Finite Group Databasebeta

← C2×#20253523 #27084387

Subgroups — C2×#20253523 #27084387

Order 12032.

2582 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689654C211yesmaximal, characteristic, complemented
2C22×#13093986C211yesmaximal, characteristic, complemented
3#20253523C2116yesmaximal, direct product factor
4C2×#15689453C211yesmaximal, characteristic, complemented
5C2×#15689426C212yesmaximal, complemented
6C2×#15689337C212yesmaximal, complemented
7C2×#15689276C211yesmaximal, characteristic, complemented
8C2×#15689256C211yesmaximal, characteristic
9C2×#15689232C212yesmaximal, complemented
10C2×#15689222C212yesmaximal, complemented
11C2×#15689177C211yesmaximal, characteristic, complemented
12C2×C47×#480C211yesmaximal, characteristic, complemented
13C23×D188C2211yescharacteristic
14C23×C4×D47—21no—
15C22×#10625325C2212yes—
16C22×#10625334C2212yes—
17#15689654—24no—
18#15689654C2218yescomplemented
19C2×#13094017—21no—
20C2×#13094015C2211yescharacteristic, complemented
21C2×#13094011C2211yescharacteristic, complemented
22C2×#13094005—21no—
23C2×#13094003C2211yescharacteristic
24C2×#13093989C2211yescharacteristic, complemented
25C2×D4×Dic47—21no—
26C2×D4×Dic47C2211yescharacteristic, complemented
27C2×#13093986—21no—
28C2×#13093986—21no—
29C2×#13093986—24no—
30C2×#13093986C2212yes—
31C2×#13093986C2212yes—
32C2×#13093986C2218yescomplemented
33C2×#13093980—21no—
34C22×(C2×D47)⋊C4—21no—
35C22×C4×Dic47C2211yescharacteristic
36#15689453C2218yescomplemented
37#15689426C22116yescomplemented
38#15689337C22116yescomplemented
39#15689276C2218yescomplemented
40#15689256C2218yes—
41#15689232C22116yescomplemented
42#15689222C22116yescomplemented
43#15689177C2218yescomplemented
44C2×#13093955C2212yescomplemented
45C2×Dic47⋊C8C2212yescomplemented
46C2×#13093947C2212yescomplemented
47C2×#13093946C2212yes—
48C2×#13093944C2212yes—
49C2×C22⋊(C47⋊C8)C2211yescharacteristic
50C2×#13093934C2212yescomplemented
51C2×#121×C47C2211yescharacteristic
52C22×C4⋊C4×C47C2211yescharacteristic
53C47×#480C2218yescomplemented
54C2×#107×C47C2212yescomplemented
55C2×#102×C47C2212yescomplemented
56C2×C22⋊C8×C47C2211yescharacteristic
57C24×D47—21no—
58C22×Dic94C2311yescharacteristic
59C22×D188—21no—
60C22×D188—22no—
61C22×D188—28no—
62C22×D188C2314yes—
63C22×D188C2312yes—
64C23×Dic47—21no—
65C23×Dic47D411yescharacteristic
66C23×Dic47D411yescharacteristic
67C22×C4×D47—22no—
68C22×C4×D47—22no—
69C22×C4×D47—28no—
70C22×C4×D47—48no—
71C2×#10625325—28no—
72C2×#10625325C2318yes—
73C2×#10625334—28no—
74C2×#10625334C2318yes—
75C22×C47⋊C8C2312yes—
76#13094017—28no—
77#13094015—22no—
78#13094015C2314yescomplemented
79#13094011—22no—
80#13094011C2314yescomplemented
81#13094005—28no—
82#13094003—22no—
83#13094003C2314yes—
84#13093989—22no—
85#13093989C2314yescomplemented
86D4×Dic47—28no—
87D4×Dic47—22no—
88D4×Dic47C2314yescomplemented
89#13093986—24no—
90#13093986—24no—
91#13093986—28no—
92#13093986—28no—
93#13093986C2318yes—
94#13093986C2318yes—
95#13093980—28no—
96C2×C4⋊Dic47—21no—
