Finite Group Databasebeta

← C2×#20243741 #26217616

Subgroups — C2×#20243741 #26217616

Order 12032.

2038 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
1C23×#10625336C211yesmaximal, characteristic
2C22×Q8×Dic47C211yesmaximal, characteristic, complemented
3C22×#13093946C211yesmaximal, characteristic
4C2×#15689024C211yesmaximal, characteristic
5#20243741C218yesmaximal, direct product factor
6C2×#15688885C211yesmaximal, characteristic, complemented
7C2×#15688877C211yesmaximal, characteristic, complemented
8C22×#103×C47C211yesmaximal, characteristic, complemented
9C23×D188C2211yescharacteristic
10C22×#10625336—24no—
11C22×#10625336—24no—
12C22×#10625336C418yescomplemented
13C22×#10625336C2214yes—
14C23×C47⋊C8C2211yescharacteristic
15C2×Q8×Dic47—24no—
16C2×Q8×Dic47—22no—
17C2×Q8×Dic47—24no—
18C2×Q8×Dic47C2214yescomplemented
19C22×C4⋊Dic47—21no—
20C22×C4⋊Dic47C2211yescharacteristic
21C22×(C2×D47)⋊C4—21no—
22C22×(C2×D47)⋊C4—21no—
23C22×C4×Dic47—21no—
24C22×C4×Dic47C2211yescharacteristic
25C2×#13093946—24no—
26C2×#13093946C2214yes—
27#15689024—22no—
28#15689024C2214yes—
29#15688885C2214yescomplemented
30#15688877C2214yescomplemented
31C23×Q8×C47C2211yescharacteristic
32C23×C8×C47C2211yescharacteristic
33C22×C4⋊C4×C47C2211yescharacteristic
34C2×#103×C47—24no—
35C2×#103×C47C2214yescomplemented
36C24×D47—21no—
37C22×D188—22no—
38C22×D188—22no—
39C22×D188—22no—
40C22×D188—22no—
41C22×D188—21no—
42C22×D188—22no—
43C22×D188C2×C414yes—
44C22×D188C2312yes—
45C23×Dic47—21no—
46C23×Dic47D411yescharacteristic
47C23×Dic47D411yescharacteristic
48C2×#10625336—232no—
49C2×#10625336—28no—
50C2×#10625336—28no—
51C2×#10625336C2×C4116yescomplemented
52C22×C47⋊C8—22no—
53C22×C47⋊C8—22no—
54C22×C47⋊C8C2×C414yes—
55C22×C47⋊C8C2312yes—
56Q8×Dic47—216no—
57Q8×Dic47—28no—
58Q8×Dic47—28no—
59C2×C4⋊Dic47—28no—
60C2×C4⋊Dic47—21no—
61C2×C4⋊Dic47—22no—
62C2×C4⋊Dic47—24no—
63C2×C4⋊Dic47D414yes—
64C2×C4⋊Dic47C2312yes—
65C2×(C2×D47)⋊C4—24no—
66C2×(C2×D47)⋊C4—24no—
67C2×(C2×D47)⋊C4—44no—
68C2×(C2×D47)⋊C4—44no—
69C2×C4×Dic47—28no—
70C2×C4×Dic47—22no—
71C2×C4×Dic47—22no—
72C2×C4×Dic47—24no—
73C2×C4×Dic47D412yes—
74C2×C4×Dic47C2312yes—
75#13093946—28no—
76C22×Q8×C47—22no—
77C22×Q8×C47—21no—
78C22×Q8×C47—22no—
79C22×Q8×C47—22no—
80C22×Q8×C47C2×C414yes—
81C22×Q8×C47D414yes—
82C22×Q8×C47D414yes—
83C22×Q8×C47C2312yes—
84C23×C4×C47—21no—
85C23×C4×C47—21no—
86C23×C4×C47C2311yescharacteristic
87C22×C8×C47—22no—
88C22×C8×C47—22no—
89C22×C8×C47—22no—
90C22×C8×C47C2312yes—
91C2×C4⋊C4×C47—22no—
92C2×C4⋊C4×C47—22no—
93C2×C4⋊C4×C47—21no—
94C2×C4⋊C4×C47C2312yes—
95#103×C47—28no—
96C24×C47C2×D411yescharacteristic
97C23×D47—24no—
98C23×D47—22no—
99C23×D47—42no—
100C23×D47—42no—
101C23×D47—42no—
102C23×D47—42no—
