Finite Group Databasebeta

← C4×#15689054 #26138112

Subgroups — C4×#15689054 #26138112

Order 12032.

1574 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689054C211yesmaximal, characteristic
2C2×C4×Dic47⋊C4C212yesmaximal
3C2×C4×Dic47⋊C4C211yesmaximal, characteristic
4#20241656C211yesmaximal, characteristic
5#20241651C211yesmaximal, characteristic
6#20241643C212yesmaximal
7#20241639C212yesmaximal
8#20241638C211yesmaximal, characteristic
9C4×C47⋊#95C212yesmaximal
10C4×C47⋊#95C211yesmaximal, characteristic
11C2×C4×C4⋊C4×C47C211yesmaximal, characteristic
12C22×Dic47⋊C4C2211yescharacteristic
13C22×Dic47⋊C4C2212yes—
14C22×Dic47⋊C4C2211yescharacteristic
15C22×Dic47⋊C4C2212yes—
16C22×C4×Dic47C2211yescharacteristic
17C22×C4×Dic47C2211yescharacteristic
18C22×C4×Dic47C2212yes—
19#15689054C418yesdirect product factor
20C4×Dic47⋊C4—28no—
21C4×Dic47⋊C4—24no—
22C2×C47⋊#95C2212yes—
23C2×C47⋊#95C2211yescharacteristic
24C2×C47⋊#95C2212yes—
25C2×C47⋊#95C2212yes—
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2211yescharacteristic
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2211yescharacteristic
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2211yescharacteristic
33C22×C4⋊C4×C47C2211yescharacteristic
34C22×C4⋊C4×C47C2211yescharacteristic
35C22×C42×C47C2212yes—
36C22×C42×C47C2211yescharacteristic
37C4×C4⋊C4×C47—24no—
38C2×#95×C47C2212yes—
39C23×Dic47C2311yescharacteristic
40C23×Dic47C2311yescharacteristic
41C23×Dic47C2312yes—
42C23×Dic47C2311yescharacteristic
43C23×Dic47C2311yescharacteristic
44C23×Dic47C2312yes—
45C2×Dic47⋊C4—22no—
46C2×Dic47⋊C4—22no—
47C2×Dic47⋊C4—24no—
48C2×Dic47⋊C4—22no—
49C2×Dic47⋊C4—24no—
50C2×Dic47⋊C4—24no—
51C2×Dic47⋊C4—22no—
52C2×Dic47⋊C4—22no—
53C2×Dic47⋊C4—24no—
54C2×Dic47⋊C4—24no—
55C2×Dic47⋊C4C2×C414yes—
56C2×Dic47⋊C4C2×C418yes—
57C2×C4×Dic47—22no—
58C2×C4×Dic47—24no—
59C2×C4×Dic47—22no—
60C2×C4×Dic47—24no—
61C2×C4×Dic47—22no—
62C2×C4×Dic47—24no—
63C2×C4×Dic47D414yes—
64C2×C4×Dic47Q818yes—
65C47⋊#95—22no—
66C47⋊#95—22no—
67C47⋊#95—24no—
68C47⋊#95—22no—
69C47⋊#95—24no—
70C47⋊#95—24no—
71C47⋊#95—24no—
72C47⋊#95—24no—
73C47⋊#95—24no—
74C47⋊#95C2×C418yes—
75C47⋊#95C2×C414yes—
76C23×C4×C47C2312yes—
77C23×C4×C47C2311yescharacteristic
78C23×C4×C47C2312yes—
79C23×C4×C47C2311yescharacteristic
80C23×C4×C47C2311yescharacteristic
81C2×C4⋊C4×C47—22no—
82C2×C4⋊C4×C47—22no—
83C2×C4⋊C4×C47—24no—
84C2×C4⋊C4×C47—22no—
85C2×C4⋊C4×C47C2×C414yes—
86C2×C42×C47—24no—
87C2×C42×C47—24no—
88C2×C42×C47—24no—
89C2×C42×C47—24no—
90C2×C42×C47D414yes—
91#95×C47—24no—
92C24×C47C2411yescharacteristic
