Finite Group Databasebeta

← C24×#10621898 #26010480

Subgroups — C24×#10621898 #26010480

Order 11008.

65470 conjugacy classes of subgroups; only the 32651 normal subgroups are shown.

normal subgroups only

This group has 65470 conjugacy classes of subgroups — too many to draw. Only its 32651 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
1C23×#10621898C21120yesmaximal, direct product factor
2C24×Dic86C211yesmaximal, characteristic, complemented
3C24×D172C211yesmaximal, characteristic, complemented
4C24×C22⋊D43C212yesmaximal, complemented
5C24×C4×D43C212yesmaximal, complemented
6C25×C4×C43C211yesmaximal, characteristic, complemented
7C25×D43C2212yes—
8C22×#10621898C2212240yesdirect product factor
9C23×Dic86C22160yescomplemented
10C23×D172C22160yescomplemented
11C23×C22⋊D43C221120yescomplemented
12C24×Dic43C2212yes—
13C23×C4×D43C221120yescomplemented
14C26×C43C2211yescharacteristic
15C24×C4×C43C2211yescharacteristic
16C24×C4×C43C2211yescharacteristic
17C24×C4×C43C22160yescomplemented
18C24×D43—232no—
19C24×D43C23160yes—
20C2×#10621898C2317680yesdirect product factor
21C22×Dic86C231560yescomplemented
22C22×D172C231560yescomplemented
23C22×C22⋊D43C2311120yescomplemented
24C23×Dic43C23160yes—
25C22×C4×D43C2311120yescomplemented
26C25×C43—216no—
27C25×C43C23130yes—
28C25×C43C2311yescharacteristic
29C23×C4×C43C23130yes—
30C23×C4×C43C23130yes—
31C23×C4×C43C231560yescomplemented
32C24×C43—2240no—
33C24×C43#41116yescomplemented
34C24×C43C241140yes—
35C24×C43C24115yes—
36C23×D43—2480no—
37C23×D43C241280yes—
38C22×C4×C43C241140yes—
39C22×C4×C43C241140yes—
40C22×C4×C43C241960yescomplemented
41C2×C22⋊D43C2411920yescomplemented
42C22×Dic43C241280yes—
43#10621898C2414096yesdirect product factor
44C2×D172C241960yescomplemented
45C2×C4×D43C2411920yescomplemented
46C2×Dic86C241960yescomplemented
47C23×C43—2560no—
48C23×C43C2×#411120yescomplemented
49C23×C43C251120yes—
50C23×C43C25135yes—
51C22×D43—21120no—
52C22×D43C251240yes—
53C2×C4×C43C251120yes—
54C2×C4×C43C251120yes—
55C2×C4×C43C251256yescomplemented
56C22⋊D43C251512yescomplemented
57C2×Dic43C251240yes—
58D172C251256yescomplemented
59C4×D43C251512yescomplemented
60Dic86C251256yescomplemented
61C24×#41—431nomaximal, Sylow
62C22×C43—2240no—
63C22×C43C22×#411140yescomplemented
64C22×C43C26116yes—
65C22×C43C26115yes—
66C2×D43—2480no—
67C2×D43C26132yes—
68C4×C43C26116yes—
69C4×C43C26116yes—
70Dic43C26132yes—
71C23×#41—43120no—
72C24×Q8—431no—
73C24×D4—432no—
74C24×D4—431no—
75C25×C4—432no—
76C25×C4D4311yescharacteristic, complemented
77C2×C43—216no—
78C2×C43C23×#41130yescomplemented
79C2×C43C2711yescharacteristic
80D43—232no—
81C26—432no—
82C26C2×D4311yescharacteristic
83C22×#41—432240no—
84C23×Q8—4360no—
85C23×D4—43120no—
86C23×D4—4360no—
87C24×C4—432no—
88C24×C4—43120no—
89C24×C4C2×D4311yescharacteristic
90C24×C4C2×D4311yescharacteristic
91C24×C4C2×D43160yescomplemented
92C43C24×#4111yescharacteristic, complemented, Sylow
93C25—216no—
94C25—4360no—
95C25—8632no—
96C25C22×D43130yes—
97C25C22×D4311yescharacteristic
98C2×#41—437680no—
99C22×Q8—43560no—
100C22×D4—431120no—
101C22×D4—43560no—
102C23×C4—4360no—
103C23×C4—431120no—
104C23×C4C22×D43130yes—
105C23×C4C22×D43130yes—
106C23×C4C22×D431560yescomplemented
107C24—2240no—
108C24—43280no—
109C24—86480no—
110C24#10621898116yesdirect product factor
111C24C23×D431140yes—
112C24C23×D43115yes—
113#41—434096no—
114C2×Q8—43960no—
115C2×D4—431920no—
116C2×D4—43960no—
117C22×C4—43280no—
118C22×C4—431920no—
119C22×C4C23×D431140yes—
120C22×C4C23×D431140yes—
121C22×C4C23×D431960yescomplemented
122C23—2560no—
123C23—43240no—
124C23—861120no—
125C23C2×#106218981120yesdirect product factor
126C23C24×D431120yes—
127C23C24×D43135yes—
128Q8—43256no—
129D4—43512no—
130D4—43256no—
131C2×C4—43240no—
132C2×C4—43512no—
133C2×C4C24×D431120yes—
134C2×C4C24×D431120yes—
135C2×C4C24×D431256yescomplemented
136C22—2240no—
137C22—4332no—
138C22—86480no—
139C22C22×#106218981140yesdirect product factor
140C22C25×D43116yes—
141C22C25×D43115yes—
142C4—4332no—
143C4C25×D43116yes—
144C4C25×D43116yes—
145C2—216no—
146C2—8632no—
147C2C23×#10621898130yesdirect product factor
148C2C26×D4311yescharacteristic
subgroupG/H
centerC24×C4C2×D43
commutator, cosocleC2×C43C27
FrattiniC2C26×D43
FittingC25×C4×C43C2
socleC25×C43C23
hypercenterC25×C4D43
hypocenterC43C24×#41
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C24×C4 ◁ C25×C4

