Finite Group Databasebeta

← #26143054

Subgroups — #26143054

Order 12032.

1634 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
1C22×#13093989C211yesmaximal, characteristic
2C2×#15689044C211yesmaximal, characteristic
3C2×#15689006C212yesmaximal
4C2×#15689005C211yesmaximal, characteristic
5#20241658C211yesmaximal, characteristic
6#20241646C212yesmaximal
7#20241640C212yesmaximal
8#20241638C211yesmaximal, characteristic
9#20241614C212yesmaximal
10#20241613C211yesmaximal, characteristic
11C47×#1442C211yesmaximal, characteristic
12C23×Dic94C2211yescharacteristic
13C2×#13093989—24no—
14C2×#13093989—28no—
15C22×C4⋊Dic47C2212yes—
16C22×Dic47⋊C4C2212yes—
17C22×Dic47⋊C4C2211yescharacteristic
18C22×Dic47⋊C4C2211yescharacteristic
19C22×C4×Dic47C2211yescharacteristic
20C22×C4×Dic47C2212yes—
21#15689044C418yescomplemented
22#15689006—28no—
23#15689005—24no—
24C2×C47⋊#95C2211yescharacteristic
25C2×C47⋊#95C2211yescharacteristic
26C2×C47⋊#95C2211yescharacteristic
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2211yescharacteristic
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C22×C4⋊C4×C47C2211yescharacteristic
36C2×#95×C47C2211yescharacteristic
37C2×#95×C47C2212yes—
38C2×#95×C47C2212yes—
39C2×#95×C47C2211yescharacteristic
40C22×Dic94—22no—
41C22×Dic94—22no—
42C22×Dic94—24no—
43C22×Dic94—24no—
44C22×Dic94C2×C414yes—
45C23×Dic47C2312yes—
46C23×Dic47C2311yescharacteristic
47C23×Dic47C2311yescharacteristic
48C23×Dic47C2311yescharacteristic
49C23×Dic47C2312yes—
50C23×Dic47C2311yescharacteristic
51#13093989—232no—
52C2×C4⋊Dic47—24no—
53C2×C4⋊Dic47—24no—
54C2×C4⋊Dic47C2×C418yes—
55C2×Dic47⋊C4—22no—
56C2×Dic47⋊C4—24no—
57C2×Dic47⋊C4—22no—
58C2×Dic47⋊C4—24no—
59C2×Dic47⋊C4—24no—
60C2×Dic47⋊C4—22no—
61C2×Dic47⋊C4—24no—
62C2×Dic47⋊C4C2×C414yes—
63C2×C4×Dic47—24no—
64C2×C4×Dic47—24no—
65C2×C4×Dic47—24no—
66C2×C4×Dic47D414yes—
67C2×C4×Dic47D418yes—
68C47⋊#95—24no—
69C47⋊#95—22no—
70C47⋊#95—22no—
71C47⋊#95—22no—
72C47⋊#95—22no—
73C47⋊#95—24no—
74C47⋊#95—24no—
75C47⋊#95—24no—
76C47⋊#95—42no—
77C47⋊#95—42no—
78C47⋊#95C2×C418yes—
79C23×C4×C47C2311yescharacteristic
80C23×C4×C47C2311yescharacteristic
81C23×C4×C47C2312yes—
82C23×C4×C47C2312yes—
83C23×C4×C47C2311yescharacteristic
84C2×C4⋊C4×C47—24no—
85C2×C4⋊C4×C47—22no—
86#95×C47—22no—
87#95×C47—24no—
88#95×C47—42no—
89#95×C47C2×C414yes—
90C24×C47C2411yescharacteristic
91C22×C4×C47—22no—
92C22×C4×C47—22no—
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—21no—
106C22×C4×C47—21no—
107C22×C4×C47—22no—
108C22×C4×C47—22no—
109C22×C4×C47—21no—
110C22×C4×C47—22no—
111C22×C4×C47—21no—
112C22×C4×C47—21no—
113C22×C4×C47—22no—
114C22×C4×C47—21no—
115C22×C4×C47C22×C414yes—
116C22×C4×C47C22×C412yes—
117C22×C4×C47C2×D414yes—
118C22×C4×C47C2×D412yes—
119C22×C4×C47#4112yes—
120C22×Dic47—22no—
121C22×Dic47—22no—
122C22×Dic47—22no—
123C22×Dic47—22no—
124C22×Dic47—22no—
125C22×Dic47—21no—
126C22×Dic47—21no—
127C22×Dic47—21no—
128C22×Dic47—21no—
129C22×Dic47—22no—
