Finite Group Databasebeta

← C2×#20247661 #26386044

Subgroups — C2×#20247661 #26386044

Order 12032.

4166 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093980C211yesmaximal, characteristic, complemented
2C23×(C2×D47)⋊C4C211yesmaximal, characteristic
3#20247661C2116yesmaximal, direct product factor
4C2×#15689058C212yesmaximal, complemented
5C2×#15689052C212yesmaximal, complemented
6C2×#15689013C212yesmaximal, complemented
7C2×#15689012C212yesmaximal, complemented
8C2×#15688996C211yesmaximal, characteristic, complemented
9C2×#15688984C211yesmaximal, characteristic, complemented
10C2×#15688978C211yesmaximal, characteristic
11C2×#15688978C211yesmaximal, characteristic
12C2×C47×#385C211yesmaximal, characteristic, complemented
13C25×D47C2211yescharacteristic
14C24×Dic47C2211yescharacteristic
15C2×#13093980—28no—
16C2×#13093980C2218yescomplemented
17C22×Dic47⋊C4C2211yescharacteristic, complemented
18C22×Dic47⋊C4C2211yescharacteristic, complemented
19C22×Dic47⋊C4C2212yescomplemented
20C22×C22⋊Dic47C2211yescharacteristic
21C22×C22⋊Dic47C2211yescharacteristic
22C22×(C2×D47)⋊C4—28no—
23C22×(C2×D47)⋊C4C2212yes—
24C22×(C2×D47)⋊C4C2212yes—
25C22×(C2×D47)⋊C4C2218yes—
26C22×(C2×D47)⋊C4C2212yes—
27C22×(C2×D47)⋊C4C2212yes—
28C22×(C2×D47)⋊C4C2212yes—
29C22×(C2×D47)⋊C4C2212yes—
30C22×C4×Dic47C2211yescharacteristic, complemented
31C22×C4×Dic47C2211yescharacteristic, complemented
32#15689058C22116yescomplemented
33#15689052C22116yescomplemented
34#15689013C22116yescomplemented
35#15689012C22116yescomplemented
36#15688996C2218yescomplemented
37#15688984C2218yescomplemented
38#15688978C2218yes—
39#15688978C2218yes—
40C2×C47⋊#95C2212yescomplemented
41C2×C47⋊#95C2212yescomplemented
42C2×C47⋊#95C2212yescomplemented
43C24×C4×C47C2211yescharacteristic
44C22×C4⋊C4×C47C2212yescomplemented
45C22×C22⋊C4×C47C2211yescharacteristic
46C22×C22⋊C4×C47C2211yescharacteristic
47C47×#385C2218yescomplemented
48C2×#95×C47C2212yescomplemented
49C24×D47—24no—
50C24×D47—28no—
51C24×D47—24no—
52C24×D47—24no—
53C24×D47—44no—
54C24×D47C2312yes—
55C24×D47C2314yes—
56C23×Dic47—24no—
57C23×Dic47—24no—
58C23×Dic47D418yes—
59C23×Dic47C2312yes—
60C23×Dic47C2311yescharacteristic
61C23×Dic47C2311yescharacteristic
62C23×Dic47C2311yescharacteristic
63C23×Dic47C2311yescharacteristic
64C23×Dic47C2314yes—
65#13093980—232no—
66C2×Dic47⋊C4—24no—
67C2×Dic47⋊C4—24no—
68C2×Dic47⋊C4—44no—
69C2×Dic47⋊C4C2314yescomplemented
70C2×Dic47⋊C4C2314yescomplemented
71C2×Dic47⋊C4C2318yescomplemented
72C2×C22⋊Dic47—24no—
73C2×C22⋊Dic47—24no—
74C2×C22⋊Dic47C2314yes—
75C2×C22⋊Dic47C2314yes—
76C2×(C2×D47)⋊C4—28no—
77C2×(C2×D47)⋊C4—28no—
78C2×(C2×D47)⋊C4—28no—
79C2×(C2×D47)⋊C4—28no—
80C2×(C2×D47)⋊C4—232no—
81C2×(C2×D47)⋊C4—44no—
82C2×(C2×D47)⋊C4—44no—
