Finite Group Databasebeta

← #22608032

Subgroups — #22608032

Order 9344.

132 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 69 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×#14556531C211yesmaximal, characteristic
2#17988625C211yesmaximal, characteristic
3#427×C73C211yesmaximal, characteristic
4#14556550—21no—
5#14556531—21no—
6#14556531—21no—
7C2×#11924003C412yescomplemented
8#14556525—21no—
9#14556523C412yescomplemented
10C22×C8×C73C2211yescharacteristic
11#117×C73—21no—
12#107×C73—21no—
13#106×C73C412yescomplemented
14C4⋊Dic73—22no—
15C22⋊Dic73—41no—
16C4×Dic73—41no—
17#11924003—22no—
18C22×C4×C73D411yescharacteristic
19C2×C8×C73C2×C411yescharacteristic
20C2×C8×C73C2×C411yescharacteristic
21C2×C8×C73C2×C411yescharacteristic
22C2×C8×C73D411yescharacteristic
23C2×C8×C73D411yescharacteristic
24C2×C8×C73Q811yescharacteristic
25C4⋊C4×C73—22no—
26C22⋊C4×C73—41no—
27C42×C73—41no—
28C23×C73D811yescharacteristic
29C2×C4×C73—42no—
30C2×C4×C73C22⋊C411yescharacteristic
31C2×C4×C73C22⋊C411yescharacteristic
32C2×C4×C73C4⋊C411yescharacteristic
33C2×C4×C73SD1611yescharacteristic
34C2×C4×C73SD1611yescharacteristic
35C2×C4×C73Q1611yescharacteristic
36C2×Dic73—42no—
37C8×C73C4211yescharacteristic
38C8×C73C22⋊C411yescharacteristic
39C8×C73C4⋊C411yescharacteristic
40C8×C73C4⋊C411yescharacteristic
41C22×C73—41no—
42C22×C73#10211yescharacteristic
43C22×C73#10211yescharacteristic
44C22×C73#10711yescharacteristic
45C4×C73—82no—
46C4×C73#9511yescharacteristic
47C4×C73#10311yescharacteristic
48C4×C73#10311yescharacteristic
49C4×C73#10611yescharacteristic
50Dic73—82no—
51C2×C73—21no—
52C2×C73—21no—
53C2×C73—21no—
54C2×C73#34011yescharacteristic
55#1384—731nomaximal, Sylow
56C73#138411yescharacteristic, complemented, Sylow
57C2×M32—731no—
58#427—731no—
59#427D7311yescharacteristic
60C22×C8C2×D7311yescharacteristic
61#117—21no—
62#117—1461no—
63M32—1461no—
64M32—1461no—
65C2×C16—732no—
66#107—21no—
67#107—1461no—
68#106—732no—
69#106Dic7312yescomplemented
70C22×C4C22⋊D7311yescharacteristic
71C2×C8Dic14611yescharacteristic
72C2×C8C4×D7311yescharacteristic
73C2×C8C4×D7311yescharacteristic
74C2×C8D29211yescharacteristic
75C2×C8C2×Dic7311yescharacteristic
76C2×C8C22⋊D7311yescharacteristic
77C4⋊C4—22no—
78C4⋊C4—1462no—
79C22⋊C4—41no—
80C22⋊C4—2921no—
81C42—41no—
82C42—2921no—
83C16—1462no—
84C23#1192401311yescharacteristic
85C2×C4—42no—
86C2×C4—2922no—
87C2×C4#1192400511yescharacteristic
88C2×C4C22⋊Dic7311yescharacteristic
89C2×C4#1192400711yescharacteristic
90C2×C4#1192401511yescharacteristic
91C2×C4#1192401611yescharacteristic
92C2×C4#1192401811yescharacteristic
93C8C4×Dic7311yescharacteristic
94C8#1192400511yescharacteristic
95C8#1192400711yescharacteristic
96C8C4⋊Dic7311yescharacteristic
97C22—41no—
98C22#1455651111yescharacteristic
99C22#1455651211yescharacteristic
100C22#1455652411yescharacteristic
101C4—82no—
102C4—5842no—
103C4#1455649811yescharacteristic
104C4#1455651411yescharacteristic
105C4#1455651511yescharacteristic
106C4#1455652211yescharacteristic
107C2—21no—
108C2—21no—
109C2—21no—
110C2#1798834911yescharacteristic
subgroupG/H
centerC4#14556522
commutatorC8×C73C42
FrattiniC22×C8C2×D73
Fitting#427×C73C2
socleC2×C73#340
hypercenter#427D73
hypocenterC73#1384
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #427

Complements

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

NH ≅ G/Ntype
7. C2×#11924003C4semidirect
9. #14556523C4semidirect
13. #106×C73C4semidirect
56. C73#1384semidirect
69. #106Dic73semidirect