Finite Group Databasebeta

← #120×D383 #37588835

Subgroups — #120×D383 #37588835

Order 24512.

662 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 131 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
1C24×D383C211yesmaximal, characteristic, complemented
2C2×D4×D383C213yesmaximal, complemented
3#27133811C213yesmaximal, complemented
4#27133810C211yesmaximal, characteristic, complemented
5#27133809C213yesmaximal, complemented
6C22⋊C4×D383C213yesmaximal, complemented
7#120×C383C211yesmaximal, characteristic, complemented
8C23×D383—212no—
9C23×D383C2213yes—
10C23×D383C2213yescomplemented
11C23×D383C2211yescharacteristic, complemented
12C2×D1532C2213yescomplemented
13C2×C22⋊D383C2213yescomplemented
14C2×C22⋊D383C2213yescomplemented
15D4×D383—212no—
16C2×C4×D383C2213yescomplemented
17C22⋊Dic383C2213yescomplemented
18(C2×D383)⋊C4C2216yescomplemented
19C24×C383C2211yescharacteristic, complemented
20C2×D4×C383C2213yescomplemented
21C22⋊C4×C383C2213yescomplemented
22C22×D383—232no—
23C22×D383—26no—
24C22×D383—212no—
25C22×D383—212no—
26C22×D383—26no—
27C22×D383D4112yescomplemented
28C22×D383C2313yes—
29C22×D383C2311yescharacteristic
30C22×D383C2311yescharacteristic, complemented
31D1532—26no—
32C22⋊D383—26no—
33C22⋊D383—26no—
34C2×Dic383C2313yescomplemented
35C4×D383—26no—
36C23×C383—26no—
37C23×C383C2313yes—
38C23×C383C2311yescharacteristic, complemented
39D4×C383—26no—
40C2×C4×C383C2313yescomplemented
41C22×C383—28no—
42C22×C383—26no—
43C22×C383—23no—
44C22×C383C2×D416yescomplemented
45C22×C383C2411yescharacteristic
46C2×D383—224no—
47C2×D383—26no—
48C2×D383—224no—
49C2×D383—23no—
50C2×D383—44no—
51C2×D383C2×D416yes—
52C2×D383C2×D416yescomplemented
53C4×C383—23no—
54Dic383—23no—
55C2×C383—26no—
56C2×C383—41no—
57C2×C383C22×D413yes—
58D383—26no—
59D383—41no—
60D383#12014yesdirect product factor
61C383C2×#12011yescharacteristic, complemented, Sylow
62C2×#120—3831nomaximal, Sylow
63C25—3831no—
64C22×D4—3833no—
65#120—3831no—
66#120—3833no—
67#120—3833no—
68#120D38311yescharacteristic, direct product factor
69C2×C22⋊C4—3833no—
70C24—3833no—
71C24—3833no—
72C24—3831no—
73C24—76612no—
74C24C2×D38311yescharacteristic, complemented
75C2×D4—3833no—
76C2×D4—3833no—
77C2×D4—3833no—
78C2×D4—76612no—
79C2×D4C2×D38313yescomplemented
80C22×C4—3833no—
81C22⋊C4—3833no—
82C22⋊C4—3836no—
83C22⋊C4C2×D38313yescomplemented
84C23—26no—
85C23—3831no—
86C23—38312no—
87C23—3833no—
88C23—3831no—
89C23—7666no—
90C23—76612no—
91C23—76612no—
92C23—76632no—
93C23—7666no—
94C23C22×D38313yes—
95C23C22×D38311yescharacteristic, complemented
96D4—26no—
97D4—7666no—
98D4—7666no—
99D4—7666no—
100C2×C4—3833no—
101C2×C4—7666no—
102C2×C4C22×D38313yescomplemented
103C22—28no—
104C22—26no—
105C22—23no—
106C22—3836no—
107C22—3836no—
108C22—15324no—
109C22—76624no—
110C22—76624no—
111C22—7663no—
112C22—7666no—
113C22D4×D38316yescomplemented
114C22C23×D38311yescharacteristic
115C4—23no—
116C4—7663no—
117C2—26no—
118C2—41no—
119C2—3834no—
120C2—15321no—
121C2—7666no—
122C2C2×D4×D38313yes—
subgroupG/H
center, FrattiniC22C23×D383
commutator, socle, cosocleC22×C383C24
Fitting#120×C383C2
hypercenter#120D383
hypocenterC383C2×#120
LCSG ▷ C22×C383 ▷ C383
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C24×D383C2semidirect
2. C2×D4×D383C2semidirect
3. #27133811C2semidirect
4. #27133810C2semidirect
5. #27133809C2semidirect
6. C22⋊C4×D383C2semidirect
7. #120×C383C2semidirect
10. C23×D383C22semidirect
11. C23×D383C22semidirect
12. C2×D1532C22semidirect
13. C2×C22⋊D383C22semidirect
14. C2×C22⋊D383C22semidirect
16. C2×C4×D383C22semidirect
17. C22⋊Dic383C22semidirect
18. (C2×D383)⋊C4C22semidirect
19. C24×C383C22semidirect
20. C2×D4×C383C22semidirect
21. C22⋊C4×C383C22semidirect
27. C22×D383D4semidirect
30. C22×D383C23semidirect
34. C2×Dic383C23semidirect
38. C23×C383C23semidirect
40. C2×C4×C383C23semidirect
44. C22×C383C2×D4semidirect
52. C2×D383C2×D4semidirect
60. D383#120direct (N × H)
61. C383C2×#120semidirect
68. #120D383direct (N × H)
74. C24C2×D383semidirect
79. C2×D4C2×D383semidirect
83. C22⋊C4C2×D383semidirect
95. C23C22×D383semidirect
102. C2×C4C22×D383semidirect
113. C22D4×D383semidirect

Maximal subgroups

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

subgroupindex
C24×D3832
C2×D4×D3832
#271338112
#271338102
#271338092
C22⋊C4×D3832
#120×C3832
C2×#120383