Finite Group Databasebeta

← C2×#20244685 #26244151

Subgroups — C2×#20244685 #26244151

Order 12032.

1362 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094054C211yesmaximal, characteristic
2C22×#13093959C211yesmaximal, characteristic, complemented
3C22×#13093947C211yesmaximal, characteristic, complemented
4C22×#13093942C211yesmaximal, characteristic, complemented
5C2×#15689090C211yesmaximal, characteristic
6#20244685C218yesmaximal, direct product factor
7C2×#15688892C211yesmaximal, characteristic, complemented
8C2×C47×#417C211yesmaximal, characteristic
9C23×Dic94C2211yescharacteristic
10C2×#13094054—24no—
11C2×#13094054—24no—
12C2×#13094054—22no—
13C2×#13094054C2214yes—
14C22×#10625337—21no—
15C22×#10625335—21no—
16C22×#10625329C2211yescharacteristic
17C22×#10625329C2211yescharacteristic
18C23×C47⋊C8C2211yescharacteristic
19C2×#13093959—24no—
20C2×#13093959C2214yescomplemented
21C2×#13093947—22no—
22C2×#13093947—22no—
23C2×#13093947C2214yescomplemented
24C2×#13093942—24no—
25C2×#13093942C2214yescomplemented
26#15689090—22no—
27#15689090C2214yes—
28C2×C22⋊(C47⋊C8)—22no—
29#15688892C2214yescomplemented
30C22×#41×C47C2211yescharacteristic
31C22×M16×C47C2211yescharacteristic
32C22×C4⋊C4×C47C2211yescharacteristic
33C47×#417—22no—
34C47×#417C2214yes—
35C2×#103×C47—21no—
36C2×#102×C47—21no—
37C22×Dic94—21no—
38C22×Dic94—21no—
39C22×Dic94—21no—
40C22×Dic94—22no—
41C22×Dic94—21no—
42C22×Dic94—22no—
43C22×Dic94—21no—
44C22×Dic94—22no—
45C22×Dic94D414yes—
46C22×Dic94C2312yes—
47C23×Dic47—21no—
48#13094054—216no—
49#13094054—28no—
50#13094054—28no—
51C2×#10625337—28no—
52C2×#10625337—24no—
53C2×#10625335—28no—
54C2×#10625335—24no—
55C2×#10625329—22no—
56C2×#10625329—21no—
57C2×#10625329—21no—
58C2×#10625329—22no—
59C2×#10625329—22no—
60C2×#10625329D414yes—
61C2×#10625329C2312yes—
62C2×#10625329C2312yes—
63C22×C47⋊C8—22no—
64C22×C47⋊C8—21no—
65C22×C47⋊C8—22no—
66C22×C47⋊C8—21no—
67C22×C47⋊C8D412yes—
68C22×C47⋊C8D412yes—
69C22×C47⋊C8C2312yes—
70#13093959—28no—
71#13093947—28no—
72#13093942—28no—
73C22⋊(C47⋊C8)—28no—
74C2×#41×C47—21no—
75C2×#41×C47—21no—
76C2×#41×C47—22no—
77C2×#41×C47—22no—
78C2×#41×C47—22no—
79C2×#41×C47—22no—
80C2×#41×C47D412yes—
81C2×#41×C47C2312yes—
82C22×Q8×C47D411yescharacteristic
83C22×D4×C47—21no—
84C22×D4×C47D411yescharacteristic
85C23×C4×C47—21no—
86C23×C4×C47—21no—
87C23×C4×C47C2311yescharacteristic
88C2×M16×C47—21no—
89C2×M16×C47—22no—
90C2×M16×C47—22no—
91C2×M16×C47C2312yes—
92C22×C8×C47—21no—
93C2×C4⋊C4×C47—21no—
94C2×C4⋊C4×C47—21no—
95C2×C4⋊C4×C47—21no—
96C2×C4⋊C4×C47—21no—
97C2×C4⋊C4×C47—21no—
