Finite Group Databasebeta

← #27386701

Subgroups — #27386701

Order 13568.

1178 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810618C211yesmaximal, characteristic
2C2×#16810618C211yesmaximal, characteristic
3C2×C4×C8×D53C211yesmaximal, characteristic, complemented
4#20277204C211yesmaximal, characteristic
5#20277196C211yesmaximal, characteristic, complemented
6#20275399C211yesmaximal, characteristic, complemented
7#20275398C211yesmaximal, characteristic, complemented
8#20275397C211yesmaximal, characteristic, complemented
9#20275396C211yesmaximal, characteristic, complemented
10#20275394C211yesmaximal, characteristic, complemented
11#20275393C211yesmaximal, characteristic, complemented
12#20275388C211yesmaximal, characteristic, complemented
13#20274430C211yesmaximal, characteristic, complemented
14#20274430C211yesmaximal, characteristic, complemented
15C53×#1933C211yesmaximal, characteristic, complemented
16C22×#11719949C2211yescharacteristic
17C22×C8×D53C2211yescharacteristic
18C22×C8×D53C2211yescharacteristic
19C2×#13133175C2211yescharacteristic
20C2×#13133175C2211yescharacteristic
21C2×#13133175C2211yescharacteristic
22C2×C42×D53C2211yescharacteristic
23#16810618—24no—
24#16810618C418yescomplemented
25C2×#13133141C2211yescharacteristic
26C2×#13133141C2211yescharacteristic
27C2×#13133139C2211yescharacteristic
28C2×#13133139C2211yescharacteristic
29C2×#13133137C2211yescharacteristic
30C2×#13133137C2211yescharacteristic
31C2×C4×#88322C2211yescharacteristic
32C2×C8×Dic53C2211yescharacteristic
33C2×C8×Dic53C2211yescharacteristic
34C4×C8×D53—24no—
35#16810530C2211yescharacteristic
36#16810525C2211yescharacteristic
37#16810524C2211yescharacteristic
38#16810522C2211yescharacteristic
39#16810521C2211yescharacteristic
40#16810519C2211yescharacteristic
41#16810501—21no—
42#16810501—21no—
43#16810497—21no—
44#16810494—21no—
45C4⋊C4×Dic53—21no—
46#16810474—21no—
47#16810470—21no—
48#16810470—21no—
49#16810386C2211yescharacteristic
50#16810386C2211yescharacteristic
51#16810385C2211yescharacteristic
52#16810385C2211yescharacteristic
53#16810385C2211yescharacteristic
54#16810385C2211yescharacteristic
55C2×#103×C53C2211yescharacteristic
56C2×#103×C53C2211yescharacteristic
57C2×C4×C8×C53C2211yescharacteristic
58C53×#391C2211yescharacteristic
59C53×#389C2211yescharacteristic
60C53×#340C2211yescharacteristic
61C53×#340C2211yescharacteristic
62C2×#11719949—22no—
63C2×#11719949—22no—
64C2×#11719949—22no—
65C2×#11719949—22no—
66C2×#11719949—22no—
67C2×#11719949C2×C414yes—
68C22×D212—21no—
69C22×D212C2311yescharacteristic
70C22×C4×D53—21no—
71C22×C4×D53D411yescharacteristic
72C22×C4×D53D411yescharacteristic
73C22×C4×D53C2311yescharacteristic
74C22×#88322C2311yescharacteristic
