Finite Group Databasebeta

← C2×#520⋊C9 #11919683

Subgroups — C2×#520⋊C9 #11919683

Order 1152.

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

normal subgroups only

This group has 717 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
1C22×#41⋊C9C211yesmaximal, characteristic
2#520⋊C9C214yesmaximal, direct product factor
3C2×C4×Q8⋊C9C212yesmaximal, complemented
4C2×C3×#520C311yesmaximal, characteristic
5C2×#41⋊C9C414yescomplemented
6C2×#41⋊C9C2212yes—
7C22×Q8⋊C9C2211yescharacteristic
8C2×C9×C4⋊C4—41nomaximal
9C4×Q8⋊C9C2214yescomplemented
10C22×C3×#41C2×C311yescharacteristic
11C3×#520—34no—
12C3×#520C2×C314yes—
13C2×C3×C4×Q8C2×C312yes—
14C2×C3×C4×D4—32no—
15C2×C3×#117—31no—
16C22×C3×C4⋊C4—31no—
17C22×C4×C9—41no—
18C22×C4×C9—42no—
19#41⋊C9C2×C414yescomplemented
20C2×Q8⋊C9C2×C412yescomplemented
21C2×Q8⋊C9C2311yescharacteristic
22C9×C4⋊C4—44no—
23C2×#520C911yescharacteristic, complemented, Sylow
24C2×C3×#41—34no—
25C2×C3×#41—32no—
26C2×C3×#41C3×C414yes—
27C2×C3×#41C22×C312yes—
28C22×C3×Q8C22×C311yescharacteristic
29C22×C3×D4—31no—
30C23×C3×C4—31no—
31C23×C3×C4—32no—
32C3×C4×Q8—34no—
33C3×C4×Q8C22×C314yes—
34C3×C4×D4—38no—
35C3×C4×D4—38no—
36C3×#117—34no—
37C3×#117—34no—
38C2×C3×C4⋊C4—32no—
39C2×C3×C4⋊C4—34no—
40C2×C3×C4⋊C4—31no—
41C2×C3×C4⋊C4—34no—
42C2×C3×C4⋊C4A411yescharacteristic
43C2×C3×C22⋊C4—32no—
44C2×C3×C42—32no—
45C23×C9—41no—
46C2×C4×C9—44no—
47C2×C4×C9—42no—
48C2×C4×C9—44no—
49C2×C4×C9—84no—
50Q8⋊C9C22×C411yescharacteristic, complemented
51C22×#41C2×C911yescharacteristic
52#520—34no—
53#520C2×C914yescomplemented
54C2×C4×Q8C2×C912yes—
55C2×C4×D4—32no—
56C2×#117—31no—
57C22×C4⋊C4—31no—
58C24×C3—31no—
59C3×#41—38no—
60C3×#41—38no—
61C3×#41—34no—
62C3×#41C2×C3×C414yes—
63C2×C3×Q8—31no—
64C2×C3×Q8—32no—
65C2×C3×Q8C2×C3×C412yes—
66C2×C3×Q8C23×C311yescharacteristic
67C2×C3×D4—32no—
68C2×C3×D4—34no—
69C2×C3×D4—32no—
70C2×C3×D4—34no—
71C22×C3×C4—31no—
72C22×C3×C4—34no—
73C22×C3×C4—34no—
74C22×C3×C4—32no—
75C22×C3×C4—32no—
76C22×C3×C4—32no—
77C22×C3×C4—38no—
78C22×C3×C4—124no—
79C22×C3×C4C2×A412yes—
80C22×C3×C4C2×A411yescharacteristic
81C3×C4⋊C4—34no—
82C3×C4⋊C4—34no—
83C3×C4⋊C4—34no—
84C3×C4⋊C4C2×A414yes—
85C3×C22⋊C4—38no—
86C3×C42—34no—
87C3×C42—34no—
88C22×C9—42no—
89C22×C9—42no—
90C22×C9—42no—
91C22×C9—41no—
92C4×C9—44no—
93C4×C9—84no—
94C2×#41—32no—
95C2×#41—34no—
96C2×#41C4×C914yescomplemented
97C2×#41C22×C912yes—
98C22×Q8C22×C911yescharacteristic
99C22×D4—31no—
100C23×C4—31no—
101C23×C4—32no—
102C4×Q8—34no—
103C4×Q8C22×C914yes—
104C4×D4—38no—
105C4×D4—38no—
106#117—34no—
107#117—34no—
108C2×C4⋊C4—32no—
109C2×C4⋊C4—34no—
110C2×C4⋊C4—31no—
111C2×C4⋊C4—34no—
112C2×C4⋊C4C22⋊C911yescharacteristic
113C2×C22⋊C4—32no—
114C2×C42—32no—
115C23×C3—34no—
116C23×C3—32no—
117C23×C3—62no—
118C23×C3—62no—
119C23×C3C22×A411yescharacteristic
120C3×Q8—32no—
121C3×Q8—31no—
122C3×Q8—32no—
123C3×Q8C22×C3×C411yescharacteristic
