Finite Group Databasebeta

← #16845307

Subgroups — #16845307

Order 3968.

180 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 65 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#14521445C211yesmaximal, characteristic
3#14521445C211yesmaximal, characteristic
4#14521428C211yesmaximal, characteristic
5#14521400C211yesmaximal, characteristic
6C8×C31⋊C8C211yesmaximal, characteristic
7C31×#487C211yesmaximal, characteristic
8C31×C4⋊Q8C2211yescharacteristic
9C31×C4⋊Q8C2211yescharacteristic
10C2×#92482—22no—
11#11758446C2211yescharacteristic
12#11758446C2211yescharacteristic
13C31×#103—22no—
14C4×C8×C31C2211yescharacteristic
15#11758404—22no—
16#11758396—22no—
17#11758396—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
31#92482—44no—
32C4⋊Dic31—21no—
33C4⋊Dic31—21no—
34C4⋊Dic31—21no—
35C4⋊Dic31—21no—
36C2×C31⋊C8D412yes—
37C2×C31⋊C8D412yes—
38Q8×C31—42no—
39Q8×C31—42no—
40C2×C4×C31—41no—
41C2×C4×C31—41no—
42C2×C4×C31C2×D411yescharacteristic
43C2×C4×C31C2×D411yescharacteristic
44C2×C4×C31C2×D411yescharacteristic
45C2×Dic31—41no—
46C2×Dic31—41no—
47Dic62—42no—
48Dic62—42no—
49C8×C31—22no—
50C31⋊C8SD1614yes—
51C31⋊C8Q1614yescomplemented
52#1707—311nomaximal, Sylow
53C22×C31#12711yescharacteristic
54C4×C31—81no—
55C4×C31—81no—
56C4×C31C2×SD1612yes—
57C4×C31C2×Q1612yes—
58C4×C31#13512yes—
59Dic31—81no—
60Dic31—81no—
61#500—311no—
62#498—311no—
63#498—311no—
64#494—311no—
65#487—311no—
66#487D3111yescharacteristic
67C82—311no—
68C2×C31#49211yescharacteristic
69C2×C31#49411yescharacteristic
70C2×C31#49511yescharacteristic
71C2×Q16—622no—
72C4⋊Q8—311no—
73C4⋊Q8—311no—
74C4⋊Q8C2×D3111yescharacteristic
75C4⋊Q8C2×D3111yescharacteristic
76#107—622no—
77#106—622no—
78#106—622no—
79#103—22no—
80#103—622no—
81C4×C8—311no—
82C4×C8—311no—
83C4×C8C2×D3111yescharacteristic
84C31#170711yescharacteristic, complemented, Sylow
85C2×Q8—21no—
86C2×Q8—21no—
87C2×Q8—621no—
88C2×Q8—621no—
89Q16—1244no—
90C2×C8—312no—
91C2×C8—312no—
92C2×C8C22⋊D3112yes—
93C4⋊C4—21no—
94C4⋊C4—21no—
95C4⋊C4—21no—
96C4⋊C4—21no—
97C4⋊C4—621no—
98C4⋊C4—621no—
99C4⋊C4—621no—
100C4⋊C4—621no—
101C42C22×D3111yescharacteristic
102Q8—42no—
103Q8—42no—
104Q8—1242no—
105Q8—1242no—
106C2×C4—41no—
107C2×C4—41no—
108C2×C4—1241no—
109C2×C4—1241no—
110C2×C4D4×D3111yescharacteristic
111C2×C4D4×D3111yescharacteristic
112C2×C4C2×C22⋊D3111yescharacteristic
113C8—22no—
114C8—314no—
115C8—314no—
116C22#1175851711yescharacteristic
117C4—81no—
118C4—81no—
119C4—2481no—
120C4—2481no—
121C4SD16×D3112yes—
122C4Q16×D3112yes—
123C4#1175852712yes—
124C2#1452142011yescharacteristic
125C2#1452142711yescharacteristic
126C2#1452143111yescharacteristic
subgroupG/H
centerC22#11758517
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
FittingC31×#487C2
socle, prime radicalC22×C31#127
hypercenter#487D31
hypocenterC31#1707
LCSG ▷ C42×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
51. C31⋊C8Q16semidirect
84. C31#1707semidirect

Maximal subgroups

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

subgroupindex
#145214522
#145214452
#145214282
#145214002
C8×C31⋊C82
C31×#4872
#170731