Finite Group Databasebeta

← #24984441

Subgroups — #24984441

Order 11008.

134 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 25 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#19133896C211yesmaximal, characteristic
2#19132766C211yesmaximal, characteristic
3C43×#1355C211yesmaximal, characteristic
4C43⋊#564C411yescharacteristic, complemented
5#14583263—21no—
6#14582692—21no—
7#14582641C411yescharacteristic, complemented
8#14582640—21no—
9C43×#490C2211yescharacteristic
10C43×#347—21no—
11#13063317—21no—
12#13063316—41no—
13#13063315—41no—
14#13063315—41no—
15#13063246—41no—
16#13063246—41no—
17#13063240—41no—
18#13063236—21no—
19#127×C43D411yescharacteristic
20#125×C43C2×C411yescharacteristic
21M32×C43—41no—
22#102×C43—41no—
23#97×C43D411yescharacteristic
24C2×D4×C43—21no—
25C2×D4×C43—41no—
26C2×C8×C43—21no—
27C4⋊C4×C43—21no—
28C4⋊C4×C43—41no—
29C42×C43C22⋊C411yescharacteristic
30C22⋊Dic43—81no—
31C4⋊Dic43—21no—
32C4⋊Dic43—21no—
33C4⋊Dic43—41no—
34Dic43⋊C4—41no—
35Dic43⋊C4—41no—
36Dic43⋊C4—41no—
37Dic43⋊C4—41no—
38C4×Dic43—41no—
39C2×C43⋊C8—41no—
40C16×C43—42no—
41C23×C43—41no—
42D4×C43—81no—
43D4×C43—82no—
44C2×C4×C43—21no—
45C2×C4×C43—41no—
46C2×C4×C43#9911yescharacteristic
47C2×Dic43—41no—
48C2×Dic43—41no—
49C2×Dic43—161no—
50C8×C43—41no—
51C43⋊C8—81no—
52#7524—431nomaximal, Sylow
53C22×C43—81no—
54C22×C43—161no—
55C22×C43AΣL(1,𝔽16)11yescharacteristic
56C4×C43—21no—
57C4×C43—41no—
58C4×C43—81no—
59Dic43—81no—
60Dic43—81no—
61Dic43—321no—
62#1658—431no—
63#1412—431no—
64#1355D4311yescharacteristic
65C2×C43—21no—
66C2×C43—161no—
67C2×C43#140411yescharacteristic
68#564—431no—
69#490—861no—
70#490C2×D4311yescharacteristic
71#353—861no—
72#347—21no—
73#330—431no—
74#330—861no—
75C43#752411yescharacteristic, complemented, Sylow
76#127D17211yescharacteristic
77#125—861no—
78#125—1721no—
79#125—1721no—
80#125—1721no—
81#125C4×D4311yescharacteristic
82M32—41no—
83#102—41no—
84#102—1721no—
85#102—1721no—
86#99—1721no—
87#97—861no—
88#97C22⋊D4311yescharacteristic
89C2×D4—21no—
90C2×D4—41no—
91C2×C8—21no—
92C2×C8—1721no—
93C4⋊C4—21no—
94C4⋊C4—41no—
95C4⋊C4—861no—
96C4⋊C4—861no—
97C4⋊C4—1721no—
98C4⋊C4—1721no—
99C4⋊C4—1721no—
100C4⋊C4—1721no—
101C4⋊C4—1721no—
102C22⋊C4—3441no—
103C42—1721no—
104C42(C2×D43)⋊C411yescharacteristic
105C16—42no—
106C23—41no—
107D4—81no—
108D4—82no—
109C2×C4—21no—
110C2×C4—41no—
111C2×C4—1721no—
112C2×C4—1721no—
113C2×C4—6881no—
114C2×C4#1306323911yescharacteristic
115C8—41no—
116C8—3441no—
117C22—81no—
118C22—161no—
119C22#1458268711yescharacteristic
120C4—21no—
121C4—41no—
122C4—81no—
123C4—3441no—
124C4—3441no—
125C4—13761no—
126C2—21no—
127C2—161no—
128C2#1913274711yescharacteristic
subgroupG/H
centerC2#19132747
commutator#125×C43C2×C4
Frattini#490C2×D43
FittingC43×#1355C2
socleC2×C43#1404
prime radical#127×C43D4
cosocleC43×#490C22
hypercenter#1355D43
hypocenterC43#7524
LCSG ▷ #125×C43 ▷ C42×C43 ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #490 ◁ #1355

Complements

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

NH ≅ G/Ntype
4. C43⋊#564C4semidirect
7. #14582641C4semidirect
75. C43#7524semidirect

Maximal subgroups

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

subgroupindex
#191338962
#191327662
C43×#13552
#752443