Finite Group Databasebeta

← #27385071

Subgroups — #27385071

Order 13568.

1550 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×Dic53C211yesmaximal, characteristic
2C2×#16810665C211yesmaximal, characteristic, complemented
3C2×#16810624C211yesmaximal, characteristic
4C2×#16810522C211yesmaximal, characteristic, complemented
5#20274985C212yesmaximal, complemented
6#20274978C212yesmaximal, complemented
7#20274971C212yesmaximal, complemented
8#20274964C212yesmaximal, complemented
9#20274434C211yesmaximal, characteristic, complemented
10#20274408C211yesmaximal, characteristic, complemented
11C2×C53×#417C211yesmaximal, characteristic
12C22×#11719917C2211yescharacteristic
13#41×Dic53—24no—
14#41×Dic53—24no—
15C2×Q8×Dic53C2211yescharacteristic
16C2×Q8×Dic53C2211yescharacteristic
17C2×D4×Dic53—21no—
18C2×D4×Dic53—21no—
19C2×D4×Dic53C2211yescharacteristic
20C2×D4×Dic53C2211yescharacteristic
21C2×#13133176—21no—
22C2×#13133176C2211yescharacteristic
23C22×C4⋊Dic53—21no—
24C22×C4⋊Dic53C2211yescharacteristic
25C22×C4×Dic53—21no—
26C22×C4×Dic53C2211yescharacteristic
27#16810665—24no—
28C2×#13133151C2212yes—
29C2×#13133149C2212yes—
30#16810624—24no—
31C2×#13133141C2212yes—
32C2×#13133138C2212yes—
33#16810522—21no—
34#16810522—21no—
35#16810522C2212yes—
36#16810522C2212yes—
37C2×#13133124—21no—
38#16810385C2212yes—
39#16810385C2212yes—
40#16810377C2212yes—
41#16810377C2212yes—
42C22×#41×C53C2211yescharacteristic
43C22×M16×C53C2211yescharacteristic
44C22×C4⋊C4×C53C2211yescharacteristic
45C53×#417C418yescomplemented
46C2×#103×C53C2212yes—
47C2×#102×C53C2212yes—
48C23×Dic53—21no—
49C23×Dic53—21no—
50C23×Dic53—21no—
51C23×Dic53D411yescharacteristic
52C23×Dic53D411yescharacteristic
53C2×#11719917—22no—
54C2×#11719917—22no—
55C2×#11719917—22no—
56C22×#88322C2312yes—
57Q8×Dic53—22no—
58Q8×Dic53—22no—
59Q8×Dic53—22no—
60Q8×Dic53—22no—
61D4×Dic53—28no—
62D4×Dic53—28no—
63D4×Dic53—22no—
64D4×Dic53—22no—
65D4×Dic53—22no—
66D4×Dic53—22no—
67#13133176—28no—
68#13133176—22no—
69#13133176D414yes—
70C2×C4⋊Dic53—21no—
71C2×C4⋊Dic53—21no—
72C2×C4⋊Dic53—21no—
73C2×C4⋊Dic53—22no—
74C2×C4⋊Dic53—22no—
75C2×C4⋊Dic53—22no—
76C2×C4⋊Dic53—22no—
77C2×C4⋊Dic53—44no—
78C2×C4⋊Dic53C2312yes—
79C2×C4⋊Dic53C2311yescharacteristic
80C2×C4⋊Dic53C2311yescharacteristic
81C2×C22⋊Dic53—21no—
82C2×C22⋊Dic53—21no—
83C2×C22⋊Dic53—21no—
84C2×C4×Dic53—28no—
85C2×C4×Dic53—21no—
86C2×C4×Dic53—22no—
87C2×C4×Dic53—22no—
88C2×C4×Dic53—21no—
89C2×C4×Dic53—21no—
90C2×C4×Dic53D411yescharacteristic
91C2×C4×Dic53D411yescharacteristic
92C2×C4×Dic53C2311yescharacteristic
93C2×C4×Dic53C2311yescharacteristic
