Finite Group Databasebeta

← C2×#397×D47 #26382482

Subgroups — C2×#397×D47 #26382482

Order 12032.

5230 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D47C211yesmaximal, characteristic, complemented
2C22×C22⋊C4×D47C211yesmaximal, characteristic
3C22×C22⋊C4×D47C212yesmaximal
4C2×#15689052C212yesmaximal, complemented
5C2×#15689051C212yesmaximal, complemented
6C2×#15689050C211yesmaximal, characteristic, complemented
7C2×#15689049C211yesmaximal, characteristic, complemented
8C2×#15689048C211yesmaximal, characteristic, complemented
9#397×D47C2116yesmaximal, direct product factor
10C2×#95×D47C211yesmaximal, characteristic, complemented
11C2×#95×D47C212yesmaximal, complemented
12C2×C47×#397C211yesmaximal, characteristic, complemented
13C25×D47C2211yescharacteristic
14C23×C4×D47C2212yes—
15C23×C4×D47C2211yescharacteristic
16C23×C4×D47C2212yes—
17C23×C4×D47C2211yescharacteristic
18C22×C4⋊Dic47C2211yescharacteristic, complemented
19C22×Dic47⋊C4C2212yescomplemented
20C2×C4⋊C4×D47—28no—
21C2×C4⋊C4×D47C2218yescomplemented
22C22×C22⋊Dic47C2212yes—
23C22×C22⋊Dic47C2211yescharacteristic
24C22×(C2×D47)⋊C4C2211yescharacteristic
25C22×(C2×D47)⋊C4C2212yes—
26C22×(C2×D47)⋊C4C2212yes—
27C22×(C2×D47)⋊C4C2211yescharacteristic
28C2×C22⋊C4×D47—216no—
29C2×C22⋊C4×D47—28no—
30C2×C22⋊C4×D47C2218yes—
31C2×C22⋊C4×D47C22116yes—
32#15689052C22116yescomplemented
33#15689051C22116yescomplemented
34#15689050C2218yescomplemented
35#15689049C2218yescomplemented
36#15689048C2218yescomplemented
37C2×C47⋊#95C2211yescharacteristic, complemented
38C2×C47⋊#95C2212yescomplemented
39C2×C47⋊#95C2212yescomplemented
40C2×C47⋊#95C2212yescomplemented
41C2×C47⋊#95C2212yescomplemented
42#95×D47C2218yescomplemented
43#95×D47C22116yescomplemented
44C22×C4⋊C4×C47C2211yescharacteristic, complemented
45C22×C22⋊C4×C47C2211yescharacteristic
46C22×C22⋊C4×C47C2212yes—
47C47×#397C2218yescomplemented
48C2×#95×C47C2211yescharacteristic, complemented
49C2×#95×C47C2212yescomplemented
50C24×D47—24no—
51C24×D47—24no—
52C24×D47—28no—
53C24×D47—28no—
54C24×D47D418yes—
55C24×D47C2314yes—
56C24×D47C2311yescharacteristic
57C24×D47C2311yescharacteristic
58C23×Dic47C2312yes—
59C23×Dic47C2311yescharacteristic
60C23×Dic47C2312yes—
61C23×Dic47C2311yescharacteristic
62C22×C4×D47—28no—
63C22×C4×D47—28no—
64C22×C4×D47—28no—
65C22×C4×D47—24no—
66C22×C4×D47—28no—
67C22×C4×D47—28no—
68C22×C4×D47—28no—
69C22×C4×D47—28no—
70C22×C4×D47—28no—
71C22×C4×D47D418yes—
72C22×C4×D47C2318yes—
73C22×C4×D47C2314yes—
74C22×C4×D47C2318yes—
75C22×C4×D47C2314yes—
