Finite Group Databasebeta

← #22612053

Subgroups — #22612053

Order 9344.

140 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 45 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#17989003C211yesmaximal, characteristic
2#17988859C212yesmaximal
3#17988417C211yesmaximal, characteristic, complemented
4#17988403C212yesmaximal, complemented
5C2×Q32×C73C211yesmaximal, characteristic, complemented
6#14556622—22no—
7#14556597C2211yescharacteristic
8#14556531C2211yescharacteristic
9#14556530—21no—
10C16×D73—21no—
11#14556527C2212yes—
12#14556510—22no—
13C2×Q16×C73C2212yes—
14Q32×C73—21no—
15Q32×C73—21no—
16C2×C16×C73C2211yescharacteristic
17#11924028D411yescharacteristic
18#11924018—42no—
19#11924015—42no—
20#11924012—22no—
21#11924012D411yescharacteristic
22#11924011—21no—
23C8×D73—21no—
24#11924003—21no—
25C2×Q8×C73—22no—
26Q16×C73—22no—
27Q16×C73—22no—
28C2×C8×C73C2311yescharacteristic
29C16×C73D411yescharacteristic
30C16×C73D411yescharacteristic
31Q8×C73—42no—
32Q8×C73—42no—
33C2×C4×C73—42no—
34C2×C4×C73C2×D411yescharacteristic
35C22⋊D73—21no—
36D292D811yescharacteristic
37C4×D73—21no—
38Dic146D811yescharacteristic
39C8×C73C2×D411yescharacteristic
40C8×C73#4111yescharacteristic
41#10596831—21no—
42#10596831—42no—
43C22×C73#13511yescharacteristic
44C2×D73—21no—
45C4×C73—82no—
46C4×C73#12111yescharacteristic
47C4×C73C2×D811yescharacteristic
48Dic73—21no—
49C2×C73—21no—
50C2×C73#46611yescharacteristic
51D73—41no—
52#2222—731nomaximal, Sylow
53C73#222211yescharacteristic, complemented, Sylow
54C2×Q32D7311yescharacteristic, complemented
55#504—731no—
56#473—732no—
57#368—731no—
58#362—732no—
59#137—1462no—
60C2×Q16C2×D7312yes—
61#131—731no—
62Q32—21no—
63Q32—21no—
64M32—731no—
65M32—1461no—
66C2×C16—1461no—
67C2×C16C2×D7311yescharacteristic
68#108—732no—
69#101—1462no—
70#41—731no—
71C2×Q8—22no—
72Q16—22no—
73Q16—22no—
74Q16—2922no—
75SD16—2922no—
76M16—731no—
77M16—1462no—
78M16—1461no—
79C2×C8—1461no—
80C2×C8C22×D7311yescharacteristic
81C16—1461no—
82C16C22⋊D7311yescharacteristic
83C16C22⋊D7311yescharacteristic
84Q8—42no—
85Q8—42no—
86Q8—731no—
87D4—731no—
88D4—1461no—
89C2×C4—42no—
90C2×C4—1461no—
91C2×C4D4×D7311yescharacteristic
92C8—2922no—
93C8—1461no—
94C8C2×C22⋊D7311yescharacteristic
95C8#1192402711yescharacteristic
96C22—1461no—
97C22#1455661011yescharacteristic
98C4—82no—
99C4—1461no—
100C4#1455656211yescharacteristic
101C4D8×D7311yescharacteristic
102C2—21no—
103C2—2921no—
104C2#1798882011yescharacteristic
subgroupG/H
centerC2#17988820
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
FittingC2×Q32×C73C2
socleC2×C73#466
hypercenterC2×Q32D73
hypocenterC73#2222
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q32

Complements

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

NH ≅ G/Ntype
3. #17988417C2semidirect
4. #17988403C2semidirect
5. C2×Q32×C73C2semidirect
53. C73#2222semidirect
54. C2×Q32D73semidirect