75C22×#88322C2311yescharacteristic
76C2×C8×D53—22no—
77C2×C8×D53—22no—
78C2×C8×D53—22no—
79C2×C8×D53—22no—
80C2×C8×D53C2×C414yes—
81C2×C8×D53D414yes—
82#13133175—22no—
83#13133175—22no—
84#13133175—22no—
85#13133175—22no—
86#13133175—22no—
87#13133175C2×C414yes—
88C2×C4⋊Dic53—21no—
89C2×C4⋊Dic53C2311yescharacteristic
90C2×C4⋊Dic53C2311yescharacteristic
91C2×C4⋊Dic53C2311yescharacteristic
92C2×#11719919—21no—
93C2×#11719919—21no—
94C2×#11719921—21no—
95C2×#11719921—21no—
96C2×#11719921—21no—
97C2×#11719921—21no—
98C2×#11719921—21no—
99C2×#11719921—21no—
100C2×#11719921—21no—
101C2×C4×Dic53—21no—
102C2×C4×Dic53—21no—
103C2×C4×Dic53—21no—
104C2×C4×Dic53D411yescharacteristic
105C2×C4×Dic53D411yescharacteristic
106C2×C4×Dic53C2311yescharacteristic
107C42×D53—22no—
108C42×D53—22no—
109#13133141—22no—
110#13133141C2×C414yescomplemented
111#13133139—22no—
112#13133139C2×C414yescomplemented
113#13133137—22no—
114#13133137C2×C414yescomplemented
115C4×#88322—22no—
116C8×Dic53—22no—
117C8×Dic53—22no—
118#13133124—21no—
119#13133124—21no—
120#13133124—21no—
121#13133124—21no—
122#13133124—21no—
123C22×Q8×C53C2311yescharacteristic
124C22×C8×C53C2311yescharacteristic
125C22×C8×C53C2311yescharacteristic
126C2×C4⋊C4×C53—21no—
127C2×C4⋊C4×C53C2311yescharacteristic
128C2×C4⋊C4×C53C2311yescharacteristic
129C2×C4⋊C4×C53C2311yescharacteristic
130C2×C42×C53C2311yescharacteristic
131#103×C53—22no—
132#103×C53C2×C414yescomplemented
133C4×C8×C53—22no—
134#95×C53—21no—
135#95×C53—21no—
136#95×C53—21no—
137C23×D53—21no—
138C23×D53C2×D411yescharacteristic
139C2×Q8×C53—21no—
140C2×Q8×C53—21no—
141C2×Q8×C53—21no—
142C2×Q8×C53—21no—
143C2×Q8×C53—21no—
144C2×Q8×C53C22×C412yes—
145C22×C4×C53—21no—
146C22×C4×C53—21no—
147C22×C4×C53—21no—
148C22×C4×C53—21no—
149C22×C4×C53C2×D411yescharacteristic
150C22×C4×C53C2×D411yescharacteristic
151C22×C4×C53C2411yescharacteristic
152C22×Dic53—21no—
153C22×Dic53—21no—
154C22×Dic53—21no—
155C22×Dic53C2×D411yescharacteristic
156C22×Dic53C2×D411yescharacteristic
157C22×Dic53C2×D411yescharacteristic
158#11719949—28no—
159#11719949—28no—
160#11719949—44no—
161#11719949—44no—
162C2×D212—21no—
163C2×D212—21no—
164C2×D212—21no—
165C2×D212—21no—
166C2×D212—24no—
167C2×D212—21no—
168C2×D212—42no—
169C2×D212—42no—
170C2×D212C22×C412yes—
171C2×C4×D53—22no—
172C2×C4×D53—22no—
173C2×C4×D53—22no—
174C2×C4×D53—22no—
175C2×C4×D53—22no—
176C2×C4×D53—22no—
177C2×C4×D53—24no—
178C2×C4×D53—42no—
179C2×C4×D53—42no—
180C2×C4×D53C22×C412yes—
181C2×C4×D53C2×D412yes—
182C2×C4×D53#4112yes—
183C2×C4×D53#4112yes—
184C2×C4×D53#4112yes—
185C2×C4×D53#4112yes—
186C2×C8×C53—21no—
187C2×C8×C53—21no—
188C2×C8×C53—21no—
189C2×C8×C53—21no—
190C2×C8×C53C22×C412yes—
191C2×C8×C53C2×D412yes—
