195C3×D12C2×D412yes—
196C3×C4×D3—24no—
197C3×C4×D3—22no—
198C3×C4×D3—22no—
199C3×Dic6—22no—
200C3×Dic6—21no—
201C3×Dic6C2×D412yes—
202C32×C8—22no—
203C3×C3⋊C8—22no—
204C2×H(5,𝔽2)—31no—
205C2×AGL(1,ℤ/8)—31no—
206C22×D8—31no—
207#535—31no—
208#449—34no—
209#447—34no—
210#418C3×D311yescharacteristic, complemented
211#416—31no—
212#408—31no—
213C24×C3—21no—
214C24×C3—21no—
215C24×C3—41no—
216C24×C3—62no—
217C24×C3—61no—
218C23×D3—22no—
219C23×D3—21no—
220C3×#41—34no—
221C3×#41—64no—
222C3×#41—68no—
223C3×#41—64no—
224C3×#41—62no—
225C3×#41—62no—
226C3×#41—62no—
227C2×C3×Q8—31no—
228C2×C3×Q8—31no—
229C2×C3×D4—21no—
230C2×C3×D4—22no—
231C2×C3×D4—21no—
232C2×C3×D4—22no—
233C2×C3×D4—24no—
234C2×C3×D4—22no—
235C2×C3×D4—32no—
236C2×C3×D4—31no—
237C2×C3×D4—31no—
238C2×C3×D4—32no—
239C2×C3×D4—41no—
240C2×C3×D4—42no—
241C2×C3×D4—64no—
242C2×C3×D4—62no—
243C2×C3×D4—64no—
244C2×C3×D4—68no—
245C2×C3×D4—62no—
246C2×C3×D4—616no—
247C2×C3×D4—61no—
248C2×C3×D4—64no—
249C2×C3×D4—62no—
250C2×C3×D4—62no—
251C2×C3×D4—61no—
252C2×C3×D4D1214yescomplemented
253C2×C3×D4C3×D414yescomplemented
254C2×C3×D4C22×D312yes—
255C2×C3×D4C23×C312yes—
256C22×C3×C4—21no—
257C22×C3×C4—32no—
258C22×C3×C4—62no—
259C22×C3×C4—61no—
260C22×C3×C4C22×D311yescharacteristic
261C22×C3×C4C23×C311yescharacteristic
262C2×#67—216no—
263C2×#67—21no—
264C2×#67—22no—
265C2×#67—22no—
266C2×#67C3×D412yes—
267C22×Dic3—22no—
268#237—28no—
269#237—24no—
270#237—24no—
271D3×D4—28no—
272D3×D4—24no—
273D3×D4—24no—
274#235—22no—
275#235—22no—
276#235—22no—
277#235C3×D414yescomplemented
278C2×D12—22no—
279C2×D12—22no—
280C2×D12—21no—
281C2×D12—24no—
282C2×D12C3×D411yescharacteristic
283C2×D12C23×C312yes—
284C2×D12C23×C311yescharacteristic
285C2×C4×D3—21no—
286C2×C4×D3C23×C312yes—
287C2×Dic6C3×D411yescharacteristic
288C2×Dic6C23×C311yescharacteristic
289C3×SD16—64no—
290C3×D8—64no—
291C3×D8—68no—
292C3×M16—22no—
293C3×M16—22no—
294C3×M16—42no—
295C2×C3×C8—22no—
296C2×C3×C8—32no—
297C2×C3×C8—62no—
298C2×C3×C8C22×D312yes—
299C2×C3×C8C23×C312yes—
300C3×C4⋊C4—22no—
301C3×C4⋊C4C22×D312yes—
302C3×C4⋊C4C23×C312yes—
303C3×C22⋊C4—21no—
304C3×C22⋊C4—21no—
305C3×C22⋊C4—41no—
306C3×C22⋊C4—64no—
307C3×C42—21no—
308C3×C42—21no—
309C3×C42—41no—
310#213—28no—
311(C2×D3)⋊C4—24no—
312C2×C3⋊C8—22no—
313C2×C3⋊C8C23×C312yes—
314D24—24no—
315#204—24no—
316C22×C32—22no—
317C22×C32—24no—
318C22×C32—44no—
319C22×C32—84no—
320C22×C32#12012yes—
321C22×C32C22×D411yescharacteristic
322C2×C3×D3—22no—
323C2×C3×D3—22no—
324C2×C3×D3—24no—
325C2×C3×D3—42no—
326C2×C3×D3—42no—
327C2×C3×D3—44no—
328C2×C3×D3—88no—
329C2×C3×D3—84no—
330C32×C4—42no—
331C32×C4#12012yes—