97C2×C4⋊Dic47C2311yescharacteristic
98C2×Dic47⋊C4—21no—
99C2×Dic47⋊C4—21no—
100C2×Dic47⋊C4—21no—
101C2×C22⋊Dic47—21no—
102C2×C22⋊Dic47—21no—
103C2×C22⋊Dic47—21no—
104C2×C22⋊Dic47—21no—
105C2×(C2×D47)⋊C4—22no—
106C2×(C2×D47)⋊C4—22no—
107C2×(C2×D47)⋊C4—28no—
108C2×C4×Dic47—21no—
109C2×C4×Dic47D411yescharacteristic
110C2×C4×Dic47D411yescharacteristic
111C2×C4×Dic47D414yes—
112C2×C4×Dic47C2311yescharacteristic
113C2×C4×Dic47C2311yescharacteristic
114C2×C4×Dic47C2314yes—
115#13093955C2318yescomplemented
116Dic47⋊C8C2318yescomplemented
117#13093947C2318yescomplemented
118#13093946C2318yes—
119#13093944C2318yes—
120C22⋊(C47⋊C8)C2314yes—
121#13093934C2318yescomplemented
122C22×D4×C47—21no—
123C22×D4×C47C2311yescharacteristic
124C23×C4×C47—21no—
125C23×C4×C47C2311yescharacteristic
126C22×C8×C47C2312yes—
127#121×C47—22no—
128#121×C47C2314yes—
129C2×C4⋊C4×C47—21no—
130C2×C4⋊C4×C47—22no—
131C2×C4⋊C4×C47C2314yes—
132C2×C4⋊C4×C47C2312yes—
133C2×C4⋊C4×C47C2311yescharacteristic
134C2×C22⋊C4×C47—21no—
135#107×C47C2318yescomplemented
136#102×C47C2318yescomplemented
137C22⋊C8×C47C2314yes—
138C24×C47—21no—
139C24×C47C2×D411yescharacteristic
140C23×D47—28no—
141C23×D47—24no—
142C23×D47—22no—
143C23×D47—44no—
144C23×D47—44no—
145C2×D4×C47—24no—
146C2×D4×C47—21no—
147C2×D4×C47—24no—
148C2×D4×C47—44no—
149C2×D4×C47C2412yes—
150C22×C4×C47—24no—
151C22×C4×C47—21no—
152C22×C4×C47—24no—
153C22×C4×C47—22no—
154C22×C4×C47—44no—
155C22×C4×C47C2×D411yescharacteristic
156C22×C4×C47C2×D412yes—
157C22×C4×C47C2412yes—
158C22×C4×C47C2411yescharacteristic
159C22×Dic47—24no—
160C22×Dic47—21no—
161C22×Dic47—21no—
162C22×Dic47—24no—
163C22×Dic47—42no—
164C22×Dic47—44no—
165C22×Dic47C2×D411yescharacteristic
166C22×Dic47C2×D411yescharacteristic
167C22×Dic47C2×D411yescharacteristic
168C22×Dic47C2×D411yescharacteristic
169C22×Dic47C2×D414yes—
170C22×Dic47C2×D414yes—
171C2×D188—28no—
172C2×D188—216no—
173C2×D188—24no—
174C2×D188—22no—
175C2×D188—24no—
176C2×D188—216no—
177C2×D188#4118yes—
178C2×D188C2414yes—
179C2×C4×D47—28no—
180C2×C4×D47—28no—
181C2×C4×D47—48no—
182C2×C4×D47—48no—
183C2×C4×D47—432no—
184C2×Dic94—24no—
185C2×Dic94—21no—
186C2×Dic94C2412yes—
187C2×C8×C47—24no—
188C2×C8×C47C2414yes—
189C4⋊C4×C47—24no—
190C4⋊C4×C47—22no—
191C4⋊C4×C47—21no—
192C4⋊C4×C47C2412yes—
193C4⋊C4×C47C2414yes—
194C22⋊C4×C47—24no—
195C22⋊Dic47—24no—
196C22⋊Dic47—24no—
197C22⋊Dic47—24no—
198C22⋊Dic47—24no—
199#10625334—216no—
200(C2×D47)⋊C4—28no—
201(C2×D47)⋊C4—28no—
202C4⋊Dic47—21no—
203C4⋊Dic47—24no—
204C4⋊Dic47C2412yes—
205Dic47⋊C4—24no—
206Dic47⋊C4—24no—
207Dic47⋊C4—24no—
208C4×Dic47—24no—
209C4×Dic47C2×D414yes—
210C4×Dic47C2×D412yes—
211C4×Dic47C2×D412yes—
212C4×Dic47C2×D414yes—
213C4×Dic47C2412yes—
214C4×Dic47C2412yes—
215C2×C47⋊C8—24no—
216C2×C47⋊C8C2414yes—
217#10625325—216no—
218C23×C47—22no—
219C23×C47—22no—
220C23×C47—22no—
221C23×C47—42no—
222C23×C47—42no—
223C23×C47—42no—
224C23×C47AGL(1,ℤ/8)14yes—
225C23×C47C22×D412yes—
226C23×C47C22×D411yescharacteristic
227C22×D47—216no—
228C22×D47—28no—
229C22×D47—24no—
