Finite Group Databasebeta

← #30570385

Subgroups — #30570385

Order 15616.

1716 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21460230C211yesmaximal, characteristic, complemented
2#21459620C211yesmaximal, characteristic, complemented
3#21458732C214yesmaximal, complemented
4#21458723C212yesmaximal, complemented
5#21458671C212yesmaximal, complemented
6#21458575C214yesmaximal, complemented
7#21458542C212yesmaximal, complemented
8#21458473C212yesmaximal, complemented
9#21457108C214yesmaximal, complemented
10#21457017C211yesmaximal, characteristic, complemented
11#21456006C214yesmaximal, complemented
12#21455914C211yesmaximal, characteristic, complemented
13#21455820C211yesmaximal, characteristic
14#21454913C211yesmaximal, characteristic, complemented
15C61×#3231C211yesmaximal, characteristic, complemented
16#16840516—22no—
17#16840497C2212yescomplemented
18Q8×Dic122C2212yescomplemented
19#16840486C2212yescomplemented
20#16840485—21no—
21#16840473C2212yes—
22#16840472—21no—
23#16840472—22no—
24#16840468C2214yes—
25Q8×D244—21no—
26Q8×D244—21no—
27#16840427C2212yes—
28#16840427C2212yescomplemented
29#16840390C2212yes—
30#16840387—22no—
31#16840385C2214yes—
32#16840383—22no—
33#16840335—22no—
34#16840319C2211yescharacteristic
35#16840312C2211yescharacteristic
36C22⋊Q8×D61—22no—
37#16840236C2212yes—
38C2×C4×D244C2211yescharacteristic
39#16840172C2212yescomplemented
40#16840169C2214yescomplemented
41#16840166C2214yescomplemented
42#16840128C2212yescomplemented
43#16840123C2214yescomplemented
44#16840118C2214yescomplemented
45#16840095C2212yes—
46#16840086C2214yes—
47#16840076C2212yes—
48#16840071C2214yescomplemented
49#16840061C2214yescomplemented
50#16840055C2214yescomplemented
51#16840051C2214yes—
52#16840049C2212yescomplemented
53#16840043C2212yes—
54#16840041C2214yes—
55#16840041C2214yescomplemented
56#16840039C2212yes—
57#16840039C2212yescomplemented
58#16839980C2214yes—
59#16839980C2214yes—
60#16839964C2212yes—
61#16839958C2212yes—
62#16839912C2212yes—
63#16839898C2212yes—
64#16839892C2212yescomplemented
65#16839891C2214yescomplemented
66C8×Dic122C2212yescomplemented
67#16839873C2214yes—
68#16839865C2214yes—
69#16839860C2214yes—
70#16839847C2214yes—
71C4×D488C2212yes—
72C4×D488C2212yes—
73#16839844C2214yes—
74#16839820C2214yes—
75#16839819C2211yescharacteristic
76C61×#533C2211yescharacteristic
77C61×#533C2211yescharacteristic
78C61×#500C2211yescharacteristic, complemented
79C61×#498C2211yescharacteristic, complemented
80C61×#487C2211yescharacteristic, complemented
81C61×#487C2211yescharacteristic, complemented
82C61×#485C2214yes—
83C61×#479C2214yescomplemented
84C61×#431C2211yescharacteristic
85C2×#11758222—21no—
86C2×Q8×D61—22no—
87C2×Q8×D61—22no—
88C22×D244C2311yescharacteristic
89C22×C4×D61—21no—