332C32×C4C22×D411yescharacteristic
333C32×C4C22×D411yescharacteristic
334C3×Dic3—22no—
335C3×Dic3—22no—
336H(5,𝔽2)—64no—
337H(5,𝔽2)—64no—
338C2×#41—31no—
339C2×#41—32no—
340C2×#41—31no—
341C2×#41—61no—
342C22×D4—32no—
343C22×D4—31no—
344C22×D4—61no—
345C22×D4—62no—
346C22×D4C2×C3×D311yescharacteristic
347AGL(1,ℤ/8)—64no—
348C2×SD16—32no—
349C2×D8—34no—
350C2×D8—32no—
351C2×D8—64no—
352C2×M16C2×C3×D311yescharacteristic, complemented
353C22×C8—31no—
354#127—61no—
355#124—61no—
356#121—34no—
357#120—62no—
358#117C2×C3×D311yescharacteristic, complemented
359#103—32no—
360#102—32no—
361#102C2×C3×D314yescomplemented
362C22⋊C8—34no—
363C23×C3—22no—
364C23×C3—22no—
365C23×C3—24no—
366C23×C3—24no—
367C23×C3—21no—
368C23×C3—32no—
369C23×C3—42no—
370C23×C3—44no—
371C23×C3—68no—
372C23×C3—61no—
373C23×C3—62no—
374C23×C3—82no—
375C23×C3—82no—
376C23×C3—84no—
377C23×C3—122no—
378C23×C3—242no—
379C23×C3—244no—
380C23×C3D3×D411yescharacteristic
381C23×C3C2×C3×D411yescharacteristic
382C22×D3—21no—
383C22×D3—28no—
384C22×D3—22no—
385C22×D3—42no—
386C22×D3—84no—
387C22×D3—82no—
388C22×D3C2×C3×D412yes—
389C3×Q8—32no—
390C3×Q8—62no—
391C3×Q8—61no—
392C3×D4—24no—
393C3×D4—24no—
394C3×D4—22no—
395C3×D4—22no—
396C3×D4—24no—
397C3×D4—32no—
398C3×D4—44no—
399C3×D4—42no—
400C3×D4—68no—
401C3×D4—68no—
402C3×D4—64no—
403C3×D4—64no—
404C3×D4—62no—
405C3×D4—61no—
406C3×D4—62no—
407C3×D4—62no—
408C3×D4—122no—
409C3×D4—244no—
410C3×D4C2×D1214yes—
411C3×D4C2×C3×D414yes—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—21no—
415C2×C3×C4—22no—
416C2×C3×C4—21no—
417C2×C3×C4—22no—
418C2×C3×C4—32no—
419C2×C3×C4—42no—
420C2×C3×C4—68no—
421C2×C3×C4—61no—
422C2×C3×C4—64no—
423C2×C3×C4—62no—
424C2×C3×C4—62no—
425C2×C3×C4C2×D1212yes—
426C2×C3×C4D3×D411yescharacteristic
427C2×C3×C4D3×D412yes—
428C2×C3×C4C2×C3×D412yes—
429C2×C3×C4C2×C3×D411yescharacteristic
430C2×C3×C4C2×C3×D412yes—
431C2×C3×C4C23×D311yescharacteristic
432C2×C3×C4C24×C311yescharacteristic
433#67—28no—
434#67—28no—
435#67—24no—
436#67—24no—
437C2×Dic3—28no—
438C2×Dic3—21no—
439C2×Dic3C2×C3×D412yes—
440D12—22no—
441D12—21no—
442D12—22no—
443D12—22no—
444D12—42no—
445D12—84no—
446D12C2×C3×D412yes—
447C4×D3—24no—
448C4×D3—22no—
449C4×D3—22no—
450Dic6—22no—
451Dic6—21no—
452Dic6C2×C3×D412yes—
453C3×C8—22no—
454C3×C8—22no—
455C3×C8—42no—
456C3×C8—62no—
457C3⋊C8—22no—
458C2×C32—22no—
459C2×C32—44no—
460C2×C32C2×#12011yescharacteristic
461C2×C32#57612yes—
462C3×D3—42no—
463C3×D3—42no—
464C3×D3—82no—
465C24—21no—
466C24—62no—
467C24—61no—
468#41—34no—
469#41—64no—
470#41—68no—
471#41—64no—
472#41—62no—
473#41—62no—
474#41—62no—
475C2×Q8—31no—