76C2×C4⋊Dic47—24no—
77C2×C4⋊Dic47C2314yescomplemented
78C2×Dic47⋊C4—28no—
79C2×Dic47⋊C4C2318yescomplemented
80C4⋊C4×D47—232no—
81C2×C22⋊Dic47—28no—
82C2×C22⋊Dic47—24no—
83C2×C22⋊Dic47C2318yes—
84C2×C22⋊Dic47C2314yes—
85C2×(C2×D47)⋊C4—28no—
86C2×(C2×D47)⋊C4—28no—
87C2×(C2×D47)⋊C4—24no—
88C2×(C2×D47)⋊C4—24no—
89C2×(C2×D47)⋊C4C2314yes—
90C2×(C2×D47)⋊C4C2318yes—
91C2×(C2×D47)⋊C4C2318yes—
92C2×(C2×D47)⋊C4C2314yes—
93C22⋊C4×D47—264no—
94C22⋊C4×D47—232no—
95C47⋊#95C2314yescomplemented
96C47⋊#95C2318yescomplemented
97C47⋊#95C2318yescomplemented
98C47⋊#95C2318yescomplemented
99C47⋊#95C2318yescomplemented
100C25×C47C2311yescharacteristic
101C23×C4×C47C2311yescharacteristic
102C23×C4×C47C2312yes—
103C23×C4×C47C2312yes—
104C23×C4×C47C2311yescharacteristic
105C2×C4⋊C4×C47—24no—
106C2×C4⋊C4×C47C2314yescomplemented
107C2×C22⋊C4×C47—28no—
108C2×C22⋊C4×C47—24no—
109C2×C22⋊C4×C47C2314yes—
110C2×C22⋊C4×C47C2318yes—
111#95×C47C2314yescomplemented
112#95×C47C2318yescomplemented
113C24×C47—22no—
114C24×C47—22no—
115C24×C47—24no—
116C24×C47—24no—
117C24×C47C2×D414yes—
118C24×C47C2412yes—
119C24×C47C2411yescharacteristic
120C23×D47—22no—
121C23×D47—22no—
122C23×D47—24no—
123C23×D47—24no—
124C23×D47—232no—
125C23×D47—264no—
126C23×D47—28no—
127C23×D47—28no—
128C23×D47—216no—
129C23×D47—216no—
130C23×D47—416no—
131C23×D47—416no—
132C23×D47—432no—
133C23×D47C2×D4116yes—
134C23×D47C2×D414yes—
135C23×D47C2×D414yes—
136C23×D47C2×D414yes—
137C23×D47#4114yes—
138C23×D47#4118yes—
139C23×D47#4118yes—
140C23×D47C2412yes—
141C23×D47C2412yes—
142C22×C4×C47—24no—
143C22×C4×C47—24no—
144C22×C4×C47—24no—
145C22×C4×C47—22no—
146C22×C4×C47—24no—
147C22×C4×C47—24no—
148C22×C4×C47—24no—
149C22×C4×C47—24no—
150C22×C4×C47—24no—
151C22×C4×C47C2×D414yes—
152C22×C4×C47C2414yes—
153C22×C4×C47C2412yes—
154C22×C4×C47C2414yes—
155C22×C4×C47C2412yes—
156C22×Dic47—24no—
157C22×Dic47—24no—
158C22×Dic47—24no—
159C22×Dic47—22no—
160C22×Dic47—24no—
161C22×Dic47—24no—
162C22×Dic47—24no—
163C22×Dic47—24no—
164C22×Dic47—24no—
165C22×Dic47C2×D414yes—
166C22×Dic47C2414yes—
167C22×Dic47C2412yes—
168C22×Dic47C2414yes—
169C22×Dic47C2412yes—
170C2×C4×D47—232no—
171C2×C4×D47—216no—
172C2×C4×D47—216no—
173C2×C4×D47—216no—
174C2×C4×D47—28no—
175C2×C4×D47—216no—
176C2×C4×D47—216no—
177C2×C4×D47—216no—
178C2×C4×D47—216no—
179C2×C4×D47—216no—
180C2×C4×D47—432no—
181C2×C4×D47—432no—
182C2×C4×D47—416no—
183C2×C4×D47C2×D4116yes—
184C4⋊C4×C47—28no—
185C22⋊C4×C47—216no—
186C22⋊C4×C47—28no—
187C22⋊Dic47—216no—
188C22⋊Dic47—28no—
