Finite Group Databasebeta

← H(3,𝔽4)×D283 #49135380

Subgroups — H(3,𝔽4)×D283 #49135380

Order 36224.

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#31827208C216yesmaximal, complemented
2#31827207C219yesmaximal, complemented
3#124×D283C219yesmaximal, complemented
4#120×D283C216yesmaximal, complemented
5H(3,𝔽4)×C283C211yesmaximal, characteristic, complemented
6C24×D283C2212yescomplemented
7C2×Q8×D283C2213yescomplemented
8C2×D4×D283C2219yes—
9#22583599C2219yescomplemented
10#22583598C2219yescomplemented
11#22583597C2219yescomplemented
12#22583596C22136yescomplemented
13#22583580C22118yescomplemented
14#22583579C2216yescomplemented
15#22583578C22118yescomplemented
16C22⋊C4×D283C22118yescomplemented
17C42×D283C2213yescomplemented
18#124×C283C2219yescomplemented
19#120×C283C2216yescomplemented
20C23×D283—412no—
21C23×D283C2316yes—
22C23×D283C2316yescomplemented
23C2×Dic566C2319yescomplemented
24Q8×D283—46no—
25C2×D1132C2319yes—
26C2×C22⋊D283C23118yes—
27D4×D283—418no—
28C2×C4×D283C2319yes—
29C22⋊Dic283C23118yescomplemented
30(C2×D283)⋊C4C23136yescomplemented
31C4×Dic283C2319yescomplemented
32C24×C283C2312yescomplemented
33C2×Q8×C283C2313yescomplemented
34C2×D4×C283C2319yes—
35C22⋊C4×C283C23118yescomplemented
36C42×C283C2313yescomplemented
37C22×D283—236no—
38C22×D283—418no—
39C22×D283—432no—
40C22×D283C2416yes—
41C22×D283C2411yescharacteristic
42Dic566—49no—
43D1132—49no—
44C22⋊D283—418no—
45C2×Dic283C2419yes—
46C4×D283—218no—
47C23×C283—46no—
48C23×C283C2416yes—
49Q8×C283—43no—
50D4×C283—49no—
51C2×C4×C283C2419yes—
52C22×C283—218no—
53C22×C283—48no—
54C22×C283C2511yescharacteristic
55C2×D283—218no—
56C2×D283—424no—
57C2×D283—424no—
58C2×D283H(5,𝔽2)16yes—
59C4×C283—29no—
60Dic283—29no—
61C2×C283—46no—
62C2×C283C2×H(5,𝔽2)13yes—
63D283—46no—
64D283H(3,𝔽4)14yesdirect product factor
65C283C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
66C2×H(3,𝔽4)—2831nomaximal, Sylow
67H(3,𝔽4)—2839no—
68H(3,𝔽4)—2836no—
69H(3,𝔽4)D28311yescharacteristic, direct product factor
70C2×#124—2839no—
71C2×#120—2836no—
72C25—2832no—
73C22×Q8—2833no—
74C22×D4—2839no—
75#124—2839no—
76#124—2839no—
77#124—28336no—
78#124—2839no—
79#124C2×D28319yescomplemented
80#120—2836no—
81#120—28318no—
82#120—28318no—
83#120C2×D28316yescomplemented
84C2×C22⋊C4—28318no—
85C2×C42—2833no—
86C24—2836no—
87C24—2836no—
88C24—113212no—
89C24C22×D28312yescomplemented
90C2×Q8—2839no—
91C2×Q8—11326no—
92C2×Q8C22×D28313yescomplemented
93C2×D4—28318no—
94C2×D4—2839no—
95C2×D4—113218no—
96C2×D4C22×D28319yes—
97C22×C4—2839no—
98C22⋊C4—28318no—
99C22⋊C4—28336no—
100C22⋊C4C22×D283118yescomplemented
101C42—2839no—
102C42C22×D28313yescomplemented
103C23—46no—
104C23—2831no—
105C23—2836no—
106C23—56636no—
107C23—113218no—
108C23—113232no—
109C23C23×D28316yes—
110Q8—43no—
111Q8—11329no—
112D4—49no—
113D4—11329no—
114D4—113218no—
115C2×C4—2839no—
116C2×C4—56618no—
117C2×C4C23×D28319yes—
118C22—218no—
119C22—48no—
120C22—2836no—
121C22—56618no—
122C22—113224no—
123C22—113224no—
124C22C24×D28311yescharacteristic
125C4—29no—
126C4—5669no—
127C2—46no—
128C2—2834no—
129C2—11326no—
130C2H(5,𝔽2)×D28313yes—
subgroupG/H
center, FrattiniC22C24×D283
commutator, socle, cosocleC22×C283C25
FittingH(3,𝔽4)×C283C2
hypercenterH(3,𝔽4)D283
hypocenterC283C2×H(3,𝔽4)
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ H(3,𝔽4)

Complements

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

NH ≅ G/Ntype
1. #31827208C2semidirect
2. #31827207C2semidirect
3. #124×D283C2semidirect
4. #120×D283C2semidirect
5. H(3,𝔽4)×C283C2semidirect
6. C24×D283C22semidirect
7. C2×Q8×D283C22semidirect
9. #22583599C22semidirect
10. #22583598C22semidirect
11. #22583597C22semidirect
12. #22583596C22semidirect
13. #22583580C22semidirect
14. #22583579C22semidirect
15. #22583578C22semidirect
16. C22⋊C4×D283C22semidirect
17. C42×D283C22semidirect
18. #124×C283C22semidirect
19. #120×C283C22semidirect
22. C23×D283C23semidirect
23. C2×Dic566C23semidirect
29. C22⋊Dic283C23semidirect
30. (C2×D283)⋊C4C23semidirect
31. C4×Dic283C23semidirect
32. C24×C283C23semidirect
33. C2×Q8×C283C23semidirect
35. C22⋊C4×C283C23semidirect
36. C42×C283C23semidirect
64. D283H(3,𝔽4)direct (N × H)
65. C283C2×H(3,𝔽4)semidirect
69. H(3,𝔽4)D283direct (N × H)
79. #124C2×D283semidirect
83. #120C2×D283semidirect
89. C24C22×D283semidirect
92. C2×Q8C22×D283semidirect
100. C22⋊C4C22×D283semidirect
102. C42C22×D283semidirect

Maximal subgroups

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

subgroupindex
#318272082
#318272072
#124×D2832
#120×D2832
H(3,𝔽4)×C2832
C2×H(3,𝔽4)283