Finite Group Databasebeta

← #20245523

Subgroups — #20245523

Order 6016.

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

normal subgroups only

This group has 142 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
1#15689527C211yesmaximal, characteristic, complemented
2D8×Dic47C211yesmaximal, characteristic
3#15688949C211yesmaximal, characteristic, complemented
4#15688948C211yesmaximal, characteristic, complemented
5Dic47⋊C16C211yesmaximal, characteristic, complemented
6#15688924C211yesmaximal, characteristic
7C47×#357C211yesmaximal, characteristic
8#13094023—21no—
9D4×Dic47—21no—
10C2×C47⋊C16C2211yescharacteristic
11#13093958C2211yescharacteristic
12#13093958C2211yescharacteristic
13#13093957—21no—
14#13093945—21no—
15C8×Dic47C2211yescharacteristic
16C2×D8×C47C2211yescharacteristic
17C2×C16×C47C2211yescharacteristic
18#107×C47C2211yescharacteristic
19C2×D4×C47—21no—
20C22×Dic47—41no—
21C2×Dic94—41no—
22D8×C47—21no—
23D8×C47Q812yescomplemented
24C2×C8×C47C2311yescharacteristic
25C4⋊C4×C47—21no—
26C22⋊Dic47—41no—
27C4⋊Dic47—21no—
28C4⋊Dic47—21no—
29Dic47⋊C4—41no—
30C4×Dic47D411yescharacteristic
31C2×C47⋊C8D411yescharacteristic
32C16×C47—21no—
33C47⋊C16—21no—
34C23×C47—41no—
35D4×C47—22no—
36D4×C47—41no—
37C2×C4×C47—41no—
38C2×C4×C47C2×D411yescharacteristic
39C2×Dic47—41no—
40C2×Dic47—41no—
41C2×Dic47—82no—
42C2×Dic47D811yescharacteristic
43C2×Dic47D811yescharacteristic
44Dic94—82no—
45C8×C47C2×Q811yescharacteristic
46C8×C47#4111yescharacteristic
47C47⋊C8—21no—
48C22×C47—42no—
49C22×C47—81no—
50C22×C47—81no—
51C22×C47C2×D811yescharacteristic
52C4×C47—81no—
53C4×C47C22⋊Q811yescharacteristic
54C4×C47#13711yescharacteristic
55Dic47—21no—
56Dic47—81no—
57Dic47—81no—
58Dic47D1612yes—
59#2224—471nomaximal, Sylow
60C2×C47—82no—
61C2×C47#47411yescharacteristic
62C2×C47C2×D1611yescharacteristic
63C2×C47#51011yescharacteristic
64#500—471no—
65C4×D8—471no—
66#366—471no—
67#366—471no—
68C4⋊C16—471no—
69#357—471no—
70#357D4711yescharacteristic
71C47#222411yescharacteristic, complemented, Sylow
72C2×D8C2×D4711yescharacteristic
73C4⋊Q8—941no—
74C4×D4—941no—
75C2×C16—471no—
76C2×C16C2×D4711yescharacteristic
77#107—471no—
78#107—471no—
79#107—941no—
80#107C2×D4711yescharacteristic
81#102—941no—
82C4×C8—471no—
83C2×Q8—1881no—
84C2×D4—21no—
85C22×C4—1881no—
86D8—21no—
87D8Dic9412yescomplemented
88C2×C8—471no—
89C2×C8C22×D4711yescharacteristic
90C4⋊C4—21no—
91C4⋊C4—941no—
92C4⋊C4—941no—
93C4⋊C4—1881no—
94C22⋊C4—1881no—
95C42—471no—
96C16—21no—
97C16—941no—
98C23—41no—
99Q8—3762no—
100D4—22no—
101D4—41no—
102C2×C4—41no—
103C2×C4—471no—
104C2×C4—471no—
105C2×C4—3762no—
106C2×C4—1881no—
107C2×C4—1881no—
108C2×C4D4×D4711yescharacteristic
109C8—941no—
110C8C2×Dic9411yescharacteristic
111C8#1062535211yescharacteristic
112C22—42no—
113C22—81no—
114C22—81no—
115C22D8×D4711yescharacteristic
116C4—81no—
117C4—472no—
118C4—941no—
119C4—3761no—
120C4—3761no—
121C4#1309400111yescharacteristic
122C4#1309405311yescharacteristic
123C2—82no—
124C2#1568940111yescharacteristic
125C2D16×D4711yescharacteristic
126C2#1568956211yescharacteristic
subgroupG/H
centerC22D8×D47
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×#357C2
socleC22×C47C2×D8
hypercenter#357D47
hypocenterC47#2224
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #357

Complements

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

NH ≅ G/Ntype
1. #15689527C2semidirect
3. #15688949C2semidirect
4. #15688948C2semidirect
5. Dic47⋊C16C2semidirect
23. D8×C47Q8semidirect
71. C47#2224semidirect
87. D8Dic94semidirect