83C2×(C2×D47)⋊C4C2318yes—
84C2×(C2×D47)⋊C4C2318yes—
85C2×(C2×D47)⋊C4C2318yes—
86C2×(C2×D47)⋊C4C2318yes—
87C2×(C2×D47)⋊C4C2318yes—
88C2×(C2×D47)⋊C4C2318yes—
89C2×C4×Dic47—24no—
90C2×C4×Dic47—24no—
91C2×C4×Dic47C2314yescomplemented
92C2×C4×Dic47C2314yescomplemented
93C47⋊#95C2318yescomplemented
94C47⋊#95C2318yescomplemented
95C47⋊#95C2318yescomplemented
96C25×C47C2311yescharacteristic
97C23×C4×C47—24no—
98C23×C4×C47—44no—
99C23×C4×C47C2312yes—
100C23×C4×C47C2312yes—
101C23×C4×C47C2311yescharacteristic
102C23×C4×C47C2311yescharacteristic
103C23×C4×C47C2314yes—
104C2×C4⋊C4×C47—44no—
105C2×C4⋊C4×C47C2318yescomplemented
106C2×C22⋊C4×C47—24no—
107C2×C22⋊C4×C47—24no—
108C2×C22⋊C4×C47C2314yes—
109C2×C22⋊C4×C47C2314yes—
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—24no—
142C22×C4×C47—24no—
143C22×C4×C47—24no—
144C22×C4×C47—24no—
145C22×C4×C47—24no—
146C22×C4×C47—24no—
147C22×C4×C47—48no—
148C22×C4×C47—416no—
149C22×C4×C47C2412yes—
150C22×C4×C47C2414yes—
151C22×C4×C47C2412yes—
152C22×C4×C47C2414yes—
153C22×Dic47—232no—
154C22×Dic47—28no—
155C22×Dic47—22no—
156C22×Dic47—22no—
157C22×Dic47—28no—
158C22×Dic47—22no—
159C22×Dic47—22no—
160C22×Dic47—22no—
161C22×Dic47—22no—
162C22×Dic47—24no—
163C22×Dic47—24no—
164C22×Dic47—24no—
165C22×Dic47—24no—
166C22×Dic47—24no—
167C22×Dic47C2×D414yes—
168C22×Dic47C2×D414yes—
169C22×Dic47C2×D4116yes—
170C22×Dic47C2414yes—
171C22×Dic47C2412yes—
172C22×Dic47C2412yes—
173C22×Dic47C2412yes—
174C22×Dic47C2412yes—
175C4⋊C4×C47—48no—
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—
186Dic47⋊C4—28no—
187Dic47⋊C4—28no—
188Dic47⋊C4—48no—
189C4×Dic47—28no—
190C4×Dic47—28no—
191C23×C47—28no—
192C23×C47—28no—
193C23×C47—216no—
194C23×C47—216no—
195C23×C47—24no—
196C23×C47—24no—
197C23×C47#123116yes—
198C23×C47C22×D414yes—
199C23×C47C22×D412yes—
200C23×C47C2×#4114yes—
201C23×C47C2×#4114yes—
202C23×C47C2×#4112yes—
203C23×C47C2×#4114yes—
204C23×C47C2×#4112yes—
205C23×C47H(5,𝔽2)14yes—
206C23×C47C2511yescharacteristic
207C22×D47—232no—
208C22×D47—216no—
209C22×D47—216no—
210C22×D47—216no—
211C22×D47—24no—
212C22×D47—24no—
213C22×D47—24no—
214C22×D47—24no—
215C22×D47—24no—
216C22×D47—24no—
217C22×D47—432no—
218C22×D47—432no—
219C22×D47—416no—
220C22×D47—4128no—
221C22×D47—416no—
222C22×D47—48no—
223C22×D47—48no—
224C22×D47—48no—
225C22×D47—48no—
226C22×D47C2×#4118yes—
227C2×C4×C47—22no—
228C2×C4×C47—22no—
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—24no—
237C2×C4×C47—416no—
238C2×C4×C47—44no—
239C2×C4×C47—44no—
240C2×C4×C47—48no—
241C2×C4×C47—48no—
242C2×Dic47—232no—
243C2×Dic47—28no—
244C2×Dic47—28no—
245C2×Dic47—22no—
246C2×Dic47—22no—
247C2×Dic47—22no—
248C2×Dic47—22no—
249C2×Dic47—22no—
250C2×Dic47—22no—
251C2×Dic47—24no—
252C2×Dic47—24no—
253C2×Dic47—24no—
