Finite Group Databasebeta

← D19×H(3,𝔽4) #14577754

Subgroups — D19×H(3,𝔽4) #14577754

Order 2432.

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#11927287C216yesmaximal, complemented
2#11927286C219yesmaximal, complemented
3#124×D19C219yesmaximal, complemented
4#120×D19C216yesmaximal, complemented
5C19×H(3,𝔽4)C211yesmaximal, characteristic, complemented
6C24×D19C2212yescomplemented
7C2×Q8×D19C2213yescomplemented
8C2×D4×D19C2219yes—
9C19×#124C2219yescomplemented
10C19×#120C2216yescomplemented
11#10597399C2216yescomplemented
12#10597393C2219yescomplemented
13#10597383C22118yescomplemented
14#10597382C2219yescomplemented
15#10597331C22136yescomplemented
16#10597328C22118yescomplemented
17C22⋊C4×D19C22118yescomplemented
18#10597321C2219yescomplemented
19C42×D19C2213yescomplemented
20C24×C19C2312yescomplemented
21C23×D19—412no—
22C23×D19C2316yes—
23C23×D19C2316yescomplemented
24C2×Q8×C19C2313yescomplemented
25C2×D4×C19C2319yes—
26C2×C22⋊D19C23118yes—
27Q8×D19—46no—
28D4×D19—418no—
29C2×D76C2319yes—
30C2×C4×D19C2319yes—
31C2×Dic38C2319yescomplemented
32C22⋊C4×C19C23118yescomplemented
33C42×C19C2313yescomplemented
34C22⋊Dic19C23118yescomplemented
35(C2×D19)⋊C4C23136yescomplemented
36C4×Dic19C2319yescomplemented
37C23×C19—46no—
38C23×C19C2416yes—
39C22×D19—236no—
40C22×D19—418no—
41C22×D19—432no—
42C22×D19C2416yes—
43C22×D19C2411yescharacteristic
44Q8×C19—43no—
45D4×C19—49no—
46C2×C4×C19C2419yes—
47C22⋊D19—418no—
48C2×Dic19C2419yes—
49D76—49no—
50C4×D19—218no—
51Dic38—49no—
52C2×H(3,𝔽4)—191nomaximal, Sylow
53C22×C19—218no—
54C22×C19—48no—
55C22×C19C2511yescharacteristic
56C2×D19—218no—
57C2×D19—424no—
58C2×D19—424no—
59C2×D19H(5,𝔽2)16yes—
60C4×C19—29no—
61Dic19—29no—
62H(3,𝔽4)—199no—
63H(3,𝔽4)—196no—
64H(3,𝔽4)D1911yescharacteristic, direct product factor
65C2×#124—199no—
66C2×#120—196no—
67C2×C19—46no—
68C2×C19C2×H(5,𝔽2)13yes—
69D19—46no—
70D19H(3,𝔽4)14yesdirect product factor
71C25—192no—
72C22×Q8—193no—
73C22×D4—199no—
74#124—199no—
75#124—199no—
76#124—1936no—
77#124—199no—
78#124C2×D1919yescomplemented
79#120—196no—
80#120—1918no—
81#120—1918no—
82#120C2×D1916yescomplemented
83C2×C22⋊C4—1918no—
84C2×C42—193no—
85C19C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
86C24—196no—
87C24—196no—
88C24—7612no—
89C24C22×D1912yescomplemented
90C2×Q8—199no—
91C2×Q8—766no—
92C2×Q8C22×D1913yescomplemented
93C2×D4—1918no—
94C2×D4—199no—
95C2×D4—7618no—
96C2×D4C22×D1919yes—
97C22×C4—199no—
98C22⋊C4—1918no—
99C22⋊C4—1936no—
100C22⋊C4C22×D19118yescomplemented
101C42—199no—
102C42C22×D1913yescomplemented
103C23—46no—
104C23—191no—
105C23—196no—
106C23—3836no—
107C23—7618no—
108C23—7632no—
109C23C23×D1916yes—
110Q8—43no—
111Q8—769no—
112D4—49no—
113D4—769no—
114D4—7618no—
115C2×C4—199no—
116C2×C4—3818no—
117C2×C4C23×D1919yes—
118C22—218no—
119C22—48no—
120C22—196no—
121C22—3818no—
122C22—7624no—
123C22—7624no—
124C22C24×D1911yescharacteristic
125C4—29no—
126C4—389no—
127C2—46no—
128C2—194no—
129C2—766no—
130C2H(5,𝔽2)×D1913yes—
subgroupG/H
center, FrattiniC22C24×D19
commutator, socle, cosocleC22×C19C25
FittingC19×H(3,𝔽4)C2
hypercenterH(3,𝔽4)D19
hypocenterC19C2×H(3,𝔽4)
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ H(3,𝔽4)

Complements

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

NH ≅ G/Ntype
1. #11927287C2semidirect
2. #11927286C2semidirect
3. #124×D19C2semidirect
4. #120×D19C2semidirect
5. C19×H(3,𝔽4)C2semidirect
6. C24×D19C22semidirect
7. C2×Q8×D19C22semidirect
9. C19×#124C22semidirect
10. C19×#120C22semidirect
11. #10597399C22semidirect
12. #10597393C22semidirect
13. #10597383C22semidirect
14. #10597382C22semidirect
15. #10597331C22semidirect
16. #10597328C22semidirect
17. C22⋊C4×D19C22semidirect
18. #10597321C22semidirect
19. C42×D19C22semidirect
20. C24×C19C23semidirect
23. C23×D19C23semidirect
24. C2×Q8×C19C23semidirect
31. C2×Dic38C23semidirect
32. C22⋊C4×C19C23semidirect
33. C42×C19C23semidirect
34. C22⋊Dic19C23semidirect
35. (C2×D19)⋊C4C23semidirect
36. C4×Dic19C23semidirect
64. H(3,𝔽4)D19direct (N × H)
70. D19H(3,𝔽4)direct (N × H)
78. #124C2×D19semidirect
82. #120C2×D19semidirect
85. C19C2×H(3,𝔽4)semidirect
89. C24C22×D19semidirect
92. C2×Q8C22×D19semidirect
100. C22⋊C4C22×D19semidirect
102. C42C22×D19semidirect

Maximal subgroups

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

subgroupindex
#119272872
#119272862
#124×D192
#120×D192
C19×H(3,𝔽4)2
C2×H(3,𝔽4)19