Finite Group Databasebeta

← #22624997

Subgroups — #22624997

Order 9344.

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

normal subgroups only

This group has 136 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
1#17989643C211yesmaximal, characteristic
2C2×#14556659C211yesmaximal, characteristic
3#108×D73C211yesmaximal, characteristic
4C2×C4⋊#64408—21no—
5#14556666—21no—
6#14556665—21no—
7#14556664C412yescomplemented
8#14556659—21no—
9#14556659C412yes—
10M16×D73—21no—
11C2×C8×D73C2211yescharacteristic
12#14556527C411yescharacteristic, complemented
13#14556526—21no—
14#108×C73C411yescharacteristic, complemented
15C22×#64408—41no—
16C4⋊#64408—22no—
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×#64408—82no—
33C2×C4×C73C22⋊C411yescharacteristic
34C2×Dic73Q1611yescharacteristic
35C4×D73C22⋊C411yescharacteristic
36C4×D73C4⋊C411yescharacteristic
37C4×D73D811yescharacteristic
38C4×D73SD1611yescharacteristic
39C8×C73—41no—
40C8×C73C4211yescharacteristic
41C8×C73C4⋊C411yescharacteristic
42#10596831—41no—
43#10596831C22⋊C411yescharacteristic
44#10596831C4⋊C411yescharacteristic
45C22×C73#10311yescharacteristic
46C2×D73—22no—
47C2×D73#10211yescharacteristic
48C2×D73#10611yescharacteristic
49#64408—82no—
50C4×C73#9511yescharacteristic
51C4×C73#10211yescharacteristic
52Dic73#10311yescharacteristic
53Dic73#10711yescharacteristic
54C2×C73—21no—
55C2×C73#34011yescharacteristic
56D73—21no—
57D73#36512yes—
58#1383—731nomaximal, Sylow
59C73#138311yescharacteristic, complemented, Sylow
60C2×M32—731no—
61C2×#108—731no—
62C2×#106—731no—
63C2×M16—1461no—
64C22×C8—731no—
65C2×C4⋊C4—1461no—
66M32—1461no—
67M32—1461no—
68C2×C16—732no—
69#108—731no—
70#108—1461no—
71#108#6440811yescharacteristic, complemented
72#106—732no—
73#106—1461no—
74C22×C4—2921no—
75C22×C4—731no—
76M16—21no—
77M16—2921no—
78M16—1461no—
79C2×C8—2921no—
80C2×C8—731no—
81C2×C8—731no—
82C2×C8—731no—
83C2×C8—731no—
84C2×C8—731no—
85C2×C8C2×#6440811yescharacteristic
86C4⋊C4—2921no—
87C4⋊C4—1462no—
88C16—1462no—
89C23—731no—
90C2×C4—2922no—
91C2×C4—5842no—
92C2×C4—731no—
93C2×C4—731no—
94C2×C4—731no—
95C2×C4—731no—
96C2×C4—731no—
97C2×C4C22⋊#6440811yescharacteristic
98C8—41no—
99C8—2921no—
100C8—731no—
101C8—731no—
102C8C4×#6440811yescharacteristic
103C8C4⋊#6440811yescharacteristic
104C22—731no—
105C22—731no—
106C22—1462no—
107C22#1455665411yescharacteristic
108C4—5842no—
109C4—731no—
110C4—731no—
111C4(C2×#64408)⋊C411yescharacteristic
112C4#1455665311yescharacteristic
113C2—21no—
114C2—732no—
115C2—1461no—
116C2#1798946011yescharacteristic
subgroupG/H
centerC2#17989460
commutatorC8×C73C42
FrattiniC2×C8C2×#64408
Fitting#108×C73C4
socleC2×C73#340
hypercenter#108#64408
hypocenterC73#1383
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #108

Complements

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

NH ≅ G/Ntype
7. #14556664C4semidirect
12. #14556527C4semidirect
14. #108×C73C4semidirect
59. C73#1383semidirect
71. #108#64408semidirect