Finite Group Databasebeta

← C2×#20248545 #26386655

Subgroups — C2×#20248545 #26386655

Order 12032.

4166 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094001C211yesmaximal, characteristic, complemented
2C23×(C2×D47)⋊C4C211yesmaximal, characteristic
3#20248545C2116yesmaximal, direct product factor
4C2×#15689052C212yesmaximal, complemented
5C2×#15689036C212yesmaximal, complemented
6C2×#15689015C212yesmaximal, complemented
7C2×#15689012C212yesmaximal, complemented
8C2×#15688986C211yesmaximal, characteristic, complemented
9C2×#15688978C211yesmaximal, characteristic
10C2×#15688978C211yesmaximal, characteristic
11C2×C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
12C2×C47×#381C211yesmaximal, characteristic, complemented
13C25×D47C2211yescharacteristic
14C23×Dic94C2211yescharacteristic, complemented
15C24×Dic47C2211yescharacteristic
16C2×#13094001—28no—
17C2×#13094001C2218yescomplemented
18C22×C4⋊Dic47C2211yescharacteristic, complemented
19C22×Dic47⋊C4C2211yescharacteristic, complemented
20C22×Dic47⋊C4C2211yescharacteristic, complemented
21C22×C22⋊Dic47C2211yescharacteristic
22C22×C22⋊Dic47C2211yescharacteristic
23C22×(C2×D47)⋊C4—28no—
24C22×(C2×D47)⋊C4C2212yes—
25C22×(C2×D47)⋊C4C2212yes—
26C22×(C2×D47)⋊C4C2218yes—
27C22×(C2×D47)⋊C4C2212yes—
28C22×(C2×D47)⋊C4C2212yes—
29C22×(C2×D47)⋊C4C2212yes—
30C22×(C2×D47)⋊C4C2212yes—
31C22×C4×Dic47C2212yescomplemented
32#15689052C22116yescomplemented
33#15689036C22116yescomplemented
34#15689015C22116yescomplemented
35#15689012C22116yescomplemented
36#15688986C2218yescomplemented
37#15688978C2218yes—
38#15688978C2218yes—
39C22⋊C4×Dic47C2218yescomplemented
40C2×C47⋊#95C2212yescomplemented
41C2×C47⋊#95C2212yescomplemented
42C2×C47⋊#95C2212yescomplemented
43C24×C4×C47C2211yescharacteristic
44C22×C22⋊C4×C47C2211yescharacteristic
45C22×C22⋊C4×C47C2211yescharacteristic
46C47×#381C2218yescomplemented
47C2×#95×C47C2212yescomplemented
48C2×#95×C47C2212yescomplemented
49C24×D47—24no—
50C24×D47—28no—
51C24×D47—24no—
52C24×D47—24no—
53C24×D47—44no—
54C24×D47C2312yes—
55C24×D47C2314yes—
56C22×Dic94—24no—
57C22×Dic94—44no—
58C22×Dic94C2314yescomplemented
59C23×Dic47—44no—
60C23×Dic47D418yes—
61C23×Dic47C2312yes—
62C23×Dic47C2311yescharacteristic
63C23×Dic47C2311yescharacteristic
64C23×Dic47C2311yescharacteristic
65C23×Dic47C2311yescharacteristic
66C23×Dic47C2314yes—
67#13094001—232no—
68C2×C4⋊Dic47—24no—
69C2×C4⋊Dic47C2314yescomplemented
70C2×Dic47⋊C4—24no—
71C2×Dic47⋊C4—24no—
72C2×Dic47⋊C4C2314yescomplemented
73C2×Dic47⋊C4C2314yescomplemented
74C2×C22⋊Dic47—24no—
75C2×C22⋊Dic47—24no—
76C2×C22⋊Dic47C2314yes—
77C2×C22⋊Dic47C2314yes—
78C2×(C2×D47)⋊C4—28no—
79C2×(C2×D47)⋊C4—28no—
80C2×(C2×D47)⋊C4—28no—
81C2×(C2×D47)⋊C4—28no—
82C2×(C2×D47)⋊C4—232no—
83C2×(C2×D47)⋊C4—44no—
84C2×(C2×D47)⋊C4—44no—
85C2×(C2×D47)⋊C4C2318yes—
86C2×(C2×D47)⋊C4C2318yes—
87C2×(C2×D47)⋊C4C2318yes—
88C2×(C2×D47)⋊C4C2318yes—
