Finite Group Databasebeta

← #16845355

Subgroups — #16845355

Order 3968.

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

normal subgroups only

This group has 164 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#14521452C211yesmaximal, characteristic
2#14521401C211yesmaximal, characteristic
3#14521400C211yesmaximal, characteristic
4#14521399C211yesmaximal, characteristic
5#14521399C211yesmaximal, characteristic
6#14520771C211yesmaximal, characteristic
7C31×#498C211yesmaximal, characteristic
8C31×C4⋊Q8C2211yescharacteristic
9C31×C4⋊Q8C2211yescharacteristic
10#11758446C2211yescharacteristic
11#11758446C2211yescharacteristic
12C31×#106—22no—
13C4×C8×C31C2211yescharacteristic
14#11758423—22no—
15#11758423—22no—
16#11758404—22no—
17#11758398—22no—
18#11758395—22no—
19C4×C31⋊C8C2211yescharacteristic
20C4×C31⋊C8C2211yescharacteristic
21C2×Q8×C31—21no—
22C2×Q8×C31—21no—
23C2×Dic62—21no—
24C2×Dic62—21no—
25C2×C8×C31D412yes—
26C4⋊C4×C31—21no—
27C4⋊C4×C31—21no—
28C4⋊C4×C31—21no—
29C4⋊C4×C31—21no—
30C42×C31C2311yescharacteristic
31C4⋊Dic31—21no—
32C4⋊Dic31—21no—
33C4⋊Dic31—21no—
34C4⋊Dic31—21no—
35C2×C31⋊C8D412yes—
36C2×C31⋊C8D412yes—
37Q8×C31—42no—
38Q8×C31—42no—
39C2×C4×C31—41no—
40C2×C4×C31—41no—
41C2×C4×C31C2×D411yescharacteristic
42C2×C4×C31C2×D411yescharacteristic
43C2×C4×C31C2×D411yescharacteristic
44C2×Dic31—41no—
45C2×Dic31—41no—
46Dic62—42no—
47Dic62—42no—
48C8×C31—22no—
49C31⋊C8—22no—
50C31⋊C8—22no—
51#1718—311nomaximal, Sylow
52C22×C31#12711yescharacteristic
53C4×C31—81no—
54C4×C31—81no—
55C4×C31#13512yes—
56C4×C31#13712yes—
57C4×C31#13712yes—
58Dic31—81no—
59Dic31—81no—
60#500—311no—
61#498D3111yescharacteristic
62#487—311no—
63#487—311no—
64#487—311no—
65#487—311no—
66#322—311no—
67C2×C31#49511yescharacteristic
68C2×C31#49711yescharacteristic
69C2×C31#49711yescharacteristic
70C4⋊Q8—311no—
71C4⋊Q8—311no—
72C4⋊Q8C2×D3111yescharacteristic
73C4⋊Q8C2×D3111yescharacteristic
74#107—622no—
75#106—22no—
76#103—622no—
77#103—622no—
78#103—622no—
79#103—622no—
80C4×C8—311no—
81C4×C8—311no—
82C4×C8C2×D3111yescharacteristic
83C31#171811yescharacteristic, complemented, Sylow
84C2×Q8—21no—
85C2×Q8—21no—
86C2×Q8—621no—
87C2×Q8—621no—
88C2×C8—312no—
89C2×C8—312no—
90C2×C8C22⋊D3112yes—
91C4⋊C4—21no—
92C4⋊C4—21no—
93C4⋊C4—21no—
94C4⋊C4—21no—
95C4⋊C4—621no—
96C4⋊C4—621no—
97C4⋊C4—621no—
98C4⋊C4—621no—
99C42C22×D3111yescharacteristic
100Q8—42no—
101Q8—42no—
102Q8—1242no—
103Q8—1242no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—1241no—
107C2×C4—1241no—
108C2×C4D4×D3111yescharacteristic
109C2×C4D4×D3111yescharacteristic
110C2×C4C2×C22⋊D3111yescharacteristic
111C8—22no—
112C8—622no—
113C8—622no—
114C22#1175851711yescharacteristic
115C4—81no—
116C4—81no—
117C4—2481no—
118C4—2481no—
119C4#1175849212yes—
120C4#1175849312yes—
121C4#1175851912yes—
122C2#1452143011yescharacteristic
123C2#1452144011yescharacteristic
124C2#1452144111yescharacteristic
subgroupG/H
centerC22#11758517
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
FittingC31×#498C2
socle, prime radicalC22×C31#127
hypercenter#498D31
hypocenterC31#1718
LCSG ▷ C42×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
83. C31#1718semidirect

Maximal subgroups

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

subgroupindex
#145214522
#145214012
#145214002
#145213992
#145207712
C31×#4982
#171831