Finite Group Databasebeta

← C3×#575 #5905

Subgroups — C3×#575 #5905

Order 192.

262 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 158 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×C3×#41C212yesmaximal, complemented
2C3×#137C214yesmaximal, complemented
3C3×AGL(1,ℤ/8)C214yesmaximal, complemented
4C3×#135C214yesmaximal, complemented
5C2×C3×M16C211yesmaximal, characteristic, complemented
6#575C311yesmaximal, characteristic, direct product factor, Sylow
7C3×#41—22no—
8C3×#41—22no—
9C3×#41C2214yes—
10C3×#41C2214yescomplemented
11C2×C3×Q8C2212yescomplemented
12C2×C3×D4—22no—
13C2×C3×D4C2212yescomplemented
14C22×C3×C4—22no—
15C22×C3×C4C2211yescharacteristic
16C3×Q16C2214yescomplemented
17C3×SD16C2218yescomplemented
18C3×D8C2214yescomplemented
19C3×M16C2214yescomplemented
20C2×C3×C8C2212yescomplemented
21C2×#41C2×C312yescomplemented
22#137C2×C314yescomplemented
23AGL(1,ℤ/8)C2×C314yescomplemented
24#135C2×C314yescomplemented
25C2×M16C2×C311yescharacteristic, complemented
26C23×C3—22no—
27C23×C3D411yescharacteristic
28C3×Q8—22no—
29C3×Q8C2314yes—
30C3×D4—24no—
31C3×D4—24no—
32C3×D4—22no—
33C3×D4C2314yes—
34C2×C3×C4—22no—
35C2×C3×C4—24no—
36C2×C3×C4—24no—
37C2×C3×C4D411yescharacteristic
38C2×C3×C4D412yes—
39C2×C3×C4C2312yes—
40C2×C3×C4C2311yescharacteristic
41C3×C8C2314yes—
42#41—22no—
43#41—22no—
44#41C22×C314yes—
45#41C22×C314yescomplemented
46C2×Q8C22×C312yescomplemented
47C2×D4—22no—
48C2×D4C22×C312yescomplemented
49C22×C4—22no—
50C22×C4C22×C311yescharacteristic
51Q16C22×C314yescomplemented
52SD16C22×C318yescomplemented
53D8C22×C314yescomplemented
54M16C22×C314yescomplemented
55C2×C8C22×C312yescomplemented
56C22×C3—24no—
57C22×C3—41no—
58C22×C3—44no—
59C22×C3C2×D412yes—
60C22×C3C2×D411yescharacteristic
61C3×C4—24no—
62C3×C4C2×D412yes—
63C3×C4C2×D411yescharacteristic
64C3×C4C2411yescharacteristic
65C23—22no—
66C23C3×D411yescharacteristic
67Q8—22no—
68Q8C23×C314yes—
69D4—24no—
70D4—24no—
71D4—22no—
72D4C23×C314yes—
73C2×C4—22no—
74C2×C4—24no—
75C2×C4—24no—
76C2×C4C3×D412yes—
77C2×C4C3×D411yescharacteristic
78C2×C4C23×C311yescharacteristic
79C2×C4C23×C312yes—
80C8C23×C314yes—
81C2×C3—22no—
82C2×C3—21no—
83C2×C3—44no—
84C2×C3C22×D411yescharacteristic
85C22—24no—
86C22—41no—
87C22—44no—
88C22C2×C3×D412yes—
89C22C2×C3×D411yescharacteristic
90C4—24no—
91C4C2×C3×D411yescharacteristic
92C4C2×C3×D412yes—
93C4C24×C311yescharacteristic
94C3#57511yescharacteristic, direct product factor, Sylow
95C2—22no—
96C2—21no—
97C2—44no—
98C2C22×C3×D411yescharacteristic
subgroupG/H
centerC3×C4C2×D4
commutator, Frattini, cosocleC4C24×C3
socleC2×C3C22×D4
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#41C2semidirect
2. C3×#137C2semidirect
3. C3×AGL(1,ℤ/8)C2semidirect
4. C3×#135C2semidirect
5. C2×C3×M16C2semidirect
6. #575C3direct (N × H)
10. C3×#41C22semidirect
11. C2×C3×Q8C22semidirect
13. C2×C3×D4C22semidirect
16. C3×Q16C22semidirect
17. C3×SD16C22semidirect
18. C3×D8C22semidirect
19. C3×M16C22semidirect
20. C2×C3×C8C22semidirect
21. C2×#41C2×C3semidirect
22. #137C2×C3semidirect
23. AGL(1,ℤ/8)C2×C3semidirect
24. #135C2×C3semidirect
25. C2×M16C2×C3semidirect
45. #41C22×C3semidirect
46. C2×Q8C22×C3semidirect
48. C2×D4C22×C3semidirect
51. Q16C22×C3semidirect
52. SD16C22×C3semidirect
53. D8C22×C3semidirect
54. M16C22×C3semidirect
55. C2×C8C22×C3semidirect
94. C3#575direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#412
C3×#1372
C3×AGL(1,ℤ/8)2
C3×#1352
C2×C3×M162
#5753