Finite Group Databasebeta

← #20245302

Subgroups — #20245302

Order 6016.

266 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 57 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
1C22×D376C211yesmaximal, characteristic, complemented
2C2×D752C212yesmaximal, complemented
3#15689359C211yesmaximal, characteristic, complemented
4#15688925C212yesmaximal, complemented
5C47×C22⋊C16C211yesmaximal, characteristic, complemented
6C22×D188—21no—
7C2×D376—21no—
8C2×D376—24no—
9C2×D376C2212yes—
10C2×D376C2211yescharacteristic, complemented
11#13093998—21no—
12D752—24no—
13#13093958C2211yescharacteristic, complemented
14#13093946—21no—
15C22×C8×C47C2211yescharacteristic
16C2×C16×C47C2212yescomplemented
17C23×D47—41no—
18C22×C4×C47D411yescharacteristic
19C2×C22⋊D47—41no—
20C2×D188—24no—
21C2×D188—22no—
22C2×D188—21no—
23C2×D188—42no—
24C2×D188—41no—
25C2×C8×C47—22no—
26C2×C8×C47D411yescharacteristic
27C2×C8×C47C2311yescharacteristic
28(C2×D47)⋊C4—41no—
29C4⋊Dic47—21no—
30D376—24no—
31D376—22no—
32D376—22no—
33D376D414yescomplemented
34C16×C47—22no—
35C23×C47D811yescharacteristic
36C22×D47—44no—
37C22×D47—42no—
38C22×D47—41no—
39C22×D47—82no—
40C22×D47—82no—
41C2×C4×C47—21no—
42C2×C4×C47—21no—
43C2×C4×C47D811yescharacteristic
44C2×C4×C47C2×D411yescharacteristic
45C22⋊D47—82no—
46C2×Dic47—41no—
47D188—24no—
48D188—44no—
49D188—41no—
50D188—42no—
51D188—41no—
52C8×C47—21no—
53C8×C47C2×D412yes—
54C22×C47—21no—
55C22×C47—21no—
56C22×C47D1612yescomplemented
57C22×C47C2×D811yescharacteristic
58C2×D47—44no—
59C2×D47—88no—
60C2×D47—82no—
61C2×D47—82no—
62C2×D47—81no—
63C2×D47—81no—
64C2×D47—81no—
65C4×C47—21no—
66C4×C47#12011yescharacteristic
67C4×C47AGL(1,ℤ/8)11yescharacteristic
68Dic47—81no—
69#2184—471nomaximal, Sylow
70C2×C47—22no—
71C2×C47#44711yescharacteristic
72C2×C47C2×D1611yescharacteristic
73C2×C47#50911yescharacteristic
74D47—84no—
75D47—161no—
76C22×D8—471no—
77C2×D16—472no—
78#466—471no—
79#357—472no—
80C22⋊C16D4711yescharacteristic, complemented
81C47#218411yescharacteristic, complemented, Sylow
82C22×D4—941no—
83C2×D8—472no—
84C2×D8—471no—
85C2×D8—944no—
86C2×D8—941no—
87C22×C8C2×D4711yescharacteristic
88#121—941no—
89D16—944no—
90C2×C16C2×D4712yescomplemented
91#107—471no—
92#102—941no—
93C24—1881no—
94C2×D4—944no—
95C2×D4—942no—
96C2×D4—941no—
97C2×D4—1882no—
98C2×D4—1881no—
99C2×D4—1881no—
100C22×C4D18811yescharacteristic
101D8—474no—
102D8—944no—
103D8—942no—
104D8—942no—
105C2×C8—22no—
106C2×C8D18811yescharacteristic
107C2×C8C22×D4711yescharacteristic
108C4⋊C4—941no—
109C22⋊C4—1881no—
110C16—22no—
111C23—3762no—
112C23—3762no—
113C23—1884no—
114C23—1881no—
115C23—1882no—
116C23D37611yescharacteristic
117D4—944no—
118D4—3762no—
119D4—1884no—
120D4—1881no—
121D4—1881no—
122D4—1882no—
123C2×C4—21no—
124C2×C4—21no—
125C2×C4—1881no—
126C2×C4D37611yescharacteristic
127C2×C4C2×D18811yescharacteristic
128C8—21no—
129C8D4×D4712yes—
130C22—21no—
131C22—21no—
132C22—3768no—
133C22—3762no—
134C22—3762no—
135C22—3761no—
136C22—3761no—
137C22—3761no—
138C22—1884no—
139C22D75212yescomplemented
140C22C2×D37611yescharacteristic
141C4—21no—
142C4—3761no—
143C4#1309399411yescharacteristic
144C4#1309405211yescharacteristic
145C2—22no—
146C2—3764no—
147C2—7521no—
148C2#1568925911yescharacteristic
149C2C2×D75211yescharacteristic
150C2#1568956111yescharacteristic
subgroupG/H
centerC22C2×D376
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×C22⋊C16C2
socleC22×C47C2×D8
hypercenterC22⋊C16D47
hypocenterC47#2184
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22⋊C16

Complements

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

NH ≅ G/Ntype
1. C22×D376C2semidirect
2. C2×D752C2semidirect
3. #15689359C2semidirect
4. #15688925C2semidirect
5. C47×C22⋊C16C2semidirect
10. C2×D376C22semidirect
13. #13093958C22semidirect
16. C2×C16×C47C22semidirect
33. D376D4semidirect
56. C22×C47D16semidirect
80. C22⋊C16D47semidirect
81. C47#2184semidirect
90. C2×C16C2×D47semidirect
139. C22D752semidirect