192C4⋊C4×C53—21no—
193C4⋊C4×C53—21no—
194C4⋊C4×C53—21no—
195C4⋊C4×C53—21no—
196C4⋊C4×C53—21no—
197C4⋊C4×C53—42no—
198C4⋊C4×C53C22×C412yes—
199C42×C53—21no—
200C42×C53—21no—
201#11719921—24no—
202#11719921—42no—
203#11719921—42no—
204#11719921—42no—
205#11719921—42no—
206#11719921—42no—
207#11719921—42no—
208C4⋊Dic53—21no—
209C4⋊Dic53—21no—
210C4⋊Dic53—21no—
211C4⋊Dic53—21no—
212C4⋊Dic53—21no—
213C4⋊Dic53—42no—
214C4⋊Dic53C22×C412yes—
215#11719919—42no—
216#11719919—42no—
217C4×Dic53—21no—
218C4×Dic53—21no—
219C4×Dic53—24no—
220C4×Dic53—22no—
221C4×Dic53—22no—
222C4×Dic53—42no—
223C4×Dic53—42no—
224C2×#88322—21no—
225C2×#88322—21no—
226C2×#88322—21no—
227C2×#88322—21no—
228C2×#88322C22×C412yes—
229C2×#88322C2×D412yes—
230C8×D53—28no—
231C8×D53—28no—
232C23×C53C22×D411yescharacteristic
233C22×D53—21no—
234C22×D53—21no—
235C22×D53—21no—
236C22×D53—21no—
237C22×D53—22no—
238C22×D53—41no—
239C22×D53—41no—
240C22×D53—41no—
241C22×D53—41no—
242C22×D53—41no—
243C22×D53—41no—
244C22×D53C4×D412yes—
245C22×D53#12112yes—
246C22×D53#12412yes—
247Q8×C53—22no—
248Q8×C53—22no—
249Q8×C53—41no—
250Q8×C53—41no—
251C2×C4×C53—21no—
252C2×C4×C53—21no—
253C2×C4×C53—21no—
254C2×C4×C53—21no—
255C2×C4×C53—22no—
256C2×C4×C53—22no—
257C2×C4×C53—41no—
258C2×C4×C53—41no—
259C2×C4×C53—41no—
260C2×C4×C53—41no—
261C2×C4×C53—41no—
262C2×C4×C53—41no—
263C2×C4×C53—41no—
264C2×C4×C53—41no—
265C2×C4×C53—41no—
266C2×C4×C53—41no—
267C2×C4×C53#13512yes—
268C2×C4×C53#13512yes—
269C2×C4×C53C23×C411yescharacteristic
270C2×C4×C53C22×D411yescharacteristic
271C2×C4×C53C2×#4111yescharacteristic
272C2×C4×C53C2×#4111yescharacteristic
273C2×C4×C53C2×#4111yescharacteristic
274C2×C4×C53C2×#4111yescharacteristic
275C2×Dic53—21no—
276C2×Dic53—21no—
277C2×Dic53—21no—
278C2×Dic53—21no—
279C2×Dic53—22no—
280C2×Dic53—41no—
281C2×Dic53—41no—
282C2×Dic53—41no—
283C2×Dic53—41no—
284C2×Dic53—41no—
285C2×Dic53—41no—
286C2×Dic53—41no—
287C2×Dic53—41no—
288C2×Dic53C4×D412yes—
289C2×Dic53#12112yes—
290C2×Dic53#12412yes—
291C2×Dic53#13512yes—
292C2×Dic53#13512yes—
293D212—22no—
294D212—22no—
295D212—48no—
296D212—41no—
297D212—41no—
298C4×D53—28no—
299C4×D53—28no—
300C4×D53—48no—
301C4×D53#11714yes—
302C4×D53C4×D414yes—
303C4×D53#12314yes—
304C4×D53#12614yes—
305C8×C53—22no—
306C8×C53—22no—
307#88322—22no—
308#88322—22no—
309#21083—531nomaximal, Sylow
310C22×C53C2×C4×D411yescharacteristic
311C22×C53C2×#12111yescharacteristic
312C22×C53C2×#12411yescharacteristic
313C22×C53C2×#13511yescharacteristic
314C22×C53C2×#13511yescharacteristic
315C22×C53C2×#13511yescharacteristic
316C22×C53C2×#13511yescharacteristic
317C2×D53—22no—
318C2×D53—22no—
319C2×D53—22no—
320C2×D53—22no—
321C2×D53—22no—
322C2×D53—22no—
323C2×D53—42no—
324C2×D53—42no—
