Finite Group Databasebeta

← #20242432

Subgroups — #20242432

Order 6016.

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

normal subgroups only

This group has 202 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#15689459C212yesmaximal
3#15689062C211yesmaximal, characteristic
4#15688861C212yesmaximal
5C47×#324C211yesmaximal, characteristic
6#13094023—22no—
7#13094015—22no—
8#13094003—21no—
9#13094003C2212yes—
10#13093983—21no—
11C2×C4⋊Dic47C2211yescharacteristic
12#13093958—22no—
13#13093949—22no—
14C47⋊#95—21no—
15C47⋊#95—21no—
16C47⋊#95C2211yescharacteristic
17C2×C4⋊C4×C47C2211yescharacteristic
18C22⋊C8×C47C2212yes—
19C22×C4×C47D411yescharacteristic
20C22×C4×C47D411yescharacteristic
21C22×C4×C47C2311yescharacteristic
22C22×Dic47—21no—
23C22×Dic47—21no—
24C2×Dic94—21no—
25C2×Dic94D412yes—
26C2×C8×C47—22no—
27C4⋊C4×C47—22no—
28C22⋊Dic47—22no—
29C4⋊Dic47—21no—
30C4⋊Dic47—21no—
31C4⋊Dic47—21no—
32C4⋊Dic47—22no—
33C4⋊Dic47D412yes—
34Dic47⋊C4—22no—
35Dic47⋊C4—22no—
36C4×Dic47—22no—
37C23×C47C2×D411yescharacteristic
38C2×C4×C47—21no—
39C2×C4×C47—21no—
40C2×C4×C47—21no—
41C2×C4×C47—41no—
42C2×C4×C47—41no—
43C2×C4×C47Q1612yes—
44C2×C4×C47C2×D412yes—
45C2×Dic47—22no—
46C2×Dic47—22no—
47C2×Dic47—41no—
48C2×Dic47—41no—
49C2×Dic47—42no—
50C2×Dic47—41no—
51C2×Dic47—41no—
52Dic94—42no—
53Dic94—81no—
54C8×C47—42no—
55C22×C47—21no—
56C22×C47—21no—
57C22×C47#12011yescharacteristic
58C22×C47C2×Q1611yescharacteristic
59C22×C47#13711yescharacteristic
60C4×C47—22no—
61C4×C47—22no—
62C4×C47—41no—
63Dic47—42no—
64Dic47—42no—
65Dic47—81no—
66Dic47—81no—
67#1617—471nomaximal, Sylow
68C2×C47—21no—
69C2×C47—21no—
70C2×C47#45111yescharacteristic
71C2×C47#45411yescharacteristic
72C2×C47#45811yescharacteristic
73#544—471no—
74#484—472no—
75#400—471no—
76#328—472no—
77#324D4711yescharacteristic
78C47#161711yescharacteristic, complemented, Sylow
79C4⋊Q8—942no—
80#125—942no—
81C22⋊Q8—472no—
82C22⋊Q8—941no—
83#117—941no—
84C2×C4⋊C4—471no—
85C2×C4⋊C4C2×D4711yescharacteristic
86#107—942no—
87#103—942no—
88C22⋊C8C2×D4712yes—
89#95—471no—
90#95—941no—
91#95—941no—
92C2×Q8—472no—
93C2×Q8—941no—
94C22×C4—941no—
95C22×C4—941no—
96C22×C4D18811yescharacteristic
97C22×C4D18811yescharacteristic
98C22×C4C22×D4711yescharacteristic
99C2×C8—22no—
100C4⋊C4—22no—
101C4⋊C4—472no—
102C4⋊C4—942no—
103C4⋊C4—941no—
104C4⋊C4—941no—
105C4⋊C4—941no—
106C4⋊C4—942no—
107C4⋊C4—942no—
108C22⋊C4—942no—
109C42—942no—
110C23C2×D18811yescharacteristic
111Q8—3761no—
112Q8—1882no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—942no—
119C2×C4—942no—
120C2×C4—1881no—
121C2×C4—1881no—
122C2×C4—1882no—
123C2×C4—1881no—
124C2×C4—1881no—
125C2×C4Dic18812yes—
126C2×C4D4×D4712yes—
127C8—42no—
128C22—21no—
129C22—21no—
130C22#1309399411yescharacteristic
131C22C2×Dic18811yescharacteristic
132C22#1309405711yescharacteristic
133C4—22no—
134C4—22no—
135C4—41no—
136C4—3761no—
137C4—3761no—
138C4—1882no—
139C4—1882no—
140C2—21no—
141C2—21no—
142C2#1568928111yescharacteristic
143C2#1568929811yescharacteristic
144C2#1568931411yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#324C2
socleC22×C47#120
hypercenter#324D47
hypocenterC47#1617
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
78. C47#1617semidirect