Finite Group Databasebeta

← #22625007

Subgroups — #22625007

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×#14556660C211yesmaximal, characteristic
3#108×D73C211yesmaximal, characteristic
4C2×C4⋊#64408—21no—
5#14556666C412yescomplemented
6#14556665—21no—
7#14556664—21no—
8#14556660—21no—
9#14556660C412yes—
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—21no—
47C2×D73—21no—
48C2×D73#10211yescharacteristic
49C2×D73#10611yescharacteristic
50#64408—82no—
51C4×C73#9511yescharacteristic
52C4×C73#10211yescharacteristic
53Dic73#10311yescharacteristic
54Dic73#10711yescharacteristic
55C2×C73—21no—
56C2×C73#34011yescharacteristic
57D73—21no—
58D73#36111yescharacteristic
59D73#36211yescharacteristic
60#1387—731nomaximal, Sylow
61C73#138711yescharacteristic, complemented, Sylow
62C2×M32—731no—
63C2×#108—731no—
64C2×#107—731no—
65C2×M16—1461no—
66C22×C8—731no—
67C2×C4⋊C4—1461no—
68M32—732no—
69M32—1461no—
70C2×C16—1461no—
71#108—731no—
72#108—1461no—
73#108#6440811yescharacteristic, complemented
74#107—732no—
75#107—1461no—
76C22×C4—2921no—
77C22×C4—731no—
78M16—21no—
79M16—2921no—
80M16—1461no—
81C2×C8—2921no—
82C2×C8—731no—
83C2×C8—731no—
84C2×C8—731no—
85C2×C8—731no—
86C2×C8—731no—
87C2×C8C2×#6440811yescharacteristic
88C4⋊C4—2921no—
89C4⋊C4—1462no—
90C16—1462no—
91C23—731no—
92C2×C4—2922no—
93C2×C4—5842no—
94C2×C4—731no—
95C2×C4—731no—
96C2×C4—731no—
97C2×C4—731no—
98C2×C4—731no—
99C2×C4C22⋊#6440811yescharacteristic
100C8—41no—
101C8—2921no—
102C8—731no—
103C8—731no—
104C8C4×#6440811yescharacteristic
105C8C4⋊#6440811yescharacteristic
106C22—731no—
107C22—731no—
108C22—1461no—
109C22—1461no—
110C22#1455665411yescharacteristic
111C4—5842no—
112C4—731no—
113C4—731no—
114C4(C2×#64408)⋊C411yescharacteristic
115C4#1455665311yescharacteristic
116C2—21no—
117C2—731no—
118C2—731no—
119C2—1461no—
120C2#1798946011yescharacteristic
subgroupG/H
centerC2#17989460
commutatorC8×C73C42
FrattiniC2×C8C2×#64408
Fitting#108×C73C4
socleC2×C73#340
hypercenter#108#64408
hypocenterC73#1387
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
5. #14556666C4semidirect
12. #14556527C4semidirect
14. #108×C73C4semidirect
61. C73#1387semidirect
73. #108#64408semidirect