Finite Group Databasebeta

← #24984429

Subgroups — #24984429

Order 11008.

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

normal subgroups only

This group has 156 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#19133671C211yesmaximal, characteristic
2#19132760C211yesmaximal, characteristic
3C43×#1359C211yesmaximal, characteristic
4#14583629C411yescharacteristic, complemented
5#14583096—21no—
6#14582692—21no—
7#14582648C411yescharacteristic, complemented
8#14582631—21no—
9C43×#492C2211yescharacteristic
10C43×#364—21no—
11C2×#10621883—41no—
12#13063324—41no—
13#13063323—41no—
14C4×Dic86—21no—
15#13063290—41no—
16C4⋊(C43⋊C8)—21no—
17#13063246—41no—
18#13063240—41no—
19C2×SD16×C43—41no—
20C4⋊Q8×C43C2×C411yescharacteristic
21#127×C43D411yescharacteristic
22M32×C43—41no—
23C4×C8×C43D411yescharacteristic
24C2×Q8×C43—21no—
25C2×D4×C43—21no—
26C2×D4×C43—41no—
27C2×Dic86—21no—
28C2×Dic86—41no—
29SD16×C43—81no—
30SD16×C43—81no—
31C2×C8×C43—21no—
32C4⋊C4×C43—41no—
33C42×C43C22⋊C411yescharacteristic
34C22⋊Dic43—81no—
35#10621883—82no—
36C4⋊Dic43—21no—
37Dic43⋊C4—42no—
38Dic43⋊C4—41no—
39C4×Dic43—41no—
40C4×Dic43—41no—
41C2×C43⋊C8—41no—
42C16×C43—81no—
43C23×C43—41no—
44Q8×C43—81no—
45D4×C43—81no—
46D4×C43—81no—
47D4×C43—81no—
48C2×C4×C43—21no—
49C2×C4×C43—41no—
50C2×C4×C43#9911yescharacteristic
51C2×Dic43—41no—
52C2×Dic43—41no—
53C2×Dic43—161no—
54Dic86—22no—
55Dic86—41no—
56Dic86—161no—
57C8×C43—21no—
58C8×C43—21no—
59C43⋊C8—81no—
60#7520—431nomaximal, Sylow
61C22×C43—81no—
62C22×C43—161no—
63C22×C43AΣL(1,𝔽16)11yescharacteristic
64C4×C43—21no—
65C4×C43—21no—
66C4×C43—21no—
67C4×C43—81no—
68Dic43—42no—
69Dic43—81no—
70Dic43—321no—
71#1623—431no—
72#1409—431no—
73#1359D4311yescharacteristic
74C2×C43—21no—
75C2×C43—161no—
76C2×C43#140211yescharacteristic
77Q82—431no—
78#492C2×D4311yescharacteristic
79#460—861no—
80#364—21no—
81#353—861no—
82#333—431no—
83Q8⋊C8—861no—
84C43#752011yescharacteristic, complemented, Sylow
85C2×SD16—41no—
86C2×SD16—1721no—
87C4⋊Q8—1721no—
88C4⋊Q8—1721no—
89C4⋊Q8C4×D4311yescharacteristic
90#127D17211yescharacteristic
91C4×Q8—861no—
92C4×Q8—1721no—
93M32—41no—
94C4⋊C8—861no—
95#102—1721no—
96#99—1721no—
97C4×C8C22⋊D4311yescharacteristic
98C2×Q8—21no—
99C2×Q8—861no—
100C2×Q8—1721no—
101C2×D4—21no—
102C2×D4—41no—
103SD16—81no—
104SD16—81no—
105SD16—3442no—
106C2×C8—21no—
107C2×C8—1721no—
108C4⋊C4—41no—
109C4⋊C4—861no—
110C4⋊C4—1722no—
111C4⋊C4—1721no—
112C22⋊C4—3441no—
113C42—1721no—
114C42—1721no—
115C42(C2×D43)⋊C411yescharacteristic
116C16—81no—
117C23—41no—
118Q8—81no—
119Q8—862no—
120Q8—1721no—
121Q8—6881no—
122D4—81no—
123D4—81no—
124D4—81no—
125C2×C4—21no—
126C2×C4—41no—
127C2×C4—1721no—
128C2×C4—1721no—
129C2×C4—6881no—
130C2×C4#1306323911yescharacteristic
131C8—21no—
132C8—21no—
133C8—3441no—
134C22—81no—
135C22—161no—
136C22#1458268711yescharacteristic
137C4—21no—
138C4—21no—
139C4—21no—
140C4—81no—
141C4—3441no—
142C4—13761no—
143C4—1722no—
144C2—21no—
145C2—161no—
146C2#1913274111yescharacteristic
subgroupG/H
centerC2#19132741
commutatorC4⋊Q8×C43C2×C4
Frattini#492C2×D43
FittingC43×#1359C2
socleC2×C43#1402
prime radical#127×C43D4
cosocleC43×#492C22
hypercenter#1359D43
hypocenterC43#7520
LCSG ▷ C4⋊Q8×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
4. #14583629C4semidirect
7. #14582648C4semidirect
84. C43#7520semidirect

Maximal subgroups

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

subgroupindex
#191336712
#191327602
C43×#13592
#752043