90C2×#11758201C2314yes—
91C2×D488C2312yes—
92C2×D488C2312yes—
93#14519777—22no—
94#14519777—22no—
95#14519777D411yescharacteristic
96#14519777D411yescharacteristic
97#14519777C2311yescharacteristic
98#14519776—24no—
99#14519776C2314yes—
100#14519776C2314yes—
101#14519774C2311yescharacteristic
102#14519772—24no—
103#14519772—24no—
104#14519769—22no—
105#14519769D412yes—
106#14519768C2314yes—
107#14519766C2314yes—
108#14519765—22no—
109#14519765—21no—
110#14519763—24no—
111#14519762—24no—
112#14519759—24no—
113#14519757—22no—
114#14519757—22no—
115#14519757—24no—
116#14519757—24no—
117#14519756D412yes—
118#14519756D412yes—
119#14519755—24no—
120#14519755—24no—
121#14519755—24no—
122#14519755—24no—
123#14519754—24no—
124#14519753—22no—
125#14519753—22no—
126#14519753—24no—
127#14519751—21no—
128#14519751C2312yes—
129Q8×Dic61C2314yes—
130C4×Dic122—22no—
131C4×Dic122C2312yes—
132C4×Dic122C2312yes—
133C4×D244—21no—
134C4×D244—21no—
135C4×D244—21no—
136C4×D244—22no—
137C4×D244—22no—
138C4×D244—22no—
139C4×D244C2312yes—
140C4×D244C2312yes—
141C4×D244C2312yes—
142#14519739C2314yes—
143#14519739C2314yes—
144#14519739C2314yes—
145#14519736C2312yes—
146#14519735—22no—
147C2×C4⋊Dic61C2311yescharacteristic
148C4⋊C4×D61—22no—
149C4⋊C4×D61—24no—
150C2×#11758198—21no—
151C22⋊C4×D61—24no—
152#14519711C2312yes—
153#14519711C2312yes—
154#14519710C2314yes—
155#14519710C2314yes—
156#14519708C2314yes—
157C4⋊#92418C2312yes—
158#14519706C2314yes—
159#14519706C2314yes—
160#14519701C2314yes—
161#14519699C2312yes—
162#14519699C2312yes—
163#14519699C2312yes—
164#14519699C2312yes—
165#14519697C2314yes—
166#14519697C2314yes—
167#14519697C2314yes—
168C22⋊#92418C2312yes—
169#14519688C2312yes—
170#14519687C2314yes—
171C8×Dic61C2314yes—
172C4⋊Q8×C61C2311yescharacteristic
173C4⋊Q8×C61C2311yescharacteristic
174C4⋊Q8×C61C2311yescharacteristic
175C4⋊Q8×C61C2311yescharacteristic
176#125×C61—21no—
177#125×C61C2312yes—
178C22⋊Q8×C61—21no—
179C22⋊Q8×C61—21no—
180C22⋊Q8×C61—21no—
181C22⋊Q8×C61C2312yes—
182C4×Q8×C61—21no—
183C4×Q8×C61—21no—
184C4×Q8×C61—21no—
185C4×Q8×C61C2312yes—
186#117×C61—21no—
187#117×C61C2312yes—
188C2×C42×C61C2311yescharacteristic
189#107×C61C2314yes—
190#106×C61C2314yes—
191C4⋊C8×C61C2312yes—
192#103×C61C2314yes—
193#103×C61C2314yes—
194C22⋊C8×C61C2312yes—
195C4×C8×C61C2311yescharacteristic
196C4×C8×C61C2311yescharacteristic
197C23×D61—21no—
198C2×Q8×C61—21no—
199C2×Q8×C61—21no—
200C2×Q8×C61—21no—
201C2×Q8×C61C2412yes—
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2411yescharacteristic
205C2×C22⋊D61—22no—
206C22×Dic61—21no—
207Q8×D61—84no—
208Q8×D61—84no—
209#11758222—82no—
210C2×D244—21no—
211C2×D244—24no—
212C2×D244—21no—
213C2×D244—21no—
214C2×D244C2412yes—
215C2×D244C2412yes—
216C2×C4×D61—22no—
217C2×C4×D61—22no—
