Finite Group Databasebeta

← C2×C4×C42⋊C9 #11919387

Subgroups — C2×C4×C42⋊C9 #11919387

Order 1152.

480 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 56 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
1C22×C42⋊C9C211yesmaximal, characteristic
2C4×C42⋊C9C212yesmaximal, direct product factor
3C2×C3×C43C311yesmaximal, characteristic
4C2×C4×C22⋊C9—41nomaximal
5C2×C42⋊C9C412yesdirect product factor
6C2×C42⋊C9C2211yescharacteristic
7C22×C3×C42—31no—
8C22×C3×C42—31no—
9C22×C3×C42C2×C311yescharacteristic
10C3×C43—32no—
11C3×C43C2×C312yes—
12C22×C22⋊C9—41no—
13C4×C22⋊C9—42no—
14C42⋊C9C2×C411yescharacteristic, direct product factor
15C2×C43C911yescharacteristic, complemented, Sylow
16C23×C3×C4—31no—
17C23×C3×C4—31no—
18C23×C3×C4A411yescharacteristic
19C2×C3×C42—31no—
20C2×C3×C42—32no—
21C2×C3×C42—32no—
22C2×C3×C42—32no—
23C2×C3×C42—38no—
24C2×C3×C42—32no—
25C2×C3×C42—34no—
26C2×C3×C42—32no—
27C2×C3×C42—32no—
28C2×C3×C42—32no—
29C2×C3×C42C3×C412yes—
30C2×C3×C42C22×C311yescharacteristic
31C2×C22⋊C9—42no—
32C2×C22⋊C9—41no—
33C2×C4×C9—161no—
34C22×C42—31no—
35C22×C42—31no—
36C22×C42C2×C911yescharacteristic
37C43—32no—
38C43C2×C912yescomplemented
39C24×C3C2×A411yescharacteristic
40C22×C3×C4—38no—
41C22×C3×C4—32no—
42C22×C3×C4—34no—
43C22×C3×C4—32no—
44C22×C3×C4—32no—
45C22×C3×C4—32no—
46C22×C3×C4—32no—
47C22×C3×C4—32no—
48C22×C3×C4—31no—
49C22×C3×C4—32no—
50C22×C3×C4—31no—
51C22×C3×C4—31no—
52C22×C3×C4—31no—
53C22×C3×C4—32no—
54C22×C3×C4C2×A412yes—
55C3×C42—32no—
56C3×C42—31no—
57C3×C42—38no—
58C3×C42—38no—
59C3×C42—34no—
60C3×C42—34no—
61C3×C42—34no—
62C3×C42—34no—
63C3×C42—32no—
64C3×C42C2×C3×C411yescharacteristic
65C22×C9—161no—
66C22⋊C9—41no—
67C4×C9—162no—
68C23×C4—31no—
69C23×C4—31no—
70C23×C4C22⋊C911yescharacteristic
71C2×C42—31no—
72C2×C42—32no—
73C2×C42—32no—
74C2×C42—32no—
75C2×C42—38no—
76C2×C42—32no—
77C2×C42—34no—
78C2×C42—32no—
79C2×C42—32no—
80C2×C42—32no—
81C2×C42C4×C912yescomplemented
82C2×C42C22×C911yescharacteristic
83C23×C3—32no—
84C23×C3—31no—
85C23×C3—31no—
86C23×C3C4×A412yes—
87C23×C3C22×A411yescharacteristic
88C2×C3×C4—32no—
89C2×C3×C4—38no—
90C2×C3×C4—32no—
91C2×C3×C4—32no—
92C2×C3×C4—34no—
93C2×C3×C4—32no—
94C2×C3×C4—34no—
95C2×C3×C4—34no—
96C2×C3×C4—38no—
97C2×C3×C4—38no—
98C2×C3×C4—34no—
99C2×C3×C4—34no—
100C2×C3×C4—32no—
101C2×C3×C4—31no—
102C2×C3×C4—31no—
103C2×C3×C4—32no—
104C2×C3×C4—31no—
105C2×C3×C4—32no—
106C2×C3×C4—32no—
107C2×C3×C4—32no—
