Finite Group Databasebeta

← C2×#20246625 #26382497

Subgroups — C2×#20246625 #26382497

Order 12032.

4134 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093986C211yesmaximal, characteristic, complemented
2C22×(C22⋊D47)⋊C4C212yesmaximal, complemented
3C22×#13093980C211yesmaximal, characteristic, complemented
4#20246625C2116yesmaximal, direct product factor
5C2×#15689054C211yesmaximal, characteristic, complemented
6C2×#15689047C212yesmaximal, complemented
7C2×#15689041C211yesmaximal, characteristic, complemented
8C2×#15689038C212yesmaximal, complemented
9C2×#15689032C211yesmaximal, characteristic
10C2×#15688974C211yesmaximal, characteristic, complemented
11C2×#15688970C212yesmaximal, complemented
12C2×C47×#397C211yesmaximal, characteristic, complemented
13C23×D188C2211yescharacteristic
14C23×C22⋊D47C2212yes—
15C24×Dic47C2211yescharacteristic
16C23×C4×D47C2212yes—
17C2×#13093986—28no—
18C2×#13093986C2218yescomplemented
19C2×(C22⋊D47)⋊C4—216no—
20C2×(C22⋊D47)⋊C4C22116yescomplemented
21C2×#13093980—28no—
22C2×#13093980C2218yescomplemented
23C22×Dic47⋊C4C2211yescharacteristic
24C22×Dic47⋊C4C2211yescharacteristic
25C22×Dic47⋊C4C2212yes—
26C22×Dic47⋊C4C2212yes—
27C22×C22⋊Dic47C2211yescharacteristic
28C22×(C2×D47)⋊C4C2212yes—
29C22×(C2×D47)⋊C4C2212yes—
30C22×(C2×D47)⋊C4C2212yes—
31C22×(C2×D47)⋊C4C2212yes—
32C22×C4×Dic47C2211yescharacteristic
33C22×C4×Dic47C2212yes—
34C22×C4×Dic47C2211yescharacteristic
35#15689054C2218yescomplemented
36#15689047C22116yescomplemented
37#15689041C2218yescomplemented
38#15689038C22116yescomplemented
39#15689032C2218yes—
40#15688974C2218yescomplemented
41#15688970C22116yescomplemented
42C2×C47⋊#95C2211yescharacteristic
43C2×C47⋊#95C2212yes—
44C22×C4⋊C4×C47C2211yescharacteristic
45C22×C22⋊C4×C47C2211yescharacteristic
46C22×C22⋊C4×C47C2212yes—
47C47×#397C2218yescomplemented
48C2×#95×C47C2211yescharacteristic
49C2×#95×C47C2212yes—
50C24×D47C2312yes—
51C22×D188—28no—
52C22×D188—24no—
53C22×D188C2314yes—
54C22×C22⋊D47—28no—
55C22×C22⋊D47—28no—
56C22×C22⋊D47—28no—
57C22×C22⋊D47C2318yes—
58C23×Dic47—24no—
59C23×Dic47—24no—
60C23×Dic47D418yescomplemented
61C23×Dic47C2311yescharacteristic
62C23×Dic47C2311yescharacteristic
63C23×Dic47C2311yescharacteristic
64C23×Dic47C2314yes—
65C23×Dic47C2312yes—
66C23×Dic47C2311yescharacteristic
67C22×C4×D47—28no—
68C22×C4×D47—28no—
69C22×C4×D47—28no—
70C22×C4×D47C2318yes—
71#13093986—232no—
72(C22⋊D47)⋊C4—264no—
73#13093980—232no—
74C2×Dic47⋊C4—24no—
75C2×Dic47⋊C4—24no—
76C2×Dic47⋊C4—28no—
77C2×Dic47⋊C4—28no—
78C2×Dic47⋊C4C2318yes—
79C2×Dic47⋊C4C2314yes—
80C2×Dic47⋊C4C2314yes—
81C2×Dic47⋊C4C2318yes—
82C2×C22⋊Dic47—24no—
83C2×C22⋊Dic47C2314yes—
84C2×(C2×D47)⋊C4—28no—
85C2×(C2×D47)⋊C4—28no—
86C2×(C2×D47)⋊C4—28no—
87C2×(C2×D47)⋊C4—28no—
88C2×(C2×D47)⋊C4C2318yes—
