Finite Group Databasebeta

← #20242115

Subgroups — #20242115

Order 6016.

202 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 65 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#15689678C211yesmaximal, characteristic
2#15689179C211yesmaximal, characteristic
3#15689145C211yesmaximal, characteristic
4#15688872C211yesmaximal, characteristic, complemented
5#15688870C211yesmaximal, characteristic, complemented
6#15688868C211yesmaximal, characteristic, complemented
7C47×#333C211yesmaximal, characteristic, complemented
8C2×#10625324—21no—
9#13094024C2211yescharacteristic
10#13094015—21no—
11#13094004—21no—
12#13094000C412yes—
13Q8×Dic47C412yes—
14#13093989—21no—
15#13093982—21no—
16C42×D47C2211yescharacteristic
17C4⋊(C47⋊C8)C2211yescharacteristic
18C4⋊(C47⋊C8)C2211yescharacteristic
19Dic47⋊C8—21no—
20(C2×D47)⋊C8—21no—
21#13093934—21no—
22C4⋊Q8×C47C2211yescharacteristic
23C4⋊C8×C47C2211yescharacteristic
24C4⋊C8×C47C2211yescharacteristic
25C2×Q8×C47C2×C412yes—
26C2×C4×D47C2×C411yescharacteristic
27C2×C4×D47D411yescharacteristic
28C2×C4×D47D411yescharacteristic
29C2×Dic94—21no—
30C2×C8×C47—21no—
31C2×C8×C47—21no—
32C4⋊C4×C47—21no—
33C4⋊C4×C47—21no—
34C42×C47C2311yescharacteristic
35(C2×D47)⋊C4—22no—
36C4⋊Dic47—21no—
37C4⋊Dic47—22no—
38C4⋊Dic47C2×C412yes—
39Dic47⋊C4—22no—
40C4×Dic47—22no—
41C4×Dic47C2×C411yescharacteristic
42C4×Dic47D411yescharacteristic
43C4×Dic47D411yescharacteristic
44C2×C47⋊C8—21no—
45C2×C47⋊C8—21no—
46#10625324—42no—
47C22×D47C22⋊C411yescharacteristic
48Q8×C47—42no—
49C2×C4×C47—22no—
50C2×C4×C47C22×C411yescharacteristic
51C2×C4×C47C2×D411yescharacteristic
52C2×C4×C47C2×D411yescharacteristic
53C2×Dic47—22no—
54C2×Dic47C22⋊C411yescharacteristic
55C2×Dic47C22⋊C411yescharacteristic
56C2×Dic47C22⋊C411yescharacteristic
57C4×D47—21no—
58C4×D47—21no—
59C4×D47—21no—
60C4×D47—21no—
61C4×D47—41no—
62Dic94—41no—
63Dic94—41no—
64C8×C47—41no—
65C8×C47—41no—
66C47⋊C8—41no—
67C47⋊C8—41no—
68C22×C47C2×C22⋊C411yescharacteristic
69C2×D47—21no—
70C2×D47—21no—
71C2×D47—21no—
72C4×C47—21no—
73C4×C47—42no—
74C4×C47AGL(1,ℤ/8)11yescharacteristic
75C4×C47#13711yescharacteristic
76C4×C47#13711yescharacteristic
77C4×C47#13711yescharacteristic
78Dic47—21no—
79Dic47—21no—
80Dic47—21no—
81Dic47—42no—
82#1559—471nomaximal, Sylow
83C2×C47#41311yescharacteristic
84C2×C47#41711yescharacteristic
85C2×C47#41911yescharacteristic
86D47—41no—
87#533—471no—
88#432—471no—
89#423—471no—
90#333—471no—
91#333D4711yescharacteristic, complemented
92#332—471no—
93#332—471no—
94C47#155911yescharacteristic, complemented, Sylow
95C2×M16—941no—
96C4⋊Q8—471no—
97C4⋊Q8C2×D4711yescharacteristic
98#125—941no—
99C22⋊Q8—472no—
100C22⋊Q8—941no—
101C4×Q8—472no—
102C4×Q8—941no—
103#117—941no—
104C2×C42—471no—
105C4⋊C8—471no—
106C4⋊C8—471no—
107C4⋊C8—941no—
108C4⋊C8C2×D4711yescharacteristic
109C4⋊C8C2×D4711yescharacteristic
110C22⋊C8—941no—
111#97—941no—
112C2×Q8—941no—
113C2×Q8C4×D4712yes—
114C22×C4—471no—
115C22×C4—471no—
116C22×C4—471no—
117M16—1882no—
118C2×C8—21no—
119C2×C8—21no—
120C2×C8—941no—
121C2×C8—941no—
122C4⋊C4—21no—
123C4⋊C4—21no—
124C4⋊C4—472no—
125C4⋊C4—942no—
126C4⋊C4—942no—
127C4⋊C4—941no—
128C22⋊C4—942no—
129C42—471no—
130C42—471no—
131C42—471no—
132C42—942no—
133C42C22×D4711yescharacteristic
134C23—471no—
135Q8—42no—
136Q8—1881no—
137Q8—1881no—
138C2×C4—22no—
139C2×C4—471no—
140C2×C4—471no—
141C2×C4—471no—
142C2×C4—941no—
143C2×C4—941no—
144C2×C4—941no—
145C2×C4—941no—
146C2×C4—942no—
147C2×C4—1881no—
148C2×C4C2×C4×D4711yescharacteristic
149C2×C4D4×D4711yescharacteristic
150C2×C4D4×D4711yescharacteristic
151C8—41no—
152C8—41no—
153C8—1881no—
154C8—1881no—
155C22—941no—
156C22—941no—
157C22—941no—
158C22C22⋊C4×D4711yescharacteristic
159C4—21no—
160C4—42no—
161C4—941no—
162C4—941no—
163C4—941no—
164C4—1882no—
165C4#1309405111yescharacteristic
166C4#1309405311yescharacteristic
167C4#1309405611yescharacteristic
168C4#1309405611yescharacteristic
169C2—1881no—
170C2#1568910411yescharacteristic
171C2#1568912311yescharacteristic
172C2#1568913011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D47
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC47×#333C2
socleC22×C47C2×C22⋊C4
hypercenter#333D47
hypocenterC47#1559
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
4. #15688872C2semidirect
5. #15688870C2semidirect
6. #15688868C2semidirect
7. C47×#333C2semidirect
91. #333D47semidirect
94. C47#1559semidirect