Finite Group Databasebeta

← #26111864

Subgroups — #26111864

Order 12032.

1030 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
1C2×#15689087C211yesmaximal, characteristic, complemented
2C2×#15688857C212yesmaximal, complemented
3#20241611C211yesmaximal, characteristic, complemented
4#20241266C212yesmaximal, complemented
5C47×#2847C211yesmaximal, characteristic
6C22×#10625329—21no—
7C22×C22⋊Dic47—21no—
8#15689087—24no—
9C2×C22⋊(C47⋊C8)—21no—
10C2×C22⋊(C47⋊C8)C2212yes—
11C2×C47⋊#95—21no—
12C2×C47⋊#95C2212yes—
13#15688857—24no—
14C24×C4×C47C2211yescharacteristic
15C2×#121×C47C411yescharacteristic, complemented
16C2×#121×C47C411yescharacteristic, complemented
17C2×#121×C47C2211yescharacteristic
18C2×#120×C47—21no—
19C47×#386—21no—
20C47×#386—21no—
21C47×#386—21no—
22C47×#380C411yescharacteristic, complemented
23C47×#380C411yescharacteristic, complemented
24C47×#380C2211yescharacteristic
25C23×Dic47—22no—
26C2×#10625329—24no—
27C2×#10625329—42no—
28C2×#10625329—42no—
29C22×C47⋊C8—22no—
30C2×C22⋊Dic47—24no—
31C2×C22⋊Dic47—42no—
32C2×C22⋊Dic47—42no—
33C22⋊(C47⋊C8)—24no—
34C22⋊(C47⋊C8)—22no—
35C22⋊(C47⋊C8)D414yescomplemented
36C47⋊#95—22no—
37C47⋊#95—22no—
38C47⋊#95—42no—
39C25×C47D411yescharacteristic
40C22×D4×C47—21no—
41C22×D4×C47—21no—
42C22×D4×C47—21no—
43C22×D4×C47C2×C411yescharacteristic
44C23×C4×C47—22no—
45C23×C4×C47—22no—
46C23×C4×C47—42no—
47C23×C4×C47—42no—
48C23×C4×C47C2×C411yescharacteristic
49C23×C4×C47C2×C411yescharacteristic
50C23×C4×C47D411yescharacteristic
51C23×C4×C47D411yescharacteristic
52C23×C4×C47D411yescharacteristic
53C23×C4×C47C2311yescharacteristic
54#121×C47—22no—
55#121×C47—22no—
56#121×C47—42no—
57#121×C47—42no—
58#120×C47—44no—
59C2×C4⋊C4×C47C2×C411yescharacteristic
60C2×C4⋊C4×C47C2×C411yescharacteristic
61C2×C4⋊C4×C47C2×C411yescharacteristic
62C2×C22⋊C4×C47—21no—
63C2×C22⋊C4×C47—21no—
64C2×C22⋊C4×C47—21no—
65C2×C22⋊C4×C47—21no—
66C2×C22⋊C4×C47—21no—
67C2×C22⋊C4×C47—21no—
68#95×C47—21no—
69#95×C47—21no—
70#95×C47—21no—
71C24×C47—22no—
72C24×C47—22no—
73C24×C47—21no—
74C24×C47—21no—
75C24×C47—22no—
76C24×C47—22no—
77C24×C47—21no—
78C24×C47—41no—
79C24×C47—41no—
80C24×C47C22⋊C411yescharacteristic
81C24×C47C22⋊C411yescharacteristic
82C24×C47C2×D411yescharacteristic
83C2×D4×C47—22no—
84C2×D4×C47—41no—
85C2×D4×C47—41no—
86C2×D4×C47—42no—
87C2×D4×C47—42no—
88C2×D4×C47—42no—
89C2×D4×C47—42no—
90C2×D4×C47—42no—
91C2×D4×C47—42no—
92C2×D4×C47—42no—
93C2×D4×C47—42no—
94C2×D4×C47—41no—
95C2×D4×C47—41no—
96C22×C4×C47—22no—
97C22×C4×C47—22no—
98C22×C4×C47—21no—
99C22×C4×C47—21no—
100C22×C4×C47—22no—
101C22×C4×C47—22no—
102C22×C4×C47—22no—
103C22×C4×C47—22no—
104C22×C4×C47—22no—
105C22×C4×C47—22no—
106C22×C4×C47—21no—
107C22×C4×C47—21no—
108C22×C4×C47—21no—
109C22×C4×C47—21no—
110C22×C4×C47—21no—
111C22×C4×C47—41no—
112C22×C4×C47—41no—
113C22×C4×C47—41no—
114C22×C4×C47—41no—
115C22×C4×C47—41no—
116C22×C4×C47—41no—
117C22×C4×C47—41no—
118C22×C4×C47—48no—
119C22×C4×C47—48no—
120C22×C4×C47C22⋊C411yescharacteristic
