Finite Group Databasebeta

← #26136143

Subgroups — #26136143

Order 12032.

342 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15688948C211yesmaximal, characteristic, complemented
2C2×(C2×D47)⋊C16C211yesmaximal, characteristic
3#20243414C211yesmaximal, characteristic
4#20243414C211yesmaximal, characteristic
5#20241480C211yesmaximal, characteristic, complemented
6#20241479C211yesmaximal, characteristic, complemented
7C47×#1380C211yesmaximal, characteristic, complemented
8C22×C8×D47C2211yescharacteristic
9C22×C47⋊C16C2211yescharacteristic
10C2×#13093958C2211yescharacteristic
11C2×#13093958C2211yescharacteristic
12#15688980—21no—
13#15688980—21no—
14#15688948—22no—
15(C2×D47)⋊C16—22no—
16#15688885—21no—
17#15688885—21no—
18C22×C16×C47C2211yescharacteristic
19C2×#107×C47C2211yescharacteristic
20C2×#107×C47C2211yescharacteristic
21C22×C4×D47D411yescharacteristic
22C22×C47⋊C8D411yescharacteristic
23C2×C8×D47—21no—
24C2×C8×D47—21no—
25C2×C8×D47—21no—
26C2×C8×D47—21no—
27C2×C8×D47—21no—
28C2×C8×D47—21no—
29C2×C4⋊Dic47—21no—
30C2×C4⋊Dic47—21no—
31C2×(C2×D47)⋊C4—41no—
32C2×(C2×D47)⋊C4—41no—
33C2×C47⋊C16—21no—
34C2×C47⋊C16—21no—
35C2×C47⋊C16D412yes—
36#13093958—21no—
37#13093958—21no—
38#13093958—21no—
39#13093958—21no—
40C47⋊#95—41no—
41C47⋊#95—41no—
42C22×C8×C47C2311yescharacteristic
43C2×C4⋊C4×C47—21no—
44C2×C4⋊C4×C47—21no—
45C2×C16×C47—21no—
46C2×C16×C47—21no—
47C2×C16×C47—21no—
48#107×C47—21no—
49#107×C47—21no—
50#107×C47—21no—
51#107×C47—21no—
52C23×D47D811yescharacteristic
53C22×C4×C47—41no—
54C22×C4×C47—41no—
55C22×C4×C47C2×D411yescharacteristic
56C22×Dic47—41no—
57C22×Dic47—41no—
58C22×Dic47D811yescharacteristic
59C2×C4×D47—21no—
60C2×C4×D47—21no—
61C2×C4×D47—21no—
62C2×C4×D47—21no—
63C2×C4×D47—21no—
64C2×C4×D47—21no—
65C2×C8×C47C2×D411yescharacteristic
66C2×C8×C47#4111yescharacteristic
67C2×C8×C47#4111yescharacteristic
68C2×C8×C47#4111yescharacteristic
69C2×C8×C47#4111yescharacteristic
70C2×C8×C47#4111yescharacteristic
71C4⋊C4×C47—41no—
72C4⋊C4×C47—41no—
73C4⋊C4×C47—41no—
74C4⋊C4×C47—41no—
75(C2×D47)⋊C4—82no—
76(C2×D47)⋊C4—82no—
77C4⋊Dic47—41no—
78C4⋊Dic47—41no—
79C4⋊Dic47—41no—
80C4⋊Dic47—41no—
81C2×C47⋊C8—21no—
82C2×C47⋊C8—21no—
83C2×C47⋊C8—21no—
84C8×D47—41no—
85C8×D47—41no—
86C8×D47—41no—
87C8×D47—41no—
88C16×C47—41no—
89C47⋊C16—22no—
90C23×C47C2×D811yescharacteristic
91C22×D47—21no—
92C22×D47—21no—
93C22×D47—21no—
94C22×D47—21no—
95C22×D47—21no—
96C22×D47—21no—
97C22×D47Q3212yes—
98C2×C4×C47—81no—
99C2×C4×C47—81no—
100C2×C4×C47—81no—
101C2×C4×C47—81no—
102C2×C4×C47—81no—
103C2×C4×C47—81no—
104C2×C4×C47#12111yescharacteristic
105C2×C4×C47#12311yescharacteristic
106C2×C4×C47#12311yescharacteristic
107C2×C4×C47#13511yescharacteristic
108C2×C4×C47#13711yescharacteristic
109C2×C4×C47#13711yescharacteristic
110C2×Dic47—21no—
111C2×Dic47—21no—
112C2×Dic47—21no—
113C2×Dic47—81no—
114C2×Dic47—81no—
115C2×Dic47—81no—
116C2×Dic47—81no—
117C2×Dic47—81no—
118C2×Dic47—81no—
119C4×D47—41no—
120C4×D47—41no—
121C4×D47—41no—
122C4×D47—41no—
123C8×C47#12311yescharacteristic
124C8×C47#12411yescharacteristic
125C8×C47#12611yescharacteristic
126C8×C47#12611yescharacteristic
127C47⋊C8—41no—
128#13493—471nomaximal, Sylow
129C22×C47#46611yescharacteristic
130C22×C47#48011yescharacteristic
131C22×C47#48011yescharacteristic
132C22×C47C2×Q3211yescharacteristic
133C22×C47#50811yescharacteristic
134C22×C47#50911yescharacteristic
135C22×C47#50911yescharacteristic
136C2×D47—22no—
137C2×D47—22no—
138C2×D47—22no—
139C2×D47—41no—
140C2×D47—41no—
141C2×D47—41no—
142C2×D47—41no—
143C4×C47—161no—
144C4×C47—161no—
145C4×C47#39711yescharacteristic
146C4×C47#47011yescharacteristic
147C4×C47#48511yescharacteristic
148C4×C47#48511yescharacteristic
149Dic47—41no—
150Dic47—161no—
151Dic47—161no—
152C2×#366—471no—
153C2×C22⋊C16—471no—
154#1808—471no—
155#1808—471no—
156#1380—471no—
157#1380—471no—
158#1380D4711yescharacteristic, complemented
159C2×C47#207511yescharacteristic
160C2×C47#221611yescharacteristic
161C2×C47#221811yescharacteristic
