Finite Group Databasebeta

← #106×Dic73 #22609822

Subgroups — #106×Dic73 #22609822

Order 9344.

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

normal subgroups only

This group has 280 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×#14556523C211yesmaximal, characteristic
2C2×C8×Dic73C211yesmaximal, characteristic
3C4⋊C4×Dic73C212yesmaximal
4#17988349C212yesmaximal
5C2×#106×C73C211yesmaximal, characteristic
6C22×#10596831C2211yescharacteristic
7C2×C4⋊Dic73C2212yes—
8C2×C4×Dic73—22no—
9C2×C4×Dic73C2211yescharacteristic
10#14556523C414yescomplemented
11C8×Dic73C414yescomplemented
12#14556498—22no—
13C22×C8×C73C2211yescharacteristic
14C2×C4⋊C4×C73C2212yes—
15#106×C73C414yescomplemented
16C22×Dic73—22no—
17C22×Dic73D411yescharacteristic
18C22×Dic73D411yescharacteristic
19C2×#10596831—21no—
20C2×#10596831—21no—
21C2×#10596831C2×C412yes—
22C4⋊Dic73—22no—
23C4⋊Dic73C2×C414yes—
24C4×Dic73—44no—
25C4×Dic73C2×C412yes—
26C4×Dic73Q812yes—
27C22×C4×C73—22no—
28C22×C4×C73C2311yescharacteristic
29C2×C8×C73C2×C412yes—
30C2×C8×C73C2×C412yes—
31C2×C8×C73C2×C412yes—
32C4⋊C4×C73—22no—
33C4⋊C4×C73C2×C414yes—
34C23×C73C2×D411yescharacteristic
35C2×C4×C73—24no—
36C2×C4×C73—42no—
37C2×C4×C73—42no—
38C2×C4×C73C22×C411yescharacteristic
39C2×C4×C73C22×C411yescharacteristic
40C2×C4×C73C22×C411yescharacteristic
41C2×C4×C73C2×Q811yescharacteristic
42C2×C4×C73#4111yescharacteristic
43C2×C4×C73#4111yescharacteristic
44C2×Dic73—22no—
45C2×Dic73—24no—
46C2×Dic73—42no—
47C2×Dic73—42no—
48C2×Dic73C4⋊C412yes—
49C2×Dic73C4⋊C412yes—
50C2×Dic73SD1614yes—
51C8×C73C4214yescomplemented
52#10596831—22no—
53C22×C73C2×C4⋊C411yescharacteristic
54C22×C73C4×D411yescharacteristic
55C22×C73C4×D411yescharacteristic
56C22×C73C2×SD1612yes—
57C22×C73#13512yes—
58C4×C73—44no—
59C4×C73C2×C4211yescharacteristic
60C4×C73#11711yescharacteristic
61C4×C73C4×Q811yescharacteristic
62C4×C73C4×Q811yescharacteristic
63Dic73—22no—
64Dic73—44no—
65Dic73#10614yesdirect product factor
66C2×C73C4×C4⋊C411yescharacteristic
67C2×C73C2×#10611yescharacteristic
68C2×C73#42711yescharacteristic
69C2×C73C4×SD1612yes—
70C2×C73C4×SD1612yes—
71C4×#106—731nomaximal, Sylow
72C73C4×#10611yescharacteristic, complemented, Sylow
73C2×#106—731no—
74C2×#106D7311yescharacteristic
75C2×C4×C8—731no—
76C4×C4⋊C4—732no—
77#340—732no—
78C22×C8—731no—
79C22×C8C2×D7311yescharacteristic
80C2×C4⋊C4—732no—
81C2×C4⋊C4C2×D7312yes—
82C2×C42—731no—
83C2×C42—1462no—
84#106—734no—
85#106Dic7314yesdirect product factor
86C4×C8—734no—
87#95—1462no—
88C22×C4—22no—
89C22×C4—731no—
90C22×C4—731no—
91C22×C4—1462no—
92C22×C4C22×D7311yescharacteristic
93C2×C8—732no—
94C2×C8—1461no—
95C2×C8—1461no—
96C2×C8C4×D7312yes—
97C2×C8C4×D7312yes—
98C2×C8C2×Dic7312yes—
99C4⋊C4—22no—
100C4⋊C4—734no—
101C4⋊C4—1462no—
102C4⋊C4C2×Dic7314yes—
103C42—2924no—
104C42—732no—
105C42—732no—
106C23D4×D7311yescharacteristic
107C2×C4—24no—
108C2×C4—42no—
109C2×C4—42no—
110C2×C4—2922no—
111C2×C4—2922no—
112C2×C4—732no—
113C2×C4—734no—
114C2×C4—732no—
115C2×C4—1464no—
116C2×C4—1462no—
117C2×C4C2×C4×D7311yescharacteristic
118C2×C4C2×C4×D7311yescharacteristic
119C2×C4C22×Dic7311yescharacteristic
120C2×C4Q8×D7311yescharacteristic
121C2×C4#1192402711yescharacteristic
122C2×C4#1192402911yescharacteristic
123C8—1462no—
124C8C4×Dic7314yescomplemented
125C22C4⋊C4×D7311yescharacteristic
126C22#1455655311yescharacteristic
127C22D4×Dic7311yescharacteristic
128C22SD16×D7312yes—
129C22#1455661212yes—
130C4—44no—
131C4—2924no—
132C4—734no—
133C4—1462no—
134C4C2×C4×Dic7311yescharacteristic
135C4#1455654911yescharacteristic
136C4#1455655611yescharacteristic
137C4Q8×Dic7311yescharacteristic
138C2C4⋊C4×Dic7311yescharacteristic
139C2#106×D7311yescharacteristic
140C2#1798862211yescharacteristic
141C2#1798867412yes—
142C2SD16×Dic7312yes—
subgroupG/H
centerC23D4×D73
commutatorC4×C73C2×C42
FrattiniC22×C4C22×D73
FittingC2×#106×C73C2
socleC23×C73C2×D4
hypercenterC2×#106D73
hypocenterC73C4×#106
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
10. #14556523C4semidirect
11. C8×Dic73C4semidirect
15. #106×C73C4semidirect
51. C8×C73C42semidirect
65. Dic73#106direct (N × H)
72. C73C4×#106semidirect
85. #106Dic73direct (N × H)
124. C8C4×Dic73semidirect