Finite Group Databasebeta

← #24984468

Subgroups — #24984468

Order 11008.

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

normal subgroups only

This group has 150 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#19134181C211yesmaximal, characteristic
2#19132762C211yesmaximal, characteristic
3C43×#1409C211yesmaximal, characteristic
4#14583297C411yescharacteristic, complemented
5#14583295—21no—
6#14583271—21no—
7#14582698—21no—
8C8×C43⋊C8C411yescharacteristic, complemented
9C43×#492C2211yescharacteristic
10C43×#353—21no—
11C2×#10621883—42no—
12#13063325—21no—
13#13063257—41no—
14#13063256—42no—
15#13063244—41no—
16C4×C43⋊C8—21no—
17C2×SD16×C43—41no—
18C4⋊Q8×C43D411yescharacteristic
19#127×C43D411yescharacteristic
20#99×C43—41no—
21C4×C8×C43C2×C411yescharacteristic
22C2×Q8×C43—21no—
23C2×D4×C43—21no—
24C2×D4×C43—41no—
25C2×Dic86—41no—
26SD16×C43—82no—
27C2×C8×C43—21no—
28C4⋊C4×C43—41no—
29C22⋊C4×C43—81no—
30C42×C43C22⋊C411yescharacteristic
31#10621883—84no—
32C4⋊Dic43—41no—
33C4⋊Dic43—41no—
34#10621877—81no—
35C2×C43⋊C8—22no—
36C23×C43—41no—
37Q8×C43—81no—
38D4×C43—81no—
39D4×C43—82no—
40C2×C4×C43—21no—
41C2×C4×C43—41no—
42C2×C4×C43—161no—
43C2×C4×C43#9911yescharacteristic
44C2×Dic43—81no—
45Dic86—82no—
46C8×C43—22no—
47C43⋊C8—24no—
48C43⋊C8—161no—
49#7535—431nomaximal, Sylow
50C22×C43—81no—
51C22×C43—161no—
52C22×C43#35311yescharacteristic
53C4×C43—22no—
54C4×C43—21no—
55C4×C43—81no—
56C4×C43—321no—
57Dic43—161no—
58#1705—431no—
59#1410—431no—
60#1409D4311yescharacteristic
61C2×C43—21no—
62C2×C43—161no—
63C2×C43#140911yescharacteristic
64#498—431no—
65#498—861no—
66#492—861no—
67#492C2×D4311yescharacteristic
68#356—861no—
69#353—21no—
70C82—431no—
71C43#753511yescharacteristic, complemented, Sylow
72C2×SD16—41no—
73C2×SD16—1722no—
74C4⋊Q8—861no—
75C4⋊Q8D17211yescharacteristic
76#127C22⋊D4311yescharacteristic
77#106—1722no—
78#106—1721no—
79#101—1721no—
80#99—41no—
81C4×C8—861no—
82C4×C8C4×D4311yescharacteristic
83C2×Q8—21no—
84C2×Q8—1721no—
85C2×D4—21no—
86C2×D4—41no—
87SD16—82no—
88SD16—3444no—
89M16—3441no—
90C2×C8—21no—
91C2×C8—862no—
92C4⋊C4—41no—
93C4⋊C4—1721no—
94C4⋊C4—1721no—
95C22⋊C4—81no—
96C42(C2×D43)⋊C411yescharacteristic
97C23—41no—
98Q8—81no—
99Q8—3442no—
100D4—81no—
101D4—82no—
102C2×C4—21no—
103C2×C4—41no—
104C2×C4—161no—
105C2×C4—3441no—
106C2×C4#1306323911yescharacteristic
107C8—22no—
108C8—864no—
109C8—6881no—
110C22—81no—
111C22—161no—
112C22#1458269111yescharacteristic
113C4—22no—
114C4—21no—
115C4—81no—
116C4—321no—
117C4—6881no—
118C2—21no—
119C2—161no—
120C2#1913275911yescharacteristic
subgroupG/H
centerC2#19132759
commutatorC4×C8×C43C2×C4
Frattini#492C2×D43
FittingC43×#1409C2
socleC2×C43#1409
prime radical#127×C43D4
cosocleC43×#492C22
hypercenter#1409D43
hypocenterC43#7535
LCSG ▷ C4×C8×C43 ▷ C42×C43 ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #492 ◁ #1409

Complements

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

NH ≅ G/Ntype
4. #14583297C4semidirect
8. C8×C43⋊C8C4semidirect
71. C43#7535semidirect

Maximal subgroups

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

subgroupindex
#191341812
#191327622
C43×#14092
#753543