Finite Group Databasebeta

← C2×#20243743 #26217618

Subgroups — C2×#20243743 #26217618

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×#13093948C211yesmaximal, characteristic, complemented
3C22×#13093944C211yesmaximal, characteristic
4C2×#15689025C211yesmaximal, characteristic
5#20243743C218yesmaximal, direct product factor
6C2×#15688885C211yesmaximal, characteristic, complemented
7C2×#15688878C211yesmaximal, characteristic, complemented
8C22×C4×Q8×C47C211yesmaximal, characteristic, complemented
9C23×D188C2211yescharacteristic
10C22×#10625336—24no—
11C22×#10625336—24no—
12C22×#10625336C418yescomplemented
13C22×#10625336C2214yes—
14C23×C47⋊C8C2211yescharacteristic
15C23×C47⋊C8C2211yescharacteristic
16C22×C4⋊Dic47C2211yescharacteristic
17C22×(C2×D47)⋊C4—21no—
18C22×(C2×D47)⋊C4—21no—
19C2×#13093948—24no—
20C2×#13093948C2214yescomplemented
21C2×#13093944—24no—
22C2×#13093944C2214yes—
23#15689025—22no—
24#15689025C2214yes—
25#15688885C2214yescomplemented
26#15688878C2214yescomplemented
27C23×Q8×C47C2211yescharacteristic
28C2×C4×Q8×C47—24no—
29C2×C4×Q8×C47—24no—
30C2×C4×Q8×C47—22no—
31C2×C4×Q8×C47C2214yescomplemented
32C22×C4⋊C4×C47—21no—
33C22×C4⋊C4×C47C2211yescharacteristic
34C22×C42×C47—21no—
35C22×C42×C47C2211yescharacteristic
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—
46C2×#10625336—232no—
47C2×#10625336—28no—
48C2×#10625336—28no—
49C2×#10625336C2×C4116yescomplemented
50C22×C47⋊C8—22no—
51C22×C47⋊C8—22no—
52C22×C47⋊C8—22no—
53C22×C47⋊C8—22no—
54C22×C47⋊C8—22no—
55C22×C47⋊C8C2×C414yes—
56C22×C47⋊C8C2312yes—
57C22×C47⋊C8C2312yes—
58C2×C4⋊Dic47—22no—
59C2×C4⋊Dic47—22no—
60C2×C4⋊Dic47—21no—
61C2×C4⋊Dic47C2312yes—
62C2×(C2×D47)⋊C4—24no—
63C2×(C2×D47)⋊C4—24no—
64C2×(C2×D47)⋊C4—44no—
65C2×(C2×D47)⋊C4—44no—
66#13093948—28no—
67#13093944—28no—
68C22×Q8×C47—22no—
69C22×Q8×C47—21no—
70C22×Q8×C47—22no—
71C22×Q8×C47—22no—
72C22×Q8×C47C2×C414yes—
73C22×Q8×C47D414yes—
74C22×Q8×C47D414yes—
75C22×Q8×C47C2312yes—
76C23×C4×C47—21no—
77C23×C4×C47—21no—
78C23×C4×C47D411yescharacteristic
79C23×C4×C47D411yescharacteristic
80C23×C4×C47C2311yescharacteristic
81C4×Q8×C47—216no—
82C4×Q8×C47—28no—
83C4×Q8×C47—28no—
84C2×C4⋊C4×C47—28no—
85C2×C4⋊C4×C47—24no—
86C2×C4⋊C4×C47—21no—
87C2×C4⋊C4×C47—22no—
88C2×C4⋊C4×C47D414yes—
89C2×C4⋊C4×C47C2312yes—
90C2×C42×C47—28no—
91C2×C42×C47—24no—
92C2×C42×C47—22no—
93C2×C42×C47—22no—
94C2×C42×C47D412yes—
95C2×C42×C47C2312yes—
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—22no—
120C22×C4×C47—24no—
121C22×C4×C47—24no—
122C22×C4×C47—22no—
123C22×C4×C47—22no—
124C22×C4×C47—22no—
125C22×C4×C47—24no—
126C22×C4×C47—22no—
127C22×C4×C47—22no—
