Finite Group Databasebeta

← #2273⋊C9 #11919641

Subgroups — #2273⋊C9 #11919641

Order 1152.

353 conjugacy classes of subgroups; only the 29 normal subgroups are shown.

normal subgroups only

This group has 353 conjugacy classes of subgroups — too many to draw. Only its 29 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
1C3×#2273C311yesmaximal, characteristic
2C2×C22⋊(C22⋊C9)—41nomaximal
3C2×C42⋊C9—42nomaximal
4#95⋊C9—42nomaximal
5C22×C3×C22⋊C4—31no—
6C3×C4×C22⋊C4—32no—
7C3×C4×C22⋊C4—32no—
8C22⋊(C22⋊C9)—41no—
9C42⋊C9—42no—
10#2273C911yescharacteristic, complemented, Sylow
11C25×C3A411yescharacteristic
12C23×C3×C4—31no—
13C23×C3×C4—31no—
14C2×C3×C22⋊C4—34no—
15C2×C3×C22⋊C4—38no—
16C2×C3×C42—32no—
17C2×C3×C42A412yes—
18C3×#95—32no—
19C3×#95A412yes—
20C2×C22⋊C9—164no—
21C2×C22⋊C9—161no—
22C22×C22⋊C4—31no—
23C4×C22⋊C4—32no—
24C4×C22⋊C4—32no—
25C24×C3—31no—
26C24×C3—34no—
27C24×C3—41no—
28C24×C3—121no—
29C22×C3×C4—32no—
30C22×C3×C4—32no—
31C22×C3×C4—34no—
32C22×C3×C4—34no—
33C22×C3×C4—121no—
34C22×C3×C4—122no—
35C22×C3×C4—121no—
36C3×C22⋊C4—316no—
37C3×C42—42no—
38C3×C42—122no—
39C22⋊C9—164no—
40C22⋊C9—161no—
41C25C22⋊C911yescharacteristic
42C23×C4—31no—
43C23×C4—31no—
44C2×C22⋊C4—34no—
45C2×C22⋊C4—38no—
46C2×C42—32no—
47C2×C42C22⋊C912yescomplemented
48#95—32no—
49#95C22⋊C912yescomplemented
50C23×C3—34no—
51C23×C3—32no—
52C23×C3—34no—
53C23×C3—62no—
54C23×C3—61no—
55C23×C3—61no—
56C23×C3—124no—
57C23×C3—124no—
58C23×C3C42⋊C314yes—
59C23×C3C22⋊A411yescharacteristic
60C2×C3×C4—34no—
61C2×C3×C4—34no—
62C2×C3×C4—62no—
63C2×C3×C4—64no—
64C2×C3×C4—62no—
65C2×C3×C4—124no—
66C2×C3×C4—124no—
67C2×C9—641no—
68C24—31no—
69C24—34no—
70C24—41no—
71C24—121no—
72C22×C4—32no—
73C22×C4—32no—
74C22×C4—34no—
75C22×C4—34no—
76C22×C4—121no—
77C22×C4—122no—
78C22×C4—121no—
79C22⋊C4—316no—
80C42—42no—
81C42—122no—
82C22×C3—31no—
83C22×C3—31no—
84C22×C3—34no—
85C22×C3—44no—
86C22×C3—62no—
87C22×C3—62no—
88C22×C3—64no—
89C22×C3—64no—
90C22×C3—124no—
91C22×C3#99711yescharacteristic
92C3×C4—64no—
93C3×C4—64no—
94C9—641noSylow
95C23—34no—
96C23—32no—
97C23—34no—
98C23—61no—
99C23—62no—
100C23—61no—
101C23—124no—
102C23—124no—
103C23C42⋊C914yescomplemented
104C23C22⋊(C22⋊C9)11yescharacteristic
105C2×C4—34no—
106C2×C4—34no—
107C2×C4—62no—
108C2×C4—64no—
109C2×C4—62no—
110C2×C4—124no—
111C2×C4—124no—
112C2×C3—31no—
113C2×C3—31no—
114C2×C3—64no—
115C2×C3C22⋊(C42⋊C3)11yescharacteristic
116C22—31no—
117C22—31no—
118C22—34no—
119C22—44no—
120C22—62no—
121C22—62no—
122C22—64no—
123C22—64no—
124C22—124no—
125C22#6370311yescharacteristic
126C4—64no—
127C4—64no—
128C3#2273⋊C311yescharacteristic
129C2—31no—
130C2—31no—
131C2—64no—
132C2C22⋊(C42⋊C9)11yescharacteristic
subgroupG/H
center, hypercenterC2×C3C22⋊(C42⋊C3)
commutator, hypocenter#2273C9
Frattini, socleC23×C3C22⋊A4
Fitting, cosocleC3×#2273C3
prime radicalC25×C3A4
LCSG ▷ #2273
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
10. #2273C9semidirect
47. C2×C42C22⋊C9semidirect
49. #95C22⋊C9semidirect
103. C23C42⋊C9semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×#22733
C2×C22⋊(C22⋊C9)4
C2×C42⋊C94
#95⋊C94