325C2×D53—42no—
326C2×D53—81no—
327C2×D53—81no—
328C2×D53—81no—
329C2×D53—81no—
330C2×D53#38814yes—
331C4×C53—22no—
332C4×C53—22no—
333C4×C53—42no—
334C4×C53—42no—
335C4×C53—81no—
336C4×C53—81no—
337C4×C53C2×#11711yescharacteristic
338C4×C53C2×C4×D411yescharacteristic
339C4×C53C2×#12311yescharacteristic
340C4×C53C2×#12611yescharacteristic
341Dic53—22no—
342Dic53—22no—
343Dic53—42no—
344Dic53—81no—
345Dic53—81no—
346Dic53#38814yes—
347C2×#416—531no—
348C2×#416—531no—
349C22×C4×C8—531no—
350#2297—531no—
351#2296—531no—
352#1934—531no—
353#1934—531no—
354#1934—531no—
355#1934—531no—
356#1933—531no—
357#1933—531no—
358#1933—531no—
359#1933D5311yescharacteristic, complemented
360#1735—531no—
361#1735—531no—
362C2×C53C2×#38811yescharacteristic
363C2×C53C4×#13511yescharacteristic
364C2×C53C4×#13511yescharacteristic
365C2×C53#305011yescharacteristic
366C2×C53#305011yescharacteristic
367C2×C53#313111yescharacteristic
368C2×C53#313111yescharacteristic
369D53—24no—
370D53—82no—
371C22×#41—531no—
372C23×C8—531no—
373C23×C8—531no—
374C2×#117—531no—
375C2×#117—531no—
376C2×#117—531no—
377C22×C42—531no—
378#416—538no—
379#416—1064no—
380C2×#103—531no—
381C2×#103—531no—
382C2×#103C2×D5311yescharacteristic
383C2×#103C2×D5311yescharacteristic
384C2×#102—531no—
385C2×#102—531no—
386C2×#102—531no—
387C2×#102—531no—
388C2×C4×C8—531no—
389C2×C4×C8—531no—
390C2×C4×C8—531no—
391C2×C4×C8—1064no—
392C2×C4×C8C2×D5311yescharacteristic
393#391—531no—
394#391C2×D5311yescharacteristic
395#390—531no—
396#390—531no—
397#389—531no—
398#389—531no—
399#389—531no—
400#389C2×D5311yescharacteristic
401#386—1061no—
402#386—1061no—
403#385—1061no—
404#385—1061no—
405C4×C4⋊C4—1061no—
406C4×C4⋊C4—1061no—
407C4×C22⋊C4—1061no—
408C4×C22⋊C4—1061no—
409#340—531no—
410#340—531no—
411#340—531no—
412#340—531no—
413#340—531no—
414#340—531no—
415#340C2×D5311yescharacteristic
416#340C2×D5311yescharacteristic
417C53#2108311yescharacteristic, complemented, Sylow
418C2×#41—534no—
419C2×#41—1062no—
420C2×#41—1062no—
421C2×#41—1062no—
422C2×#41—1062no—
423C2×#41—1062no—
424C22×Q8C22×D5311yescharacteristic
425C22×D4—531no—
426C22×D4—1061no—
427C23×C4—531no—
428C23×C4—531no—
429C23×C4—531no—
430C23×C4—1061no—
431C22×C8—531no—
432C22×C8—531no—
433C22×C8—534no—
434C22×C8—534no—
435C22×C8—1062no—
436C22×C8—1062no—
437C22×C8—1062no—
438C22×C8—1062no—
439C22×C8C22×D5311yescharacteristic
440C22×C8C22×D5311yescharacteristic
441#117—534no—
442#117—1062no—
443#117—1062no—
444#117—1062no—
445#117—1062no—
446#117—1062no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—531no—
449C2×C4⋊C4—531no—
450C2×C4⋊C4—531no—
451C2×C4⋊C4—1061no—
452C2×C4⋊C4—1061no—
453C2×C4⋊C4—1061no—
454C2×C4⋊C4C22×D5311yescharacteristic
