Finite Group Databasebeta

← #16846102

Subgroups — #16846102

Order 3968.

324 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 89 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×#11758521C211yesmaximal, characteristic
2#14521527C211yesmaximal, characteristic
3#14521059C212yesmaximal
4#14520810C212yesmaximal
5C2×C31×#101C211yesmaximal, characteristic
6C22×Q8×C31C2211yescharacteristic
7C22×Dic62C2211yescharacteristic
8C2×M16×C31C2212yes—
9Q8×Dic31—24no—
10#11758521—22no—
11#11758521C414yescomplemented
12#11758503—22no—
13#11758503C2212yes—
14C2×Dic31⋊C4—22no—
15C2×C4×Dic31C2211yescharacteristic
16C31×#101—22no—
17#11758404—24no—
18C2×Q8×C31—22no—
19C2×Q8×C31—22no—
20C2×Q8×C31C2×C412yes—
21C2×Q8×C31D412yes—
22C22×C4×C31D412yes—
23C22×C4×C31C2311yescharacteristic
24C22×Dic31—21no—
25C22×Dic31—21no—
26C2×Dic62—22no—
27C2×Dic62—22no—
28C2×Dic62—21no—
29C2×Dic62C2×C412yes—
30M16×C31—22no—
31M16×C31—22no—
32C2×C8×C31—22no—
33C22⋊Dic31—22no—
34C4⋊Dic31—24no—
35C4⋊Dic31D414yes—
36Dic31⋊C4—28no—
37C4×Dic31—24no—
38C4×Dic31—21no—
39C4×Dic31—22no—
40C4×Dic31C2×C412yes—
41C23×C31C2×D411yescharacteristic
42Q8×C31—24no—
43Q8×C31—24no—
44C2×C4×C31—22no—
45C2×C4×C31—22no—
46C2×C4×C31C22⋊C414yes—
47C2×C4×C31C22×C411yescharacteristic
48C2×C4×C31C2×D412yes—
49C2×C4×C31C2×D411yescharacteristic
50C2×C4×C31#4112yes—
51C2×Dic31—24no—
52C2×Dic31—22no—
53C2×Dic31—22no—
54C2×Dic31—24no—
55C2×Dic31—41no—
56C2×Dic31—41no—
57Dic62—24no—
58Dic62—42no—
59C8×C31—42no—
60#1886—311nomaximal, Sylow
61C22×C31—22no—
62C22×C31C2×C22⋊C411yescharacteristic
63C22×C31#12011yescharacteristic
64C22×C31#12311yescharacteristic
65C4×C31—24no—
66C4×C31C4×D412yes—
67C4×C31#12112yes—
68Dic31—24no—
69Dic31—42no—
70Dic31—44no—
71C2×C4⋊Q8—311no—
72#519—311no—
73#419—312no—
74C2×#101D3111yescharacteristic
75#339—312no—
76C2×C31—21no—
77C2×C31—21no—
78C2×C31#38611yescharacteristic
79C2×C31#45612yes—
80C22×Q8—311no—
81C22×Q8C2×D3111yescharacteristic
82C2×M16C2×D3112yes—
83C4⋊Q8—314no—
84C4⋊Q8—622no—
85C4×Q8—624no—
86#117—312no—
87#117—622no—
88C2×C4⋊C4—622no—
89C2×C42—311no—
90#103—624no—
91#101—22no—
92C31#188611yescharacteristic, complemented, Sylow
93C2×Q8—22no—
94C2×Q8—22no—
95C2×Q8—312no—
96C2×Q8—621no—
97C2×Q8—622no—
98C2×Q8—622no—
99C2×Q8C4×D3112yes—
100C2×Q8C22⋊D3112yes—
101C22×C4—621no—
102C22×C4—621no—
103C22×C4D12412yes—
104C22×C4C22×D3111yescharacteristic
105M16—22no—
106M16—22no—
107C2×C8—22no—
108C4⋊C4—314no—
109C4⋊C4—624no—
110C4⋊C4—628no—
111C22⋊C4—622no—
112C42—312no—
113C42—624no—
114C42—622no—
115C42—621no—
116C23C2×D12411yescharacteristic
117Q8—24no—
118Q8—24no—
119Q8—624no—
120Q8—1242no—
121C2×C4—22no—
122C2×C4—22no—
123C2×C4—624no—
124C2×C4—622no—
125C2×C4—624no—
126C2×C4—622no—
127C2×C4—1241no—
128C2×C4—1241no—
129C2×C4(C2×D31)⋊C414yes—
130C2×C4C2×C4×D3111yescharacteristic
131C2×C4D4×D3112yes—
132C2×C4#9249712yes—
133C2×C4C2×C22⋊D3111yescharacteristic
134C8—42no—
135C22—22no—
136C22#1175845911yescharacteristic
137C22#1175846311yescharacteristic
138C22C2×(C2×D31)⋊C411yescharacteristic
139C4—24no—
140C4—624no—
141C4—1242no—
142C4—1244no—
143C4(C22⋊D31)⋊C412yes—
144C4#1175851612yes—
145C2—21no—
146C2—21no—
147C2#1452092611yescharacteristic
148C2#1452123412yes—
subgroupG/H
centerC22#11758459
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC2×C31×#101C2
socleC22×C31#120
prime radicalC23×C31C2×D4
cosocleC22×C4×C31C23
hypercenterC2×#101D31
hypocenterC31#1886
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
11. #11758521C4semidirect
92. C31#1886semidirect

Maximal subgroups

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

subgroupindex
C2×#117585212
#145215272
#145210592
#145208102
C2×C31×#1012
#188631