130C22×Dic47—22no—
131C22×Dic47—21no—
132C22×Dic47—21no—
133C22×Dic47—22no—
134C22×Dic47—21no—
135C22×Dic47—21no—
136C22×Dic47—21no—
137C22×Dic47—21no—
138C22×Dic47—21no—
139C22×Dic47—22no—
140C22×Dic47—21no—
141C22×Dic47—22no—
142C22×Dic47—22no—
143C22×Dic47—22no—
144C22×Dic47—22no—
145C22×Dic47—22no—
146C22×Dic47—22no—
147C22×Dic47—22no—
148C22×Dic47C22×C412yes—
149C22×Dic47C22×C412yes—
150C22×Dic47C22×C414yes—
151C22×Dic47C2×D412yes—
152C22×Dic47C2×D414yes—
153C22×Dic47C2×D412yes—
154C22×Dic47C2×D414yes—
155C22×Dic47#4114yes—
156C2×Dic94—28no—
157C2×Dic94—216no—
158C2×Dic94—28no—
159C2×Dic94—28no—
160C2×Dic94—216no—
161C4⋊C4×C47—28no—
162C4⋊Dic47—216no—
163Dic47⋊C4—216no—
164Dic47⋊C4—28no—
165Dic47⋊C4—44no—
166C4×Dic47—216no—
167C4×Dic47—28no—
168C23×C47C23×C411yescharacteristic
169C23×C47C22×D412yes—
170C23×C47C22×D411yescharacteristic
171C23×C47C2×#4112yes—
172C23×C47C2×#4111yescharacteristic
173C23×C47H(5,𝔽2)11yescharacteristic
174C23×C472−1+412yes—
175C23×C472−1+411yescharacteristic
176C23×C472−1+412yes—
177C23×C472−1+411yescharacteristic
178C23×C472−1+411yescharacteristic
179C2×C4×C47—24no—
180C2×C4×C47—22no—
181C2×C4×C47—22no—
182C2×C4×C47—24no—
183C2×C4×C47—24no—
184C2×C4×C47—24no—
185C2×C4×C47—24no—
186C2×C4×C47—24no—
187C2×C4×C47—24no—
188C2×C4×C47—24no—
189C2×C4×C47—42no—
190C2×C4×C47—42no—
191C2×C4×C47—42no—
192C2×C4×C47—42no—
193C2×C4×C47—42no—
194C2×C4×C47—42no—
195C2×C4×C47—42no—
196C2×C4×C47—42no—
197C2×C4×C47—41no—
198C2×C4×C47—41no—
199C2×C4×C47—42no—
200C2×C4×C47—41no—
201C2×C4×C47—41no—
202C2×C4×C47—41no—
203C2×C4×C47—42no—
204C2×C4×C47—41no—
205C2×C4×C47—42no—
206C2×C4×C47—42no—
207C2×C4×C47C4×D414yes—
208C2×Dic47—24no—
209C2×Dic47—24no—
210C2×Dic47—24no—
211C2×Dic47—24no—
212C2×Dic47—24no—
213C2×Dic47—24no—
214C2×Dic47—24no—
215C2×Dic47—22no—
216C2×Dic47—22no—
217C2×Dic47—24no—
218C2×Dic47—22no—
219C2×Dic47—22no—
220C2×Dic47—24no—
221C2×Dic47—22no—
222C2×Dic47—22no—
223C2×Dic47—22no—
224C2×Dic47—22no—
225C2×Dic47—22no—
226C2×Dic47—41no—
227C2×Dic47—41no—
228C2×Dic47—42no—
229C2×Dic47—42no—
230C2×Dic47—41no—
231C2×Dic47—42no—
232C2×Dic47—41no—
233C2×Dic47—41no—
234C2×Dic47—41no—
235C2×Dic47—42no—
236C2×Dic47—42no—
237C2×Dic47—42no—
238C2×Dic47—42no—
239C2×Dic47—42no—
240C2×Dic47—42no—
241C2×Dic47—42no—
242C2×Dic47C4×D418yes—
243C2×Dic47#12014yes—
244Dic94—232no—
245#14302—471nomaximal, Sylow
246C22×C47C2×C4×D412yes—
247C22×C47C2×C4×D411yescharacteristic
248C22×C47#51911yescharacteristic
249C22×C47#51912yes—
250C22×C47#52011yescharacteristic
251C22×C47C2×#12011yescharacteristic
252C22×C47#52511yescharacteristic
253C22×C47#52512yes—
254C22×C47#53612yes—
255C22×C47#53611yescharacteristic
256C22×C47#53611yescharacteristic
257C22×C47#53612yes—
258C22×C47#53611yescharacteristic
259C22×C47#53612yes—
260C22×C47#53712yes—
261C22×C47#53711yescharacteristic
262C22×C47#54112yes—
263C22×C47#54112yes—
264C22×C47#54112yes—
265C22×C47#54111yescharacteristic
266C22×C47#54112yes—
267C22×C47#54212yes—
