Finite Group Databasebeta

← #22612057

Subgroups — #22612057

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
1C2×Dic584C211yesmaximal, characteristic, complemented
2#17989003C211yesmaximal, characteristic
3#17988863C212yesmaximal
4#17988402C212yesmaximal, complemented
5#368×C73C211yesmaximal, characteristic, complemented
6#14556624—22no—
7C2×Dic292C2212yes—
8#14556597C2211yescharacteristic
9Dic584—21no—
10Dic584—21no—
11#14556531C2211yescharacteristic
12#14556530—21no—
13C16×D73—21no—
14#14556509—22no—
15C2×C16×C73C2211yescharacteristic
16#108×C73C2212yes—
17#11924028D411yescharacteristic
18C2×Dic146—22no—
19Dic292—22no—
20Dic292—22no—
21Dic292—42no—
22#11924017—42no—
23#11924012D411yescharacteristic
24#11924011—21no—
25C8×D73—21no—
26#11924003—21no—
27M16×C73—22no—
28C2×C8×C73C2311yescharacteristic
29C16×C73D411yescharacteristic
30C16×C73D411yescharacteristic
31C2×C4×C73C2×D411yescharacteristic
32C22⋊D73—21no—
33C2×Dic73—42no—
34D292D811yescharacteristic
35C4×D73—21no—
36Dic146—42no—
37Dic146—42no—
38Dic146D811yescharacteristic
39C8×C73—42no—
40C8×C73C2×D411yescharacteristic
41C8×C73#4111yescharacteristic
42#10596831—21no—
43C22×C73#13511yescharacteristic
44C2×D73—21no—
45C4×C73#12111yescharacteristic
46C4×C73C2×D811yescharacteristic
47Dic73—21no—
48Dic73—82no—
49C2×C73—21no—
50C2×C73#46611yescharacteristic
51D73—41no—
52#2222—731nomaximal, Sylow
53C73#222211yescharacteristic, complemented, Sylow
54C2×Q32—731no—
55#504—731no—
56#473—732no—
57#368D7311yescharacteristic, complemented
58#362—732no—
59#137—1462no—
60C2×Q16—732no—
61#131—731no—
62Q32—1461no—
63Q32—1461no—
64M32—731no—
65M32—1461no—
66C2×C16—1461no—
67C2×C16C2×D7311yescharacteristic
68#108C2×D7312yes—
69#101—1462no—
70#41—731no—
71C2×Q8—1462no—
72Q16—2922no—
73Q16—1462no—
74Q16—1462no—
75SD16—2922no—
76M16—22no—
77M16—731no—
78M16—1461no—
79C2×C8—1461no—
80C2×C8C22×D7311yescharacteristic
81C16—1461no—
82C16D29211yescharacteristic
83C16D29211yescharacteristic
84Q8—2922no—
85Q8—2922no—
86Q8—731no—
87D4—731no—
88D4—1461no—
89C2×C4—2922no—
90C2×C4—1461no—
91C2×C4D4×D7311yescharacteristic
92C8—42no—
93C8—1461no—
94C8C2×D29211yescharacteristic
95C8#1192402911yescharacteristic
96C22—1461no—
97C22#1455661411yescharacteristic
98C4—5842no—
99C4—1461no—
100C4#1455656611yescharacteristic
101C4D8×D7311yescharacteristic
102C2—21no—
103C2—2921no—
104C2#1798882411yescharacteristic
subgroupG/H
centerC2#17988824
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#368×C73C2
socleC2×C73#466
hypercenter#368D73
hypocenterC73#2222
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #368

Complements

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

NH ≅ G/Ntype
1. C2×Dic584C2semidirect
4. #17988402C2semidirect
5. #368×C73C2semidirect
53. C73#2222semidirect
57. #368D73semidirect