94#13133151—24no—
95#13133149—24no—
96#13133141—24no—
97#13133138—24no—
98#13133124—22no—
99#13133124—22no—
100C2×#41×C53—22no—
101C2×#41×C53—22no—
102C2×#41×C53—22no—
103C2×#41×C53C2×C414yes—
104C2×#41×C53D414yes—
105C2×#41×C53Q814yes—
106C22×Q8×C53C2311yescharacteristic
107C22×D4×C53—21no—
108C22×D4×C53C2311yescharacteristic
109C23×C4×C53—21no—
110C23×C4×C53—21no—
111C23×C4×C53C2311yescharacteristic
112C2×M16×C53—22no—
113C2×M16×C53—22no—
114C2×M16×C53C2×C414yescomplemented
115C22×C8×C53C2312yes—
116C2×C4⋊C4×C53—21no—
117C2×C4⋊C4×C53—22no—
118C2×C4⋊C4×C53C2×C414yescomplemented
119C2×C4⋊C4×C53C2312yes—
120#103×C53C2×C418yescomplemented
121#102×C53C2×C418yescomplemented
122C24×C53—21no—
123C24×C53C2×D411yescharacteristic
124#41×C53—28no—
125#41×C53—28no—
126#41×C53—28no—
127#41×C53C4⋊C4116yescomplemented
128C2×Q8×C53—21no—
129C2×Q8×C53—21no—
130C2×Q8×C53—21no—
131C2×Q8×C53C22×C412yes—
132C2×Q8×C53C2×D412yes—
133C2×Q8×C53C2×Q812yes—
134C2×D4×C53—24no—
135C2×D4×C53—24no—
136C2×D4×C53—24no—
137C2×D4×C53—21no—
138C2×D4×C53—21no—
139C2×D4×C53—21no—
140C2×D4×C53C22×C412yes—
141C2×D4×C53C2×D412yes—
142C2×D4×C53C2×Q812yes—
143C22×C4×C53—21no—
144C22×C4×C53—24no—
145C22×C4×C53—24no—
146C22×C4×C53—24no—
147C22×C4×C53—24no—
148C22×C4×C53—22no—
149C22×C4×C53—42no—
150C22×C4×C53—42no—
151C22×C4×C53C22×C412yes—
152C22×C4×C53C2×D412yes—
153C22×C4×C53C2×D411yescharacteristic
154C22×C4×C53C2×D412yes—
155C22×C4×C53C2×Q812yes—
156C22×C4×C53#4112yes—
157C22×C4×C53#4112yes—
158C22×C4×C53C2411yescharacteristic
159C22×Dic53—24no—
160C22×Dic53—24no—
161C22×Dic53—22no—
162C22×Dic53—22no—
163C22×Dic53—21no—
164C22×Dic53—21no—
165C22×Dic53—22no—
166C22×Dic53—22no—
167C22×Dic53—22no—
168C22×Dic53—41no—
169C22×Dic53—41no—
170C22×Dic53—42no—
171C22×Dic53—42no—
172C22×Dic53—42no—
173C22×Dic53—42no—
174C22×Dic53—42no—
175C22×Dic53—42no—
176C22×Dic53—42no—
177C22×Dic53C2×D411yescharacteristic
178C22×Dic53C2×D411yescharacteristic
179C22×Dic53C2×D411yescharacteristic
180C22×Dic53C2×D411yescharacteristic
181M16×C53—28no—
182C2×C8×C53—22no—
183C2×C8×C53—22no—
184C2×C8×C53C22×C414yes—
185C4⋊C4×C53—24no—
186C4⋊C4×C53—22no—
187C4⋊C4×C53C22×C414yes—
188C22⋊Dic53—24no—
189C22⋊Dic53—24no—
190C22⋊Dic53—24no—
191C4⋊Dic53—24no—
192C4⋊Dic53—24no—
193C4⋊Dic53—21no—
194C4⋊Dic53—21no—
195C4⋊Dic53—22no—
196C4⋊Dic53—22no—
197C4⋊Dic53—44no—
198C4⋊Dic53—42no—
199C4⋊Dic53—44no—
200C4⋊Dic53C2×D412yes—
201C4⋊Dic53C2×D412yes—
202C4×Dic53—24no—
203C4×Dic53—24no—
204C4×Dic53—22no—
205C4×Dic53—24no—
206C4×Dic53—22no—
207C4×Dic53—21no—
208C4×Dic53—21no—
209C4×Dic53—21no—
210C4×Dic53—21no—
211#11719917—44no—
