Finite Group Databasebeta

← C4×#15689000 #26137430

Subgroups — C4×#15689000 #26137430

Order 12032.

3366 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D47C211yesmaximal, characteristic
2C23×C4×Dic47C211yesmaximal, characteristic, complemented
3C2×#15689000C212yesmaximal
4C2×C4×(C2×D47)⋊C4C212yesmaximal, complemented
5#20241624C212yesmaximal, complemented
6#20241623C212yesmaximal, complemented
7#20241610C212yesmaximal, complemented
8C4×C47⋊#95C212yesmaximal, complemented
9C2×C4×C22⋊C4×C47C211yesmaximal, characteristic, complemented
10C23×C22⋊D47C2211yescharacteristic
11C24×Dic47C2212yes—
12C23×C4×D47C2211yescharacteristic
13C2×C4×C22⋊D47—24no—
14C2×C4×C22⋊D47—24no—
15C2×C4×C22⋊D47C418yescomplemented
16C22×Dic47⋊C4C2211yescharacteristic
17C22×C22⋊Dic47C2211yescharacteristic
18C22×(C2×D47)⋊C4C2214yes—
19C22×(C2×D47)⋊C4C2211yescharacteristic
20C22×C4×Dic47—28no—
21C22×C4×Dic47—24no—
22C22×C4×Dic47C2212yes—
23C22×C4×Dic47C2211yescharacteristic
24C22×C4×Dic47C2212yes—
25#15689000C4116yesdirect product factor
26C4×(C2×D47)⋊C4—28no—
27C2×C47⋊#95C2214yes—
28C2×C47⋊#95C2214yes—
29C2×C47⋊#95C2214yes—
30C24×C4×C47C2211yescharacteristic
31C22×C22⋊C4×C47C2212yes—
32C22×C42×C47C2212yes—
33C4×C22⋊C4×C47—24no—
34C2×#95×C47C2212yes—
35C24×D47C2311yescharacteristic
36C22×C22⋊D47—22no—
37C22×C22⋊D47—22no—
38C22×C22⋊D47—24no—
39C22×C22⋊D47C2×C418yes—
40C22×C22⋊D47C2×C414yes—
41C23×Dic47—24no—
42C23×Dic47—24no—
43C23×Dic47—28no—
44C23×Dic47—28no—
45C23×Dic47C2×C418yescomplemented
46C23×Dic47C2311yescharacteristic
47C23×Dic47C2311yescharacteristic
48C23×Dic47C2311yescharacteristic
49C23×Dic47C2314yes—
50C22×C4×D47—24no—
51C22×C4×D47—22no—
52C22×C4×D47—22no—
53C22×C4×D47—24no—
54C22×C4×D47C2×C414yescomplemented
55C4×C22⋊D47—232no—
56C2×Dic47⋊C4—22no—
57C2×Dic47⋊C4—22no—
58C2×Dic47⋊C4C2×C414yescomplemented
59C2×C22⋊Dic47—22no—
60C2×C22⋊Dic47—22no—
61C2×C22⋊Dic47C2×C414yes—
62C2×(C2×D47)⋊C4—22no—
63C2×(C2×D47)⋊C4—22no—
64C2×(C2×D47)⋊C4—28no—
65C2×(C2×D47)⋊C4—28no—
66C2×(C2×D47)⋊C4C2×C4116yescomplemented
67C2×(C2×D47)⋊C4C2×C414yescomplemented
68C2×C4×Dic47—232no—
69C2×C4×Dic47—24no—
70C2×C4×Dic47—24no—
71C2×C4×Dic47—24no—
72C2×C4×Dic47—22no—
73C2×C4×Dic47—22no—
74C2×C4×Dic47—28no—
75C2×C4×Dic47C2×C414yescomplemented
76C2×C4×Dic47D418yescomplemented
77C47⋊#95—28no—
78C47⋊#95—28no—
79C47⋊#95C2×C4116yescomplemented
80C25×C47C2311yescharacteristic
81C23×C4×C47—24no—
82C23×C4×C47—24no—
83C23×C4×C47C2×C414yes—