89C2×(C2×D47)⋊C4C2318yes—
90C2×(C2×D47)⋊C4C2318yes—
91C2×C4×Dic47—44no—
92C2×C4×Dic47C2318yescomplemented
93C47⋊#95C2318yescomplemented
94C47⋊#95C2318yescomplemented
95C47⋊#95C2318yescomplemented
96C25×C47C2311yescharacteristic
97C23×C4×C47—24no—
98C23×C4×C47—24no—
99C23×C4×C47—24no—
100C23×C4×C47C2312yes—
101C23×C4×C47C2312yes—
102C23×C4×C47C2314yes—
103C23×C4×C47C2311yescharacteristic
104C23×C4×C47C2311yescharacteristic
105C2×C22⋊C4×C47—24no—
106C2×C22⋊C4×C47—24no—
107C2×C22⋊C4×C47C2314yes—
108C2×C22⋊C4×C47C2314yes—
109#95×C47C2318yescomplemented
110#95×C47C2318yescomplemented
111C24×C47—24no—
112C24×C47—24no—
113C24×C47C2×D414yes—
114C24×C47#4114yes—
115C24×C47#4114yes—
116C24×C47C2412yes—
117C24×C47C2411yescharacteristic
118C23×D47—232no—
119C23×D47—28no—
120C23×D47—24no—
121C23×D47—24no—
122C23×D47—24no—
123C23×D47—24no—
124C23×D47—24no—
125C23×D47—24no—
126C23×D47—216no—
127C23×D47—28no—
128C23×D47—28no—
129C23×D47—48no—
130C23×D47—432no—
131C23×D47—432no—
132C23×D47—416no—
133C23×D47—416no—
134C23×D47#4118yes—
135C23×D47C2414yes—
136C22×C4×C47—22no—
137C22×C4×C47—22no—
138C22×C4×C47—28no—
139C22×C4×C47—24no—
140C22×C4×C47—24no—
141C22×C4×C47—28no—
142C22×C4×C47—24no—
143C22×C4×C47—28no—
144C22×C4×C47—24no—
145C22×C4×C47—24no—
146C22×C4×C47—24no—
147C22×C4×C47—24no—
148C22×C4×C47—24no—
149C22×C4×C47—416no—
150C22×C4×C47C2414yes—
151C22×C4×C47C2412yes—
152C22×C4×C47C2412yes—
153C22×C4×C47C2414yes—
154C22×Dic47—24no—
155C22×Dic47—24no—
156C22×Dic47—22no—
157C22×Dic47—22no—
158C22×Dic47—24no—
159C22×Dic47—24no—
160C22×Dic47—24no—
161C22×Dic47—24no—
162C22×Dic47—24no—
163C22×Dic47—416no—
164C22×Dic47—48no—
165C22×Dic47C2×D414yes—
166C22×Dic47C2×D414yes—
167C22×Dic47C2×D4116yes—
168C22×Dic47C2414yes—
169C22×Dic47C2412yes—
170C22×Dic47C2412yes—
171C22×Dic47C2412yes—
172C22×Dic47C2412yes—
173C2×Dic94—28no—
174C2×Dic94—48no—
175C2×Dic94—416no—
176C22⋊C4×C47—28no—
177C22⋊C4×C47—28no—
178C22⋊Dic47—28no—
179C22⋊Dic47—28no—
180(C2×D47)⋊C4—216no—
181(C2×D47)⋊C4—216no—
182(C2×D47)⋊C4—216no—
183(C2×D47)⋊C4—216no—
184(C2×D47)⋊C4—48no—
185(C2×D47)⋊C4—48no—
186C4⋊Dic47—28no—
187Dic47⋊C4—28no—
188Dic47⋊C4—28no—
189C4×Dic47—48no—
190C23×C47—28no—
191C23×C47—28no—
192C23×C47—216no—
193C23×C47—216no—
194C23×C47—24no—
195C23×C47—24no—
196C23×C47#124116yes—
197C23×C47C22×D414yes—
198C23×C47C22×D412yes—
199C23×C47C2×#4114yes—
200C23×C47C2×#4114yes—
201C23×C47C2×#4112yes—
202C23×C47C2×#4114yes—
203C23×C47C2×#4112yes—
204C23×C47H(5,𝔽2)14yes—
205C23×C47C2511yescharacteristic
206C22×D47—232no—
207C22×D47—216no—
208C22×D47—216no—
209C22×D47—216no—
210C22×D47—24no—
211C22×D47—24no—
212C22×D47—24no—
213C22×D47—24no—
214C22×D47—24no—
215C22×D47—24no—
216C22×D47—432no—
217C22×D47—432no—
218C22×D47—4128no—
219C22×D47—416no—
220C22×D47—416no—
221C22×D47—48no—
222C22×D47—48no—
223C22×D47—48no—
224C22×D47—48no—
225C22×D47C2×#4118yes—
226C2×C4×C47—22no—
227C2×C4×C47—22no—
