Finite Group Databasebeta

← #26114666

Subgroups — #26114666

Order 12032.

454 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20244314C211yesmaximal, characteristic
2#20244193C211yesmaximal, characteristic
3#20244149C211yesmaximal, characteristic, complemented
4#20243258C211yesmaximal, characteristic, complemented
5C2×#15688866C211yesmaximal, characteristic
6#20241222C211yesmaximal, characteristic, complemented
7C47×#1296C211yesmaximal, characteristic, complemented
8C2×#13094021C2211yescharacteristic
9C2×#13093955—21no—
10C2×C4⋊(C47⋊C8)C2211yescharacteristic
11C2×#13093946—21no—
12C2×#13093946—21no—
13C2×#13093944—21no—
14C2×#13093944—21no—
15C2×#13093934—21no—
16C2×C4×C47⋊C8C2211yescharacteristic
17C4×C4⋊Dic47C2211yescharacteristic
18#15688885—21no—
19#15688877—21no—
20#15688866C414yescomplemented
21C2×C4⋊C8×C47C2211yescharacteristic
22C2×C4⋊C8×C47C2211yescharacteristic
23C47×#384C2211yescharacteristic
24C22×D188—21no—
25C22×D188—21no—
26C22×D188—21no—
27C22×C47⋊C8—21no—
28C22×C47⋊C8D411yescharacteristic
29C22×C47⋊C8D411yescharacteristic
30#13094021—21no—
31#13094021—21no—
32#13094021—21no—
33#13094021C2×C412yes—
34C2×C4⋊Dic47D411yescharacteristic
35C2×C4⋊Dic47D411yescharacteristic
36C2×C4×Dic47—21no—
37#13093955—42no—
38C4⋊(C47⋊C8)—21no—
39C4⋊(C47⋊C8)C2×C412yes—
40#13093946—42no—
41#13093946—42no—
42#13093944—42no—
43#13093944—42no—
44#13093934—42no—
45C4×C47⋊C8—21no—
46C4×C47⋊C8—21no—
47C47⋊#95—21no—
48C22×C8×C47—21no—
49C22×C8×C47—21no—
50C2×C4⋊C4×C47—21no—
51C2×C4⋊C4×C47—21no—
52C2×C4⋊C4×C47—21no—
53C2×C42×C47C2311yescharacteristic
54C4⋊C8×C47—21no—
55C4⋊C8×C47—21no—
56C4⋊C8×C47—21no—
57C4⋊C8×C47C2×C412yes—
58C23×D47—41no—
59C22×C4×C47—41no—
60C22×C4×C47C2×D411yescharacteristic
61C22×C4×C47C2×D411yescharacteristic
62C22×C4×C47#4111yescharacteristic
63C22×Dic47—21no—
64C22×Dic47—21no—
65C2×D188—22no—
66C2×D188—22no—
67C2×D188—22no—
68C2×D188—41no—
69C2×D188—41no—
70C2×D188—41no—
71C2×D188—41no—
72C2×D188—41no—
73C2×D188—41no—
74C2×D188—41no—
75C2×D188—41no—
76C2×D188—41no—
77C2×D188—41no—
78C2×D188—41no—
79C2×D188—81no—
80C2×D188—81no—
81C2×C8×C47—22no—
82C2×C8×C47—41no—
83C2×C8×C47—41no—
84C2×C8×C47—41no—
85C2×C8×C47—41no—
86C2×C8×C47—41no—
87C4⋊C4×C47—41no—
88C4⋊C4×C47—41no—
89C4⋊C4×C47—41no—
90C4⋊C4×C47—41no—
91C4⋊C4×C47—81no—
92C42×C47C22×C411yescharacteristic
93C42×C47#4111yescharacteristic
94C42×C47#4111yescharacteristic
95C42×C47#4111yescharacteristic
96C4⋊Dic47—21no—
97C4⋊Dic47—21no—
98C4⋊Dic47—21no—
99C4⋊Dic47—21no—
100C4×Dic47—41no—
101C4×Dic47—41no—
102C2×C47⋊C8—21no—
103C2×C47⋊C8—21no—
104C2×C47⋊C8—22no—
105C2×C47⋊C8—21no—
106C2×C47⋊C8—21no—
107C2×C47⋊C8—21no—
108C2×C47⋊C8—41no—
109C2×C47⋊C8—41no—
110C2×C47⋊C8SD1612yes—
111C23×C47#12111yescharacteristic
112C22×D47—42no—
113C22×D47—81no—
114C22×D47—81no—
115C22×D47—81no—
116C22×D47—81no—
117C22×D47—81no—
118C22×D47—81no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—81no—
122C2×C4×C47—81no—
123C2×C4×C47—81no—
124C2×C4×C47#11711yescharacteristic
125C2×C4×C47C4×D411yescharacteristic
126C2×C4×C47C4×D411yescharacteristic
127C2×C4×C47#12311yescharacteristic