230C22×D47—432no—
231C22×D47—48no—
232C22×D47—48no—
233C22×D47—44no—
234C22×D47—44no—
235D4×C47—24no—
236D4×C47—48no—
237D4×C47—42no—
238C2×C4×C47—22no—
239C2×C4×C47—24no—
240C2×C4×C47—24no—
241C2×C4×C47—22no—
242C2×C4×C47—24no—
243C2×C4×C47—48no—
244C2×C4×C47—44no—
245C2×C4×C47—42no—
246C2×C4×C47C22×D412yes—
247C2×C4×C47C22×D411yescharacteristic
248C2×C4×C47C2×#4114yes—
249C2×C4×C47C2511yescharacteristic
250C2×Dic47—28no—
251C2×Dic47—22no—
252C2×Dic47—22no—
253C2×Dic47—22no—
254C2×Dic47—22no—
255C2×Dic47—22no—
256C2×Dic47—22no—
257C2×Dic47—44no—
258C2×Dic47—48no—
259C2×Dic47—42no—
260C2×Dic47—42no—
261C2×Dic47C22×D412yes—
262C2×Dic47C22×D412yes—
263C2×Dic47C22×D412yes—
264C2×Dic47C22×D412yes—
265D188—216no—
266D188—28no—
267D188—24no—
268D188C2×#4118yes—
269C4×D47—416no—
270C4×D47—416no—
271Dic94—24no—
272Dic94—42no—
273C8×C47—24no—
274C47⋊C8—24no—
275C2×#3114—471nomaximal, Sylow
276C22×C47—28no—
277C22×C47—22no—
278C22×C47—22no—
279C22×C47—42no—
280C22×C47—42no—
281C22×C47—42no—
282C22×C47—84no—
283C22×C47#52512yes—
284C22×C47C2×AGL(1,ℤ/8)14yes—
285C22×C47C2×AGL(1,ℤ/8)12yes—
286C22×C47#57512yes—
287C22×C47C23×D411yescharacteristic
288C2×D47—28no—
289C2×D47—432no—
290C2×D47—416no—
291C2×D47—44no—
292C2×D47—44no—
293C4×C47—22no—
294C4×C47—44no—
295C4×C47—42no—
296C4×C47#52512yes—
297C4×C47C22×#4112yes—
298Dic47—22no—
299Dic47—22no—
300Dic47—22no—
301Dic47—22no—
302Dic47—42no—
303Dic47—42no—
304C2×#529—471no—
305C22×C4×D4—471no—
306#3114—4716no—
307C2×#483—471no—
308C2×#480D4711yescharacteristic, complemented
309C2×#478—472no—
310C2×#463—472no—
311C2×#450—471no—
312C2×#447—471no—
313C2×#442—472no—
314C2×#440—472no—
315C2×#432—471no—
316C2×C47—24no—
317C2×C47—82no—
318C2×C47#311414yescomplemented
319C2×C47C2×#52511yescharacteristic
320C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
321C2×C47C2×#57511yescharacteristic
322D47—48no—
323C23×D4—471no—
324C24×C4—941no—
325C22×SD16—472no—
326C22×D8—472no—
327#529—478no—
328#529—944no—
329C2×#126—941no—
330C2×#125—471no—
331C2×#124—471no—
332C2×#123—941no—
333C2×C22⋊Q8—471no—
334C2×#121C2×D4711yescharacteristic
335C2×C4×Q8—471no—
336C2×C4×D4—471no—
337C2×C4×D4—472no—
338C2×C4×D4—478no—
339C2×C4×D4—472no—
340C2×C4×D4—941no—
341C2×C4×D4—941no—
342C2×C4×D4—944no—
343C2×C4×D4—941no—
344C2×#117—941no—
345C22×C4⋊C4C2×D4711yescharacteristic
346C22×C22⋊C4—941no—
347C22×C42—471no—
348#483—478no—
349#480C2×D4718yescomplemented
350#478—4716no—
351#463—4716no—
352#450—478no—
353#447—478no—
354#442—4716no—
355#440—4716no—
356#432—478no—
357C2×#107C2×D4712yescomplemented
358C2×#106—472no—
359C2×C4⋊C8—472no—
360C2×#103—472no—
361C2×#102—472no—
362C2×#102—472no—
363C2×#102C2×D4712yescomplemented
364C2×C22⋊C8—471no—
365C2×C22⋊C8C2×D4711yescharacteristic
366C2×#97—472no—
367C47C2×#311411yescharacteristic, complemented, Sylow
368C25—941no—
369C22×Q8—471no—
370C22×D4—21no—
371C22×D4—472no—
372C22×D4—474no—
373C22×D4—948no—
374C22×D4—942no—
375C22×D4—941no—
376C22×D4C22×D4711yescharacteristic
377C23×C4—21no—
378C23×C4—471no—