84C23×C4×C47D414yes—
85C23×C4×C47D414yes—
86C23×C4×C47C2314yes—
87C23×C4×C47C2311yescharacteristic
88C23×C4×C47C2311yescharacteristic
89C2×C22⋊C4×C47—24no—
90C2×C22⋊C4×C47—24no—
91C2×C22⋊C4×C47C2×C418yescomplemented
92C2×C42×C47—24no—
93C2×C42×C47—24no—
94C2×C42×C47—24no—
95#95×C47—24no—
96C24×C47—22no—
97C24×C47—22no—
98C24×C47—24no—
99C24×C47C22×C412yes—
100C24×C47C22×C414yes—
101C24×C47C2×D412yes—
102C24×C47C2×D412yes—
103C24×C47#4114yes—
104C24×C47C2411yescharacteristic
105C23×D47—22no—
106C23×D47—21no—
107C23×D47—21no—
108C23×D47—24no—
109C23×D47—22no—
110C23×D47—22no—
111C23×D47C22×C414yes—
112C23×D47C22×C412yes—
113C22×C4×C47—22no—
114C22×C4×C47—22no—
115C22×C4×C47—216no—
116C22×C4×C47—28no—
117C22×C4×C47—216no—
118C22×C4×C47—28no—
119C22×C4×C47—24no—
120C22×C4×C47—24no—
121C22×C4×C47—24no—
122C22×C4×C47—24no—
123C22×C4×C47—24no—
124C22×C4×C47—24no—
125C22×C4×C47C22⋊C4116yescomplemented
126C22×C4×C47C22×C418yes—
127C22×C4×C47C22×C412yes—
128C22×C4×C47C22×C412yes—
129C22×C4×C47C2×D412yes—
130C22×C4×C47C2×D412yes—
131C22×C4×C47C2×D412yes—
132C22×C4×C47C2×D412yes—
133C22×C4×C47C2×D414yes—
134C22×C4×C47#4114yes—
135C2×C22⋊D47—28no—
136C2×C22⋊D47—28no—
137C2×C22⋊D47—216no—
138C2×C22⋊D47—216no—
139C2×C22⋊D47C42116yescomplemented
140C22×Dic47—216no—
141C22×Dic47—232no—
142C22×Dic47—216no—
143C22×Dic47—216no—
144C22×Dic47—24no—
145C22×Dic47—24no—
146C22×Dic47—21no—
147C22×Dic47—21no—
148C22×Dic47—24no—
149C22×Dic47—24no—
150C22×Dic47—22no—
151C22×Dic47—232no—
152C22×Dic47—22no—
153C22×Dic47—21no—
154C22×Dic47—21no—
155C22×Dic47—21no—
156C22×Dic47—21no—
157C22×Dic47—24no—
158C22×Dic47—22no—
159C22×Dic47C22×C412yes—
160C22×Dic47C22×C412yes—
161C22×Dic47C22×C414yes—
162C22×Dic47C22×C412yes—
163C22×Dic47C22×C418yes—
164C22×Dic47C2×D418yes—
165C22×Dic47#4118yes—
166C2×C4×D47—28no—
167C2×C4×D47—216no—
168C2×C4×D47—44no—
169C2×C4×D47—48no—
170C2×C4×D47—44no—
171C22⋊C4×C47—216no—
172C42×C47—48no—
173C22⋊Dic47—28no—
174(C2×D47)⋊C4—28no—
175(C2×D47)⋊C4—232no—
176Dic47⋊C4—28no—
177C4×Dic47—216no—
178C4×Dic47—28no—
179C4×Dic47—216no—
180C23×C47—28no—
181C23×C47—24no—
182C23×C47—28no—
183C23×C47—24no—
184C23×C47—22no—
185C23×C47—24no—
186C23×C47—22no—
187C23×C47—24no—
188C23×C47—28no—
189C23×C47—28no—
190C23×C47—24no—
191C23×C47C2×C4214yes—
192C23×C47C2×C22⋊C414yes—
193C23×C47#11714yes—
194C23×C47C4×D418yes—
195C23×C47C4×D418yes—
196C23×C47C23×C411yescharacteristic
197C23×C47C23×C412yes—
