Finite Group Databasebeta

← C2×#20247693 #26385325

Subgroups — C2×#20247693 #26385325

Order 12032.

3678 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094005C211yesmaximal, characteristic
2C22×D4×Dic47C211yesmaximal, characteristic
3C23×Dic47⋊C4C211yesmaximal, characteristic, complemented
4#20247693C2116yesmaximal, direct product factor
5C2×#15689056C212yesmaximal, complemented
6C2×#15689051C212yesmaximal, complemented
7C2×#15689018C212yesmaximal, complemented
8C2×#15688986C211yesmaximal, characteristic, complemented
9C2×#15688984C211yesmaximal, characteristic, complemented
10C2×#15688981C212yesmaximal, complemented
11C2×#15688981C211yesmaximal, characteristic, complemented
12C22×#123×C47C211yesmaximal, characteristic
13C24×Dic47C2211yescharacteristic
14C24×Dic47C2211yescharacteristic
15C24×Dic47C2211yescharacteristic
16C2×#13094005—28no—
17C2×#13094005C2218yes—
18C2×D4×Dic47—28no—
19C2×D4×Dic47C2218yes—
20C22×C4⋊Dic47C2211yescharacteristic
21C22×Dic47⋊C4—28no—
22C22×Dic47⋊C4C2212yes—
23C22×Dic47⋊C4C2212yes—
24C22×Dic47⋊C4C2212yes—
25C22×Dic47⋊C4C2212yes—
26C22×Dic47⋊C4C2218yescomplemented
27C22×C22⋊Dic47C2211yescharacteristic
28C22×C22⋊Dic47C2211yescharacteristic
29C22×C22⋊Dic47C2211yescharacteristic
30C22×C22⋊Dic47C2212yes—
31C22×C4×Dic47C2211yescharacteristic
32#15689056C22116yescomplemented
33#15689051C22116yescomplemented
34#15689018C22116yescomplemented
35#15688986C2218yescomplemented
36#15688984C2218yescomplemented
37#15688981C2218yescomplemented
38#15688981C22116yescomplemented
39C2×C47⋊#95C2212yes—
40C2×C47⋊#95C2212yes—
41C2×C47⋊#95C2212yes—
42C2×C47⋊#95C2212yes—
43C2×C47⋊#95C2212yes—
44C23×D4×C47C2211yescharacteristic
45C24×C4×C47C2211yescharacteristic
46C2×#123×C47—28no—
47C2×#123×C47C2218yes—
48C22×C4⋊C4×C47C2212yes—
49C22×C22⋊C4×C47C2211yescharacteristic
50C22×C22⋊C4×C47C2212yes—
51C23×Dic47—28no—
52C23×Dic47—24no—
53C23×Dic47—24no—
54C23×Dic47—24no—
55C23×Dic47—24no—
56C23×Dic47—28no—
57C23×Dic47D418yes—
58C23×Dic47C2311yescharacteristic
59C23×Dic47C2311yescharacteristic
60C23×Dic47C2312yes—
61C23×Dic47C2312yes—
62C23×Dic47C2314yes—
63C23×Dic47C2314yes—
64C23×Dic47C2311yescharacteristic
65C23×Dic47C2314yes—
66C23×Dic47C2311yescharacteristic
67#13094005—232no—
68D4×Dic47—232no—
69C2×C4⋊Dic47—24no—
70C2×C4⋊Dic47C2314yes—
71C2×Dic47⋊C4—28no—
72C2×Dic47⋊C4—28no—
73C2×Dic47⋊C4—28no—
74C2×Dic47⋊C4—232no—
75C2×Dic47⋊C4—28no—
76C2×Dic47⋊C4C2318yes—
77C2×Dic47⋊C4C2318yes—
78C2×Dic47⋊C4C2318yes—
79C2×Dic47⋊C4C2318yes—
80C2×C22⋊Dic47—24no—
81C2×C22⋊Dic47—24no—
82C2×C22⋊Dic47—28no—
83C2×C22⋊Dic47—24no—
84C2×C22⋊Dic47C2314yes—
85C2×C22⋊Dic47C2318yes—
86C2×C22⋊Dic47C2314yes—
87C2×C22⋊Dic47C2314yes—
88C2×C4×Dic47—24no—