212C2×#88322—22no—
213C2×#88322—22no—
214C2×#88322—22no—
215C23×C53—21no—
216C23×C53—21no—
217C23×C53—21no—
218C23×C53—21no—
219C23×C53—22no—
220C23×C53—22no—
221C23×C53—22no—
222C23×C53—41no—
223C23×C53—41no—
224C23×C53—41no—
225C23×C53—41no—
226C23×C53C4×D412yes—
227C23×C53#12012yes—
228C23×C53C22⋊Q812yes—
229C23×C53C22×D411yescharacteristic
230Q8×C53—22no—
231Q8×C53—22no—
232Q8×C53—22no—
233Q8×C53C2×C4⋊C414yescomplemented
234D4×C53—216no—
235D4×C53—22no—
236D4×C53—22no—
237D4×C53—22no—
238D4×C53C2×C4⋊C414yescomplemented
239C2×C4×C53—22no—
240C2×C4×C53—22no—
241C2×C4×C53—22no—
242C2×C4×C53—216no—
243C2×C4×C53—24no—
244C2×C4×C53—48no—
245C2×C4×C53—42no—
246C2×C4×C53—42no—
247C2×C4×C53C2×C4⋊C414yes—
248C2×C4×C53C4×D414yes—
249C2×C4×C53C4×D412yes—
250C2×C4×C53#12012yes—
251C2×C4×C53C22⋊Q814yes—
252C2×C4×C53C22⋊Q812yes—
253C2×C4×C53#12314yes—
254C2×C4×C53C23×C411yescharacteristic
255C2×C4×C53C22×D411yescharacteristic
256C2×C4×C53C22×D411yescharacteristic
257C2×C4×C53C22×Q811yescharacteristic
258C2×C4×C53C2×#4111yescharacteristic
259C2×C4×C53C2×#4111yescharacteristic
260C2×Dic53—21no—
261C2×Dic53—21no—
262C2×Dic53—21no—
263C2×Dic53—21no—
264C2×Dic53—22no—
265C2×Dic53—22no—
266C2×Dic53—21no—
267C2×Dic53—21no—
268C2×Dic53—21no—
269C2×Dic53—21no—
270C2×Dic53—21no—
271C2×Dic53—21no—
272C2×Dic53—44no—
273C2×Dic53—44no—
274C2×Dic53—48no—
275C2×Dic53—48no—
276C2×Dic53—41no—
277C2×Dic53—41no—
278C2×Dic53—41no—
279C2×Dic53—41no—
280C2×Dic53—42no—
281C2×Dic53—42no—
282C2×Dic53—42no—
283C2×Dic53—84no—
284C2×Dic53AGL(1,ℤ/8)12yes—
285C2×Dic53#13712yes—
286C8×C53—24no—
287#88322—42no—
288#20875—531nomaximal, Sylow
289C22×C53—22no—
290C22×C53—22no—
291C22×C53—22no—
292C22×C53—22no—
293C22×C53—22no—
294C22×C53—22no—
295C22×C53—24no—
296C22×C53—42no—
297C22×C53—42no—
298C22×C53—42no—
299C22×C53—42no—
300C22×C53—42no—
301C22×C53—42no—
302C22×C53#38514yes—
303C22×C53C2×C4×D411yescharacteristic
304C22×C53C2×#12011yescharacteristic
305C22×C53C2×C22⋊Q811yescharacteristic
306C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
307C22×C53C2×#13711yescharacteristic
308C22×C53#57511yescharacteristic
309C22×C53#57511yescharacteristic
310C4×C53—24no—
311C4×C53—44no—
312C4×C53#38514yes—
313C4×C53C22×C4⋊C411yescharacteristic
314C4×C53C2×C4×D411yescharacteristic
315C4×C53C2×C22⋊Q811yescharacteristic
316C4×C53C2×#12311yescharacteristic
317Dic53—22no—
318Dic53—22no—
319Dic53—41no—
320Dic53—42no—
321Dic53—41no—
322Dic53—42no—
323Dic53—82no—
324C2×C4×#41—531no—
325C2×#428—531no—
326C2×#417—531no—
327C2×#417D5311yescharacteristic
328C2×#389—531no—
329#1865—532no—
330#1864—532no—