89C2×(C2×D47)⋊C4C2318yes—
90C2×(C2×D47)⋊C4C2318yes—
91C2×(C2×D47)⋊C4C2318yes—
92C2×C4×Dic47—24no—
93C2×C4×Dic47—28no—
94C2×C4×Dic47D418yescomplemented
95C2×C4×Dic47C2314yes—
96C2×C4×Dic47C2318yes—
97C2×C4×Dic47C2314yes—
98C47⋊#95C2318yes—
99C47⋊#95C2314yes—
100C25×C47C2311yescharacteristic
101C23×C4×C47C2312yes—
102C23×C4×C47C2312yes—
103C23×C4×C47C2311yescharacteristic
104C23×C4×C47C2311yescharacteristic
105C2×C4⋊C4×C47—24no—
106C2×C4⋊C4×C47C2314yes—
107C2×C22⋊C4×C47—28no—
108C2×C22⋊C4×C47—24no—
109C2×C22⋊C4×C47C2314yes—
110C2×C22⋊C4×C47C2318yes—
111#95×C47C2318yes—
112#95×C47C2314yes—
113C24×C47—22no—
114C24×C47—22no—
115C24×C47—24no—
116C24×C47—24no—
117C24×C47C2×D414yes—
118C24×C47C2412yes—
119C24×C47C2411yescharacteristic
120C23×D47—24no—
121C23×D47—24no—
122C23×D47—24no—
123C23×D47—24no—
124C23×D47—24no—
125C23×D47—24no—
126C23×D47#4118yes—
127C23×D47C2414yes—
128C22×C4×C47—24no—
129C22×C4×C47—24no—
130C22×C4×C47—22no—
131C22×C4×C47—24no—
132C22×C4×C47—24no—
133C22×C4×C47—24no—
134C22×C4×C47—24no—
135C22×C4×C47—24no—
136C22×C4×C47—24no—
137C22×C4×C47C2×D414yes—
138C22×C4×C47C2414yes—
139C22×C4×C47C2412yes—
140C22×C4×C47C2414yes—
141C22×C4×C47C2412yes—
142C2×C22⋊D47—264no—
143C2×C22⋊D47—216no—
144C2×C22⋊D47—216no—
145C2×C22⋊D47—216no—
146C22×Dic47—24no—
147C22×Dic47—22no—
148C22×Dic47—24no—
149C22×Dic47—22no—
150C22×Dic47—24no—
151C22×Dic47—232no—
152C22×Dic47—28no—
153C22×Dic47—28no—
154C22×Dic47—22no—
155C22×Dic47—24no—
156C22×Dic47C2×D414yes—
157C22×Dic47C2×D414yes—
158C22×Dic47C2×D414yes—
159C22×Dic47C2×D414yes—
160C22×Dic47C2×D4116yescomplemented
161C22×Dic47#4118yes—
162C22×Dic47#4114yes—
163C22×Dic47C2412yes—
164C22×Dic47C2412yes—
165C22×Dic47C2412yes—
166C22×Dic47C2414yes—
167C22×Dic47C2412yes—
168C2×D188—232no—
169C2×D188—216no—
170C2×D188—28no—
171C2×C4×D47—216no—
172C2×C4×D47—216no—
173C2×C4×D47—216no—
174C2×C4×D47—432no—
175C4⋊C4×C47—28no—
176C22⋊C4×C47—216no—
177C22⋊C4×C47—28no—
178C22⋊Dic47—28no—
179(C2×D47)⋊C4—216no—
180(C2×D47)⋊C4—216no—
181(C2×D47)⋊C4—216no—
182(C2×D47)⋊C4—216no—
183Dic47⋊C4—28no—
184Dic47⋊C4—28no—
185Dic47⋊C4—216no—
186Dic47⋊C4—216no—
187C4×Dic47—28no—
188C4×Dic47—216no—
189C4×Dic47C2×D4116yescomplemented
190C23×C47—28no—
191C23×C47—216no—
192C23×C47—22no—
193C23×C47—22no—
194C23×C47—24no—
195C23×C47—24no—
196C23×C47—44no—
197C23×C47—48no—
198C23×C47—44no—
199C23×C47C22×D414yes—
200C23×C47C22×D412yes—
201C23×C47C22×D412yes—
202C23×C47C2×#4112yes—
203C23×C47C2×#4114yes—
204C23×C47C2×#4114yes—
205C23×C47C2511yescharacteristic
206C22×D47—216no—
207C22×D47—216no—
208C22×D47—216no—
209C22×D47—24no—
210C22×D47—24no—
211C22×D47—24no—
212C22×D47—24no—
213C22×D47—24no—
214C22×D47—24no—
215C22×D47—48no—
216C22×D47—48no—
217C22×D47—48no—
218C22×D47—48no—
219C22×D47C2×#4118yes—
