Finite Group Databasebeta

← #26113902

Subgroups — #26113902

Order 12032.

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

normal subgroups only

This group has 434 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#20253937C211yesmaximal, characteristic
2#20242015C211yesmaximal, characteristic
3#20241899C212yesmaximal
4#20241281C212yesmaximal
5C47×#2371C211yesmaximal, characteristic
6#15689680C2211yescharacteristic
7#15689533C414yescomplemented
8#15689522—22no—
9#15689180C2212yes—
10#15689163—22no—
11C4×#10625329C2211yescharacteristic
12#15688865—22no—
13#15688859—22no—
14#15688859—22no—
15C2×#125×C47C2211yescharacteristic
16C47×#387—22no—
17C47×#387—22no—
18C4×C4⋊C4×C47—22no—
19C47×#376C2212yes—
20C2×#10625329—21no—
21#13094024C2×C412yes—
22#13094016—21no—
23#13094003—22no—
24C4×Dic94—22no—
25#13093983—21no—
26#13093957—24no—
27#13093955—24no—
28C4⋊(C47⋊C8)—22no—
29C22⋊(C47⋊C8)—22no—
30#13093935—22no—
31#13093935C2×C412yes—
32C4×C47⋊C8—21no—
33#125×C47—22no—
34#125×C47C2×C412yes—
35#125×C47D412yes—
36C2×C4⋊C4×C47—22no—
37C2×C4⋊C4×C47—22no—
38C2×C4⋊C4×C47D412yes—
39C2×C42×C47—22no—
40C2×C42×C47—22no—
41C2×C42×C47C2311yescharacteristic
42#95×C47—22no—
43#95×C47—22no—
44#95×C47—22no—
45#95×C47D412yes—
46#95×C47D412yes—
47C22×C4×C47—22no—
48C22×C4×C47—22no—
49C22×C4×C47—22no—
50C22×C4×C47C2×D411yescharacteristic
51C22×C4×C47C2×D412yes—
52C2×Dic94—22no—
53C4⋊C4×C47—24no—
54C4⋊C4×C47—24no—
55C4⋊C4×C47—22no—
56C4⋊C4×C47—44no—
57C4⋊C4×C47C22⋊C414yes—
58C42×C47—44no—
59C42×C47—44no—
60C42×C47C22×C411yescharacteristic
61C42×C47C2×D411yescharacteristic
62C42×C47#4112yes—
63C22⋊Dic47—41no—
64C4⋊Dic47—22no—
65C4⋊Dic47—22no—
66Dic47⋊C4—42no—
67C4×Dic47—41no—
68#10625329—24no—
69C2×C47⋊C8—22no—
70C2×C47⋊C8—42no—
71C23×C47#12011yescharacteristic
72C2×C4×C47—22no—
73C2×C4×C47—24no—
74C2×C4×C47—24no—
75C2×C4×C47—42no—
76C2×C4×C47—42no—
77C2×C4×C47—42no—
78C2×C4×C47—42no—
79C2×C4×C47—42no—
80C2×C4×C47—42no—
81C2×C4×C47—42no—
82C2×C4×C47—42no—
83C2×C4×C47C2×C22⋊C411yescharacteristic
84C2×C4×C47C4×D412yes—
85C2×C4×C47#12112yes—
86C2×C4×C47#12311yescharacteristic
87C2×Dic47—42no—
88Dic94—82no—
89C47⋊C8—24no—
90C47⋊C8—82no—
91#9440—471nomaximal, Sylow
92C22×C47—22no—
93C22×C47#38611yescharacteristic
94C22×C47#45612yes—
95C4×C47—21no—
96C4×C47—21no—
97C4×C47—22no—
98C4×C47—22no—
99C4×C47—44no—
100C4×C47—44no—
101C4×C47—82no—
102Dic47—82no—
103#3166—471no—
104#2371D4711yescharacteristic
105#1534—471no—
106#1506—472no—
107#1300—472no—
108C2×C47—22no—
109C2×C47#188611yescharacteristic
110C2×C47#190612yes—
111#533—471no—
112C2×#125C2×D4711yescharacteristic
113#501—474no—
114#499—942no—
115#432—472no—
116#428—942no—
117C4×M16—471no—
118#387—22no—
119#387—22no—
120C4×C4⋊C4—22no—
121#376C2×D4712yes—
122#330—942no—
123#328—942no—
124#328—942no—
125C47#944011yescharacteristic, complemented, Sylow
126C2×M16—941no—
127C4⋊Q8—472no—
128#125—22no—
129#125—941no—
130#125C4×D4712yes—
131#125D18812yes—
132C22⋊Q8—942no—
133C4×Q8—942no—
134#117—941no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4C22⋊D4712yes—
138C2×C42—22no—
139C2×C42—22no—
140C2×C42C22×D4711yescharacteristic
141#107—944no—
142#106—944no—
143C4⋊C8—942no—
144C22⋊C8—942no—
145#97—472no—
146#97—942no—
147C4×C8—941no—
148#95—22no—
149#95—22no—
150#95—22no—
151#95C22⋊D4712yes—
152#95C22⋊D4712yes—
153C2×Q8—942no—
154C22×C4—22no—
155C22×C4—22no—
156C22×C4—22no—
157C22×C4C2×C22⋊D4711yescharacteristic
158C22×C4C2×C22⋊D4712yes—
159M16—944no—
160C2×C8—942no—
161C2×C8—1882no—
162C4⋊C4—24no—
163C4⋊C4—24no—
164C4⋊C4—22no—
165C4⋊C4—44no—
166C4⋊C4—942no—
167C4⋊C4—942no—
168C4⋊C4—1882no—
169C4⋊C4(C2×D47)⋊C414yes—
170C22⋊C4—1881no—
171C42—44no—
172C42—44no—
173C42—1881no—
174C42C2×C4×D4711yescharacteristic
175C42C2×D18811yescharacteristic
176C42#1062535012yes—
177C23#1309399311yescharacteristic
178Q8—3762no—
179C2×C4—22no—
180C2×C4—24no—
181C2×C4—24no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—1882no—
191C2×C4C2×(C2×D47)⋊C411yescharacteristic
192C2×C4C4×C22⋊D4712yes—
193C2×C4#1309399812yes—
194C2×C4#1309400711yescharacteristic
195C8—944no—
196C8—3762no—
197C22—22no—
198C22#1568900211yescharacteristic
199C22#1568930612yes—
200C4—21no—
201C4—21no—
202C4—22no—
203C4—22no—
204C4—44no—
205C4—44no—
206C4—82no—
207C4—3762no—
208C2—22no—
209C2#2024378111yescharacteristic
210C2#2024388912yes—
subgroupG/H
centerC22#15689002
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#2371C2
socleC22×C47#386
prime radicalC23×C47#120
cosocleC2×C42×C47C23
hypercenter#2371D47
hypocenterC47#9440
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2371

Complements

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

NH ≅ G/Ntype
7. #15689533C4semidirect
125. C47#9440semidirect

Maximal subgroups

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

subgroupindex
#202539372
#202420152
#202418992
#202412812
C47×#23712
#944047