Finite Group Databasebeta

← #22626210

Subgroups — #22626210

Order 9344.

270 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 54 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#17989566C212yesmaximal, complemented
2#17989491C214yesmaximal, complemented
3#17989154C211yesmaximal, characteristic
4#14556670—22no—
5#14556650C2214yescomplemented
6#14556649—22no—
7C2×#11924028C2211yescharacteristic
8#14556587C2212yes—
9#14556578C412yescomplemented
10#14556562—22no—
11#14556560—22no—
12#14556550C411yescharacteristic, complemented
13C22×D4×C73C411yescharacteristic, complemented
14C4⋊#64408—42no—
15C22⋊#64408—24no—
16C4×#64408—42no—
17#11924028—42no—
18C2×Dic146C2×C411yescharacteristic
19C2×D292C2311yescharacteristic
20C2×C22⋊D73—24no—
21C2×C22⋊D73D412yes—
22C2×C4×D73D412yes—
23C4⋊Dic73—21no—
24C22⋊Dic73—21no—
25C22⋊Dic73—24no—
26C4×Dic73C2×C412yes—
27C24×C73—21no—
28C2×D4×C73—21no—
29C2×D4×C73—42no—
30C2×D4×C73C2×C412yes—
31C22×C4×C73C2×C411yescharacteristic
32C23×C73—22no—
33C23×C73—42no—
34C23×C73—82no—
35C23×C73C22⋊C411yescharacteristic
36C22×D73C2×D412yes—
37C2×#64408—44no—
38D4×C73—42no—
39D4×C73—42no—
40C2×C4×C73—22no—
41C2×C4×C73C22⋊C411yescharacteristic
42C2×C4×C73C22×C411yescharacteristic
43C22⋊D73—42no—
44C22⋊D73—84no—
45C2×Dic73—22no—
46C2×Dic73C22⋊C412yes—
47D292—41no—
48C4×D73—22no—
49C4×D73—22no—
50Dic146—41no—
51C22×C73—21no—
52C22×C73—41no—
53C22×C73—44no—
54C22×C73—42no—
55C22×C73—84no—
56C22×C73C2×C22⋊C411yescharacteristic
57C2×D73—22no—
58C2×D73—42no—
59#64408—84no—
60C4×C73—21no—
61C4×C73#9912yes—
62Dic73—22no—
63Dic73—42no—
64C2×C73—21no—
65C2×C73—41no—
66C2×C73—82no—
67C2×C73C2×#9911yescharacteristic
68D73—42no—
69#2128—731nomaximal, Sylow
70C73#212811yescharacteristic, complemented, Sylow
71#535—731no—
72#410—732no—
73#353—734no—
74C2×#41—731no—
75C22×D4#6440811yescharacteristic, complemented
76#127—732no—
77#124—732no—
78#121—1462no—
79#120—1462no—
80#117—731no—
81#117—1462no—
82#99—734no—
83#99—1462no—
84C24—21no—
85#41—2922no—
86C2×Q8—731no—
87C2×D4—21no—
88C2×D4—42no—
89C2×D4—732no—
90C2×D4—731no—
91C2×D4—1464no—
92C2×D4C2×#6440812yes—
93C22×C4—732no—
94C22×C4C2×#6440811yescharacteristic
95C4⋊C4—2922no—
96C4⋊C4—1461no—
97C22⋊C4—1464no—
98C22⋊C4—1464no—
99C22⋊C4—1461no—
100C42—2922no—
101C42—732no—
102C23—22no—
103C23—42no—
104C23—82no—
105C23—732no—
106C23C22⋊#6440811yescharacteristic
107Q8—2921no—
108D4—42no—
109D4—42no—
110D4—2921no—
111D4—2922no—
112D4—5844no—
113C2×C4—22no—
114C2×C4—2924no—
115C2×C4—732no—
116C2×C4—1462no—
117C2×C4—1462no—
118C2×C4—1462no—
119C2×C4C22⋊#6440811yescharacteristic
120C2×C4C22×#6440811yescharacteristic
121C22—21no—
122C22—41no—
123C22—44no—
124C22—42no—
125C22—84no—
126C22—2922no—
127C22—1462no—
128C22C2×C22⋊#6440811yescharacteristic
129C4—21no—
130C4—2922no—
131C4—5844no—
132C4—1462no—
133C4#1455664912yes—
134C2—21no—
135C2—41no—
136C2—82no—
137C2—2922no—
138C2C2×#1455664911yescharacteristic
subgroupG/H
centerC2C2×#14556649
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC22×D4×C73C4
socleC2×C73C2×#99
hypercenterC22×D4#64408
hypocenterC73#2128
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #17989566C2semidirect
2. #17989491C2semidirect
5. #14556650C22semidirect
9. #14556578C4semidirect
12. #14556550C4semidirect
13. C22×D4×C73C4semidirect
70. C73#2128semidirect
75. C22×D4#64408semidirect