Finite Group Databasebeta

← #26114110

Subgroups — #26114110

Order 12032.

518 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20247675C211yesmaximal, characteristic
2#20245991C211yesmaximal, characteristic
3#20243485C212yesmaximal
4#20241242C212yesmaximal
5C47×#1463C211yesmaximal, characteristic
6C2×#13093983C2211yescharacteristic
7#15689062C412yescomplemented
8#15689053C412yescomplemented
9#15689009—24no—
10#15689004—22no—
11#15688996—21no—
12#15688986—21no—
13#15688986—21no—
14#15688986C2211yescharacteristic
15#15688983—21no—
16C4×C22⋊Dic47C2212yes—
17#15688884—24no—
18C22×C4⋊C4×C47C2211yescharacteristic
19C47×#407C2212yes—
20C47×#324—22no—
21#13093983—22no—
22#13093983—22no—
23C2×C4⋊Dic47—22no—
24C2×C4⋊Dic47C2×C411yescharacteristic
25C2×C4⋊Dic47C2×C411yescharacteristic
26C2×Dic47⋊C4—22no—
27C2×C22⋊Dic47—22no—
28C2×C22⋊Dic47—21no—
29C2×C22⋊Dic47—21no—
30C2×C4×Dic47—21no—
31C2×C4×Dic47D414yes—
32C47⋊#95—22no—
33C47⋊#95—24no—
34C47⋊#95—22no—
35C47⋊#95—22no—
36C47⋊#95—22no—
37C47⋊#95—22no—
38C47⋊#95—21no—
39C47⋊#95C2×C412yes—
40C23×C4×C47D411yescharacteristic
41C23×C4×C47D411yescharacteristic
42C23×C4×C47C2311yescharacteristic
43C2×M16×C47—22no—
44C2×C4⋊C4×C47—22no—
45C2×C4⋊C4×C47—22no—
46C2×C4⋊C4×C47C2×C412yes—
47C2×C4⋊C4×C47D412yes—
48C22⋊C8×C47—22no—
49C22⋊C8×C47—22no—
50C24×C47C2×D411yescharacteristic
51C22×C4×C47—21no—
52C22×C4×C47—21no—
53C22×C4×C47—21no—
54C22×C4×C47—21no—
55C22×C4×C47—42no—
56C22×C4×C47—42no—
57C22×C4×C47—42no—
58C22×C4×C47C22⋊C412yes—
59C22×C4×C47C22⋊C412yes—
60C22×C4×C47C22×C411yescharacteristic
61C22×C4×C47C2×D412yes—
62C22×C4×C47C2×D411yescharacteristic
63C22×C4×C47#4112yes—
64C22×Dic47—22no—
65C22×Dic47—21no—
66C22×Dic47—21no—
67C22×Dic47—24no—
68M16×C47—44no—
69C2×C8×C47—42no—
70C4⋊C4×C47—24no—
71C4⋊C4×C47—24no—
72C22⋊Dic47—44no—
73C22⋊Dic47—42no—
74C22⋊Dic47—41no—
75C22⋊Dic47—41no—
76C4⋊Dic47—22no—
77C4⋊Dic47—22no—
78C4⋊Dic47—82no—
79Dic47⋊C4—44no—
80C4×Dic47—42no—
81C4×Dic47—44no—
82C23×C47—22no—
83C23×C47—22no—
84C23×C47—41no—
85C23×C47C2×C22⋊C411yescharacteristic
86C23×C47#12011yescharacteristic
87C23×C47#12311yescharacteristic
88C2×C4×C47—24no—
89C2×C4×C47—22no—
90C2×C4×C47—22no—
91C2×C4×C47—22no—
92C2×C4×C47—22no—
93C2×C4×C47—41no—
94C2×C4×C47—41no—
95C2×C4×C47—42no—
96C2×C4×C47—42no—
97C2×C4×C47—42no—
98C2×C4×C47—42no—
99C2×C4×C47—42no—
100C2×C4×C47—81no—
101C2×C4×C47C4×D412yes—
102C2×C4×C47#12112yes—
103C2×Dic47—42no—
104C2×Dic47—44no—
105C2×Dic47—42no—
106C2×Dic47—44no—
107C2×Dic47—42no—
108C2×Dic47—41no—
109C2×Dic47—41no—
110C2×Dic47—42no—
111C2×Dic47—42no—
112C2×Dic47—44no—
113C8×C47—82no—
114#9482—471nomaximal, Sylow
115C22×C47—21no—
116C22×C47—21no—
117C22×C47—21no—
118C22×C47—21no—
119C22×C47—21no—
120C22×C47—21no—
121C22×C47—21no—
122C22×C47—44no—
123C22×C47#38611yescharacteristic
124C22×C47#42112yes—
125C22×C47#45812yes—
126C4×C47—22no—
127C4×C47—22no—
128C4×C47—42no—
129C4×C47—42no—
130Dic47—84no—
131Dic47—82no—
132Dic47—81no—
133Dic47—81no—
134#2484—471no—
135#2313—471no—
136#1826—472no—
137#1463D4711yescharacteristic
