Finite Group Databasebeta

← C2×#519⋊C9 #11919681

Subgroups — C2×#519⋊C9 #11919681

Order 1152.

713 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 713 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C23×Q8⋊C9C211yesmaximal, characteristic
2#519⋊C9C214yesmaximal, direct product factor
3C2×C4×Q8⋊C9C212yesmaximal, complemented
4C2×C3×#519C311yesmaximal, characteristic
5C22×Q8⋊C9C414yescomplemented
6C22×Q8⋊C9C2211yescharacteristic
7C22×Q8⋊C9C2212yes—
8C2×C9×C22⋊C4—41nomaximal
9C4×Q8⋊C9C2214yescomplemented
10C23×C3×Q8C2×C311yescharacteristic
11C3×#519—34no—
12C3×#519C2×C314yes—
13C2×C3×C4×Q8—32no—
14C2×C3×C4×Q8C2×C312yes—
15C2×C3×#117—31no—
16C2×C3×#117—31no—
17C24×C9—41no—
18C22×C4×C9—42no—
19C2×Q8⋊C9C2×C412yes—
20C2×Q8⋊C9C2×C414yescomplemented
21C2×Q8⋊C9C2311yescharacteristic
22C9×C22⋊C4—44no—
23C2×#519C911yescharacteristic, complemented, Sylow
24C22×C3×Q8—34no—
25C22×C3×Q8—31no—
26C22×C3×Q8—32no—
27C22×C3×Q8C3×C414yes—
28C22×C3×Q8C22×C311yescharacteristic
29C22×C3×Q8C22×C312yes—
30C23×C3×C4—31no—
31C3×C4×Q8—38no—
32C3×C4×Q8—38no—
33C3×C4×Q8—34no—
34C3×C4×Q8C22×C314yes—
35C3×#117—34no—
36C3×#117—34no—
37C3×#117—34no—
38C3×#117—34no—
39C2×C3×C4⋊C4—32no—
40C2×C3×C4⋊C4—32no—
41C2×C3×C22⋊C4—31no—
42C2×C3×C22⋊C4A411yescharacteristic
43C2×C3×C42—32no—
44C2×C3×C42—32no—
45C23×C9—44no—
46C23×C9—42no—
47C23×C9—41no—
48C23×C9—84no—
49C2×C4×C9—44no—
50C2×C4×C9—84no—
51Q8⋊C9C22×C411yescharacteristic
52C23×Q8C2×C911yescharacteristic
53#519—34no—
54#519C2×C914yescomplemented
55C2×C4×Q8—32no—
56C2×C4×Q8C2×C912yescomplemented
57C2×#117—31no—
58C2×#117—31no—
59C24×C3C2×A411yescharacteristic
60C2×C3×Q8—32no—
61C2×C3×Q8—34no—
62C2×C3×Q8—38no—
63C2×C3×Q8—32no—
64C2×C3×Q8—31no—
65C2×C3×Q8—34no—
66C2×C3×Q8—38no—
67C2×C3×Q8—32no—
68C2×C3×Q8—34no—
69C2×C3×Q8C2×C3×C412yes—
70C2×C3×Q8C2×C3×C414yes—
71C2×C3×Q8C23×C311yescharacteristic
72C22×C3×C4—34no—
73C22×C3×C4—34no—
74C22×C3×C4—32no—
75C22×C3×C4—32no—
76C22×C3×C4—31no—
77C22×C3×C4—31no—
78C22×C3×C4—32no—
79C22×C3×C4C2×A412yes—
80C3×C4⋊C4—34no—
81C3×C4⋊C4—34no—
82C3×C4⋊C4—38no—
83C3×C22⋊C4—34no—
84C3×C22⋊C4C2×A414yes—
85C3×C42—38no—
86C3×C42—34no—
87C3×C42—34no—
88C22×C9—42no—
89C22×C9—44no—
90C22×C9—44no—
91C22×C9—41no—
92C22×C9—84no—
93C22×C9—88no—
94C4×C9—84no—
95C22×Q8—31no—
96C22×Q8—32no—
97C22×Q8—34no—
98C22×Q8C4×C914yescomplemented
99C22×Q8C22×C911yescharacteristic
100C22×Q8C22×C912yes—
101C23×C4—31no—
102C4×Q8—38no—
103C4×Q8—38no—
104C4×Q8—34no—
105C4×Q8C22×C914yescomplemented
106#117—34no—
107#117—34no—
108#117—34no—
109#117—34no—
110C2×C4⋊C4—32no—
111C2×C4⋊C4—32no—
112C2×C22⋊C4—31no—
113C2×C22⋊C4C22⋊C911yescharacteristic
114C2×C42—32no—
115C2×C42—32no—
116C23×C3—24no—
117C23×C3C4×A414yes—
118C23×C3C22×A412yes—
119C23×C3C22×A411yescharacteristic
120C3×Q8—32no—
