Finite Group Databasebeta

← #26113815

Subgroups — #26113815

Order 12032.

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

normal subgroups only

This group has 534 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#20253762C211yesmaximal, characteristic
2#20242102C211yesmaximal, characteristic
3#20241938C212yesmaximal, complemented
4#20241252C212yesmaximal, complemented
5C47×#2380C211yesmaximal, characteristic
6#15689680C2211yescharacteristic
7#15689487—22no—
8#15689469C414yescomplemented
9#15689180C2212yes—
10#15689128—22no—
11C4×#10625329C2211yescharacteristic
12#15688867—22no—
13#15688859—24no—
14C2×#127×C47C2211yescharacteristic
15C47×#386—24no—
16C47×#386—22no—
17C47×#383C2212yes—
18C2×#10625329—21no—
19#13094024C2×C412yescomplemented
20#13094016—21no—
21#13094003—22no—
22C4×Dic94—22no—
23#13093983—21no—
24C4⋊(C47⋊C8)—22no—
25#13093945—28no—
26C22⋊(C47⋊C8)—22no—
27#13093935—21no—
28#13093935—22no—
29C4×C47⋊C8C2×C412yescomplemented
30C22×D4×C47—22no—
31C22×D4×C47D412yes—
32C23×C4×C47—22no—
33#127×C47—22no—
34#127×C47C2×C412yes—
35#127×C47D412yes—
36C2×C22⋊C4×C47—24no—
37C2×C22⋊C4×C47—22no—
38C2×C42×C47C2311yescharacteristic
39#95×C47—22no—
40#95×C47—22no—
41#95×C47D414yes—
42C24×C47—22no—
43C2×D4×C47—24no—
44C2×D4×C47—24no—
45C2×D4×C47—22no—
46C2×D4×C47—42no—
47C2×D4×C47—42no—
48C2×D4×C47—82no—
49C2×D4×C47—82no—
50C2×D4×C47C22⋊C414yes—
51C22×C4×C47—24no—
52C22×C4×C47—84no—
53C22×C4×C47—82no—
54C22×C4×C47C2×D411yescharacteristic
55C22×C4×C47C2×D412yes—
56C2×Dic94—22no—
57C22⋊C4×C47—84no—
58C22⋊C4×C47—82no—
59C42×C47C22×C411yescharacteristic
60C42×C47C2×D411yescharacteristic
61C42×C47#4112yes—
62C22⋊Dic47—41no—
63C4⋊Dic47—22no—
64C4⋊Dic47—22no—
65Dic47⋊C4—42no—
66C4×Dic47—41no—
67#10625329—42no—
68C2×C47⋊C8—22no—
69C2×C47⋊C8—42no—
70C23×C47—24no—
71C23×C47—44no—
72C23×C47—44no—
73C23×C47—42no—
74C23×C47—42no—
75C23×C47#12011yescharacteristic
76D4×C47—44no—
77D4×C47—82no—
78D4×C47—84no—
79D4×C47—84no—
80C2×C4×C47—22no—
81C2×C4×C47—42no—
82C2×C4×C47—48no—
83C2×C4×C47—44no—
84C2×C4×C47—88no—
85C2×C4×C47C2×C22⋊C411yescharacteristic
86C2×C4×C47C4×D412yes—
87C2×C4×C47#12112yes—
88C2×C4×C47#12311yescharacteristic
89C2×Dic47—42no—
90Dic94—82no—
91C47⋊C8—42no—
92C47⋊C8—82no—
93#9425—471nomaximal, Sylow
94C22×C47—22no—
95C22×C47—44no—
96C22×C47—48no—
97C22×C47—82no—
98C22×C47—82no—
99C22×C47—84no—
100C22×C47#38611yescharacteristic
101C22×C47#45512yes—
102C4×C47—21no—
103C4×C47—21no—
104C4×C47—22no—
105C4×C47—22no—
106C4×C47—84no—
107Dic47—82no—
108#3138—471no—
109#2380D4711yescharacteristic
110#1555—471no—
111#1515—472no—
112#1288—472no—
113C2×C47—22no—