89C2×C4×Dic47C2314yes—
90C47⋊#95C2318yes—
91C47⋊#95C2318yes—
92C47⋊#95C2318yes—
93C47⋊#95C2318yes—
94C47⋊#95C2318yes—
95C25×C47C2311yescharacteristic
96C25×C47C2311yescharacteristic
97C22×D4×C47—24no—
98C22×D4×C47—24no—
99C22×D4×C47D418yes—
100C22×D4×C47C2314yes—
101C23×C4×C47—24no—
102C23×C4×C47—24no—
103C23×C4×C47—24no—
104C23×C4×C47C2312yes—
105C23×C4×C47C2312yes—
106C23×C4×C47C2314yes—
107C23×C4×C47C2311yescharacteristic
108#123×C47—232no—
109C2×C4⋊C4×C47—28no—
110C2×C4⋊C4×C47C2318yes—
111C2×C22⋊C4×C47—24no—
112C2×C22⋊C4×C47—28no—
113C2×C22⋊C4×C47C2314yes—
114C2×C22⋊C4×C47C2318yes—
115C24×C47—24no—
116C24×C47—24no—
117C24×C47—22no—
118C24×C47—22no—
119C24×C47—24no—
120C24×C47—24no—
121C24×C47C2×D414yes—
122C24×C47C2×D414yes—
123C24×C47C2×D414yes—
124C24×C47#4114yes—
125C24×C47C2412yes—
126C24×C47C2412yes—
127C24×C47C2411yescharacteristic
128C2×D4×C47—232no—
129C2×D4×C47—28no—
130C2×D4×C47—28no—
131C2×D4×C47C2×D4116yes—
132C22×C4×C47—22no—
133C22×C4×C47—22no—
134C22×C4×C47—24no—
135C22×C4×C47—24no—
136C22×C4×C47—28no—
137C22×C4×C47—28no—
138C22×C4×C47—24no—
139C22×C4×C47—28no—
140C22×C4×C47—24no—
141C22×C4×C47—24no—
142C22×C4×C47—24no—
143C22×C4×C47—416no—
144C22×C4×C47C2×D414yes—
145C22×C4×C47C2414yes—
146C22×C4×C47C2414yes—
147C22×C4×C47C2412yes—
148C22×Dic47—24no—
149C22×Dic47—232no—
150C22×Dic47—216no—
151C22×Dic47—22no—
152C22×Dic47—24no—
153C22×Dic47—24no—
154C22×Dic47—22no—
155C22×Dic47—28no—
156C22×Dic47—24no—
157C22×Dic47—28no—
158C22×Dic47—24no—
159C22×Dic47—28no—
160C22×Dic47—24no—
161C22×Dic47—24no—
162C22×Dic47—24no—
163C22×Dic47—24no—
164C22×Dic47—28no—
165C22×Dic47—216no—
166C22×Dic47—416no—
167C22×Dic47—416no—
168C22×Dic47C2×D414yes—
169C22×Dic47C2×D4116yes—
170C22×Dic47C2×D414yes—
171C22×Dic47#4118yes—
172C22×Dic47C2412yes—
173C22×Dic47C2412yes—
174C22×Dic47C2414yes—
175C22×Dic47C2414yes—
176C22×Dic47C2412yes—
177C22×Dic47C2412yes—
178C4⋊C4×C47—216no—
179C22⋊C4×C47—28no—
180C22⋊C4×C47—216no—
181C22⋊Dic47—28no—
182C22⋊Dic47—28no—
183C22⋊Dic47—216no—
184C22⋊Dic47—28no—
185C4⋊Dic47—28no—
186Dic47⋊C4—216no—
187Dic47⋊C4—216no—
188Dic47⋊C4—216no—
189Dic47⋊C4—216no—
190C4×Dic47—28no—
191C23×C47—28no—
192C23×C47—28no—
193C23×C47—216no—
194C23×C47—216no—
195C23×C47—24no—
196C23×C47—24no—
197C23×C47—28no—
198C23×C47—216no—
199C23×C47—22no—
200C23×C47—24no—
201C23×C47—22no—
202C23×C47—24no—
203C23×C47—44no—
204C23×C47—44no—
205C23×C47—48no—
206C23×C47#121116yes—
207C23×C47C22×D414yes—
208C23×C47C22×D412yes—
209C23×C47C22×D414yes—
210C23×C47C22×D414yes—
211C23×C47C22×D412yes—
212C23×C47C2×#4114yes—
213C23×C47C2×#4114yes—
214C23×C47C2×#4112yes—
215C23×C472−1+414yes—
216C23×C47C2511yescharacteristic
217D4×C47—232no—