128C22×C4×C47—22no—
129C22×C4×C47—42no—
130C22×C4×C47—42no—
131C22×C4×C47SD1614yescomplemented
132C22×C4×C47C22×C412yes—
133C22×C4×C47C2×D412yes—
134C22×C4×C47C2×D412yes—
135C22×C4×C47C2×D412yes—
136C22×C4×C47C2×D412yes—
137C22×C4×C47C2×D411yescharacteristic
138C22×C4×C47C2×D412yes—
139C22×C4×C47#4112yes—
140C22×C4×C47#4112yes—
141C22×C4×C47C2411yescharacteristic
142C22×Dic47—22no—
143C22×Dic47—42no—
144C22×Dic47—42no—
145C22×Dic47—42no—
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—
159C4⋊C4×C47—216no—
160C4⋊C4×C47—24no—
161C4⋊C4×C47—22no—
162C4⋊C4×C47C2×D414yes—
163C42×C47—216no—
164C42×C47—24no—
165C42×C47—22no—
166C42×C47—22no—
167#10625336—232no—
168(C2×D47)⋊C4—48no—
169(C2×D47)⋊C4—48no—
170C4⋊Dic47—22no—
171C4⋊Dic47—22no—
172C4⋊Dic47—42no—
173C2×C47⋊C8—28no—
174C2×C47⋊C8—22no—
175C2×C47⋊C8—22no—
176C2×C47⋊C8—22no—
177C2×C47⋊C8—22no—
178C2×C47⋊C8—22no—
179C2×C47⋊C8—44no—
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—22no—
210C2×C4×C47—24no—
211C2×C4×C47—24no—
212C2×C4×C47—22no—
213C2×C4×C47—216no—
214C2×C4×C47—28no—
215C2×C4×C47—22no—
216C2×C4×C47—24no—
217C2×C4×C47—22no—
218C2×C4×C47—22no—
219C2×C4×C47—42no—
220C2×C4×C47—42no—
221C2×C4×C47—44no—
222C2×C4×C47—48no—
223C2×C4×C47C2×C22⋊C414yes—
224C2×C4×C47C4×D414yes—
225C2×C4×C47C4×D412yes—
226C2×C4×C47#12012yes—
227C2×C4×C47#12114yes—
228C2×C4×C47#12112yes—
229C2×C4×C47#12314yes—
230C2×C4×C47C2×SD1614yescomplemented
231C2×C4×C47C23×C411yescharacteristic
232C2×C4×C47C22×D411yescharacteristic
233C2×C4×C47C22×D411yescharacteristic
234C2×C4×C47C22×D411yescharacteristic
235C2×C4×C47C2×#4111yescharacteristic
236C2×C4×C47C2×#4111yescharacteristic
237C2×Dic47—42no—
238C2×Dic47—42no—
239C2×Dic47—42no—
240C2×Dic47—84no—
241D188—24no—
242D188—24no—
243D188—42no—
244D188—42no—
245D188—48no—
246C47⋊C8—24no—
247C47⋊C8—42no—
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—24no—
272C4×C47—28no—
273C4×C47—42no—
274C4×C47—44no—
275C4×C47#38614yes—
276C4×C47C22×C22⋊C411yescharacteristic
277C4×C47C2×C4×D411yescharacteristic
278C4×C47C2×#12111yescharacteristic
279C4×C47C2×#12311yescharacteristic
280Dic47—82no—
281C23×SD16—471no—
282C22×C4×Q8D4711yescharacteristic, complemented
283C22×#103—471no—
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×C8—471no—
306C2×C4×Q8—24no—
307C2×C4×Q8—24no—
308C2×C4×Q8—22no—
309C2×C4×Q8C2×D4714yescomplemented
310C22×C4⋊C4—21no—
311C22×C4⋊C4—471no—
312C22×C4⋊C4C2×D4711yescharacteristic
313C22×C22⋊C4—941no—
314C22×C22⋊C4—941no—
315C22×C42—21no—
316C22×C42C2×D4711yescharacteristic
317C2×#103—474no—
318C2×#103—944no—
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—22no—
