Finite Group Databasebeta

← #22609960

Subgroups — #22609960

Order 9344.

336 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14556525C212yesmaximal, complemented
2#17988447C212yesmaximal
3#17988350C212yesmaximal, complemented
4C23×C8×C73C211yesmaximal, characteristic
5C2×C4⋊Dic73C2214yes—
6C2×C22⋊Dic73—22no—
7#14556525—24no—
8#14556498—22no—
9C23×C4×C73C2211yescharacteristic
10C22×C8×C73—24no—
11C22×C8×C73C414yescomplemented
12C22×C8×C73C2211yescharacteristic
13C22×C8×C73C2211yescharacteristic
14C22×Dic73—24no—
15C4⋊Dic73—24no—
16C4⋊Dic73—24no—
17C22⋊Dic73—44no—
18C24×C73D411yescharacteristic
19C22×C4×C73—22no—
20C22×C4×C73—22no—
21C22×C4×C73C2×C412yes—
22C22×C4×C73D411yescharacteristic
23C22×C4×C73Q812yes—
24C22×C4×C73C2311yescharacteristic
25C2×C8×C73—22no—
26C2×C8×C73—28no—
27C2×C8×C73C2×C412yes—
28C2×C8×C73C2×C412yes—
29C2×C8×C73D414yes—
30C23×C73—22no—
31C23×C73—22no—
32C23×C73C4⋊C412yes—
33C23×C73D812yes—
34C23×C73Q1612yes—
35C23×C73C2×D411yescharacteristic
36C2×C4×C73—22no—
37C2×C4×C73—22no—
38C2×C4×C73—22no—
39C2×C4×C73—24no—
40C2×C4×C73C4⋊C412yes—
41C2×C4×C73C22×C411yescharacteristic
42C2×C4×C73C2×D412yes—
43C2×C4×C73C2×Q811yescharacteristic
44C2×C4×C73#4112yes—
45C2×Dic73—44no—
46C2×Dic73—44no—
47C2×Dic73—44no—
48C8×C73—22no—
49C8×C73C22⋊C414yescomplemented
50C22×C73—22no—
51C22×C73—22no—
52C22×C73—24no—
53C22×C73—24no—
54C22×C73#10714yescomplemented
55C22×C73C2×C4⋊C411yescharacteristic
56C22×C73#12112yes—
57C22×C73C2×D811yescharacteristic
58C22×C73C2×Q1611yescharacteristic
59C22×C73#13512yes—
60C4×C73—22no—
61C4×C73C2×C22⋊C411yescharacteristic
62C4×C73#11711yescharacteristic
63C4×C73C22⋊Q812yes—
64Dic73—84no—
65C2×C73—24no—
66C2×C73#38011yescharacteristic
67C2×C73C2×#10711yescharacteristic
68C2×C73#42711yescharacteristic
69C2×C73#46612yes—
70C2×C73#46712yes—
71#1808—731nomaximal, Sylow
72C73#180811yescharacteristic, complemented, Sylow
73C23×C8D7311yescharacteristic
74C2×#107—732no—
75#380—732no—
76#340—732no—
77C23×C4C2×D7311yescharacteristic
78C22×C8—24no—
79C22×C8Dic7314yescomplemented
80C22×C8C2×D7311yescharacteristic
81C22×C8C2×D7311yescharacteristic
82C2×C4⋊C4—734no—
83C2×C22⋊C4—1462no—
84#107—1464no—
85#95—1462no—
86C24D29211yescharacteristic
87C22×C4—22no—
88C22×C4—22no—
89C22×C4—1464no—
90C22×C4Dic14612yes—
91C22×C4D29211yescharacteristic
92C22×C4C2×Dic7312yes—
93C22×C4C22×D7311yescharacteristic
94C2×C8—22no—
95C2×C8—28no—
96C2×C8C2×Dic7312yes—
97C2×C8C2×Dic7312yes—
98C2×C8C22⋊D7314yes—
99C4⋊C4—1464no—
100C4⋊C4—1464no—
101C22⋊C4—2924no—
102C23—22no—
103C23—22no—
104C23C4⋊Dic7312yes—
105C23D58412yes—
106C23Dic29212yes—
107C23C2×D29211yescharacteristic
108C2×C4—22no—
109C2×C4—22no—
110C2×C4—22no—
111C2×C4—24no—
112C2×C4—2924no—
113C2×C4—2924no—
114C2×C4—2924no—
115C2×C4C4⋊Dic7312yes—
116C2×C4C22×Dic7311yescharacteristic
117C2×C4C2×C22⋊D7312yes—
118C2×C4C2×Dic14611yescharacteristic
119C2×C4#1192402812yes—
120C8—22no—
121C8C22⋊Dic7314yescomplemented
122C22—22no—
123C22—22no—
124C22—24no—
125C22—24no—
126C22#1455652514yescomplemented
127C22C2×C4⋊Dic7311yescharacteristic
128C22#1455656512yes—
129C22C2×D58411yescharacteristic
130C22C2×Dic29211yescharacteristic
131C22#1455661312yes—
132C4—22no—
133C4—5844no—
134C4C2×C22⋊Dic7311yescharacteristic
135C4#1455655011yescharacteristic
136C4#1455657012yes—
137C2—24no—
138C2#1798844711yescharacteristic
139C2C2×#1455652511yescharacteristic
140C2#1798862511yescharacteristic
141C2#1798882312yes—
142C2#1798882812yes—
subgroupG/H
centerC23C2×D292
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
FittingC23×C8×C73C2
socleC23×C73C2×D4
hypercenterC23×C8D73
hypocenterC73#1808
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
1. C2×#14556525C2semidirect
3. #17988350C2semidirect
11. C22×C8×C73C4semidirect
49. C8×C73C22⋊C4semidirect
54. C22×C73#107semidirect
72. C73#1808semidirect
79. C22×C8Dic73semidirect
121. C8C22⋊Dic73semidirect
126. C22#14556525semidirect