455C2×C4⋊C4C22×D5311yescharacteristic
456C2×C4⋊C4C22×D5311yescharacteristic
457C2×C22⋊C4—1061no—
458C2×C22⋊C4—1061no—
459C2×C22⋊C4—1061no—
460C2×C22⋊C4—1061no—
461C2×C22⋊C4—1061no—
462C2×C22⋊C4—1061no—
463C2×C22⋊C4—1061no—
464C2×C42—531no—
465C2×C42—531no—
466C2×C42—531no—
467C2×C42—1062no—
468C2×C42—1062no—
469C2×C42—1061no—
470C2×C42—1061no—
471C2×C42—1061no—
472C2×C42C22×D5311yescharacteristic
473#103—22no—
474#103—534no—
475#103—1062no—
476#103C4×D5314yescomplemented
477#102—534no—
478#102—534no—
479#102—1062no—
480#102—1062no—
481C4×C8—22no—
482C4×C8—1062no—
483C4×C8—1062no—
484C4×C8—1062no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—1061no—
489#95—1061no—
490#95—1061no—
491#95—1061no—
492#95—1061no—
493C24—531no—
494C24—1061no—
495#41—1068no—
496#41—1068no—
497#41—2124no—
498#41—2124no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8C2×C4×D5312yes—
505C2×D4—532no—
506C2×D4—1064no—
507C2×D4—1061no—
508C2×D4—1061no—
509C2×D4—1061no—
510C2×D4—1061no—
511C2×D4—1061no—
512C2×D4—2122no—
513C2×D4—2122no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—531no—
519C22×C4—532no—
520C22×C4—532no—
521C22×C4—532no—
522C22×C4—532no—
523C22×C4—532no—
524C22×C4—532no—
525C22×C4—531no—
526C22×C4—531no—
527C22×C4—1062no—
528C22×C4—1062no—
529C22×C4—1064no—
530C22×C4—1062no—
531C22×C4—1062no—
532C22×C4—1062no—
533C22×C4—1062no—
534C22×C4—1061no—
535C22×C4—1061no—
536C22×C4—1061no—
537C22×C4—2122no—
538C22×C4—2122no—
539C22×C4D4×D5311yescharacteristic
540C22×C4D4×D5311yescharacteristic
541C22×C4C23×D5311yescharacteristic
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—532no—
547C2×C8—532no—
548C2×C8—1068no—
549C2×C8—1068no—
550C2×C8—1061no—
551C2×C8—1061no—
552C2×C8—1061no—
553C2×C8—1061no—
554C2×C8C2×C4×D5312yes—
555C2×C8D4×D5312yes—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—42no—
562C4⋊C4—532no—
563C4⋊C4—1061no—
564C4⋊C4—1061no—
565C4⋊C4—1061no—
566C4⋊C4—1061no—
567C4⋊C4—1061no—
568C4⋊C4—2122no—
569C4⋊C4—2122no—
570C4⋊C4—2122no—
571C4⋊C4C2×C4×D5312yes—
572C22⋊C4—1064no—
573C22⋊C4—2122no—
574C22⋊C4—2122no—
575C22⋊C4—2122no—
576C22⋊C4—2122no—
577C22⋊C4—2122no—
578C22⋊C4—2122no—
579C42—21no—
580C42—21no—
581C42—1062no—
582C42—1062no—
583C42—1064no—
584C42—1061no—
585C42—1061no—
586C42—2122no—
587C42—2122no—
588C23—532no—
589C23—532no—
590C23—532no—
591C23—1061no—
592C23—1061no—
593C23—1061no—
594C23—1061no—
595C23—1062no—
596C23—2121no—
597C23—2121no—
598C23—2121no—
599C23—2121no—
600C23—2121no—
601C23—2121no—
602C23C2×D4×D5311yescharacteristic
603Q8—22no—
604Q8—22no—
605Q8—41no—
606Q8—41no—
607D4—1062no—
608D4—1062no—
609D4—2128no—
610D4—2121no—
611D4—2121no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—532no—
629C2×C4—532no—
630C2×C4—532no—