218C2×C4×D61—22no—
219C2×C4×D61—24no—
220C2×C4×D61—24no—
221C2×C4×D61—24no—
222C2×C4×D61—82no—
223C2×Dic122—21no—
224C2×Dic122—24no—
225C2×Dic122—24no—
226C2×Dic122C2×D412yes—
227C2×Dic122C2×D412yes—
228C2×C8×C61C2412yes—
229C2×C8×C61C2412yes—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—22no—
233C4⋊C4×C61—22no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—22no—
238C4⋊C4×C61—22no—
239C4⋊C4×C61C2412yes—
240C4⋊C4×C61C2412yes—
241C4⋊C4×C61C2412yes—
242C22⋊C4×C61—22no—
243C22⋊C4×C61—22no—
244C42×C61—22no—
245C42×C61—22no—
246C42×C61C2×D411yescharacteristic
247C42×C61C2×D411yescharacteristic
248C42×C61C2411yescharacteristic
249C42×C61C2411yescharacteristic
250C22⋊Dic61C2×D414yes—
251#11758201—28no—
252#11758198—22no—
253#11758198—22no—
254#11758198—22no—
255#11758198—22no—
256#11758198—24no—
257#11758198—24no—
258#11758198—24no—
259#11758198—24no—
260#11758198—24no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61—24no—
264C4⋊Dic61—24no—
265C4⋊Dic61C2×D412yes—
266C4⋊Dic61C2×D412yes—
267C4⋊Dic61C2×D412yes—
268C4⋊Dic61C2×D412yes—
269C4⋊Dic61C2412yes—
270C4⋊Dic61C2412yes—
271#11758196—24no—
272#11758196—24no—
273#11758196—24no—
274#11758196C2×D414yes—
275#11758196C2×D414yes—
276C4×Dic61—24no—
277C4×Dic61C2414yes—
278C2×#92418C2414yes—
279D488—24no—
280D488—24no—
281C23×C61C22×D411yescharacteristic
282C22×D61—22no—
283C22×D61—24no—
284C22×D61—22no—
285C22×D61—81no—
286C22×D61—81no—
287Q8×C61—24no—
288Q8×C61—42no—
289Q8×C61—42no—
290Q8×C61—81no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—41no—
298C2×C4×C61C22×D411yescharacteristic
299C2×C4×C61C22×D411yescharacteristic
300C2×C4×C61C22×D411yescharacteristic
301C2×C4×C61C22×D411yescharacteristic
302C2×C4×C61C22×D411yescharacteristic
303C2×C4×C61C2511yescharacteristic
304C22⋊D61—82no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—81no—
308C2×Dic61C22×D414yes—
309C2×Dic61C22×D414yes—
310D244—24no—
311D244—22no—
312D244—22no—
313D244—22no—
314D244—42no—
315D244—81no—
316D2442−1+414yes—
317C4×D61—44no—
318C4×D61—44no—
319C4×D61—84no—
320C4×D61—84no—
321C4×D61—84no—
322C4×D61—82no—
323Dic122—24no—
324Dic122—42no—
325Dic122—84no—
326Dic122—84no—
327Dic122—81no—
328C8×C61—22no—
329C8×C61—22no—
330#92418—24no—
331#61849—611nomaximal, Sylow
332C22×C61—21no—
333C22×C61—21no—
334C22×C61—21no—
335C22×C61C23×D411yescharacteristic
336C2×D61—24no—
337C2×D61—42no—
338C2×D61—42no—
339C2×D61—42no—
340C2×D61—42no—
341C2×D61—42no—
342C2×D61—84no—
343C4×C61—21no—
344C4×C61—21no—
345C4×C61—21no—
346C4×C61—21no—
347C4×C61—42no—
348C4×C61—42no—
349C4×C61—42no—
350C4×C61—42no—
351C4×C61#57612yes—
352C4×C61C2×2−1+412yes—
353Dic61—24no—
354Dic61—24no—
355Dic61—42no—
356Dic61—42no—
357#3550—611no—
358#3501—611no—
359#3385—614no—
360#3384—612no—
361Q8×D8—612no—
362#3370—614no—
