Finite Group Databasebeta

← #22625867

Subgroups — #22625867

Order 9344.

280 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 114 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×#14556660C214yesmaximal
2#17989533C212yesmaximal
3C4×C8×D73C211yesmaximal, characteristic
4C2×C4⋊#64408—24no—
5C2×C4⋊#64408C2214yes—
6#14556660—28no—
7C2×C8×D73C2212yes—
8C42×D73C2211yescharacteristic
9C4×#10596831C411yescharacteristic, complemented
10C8×Dic73C412yescomplemented
11C4×C8×C73C411yescharacteristic, complemented
12C22×#64408—24no—
13C4⋊#64408—28no—
14C4⋊#64408—48no—
15C2×C4×D73D412yes—
16C2×C4×D73C2311yescharacteristic
17C2×#10596831C2×C412yes—
18C8×D73D414yes—
19C8×D73Q814yes—
20C4×Dic73C2×C411yescharacteristic
21C4×Dic73Q812yes—
22C2×C8×C73C2×C412yes—
23C42×C73C2×C411yescharacteristic
24C22×D73C2×D411yescharacteristic
25C2×#64408—44no—
26C2×#64408—48no—
27C2×C4×C73C4⋊C412yes—
28C2×C4×C73C22×C411yescharacteristic
29C2×Dic73C4⋊C412yes—
30C2×Dic73C2×Q811yescharacteristic
31C4×D73D814yes—
32C4×D73Q1614yes—
33C4×D73C2×D412yes—
34C4×D73C2×Q812yes—
35C8×C73C4⋊C414yescomplemented
36#10596831C4⋊C414yescomplemented
37C22×C73C2×C4⋊C411yescharacteristic
38C2×D73#12711yescharacteristic
39C2×D73C4⋊Q811yescharacteristic
40C2×D73C2×D812yes—
41C2×D73C2×Q1612yes—
42#64408—84no—
43C4×C73#10714yescomplemented
44C4×C73C2×C4⋊C412yes—
45Dic73#10714yescomplemented
46Dic73C4⋊Q812yes—
47C2×C73#38411yescharacteristic
48C2×C73C2×#10712yes—
49D73#49311yescharacteristic
50D73#49411yescharacteristic
51D73#50012yes—
52#1845—731nomaximal, Sylow
53C73#184511yescharacteristic, complemented, Sylow
54C2×#107—734no—
55C2×C4×C8—731no—
56#384—732no—
57C22×C8—732no—
58C2×C4⋊C4—734no—
59C2×C4⋊C4—1464no—
60C2×C42—731no—
61#107—1468no—
62C4×C8—732no—
63C4×C8—731no—
64C4×C8#6440811yescharacteristic, complemented
65C22×C4—732no—
66C22×C4—731no—
67C22×C4—1464no—
68C2×C8—732no—
69C2×C8—734no—
70C2×C8—734no—
71C2×C8C2×#6440812yes—
72C4⋊C4—2928no—
73C4⋊C4—1468no—
74C42—732no—
75C42—731no—
76C42C2×#6440811yescharacteristic
77C23—731no—
78C2×C4—2928no—
79C2×C4—2924no—
80C2×C4—732no—
81C2×C4—731no—
82C2×C4—734no—
83C2×C4—734no—
84C2×C4—732no—
85C2×C4—732no—
86C2×C4C4⋊#6440812yes—
87C2×C4C22×#6440811yescharacteristic
88C8—734no—
89C8C4⋊#6440814yescomplemented
90C22—731no—
91C22—731no—
92C22—732no—
93C22—732no—
94C22C2×C4⋊#6440811yescharacteristic
95C4—5844no—
96C4—732no—
97C4—734no—
98C4#1455666014yescomplemented
99C4C2×C4⋊#6440812yes—
100C2—731no—
101C2—731no—
102C2—732no—
103C2#1798953311yescharacteristic
104C2C2×#1455666012yes—
subgroupG/H
centerC22C2×C4⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC4×C8×C73C4
socleC22×C73C2×C4⋊C4
hypercenterC4×C8#64408
hypocenterC73#1845
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
9. C4×#10596831C4semidirect
10. C8×Dic73C4semidirect
11. C4×C8×C73C4semidirect
35. C8×C73C4⋊C4semidirect
36. #10596831C4⋊C4semidirect
43. C4×C73#107semidirect
45. Dic73#107semidirect
53. C73#1845semidirect
64. C4×C8#64408semidirect
89. C8C4⋊#64408semidirect
98. C4#14556660semidirect