Finite Group Databasebeta

← #20245494

Subgroups — #20245494

Order 6016.

150 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 51 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×#13093970C211yesmaximal, characteristic, complemented
2C2×#13093964C211yesmaximal, characteristic
3#15689364C211yesmaximal, characteristic
4#15688950C211yesmaximal, characteristic, complemented
5#15688927C211yesmaximal, characteristic, complemented
6#15688926C211yesmaximal, characteristic, complemented
7C47×#467C211yesmaximal, characteristic
8C2×Dic188C2211yescharacteristic
9#13094003—21no—
10#13093970—22no—
11#13093964—22no—
12C2×C47⋊C16C2211yescharacteristic
13C2×C47⋊C16C2211yescharacteristic
14#13093958C2211yescharacteristic
15#13093949—21no—
16C2×Q16×C47C2211yescharacteristic
17C22×C8×C47C2211yescharacteristic
18C22⋊Q8×C47—21no—
19#107×C47C2211yescharacteristic
20#103×C47—21no—
21C2×Q8×C47—21no—
22C22×C4×C47D411yescharacteristic
23C2×Dic94—21no—
24Q16×C47—21no—
25Q16×C47—21no—
26C2×C8×C47—21no—
27C2×C8×C47—21no—
28C2×C8×C47D411yescharacteristic
29C2×C8×C47C2311yescharacteristic
30C4⋊C4×C47—21no—
31C4⋊C4×C47—41no—
32C22⋊C4×C47—41no—
33C22⋊Dic47—41no—
34C4⋊Dic47—21no—
35Dic47⋊C4—41no—
36Dic188—21no—
37Dic188—21no—
38C47⋊C16—21no—
39C47⋊C16D412yes—
40C23×C47D811yescharacteristic
41Q8×C47—41no—
42Q8×C47—41no—
43C2×C4×C47—21no—
44C2×C4×C47—21no—
45C2×C4×C47—41no—
46C2×C4×C47—41no—
47C2×C4×C47D811yescharacteristic
48C2×C4×C47C2×D411yescharacteristic
49C2×Dic47—41no—
50C2×Dic47—41no—
51Dic94—41no—
52Dic94—41no—
53C8×C47—21no—
54C8×C47C2×D411yescharacteristic
55C8×C47#4111yescharacteristic
56C22×C47—21no—
57C22×C47—21no—
58C22×C47—21no—
59C22×C47C2×D811yescharacteristic
60C4×C47—21no—
61C4×C47—81no—
62C4×C47—81no—
63C4×C47#12111yescharacteristic
64C4×C47#13511yescharacteristic
65Dic47—81no—
66Dic47—81no—
67#2219—471nomaximal, Sylow
68C2×C47—41no—
69C2×C47#46611yescharacteristic
70C2×C47#51011yescharacteristic
71C2×C47#51011yescharacteristic
72C2×Q32—471no—
73C2×M32—471no—
74#467—471no—
75#467D4711yescharacteristic
76#367—471no—
77#358—471no—
78#358—471no—
79C47#221911yescharacteristic, complemented, Sylow
80C2×Q16—471no—
81C2×Q16C2×D4711yescharacteristic
82C22×C8C2×D4711yescharacteristic
83C22⋊Q8—21no—
84C22⋊Q8—941no—
85Q32—942no—
86M32—942no—
87C2×C16—471no—
88C2×C16—471no—
89#107—471no—
90#107C2×D4711yescharacteristic
91#103—21no—
92#103—941no—
93C2×Q8—21no—
94C2×Q8—941no—
95C22×C4C22⋊D4711yescharacteristic
96Q16—21no—
97Q16—21no—
98Q16—941no—
99Q16—941no—
100C2×C8—21no—
101C2×C8—21no—
102C2×C8C22⋊D4711yescharacteristic
103C2×C8C22×D4711yescharacteristic
104C4⋊C4—21no—
105C4⋊C4—41no—
106C4⋊C4—941no—
107C4⋊C4—1881no—
108C22⋊C4—41no—
109C22⋊C4—1881no—
110C16—472no—
111C16—941no—
112C23#1062533411yescharacteristic
113Q8—41no—
114Q8—41no—
115Q8—1881no—
116Q8—1881no—
117C2×C4—21no—
118C2×C4—21no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—1881no—
122C2×C4—1881no—
123C2×C4#1062533411yescharacteristic
124C2×C4C2×C22⋊D4711yescharacteristic
125C8—21no—
126C8D4×D4711yescharacteristic
127C8#1062535211yescharacteristic
128C22—21no—
129C22—21no—
130C22—21no—
131C22C2×#1062533411yescharacteristic
132C4—21no—
133C4—81no—
134C4—81no—
135C4—3761no—
136C4—3761no—
137C4#1309399611yescharacteristic
138C4#1309404411yescharacteristic
139C2—41no—
140C2#1568935711yescharacteristic
141C2#1568956311yescharacteristic
142C2#1568956411yescharacteristic
subgroupG/H
centerC22C2×#10625334
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×#467C2
socleC22×C47C2×D8
hypercenter#467D47
hypocenterC47#2219
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #467

Complements

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

NH ≅ G/Ntype
1. C2×#13093970C2semidirect
4. #15688950C2semidirect
5. #15688927C2semidirect
6. #15688926C2semidirect
79. C47#2219semidirect