Finite Group Databasebeta

← #26143358

Subgroups — #26143358

Order 12032.

1282 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689055C211yesmaximal, characteristic
2C2×#15689019C211yesmaximal, characteristic
3C2×#15689005C211yesmaximal, characteristic
4#20241655C211yesmaximal, characteristic
5#20241651C212yesmaximal
6#20241640C212yesmaximal
7#20241638C211yesmaximal, characteristic
8#20241617C212yesmaximal
9#20241613C212yesmaximal
10#95×Dic47C211yesmaximal, characteristic
11C47×#1444C211yesmaximal, characteristic
12C22×C4⋊Dic47C2211yescharacteristic
13C22×C4⋊Dic47C2212yes—
14C22×Dic47⋊C4C2211yescharacteristic
15C22×Dic47⋊C4C2211yescharacteristic
16C22×Dic47⋊C4C2212yes—
17C22×C4×Dic47C2211yescharacteristic
18C22×C4×Dic47C2212yes—
19#15689055C418yescomplemented
20#15689019—24no—
21#15689005—24no—
22C2×C47⋊#95C2211yescharacteristic
23C2×C47⋊#95C2211yescharacteristic
24C2×C47⋊#95C2211yescharacteristic
25C2×C47⋊#95C2212yes—
26C2×C47⋊#95C2211yescharacteristic
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C22×C4⋊C4×C47C2211yescharacteristic
34C22×C4⋊C4×C47C2212yes—
35C2×#95×C47C2211yescharacteristic
36C2×#95×C47C2212yes—
37C2×#95×C47C2211yescharacteristic
38C23×Dic47C2311yescharacteristic
39C23×Dic47C2311yescharacteristic
40C23×Dic47C2312yes—
41C23×Dic47C2311yescharacteristic
42C23×Dic47C2312yes—
43C23×Dic47C2311yescharacteristic
44C2×C4⋊Dic47—22no—
45C2×C4⋊Dic47—22no—
46C2×C4⋊Dic47—42no—
47C2×C4⋊Dic47—42no—
48C2×C4⋊Dic47C2×C414yes—
49C2×C4⋊Dic47C2×C418yes—
50C2×Dic47⋊C4—22no—
51C2×Dic47⋊C4—22no—
52C2×Dic47⋊C4—22no—
53C2×Dic47⋊C4—24no—
54C2×Dic47⋊C4—42no—
55C2×Dic47⋊C4—42no—
56C2×Dic47⋊C4—42no—
57C2×Dic47⋊C4C2×C414yes—
58C2×C4×Dic47—42no—
59C2×C4×Dic47—42no—
60C2×C4×Dic47—42no—
61C2×C4×Dic47D414yes—
62C2×C4×Dic47Q818yes—
63C47⋊#95—22no—
64C47⋊#95—24no—
65C47⋊#95—22no—
66C47⋊#95—22no—
67C47⋊#95—22no—
68C47⋊#95—24no—
69C47⋊#95—42no—
70C47⋊#95—42no—
71C47⋊#95—42no—
72C47⋊#95—42no—
73C47⋊#95C2×C418yes—
74C23×C4×C47C2311yescharacteristic
75C23×C4×C47C2312yes—
76C23×C4×C47C2311yescharacteristic
77C23×C4×C47C2311yescharacteristic
78C23×C4×C47C2312yes—
79C2×C4⋊C4×C47—22no—
80C2×C4⋊C4×C47—24no—
81C2×C4⋊C4×C47—42no—
82C2×C4⋊C4×C47—42no—
83C2×C4⋊C4×C47—42no—
84#95×C47—22no—
85#95×C47—24no—
86#95×C47C2×C414yes—
87C24×C47C2411yescharacteristic
88C22×C4×C47—22no—
89C22×C4×C47—22no—
90C22×C4×C47—22no—
91C22×C4×C47—22no—
92C22×C4×C47—22no—
93C22×C4×C47—22no—
94C22×C4×C47—22no—
95C22×C4×C47—21no—
96C22×C4×C47—21no—
97C22×C4×C47—22no—
98C22×C4×C47—22no—
99C22×C4×C47—22no—
100C22×C4×C47—22no—
101C22×C4×C47—22no—
102C22×C4×C47—21no—
103C22×C4×C47—22no—
104C22×C4×C47—22no—
105C22×C4×C47—22no—
106C22×C4×C47—21no—
107C22×C4×C47—21no—
108C22×C4×C47—22no—
109C22×C4×C47—22no—
110C22×C4×C47—21no—
111C22×C4×C47C22×C412yes—
112C22×C4×C47C22×C414yes—
113C22×C4×C47C2×D412yes—
114C22×C4×C47C2×Q814yes—
115C22×C4×C47#4112yes—
116C22×C4×C47#4114yes—
117C22×Dic47—22no—
118C22×Dic47—21no—