98C2×C4⋊C4×C47C2312yes—
99#103×C47—24no—
100#102×C47—24no—
101C24×C47—21no—
102C24×C47#4111yescharacteristic
103#41×C47—24no—
104#41×C47—24no—
105#41×C47—22no—
106#41×C47—22no—
107#41×C47—22no—
108#41×C47—22no—
109#41×C47—42no—
110#41×C47—42no—
111#41×C47—42no—
112#41×C47—42no—
113C2×Q8×C47—21no—
114C2×Q8×C47—22no—
115C2×Q8×C47—22no—
116C2×Q8×C47C2×D412yes—
117C2×D4×C47—22no—
118C2×D4×C47—22no—
119C2×D4×C47—22no—
120C2×D4×C47—21no—
121C2×D4×C47—22no—
122C2×D4×C47—42no—
123C2×D4×C47—42no—
124C2×D4×C47C2×D412yes—
125C22×C4×C47—21no—
126C22×C4×C47—22no—
127C22×C4×C47—22no—
128C22×C4×C47—22no—
129C22×C4×C47—42no—
130C22×C4×C47—42no—
131C22×C4×C47—41no—
132C22×C4×C47—41no—
133C22×C4×C47—82no—
134C22×C4×C47C2×D412yes—
135C22×C4×C47C2×D412yes—
136C22×C4×C47C2×D411yescharacteristic
137C22×C4×C47C2×D411yescharacteristic
138C22×C4×C47C2×D411yescharacteristic
139C22×C4×C47C2×D411yescharacteristic
140C22×C4×C47#4112yes—
141C22×C4×C47#4111yescharacteristic
142C22×C4×C47#4112yes—
143C22×C4×C47C2411yescharacteristic
144C22×Dic47—24no—
145C22×Dic47—22no—
146C22×Dic47—41no—
147C22×Dic47—41no—
148C22×Dic47—42no—
149C2×Dic94—24no—
150C2×Dic94—24no—
151C2×Dic94—24no—
152C2×Dic94—24no—
153C2×Dic94—22no—
154C2×Dic94—22no—
155C2×Dic94—22no—
156C2×Dic94—22no—
157C2×Dic94—24no—
158C2×Dic94—22no—
159C2×Dic94—42no—
160C2×Dic94—42no—
161C2×Dic94—41no—
162C2×Dic94—41no—
163C2×Dic94—42no—
164C2×Dic94—42no—
165C2×Dic94—42no—
166C2×Dic94C2×D414yes—
167M16×C47—22no—
168M16×C47—22no—
169M16×C47—42no—
170C2×C8×C47—22no—
171C2×C8×C47—42no—
172C4⋊C4×C47—22no—
173C4⋊C4×C47—22no—
174C4⋊C4×C47—41no—
175C4⋊C4×C47—41no—
176#10625337—216no—
177#10625335—216no—
178#10625329—24no—
179#10625329—22no—
180#10625329—22no—
181#10625329—22no—
182#10625329—42no—
183#10625329C2×D414yes—
184C2×C47⋊C8—24no—
185C2×C47⋊C8—24no—
186C2×C47⋊C8—24no—
187C2×C47⋊C8—22no—
188C2×C47⋊C8—22no—
189C2×C47⋊C8—22no—
190C2×C47⋊C8—22no—
191C2×C47⋊C8—42no—
192C2×C47⋊C8C2×D414yes—
193C23×C47—22no—
194C23×C47—22no—
195C23×C47—22no—
196C23×C47—42no—
197C23×C47—42no—
198C23×C47—42no—
199C23×C47#12111yescharacteristic
200C23×C47#12111yescharacteristic
201C23×C47#12312yes—
202C23×C47#12412yes—
203C23×C47C2×#4111yescharacteristic
204Q8×C47—22no—
205Q8×C47—22no—
206Q8×C47—42no—
207D4×C47—22no—
208D4×C47—22no—
209D4×C47—42no—
210D4×C47—42no—
211D4×C47—44no—
212D4×C47—42no—
213C2×C4×C47—22no—
214C2×C4×C47—42no—
215C2×C4×C47—42no—
216C2×C4×C47—42no—
217C2×C4×C47—44no—
218C2×C4×C47—42no—
219C2×C4×C47—82no—
220C2×C4×C47—82no—
221C2×C4×C47—82no—
222C2×C4×C47#12012yes—
223C2×C4×C47#12012yes—
