Finite Group Databasebeta

← #14583078

Subgroups — #14583078

Order 2752.

152 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 39 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#13063371C211yesmaximal, characteristic
2#13063358C211yesmaximal, characteristic, complemented
3#13063355C211yesmaximal, characteristic, complemented
4#13063313C211yesmaximal, characteristic, complemented
5#13063253C211yesmaximal, characteristic, complemented
6#13063241C211yesmaximal, characteristic, complemented
7#104×C43C211yesmaximal, characteristic, complemented
8#41×C43C2211yescharacteristic
9#10621902—21no—
10D4×D43—21no—
11D4×D43—22no—
12#10621898—21no—
13#10621898C2211yescharacteristic
14C2×D172—21no—
15C2×D172C2211yescharacteristic
16C2×Dic86C2211yescharacteristic, complemented
17M16×C43C2211yescharacteristic, complemented
18C42×C43C2211yescharacteristic, complemented
19#10621885—21no—
20#10621883—21no—
21(C2×D43)⋊C4—22no—
22#10621877C2211yescharacteristic, complemented
23Dic172—21no—
24#10621873—21no—
25C22×D43—22no—
26C22×D43D412yes—
27Q8×C43D411yescharacteristic
28D4×C43—21no—
29D4×C43D411yescharacteristic
30C2×C4×C43—21no—
31C2×C4×C43—21no—
32C2×C4×C43C2311yescharacteristic
33C22⋊D43—22no—
34C22⋊D43—21no—
35C2×Dic43—21no—
36D172—22no—
37D172—21no—
38D172—21no—
39D172D411yescharacteristic
40C4×D43—22no—
41C4×D43—21no—
42Dic86—21no—
43Dic86—21no—
44Dic86D411yescharacteristic
45C8×C43—21no—
46C43⋊C8—21no—
47C22×C43—21no—
48C22×C43C2×D411yescharacteristic
49C2×D43—21no—
50C2×D43—22no—
51C2×D43—42no—
52C2×D43—82no—
53C4×C43—21no—
54C4×C43—41no—
55C4×C43C2×D411yescharacteristic
56C4×C43C2×D411yescharacteristic
57Dic43—21no—
58Dic43—41no—
59C2×C43—21no—
60C2×C43—41no—
61C2×C43#12011yescharacteristic
62D43—42no—
63D43—41no—
64#455—431nomaximal, Sylow
65C43#45511yescharacteristic, complemented, Sylow
66H(5,𝔽2)—431no—
67#137—431no—
68#137—431no—
69#124—431no—
70#104—431no—
71#104D4311yescharacteristic, complemented
72#100—431no—
73#41—431no—
74#41—861no—
75#41—861no—
76#41C2×D4311yescharacteristic
77C2×Q8—431no—
78C2×D4—431no—
79C2×D4—861no—
80C2×D4—862no—
81C2×D4—861no—
82Q16—861no—
83Q16—861no—
84SD16—861no—
85SD16—861no—
86M16—431no—
87M16C2×D4311yescharacteristic, complemented
88C22⋊C4—862no—
89C42C2×D4311yescharacteristic, complemented
90C23—432no—
91C23—862no—
92Q8—431no—
93Q8—861no—
94Q8—861no—
95Q8D17211yescharacteristic
96D4—21no—
97D4—431no—
98D4—862no—
99D4—862no—
100D4—861no—
101D4—861no—
102D4—861no—
103D4D17211yescharacteristic
104C2×C4—21no—
105C2×C4—21no—
106C2×C4—862no—
107C2×C4—861no—
108C2×C4—861no—
109C2×C4C22×D4311yescharacteristic
110C8—21no—
111C8—861no—
112C22—21no—
113C22—861no—
114C22—862no—
115C22—3442no—
116C22—1722no—
117C22D4×D4311yescharacteristic
118C4—21no—
119C4—41no—
120C4—861no—
121C4—1721no—
122C4C2×D17211yescharacteristic
123C4D4×D4311yescharacteristic
124C2—21no—
125C2—41no—
126C2—1721no—
127C2—1722no—
128C2#1306329511yescharacteristic
subgroupG/H
centerC2#13063295
commutator, cosocleC2×C4×C43C23
FrattiniC2×C4C22×D43
Fitting#104×C43C2
socleC2×C43#120
prime radical#13063371C2
hypercenter#104D43
hypocenterC43#455
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #13063358C2semidirect
3. #13063355C2semidirect
4. #13063313C2semidirect
5. #13063253C2semidirect
6. #13063241C2semidirect
7. #104×C43C2semidirect
16. C2×Dic86C22semidirect
17. M16×C43C22semidirect
18. C42×C43C22semidirect
22. #10621877C22semidirect
65. C43#455semidirect
71. #104D43semidirect
87. M16C2×D43semidirect
89. C42C2×D43semidirect

Maximal subgroups

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

subgroupindex
#130633712
#130633582
#130633552
#130633132
#130632532
#130632412
#104×C432
#45543