103C23×D47—42no—
104C23×D47—42no—
105C2×Q8×C47—24no—
106C2×Q8×C47—28no—
107C2×Q8×C47—24no—
108C2×Q8×C47—24no—
109C2×Q8×C47—28no—
110C2×Q8×C47—28no—
111C2×Q8×C47—22no—
112C2×Q8×C47—22no—
113C2×Q8×C47—22no—
114C2×Q8×C47C22⋊C4116yescomplemented
115C2×Q8×C47C22×C414yes—
116C2×Q8×C47C2×D414yes—
117C2×Q8×C47C2×D414yes—
118C22×C4×C47—24no—
119C22×C4×C47—24no—
120C22×C4×C47—24no—
121C22×C4×C47—22no—
122C22×C4×C47—22no—
123C22×C4×C47—42no—
124C22×C4×C47—42no—
125C22×C4×C47—42no—
126C22×C4×C47C22×C412yes—
127C22×C4×C47C2×D412yes—
128C22×C4×C47C2×D412yes—
129C22×C4×C47C2×D411yescharacteristic
130C22×C4×C47C2×D412yes—
131C22×C4×C47#4112yes—
132C22×C4×C47#4112yes—
133C22×C4×C47C2411yescharacteristic
134C22×Dic47—22no—
135C22×Dic47—22no—
136C22×Dic47—22no—
137C22×Dic47—24no—
138C22×Dic47—22no—
139C22×Dic47—22no—
140C22×Dic47—22no—
141C22×Dic47—42no—
142C22×Dic47—42no—
143C22×Dic47SD1614yescomplemented
144C22×Dic47C2×D412yes—
145C22×Dic47C2×D412yes—
146C2×D188—28no—
147C2×D188—28no—
148C2×D188—22no—
149C2×D188—22no—
150C2×D188—22no—
151C2×D188—22no—
152C2×D188—24no—
153C2×D188—22no—
154C2×D188—42no—
155C2×D188—44no—
156C2×D188—42no—
157C2×D188—44no—
158C2×D188C22×C414yes—
159C2×C8×C47—22no—
160C2×C8×C47—22no—
161C2×C8×C47—22no—
162C2×C8×C47—44no—
163C4⋊C4×C47—22no—
164C4⋊C4×C47—22no—
165C4⋊C4×C47—42no—
166#10625336—232no—
167(C2×D47)⋊C4—48no—
168(C2×D47)⋊C4—48no—
169C4⋊Dic47—216no—
170C4⋊Dic47—24no—
171C4⋊Dic47—22no—
172C4⋊Dic47C2×D414yes—
173C4×Dic47—216no—
174C4×Dic47—24no—
175C4×Dic47—22no—
176C4×Dic47—22no—
177C2×C47⋊C8—28no—
178C2×C47⋊C8—22no—
179C2×C47⋊C8—22no—
180C2×C47⋊C8C22×C414yes—
181C23×C47C4×D412yes—
182C23×C47#12012yes—
183C23×C47#12112yes—
184C23×C47C2×SD1612yes—
185C23×C47#13512yes—
186C23×C47AGL(1,ℤ/8)12yes—
187C23×C47#13712yes—
188C23×C47C22×D411yescharacteristic
189C22×D47—24no—
190C22×D47—42no—
191C22×D47—42no—
192C22×D47—42no—
193C22×D47—42no—
194C22×D47—42no—
195C22×D47—42no—
196C22×D47—48no—
197C22×D47—48no—
198C22×D47—48no—
199C22×D47—84no—
200C22×D47—84no—
201C22×D47—84no—
202C22×D47—84no—
203Q8×C47—24no—
204Q8×C47—24no—
205Q8×C47—24no—
206Q8×C47—216no—
207Q8×C47C2×C22⋊C418yescomplemented
208C2×C4×C47—24no—
209C2×C4×C47—24no—
210C2×C4×C47—24no—
211C2×C4×C47—216no—
212C2×C4×C47—42no—
213C2×C4×C47—42no—
214C2×C4×C47—42no—
215C2×C4×C47—84no—
216C2×C4×C47C2×C22⋊C414yes—
217C2×C4×C47C4×D414yes—
218C2×C4×C47C4×D412yes—
219C2×C4×C47#12012yes—
220C2×C4×C47#12114yes—
221C2×C4×C47#12112yes—
222C2×C4×C47#12314yes—
223C2×C4×C47C23×C411yescharacteristic
224C2×C4×C47C22×D411yescharacteristic
225C2×C4×C47C22×D411yescharacteristic
226C2×C4×C47C22×D411yescharacteristic
227C2×C4×C47C2×#4111yescharacteristic
228C2×C4×C47C2×#4111yescharacteristic
229C2×Dic47—22no—
230C2×Dic47—22no—