198C23×C47C22×D412yes—
199C23×C47C22×D411yescharacteristic
200C23×C47C22×D411yescharacteristic
201C23×C47C2×#4114yes—
202C23×C47C2×#4112yes—
203C23×C47C2×#4112yes—
204C22×D47—22no—
205C22×D47—22no—
206C22×D47—28no—
207C22×D47—24no—
208C22×D47—24no—
209C22×D47—24no—
210C22×D47—28no—
211C22×D47—24no—
212C22×D47—41no—
213C22×D47—42no—
214C22×D47—41no—
215C22×D47—44no—
216C22×D47—42no—
217C22×D47—44no—
218C22×D47—42no—
219C22×D47C2×C4214yescomplemented
220C2×C4×C47—24no—
221C2×C4×C47—22no—
222C2×C4×C47—24no—
223C2×C4×C47—22no—
224C2×C4×C47—232no—
225C2×C4×C47—28no—
226C2×C4×C47—28no—
227C2×C4×C47—28no—
228C2×C4×C47—44no—
229C2×C4×C47—44no—
230C2×C4×C47—44no—
231C2×C4×C47—44no—
232C2×C4×C47C2×C22⋊C414yes—
233C2×C4×C47C2×C22⋊C414yes—
234C2×C4×C47C4×D418yes—
235C2×C4×C47#12014yes—
236C2×C4×C47#12118yes—
237C2×C4×C47#12314yes—
238C22⋊D47—232no—
239C2×Dic47—264no—
240C2×Dic47—22no—
241C2×Dic47—22no—
242C2×Dic47—28no—
243C2×Dic47—28no—
244C2×Dic47—24no—
245C2×Dic47—24no—
246C2×Dic47—28no—
247C2×Dic47—28no—
248C2×Dic47—28no—
249C2×Dic47—28no—
250C2×Dic47—22no—
251C2×Dic47—22no—
252C2×Dic47—24no—
253C2×Dic47—24no—
254C2×Dic47—41no—
255C2×Dic47—42no—
256C2×Dic47—41no—
257C2×Dic47—42no—
258C2×Dic47—42no—
259C2×Dic47C2×C4214yescomplemented
260C2×Dic47C4×D4116yescomplemented
261C4×D47—416no—
262C4×#386—471nomaximal, Sylow
263C22×C47—28no—
264C22×C47—24no—
265C22×C47—28no—
266C22×C47—24no—
267C22×C47—28no—
268C22×C47—216no—
269C22×C47—28no—
270C22×C47C4×C22⋊C418yescomplemented
271C22×C47C22×C4211yescharacteristic
272C22×C47C22×C22⋊C411yescharacteristic
273C22×C47C2×#11711yescharacteristic
274C22×C47C2×C4×D414yes—
275C22×C47C2×C4×D412yes—
276C22×C47C2×C4×D412yes—
277C22×C47C2×C4×D412yes—
278C22×C47C4×#4114yes—
279C22×C47C4×#4112yes—
280C22×C47C2×#12011yescharacteristic
281C22×C47C2×#12112yes—
282C22×C47C2×#12311yescharacteristic
283C22×C47#52514yes—
284C22×C47#52512yes—
285C22×C47#52914yes—
286C22×C47#53212yes—
287C2×D47—24no—
288C2×D47—28no—
289C2×D47—42no—
290C2×D47—44no—
291C2×D47—42no—
292C2×D47—44no—
293C2×D47—48no—
294C2×D47—44no—
295C4×C47—24no—
296C4×C47—48no—
297C4×C47#38618yescomplemented
298Dic47—24no—
299Dic47—216no—
300Dic47—42no—
301Dic47—42no—
302C22×C4×D4—471no—
303C23×C42—471no—
304C2×#386—472no—
305C2×C4×C22⋊C4—472no—
306C2×C4×C22⋊C4D4711yescharacteristic, complemented
307#1437—472no—
308#1436—472no—
309C22⋊#95—472no—
310C4×#95—472no—
311C2×C47—28no—
312C2×C47C2×C4×C22⋊C411yescharacteristic
