Finite Group Databasebeta

← #24984464

Subgroups — #24984464

Order 11008.

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

normal subgroups only

This group has 156 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#19134221C211yesmaximal, characteristic
2#19132758C211yesmaximal, characteristic
3C43×#1408C211yesmaximal, characteristic
4#14583297C411yescharacteristic, complemented
5#14583271—21no—
6#14583245—21no—
7#14582692—21no—
8#14582620C411yescharacteristic, complemented
9C43×#493C2211yescharacteristic
10C43×#353—21no—
11C2×#10621883—42no—
12#13063325—21no—
13#13063257—41no—
14#13063246—42no—
15#13063240—41no—
16C4×C43⋊C8—21no—
17C2×D8×C43—41no—
18#127×C43D411yescharacteristic
19#127×C43D411yescharacteristic
20#99×C43—41no—
21C4×C8×C43C2×C411yescharacteristic
22C2×D4×C43—21no—
23C2×D4×C43—21no—
24C2×D4×C43—41no—
25C2×D4×C43—41no—
26C2×Dic86—41no—
27D8×C43—82no—
28C2×C8×C43—21no—
29C22⋊C4×C43—81no—
30C42×C43C22⋊C411yescharacteristic
31C22⋊Dic43—81no—
32#10621883—84no—
33C4⋊Dic43—41no—
34C4⋊Dic43—41no—
35C2×C43⋊C8—22no—
36C23×C43—41no—
37C23×C43—41no—
38D4×C43—81no—
39D4×C43—81no—
40D4×C43—82no—
41D4×C43—82no—
42C2×C4×C43—21no—
43C2×C4×C43—161no—
44C2×C4×C43#9911yescharacteristic
45C2×Dic43—81no—
46C2×Dic43—161no—
47Dic86—82no—
48C8×C43—22no—
49C43⋊C8—42no—
50#7533—431nomaximal, Sylow
51C22×C43—81no—
52C22×C43—81no—
53C22×C43—161no—
54C22×C43—161no—
55C22×C43#35311yescharacteristic
56C4×C43—22no—
57C4×C43—21no—
58C4×C43—321no—
59Dic43—161no—
60Dic43—321no—
61#1715—431no—
62#1408—431no—
63#1408D4311yescharacteristic
64C2×C43—21no—
65C2×C43—161no—
66C2×C43—161no—
67C2×C43#140911yescharacteristic
68#498—431no—
69#493C2×D4311yescharacteristic
70#492—861no—
71#486—861no—
72#353—21no—
73#353—861no—
74#322—431no—
75C43#753311yescharacteristic, complemented, Sylow
76C2×SD16—1722no—
77C2×D8—41no—
78C4⋊Q8—861no—
79#127D17211yescharacteristic
80#127C22⋊D4311yescharacteristic
81#106—1721no—
82#102—1722no—
83#99—41no—
84#99—1721no—
85C4×C8—861no—
86C4×C8C4×D4311yescharacteristic
87C2×Q8—1721no—
88C2×D4—21no—
89C2×D4—21no—
90C2×D4—41no—
91C2×D4—41no—
92SD16—3444no—
93D8—82no—
94C2×C8—21no—
95C2×C8—862no—
96C4⋊C4—1721no—
97C4⋊C4—1721no—
98C22⋊C4—81no—
99C22⋊C4—3441no—
100C42(C2×D43)⋊C411yescharacteristic
101C23—41no—
102C23—41no—
103Q8—3442no—
104D4—81no—
105D4—81no—
106D4—82no—
107D4—82no—
108C2×C4—21no—
109C2×C4—161no—
110C2×C4—3441no—
111C2×C4—6881no—
112C2×C4#1306323911yescharacteristic
113C8—22no—
114C8—1722no—
115C22—81no—
116C22—81no—
117C22—161no—
118C22—161no—
119C22#1458269111yescharacteristic
120C4—22no—
121C4—21no—
122C4—321no—
123C4—13761no—
124C4—6881no—
125C2—21no—
126C2—161no—
127C2—161no—
128C2#1913275911yescharacteristic
subgroupG/H
centerC2#19132759
commutatorC4×C8×C43C2×C4
Frattini#493C2×D43
FittingC43×#1408C2
socleC2×C43#1409
prime radical, cosocleC43×#493C22
hypercenter#1408D43
hypocenterC43#7533
LCSG ▷ C4×C8×C43 ▷ C42×C43 ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #493 ◁ #1408

Complements

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

NH ≅ G/Ntype
4. #14583297C4semidirect
8. #14582620C4semidirect
75. C43#7533semidirect

Maximal subgroups

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

subgroupindex
#191342212
#191327582
C43×#14082
#753343