121C22×C4×C47C22⋊C411yescharacteristic
122C22×C4×C47C22×C411yescharacteristic
123C22×C4×C47C2×D411yescharacteristic
124C22×C4×C47C2×D412yes—
125C22×C4×C47#4112yes—
126C22×Dic47—24no—
127C22×Dic47—42no—
128C22×Dic47—42no—
129C22×Dic47—42no—
130C22×Dic47—42no—
131C22×Dic47—42no—
132C22×Dic47—42no—
133C4⋊C4×C47—22no—
134C4⋊C4×C47—41no—
135C4⋊C4×C47—41no—
136C22⋊C4×C47—42no—
137C22⋊C4×C47—42no—
138C22⋊C4×C47—42no—
139C22⋊C4×C47—42no—
140C22⋊C4×C47—42no—
141C22⋊C4×C47—41no—
142C22⋊C4×C47—41no—
143C22⋊Dic47—48no—
144#10625329—48no—
145C2×C47⋊C8—24no—
146C2×C47⋊C8—42no—
147C2×C47⋊C8—42no—
148C23×C47—21no—
149C23×C47—21no—
150C23×C47—21no—
151C23×C47—21no—
152C23×C47—24no—
153C23×C47—24no—
154C23×C47—21no—
155C23×C47—21no—
156C23×C47—21no—
157C23×C47—21no—
158C23×C47—21no—
159C23×C47—21no—
160C23×C47—21no—
161C23×C47—21no—
162C23×C47—21no—
163C23×C47—21no—
164C23×C47—21no—
165C23×C47—21no—
166C23×C47—44no—
167C23×C47—44no—
168C23×C47—44no—
169C23×C47—44no—
170C23×C47—42no—
171C23×C47—42no—
172C23×C47—42no—
173C23×C47—42no—
174C23×C47—41no—
175C23×C47—41no—
176C23×C47—41no—
177C23×C47—41no—
178C23×C47—41no—
179C23×C47—41no—
180C23×C47—41no—
181C23×C47#9912yes—
182C23×C47#10412yes—
183C23×C47C2×C22⋊C411yescharacteristic
184C23×C47#12112yes—
185C23×C47AGL(1,ℤ/8)11yescharacteristic
186C23×C47AGL(1,ℤ/8)12yes—
187C23×C47#13711yescharacteristic
188D4×C47—82no—
189D4×C47—84no—
190D4×C47—84no—
191D4×C47—82no—
192D4×C47—82no—
193C2×C4×C47—24no—
194C2×C4×C47—24no—
195C2×C4×C47—21no—
196C2×C4×C47—21no—
197C2×C4×C47—21no—
198C2×C4×C47—21no—
199C2×C4×C47—21no—
200C2×C4×C47—21no—
201C2×C4×C47—21no—
202C2×C4×C47—21no—
203C2×C4×C47—21no—
204C2×C4×C47—42no—
205C2×C4×C47—42no—
206C2×C4×C47—44no—
207C2×C4×C47—44no—
208C2×C4×C47—44no—
209C2×C4×C47—42no—
210C2×C4×C47—42no—
211C2×C4×C47—41no—
212C2×C4×C47—41no—
213C2×C4×C47—41no—
214C2×C4×C47—41no—
215C2×C4×C47—41no—
216C2×C4×C47—41no—
217C2×C4×C47—41no—
218C2×C4×C47—41no—
219C2×C4×C47—41no—
220C2×C4×C47#9912yes—
221C2×C4×C47C4×D412yes—
222C2×C4×C47#12011yescharacteristic
223C2×C4×C47#12311yescharacteristic
224C2×Dic47—44no—
225C2×Dic47—44no—
226C2×Dic47—44no—
227C2×Dic47—82no—
228C2×Dic47—82no—
229C2×Dic47—82no—
230C2×Dic47—82no—
231C47⋊C8—44no—
232#9117—471nomaximal, Sylow
233C22×C47—22no—
234C22×C47—22no—
235C22×C47—21no—
236C22×C47—21no—
237C22×C47—22no—
238C22×C47—22no—
239C22×C47—21no—
240C22×C47—21no—
241C22×C47—22no—
242C22×C47—22no—
243C22×C47—22no—
244C22×C47—22no—
245C22×C47—22no—
246C22×C47—22no—
247C22×C47—48no—
248C22×C47—48no—
249C22×C47—41no—
250C22×C47—41no—
251C22×C47—41no—
252C22×C47—41no—
253C22×C47—41no—
254C22×C47—41no—
255C22×C47—41no—
256C22×C47—41no—
257C22×C47—81no—
258C22×C47—81no—
259C22×C47—81no—
260C22×C47—81no—
261C22×C47—81no—
262C22×C47—81no—
263C22×C47—81no—
264C22×C47#38611yescharacteristic
265C22×C47C2×#9911yescharacteristic
266C22×C47C2×#9911yescharacteristic
267C22×C47#41711yescharacteristic
268C22×C47#41811yescharacteristic
269C22×C47C2×#10411yescharacteristic
