Finite Group Databasebeta

← #2912⋊C9 #11919561

Subgroups — #2912⋊C9 #11919561

Order 1152.

231 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 231 conjugacy classes of subgroups — too many to draw. Only its 61 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×#131⋊C9C211yesmaximal, characteristic
2#520⋊C9C212yesmaximal
3C3×#2912C311yesmaximal, characteristic
4C2×#41⋊C9C2211yescharacteristic
5#131⋊C9C412yescomplemented
6C4×Q8⋊C9—22no—
7C9×#106—41nomaximal
8C2×C3×#131C2×C311yescharacteristic
9C3×#520C2×C312yes—
10C3×#428—32no—
11C3×#427—31no—
12C2×C3×#106—31no—
13#41⋊C9C2×C411yescharacteristic
14#41⋊C9Q811yescharacteristic
15C2×Q8⋊C9D411yescharacteristic
16C2×C8×C9—41no—
17C9×C4⋊C4—42no—
18#2912C911yescharacteristic, complemented, Sylow
19C2×C3×#41C22×C311yescharacteristic
20C3×#131—32no—
21C3×#131C3×C412yes—
22C2×C3×M16—31no—
23C22×C3×C8—31no—
24C3×C4×Q8—22no—
25C3×C4×D4—62no—
26C3×#117—32no—
27C2×C3×C4⋊C4—32no—
28C3×#107—32no—
29C3×#106—32no—
30C3×#106—31no—
31C3×#106A411yescharacteristic
32C2×C4×C9—41no—
33C2×C4×C9—82no—
34Q8⋊C9C4⋊C411yescharacteristic
35C8×C9—42no—
36C2×#131C2×C911yescharacteristic
37#520C2×C912yes—
38#428—32no—
39#427—31no—
40C2×#106—31no—
41C3×#41—31no—
42C3×#41—31no—
43C3×#41C2×C3×C411yescharacteristic
44C3×#41C3×Q811yescharacteristic
45C2×C3×Q8C3×D411yescharacteristic
46C2×C3×D4—31no—
47C22×C3×C4—31no—
48C22×C3×C4—62no—
49C3×M16—32no—
50C3×M16—32no—
51C2×C3×C8—31no—
52C2×C3×C8—32no—
53C2×C3×C8—32no—
54C2×C3×C8C2×A411yescharacteristic
55C3×C4⋊C4—32no—
56C3×C4⋊C4—62no—
57C3×C4⋊C4C2×A412yes—
58C3×C22⋊C4—62no—
59C3×C42—62no—
60C22×C9—41no—
61C4×C9—41no—
62C4×C9—41no—
63C4×C9—162no—
64C2×#41C22×C911yescharacteristic
65#131—32no—
66#131C4×C912yescomplemented
67C2×M16—31no—
68C22×C8—31no—
69C4×Q8—22no—
70C4×D4—62no—
71#117—32no—
72C2×C4⋊C4—32no—
73#107—32no—
74#106—32no—
75#106—31no—
76#106C22⋊C911yescharacteristic
77C23×C3—31no—
78C3×Q8—31no—
79C3×Q8C3×C4⋊C411yescharacteristic
80C3×D4—31no—
81C3×D4—31no—
82C3×D4—32no—
83C2×C3×C4—22no—
84C2×C3×C4—31no—
85C2×C3×C4—31no—
86C2×C3×C4—31no—
87C2×C3×C4—31no—
88C2×C3×C4—31no—
89C2×C3×C4—62no—
90C2×C3×C4—242no—
91C2×C3×C4C22×A411yescharacteristic
92C3×C8—32no—
93C3×C8C4×A412yes—
94C2×C9—41no—
95C2×C9—42no—
96#41—31no—
97#41—31no—
98#41C2×C4×C911yescharacteristic
99#41Q8×C911yescharacteristic
100C2×Q8D4×C911yescharacteristic
101C2×D4—31no—
102C22×C4—31no—
103C22×C4—62no—
104M16—32no—
105M16—32no—
106C2×C8—31no—
107C2×C8—32no—
108C2×C8—32no—
109C2×C8C2×C22⋊C911yescharacteristic
110C4⋊C4—32no—
111C4⋊C4—62no—
112C4⋊C4C2×C22⋊C912yes—
113C22⋊C4—62no—
114C42—62no—
115C22×C3—31no—
116C22×C3—31no—
117C22×C3—62no—
118C22×C3D4×A411yescharacteristic
119C3×C4—31no—
120C3×C4—31no—
121C3×C4—42no—
122C3×C4—122no—
123C3×C4C2×C4×A411yescharacteristic
124C3×C4Q8×A411yescharacteristic
125C9—41noSylow
126C23—31no—
127Q8—31no—
128Q8C9×C4⋊C411yescharacteristic
129D4—31no—
130D4—31no—
131D4—32no—
132C2×C4—22no—
133C2×C4—31no—
134C2×C4—31no—
135C2×C4—31no—
136C2×C4—31no—
137C2×C4—31no—
138C2×C4—62no—
139C2×C4—242no—
140C2×C4C22×C22⋊C911yescharacteristic
141C8—32no—
142C8C4×C22⋊C912yes—
143C2×C3—61no—
144C2×C3—61no—
145C2×C3A4×C4⋊C411yescharacteristic
146C2×C3#577⋊C312yes—
147C22—31no—
148C22—31no—
149C22—62no—
150C22D4×C22⋊C911yescharacteristic
151C4—31no—
152C4—31no—
153C4—42no—
154C4—122no—
155C4C2×C4×C22⋊C911yescharacteristic
156C4Q8×C22⋊C911yescharacteristic
157C3#2912⋊C311yescharacteristic
158C2—61no—
159C2—61no—
160C2C4⋊C4×C22⋊C911yescharacteristic
161C2#577⋊C912yes—
subgroupG/H
center, socleC22×C3D4×A4
commutator#41C2×C4×C9
FrattiniC2×C3×C4C22×A4
FittingC3×#2912C3
prime radical, cosocleC2×C3×#41C22×C3
hypercenterC3×#106A4
hypocenterQ8C9×C4⋊C4
LCSG ▷ #41 ▷ Q8
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×#106

Complements

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

NH ≅ G/Ntype
5. #131⋊C9C4semidirect
18. #2912C9semidirect
66. #131C4×C9semidirect

Maximal subgroups

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

subgroupindex
C2×#131⋊C92
#520⋊C92
C3×#29123
C9×#1064