119C22×Dic47—21no—
120C22×Dic47—21no—
121C22×Dic47—21no—
122C22×Dic47—22no—
123C22×Dic47—22no—
124C22×Dic47—22no—
125C22×Dic47—22no—
126C22×Dic47—21no—
127C22×Dic47—21no—
128C22×Dic47—22no—
129C22×Dic47—21no—
130C22×Dic47—22no—
131C22×Dic47—22no—
132C22×Dic47—22no—
133C22×Dic47—22no—
134C22×Dic47—22no—
135C22×Dic47—22no—
136C22×Dic47—22no—
137C22×Dic47—21no—
138C22×Dic47—21no—
139C22×Dic47—22no—
140C22×Dic47—21no—
141C22×Dic47—21no—
142C22×Dic47—22no—
143C22×Dic47—21no—
144C22×Dic47—22no—
145C22×Dic47—22no—
146C22×Dic47C22×C412yes—
147C22×Dic47C22×C414yes—
148C22×Dic47C22×C412yes—
149C22×Dic47C2×D412yes—
150C22×Dic47C2×D412yes—
151C22×Dic47C2×Q814yes—
152C22×Dic47C2×Q814yes—
153C4⋊C4×C47—44no—
154C4⋊C4×C47—48no—
155C4⋊Dic47—28no—
156C4⋊Dic47—48no—
157Dic47⋊C4—28no—
158Dic47⋊C4—44no—
159Dic47⋊C4—48no—
160C4×Dic47—44no—
161C4×Dic47—48no—
162C23×C47C23×C411yescharacteristic
163C23×C47C22×D411yescharacteristic
164C23×C47C22×Q812yes—
165C23×C47C2×#4112yes—
166C23×C47C2×#4111yescharacteristic
167C23×C47H(5,𝔽2)11yescharacteristic
168C23×C47H(5,𝔽2)12yes—
169C23×C47H(5,𝔽2)11yescharacteristic
170C23×C47H(5,𝔽2)11yescharacteristic
171C23×C472−1+412yes—
172C23×C472−1+411yescharacteristic
173C2×C4×C47—24no—
174C2×C4×C47—24no—
175C2×C4×C47—24no—
176C2×C4×C47—22no—
177C2×C4×C47—22no—
178C2×C4×C47—24no—
179C2×C4×C47—24no—
180C2×C4×C47—24no—
181C2×C4×C47—24no—
182C2×C4×C47—24no—
183C2×C4×C47—42no—
184C2×C4×C47—41no—
185C2×C4×C47—41no—
186C2×C4×C47—41no—
187C2×C4×C47—42no—
188C2×C4×C47—42no—
189C2×C4×C47—41no—
190C2×C4×C47—41no—
191C2×C4×C47—41no—
192C2×C4×C47—42no—
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×C47C4×D414yes—
201C2×C4×C47C4×Q818yes—
202C2×Dic47—22no—
203C2×Dic47—22no—
204C2×Dic47—24no—
205C2×Dic47—24no—
206C2×Dic47—22no—
207C2×Dic47—22no—
208C2×Dic47—24no—
209C2×Dic47—22no—
210C2×Dic47—24no—
211C2×Dic47—24no—
212C2×Dic47—22no—
213C2×Dic47—24no—
214C2×Dic47—22no—
215C2×Dic47—24no—
216C2×Dic47—22no—
217C2×Dic47—22no—
218C2×Dic47—24no—
219C2×Dic47—24no—
220C2×Dic47—41no—
221C2×Dic47—42no—
222C2×Dic47—41no—
223C2×Dic47—41no—
224C2×Dic47—41no—
225C2×Dic47—42no—
226C2×Dic47—42no—
227C2×Dic47—42no—
228C2×Dic47—42no—
229C2×Dic47—42no—
230C2×Dic47—41no—
231C2×Dic47—42no—
232C2×Dic47—42no—
233C2×Dic47—42no—
234C2×Dic47—42no—
235C2×Dic47—41no—
236C2×Dic47—42no—
237C2×Dic47C4⋊Q814yes—
238#14328—471nomaximal, Sylow
239C22×C47C2×C4×D411yescharacteristic
240C22×C47C2×C4×Q812yes—
241C22×C47#51811yescharacteristic
242C22×C47#52012yes—
243C22×C47#52011yescharacteristic
244C22×C47C2×C4⋊Q811yescharacteristic
245C22×C47#53211yescharacteristic
246C22×C47#53312yes—
247C22×C47#53411yescharacteristic
248C22×C47#53511yescharacteristic
249C22×C47#53611yescharacteristic
250C22×C47#53711yescharacteristic
251C22×C47#53812yes—
252C22×C47#53912yes—
253C22×C47#53912yes—
254C22×C47#54011yescharacteristic
255C22×C47#54012yes—
256C22×C47#54112yes—
257C22×C47#54211yescharacteristic
