Finite Group Databasebeta

← #20245262

Subgroups — #20245262

Order 6016.

172 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 61 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×#13093965C211yesmaximal, characteristic
2C4×D376C211yesmaximal, characteristic, complemented
3#15688950C211yesmaximal, characteristic, complemented
4#15688924C211yesmaximal, characteristic, complemented
5#15688923C211yesmaximal, characteristic, complemented
6#15688899C211yesmaximal, characteristic, complemented
7C4×D8×C47C211yesmaximal, characteristic, complemented
8C2×D376C2211yescharacteristic
9C4×D188—21no—
10#13093965C414yescomplemented
11C2×C47⋊C16C2211yescharacteristic
12C2×C47⋊C16C2211yescharacteristic
13#13093958C2211yescharacteristic
14#13093946—21no—
15C2×D8×C47C2211yescharacteristic
16C4×D4×C47—21no—
17#107×C47C2211yescharacteristic
18#102×C47—21no—
19C4×C8×C47C2211yescharacteristic
20C2×D4×C47—21no—
21C22×C4×C47—41no—
22C2×D188—21no—
23C2×C4×D47—41no—
24D8×C47—21no—
25D8×C47C2×C412yescomplemented
26C2×C8×C47D411yescharacteristic
27C2×C8×C47C2311yescharacteristic
28C4⋊C4×C47—21no—
29C22⋊C4×C47—41no—
30C42×C47D411yescharacteristic
31(C2×D47)⋊C4—41no—
32C4⋊Dic47—21no—
33D376—21no—
34D376C2×C412yescomplemented
35C47⋊C16—21no—
36C47⋊C16C2×C412yescomplemented
37C23×C47—41no—
38C22×D47—41no—
39D4×C47—22no—
40D4×C47—41no—
41C2×C4×C47—41no—
42C2×C4×C47—82no—
43C2×C4×C47D811yescharacteristic
44C2×C4×C47D811yescharacteristic
45C2×C4×C47C2×D411yescharacteristic
46C2×Dic47—41no—
47D188—22no—
48D188—41no—
49C4×D47—82no—
50C8×C47—21no—
51C8×C47C22×C411yescharacteristic
52C8×C47#4111yescharacteristic
53C22×C47—42no—
54C22×C47—81no—
55C22×C47—81no—
56C22×C47C2×D811yescharacteristic
57C2×D47—42no—
58C2×D47—81no—
59C2×D47—81no—
60C4×C47—21no—
61C4×C47—21no—
62C4×C47—81no—
63C4×C47C4×D411yescharacteristic
64C4×C47#13511yescharacteristic
65Dic47—81no—
66#2177—471nomaximal, Sylow
67C2×C47—82no—
68C2×C47C4×D811yescharacteristic
69C2×C47#50911yescharacteristic
70C2×C47#50911yescharacteristic
71D47—82no—
72C2×D16—471no—
73C4×D8—471no—
74C4×D8D4711yescharacteristic, complemented
75#367—471no—
76#357—471no—
77#357—471no—
78#346—471no—
79C47#217711yescharacteristic, complemented, Sylow
80C2×D8—471no—
81C2×D8C2×D4711yescharacteristic
82C4×D4—21no—
83C4×D4—941no—
84D16—474no—
85C2×C16—471no—
86C2×C16—471no—
87#107—471no—
88#107C2×D4711yescharacteristic
89#102—21no—
90#102—941no—
91C4×C8C2×D4711yescharacteristic
92C2×D4—21no—
93C2×D4—941no—
94C22×C4—41no—
95C22×C4—1881no—
96D8—21no—
97D8—472no—
98D8—941no—
99D8C4×D4712yescomplemented
100C2×C8C22⋊D4711yescharacteristic
101C2×C8C22×D4711yescharacteristic
102C4⋊C4—21no—
103C4⋊C4—941no—
104C22⋊C4—41no—
105C22⋊C4—1881no—
106C42C22⋊D4711yescharacteristic
107C16—472no—
108C16—941no—
109C23—41no—
110C23—1881no—
111D4—22no—
112D4—41no—
113D4—942no—
114D4—1881no—
115C2×C4—41no—
116C2×C4—82no—
117C2×C4—3762no—
118C2×C4—1881no—
119C2×C4#1062533411yescharacteristic
120C2×C4#1062533411yescharacteristic
121C2×C4C2×C22⋊D4711yescharacteristic
122C8—21no—
123C8C2×C4×D4711yescharacteristic
124C8#1062535011yescharacteristic
125C22—42no—
126C22—81no—
127C22—81no—
128C22—3761no—
129C22—3761no—
130C22—1882no—
131C22C2×#1062533411yescharacteristic
132C4—21no—
133C4—21no—
134C4—81no—
135C4—3761no—
136C4C4×C22⋊D4711yescharacteristic
137C4#1309404411yescharacteristic
138C2—82no—
139C2—3762no—
140C2C4×#1062533411yescharacteristic
141C2#1568955811yescharacteristic
142C2#1568955911yescharacteristic
subgroupG/H
centerC22C2×#10625334
commutatorC8×C47C22×C4
FrattiniC2×C8C22×D47
FittingC4×D8×C47C2
socleC22×C47C2×D8
hypercenterC4×D8D47
hypocenterC47#2177
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
2. C4×D376C2semidirect
3. #15688950C2semidirect
4. #15688924C2semidirect
5. #15688923C2semidirect
6. #15688899C2semidirect
7. C4×D8×C47C2semidirect
10. #13093965C4semidirect
25. D8×C47C2×C4semidirect
34. D376C2×C4semidirect
36. C47⋊C16C2×C4semidirect
74. C4×D8D47semidirect
79. C47#2177semidirect
99. D8C4×D47semidirect