93C22×C4×C47—22no—
94C22×C4×C47—22no—
95C22×C4×C47—22no—
96C22×C4×C47—22no—
97C22×C4×C47—22no—
98C22×C4×C47—22no—
99C22×C4×C47—22no—
100C22×C4×C47—22no—
101C22×C4×C47—22no—
102C22×C4×C47—22no—
103C22×C4×C47—22no—
104C22×C4×C47—22no—
105C22×C4×C47—22no—
106C22×C4×C47—22no—
107C22×C4×C47—22no—
108C22×C4×C47—21no—
109C22×C4×C47—21no—
110C22×C4×C47—22no—
111C22×C4×C47C22×C414yes—
112C22×C4×C47C22×C412yes—
113C22×C4×C47C2×D412yes—
114C22×C4×C47C2×D412yes—
115C22×C4×C47C2×D412yes—
116C22×C4×C47C2×D412yes—
117C22×C4×C47C2×Q814yes—
118C22×C4×C47#4114yes—
119C22×C4×C47#4112yes—
120C22×C4×C47#4112yes—
121C22×C4×C47#4114yes—
122C22×Dic47—21no—
123C22×Dic47—22no—
124C22×Dic47—21no—
125C22×Dic47—22no—
126C22×Dic47—21no—
127C22×Dic47—22no—
128C22×Dic47—21no—
129C22×Dic47—22no—
130C22×Dic47—21no—
131C22×Dic47—22no—
132C22×Dic47—21no—
133C22×Dic47—21no—
134C22×Dic47—22no—
135C22×Dic47—22no—
136C22×Dic47—22no—
137C22×Dic47—22no—
138C22×Dic47—22no—
139C22×Dic47—22no—
140C22×Dic47—22no—
141C22×Dic47—21no—
142C22×Dic47—22no—
143C22×Dic47—22no—
144C22×Dic47—21no—
145C22×Dic47—22no—
146C22×Dic47—22no—
147C22×Dic47—21no—
148C22×Dic47C22×C412yes—
149C22×Dic47C22×C412yes—
150C22×Dic47C22×C414yes—
151C22×Dic47C2×D412yes—
152C22×Dic47C2×D412yes—
153C22×Dic47C2×Q814yes—
154C22×Dic47C2×Q814yes—
155C22×Dic47#4112yes—
156C22×Dic47#4112yes—
157C22×Dic47#4114yes—
158C4⋊C4×C47—28no—
159C4⋊C4×C47—28no—
160C42×C47—28no—
161C42×C47—48no—
162Dic47⋊C4—216no—
163Dic47⋊C4—28no—
164Dic47⋊C4—28no—
165Dic47⋊C4—216no—
166C4×Dic47—28no—
167C4×Dic47—216no—
168C4×Dic47—44no—
169C23×C47C23×C411yescharacteristic
170C23×C47C22×D411yescharacteristic
171C23×C47C22×D411yescharacteristic
172C23×C47C22×Q812yes—
173C23×C47C2×#4111yescharacteristic
174C23×C47C2×#4112yes—
175C23×C47C2×#4111yescharacteristic
176C23×C47C2×#4111yescharacteristic
177C23×C47C2×#4111yescharacteristic
178C23×C47C2×#4112yes—
179C23×C47C2×#4112yes—
180C2×C4×C47—24no—
181C2×C4×C47—22no—
182C2×C4×C47—22no—
183C2×C4×C47—24no—
184C2×C4×C47—24no—
185C2×C4×C47—24no—
186C2×C4×C47—24no—
187C2×C4×C47—22no—
188C2×C4×C47—22no—
189C2×C4×C47—24no—
190C2×C4×C47—24no—
191C2×C4×C47—24no—
192C2×C4×C47—22no—
193C2×C4×C47—42no—
194C2×C4×C47—42no—
195C2×C4×C47—42no—
196C2×C4×C47—42no—
197C2×C4×C47—42no—
198C2×C4×C47—42no—
199C2×C4×C47—42no—
200C2×C4×C47—42no—
201C2×C4×C47—42no—
202C2×C4×C47—42no—
203C2×C4×C47C4×D414yes—
204C2×C4×C47#12114yes—
205C2×C4×C47C22⋊Q818yes—
206C2×C4×C47#12314yes—
207C2×C4×C47#12518yes—
208C2×C4×C47C4⋊Q814yes—
209C2×Dic47—24no—
210C2×Dic47—22no—
211C2×Dic47—22no—