220C2×C4×C47—28no—
221C2×C4×C47—24no—
222C2×C4×C47—22no—
223C2×C4×C47—24no—
224C2×C4×C47—24no—
225C2×C4×C47—24no—
226C2×C4×C47—24no—
227C2×C4×C47—24no—
228C2×C4×C47—24no—
229C2×C4×C47—24no—
230C2×C4×C47—48no—
231C2×C4×C47—48no—
232C2×C4×C47—44no—
233C2×C4×C47C22×D414yes—
234C22⋊D47—264no—
235C2×Dic47—28no—
236C2×Dic47—216no—
237C2×Dic47—28no—
238C2×Dic47—24no—
239C2×Dic47—22no—
240C2×Dic47—24no—
241C2×Dic47—22no—
242C2×Dic47—24no—
243C2×Dic47—232no—
244C2×Dic47—22no—
245C2×Dic47—24no—
246C2×Dic47—44no—
247C2×Dic47#121116yes—
248C2×Dic47C22×D414yes—
249C2×Dic47C22×D414yes—
250C2×Dic47C22×D414yes—
251C2×Dic47C22×D414yes—
252C2×Dic47C2×#4118yes—
253C2×Dic47C2×#4114yes—
254D188—232no—
255C4×D47—432no—
256C2×#2392—471nomaximal, Sylow
257C22×C47—24no—
258C22×C47—28no—
259C22×C47—416no—
260C22×C47—42no—
261C22×C47—44no—
262C22×C47—42no—
263C22×C47C2×#12114yes—
264C22×C47#52518yes—
265C22×C47#52514yes—
266C22×C47#52918yes—
267C22×C47#53214yes—
268C22×C47C23×D411yescharacteristic
269C22×C47C23×D411yescharacteristic
270C22×C47C22×#4111yescharacteristic
271C22×C47C22×#4112yes—
272C22×C47C22×#4112yes—
273C2×D47—28no—
274C2×D47—28no—
275C2×D47—28no—
276C2×D47—432no—
277C2×D47—44no—
278C2×D47—44no—
279C2×D47—44no—
280C2×D47—44no—
281C4×C47—24no—
282C4×C47—44no—
283C4×C47—44no—
284C4×C47—42no—
285Dic47—24no—
286Dic47—28no—
287Dic47—24no—
288Dic47—42no—
289Dic47C2×#12118yes—
290C22×C4×D4—471no—
291C22×C4×D4—472no—
292C22×#117—471no—
293#2392—4716no—
294C2×#398—471no—
295C2×#397D4711yescharacteristic, complemented
296C2×#396—472no—
297C2×#394—471no—
298C2×#394—472no—
299C2×#392—471no—
300C2×C4×C4⋊C4—471no—
301C2×C4×C22⋊C4—472no—
302C2×C47—44no—
303C2×C47#239218yescomplemented
304C2×C47C22×#12111yescharacteristic
305C2×C47C2×#52512yes—
306C2×C47C2×#52511yescharacteristic
307C2×C47C2×#52912yes—
308C2×C47C2×#53211yescharacteristic
309D47—48no—
310C23×D4—472no—
311C23×D4—471no—
312C24×C4—471no—
313C24×C4—472no—
314C2×C4×D4—478no—
315C2×C4×D4—4716no—
316C2×C4×D4—948no—
317C2×C4×D4—9416no—
318C2×#117—478no—
319C2×#117—948no—
320C22×C4⋊C4—472no—
321C22×C4⋊C4—471no—
322C22×C4⋊C4—471no—
323C22×C4⋊C4—472no—
324C22×C4⋊C4C2×D4711yescharacteristic
325C22×C22⋊C4—471no—
326C22×C22⋊C4—472no—
327C22×C22⋊C4—472no—
328C22×C22⋊C4—472no—
329C22×C22⋊C4—472no—
330C22×C22⋊C4C2×D4711yescharacteristic
331C22×C22⋊C4C2×D4712yes—
332C22×C42—471no—
333C22×C42—471no—
334C22×C42—472no—
335#398—478no—
336#397C2×D4718yescomplemented
337#396—4716no—
338#394—4716no—
339#394—478no—
340#392—478no—
341C4×C4⋊C4—478no—
342C4×C22⋊C4—4716no—
343C2×#95—471no—
344C2×#95—472no—
345C2×#95C2×D4711yescharacteristic
346C2×#95C2×D4712yes—
347C47C2×#239211yescharacteristic, complemented, Sylow
348C25—472no—
349C25C22×D4711yescharacteristic
350C22×D4—478no—