224C2×C4×C47#12111yescharacteristic
225C2×C4×C47#12111yescharacteristic
226C2×C4×C47#12112yes—
227C2×C4×C47#12112yes—
228C2×C4×C47#12112yes—
229C2×C4×C47#12112yes—
230C2×C4×C47#12312yes—
231C2×C4×C47#12312yes—
232C2×C4×C47#12312yes—
233C2×C4×C47#12412yes—
234C2×C4×C47C22×D411yescharacteristic
235C2×C4×C47C22×D411yescharacteristic
236C2×C4×C47C22×D411yescharacteristic
237C2×C4×C47C22×D411yescharacteristic
238C2×C4×C47C2×#4111yescharacteristic
239C2×C4×C47C2×#4111yescharacteristic
240C2×Dic47—24no—
241C2×Dic47—42no—
242C2×Dic47—42no—
243C2×Dic47—44no—
244C2×Dic47—44no—
245Dic94—24no—
246Dic94—24no—
247Dic94—42no—
248Dic94—42no—
249Dic94—44no—
250Dic94—44no—
251C8×C47—42no—
252C47⋊C8—24no—
253C47⋊C8—24no—
254C47⋊C8—42no—
255C2×#2052—471nomaximal, Sylow
256C22×C47—24no—
257C22×C47—24no—
258C22×C47—21no—
259C22×C47—21no—
260C22×C47—21no—
261C22×C47—21no—
262C22×C47—42no—
263C22×C47—42no—
264C22×C47—42no—
265C22×C47—84no—
266C22×C47#39412yes—
267C22×C47#39412yes—
268C22×C47#47112yes—
269C22×C47#47312yes—
270C22×C47C2×#12111yescharacteristic
271C22×C47C2×#12311yescharacteristic
272C22×C47C2×#12411yescharacteristic
273C4×C47—42no—
274C4×C47—82no—
275C4×C47#39412yes—
276C4×C47#39412yes—
277C4×C47C2×#12011yescharacteristic
278C4×C47C2×#12111yescharacteristic
279C4×C47C2×#12111yescharacteristic
280C4×C47C2×#12311yescharacteristic
281Dic47—44no—
282C22×#137—471no—
283C22×#108—471no—
284C2×#417D4711yescharacteristic
285C22×#103—471no—
286C22×#101—471no—
287C2×#408—471no—
288#2052—478no—
289C2×#343—471no—
290C2×C47—21no—
291C2×C47—21no—
292C2×C47—22no—
293C2×C47—82no—
294C2×C47#205214yescomplemented
295C2×C47C2×#39411yescharacteristic
296C2×C47C2×#47111yescharacteristic
297C2×C47C2×#47311yescharacteristic
298C22×#41C2×D4711yescharacteristic
299C23×Q8—471no—
300C2×#137—474no—
301C2×#137—944no—
302C2×#137—944no—
303C2×#137—942no—
304C22×Q16—941no—
305C22×SD16—941no—
306C22×M16—471no—
307C22×M16—471no—
308C22×M16C2×D4711yescharacteristic
309C23×C8—471no—
310C22×C4⋊C4C2×D4711yescharacteristic
311C2×#108—474no—
312C2×#108—944no—
313#417—22no—
314#417C2×D4714yes—
315C2×#103—21no—
316C2×#103—474no—
317C2×#103—942no—
318C2×#103—942no—
319C2×#102—21no—
320C2×#101—474no—
321C2×#101—944no—
322#408—474no—
323#408—942no—
324C2×C22⋊C8—942no—
325#343—474no—
326C47C2×#205211yescharacteristic, complemented, Sylow
327C2×#41—21no—
328C2×#41—21no—
329C2×#41—22no—
330C2×#41—22no—
331C2×#41—22no—
332C2×#41—22no—
333C2×#41C22⋊D4712yes—
334C2×#41C22×D4712yes—
335C22×Q8—474no—
336C22×Q8—472no—
337C22×Q8—942no—
338C22×Q8—941no—
339C22×Q8—942no—
340C22×Q8—942no—