114C2×C47—84no—
115C2×C47#188511yescharacteristic
116C2×C47#190412yes—
117#533—471no—
118C2×#127C2×D4711yescharacteristic
119#490—942no—
120#486—474no—
121#432—472no—
122#418—942no—
123C4×M16—471no—
124#386—22no—
125#386—24no—
126#383C2×D4712yes—
127#331—942no—
128#328—944no—
129C47#942511yescharacteristic, complemented, Sylow
130C22×D4—22no—
131C22×D4C22⋊D4712yes—
132C23×C4—22no—
133C2×M16—941no—
134C4⋊Q8—472no—
135#127—22no—
136#127C4×D4712yes—
137#127D18812yes—
138#125—941no—
139C22⋊Q8—942no—
140C4×Q8—942no—
141#117—941no—
142C2×C22⋊C4—24no—
143C2×C22⋊C4—22no—
144C2×C42C22×D4711yescharacteristic
145C4⋊C8—942no—
146#102—948no—
147C22⋊C8—942no—
148#97—941no—
149#97—942no—
150C4×C8—472no—
151#95—22no—
152#95—22no—
153#95C22⋊D4714yes—
154C24—22no—
155C2×Q8—942no—
156C2×D4—24no—
157C2×D4—24no—
158C2×D4—22no—
159C2×D4—42no—
160C2×D4—42no—
161C2×D4—82no—
162C2×D4—82no—
163C2×D4(C2×D47)⋊C414yes—
164C22×C4—24no—
165C22×C4—84no—
166C22×C4—82no—
167C22×C4C2×C22⋊D4711yescharacteristic
168C22×C4C2×C22⋊D4712yes—
169M16—1882no—
170C2×C8—942no—
171C2×C8—1882no—
172C4⋊C4—942no—
173C4⋊C4—942no—
174C4⋊C4—1882no—
175C22⋊C4—84no—
176C22⋊C4—82no—
177C22⋊C4—1881no—
178C42—1881no—
179C42C2×C4×D4711yescharacteristic
180C42C2×D18811yescharacteristic
181C42#1062535012yes—
182C23—24no—
183C23—44no—
184C23—44no—
185C23—42no—
186C23—42no—
187C23#1309399311yescharacteristic
188Q8—3762no—
189D4—44no—
190D4—82no—
191D4—84no—
192D4—84no—
193C2×C4—22no—
194C2×C4—42no—
195C2×C4—48no—
196C2×C4—44no—
197C2×C4—88no—
198C2×C4—1882no—
199C2×C4C2×(C2×D47)⋊C411yescharacteristic
200C2×C4C4×C22⋊D4712yes—
201C2×C4#1309399812yes—
202C2×C4#1309400711yescharacteristic
203C8—3762no—
204C8—1882no—
205C22—22no—
206C22—44no—
207C22—48no—
208C22—82no—
209C22—82no—
210C22—84no—
211C22#1568900211yescharacteristic
212C22#1568930112yes—
213C4—21no—
214C4—21no—
215C4—22no—
216C4—22no—
217C4—84no—
218C4—3762no—
219C2—22no—
220C2—84no—
221C2#2024377611yescharacteristic
222C2#2024387512yes—
subgroupG/H
centerC22#15689002
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#2380C2
socleC22×C47#386
prime radicalC2×#127×C47C22
cosocleC2×C42×C47C23
hypercenter#2380D47
hypocenterC47#9425
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2380

Complements

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

NH ≅ G/Ntype
3. #20241938C2semidirect
4. #20241252C2semidirect
8. #15689469C4semidirect
19. #13094024C2×C4semidirect
29. C4×C47⋊C8C2×C4semidirect
129. C47#9425semidirect

Maximal subgroups

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

subgroupindex
#202537622
#202421022
#202419382
#202412522
C47×#23802
#942547