189(C2×D47)⋊C4—216no—
190(C2×D47)⋊C4—216no—
191(C2×D47)⋊C4—28no—
192(C2×D47)⋊C4—28no—
193C4⋊Dic47—28no—
194Dic47⋊C4—216no—
195C23×C47—28no—
196C23×C47—216no—
197C23×C47—22no—
198C23×C47—22no—
199C23×C47—24no—
200C23×C47—24no—
201C23×C47—44no—
202C23×C47—44no—
203C23×C47—48no—
204C23×C47C22×D414yes—
205C23×C47C22×D412yes—
206C23×C47C22×D412yes—
207C23×C47C2×#4112yes—
208C23×C47C2×#4114yes—
209C23×C47C2×#4114yes—
210C23×C47C2511yescharacteristic
211C22×D47—28no—
212C22×D47—216no—
213C22×D47—22no—
214C22×D47—22no—
215C22×D47—24no—
216C22×D47—24no—
217C22×D47—232no—
218C22×D47—264no—
219C22×D47—44no—
220C22×D47—44no—
221C22×D47—48no—
222C22×D47—416no—
223C22×D47—416no—
224C22×D47—432no—
225C22×D47—4128no—
226C22×D47#121116yes—
227C22×D47#123116yes—
228C22×D47#123132yes—
229C22×D47#124116yes—
230C22×D47#126132yes—
231C22×D47C22×D414yes—
232C22×D47C22×D414yes—
233C22×D47C22×D414yes—
234C22×D47C2×#4114yes—
235C22×D47C2×#4118yes—
236C22×D47C2×#4118yes—
237C2×C4×C47—28no—
238C2×C4×C47—24no—
239C2×C4×C47—24no—
240C2×C4×C47—24no—
241C2×C4×C47—24no—
242C2×C4×C47—22no—
243C2×C4×C47—24no—
244C2×C4×C47—24no—
245C2×C4×C47—24no—
246C2×C4×C47—24no—
247C2×C4×C47—48no—
248C2×C4×C47—48no—
249C2×C4×C47—44no—
250C2×C4×C47C22×D414yes—
251C2×Dic47—28no—
252C2×Dic47—24no—
253C2×Dic47—24no—
254C2×Dic47—24no—
255C2×Dic47—24no—
256C2×Dic47—22no—
257C2×Dic47—24no—
258C2×Dic47—24no—
259C2×Dic47—24no—
260C2×Dic47—24no—
261C2×Dic47—48no—
262C2×Dic47—48no—
263C2×Dic47—44no—
264C2×Dic47C22×D414yes—
265C4×D47—232no—
266C4×D47—432no—
267C4×D47—432no—
268C4×D47—416no—
269C22×#397—471nomaximal, Sylow
270C22×C47—24no—
271C22×C47—28no—
272C22×C47—416no—
273C22×C47—42no—
274C22×C47—42no—
275C22×C47—44no—
276C22×C47C2×#12114yes—
277C22×C47C2×#12314yes—
278C22×C47C2×#12318yes—
279C22×C47C2×#12414yes—
280C22×C47C2×#12618yes—
281C22×C47C23×D411yescharacteristic
282C22×C47C23×D411yescharacteristic
283C22×C47C22×#4111yescharacteristic
284C22×C47C22×#4112yes—
285C22×C47C22×#4112yes—
286C2×D47—24no—
287C2×D47—28no—
288C2×D47—416no—
289C2×D47—42no—
290C2×D47—42no—
291C2×D47—44no—
292C2×D47—464no—
293C2×D47#397164yesdirect product factor
294C2×D47C2×#12118yes—
295C2×D47C2×#12318yes—
296C2×D47C2×#123116yes—
297C2×D47C2×#12418yes—
298C2×D47C2×#126116yes—
299C4×C47—24no—
300C4×C47—44no—
301C4×C47—44no—
302C4×C47—42no—
303Dic47—24no—
304Dic47—44no—
305Dic47—44no—
306Dic47—42no—
307C23×C4⋊C4—471no—
308C23×C22⋊C4—471no—
309C23×C22⋊C4—472no—
310C2×#397—4716no—
311C2×#397—471no—
312C2×#397—472no—
313C2×#397—471no—
314C2×#397—471no—
