Finite Group Databasebeta

← #16844792

Subgroups — #16844792

Order 3968.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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#14521765C211yesmaximal, characteristic, complemented
2#14521241C212yesmaximal, complemented
3#14520798C211yesmaximal, characteristic, complemented
4#14520778C212yesmaximal, complemented
5C31×#492C211yesmaximal, characteristic, complemented
6C2×SD16×C31—22no—
7C31×C4⋊Q8C2211yescharacteristic
8C31×#127C2211yescharacteristic
9#11758524—22no—
10C2×#92479—22no—
11#11758472—22no—
12#11758469—22no—
13C4×D124C2212yes—
14C4×C8×C31C2211yescharacteristic
15#11758420—22no—
16C4⋊(C31⋊C8)C2212yes—
17C2×Q8×C31D412yes—
18C2×D4×C31—22no—
19C2×D4×C31—21no—
20C2×D124—22no—
21C2×D124D412yes—
22C2×C4×D31—22no—
23SD16×C31—44no—
24C2×C8×C31—21no—
25C4⋊C4×C31—22no—
26C42×C31C2311yescharacteristic
27#92479—44no—
28(C2×D31)⋊C4—24no—
29(C2×D31)⋊C4—22no—
30C4⋊Dic31D412yes—
31C4×Dic31—22no—
32C2×C31⋊C8—22no—
33C23×C31—41no—
34C22×D31—22no—
35Q8×C31—42no—
36D4×C31—42no—
37D4×C31—42no—
38D4×C31—42no—
39C2×C4×C31—22no—
40C2×C4×C31C2×D412yes—
41C2×C4×C31C2×D411yescharacteristic
42C2×Dic31—22no—
43D124—22no—
44D124—22no—
45D124—82no—
46C4×D31—42no—
47C4×D31—42no—
48C8×C31—22no—
49C31⋊C8—42no—
50#1624—311nomaximal, Sylow
51C22×C31—82no—
52C22×C31—81no—
53C22×C31#12011yescharacteristic
54C2×D31—42no—
55C2×D31—42no—
56C2×D31—42no—
57C4×C31—21no—
58C4×C31—42no—
59C4×C31#13512yes—
60C4×C31AGL(1,ℤ/8)12yes—
61Dic31—42no—
62#555—311no—
63#492D3111yescharacteristic, complemented
64#459—312no—
65#333—311no—
66D4⋊C8—312no—
67C2×C31—161no—
68C2×C31#44912yes—
69C2×C31#45311yescharacteristic
70D31—82no—
71C2×SD16—22no—
72C2×D8—622no—
73C4⋊Q8C2×D3111yescharacteristic
74#127C2×D3111yescharacteristic
75#124—622no—
76#121—622no—
77C4×D4—312no—
78#117—622no—
79C4⋊C8—312no—
80#102—622no—
81C4×C8C2×D3111yescharacteristic
82C31#162411yescharacteristic, complemented, Sylow
83C2×Q8C22⋊D3112yes—
84C2×D4—22no—
85C2×D4—21no—
86C2×D4—312no—
87C2×D4—622no—
88C22×C4—622no—
89SD16—44no—
90D8—1244no—
91C2×C8—21no—
92C2×C8—622no—
93C4⋊C4—22no—
94C4⋊C4—312no—
95C22⋊C4—624no—
96C22⋊C4—622no—
97C42—622no—
98C42C22×D3111yescharacteristic
99C23—41no—
100C23—622no—
101Q8—42no—
102D4—42no—
103D4—42no—
104D4—42no—
105D4—622no—
106D4—622no—
107D4—2482no—
108C2×C4—22no—
109C2×C4—622no—
110C2×C4—1242no—
111C2×C4—1242no—
112C2×C4D4×D3112yes—
113C2×C4C2×C22⋊D3111yescharacteristic
114C8—22no—
115C8—1242no—
116C22—82no—
117C22—81no—
118C22—1242no—
119C22—1242no—
120C22—1242no—
121C22#1175851411yescharacteristic
122C4—21no—
123C4—42no—
124C4—1242no—
125C4#1175849112yes—
126C4#1175849312yes—
127C2—161no—
128C2—2482no—
129C2#1452119312yes—
130C2#1452121611yescharacteristic
subgroupG/H
centerC22#11758514
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
FittingC31×#492C2
socleC22×C31#120
hypercenter#492D31
hypocenterC31#1624
LCSG ▷ C42×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #14521765C2semidirect
2. #14521241C2semidirect
3. #14520798C2semidirect
4. #14520778C2semidirect
5. C31×#492C2semidirect
63. #492D31semidirect
82. C31#1624semidirect

Maximal subgroups

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

subgroupindex
#145217652
#145212412
#145207982
#145207782
C31×#4922
#162431