Finite Group Databasebeta

← H(3,𝔽4)×D151 #34083229

Subgroups — H(3,𝔽4)×D151 #34083229

Order 19328.

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#23752955C216yesmaximal, complemented
2#23752954C219yesmaximal, complemented
3#124×D151C219yesmaximal, complemented
4#120×D151C216yesmaximal, complemented
5H(3,𝔽4)×C151C211yesmaximal, characteristic, complemented
6C24×D151C2212yescomplemented
7C2×Q8×D151C2213yescomplemented
8C2×D4×D151C2219yes—
9#18012728C2219yescomplemented
10#18012727C2219yescomplemented
11#18012726C2219yescomplemented
12#18012725C22136yescomplemented
13#18012709C22118yescomplemented
14#18012708C2216yescomplemented
15#18012707C22118yescomplemented
16C22⋊C4×D151C22118yescomplemented
17C42×D151C2213yescomplemented
18#124×C151C2219yescomplemented
19#120×C151C2216yescomplemented
20C23×D151—412no—
21C23×D151C2316yes—
22C23×D151C2316yescomplemented
23C2×Dic302C2319yescomplemented
24Q8×D151—46no—
25C2×D604C2319yes—
26C2×C22⋊D151C23118yes—
27D4×D151—418no—
28C2×C4×D151C2319yes—
29C22⋊Dic151C23118yescomplemented
30(C2×D151)⋊C4C23136yescomplemented
31C4×Dic151C2319yescomplemented
32C24×C151C2312yescomplemented
33C2×Q8×C151C2313yescomplemented
34C2×D4×C151C2319yes—
35C22⋊C4×C151C23118yescomplemented
36C42×C151C2313yescomplemented
37C22×D151—236no—
38C22×D151—418no—
39C22×D151—432no—
40C22×D151C2416yes—
41C22×D151C2411yescharacteristic
42Dic302—49no—
43D604—49no—
44C22⋊D151—418no—
45C2×Dic151C2419yes—
46C4×D151—218no—
47C23×C151—46no—
48C23×C151C2416yes—
49Q8×C151—43no—
50D4×C151—49no—
51C2×C4×C151C2419yes—
52C22×C151—218no—
53C22×C151—48no—
54C22×C151C2511yescharacteristic
55C2×D151—218no—
56C2×D151—424no—
57C2×D151—424no—
58C2×D151H(5,𝔽2)16yes—
59C4×C151—29no—
60Dic151—29no—
61C2×C151—46no—
62C2×C151C2×H(5,𝔽2)13yes—
63D151—46no—
64D151H(3,𝔽4)14yesdirect product factor
65C151C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
66C2×H(3,𝔽4)—1511nomaximal, Sylow
67H(3,𝔽4)—1519no—
68H(3,𝔽4)—1516no—
69H(3,𝔽4)D15111yescharacteristic, direct product factor
70C2×#124—1519no—
71C2×#120—1516no—
72C25—1512no—
73C22×Q8—1513no—
74C22×D4—1519no—
75#124—1519no—
76#124—1519no—
77#124—15136no—
78#124—1519no—
79#124C2×D15119yescomplemented
80#120—1516no—
81#120—15118no—
82#120—15118no—
83#120C2×D15116yescomplemented
84C2×C22⋊C4—15118no—
85C2×C42—1513no—
86C24—60412no—
87C24—1516no—
88C24—1516no—
89C24C22×D15112yescomplemented
90C2×Q8—6046no—
91C2×Q8—1519no—
92C2×Q8C22×D15113yescomplemented
93C2×D4—60418no—
94C2×D4—15118no—
95C2×D4—1519no—
96C2×D4C22×D15119yes—
97C22×C4—1519no—
98C22⋊C4—15118no—
99C22⋊C4—15136no—
100C22⋊C4C22×D151118yescomplemented
101C42—1519no—
102C42C22×D15113yescomplemented
103C23—46no—
104C23—30236no—
105C23—60418no—
106C23—60432no—
107C23—1516no—
108C23—1511no—
109C23C23×D15116yes—
110Q8—43no—
111Q8—6049no—
112D4—49no—
113D4—6049no—
114D4—60418no—
115C2×C4—30218no—
116C2×C4—1519no—
117C2×C4C23×D15119yes—
118C22—218no—
119C22—48no—
120C22—30218no—
121C22—60424no—
122C22—60424no—
123C22—1516no—
124C22C24×D15111yescharacteristic
125C4—29no—
126C4—3029no—
127C2—46no—
128C2—6046no—
129C2—1514no—
130C2H(5,𝔽2)×D15113yes—
subgroupG/H
center, FrattiniC22C24×D151
commutator, socle, cosocleC22×C151C25
FittingH(3,𝔽4)×C151C2
hypercenterH(3,𝔽4)D151
hypocenterC151C2×H(3,𝔽4)
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ H(3,𝔽4)

Complements

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

NH ≅ G/Ntype
1. #23752955C2semidirect
2. #23752954C2semidirect
3. #124×D151C2semidirect
4. #120×D151C2semidirect
5. H(3,𝔽4)×C151C2semidirect
6. C24×D151C22semidirect
7. C2×Q8×D151C22semidirect
9. #18012728C22semidirect
10. #18012727C22semidirect
11. #18012726C22semidirect
12. #18012725C22semidirect
13. #18012709C22semidirect
14. #18012708C22semidirect
15. #18012707C22semidirect
16. C22⋊C4×D151C22semidirect
17. C42×D151C22semidirect
18. #124×C151C22semidirect
19. #120×C151C22semidirect
22. C23×D151C23semidirect
23. C2×Dic302C23semidirect
29. C22⋊Dic151C23semidirect
30. (C2×D151)⋊C4C23semidirect
31. C4×Dic151C23semidirect
32. C24×C151C23semidirect
33. C2×Q8×C151C23semidirect
35. C22⋊C4×C151C23semidirect
36. C42×C151C23semidirect
64. D151H(3,𝔽4)direct (N × H)
65. C151C2×H(3,𝔽4)semidirect
69. H(3,𝔽4)D151direct (N × H)
79. #124C2×D151semidirect
83. #120C2×D151semidirect
89. C24C22×D151semidirect
92. C2×Q8C22×D151semidirect
100. C22⋊C4C22×D151semidirect
102. C42C22×D151semidirect

Maximal subgroups

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

subgroupindex
#237529552
#237529542
#124×D1512
#120×D1512
H(3,𝔽4)×C1512
C2×H(3,𝔽4)151