Finite Group Databasebeta

← #26112587

Subgroups — #26112587

Order 12032.

686 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251837C211yesmaximal, characteristic
2#20243332C211yesmaximal, characteristic
3#20241908C211yesmaximal, characteristic, complemented
4#20241752C211yesmaximal, characteristic, complemented
5#20241265C211yesmaximal, characteristic, complemented
6#20241235C211yesmaximal, characteristic, complemented
7C2×C47×#452C211yesmaximal, characteristic
8C2×#13094031—21no—
9C2×#13093951—21no—
10C2×#13093951—21no—
11#15689090—22no—
12#15689090—21no—
13#15689087—21no—
14#15689087C2211yescharacteristic
15#15689087C2211yescharacteristic
16C2×C22⋊(C47⋊C8)—21no—
17C2×C22⋊(C47⋊C8)C2211yescharacteristic
18C4×C22⋊Dic47C2211yescharacteristic
19#15688860—22no—
20#15688849—21no—
21#15688849—21no—
22C22×#41×C47C2211yescharacteristic
23C22×Q16×C47C411yescharacteristic, complemented
24C22×SD16×C47C411yescharacteristic, complemented
25C2×C22⋊Q8×C47C2211yescharacteristic
26C47×#452—21no—
27C47×#452—21no—
28C47×#452—21no—
29C47×#452—21no—
30C2×#103×C47C411yescharacteristic, complemented
31C2×#102×C47C411yescharacteristic, complemented
32C2×C22⋊C8×C47C2211yescharacteristic
33#13094031—42no—
34#13094031—42no—
35C2×#10625329—22no—
36C2×#10625329—21no—
37C2×#10625329—21no—
38C22×C47⋊C8—22no—
39C22×C47⋊C8—21no—
40C2×C22⋊Dic47—21no—
41C2×C4×Dic47—21no—
42#13093951—42no—
43#13093951—42no—
44C22⋊(C47⋊C8)—22no—
45C22⋊(C47⋊C8)—22no—
46C22⋊(C47⋊C8)—21no—
47C22⋊(C47⋊C8)—21no—
48C22⋊(C47⋊C8)—21no—
49C22⋊(C47⋊C8)—21no—
50C22⋊(C47⋊C8)D411yescharacteristic
51C22⋊(C47⋊C8)D411yescharacteristic
52C22⋊(C47⋊C8)D412yes—
53C47⋊#95—21no—
54C2×#41×C47—21no—
55C2×#41×C47—21no—
56C2×#41×C47—42no—
57C2×#41×C47—42no—
58C2×#41×C47D411yescharacteristic
59C2×#41×C47D411yescharacteristic
60C2×#41×C47D411yescharacteristic
61C2×#41×C47D411yescharacteristic
62C22×Q8×C47C2×C411yescharacteristic
63C22×Q8×C47C2×C411yescharacteristic
64C22×D4×C47—21no—
65C22×D4×C47C2×C411yescharacteristic
66C23×C4×C47—21no—
67C23×C4×C47C2311yescharacteristic
68C2×Q16×C47—21no—
69C2×Q16×C47—21no—
70C2×Q16×C47—42no—
71C2×SD16×C47—21no—
72C2×SD16×C47—21no—
73C2×SD16×C47—42no—
74C22×C8×C47C2×C411yescharacteristic
75C22×C8×C47C2×C411yescharacteristic
76C22⋊Q8×C47—21no—
77C22⋊Q8×C47—21no—
78C22⋊Q8×C47—21no—
79C22⋊Q8×C47—21no—
80C2×C4⋊C4×C47—21no—
81C2×C4⋊C4×C47C2×C411yescharacteristic
82C2×C22⋊C4×C47—21no—
83#103×C47—21no—
84#103×C47—21no—
85#102×C47—21no—
86#102×C47—21no—
87C22⋊C8×C47—21no—
88C22⋊C8×C47—21no—
89C24×C47—21no—
90C24×C47#4111yescharacteristic
91#41×C47—22no—
92#41×C47—22no—
93#41×C47—22no—
94#41×C47—22no—
95#41×C47—41no—
96#41×C47—41no—
97#41×C47—41no—
98#41×C47—41no—
99#41×C47—44no—
100#41×C47—44no—
101C2×Q8×C47—21no—
102C2×Q8×C47—22no—
103C2×Q8×C47—21no—
104C2×Q8×C47—21no—
105C2×Q8×C47—41no—
106C2×Q8×C47—41no—
107C2×Q8×C47—41no—
108C2×Q8×C47C22⋊C411yescharacteristic
109C2×Q8×C47C22⋊C411yescharacteristic