121C3×Q8—34no—
122C3×Q8—31no—
123C3×Q8—38no—
124C3×Q8—34no—
125C3×Q8—32no—
126C3×Q8C22×C3×C411yescharacteristic
127C2×C3×C4—24no—
128C2×C3×C4—34no—
129C2×C3×C4—38no—
130C2×C3×C4—32no—
131C2×C3×C4—34no—
132C2×C3×C4—32no—
133C2×C3×C4—34no—
134C2×C3×C4—32no—
135C2×C3×C4—31no—
136C2×C3×C4—31no—
137C2×C3×C4—34no—
138C2×C3×C4—64no—
139C2×C3×C4C22×A414yes—
140C2×C9—41no—
141C2×C9—42no—
142C2×C9—44no—
143C2×C9—84no—
144C24C2×C22⋊C911yescharacteristic
145C2×Q8—32no—
146C2×Q8—34no—
147C2×Q8—38no—
148C2×Q8—31no—
149C2×Q8—32no—
150C2×Q8—34no—
151C2×Q8—38no—
152C2×Q8—32no—
153C2×Q8—34no—
154C2×Q8C2×C4×C912yes—
155C2×Q8C2×C4×C914yescomplemented
156C2×Q8C23×C911yescharacteristic
157C22×C4—34no—
158C22×C4—34no—
159C22×C4—31no—
160C22×C4—31no—
161C22×C4—32no—
162C22×C4—32no—
163C22×C4—32no—
164C22×C4C2×C22⋊C912yes—
165C4⋊C4—34no—
166C4⋊C4—34no—
167C4⋊C4—38no—
168C22⋊C4—34no—
169C22⋊C4C2×C22⋊C914yes—
170C42—38no—
171C42—34no—
172C42—34no—
173C22×C3—24no—
174C22×C3—28no—
175C22×C3C2×C4×A414yes—
176C22×C3C2×C4×A412yes—
177C22×C32−1+4⋊C314yes—
178C22×C3C23×A411yescharacteristic
179C3×C4—24no—
180C3×C4—31no—
181C3×C4—32no—
182C3×C4—34no—
183C3×C4—31no—
184C3×C4—64no—
185C9—41noSylow
186C23—24no—
187C23C4×C22⋊C914yes—
188C23C22×C22⋊C912yes—
189C23C22×C22⋊C911yescharacteristic
190Q8—32no—
191Q8—34no—
192Q8—31no—
193Q8—38no—
194Q8—32no—
195Q8—34no—
196Q8C22×C4×C911yescharacteristic
197C2×C4—24no—
198C2×C4—31no—
199C2×C4—32no—
200C2×C4—31no—
201C2×C4—32no—
202C2×C4—34no—
203C2×C4—38no—
204C2×C4—34no—
205C2×C4—34no—
206C2×C4—32no—
207C2×C4—34no—
208C2×C4—64no—
209C2×C4C22×C22⋊C914yes—
210C2×C3—24no—
211C2×C3#519⋊C314yes—
212C2×C3C22×C4×A411yescharacteristic
213C2×C3C2×2−1+4⋊C312yes—
214C22—24no—
215C22—28no—
216C22C2×C4×C22⋊C914yes—
217C22C2×C4×C22⋊C912yes—
218C222−1+4⋊C914yes—
219C22C23×C22⋊C911yescharacteristic
220C4—24no—
221C4—31no—
222C4—31no—
223C4—32no—
224C4—34no—
225C4—64no—
226C3C2×#519⋊C311yescharacteristic
227C2—24no—
228C2#519⋊C914yesdirect product factor
229C2C22×C4×C22⋊C911yescharacteristic
230C2C2×2−1+4⋊C912yes—
subgroupG/H
center, socleC23×C3C22×A4
commutator, hypocenterQ8C22×C4×C9
FrattiniC22×C3C23×A4
FittingC2×C3×#519C3
prime radicalC24×C3C2×A4
cosocleC2×C3×Q8C23×C3
hypercenterC2×C3×C22⋊C4A4
LCSG ▷ Q8
UCSC1 ◁ C23×C3 ◁ C2×C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #519⋊C9C2direct (N × H)
3. C2×C4×Q8⋊C9C2semidirect
5. C22×Q8⋊C9C4semidirect
9. C4×Q8⋊C9C22semidirect
20. C2×Q8⋊C9C2×C4semidirect
23. C2×#519C9semidirect
54. #519C2×C9semidirect
56. C2×C4×Q8C2×C9semidirect
98. C22×Q8C4×C9semidirect
105. C4×Q8C22×C9semidirect
155. C2×Q8C2×C4×C9semidirect
228. C2#519⋊C9direct (N × H)

Maximal subgroups

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

subgroupindex
C23×Q8⋊C92
#519⋊C92
C2×C4×Q8⋊C92
C2×C3×#5193
C2×C9×C22⋊C44