Finite Group Databasebeta

← #26109758

Subgroups — #26109758

Order 12032.

418 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 91 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#20245886C211yesmaximal, characteristic
2#20243465C211yesmaximal, characteristic
3#20241242C214yesmaximal
4C47×#1822C211yesmaximal, characteristic
5#15689016—22no—
6#15689009—22no—
7#15688986C2212yes—
8C4×C4⋊Dic47C412yescomplemented
9C4×C22⋊Dic47C2212yes—
10#15688969C411yescharacteristic, complemented
11C42×Dic47C411yescharacteristic, complemented
12#15688890—22no—
13C2×#117×C47C2211yescharacteristic
14C47×#407C2212yes—
15C47×#343—22no—
16C2×C4⋊Dic47—22no—
17C2×C22⋊Dic47—22no—
18C2×C22⋊Dic47—22no—
19C2×C4×Dic47—22no—
20C2×C4×Dic47C2×C412yes—
21C2×C4×Dic47C2×C412yes—
22C47⋊#95—22no—
23C47⋊#95—22no—
24C47⋊#95—22no—
25C47⋊#95—24no—
26C23×C4×C47C2311yescharacteristic
27C2×M16×C47—22no—
28#117×C47—24no—
29C2×C4⋊C4×C47D412yes—
30C2×C22⋊C4×C47D412yes—
31C2×C42×C47C2×C411yescharacteristic
32C2×C42×C47C2×C411yescharacteristic
33C22⋊C8×C47—24no—
34C24×C47C2×D411yescharacteristic
35C22×C4×C47—42no—
36C22×C4×C47C22⋊C412yes—
37C22×C4×C47C22⋊C412yes—
38C22×C4×C47C22×C411yescharacteristic
39C22×C4×C47C2×D411yescharacteristic
40C22×C4×C47#4114yes—
41C22×Dic47—22no—
42C22×Dic47—22no—
43C22×Dic47—42no—
44M16×C47—44no—
45C2×C8×C47—42no—
46C4⋊C4×C47—24no—
47C22⋊C4×C47—24no—
48C42×C47—22no—
49C42×C47—22no—
50C22⋊Dic47—44no—
51C22⋊Dic47—44no—
52C4⋊Dic47—44no—
53C4×Dic47—44no—
54C4×Dic47—42no—
55C4×Dic47—42no—
56C23×C47—22no—
57C23×C47—42no—
58C23×C47C2×C22⋊C411yescharacteristic
59C23×C47#12312yes—
60C2×C4×C47—22no—
61C2×C4×C47—22no—
62C2×C4×C47—22no—
63C2×C4×C47—22no—
64C2×C4×C47—44no—
65C2×C4×C47—42no—
66C2×C4×C47—42no—
67C2×C4×C47#11712yes—
68C2×C4×C47#12312yes—
69C2×Dic47—24no—
70C2×Dic47—42no—
71C2×Dic47—42no—
72C2×Dic47—42no—
73C2×Dic47—42no—
74C2×Dic47—42no—
75C2×Dic47—82no—
76C2×Dic47—84no—
77C8×C47—82no—
78#8740—471nomaximal, Sylow
79C22×C47—22no—
80C22×C47—22no—
81C22×C47—24no—
82C22×C47—82no—
83C22×C47#38111yescharacteristic
84C22×C47#41012yes—
85C4×C47—22no—
86C4×C47—22no—
87C4×C47—42no—
88C4×C47—42no—
89Dic47—44no—
90Dic47—82no—
91Dic47—162no—
92#2298—471no—
93#1822D4711yescharacteristic
94#1820—471no—
95#1284—474no—
96C2×C47—22no—
97C2×C47—42no—
98C2×C47#182011yescharacteristic
99C2×C47#182712yes—
100C2×#117C2×D4711yescharacteristic
101#407C2×D4712yes—
102#388—942no—
103#387—942no—
104#381—472no—
105C4×C4⋊C4—472no—
106C4×C22⋊C4—472no—
107#376—471no—
108C43—471no—
109#343—22no—
110#342—942no—
111C47#874011yescharacteristic, complemented, Sylow
112C23×C4C22×D4711yescharacteristic
113C2×M16—22no—
114#117—24no—
115C2×C4⋊C4—942no—
116C2×C4⋊C4C22⋊D4712yes—
117C2×C22⋊C4—942no—
118C2×C22⋊C4—942no—
119C2×C22⋊C4D18812yes—
120C2×C42—472no—
121C2×C42—472no—
122C2×C42—942no—
123C2×C42C4×D4711yescharacteristic
124C2×C42C4×D4711yescharacteristic
125C22⋊C8—24no—
126#95—942no—
127#95—942no—
128#95—942no—
129#95—944no—
130C24C2×D18811yescharacteristic
131C22×C4—42no—
132C22×C4—942no—
133C22×C4—942no—
134C22×C4—1882no—
135C22×C4(C2×D47)⋊C412yes—
136C22×C4(C2×D47)⋊C412yes—
137C22×C4C2×C4×D4711yescharacteristic
138C22×C4#1062535214yes—
139C22×C4C2×C22⋊D4711yescharacteristic
140M16—44no—
141C2×C8—42no—
142C4⋊C4—24no—
143C4⋊C4—1884no—
144C22⋊C4—24no—
145C22⋊C4—1884no—
146C22⋊C4—1884no—
147C42—22no—
148C42—22no—
149C42—1882no—
150C42—1882no—
151C42—1884no—
152C23—22no—
153C23—42no—
154C23C2×(C2×D47)⋊C411yescharacteristic
155C23#1309400812yes—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—44no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—944no—
164C2×C4—3762no—
165C2×C4—3764no—
166C2×C4—1882no—
167C2×C4—1882no—
168C2×C4—1882no—
169C2×C4—1882no—
170C2×C4—1882no—
171C2×C4#1309398012yes—
172C2×C4#1309400512yes—
173C8—82no—
174C22—22no—
175C22—22no—
176C22—24no—
177C22—82no—
178C22#1568898411yescharacteristic
179C22#1568909612yes—
180C4—22no—
181C4—22no—
182C4—42no—
183C4—42no—
184C4—3762no—
185C4—1884no—
186C4—7522no—
187C2—22no—
188C2—42no—
189C2#2024346311yescharacteristic
190C2#2024349312yes—
subgroupG/H
centerC22#15688984
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#1822C2
socleC22×C47#381
prime radicalC24×C47C2×D4
cosocleC23×C4×C47C23
hypercenter#1822D47
hypocenterC47#8740
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1822

Complements

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

NH ≅ G/Ntype
8. C4×C4⋊Dic47C4semidirect
10. #15688969C4semidirect
11. C42×Dic47C4semidirect
111. C47#8740semidirect

Maximal subgroups

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

subgroupindex
#202458862
#202434652
#202412422
C47×#18222
#874047