268C22×C47#54211yescharacteristic
269C4×C47—24no—
270C4×C47—44no—
271C4×C47—44no—
272C4×C47—81no—
273C4×C47—81no—
274Dic47—24no—
275Dic47—28no—
276Dic47—42no—
277Dic47—42no—
278Dic47—42no—
279Dic47—82no—
280C22×C4×Q8—471no—
281C2×#395—471no—
282C2×#387—471no—
283C2×#387—472no—
284#1446—471no—
285#1442—472no—
286#1442D4711yescharacteristic
287#1441—472no—
288#1441—471no—
289#1434—471no—
290#1434—472no—
291C2×C47C4×#12011yescharacteristic
292C2×C47#232312yes—
293C2×C47#232311yescharacteristic
294C2×C47#232712yes—
295C2×C47#232711yescharacteristic
296C2×C47#261411yescharacteristic
297C2×C47#261611yescharacteristic
298C2×C47#263411yescharacteristic
299C2×C47#263412yes—
300C2×C47#263711yescharacteristic
301C2×C47#263712yes—
302C23×Q8—471no—
303C2×C4×Q8—944no—
304C2×C4×Q8—948no—
305C22×C4⋊C4—471no—
306C22×C4⋊C4—472no—
307C22×C4⋊C4—472no—
308C22×C4⋊C4—471no—
309C22×C4⋊C4C2×D4711yescharacteristic
310C22×C42—472no—
311C22×C42—471no—
312#395—478no—
313#387—944no—
314#387—948no—
315C2×#95—472no—
316C2×#95—471no—
317C2×#95—472no—
318C2×#95—472no—
319C2×#95—471no—
320C2×#95—471no—
321C2×#95—472no—
322C2×#95—471no—
323C2×#95—472no—
324C2×#95—472no—
325C2×#95—472no—
326C2×#95C2×D4712yes—
327C2×#95C2×D4711yescharacteristic
328C2×#95C2×D4712yes—
329C2×#95C2×D4711yescharacteristic
330C47#1430211yescharacteristic, complemented, Sylow
331C22×Q8—474no—
332C22×Q8—944no—
333C22×Q8—944no—
334C22×Q8—942no—
335C22×Q8—942no—
336C23×C4—472no—
337C23×C4—471no—
338C23×C4—471no—
339C23×C4—471no—
340C23×C4—471no—
341C23×C4—472no—
342C23×C4C22×D4711yescharacteristic
343C23×C4C22×D4711yescharacteristic
344C23×C4C22×D4712yes—
345C23×C4C22×D4712yes—
346C23×C4C22×D4711yescharacteristic
347C4×Q8—9432no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—474no—
351C2×C4⋊C4—478no—
352C2×C4⋊C4—944no—
353C2×C4⋊C4—944no—
354C2×C4⋊C4—944no—
355C2×C4⋊C4—944no—
356C2×C4⋊C4—944no—
357C2×C4⋊C4—942no—
358C2×C4⋊C4—942no—
359C2×C4⋊C4—942no—
360C2×C4⋊C4—944no—
361C2×C42—478no—
362C2×C42—474no—
363C2×C42—944no—
364C2×C42—944no—
365C2×C42—944no—
366#95—24no—
367#95—22no—
368#95—42no—
369#95—478no—
370#95—944no—
371#95—944no—
372#95—942no—
373#95—942no—
374#95—944no—
375#95—942no—
376#95—944no—
377#95—942no—
378#95—1882no—
379#95—1882no—
380#95C4×D4714yes—
381C24C23×D4711yescharacteristic
382C2×Q8—9416no—
383C2×Q8—948no—
384C2×Q8—948no—
385C2×Q8—9416no—
386C2×Q8—948no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—474no—
412C22×C4—474no—
413C22×C4—472no—
414C22×C4—474no—
415C22×C4—474no—
416C22×C4—472no—
417C22×C4—472no—
418C22×C4—472no—
419C22×C4—942no—
420C22×C4—942no—
421C22×C4—942no—
422C22×C4—942no—
423C22×C4—941no—
424C22×C4—942no—
425C22×C4—941no—
426C22×C4—941no—
427C22×C4—942no—
428C22×C4—941no—
429C22×C4—942no—
430C22×C4—942no—
431C22×C4—941no—
432C22×C4—941no—
433C22×C4—941no—
434C22×C4—941no—
435C22×C4—941no—
436C22×C4—941no—
437C22×C4—942no—
438C22×C4—941no—
439C22×C4—941no—
440C22×C4—942no—
441C22×C4—942no—
442C22×C4—942no—
