Finite Group Databasebeta

← #20242361

Subgroups — #20242361

Order 6016.

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

normal subgroups only

This group has 238 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
2#15689279C212yesmaximal
3#15688859C212yesmaximal
4#15688849C211yesmaximal, characteristic
5C47×#395C211yesmaximal, characteristic
6C2×#10625337—22no—
7#13094023—22no—
8#13094015—22no—
9#13094003—21no—
10#13094003C2212yes—
11#13093983—21no—
12#13093948—22no—
13C22⋊(C47⋊C8)C2212yes—
14C22×Q8×C47C2211yescharacteristic
15C2×C4⋊C4×C47—21no—
16C2×C4⋊C4×C47C2211yescharacteristic
17#95×C47—21no—
18#95×C47C2211yescharacteristic
19C2×Q8×C47—22no—
20C2×Q8×C47—42no—
21C22×C4×C47—21no—
22C22×C4×C47—21no—
23C22×C4×C47D411yescharacteristic
24C22×C4×C47D411yescharacteristic
25C22×C4×C47C2311yescharacteristic
26C2×Dic94—21no—
27C2×Dic94D412yes—
28C4⋊C4×C47—22no—
29C4⋊C4×C47—42no—
30C22⋊Dic47—22no—
31#10625337—44no—
32C4⋊Dic47—21no—
33C4⋊Dic47—21no—
34C4⋊Dic47—21no—
35C4⋊Dic47D412yes—
36Dic47⋊C4—22no—
37Dic47⋊C4—22no—
38C4×Dic47—22no—
39C2×C47⋊C8—22no—
40C23×C47C2×D411yescharacteristic
41Q8×C47—24no—
42Q8×C47—42no—
43C2×C4×C47—21no—
44C2×C4×C47—21no—
45C2×C4×C47—22no—
46C2×C4×C47—22no—
47C2×C4×C47—21no—
48C2×C4×C47—41no—
49C2×C4×C47—41no—
50C2×C4×C47—41no—
51C2×C4×C47—41no—
52C2×C4×C47—41no—
53C2×C4×C47—41no—
54C2×C4×C47Q1612yescomplemented
55C2×C4×C47C2×D412yes—
56C2×Dic47—22no—
57C2×Dic47—22no—
58Dic94—42no—
59Dic94—81no—
60C47⋊C8—42no—
61C22×C47—21no—
62C22×C47—21no—
63C22×C47#12011yescharacteristic
64C22×C47C2×Q1611yescharacteristic
65C22×C47#13711yescharacteristic
66C4×C47—22no—
67C4×C47—22no—
68C4×C47—42no—
69C4×C47—41no—
70C4×C47—42no—
71Dic47—42no—
72Dic47—42no—
73#1605—471nomaximal, Sylow
74C2×C47—21no—
75C2×C47—21no—
76C2×C47#45111yescharacteristic
77C2×C47#45611yescharacteristic
78C2×C47B(4,𝔽2)11yescharacteristic
79#544—471no—
80#451—472no—
81#395D4711yescharacteristic
82#328—472no—
83#324—471no—
84C47#160511yescharacteristic, complemented, Sylow
85C22×Q8C2×D4711yescharacteristic
86C2×Q16—942no—
87C4⋊Q8—942no—
88#125—942no—
89C22⋊Q8—472no—
90C22⋊Q8—941no—
91#117—941no—
92C2×C4⋊C4—21no—
93C2×C4⋊C4C2×D4711yescharacteristic
94#103—942no—
95C22⋊C8—472no—
96#95—21no—
97#95C2×D4711yescharacteristic
98C2×Q8—22no—
99C2×Q8—42no—
100C2×Q8—472no—
101C2×Q8—941no—
102C22×C4—21no—
103C22×C4—21no—
104C22×C4C22⋊D4711yescharacteristic
105C22×C4C22⋊D4711yescharacteristic
106C22×C4C22×D4711yescharacteristic
107Q16—1884no—
108C2×C8—942no—
109C4⋊C4—22no—
110C4⋊C4—42no—
111C4⋊C4—472no—
112C4⋊C4—942no—
113C4⋊C4—941no—
114C4⋊C4—941no—
115C4⋊C4—941no—
116C4⋊C4—942no—
117C22⋊C4—942no—
118C42—942no—
119C23C2×C22⋊D4711yescharacteristic
120Q8—24no—
121Q8—42no—
122Q8—3761no—
123Q8—1882no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—22no—
127C2×C4—22no—
128C2×C4—21no—
129C2×C4—41no—
130C2×C4—41no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—942no—
136C2×C4—942no—
137C2×C4#1062533712yescomplemented
138C2×C4D4×D4712yes—
139C8—1882no—
140C22—21no—
141C22—21no—
142C22#1309399211yescharacteristic
143C22C2×#1062533711yescharacteristic
144C22#1309405411yescharacteristic
145C4—22no—
146C4—22no—
147C4—42no—
148C4—42no—
149C4—41no—
150C4—1882no—
151C4—1882no—
152C2—21no—
153C2—21no—
154C2#1568927811yescharacteristic
155C2#1568930511yescharacteristic
156C2#1568930911yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#395C2
socleC22×C47#120
hypercenter#395D47
hypocenterC47#1605
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #395

Complements

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

NH ≅ G/Ntype
54. C2×C4×C47Q16semidirect
84. C47#1605semidirect
137. C2×C4#10625337semidirect