138#1284—472no—
139C2×C47—22no—
140C2×C47—22no—
141C2×C47—41no—
142C2×C47#189011yescharacteristic
143C2×C47#189711yescharacteristic
144C2×C47#191211yescharacteristic
145C2×#117—471no—
146C22×C4⋊C4C2×D4711yescharacteristic
147#407C2×D4712yes—
148#400—472no—
149#398—472no—
150#387—944no—
151#387—942no—
152#385—941no—
153#381—471no—
154#381—941no—
155#381—941no—
156#380—941no—
157C4×C22⋊C4—472no—
158#339—944no—
159#324—22no—
160C47#948211yescharacteristic, complemented, Sylow
161C23×C4D18811yescharacteristic
162C23×C4D18811yescharacteristic
163C23×C4C22×D4711yescharacteristic
164C2×M16—22no—
165#117—942no—
166#117—942no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—471no—
170C2×C4⋊C4—471no—
171C2×C4⋊C4—942no—
172C2×C4⋊C4—942no—
173C2×C4⋊C4C4×D4712yes—
174C2×C4⋊C4C22⋊D4712yes—
175C2×C22⋊C4—941no—
176C2×C22⋊C4—942no—
177C2×C22⋊C4—941no—
178C2×C42—474no—
179C2×C42—941no—
180C22⋊C8—22no—
181C22⋊C8—22no—
182#95—472no—
183#95—942no—
184#95—944no—
185#95—942no—
186#95—942no—
187#95—942no—
188#95—942no—
189#95—941no—
190C24C2×D18811yescharacteristic
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—42no—
196C22×C4—42no—
197C22×C4—42no—
198C22×C4—942no—
199C22×C4—941no—
200C22×C4—941no—
201C22×C4—944no—
202C22×C4(C2×D47)⋊C412yes—
203C22×C4(C2×D47)⋊C412yes—
204C22×C4C2×C4×D4711yescharacteristic
205C22×C4D4×D4712yes—
206C22×C4#1062535212yes—
207C22×C4C2×C22⋊D4711yescharacteristic
208M16—44no—
209C2×C8—42no—
210C4⋊C4—24no—
211C4⋊C4—24no—
212C4⋊C4—942no—
213C4⋊C4—942no—
214C4⋊C4—3762no—
215C4⋊C4—1884no—
216C22⋊C4—1882no—
217C22⋊C4—1884no—
218C22⋊C4—1881no—
219C22⋊C4—1881no—
220C42—1884no—
221C42—1882no—
222C23—22no—
223C23—22no—
224C23—41no—
225C23C2×(C2×D47)⋊C411yescharacteristic
226C23#1309399411yescharacteristic
227C23#1309400811yescharacteristic
228C2×C4—24no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—41no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—81no—
241C2×C4—1882no—
242C2×C4—1884no—
243C2×C4—1882no—
244C2×C4—1884no—
245C2×C4—1882no—
246C2×C4—1881no—
247C2×C4—1881no—
248C2×C4—1884no—
249C2×C4—1882no—
250C2×C4—1882no—
251C2×C4(C22⋊D47)⋊C412yes—
252C2×C4#1309399612yes—
253C8—82no—
254C22—21no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—44no—
262C22#1568900011yescharacteristic
263C22#1568913912yes—
264C22#1568931412yes—
265C4—22no—
266C4—22no—
267C4—42no—
268C4—42no—
269C4—3764no—
270C4—3762no—
271C4—3761no—
272C4—3761no—
273C2—22no—
274C2—22no—
275C2—41no—
276C2#2024379911yescharacteristic
277C2#2024383411yescharacteristic
278C2#2024392311yescharacteristic
subgroupG/H
centerC22#15689000
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#1463C2
socleC22×C47#386
prime radicalC24×C47C2×D4
cosocleC23×C4×C47C23
hypercenter#1463D47
hypocenterC47#9482
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
7. #15689062C4semidirect
8. #15689053C4semidirect
160. C47#9482semidirect

Maximal subgroups

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

subgroupindex
#202476752
#202459912
#202434852
#202412422
C47×#14632
#948247