231C2×Dic47—28no—
232C2×Dic47—22no—
233C2×Dic47—24no—
234C2×Dic47—22no—
235C2×Dic47—22no—
236C2×Dic47—42no—
237C2×Dic47—42no—
238C2×Dic47—44no—
239C2×Dic47—48no—
240C2×Dic47C2×SD1614yescomplemented
241D188—24no—
242D188—24no—
243D188—42no—
244D188—42no—
245D188—48no—
246C8×C47—42no—
247C47⋊C8—24no—
248C2×#1880—471nomaximal, Sylow
249C22×C47#38614yes—
250C22×C47C4×SD1614yes—
251C22×C47#44014yes—
252C22×C47#44814yes—
253C22×C47#44914yes—
254C22×C47#46014yes—
255C22×C47#46414yes—
256C22×C47C2×C4×D411yescharacteristic
257C22×C47C2×#12011yescharacteristic
258C22×C47C2×#12111yescharacteristic
259C22×C47C22×SD1611yescharacteristic
260C22×C47C2×#13511yescharacteristic
261C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
262C22×C47C2×#13711yescharacteristic
263C2×D47—44no—
264C2×D47—44no—
265C2×D47—44no—
266C2×D47—816no—
267C2×D47—82no—
268C2×D47—82no—
269C2×D47—82no—
270C2×D47—82no—
271C4×C47—28no—
272C4×C47—82no—
273C4×C47#38614yes—
274C4×C47C22×C22⋊C411yescharacteristic
275C4×C47C2×C4×D411yescharacteristic
276C4×C47C2×#12111yescharacteristic
277C4×C47C2×#12311yescharacteristic
278Dic47—24no—
279Dic47—42no—
280Dic47—44no—
281C23×SD16—471no—
282C22×C4×Q8—471no—
283C22×#103D4711yescharacteristic, complemented
284C22×#102—471no—
285C2×#390—471no—
286#1880—478no—
287C2×#340—471no—
288C2×#336—471no—
289C2×C47#188018yescomplemented
290C2×C47C2×#38611yescharacteristic
291C2×C47C2×C4×SD1611yescharacteristic
292C2×C47C2×#44011yescharacteristic
293C2×C47C2×#44811yescharacteristic
294C2×C47C2×#44911yescharacteristic
295C2×C47C2×#46011yescharacteristic
296C2×C47C2×#46411yescharacteristic
297D47—84no—
298C23×Q8C2×D4711yescharacteristic
299C23×D4—471no—
300C22×SD16—478no—
301C22×SD16—474no—
302C22×SD16—944no—
303C22×SD16—944no—
304C23×C8—471no—
305C23×C8C2×D4711yescharacteristic
306C2×C4×Q8—474no—
307C2×C4×Q8—942no—
308C2×C4×Q8—944no—
309C2×C4×Q8—944no—
310C22×C4⋊C4—471no—
311C22×C4⋊C4—941no—
312C22×C4⋊C4C2×D4711yescharacteristic
313C22×C22⋊C4—941no—
314C22×C22⋊C4—941no—
315C22×C42—471no—
316C22×C42—941no—
317C2×#103—24no—
318C2×#103C2×D4714yescomplemented
319C2×#102—474no—
320C2×#102—944no—
321#390—474no—
322#390—942no—
323#340—474no—
324#336—474no—
325C47C2×#188011yescharacteristic, complemented, Sylow
326C25—941no—
327C22×Q8—22no—
328C22×Q8—21no—
329C22×Q8—22no—
330C22×Q8—22no—
331C22×Q8C4×D4714yes—
332C22×Q8D18814yes—
333C22×Q8C22⋊D4714yes—
334C22×Q8C22×D4712yes—
335C22×D4—474no—
336C22×D4—472no—
337C22×D4—942no—
338C22×D4—942no—
339C22×D4—941no—
340C22×D4—942no—
341C22×D4—942no—
342C22×D4—942no—
343C23×C4—21no—
344C23×C4—21no—
345C23×C4—471no—
346C23×C4—471no—
347C23×C4—941no—
348C23×C4C22×D4711yescharacteristic
349C2×SD16—4716no—
350C2×SD16—9432no—
351C2×SD16—948no—
