Finite Group Databasebeta

← H(3,𝔽4)×D37 #18008715

Subgroups — H(3,𝔽4)×D37 #18008715

Order 4736.

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#14558276C216yesmaximal, complemented
2#14558275C219yesmaximal, complemented
3#124×D37C219yesmaximal, complemented
4#120×D37C216yesmaximal, complemented
5C37×H(3,𝔽4)C211yesmaximal, characteristic, complemented
6C24×D37C2212yescomplemented
7C2×Q8×D37C2213yescomplemented
8C2×D4×D37C2219yes—
9#11924525C2219yescomplemented
10#11924524C2219yescomplemented
11#11924523C2219yescomplemented
12#11924522C22136yescomplemented
13#11924506C22118yescomplemented
14#11924505C2216yescomplemented
15#11924504C22118yescomplemented
16C22⋊C4×D37C22118yescomplemented
17C42×D37C2213yescomplemented
18#124×C37C2219yescomplemented
19#120×C37C2216yescomplemented
20C24×C37C2312yescomplemented
21C23×D37—412no—
22C23×D37C2316yes—
23C23×D37C2316yescomplemented
24C2×Q8×C37C2313yescomplemented
25C2×D4×C37C2319yes—
26C2×C22⋊D37C23118yes—
27Q8×D37—46no—
28D4×D37—418no—
29C2×D148C2319yes—
30C2×C4×D37C2319yes—
31C2×Dic74C2319yescomplemented
32C22⋊C4×C37C23118yescomplemented
33C42×C37C2313yescomplemented
34C22⋊Dic37C23118yescomplemented
35#10596938C23136yescomplemented
36C4×Dic37C2319yescomplemented
37C23×C37—46no—
38C23×C37C2416yes—
39C22×D37—236no—
40C22×D37—418no—
41C22×D37—432no—
42C22×D37C2416yes—
43C22×D37C2411yescharacteristic
44Q8×C37—43no—
45D4×C37—49no—
46C2×C4×C37C2419yes—
47C22⋊D37—418no—
48C2×Dic37C2419yes—
49D148—49no—
50C4×D37—218no—
51Dic74—49no—
52C22×C37—218no—
53C22×C37—48no—
54C22×C37C2511yescharacteristic
55C2×D37—218no—
56C2×D37—424no—
57C2×D37—424no—
58C2×D37H(5,𝔽2)16yes—
59C4×C37—29no—
60Dic37—29no—
61C2×H(3,𝔽4)—371nomaximal, Sylow
62C2×C37—46no—
63C2×C37C2×H(5,𝔽2)13yes—
64D37—46no—
65D37H(3,𝔽4)14yesdirect product factor
66H(3,𝔽4)—379no—
67H(3,𝔽4)—376no—
68H(3,𝔽4)D3711yescharacteristic, direct product factor
69C2×#124—379no—
70C2×#120—376no—
71C37C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
72C25—372no—
73C22×Q8—373no—
74C22×D4—379no—
75#124—379no—
76#124—379no—
77#124—3736no—
78#124—379no—
79#124C2×D3719yescomplemented
80#120—376no—
81#120—3718no—
82#120—3718no—
83#120C2×D3716yescomplemented
84C2×C22⋊C4—3718no—
85C2×C42—373no—
86C24—376no—
87C24—376no—
88C24—14812no—
89C24C22×D3712yescomplemented
90C2×Q8—379no—
91C2×Q8—1486no—
92C2×Q8C22×D3713yescomplemented
93C2×D4—3718no—
94C2×D4—379no—
95C2×D4—14818no—
96C2×D4C22×D3719yes—
97C22×C4—379no—
98C22⋊C4—3718no—
99C22⋊C4—3736no—
100C22⋊C4C22×D37118yescomplemented
101C42—379no—
102C42C22×D3713yescomplemented
103C23—46no—
104C23—371no—
105C23—376no—
106C23—7436no—
107C23—14818no—
108C23—14832no—
109C23C23×D3716yes—
110Q8—43no—
111Q8—1489no—
112D4—49no—
113D4—1489no—
114D4—14818no—
115C2×C4—379no—
116C2×C4—7418no—
117C2×C4C23×D3719yes—
118C22—218no—
119C22—48no—
120C22—376no—
121C22—7418no—
122C22—14824no—
123C22—14824no—
124C22C24×D3711yescharacteristic
125C4—29no—
126C4—749no—
127C2—46no—
128C2—374no—
129C2—1486no—
130C2H(5,𝔽2)×D3713yes—
subgroupG/H
center, FrattiniC22C24×D37
commutator, socle, cosocleC22×C37C25
FittingC37×H(3,𝔽4)C2
hypercenterH(3,𝔽4)D37
hypocenterC37C2×H(3,𝔽4)
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ H(3,𝔽4)

Complements

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

NH ≅ G/Ntype
1. #14558276C2semidirect
2. #14558275C2semidirect
3. #124×D37C2semidirect
4. #120×D37C2semidirect
5. C37×H(3,𝔽4)C2semidirect
6. C24×D37C22semidirect
7. C2×Q8×D37C22semidirect
9. #11924525C22semidirect
10. #11924524C22semidirect
11. #11924523C22semidirect
12. #11924522C22semidirect
13. #11924506C22semidirect
14. #11924505C22semidirect
15. #11924504C22semidirect
16. C22⋊C4×D37C22semidirect
17. C42×D37C22semidirect
18. #124×C37C22semidirect
19. #120×C37C22semidirect
20. C24×C37C23semidirect
23. C23×D37C23semidirect
24. C2×Q8×C37C23semidirect
31. C2×Dic74C23semidirect
32. C22⋊C4×C37C23semidirect
33. C42×C37C23semidirect
34. C22⋊Dic37C23semidirect
35. #10596938C23semidirect
36. C4×Dic37C23semidirect
65. D37H(3,𝔽4)direct (N × H)
68. H(3,𝔽4)D37direct (N × H)
71. C37C2×H(3,𝔽4)semidirect
79. #124C2×D37semidirect
83. #120C2×D37semidirect
89. C24C22×D37semidirect
92. C2×Q8C22×D37semidirect
100. C22⋊C4C22×D37semidirect
102. C42C22×D37semidirect

Maximal subgroups

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

subgroupindex
#145582762
#145582752
#124×D372
#120×D372
C37×H(3,𝔽4)2
C2×H(3,𝔽4)37