254C2×Dic47—24no—
255C2×Dic47—24no—
256C2×Dic47—44no—
257C2×Dic47—44no—
258C2×Dic47—48no—
259C2×Dic47C22×D414yes—
260C2×Dic47C22×D414yes—
261C2×#2482—471nomaximal, Sylow
262C22×C47—24no—
263C22×C47—24no—
264C22×C47—28no—
265C22×C47—28no—
266C22×C47—232no—
267C22×C47C2×#12318yes—
268C22×C47C2×#12314yes—
269C22×C47#52514yes—
270C22×C47#53514yes—
271C22×C47#55118yes—
272C22×C47#55118yes—
273C22×C47C23×D411yescharacteristic
274C22×C47C22×#4112yes—
275C22×C47C22×#4111yescharacteristic
276C22×C47C22×#4111yescharacteristic
277C22×C47C2×H(5,𝔽2)12yes—
278C2×D47—28no—
279C2×D47—28no—
280C2×D47—28no—
281C2×D47—464no—
282C2×D47—44no—
283C2×D47—44no—
284C2×D47—44no—
285C2×D47—44no—
286C2×D47—432no—
287C4×C47—42no—
288C4×C47—42no—
289C4×C47—44no—
290C4×C47—44no—
291Dic47—24no—
292Dic47—24no—
293Dic47—42no—
294Dic47—42no—
295Dic47—44no—
296C22×#117—471no—
297C23×C22⋊C4—471no—
298#2482—4716no—
299C2×#399—472no—
300C2×#397—472no—
301C2×#388—472no—
302C2×#388—472no—
303C2×#385—471no—
304C2×#385D4711yescharacteristic, complemented
305C2×#381—471no—
306C2×#379—471no—
307C2×#379—471no—
308C2×C47—28no—
309C2×C47#248218yescomplemented
310C2×C47C22×#12311yescharacteristic
311C2×C47C2×#52511yescharacteristic
312C2×C47C2×#53511yescharacteristic
313C2×C47C2×#55112yes—
314C2×C47C2×#55112yes—
315D47—48no—
316C26—471no—
317C24×C4—471no—
318C24×C4C2×D4711yescharacteristic
319C2×#117—478no—
320C2×#117—948no—
321C22×C4⋊C4—471no—
322C22×C4⋊C4—471no—
323C22×C4⋊C4—472no—
324C22×C4⋊C4C2×D4712yescomplemented
325C22×C22⋊C4—471no—
326C22×C22⋊C4—471no—
327C22×C22⋊C4—472no—
328C22×C22⋊C4—472no—
329C22×C22⋊C4—472no—
330C22×C22⋊C4—478no—
331C22×C22⋊C4—472no—
332C22×C22⋊C4—472no—
333C22×C22⋊C4—472no—
334C22×C22⋊C4—948no—
335C22×C22⋊C4C2×D4711yescharacteristic
336C22×C22⋊C4C2×D4711yescharacteristic
337C22×C42—471no—
338C22×C42—471no—
339#399—4716no—
340#397—4716no—
341#388—4716no—
342#388—4716no—
343#385—478no—
344#385C2×D4718yescomplemented
345#381—478no—
346#379—478no—
347#379—478no—
348C2×#95—472no—
349C2×#95—472no—
350C2×#95—472no—
351C2×#95C2×D4712yescomplemented
352C47C2×#248211yescharacteristic, complemented, Sylow
353C25—472no—
354C25—474no—
355C25—948no—
356C25—944no—
357C25—944no—
358C25—944no—
359C25—1884no—
360C25C22×D4711yescharacteristic
361C23×C4—24no—
362C23×C4—44no—
363C23×C4—478no—
364C23×C4—474no—
365C23×C4—471no—
366C23×C4—471no—
367C23×C4—471no—
368C23×C4—472no—
369C23×C4—471no—
370C23×C4—944no—
371C23×C4—944no—
372C23×C4C22×D4711yescharacteristic
373C23×C4C22×D4711yescharacteristic
374C23×C4C22×D4712yes—
375C23×C4C22×D4712yes—
376C23×C4C22×D4714yes—
377#117—9432no—
378C2×C4⋊C4—44no—
379C2×C4⋊C4—474no—
380C2×C4⋊C4—474no—
381C2×C4⋊C4—478no—
382C2×C4⋊C4—944no—
383C2×C4⋊C4—944no—
384C2×C4⋊C4—1884no—
