Finite Group Databasebeta

← C3×#3415 #85279

Subgroups — C3×#3415 #85279

Order 384.

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

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 180 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
1C3×#576C212yesmaximal, complemented
2C3×#509C216yesmaximal, complemented
3C3×#508C213yesmaximal, complemented
4C2×C3×D16C213yesmaximal, complemented
5C3×#504C211yesmaximal, characteristic, complemented
6#3415C311yesmaximal, characteristic, direct product factor, Sylow
7C3×H(5,𝔽2)—22no—
8C3×AGL(1,ℤ/8)—26no—
9C3×#135C2216yescomplemented
10C2×C3×D8C2216yescomplemented
11C3×#131C2211yescharacteristic
12C3×Q32C2211yescharacteristic, complemented
13C3×SD32C2216yescomplemented
14C3×D16C2213yescomplemented
15C3×D16C2216yescomplemented
16C3×M32C2213yescomplemented
17C2×C3×C16C2213yescomplemented
18#576C2×C312yescomplemented
19#509C2×C316yescomplemented
20#508C2×C313yescomplemented
21C2×D16C2×C313yescomplemented
22#504C2×C311yescharacteristic, complemented
23C3×#41—26no—
24C3×#41—42no—
25C3×#41D411yescharacteristic
26C2×C3×D4—26no—
27C2×C3×D4—46no—
28C3×Q16C2312yes—
29C3×SD16—26no—
30C3×D8—26no—
31C3×D8C2316yes—
32C3×M16D413yes—
33C2×C3×C8C2313yes—
34C3×C16C2311yescharacteristic
35C3×C16C2313yes—
36H(5,𝔽2)—22no—
37AGL(1,ℤ/8)—26no—
38#135C22×C316yescomplemented
39C2×D8C22×C316yescomplemented
40#131C22×C311yescharacteristic
41Q32C22×C311yescharacteristic, complemented
42SD32C22×C316yescomplemented
43D16C22×C313yescomplemented
44D16C22×C316yescomplemented
45M32C22×C313yescomplemented
46C2×C16C22×C313yescomplemented
47C23×C3—46no—
48C3×Q8—22no—
49C3×Q8D811yescharacteristic
50C3×D4—26no—
51C3×D4—46no—
52C3×D4—46no—
53C3×D4D813yes—
54C2×C3×C4—46no—
55C2×C3×C4C2×D413yes—
56C3×C8C2×D413yes—
57C3×C8C2411yescharacteristic
58#41—26no—
59#41—42no—
60#41C3×D411yescharacteristic
61C2×D4—26no—
62C2×D4—46no—
63Q16C23×C312yes—
64SD16—26no—
65D8—26no—
66D8C23×C316yes—
67M16C3×D413yes—
68C2×C8C23×C313yes—
69C16C23×C311yescharacteristic
70C16C23×C313yes—
71C22×C3—46no—
72C22×C3—166no—
73C22×C3C2×D813yes—
74C3×C4—42no—
75C3×C4C2×D813yes—
76C3×C4C22×D411yescharacteristic
77C23—46no—
78Q8—22no—
79Q8C3×D811yescharacteristic
80D4—26no—
81D4—46no—
82D4—46no—
83D4C3×D813yes—
84C2×C4—46no—
85C2×C4C2×C3×D413yes—
86C8C2×C3×D413yes—
87C8C24×C311yescharacteristic
88C2×C3—23no—
89C2×C3—86no—
90C2×C3C22×D811yescharacteristic
91C22—46no—
92C22—166no—
93C22C2×C3×D813yes—
94C4—42no—
95C4C2×C3×D813yes—
96C4C22×C3×D411yescharacteristic
97C3#341511yescharacteristic, direct product factor, Sylow
98C2—23no—
99C2—86no—
100C2C22×C3×D811yescharacteristic
subgroupG/H
center, socleC2×C3C22×D8
commutator, Frattini, cosocleC8C24×C3
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C3 ◁ C3×#41 ◁ C3×#131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#576C2semidirect
2. C3×#509C2semidirect
3. C3×#508C2semidirect
4. C2×C3×D16C2semidirect
5. C3×#504C2semidirect
6. #3415C3direct (N × H)
9. C3×#135C22semidirect
10. C2×C3×D8C22semidirect
12. C3×Q32C22semidirect
13. C3×SD32C22semidirect
14. C3×D16C22semidirect
15. C3×D16C22semidirect
16. C3×M32C22semidirect
17. C2×C3×C16C22semidirect
18. #576C2×C3semidirect
19. #509C2×C3semidirect
20. #508C2×C3semidirect
21. C2×D16C2×C3semidirect
22. #504C2×C3semidirect
38. #135C22×C3semidirect
39. C2×D8C22×C3semidirect
41. Q32C22×C3semidirect
42. SD32C22×C3semidirect
43. D16C22×C3semidirect
44. D16C22×C3semidirect
45. M32C22×C3semidirect
46. C2×C16C22×C3semidirect
97. C3#3415direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#5762
C3×#5092
C3×#5082
C2×C3×D162
C3×#5042
#34153