128C2×C4×C47#12411yescharacteristic
129C2×C4×C47#12611yescharacteristic
130C2×C4×C47C2×SD1611yescharacteristic
131C2×C4×C47#13511yescharacteristic
132C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C47#13711yescharacteristic
138C2×Dic47—41no—
139C2×Dic47—41no—
140C2×Dic47—41no—
141C2×Dic47—41no—
142C2×Dic47—41no—
143C2×Dic47—41no—
144D188—42no—
145D188—42no—
146D188—42no—
147D188—42no—
148D188—82no—
149D188—82no—
150D188—81no—
151D188—81no—
152D188—81no—
153D188—81no—
154C8×C47—42no—
155C8×C47—81no—
156C47⋊C8—22no—
157C47⋊C8—42no—
158C47⋊C8—41no—
159#9572—471nomaximal, Sylow
160C22×C47#38811yescharacteristic
161C22×C47#46011yescharacteristic
162C22×C47#46311yescharacteristic
163C22×C47#46811yescharacteristic
164C22×C47#46911yescharacteristic
165C22×C47#47111yescharacteristic
166C22×C47#47211yescharacteristic
167C2×D47—82no—
168C2×D47—82no—
169C2×D47—82no—
170C2×D47—161no—
171C2×D47—161no—
172C2×D47—161no—
173C2×D47—161no—
174C4×C47—21no—
175C4×C47—21no—
176C4×C47—161no—
177C4×C47C4×SD1611yescharacteristic
178C4×C47#44011yescharacteristic
179C4×C47#44211yescharacteristic
180C4×C47#44211yescharacteristic
181C4×C47#48111yescharacteristic
182C4×C47#48211yescharacteristic
183C4×C47#48911yescharacteristic
184C4×C47#49011yescharacteristic
185Dic47—81no—
186Dic47—81no—
187#1982—471no—
188#1957—471no—
189#1948—471no—
190#1770—471no—
191C2×#331—471no—
192#1296D4711yescharacteristic, complemented
193#1277—471no—
194C2×C47#168611yescharacteristic
195C2×C47#168811yescharacteristic
196C2×C47#169711yescharacteristic
197C2×C47#170111yescharacteristic
198C2×C47#192611yescharacteristic
199C2×C47#193111yescharacteristic
200C2×C47#193611yescharacteristic
201D47—162no—
202C2×#127—471no—
203C2×#106—941no—
204C2×C4⋊C8—471no—
205C2×C4⋊C8C2×D4711yescharacteristic
206C2×C4⋊C8C2×D4711yescharacteristic
207C2×#102—941no—
208C2×#102—941no—
209C2×#102—941no—
210C2×#102—941no—
211C2×#97—941no—
212C2×C4×C8—471no—
213#384C2×D4711yescharacteristic
214C4×C4⋊C4—471no—
215#340—941no—
216#336—941no—
217#331—474no—
218C47#957211yescharacteristic, complemented, Sylow
219C22×D4—941no—
220C22×D4—941no—
221C22×D4—941no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—471no—
225C22×C8—471no—
226C22×C8—941no—
227#127—472no—
228#127—941no—
229#127—941no—
230#127—941no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—471no—
235C2×C4⋊C4—471no—
236C2×C42—941no—
237C2×C42C22×D4711yescharacteristic
238#106—1882no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—472no—
243C4⋊C8—941no—
244C4⋊C8C4×D4712yes—
245#102—1882no—
246#102—1882no—
247#102—1882no—
248#102—1882no—
249#97—1882no—
250C4×C8—941no—
251C4×C8—941no—
252#95—941no—
253C24—1881no—
254C2×D4—942no—
255C2×D4—942no—
256C2×D4—942no—
257C2×D4—3761no—
258C2×D4—3761no—
259C2×D4—1881no—
260C2×D4—1881no—
261C2×D4—1881no—
262C2×D4—1881no—
263C2×D4—1881no—
264C2×D4—1881no—
265C2×D4—1881no—
266C2×D4—1881no—
267C2×D4—1881no—
268C2×D4—1881no—
269C2×D4—1881no—
270C22×C4—41no—
271C22×C4—941no—
272C22×C4—941no—
273C22×C4#1062535011yescharacteristic
274C22×C4D4×D4711yescharacteristic