385C2×C4⋊C4C22×D4718yescomplemented
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—474no—
389C2×C22⋊C4—474no—
390C2×C22⋊C4—478no—
391C2×C22⋊C4—478no—
392C2×C22⋊C4—478no—
393C2×C22⋊C4—478no—
394C2×C22⋊C4—478no—
395C2×C22⋊C4—478no—
396C2×C22⋊C4—948no—
397C2×C22⋊C4—948no—
398C2×C22⋊C4—9432no—
399C2×C22⋊C4—948no—
400C2×C22⋊C4—948no—
401C2×C22⋊C4—944no—
402C2×C22⋊C4—944no—
403C2×C22⋊C4—1884no—
404C2×C22⋊C4—1884no—
405C2×C22⋊C4C22×D4714yes—
406C2×C22⋊C4C22×D4714yes—
407C2×C42—474no—
408C2×C42—474no—
409C2×C42—944no—
410C2×C42—944no—
411#95—478no—
412#95—478no—
413#95—478no—
414#95C22×D4718yescomplemented
415C24—24no—
416C24—24no—
417C24—478no—
418C24—474no—
419C24—9416no—
420C24—9432no—
421C24—948no—
422C24—944no—
423C24—944no—
424C24—944no—
425C24—944no—
426C24—944no—
427C24—944no—
428C24—948no—
429C24—948no—
430C24—1888no—
431C24—18832no—
432C24—18832no—
433C24—18816no—
434C24—18816no—
435C24#1062535014yes—
436C24D4×D4714yes—
437C24#1062535414yes—
438C24C23×D4712yes—
439C24C23×D4711yescharacteristic
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—28no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—48no—
452C22×C4—416no—
453C22×C4—474no—
454C22×C4—474no—
455C22×C4—4716no—
456C22×C4—472no—
457C22×C4—472no—
458C22×C4—474no—
459C22×C4—472no—
460C22×C4—472no—
461C22×C4—9432no—
462C22×C4—948no—
463C22×C4—942no—
464C22×C4—942no—
465C22×C4—948no—
466C22×C4—942no—
467C22×C4—942no—
468C22×C4—942no—
469C22×C4—942no—
470C22×C4—944no—
471C22×C4—944no—
472C22×C4—944no—
473C22×C4—944no—
474C22×C4—944no—
475C22×C4C23×D4714yes—
476C22×C4C23×D4714yes—
477C22×C4C23×D4712yes—
478C22×C4C23×D4712yes—
479C4⋊C4—48no—
480C4⋊C4—948no—
481C4⋊C4—948no—
482C4⋊C4—1888no—
483C22⋊C4—28no—
484C22⋊C4—28no—
485C22⋊C4—9416no—
486C22⋊C4—9416no—
487C22⋊C4—9416no—
488C22⋊C4—9416no—
489C22⋊C4—948no—
490C22⋊C4—948no—
491C22⋊C4—1888no—
492C22⋊C4—1888no—
493C42—948no—
494C42—948no—
495C23—216no—
496C23—216no—
497C23—28no—
498C23—28no—
499C23—24no—
500C23—24no—
501C23—478no—
502C23—9432no—
503C23—9416no—
504C23—9416no—
505C23—9416no—
506C23—944no—
507C23—944no—
508C23—944no—
509C23—944no—
510C23—944no—
511C23—944no—
512C23—18832no—
513C23—18832no—
514C23—188128no—
515C23—18816no—
516C23—1888no—
517C23—1888no—
518C23—18816no—
519C23—1888no—
520C23—1888no—
521C23#13094009116yes—
522C23C2×D4×D4714yes—
523C23C2×D4×D4712yes—
524C23#41×D4714yes—
525C23C2×#1062535014yes—
526C23C2×#1062535012yes—
527C23C2×#1062535414yes—
528C23C2×#1062535412yes—
529C23#1309406914yes—
530C23C24×D4711yescharacteristic
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—416no—
542C2×C4—48no—
543C2×C4—44no—
544C2×C4—44no—
545C2×C4—48no—
546C2×C4—474no—
547C2×C4—474no—
548C2×C4—9432no—
549C2×C4—948no—
550C2×C4—948no—
551C2×C4—942no—
552C2×C4—942no—
