Finite Group Databasebeta

← #24984431

Subgroups — #24984431

Order 11008.

148 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 27 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#19132764C211yesmaximal, characteristic, complemented
2#19132634C211yesmaximal, characteristic, complemented
3C43×#1634C211yesmaximal, characteristic
4#14582720—21no—
5#14582698—21no—
6C43×#555C411yescharacteristic
7C43×#494C2211yescharacteristic
8C43×#476—21no—
9C43×#333C411yescharacteristic
10C43×D4⋊C8—21no—
11#13063265—41no—
12#13063244—41no—
13C2×Q16×C43—41no—
14C4⋊Q8×C43C2×C411yescharacteristic
15C4⋊Q8×C43D411yescharacteristic
16#124×C43—41no—
17#121×C43—41no—
18C4×D4×C43—21no—
19#117×C43—41no—
20#106×C43—41no—
21C4⋊C8×C43—21no—
22#102×C43—41no—
23C4×C8×C43D411yescharacteristic
24C2×Q8×C43—21no—
25C2×Q8×C43—21no—
26C2×D4×C43—21no—
27C2×D4×C43—41no—
28C22×C4×C43—41no—
29Q16×C43—81no—
30Q16×C43—81no—
31C2×C8×C43—21no—
32C2×C8×C43—41no—
33C4⋊C4×C43—21no—
34C4⋊C4×C43—41no—
35C4⋊C4×C43—41no—
36C22⋊C4×C43—42no—
37C22⋊C4×C43—41no—
38C42×C43—41no—
39C42×C43C22⋊C411yescharacteristic
40#10621877—81no—
41C43⋊C16—81no—
42C23×C43—41no—
43Q8×C43—81no—
44Q8×C43—81no—
45D4×C43—41no—
46D4×C43—41no—
47D4×C43—161no—
48C2×C4×C43—21no—
49C2×C4×C43—41no—
50C2×C4×C43—41no—
51C2×C4×C43—41no—
52C2×C4×C43—81no—
53C2×C4×C43—81no—
54C2×C4×C43#9911yescharacteristic
55C8×C43—21no—
56C8×C43—21no—
57C8×C43—81no—
58C43⋊C8—161no—
59#7521—431nomaximal, Sylow
60C22×C43—81no—
61C22×C43—81no—
62C22×C43—81no—
63C22×C43AΣL(1,𝔽16)11yescharacteristic
64C4×C43—21no—
65C4×C43—21no—
66C4×C43—21no—
67C4×C43—81no—
68C4×C43—81no—
69C4×C43—81no—
70#1634D4311yescharacteristic
71#1411—431no—
72#1358—431no—
73C2×C43—21no—
74C2×C43—161no—
75C2×C43#140211yescharacteristic
76#555Dic4311yescharacteristic
77#494C2×D4311yescharacteristic
78#476—21no—
79#364—861no—
80#356—861no—
81#333Dic4311yescharacteristic
82D4⋊C8—21no—
83C43#752111yescharacteristic, complemented, Sylow
84C2×Q16—41no—
85C4⋊Q8C2×Dic4311yescharacteristic
86C4⋊Q8C22⋊D4311yescharacteristic
87#124—41no—
88#121—41no—
89C4×D4—21no—
90#117—41no—
91M32—1721no—
92#106—41no—
93C4⋊C8—21no—
94#102—41no—
95#101—1721no—
96C4×C8C22⋊D4311yescharacteristic
97C2×Q8—21no—
98C2×Q8—21no—
99C2×D4—21no—
100C2×D4—41no—
101C22×C4—41no—
102Q16—81no—
103Q16—81no—
104M16—3441no—
105C2×C8—21no—
106C2×C8—41no—
107C4⋊C4—21no—
108C4⋊C4—41no—
109C4⋊C4—41no—
110C22⋊C4—42no—
111C22⋊C4—41no—
112C42—41no—
113C42C22⋊Dic4311yescharacteristic
114C16—3441no—
115C23—41no—
116Q8—81no—
117Q8—81no—
118D4—41no—
119D4—41no—
120D4—161no—
121C2×C4—21no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4—41no—
125C2×C4—81no—
126C2×C4—81no—
127C2×C4#1306324011yescharacteristic
128C8—21no—
129C8—21no—
130C8—81no—
131C8—6881no—
132C22—81no—
133C22—81no—
134C22—81no—
135C22#1458268611yescharacteristic
136C4—21no—
137C4—21no—
138C4—21no—
139C4—81no—
140C4—81no—
141C4—81no—
142C2—21no—
143C2—161no—
144C2#1913274011yescharacteristic
subgroupG/H
centerC2#19132740
commutatorC4⋊Q8×C43C2×C4
Frattini#494C2×D43
FittingC43×#1634C2
socleC2×C43#1402
prime radicalC43×#555C4
cosocleC43×#494C22
hypercenter#1634D43
hypocenterC43#7521
LCSG ▷ C4⋊Q8×C43 ▷ C42×C43 ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #494 ◁ #1634

Complements

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

NH ≅ G/Ntype
1. #19132764C2semidirect
2. #19132634C2semidirect
83. C43#7521semidirect

Maximal subgroups

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

subgroupindex
#191327642
#191326342
C43×#16342
#752143