110C2×D4×C47—21no—
111C2×D4×C47—22no—
112C2×D4×C47—21no—
113C2×D4×C47—21no—
114C2×D4×C47—21no—
115C2×D4×C47—21no—
116C2×D4×C47—41no—
117C2×D4×C47—44no—
118C2×D4×C47C22⋊C411yescharacteristic
119C2×D4×C47C22⋊C411yescharacteristic
120C22×C4×C47—21no—
121C22×C4×C47—21no—
122C22×C4×C47—21no—
123C22×C4×C47—21no—
124C22×C4×C47—21no—
125C22×C4×C47—21no—
126C22×C4×C47—21no—
127C22×C4×C47—41no—
128C22×C4×C47—41no—
129C22×C4×C47—44no—
130C22×C4×C47C22×C411yescharacteristic
131C22×C4×C47C2×D411yescharacteristic
132C22×C4×C47C2×D411yescharacteristic
133C22×C4×C47C2×D411yescharacteristic
134C22×C4×C47C2×D411yescharacteristic
135C22×C4×C47#4111yescharacteristic
136C22×Dic47—41no—
137Q16×C47—42no—
138Q16×C47—42no—
139SD16×C47—42no—
140SD16×C47—42no—
141C2×C8×C47—21no—
142C2×C8×C47—21no—
143C2×C8×C47—41no—
144C2×C8×C47—41no—
145C4⋊C4×C47—21no—
146C4⋊C4×C47—21no—
147C4⋊C4×C47—41no—
148C4⋊C4×C47—41no—
149C22⋊C4×C47—41no—
150C22⋊C4×C47—41no—
151C22⋊Dic47—22no—
152C22⋊Dic47—41no—
153C4×Dic47—41no—
154C4×Dic47—41no—
155#10625329—44no—
156#10625329—41no—
157#10625329—41no—
158#10625329—41no—
159#10625329—41no—
160C2×C47⋊C8—21no—
161C2×C47⋊C8—22no—
162C2×C47⋊C8—21no—
163C2×C47⋊C8—44no—
164C2×C47⋊C8—41no—
165C2×C47⋊C8—41no—
166C2×C47⋊C8—41no—
167C23×C47—21no—
168C23×C47—21no—
169C23×C47—21no—
170C23×C47—21no—
171C23×C47—41no—
172C23×C47—41no—
173C23×C47—42no—
174C23×C47—41no—
175C23×C47—41no—
176C23×C47—81no—
177C23×C47C4×D411yescharacteristic
178C23×C47#12111yescharacteristic
179C23×C47#12311yescharacteristic
180Q8×C47—21no—
181Q8×C47—21no—
182Q8×C47—21no—
183Q8×C47—42no—
184Q8×C47—41no—
185Q8×C47—41no—
186Q8×C47—81no—
187Q8×C47#9912yes—
188D4×C47—24no—
189D4×C47—21no—
190D4×C47—21no—
191D4×C47—21no—
192D4×C47—42no—
193D4×C47—42no—
194D4×C47—42no—
195D4×C47—42no—
196D4×C47#9912yes—
197C2×C4×C47—24no—
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—21no—
205C2×C4×C47—21no—
206C2×C4×C47—41no—
207C2×C4×C47—41no—
208C2×C4×C47—41no—
209C2×C4×C47—42no—
210C2×C4×C47—42no—
211C2×C4×C47—42no—
212C2×C4×C47—42no—
213C2×C4×C47—41no—
214C2×C4×C47—41no—
215C2×C4×C47—41no—
216C2×C4×C47—41no—
217C2×C4×C47—81no—
218C2×C4×C47C2×C22⋊C411yescharacteristic
219C2×C4×C47C4×D411yescharacteristic
220C2×C4×C47#12011yescharacteristic
221C2×C4×C47#12111yescharacteristic
222C2×Dic47—42no—
223C2×Dic47—81no—
224C2×Dic47—81no—
225C8×C47—41no—
226C8×C47—41no—
227C47⋊C8—41no—
228C47⋊C8—42no—
229C47⋊C8—41no—
230C47⋊C8—81no—
231#9239—471nomaximal, Sylow
232C22×C47—21no—
233C22×C47—21no—
234C22×C47—21no—
235C22×C47—21no—
236C22×C47—21no—
237C22×C47—21no—
238C22×C47—22no—
239C22×C47—21no—
240C22×C47—21no—
241C22×C47—41no—
242C22×C47—41no—
243C22×C47—41no—
244C22×C47—41no—
245C22×C47—41no—
246C22×C47—81no—
247C22×C47—81no—
248C22×C47—82no—
249C22×C47—82no—
250C22×C47#38611yescharacteristic
251C22×C47#44311yescharacteristic
252C22×C47#44411yescharacteristic
253C4×C47—21no—
254C4×C47—21no—
255C4×C47—22no—
256C4×C47—21no—
257C4×C47—41no—
