Finite Group Databasebeta

← H(3,𝔽4)×D107 #28350580

Subgroups — H(3,𝔽4)×D107 #28350580

Order 13696.

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#20293370C216yesmaximal, complemented
2#20293369C219yesmaximal, complemented
3#124×D107C219yesmaximal, complemented
4#120×D107C216yesmaximal, complemented
5H(3,𝔽4)×C107C211yesmaximal, characteristic, complemented
6C24×D107C2212yescomplemented
7C2×Q8×D107C2213yescomplemented
8C2×D4×D107C2219yes—
9#16812098C2219yescomplemented
10#16812097C2219yescomplemented
11#16812096C2219yescomplemented
12#16812095C22136yescomplemented
13#16812079C22118yescomplemented
14#16812078C2216yescomplemented
15#16812077C22118yescomplemented
16C22⋊C4×D107C22118yescomplemented
17C42×D107C2213yescomplemented
18#124×C107C2219yescomplemented
19#120×C107C2216yescomplemented
20C23×D107—412no—
21C23×D107C2316yes—
22C23×D107C2316yescomplemented
23C2×Dic214C2319yescomplemented
24Q8×D107—46no—
25C2×D428C2319yes—
26C2×C22⋊D107C23118yes—
27D4×D107—418no—
28C2×C4×D107C2319yes—
29C22⋊Dic107C23118yescomplemented
30(C2×D107)⋊C4C23136yescomplemented
31C4×Dic107C2319yescomplemented
32C24×C107C2312yescomplemented
33C2×Q8×C107C2313yescomplemented
34C2×D4×C107C2319yes—
35C22⋊C4×C107C23118yescomplemented
36C42×C107C2313yescomplemented
37C23×C107—46no—
38C23×C107C2416yes—
39C22×D107—236no—
40C22×D107—418no—
41C22×D107—432no—
42C22×D107C2416yes—
43C22×D107C2411yescharacteristic
44Q8×C107—43no—
45D4×C107—49no—
46C2×C4×C107C2419yes—
47C22⋊D107—418no—
48C2×Dic107C2419yes—
49D428—49no—
50C4×D107—218no—
51Dic214—49no—
52C22×C107—218no—
53C22×C107—48no—
54C22×C107C2511yescharacteristic
55C2×D107—218no—
56C2×D107—424no—
57C2×D107—424no—
58C2×D107H(5,𝔽2)16yes—
59C4×C107—29no—
60Dic107—29no—
61C2×C107—46no—
62C2×C107C2×H(5,𝔽2)13yes—
63D107—46no—
64D107H(3,𝔽4)14yesdirect product factor
65C2×H(3,𝔽4)—1071nomaximal, Sylow
66C107C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
67H(3,𝔽4)—1079no—
68H(3,𝔽4)—1076no—
69H(3,𝔽4)D10711yescharacteristic, direct product factor
70C2×#124—1079no—
71C2×#120—1076no—
72C25—1072no—
73C22×Q8—1073no—
74C22×D4—1079no—
75#124—1079no—
76#124—1079no—
77#124—10736no—
78#124—1079no—
79#124C2×D10719yescomplemented
80#120—1076no—
81#120—10718no—
82#120—10718no—
83#120C2×D10716yescomplemented
84C2×C22⋊C4—10718no—
85C2×C42—1073no—
86C24—1076no—
87C24—1076no—
88C24—42812no—
89C24C22×D10712yescomplemented
90C2×Q8—1079no—
91C2×Q8—4286no—
92C2×Q8C22×D10713yescomplemented
93C2×D4—10718no—
94C2×D4—1079no—
95C2×D4—42818no—
96C2×D4C22×D10719yes—
97C22×C4—1079no—
98C22⋊C4—10718no—
99C22⋊C4—10736no—
100C22⋊C4C22×D107118yescomplemented
101C42—1079no—
102C42C22×D10713yescomplemented
103C23—46no—
104C23—1071no—
105C23—1076no—
106C23—42818no—
107C23—42832no—
108C23—21436no—
109C23C23×D10716yes—
110Q8—43no—
111Q8—4289no—
112D4—49no—
113D4—4289no—
114D4—42818no—
115C2×C4—1079no—
116C2×C4—21418no—
117C2×C4C23×D10719yes—
118C22—218no—
119C22—48no—
120C22—1076no—
121C22—42824no—
122C22—42824no—
123C22—21418no—
124C22C24×D10711yescharacteristic
125C4—29no—
126C4—2149no—
127C2—46no—
128C2—1074no—
129C2—4286no—
130C2H(5,𝔽2)×D10713yes—
subgroupG/H
center, FrattiniC22C24×D107
commutator, socle, cosocleC22×C107C25
FittingH(3,𝔽4)×C107C2
hypercenterH(3,𝔽4)D107
hypocenterC107C2×H(3,𝔽4)
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ H(3,𝔽4)

Complements

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

NH ≅ G/Ntype
1. #20293370C2semidirect
2. #20293369C2semidirect
3. #124×D107C2semidirect
4. #120×D107C2semidirect
5. H(3,𝔽4)×C107C2semidirect
6. C24×D107C22semidirect
7. C2×Q8×D107C22semidirect
9. #16812098C22semidirect
10. #16812097C22semidirect
11. #16812096C22semidirect
12. #16812095C22semidirect
13. #16812079C22semidirect
14. #16812078C22semidirect
15. #16812077C22semidirect
16. C22⋊C4×D107C22semidirect
17. C42×D107C22semidirect
18. #124×C107C22semidirect
19. #120×C107C22semidirect
22. C23×D107C23semidirect
23. C2×Dic214C23semidirect
29. C22⋊Dic107C23semidirect
30. (C2×D107)⋊C4C23semidirect
31. C4×Dic107C23semidirect
32. C24×C107C23semidirect
33. C2×Q8×C107C23semidirect
35. C22⋊C4×C107C23semidirect
36. C42×C107C23semidirect
64. D107H(3,𝔽4)direct (N × H)
66. C107C2×H(3,𝔽4)semidirect
69. H(3,𝔽4)D107direct (N × H)
79. #124C2×D107semidirect
83. #120C2×D107semidirect
89. C24C22×D107semidirect
92. C2×Q8C22×D107semidirect
100. C22⋊C4C22×D107semidirect
102. C42C22×D107semidirect

Maximal subgroups

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

subgroupindex
#202933702
#202933692
#124×D1072
#120×D1072
H(3,𝔽4)×C1072
C2×H(3,𝔽4)107