Finite Group Databasebeta

← H(3,𝔽4)×D139 #31820523

Subgroups — H(3,𝔽4)×D139 #31820523

Order 17792.

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#22581696C216yesmaximal, complemented
2#22581695C219yesmaximal, complemented
3#124×D139C219yesmaximal, complemented
4#120×D139C216yesmaximal, complemented
5H(3,𝔽4)×C139C211yesmaximal, characteristic, complemented
6C24×D139C2212yescomplemented
7C2×Q8×D139C2213yescomplemented
8C2×D4×D139C2219yes—
9#17984831C2219yescomplemented
10#17984830C2219yescomplemented
11#17984829C2219yescomplemented
12#17984828C22136yescomplemented
13#17984812C22118yescomplemented
14#17984811C2216yescomplemented
15#17984810C22118yescomplemented
16C22⋊C4×D139C22118yescomplemented
17C42×D139C2213yescomplemented
18#124×C139C2219yescomplemented
19#120×C139C2216yescomplemented
20C23×D139—412no—
21C23×D139C2316yes—
22C23×D139C2316yescomplemented
23C2×Dic278C2319yescomplemented
24Q8×D139—46no—
25C2×D556C2319yes—
26C2×C22⋊D139C23118yes—
27D4×D139—418no—
28C2×C4×D139C2319yes—
29C22⋊Dic139C23118yescomplemented
30(C2×D139)⋊C4C23136yescomplemented
31C4×Dic139C2319yescomplemented
32C24×C139C2312yescomplemented
33C2×Q8×C139C2313yescomplemented
34C2×D4×C139C2319yes—
35C22⋊C4×C139C23118yescomplemented
36C42×C139C2313yescomplemented
37C22×D139—236no—
38C22×D139—418no—
39C22×D139—432no—
40C22×D139C2416yes—
41C22×D139C2411yescharacteristic
42Dic278—49no—
43D556—49no—
44C22⋊D139—418no—
45C2×Dic139C2419yes—
46C4×D139—218no—
47C23×C139—46no—
48C23×C139C2416yes—
49Q8×C139—43no—
50D4×C139—49no—
51C2×C4×C139C2419yes—
52C22×C139—218no—
53C22×C139—48no—
54C22×C139C2511yescharacteristic
55C2×D139—218no—
56C2×D139—424no—
57C2×D139—424no—
58C2×D139H(5,𝔽2)16yes—
59C4×C139—29no—
60Dic139—29no—
61C2×C139—46no—
62C2×C139C2×H(5,𝔽2)13yes—
63D139—46no—
64D139H(3,𝔽4)14yesdirect product factor
65C139C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
66C2×H(3,𝔽4)—1391nomaximal, Sylow
67H(3,𝔽4)—1399no—
68H(3,𝔽4)—1396no—
69H(3,𝔽4)D13911yescharacteristic, direct product factor
70C2×#124—1399no—
71C2×#120—1396no—
72C25—1392no—
73C22×Q8—1393no—
74C22×D4—1399no—
75#124—1399no—
76#124—1399no—
77#124—13936no—
78#124—1399no—
79#124C2×D13919yescomplemented
80#120—1396no—
81#120—13918no—
82#120—13918no—
83#120C2×D13916yescomplemented
84C2×C22⋊C4—13918no—
85C2×C42—1393no—
86C24—55612no—
87C24—1396no—
88C24—1396no—
89C24C22×D13912yescomplemented
90C2×Q8—5566no—
91C2×Q8—1399no—
92C2×Q8C22×D13913yescomplemented
93C2×D4—55618no—
94C2×D4—13918no—
95C2×D4—1399no—
96C2×D4C22×D13919yes—
97C22×C4—1399no—
98C22⋊C4—13918no—
99C22⋊C4—13936no—
100C22⋊C4C22×D139118yescomplemented
101C42—1399no—
102C42C22×D13913yescomplemented
103C23—46no—
104C23—27836no—
105C23—55618no—
106C23—55632no—
107C23—1396no—
108C23—1391no—
109C23C23×D13916yes—
110Q8—43no—
111Q8—5569no—
112D4—49no—
113D4—5569no—
114D4—55618no—
115C2×C4—27818no—
116C2×C4—1399no—
117C2×C4C23×D13919yes—
118C22—218no—
119C22—48no—
120C22—27818no—
121C22—55624no—
122C22—55624no—
123C22—1396no—
124C22C24×D13911yescharacteristic
125C4—29no—
126C4—2789no—
127C2—46no—
128C2—5566no—
129C2—1394no—
130C2H(5,𝔽2)×D13913yes—
subgroupG/H
center, FrattiniC22C24×D139
commutator, socle, cosocleC22×C139C25
FittingH(3,𝔽4)×C139C2
hypercenterH(3,𝔽4)D139
hypocenterC139C2×H(3,𝔽4)
LCSG ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ H(3,𝔽4)

Complements

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

NH ≅ G/Ntype
1. #22581696C2semidirect
2. #22581695C2semidirect
3. #124×D139C2semidirect
4. #120×D139C2semidirect
5. H(3,𝔽4)×C139C2semidirect
6. C24×D139C22semidirect
7. C2×Q8×D139C22semidirect
9. #17984831C22semidirect
10. #17984830C22semidirect
11. #17984829C22semidirect
12. #17984828C22semidirect
13. #17984812C22semidirect
14. #17984811C22semidirect
15. #17984810C22semidirect
16. C22⋊C4×D139C22semidirect
17. C42×D139C22semidirect
18. #124×C139C22semidirect
19. #120×C139C22semidirect
22. C23×D139C23semidirect
23. C2×Dic278C23semidirect
29. C22⋊Dic139C23semidirect
30. (C2×D139)⋊C4C23semidirect
31. C4×Dic139C23semidirect
32. C24×C139C23semidirect
33. C2×Q8×C139C23semidirect
35. C22⋊C4×C139C23semidirect
36. C42×C139C23semidirect
64. D139H(3,𝔽4)direct (N × H)
65. C139C2×H(3,𝔽4)semidirect
69. H(3,𝔽4)D139direct (N × H)
79. #124C2×D139semidirect
83. #120C2×D139semidirect
89. C24C22×D139semidirect
92. C2×Q8C22×D139semidirect
100. C22⋊C4C22×D139semidirect
102. C42C22×D139semidirect

Maximal subgroups

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

subgroupindex
#225816962
#225816952
#124×D1392
#120×D1392
H(3,𝔽4)×C1392
C2×H(3,𝔽4)139