Finite Group Databasebeta

← #22625004

Subgroups — #22625004

Order 9344.

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

normal subgroups only

This group has 140 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
2#17989597C211yesmaximal, characteristic
3#106×D73C211yesmaximal, characteristic
4#14556670—21no—
5#14556666C412yescomplemented
6#14556665—21no—
7#14556664—21no—
8#14556660C412yescomplemented
9#14556659—21no—
10C2×C8×D73C2211yescharacteristic
11C4⋊C4×D73—21no—
12#14556523C411yescharacteristic, complemented
13#14556522—21no—
14#106×C73C411yescharacteristic, complemented
15C4⋊#64408—22no—
16C22⋊#64408—41no—
17C4×#64408—41no—
18#11924031—22no—
19C2×C4×D73—41no—
20C2×C4×D73D411yescharacteristic
21C2×#10596831D411yescharacteristic
22C8×D73C2×C411yescharacteristic
23C8×D73C2×C411yescharacteristic
24C8×D73D411yescharacteristic
25C8×D73Q811yescharacteristic
26C4⋊Dic73—21no—
27#11924007—41no—
28C2×C8×C73C2×C411yescharacteristic
29C4⋊C4×C73—21no—
30C22×D73D811yescharacteristic
31C2×#64408—42no—
32C2×C4×C73—41no—
33C2×C4×C73C22⋊C411yescharacteristic
34C2×Dic73—41no—
35C2×Dic73SD1611yescharacteristic
36C4×D73—82no—
37C4×D73C22⋊C411yescharacteristic
38C4×D73C4⋊C411yescharacteristic
39C4×D73SD1611yescharacteristic
40C4×D73Q1611yescharacteristic
41C8×C73C4211yescharacteristic
42C8×C73C4⋊C411yescharacteristic
43#10596831C22⋊C411yescharacteristic
44#10596831C4⋊C411yescharacteristic
45C22×C73#10211yescharacteristic
46C2×D73—22no—
47C2×D73#10211yescharacteristic
48C2×D73#10711yescharacteristic
49#64408—82no—
50C4×C73—81no—
51C4×C73#9511yescharacteristic
52C4×C73#10311yescharacteristic
53Dic73—81no—
54Dic73#10311yescharacteristic
55Dic73#10611yescharacteristic
56C2×C73—21no—
57C2×C73#34011yescharacteristic
58D73—21no—
59D73#36012yes—
60#1386—731nomaximal, Sylow
61C73#138611yescharacteristic, complemented, Sylow
62C2×M32—731no—
63#427—731no—
64C2×#106—731no—
65C22×C8—731no—
66#117—1461no—
67C2×C4⋊C4—1461no—
68M32—732no—
69M32—1461no—
70C2×C16—1461no—
71#107—732no—
72#106—731no—
73#106—1461no—
74#106—1461no—
75#106#6440811yescharacteristic, complemented
76C22×C4—2921no—
77C22×C4—731no—
78C2×C8—731no—
79C2×C8—731no—
80C2×C8—731no—
81C2×C8—731no—
82C2×C8—731no—
83C2×C8C2×#6440811yescharacteristic
84C4⋊C4—21no—
85C4⋊C4—2921no—
86C4⋊C4—1462no—
87C4⋊C4—1461no—
88C22⋊C4—2921no—
89C42—2921no—
90C16—1462no—
91C23—731no—
92C2×C4—41no—
93C2×C4—2922no—
94C2×C4—2921no—
95C2×C4—5842no—
96C2×C4—731no—
97C2×C4—731no—
98C2×C4—731no—
99C2×C4—731no—
100C2×C4—731no—
101C2×C4C22⋊#6440811yescharacteristic
102C8—731no—
103C8—731no—
104C8C4×#6440811yescharacteristic
105C8C4⋊#6440811yescharacteristic
106C22—731no—
107C22—731no—
108C22—1462no—
109C22#1455665311yescharacteristic
110C4—81no—
111C4—5841no—
112C4—5842no—
113C4—731no—
114C4—731no—
115C4(C2×#64408)⋊C411yescharacteristic
116C4#1455665411yescharacteristic
117C2—21no—
118C2—732no—
119C2—1461no—
120C2#1798946011yescharacteristic
subgroupG/H
centerC2#17989460
commutatorC8×C73C42
FrattiniC2×C8C2×#64408
Fitting#106×C73C4
socleC2×C73#340
hypercenter#106#64408
hypocenterC73#1386
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #106

Complements

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

NH ≅ G/Ntype
5. #14556666C4semidirect
8. #14556660C4semidirect
12. #14556523C4semidirect
14. #106×C73C4semidirect
61. C73#1386semidirect
75. #106#64408semidirect