315C2×#397—472no—
316C2×#397D4711yescharacteristic, direct product factor
317C22×#95—471no—
318C22×#95—472no—
319C2×C47—44no—
320C2×C47C2×#39718yescomplemented
321C2×C47C22×#12111yescharacteristic
322C2×C47C22×#12311yescharacteristic
323C2×C47C22×#12312yes—
324C2×C47C22×#12411yescharacteristic
325C2×C47C22×#12612yes—
326D47—44no—
327D47C2×#397116yesdirect product factor
328C26—471no—
329C24×C4—471no—
330C24×C4—472no—
331C24×C4—471no—
332C24×C4—472no—
333C22×C4⋊C4—472no—
334C22×C4⋊C4—471no—
335C22×C4⋊C4—478no—
336C22×C4⋊C4—948no—
337C22×C4⋊C4C2×D4711yescharacteristic, complemented
338C22×C22⋊C4—471no—
339C22×C22⋊C4—472no—
340C22×C22⋊C4—471no—
341C22×C22⋊C4—472no—
342C22×C22⋊C4—472no—
343C22×C22⋊C4—471no—
344C22×C22⋊C4—478no—
345C22×C22⋊C4—4716no—
346C22×C22⋊C4—948no—
347C22×C22⋊C4—9416no—
348C22×C22⋊C4C2×D4712yes—
349C22×C22⋊C4C2×D4711yescharacteristic
350#397—478no—
351#397—478no—
352#397—4716no—
353#397—478no—
354#397—4716no—
355#397C2×D4718yesdirect product factor
356C2×#95—472no—
357C2×#95—472no—
358C2×#95—472no—
359C2×#95—472no—
360C2×#95—471no—
361C2×#95—478no—
362C2×#95—4716no—
363C2×#95C2×D4712yescomplemented
364C2×#95C2×D4711yescharacteristic, complemented
365C47C22×#39711yescharacteristic, complemented, Sylow
366C25—471no—
367C25—478no—
368C25—474no—
369C25—471no—
370C25—944no—
371C25—944no—
372C25—948no—
373C25—948no—
374C25C22×D4711yescharacteristic
375C23×C4—471no—
376C23×C4—478no—
377C23×C4—474no—
378C23×C4—472no—
379C23×C4—472no—
380C23×C4—471no—
381C23×C4—478no—
382C23×C4—474no—
383C23×C4—478no—
384C23×C4—948no—
385C23×C4—944no—
386C23×C4—948no—
387C23×C4—948no—
388C23×C4—948no—
389C23×C4—948no—
390C23×C4—948no—
391C23×C4—948no—
392C23×C4—948no—
393C23×C4C22×D4712yes—
394C23×C4C22×D4712yes—
395C23×C4C22×D4711yescharacteristic
396C23×C4C22×D4711yescharacteristic
397C2×C4⋊C4—24no—
398C2×C4⋊C4—478no—
399C2×C4⋊C4—474no—
400C2×C4⋊C4—9432no—
401C2×C4⋊C4—948no—
402C2×C4⋊C4—944no—
403C2×C4⋊C4C22×D4714yescomplemented
404C2×C22⋊C4—28no—
405C2×C22⋊C4—24no—
406C2×C22⋊C4—474no—
407C2×C22⋊C4—478no—
408C2×C22⋊C4—474no—
409C2×C22⋊C4—478no—
410C2×C22⋊C4—478no—
411C2×C22⋊C4—474no—
412C2×C22⋊C4—9432no—
413C2×C22⋊C4—9464no—
414C2×C22⋊C4—944no—
415C2×C22⋊C4—948no—
416C2×C22⋊C4—948no—
417C2×C22⋊C4—944no—
418C2×C22⋊C4—948no—
419C2×C22⋊C4—944no—
420C2×C22⋊C4C22×D4718yes—
421C2×C22⋊C4C22×D4714yes—
422#95—478no—
423#95—478no—
424#95—474no—
425#95—478no—
426#95—478no—
427#95C22×D4718yescomplemented
428#95C22×D4714yescomplemented
429C24—22no—
430C24—22no—
431C24—24no—
