Finite Group Databasebeta

← #20242430

Subgroups — #20242430

Order 6016.

202 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 57 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#15689456C212yesmaximal
2#15689062C211yesmaximal, characteristic
3#15688860C212yesmaximal
4#15688849C211yesmaximal, characteristic
5C47×#544C211yesmaximal, characteristic
6C2×C4⋊Dic47C2211yescharacteristic
7#13093957—22no—
8#13093948—22no—
9C22⋊(C47⋊C8)C2212yes—
10C47⋊#95—21no—
11C47⋊#95—21no—
12C47⋊#95C2211yescharacteristic
13C4⋊Q8×C47—22no—
14#125×C47—22no—
15C22⋊Q8×C47—21no—
16C22⋊Q8×C47C2212yes—
17#117×C47—21no—
18C2×C4⋊C4×C47C2211yescharacteristic
19C2×Q8×C47—21no—
20C2×Q8×C47D412yes—
21C22×C4×C47D411yescharacteristic
22C22×C4×C47D411yescharacteristic
23C22×C4×C47C2311yescharacteristic
24C22×Dic47—21no—
25C22×Dic47—21no—
26C4⋊C4×C47—21no—
27C4⋊C4×C47—21no—
28C4⋊C4×C47—21no—
29C4⋊C4×C47—22no—
30C4⋊C4×C47—22no—
31C4⋊C4×C47—22no—
32C4⋊C4×C47D412yes—
33C22⋊C4×C47—22no—
34C42×C47—22no—
35C4⋊Dic47—22no—
36C2×C47⋊C8—22no—
37C23×C47C2×D411yescharacteristic
38Q8×C47—42no—
39Q8×C47—81no—
40C2×C4×C47—21no—
41C2×C4×C47—21no—
42C2×C4×C47—22no—
43C2×C4×C47—22no—
44C2×C4×C47—21no—
45C2×C4×C47—41no—
46C2×C4×C47—41no—
47C2×C4×C47Q1612yes—
48C2×C4×C47C2×D412yes—
49C2×Dic47—41no—
50C2×Dic47—41no—
51C2×Dic47—42no—
52C2×Dic47—41no—
53C2×Dic47—41no—
54C47⋊C8—42no—
55C22×C47—21no—
56C22×C47—21no—
57C22×C47#12011yescharacteristic
58C22×C47C2×Q1611yescharacteristic
59C22×C47#13711yescharacteristic
60C4×C47—22no—
61C4×C47—22no—
62C4×C47—42no—
63C4×C47—41no—
64C4×C47—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#544D4711yescharacteristic
74#484—472no—
75#400—471no—
76#328—472no—
77#324—471no—
78C47#161711yescharacteristic, complemented, Sylow
79C4⋊Q8—22no—
80#125—22no—
81C22⋊Q8—21no—
82C22⋊Q8C2×D4712yes—
83#117—21no—
84C2×C4⋊C4—471no—
85C2×C4⋊C4C2×D4711yescharacteristic
86#107—942no—
87#103—942no—
88C22⋊C8—472no—
89#95—471no—
90#95—941no—
91#95—941no—
92C2×Q8—21no—
93C2×Q8C22⋊D4712yes—
94C22×C4—941no—
95C22×C4—941no—
96C22×C4C22⋊D4711yescharacteristic
97C22×C4C22⋊D4711yescharacteristic
98C22×C4C22×D4711yescharacteristic
99C2×C8—942no—
100C4⋊C4—21no—
101C4⋊C4—21no—
102C4⋊C4—21no—
103C4⋊C4—22no—
104C4⋊C4—22no—
105C4⋊C4—22no—
106C4⋊C4—942no—
107C4⋊C4C22⋊D4712yes—
108C22⋊C4—22no—
109C42—22no—
110C23C2×C22⋊D4711yescharacteristic
111Q8—42no—
112Q8—81no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—21no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—1881no—
121C2×C4—1881no—
122C2×C4—1882no—
123C2×C4—1881no—
124C2×C4—1881no—
125C2×C4#1062533712yes—
126C2×C4C2×C22⋊D4712yes—
127C8—1882no—
128C22—21no—
129C22—21no—
130C22#1309399311yescharacteristic
131C22C2×#1062533711yescharacteristic
132C22#1309405511yescharacteristic
133C4—22no—
134C4—22no—
135C4—42no—
136C4—41no—
137C4—42no—
138C4—3761no—
139C4—3761no—
140C2—21no—
141C2—21no—
142C2#1568927911yescharacteristic
143C2#1568929611yescharacteristic
144C2#1568931311yescharacteristic
subgroupG/H
centerC22#13093993
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#544C2
socleC22×C47#120
hypercenter#544D47
hypocenterC47#1617
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
78. C47#1617semidirect