Finite Group Databasebeta

← #24984423

Subgroups — #24984423

Order 11008.

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

normal subgroups only

This group has 148 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#19133714C211yesmaximal, characteristic
2#19132762C211yesmaximal, characteristic
3C43×#1359C211yesmaximal, characteristic
4#14583635C411yescharacteristic
5#14583191—21no—
6#14582698—21no—
7#14582643C411yescharacteristic
8#14582631—21no—
9C43×#492C2211yescharacteristic
10C43×#364—21no—
11#13063312—41no—
12#13063306—41no—
13C4×Dic86—21no—
14D4×Dic43—41no—
15#13063258—41no—
16C4⋊(C43⋊C8)—21no—
17#13063248—41no—
18#13063244—41no—
19C2×SD16×C43—41no—
20C4⋊Q8×C43D411yescharacteristic
21#127×C43C2×C411yescharacteristic
22M32×C43—41no—
23C4×C8×C43D411yescharacteristic
24C2×Q8×C43—21no—
25C2×D4×C43—21no—
26C2×D4×C43—41no—
27C22×Dic43—41no—
28C2×Dic86—21no—
29SD16×C43—81no—
30SD16×C43—81no—
31C2×C8×C43—21no—
32C4⋊C4×C43—41no—
33C42×C43C22⋊C411yescharacteristic
34C22⋊Dic43—41no—
35C22⋊Dic43—42no—
36C4⋊Dic43—21no—
37Dic43⋊C4—41no—
38C4×Dic43—41no—
39#10621877—81no—
40C2×C43⋊C8—41no—
41C16×C43—81no—
42C23×C43—41no—
43Q8×C43—81no—
44D4×C43—81no—
45D4×C43—81no—
46D4×C43—81no—
47C2×C4×C43—21no—
48C2×C4×C43—41no—
49C2×C4×C43#9911yescharacteristic
50C2×Dic43—41no—
51C2×Dic43—41no—
52C2×Dic43—161no—
53Dic86—41no—
54Dic86—41no—
55C8×C43—21no—
56C8×C43—21no—
57C43⋊C8—81no—
58C43⋊C8—161no—
59#7518—431nomaximal, Sylow
60C22×C43—82no—
61C22×C43—81no—
62C22×C43AΣL(1,𝔽16)11yescharacteristic
63C4×C43—21no—
64C4×C43—21no—
65C4×C43—21no—
66C4×C43—81no—
67Dic43—81no—
68Dic43—81no—
69#1630—431no—
70#1410—431no—
71#1359D4311yescharacteristic
72C2×C43—21no—
73C2×C43—161no—
74C2×C43#140211yescharacteristic
75#559—431no—
76#492C2×D4311yescharacteristic
77#477—861no—
78#364—21no—
79#356—861no—
80#331—431no—
81Q8⋊C8—861no—
82C43#751811yescharacteristic, complemented, Sylow
83C2×SD16—41no—
84C4⋊Q8D17211yescharacteristic
85#127C4×D4311yescharacteristic
86#124—1721no—
87#123—1721no—
88C4×Q8—861no—
89C4×D4—1721no—
90M32—41no—
91#107—1721no—
92C4⋊C8—861no—
93#103—1721no—
94#101—1721no—
95C4×C8C22⋊D4311yescharacteristic
96C2×Q8—21no—
97C2×Q8—861no—
98C2×D4—21no—
99C2×D4—41no—
100C22×C4—1721no—
101SD16—81no—
102SD16—81no—
103M16—3441no—
104C2×C8—21no—
105C2×C8—1721no—
106C4⋊C4—41no—
107C4⋊C4—861no—
108C4⋊C4—1721no—
109C22⋊C4—1722no—
110C22⋊C4—1721no—
111C42—1721no—
112C42(C2×D43)⋊C411yescharacteristic
113C16—81no—
114C23—41no—
115Q8—81no—
116Q8—1721no—
117Q8—1721no—
118D4—81no—
119D4—81no—
120D4—81no—
121C2×C4—21no—
122C2×C4—41no—
123C2×C4—1721no—
124C2×C4—1721no—
125C2×C4—6881no—
126C2×C4#1306323911yescharacteristic
127C8—21no—
128C8—21no—
129C8—3441no—
130C8—6881no—
131C22—82no—
132C22—81no—
133C22#1458268711yescharacteristic
134C4—21no—
135C4—21no—
136C4—21no—
137C4—81no—
138C4—3441no—
139C4—3441no—
140C2—21no—
141C2—161no—
142C2#1913274111yescharacteristic
subgroupG/H
centerC2#19132741
commutator, prime radical#127×C43C2×C4
Frattini#492C2×D43
FittingC43×#1359C2
socleC2×C43#1402
cosocleC43×#492C22
hypercenter#1359D43
hypocenterC43#7518
LCSG ▷ #127×C43 ▷ C42×C43 ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #492 ◁ #1359

Complements

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

NH ≅ G/Ntype
82. C43#7518semidirect

Maximal subgroups

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

subgroupindex
#191337142
#191327622
C43×#13592
#751843