432C24—24no—
433C24—474no—
434C24—474no—
435C24—474no—
436C24—478no—
437C24—478no—
438C24—472no—
439C24—4716no—
440C24—474no—
441C24—472no—
442C24—948no—
443C24—9432no—
444C24—9464no—
445C24—948no—
446C24—9416no—
447C24—9416no—
448C24—942no—
449C24—942no—
450C24—944no—
451C24—944no—
452C24—18816no—
453C24—18816no—
454C24—18832no—
455C24D4×D4714yes—
456C24C23×D4712yes—
457C24C23×D4711yescharacteristic
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—474no—
468C22×C4—472no—
469C22×C4—4716no—
470C22×C4—474no—
471C22×C4—472no—
472C22×C4—474no—
473C22×C4—9432no—
474C22×C4—9416no—
475C22×C4—948no—
476C22×C4—9416no—
477C22×C4—9416no—
478C22×C4—9416no—
479C22×C4—9416no—
480C22×C4—9416no—
481C22×C4—9416no—
482C22×C4—9416no—
483C22×C4—944no—
484C22×C4—944no—
485C22×C4—944no—
486C22×C4—942no—
487C22×C4—944no—
488C22×C4—944no—
489C22×C4—944no—
490C22×C4—944no—
491C22×C4—944no—
492C22×C4—18832no—
493C22×C4—18832no—
494C22×C4—18816no—
495C22×C4D4×D4714yes—
496C22×C4C23×D4714yes—
497C22×C4C23×D4712yes—
498C22×C4C23×D4714yes—
499C22×C4C23×D4712yes—
500C4⋊C4—28no—
501C4⋊C4—9416no—
502C4⋊C4—948no—
503C22⋊C4—216no—
504C22⋊C4—28no—
505C22⋊C4—948no—
506C22⋊C4—9416no—
507C22⋊C4—9416no—
508C22⋊C4—948no—
509C22⋊C4—9416no—
510C22⋊C4—948no—
511C23—28no—
512C23—216no—
513C23—22no—
514C23—22no—
515C23—24no—
516C23—24no—
517C23—44no—
518C23—44no—
519C23—48no—
520C23—4716no—
521C23—4716no—
522C23—4732no—
523C23—4716no—
524C23—4732no—
525C23—474no—
526C23—474no—
527C23—474no—
528C23—478no—
529C23—478no—
530C23—474no—
531C23—9432no—
532C23—9464no—
533C23—948no—
534C23—9416no—
535C23—942no—
536C23—942no—
537C23—944no—
538C23—944no—
539C23—188128no—
540C23—18816no—
541C23—18816no—
542C23—18832no—
543C23—1884no—
544C23—1884no—
545C23—1888no—
546C23C2×D4×D4714yes—
547C23C2×D4×D4712yes—
548C23C2×D4×D4712yes—
549C23#41×D4712yes—
550C23#41×D4714yes—
551C23#41×D4714yes—
552C23C24×D4711yescharacteristic
553C2×C4—28no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—48no—
564C2×C4—48no—
565C2×C4—44no—
566C2×C4—474no—
567C2×C4—9432no—
568C2×C4—948no—
569C2×C4—944no—
570C2×C4—944no—
571C2×C4—944no—
572C2×C4—942no—
573C2×C4—944no—
574C2×C4—944no—
575C2×C4—944no—
576C2×C4—944no—
577C2×C4—944no—
578C2×C4—18832no—
579C2×C4—18832no—
580C2×C4—18816no—
581C2×C4—1888no—
582C2×C4—1888no—
583C2×C4—1884no—
584C2×C4C2×D4×D4714yes—
585C22—24no—
586C22—28no—
587C22—416no—
588C22—42no—
589C22—42no—
590C22—44no—
591C22—4764no—
592C22—478no—
593C22—478no—
594C22—4716no—
595C22—478no—
596C22—4716no—
597C22—944no—
