Finite Group Databasebeta

← #22624994

Subgroups — #22624994

Order 9344.

132 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 50 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×#14556664C211yesmaximal, characteristic
2#17989597C211yesmaximal, characteristic
3#108×D73C211yesmaximal, characteristic
4#14556670—21no—
5#14556664—21no—
6#14556664C412yescomplemented
7C2×#11924031—21no—
8#14556660C412yes—
9#14556659—21no—
10M16×D73—21no—
11C2×C8×D73C2211yescharacteristic
12#14556527C411yescharacteristic, complemented
13#14556526—21no—
14#108×C73C411yescharacteristic, complemented
15C4⋊#64408—22no—
16C22⋊#64408—41no—
17C4×#64408—41no—
18#11924031—22no—
19C2×C4×D73D411yescharacteristic
20#11924012—21no—
21#11924011—41no—
22C2×#10596831D411yescharacteristic
23C8×D73—41no—
24C8×D73C2×C411yescharacteristic
25C8×D73C2×C411yescharacteristic
26C8×D73D411yescharacteristic
27C8×D73Q811yescharacteristic
28M16×C73—21no—
29C2×C8×C73C2×C411yescharacteristic
30C22×D73SD1611yescharacteristic
31C2×#64408—42no—
32C2×C4×C73C22⋊C411yescharacteristic
33C2×Dic73Q1611yescharacteristic
34C4×D73C22⋊C411yescharacteristic
35C4×D73C4⋊C411yescharacteristic
36C4×D73D811yescharacteristic
37C4×D73SD1611yescharacteristic
38C8×C73—41no—
39C8×C73C4211yescharacteristic
40C8×C73C4⋊C411yescharacteristic
41#10596831—41no—
42#10596831C22⋊C411yescharacteristic
43#10596831C4⋊C411yescharacteristic
44C22×C73#10311yescharacteristic
45C2×D73—22no—
46C2×D73#10211yescharacteristic
47C2×D73#10611yescharacteristic
48#64408—82no—
49C4×C73#9511yescharacteristic
50C4×C73#10211yescharacteristic
51Dic73#10311yescharacteristic
52Dic73#10711yescharacteristic
53C2×C73—21no—
54C2×C73#34011yescharacteristic
55D73—21no—
56D73#35912yes—
57#1382—731nomaximal, Sylow
58C73#138211yescharacteristic, complemented, Sylow
59C22×C16—731no—
60C2×#108—731no—
61#427—731no—
62C2×M16—1461no—
63C22×C8—731no—
64#117—1461no—
65C2×C16—732no—
66C2×C16—1461no—
67C2×C16—1461no—
68#108—731no—
69#108—1461no—
70#108#6440811yescharacteristic, complemented
71#107—732no—
72#106—1461no—
73C22×C4—731no—
74M16—21no—
75M16—2921no—
76M16—1461no—
77C2×C8—2921no—
78C2×C8—731no—
79C2×C8—731no—
80C2×C8—731no—
81C2×C8—731no—
82C2×C8—731no—
83C2×C8C2×#6440811yescharacteristic
84C4⋊C4—1462no—
85C22⋊C4—2921no—
86C42—2921no—
87C16—1462no—
88C23—731no—
89C2×C4—2922no—
90C2×C4—731no—
91C2×C4—731no—
92C2×C4—731no—
93C2×C4—731no—
94C2×C4—731no—
95C2×C4C22⋊#6440811yescharacteristic
96C8—41no—
97C8—2921no—
98C8—731no—
99C8—731no—
100C8C4×#6440811yescharacteristic
101C8C4⋊#6440811yescharacteristic
102C22—731no—
103C22—731no—
104C22—1462no—
105C22#1455665411yescharacteristic
106C4—5842no—
107C4—731no—
108C4—731no—
109C4(C2×#64408)⋊C411yescharacteristic
110C4#1455665311yescharacteristic
111C2—21no—
112C2—732no—
113C2—1461no—
114C2#1798946011yescharacteristic
subgroupG/H
centerC4#14556653
commutatorC8×C73C42
FrattiniC2×C8C2×#64408
Fitting#108×C73C4
socleC2×C73#340
hypercenter#108#64408
hypocenterC73#1382
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #108

Complements

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

NH ≅ G/Ntype
6. #14556664C4semidirect
12. #14556527C4semidirect
14. #108×C73C4semidirect
58. C73#1382semidirect
70. #108#64408semidirect