258C22×C47#54312yes—
259C22×C47#54412yes—
260C22×C47#54412yes—
261C22×C47#54412yes—
262C4×C47—24no—
263C4×C47—28no—
264C4×C47—81no—
265C4×C47—82no—
266C4×C47—81no—
267Dic47—24no—
268Dic47—42no—
269Dic47—42no—
270Dic47—44no—
271Dic47—42no—
272Dic47—44no—
273C2×#398—471no—
274C2×#389—471no—
275C2×#387—471no—
276#1445—471no—
277#1444—472no—
278#1444D4711yescharacteristic
279#1441—472no—
280#1441—471no—
281C4⋊#95—472no—
282#1434—472no—
283C4×#95—471no—
284C2×C47C4×C4⋊Q811yescharacteristic
285C2×C47#232211yescharacteristic
286C2×C47#232411yescharacteristic
287C2×C47#232912yes—
288C2×C47#233012yes—
289C2×C47#265911yescharacteristic
290C2×C47#266011yescharacteristic
291C2×C47#266111yescharacteristic
292C2×C47#266411yescharacteristic
293C2×C47#266612yes—
294C2×C47#266712yes—
295C22×C4⋊C4—471no—
296C22×C4⋊C4—471no—
297C22×C4⋊C4—472no—
298C22×C4⋊C4—472no—
299C22×C4⋊C4—471no—
300C22×C4⋊C4C2×D4712yes—
301C22×C4⋊C4C2×D4711yescharacteristic
302C22×C42—472no—
303C22×C42—471no—
304#398—478no—
305#389—944no—
306#387—944no—
307C2×#95—472no—
308C2×#95—472no—
309C2×#95—471no—
310C2×#95—471no—
311C2×#95—472no—
312C2×#95—471no—
313C2×#95—471no—
314C2×#95—472no—
315C2×#95—472no—
316C2×#95—472no—
317C2×#95—472no—
318C2×#95C2×D4712yes—
319C2×#95C2×D4711yescharacteristic
320C2×#95C2×D4711yescharacteristic
321C47#1432811yescharacteristic, complemented, Sylow
322C23×C4—471no—
323C23×C4—472no—
324C23×C4—471no—
325C23×C4—471no—
326C23×C4—471no—
327C23×C4—472no—
328C23×C4C22×D4711yescharacteristic
329C23×C4C22×D4712yes—
330C23×C4C22×D4711yescharacteristic
331C23×C4C22×D4711yescharacteristic
332C23×C4C22×D4712yes—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—474no—
339C2×C4⋊C4—474no—
340C2×C4⋊C4—478no—
341C2×C4⋊C4—942no—
342C2×C4⋊C4—942no—
343C2×C4⋊C4—942no—
344C2×C4⋊C4—942no—
345C2×C4⋊C4—942no—
346C2×C4⋊C4—944no—
347C2×C4⋊C4—1882no—
348C2×C4⋊C4—1882no—
349C2×C4⋊C4—1882no—
350C2×C4⋊C4—1882no—
351C2×C4⋊C4—1882no—
352C2×C42—474no—
353C2×C42—478no—
354C2×C42—1882no—
355C2×C42—1882no—
356C2×C42—1882no—
357#95—22no—
358#95—24no—
359#95—478no—
360#95—942no—
361#95—942no—
362#95—942no—
363#95—944no—
364#95—944no—
365#95—942no—
366#95—1882no—
367#95—1882no—
368#95—1882no—
369#95—1882no—
370#95C4×D4714yes—
371C24C23×D4711yescharacteristic
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—472no—
396C22×C4—474no—
397C22×C4—472no—
398C22×C4—474no—
399C22×C4—472no—
400C22×C4—472no—
401C22×C4—474no—
402C22×C4—942no—
403C22×C4—941no—
404C22×C4—941no—
405C22×C4—941no—
406C22×C4—941no—
407C22×C4—942no—
408C22×C4—942no—
409C22×C4—942no—
410C22×C4—942no—
411C22×C4—941no—
412C22×C4—942no—
413C22×C4—941no—
414C22×C4—942no—
415C22×C4—942no—
416C22×C4—942no—
417C22×C4—941no—
418C22×C4—942no—
419C22×C4—941no—
420C22×C4—942no—
421C22×C4—941no—
422C22×C4—942no—
423C22×C4—942no—
424C22×C4—942no—
425C22×C4—941no—
426C22×C4—941no—
427C22×C4—942no—
428C22×C4—942no—
429C22×C4—942no—
430C22×C4—941no—