341C22×Q8—941no—
342C22×Q8—941no—
343C22×Q8—941no—
344C22×Q8—941no—
345C22×Q8C22⋊D4711yescharacteristic
346C22×D4—21no—
347C22×D4C22⋊D4711yescharacteristic
348C23×C4—21no—
349C23×C4—21no—
350C23×C4—941no—
351C23×C4C22×D4711yescharacteristic
352#137—948no—
353#137—948no—
354#137—9416no—
355C2×Q16—948no—
356C2×Q16—944no—
357C2×SD16—948no—
358C2×SD16—944no—
359C2×M16—21no—
360C2×M16—22no—
361C2×M16—22no—
362C2×M16—474no—
363C2×M16—472no—
364C2×M16—472no—
365C2×M16—942no—
366C2×M16—941no—
367C2×M16—941no—
368C2×M16—942no—
369C2×M16—942no—
370C2×M16C22×D4712yes—
371C22×C8—21no—
372C22×C8—472no—
373C22×C8—472no—
374C22×C8—472no—
375C22×C8—942no—
376C22×C8—942no—
377C22×C8—941no—
378C22×C8—941no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4C22×D4712yes—
385#108—948no—
386#103—24no—
387#103—948no—
388#102—24no—
389#101—948no—
390C22⋊C8—948no—
391C24—21no—
392C24#1062535211yescharacteristic
393#41—24no—
394#41—24no—
395#41—22no—
396#41—22no—
397#41—22no—
398#41—22no—
399#41—42no—
400#41—42no—
401#41—42no—
402#41—42no—
403C2×Q8—21no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—474no—
407C2×Q8—944no—
408C2×Q8—942no—
409C2×Q8—944no—
410C2×Q8—944no—
411C2×Q8—944no—
412C2×Q8—944no—
413C2×Q8—942no—
414C2×Q8—942no—
415C2×Q8—942no—
416C2×Q8—942no—
417C2×Q8—1881no—
418C2×Q8—1881no—
419C2×Q8—1882no—
420C2×Q8—1882no—
421C2×Q8—1882no—
422C2×Q8—1882no—
423C2×Q8—1882no—
424C2×Q8C2×C22⋊D4712yes—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—21no—
429C2×D4—22no—
430C2×D4—42no—
431C2×D4—42no—
432C2×D4C2×C22⋊D4712yes—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—82no—
442C22×C4—944no—
443C22×C4—942no—
444C22×C4—1881no—
445C22×C4—1881no—
446C22×C4—1882no—
447C22×C4#1062535012yes—
448C22×C4#1062535012yes—
449C22×C4D4×D4712yes—
450C22×C4D4×D4712yes—
451C22×C4D4×D4711yescharacteristic
452C22×C4D4×D4711yescharacteristic
453C22×C4#1062535211yescharacteristic
454C22×C4C2×C22⋊D4711yescharacteristic
455C22×C4C2×C22⋊D4711yescharacteristic
456C22×C4C23×D4711yescharacteristic
457Q16—9416no—
458SD16—9416no—
459M16—22no—
460M16—22no—
461M16—42no—
462M16—474no—
463M16—944no—
464M16—942no—
465M16—942no—
466M16—942no—
467M16—1882no—
468C2×C8—22no—
469C2×C8—42no—
470C2×C8—474no—
471C2×C8—944no—
472C2×C8—944no—
473C2×C8—944no—
474C2×C8—942no—
475C2×C8—942no—
476C2×C8—942no—
477C2×C8—942no—
478C2×C8—1882no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C23—22no—
484C23—22no—
485C23—22no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23#1309399611yescharacteristic
490C23#1309399611yescharacteristic
491C23#1309400612yes—