443C22×C4—942no—
444C22×C4—942no—
445C22×C4—942no—
446C22×C4—942no—
447C22×C4C2×C4×D4714yes—
448C22×C4C2×C4×D4712yes—
449C22×C4D4×D4714yes—
450C22×C4D4×D4712yes—
451C22×C4#1062535412yes—
452C4⋊C4—28no—
453C4⋊C4—9416no—
454C4⋊C4—9416no—
455C4⋊C4—948no—
456C4⋊C4—1884no—
457C42—948no—
458C42—9416no—
459C23C22×C4×D4711yescharacteristic
460C23C2×D4×D4712yes—
461C23C2×D4×D4711yescharacteristic
462C23#41×D4712yes—
463C23C2×#1062535411yescharacteristic
464C23#1309406911yescharacteristic
465C23#1309407111yescharacteristic
466C23#1309407111yescharacteristic
467C23#1309407112yes—
468C23#1309407112yes—
469C23#1309407211yescharacteristic
470Q8—9432no—
471C2×C4—24no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—42no—
498C2×C4—41no—
499C2×C4—478no—
500C2×C4—474no—
501C2×C4—944no—
502C2×C4—944no—
503C2×C4—944no—
504C2×C4—944no—
505C2×C4—944no—
506C2×C4—944no—
507C2×C4—944no—
508C2×C4—942no—
509C2×C4—942no—
510C2×C4—944no—
511C2×C4—944no—
512C2×C4—942no—
513C2×C4—942no—
514C2×C4—942no—
515C2×C4—942no—
516C2×C4—942no—
517C2×C4—942no—
518C2×C4—942no—
519C2×C4—1882no—
520C2×C4—1882no—
521C2×C4—1882no—
522C2×C4—1882no—
523C2×C4—1882no—
524C2×C4—1882no—
525C2×C4—1882no—
526C2×C4—1881no—
527C2×C4—1881no—
528C2×C4—1881no—
529C2×C4—1881no—
530C2×C4—1882no—
531C2×C4—1882no—
532C2×C4—1881no—
533C2×C4—1882no—
534C2×C4—1881no—
535C2×C4#1309398614yes—
536C22C4×D4×D4712yes—
537C22C2×#1309398611yescharacteristic
538C22#1568959911yescharacteristic
539C22#1568960012yes—
540C22#1568960211yescharacteristic
541C22#120×D4711yescharacteristic
542C22#1568963111yescharacteristic
543C22#1568963612yes—
544C22#1568969312yes—
545C22#1568969311yescharacteristic
546C22#1568969311yescharacteristic
547C22#1568969512yes—
548C22#1568969611yescharacteristic
549C22#1568969612yes—
550C22#1568970012yes—
551C22#1568970211yescharacteristic
552C22#1568973012yes—
553C22#1568973012yes—
554C22#1568973212yes—
555C22#1568973611yescharacteristic
556C22#1568973612yes—
557C22#1568974112yes—
558C22#1568974711yescharacteristic
559C4—24no—
560C4—44no—
561C4—44no—
562C4—81no—
563C4—81no—
564C4—944no—
565C4—948no—
566C4—3762no—
567C4—1882no—
568C4—1882no—
569C4—1882no—
570C2#2024588911yescharacteristic
571C2#2024606312yes—
572C2#2024606811yescharacteristic
573C2#2024610312yes—
574C2#2024610511yescharacteristic
575C2#2024910611yescharacteristic
576C2#2024911611yescharacteristic
577C2#2024926611yescharacteristic
578C2#2024927012yes—
579C2#2024929711yescharacteristic
580C2#2024930312yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC47×#1442C2
socle, prime radical, cosocleC24×C47C24
hypercenter#1442D47
hypocenterC47#14302
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
21. #15689044C4semidirect
330. C47#14302semidirect

Maximal subgroups

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

subgroupindex
C22×#130939892
C2×#156890442
C2×#156890062
C2×#156890052
#202416582
#202416462
#202416402
#202416382
#202416142
#202416132
C47×#14422
#1430247