363#3367—612no—
364#3360—612no—
365#3243—614no—
366#3235—611no—
367#3231D6111yescharacteristic, complemented
368#3118—614no—
369#3110—611no—
370#3100—611no—
371#2985—611no—
372C2×C61—41no—
373C2×C61#348611yescharacteristic
374C2×C61C2×#57611yescharacteristic
375C2×C61#358611yescharacteristic
376D61—44no—
377D61—82no—
378#563—1222no—
379#559—612no—
380Q82—612no—
381#556—612no—
382#556—1221no—
383#554—612no—
384#554—614no—
385#554—1222no—
386#554—1221no—
387D4×Q8—612no—
388D4×Q8—612no—
389D4×Q8—1221no—
390D4×Q8—1221no—
391#544—612no—
392#543—1222no—
393#542—614no—
394#542—1222no—
395#536—1222no—
396#533—611no—
397#533C2×D6111yescharacteristic
398#533C2×D6111yescharacteristic
399#532—611no—
400C2×C22⋊Q8—1222no—
401#518—612no—
402C2×C4×D4—611no—
403#501—612no—
404#501—614no—
405#500—614no—
406#500C2×D6111yescharacteristic, complemented
407#498C2×D6111yescharacteristic, complemented
408#490—612no—
409#489—614no—
410#488—614no—
411#487C2×D6111yescharacteristic, complemented
412#487C2×D6111yescharacteristic, complemented
413#485C2×D6114yes—
414#484—612no—
415#482—614no—
416#480—612no—
417#479—614no—
418#479C2×D6114yescomplemented
419#478—614no—
420#477—614no—
421#476—612no—
422#476—614no—
423#474—612no—
424#474—612no—
425#474—614no—
426#474—614no—
427#474—612no—
428#463—614no—
429#463—614no—
430#461—612no—
431#459—612no—
432#450—612no—
433#447—612no—
434#446—614no—
435#446—612no—
436C8×Q8—612no—
437#442—614no—
438#440—614no—
439#440—614no—
440C4×SD16—614no—
441C4×D8—614no—
442C4×D8—612no—
443C4×D8—612no—
444#433—614no—
445#432—611no—
446#431C2×D6111yescharacteristic
447C61#6184911yescharacteristic, complemented, Sylow
448C2×#41—1221no—
449C22×Q8—1222no—
450C22×Q8—1222no—
451C22×D4—611no—
452C23×C4—1221no—
453C2×SD16—614no—
454C2×D8—612no—
455C2×D8—612no—
456C4⋊Q8—614no—
457C4⋊Q8—614no—
458C4⋊Q8—611no—
459C4⋊Q8—611no—
460C4⋊Q8—611no—
461C4⋊Q8—1222no—
462C4⋊Q8—1222no—
463C4⋊Q8—1224no—
464C4⋊Q8C22×D6111yescharacteristic
465C4⋊Q8C22×D6111yescharacteristic
466C4⋊Q8C22×D6111yescharacteristic
467C4⋊Q8C22×D6111yescharacteristic
468#127—611no—
469#126—1224no—
470#126—1224no—
471#125—21no—
472#125—614no—
473#125—612no—
474#125—1222no—
475#125C22×D6112yes—
476#124—614no—
477#124—1222no—
478#124—1224no—
479#124—1221no—
480#123—1224no—
481#123—1224no—
482C22⋊Q8—21no—
483C22⋊Q8—21no—
484C22⋊Q8—21no—
485C22⋊Q8—612no—
486C22⋊Q8—612no—
487C22⋊Q8—1224no—
488C22⋊Q8—1224no—
489C22⋊Q8—1224no—
490C22⋊Q8—1224no—
491C22⋊Q8—1224no—
492C22⋊Q8—1224no—
493C22⋊Q8—1222no—
494C22⋊Q8—1222no—
495C22⋊Q8—1224no—
496C22⋊Q8—1222no—
497C22⋊Q8—1222no—
498C22⋊Q8—1224no—
499C22⋊Q8C22×D6112yes—
500#121—612no—
501#121—1221no—
502C4×Q8—21no—
503C4×Q8—21no—
504C4×Q8—21no—
505C4×Q8—612no—
506C4×Q8—612no—
507C4×Q8—614no—
508C4×Q8—1222no—
509C4×Q8C22×D6112yes—