313C2×C47C42×D412yes—
314C2×C47C2×#38611yescharacteristic
315C2×C47#229012yes—
316C2×C47#229711yescharacteristic
317C2×C47C4×#12012yes—
318C2×C47C4×#12114yes—
319C2×C47C4×#12312yes—
320D47—44no—
321C23×D4—471no—
322C24×C4—472no—
323C24×C4—471no—
324C24×C4C2×D4711yescharacteristic
325C2×C4×D4—478no—
326C2×C4×D4—944no—
327C2×C4×D4—944no—
328C22×C4⋊C4—471no—
329C22×C22⋊C4—471no—
330C22×C22⋊C4—471no—
331C22×C22⋊C4—474no—
332C22×C22⋊C4C2×D4712yes—
333C22×C42—472no—
334C22×C42—471no—
335C22×C42—472no—
336C22×C42—948no—
337C22×C42—944no—
338C22×C42C2×D4712yes—
339#386—4716no—
340C4×C22⋊C4—24no—
341C4×C22⋊C4—948no—
342C2×#95—474no—
343C2×#95—474no—
344C2×#95—474no—
345C2×#95C2×D4712yes—
346C47C4×#38611yescharacteristic, complemented, Sylow
347C25—471no—
348C25C22×D4711yescharacteristic
349C22×D4—474no—
350C22×D4—478no—
351C22×D4—942no—
352C22×D4—944no—
353C22×D4—942no—
354C23×C4—24no—
355C23×C4—24no—
356C23×C4—474no—
357C23×C4—471no—
358C23×C4—478no—
359C23×C4—471no—
360C23×C4—471no—
361C23×C4—474no—
362C23×C4—948no—
363C23×C4—948no—
364C23×C4—944no—
365C23×C4—944no—
366C23×C4—942no—
367C23×C4—944no—
368C23×C4—944no—
369C23×C4—942no—
370C23×C4C4×D4714yes—
371C23×C4D18814yes—
372C23×C4C22⋊D4714yes—
373C23×C4C22×D4714yes—
374C23×C4C22×D4711yescharacteristic
375C23×C4C22×D4711yescharacteristic
376C4×D4—9432no—
377C2×C4⋊C4—474no—
378C2×C4⋊C4—942no—
379C2×C4⋊C4—942no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—474no—
383C2×C22⋊C4—474no—
384C2×C22⋊C4—4716no—
385C2×C22⋊C4—948no—
386C2×C22⋊C4—948no—
387C2×C22⋊C4—942no—
388C2×C22⋊C4—942no—
389C2×C22⋊C4—942no—
390C2×C22⋊C4—942no—
391C2×C22⋊C4C4×D4718yescomplemented
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—474no—
396C2×C42—478no—
397C2×C42—948no—
398C2×C42—9432no—
399C2×C42—942no—
400C2×C42—944no—
401C2×C42—944no—
402C2×C42—944no—
403C2×C42—942no—
404#95—24no—
405#95—4716no—
406#95—948no—
407#95—948no—
408C24—22no—
409C24—24no—
410C24—22no—
411C24—474no—
412C24—472no—
413C24—942no—
414C24—941no—
415C24—941no—
416C24—944no—
417C24—942no—
418C24—942no—
419C24C2×C4×D4712yes—
420C24C2×C4×D4714yes—
421C24C2×D18812yes—
422C24#1062535014yes—
423C24C2×C22⋊D4712yes—
424C24C23×D4711yescharacteristic
425C2×D4—4716no—
426C2×D4—948no—
427C2×D4—948no—
428C2×D4—9416no—
429C2×D4—9416no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—216no—
433C22×C4—28no—
434C22×C4—216no—
435C22×C4—28no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—24no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—474no—