431C22×C4C2×C4×D4712yes—
432C22×C4C2×C4×D4714yes—
433C22×C4D4×D4712yes—
434C22×C4#1062535214yes—
435C22×C4Q8×D4714yes—
436C22×C4#1062535412yes—
437C4⋊C4—44no—
438C4⋊C4—48no—
439C4⋊C4—948no—
440C4⋊C4—948no—
441C4⋊C4—1888no—
442C4⋊C4—1884no—
443C4⋊C4—1888no—
444C42—1888no—
445C42—1884no—
446C23C22×C4×D4711yescharacteristic
447C23C2×D4×D4711yescharacteristic
448C23C2×Q8×D4712yes—
449C23C2×#1062535212yes—
450C23C2×#1062535411yescharacteristic
451C23#1309406911yescharacteristic
452C23#1309406912yes—
453C23#1309407011yescharacteristic
454C23#1309407011yescharacteristic
455C23#1309407112yes—
456C23#1309407211yescharacteristic
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—474no—
485C2×C4—944no—
486C2×C4—944no—
487C2×C4—942no—
488C2×C4—942no—
489C2×C4—944no—
490C2×C4—944no—
491C2×C4—942no—
492C2×C4—942no—
493C2×C4—944no—
494C2×C4—942no—
495C2×C4—944no—
496C2×C4—944no—
497C2×C4—944no—
498C2×C4—942no—
499C2×C4—942no—
500C2×C4—944no—
501C2×C4—942no—
502C2×C4—942no—
503C2×C4—1881no—
504C2×C4—1882no—
505C2×C4—1882no—
506C2×C4—1881no—
507C2×C4—1882no—
508C2×C4—1881no—
509C2×C4—1882no—
510C2×C4—1881no—
511C2×C4—1881no—
512C2×C4—1881no—
513C2×C4—1882no—
514C2×C4—1882no—
515C2×C4—1882no—
516C2×C4—1882no—
517C2×C4—1882no—
518C2×C4—1882no—
519C2×C4—1882no—
520C2×C4#1309398614yes—
521C2×C4#1309398918yes—
522C22C2×#1309398611yescharacteristic
523C22C2×#1309398912yes—
524C22#1568959511yescharacteristic
525C22#1568960212yes—
526C22#1568960511yescharacteristic
527C22C4⋊Q8×D4711yescharacteristic
528C22#1568967111yescharacteristic
529C22#1568967812yes—
530C22#1568968311yescharacteristic
531C22#1568968911yescharacteristic
532C22#1568969511yescharacteristic
533C22#1568970311yescharacteristic
534C22#1568970812yes—
535C22#1568971712yes—
536C22#1568972212yes—
537C22#1568972612yes—
538C22#1568972911yescharacteristic
539C22#1568973312yes—
540C22#1568974711yescharacteristic
541C22#1568974812yes—
542C22#1568975012yes—
543C22#1568975212yes—
544C22#1568975312yes—
545C4—24no—
546C4—28no—
547C4—82no—
548C4—81no—
549C4—81no—
550C4—944no—
551C4—1882no—
552C4—1882no—
553C4—1884no—
554C4—1882no—
555C4—1884no—
556C2#2024595511yescharacteristic
557C2#2024605611yescharacteristic
558C2#2024607911yescharacteristic
559C2#2024611912yes—
560C2#2024612812yes—
561C2#2024950111yescharacteristic
562C2#2024951111yescharacteristic
563C2#2024951911yescharacteristic
564C2#2024955211yescharacteristic
565C2#2024957412yes—
566C2#2024958712yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC47×#1444C2
socle, prime radical, cosocleC24×C47C24
hypercenter#1444D47
hypocenterC47#14328
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
19. #15689055C4semidirect
321. C47#14328semidirect

Maximal subgroups

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

subgroupindex
C2×#156890552
C2×#156890192
C2×#156890052
#202416552
#202416512
#202416402
#202416382
#202416172
#202416132
#95×Dic472
C47×#14442
#1432847