258C4×C47—81no—
259C4×C47—81no—
260C4×C47C2×#9911yescharacteristic
261C4×C47C2×#9911yescharacteristic
262Dic47—82no—
263C2×#452D4711yescharacteristic
264#2880—471no—
265#1789—471no—
266#1508—471no—
267#1472—471no—
268#1293—471no—
269#1282—471no—
270C2×C47—21no—
271C2×C47—21no—
272C2×C47—41no—
273C2×C47—41no—
274C2×C47—42no—
275C2×C47—81no—
276C2×C47#187611yescharacteristic
277C2×C47#189811yescharacteristic
278C2×C47#190211yescharacteristic
279C22×#41C2×D4711yescharacteristic
280C22×Q16Dic4711yescharacteristic, complemented
281C22×SD16Dic4711yescharacteristic, complemented
282C2×#131—941no—
283C2×C22⋊Q8C2×D4711yescharacteristic
284#452—21no—
285#452—21no—
286#452—21no—
287#452—21no—
288C2×#104—941no—
289C2×#104—941no—
290C2×#103Dic4711yescharacteristic, complemented
291C2×#102Dic4711yescharacteristic, complemented
292#408—942no—
293#408—941no—
294#407—471no—
295#407—471no—
296#407—941no—
297C2×C22⋊C8—471no—
298C2×C22⋊C8—941no—
299C2×C22⋊C8C2×D4711yescharacteristic
300C4×C22⋊C4—471no—
301#328—942no—
302#324—941no—
303#324—941no—
304C47#923911yescharacteristic, complemented, Sylow
305C2×#41—21no—
306C2×#41—21no—
307C2×#41—42no—
308C2×#41—42no—
309C2×#41C22⋊D4711yescharacteristic
310C2×#41C22⋊D4711yescharacteristic
311C2×#41C22⋊D4711yescharacteristic
312C2×#41C22⋊D4711yescharacteristic
313C22×Q8C2×Dic4711yescharacteristic
314C22×Q8C2×Dic4711yescharacteristic
315C22×D4—21no—
316C22×D4C2×Dic4711yescharacteristic
317C23×C4—21no—
318C23×C4C22×D4711yescharacteristic
319C2×Q16—21no—
320C2×Q16—21no—
321C2×Q16—42no—
322C2×SD16—21no—
323C2×SD16—21no—
324C2×SD16—42no—
325#131—1882no—
326#131—1882no—
327C2×M16—942no—
328C2×M16—941no—
329C2×M16—941no—
330C22×C8—942no—
331C22×C8—941no—
332C22×C8C2×Dic4711yescharacteristic
333C22×C8C2×Dic4711yescharacteristic
334C22⋊Q8—21no—
335C22⋊Q8—21no—
336C22⋊Q8—21no—
337C22⋊Q8—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4C2×Dic4711yescharacteristic
340C2×C22⋊C4—21no—
341C2×C22⋊C4—941no—
342C2×C42—941no—
343#104—1882no—
344#104—1882no—
345#103—21no—
346#103—21no—
347#102—21no—
348#102—21no—
349C22⋊C8—21no—
350C22⋊C8—21no—
351C22⋊C8—471no—
352C22⋊C8—471no—
353C22⋊C8—472no—
354C22⋊C8—942no—
355C22⋊C8—942no—
356C22⋊C8—941no—
357C22⋊C8—941no—
358C22⋊C8—941no—
359C22⋊C8—941no—
360#95—941no—
361C24—21no—
362C24#1062535211yescharacteristic
363#41—22no—
364#41—22no—
365#41—22no—
366#41—22no—
367#41—41no—
368#41—41no—
369#41—41no—
370#41—41no—
371#41—44no—
372#41—44no—
373C2×Q8—21no—
374C2×Q8—22no—
375C2×Q8—21no—
376C2×Q8—21no—
377C2×Q8—41no—
378C2×Q8—41no—
379C2×Q8—41no—
380C2×Q8C22⋊Dic4711yescharacteristic
381C2×Q8C22⋊Dic4711yescharacteristic
382C2×D4—21no—
383C2×D4—22no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—41no—
389C2×D4—44no—
390C2×D4C22⋊Dic4711yescharacteristic
391C2×D4C22⋊Dic4711yescharacteristic
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—44no—
402C22×C4—1881no—
403C22×C4D4×D4711yescharacteristic