275C22×C4D4×D4711yescharacteristic
276C2×C8—22no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—472no—
283C2×C8—941no—
284C2×C8—941no—
285C2×C8—942no—
286C2×C8—941no—
287C2×C8—941no—
288C2×C8—941no—
289C2×C8—1881no—
290C2×C8—1881no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—81no—
296C4⋊C4—941no—
297C4⋊C4—941no—
298C4⋊C4—941no—
299C4⋊C4—941no—
300C42—1881no—
301C42—1881no—
302C42C2×C4×D4711yescharacteristic
303C42#1062535011yescharacteristic
304C42#1062535211yescharacteristic
305C42#1062535411yescharacteristic
306C23—3761no—
307C23—3761no—
308C23—3761no—
309C23—3761no—
310C23—3761no—
311C23—3761no—
312C23—1882no—
313C23#1309399711yescharacteristic
314D4—3762no—
315D4—3762no—
316D4—3761no—
317D4—3761no—
318D4—3761no—
319D4—3761no—
320D4—1882no—
321D4—1882no—
322D4—1882no—
323D4—1882no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—1881no—
330C2×C4—1881no—
331C2×C4—1881no—
332C2×C4—1881no—
333C2×C4—1881no—
334C2×C4—1881no—
335C2×C4#1309398111yescharacteristic
336C2×C4(C22⋊D47)⋊C411yescharacteristic
337C2×C4#1309398611yescharacteristic
338C2×C4#1309400911yescharacteristic
339C2×C4#1309401011yescharacteristic
340C2×C4#1309401911yescharacteristic
341C2×C4SD16×D4711yescharacteristic
342C2×C4#1309404711yescharacteristic
343C2×C4#1309404811yescharacteristic
344C2×C4#1309404811yescharacteristic
345C2×C4#1309405111yescharacteristic
346C2×C4#1309405111yescharacteristic
347C2×C4#1309405111yescharacteristic
348C2×C4#1309405611yescharacteristic
349C8—42no—
350C8—81no—
351C8—942no—
352C8—1882no—
353C8—1881no—
354C22—3762no—
355C22—3762no—
356C22—3762no—
357C22—7521no—
358C22—7521no—
359C22—7521no—
360C22—7521no—
361C22#1568901211yescharacteristic
362C22#1568932211yescharacteristic
363C22#1568934111yescharacteristic
364C22#1568937211yescharacteristic
365C22#1568937511yescharacteristic
366C22#1568938911yescharacteristic
367C22#1568939211yescharacteristic
368C4—21no—
369C4—21no—
370C4—161no—
371C4—3761no—
372C4—3761no—
373C4#1568920811yescharacteristic
374C4#1568922211yescharacteristic
375C4#1568923211yescharacteristic
376C4#1568923411yescharacteristic
377C4#1568944311yescharacteristic
378C4#1568945011yescharacteristic
379C4#1568948411yescharacteristic
380C4#1568948611yescharacteristic
381C2—7522no—
382C2#2024286311yescharacteristic
383C2#2024287111yescharacteristic
384C2#2024292411yescharacteristic
385C2#2024295211yescharacteristic
386C2#2024401311yescharacteristic
387C2#2024404811yescharacteristic
388C2#2024408311yescharacteristic
subgroupG/H
centerC23#13093997
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1296C2
socleC23×C47#121
prime radicalC2×#13094021C22
cosocleC2×C42×C47C23
hypercenter#1296D47
hypocenterC47#9572
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
3. #20244149C2semidirect
4. #20243258C2semidirect
6. #20241222C2semidirect
7. C47×#1296C2semidirect
20. #15688866C4semidirect
192. #1296D47semidirect
218. C47#9572semidirect

Maximal subgroups

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

subgroupindex
#202443142
#202441932
#202441492
#202432582
C2×#156888662
#202412222
C47×#12962
#957247