Finite Group Databasebeta

← #20241514

Subgroups — #20241514

Order 6016.

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

normal subgroups only

This group has 172 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
1C2×#13093943C211yesmaximal, characteristic
2#15689030C211yesmaximal, characteristic
3C2×#101×C47C211yesmaximal, characteristic
4C2×#10625329—21no—
5C2×C4⋊Dic47C411yescharacteristic
6C2×C4×Dic47C411yescharacteristic
7#13093943—21no—
8#13093943C412yescomplemented
9C47⋊#95—21no—
10C47⋊#95—21no—
11C22×Q8×C47C2211yescharacteristic
12C2×M16×C47—21no—
13#101×C47—21no—
14#101×C47C412yescomplemented
15C2×Q8×C47—41no—
16C2×Q8×C47—41no—
17C2×Q8×C47C2×C411yescharacteristic
18C2×Q8×C47C2×C411yescharacteristic
19C2×Q8×C47D411yescharacteristic
20C2×Q8×C47Q811yescharacteristic
21C22×C4×C47C2×C411yescharacteristic
22C22×C4×C47D411yescharacteristic
23C22×C4×C47D411yescharacteristic
24C22×Dic47—21no—
25C22×Dic47—21no—
26M16×C47—22no—
27M16×C47—41no—
28C2×C8×C47—41no—
29C4⋊Dic47—41no—
30C4×Dic47—41no—
31#10625329—22no—
32#10625329—41no—
33C2×C47⋊C8—41no—
34C23×C47C22⋊C411yescharacteristic
35Q8×C47—41no—
36Q8×C47—41no—
37Q8×C47—41no—
38Q8×C47—41no—
39C2×C4×C47—21no—
40C2×C4×C47—21no—
41C2×C4×C47—21no—
42C2×C4×C47—21no—
43C2×C4×C47—21no—
44C2×C4×C47—21no—
45C2×C4×C47C4211yescharacteristic
46C2×C4×C47C22⋊C411yescharacteristic
47C2×C4×C47C22⋊C411yescharacteristic
48C2×C4×C47C4⋊C411yescharacteristic
49C2×C4×C47C4⋊C411yescharacteristic
50C2×C4×C47C4⋊C411yescharacteristic
51C2×Dic47—22no—
52C2×Dic47—41no—
53C2×Dic47—41no—
54C2×Dic47—42no—
55C2×Dic47—41no—
56C8×C47—42no—
57C47⋊C8—42no—
58C22×C47—21no—
59C22×C47—21no—
60C22×C47#9511yescharacteristic
61C22×C47#9911yescharacteristic
62C22×C47#9911yescharacteristic
63C4×C47—21no—
64C4×C47—21no—
65C4×C47—21no—
66C4×C47—21no—
67C4×C47—21no—
68C4×C47—21no—
69Dic47—42no—
70Dic47—81no—
71#1394—471nomaximal, Sylow
72C2×C47—21no—
73C2×C47—21no—
74C2×C47#34211yescharacteristic
75C2×C47#35511yescharacteristic
76C2×C47#35611yescharacteristic
77C2×#101—471no—
78C2×#101D4711yescharacteristic
79#391—471no—
80C47#139411yescharacteristic, complemented, Sylow
81C22×Q8C2×D4711yescharacteristic
82C2×M16—21no—
83C2×M16—941no—
84C2×C4⋊C4—471no—
85C2×C42—471no—
86#101—21no—
87#101—472no—
88#101—941no—
89#101Dic4712yescomplemented
90#95—941no—
91#95—941no—
92C2×Q8—41no—
93C2×Q8—41no—
94C2×Q8Dic9411yescharacteristic
95C2×Q8C4×D4711yescharacteristic
96C2×Q8C2×Dic4711yescharacteristic
97C2×Q8C22⋊D4711yescharacteristic
98C22×C4—941no—
99C22×C4—941no—
100C22×C4C4×D4711yescharacteristic
101C22×C4D18811yescharacteristic
102C22×C4C22⋊D4711yescharacteristic
103M16—22no—
104M16—41no—
105M16—942no—
106M16—1881no—
107C2×C8—41no—
108C2×C8—1881no—
109C4⋊C4—1881no—
110C42—1881no—
111C23(C2×D47)⋊C411yescharacteristic
112Q8—41no—
113Q8—41no—
114Q8—41no—
115Q8—41no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—21no—
119C2×C4—21no—
120C2×C4—21no—
121C2×C4—21no—
122C2×C4—942no—
123C2×C4—1882no—
124C2×C4—1881no—
125C2×C4—1881no—
126C2×C4—1881no—
127C2×C4C4×Dic4711yescharacteristic
128C2×C4Dic47⋊C411yescharacteristic
129C2×C4Dic47⋊C411yescharacteristic
130C2×C4C4⋊Dic4711yescharacteristic
131C2×C4(C2×D47)⋊C411yescharacteristic
132C2×C4C22⋊Dic4711yescharacteristic
133C8—42no—
134C8—1882no—
135C22—21no—
136C22—21no—
137C22C47⋊#9511yescharacteristic
138C22#1309393811yescharacteristic
139C22#1309393811yescharacteristic
140C4—21no—
141C4—21no—
142C4—21no—
143C4—21no—
144C4—21no—
145C4—21no—
146C4—3761no—
147C4—1882no—
148C2—21no—
149C2—21no—
150C2#1568888911yescharacteristic
151C2#1568891911yescharacteristic
152C2#1568892111yescharacteristic
subgroupG/H
centerC22#13093938
commutatorC2×C4×C47C42
FrattiniC22×Q8C2×D47
FittingC2×#101×C47C2
socleC22×C47#99
hypercenterC2×#101D47
hypocenterC47#1394
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
8. #13093943C4semidirect
14. #101×C47C4semidirect
80. C47#1394semidirect
89. #101Dic47semidirect