443C22×C4—478no—
444C22×C4—472no—
445C22×C4—478no—
446C22×C4—478no—
447C22×C4—472no—
448C22×C4—472no—
449C22×C4—9432no—
450C22×C4—9416no—
451C22×C4—9432no—
452C22×C4—9416no—
453C22×C4—9416no—
454C22×C4—944no—
455C22×C4—941no—
456C22×C4—944no—
457C22×C4—941no—
458C22×C4—944no—
459C22×C4—944no—
460C22×C4—942no—
461C22×C4—942no—
462C22×C4—941no—
463C22×C4—941no—
464C22×C4—941no—
465C22×C4—941no—
466C22×C4—944no—
467C22×C4—942no—
468C22×C4—948no—
469C22×C4—9416no—
470C22×C4—1884no—
471C22×C4—1888no—
472C22×C4—1884no—
473C22×C4(C2×D47)⋊C4116yescomplemented
474C22×C4C2×C4×D4718yes—
475C22×C4C2×C4×D4712yes—
476C22×C4C2×C4×D4712yes—
477C22×C4C2×D18812yes—
478C22×C4C2×D18812yes—
479C22×C4D4×D4714yes—
480C22×C4#1062535214yes—
481C22×C4C2×C22⋊D4712yes—
482C22×C4C2×C22⋊D4712yes—
483C4⋊C4—948no—
484C22⋊C4—216no—
485C22⋊C4—9432no—
486C22⋊C4—948no—
487C22⋊C4—948no—
488C42—48no—
489C42—9416no—
490C42—948no—
491C42—9416no—
492C23—28no—
493C23—24no—
494C23—28no—
495C23—24no—
496C23—22no—
497C23—24no—
498C23—22no—
499C23—28no—
500C23—24no—
501C23—28no—
502C23—24no—
503C23—474no—
504C23—942no—
505C23—942no—
506C23—948no—
507C23—944no—
508C23—944no—
509C23—944no—
510C23—948no—
511C23—944no—
512C23—1881no—
513C23—1882no—
514C23—1881no—
515C23—1884no—
516C23—1882no—
517C23—1884no—
518C23—1882no—
519C23C42×D4714yes—
520C23C2×(C2×D47)⋊C414yes—
521C23#1309398114yes—
522C23C4×C22⋊D4718yes—
523C23C4×D18818yes—
524C23C22×C4×D4711yescharacteristic
525C23C22×C4×D4712yes—
526C23C2×D4×D4712yes—
527C23C22×C22⋊D4711yescharacteristic
528C23C22×D18811yescharacteristic
529C23#41×D4714yes—
530C23C2×#1062535212yes—
531C23C2×#1062535012yes—
532D4—9432no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—24no—
536C2×C4—22no—
537C2×C4—232no—
538C2×C4—28no—
539C2×C4—28no—
540C2×C4—28no—
541C2×C4—44no—
542C2×C4—44no—
543C2×C4—44no—
544C2×C4—44no—
545C2×C4—474no—
546C2×C4—4716no—
547C2×C4—9464no—
548C2×C4—942no—
549C2×C4—942no—
550C2×C4—948no—
551C2×C4—944no—
552C2×C4—948no—
553C2×C4—944no—
554C2×C4—948no—
555C2×C4—948no—
556C2×C4—948no—
557C2×C4—948no—
558C2×C4—942no—
559C2×C4—942no—
560C2×C4—944no—
561C2×C4—944no—
562C2×C4—1881no—
563C2×C4—1882no—
564C2×C4—1881no—
565C2×C4—1882no—
566C2×C4—1882no—
567C2×C4—18816no—
568C2×C4C2×(C2×D47)⋊C414yes—
569C2×C4C2×(C2×D47)⋊C414yes—
570C2×C4(C22⋊D47)⋊C418yes—
571C2×C4#1309399414yes—
572C2×C4#1309399618yes—
573C2×C4#1309400814yes—