Complements

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

NH ≅ G/Ntype
1. C23×#10621898C2direct (N × H)
2. C24×Dic86C2semidirect
3. C24×D172C2semidirect
4. C24×C22⋊D43C2semidirect
5. C24×C4×D43C2semidirect
6. C25×C4×C43C2semidirect
8. C22×#10621898C22direct (N × H)
9. C23×Dic86C22semidirect
10. C23×D172C22semidirect
11. C23×C22⋊D43C22semidirect
13. C23×C4×D43C22semidirect
17. C24×C4×C43C22semidirect
20. C2×#10621898C23direct (N × H)
21. C22×Dic86C23semidirect
22. C22×D172C23semidirect
23. C22×C22⋊D43C23semidirect
25. C22×C4×D43C23semidirect
31. C23×C4×C43C23semidirect
33. C24×C43#41semidirect
40. C22×C4×C43C24semidirect
41. C2×C22⋊D43C24semidirect
43. #10621898C24direct (N × H)
44. C2×D172C24semidirect
45. C2×C4×D43C24semidirect
46. C2×Dic86C24semidirect
48. C23×C43C2×#41semidirect
55. C2×C4×C43C25semidirect
56. C22⋊D43C25semidirect
58. D172C25semidirect
59. C4×D43C25semidirect
60. Dic86C25semidirect
63. C22×C43C22×#41semidirect
76. C25×C4D43semidirect
78. C2×C43C23×#41semidirect
91. C24×C4C2×D43semidirect
92. C43C24×#41semidirect
106. C23×C4C22×D43semidirect
110. C24#10621898direct (N × H)
121. C22×C4C23×D43semidirect
125. C23C2×#10621898direct (N × H)
135. C2×C4C24×D43semidirect
139. C22C22×#10621898direct (N × H)
147. C2C23×#10621898direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#106218982
C24×Dic862
C24×D1722
C24×C22⋊D432
C24×C4×D432
C25×C4×C432
C24×#4143