228C2×C4×C47—24no—
229C2×C4×C47—24no—
230C2×C4×C47—24no—
231C2×C4×C47—24no—
232C2×C4×C47—24no—
233C2×C4×C47—24no—
234C2×C4×C47—24no—
235C2×C4×C47—24no—
236C2×C4×C47—44no—
237C2×C4×C47—416no—
238C2×C4×C47—48no—
239C2×C4×C47—44no—
240C2×C4×C47—48no—
241C2×Dic47—28no—
242C2×Dic47—28no—
243C2×Dic47—24no—
244C2×Dic47—24no—
245C2×Dic47—22no—
246C2×Dic47—22no—
247C2×Dic47—24no—
248C2×Dic47—24no—
249C2×Dic47—24no—
250C2×Dic47—24no—
251C2×Dic47—24no—
252C2×Dic47—416no—
253C2×Dic47—44no—
254C2×Dic47—44no—
255C2×Dic47—48no—
256C2×Dic47C22×D414yes—
257C2×Dic47C22×D414yes—
258Dic94—416no—
259C2×#2561—471nomaximal, Sylow
260C22×C47—232no—
261C22×C47—24no—
262C22×C47—24no—
263C22×C47—28no—
264C22×C47—28no—
265C22×C47#52514yes—
266C22×C47C2×#12418yes—
267C22×C47C2×#12414yes—
268C22×C47#53414yes—
269C22×C47#55118yes—
270C22×C47#55118yes—
271C22×C47C23×D411yescharacteristic
272C22×C47C22×#4112yes—
273C22×C47C22×#4111yescharacteristic
274C22×C47C22×#4111yescharacteristic
275C22×C47C2×H(5,𝔽2)12yes—
276C2×D47—28no—
277C2×D47—28no—
278C2×D47—28no—
279C2×D47—464no—
280C2×D47—432no—
281C2×D47—44no—
282C2×D47—44no—
283C2×D47—44no—
284C2×D47—44no—
285C4×C47—42no—
286C4×C47—44no—
287C4×C47—42no—
288C4×C47—44no—
289Dic47—24no—
290Dic47—24no—
291Dic47—42no—
292Dic47—42no—
293Dic47—44no—
294C22×C22⋊Q8—471no—
295C23×C22⋊C4—471no—
296#2561—4716no—
297C2×#397—472no—
298C2×#393—472no—
299C2×#388—472no—
300C2×#388—472no—
301C2×#381—471no—
302C2×#381D4711yescharacteristic, complemented
303C2×#379—471no—
304C2×#379—471no—
305C2×C4×C22⋊C4—471no—
306C2×C47—28no—
307C2×C47#256118yescomplemented
308C2×C47C2×#52511yescharacteristic
309C2×C47C22×#12411yescharacteristic
310C2×C47C2×#53411yescharacteristic
311C2×C47C2×#55112yes—
312C2×C47C2×#55112yes—
313D47—48no—
314C26—471no—
315C23×Q8—471no—
316C24×C4—471no—
317C24×C4C2×D4711yescharacteristic
318C2×C22⋊Q8—478no—
319C2×C22⋊Q8—948no—
320C22×C4⋊C4—471no—
321C22×C4⋊C4—471no—
322C22×C4⋊C4—471no—
323C22×C22⋊C4—471no—
324C22×C22⋊C4—471no—
325C22×C22⋊C4—478no—
326C22×C22⋊C4—472no—
327C22×C22⋊C4—472no—
328C22×C22⋊C4—472no—
329C22×C22⋊C4—472no—
330C22×C22⋊C4—472no—
331C22×C22⋊C4—472no—
332C22×C22⋊C4—948no—
333C22×C22⋊C4C2×D4711yescharacteristic
334C22×C22⋊C4C2×D4711yescharacteristic
335C22×C42—472no—
336#397—4716no—
337#393—4716no—
338#388—4716no—
339#388—4716no—
340#381—478no—
341#381C2×D4718yescomplemented
342#379—478no—
343#379—478no—
344C4×C22⋊C4—478no—
345C2×#95—472no—
346C2×#95—472no—
347C2×#95—472no—
348C2×#95C2×D4712yescomplemented
349C2×#95C2×D4712yescomplemented
350C47C2×#256111yescharacteristic, complemented, Sylow
351C25—472no—
352C25—474no—
353C25—948no—
354C25—944no—
355C25—944no—
356C25—944no—
357C25—1884no—
358C25C22×D4711yescharacteristic
359C22×Q8—474no—
360C22×Q8—944no—
361C22×Q8—1884no—
362C23×C4—24no—
363C23×C4—24no—
364C23×C4—24no—
365C23×C4—471no—
366C23×C4—471no—
367C23×C4—478no—
368C23×C4—474no—
369C23×C4—471no—
