Finite Group Databasebeta

← #24984471

Subgroups — #24984471

Order 11008.

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

normal subgroups only

This group has 138 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#19134194C211yesmaximal, characteristic
2#19132762C211yesmaximal, characteristic
3C43×#1409C211yesmaximal, characteristic
4#14583297C411yescharacteristic, complemented
5#14583251—21no—
6#14583245—21no—
7#14582698—21no—
8C8×C43⋊C8C411yescharacteristic, complemented
9C43×#492C2211yescharacteristic
10C43×#353—21no—
11#13063325—21no—
12#13063257—41no—
13#13063248—42no—
14#13063246—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
31C4⋊Dic43—41no—
32C4⋊Dic43—41no—
33#10621877—81no—
34C2×C43⋊C8—22no—
35C23×C43—41no—
36Q8×C43—81no—
37D4×C43—81no—
38D4×C43—82no—
39C2×C4×C43—21no—
40C2×C4×C43—41no—
41C2×C4×C43—161no—
42C2×C4×C43#9911yescharacteristic
43C2×Dic43—81no—
44Dic86—82no—
45C8×C43—22no—
46C43⋊C8—42no—
47C43⋊C8—161no—
48#7536—431nomaximal, Sylow
49C22×C43—81no—
50C22×C43—161no—
51C22×C43#35311yescharacteristic
52C4×C43—22no—
53C4×C43—21no—
54C4×C43—81no—
55C4×C43—321no—
56Dic43—161no—
57#1708—431no—
58#1410—431no—
59#1409D4311yescharacteristic
60C2×C43—21no—
61C2×C43—161no—
62C2×C43#140911yescharacteristic
63#498—431no—
64#492C2×D4311yescharacteristic
65#487—861no—
66#486—861no—
67#356—861no—
68#353—21no—
69C82—431no—
70C43#753611yescharacteristic, complemented, Sylow
71C2×SD16—41no—
72C4⋊Q8—861no—
73C4⋊Q8D17211yescharacteristic
74#127C22⋊D4311yescharacteristic
75#106—1721no—
76#103—1722no—
77#102—1722no—
78#101—1721no—
79#99—41no—
80C4×C8—861no—
81C4×C8C4×D4311yescharacteristic
82C2×Q8—21no—
83C2×Q8—1721no—
84C2×D4—21no—
85C2×D4—41no—
86SD16—82no—
87M16—3441no—
88C2×C8—21no—
89C2×C8—862no—
90C4⋊C4—41no—
91C4⋊C4—1721no—
92C4⋊C4—1721no—
93C22⋊C4—81no—
94C42(C2×D43)⋊C411yescharacteristic
95C23—41no—
96Q8—81no—
97Q8—3442no—
98D4—81no—
99D4—82no—
100C2×C4—21no—
101C2×C4—41no—
102C2×C4—161no—
103C2×C4—3441no—
104C2×C4#1306323911yescharacteristic
105C8—22no—
106C8—1722no—
107C8—6881no—
108C22—81no—
109C22—161no—
110C22#1458269111yescharacteristic
111C4—22no—
112C4—21no—
113C4—81no—
114C4—321no—
115C4—6881no—
116C2—21no—
117C2—161no—
118C2#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#7536
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
70. C43#7536semidirect

Maximal subgroups

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

subgroupindex
#191341942
#191327622
C43×#14092
#753643