329C22×Q8—22no—
330C22×Q8—21no—
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—942no—
340C22×D4—942no—
341C22×D4—942no—
342C22×D4—941no—
343C23×C4—21no—
344C23×C4—21no—
345C23×C4—941no—
346C23×C4C22⋊D4711yescharacteristic
347C23×C4C22⋊D4711yescharacteristic
348C23×C4C22×D4711yescharacteristic
349C2×SD16—4716no—
350C2×SD16—9432no—
351C2×SD16—948no—
352C2×SD16—948no—
353C22×C8—474no—
354C22×C8—472no—
355C22×C8—472no—
356C22×C8—942no—
357C22×C8—942no—
358C22×C8—942no—
359C22×C8—942no—
360C22×C8—942no—
361C4×Q8—216no—
362C4×Q8—28no—
363C4×Q8—28no—
364C2×C4⋊C4—28no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—472no—
369C2×C4⋊C4—942no—
370C2×C4⋊C4—942no—
371C2×C4⋊C4—941no—
372C2×C4⋊C4C22⋊D4714yes—
373C2×C4⋊C4C22×D4712yes—
374C2×C22⋊C4—944no—
375C2×C22⋊C4—944no—
376C2×C22⋊C4—1884no—
377C2×C22⋊C4—1884no—
378C2×C42—28no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—24no—
382C2×C42C22⋊D4712yes—
383C2×C42C22×D4712yes—
384#103—948no—
385#102—948no—
386C24—944no—
387C24—942no—
388C24—1882no—
389C24—1882no—
390C24—1882no—
391C24—1882no—
392C24—1882no—
393C24—1882no—
394C24C2×C22⋊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—22no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—24no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—942no—
435C22×C4—1882no—
436C22×C4—1882no—
437C22×C4—1882no—
438C22×C4#1062533614yescomplemented
439C22×C4C2×C4×D4712yes—
440C22×C4C2×D18812yes—
441C22×C4#1062535012yes—
442C22×C4#1062535012yes—
443C22×C4C2×C22⋊D4712yes—
444C22×C4C2×C22⋊D4712yes—
445C22×C4C2×C22⋊D4712yes—
446C22×C4C2×C22⋊D4711yescharacteristic
447C22×C4C2×C22⋊D4712yes—
448C22×C4C23×D4711yescharacteristic
449SD16—9432no—
450C2×C8—474no—
451C2×C8—948no—
452C2×C8—942no—
453C2×C8—942no—
454C2×C8—942no—
455C2×C8—942no—
456C2×C8—942no—
457C2×C8—1884no—
458C4⋊C4—216no—
459C4⋊C4—24no—
460C4⋊C4—22no—
461C4⋊C4—942no—
462C4⋊C4—942no—
463C4⋊C4—1882no—
464C4⋊C4C2×C22⋊D4714yes—
465C22⋊C4—1888no—
466C22⋊C4—1888no—
467C42—216no—
468C42—24no—
469C42—22no—
470C42—22no—
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—
485C23C4×C22⋊D4712yes—
486C23#1309399312yes—
487C23#1309399812yes—
488C23C2×#1062533612yes—
489C23#1309404412yes—
490C23#1309404912yes—
491C23#1309405512yes—
492C23C22×C22⋊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—28no—
505C2×C4—24no—
506C2×C4—22no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—44no—
515C2×C4—48no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—3764no—
519C2×C4—1882no—
520C2×C4—1882no—
521C2×C4—1882no—
522C2×C4C2×(C2×D47)⋊C414yes—
523C2×C4C4×C22⋊D4712yes—
524C2×C4C4×C22⋊D4714yes—
