Finite Group Databasebeta

← C22×C8×C22⋊C9 #11919775

Subgroups — C22×C8×C22⋊C9 #11919775

Order 1152.

836 conjugacy classes of subgroups; only the 190 normal subgroups are shown.

normal subgroups only

This group has 836 conjugacy classes of subgroups — too many to draw. Only its 190 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×C4×C22⋊C9C211yesmaximal, characteristic
2C2×C8×C22⋊C9C216yesmaximal, direct product factor
3C24×C3×C8C311yesmaximal, characteristic
4C23×C22⋊C9C411yescharacteristic
5C2×C4×C22⋊C9C413yes—
6C2×C4×C22⋊C9C2213yes—
7C22×C8×C9—41nomaximal
8C8×C22⋊C9C2214yesdirect product factor
9C24×C3×C4C2×C311yescharacteristic
10C23×C3×C8—31no—
11C23×C3×C8—31no—
12C23×C3×C8—36no—
13C23×C3×C8C2×C316yes—
14C22×C22⋊C9C814yesdirect product factor
15C22×C22⋊C9C2×C413yes—
16C22×C4×C9—41no—
17C4×C22⋊C9C2×C413yes—
18C4×C22⋊C9C2311yescharacteristic
19C2×C8×C9—46no—
20C24×C8C911yescharacteristic, complemented, Sylow
21C25×C3C3×C411yescharacteristic
22C23×C3×C4—31no—
23C23×C3×C4—33no—
24C23×C3×C4—31no—
25C23×C3×C4—33no—
26C23×C3×C4C3×C413yes—
27C23×C3×C4C22×C313yes—
28C22×C3×C8—36no—
29C22×C3×C8—38no—
30C22×C3×C8—31no—
31C22×C3×C8—36no—
32C22×C3×C8—36no—
33C22×C3×C8—36no—
34C22×C3×C8—312no—
35C22×C3×C8A411yescharacteristic
36C22×C3×C8C22×C314yes—
37C23×C9—41no—
38C2×C22⋊C9C2×C816yesdirect product factor
39C2×C22⋊C9C22×C411yescharacteristic
40C2×C4×C9—43no—
41C2×C4×C9—43no—
42C8×C9—44no—
43C24×C4C2×C911yescharacteristic
44C23×C8—31no—
45C23×C8—31no—
46C23×C8—36no—
47C23×C8C2×C916yescomplemented
48C24×C3—34no—
49C24×C3—33no—
50C24×C3—31no—
51C24×C3C3×C814yes—
52C24×C3C2×C3×C413yes—
53C22×C3×C4—32no—
54C22×C3×C4—36no—
55C22×C3×C4—36no—
56C22×C3×C4—31no—
57C22×C3×C4—33no—
58C22×C3×C4—33no—
59C22×C3×C4—33no—
60C22×C3×C4—33no—
61C22×C3×C4—33no—
62C22×C3×C4—33no—
63C22×C3×C4—36no—
64C22×C3×C4—33no—
65C22×C3×C4—33no—
66C22×C3×C4C2×C3×C413yes—
67C22×C3×C4C2×A411yescharacteristic
68C22×C3×C4C23×C311yescharacteristic
69C2×C3×C8—312no—
70C2×C3×C8—36no—
71C2×C3×C8—312no—
72C2×C3×C8—34no—
73C2×C3×C8—34no—
74C2×C3×C8C2×A416yes—
75C22×C9—44no—
76C22×C9—43no—
77C22⋊C9C22×C811yescharacteristic, direct product factor
78C4×C9—43no—
79C4×C9—41no—
80C25C4×C911yescharacteristic
81C23×C4—31no—
82C23×C4—33no—
83C23×C4—31no—
84C23×C4—33no—
85C23×C4C4×C913yes—
86C23×C4C22×C913yes—
87C22×C8—36no—
88C22×C8—38no—
89C22×C8—31no—
90C22×C8—36no—
91C22×C8—36no—
92C22×C8—36no—
93C22×C8—312no—
94C22×C8C22⋊C911yescharacteristic, direct product factor
95C22×C8C22×C914yescomplemented
96C23×C3—33no—
97C23×C3—312no—
98C23×C3—36no—
99C23×C3—32no—
100C23×C3—312no—
101C23×C3—34no—
102C23×C3—34no—
103C23×C3—33no—
104C23×C3—33no—
105C23×C3C2×C3×C816yes—
106C23×C3C4×A411yescharacteristic
107C23×C3C22×C3×C411yescharacteristic
108C2×C3×C4—36no—
109C2×C3×C4—36no—
110C2×C3×C4—33no—
111C2×C3×C4—33no—
112C2×C3×C4—33no—
113C2×C3×C4—36no—
114C2×C3×C4—33no—
115C2×C3×C4—33no—
116C2×C3×C4—31no—