352C2×SD16—948no—
353C22×C8—22no—
354C22×C8—22no—
355C22×C8—22no—
356C22×C8—474no—
357C22×C8—472no—
358C22×C8—942no—
359C22×C8—942no—
360C22×C8C22×D4712yes—
361C4×Q8—948no—
362C4×Q8—9416no—
363C4×Q8—948no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—474no—
368C2×C4⋊C4—472no—
369C2×C4⋊C4—944no—
370C2×C4⋊C4—948no—
371C2×C4⋊C4—942no—
372C2×C4⋊C4—941no—
373C2×C4⋊C4C22×D4712yes—
374C2×C22⋊C4—944no—
375C2×C22⋊C4—944no—
376C2×C22⋊C4—1884no—
377C2×C22⋊C4—1884no—
378C2×C42—472no—
379C2×C42—472no—
380C2×C42—944no—
381C2×C42—948no—
382C2×C42—942no—
383C2×C42—942no—
384#103—28no—
385#102—948no—
386C24—944no—
387C24—942no—
388C24—1882no—
389C24—1882no—
390C24—1882no—
391C24—1882no—
392C24—1882no—
393C24—1882no—
394C24D4×D4711yescharacteristic
395C2×Q8—28no—
396C2×Q8—24no—
397C2×Q8—24no—
398C2×Q8—28no—
399C2×Q8—24no—
400C2×Q8—28no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8(C2×D47)⋊C4116yescomplemented
405C2×Q8C2×C4×D4714yes—
406C2×Q8C2×D18814yes—
407C2×Q8C2×C22⋊D4714yes—
408C2×D4—474no—
409C2×D4—948no—
410C2×D4—948no—
411C2×D4—944no—
412C2×D4—942no—
413C2×D4—942no—
414C2×D4—942no—
415C2×D4—942no—
416C2×D4—942no—
417C2×D4—1882no—
418C2×D4—1882no—
419C2×D4—1884no—
420C2×D4—1884no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—474no—
430C22×C4—472no—
431C22×C4—472no—
432C22×C4—942no—
433C22×C4—942no—
434C22×C4—944no—
435C22×C4—942no—
436C22×C4—942no—
437C22×C4—942no—
438C22×C4—942no—
439C22×C4—1882no—
440C22×C4—1882no—
441C22×C4C2×C4×D4712yes—
442C22×C4C2×D18812yes—
443C22×C4D4×D4711yescharacteristic
444C22×C4D4×D4712yes—
445C22×C4#1062535212yes—
446C22×C4#1062535212yes—
447C22×C4C2×C22⋊D4712yes—
448C22×C4C23×D4711yescharacteristic
449SD16—9432no—
450C2×C8—22no—
451C2×C8—22no—
452C2×C8—22no—
453C2×C8—44no—
454C2×C8—474no—
455C2×C8—948no—
456C2×C8—942no—
457C2×C8—942no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—42no—
461C4⋊C4—474no—
462C4⋊C4—9416no—
463C4⋊C4—944no—
464C4⋊C4—942no—
465C22⋊C4—1888no—
466C22⋊C4—1888no—
467C42—9416no—
468C42—944no—
469C42—942no—
470C42—942no—
471C23—944no—
472C23—3764no—
473C23—3764no—
474C23—3764no—
475C23—3764no—
476C23—1888no—
477C23—1888no—
478C23—1882no—
479C23—1882no—
480C23—1882no—
481C23—1882no—
482C23—1882no—
483C23—1882no—
484C23—1888no—
485C23(C22⋊D47)⋊C412yes—
486C23#1309399412yes—
487C23#1309399612yes—
488C23SD16×D4712yes—
489C23#1309404712yes—
490C23#1309405112yes—
491C23#1309405612yes—
492C23C2×D4×D4711yescharacteristic
493Q8—216no—
494Q8—24no—
495Q8—24no—
496Q8—24no—
497Q8C2×(C2×D47)⋊C418yescomplemented
498D4—944no—
499D4—944no—
500D4—1888no—
501D4—1882no—
502D4—1882no—
503C2×C4—216no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—84no—
511C2×C4—474no—
512C2×C4—948no—
513C2×C4—942no—
514C2×C4—942no—