379C23×C4—471no—
380C23×C4—948no—
381C23×C4—942no—
382C23×C4—942no—
383C23×C4—941no—
384C23×C4—1888no—
385C23×C4C22×D4711yescharacteristic
386C2×SD16—478no—
387C2×SD16—948no—
388C2×D8—478no—
389C2×D8—948no—
390C22×C8—472no—
391C22×C8C22×D4712yes—
392#126—948no—
393#125—474no—
394#125—942no—
395#124—474no—
396#124—942no—
397#123—948no—
398C22⋊Q8—474no—
399C22⋊Q8—942no—
400#121—22no—
401#121C22×D4714yes—
402C4×Q8—474no—
403C4×Q8—942no—
404C4×D4—474no—
405C4×D4—478no—
406C4×D4—478no—
407C4×D4—948no—
408C4×D4—944no—
409C4×D4—944no—
410C4×D4—948no—
411C4×D4—942no—
412C4×D4—948no—
413#117—948no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—471no—
417C2×C4⋊C4—941no—
418C2×C4⋊C4—941no—
419C2×C4⋊C4—941no—
420C2×C4⋊C4—941no—
421C2×C4⋊C4C22×D4712yes—
422C2×C4⋊C4C22×D4714yes—
423C2×C4⋊C4C22×D4711yescharacteristic
424C2×C22⋊C4—21no—
425C2×C22⋊C4—948no—
426C2×C22⋊C4—942no—
427C2×C22⋊C4—942no—
428C2×C22⋊C4—941no—
429C2×C22⋊C4—941no—
430C2×C22⋊C4—941no—
431C2×C22⋊C4—941no—
432C2×C42—471no—
433C2×C42—471no—
434C2×C42—474no—
435C2×C42—471no—
436C2×C42—471no—
437C2×C42—474no—
438C2×C42—941no—
439#107C22×D4718yescomplemented
440#106—478no—
441C4⋊C8—478no—
442#103—478no—
443#102—478no—
444#102—478no—
445#102C22×D4718yescomplemented
446C22⋊C8—474no—
447C22⋊C8C22×D4714yes—
448#97—478no—
449C24—21no—
450C24—948no—
451C24—944no—
452C24—942no—
453C24—1884no—
454C24—1884no—
455C24D4×D4711yescharacteristic
456C2×Q8—472no—
457C2×Q8—941no—
458C2×Q8—944no—
459C2×D4—24no—
460C2×D4—21no—
461C2×D4—24no—
462C2×D4—44no—
463C2×D4—478no—
464C2×D4—474no—
465C2×D4—9416no—
466C2×D4—948no—
467C2×D4—9416no—
468C2×D4—944no—
469C2×D4—942no—
470C2×D4—944no—
471C2×D4C23×D4712yes—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—44no—
477C22×C4—474no—
478C22×C4—471no—
479C22×C4—471no—
480C22×C4—471no—
481C22×C4—471no—
482C22×C4—474no—
483C22×C4—948no—
484C22×C4—948no—
485C22×C4—944no—
486C22×C4—944no—
487C22×C4—941no—
488C22×C4—941no—
489C22×C4—18832no—
490C22×C4—1888no—
491C22×C4—1888no—
492C22×C4—1882no—
493C22×C4—1884no—
494C22×C4D4×D4712yes—
495C22×C4D4×D4711yescharacteristic
496C22×C4C23×D4712yes—
497C22×C4C23×D4711yescharacteristic
498SD16—9416no—
499D8—9416no—
500C2×C8—24no—
501C2×C8—474no—
502C2×C8—944no—
503C2×C8C23×D4714yes—
504C4⋊C4—24no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—472no—
508C4⋊C4—944no—
509C4⋊C4—944no—
510C4⋊C4—944no—
511C4⋊C4—944no—
512C4⋊C4—941no—
513C4⋊C4C23×D4712yes—
514C4⋊C4C23×D4714yes—
515C22⋊C4—24no—
516C22⋊C4—948no—
517C22⋊C4—948no—
518C22⋊C4—944no—
519C22⋊C4—944no—
520C22⋊C4—944no—
521C22⋊C4—944no—
522C42—474no—
523C42—472no—
524C42—472no—
525C42—474no—
526C42—472no—
527C42—472no—
528C42—944no—
529C23—22no—
530C23—22no—
531C23—22no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—9416no—
536C23—948no—
537C23—944no—
538C23—18832no—
539C23—1888no—
540C23—1888no—
541C23—1884no—
542C23—1884no—
543C23#1309404814yes—
544C23C2×D4×D4712yes—
545C23C2×D4×D4711yescharacteristic
546Q8—944no—
547Q8—1882no—
548D4—24no—
549D4—48no—
550D4—42no—
551D4—478no—