370C23×C4—471no—
371C23×C4—472no—
372C23×C4—1884no—
373C23×C4C22×D4714yes—
374C23×C4C22×D4711yescharacteristic
375C23×C4C22×D4711yescharacteristic
376C23×C4C22×D4712yes—
377C23×C4C22×D4712yes—
378C22⋊Q8—9432no—
379C2×C4⋊C4—474no—
380C2×C4⋊C4—474no—
381C2×C4⋊C4—474no—
382C2×C4⋊C4—944no—
383C2×C4⋊C4—944no—
384C2×C4⋊C4—944no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—474no—
388C2×C22⋊C4—474no—
389C2×C22⋊C4—478no—
390C2×C22⋊C4—478no—
391C2×C22⋊C4—478no—
392C2×C22⋊C4—478no—
393C2×C22⋊C4—478no—
394C2×C22⋊C4—478no—
395C2×C22⋊C4—948no—
396C2×C22⋊C4—948no—
397C2×C22⋊C4—9432no—
398C2×C22⋊C4—948no—
399C2×C22⋊C4—948no—
400C2×C22⋊C4—944no—
401C2×C22⋊C4—944no—
402C2×C22⋊C4—1884no—
403C2×C22⋊C4—1884no—
404C2×C22⋊C4C22×D4714yes—
405C2×C22⋊C4C22×D4714yes—
406C2×C42—478no—
407C2×C42—1884no—
408#95—478no—
409#95—478no—
410#95—478no—
411#95C22×D4718yescomplemented
412#95C22×D4718yescomplemented
413C24—24no—
414C24—24no—
415C24—478no—
416C24—474no—
417C24—9416no—
418C24—9432no—
419C24—948no—
420C24—944no—
421C24—944no—
422C24—944no—
423C24—944no—
424C24—944no—
425C24—944no—
426C24—948no—
427C24—948no—
428C24—1888no—
429C24—18832no—
430C24—18832no—
431C24—18816no—
432C24—18816no—
433C24#1062535014yes—
434C24D4×D4714yes—
435C24#1062535214yes—
436C24C23×D4712yes—
437C24C23×D4711yescharacteristic
438C2×Q8—948no—
439C2×Q8—1888no—
440C2×Q8—18816no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—28no—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—28no—
449C22×C4—24no—
450C22×C4—28no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—416no—
455C22×C4—474no—
456C22×C4—474no—
457C22×C4—472no—
458C22×C4—472no—
459C22×C4—4716no—
460C22×C4—474no—
461C22×C4—472no—
462C22×C4—472no—
463C22×C4—944no—
464C22×C4—944no—
465C22×C4—942no—
466C22×C4—942no—
467C22×C4—944no—
468C22×C4—944no—
469C22×C4—944no—
470C22×C4—944no—
471C22×C4—944no—
472C22×C4—18816no—
473C22×C4—1888no—
474C22×C4C23×D4714yes—
475C22×C4C23×D4714yes—
476C22×C4C23×D4712yes—
477C22×C4C23×D4712yes—
478C4⋊C4—948no—
479C4⋊C4—948no—
480C4⋊C4—948no—
481C22⋊C4—28no—
482C22⋊C4—28no—
483C22⋊C4—9416no—
484C22⋊C4—9416no—
485C22⋊C4—9416no—
486C22⋊C4—9416no—
487C22⋊C4—948no—
488C22⋊C4—948no—
489C22⋊C4—1888no—
490C22⋊C4—1888no—
491C42—1888no—
492C23—216no—
493C23—216no—
494C23—28no—
495C23—28no—
496C23—24no—
497C23—24no—
498C23—478no—
499C23—9432no—
500C23—9416no—
501C23—9416no—
502C23—9416no—
503C23—944no—
504C23—944no—
505C23—944no—
506C23—944no—
507C23—944no—
508C23—944no—
509C23—18832no—
510C23—18832no—
511C23—18816no—
512C23—188128no—
513C23—1888no—
514C23—1888no—
515C23—18816no—
516C23—1888no—
517C23—1888no—
518C23#13094010116yes—
519C23C2×D4×D4714yes—
520C23C2×D4×D4712yes—
521C23#41×D4714yes—
522C23C2×#1062535214yes—
523C23C2×#1062535212yes—
524C23C2×#1062535014yes—
525C23C2×#1062535012yes—
526C23#1309407014yes—
527C23C24×D4711yescharacteristic
528Q8—18816no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—48no—