476C2×Q8—31no—
477C2×D4—21no—
478C2×D4—22no—
479C2×D4—32no—
480C2×D4—31no—
481C2×D4—32no—
482C2×D4—31no—
483C2×D4—64no—
484C2×D4—62no—
485C2×D4—64no—
486C2×D4—68no—
487C2×D4—62no—
488C2×D4—616no—
489C2×D4—61no—
490C2×D4—64no—
491C2×D4—62no—
492C2×D4—62no—
493C2×D4—61no—
494C2×D4C3×D1214yescomplemented
495C2×D4C22×C3×D312yes—
496C22×C4—32no—
497C22×C4—62no—
498C22×C4—61no—
499C22×C4C22×C3×D311yescharacteristic
500SD16—64no—
501D8—64no—
502D8—68no—
503M16—22no—
504C2×C8—32no—
505C2×C8—62no—
506C2×C8C22×C3×D312yes—
507C4⋊C4C22×C3×D312yes—
508C22⋊C4—21no—
509C22⋊C4—64no—
510C42—21no—
511C22×C3—22no—
512C22×C3—22no—
513C22×C3—24no—
514C22×C3—24no—
515C22×C3—22no—
516C22×C3—21no—
517C22×C3—42no—
518C22×C3—44no—
519C22×C3—44no—
520C22×C3—44no—
521C22×C3—62no—
522C22×C3—62no—
523C22×C3—64no—
524C22×C3—84no—
525C22×C3—84no—
526C22×C3—84no—
527C22×C3—88no—
528C22×C3—122no—
529C22×C3—122no—
530C22×C3—124no—
531C22×C3—244no—
532C22×C3—248no—
533C22×C3#88212yes—
534C22×C3C3×#12012yes—
535C22×C3C2×D3×D411yescharacteristic
536C22×C3C22×C3×D411yescharacteristic
537C2×D3—24no—
538C2×D3—22no—
539C2×D3—22no—
540C2×D3—42no—
541C2×D3—44no—
542C2×D3—42no—
543C2×D3—88no—
544C2×D3—84no—
545C3×C4—22no—
546C3×C4—21no—
547C3×C4—21no—
548C3×C4—42no—
549C3×C4—42no—
550C3×C4—62no—
551C3×C4—62no—
552C3×C4—82no—
553C3×C4#88212yes—
554C3×C4C3×#12012yes—
555C3×C4C22×D1211yescharacteristic
556C3×C4C2×D3×D411yescharacteristic
557C3×C4C22×C3×D411yescharacteristic
558C3×C4C22×C3×D411yescharacteristic
559Dic3—22no—
560Dic3—22no—
561C32#300811yescharacteristic, complemented, Sylow
562C23—22no—
563C23—24no—
564C23—32no—
565C23—68no—
566C23—61no—
567C23—62no—
568C23—82no—
569C23—122no—
570C23—242no—
571C23—244no—
572C23C3×D3×D411yescharacteristic
573Q8—32no—
574Q8—62no—
575Q8—61no—
576D4—24no—
577D4—22no—
578D4—32no—
579D4—68no—
580D4—68no—
581D4—64no—
582D4—64no—
583D4—62no—
584D4—61no—
585D4—62no—
586D4—62no—
587D4—122no—
588D4—244no—
589D4C2×C3×D1214yes—
590C2×C4—22no—
591C2×C4—32no—
592C2×C4—68no—
593C2×C4—61no—
594C2×C4—64no—
595C2×C4—62no—
596C2×C4—62no—
597C2×C4C2×C3×D1212yes—
598C2×C4C3×D3×D411yescharacteristic
599C2×C4C3×D3×D412yes—
600C2×C4C23×C3×D311yescharacteristic
601C8—22no—
602C8—62no—
603C2×C3—22no—
604C2×C3—22no—
605C2×C3—21no—
606C2×C3—22no—
607C2×C3—42no—
608C2×C3—44no—
609C2×C3—44no—
610C2×C3—84no—
611C2×C3—122no—
612C2×C3—122no—
613C2×C3—242no—
614C2×C3C2×#88211yescharacteristic
615C2×C3#577412yes—
616C2×C3C2×C3×#12011yescharacteristic
617C2×C3C3×#57612yes—
618D3—42no—
619D3—42no—
620D3—82no—
621C22—22no—
622C22—24no—
623C22—44no—
624C22—62no—
625C22—62no—
626C22—64no—
