Finite Group Databasebeta

← #20242327

Subgroups — #20242327

Order 6016.

266 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 53 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#15689754C211yesmaximal, characteristic, complemented
2#15689274C212yesmaximal
3#15688859C212yesmaximal, complemented
4#15688849C211yesmaximal, characteristic, complemented
5C47×#394C211yesmaximal, characteristic
6C2×#10625335—22no—
7#13094023—22no—
8#13094015—22no—
9#13094003—21no—
10#13094003C2212yes—
11#13093983—21no—
12#13093945—22no—
13C22⋊(C47⋊C8)C2212yes—
14C22×D4×C47C2211yescharacteristic
15C2×C4⋊C4×C47C2211yescharacteristic
16C2×C22⋊C4×C47—21no—
17C2×C22⋊C4×C47—21no—
18#95×C47C2211yescharacteristic
19C24×C47—21no—
20C2×D4×C47—22no—
21C2×D4×C47—42no—
22C22×C4×C47—21no—
23C22×C4×C47D411yescharacteristic
24C22×C4×C47D411yescharacteristic
25C22×C4×C47C2311yescharacteristic
26C2×Dic94—21no—
27C2×Dic94D412yes—
28C4⋊C4×C47—22no—
29C22⋊C4×C47—42no—
30C22⋊C4×C47—42no—
31C22⋊Dic47—22no—
32#10625335—44no—
33C4⋊Dic47—21no—
34C4⋊Dic47—21no—
35C4⋊Dic47—21no—
36C4⋊Dic47D412yes—
37Dic47⋊C4—22no—
38Dic47⋊C4—22no—
39C4×Dic47—22no—
40C2×C47⋊C8—22no—
41C23×C47—22no—
42C23×C47—41no—
43C23×C47—41no—
44C23×C47—41no—
45C23×C47—41no—
46C23×C47—41no—
47C23×C47—41no—
48C23×C47C2×D411yescharacteristic
49D4×C47—24no—
50D4×C47—42no—
51C2×C4×C47—21no—
52C2×C4×C47—21no—
53C2×C4×C47—21no—
54C2×C4×C47—41no—
55C2×C4×C47—41no—
56C2×C4×C47—41no—
57C2×C4×C47—41no—
58C2×C4×C47—41no—
59C2×C4×C47SD1612yescomplemented
60C2×C4×C47C2×D412yes—
61C2×Dic47—22no—
62C2×Dic47—22no—
63Dic94—42no—
64Dic94—81no—
65C47⋊C8—42no—
66C22×C47—21no—
67C22×C47—21no—
68C22×C47—42no—
69C22×C47—42no—
70C22×C47—42no—
71C22×C47—81no—
72C22×C47—81no—
73C22×C47—81no—
74C22×C47—81no—
75C22×C47#12011yescharacteristic
76C22×C47C2×SD1611yescharacteristic
77C22×C47#13711yescharacteristic
78C4×C47—22no—
79C4×C47—22no—
80C4×C47—41no—
81C4×C47—81no—
82Dic47—42no—
83Dic47—42no—
84#1599—471nomaximal, Sylow
85C2×C47—21no—
86C2×C47—21no—
87C2×C47—82no—
88C2×C47#44811yescharacteristic
89C2×C47#45411yescharacteristic
90C2×C47B(4,𝔽2)11yescharacteristic
91#544—471no—
92#450—472no—
93#394D4711yescharacteristic
94#328—472no—
95#324—471no—
96C47#159911yescharacteristic, complemented, Sylow
97C22×D4C2×D4711yescharacteristic
98C2×SD16—942no—
99C4⋊Q8—942no—
100#125—942no—
101C22⋊Q8—472no—
102C22⋊Q8—941no—
103#117—941no—
104C2×C4⋊C4C2×D4711yescharacteristic
105C2×C22⋊C4—21no—
106C2×C22⋊C4—21no—
107#102—942no—
108C22⋊C8—472no—
109#95C2×D4711yescharacteristic
110C24—21no—
111C2×Q8—472no—
112C2×Q8—941no—
113C2×D4—22no—
114C2×D4—42no—
115C22×C4—21no—
116C22×C4C22⋊D4711yescharacteristic
117C22×C4C22⋊D4711yescharacteristic
118C22×C4C22×D4711yescharacteristic
119SD16—1884no—
120C2×C8—942no—
121C4⋊C4—22no—
122C4⋊C4—472no—
123C4⋊C4—942no—
124C4⋊C4—941no—
125C4⋊C4—941no—
126C4⋊C4—941no—
127C4⋊C4—942no—
128C22⋊C4—42no—
129C22⋊C4—42no—
130C22⋊C4—942no—
131C42—942no—
132C23—22no—
133C23—41no—
134C23—41no—
135C23—41no—
136C23—41no—
137C23—41no—
138C23—41no—
139C23C2×C22⋊D4711yescharacteristic
140Q8—3761no—
141Q8—1882no—
142D4—24no—
143D4—42no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—942no—
153C2×C4—942no—
154C2×C4#1062533512yescomplemented
155C2×C4D4×D4712yes—
156C8—1882no—
157C22—21no—
158C22—21no—
159C22—42no—
160C22—42no—
161C22—42no—
162C22—81no—
163C22—81no—
164C22—81no—
165C22—81no—
166C22#1309399211yescharacteristic
167C22C2×#1062533511yescharacteristic
168C22#1309405411yescharacteristic
169C4—22no—
170C4—22no—
171C4—41no—
172C4—81no—
173C4—1882no—
174C4—1882no—
175C2—21no—
176C2—21no—
177C2—82no—
178C2#1568926111yescharacteristic
179C2#1568929511yescharacteristic
180C2#1568930911yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#394C2
socleC22×C47#120
hypercenter#394D47
hypocenterC47#1599
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #15689754C2semidirect
3. #15688859C2semidirect
4. #15688849C2semidirect
59. C2×C4×C47SD16semidirect
96. C47#1599semidirect
154. C2×C4#10625335semidirect