552D4—9416no—
553D4—948no—
554D4—944no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—48no—
561C2×C4—44no—
562C2×C4—42no—
563C2×C4—472no—
564C2×C4—472no—
565C2×C4—472no—
566C2×C4—472no—
567C2×C4—948no—
568C2×C4—942no—
569C2×C4—942no—
570C2×C4—942no—
571C2×C4—942no—
572C2×C4—942no—
573C2×C4—942no—
574C2×C4—18816no—
575C2×C4—18816no—
576C2×C4—1884no—
577C2×C4—1888no—
578C2×C4—1882no—
579C2×C4—1882no—
580C2×C4C2×D4×D4712yes—
581C2×C4C2×D4×D4711yescharacteristic
582C2×C4#41×D4714yes—
583C2×C4C24×D4711yescharacteristic
584C8—24no—
585C8—944no—
586C22—28no—
587C22—22no—
588C22—22no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—84no—
593C22—948no—
594C22—18832no—
595C22—1884no—
596C22—18816no—
597C22—1884no—
598C22#1568963112yes—
599C22C2×#1309404814yes—
600C22C2×#1309404812yes—
601C22#1568992212yes—
602C22C22×D4×D4711yescharacteristic
603C4—22no—
604C4—44no—
605C4—42no—
606C4—942no—
607C4—942no—
608C4—942no—
609C4—942no—
610C4—1882no—
611C4—1882no—
612C4#1568963112yes—
613C4C2×#41×D4712yes—
614C2—24no—
615C2—82no—
616C2—1888no—
617C2#2025352314yesdirect product factor
618C2C2×#1568963111yescharacteristic
619C2C22×#1309404811yescharacteristic
620C2C2×#1568992211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#480C2
socleC23×C47C22×D4
prime radicalC2×#15689256C2
hypercenterC2×#480D47
hypocenterC47C2×#3114
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
1. C2×#15689654C2semidirect
2. C22×#13093986C2semidirect
3. #20253523C2direct (N × H)
4. C2×#15689453C2semidirect
5. C2×#15689426C2semidirect
6. C2×#15689337C2semidirect
7. C2×#15689276C2semidirect
9. C2×#15689232C2semidirect
10. C2×#15689222C2semidirect
11. C2×#15689177C2semidirect
12. C2×C47×#480C2semidirect
18. #15689654C22semidirect
20. C2×#13094015C22semidirect
21. C2×#13094011C22semidirect
24. C2×#13093989C22semidirect
26. C2×D4×Dic47C22semidirect
32. C2×#13093986C22semidirect
36. #15689453C22semidirect
37. #15689426C22semidirect
38. #15689337C22semidirect
39. #15689276C22semidirect
41. #15689232C22semidirect
42. #15689222C22semidirect
43. #15689177C22semidirect
44. C2×#13093955C22semidirect
45. C2×Dic47⋊C8C22semidirect
46. C2×#13093947C22semidirect
50. C2×#13093934C22semidirect
53. C47×#480C22semidirect
54. C2×#107×C47C22semidirect
55. C2×#102×C47C22semidirect
78. #13094015C23semidirect
80. #13094011C23semidirect
85. #13093989C23semidirect
88. D4×Dic47C23semidirect
115. #13093955C23semidirect
116. Dic47⋊C8C23semidirect
117. #13093947C23semidirect
121. #13093934C23semidirect
135. #107×C47C23semidirect
136. #102×C47C23semidirect
308. C2×#480D47semidirect
318. C2×C47#3114semidirect
349. #480C2×D47semidirect
357. C2×#107C2×D47semidirect
363. C2×#102C2×D47semidirect
367. C47C2×#3114semidirect
439. #107C22×D47semidirect
445. #102C22×D47semidirect
617. C2#20253523direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896542
C22×#130939862
#202535232
C2×#156894532
C2×#156894262
C2×#156893372
C2×#156892762
C2×#156892562
C2×#156892322
C2×#156892222
C2×#156891772
C2×C47×#4802
C2×#311447