Finite Group Databasebeta

← #24999563

Subgroups — #24999563

Order 11008.

738 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 89 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#19138876C213yesmaximal
2#19134667C213yesmaximal
3C43×#1304C211yesmaximal, characteristic
4C22×C22⋊Dic43C2213yes—
5#14582824—26no—
6#14582774—26no—
7#14582760—26no—
8#14582755C2211yescharacteristic
9#14582665—26no—
10C43×#379C2213yes—
11C23×Dic43D416yes—
12C2×C4⋊Dic43—26no—
13C2×C22⋊Dic43—26no—
14C2×C22⋊Dic43—23no—
15C2×C22⋊Dic43—26no—
16C2×C22⋊Dic43—23no—
17C2×C22⋊Dic43—23no—
18C43⋊#95—26no—
19C43⋊#95—212no—
20C25×C43C2311yescharacteristic
21C2×C22⋊C4×C43—26no—
22C2×C22⋊C4×C43D416yes—
23C24×C43—46no—
24C24×C43C2×D413yes—
25C24×C43C2×D413yes—
26C24×C43#4111yescharacteristic
27C22×C4×C43—26no—
28C22×Dic43—26no—
29C22×Dic43—26no—
30C22×Dic43—26no—
31C22×Dic43—412no—
32C22×Dic43—41no—
33C22⋊C4×C43—46no—
34C22⋊C4×C43—412no—
35C22⋊Dic43—46no—
36C22⋊Dic43—43no—
37C22⋊Dic43—46no—
38C22⋊Dic43—43no—
39C4⋊Dic43—86no—
40C23×C43—212no—
41C23×C43—26no—
42C23×C43—43no—
43C23×C43—46no—
44C23×C43—43no—
45C23×C43—88no—
46C23×C43#12013yes—
47C23×C43#12113yes—
48C23×C43#12711yescharacteristic
49C2×C4×C43—412no—
50C2×C4×C43—46no—
51C2×Dic43—412no—
52C2×Dic43—46no—
53C2×Dic43—412no—
54C2×Dic43—86no—
55C2×Dic43—83no—
56#10339—431nomaximal, Sylow
57C22×C43—26no—
58C22×C43—23no—
59C22×C43—26no—
60C22×C43—23no—
61C22×C43—412no—
62C22×C43—86no—
63C22×C43—82no—
64C22×C43#39211yescharacteristic
65C22×C43#45816yes—
66C4×C43—86no—
67Dic43—86no—
68Dic43—161no—
69#2483—433no—
70#1819—433no—
71#1304D4311yescharacteristic
72C2×C43—26no—
73C2×C43—41no—
74C2×C43—43no—
75C2×C43#202213yes—
76C22×C22⋊C4—433no—
77#397—866no—
78#385—866no—
79#381—866no—
80#379—431no—
81#379C2×D4313yes—
82#342—866no—
83C43#1033911yescharacteristic, complemented, Sylow
84C25C22×D4311yescharacteristic
85C23×C4—436no—
86C2×C4⋊C4—866no—
87C2×C22⋊C4—26no—
88C2×C22⋊C4—863no—
89C2×C22⋊C4—866no—
90C2×C22⋊C4—866no—
91C2×C22⋊C4—863no—
92C2×C22⋊C4—863no—
93C2×C22⋊C4D17216yes—
94#95—866no—
95#95—8612no—
96C24—46no—
97C24C2×D17213yes—
98C24D4×D4313yes—
99C24#1062190211yescharacteristic
100C22×C4—26no—
101C22×C4—866no—
102C22×C4—866no—
103C22×C4—866no—
104C22×C4—1721no—
105C22×C4—17212no—
106C4⋊C4—3446no—
107C22⋊C4—412no—
108C22⋊C4—46no—
109C22⋊C4—1726no—
110C22⋊C4—1723no—
111C22⋊C4—1726no—
112C22⋊C4—1723no—
113C23—212no—
114C23—26no—
115C23—43no—
116C23—46no—
117C23—43no—
118C23—88no—
119C23#1306329513yes—
120C23#1306330013yes—
121C23#1306332211yescharacteristic
122C2×C4—412no—
123C2×C4—46no—
124C2×C4—3446no—
125C2×C4—3443no—
126C2×C4—17212no—
127C2×C4—1726no—
128C2×C4—17212no—
129C22—26no—
130C22—26no—
131C22—23no—
132C22—23no—
133C22—412no—
134C22—86no—
135C22—82no—
136C22#1458280911yescharacteristic
137C22#1458309016yes—
138C4—86no—
139C4—3446no—
140C4—6881no—
141C2—26no—
142C2—41no—
143C2—43no—
144C2#1913572713yes—
subgroupG/H
centerC22#14582809
commutator, prime radical, cosocleC25×C43C23
FrattiniC25C22×D43
FittingC43×#1304C2
socleC22×C43#392
hypercenter#1304D43
hypocenterC43#10339
LCSG ▷ C25×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C25 ◁ #1304

Complements

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

NH ≅ G/Ntype
83. C43#10339semidirect

Maximal subgroups

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

subgroupindex
#191388762
#191346672
C43×#13042
#1033943