Finite Group Databasebeta

← #20242712

Subgroups — #20242712

Order 6016.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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#15689871C211yesmaximal, characteristic
2#15689493C211yesmaximal, characteristic, complemented
3#15689483C212yesmaximal, complemented
4#15688862C212yesmaximal, complemented
5C47×#330C211yesmaximal, characteristic, complemented
6#13094024C2211yescharacteristic
7#13094012C2212yes—
8#13094009—22no—
9#13094002—22no—
10#13093999—22no—
11#13093949—22no—
12#13093947—22no—
13#13093946—22no—
14#13093935C2211yescharacteristic
15#125×C47C2211yescharacteristic
16#97×C47C2212yes—
17C2×D188—22no—
18C2×D188D412yes—
19C2×C4×D47—22no—
20C2×Dic94—21no—
21C2×Dic94D412yes—
22C2×C8×C47—22no—
23C4⋊C4×C47—22no—
24C4⋊C4×C47D412yes—
25C42×C47C2311yescharacteristic
26(C2×D47)⋊C4—22no—
27(C2×D47)⋊C4—22no—
28(C2×D47)⋊C4—22no—
29C4⋊Dic47—22no—
30Dic47⋊C4—22no—
31C2×C47⋊C8—21no—
32C22×D47—22no—
33C2×C4×C47—22no—
34C2×C4×C47C2×D411yescharacteristic
35C2×C4×C47C2×D412yes—
36C2×Dic47—22no—
37C2×Dic47—41no—
38D188—42no—
39D188—82no—
40C4×D47—82no—
41Dic94—42no—
42Dic94—42no—
43C8×C47—42no—
44C47⋊C8—41no—
45C22×C47#12011yescharacteristic
46C2×D47—42no—
47C2×D47—42no—
48C2×D47—42no—
49C4×C47—21no—
50C4×C47—22no—
51C4×C47—42no—
52Dic47—42no—
53Dic47—81no—
54#1662—471nomaximal, Sylow
55C2×C47#45411yescharacteristic
56C2×C47#45512yes—
57D47—82no—
58#562—471no—
59#491—471no—
60#489—472no—
61#330D4711yescharacteristic, complemented
62#329—472no—
63C47#166211yescharacteristic, complemented, Sylow
64C4⋊Q8—471no—
65#125C2×D4711yescharacteristic
66#124—472no—
67#123—942no—
68C22⋊Q8—942no—
69#121—942no—
70#103—942no—
71#103—942no—
72#102—942no—
73#97—471no—
74#97C2×D4712yes—
75C2×Q8—472no—
76C2×Q8—941no—
77C2×D4—472no—
78C2×D4—942no—
79C22×C4—942no—
80C2×C8—22no—
81C2×C8—941no—
82C4⋊C4—22no—
83C4⋊C4—942no—
84C4⋊C4—942no—
85C4⋊C4D18812yes—
86C22⋊C4—942no—
87C22⋊C4—942no—
88C22⋊C4—942no—
89C42C22×D4711yescharacteristic
90C23—942no—
91Q8—1882no—
92Q8—1882no—
93D4—3762no—
94D4—1882no—
95C2×C4—22no—
96C2×C4—942no—
97C2×C4—3762no—
98C2×C4—1881no—
99C2×C4C2×D18811yescharacteristic
100C2×C4D4×D4712yes—
101C8—42no—
102C8—1881no—
103C22—1882no—
104C22—1882no—
105C22—1882no—
106C22#1309399411yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—3761no—
111C4—1882no—
112C2—3762no—
113C2#1568929811yescharacteristic
114C2#1568930212yes—
subgroupG/H
centerC22#13093994
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#330C2
socleC22×C47#120
hypercenter#330D47
hypocenterC47#1662
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #15689493C2semidirect
3. #15689483C2semidirect
4. #15688862C2semidirect
5. C47×#330C2semidirect
61. #330D47semidirect
63. C47#1662semidirect