Finite Group Databasebeta

← C24×#11929625 #35202153

Subgroups — C24×#11929625 #35202153

Order 20224.

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×#11929625C21120yesmaximal, direct product factor
2C24×D316C213yesmaximal, complemented
3C24×C4×D79C213yesmaximal, complemented
4C24×Q8×C79C211yesmaximal, characteristic, complemented
5C25×D79C2213yes—
6C22×#11929625C2212240yesdirect product factor
7C23×D316C221180yescomplemented
8C24×Dic79C2211yescharacteristic
9C23×C4×D79C221180yescomplemented
10C23×Q8×C79C22160yescomplemented
11C24×C4×C79C2213yes—
12C24×D79—248no—
13C24×D79C23190yes—
14C2×#11929625C2317680yesdirect product factor
15C22×D316C2311680yescomplemented
16C23×Dic79C23130yes—
17C22×C4×D79C2311680yescomplemented
18C25×C79C2311yescharacteristic
19C22×Q8×C79C231560yescomplemented
20C23×C4×C79C23190yes—
21C23×D79—2720no—
22C23×D79C241420yes—
23#11929625C2414096yesdirect product factor
24C2×D316C2412880yescomplemented
25C22×Dic79C241140yes—
26C2×C4×D79C2412880yescomplemented
27C24×C79#41116yescomplemented
28C24×C79C24115yes—
29C2×Q8×C79C241960yescomplemented
30C22×C4×C79C241420yes—
31C23×C79C2×#411120yescomplemented
32C23×C79C25135yes—
33C22×D79—21680no—
34C22×D79C251360yes—
35Q8×C79C251256yescomplemented
36C2×C4×C79C251360yes—
37C2×Dic79C251120yes—
38D316C251768yescomplemented
39C4×D79C251768yescomplemented
40C22×C79C22×#411140yescomplemented
41C22×C79C26115yes—
42C2×D79—2720no—
43C2×D79C26148yes—
44C4×C79C26148yes—
45Dic79C26116yes—
46C24×#41—791nomaximal, Sylow
47C2×C79C23×#41130yescomplemented
48C2×C79C2711yescharacteristic
49D79—248no—
50C23×#41—79120no—
51C24×Q8D7911yescharacteristic, complemented
52C24×D4—793no—
53C25×C4—793no—
54C79C24×#4111yescharacteristic, complemented, Sylow
55C26—793no—
56C22×#41—792240no—
57C23×Q8C2×D79160yescomplemented
58C23×D4—79180no—
59C24×C4—791no—
60C24×C4—79180no—
61C24×C4C2×D7913yes—
62C25—7990no—
63C25—15848no—
64C25C22×D7911yescharacteristic
65C2×#41—797680no—
66C22×Q8C22×D791560yescomplemented
67C22×D4—791680no—
68C23×C4—7930no—
69C23×C4—791680no—
70C23×C4C22×D79190yes—
71C24—79420no—
72C24—158720no—
73C24#11929625116yesdirect product factor
74C24C23×D79115yes—
75#41—794096no—
76C2×Q8C23×D791960yescomplemented
77C2×D4—792880no—
78C22×C4—79140no—
79C22×C4—792880no—
80C22×C4C23×D791420yes—
81C23—79360no—
82C23—1581680no—
83C23C2×#119296251120yesdirect product factor
84C23C24×D79135yes—
85Q8C24×D791256yescomplemented
86D4—79768no—
87C2×C4—79120no—
88C2×C4—79768no—
89C2×C4C24×D791360yes—
90C22—7948no—
91C22—158720no—
92C22C22×#119296251140yesdirect product factor
93C22C25×D79115yes—
94C4—7916no—
95C4C25×D79148yes—
96C2—15848no—
97C2C23×#11929625130yesdirect product factor
98C2C26×D7911yescharacteristic
subgroupG/H
centerC25C22×D79
commutator, cosocleC2×C79C27
FrattiniC2C26×D79
FittingC24×Q8×C79C2
socleC25×C79C23
hypercenterC24×Q8D79
hypocenterC79C24×#41
LCSG ▷ C2×C79 ▷ C79
UCSC1 ◁ C25 ◁ C24×Q8

Complements

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

NH ≅ G/Ntype
1. C23×#11929625C2direct (N × H)
2. C24×D316C2semidirect
3. C24×C4×D79C2semidirect
4. C24×Q8×C79C2semidirect
6. C22×#11929625C22direct (N × H)
7. C23×D316C22semidirect
9. C23×C4×D79C22semidirect
10. C23×Q8×C79C22semidirect
14. C2×#11929625C23direct (N × H)
15. C22×D316C23semidirect
17. C22×C4×D79C23semidirect
19. C22×Q8×C79C23semidirect
23. #11929625C24direct (N × H)
24. C2×D316C24semidirect
26. C2×C4×D79C24semidirect
27. C24×C79#41semidirect
29. C2×Q8×C79C24semidirect
31. C23×C79C2×#41semidirect
35. Q8×C79C25semidirect
38. D316C25semidirect
39. C4×D79C25semidirect
40. C22×C79C22×#41semidirect
47. C2×C79C23×#41semidirect
51. C24×Q8D79semidirect
54. C79C24×#41semidirect
57. C23×Q8C2×D79semidirect
66. C22×Q8C22×D79semidirect
73. C24#11929625direct (N × H)
76. C2×Q8C23×D79semidirect
83. C23C2×#11929625direct (N × H)
85. Q8C24×D79semidirect
92. C22C22×#11929625direct (N × H)
97. C2C23×#11929625direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#119296252
C24×D3162
C24×C4×D792
C24×Q8×C792
C24×#4179