218C2×C4×C47—28no—
219C2×C4×C47—22no—
220C2×C4×C47—22no—
221C2×C4×C47—24no—
222C2×C4×C47—24no—
223C2×C4×C47—24no—
224C2×C4×C47—24no—
225C2×C4×C47—24no—
226C2×C4×C47—24no—
227C2×C4×C47—416no—
228C2×C4×C47—48no—
229C2×C4×C47—48no—
230C2×C4×C47C22×D414yes—
231C2×Dic47—28no—
232C2×Dic47—24no—
233C2×Dic47—232no—
234C2×Dic47—22no—
235C2×Dic47—24no—
236C2×Dic47—24no—
237C2×Dic47—24no—
238C2×Dic47—22no—
239C2×Dic47—24no—
240C2×Dic47—24no—
241C2×Dic47—24no—
242C2×Dic47—24no—
243C2×Dic47—24no—
244C2×Dic47—416no—
245C2×Dic47—48no—
246C2×Dic47—44no—
247C2×Dic47—44no—
248C2×Dic47—48no—
249C2×Dic47—416no—
250C2×Dic47#123116yescomplemented
251C2×Dic47C22×D414yes—
252C2×Dic47C22×D414yes—
253C2×Dic47C2×#4118yes—
254C2×#2486—471nomaximal, Sylow
255C22×C47—24no—
256C22×C47—24no—
257C22×C47—28no—
258C22×C47—28no—
259C22×C47—232no—
260C22×C47—24no—
261C22×C47—28no—
262C22×C47—42no—
263C22×C47—42no—
264C22×C47—44no—
265C22×C47—416no—
266C22×C47C2×#12118yes—
267C22×C47C2×#12114yes—
268C22×C47C2×#12314yes—
269C22×C47#53614yes—
270C22×C47#54718yes—
271C22×C47#55218yes—
272C22×C47C23×D411yescharacteristic
273C22×C47C23×D411yescharacteristic
274C22×C47C22×#4112yes—
275C22×C47C22×#4111yescharacteristic
276C22×C47C2×2−1+412yes—
277C4×C47—24no—
278C4×C47—44no—
279C4×C47—44no—
280Dic47—24no—
281Dic47—44no—
282Dic47—42no—
283Dic47—42no—
284Dic47—44no—
285Dic47C2×#12318yescomplemented
286C22×#123—471no—
287C22×#123D4711yescharacteristic
288C22×C4×D4—471no—
289C23×C4⋊C4—471no—
290#2486—4716no—
291C2×#398—472no—
292C2×#397—472no—
293C2×#389—472no—
294C2×#381—471no—
295C2×#381—471no—
296C2×#380—472no—
297C2×#380—471no—
298C2×C47—28no—
299C2×C47—44no—
300C2×C47#248618yescomplemented
301C2×C47C22×#12111yescharacteristic
302C2×C47C22×#12311yescharacteristic
303C2×C47C2×#53611yescharacteristic
304C2×C47C2×#54712yes—
305C2×C47C2×#55212yes—
306C23×D4C2×D4711yescharacteristic
307C24×C4—471no—
308C24×C4—471no—
309C24×C4—471no—
310C24×C4C2×D4711yescharacteristic
311C2×#123—28no—
312C2×#123—478no—
313C2×#123—948no—
314C2×#123C2×D4718yes—
315C2×C4×D4—478no—
316C2×C4×D4—948no—
317C22×C4⋊C4—472no—
318C22×C4⋊C4—471no—
319C22×C4⋊C4—472no—
320C22×C4⋊C4—472no—
321C22×C4⋊C4—478no—
322C22×C4⋊C4—472no—
323C22×C4⋊C4—948no—
324C22×C4⋊C4C2×D4712yes—
325C22×C22⋊C4—471no—
326C22×C22⋊C4—472no—
327C22×C22⋊C4—471no—
328C22×C22⋊C4—471no—
329C22×C22⋊C4C2×D4712yes—
330C22×C22⋊C4C2×D4711yescharacteristic
331C22×C42—471no—
332#398—4716no—
333#397—4716no—
334#389—4716no—
335#381—478no—
336#381—478no—
337#380—4716no—
338#380—478no—
339C2×#95—472no—
340C2×#95—472no—
341C2×#95—472no—
342C2×#95—472no—
343C2×#95—472no—
344C47C2×#248611yescharacteristic, complemented, Sylow
345C25C22×D4711yescharacteristic