108C2×C3×C4C42⋊C311yescharacteristic
109C2×C9—162no—
110C2×C9—161no—
111C24C2×C22⋊C911yescharacteristic
112C22×C4—38no—
113C22×C4—32no—
114C22×C4—34no—
115C22×C4—32no—
116C22×C4—32no—
117C22×C4—32no—
118C22×C4—32no—
119C22×C4—32no—
120C22×C4—31no—
121C22×C4—32no—
122C22×C4—31no—
123C22×C4—31no—
124C22×C4—31no—
125C22×C4—32no—
126C22×C4C2×C22⋊C912yes—
127C42—32no—
128C42—31no—
129C42—38no—
130C42—38no—
131C42—34no—
132C42—34no—
133C42—34no—
134C42—34no—
135C42—32no—
136C42C2×C4×C911yescharacteristic, complemented
137C22×C3—31no—
138C22×C3—32no—
139C22×C3—32no—
140C22×C3—32no—
141C22×C3—32no—
142C22×C3—31no—
143C22×C3—31no—
144C22×C3C2×C42⋊C311yescharacteristic
145C22×C3C2×C4×A411yescharacteristic
146C3×C4—38no—
147C3×C4—32no—
148C3×C4—32no—
149C3×C4—34no—
150C3×C4—32no—
151C3×C4C2×C42⋊C312yes—
152C9—161noSylow
153C23—32no—
154C23—31no—
155C23—31no—
156C23C4×C22⋊C912yes—
157C23C22×C22⋊C911yescharacteristic
158C2×C4—32no—
159C2×C4—32no—
160C2×C4—38no—
161C2×C4—32no—
162C2×C4—32no—
163C2×C4—34no—
164C2×C4—34no—
165C2×C4—34no—
166C2×C4—38no—
167C2×C4—34no—
168C2×C4—34no—
169C2×C4—38no—
170C2×C4—32no—
171C2×C4—31no—
172C2×C4—31no—
173C2×C4—32no—
174C2×C4—31no—
175C2×C4—32no—
176C2×C4—32no—
177C2×C4—32no—
178C2×C4C42⋊C911yescharacteristic, direct product factor
179C2×C3—31no—
180C2×C3—31no—
181C2×C3—32no—
182C2×C3C4×C42⋊C312yes—
183C2×C3C22×C42⋊C311yescharacteristic
184C22—31no—
185C22—32no—
186C22—32no—
187C22—31no—
188C22—31no—
189C22—32no—
190C22—32no—
191C22C2×C42⋊C911yescharacteristic
192C22C2×C4×C22⋊C911yescharacteristic
193C4—32no—
194C4—32no—
195C4—34no—
196C4—38no—
197C4—32no—
198C4C2×C42⋊C912yesdirect product factor
199C3C2×C4×C42⋊C311yescharacteristic
200C2—31no—
201C2—31no—
202C2—32no—
203C2C4×C42⋊C912yesdirect product factor
204C2C22×C42⋊C911yescharacteristic
subgroupG/H
center, hypercenterC2×C3×C4C42⋊C3
commutator, hypocenterC42C2×C4×C9
FrattiniC23×C3C22×A4
FittingC2×C3×C43C3
socle, prime radicalC24×C3C2×A4
cosocleC2×C3×C42C22×C3
LCSG ▷ C42
UCSC1 ◁ C2×C3×C4

Complements

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

NH ≅ G/Ntype
2. C4×C42⋊C9C2direct (N × H)
5. C2×C42⋊C9C4direct (N × H)
14. C42⋊C9C2×C4direct (N × H)
15. C2×C43C9semidirect
38. C43C2×C9semidirect
81. C2×C42C4×C9semidirect
136. C42C2×C4×C9semidirect
178. C2×C4C42⋊C9direct (N × H)
198. C4C2×C42⋊C9direct (N × H)
203. C2C4×C42⋊C9direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C42⋊C92
C4×C42⋊C92
C2×C3×C433
C2×C4×C22⋊C94