270C22×C47#42111yescharacteristic
271C22×C47#46812yes—
272C22×C47#46912yes—
273C4×C47—21no—
274C4×C47—22no—
275C4×C47—21no—
276C4×C47—22no—
277C4×C47—41no—
278C4×C47—81no—
279C4×C47—81no—
280C4×C47—81no—
281Dic47—84no—
282C2×#407—471no—
283#2847D4711yescharacteristic
284C2×#327—472no—
285C22⋊#95—471no—
286#1294—472no—
287C2×C47—22no—
288C2×C47—22no—
289C2×C47—42no—
290C2×C47—42no—
291C2×C47—161no—
292C2×C47#150411yescharacteristic
293C2×C47#150711yescharacteristic
294C2×C47#151011yescharacteristic
295C2×C47#151311yescharacteristic
296C2×C47#187111yescharacteristic
297C2×C47#189511yescharacteristic
298C2×C47#189811yescharacteristic
299C24×C4C2×D4711yescharacteristic
300C22×M16—941no—
301C2×#121Dic4711yescharacteristic, complemented
302C2×#121Dic4711yescharacteristic, complemented
303C2×#121C2×D4711yescharacteristic
304C2×#120—21no—
305C22×C22⋊C4—941no—
306#407—944no—
307C2×C22⋊C8—472no—
308C2×C22⋊C8—941no—
309#386—21no—
310#386—21no—
311#386—21no—
312#380Dic4711yescharacteristic, complemented
313#380Dic4711yescharacteristic, complemented
314#380C2×D4711yescharacteristic
315C2×#95—472no—
316C2×#95—941no—
317#327—944no—
318C47#911711yescharacteristic, complemented, Sylow
319C25C22⋊D4711yescharacteristic
320C22×D4—21no—
321C22×D4—21no—
322C22×D4—21no—
323C22×D4C2×Dic4711yescharacteristic
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—42no—
327C23×C4—42no—
328C23×C4—942no—
329C23×C4C2×Dic4711yescharacteristic
330C23×C4C2×Dic4711yescharacteristic
331C23×C4C22⋊D4711yescharacteristic
332C23×C4C22⋊D4711yescharacteristic
333C23×C4C22⋊D4711yescharacteristic
334C23×C4C22×D4711yescharacteristic
335C2×M16—944no—
336C2×M16—1882no—
337C2×M16—1882no—
338C22×C8—942no—
339#121—22no—
340#121—22no—
341#121—42no—
342#121—42no—
343#120—44no—
344C2×C4⋊C4C2×Dic4711yescharacteristic
345C2×C4⋊C4C2×Dic4711yescharacteristic
346C2×C4⋊C4C2×Dic4711yescharacteristic
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—944no—
354C2×C22⋊C4—1882no—
355C2×C22⋊C4—1882no—
356C22⋊C8—474no—
357C22⋊C8—944no—
358C22⋊C8—942no—
359#95—21no—
360#95—21no—
361#95—21no—
362#95—942no—
363#95—942no—
364#95—1882no—
365C24—22no—
366C24—22no—
367C24—21no—
368C24—21no—
369C24—22no—
370C24—22no—
371C24—21no—
372C24—41no—
373C24—41no—
374C24C22⋊Dic4711yescharacteristic
375C24C22⋊Dic4711yescharacteristic
376C24C2×C22⋊D4711yescharacteristic
377C2×D4—22no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4—42no—
381C2×D4—42no—
382C2×D4—42no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4—41no—
388C2×D4—42no—
389C2×D4—41no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—48no—
413C22×C4—48no—
414C22×C4—944no—
415C22×C4—1882no—
416C22×C4—1882no—
417C22×C4—1882no—
418C22×C4—1882no—
419C22×C4—1882no—
420C22×C4—1882no—
421C22×C4C22⋊Dic4711yescharacteristic
422C22×C4C22⋊Dic4711yescharacteristic
423C22×C4D4×D4712yes—
424C22×C4#1062535212yes—
425C22×C4C22×Dic4711yescharacteristic
426C22×C4C2×C22⋊D4711yescharacteristic
427M16—1888no—
428C2×C8—944no—
429C2×C8—1882no—