553C2×C4—942no—
554C2×C4—942no—
555C2×C4—942no—
556C2×C4—942no—
557C2×C4—944no—
558C2×C4—944no—
559C2×C4—944no—
560C2×C4—944no—
561C2×C4—944no—
562C2×C4—1888no—
563C2×C4—1884no—
564C2×C4—1884no—
565C22—232no—
566C22—24no—
567C22—28no—
568C22—28no—
569C22—24no—
570C22—948no—
571C22—948no—
572C22—948no—
573C22—18864no—
574C22—18832no—
575C22—1884no—
576C22—1884no—
577C22—1884no—
578C22—1884no—
579C22C2×#1309400918yes—
580C22C2×#1309400914yes—
581C22#1568963114yes—
582C22#1568968814yes—
583C22#1568980018yes—
584C22#1568980218yes—
585C22C22×D4×D4711yescharacteristic
586C22C2×#41×D4712yes—
587C22C22×#1062535011yescharacteristic
588C22C22×#1062535411yescharacteristic
589C22C2×#1309406912yes—
590C4—42no—
591C4—44no—
592C4—44no—
593C4—42no—
594C4—944no—
595C4—944no—
596C4—1882no—
597C4—1884no—
598C4—1882no—
599C2—28no—
600C2—1888no—
601C2#2024766118yesdirect product factor
602C2C22×#1309400911yescharacteristic
603C2C2×#1568963111yescharacteristic
604C2C2×#1568968811yescharacteristic
605C2C2×#1568980012yes—
606C2C2×#1568980212yes—
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#385C2
socleC24×C47C24
prime radicalC25×D47C22
hypercenterC2×#385D47
hypocenterC47C2×#2482
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#13093980C2semidirect
3. #20247661C2direct (N × H)
4. C2×#15689058C2semidirect
5. C2×#15689052C2semidirect
6. C2×#15689013C2semidirect
7. C2×#15689012C2semidirect
8. C2×#15688996C2semidirect
9. C2×#15688984C2semidirect
12. C2×C47×#385C2semidirect
16. C2×#13093980C22semidirect
17. C22×Dic47⋊C4C22semidirect
18. C22×Dic47⋊C4C22semidirect
19. C22×Dic47⋊C4C22semidirect
30. C22×C4×Dic47C22semidirect
31. C22×C4×Dic47C22semidirect
32. #15689058C22semidirect
33. #15689052C22semidirect
34. #15689013C22semidirect
35. #15689012C22semidirect
36. #15688996C22semidirect
37. #15688984C22semidirect
40. C2×C47⋊#95C22semidirect
41. C2×C47⋊#95C22semidirect
42. C2×C47⋊#95C22semidirect
44. C22×C4⋊C4×C47C22semidirect
47. C47×#385C22semidirect
48. C2×#95×C47C22semidirect
69. C2×Dic47⋊C4C23semidirect
70. C2×Dic47⋊C4C23semidirect
71. C2×Dic47⋊C4C23semidirect
91. C2×C4×Dic47C23semidirect
92. C2×C4×Dic47C23semidirect
93. C47⋊#95C23semidirect
94. C47⋊#95C23semidirect
95. C47⋊#95C23semidirect
105. C2×C4⋊C4×C47C23semidirect
110. #95×C47C23semidirect
304. C2×#385D47semidirect
309. C2×C47#2482semidirect
324. C22×C4⋊C4C2×D47semidirect
344. #385C2×D47semidirect
351. C2×#95C2×D47semidirect
352. C47C2×#2482semidirect
385. C2×C4⋊C4C22×D47semidirect
414. #95C22×D47semidirect
601. C2#20247661direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130939802
C23×(C2×D47)⋊C42
#202476612
C2×#156890582
C2×#156890522
C2×#156890132
C2×#156890122
C2×#156889962
C2×#156889842
C2×#156889782
C2×C47×#3852
C2×#248247