Finite Group Databasebeta

← #5748

Subgroups — #5748

Order 192.

262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 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×#235C212yesmaximal, complemented
2C2×C3×M16C211yesmaximal, characteristic, complemented
3#909C214yesmaximal, complemented
4#908C214yesmaximal, complemented
5#904C214yesmaximal, complemented
6#575—31nomaximal, Sylow
7C22×C3×C4C2211yescharacteristic
8C2×#67—22no—
9#235—22no—
10#235—22no—
11#235C2214yes—
12#235C2214yescomplemented
13C2×D12C2212yescomplemented
14C2×C4×D3—22no—
15C2×Dic6C2212yescomplemented
16C3×M16C2214yescomplemented
17C2×C3×C8C2212yescomplemented
18Dic12C2214yescomplemented
19D24C2214yescomplemented
20#204C2218yescomplemented
21C2×#41—32no—
22#137—34no—
23AGL(1,ℤ/8)—34no—
24#135—34no—
25C2×M16D311yescharacteristic, complemented
26C23×C3D411yescharacteristic
27C22×D3—22no—
28C2×C3×C4D412yes—
29C2×C3×C4D411yescharacteristic
30C2×C3×C4C2311yescharacteristic
31C2×C3×C4C2312yes—
32#67—24no—
33#67—24no—
34C2×Dic3—22no—
35D12—22no—
36D12C2314yes—
37C4×D3—24no—
38C4×D3—24no—
39Dic6—22no—
40Dic6C2314yes—
41C3×C8C2314yes—
42#41—34no—
43#41—34no—
44#41—62no—
45#41—62no—
46C2×Q8—32no—
47C2×D4—32no—
48C2×D4—62no—
49C22×C4—62no—
50C22×C4C2×D311yescharacteristic
51Q16—34no—
52SD16—38no—
53D8—34no—
54M16C2×D314yescomplemented
55C2×C8C2×D312yescomplemented
56C22×C3—41no—
57C22×C3C2×D412yes—
58C22×C3C2×D411yescharacteristic
59C2×D3—24no—
60C2×D3—44no—
61C3×C4C2×D412yes—
62C3×C4C2×D411yescharacteristic
63C3×C4C2411yescharacteristic
64Dic3—24no—
65C23—62no—
66C23D1211yescharacteristic
67Q8—34no—
68Q8—62no—
69D4—34no—
70D4—64no—
71D4—64no—
72D4—62no—
73C2×C4—62no—
74C2×C4—64no—
75C2×C4—64no—
76C2×C4D1211yescharacteristic
77C2×C4D1212yes—
78C2×C4C22×D312yes—
79C2×C4C22×D311yescharacteristic
80C8C22×D314yes—
81C2×C3—22no—
82C2×C3—21no—
83C2×C3C22×D411yescharacteristic
84D3—44no—
85C22—41no—
86C22—64no—
87C22—124no—
88C22C2×D1212yes—
89C22C2×D1211yescharacteristic
90C4—64no—
91C4C2×D1212yes—
92C4C2×D1211yescharacteristic
93C4C23×D311yescharacteristic
94C3#57511yescharacteristic, complemented, Sylow
95C2—22no—
96C2—21no—
97C2—124no—
98C2C22×D1211yescharacteristic
subgroupG/H
centerC4C2×D12
commutator, cosocleC3×C4C24
FrattiniC4C23×D3
FittingC2×C3×M16C2
socleC2×C3C22×D4
hypercenterC2×M16D3
hypocenterC3#575
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×#235C2semidirect
2. C2×C3×M16C2semidirect
3. #909C2semidirect
4. #908C2semidirect
5. #904C2semidirect
12. #235C22semidirect
13. C2×D12C22semidirect
15. C2×Dic6C22semidirect
16. C3×M16C22semidirect
17. C2×C3×C8C22semidirect
18. Dic12C22semidirect
19. D24C22semidirect
20. #204C22semidirect
25. C2×M16D3semidirect
54. M16C2×D3semidirect
55. C2×C8C2×D3semidirect
94. C3#575semidirect

Maximal subgroups

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

subgroupindex
C2×#2352
C2×C3×M162
#9092
#9082
#9042
#5753