331#1863—532no—
332#1862—532no—
333#1736—531no—
334#1728—531no—
335C2×C53—24no—
336C2×C53—44no—
337C2×C53C2×#38511yescharacteristic
338C2×C53C4×AGL(1,ℤ/8)11yescharacteristic
339C2×C53C4×#13711yescharacteristic
340C2×C53#300611yescharacteristic
341C2×C53#300711yescharacteristic
342C2×C53#307911yescharacteristic
343C2×C53#308011yescharacteristic
344C22×#41C2×D5311yescharacteristic
345C22×M16—531no—
346C22×M16C2×D5311yescharacteristic
347C4×#41—1064no—
348C4×#41—1064no—
349C2×C4×Q8—531no—
350C2×C4×Q8—531no—
351C2×C4×D4—531no—
352C2×C4×D4—531no—
353C2×C4×D4—1061no—
354C2×C4×D4—1061no—
355C2×#117—531no—
356C2×#117—1061no—
357C22×C4⋊C4—531no—
358C22×C4⋊C4—1061no—
359C22×C4⋊C4C2×D5311yescharacteristic
360C22×C42—531no—
361C22×C42—1061no—
362#428—1064no—
363C2×#107—532no—
364C2×#106—532no—
365#417—1064no—
366#417Dic5318yescomplemented
367C2×#103—532no—
368C2×#103C2×D5312yes—
369C2×#102—532no—
370C2×#102C2×D5312yes—
371#389—532no—
372#389—532no—
373#389—1061no—
374#389—1061no—
375C2×#95—1061no—
376#340—532no—
377#340—532no—
378#336—532no—
379#336—532no—
380C53#2087511yescharacteristic, complemented, Sylow
381C2×#41—22no—
382C2×#41—22no—
383C2×#41—22no—
384C2×#41Dic10614yes—
385C2×#41D21214yes—
386C2×#41C2×Dic5314yes—
387C22×Q8C22×D5311yescharacteristic
388C22×D4—21no—
389C22×D4C22×D5311yescharacteristic
390C23×C4—21no—
391C23×C4—21no—
392C23×C4—531no—
393C23×C4—531no—
394C23×C4—1061no—
395C23×C4—1061no—
396C23×C4—1061no—
397C23×C4C22×D5311yescharacteristic
398C2×M16—22no—
399C2×M16—22no—
400C2×M16—1062no—
401C2×M16—1062no—
402C2×M16—1062no—
403C2×M16C2×Dic5314yescomplemented
404C22×C8—532no—
405C22×C8C22×D5312yes—
406C4×Q8—1062no—
407C4×Q8—1062no—
408C4×Q8—1062no—
409C4×Q8—1062no—
410C4×D4—1062no—
411C4×D4—1062no—
412C4×D4—1068no—
413C4×D4—1068no—
414C4×D4—1062no—
415C4×D4—1062no—
416#117—534no—
417#117—1068no—
418#117—1062no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—531no—
422C2×C4⋊C4—531no—
423C2×C4⋊C4—532no—
424C2×C4⋊C4—1061no—
425C2×C4⋊C4—1061no—
426C2×C4⋊C4—1062no—
427C2×C4⋊C4—1062no—
428C2×C4⋊C4—1062no—
429C2×C4⋊C4—1062no—
430C2×C4⋊C4—1061no—
431C2×C4⋊C4—2124no—
432C2×C4⋊C4C2×Dic5314yescomplemented
433C2×C4⋊C4C22×D5312yes—
434C2×C22⋊C4—1061no—
435C2×C22⋊C4—1061no—
436C2×C22⋊C4—1061no—
437C2×C42—531no—
438C2×C42—531no—
439C2×C42—531no—
440C2×C42—531no—
441C2×C42—1061no—
442C2×C42—1061no—
443C2×C42—1068no—
444C2×C42—1062no—
445C2×C42—1061no—
446C2×C42—1062no—
447#107—1064no—
448#106—1064no—
449#103—1064no—
450#103C2×Dic5318yescomplemented
451#102—1064no—
452#102C2×Dic5318yescomplemented
453#95—1062no—
454#95—1062no—
455C24—21no—
