Finite Group Databasebeta

← #20245243

Subgroups — #20245243

Order 6016.

162 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 59 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×#13093968C211yesmaximal, characteristic
2#15689217C211yesmaximal, characteristic, complemented
3D8×Dic47C211yesmaximal, characteristic
4#15688950C211yesmaximal, characteristic, complemented
5#15688928C211yesmaximal, characteristic, complemented
6C16×Dic47C211yesmaximal, characteristic, complemented
7C47×#357C211yesmaximal, characteristic
8C2×Dic188C2211yescharacteristic
9#13093989—21no—
10D4×Dic47—21no—
11#13093968C414yescomplemented
12C2×C47⋊C16C2211yescharacteristic
13#13093958C2211yescharacteristic
14#13093947—21no—
15#13093945—21no—
16C8×Dic47C2211yescharacteristic
17C2×D8×C47C2211yescharacteristic
18C2×C16×C47C2211yescharacteristic
19#107×C47C2211yescharacteristic
20C2×D4×C47—21no—
21C22×Dic47—41no—
22C2×Dic94—21no—
23D8×C47—21no—
24D8×C47C2×C412yes—
25C2×C8×C47C2311yescharacteristic
26C4⋊C4×C47—21no—
27C22⋊Dic47—41no—
28C4⋊Dic47—21no—
29Dic47⋊C4—41no—
30C4×Dic47—41no—
31C4×Dic47D411yescharacteristic
32C2×C47⋊C8D411yescharacteristic
33Dic188—21no—
34Dic188C2×C412yescomplemented
35C16×C47—21no—
36C47⋊C16C2×C412yescomplemented
37C23×C47—41no—
38D4×C47—22no—
39D4×C47—41no—
40C2×C4×C47—41no—
41C2×C4×C47C2×D411yescharacteristic
42C2×Dic47—41no—
43C2×Dic47—41no—
44C2×Dic47—82no—
45C2×Dic47D811yescharacteristic
46C2×Dic47D811yescharacteristic
47Dic94—22no—
48Dic94—41no—
49C8×C47C22×C411yescharacteristic
50C8×C47#4111yescharacteristic
51C47⋊C8—21no—
52C22×C47—42no—
53C22×C47—81no—
54C22×C47—81no—
55C22×C47C2×D811yescharacteristic
56C4×C47—81no—
57C4×C47C4×D411yescharacteristic
58C4×C47#13511yescharacteristic
59Dic47—21no—
60Dic47—42no—
61Dic47—81no—
62Dic47SD3212yescomplemented
63C4×SD32—471nomaximal, Sylow
64C2×C47—82no—
65C2×C47C4×D811yescharacteristic
66C2×C47C2×SD3211yescharacteristic
67C2×C47#50811yescharacteristic
68C2×SD32—471no—
69C4×Q16—471no—
70C4×D8—471no—
71#367—471no—
72#358—471no—
73#357D4711yescharacteristic
74C4×C16—471no—
75C47C4×SD3211yescharacteristic, complemented, Sylow
76C2×Q16—471no—
77C2×D8C2×D4711yescharacteristic
78C4×Q8—941no—
79C4×D4—941no—
80SD32—474no—
81C2×C16—471no—
82C2×C16C2×D4711yescharacteristic
83#107—471no—
84#107C2×D4711yescharacteristic
85#103—941no—
86#102—941no—
87C4×C8—471no—
88C2×Q8—941no—
89C2×D4—21no—
90C22×C4—1881no—
91Q16—472no—
92Q16—941no—
93D8—21no—
94D8C4×D4712yes—
95C2×C8—471no—
96C2×C8C22×D4711yescharacteristic
97C4⋊C4—21no—
98C4⋊C4—941no—
99C4⋊C4—1881no—
100C22⋊C4—1881no—
101C42—471no—
102C42—1881no—
103C16—21no—
104C16—472no—
105C23—41no—
106Q8—942no—
107Q8—1881no—
108D4—22no—
109D4—41no—
110C2×C4—41no—
111C2×C4—471no—
112C2×C4—471no—
113C2×C4—3762no—
114C2×C4—1881no—
115C2×C4—1881no—
116C2×C4D4×D4711yescharacteristic
117C8—941no—
118C8C2×C4×D4711yescharacteristic
119C8#1062535211yescharacteristic
120C22—42no—
121C22—81no—
122C22—81no—
123C22D8×D4711yescharacteristic
124C4—81no—
125C4—472no—
126C4—941no—
127C4—3761no—
128C4—1882no—
129C4(C22⋊D47)⋊C411yescharacteristic
130C4#1309404511yescharacteristic
131C2—82no—
132C2#1568920311yescharacteristic
133C2SD32×D4711yescharacteristic
134C2#1568955211yescharacteristic
subgroupG/H
centerC22D8×D47
commutatorC8×C47C22×C4
FrattiniC2×C8C22×D47
FittingC47×#357C2
socleC22×C47C2×D8
hypercenter#357D47
hypocenterC47C4×SD32
LCSG ▷ 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
2. #15689217C2semidirect
4. #15688950C2semidirect
5. #15688928C2semidirect
6. C16×Dic47C2semidirect
11. #13093968C4semidirect
34. Dic188C2×C4semidirect
36. C47⋊C16C2×C4semidirect
62. Dic47SD32semidirect
75. C47C4×SD32semidirect