Finite Group Databasebeta

← H(3,𝔽4)×D83 #24921582

Subgroups — H(3,𝔽4)×D83 #24921582

Order 10624.

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#19128444C216yesmaximal, complemented
2#19128443C219yesmaximal, complemented
3#124×D83C219yesmaximal, complemented
4#120×D83C216yesmaximal, complemented
5H(3,𝔽4)×C83C211yesmaximal, characteristic, complemented
6C24×D83C2212yescomplemented
7C2×Q8×D83C2213yescomplemented
8C2×D4×D83C2219yes—
9#14581781C2219yescomplemented
10#14581780C2219yescomplemented
11#14581779C2219yescomplemented
12#14581778C22136yescomplemented
13#14581762C22118yescomplemented
14#14581761C2216yescomplemented
15#14581760C22118yescomplemented
16C22⋊C4×D83C22118yescomplemented
17C42×D83C2213yescomplemented
18#124×C83C2219yescomplemented
19#120×C83C2216yescomplemented
20C23×D83—412no—
21C23×D83C2316yes—
22C23×D83C2316yescomplemented
23C2×Dic166C2319yescomplemented
24Q8×D83—46no—
25C2×D332C2319yes—
26C2×C22⋊D83C23118yes—
27D4×D83—418no—
28C2×C4×D83C2319yes—
29C22⋊Dic83C23118yescomplemented
30(C2×D83)⋊C4C23136yescomplemented
31C4×Dic83C2319yescomplemented
32C24×C83C2312yescomplemented
33C2×Q8×C83C2313yescomplemented
34C2×D4×C83C2319yes—
35C22⋊C4×C83C23118yescomplemented
36C42×C83C2313yescomplemented
37C23×C83—46no—
38C23×C83C2416yes—
39C22×D83—236no—
40C22×D83—418no—
41C22×D83—432no—
42C22×D83C2416yes—
43C22×D83C2411yescharacteristic
44Q8×C83—43no—
45D4×C83—49no—
46C2×C4×C83C2419yes—
47C22⋊D83—418no—
48C2×Dic83C2419yes—
49D332—49no—
50C4×D83—218no—
51Dic166—49no—
52C22×C83—218no—
53C22×C83—48no—
54C22×C83C2511yescharacteristic
55C2×D83—218no—
56C2×D83—424no—
57C2×D83—424no—
58C2×D83H(5,𝔽2)16yes—
59C4×C83—29no—
60Dic83—29no—
61C2×C83—46no—
62C2×C83C2×H(5,𝔽2)13yes—
63D83—46no—
64D83H(3,𝔽4)14yesdirect product factor
65C2×H(3,𝔽4)—831nomaximal, Sylow
66C83C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
67H(3,𝔽4)—839no—
68H(3,𝔽4)—836no—
69H(3,𝔽4)D8311yescharacteristic, direct product factor
70C2×#124—839no—
71C2×#120—836no—
72C25—832no—
73C22×Q8—833no—
74C22×D4—839no—
75#124—839no—
76#124—839no—
77#124—8336no—
78#124—839no—
79#124C2×D8319yescomplemented
80#120—836no—
81#120—8318no—
82#120—8318no—
83#120C2×D8316yescomplemented
84C2×C22⋊C4—8318no—
85C2×C42—833no—
86C24—33212no—
87C24—836no—
88C24—836no—
89C24C22×D8312yescomplemented
90C2×Q8—3326no—
91C2×Q8—839no—
92C2×Q8C22×D8313yescomplemented
93C2×D4—33218no—
94C2×D4—8318no—
95C2×D4—839no—
96C2×D4C22×D8319yes—
97C22×C4—839no—
98C22⋊C4—8318no—
99C22⋊C4—8336no—
100C22⋊C4C22×D83118yescomplemented
101C42—839no—
102C42C22×D8313yescomplemented
103C23—46no—
104C23—33218no—
105C23—33232no—
106C23—831no—
107C23—836no—
108C23—16636no—
109C23C23×D8316yes—
110Q8—43no—
111Q8—3329no—
112D4—49no—
113D4—3329no—
114D4—33218no—
115C2×C4—839no—
116C2×C4—16618no—
117C2×C4C23×D8319yes—
118C22—218no—
119C22—48no—
120C22—33224no—
121C22—33224no—
122C22—836no—
123C22—16618no—
124C22C24×D8311yescharacteristic
125C4—29no—
126C4—1669no—
127C2—46no—
128C2—3326no—
129C2—834no—
130C2H(5,𝔽2)×D8313yes—
subgroupG/H
center, FrattiniC22C24×D83
commutator, socle, cosocleC22×C83C25
FittingH(3,𝔽4)×C83C2
hypercenterH(3,𝔽4)D83
hypocenterC83C2×H(3,𝔽4)
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ H(3,𝔽4)

Complements

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

NH ≅ G/Ntype
1. #19128444C2semidirect
2. #19128443C2semidirect
3. #124×D83C2semidirect
4. #120×D83C2semidirect
5. H(3,𝔽4)×C83C2semidirect
6. C24×D83C22semidirect
7. C2×Q8×D83C22semidirect
9. #14581781C22semidirect
10. #14581780C22semidirect
11. #14581779C22semidirect
12. #14581778C22semidirect
13. #14581762C22semidirect
14. #14581761C22semidirect
15. #14581760C22semidirect
16. C22⋊C4×D83C22semidirect
17. C42×D83C22semidirect
18. #124×C83C22semidirect
19. #120×C83C22semidirect
22. C23×D83C23semidirect
23. C2×Dic166C23semidirect
29. C22⋊Dic83C23semidirect
30. (C2×D83)⋊C4C23semidirect
31. C4×Dic83C23semidirect
32. C24×C83C23semidirect
33. C2×Q8×C83C23semidirect
35. C22⋊C4×C83C23semidirect
36. C42×C83C23semidirect
64. D83H(3,𝔽4)direct (N × H)
66. C83C2×H(3,𝔽4)semidirect
69. H(3,𝔽4)D83direct (N × H)
79. #124C2×D83semidirect
83. #120C2×D83semidirect
89. C24C22×D83semidirect
92. C2×Q8C22×D83semidirect
100. C22⋊C4C22×D83semidirect
102. C42C22×D83semidirect

Maximal subgroups

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

subgroupindex
#191284442
#191284432
#124×D832
#120×D832
H(3,𝔽4)×C832
C2×H(3,𝔽4)83