212C2×Dic47—24no—
213C2×Dic47—22no—
214C2×Dic47—24no—
215C2×Dic47—22no—
216C2×Dic47—24no—
217C2×Dic47—24no—
218C2×Dic47—22no—
219C2×Dic47—22no—
220C2×Dic47—24no—
221C2×Dic47—22no—
222C2×Dic47—24no—
223C2×Dic47—22no—
224C2×Dic47—24no—
225C2×Dic47—24no—
226C2×Dic47—22no—
227C2×Dic47—24no—
228C2×Dic47—24no—
229C2×Dic47—24no—
230C2×Dic47—41no—
231C2×Dic47—41no—
232C2×Dic47—42no—
233C2×Dic47—41no—
234C2×Dic47—41no—
235C2×Dic47—42no—
236C2×Dic47—42no—
237C2×Dic47—42no—
238C2×Dic47—42no—
239C2×Dic47—42no—
240C2×Dic47—41no—
241C2×Dic47—41no—
242C2×Dic47—42no—
243C2×Dic47C4×D414yes—
244C2×Dic47C4×Q818yes—
245C4×#398—471nomaximal, Sylow
246C22×C47C2×C4×D411yescharacteristic
247C22×C47C2×C4×D411yescharacteristic
248C22×C47C2×C4×Q812yes—
249C22×C47C4×#4111yescharacteristic
250C22×C47C4×#4112yes—
251C22×C47C2×#12111yescharacteristic
252C22×C47C2×C22⋊Q812yes—
253C22×C47C2×#12311yescharacteristic
254C22×C47#52511yescharacteristic
255C22×C47#52512yes—
256C22×C47#52511yescharacteristic
257C22×C47C2×#12512yes—
258C22×C47#52912yes—
259C22×C47#52912yes—
260C22×C47#52912yes—
261C22×C47#52911yescharacteristic
262C22×C47#52912yes—
263C22×C47C2×C4⋊Q811yescharacteristic
264C22×C47#53211yescharacteristic
265C22×C47#53211yescharacteristic
266C22×C47#53312yes—
267C22×C47#53312yes—
268C22×C47#53312yes—
269C4×C47—24no—
270C4×C47—44no—
271C4×C47—42no—
272C4×C47—44no—
273C4×C47#39818yescomplemented
274Dic47—24no—
275Dic47—28no—
276Dic47—42no—
277Dic47—42no—
278Dic47—44no—
279Dic47—42no—
280C2×#398—471no—
281C2×C4×C4⋊C4—471no—
282C2×C4×C4⋊C4—472no—
283C2×C4×C4⋊C4D4711yescharacteristic
284#1445—471no—
285#1444—471no—
286#1442—472no—
287#1441—472no—
288#1441—471no—
289C4×#95—472no—
290C4×#95—471no—
291C2×C47C4×#12111yescharacteristic
292C2×C47C4×#12311yescharacteristic
293C2×C47C4×C22⋊Q812yes—
294C2×C47C4×#12512yes—
295C2×C47C4×C4⋊Q811yescharacteristic
296C2×C47C2×#39811yescharacteristic
297C2×C47#239211yescharacteristic
298C2×C47#239511yescharacteristic
299C2×C47#239612yes—
300C2×C47#239911yescharacteristic
301C2×C47#240212yes—
302C22×C4⋊C4—472no—
303C22×C4⋊C4—471no—
304C22×C4⋊C4—471no—
305C22×C4⋊C4—472no—
306C22×C4⋊C4C2×D4711yescharacteristic
307C22×C4⋊C4C2×D4711yescharacteristic
308C22×C42—472no—
309C22×C42—471no—
310C22×C42—471no—
311C22×C42C2×D4712yes—
312C22×C42C2×D4711yescharacteristic
313#398—478no—
314C4×C4⋊C4—24no—
315C4×C4⋊C4—948no—
316C4×C4⋊C4—944no—
317C2×#95—472no—
318C2×#95—471no—
319C2×#95—472no—
320C2×#95—472no—
321C2×#95—472no—
322C2×#95—472no—
323C2×#95—471no—
324C2×#95—472no—
325C2×#95—471no—
326C2×#95—472no—
