Finite Group Databasebeta

← #2736⋊C9 #11919647

Subgroups — #2736⋊C9 #11919647

Order 1152.

245 conjugacy classes of subgroups; only the 21 normal subgroups are shown.

normal subgroups only

This group has 245 conjugacy classes of subgroups — too many to draw. Only its 21 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×#2736C311yesmaximal, characteristic
2C2×C22⋊(C22⋊C9)—41nomaximal
3C22⋊(Q8⋊C9)—41nomaximal
4C2×C42⋊C9—42nomaximal
5#95⋊C9—41nomaximal
6C3×#397—31no—
7C3×#393—31no—
8C3×#388—32no—
9C3×#379—31no—
10C22⋊(C22⋊C9)—41no—
11C42⋊C9—42no—
12#2736C911yescharacteristic, complemented, Sylow
13C25×C3A411yescharacteristic
14C22×C3×Q8A411yescharacteristic
15C2×C3×C4⋊C4—31no—
16C2×C3×C22⋊C4—32no—
17C2×C3×C22⋊C4—31no—
18C2×C3×C22⋊C4—32no—
19C2×C3×C22⋊C4—31no—
20C2×C3×C42A412yes—
21C3×#95—31no—
22C3×#95—32no—
23C3×#95A411yescharacteristic
24C2×C22⋊C9—164no—
25C2×C22⋊C9—161no—
26Q8⋊C9—164no—
27#397—31no—
28#393—31no—
29#388—32no—
30#379—31no—
31C24×C3—31no—
32C24×C3—41no—
33C24×C3—62no—
34C24×C3—121no—
35C2×C3×Q8—121no—
36C22×C3×C4—31no—
37C22×C3×C4—31no—
38C22×C3×C4—32no—
39C3×C4⋊C4—121no—
40C3×C22⋊C4—64no—
41C3×C22⋊C4—122no—
42C3×C22⋊C4—121no—
43C3×C22⋊C4—121no—
44C3×C42—42no—
45C22⋊C9—164no—
46C22⋊C9—161no—
47C25C22⋊C911yescharacteristic
48C22×Q8C22⋊C911yescharacteristic, complemented
49C2×C4⋊C4—31no—
50C2×C22⋊C4—32no—
51C2×C22⋊C4—31no—
52C2×C22⋊C4—32no—
53C2×C22⋊C4—31no—
54C2×C42C22⋊C912yescomplemented
55#95—31no—
56#95—32no—
57#95C22⋊C911yescharacteristic, complemented
58C23×C3—32no—
59C23×C3—44no—
60C23×C3—61no—
61C23×C3—62no—
62C23×C3—62no—
63C23×C3—61no—
64C23×C3—122no—
65C23×C3—124no—
66C23×C3—122no—
67C23×C3C22⋊A411yescharacteristic
68C3×Q8—44no—
69C2×C3×C4—62no—
70C2×C3×C4—62no—
71C2×C3×C4—61no—
72C2×C3×C4—62no—
73C2×C3×C4—62no—
74C2×C3×C4—61no—
75C2×C3×C4—62no—
76C2×C9—641no—
77C24—31no—
78C24—41no—
79C24—62no—
80C24—121no—
81C2×Q8—121no—
82C22×C4—31no—
83C22×C4—31no—
84C22×C4—32no—
85C4⋊C4—121no—
86C22⋊C4—64no—
87C22⋊C4—122no—
88C22⋊C4—121no—
89C22⋊C4—121no—
90C42—42no—
91C22×C3—31no—
92C22×C3—31no—
93C22×C3—44no—
94C22×C3—62no—
95C22×C3—64no—
96C22×C3—122no—
97C22×C3—121no—
98C22×C3—124no—
99C22×C3—121no—
100C22×C3#99711yescharacteristic
101C3×C4—122no—
102C3×C4—121no—
103C3×C4—121no—
104C9—641noSylow
105C23—32no—
106C23—44no—
107C23—61no—
108C23—62no—
109C23—62no—
110C23—61no—
111C23—122no—
112C23—124no—
113C23—122no—
114C23C22⋊(C22⋊C9)11yescharacteristic
115Q8—44no—
116C2×C4—62no—
117C2×C4—62no—
118C2×C4—61no—
119C2×C4—62no—
120C2×C4—62no—
121C2×C4—61no—
122C2×C4—62no—
123C2×C3—31no—
124C2×C3—31no—
125C2×C3—122no—
126C2×C3#546411yescharacteristic
127C22—31no—
128C22—31no—
129C22—44no—
130C22—62no—
131C22—64no—
132C22—122no—
133C22—121no—
134C22—124no—
135C22—121no—
136C22#6370311yescharacteristic
137C4—122no—
138C4—121no—
139C4—121no—
140C3#2736⋊C311yescharacteristic
141C2—31no—
142C2—31no—
143C2—122no—
144C2#1058956611yescharacteristic
subgroupG/H
center, hypercenterC2×C3#5464
commutator, hypocenter#2736C9
Frattini, socleC23×C3C22⋊A4
Fitting, cosocleC3×#2736C3
prime radicalC25×C3A4
LCSG ▷ #2736
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
12. #2736C9semidirect
48. C22×Q8C22⋊C9semidirect
54. C2×C42C22⋊C9semidirect
57. #95C22⋊C9semidirect

Maximal subgroups

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

subgroupindex
C3×#27363
C2×C22⋊(C22⋊C9)4
C22⋊(Q8⋊C9)4
C2×C42⋊C94
#95⋊C94