346C25C22×D4711yescharacteristic
347C22×D4—24no—
348C22×D4—24no—
349C22×D4C22⋊D4718yes—
350C22×D4C22×D4714yes—
351C23×C4—24no—
352C23×C4—24no—
353C23×C4—24no—
354C23×C4—471no—
355C23×C4—478no—
356C23×C4—474no—
357C23×C4—471no—
358C23×C4—474no—
359C23×C4—474no—
360C23×C4—472no—
361C23×C4—471no—
362C23×C4—472no—
363C23×C4—471no—
364C23×C4—948no—
365C23×C4—944no—
366C23×C4—948no—
367C23×C4—944no—
368C23×C4—944no—
369C23×C4—944no—
370C23×C4C22×D4714yes—
371C23×C4C22×D4712yes—
372C23×C4C22×D4712yes—
373C23×C4C22×D4711yescharacteristic
374#123—232no—
375#123—9432no—
376C4×D4—9432no—
377C2×C4⋊C4—28no—
378C2×C4⋊C4—478no—
379C2×C4⋊C4—478no—
380C2×C4⋊C4—474no—
381C2×C4⋊C4—478no—
382C2×C4⋊C4—478no—
383C2×C4⋊C4—948no—
384C2×C4⋊C4—948no—
385C2×C4⋊C4—9432no—
386C2×C4⋊C4—944no—
387C2×C4⋊C4—948no—
388C2×C4⋊C4—948no—
389C2×C4⋊C4C22×D4718yes—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—474no—
393C2×C22⋊C4—474no—
394C2×C22⋊C4—474no—
395C2×C22⋊C4—478no—
396C2×C22⋊C4—944no—
397C2×C22⋊C4—944no—
398C2×C22⋊C4—944no—
399C2×C22⋊C4—948no—
400C2×C22⋊C4C22×D4714yes—
401C2×C22⋊C4C22×D4718yes—
402C2×C42—474no—
403C2×C42—944no—
404#95—478no—
405#95—478no—
406#95—478no—
407#95—478no—
408#95—478no—
409C24—24no—
410C24—24no—
411C24—22no—
412C24—24no—
413C24—22no—
414C24—24no—
415C24D4×D4714yes—
416C24#1062535214yes—
417C24C2×C22⋊D4714yes—
418C24C2×C22⋊D4714yes—
419C24C23×D4712yes—
420C24C23×D4712yes—
421C24C23×D4711yescharacteristic
422C2×D4—232no—
423C2×D4—28no—
424C2×D4—28no—
425C2×D4C2×C22⋊D47116yes—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—28no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—28no—
433C22×C4—24no—
434C22×C4—28no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—416no—
438C22×C4—474no—
439C22×C4—478no—
440C22×C4—472no—
441C22×C4—474no—
442C22×C4—4716no—
443C22×C4—472no—
444C22×C4—472no—
445C22×C4—472no—
446C22×C4—474no—
447C22×C4—474no—
448C22×C4—9432no—
449C22×C4—9416no—
450C22×C4—948no—
451C22×C4—9416no—
452C22×C4—944no—
453C22×C4—942no—
454C22×C4—942no—
455C22×C4—948no—
456C22×C4—944no—
457C22×C4—944no—
458C22×C4—944no—
459C22×C4—948no—
460C22×C4—944no—
461C22×C4—944no—
462C22×C4—948no—
463C22×C4—944no—
464C22×C4—944no—
465C22×C4—944no—
466C22×C4—18816no—
467C22×C4—18816no—
468C22×C4C2×C22⋊D4714yes—
469C22×C4C23×D4714yes—
470C22×C4C23×D4714yes—
471C22×C4C23×D4712yes—
472C4⋊C4—216no—
473C4⋊C4—9416no—
474C4⋊C4—9416no—
475C4⋊C4—9416no—
476C4⋊C4—948no—
477C4⋊C4—9416no—
478C22⋊C4—28no—
479C22⋊C4—216no—
480C22⋊C4—948no—
481C22⋊C4—948no—
482C22⋊C4—948no—
483C22⋊C4—9416no—
484C42—948no—
485C23—216no—
486C23—216no—
487C23—28no—
488C23—24no—
489C23—28no—
490C23—24no—
491C23—216no—
492C23—28no—
493C23—22no—