540C2×C4—44no—
541C2×C4—416no—
542C2×C4—48no—
543C2×C4—44no—
544C2×C4—474no—
545C2×C4—474no—
546C2×C4—948no—
547C2×C4—948no—
548C2×C4—944no—
549C2×C4—944no—
550C2×C4—942no—
551C2×C4—942no—
552C2×C4—944no—
553C2×C4—944no—
554C2×C4—944no—
555C2×C4—944no—
556C2×C4—944no—
557C2×C4—18816no—
558C2×C4—1888no—
559C2×C4—1884no—
560C2×C4—1884no—
561C22—28no—
562C22—24no—
563C22—28no—
564C22—24no—
565C22—232no—
566C22—948no—
567C22—948no—
568C22—948no—
569C22—18864no—
570C22—1884no—
571C22—1884no—
572C22—1884no—
573C22—1884no—
574C22—18832no—
575C22#1568963114yes—
576C22C2×#1309401018yes—
577C22C2×#1309401014yes—
578C22#1568968414yes—
579C22#1568979618yes—
580C22#1568979718yes—
581C22C22×D4×D4711yescharacteristic
582C22C2×#41×D4712yes—
583C22C22×#1062535211yescharacteristic
584C22C22×#1062535011yescharacteristic
585C22C2×#1309407012yes—
586C4—44no—
587C4—42no—
588C4—44no—
589C4—42no—
590C4—944no—
591C4—944no—
592C4—1882no—
593C4—1884no—
594C4—1882no—
595C2—28no—
596C2—1888no—
597C2#2024854518yesdirect product factor
598C2C2×#1568963111yescharacteristic
599C2C22×#1309401011yescharacteristic
600C2C2×#1568968411yescharacteristic
601C2C2×#1568979612yes—
602C2C2×#1568979712yes—
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#381C2
socleC24×C47C24
prime radicalC25×D47C22
hypercenterC2×#381D47
hypocenterC47C2×#2561
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
1. C22×#13094001C2semidirect
3. #20248545C2direct (N × H)
4. C2×#15689052C2semidirect
5. C2×#15689036C2semidirect
6. C2×#15689015C2semidirect
7. C2×#15689012C2semidirect
8. C2×#15688986C2semidirect
11. C2×C22⋊C4×Dic47C2semidirect
12. C2×C47×#381C2semidirect
14. C23×Dic94C22semidirect
17. C2×#13094001C22semidirect
18. C22×C4⋊Dic47C22semidirect
19. C22×Dic47⋊C4C22semidirect
20. C22×Dic47⋊C4C22semidirect
31. C22×C4×Dic47C22semidirect
32. #15689052C22semidirect
33. #15689036C22semidirect
34. #15689015C22semidirect
35. #15689012C22semidirect
36. #15688986C22semidirect
39. C22⋊C4×Dic47C22semidirect
40. C2×C47⋊#95C22semidirect
41. C2×C47⋊#95C22semidirect
42. C2×C47⋊#95C22semidirect
46. C47×#381C22semidirect
47. C2×#95×C47C22semidirect
48. C2×#95×C47C22semidirect
58. C22×Dic94C23semidirect
69. C2×C4⋊Dic47C23semidirect
72. C2×Dic47⋊C4C23semidirect
73. C2×Dic47⋊C4C23semidirect
92. C2×C4×Dic47C23semidirect
93. C47⋊#95C23semidirect
94. C47⋊#95C23semidirect
95. C47⋊#95C23semidirect
109. #95×C47C23semidirect
110. #95×C47C23semidirect
302. C2×#381D47semidirect
307. C2×C47#2561semidirect
341. #381C2×D47semidirect
348. C2×#95C2×D47semidirect
349. C2×#95C2×D47semidirect
350. C47C2×#2561semidirect
411. #95C22×D47semidirect
412. #95C22×D47semidirect
597. C2#20248545direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940012
C23×(C2×D47)⋊C42
#202485452
C2×#156890522
C2×#156890362
C2×#156890152
C2×#156890122
C2×#156889862
C2×#156889782
C2×C22⋊C4×Dic472
C2×C47×#3812
C2×#256147