327C2×#95—471no—
328C2×#95C2×D4712yes—
329C47C4×#39811yescharacteristic, complemented, Sylow
330C23×C4—471no—
331C23×C4—472no—
332C23×C4—471no—
333C23×C4—471no—
334C23×C4—471no—
335C23×C4—472no—
336C23×C4C22×D4712yes—
337C23×C4C22×D4712yes—
338C23×C4C22×D4711yescharacteristic
339C23×C4C22×D4711yescharacteristic
340C23×C4C22×D4711yescharacteristic
341C2×C4⋊C4—24no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—478no—
346C2×C4⋊C4—474no—
347C2×C4⋊C4—944no—
348C2×C4⋊C4—944no—
349C2×C4⋊C4—942no—
350C2×C4⋊C4—942no—
351C2×C4⋊C4—944no—
352C2×C4⋊C4—944no—
353C2×C4⋊C4—944no—
354C2×C4⋊C4—942no—
355C2×C4⋊C4—942no—
356C2×C4⋊C4—942no—
357C2×C4⋊C4C4×D4714yes—
358C2×C42—24no—
359C2×C42—24no—
360C2×C42—24no—
361C2×C42—24no—
362C2×C42—474no—
363C2×C42—478no—
364C2×C42—944no—
365C2×C42—944no—
366C2×C42—942no—
367C2×C42—942no—
368C2×C42—944no—
369C2×C42—942no—
370C2×C42C22⋊D4714yes—
371#95—24no—
372#95—474no—
373#95—478no—
374#95—944no—
375#95—944no—
376#95—944no—
377#95—944no—
378#95—944no—
379#95—944no—
380#95—942no—
381#95—942no—
382#95—942no—
383C24C23×D4711yescharacteristic
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—474no—
403C22×C4—472no—
404C22×C4—472no—
405C22×C4—474no—
406C22×C4—474no—
407C22×C4—472no—
408C22×C4—472no—
409C22×C4—472no—
410C22×C4—474no—
411C22×C4—472no—
412C22×C4—942no—
413C22×C4—941no—
414C22×C4—942no—
415C22×C4—941no—
416C22×C4—941no—
417C22×C4—942no—
418C22×C4—941no—
419C22×C4—942no—
420C22×C4—942no—
421C22×C4—941no—
422C22×C4—941no—
423C22×C4—941no—
424C22×C4—942no—
425C22×C4—942no—
426C22×C4—942no—
427C22×C4—941no—
428C22×C4—942no—
429C22×C4—941no—
430C22×C4—942no—
431C22×C4—942no—
432C22×C4—942no—
433C22×C4—942no—
434C22×C4—942no—
435C22×C4—942no—
436C22×C4—941no—
437C22×C4—942no—
438C22×C4C2×C4×D4714yes—
439C22×C4C2×C4×D4712yes—
440C22×C4#1062535014yes—
441C22×C4#1062535012yes—
442C22×C4#1062535014yes—
443C22×C4D4×D4712yes—
444C22×C4#1062535212yes—
445C22×C4Q8×D4714yes—
446C22×C4C2×C22⋊D4712yes—
447C22×C4C2×C22⋊D4712yes—
448C22×C4C2×C22⋊D4712yes—
449C4⋊C4—28no—
450C4⋊C4—28no—
451C4⋊C4—9416no—
452C4⋊C4—948no—
453C4⋊C4—9416no—
454C4⋊C4—948no—
455C42—28no—
456C42—48no—
457C42—948no—
458C42—9416no—
459C42—1884no—
460C23C22×C4×D4711yescharacteristic
461C23C2×D4×D4711yescharacteristic
462C23C22×C22⋊D4711yescharacteristic
463C23C2×Q8×D4712yes—
464C23#41×D4711yescharacteristic
465C23#41×D4712yes—
466C23#41×D4711yescharacteristic
467C23C2×#1062535211yescharacteristic
468C23C2×#1062535011yescharacteristic
469C23C2×#1062535012yes—
470C23C2×#1062535012yes—