430C2×C8—1882no—
431C4⋊C4—22no—
432C4⋊C4—41no—
433C4⋊C4—41no—
434C22⋊C4—42no—
435C22⋊C4—42no—
436C22⋊C4—42no—
437C22⋊C4—42no—
438C22⋊C4—42no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C22⋊C4—1888no—
442C23—21no—
443C23—21no—
444C23—21no—
445C23—21no—
446C23—24no—
447C23—24no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—44no—
461C23—44no—
462C23—44no—
463C23—44no—
464C23—42no—
465C23—42no—
466C23—42no—
467C23—42no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23#1309393912yes—
476C23#1309395112yes—
477C23C2×C22⋊Dic4711yescharacteristic
478C23#1309399612yes—
479C23#1309404911yescharacteristic
480C23#1309405012yes—
481C23#1309405411yescharacteristic
482D4—82no—
483D4—84no—
484D4—84no—
485D4—82no—
486D4—82no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—44no—
501C2×C4—44no—
502C2×C4—44no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—3762no—
515C2×C4—3762no—
516C2×C4—3762no—
517C2×C4—3762no—
518C2×C4—1884no—
519C2×C4—1884no—
520C2×C4—1884no—
521C2×C4#1309393912yes—
522C2×C4D4×Dic4712yes—
523C2×C4#1309399211yescharacteristic
524C2×C4#1309400511yescharacteristic
525C8—1884no—
526C22—21no—
527C22—21no—
528C22—22no—
529C22—21no—
530C22—21no—
531C22—22no—
532C22—22no—
533C22—22no—
534C22—22no—
535C22—22no—
536C22—22no—
537C22—22no—
538C22—22no—
539C22—22no—
540C22—48no—
541C22—48no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22#1568900311yescharacteristic
558C22C2×#1309393911yescharacteristic
559C22C2×#1309393911yescharacteristic
560C22#1568912411yescharacteristic
561C22#1568912811yescharacteristic
562C22C2×#1309395111yescharacteristic
563C22#1568914011yescharacteristic
564C22#1568936712yes—
565C22#1568937412yes—
566C4—21no—
567C4—22no—
568C4—21no—
569C4—22no—
570C4—41no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4—3764no—
575C2—22no—
576C2—22no—
577C2—42no—
578C2—42no—
579C2—161no—
580C2#2024189211yescharacteristic
581C2#2024190411yescharacteristic
582C2#2024191711yescharacteristic
583C2#2024193111yescharacteristic
584C2#2024369111yescharacteristic
585C2#2024382711yescharacteristic
586C2#2024384211yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic47
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
Fitting, prime radicalC47×#2847C2
socleC23×C47C2×C22⋊C4
cosocleC23×C4×C47C23
hypercenter#2847D47
hypocenterC47#9117
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C24×C4 ◁ #2847

Complements

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

NH ≅ G/Ntype
1. C2×#15689087C2semidirect
2. C2×#15688857C2semidirect
3. #20241611C2semidirect
4. #20241266C2semidirect
15. C2×#121×C47C4semidirect
16. C2×#121×C47C4semidirect
22. C47×#380C4semidirect
23. C47×#380C4semidirect
35. C22⋊(C47⋊C8)D4semidirect
301. C2×#121Dic47semidirect
302. C2×#121Dic47semidirect
312. #380Dic47semidirect
313. #380Dic47semidirect
318. C47#9117semidirect

Maximal subgroups

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

subgroupindex
C2×#156890872
C2×#156888572
#202416112
#202412662
C47×#28472
#911747