Finite Group Databasebeta

← #20242396

Subgroups — #20242396

Order 6016.

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

normal subgroups only

This group has 210 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
1#15689451C212yesmaximal
2#15689053C211yesmaximal, characteristic
3#15688860C212yesmaximal
4#15688849C211yesmaximal, characteristic
5C47×#544C211yesmaximal, characteristic
6C2×C4⋊Dic47C2211yescharacteristic
7C2×Dic47⋊C4—21no—
8#13093955—22no—
9#13093948—22no—
10C22⋊(C47⋊C8)C2212yes—
11C47⋊#95—21no—
12C47⋊#95C2211yescharacteristic
13C4⋊Q8×C47—22no—
14#125×C47—22no—
15C22⋊Q8×C47—21no—
16C22⋊Q8×C47C2212yes—
17#117×C47—21no—
18C2×C4⋊C4×C47C2211yescharacteristic
19C2×Q8×C47—21no—
20C2×Q8×C47D412yes—
21C22×C4×C47D411yescharacteristic
22C22×C4×C47D411yescharacteristic
23C22×C4×C47C2311yescharacteristic
24C22×Dic47—21no—
25C22×Dic47—21no—
26C4⋊C4×C47—21no—
27C4⋊C4×C47—21no—
28C4⋊C4×C47—21no—
29C4⋊C4×C47—22no—
30C4⋊C4×C47—22no—
31C4⋊C4×C47—22no—
32C4⋊C4×C47D412yes—
33C22⋊C4×C47—22no—
34C42×C47—22no—
35C4⋊Dic47—22no—
36Dic47⋊C4—42no—
37C2×C47⋊C8—22no—
38C23×C47C2×D411yescharacteristic
39Q8×C47—42no—
40Q8×C47—81no—
41C2×C4×C47—21no—
42C2×C4×C47—21no—
43C2×C4×C47—22no—
44C2×C4×C47—22no—
45C2×C4×C47—21no—
46C2×C4×C47—41no—
47C2×C4×C47—41no—
48C2×C4×C47SD1612yes—
49C2×C4×C47C2×D412yes—
50C2×Dic47—22no—
51C2×Dic47—41no—
52C2×Dic47—41no—
53C2×Dic47—41no—
54C2×Dic47—41no—
55C2×Dic47—41no—
56C47⋊C8—42no—
57C22×C47—21no—
58C22×C47—21no—
59C22×C47#12011yescharacteristic
60C22×C47C2×SD1611yescharacteristic
61C22×C47#13711yescharacteristic
62C4×C47—22no—
63C4×C47—22no—
64C4×C47—42no—
65C4×C47—41no—
66C4×C47—42no—
67Dic47—42no—
68Dic47—81no—
69#1611—471nomaximal, Sylow
70C2×C47—21no—
71C2×C47—21no—
72C2×C47#44811yescharacteristic
73C2×C47#45611yescharacteristic
74C2×C47#45811yescharacteristic
75#544D4711yescharacteristic
76#483—472no—
77#398—471no—
78#328—472no—
79#324—471no—
80C47#161111yescharacteristic, complemented, Sylow
81C4⋊Q8—22no—
82#125—22no—
83C22⋊Q8—21no—
84C22⋊Q8C2×D4712yes—
85#117—21no—
86C2×C4⋊C4—471no—
87C2×C4⋊C4—941no—
88C2×C4⋊C4C2×D4711yescharacteristic
89#106—942no—
90#103—942no—
91C22⋊C8—472no—
92#95—471no—
93#95—941no—
94C2×Q8—21no—
95C2×Q8C22⋊D4712yes—
96C22×C4—941no—
97C22×C4—941no—
98C22×C4C22⋊D4711yescharacteristic
99C22×C4C22⋊D4711yescharacteristic
100C22×C4C22×D4711yescharacteristic
101C2×C8—942no—
102C4⋊C4—21no—
103C4⋊C4—21no—
104C4⋊C4—21no—
105C4⋊C4—22no—
106C4⋊C4—22no—
107C4⋊C4—22no—
108C4⋊C4—942no—
109C4⋊C4—1882no—
110C4⋊C4C22⋊D4712yes—
111C22⋊C4—22no—
112C42—22no—
113C23C2×C22⋊D4711yescharacteristic
114Q8—42no—
115Q8—81no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—22no—
119C2×C4—22no—
120C2×C4—21no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—942no—
124C2×C4—1881no—
125C2×C4—1881no—
126C2×C4—1881no—
127C2×C4—1881no—
128C2×C4—1881no—
129C2×C4#1062533612yes—
130C2×C4C2×C22⋊D4712yes—
131C8—1882no—
132C22—21no—
133C22—21no—
134C22#1309399311yescharacteristic
135C22C2×#1062533611yescharacteristic
136C22#1309405511yescharacteristic
137C4—22no—
138C4—22no—
139C4—42no—
140C4—41no—
141C4—42no—
142C4—3761no—
143C4—1882no—
144C2—21no—
145C2—21no—
146C2#1568926211yescharacteristic
147C2#1568930611yescharacteristic
148C2#1568931311yescharacteristic
subgroupG/H
centerC22#13093993
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#544C2
socleC22×C47#120
hypercenter#544D47
hypocenterC47#1611
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
80. C47#1611semidirect