Finite Group Databasebeta

← #22590465

Subgroups — #22590465

Order 9088.

140 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 49 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
1C2×Dic568C211yesmaximal, characteristic, complemented
2#17986274C212yesmaximal
3#17985829C211yesmaximal, characteristic, complemented
4#17985816C212yesmaximal, complemented
5#504×C71C211yesmaximal, characteristic
6#14556158—22no—
7C2×Dic284C2212yes—
8Dic568—21no—
9Dic568—21no—
10#14556064C2212yes—
11#14556046—22no—
12#131×C71C2211yescharacteristic
13M32×C71—21no—
14M32×C71C2211yescharacteristic
15C2×C16×C71—21no—
16C2×C16×C71C2211yescharacteristic
17C2×Dic142—22no—
18Dic284—22no—
19Dic284—22no—
20#11765855—42no—
21#11765853—42no—
22#11765849—22no—
23#41×C71D411yescharacteristic
24M16×C71—21no—
25M16×C71D411yescharacteristic
26C2×C8×C71—21no—
27C2×C8×C71C2311yescharacteristic
28C16×C71—21no—
29C16×C71D411yescharacteristic
30C16×C71D411yescharacteristic
31Q8×C71D811yescharacteristic
32D4×C71—21no—
33D4×C71D811yescharacteristic
34C2×C4×C71—21no—
35C2×C4×C71C2×D411yescharacteristic
36C2×Dic71—42no—
37Dic142—42no—
38Dic142—42no—
39C8×C71—21no—
40C8×C71C2×D411yescharacteristic
41C8×C71#4111yescharacteristic
42C71⋊C8—42no—
43C22×C71—21no—
44C22×C71#13511yescharacteristic
45C4×C71—21no—
46C4×C71#12111yescharacteristic
47C4×C71C2×D811yescharacteristic
48Dic71—82no—
49C2×C71—21no—
50C2×C71—41no—
51C2×C71#46611yescharacteristic
52#2222—711nomaximal, Sylow
53C71#222211yescharacteristic, complemented, Sylow
54C2×Q32—711no—
55#504D7111yescharacteristic
56#473—712no—
57#368—711no—
58#362—712no—
59#137—1422no—
60C2×Q16—712no—
61#131C2×D7111yescharacteristic
62Q32—1421no—
63Q32—1421no—
64M32—21no—
65M32C2×D7111yescharacteristic
66C2×C16—21no—
67C2×C16C2×D7111yescharacteristic
68#108—712no—
69#101—1422no—
70#41D28411yescharacteristic
71C2×Q8—1422no—
72Q16—2842no—
73Q16—1422no—
74Q16—1422no—
75SD16—2842no—
76M16—21no—
77M16—1422no—
78M16D28411yescharacteristic
79C2×C8—21no—
80C2×C8C22×D7111yescharacteristic
81C16—21no—
82C16C22⋊D7111yescharacteristic
83C16C22⋊D7111yescharacteristic
84Q8—2842no—
85Q8—2842no—
86Q8D56811yescharacteristic
87D4—21no—
88D4D56811yescharacteristic
89C2×C4—21no—
90C2×C4—2842no—
91C2×C4C2×D28411yescharacteristic
92C8—21no—
93C8—2842no—
94C8C2×C22⋊D7111yescharacteristic
95C8#1176586511yescharacteristic
96C22—21no—
97C22#1455615011yescharacteristic
98C4—21no—
99C4—5682no—
100C4#1455610211yescharacteristic
101C4C2×D56811yescharacteristic
102C2—21no—
103C2—41no—
104C2#1798623511yescharacteristic
subgroupG/H
centerC2#17986235
commutatorC2×C8×C71C23
FrattiniC2×C8C22×D71
Fitting#504×C71C2
socleC2×C71#466
hypercenter#504D71
hypocenterC71#2222
LCSG ▷ C2×C8×C71 ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131 ◁ #504

Complements

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

NH ≅ G/Ntype
1. C2×Dic568C2semidirect
3. #17985829C2semidirect
4. #17985816C2semidirect
53. C71#2222semidirect