Finite Group Databasebeta

← #20245442

Subgroups — #20245442

Order 6016.

170 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 47 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×#13093969C211yesmaximal, characteristic, complemented
2C2×#13093965C211yesmaximal, characteristic
3#15689506C211yesmaximal, characteristic, complemented
4#15689205C211yesmaximal, characteristic, complemented
5Dic47⋊C16C211yesmaximal, characteristic, complemented
6#15688926C211yesmaximal, characteristic, complemented
7C47×#357C211yesmaximal, characteristic, complemented
8C2×Dic188C2211yescharacteristic
9C2×#10625335—21no—
10C2×D376C2211yescharacteristic
11#13094011—21no—
12#13093986—21no—
13#13093969—22no—
14#13093965—22no—
15C2×C47⋊C16C2211yescharacteristic
16#13093944—21no—
17C8×Dic47C2211yescharacteristic
18C2×D8×C47C2211yescharacteristic
19C2×C16×C47C2211yescharacteristic
20#107×C47C2211yescharacteristic
21C2×D4×C47—21no—
22C2×D188—21no—
23C2×C4×D47—41no—
24C2×Dic94—21no—
25D8×C47—21no—
26D8×C47—21no—
27C2×C8×C47C2311yescharacteristic
28C4⋊C4×C47—21no—
29C22⋊Dic47—41no—
30C22⋊Dic47—41no—
31#10625335—42no—
32(C2×D47)⋊C4—41no—
33C4×Dic47D411yescharacteristic
34C2×C47⋊C8D411yescharacteristic
35Dic188—21no—
36Dic188—21no—
37D376—21no—
38D376D412yes—
39C16×C47—21no—
40C47⋊C16—21no—
41C23×C47—41no—
42C22×D47—41no—
43D4×C47—41no—
44D4×C47—41no—
45C2×C4×C47—41no—
46C2×C4×C47C2×D411yescharacteristic
47C2×Dic47—41no—
48C2×Dic47D811yescharacteristic
49C2×Dic47D811yescharacteristic
50D188—22no—
51D188—41no—
52C4×D47—82no—
53Dic94—41no—
54Dic94—41no—
55C8×C47C2×D411yescharacteristic
56C8×C47#4111yescharacteristic
57C47⋊C8—21no—
58C22×C47—81no—
59C22×C47—81no—
60C22×C47—81no—
61C22×C47C2×D811yescharacteristic
62C2×D47—42no—
63C2×D47—81no—
64C2×D47—81no—
65C4×C47—81no—
66C4×C47#12111yescharacteristic
67C4×C47AGL(1,ℤ/8)11yescharacteristic
68Dic47—21no—
69Dic47—21no—
70Dic47—81no—
71#2210—471nomaximal, Sylow
72C2×C47—161no—
73C2×C47#45911yescharacteristic
74C2×C47#50811yescharacteristic
75C2×C47#50911yescharacteristic
76D47—82no—
77C2×SD32—471no—
78C2×D16—471no—
79#495—471no—
80C4×D8—471no—
81C4⋊C16—471no—
82#358—471no—
83#357D4711yescharacteristic, complemented
84C47#221011yescharacteristic, complemented, Sylow
85C2×Q16—471no—
86C2×SD16—941no—
87C2×D8—471no—
88C2×D8C2×D4711yescharacteristic
89#124—941no—
90C4×D4—941no—
91SD32—942no—
92D16—942no—
93C2×C16—471no—
94C2×C16C2×D4711yescharacteristic
95#107C2×D4711yescharacteristic
96#102—941no—
97C4×C8—471no—
98C2×Q8—941no—
99C2×D4—21no—
100C2×D4—941no—
101C22×C4—1881no—
102Q16—941no—
103Q16—941no—
104SD16—1882no—
105D8—21no—
106D8—21no—
107D8—472no—
108D8—941no—
109C2×C8—471no—
110C2×C8C22×D4711yescharacteristic
111C4⋊C4—21no—
112C22⋊C4—1881no—
113C22⋊C4—1881no—
114C22⋊C4—1881no—
115C42—471no—
116C16—21no—
117C16—941no—
118C23—41no—
119C23—1881no—
120Q8—1881no—
121Q8—1881no—
122D4—41no—
123D4—41no—
124D4—942no—
125D4—1881no—
126C2×C4—41no—
127C2×C4—471no—
128C2×C4—471no—
129C2×C4—3762no—
130C2×C4—1881no—
131C2×C4D4×D4711yescharacteristic
132C8—941no—
133C8#1062535011yescharacteristic
134C8D4×D4711yescharacteristic
135C22—81no—
136C22—81no—
137C22—81no—
138C22—3761no—
139C22—3761no—
140C22—1882no—
141C22D8×D4711yescharacteristic
142C4—81no—
143C4—941no—
144C4—941no—
145C4—3761no—
146C4#1309399711yescharacteristic
147C4#1309405111yescharacteristic
148C2—161no—
149C2—3762no—
150C2#1568931711yescharacteristic
151C2#1568955411yescharacteristic
152C2#1568955711yescharacteristic
subgroupG/H
centerC22D8×D47
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×#357C2
socleC22×C47C2×D8
hypercenter#357D47
hypocenterC47#2210
LCSG ▷ C2×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
1. C2×#13093969C2semidirect
3. #15689506C2semidirect
4. #15689205C2semidirect
5. Dic47⋊C16C2semidirect
6. #15688926C2semidirect
7. C47×#357C2semidirect
83. #357D47semidirect
84. C47#2210semidirect