Finite Group Databasebeta

← #22610771

Subgroups — #22610771

Order 9344.

396 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 101 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×#14556588C211yesmaximal, characteristic
2#17988611C211yesmaximal, characteristic, complemented
3C2×#14556507C214yesmaximal, complemented
4C4×M16×C73C211yesmaximal, characteristic, complemented
5C22×D292C414yes—
6C22×D292C2212yes—
7C2×#11924012C2212yes—
8#14556588—22no—
9#14556588—21no—
10#14556588—21no—
11C4⋊#10596831—22no—
12#14556507—28no—
13C2×M16×C73C2212yes—
14C2×C42×C73C2211yescharacteristic
15#97×C73—21no—
16C4×C8×C73—21no—
17C23×D73C2×C414yes—
18C2×D292—24no—
19C2×D292—24no—
20C2×D292—24no—
21C2×D292—22no—
22C2×D292—22no—
23C2×D292—24no—
24C2×D292—48no—
25#11924012—24no—
26C2×#10596831—22no—
27C22×C4×C73C2×C412yes—
28C22×C4×C73C2311yescharacteristic
29M16×C73—22no—
30M16×C73D414yescomplemented
31C2×C8×C73—22no—
32C42×C73D412yes—
33C42×C73D411yescharacteristic
34C42×C73D411yescharacteristic
35C23×C73C22×C411yescharacteristic
36C22×D73—24no—
37C22×D73—28no—
38C22×D73—48no—
39C2×C4×C73—24no—
40C2×C4×C73C22⋊C412yes—
41C2×C4×C73C22⋊C412yes—
42C2×C4×C73C2×D411yescharacteristic
43C2×C4×C73C2×D412yes—
44C2×C4×C73C2×D411yescharacteristic
45C2×C4×C73#4112yes—
46D292—48no—
47D292—48no—
48D292—44no—
49D292—42no—
50D292—42no—
51C8×C73—24no—
52#10596831—42no—
53C22×C73—22no—
54C22×C73C2×C22⋊C411yescharacteristic
55C22×C73C4×D412yes—
56C2×D73—44no—
57C2×D73—48no—
58C2×D73—88no—
59C4×C73—22no—
60C4×C73#10014yescomplemented
61C4×C73#12112yes—
62C4×C73#12411yescharacteristic
63C4×C73#12711yescharacteristic
64C2×C73—22no—
65C2×C73#39011yescharacteristic
66C2×C73C2×#10012yes—
67D73—84no—
68#1965—731nomaximal, Sylow
69C73#196511yescharacteristic, complemented, Sylow
70C2×#127—731no—
71#423—731no—
72C2×#100—734no—
73C4×M16D7311yescharacteristic, complemented
74C22×D4—734no—
75C22×D4—732no—
76C2×M16—732no—
77C2×M16C2×D7312yes—
78#127—1462no—
79#127—1461no—
80#127—1461no—
81C2×C42C2×D7311yescharacteristic
82C4⋊C8—1462no—
83#100—1468no—
84#97—21no—
85C4×C8—21no—
86C24—734no—
87C2×D4—2928no—
88C2×D4—1464no—
89C2×D4—1464no—
90C2×D4—1462no—
91C2×D4—1464no—
92C2×D4—1462no—
93C2×D4—1464no—
94C22×C4C4×D7312yes—
95C22×C4C22×D7311yescharacteristic
96M16—22no—
97M16—1464no—
98M16D29214yescomplemented
99C2×C8—22no—
100C2×C8—1462no—
101C42D29212yes—
102C42C22⋊D7311yescharacteristic
103C42C22⋊D7311yescharacteristic
104C23—2928no—
105C23—1464no—
106C23—1468no—
107C23C2×C4×D7311yescharacteristic
108D4—2928no—
109D4—2928no—
110D4—2924no—
111D4—2922no—
112D4—2922no—
113C2×C4—24no—
114C2×C4#1192400512yes—
115C2×C4#1192400512yes—
116C2×C4C2×C22⋊D7311yescharacteristic
117C2×C4C2×D29212yes—
118C2×C4C2×D29211yescharacteristic
119C2×C4#1192402812yes—
120C8—24no—
121C8—2922no—
122C22—22no—
123C22—2924no—
124C22—2928no—
125C22—5848no—
126C22C2×#1192400511yescharacteristic
127C22C4×D29212yes—
128C4—22no—
129C4#1455650714yescomplemented
130C4#1455656512yes—
131C4#1455657911yescharacteristic
132C4#1455658811yescharacteristic
133C2—22no—
134C2—5844no—
135C2#1798848911yescharacteristic
136C2C2×#1455650712yes—
subgroupG/H
centerC22C2×#11924005
commutatorC23×C73C22×C4
FrattiniC22×C4C22×D73
FittingC4×M16×C73C2
socleC22×C73C2×C22⋊C4
hypercenterC4×M16D73
hypocenterC73#1965
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
2. #17988611C2semidirect
3. C2×#14556507C2semidirect
4. C4×M16×C73C2semidirect
30. M16×C73D4semidirect
60. C4×C73#100semidirect
69. C73#1965semidirect
73. C4×M16D73semidirect
98. M16D292semidirect
129. C4#14556507semidirect