162C2×C47#223411yescharacteristic
163C2×C47#223411yescharacteristic
164C2×C47#223611yescharacteristic
165C2×C47#223611yescharacteristic
166D47—42no—
167C23×C8—471no—
168C22×C16—471no—
169C22×C16C2×D4711yescharacteristic
170C2×#107—471no—
171C2×#107—471no—
172C2×#107C2×D4711yescharacteristic
173C2×#107C2×D4711yescharacteristic
174#380—941no—
175#380—941no—
176#366—942no—
177C22⋊C16—942no—
178#340—941no—
179#340—941no—
180C47#1349311yescharacteristic, complemented, Sylow
181C23×C4—471no—
182C22×C8—471no—
183C22×C8—941no—
184C22×C8—941no—
185C22×C8—941no—
186C22×C8—941no—
187C22×C8—941no—
188C22×C8—941no—
189C22×C8C22×D4711yescharacteristic
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—941no—
193C2×C4⋊C4—941no—
194C2×C22⋊C4—1881no—
195C2×C22⋊C4—1881no—
196C2×C16—21no—
197C2×C16—21no—
198C2×C16—21no—
199C2×C16—472no—
200C2×C16—941no—
201C2×C16—941no—
202#107—21no—
203#107—21no—
204#107—21no—
205#107—21no—
206#107—941no—
207#107—941no—
208#107—941no—
209#107—941no—
210#95—1881no—
211#95—1881no—
212C24—471no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—471no—
216C22×C4—941no—
217C22×C4—941no—
218C22×C4—941no—
219C22×C4—941no—
220C22×C4—941no—
221C22×C4—941no—
222C22×C4—1881no—
223C22×C4—1881no—
224C22×C4D4×D4711yescharacteristic
225C2×C8—941no—
226C2×C8—941no—
227C2×C8—941no—
228C2×C8—1881no—
229C2×C8—1881no—
230C2×C8—1881no—
231C2×C8—1881no—
232C2×C8#1062535011yescharacteristic
233C2×C8#1062535011yescharacteristic
234C2×C8#1062535011yescharacteristic
235C2×C8D4×D4711yescharacteristic
236C2×C8#1062535211yescharacteristic
237C2×C8#1062535411yescharacteristic
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—1881no—
243C4⋊C4—1881no—
244C4⋊C4—1881no—
245C4⋊C4—1881no—
246C22⋊C4—3762no—
247C22⋊C4—3762no—
248C16—41no—
249C16—942no—
250C23—472no—
251C23—941no—
252C23—941no—
253C23—941no—
254C23—941no—
255C23—941no—
256C23—941no—
257C23D8×D4711yescharacteristic
258C2×C4—81no—
259C2×C4—81no—
260C2×C4—81no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4—81no—
264C2×C4—941no—
265C2×C4—941no—
266C2×C4—941no—
267C2×C4—3761no—
268C2×C4—3761no—
269C2×C4—3761no—
270C2×C4—3761no—
271C2×C4—3761no—
272C2×C4—3761no—
273C2×C4—1881no—
274C2×C4—1881no—
275C2×C4—1881no—
276C2×C4—1881no—
277C2×C4#1309399711yescharacteristic
278C2×C4#1309400611yescharacteristic
279C2×C4#1309400911yescharacteristic
280C2×C4#1309404511yescharacteristic
281C2×C4#1309405311yescharacteristic
282C2×C4#1309405611yescharacteristic
283C8—1881no—
284C8#1309400911yescharacteristic
285C8#1309401011yescharacteristic
286C8#1309401811yescharacteristic
287C8#1309401911yescharacteristic
288C22—942no—
289C22—942no—
290C22—942no—
291C22—1881no—
292C22—1881no—
293C22—1881no—
294C22—1881no—
295C22#1568935811yescharacteristic
296C22#1568943511yescharacteristic
297C22#1568943811yescharacteristic
298C22Q32×D4711yescharacteristic
299C22#1568955411yescharacteristic
300C22#1568955711yescharacteristic
301C22#1568956011yescharacteristic
302C4—161no—
303C4—161no—
304C4—1881no—
305C4—7521no—
306C4—7521no—
307C4#1568905211yescharacteristic
308C4#1568938011yescharacteristic
309C4#1568946211yescharacteristic
310C4#1568946711yescharacteristic
311C2—1882no—
312C2#2024481511yescharacteristic
313C2#2024547811yescharacteristic
314C2#2024549011yescharacteristic
315C2#2024557811yescharacteristic
316C2#2024558111yescharacteristic
317C2#2024558911yescharacteristic
318C2#2024559211yescharacteristic
subgroupG/H
centerC23D8×D47
commutator, cosocleC22×C8×C47C23
FrattiniC22×C8C22×D47
FittingC47×#1380C2
socleC23×C47C2×D8
prime radicalC23×D47D8
hypercenter#1380D47
hypocenterC47#13493
LCSG ▷ C22×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
1. C2×#15688948C2semidirect
5. #20241480C2semidirect
6. #20241479C2semidirect
7. C47×#1380C2semidirect
158. #1380D47semidirect
180. C47#13493semidirect

Maximal subgroups

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

subgroupindex
C2×#156889482
C2×(C2×D47)⋊C162
#202434142
#202414802
#202414792
C47×#13802
#1349347