Finite Group Databasebeta

← #20242364

Subgroups — #20242364

Order 6016.

238 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 53 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#15689754C211yesmaximal, characteristic
2#15689281C212yesmaximal
3#15689043C211yesmaximal, characteristic
4#15688861C212yesmaximal
5C47×#324C211yesmaximal, characteristic
6C22×Dic94C2211yescharacteristic
7C2×Dic188—22no—
8#13094023—22no—
9#13094015—22no—
10#13094003—21no—
11#13094003C2212yes—
12#13093983—21no—
13C2×Dic47⋊C4—21no—
14#13093949—22no—
15C47⋊#95—21no—
16C47⋊#95C2211yescharacteristic
17C2×C4⋊C4×C47C2211yescharacteristic
18C22⋊C8×C47C2212yes—
19C22×C4×C47D411yescharacteristic
20C22×C4×C47D411yescharacteristic
21C22×C4×C47C2311yescharacteristic
22C22×Dic47—21no—
23C22×Dic47—21no—
24C2×Dic94—22no—
25C2×Dic94—21no—
26C2×Dic94—42no—
27C2×Dic94D412yes—
28C2×C8×C47—22no—
29C4⋊C4×C47—22no—
30C22⋊Dic47—22no—
31C4⋊Dic47—21no—
32C4⋊Dic47—21no—
33C4⋊Dic47—21no—
34C4⋊Dic47D412yes—
35Dic47⋊C4—22no—
36Dic47⋊C4—22no—
37Dic47⋊C4—42no—
38C4×Dic47—22no—
39Dic188—44no—
40C23×C47C2×D411yescharacteristic
41C2×C4×C47—21no—
42C2×C4×C47—21no—
43C2×C4×C47—21no—
44C2×C4×C47—41no—
45C2×C4×C47—41no—
46C2×C4×C47Q1612yescomplemented
47C2×C4×C47C2×D412yes—
48C2×Dic47—22no—
49C2×Dic47—22no—
50C2×Dic47—22no—
51C2×Dic47—22no—
52C2×Dic47—41no—
53C2×Dic47—41no—
54C2×Dic47—41no—
55C2×Dic47—41no—
56Dic94—24no—
57Dic94—42no—
58Dic94—42no—
59Dic94—81no—
60C8×C47—42no—
61C22×C47—21no—
62C22×C47—21no—
63C22×C47#12011yescharacteristic
64C22×C47C2×Q1611yescharacteristic
65C22×C47#13711yescharacteristic
66C4×C47—22no—
67C4×C47—22no—
68C4×C47—41no—
69Dic47—42no—
70Dic47—42no—
71Dic47—42no—
72Dic47—42no—
73#1605—471nomaximal, Sylow
74C2×C47—21no—
75C2×C47—21no—
76C2×C47#45111yescharacteristic
77C2×C47#45611yescharacteristic
78C2×C47B(4,𝔽2)11yescharacteristic
79#544—471no—
80#451—472no—
81#395—471no—
82#328—472no—
83#324D4711yescharacteristic
84C47#160511yescharacteristic, complemented, Sylow
85C22×Q8—471no—
86C2×Q16—942no—
87C4⋊Q8—942no—
88#125—942no—
89C22⋊Q8—472no—
90C22⋊Q8—941no—
91#117—941no—
92C2×C4⋊C4—941no—
93C2×C4⋊C4C2×D4711yescharacteristic
94#103—942no—
95C22⋊C8C2×D4712yes—
96#95—471no—
97#95—941no—
98C2×Q8—472no—
99C2×Q8—941no—
100C2×Q8—942no—
101C2×Q8—1882no—
102C22×C4—941no—
103C22×C4—941no—
104C22×C4D18811yescharacteristic
105C22×C4D18811yescharacteristic
106C22×C4C22×D4711yescharacteristic
107Q16—1884no—
108C2×C8—22no—
109C4⋊C4—22no—
110C4⋊C4—472no—
111C4⋊C4—942no—
112C4⋊C4—941no—
113C4⋊C4—941no—
114C4⋊C4—941no—
115C4⋊C4—942no—
116C4⋊C4—1882no—
117C22⋊C4—942no—
118C42—942no—
119C23C2×D18811yescharacteristic
120Q8—944no—
121Q8—3761no—
122Q8—1882no—
123Q8—1882no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—21no—
127C2×C4—41no—
128C2×C4—41no—
129C2×C4—942no—
130C2×C4—942no—
131C2×C4—942no—
132C2×C4—942no—
133C2×C4—1881no—
134C2×C4—1881no—
135C2×C4—1881no—
136C2×C4—1881no—
137C2×C4Dic18812yescomplemented
138C2×C4D4×D4712yes—
139C8—42no—
140C22—21no—
141C22—21no—
142C22#1309399411yescharacteristic
143C22C2×Dic18811yescharacteristic
144C22#1309405711yescharacteristic
145C4—22no—
146C4—22no—
147C4—41no—
148C4—1882no—
149C4—1882no—
150C4—1882no—
151C4—1882no—
152C2—21no—
153C2—21no—
154C2#1568928111yescharacteristic
155C2#1568930811yescharacteristic
156C2#1568931111yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#324C2
socleC22×C47#120
hypercenter#324D47
hypocenterC47#1605
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
46. C2×C4×C47Q16semidirect
84. C47#1605semidirect
137. C2×C4Dic188semidirect