Finite Group Databasebeta

← C4×C8×C22⋊C9 #11919517

Subgroups — C4×C8×C22⋊C9 #11919517

Order 1152.

356 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 110 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×C8×C22⋊C9C212yesmaximal
2C42×C22⋊C9C211yesmaximal, characteristic
3C22×C3×C4×C8C311yesmaximal, characteristic
4C2×C4×C22⋊C9C412yes—
5C2×C4×C22⋊C9C2211yescharacteristic
6C8×C22⋊C9C414yesdirect product factor
7C4×C8×C9—41nomaximal
8C23×C3×C8C2×C312yes—
9C22×C3×C42C2×C311yescharacteristic
10C2×C3×C4×C8—31no—
11C2×C3×C4×C8—32no—
12C2×C3×C4×C8—31no—
13C22×C22⋊C9C2×C411yescharacteristic
14C4×C22⋊C9C814yesdirect product factor
15C4×C22⋊C9C2×C412yes—
16C2×C8×C9—42no—
17C42×C9—41no—
18C22×C4×C8C911yescharacteristic, complemented, Sylow
19C23×C3×C4C3×C412yes—
20C23×C3×C4C22×C311yescharacteristic
21C22×C3×C8—32no—
22C22×C3×C8—34no—
23C22×C3×C8—32no—
24C22×C3×C8C3×C414yes—
25C2×C3×C42—31no—
26C2×C3×C42—31no—
27C2×C3×C42—32no—
28C3×C4×C8—32no—
29C3×C4×C8—32no—
30C3×C4×C8—31no—
31C3×C4×C8A411yescharacteristic
32C2×C22⋊C9C4211yescharacteristic
33C2×C22⋊C9C2×C812yes—
34C2×C4×C9—42no—
35C2×C4×C9—41no—
36C8×C9—44no—
37C23×C8C2×C912yes—
38C22×C42C2×C911yescharacteristic
39C2×C4×C8—31no—
40C2×C4×C8—32no—
41C2×C4×C8—31no—
42C24×C3C2×C3×C411yescharacteristic
43C22×C3×C4—32no—
44C22×C3×C4—31no—
45C22×C3×C4—32no—
46C22×C3×C4—31no—
47C22×C3×C4—32no—
48C22×C3×C4—34no—
49C22×C3×C4C3×C814yes—
50C22×C3×C4C2×C3×C412yes—
51C2×C3×C8—34no—
52C2×C3×C8—32no—
53C2×C3×C8—34no—
54C2×C3×C8—34no—
55C2×C3×C8—34no—
56C2×C3×C8C2×A412yes—
57C3×C42—32no—
58C3×C42—32no—
59C3×C42—31no—
60C3×C42C2×A411yescharacteristic
61C22×C9—41no—
62C22⋊C9C4×C811yescharacteristic, direct product factor
63C4×C9—44no—
64C4×C9—42no—
65C23×C4C4×C912yes—
66C23×C4C22×C911yescharacteristic
67C22×C8—32no—
68C22×C8—32no—
69C22×C8—34no—
70C22×C8C4×C914yescomplemented
71C2×C42—31no—
72C2×C42—31no—
73C2×C42—32no—
74C4×C8—32no—
75C4×C8—32no—
76C4×C8—31no—
77C4×C8C22⋊C911yescharacteristic, direct product factor
78C23×C3—32no—
79C23×C3—31no—
80C23×C3—31no—
81C23×C3C3×C4211yescharacteristic
82C23×C3C2×C3×C812yes—
83C2×C3×C4—32no—
84C2×C3×C4—34no—
85C2×C3×C4—31no—
86C2×C3×C4—32no—
87C2×C3×C4—34no—
88C2×C3×C4—34no—
89C2×C3×C4—32no—
90C2×C3×C4—32no—
91C2×C3×C4—34no—
92C2×C3×C4—32no—
93C2×C3×C4C4×A412yes—
94C2×C3×C4C22×A411yescharacteristic
95C3×C8—34no—
96C3×C8C4×A414yes—
97C2×C9—41no—
98C2×C9—42no—
99C24C2×C4×C911yescharacteristic
100C22×C4—32no—
101C22×C4—31no—
102C22×C4—32no—
103C22×C4—31no—
104C22×C4—32no—
105C22×C4—34no—
106C22×C4C8×C914yescomplemented
107C22×C4C2×C4×C912yes—
108C2×C8—34no—
109C2×C8—32no—
110C2×C8—34no—
111C2×C8—34no—
112C2×C8—34no—
113C2×C8C2×C22⋊C912yes—
114C42—32no—
115C42—32no—
116C42—31no—
117C42C2×C22⋊C911yescharacteristic
118C22×C3—31no—
119C22×C3—32no—
120C22×C3—32no—
121C22×C3—31no—
122C22×C3—31no—
123C22×C3—32no—
124C22×C3—32no—
125C22×C3C3×C4×C811yescharacteristic
126C22×C3C2×C4×A411yescharacteristic
127C3×C4—32no—
128C3×C4—34no—
129C3×C4C8×A414yes—
130C3×C4C2×C4×A412yes—
131C9—41noSylow
132C23—32no—
133C23—31no—
134C23—31no—
135C23C42×C911yescharacteristic
136C23C2×C8×C912yes—
137C2×C4—32no—
138C2×C4—34no—
139C2×C4—31no—
140C2×C4—32no—
141C2×C4—34no—
142C2×C4—34no—
143C2×C4—32no—
144C2×C4—32no—
145C2×C4—34no—
146C2×C4—32no—
147C2×C4C4×C22⋊C912yes—
148C2×C4C22×C22⋊C911yescharacteristic
149C8—34no—
150C8C4×C22⋊C914yesdirect product factor
151C2×C3—31no—
152C2×C3—32no—
153C2×C3—31no—
154C2×C3C42×A411yescharacteristic
155C2×C3C2×C8×A412yes—
156C22—31no—
157C22—32no—
158C22—32no—
159C22—31no—
160C22—31no—
161C22—32no—
162C22—32no—
163C22C4×C8×C911yescharacteristic, complemented
164C22C2×C4×C22⋊C911yescharacteristic
165C4—32no—
166C4—34no—
167C4C8×C22⋊C914yesdirect product factor
168C4C2×C4×C22⋊C912yes—
169C3C4×C8×A411yescharacteristic
170C2—31no—
171C2—31no—
172C2—32no—
173C2C42×C22⋊C911yescharacteristic
174C2C2×C8×C22⋊C912yes—
subgroupG/H
center, hypercenterC3×C4×C8A4
commutator, hypocenterC22C4×C8×C9
FrattiniC2×C3×C4C22×A4
FittingC22×C3×C4×C8C3
socle, prime radicalC24×C3C2×C3×C4
cosocleC23×C3×C4C22×C3
LCSG ▷ C22
UCSC1 ◁ C3×C4×C8

Complements

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

NH ≅ G/Ntype
6. C8×C22⋊C9C4direct (N × H)
14. C4×C22⋊C9C8direct (N × H)
18. C22×C4×C8C9semidirect
62. C22⋊C9C4×C8direct (N × H)
70. C22×C8C4×C9semidirect
77. C4×C8C22⋊C9direct (N × H)
106. C22×C4C8×C9semidirect
150. C8C4×C22⋊C9direct (N × H)
163. C22C4×C8×C9semidirect
167. C4C8×C22⋊C9direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C8×C22⋊C92
C42×C22⋊C92
C22×C3×C4×C83
C4×C8×C94