Finite Group Databasebeta

← #16847605

Subgroups — #16847605

Order 3968.

142 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 51 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#14521490C211yesmaximal, characteristic
2#14521170C211yesmaximal, characteristic
3#14521156C211yesmaximal, characteristic, complemented
4#14520873C211yesmaximal, characteristic, complemented
5#14520860C211yesmaximal, characteristic
6#14520826C211yesmaximal, characteristic, complemented
7C31×#362C211yesmaximal, characteristic, complemented
8C2×Q16×C31C2211yescharacteristic
9Q8×Dic31—21no—
10#11758484—21no—
11#11758481C2211yescharacteristic
12C31×M32C2211yescharacteristic
13C31×#108C2211yescharacteristic
14#11758423—21no—
15#11758417C412yescomplemented
16#11758416C412yescomplemented
17#11758413—21no—
18#11758405C2211yescharacteristic
19#11758403C2211yescharacteristic
20#11758400C2211yescharacteristic
21C2×Q8×C31—21no—
22#92495—21no—
23Q16×C31—21no—
24Q16×C31C2×C412yes—
25M16×C31—21no—
26C2×C8×C31C2311yescharacteristic
27C4⋊Dic31—21no—
28C4⋊Dic31—41no—
29C4×Dic31—41no—
30C4×Dic31D411yescharacteristic
31C2×C31⋊C8D411yescharacteristic
32Dic124C2×C411yescharacteristic
33D248C2×C411yescharacteristic
34#92470—21no—
35#92469—41no—
36C8×D31—41no—
37C16×C31—21no—
38C31⋊C16C2×C412yes—
39Q8×C31—22no—
40Q8×C31—41no—
41C2×C4×C31—41no—
42C2×C4×C31C2×D411yescharacteristic
43C22⋊D31—41no—
44C2×Dic31—21no—
45C2×Dic31—41no—
46D124—21no—
47C4×D31—41no—
48Dic62—21no—
49C8×C31—41no—
50C8×C31C22×C411yescharacteristic
51C8×C31#4111yescharacteristic
52C31⋊C8—21no—
53#2180—311nomaximal, Sylow
54C22×C31AGL(1,ℤ/8)11yescharacteristic
55C2×D31—41no—
56C4×C31—42no—
57C4×C31C4×D411yescharacteristic
58C4×C31AGL(1,ℤ/8)11yescharacteristic
59Dic31—41no—
60Dic31—41no—
61Dic31—81no—
62#510—311no—
63#444—311no—
64#441—311no—
65#365—311no—
66#362D3111yescharacteristic, complemented
67#360—311no—
68#347—311no—
69C2×C31—21no—
70C2×C31#44211yescharacteristic
71D31—81no—
72#135—311no—
73C2×Q16C2×D3111yescharacteristic
74#131—621no—
75C4×Q8—621no—
76Q32—312no—
77SD32—312no—
78M32—311no—
79M32C2×D3111yescharacteristic
80#108C2×D3111yescharacteristic
81#106—311no—
82#104—621no—
83#103—621no—
84#97—311no—
85C31#218011yescharacteristic, complemented, Sylow
86#41—621no—
87C2×Q8—21no—
88Q16—21no—
89Q16—311no—
90Q16C4×D3112yes—
91SD16—621no—
92D8—311no—
93M16—21no—
94M16—1241no—
95C2×C8—311no—
96C2×C8—1241no—
97C2×C8C22×D3111yescharacteristic
98C4⋊C4—621no—
99C4⋊C4—1241no—
100C42—311no—
101C42—1241no—
102C16—21no—
103C16—312no—
104Q8—22no—
105Q8—41no—
106Q8—621no—
107D4—621no—
108D4—1241no—
109C2×C4—41no—
110C2×C4—621no—
111C2×C4—1241no—
112C2×C4—1241no—
113C2×C4D4×D3111yescharacteristic
114C8—41no—
115C8—621no—
116C8C2×C4×D3111yescharacteristic
117C8#9249711yescharacteristic
118C22—1241no—
119C22#1175849111yescharacteristic
120C4—42no—
121C4—1241no—
122C4—1241no—
123C4—2481no—
124C4(C22⋊D31)⋊C411yescharacteristic
125C4#1175848811yescharacteristic
126C2—21no—
127C2—2481no—
128C2#1452115811yescharacteristic
subgroupG/H
centerC2#14521158
commutatorC8×C31C22×C4
FrattiniC2×C8C22×D31
FittingC31×#362C2
socleC2×C31#442
prime radical#11758481C22
cosocleC2×C8×C31C23
hypercenter#362D31
hypocenterC31#2180
LCSG ▷ C8×C31 ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #362

Complements

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

NH ≅ G/Ntype
3. #14521156C2semidirect
4. #14520873C2semidirect
6. #14520826C2semidirect
7. C31×#362C2semidirect
15. #11758417C4semidirect
16. #11758416C4semidirect
66. #362D31semidirect
85. C31#2180semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145214902
#145211702
#145211562
#145208732
#145208602
#145208262
C31×#3622
#218031