351C22×D4—474no—
352C22×D4—948no—
353C22×D4—948no—
354C22×D4—948no—
355C22×D4—948no—
356C22×D4—944no—
357C23×C4—471no—
358C23×C4—478no—
359C23×C4—474no—
360C23×C4—471no—
361C23×C4—471no—
362C23×C4—472no—
363C23×C4—471no—
364C23×C4—478no—
365C23×C4—948no—
366C23×C4—948no—
367C23×C4—948no—
368C23×C4—944no—
369C23×C4—944no—
370C23×C4C22×D4712yes—
371C23×C4C22×D4711yescharacteristic
372C23×C4C22×D4712yes—
373C23×C4C22×D4711yescharacteristic
374C4×D4—9432no—
375C4×D4—9464no—
376#117—9432no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—474no—
379C2×C4⋊C4—474no—
380C2×C4⋊C4—478no—
381C2×C4⋊C4—478no—
382C2×C4⋊C4—944no—
383C2×C4⋊C4—948no—
384C2×C4⋊C4—948no—
385C2×C4⋊C4—944no—
386C2×C4⋊C4C22×D4714yes—
387C2×C22⋊C4—28no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—474no—
390C2×C22⋊C4—478no—
391C2×C22⋊C4—478no—
392C2×C22⋊C4—478no—
393C2×C22⋊C4—478no—
394C2×C22⋊C4—948no—
395C2×C22⋊C4—948no—
396C2×C22⋊C4—948no—
397C2×C22⋊C4—948no—
398C2×C22⋊C4—944no—
399C2×C22⋊C4C22×D4714yes—
400C2×C22⋊C4C22×D4718yes—
401C2×C42—478no—
402C2×C42—474no—
403C2×C42—474no—
404C2×C42—478no—
405C2×C42—944no—
406C2×C42—948no—
407#95—478no—
408#95—474no—
409#95C22×D4718yes—
410#95C22×D4714yes—
411C24—22no—
412C24—22no—
413C24—24no—
414C24—24no—
415C24—478no—
416C24—474no—
417C24—944no—
418C24—944no—
419C24—944no—
420C24—944no—
421C24—944no—
422C24—944no—
423C24D4×D4714yes—
424C24C23×D4712yes—
425C24C23×D4711yescharacteristic
426C2×D4—9416no—
427C2×D4—9432no—
428C2×D4—9416no—
429C2×D4—9416no—
430C2×D4—9464no—
431C2×D4—9416no—
432C2×D4—948no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—24no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—474no—
443C22×C4—474no—
444C22×C4—474no—
445C22×C4—472no—
446C22×C4—474no—
447C22×C4—474no—
448C22×C4—4716no—
449C22×C4—478no—
450C22×C4—474no—
451C22×C4—472no—
452C22×C4—472no—
453C22×C4—472no—
454C22×C4—9416no—
455C22×C4—9416no—
456C22×C4—9416no—
457C22×C4—948no—
458C22×C4—9432no—
459C22×C4—948no—
460C22×C4—944no—
461C22×C4—942no—
462C22×C4—944no—
463C22×C4—942no—
464C22×C4—944no—
465C22×C4—942no—
466C22×C4—944no—
467C22×C4—18832no—
468C22×C4D4×D4714yes—
469C22×C4C23×D4714yes—
470C22×C4C23×D4714yes—
471C22×C4C23×D4712yes—
472C22×C4C23×D4712yes—
473C4⋊C4—28no—
474C4⋊C4—9416no—
475C4⋊C4—948no—
476C4⋊C4—9416no—
477C4⋊C4—948no—
478C22⋊C4—216no—
479C22⋊C4—28no—
480C22⋊C4—9416no—
481C22⋊C4—9416no—
482C22⋊C4—9416no—
483C22⋊C4—9416no—
484C22⋊C4—948no—
485C42—4716no—
486C42—948no—
487C42—9416no—
488C23—28no—
489C23—216no—
490C23—22no—
491C23—22no—
492C23—24no—
493C23—24no—
494C23—44no—
495C23—48no—
496C23—44no—
497C23—478no—
498C23—9416no—
499C23—9416no—
500C23—9416no—
501C23—944no—
502C23—944no—
503C23—944no—
504C23—944no—
505C23—944no—
506C23—944no—
507C23—1888no—
508C23—1888no—
509C23—1888no—
