Finite Group Databasebeta

← H(3,𝔽4)×D149 #34058810

Subgroups — H(3,𝔽4)×D149 #34058810

Order 19072.

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#23750368C216yesmaximal, complemented
2#23750367C219yesmaximal, complemented
3#124×D149C219yesmaximal, complemented
4#120×D149C216yesmaximal, complemented
5H(3,𝔽4)×C149C211yesmaximal, characteristic, complemented
6C24×D149C2212yescomplemented
7C2×Q8×D149C2213yescomplemented
8C2×D4×D149C2219yes—
9#18011900C2219yescomplemented
10#18011899C2219yescomplemented
11#18011898C2219yescomplemented
12#18011897C22136yescomplemented
13#18011881C22118yescomplemented
14#18011880C2216yescomplemented
15#18011879C22118yescomplemented
16C22⋊C4×D149C22118yescomplemented
17C42×D149C2213yescomplemented
18#124×C149C2219yescomplemented
19#120×C149C2216yescomplemented
20C23×D149—412no—
21C23×D149C2316yes—
22C23×D149C2316yescomplemented
23C2×Dic298C2319yescomplemented
24Q8×D149—46no—
25C2×D596C2319yes—
26C2×C22⋊D149C23118yes—
27D4×D149—418no—
28C2×C4×D149C2319yes—
29C22⋊Dic149C23118yescomplemented
30#14558713C23136yescomplemented
31C4×Dic149C2319yescomplemented
32C24×C149C2312yescomplemented
33C2×Q8×C149C2313yescomplemented
34C2×D4×C149C2319yes—
35C22⋊C4×C149C23118yescomplemented
36C42×C149C2313yescomplemented
37C22×D149—236no—
38C22×D149—418no—
39C22×D149—432no—
40C22×D149C2416yes—
41C22×D149C2411yescharacteristic
42Dic298—49no—
43D596—49no—
44C22⋊D149—418no—
45C2×Dic149C2419yes—
46C4×D149—218no—
47C23×C149—46no—
48C23×C149C2416yes—
49Q8×C149—43no—
50D4×C149—49no—
51C2×C4×C149C2419yes—
52C22×C149—218no—
53C22×C149—48no—
54C22×C149C2511yescharacteristic
55C2×D149—218no—
56C2×D149—424no—
57C2×D149—424no—
58C2×D149H(5,𝔽2)16yes—
59C4×C149—29no—
60Dic149—29no—
61C2×C149—46no—
62C2×C149C2×H(5,𝔽2)13yes—
63D149—46no—
64D149H(3,𝔽4)14yesdirect product factor
65C149C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
66C2×H(3,𝔽4)—1491nomaximal, Sylow
67H(3,𝔽4)—1499no—
68H(3,𝔽4)—1496no—
69H(3,𝔽4)D14911yescharacteristic, direct product factor
70C2×#124—1499no—
71C2×#120—1496no—
72C25—1492no—
73C22×Q8—1493no—
74C22×D4—1499no—
75#124—1499no—
76#124—1499no—
77#124—14936no—
78#124—1499no—
79#124C2×D14919yescomplemented
80#120—1496no—
81#120—14918no—
82#120—14918no—
83#120C2×D14916yescomplemented
84C2×C22⋊C4—14918no—
85C2×C42—1493no—
86C24—59612no—
87C24—1496no—
88C24—1496no—
89C24C22×D14912yescomplemented
90C2×Q8—5966no—
91C2×Q8—1499no—
92C2×Q8C22×D14913yescomplemented
93C2×D4—59618no—
94C2×D4—14918no—
95C2×D4—1499no—
96C2×D4C22×D14919yes—
97C22×C4—1499no—
98C22⋊C4—14918no—
99C22⋊C4—14936no—
100C22⋊C4C22×D149118yescomplemented
101C42—1499no—
102C42C22×D14913yescomplemented
103C23—46no—
104C23—29836no—
105C23—59618no—
106C23—59632no—
107C23—1496no—
108C23—1491no—
109C23C23×D14916yes—
110Q8—43no—
111Q8—5969no—
112D4—49no—
113D4—5969no—
114D4—59618no—
115C2×C4—29818no—
116C2×C4—1499no—
117C2×C4C23×D14919yes—
118C22—218no—
119C22—48no—
120C22—29818no—
121C22—59624no—
122C22—59624no—
123C22—1496no—
124C22C24×D14911yescharacteristic
125C4—29no—
126C4—2989no—
127C2—46no—
128C2—5966no—
129C2—1494no—
130C2H(5,𝔽2)×D14913yes—
subgroupG/H
center, FrattiniC22C24×D149
commutator, socle, cosocleC22×C149C25
FittingH(3,𝔽4)×C149C2
hypercenterH(3,𝔽4)D149
hypocenterC149C2×H(3,𝔽4)
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ H(3,𝔽4)

Complements

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

NH ≅ G/Ntype
1. #23750368C2semidirect
2. #23750367C2semidirect
3. #124×D149C2semidirect
4. #120×D149C2semidirect
5. H(3,𝔽4)×C149C2semidirect
6. C24×D149C22semidirect
7. C2×Q8×D149C22semidirect
9. #18011900C22semidirect
10. #18011899C22semidirect
11. #18011898C22semidirect
12. #18011897C22semidirect
13. #18011881C22semidirect
14. #18011880C22semidirect
15. #18011879C22semidirect
16. C22⋊C4×D149C22semidirect
17. C42×D149C22semidirect
18. #124×C149C22semidirect
19. #120×C149C22semidirect
22. C23×D149C23semidirect
23. C2×Dic298C23semidirect
29. C22⋊Dic149C23semidirect
30. #14558713C23semidirect
31. C4×Dic149C23semidirect
32. C24×C149C23semidirect
33. C2×Q8×C149C23semidirect
35. C22⋊C4×C149C23semidirect
36. C42×C149C23semidirect
64. D149H(3,𝔽4)direct (N × H)
65. C149C2×H(3,𝔽4)semidirect
69. H(3,𝔽4)D149direct (N × H)
79. #124C2×D149semidirect
83. #120C2×D149semidirect
89. C24C22×D149semidirect
92. C2×Q8C22×D149semidirect
100. C22⋊C4C22×D149semidirect
102. C42C22×D149semidirect

Maximal subgroups

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

subgroupindex
#237503682
#237503672
#124×D1492
#120×D1492
H(3,𝔽4)×C1492
C2×H(3,𝔽4)149