598C22—948no—
599C22—18864no—
600C22—18816no—
601C22—1882no—
602C22—1882no—
603C22—1884no—
604C22#121×D4714yes—
605C22#123×D4714yes—
606C22#123×D4718yes—
607C22#124×D4714yes—
608C22#126×D4718yes—
609C22C22×D4×D4711yescharacteristic
610C22C22×D4×D4711yescharacteristic
611C22C2×#41×D4711yescharacteristic
612C22C2×#41×D4712yes—
613C22C2×#41×D4712yes—
614C4—24no—
615C4—44no—
616C4—44no—
617C4—42no—
618C4—944no—
619C4—1884no—
620C4—1884no—
621C4—1882no—
622C2—44no—
623C2—4716no—
624C2—1884no—
625C2#397×D4718yesdirect product factor
626C2C2×#121×D4711yescharacteristic
627C2C2×#123×D4711yescharacteristic
628C2C2×#123×D4712yes—
629C2C2×#124×D4711yescharacteristic
630C2C2×#126×D4712yes—
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#397C2
socleC24×C47C24
prime radicalC25×D47C22
hypercenterC2×#397D47
hypocenterC47C22×#397
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. C22×C4⋊C4×D47C2semidirect
4. C2×#15689052C2semidirect
5. C2×#15689051C2semidirect
6. C2×#15689050C2semidirect
7. C2×#15689049C2semidirect
8. C2×#15689048C2semidirect
9. #397×D47C2direct (N × H)
10. C2×#95×D47C2semidirect
11. C2×#95×D47C2semidirect
12. C2×C47×#397C2semidirect
18. C22×C4⋊Dic47C22semidirect
19. C22×Dic47⋊C4C22semidirect
21. C2×C4⋊C4×D47C22semidirect
32. #15689052C22semidirect
33. #15689051C22semidirect
34. #15689050C22semidirect
35. #15689049C22semidirect
36. #15689048C22semidirect
37. C2×C47⋊#95C22semidirect
38. C2×C47⋊#95C22semidirect
39. C2×C47⋊#95C22semidirect
40. C2×C47⋊#95C22semidirect
41. C2×C47⋊#95C22semidirect
42. #95×D47C22semidirect
43. #95×D47C22semidirect
44. C22×C4⋊C4×C47C22semidirect
47. C47×#397C22semidirect
48. C2×#95×C47C22semidirect
49. C2×#95×C47C22semidirect
77. C2×C4⋊Dic47C23semidirect
79. C2×Dic47⋊C4C23semidirect
95. C47⋊#95C23semidirect
96. C47⋊#95C23semidirect
97. C47⋊#95C23semidirect
98. C47⋊#95C23semidirect
99. C47⋊#95C23semidirect
106. C2×C4⋊C4×C47C23semidirect
111. #95×C47C23semidirect
112. #95×C47C23semidirect
293. C2×D47#397direct (N × H)
316. C2×#397D47direct (N × H)
320. C2×C47C2×#397semidirect
327. D47C2×#397direct (N × H)
337. C22×C4⋊C4C2×D47semidirect
355. #397C2×D47direct (N × H)
363. C2×#95C2×D47semidirect
364. C2×#95C2×D47semidirect
365. C47C22×#397semidirect
403. C2×C4⋊C4C22×D47semidirect
427. #95C22×D47semidirect
428. #95C22×D47semidirect
625. C2#397×D47direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D472
C22×C22⋊C4×D472
C2×#156890522
C2×#156890512
C2×#156890502
C2×#156890492
C2×#156890482
#397×D472
C2×#95×D472
C2×C47×#3972
C22×#39747