515C2×C4—944no—
516C2×C4—942no—
517C2×C4—942no—
518C2×C4—942no—
519C2×C4—1884no—
520C2×C4—1888no—
521C2×C4—1882no—
522C2×C4—1882no—
523C2×C4C2×(C2×D47)⋊C414yes—
524C2×C4(C22⋊D47)⋊C412yes—
525C2×C4(C22⋊D47)⋊C414yes—
526C2×C4#1309399412yes—
527C2×C4#1309399612yes—
528C2×C4#1309399614yes—
529C2×C4#1309400814yes—
530C2×C4C22×C4×D4711yescharacteristic
531C2×C4C2×D4×D4711yescharacteristic
532C2×C4C22×C22⋊D4711yescharacteristic
533C2×C4C22×D18811yescharacteristic
534C2×C4C2×#1062535211yescharacteristic
535C2×C4C2×#1062535211yescharacteristic
536C8—42no—
537C8—944no—
538C22—37616no—
539C22—3762no—
540C22—3762no—
541C22—3762no—
542C22—3762no—
543C22—1884no—
544C22—1884no—
545C22—1884no—
546C22#1568900014yes—
547C22#1568920814yes—
548C22#1568922614yes—
549C22#1568926314yes—
550C22#1568927114yes—
551C22#1568932114yes—
552C22#1568934714yes—
553C22C2×(C22⋊D47)⋊C411yescharacteristic
554C22C2×#1309399411yescharacteristic
555C22C2×#1309399611yescharacteristic
556C22C2×SD16×D4711yescharacteristic
557C22C2×#1309404711yescharacteristic
558C22C2×#1309405111yescharacteristic
559C22C2×#1309405611yescharacteristic
560C4—28no—
561C4—82no—
562C4—944no—
563C4—1882no—
564C4—1884no—
565C4#1568900014yes—
566C4C22×(C2×D47)⋊C411yescharacteristic
567C4C2×(C22⋊D47)⋊C411yescharacteristic
568C4C2×#1309399611yescharacteristic
569C4C2×#1309400811yescharacteristic
570C2—3764no—
571C2#2024374118yesdirect product factor
572C2C2×#1568900011yescharacteristic
573C2C2×#1568920811yescharacteristic
574C2C2×#1568922611yescharacteristic
575C2C2×#1568926311yescharacteristic
576C2C2×#1568927111yescharacteristic
577C2C2×#1568932111yescharacteristic
578C2C2×#1568934711yescharacteristic
subgroupG/H
centerC24D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC22×#103×C47C2
socleC24×C47C2×D4
prime radicalC23×D188C22
cosocleC22×C4×C47C24
hypercenterC22×#103D47
hypocenterC47C2×#1880
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
2. C22×Q8×Dic47C2semidirect
5. #20243741C2direct (N × H)
6. C2×#15688885C2semidirect
7. C2×#15688877C2semidirect
8. C22×#103×C47C2semidirect
12. C22×#10625336C4semidirect
18. C2×Q8×Dic47C22semidirect
29. #15688885C22semidirect
30. #15688877C22semidirect
35. C2×#103×C47C22semidirect
51. C2×#10625336C2×C4semidirect
114. C2×Q8×C47C22⋊C4semidirect
143. C22×Dic47SD16semidirect
207. Q8×C47C2×C22⋊C4semidirect
240. C2×Dic47C2×SD16semidirect
283. C22×#103D47semidirect
289. C2×C47#1880semidirect
318. C2×#103C2×D47semidirect
325. C47C2×#1880semidirect
404. C2×Q8(C2×D47)⋊C4semidirect
497. Q8C2×(C2×D47)⋊C4semidirect
571. C2#20243741direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#106253362
C22×Q8×Dic472
C22×#130939462
C2×#156890242
#202437412
C2×#156888852
C2×#156888772
C22×#103×C472
C2×#188047