510C4×D4—614no—
511C4×D4—614no—
512C4×D4—614no—
513C4×D4—612no—
514C4×D4—612no—
515C4×D4—612no—
516C4×D4—1222no—
517C4×D4—1222no—
518C4×D4—1222no—
519C4×D4—1221no—
520C4×D4—1221no—
521C4×D4—1221no—
522#117—21no—
523#117—612no—
524#117—1222no—
525#117C22×D6112yes—
526C2×C4⋊C4—611no—
527C2×C4⋊C4—1224no—
528C2×C4⋊C4—1222no—
529C2×C22⋊C4—1224no—
530C2×C22⋊C4—1221no—
531C2×C42C22×D6111yescharacteristic
532#107—612no—
533#107—612no—
534#107—614no—
535#107—614no—
536#107C22×D6114yes—
537#106—614no—
538#106C22×D6114yes—
539C4⋊C8—614no—
540C4⋊C8—614no—
541C4⋊C8—612no—
542C4⋊C8C22×D6112yes—
543#103—614no—
544#103C22×D6114yes—
545#103C22×D6114yes—
546#102—612no—
547#102—612no—
548#102—612no—
549#102—612no—
550#102—614no—
551#102—614no—
552#102—614no—
553C22⋊C8—612no—
554C22⋊C8C22×D6112yes—
555#97—614no—
556#97—612no—
557C4×C8—614no—
558C4×C8C22×D6111yescharacteristic
559C4×C8C22×D6111yescharacteristic
560C24—1221no—
561#41—4882no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—612no—
566C2×Q8—612no—
567C2×Q8—1224no—
568C2×Q8—1224no—
569C2×Q8—1221no—
570C2×Q8—4884no—
571C2×Q8—4884no—
572C2×Q8C23×D6112yes—
573C2×D4—612no—
574C2×D4—612no—
575C2×D4—1224no—
576C2×D4—1222no—
577C2×D4—1221no—
578C2×D4—1221no—
579C2×D4—1221no—
580C22×C4—1224no—
581C22×C4—1224no—
582C22×C4—1224no—
583C22×C4—1221no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—4882no—
588C22×C4D4×D6111yescharacteristic
589C22×C4D4×D6111yescharacteristic
590C22×C4C23×D6111yescharacteristic
591SD16—1228no—
592D8—1224no—
593D8—1224no—
594C2×C8—614no—
595C2×C8C23×D6112yes—
596C2×C8C23×D6112yes—
597C4⋊C4—22no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—22no—
603C4⋊C4—21no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—614no—
607C4⋊C4—612no—
608C4⋊C4—614no—
609C4⋊C4—612no—
610C4⋊C4—612no—
611C4⋊C4—612no—
612C4⋊C4—612no—
613C4⋊C4—612no—
614C4⋊C4—1224no—
615C4⋊C4—1224no—
616C4⋊C4—1224no—
617C4⋊C4—1224no—
618C4⋊C4—1224no—
619C4⋊C4—1221no—
620C4⋊C4—1221no—
621C4⋊C4C23×D6112yes—
622C4⋊C4C23×D6112yes—
623C4⋊C4C23×D6112yes—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—614no—
627C22⋊C4—1224no—
628C22⋊C4—1224no—
629C22⋊C4—1224no—
630C22⋊C4—1224no—
631C22⋊C4—1224no—
632C22⋊C4—1222no—
633C22⋊C4—1222no—
634C22⋊C4—1222no—
635C22⋊C4—1222no—
636C42—22no—
637C42—22no—
638C42—614no—
639C42—1224no—
640C42D4×D6111yescharacteristic
641C42D4×D6111yescharacteristic
642C42C23×D6111yescharacteristic
643C42C23×D6111yescharacteristic
644C23—1224no—
645C23—1222no—
646C23—1222no—
647C23—4881no—
648C23—4881no—
649C23C2×D4×D6111yescharacteristic
650Q8—24no—
651Q8—42no—
652Q8—42no—
653Q8—81no—
654Q8—1224no—
655Q8—4881no—
656Q8—4884no—
657Q8—4884no—
658Q8—2442no—
659D4—614no—
660D4—1224no—
661D4—1222no—
662D4—1222no—
663D4—1222no—
664D4—4881no—
665D4—4882no—
