Finite Group Databasebeta

← #120×D359 #37526927

Subgroups — #120×D359 #37526927

Order 22976.

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×D359C211yesmaximal, characteristic, complemented
2C2×D4×D359C213yesmaximal, complemented
3#26039985C213yesmaximal, complemented
4#26039984C211yesmaximal, characteristic, complemented
5#26039983C213yesmaximal, complemented
6C22⋊C4×D359C213yesmaximal, complemented
7#120×C359C211yesmaximal, characteristic, complemented
8C23×D359—212no—
9C23×D359C2213yes—
10C23×D359C2213yescomplemented
11C23×D359C2211yescharacteristic, complemented
12C2×D1436C2213yescomplemented
13C2×C22⋊D359C2213yescomplemented
14C2×C22⋊D359C2213yescomplemented
15D4×D359—212no—
16C2×C4×D359C2213yescomplemented
17C22⋊Dic359C2213yescomplemented
18(C2×D359)⋊C4C2216yescomplemented
19C24×C359C2211yescharacteristic, complemented
20C2×D4×C359C2213yescomplemented
21C22⋊C4×C359C2213yescomplemented
22C22×D359—232no—
23C22×D359—26no—
24C22×D359—212no—
25C22×D359—212no—
26C22×D359—26no—
27C22×D359D4112yescomplemented
28C22×D359C2313yes—
29C22×D359C2311yescharacteristic
30C22×D359C2311yescharacteristic, complemented
31D1436—26no—
32C22⋊D359—26no—
33C22⋊D359—26no—
34C2×Dic359C2313yescomplemented
35C4×D359—26no—
36C23×C359—26no—
37C23×C359C2313yes—
38C23×C359C2311yescharacteristic, complemented
39D4×C359—26no—
40C2×C4×C359C2313yescomplemented
41C22×C359—28no—
42C22×C359—26no—
43C22×C359—23no—
44C22×C359C2×D416yescomplemented
45C22×C359C2411yescharacteristic
46C2×D359—224no—
47C2×D359—26no—
48C2×D359—224no—
49C2×D359—23no—
50C2×D359—44no—
51C2×D359C2×D416yes—
52C2×D359C2×D416yescomplemented
53C4×C359—23no—
54Dic359—23no—
55C2×C359—26no—
56C2×C359—41no—
57C2×C359C22×D413yes—
58D359—26no—
59D359—41no—
60D359#12014yesdirect product factor
61C359C2×#12011yescharacteristic, complemented, Sylow
62C2×#120—3591nomaximal, Sylow
63C25—3591no—
64C22×D4—3593no—
65#120—3591no—
66#120—3593no—
67#120—3593no—
68#120D35911yescharacteristic, direct product factor
69C2×C22⋊C4—3593no—
70C24—3593no—
71C24—3593no—
72C24—3591no—
73C24—71812no—
74C24C2×D35911yescharacteristic, complemented
75C2×D4—3593no—
76C2×D4—3593no—
77C2×D4—3593no—
78C2×D4—71812no—
79C2×D4C2×D35913yescomplemented
80C22×C4—3593no—
81C22⋊C4—3593no—
82C22⋊C4—3596no—
83C22⋊C4C2×D35913yescomplemented
84C23—26no—
85C23—3591no—
86C23—35912no—
87C23—3593no—
88C23—3591no—
89C23—7186no—
90C23—71812no—
91C23—71812no—
92C23—71832no—
93C23—7186no—
94C23C22×D35913yes—
95C23C22×D35911yescharacteristic, complemented
96D4—26no—
97D4—7186no—
98D4—7186no—
99D4—7186no—
100C2×C4—3593no—
101C2×C4—7186no—
102C2×C4C22×D35913yescomplemented
103C22—28no—
104C22—26no—
105C22—23no—
106C22—3596no—
107C22—3596no—
108C22—14364no—
109C22—71824no—
110C22—71824no—
111C22—7183no—
112C22—7186no—
113C22D4×D35916yescomplemented
114C22C23×D35911yescharacteristic
115C4—23no—
116C4—7183no—
117C2—26no—
118C2—41no—
119C2—3594no—
120C2—14361no—
121C2—7186no—
122C2C2×D4×D35913yes—
subgroupG/H
center, FrattiniC22C23×D359
commutator, socle, cosocleC22×C359C24
Fitting#120×C359C2
hypercenter#120D359
hypocenterC359C2×#120
LCSG ▷ C22×C359 ▷ C359
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C24×D359C2semidirect
2. C2×D4×D359C2semidirect
3. #26039985C2semidirect
4. #26039984C2semidirect
5. #26039983C2semidirect
6. C22⋊C4×D359C2semidirect
7. #120×C359C2semidirect
10. C23×D359C22semidirect
11. C23×D359C22semidirect
12. C2×D1436C22semidirect
13. C2×C22⋊D359C22semidirect
14. C2×C22⋊D359C22semidirect
16. C2×C4×D359C22semidirect
17. C22⋊Dic359C22semidirect
18. (C2×D359)⋊C4C22semidirect
19. C24×C359C22semidirect
20. C2×D4×C359C22semidirect
21. C22⋊C4×C359C22semidirect
27. C22×D359D4semidirect
30. C22×D359C23semidirect
34. C2×Dic359C23semidirect
38. C23×C359C23semidirect
40. C2×C4×C359C23semidirect
44. C22×C359C2×D4semidirect
52. C2×D359C2×D4semidirect
60. D359#120direct (N × H)
61. C359C2×#120semidirect
68. #120D359direct (N × H)
74. C24C2×D359semidirect
79. C2×D4C2×D359semidirect
83. C22⋊C4C2×D359semidirect
95. C23C22×D359semidirect
102. C2×C4C22×D359semidirect
113. C22D4×D359semidirect

Maximal subgroups

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

subgroupindex
C24×D3592
C2×D4×D3592
#260399852
#260399842
#260399832
C22⋊C4×D3592
#120×C3592
C2×#120359