Finite Group Databasebeta

← H(3,𝔽4)×D103 #27209263

Subgroups — H(3,𝔽4)×D103 #27209263

Order 13184.

1408 conjugacy classes of subgroups; only the 459 normal subgroups are shown.

normal subgroups only

This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 459 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
1#20268534C216yesmaximal, complemented
2#20268533C219yesmaximal, complemented
3#124×D103C219yesmaximal, complemented
4#120×D103C216yesmaximal, complemented
5H(3,𝔽4)×C103C211yesmaximal, characteristic, complemented
6C24×D103C2212yescomplemented
7C2×Q8×D103C2213yescomplemented
8C2×D4×D103C2219yes—
9#15693010C2219yescomplemented
10#15693009C2219yescomplemented
11#15693008C2219yescomplemented
12#15693007C22136yescomplemented
13#15692991C22118yescomplemented
14#15692990C2216yescomplemented
15#15692989C22118yescomplemented
16C22⋊C4×D103C22118yescomplemented
17C42×D103C2213yescomplemented
18#124×C103C2219yescomplemented
19#120×C103C2216yescomplemented
20C23×D103—412no—
21C23×D103C2316yes—
22C23×D103C2316yescomplemented
23C2×Dic206C2319yescomplemented
24Q8×D103—46no—
25C2×D412C2319yes—
26C2×C22⋊D103C23118yes—
27D4×D103—418no—
28C2×C4×D103C2319yes—
29C22⋊Dic103C23118yescomplemented
30(C2×D103)⋊C4C23136yescomplemented
31C4×Dic103C2319yescomplemented
32C24×C103C2312yescomplemented
33C2×Q8×C103C2313yescomplemented
34C2×D4×C103C2319yes—
35C22⋊C4×C103C23118yescomplemented
36C42×C103C2313yescomplemented
37C23×C103—46no—
38C23×C103C2416yes—
39C22×D103—236no—
40C22×D103—418no—
41C22×D103—432no—
42C22×D103C2416yes—
43C22×D103C2411yescharacteristic
44Q8×C103—43no—
45D4×C103—49no—
46C2×C4×C103C2419yes—
47C22⋊D103—418no—
48C2×Dic103C2419yes—
49D412—49no—
50C4×D103—218no—
51Dic206—49no—
52C22×C103—218no—
53C22×C103—48no—
54C22×C103C2511yescharacteristic
55C2×D103—218no—
56C2×D103—424no—
57C2×D103—424no—
58C2×D103H(5,𝔽2)16yes—
59C4×C103—29no—
60Dic103—29no—
61C2×C103—46no—
62C2×C103C2×H(5,𝔽2)13yes—
63D103—46no—
64D103H(3,𝔽4)14yesdirect product factor
65C2×H(3,𝔽4)—1031nomaximal, Sylow
66C103C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
67H(3,𝔽4)—1039no—
68H(3,𝔽4)—1036no—
69H(3,𝔽4)D10311yescharacteristic, direct product factor
70C2×#124—1039no—
71C2×#120—1036no—
72C25—1032no—
73C22×Q8—1033no—
74C22×D4—1039no—
75#124—1039no—
76#124—1039no—
77#124—10336no—
78#124—1039no—
79#124C2×D10319yescomplemented
80#120—1036no—
81#120—10318no—
82#120—10318no—
83#120C2×D10316yescomplemented
84C2×C22⋊C4—10318no—
85C2×C42—1033no—
86C24—1036no—
87C24—1036no—
88C24—41212no—
89C24C22×D10312yescomplemented
90C2×Q8—1039no—
91C2×Q8—4126no—
92C2×Q8C22×D10313yescomplemented
93C2×D4—10318no—
94C2×D4—1039no—
95C2×D4—41218no—
96C2×D4C22×D10319yes—
97C22×C4—1039no—
98C22⋊C4—10318no—
99C22⋊C4—10336no—
100C22⋊C4C22×D103118yescomplemented
101C42—1039no—
102C42C22×D10313yescomplemented
103C23—46no—
104C23—1031no—
105C23—1036no—
106C23—41218no—
107C23—41232no—
108C23—20636no—
109C23C23×D10316yes—
110Q8—43no—
111Q8—4129no—
112D4—49no—
113D4—4129no—
114D4—41218no—
115C2×C4—1039no—
116C2×C4—20618no—
117C2×C4C23×D10319yes—
118C22—218no—
119C22—48no—
120C22—1036no—
121C22—41224no—
122C22—41224no—
123C22—20618no—
124C22C24×D10311yescharacteristic
125C4—29no—
126C4—2069no—
127C2—46no—
128C2—1034no—
129C2—4126no—
130C2H(5,𝔽2)×D10313yes—
subgroupG/H
center, FrattiniC22C24×D103
commutator, socle, cosocleC22×C103C25
FittingH(3,𝔽4)×C103C2
hypercenterH(3,𝔽4)D103
hypocenterC103C2×H(3,𝔽4)
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ H(3,𝔽4)

Complements

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

NH ≅ G/Ntype
1. #20268534C2semidirect
2. #20268533C2semidirect
3. #124×D103C2semidirect
4. #120×D103C2semidirect
5. H(3,𝔽4)×C103C2semidirect
6. C24×D103C22semidirect
7. C2×Q8×D103C22semidirect
9. #15693010C22semidirect
10. #15693009C22semidirect
11. #15693008C22semidirect
12. #15693007C22semidirect
13. #15692991C22semidirect
14. #15692990C22semidirect
15. #15692989C22semidirect
16. C22⋊C4×D103C22semidirect
17. C42×D103C22semidirect
18. #124×C103C22semidirect
19. #120×C103C22semidirect
22. C23×D103C23semidirect
23. C2×Dic206C23semidirect
29. C22⋊Dic103C23semidirect
30. (C2×D103)⋊C4C23semidirect
31. C4×Dic103C23semidirect
32. C24×C103C23semidirect
33. C2×Q8×C103C23semidirect
35. C22⋊C4×C103C23semidirect
36. C42×C103C23semidirect
64. D103H(3,𝔽4)direct (N × H)
66. C103C2×H(3,𝔽4)semidirect
69. H(3,𝔽4)D103direct (N × H)
79. #124C2×D103semidirect
83. #120C2×D103semidirect
89. C24C22×D103semidirect
92. C2×Q8C22×D103semidirect
100. C22⋊C4C22×D103semidirect
102. C42C22×D103semidirect

Maximal subgroups

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

subgroupindex
#202685342
#202685332
#124×D1032
#120×D1032
H(3,𝔽4)×C1032
C2×H(3,𝔽4)103