404C22×C4D4×D4711yescharacteristic
405C22×C4#1062535211yescharacteristic
406C22×C4C22×Dic4711yescharacteristic
407C22×C4C2×C22⋊D4711yescharacteristic
408C22×C4C2×C22⋊D4711yescharacteristic
409Q16—42no—
410Q16—42no—
411SD16—42no—
412SD16—42no—
413M16—1881no—
414M16—1881no—
415M16—1884no—
416M16—1881no—
417M16—1881no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—41no—
421C2×C8—41no—
422C2×C8—941no—
423C2×C8—941no—
424C2×C8—942no—
425C2×C8—1881no—
426C2×C8—1884no—
427C2×C8—1881no—
428C2×C8—1881no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—41no—
432C4⋊C4—41no—
433C22⋊C4—41no—
434C22⋊C4—41no—
435C22⋊C4—942no—
436C22⋊C4—1881no—
437C42—1881no—
438C42—1881no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23—21no—
443C23—41no—
444C23—41no—
445C23—42no—
446C23—41no—
447C23—41no—
448C23—81no—
449C23D4×Dic4711yescharacteristic
450C23#1309399611yescharacteristic
451C23#1309400511yescharacteristic
452Q8—21no—
453Q8—21no—
454Q8—21no—
455Q8—42no—
456Q8—41no—
457Q8—41no—
458Q8—81no—
459Q8#1309393912yes—
460D4—24no—
461D4—21no—
462D4—21no—
463D4—21no—
464D4—42no—
465D4—42no—
466D4—42no—
467D4—42no—
468D4#1309393912yes—
469C2×C4—24no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—81no—
490C2×C4—3761no—
491C2×C4—3761no—
492C2×C4—1882no—
493C2×C4C2×C22⋊Dic4711yescharacteristic
494C2×C4D4×Dic4711yescharacteristic
495C2×C4#1309399211yescharacteristic
496C2×C4#1309399611yescharacteristic
497C8—41no—
498C8—41no—
499C8—3761no—
500C8—1881no—
501C8—1881no—
502C8—1882no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—22no—
510C22—21no—
511C22—21no—
512C22—41no—
513C22—41no—
514C22—41no—
515C22—41no—
516C22—41no—
517C22—81no—
518C22—81no—
519C22—82no—
520C22—82no—
521C22#1568900311yescharacteristic
522C22#1568924011yescharacteristic
523C22#1568924511yescharacteristic
524C4—21no—
525C4—21no—
526C4—22no—
527C4—21no—
528C4—41no—
529C4—81no—
530C4—81no—
531C4—3762no—
532C4C2×#1309393911yescharacteristic
533C4C2×#1309393911yescharacteristic
534C2—21no—
535C2—21no—
536C2—41no—
537C2—41no—
538C2—42no—
539C2—81no—
540C2#2024371711yescharacteristic
541C2#2024384211yescharacteristic
542C2#2024386311yescharacteristic
subgroupG/H
centerC22#15689003
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC2×C47×#452C2
socleC22×C47#386
prime radicalC22×#41×C47C22
cosocleC23×C4×C47C23
hypercenterC2×#452D47
hypocenterC47#9239
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
3. #20241908C2semidirect
4. #20241752C2semidirect
5. #20241265C2semidirect
6. #20241235C2semidirect
23. C22×Q16×C47C4semidirect
24. C22×SD16×C47C4semidirect
30. C2×#103×C47C4semidirect
31. C2×#102×C47C4semidirect
280. C22×Q16Dic47semidirect
281. C22×SD16Dic47semidirect
290. C2×#103Dic47semidirect
291. C2×#102Dic47semidirect
304. C47#9239semidirect

Maximal subgroups

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

subgroupindex
#202518372
#202433322
#202419082
#202417522
#202412652
#202412352
C2×C47×#4522
#923947