Finite Group Databasebeta

← #24984444

Subgroups — #24984444

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#19133916C211yesmaximal, characteristic
2#19132768C211yesmaximal, characteristic, complemented
3C43×#1356C211yesmaximal, characteristic, complemented
4#14583647C411yescharacteristic
5#14583261—21no—
6#14582698—21no—
7#14582641C411yescharacteristic
8#14582638—21no—
9C43×#491C2211yescharacteristic
10C43×#347—21no—
11#13063313—21no—
12#13063310—41no—
13#13063303—41no—
14#13063300—41no—
15#13063248—41no—
16#13063245—41no—
17#13063244—41no—
18#13063236—21no—
19C4⋊Q8×C43D411yescharacteristic
20#125×C43C2×C411yescharacteristic
21M32×C43—41no—
22#103×C43—41no—
23#97×C43D411yescharacteristic
24C2×Q8×C43—21no—
25C2×D172—21no—
26C2×D172—41no—
27C2×C4×D43—41no—
28C2×Dic86—21no—
29C2×C8×C43—21no—
30C4⋊C4×C43—21no—
31C4⋊C4×C43—41no—
32C4⋊C4×C43—41no—
33C42×C43C22⋊C411yescharacteristic
34(C2×D43)⋊C4—41no—
35(C2×D43)⋊C4—41no—
36(C2×D43)⋊C4—41no—
37Dic43⋊C4—41no—
38#10621877—81no—
39C2×C43⋊C8—41no—
40C16×C43—42no—
41C22×D43—41no—
42Q8×C43—81no—
43C2×C4×C43—21no—
44C2×C4×C43—41no—
45C2×C4×C43—41no—
46C2×C4×C43#9911yescharacteristic
47C2×Dic43—41no—
48D172—81no—
49D172—161no—
50C4×D43—161no—
51Dic86—81no—
52C8×C43—41no—
53C43⋊C8—81no—
54C43⋊C8—161no—
55#7525—431nomaximal, Sylow
56C22×C43AΣL(1,𝔽16)11yescharacteristic
57C2×D43—81no—
58C2×D43—81no—
59C2×D43—81no—
60C4×C43—21no—
61C4×C43—41no—
62C4×C43—81no—
63C4×C43—81no—
64Dic43—81no—
65#1662—431no—
66#1413—431no—
67#1356D4311yescharacteristic, complemented
68C2×C43—21no—
69C2×C43#140411yescharacteristic
70D43—161no—
71#562—431no—
72#491C2×D4311yescharacteristic
73#489—861no—
74#356—861no—
75#347—21no—
76#330—431no—
77#329—861no—
78C43#752511yescharacteristic, complemented, Sylow
79C4⋊Q8D17211yescharacteristic
80#125C4×D4311yescharacteristic
81#124—861no—
82#123—1721no—
83C22⋊Q8—1721no—
84#121—1721no—
85M32—41no—
86#103—41no—
87#103—1721no—
88#102—1721no—
89#101—1721no—
90#97—861no—
91#97C22⋊D4311yescharacteristic
92C2×Q8—21no—
93C2×Q8—861no—
94C2×D4—861no—
95C2×D4—1721no—
96C22×C4—1721no—
97M16—3441no—
98C2×C8—21no—
99C2×C8—1721no—
100C4⋊C4—21no—
101C4⋊C4—41no—
102C4⋊C4—41no—
103C4⋊C4—1721no—
104C22⋊C4—1721no—
105C22⋊C4—1721no—
106C22⋊C4—1721no—
107C42(C2×D43)⋊C411yescharacteristic
108C16—42no—
109C23—1721no—
110Q8—81no—
111Q8—3441no—
112D4—3441no—
113D4—6881no—
114C2×C4—21no—
115C2×C4—41no—
116C2×C4—41no—
117C2×C4—1721no—
118C2×C4—6881no—
119C2×C4#1306323911yescharacteristic
120C8—41no—
121C8—3441no—
122C8—6881no—
123C22—3441no—
124C22—3441no—
125C22—3441no—
126C22#1458268711yescharacteristic
127C4—21no—
128C4—41no—
129C4—81no—
130C4—81no—
131C4—3441no—
132C2—21no—
133C2—6881no—
134C2#1913274711yescharacteristic
subgroupG/H
centerC2#19132747
commutator#125×C43C2×C4
Frattini#491C2×D43
FittingC43×#1356C2
socleC2×C43#1404
prime radical#14583647C4
cosocleC43×#491C22
hypercenter#1356D43
hypocenterC43#7525
LCSG ▷ #125×C43 ▷ C42×C43 ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #491 ◁ #1356

Complements

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

NH ≅ G/Ntype
2. #19132768C2semidirect
3. C43×#1356C2semidirect
67. #1356D43semidirect
78. C43#7525semidirect

Maximal subgroups

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

subgroupindex
#191339162
#191327682
C43×#13562
#752543