Finite Group Databasebeta

← #24984430

Subgroups — #24984430

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#19133738C211yesmaximal, characteristic
2#19132634C211yesmaximal, characteristic, complemented
3C43×#1411C211yesmaximal, characteristic, complemented
4#14583615C411yescharacteristic
5#14583186—21no—
6#14582720—21no—
7#14582648C411yescharacteristic
8#14582628—21no—
9C43×#494C2211yescharacteristic
10C43×#356—21no—
11#13063314—41no—
12#13063300—41no—
13C4×D172—21no—
14#13063283—41no—
15#13063265—41no—
16#13063256—41no—
17C4⋊(C43⋊C8)—21no—
18#13063245—41no—
19C2×Q16×C43—41no—
20C4⋊Q8×C43C2×C411yescharacteristic
21C4⋊Q8×C43D411yescharacteristic
22#101×C43—41no—
23C4×C8×C43D411yescharacteristic
24C2×Q8×C43—21no—
25C2×Q8×C43—21no—
26C2×D172—21no—
27C2×D172—41no—
28C2×C4×D43—41no—
29Q16×C43—81no—
30Q16×C43—81no—
31M16×C43—81no—
32C2×C8×C43—21no—
33C4⋊C4×C43—41no—
34C4⋊C4×C43—41no—
35C42×C43C22⋊C411yescharacteristic
36(C2×D43)⋊C4—42no—
37(C2×D43)⋊C4—41no—
38C4⋊Dic43—21no—
39C4×Dic43—41no—
40C2×C43⋊C8—41no—
41C43⋊C16—81no—
42C22×D43—41no—
43Q8×C43—81no—
44Q8×C43—81no—
45C2×C4×C43—21no—
46C2×C4×C43—41no—
47C2×C4×C43—41no—
48C2×C4×C43#9911yescharacteristic
49C2×Dic43—41no—
50D172—41no—
51D172—41no—
52D172—161no—
53C4×D43—81no—
54C4×D43—81no—
55C8×C43—21no—
56C8×C43—21no—
57C8×C43—161no—
58C43⋊C8—81no—
59#7521—431nomaximal, Sylow
60C22×C43AΣL(1,𝔽16)11yescharacteristic
61C2×D43—81no—
62C2×D43—81no—
63C2×D43—81no—
64C4×C43—21no—
65C4×C43—21no—
66C4×C43—21no—
67C4×C43—81no—
68C4×C43—81no—
69Dic43—81no—
70#1634—431no—
71#1411D4311yescharacteristic, complemented
72#1358—431no—
73C2×C43—21no—
74C2×C43#140211yescharacteristic
75D43—161no—
76#555—431no—
77#494C2×D4311yescharacteristic
78#476—861no—
79#364—861no—
80#356—21no—
81#333—431no—
82D4⋊C8—861no—
83C43#752111yescharacteristic, complemented, Sylow
84C2×Q16—41no—
85C4⋊Q8C4×D4311yescharacteristic
86C4⋊Q8C22⋊D4311yescharacteristic
87#124—1721no—
88#121—1721no—
89C4×D4—861no—
90#117—1721no—
91M32—1721no—
92#106—1721no—
93C4⋊C8—861no—
94#102—1721no—
95#101—41no—
96C4×C8D17211yescharacteristic
97C2×Q8—21no—
98C2×Q8—21no—
99C2×D4—861no—
100C2×D4—1721no—
101C22×C4—1721no—
102Q16—81no—
103Q16—81no—
104M16—81no—
105C2×C8—21no—
106C2×C8—1721no—
107C4⋊C4—41no—
108C4⋊C4—41no—
109C4⋊C4—861no—
110C22⋊C4—1722no—
111C22⋊C4—1721no—
112C42—1721no—
113C42(C2×D43)⋊C411yescharacteristic
114C16—3441no—
115C23—1721no—
116Q8—81no—
117Q8—81no—
118D4—1721no—
119D4—1721no—
120D4—6881no—
121C2×C4—21no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4—3441no—
125C2×C4—3441no—
126C2×C4—1721no—
127C2×C4#1306323911yescharacteristic
128C8—21no—
129C8—21no—
130C8—161no—
131C8—3441no—
132C22—3441no—
133C22—3441no—
134C22—3441no—
135C22#1458268511yescharacteristic
136C4—21no—
137C4—21no—
138C4—21no—
139C4—81no—
140C4—81no—
141C4—3441no—
142C2—21no—
143C2—6881no—
144C2#1913273911yescharacteristic
subgroupG/H
centerC2#19132739
commutatorC4⋊Q8×C43C2×C4
Frattini#494C2×D43
FittingC43×#1411C2
socleC2×C43#1402
prime radical#14583615C4
cosocleC43×#494C22
hypercenter#1411D43
hypocenterC43#7521
LCSG ▷ C4⋊Q8×C43 ▷ C42×C43 ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #494 ◁ #1411

Complements

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

NH ≅ G/Ntype
2. #19132634C2semidirect
3. C43×#1411C2semidirect
71. #1411D43semidirect
83. C43#7521semidirect

Maximal subgroups

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

subgroupindex
#191337382
#191326342
C43×#14112
#752143