471C2×C4—24no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—22no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—474no—
495C2×C4—478no—
496C2×C4—944no—
497C2×C4—942no—
498C2×C4—942no—
499C2×C4—944no—
500C2×C4—942no—
501C2×C4—944no—
502C2×C4—942no—
503C2×C4—944no—
504C2×C4—944no—
505C2×C4—942no—
506C2×C4—942no—
507C2×C4—944no—
508C2×C4—942no—
509C2×C4—944no—
510C2×C4—942no—
511C2×C4—944no—
512C2×C4—942no—
513C2×C4—944no—
514C2×C4—944no—
515C2×C4—944no—
516C2×C4—944no—
517C2×C4—1881no—
518C2×C4—1881no—
519C2×C4—1882no—
520C2×C4—1881no—
521C2×C4—1881no—
522C2×C4—1882no—
523C2×C4—1882no—
524C2×C4—1882no—
525C2×C4—1882no—
526C2×C4—1882no—
527C2×C4—1881no—
528C2×C4—1881no—
529C2×C4—1882no—
530C2×C4C4×C22⋊D4714yes—
531C2×C4#1309399514yes—
532C2×C4#1309400218yes—
533C2×C4#1309400714yes—
534C2×C4#1309401418yes—
535C2×C4#1309402214yes—
536C22C4×D4×D4711yescharacteristic
537C22C2×C4×C22⋊D4711yescharacteristic
538C22C4×Q8×D4712yes—
539C22C4×#1062535211yescharacteristic
540C22C4×#1062535012yes—
541C22C2×#1309399511yescharacteristic
542C22C2×#1309400212yes—
543C22C2×#1309400711yescharacteristic
544C22#1568963011yescharacteristic
545C22#1568963212yes—
546C22#1568963411yescharacteristic
547C22C2×#1309401412yes—
548C22#1568965112yes—
549C22#1568965112yes—
550C22#1568965312yes—
551C22#1568965511yescharacteristic
552C22#1568965712yes—
553C22C2×#1309402211yescharacteristic
554C22#1568966911yescharacteristic
555C22#1568967011yescharacteristic
556C22#1568967712yes—
557C22#1568967712yes—
558C22#1568967712yes—
559C4—24no—
560C4—44no—
561C4—42no—
562C4—44no—
563C4—944no—
564C4—948no—
565C4—1882no—
566C4—1882no—
567C4—1884no—
568C4—1882no—
569C4#1568905418yesdirect product factor
570C2C4×#1309399511yescharacteristic
571C2C4×#1309400711yescharacteristic
572C2C4×#1309400212yes—
573C2C4×#1309401412yes—
574C2C4×#1309402211yescharacteristic
575C2C2×#1568905411yescharacteristic
576C2#2024662611yescharacteristic
577C2#2024664511yescharacteristic
578C2#2024666412yes—
579C2#2024667911yescharacteristic
580C2#2024669512yes—
subgroupG/H
centerC23×C4C22×D47
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC2×C4×C4⋊C4×C47C2
socle, prime radical, cosocleC24×C47C24
hypercenterC2×C4×C4⋊C4D47
hypocenterC47C4×#398
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
19. #15689054C4direct (N × H)
273. C4×C47#398semidirect
329. C47C4×#398semidirect
569. C4#15689054direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156890542
C2×C4×Dic47⋊C42
#202416562
#202416512
#202416432
#202416392
#202416382
C4×C47⋊#952
C2×C4×C4⋊C4×C472
C4×#39847