492C23#1309401012yes—
493C23C2×#1062535211yescharacteristic
494Q8—22no—
495Q8—22no—
496Q8—42no—
497Q8—944no—
498Q8—944no—
499Q8—1884no—
500Q8—1884no—
501Q8—1882no—
502Q8—1882no—
503D4—22no—
504D4—22no—
505D4—44no—
506D4—42no—
507D4—42no—
508D4—42no—
509C2×C4—22no—
510C2×C4—42no—
511C2×C4—44no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—82no—
516C2×C4—82no—
517C2×C4—82no—
518C2×C4—944no—
519C2×C4—1884no—
520C2×C4—1884no—
521C2×C4—1882no—
522C2×C4—1882no—
523C2×C4#1309399212yes—
524C2×C4#1309399212yes—
525C2×C4#1309399611yescharacteristic
526C2×C4#1309399611yescharacteristic
527C2×C4#1309399712yes—
528C2×C4#1309399712yes—
529C2×C4#1309399712yes—
530C2×C4#1309399712yes—
531C2×C4#1309400612yes—
532C2×C4#1309400712yes—
533C2×C4#1309400712yes—
534C2×C4#1309401012yes—
535C2×C4C2×D4×D4711yescharacteristic
536C2×C4C2×D4×D4711yescharacteristic
537C2×C4C2×D4×D4711yescharacteristic
538C2×C4C22×C22⋊D4711yescharacteristic
539C2×C4C2×#1062535011yescharacteristic
540C2×C4C2×#1062535011yescharacteristic
541C8—42no—
542C8—944no—
543C8—944no—
544C8—1882no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—24no—
550C22—24no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—84no—
555C22#1568903812yes—
556C22#1568903812yes—
557C22#1568938412yes—
558C22#1568939612yes—
559C22C2×#1309399611yescharacteristic
560C22C2×#1309400611yescharacteristic
561C22C2×#1309401011yescharacteristic
562C4—42no—
563C4—82no—
564C4—1884no—
565C4#1568903812yes—
566C4#1568903812yes—
567C4C2×#1309399211yescharacteristic
568C4C2×#1309399711yescharacteristic
569C4C2×#1309399711yescharacteristic
570C4C2×#1309400711yescharacteristic
571C2—22no—
572C2—21no—
573C2—21no—
574C2—82no—
575C2#2024468514yesdirect product factor
576C2C2×#1568903811yescharacteristic
577C2C2×#1568938411yescharacteristic
578C2C2×#1568939611yescharacteristic
subgroupG/H
centerC23#13093996
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC2×C47×#417C2
socleC23×C47#121
prime radicalC22×#41×C47C22
hypercenterC2×#417D47
hypocenterC47C2×#2052
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C22×#13093959C2semidirect
3. C22×#13093947C2semidirect
4. C22×#13093942C2semidirect
6. #20244685C2direct (N × H)
7. C2×#15688892C2semidirect
20. C2×#13093959C22semidirect
23. C2×#13093947C22semidirect
25. C2×#13093942C22semidirect
29. #15688892C22semidirect
294. C2×C47#2052semidirect
326. C47C2×#2052semidirect
575. C2#20244685direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940542
C22×#130939592
C22×#130939472
C22×#130939422
C2×#156890902
#202446852
C2×#156888922
C2×C47×#4172
C2×#205247