456C24D4×D5311yescharacteristic
457#41—28no—
458#41—28no—
459#41—28no—
460#41C4⋊Dic53116yescomplemented
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8C2×Dic10612yes—
465C2×Q8C2×D21212yes—
466C2×Q8C22×Dic5312yes—
467C2×D4—24no—
468C2×D4—24no—
469C2×D4—24no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4C2×Dic10612yes—
474C2×D4C2×D21212yes—
475C2×D4C22×Dic5312yes—
476C22×C4—21no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—22no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—531no—
485C22×C4—531no—
486C22×C4—531no—
487C22×C4—531no—
488C22×C4—1062no—
489C22×C4—1062no—
490C22×C4—1064no—
491C22×C4—1064no—
492C22×C4—1062no—
493C22×C4—1062no—
494C22×C4—1061no—
495C22×C4—1061no—
496C22×C4—1062no—
497C22×C4—2122no—
498C22×C4—2122no—
499C22×C4—2121no—
500C22×C4—2121no—
501C22×C4—2122no—
502C22×C4—2122no—
503C22×C4—2122no—
504C22×C4—2122no—
505C22×C4—2122no—
506C22×C4C2×Dic10612yes—
507C22×C4C2×D21212yes—
508C22×C4D4×D5311yescharacteristic
509C22×C4D4×D5312yes—
510C22×C4#1171994712yes—
511C22×C4#1171994712yes—
512C22×C4C22×Dic5312yes—
513C22×C4C23×D5311yescharacteristic
514M16—28no—
515M16—2124no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—1062no—
519C2×C8—1062no—
520C2×C8—1062no—
521C2×C8C22×Dic5314yes—
522C4⋊C4—24no—
523C4⋊C4—22no—
524C4⋊C4—532no—
525C4⋊C4—532no—
526C4⋊C4—1064no—
527C4⋊C4—1064no—
528C4⋊C4—1061no—
529C4⋊C4—1061no—
530C4⋊C4—1062no—
531C4⋊C4—1062no—
532C4⋊C4—2124no—
533C4⋊C4—2124no—
534C4⋊C4—2122no—
535C4⋊C4C22×Dic5314yes—
536C22⋊C4—1064no—
537C22⋊C4—1064no—
538C22⋊C4—1064no—
539C42—1064no—
540C42—1064no—
541C42—1062no—
542C42—1062no—
543C42—1064no—
544C42—1061no—
545C42—1061no—
546C42—1061no—
547C42—1061no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—22no—
553C23—22no—
554C23—22no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23D4×Dic5312yes—
560C23#1313318712yes—
561C23#1313319412yes—
562C23C2×D4×D5311yescharacteristic
563Q8—22no—
564Q8—22no—
565Q8—22no—
566Q8C2×C4⋊Dic5314yescomplemented
567D4—216no—
568D4—22no—
569D4—22no—
570D4—22no—
571D4C2×C4⋊Dic5314yescomplemented
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—216no—
576C2×C4—24no—
577C2×C4—48no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—532no—
581C2×C4—532no—
582C2×C4—1061no—
583C2×C4—1061no—
584C2×C4—1061no—
585C2×C4—1061no—
586C2×C4—1062no—
587C2×C4—1062no—
588C2×C4—1061no—
589C2×C4—1061no—
590C2×C4—1061no—
591C2×C4—1061no—
592C2×C4—1061no—
593C2×C4—1061no—
594C2×C4—4244no—
595C2×C4—2124no—
596C2×C4—2124no—
597C2×C4—2128no—
598C2×C4—2128no—
599C2×C4—2122no—
600C2×C4—2122no—
601C2×C4—2122no—
602C2×C4—2121no—
603C2×C4—2121no—