574C22—24no—
575C22—28no—
576C22—24no—
577C22—28no—
578C22—216no—
579C22—28no—
580C22—28no—
581C22—944no—
582C22—948no—
583C22—1882no—
584C22—1884no—
585C22—1882no—
586C22—1884no—
587C22—1888no—
588C22—1884no—
589C22C4×(C2×D47)⋊C418yescomplemented
590C22C2×C42×D4711yescharacteristic
591C22C22×(C2×D47)⋊C411yescharacteristic
592C22C2×#1309398111yescharacteristic
593C22C4×D4×D4714yes—
594C22C2×(C22⋊D47)⋊C412yes—
595C22C2×C4×C22⋊D4712yes—
596C22C2×C4×D18812yes—
597C22C4×#1062535214yes—
598C22#1568959112yes—
599C22C2×#1309399411yescharacteristic
600C22C2×#1309399612yes—
601C22C2×#1309400811yescharacteristic
602C22#1568963214yes—
603C22#1568963512yes—
604C22#1568965314yes—
605C22#1568966912yes—
606C4—24no—
607C4—48no—
608C4—9416no—
609C4—944no—
610C4—1882no—
611C4—1882no—
612C4#1568900018yesdirect product factor
613C2—28no—
614C2—1884no—
615C2C2×C4×(C2×D47)⋊C411yescharacteristic
616C2C4×(C22⋊D47)⋊C412yes—
617C2C2×#1568900011yescharacteristic
618C2#2024582712yes—
619C2#2024587611yescharacteristic
620C2C4×#1309399412yes—
621C2C4×#1309399614yes—
622C2C4×#1309400812yes—
subgroupG/H
centerC23×C4C22×D47
commutatorC22×C47C22×C42
FrattiniC24C23×D47
FittingC2×C4×C22⋊C4×C47C2
socle, cosocleC24×C47C24
prime radicalC23×C22⋊D47C22
hypercenterC2×C4×C22⋊C4D47
hypocenterC47C4×#386
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C23×C4×Dic47C2semidirect
4. C2×C4×(C2×D47)⋊C4C2semidirect
5. #20241624C2semidirect
6. #20241623C2semidirect
7. #20241610C2semidirect
8. C4×C47⋊#95C2semidirect
9. C2×C4×C22⋊C4×C47C2semidirect
15. C2×C4×C22⋊D47C4semidirect
25. #15689000C4direct (N × H)
45. C23×Dic47C2×C4semidirect
54. C22×C4×D47C2×C4semidirect
58. C2×Dic47⋊C4C2×C4semidirect
66. C2×(C2×D47)⋊C4C2×C4semidirect
67. C2×(C2×D47)⋊C4C2×C4semidirect
75. C2×C4×Dic47C2×C4semidirect
76. C2×C4×Dic47D4semidirect
79. C47⋊#95C2×C4semidirect
91. C2×C22⋊C4×C47C2×C4semidirect
125. C22×C4×C47C22⋊C4semidirect
139. C2×C22⋊D47C42semidirect
219. C22×D47C2×C42semidirect
259. C2×Dic47C2×C42semidirect
260. C2×Dic47C4×D4semidirect
270. C22×C47C4×C22⋊C4semidirect
297. C4×C47#386semidirect
306. C2×C4×C22⋊C4D47semidirect
346. C47C4×#386semidirect
391. C2×C22⋊C4C4×D47semidirect
473. C22×C4(C2×D47)⋊C4semidirect
589. C22C4×(C2×D47)⋊C4semidirect
612. C4#15689000direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D472
C23×C4×Dic472
C2×#156890002
C2×C4×(C2×D47)⋊C42
#202416242
#202416232
#202416102
C4×C47⋊#952
C2×C4×C22⋊C4×C472
C4×#38647