631C2×C4—534no—
632C2×C4—534no—
633C2×C4—534no—
634C2×C4—534no—
635C2×C4—532no—
636C2×C4—532no—
637C2×C4—1068no—
638C2×C4—1068no—
639C2×C4—1061no—
640C2×C4—1061no—
641C2×C4—1061no—
642C2×C4—1061no—
643C2×C4—1062no—
644C2×C4—2128no—
645C2×C4—2121no—
646C2×C4—2121no—
647C2×C4—2121no—
648C2×C4—2121no—
649C2×C4—2121no—
650C2×C4—2121no—
651C2×C4—2121no—
652C2×C4—2121no—
653C2×C4#1313323812yes—
654C2×C4#1313324012yes—
655C2×C4C22×C4×D5311yescharacteristic
656C2×C4C2×D4×D5311yescharacteristic
657C2×C4#41×D5311yescharacteristic
658C2×C4#41×D5311yescharacteristic
659C2×C4#41×D5311yescharacteristic
660C2×C4#41×D5311yescharacteristic
661C8—22no—
662C8—22no—
663C8—1062no—
664C8—1062no—
665C22—534no—
666C22—1062no—
667C22—1062no—
668C22—1062no—
669C22—1062no—
670C22—1062no—
671C22—1062no—
672C22—4241no—
673C22—4241no—
674C22—4241no—
675C22—4241no—
676C22—2122no—
677C22—2122no—
678C22—2122no—
679C22C4×D4×D5311yescharacteristic
680C22#121×D5311yescharacteristic
681C22#124×D5311yescharacteristic
682C22#135×D5311yescharacteristic
683C22#135×D5311yescharacteristic
684C22C2×#1313323811yescharacteristic
685C22C2×#1313324011yescharacteristic
686C4—22no—
687C4—22no—
688C4—42no—
689C4—42no—
690C4—81no—
691C4—81no—
692C4—534no—
693C4—1062no—
694C4—1062no—
695C4—4241no—
696C4—4241no—
697C4—2122no—
698C4#117×D5311yescharacteristic
699C4C4×D4×D5311yescharacteristic
700C4#123×D5311yescharacteristic
701C4#126×D5311yescharacteristic
702C2—1064no—
703C2—4242no—
704C2#388×D5311yescharacteristic
705C2C4×#1313323811yescharacteristic
706C2C4×#1313324011yescharacteristic
707C2#2028429111yescharacteristic
708C2#2028429811yescharacteristic
709C2#2028503611yescharacteristic
710C2#2028503911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1933C2
socleC23×C53C22×D4
prime radicalC22×#11719949C22
cosocleC22×C4×C53C24
hypercenter#1933D53
hypocenterC53#21083
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1933

Complements

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

NH ≅ G/Ntype
3. C2×C4×C8×D53C2semidirect
5. #20277196C2semidirect
6. #20275399C2semidirect
7. #20275398C2semidirect
8. #20275397C2semidirect
9. #20275396C2semidirect
10. #20275394C2semidirect
11. #20275393C2semidirect
12. #20275388C2semidirect
13. #20274430C2semidirect
14. #20274430C2semidirect
15. C53×#1933C2semidirect
24. #16810618C4semidirect
110. #13133141C2×C4semidirect
112. #13133139C2×C4semidirect
114. #13133137C2×C4semidirect
132. #103×C53C2×C4semidirect
359. #1933D53semidirect
417. C53#21083semidirect
476. #103C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168106182
C2×C4×C8×D532
#202772042
#202771962
#202753992
#202753982
#202753972
#202753962
#202753942
#202753932
#202753882
#202744302
C53×#19332
#2108353