604C2×C4—2121no—
605C2×C4—2121no—
606C2×C4C2×C4⋊Dic5314yes—
607C2×C4D4×Dic5312yes—
608C2×C4D4×Dic5314yes—
609C2×C4#1313318712yes—
610C2×C4#1313319412yes—
611C2×C4#1313319414yes—
612C2×C4#1313320114yes—
613C2×C4C23×Dic5311yescharacteristic
614C2×C4C2×D4×D5311yescharacteristic
615C2×C4C22×D21211yescharacteristic
616C2×C4C22×Dic10611yescharacteristic
617C2×C4C2×#1171994711yescharacteristic
618C2×C4C2×#1171994711yescharacteristic
619C8—24no—
620C8—2122no—
621C22—22no—
622C22—22no—
623C22—22no—
624C22—22no—
625C22—22no—
626C22—22no—
627C22—24no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—42no—
633C22—42no—
634C22#1681049814yes—
635C22C2×D4×Dic5311yescharacteristic
636C22C2×#1313318711yescharacteristic
637C22C2×#1313319411yescharacteristic
638C22AGL(1,ℤ/8)×D5311yescharacteristic
639C22#137×D5311yescharacteristic
640C22#1681141911yescharacteristic
641C22#1681142211yescharacteristic
642C4—24no—
643C4—44no—
644C4—1062no—
645C4—1062no—
646C4—4242no—
647C4—2121no—
648C4—2122no—
649C4—2121no—
650C4—2122no—
651C4#1681049814yes—
652C4C22×C4⋊Dic5311yescharacteristic
653C4C2×D4×Dic5311yescharacteristic
654C4C2×#1313319411yescharacteristic
655C4C2×#1313320111yescharacteristic
656C2—24no—
657C2—44no—
658C2C2×#1681049811yescharacteristic
659C2AGL(1,ℤ/8)×Dic5311yescharacteristic
660C2#137×Dic5311yescharacteristic
661C2#2028396811yescharacteristic
662C2#2028397611yescharacteristic
663C2#2028452611yescharacteristic
664C2#2028453511yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#417C2
socleC23×C53C22×D4
prime radicalC22×#41×C53C22
cosocleC22×C4×C53C24
hypercenterC2×#417D53
hypocenterC53#20875
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×#16810665C2semidirect
4. C2×#16810522C2semidirect
5. #20274985C2semidirect
6. #20274978C2semidirect
7. #20274971C2semidirect
8. #20274964C2semidirect
9. #20274434C2semidirect
10. #20274408C2semidirect
45. C53×#417C4semidirect
114. C2×M16×C53C2×C4semidirect
118. C2×C4⋊C4×C53C2×C4semidirect
120. #103×C53C2×C4semidirect
121. #102×C53C2×C4semidirect
127. #41×C53C4⋊C4semidirect
233. Q8×C53C2×C4⋊C4semidirect
238. D4×C53C2×C4⋊C4semidirect
366. #417Dic53semidirect
380. C53#20875semidirect
403. C2×M16C2×Dic53semidirect
432. C2×C4⋊C4C2×Dic53semidirect
450. #103C2×Dic53semidirect
452. #102C2×Dic53semidirect
460. #41C4⋊Dic53semidirect
566. Q8C2×C4⋊Dic53semidirect
571. D4C2×C4⋊Dic53semidirect

Maximal subgroups

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

subgroupindex
C2×#41×Dic532
C2×#168106652
C2×#168106242
C2×#168105222
#202749852
#202749782
#202749712
#202749642
#202744342
#202744082
C2×C53×#4172
#2087553