494C23—24no—
495C23—22no—
496C23—24no—
497C23—48no—
498C23—44no—
499C23—44no—
500C23#13093996116yes—
501C23C2×D4×D4714yes—
502C23C2×D4×D4712yes—
503C23C22×C22⋊D4714yes—
504C23C22×C22⋊D4714yes—
505C23C22×C22⋊D4712yes—
506C23#41×D4714yes—
507C23C2×#1062535214yes—
508C23C2×#1062535212yes—
509C23#1309407114yes—
510C23C24×D4711yescharacteristic
511D4—232no—
512C2×C4—28no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—48no—
522C2×C4—416no—
523C2×C4—48no—
524C2×C4—4716no—
525C2×C4—474no—
526C2×C4—478no—
527C2×C4—474no—
528C2×C4—9432no—
529C2×C4—948no—
530C2×C4—944no—
531C2×C4—942no—
532C2×C4—942no—
533C2×C4—944no—
534C2×C4—944no—
535C2×C4—944no—
536C2×C4—944no—
537C2×C4—944no—
538C2×C4—944no—
539C2×C4—944no—
540C2×C4—944no—
541C2×C4—18816no—
542C2×C4—1888no—
543C2×C4—18816no—
544C2×C4—1888no—
545C2×C4—1884no—
546C2×C4—1884no—
547C2×C4C22×C22⋊D4714yes—
548C22—28no—
549C22—24no—
550C22—28no—
551C22—232no—
552C22—24no—
553C22—28no—
554C22—24no—
555C22—42no—
556C22—44no—
557C22—416no—
558C22—42no—
559C22C2×#1309399618yes—
560C22C2×#1309399614yes—
561C22#123×D4714yes—
562C22#1568969514yes—
563C22#1568977218yes—
564C22#1568981018yes—
565C22C22×D4×D4711yescharacteristic
566C22C23×C22⋊D4711yescharacteristic
567C22C2×#41×D4712yes—
568C22C22×#1062535211yescharacteristic
569C22C2×#1309407112yes—
570C4—24no—
571C4—44no—
572C4—44no—
573C4—478no—
574C4—944no—
575C4—1884no—
576C4—1884no—
577C4—1882no—
578C4—1882no—
579C2—28no—
580C2—44no—
581C2#2024769318yesdirect product factor
582C2C22×#1309399611yescharacteristic
583C2C2×#123×D4711yescharacteristic
584C2C2×#1568969511yescharacteristic
585C2C2×#1568977212yes—
586C2C2×#1568981012yes—
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC22×#123×C47C2
socleC24×C47C24
prime radicalC23×D4×C47C22
hypercenterC22×#123D47
hypocenterC47C2×#2486
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
3. C23×Dic47⋊C4C2semidirect
4. #20247693C2direct (N × H)
5. C2×#15689056C2semidirect
6. C2×#15689051C2semidirect
7. C2×#15689018C2semidirect
8. C2×#15688986C2semidirect
9. C2×#15688984C2semidirect
10. C2×#15688981C2semidirect
11. C2×#15688981C2semidirect
26. C22×Dic47⋊C4C22semidirect
32. #15689056C22semidirect
33. #15689051C22semidirect
34. #15689018C22semidirect
35. #15688986C22semidirect
36. #15688984C22semidirect
37. #15688981C22semidirect
38. #15688981C22semidirect
250. C2×Dic47#123semidirect
285. Dic47C2×#123semidirect
300. C2×C47#2486semidirect
344. C47C2×#2486semidirect
581. C2#20247693direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940052
C22×D4×Dic472
C23×Dic47⋊C42
#202476932
C2×#156890562
C2×#156890512
C2×#156890182
C2×#156889862
C2×#156889842
C2×#156889812
C22×#123×C472
C2×#248647