Finite Group Databasebeta

← H(3,𝔽4)×D293 #49172904

Subgroups — H(3,𝔽4)×D293 #49172904

Order 37504.

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#34036872C216yesmaximal, complemented
2#34036871C219yesmaximal, complemented
3#124×D293C219yesmaximal, complemented
4#120×D293C216yesmaximal, complemented
5H(3,𝔽4)×C293C211yesmaximal, characteristic, complemented
6C24×D293C2212yescomplemented
7C2×Q8×D293C2213yescomplemented
8C2×D4×D293C2219yes—
9#22627613C2219yescomplemented
10#22627612C2219yescomplemented
11#22627611C2219yescomplemented
12#22627610C22136yescomplemented
13#22627594C22118yescomplemented
14#22627593C2216yescomplemented
15#22627592C22118yescomplemented
16C22⋊C4×D293C22118yescomplemented
17C42×D293C2213yescomplemented
18#124×C293C2219yescomplemented
19#120×C293C2216yescomplemented
20C23×D293—412no—
21C23×D293C2316yes—
22C23×D293C2316yescomplemented
23C2×Dic586C2319yescomplemented
24Q8×D293—46no—
25C2×D1172C2319yes—
26C2×C22⋊D293C23118yes—
27D4×D293—418no—
28C2×C4×D293C2319yes—
29C22⋊Dic293C23118yescomplemented
30#17989779C23136yescomplemented
31C4×Dic293C2319yescomplemented
32C24×C293C2312yescomplemented
33C2×Q8×C293C2313yescomplemented
34C2×D4×C293C2319yes—
35C22⋊C4×C293C23118yescomplemented
36C42×C293C2313yescomplemented
37C22×D293—236no—
38C22×D293—418no—
39C22×D293—432no—
40C22×D293C2416yes—
41C22×D293C2411yescharacteristic
42Dic586—49no—
43D1172—49no—
44C22⋊D293—418no—
45C2×Dic293C2419yes—
46C4×D293—218no—
47C23×C293—46no—
48C23×C293C2416yes—
49Q8×C293—43no—
50D4×C293—49no—
51C2×C4×C293C2419yes—
52C22×C293—218no—
53C22×C293—48no—
54C22×C293C2511yescharacteristic
55C2×D293—218no—
56C2×D293—424no—
57C2×D293—424no—
58C2×D293H(5,𝔽2)16yes—
59C4×C293—29no—
60Dic293—29no—
61C2×C293—46no—
62C2×C293C2×H(5,𝔽2)13yes—
63D293—46no—
64D293H(3,𝔽4)14yesdirect product factor
65C293C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
66C2×H(3,𝔽4)—2931nomaximal, Sylow
67H(3,𝔽4)—2939no—
68H(3,𝔽4)—2936no—
69H(3,𝔽4)D29311yescharacteristic, direct product factor
70C2×#124—2939no—
71C2×#120—2936no—
72C25—2932no—
73C22×Q8—2933no—
74C22×D4—2939no—
75#124—2939no—
76#124—2939no—
77#124—29336no—
78#124—2939no—
79#124C2×D29319yescomplemented
80#120—2936no—
81#120—29318no—
82#120—29318no—
83#120C2×D29316yescomplemented
84C2×C22⋊C4—29318no—
85C2×C42—2933no—
86C24—2936no—
87C24—2936no—
88C24—117212no—
89C24C22×D29312yescomplemented
90C2×Q8—2939no—
91C2×Q8—11726no—
92C2×Q8C22×D29313yescomplemented
93C2×D4—29318no—
94C2×D4—2939no—
95C2×D4—117218no—
96C2×D4C22×D29319yes—
97C22×C4—2939no—
98C22⋊C4—29318no—
99C22⋊C4—29336no—
100C22⋊C4C22×D293118yescomplemented
101C42—2939no—
102C42C22×D29313yescomplemented
103C23—46no—
104C23—2931no—
105C23—2936no—
106C23—58636no—
107C23—117218no—
108C23—117232no—
109C23C23×D29316yes—
110Q8—43no—
111Q8—11729no—
112D4—49no—
113D4—11729no—
114D4—117218no—
115C2×C4—2939no—
116C2×C4—58618no—
117C2×C4C23×D29319yes—
118C22—218no—
119C22—48no—
120C22—2936no—
121C22—58618no—
122C22—117224no—
123C22—117224no—
124C22C24×D29311yescharacteristic
125C4—29no—
126C4—5869no—
127C2—46no—
128C2—2934no—
129C2—11726no—
130C2H(5,𝔽2)×D29313yes—
subgroupG/H
center, FrattiniC22C24×D293
commutator, socle, cosocleC22×C293C25
FittingH(3,𝔽4)×C293C2
hypercenterH(3,𝔽4)D293
hypocenterC293C2×H(3,𝔽4)
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ H(3,𝔽4)

Complements

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

NH ≅ G/Ntype
1. #34036872C2semidirect
2. #34036871C2semidirect
3. #124×D293C2semidirect
4. #120×D293C2semidirect
5. H(3,𝔽4)×C293C2semidirect
6. C24×D293C22semidirect
7. C2×Q8×D293C22semidirect
9. #22627613C22semidirect
10. #22627612C22semidirect
11. #22627611C22semidirect
12. #22627610C22semidirect
13. #22627594C22semidirect
14. #22627593C22semidirect
15. #22627592C22semidirect
16. C22⋊C4×D293C22semidirect
17. C42×D293C22semidirect
18. #124×C293C22semidirect
19. #120×C293C22semidirect
22. C23×D293C23semidirect
23. C2×Dic586C23semidirect
29. C22⋊Dic293C23semidirect
30. #17989779C23semidirect
31. C4×Dic293C23semidirect
32. C24×C293C23semidirect
33. C2×Q8×C293C23semidirect
35. C22⋊C4×C293C23semidirect
36. C42×C293C23semidirect
64. D293H(3,𝔽4)direct (N × H)
65. C293C2×H(3,𝔽4)semidirect
69. H(3,𝔽4)D293direct (N × H)
79. #124C2×D293semidirect
83. #120C2×D293semidirect
89. C24C22×D293semidirect
92. C2×Q8C22×D293semidirect
100. C22⋊C4C22×D293semidirect
102. C42C22×D293semidirect

Maximal subgroups

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

subgroupindex
#340368722
#340368712
#124×D2932
#120×D2932
H(3,𝔽4)×C2932
C2×H(3,𝔽4)293