666D4—2442no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—41no—
674C2×C4—614no—
675C2×C4—614no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—4882no—
679C2×C4—4884no—
680C2×C4—4884no—
681C2×C4—4884no—
682C2×C4—4881no—
683C2×C4—2444no—
684C2×C4—2444no—
685C2×C4C2×D4×D6111yescharacteristic
686C2×C4C2×D4×D6111yescharacteristic
687C2×C4C2×D4×D6111yescharacteristic
688C2×C4C2×D4×D6111yescharacteristic
689C2×C4C2×D4×D6111yescharacteristic
690C2×C4C24×D6111yescharacteristic
691C8—22no—
692C8—22no—
693C8—1224no—
694C22—21no—
695C22—21no—
696C22—21no—
697C22—1224no—
698C22—4884no—
699C22—2442no—
700C22—2442no—
701C22—2442no—
702C22—2442no—
703C22—2442no—
704C22C22×D4×D6111yescharacteristic
705C4—21no—
706C4—21no—
707C4—21no—
708C4—21no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—42no—
713C4—1224no—
714C4—1224no—
715C4—2442no—
716C4—2442no—
717C4#1684056412yes—
718C42−1+4×D6112yes—
719C2—41no—
720C2—4882no—
721C2—2444no—
722C2#2145946811yescharacteristic
723C2C2×#1684056411yescharacteristic
724C2#2146060211yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3231C2
socleC22×C61C23×D4
prime radical#21455820C2
hypercenter#3231D61
hypocenterC61#61849
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3231

Complements

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

NH ≅ G/Ntype
1. #21460230C2semidirect
2. #21459620C2semidirect
3. #21458732C2semidirect
4. #21458723C2semidirect
5. #21458671C2semidirect
6. #21458575C2semidirect
7. #21458542C2semidirect
8. #21458473C2semidirect
9. #21457108C2semidirect
10. #21457017C2semidirect
11. #21456006C2semidirect
12. #21455914C2semidirect
14. #21454913C2semidirect
15. C61×#3231C2semidirect
17. #16840497C22semidirect
18. Q8×Dic122C22semidirect
19. #16840486C22semidirect
28. #16840427C22semidirect
39. #16840172C22semidirect
40. #16840169C22semidirect
41. #16840166C22semidirect
42. #16840128C22semidirect
43. #16840123C22semidirect
44. #16840118C22semidirect
48. #16840071C22semidirect
49. #16840061C22semidirect
50. #16840055C22semidirect
52. #16840049C22semidirect
55. #16840041C22semidirect
57. #16840039C22semidirect
64. #16839892C22semidirect
65. #16839891C22semidirect
66. C8×Dic122C22semidirect
78. C61×#500C22semidirect
79. C61×#498C22semidirect
80. C61×#487C22semidirect
81. C61×#487C22semidirect
83. C61×#479C22semidirect
367. #3231D61semidirect
406. #500C2×D61semidirect
407. #498C2×D61semidirect
411. #487C2×D61semidirect
412. #487C2×D61semidirect
418. #479C2×D61semidirect
447. C61#61849semidirect

Maximal subgroups

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

subgroupindex
#214602302
#214596202
#214587322
#214587232
#214586712
#214585752
#214585422
#214584732
#214571082
#214570172
#214560062
#214559142
#214558202
#214549132
C61×#32312
#6184961