510C23—1888no—
511C23C2×D4×D4714yes—
512C23C2×D4×D4712yes—
513C23C2×D4×D4712yes—
514C23#41×D4712yes—
515C23#41×D4714yes—
516C23#41×D4714yes—
517C23C24×D4711yescharacteristic
518D4—9432no—
519D4—9464no—
520C2×C4—28no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—22no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—48no—
531C2×C4—48no—
532C2×C4—44no—
533C2×C4—4716no—
534C2×C4—474no—
535C2×C4—474no—
536C2×C4—474no—
537C2×C4—474no—
538C2×C4—474no—
539C2×C4—478no—
540C2×C4—9432no—
541C2×C4—948no—
542C2×C4—9416no—
543C2×C4—948no—
544C2×C4—944no—
545C2×C4—942no—
546C2×C4—944no—
547C2×C4—942no—
548C2×C4—944no—
549C2×C4—942no—
550C2×C4—944no—
551C2×C4—18832no—
552C2×C4—1884no—
553C2×C4C2×D4×D4714yes—
554C22—24no—
555C22—28no—
556C22—416no—
557C22—42no—
558C22—44no—
559C22—42no—
560C22—948no—
561C22—948no—
562C22—948no—
563C22—1884no—
564C22—18832no—
565C22—1884no—
566C22—1884no—
567C22—1884no—
568C22#121×D4714yes—
569C22#1568963114yes—
570C22#1568963118yes—
571C22#1568965618yes—
572C22#1568967214yes—
573C22C22×D4×D4711yescharacteristic
574C22C22×D4×D4711yescharacteristic
575C22C2×#41×D4711yescharacteristic
576C22C2×#41×D4712yes—
577C22C2×#41×D4712yes—
578C4—24no—
579C4—44no—
580C4—44no—
581C4—42no—
582C4—478no—
583C4—944no—
584C4—948no—
585C4—944no—
586C4—1882no—
587C2—44no—
588C2—1888no—
589C2#2024662518yesdirect product factor
590C2C2×#121×D4711yescharacteristic
591C2C2×#1568963111yescharacteristic
592C2C2×#1568963112yes—
593C2C2×#1568965612yes—
594C2C2×#1568967211yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#397C2
socleC24×C47C24
prime radicalC2×#15689032C2
hypercenterC2×#397D47
hypocenterC47C2×#2392
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. C22×#13093986C2semidirect
2. C22×(C22⋊D47)⋊C4C2semidirect
3. C22×#13093980C2semidirect
4. #20246625C2direct (N × H)
5. C2×#15689054C2semidirect
6. C2×#15689047C2semidirect
7. C2×#15689041C2semidirect
8. C2×#15689038C2semidirect
10. C2×#15688974C2semidirect
11. C2×#15688970C2semidirect
12. C2×C47×#397C2semidirect
18. C2×#13093986C22semidirect
20. C2×(C22⋊D47)⋊C4C22semidirect
22. C2×#13093980C22semidirect
35. #15689054C22semidirect
36. #15689047C22semidirect
37. #15689041C22semidirect
38. #15689038C22semidirect
40. #15688974C22semidirect
41. #15688970C22semidirect
47. C47×#397C22semidirect
60. C23×Dic47D4semidirect
94. C2×C4×Dic47D4semidirect
160. C22×Dic47C2×D4semidirect
189. C4×Dic47C2×D4semidirect
295. C2×#397D47semidirect
303. C2×C47#2392semidirect
336. #397C2×D47semidirect
347. C47C2×#2392semidirect
589. C2#20246625direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130939862
C22×(C22⋊D47)⋊C42
C22×#130939802
#202466252
C2×#156890542
C2×#156890472
C2×#156890412
C2×#156890382
C2×#156890322
C2×#156889742
C2×#156889702
C2×C47×#3972
C2×#239247