117C2×C3×C4—33no—
118C2×C3×C4—31no—
119C2×C3×C4C4×A413yes—
120C2×C3×C4C22×A413yes—
121C3×C8—34no—
122C3×C8C22×A414yes—
123C2×C9—41no—
124C2×C9—46no—
125C24—33no—
126C24—34no—
127C24—31no—
128C24C8×C914yescomplemented
129C24C2×C4×C913yes—
130C22×C4—32no—
131C22×C4—36no—
132C22×C4—36no—
133C22×C4—31no—
134C22×C4—33no—
135C22×C4—33no—
136C22×C4—33no—
137C22×C4—33no—
138C22×C4—33no—
139C22×C4—33no—
140C22×C4—36no—
141C22×C4—33no—
142C22×C4—33no—
143C22×C4C2×C4×C913yes—
144C22×C4C2×C22⋊C911yescharacteristic
145C22×C4C23×C911yescharacteristic
146C2×C8—312no—
147C2×C8—36no—
148C2×C8—34no—
149C2×C8—312no—
150C2×C8—34no—
151C2×C8C2×C22⋊C916yesdirect product factor
152C22×C3—36no—
153C22×C3—31no—
154C22×C3—36no—
155C22×C3—38no—
156C22×C3—33no—
157C22×C3—31no—
158C22×C3—312no—
159C22×C3—36no—
160C22×C3—36no—
161C22×C3C8×A414yes—
162C22×C3C22×C3×C811yescharacteristic
163C22×C3C2×C4×A413yes—
164C3×C4—31no—
165C3×C4—33no—
166C3×C4C2×C4×A413yes—
167C3×C4C23×A411yescharacteristic
168C9—41noSylow
169C23—33no—
170C23—312no—
171C23—36no—
172C23—32no—
173C23—312no—
174C23—34no—
175C23—34no—
176C23—33no—
177C23—33no—
178C23C2×C8×C916yescomplemented
179C23C4×C22⋊C911yescharacteristic
180C23C22×C4×C911yescharacteristic
181C2×C4—36no—
182C2×C4—36no—
183C2×C4—33no—
184C2×C4—33no—
185C2×C4—31no—
186C2×C4—33no—
187C2×C4—33no—
188C2×C4—36no—
189C2×C4—33no—
190C2×C4—33no—
191C2×C4—31no—
192C2×C4C4×C22⋊C913yes—
193C2×C4C22×C22⋊C913yes—
194C8—34no—
195C8C22×C22⋊C914yesdirect product factor
196C2×C3—36no—
197C2×C3—31no—
198C2×C3—31no—
199C2×C3C2×C8×A416yes—
200C2×C3C22×C4×A411yescharacteristic
201C22—36no—
202C22—31no—
203C22—36no—
204C22—38no—
205C22—31no—
206C22—33no—
207C22—36no—
208C22—312no—
209C22—36no—
210C22C8×C22⋊C914yesdirect product factor
211C22C22×C8×C911yescharacteristic, complemented
212C22C2×C4×C22⋊C913yes—
213C4—31no—
214C4—33no—
215C4C2×C4×C22⋊C913yes—
216C4C23×C22⋊C911yescharacteristic
217C3C22×C8×A411yescharacteristic
218C2—31no—
219C2—36no—
220C2—31no—
221C2C2×C8×C22⋊C916yesdirect product factor
222C2C22×C4×C22⋊C911yescharacteristic
subgroupG/H
center, hypercenterC22×C3×C8A4
commutator, hypocenterC22C22×C8×C9
FrattiniC3×C4C23×A4
FittingC24×C3×C8C3
socle, prime radicalC25×C3C3×C4
cosocleC22×C3×C4C23×C3
LCSG ▷ C22
UCSC1 ◁ C22×C3×C8

Complements

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

NH ≅ G/Ntype
2. C2×C8×C22⋊C9C2direct (N × H)
8. C8×C22⋊C9C22direct (N × H)
14. C22×C22⋊C9C8direct (N × H)
20. C24×C8C9semidirect
38. C2×C22⋊C9C2×C8direct (N × H)
47. C23×C8C2×C9semidirect
77. C22⋊C9C22×C8direct (N × H)
94. C22×C8C22⋊C9direct (N × H)
95. C22×C8C22×C9semidirect
128. C24C8×C9semidirect
151. C2×C8C2×C22⋊C9direct (N × H)
178. C23C2×C8×C9semidirect
195. C8C22×C22⋊C9direct (N × H)
210. C22C8×C22⋊C9direct (N × H)
211. C22C22×C8×C9semidirect
221. C2C2×C8×C22⋊C9direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊C92
C2×C8×C22⋊C92
C24×C3×C83
C22×C8×C94