525C2×C4#1309399312yes—
526C2×C4#1309399812yes—
527C2×C4#1309399814yes—
528C2×C4#1309400714yes—
529C2×C4C2×#1062533614yescomplemented
530C2×C4C22×C4×D4711yescharacteristic
531C2×C4C22×C22⋊D4711yescharacteristic
532C2×C4C22×C22⋊D4711yescharacteristic
533C2×C4C22×D18811yescharacteristic
534C2×C4C2×#1062535011yescharacteristic
535C2×C4C2×#1062535011yescharacteristic
536C8—944no—
537C8—1882no—
538C22—37616no—
539C22—3762no—
540C22—3762no—
541C22—3762no—
542C22—3762no—
543C22—1884no—
544C22—1884no—
545C22—1884no—
546C22#1568900214yes—
547C22C4×#1062533614yes—
548C22#1568922114yes—
549C22#1568926214yes—
550C22#1568926814yes—
551C22#1568932314yes—
552C22#1568934514yes—
553C22C2×C4×C22⋊D4711yescharacteristic
554C22C2×#1309399311yescharacteristic
555C22C2×#1309399811yescharacteristic
556C22C22×#1062533611yescharacteristic
557C22C2×#1309404411yescharacteristic
558C22C2×#1309404911yescharacteristic
559C22C2×#1309405511yescharacteristic
560C4—28no—
561C4—24no—
562C4—42no—
563C4—44no—
564C4—3762no—
565C4#1568900214yes—
566C4C22×(C2×D47)⋊C411yescharacteristic
567C4C2×C4×C22⋊D4711yescharacteristic
568C4C2×#1309399811yescharacteristic
569C4C2×#1309400711yescharacteristic
570C2—3764no—
571C2#2024374318yesdirect product factor
572C2C2×#1568900211yescharacteristic
573C2C2×C4×#1062533611yescharacteristic
574C2C2×#1568922111yescharacteristic
575C2C2×#1568926211yescharacteristic
576C2C2×#1568926811yescharacteristic
577C2C2×#1568932311yescharacteristic
578C2C2×#1568934511yescharacteristic
subgroupG/H
centerC24C2×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC22×C4×Q8×C47C2
socleC24×C47C2×D4
prime radicalC23×D188C22
cosocleC22×C4×C47C24
hypercenterC22×C4×Q8D47
hypocenterC47C2×#1880
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
2. C22×#13093948C2semidirect
5. #20243743C2direct (N × H)
6. C2×#15688885C2semidirect
7. C2×#15688878C2semidirect
8. C22×C4×Q8×C47C2semidirect
12. C22×#10625336C4semidirect
20. C2×#13093948C22semidirect
25. #15688885C22semidirect
26. #15688878C22semidirect
31. C2×C4×Q8×C47C22semidirect
49. C2×#10625336C2×C4semidirect
114. C2×Q8×C47C22⋊C4semidirect
131. C22×C4×C47SD16semidirect
207. Q8×C47C2×C22⋊C4semidirect
230. C2×C4×C47C2×SD16semidirect
282. C22×C4×Q8D47semidirect
289. C2×C47#1880semidirect
309. C2×C4×Q8C2×D47semidirect
325. C47C2×#1880semidirect
404. C2×Q8(C2×D47)⋊C4semidirect
438. C22×C4#10625336semidirect
497. Q8C2×(C2×D47)⋊C4semidirect
529. C2×C4C2×#10625336semidirect
571. C2#20243743direct (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×#130939482
C22×#130939442
C2×#156890252
#202437432
C2×#156888852
C2×#156888782
C22×C4×Q8×C472
C2×#188047