124C3×D4—34no—
125C3×D4—34no—
126C3×D4—38no—
127C2×C3×C4—24no—
128C2×C3×C4—32no—
129C2×C3×C4—32no—
130C2×C3×C4—31no—
131C2×C3×C4—31no—
132C2×C3×C4—34no—
133C2×C3×C4—38no—
134C2×C3×C4—34no—
135C2×C3×C4—34no—
136C2×C3×C4—64no—
137C2×C3×C4—128no—
138C2×C3×C4C4×A414yes—
139C2×C3×C4C22×A414yes—
140C2×C3×C4C22×A412yes—
141C2×C9—41no—
142C2×C9—41no—
143C2×C9—41no—
144C2×C9—44no—
145C24—31no—
146#41—38no—
147#41—38no—
148#41—34no—
149#41C2×C4×C914yescomplemented
150C2×Q8—31no—
151C2×Q8—32no—
152C2×Q8C2×C4×C912yes—
153C2×Q8C23×C911yescharacteristic
154C2×D4—32no—
155C2×D4—34no—
156C2×D4—32no—
157C2×D4—34no—
158C22×C4—31no—
159C22×C4—34no—
160C22×C4—34no—
161C22×C4—32no—
162C22×C4—32no—
163C22×C4—32no—
164C22×C4—38no—
165C22×C4—124no—
166C22×C4C2×C22⋊C912yes—
167C22×C4C2×C22⋊C911yescharacteristic
168C4⋊C4—34no—
169C4⋊C4—34no—
170C4⋊C4—34no—
171C4⋊C4C2×C22⋊C914yes—
172C22⋊C4—38no—
173C42—34no—
174C42—34no—
175C22×C3—34no—
176C22×C3—62no—
177C22×C3—62no—
178C22×C3—68no—
179C22×C3C2×C4×A412yes—
180C22×C3#99412yes—
181C22×C32−1+4⋊C312yes—
182C22×C3C23×A411yescharacteristic
183C3×C4—24no—
184C3×C4—31no—
185C3×C4—32no—
186C3×C4—31no—
187C3×C4—64no—
188C3×C4C2×C4×A414yes—
189C9—41noSylow
190C23—32no—
191C23—34no—
192C23—62no—
193C23—62no—
194C23C22×C22⋊C911yescharacteristic
195Q8—32no—
196Q8—31no—
197Q8—32no—
198Q8C22×C4×C911yescharacteristic
199D4—34no—
200D4—34no—
201D4—38no—
202C2×C4—24no—
203C2×C4—31no—
204C2×C4—31no—
205C2×C4—32no—
206C2×C4—32no—
207C2×C4—34no—
208C2×C4—38no—
209C2×C4—34no—
210C2×C4—34no—
211C2×C4—64no—
212C2×C4—128no—
213C2×C4C4×C22⋊C914yes—
214C2×C4C22×C22⋊C914yes—
215C2×C4C22×C22⋊C912yes—
216C2×C3—64no—
217C2×C3#520⋊C314yes—
218C2×C3C22×C4×A411yescharacteristic
219C2×C3C2×#99411yescharacteristic
220C2×C3C2×2−1+4⋊C311yescharacteristic
221C22—34no—
222C22—62no—
223C22—62no—
224C22—68no—
225C22C2×C4×C22⋊C912yes—
226C22#6370012yes—
227C222−1+4⋊C912yes—
228C22C23×C22⋊C911yescharacteristic
229C4—24no—
230C4—31no—
231C4—31no—
232C4—32no—
233C4—64no—
234C4C2×C4×C22⋊C914yes—
235C3C2×#520⋊C311yescharacteristic
236C2—64no—
237C2#520⋊C914yesdirect product factor
238C2C22×C4×C22⋊C911yescharacteristic
239C2C2×#6370011yescharacteristic
240C2C2×2−1+4⋊C911yescharacteristic
subgroupG/H
center, socleC23×C3C22×A4
commutator, hypocenterQ8C22×C4×C9
FrattiniC22×C3C23×A4
FittingC2×C3×#520C3
prime radicalC22×C3×#41C2×C3
cosocleC2×C3×Q8C23×C3
hypercenterC2×C3×C4⋊C4A4
LCSG ▷ Q8
UCSC1 ◁ C23×C3 ◁ C2×C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #520⋊C9C2direct (N × H)
3. C2×C4×Q8⋊C9C2semidirect
5. C2×#41⋊C9C4semidirect
9. C4×Q8⋊C9C22semidirect
19. #41⋊C9C2×C4semidirect
20. C2×Q8⋊C9C2×C4semidirect
23. C2×#520C9semidirect
50. Q8⋊C9C22×C4semidirect
53. #520C2×C9semidirect
96. C2×#41C4×C9semidirect
149. #41C2×C4×C9semidirect
237. C2#520⋊C9direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#41⋊C92
#520⋊C92
C2×C4×Q8⋊C92
C2×C3×#5203
C2×C9×C4⋊C44