627C22—84no—
628C22—122no—
629C22—122no—
630C22—124no—
631C22—244no—
632C22—248no—
633C22C3×#88212yes—
634C22C2×C3×D3×D411yescharacteristic
635C4—42no—
636C4—62no—
637C4—62no—
638C4C3×#88212yes—
639C4C22×C3×D1211yescharacteristic
640C4C2×C3×D3×D411yescharacteristic
641C3—21no—
642C3#7892811yescharacteristic, direct product factor
643C3C3×#300811yescharacteristic, complemented
644C2—22no—
645C2—44no—
646C2—122no—
647C2—122no—
648C2—242no—
649C2C2×C3×#88211yescharacteristic
650C2C3×#577412yes—
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#418C2
socleC22×C32C22×D4
hypercenterC3×#418D3
hypocenterC3C3×#3008
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#418

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1004C2semidirect
2. C22×C3×#213C2semidirect
3. C2×C3×#908C2semidirect
4. C3×#5525C2semidirect
5. C32×#418C2semidirect
6. C3×#5129C2semidirect
7. C3×#5002C2semidirect
8. C3×#4781C2semidirect
9. C3×#4773C2semidirect
11. #78928C3direct (N × H)
17. C2×C3×#237C22semidirect
19. C2×C3×D3×D4C22semidirect
22. C22×C3×D12C22semidirect
23. C2×C32×M16C22semidirect
24. C32×#117C22semidirect
26. C2×C3×#213C22semidirect
27. C22×C3×C3⋊C8C22semidirect
29. C2×C3×D24C22semidirect
30. C2×C3×#204C22semidirect
31. C3×#895C22semidirect
35. C32×#102C22semidirect
36. C3×(C2×D3)⋊C8C22semidirect
37. C3×#810C22semidirect
38. C3×#809C22semidirect
40. C2×#1004C2×C3semidirect
44. C22×#213C2×C3semidirect
45. C2×#908C2×C3semidirect
46. #5525C2×C3semidirect
50. C3×#418D3semidirect
51. C3×#418C2×C3semidirect
54. #5129C2×C3semidirect
55. #5002C2×C3semidirect
56. #4781C2×C3semidirect
57. #4773C2×C3semidirect
63. C2×C32×D4D4semidirect
81. C3×#235D4semidirect
122. C2×#237C22×C3semidirect
124. C2×D3×D4C22×C3semidirect
127. C22×D12C22×C3semidirect
134. C2×C3×M16C2×D3semidirect
135. C2×C3×M16C22×C3semidirect
142. C3×#117C2×D3semidirect
143. C3×#117C22×C3semidirect
145. C2×#213C22×C3semidirect
146. C22×C3⋊C8C22×C3semidirect
148. C2×D24C22×C3semidirect
149. C2×#204C22×C3semidirect
150. #895C22×C3semidirect
157. C3×#102C2×D3semidirect
158. C3×#102C22×C3semidirect
160. (C2×D3)⋊C8C22×C3semidirect
161. #810C22×C3semidirect
162. #809C22×C3semidirect
210. #418C3×D3semidirect
252. C2×C3×D4D12semidirect
253. C2×C3×D4C3×D4semidirect
277. #235C3×D4semidirect
352. C2×M16C2×C3×D3semidirect
358. #117C2×C3×D3semidirect
361. #102C2×C3×D3semidirect
494. C2×D4C3×D12semidirect
561. C32#3008semidirect
642. C3#78928direct (N × H)
643. C3C3×#3008semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10042
C22×C3×#2132
C2×C3×#9082
C3×#55252
C32×#4182
C3×#51292
C3×#50022
C3×#47812
C3×#47732
C3×#30083
#789283