Finite Group Databasebeta

← #22608694

Subgroups — #22608694

Order 9344.

168 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 93 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#17988644C212yesmaximal
2#17988340C212yesmaximal, complemented
3#17988338C212yesmaximal, complemented
4C2×C4×C8×C73C211yesmaximal, characteristic
5C4⋊#10596831C2214yes—
6C22⋊#10596831—22no—
7#14556502—22no—
8C22×C8×C73C411yescharacteristic
9C22×C8×C73C411yescharacteristic
10C2×C42×C73C2211yescharacteristic
11C4×C8×C73C411yescharacteristic
12C4×C8×C73C411yescharacteristic
13C4×C8×C73C2211yescharacteristic
14C4×C8×C73C2211yescharacteristic
15C2×#10596831—24no—
16C22×C4×C73C2×C411yescharacteristic
17C22×C4×C73D411yescharacteristic
18C22×C4×C73Q811yescharacteristic
19C2×C8×C73—22no—
20C2×C8×C73—22no—
21C2×C8×C73C2×C411yescharacteristic
22C2×C8×C73C2×C411yescharacteristic
23C2×C8×C73C2×C411yescharacteristic
24C2×C8×C73C2×C411yescharacteristic
25C42×C73C2×C411yescharacteristic
26C42×C73D411yescharacteristic
27C42×C73Q811yescharacteristic
28C42×C73C2311yescharacteristic
29C23×C73C4⋊C411yescharacteristic
30C2×C4×C73—22no—
31C2×C4×C73—21no—
32C2×C4×C73—21no—
33C2×C4×C73—22no—
34C2×C4×C73C4⋊C411yescharacteristic
35C2×C4×C73C4⋊C411yescharacteristic
36C2×C4×C73C4⋊C411yescharacteristic
37C2×C4×C73C22×C411yescharacteristic
38C2×C4×C73C2×D411yescharacteristic
39C2×C4×C73C2×Q811yescharacteristic
40C8×C73—21no—
41C8×C73—21no—
42C8×C73M1612yes—
43C8×C73M1612yes—
44#10596831—44no—
45C22×C73—21no—
46C22×C73—21no—
47C22×C73#10812yes—
48C22×C73C2×C4⋊C411yescharacteristic
49C4×C73—21no—
50C4×C73—21no—
51C4×C73—21no—
52C4×C73—21no—
53C4×C73C2×M1611yescharacteristic
54C4×C73C2×M1611yescharacteristic
55C4×C73#13512yes—
56C2×C73—22no—
57C2×C73#42311yescharacteristic
58C2×C73#42711yescharacteristic
59C2×C73C2×#10811yescharacteristic
60#1568—731nomaximal, Sylow
61C73#156811yescharacteristic, complemented, Sylow
62#432—732no—
63C2×C4×C8D7311yescharacteristic
64#335—732no—
65#334—732no—
66C22×C8Dic7311yescharacteristic
67C22×C8Dic7311yescharacteristic
68C2×C42C2×D7311yescharacteristic
69C4⋊C8—734no—
70C22⋊C8—1462no—
71#97—1462no—
72C4×C8Dic7311yescharacteristic
73C4×C8Dic7311yescharacteristic
74C4×C8C2×D7311yescharacteristic
75C4×C8C2×D7311yescharacteristic
76C22×C4Dic14611yescharacteristic
77C22×C4D29211yescharacteristic
78C22×C4C2×Dic7311yescharacteristic
79C2×C8—22no—
80C2×C8—22no—
81C2×C8—1464no—
82C2×C8C2×Dic7311yescharacteristic
83C2×C8C2×Dic7311yescharacteristic
84C2×C8C2×Dic7311yescharacteristic
85C2×C8C2×Dic7311yescharacteristic
86C42Dic14611yescharacteristic
87C42D29211yescharacteristic
88C42C2×Dic7311yescharacteristic
89C42C22×D7311yescharacteristic
90C23C4⋊Dic7311yescharacteristic
91C2×C4—22no—
92C2×C4—21no—
93C2×C4—21no—
94C2×C4—22no—
95C2×C4C4⋊Dic7311yescharacteristic
96C2×C4C4⋊Dic7311yescharacteristic
97C2×C4C4⋊Dic7311yescharacteristic
98C2×C4C22×Dic7311yescharacteristic
99C2×C4C2×D29211yescharacteristic
100C2×C4C2×Dic14611yescharacteristic
101C8—21no—
102C8—21no—
103C8—2924no—
104C8#1192401212yes—
105C8#1192401212yes—
106C22—21no—
107C22—21no—
108C22#1455652712yes—
109C22C2×C4⋊Dic7311yescharacteristic
110C4—21no—
111C4—21no—
112C4—21no—
113C4—21no—
114C4C2×#1192401211yescharacteristic
115C4C2×#1192401211yescharacteristic
116C4#1455661312yes—
117C2—22no—
118C2#1798861111yescharacteristic
119C2#1798862511yescharacteristic
120C2C2×#1455652711yescharacteristic
subgroupG/H
centerC2×C4C2×D292
commutatorC2×C4×C73C22×C4
FrattiniC42C22×D73
FittingC2×C4×C8×C73C2
socleC22×C73C2×C4⋊C4
hypercenterC2×C4×C8D73
hypocenterC73#1568
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
2. #17988340C2semidirect
3. #17988338C2semidirect
61. C73#1568semidirect