Finite Group Databasebeta

← C2×C4⋊(#41⋊C9) #11919719

Subgroups — C2×C4⋊(#41⋊C9) #11919719

Order 1152.

749 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 749 conjugacy classes of subgroups — too many to draw. Only its 133 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⋊C9C212yesmaximal, complemented
2C4⋊(#41⋊C9)C214yesmaximal, direct product factor
3C2×C4×Q8⋊C9C211yesmaximal, characteristic, complemented
4C2×C3×#550C311yesmaximal, characteristic
5C2×#41⋊C9—24no—
6C2×#41⋊C9C2214yescomplemented
7C22×Q8⋊C9C2211yescharacteristic
8C2×C9×C4⋊C4—41nomaximal
9C4×Q8⋊C9C2212yescomplemented
10C22×C3×#41C2×C312yes—
11C3×#550—34no—
12C3×#550C2×C314yes—
13C2×C3×#127—31no—
14C2×C3×#121—32no—
15C2×C3×C4×Q8C2×C311yescharacteristic
16C2×C3×C4×D4—31no—
17C22×C4×C9—41no—
18C22×C4×C9—42no—
19#41⋊C9—24no—
20C2×Q8⋊C9D412yescomplemented
21C2×Q8⋊C9C2311yescharacteristic
22C9×C4⋊C4—44no—
23C2×#550C911yescharacteristic, complemented, Sylow
24C2×C3×#41—24no—
25C2×C3×#41—34no—
26C2×C3×#41—64no—
27C2×C3×#41C22×C314yes—
28C22×C3×Q8C22×C311yescharacteristic
29C22×C3×D4—32no—
30C22×C3×D4—32no—
31C22×C3×D4—31no—
32C23×C3×C4—32no—
33C3×#127—34no—
34C3×#127—34no—
35C3×#121—38no—
36C3×#121—38no—
37C3×C4×Q8—32no—
38C3×C4×Q8C22×C312yes—
39C3×C4×D4—34no—
40C3×C4×D4—34no—
41C2×C3×C4⋊C4—31no—
42C2×C3×C4⋊C4A411yescharacteristic
43C2×C3×C22⋊C4—32no—
44C2×C3×C42—31no—
45C23×C9—41no—
46C2×C4×C9—44no—
47C2×C4×C9—42no—
48C2×C4×C9—44no—
49C2×C4×C9—84no—
50Q8⋊C9C2×D411yescharacteristic, complemented
51C22×#41C2×C912yes—
52#550—34no—
53#550C2×C914yescomplemented
54C2×#127—31no—
55C2×#121—32no—
56C2×C4×Q8C2×C911yescharacteristic
57C2×C4×D4—31no—
58C24×C3—32no—
59C3×#41—24no—
60C3×#41—68no—
61C3×#41—68no—
62C3×#41—64no—
63C2×C3×Q8—31no—
64C2×C3×Q8—32no—
65C2×C3×Q8C3×D412yes—
66C2×C3×Q8C23×C311yescharacteristic
67C2×C3×D4—34no—
68C2×C3×D4—34no—
69C2×C3×D4—38no—
70C2×C3×D4—34no—
71C2×C3×D4—64no—
72C2×C3×D4—64no—
73C2×C3×D4—64no—
74C2×C3×D4—124no—
75C22×C3×C4—31no—
76C22×C3×C4—31no—
77C22×C3×C4—34no—
78C22×C3×C4—34no—
79C22×C3×C4—64no—
80C22×C3×C4—64no—
81C22×C3×C4C2×A412yes—
82C22×C3×C4C2×A411yescharacteristic
83C3×C4⋊C4—32no—
84C3×C4⋊C4—32no—
85C3×C4⋊C4C2×A414yes—
86C3×C22⋊C4—38no—
87C3×C42—32no—
88C3×C42—32no—
89C22×C9—42no—
90C22×C9—42no—
91C22×C9—42no—
92C22×C9—41no—
93C4×C9—44no—
94C4×C9—84no—
95C2×#41—24no—
96C2×#41—34no—
97C2×#41—64no—
98C2×#41C22×C914yes—
99C22×Q8C22×C911yescharacteristic
100C22×D4—32no—
101C22×D4—32no—
102C22×D4—31no—
103C23×C4—32no—
104#127—34no—
105#127—34no—
106#121—38no—
107#121—38no—
108C4×Q8—32no—
109C4×Q8C22×C912yes—
110C4×D4—34no—
111C4×D4—34no—
112C2×C4⋊C4—31no—
113C2×C4⋊C4C22⋊C911yescharacteristic
114C2×C22⋊C4—32no—
115C2×C42—31no—
116C23×C3—34no—
117C23×C3—64no—
118C23×C3—64no—
119C23×C3—64no—
120C23×C3C22×A411yescharacteristic
121C3×Q8—32no—
122C3×Q8—31no—
123C3×Q8—32no—
124C3×Q8C2×C3×D411yescharacteristic
125C3×D4—64no—
126C3×D4—64no—
127C3×D4—68no—
128C3×D4—68no—
129C3×D4—128no—
130C2×C3×C4—24no—
131C2×C3×C4—32no—
132C2×C3×C4—32no—
133C2×C3×C4—31no—
134C2×C3×C4—31no—
135C2×C3×C4—32no—
136C2×C3×C4—64no—
137C2×C3×C4—68no—
138C2×C3×C4—64no—
139C2×C3×C4—62no—
140C2×C3×C4#41⋊C314yes—
141C2×C3×C4C22×A414yes—
142C2×C3×C4C22×A412yes—
143C2×C9—41no—
144C2×C9—41no—
145C2×C9—41no—
146C2×C9—44no—
147C24—32no—
148#41—24no—
149#41—68no—
150#41—68no—
151#41—64no—
152C2×Q8—31no—
153C2×Q8—32no—
154C2×Q8D4×C912yes—
155C2×Q8C23×C911yescharacteristic
156C2×D4—34no—
157C2×D4—34no—
158C2×D4—38no—
159C2×D4—34no—
160C2×D4—64no—
161C2×D4—64no—
162C2×D4—64no—
163C2×D4—124no—
164C22×C4—31no—
165C22×C4—31no—
166C22×C4—34no—
167C22×C4—34no—
168C22×C4—64no—
169C22×C4—64no—
170C22×C4C2×C22⋊C912yes—
171C22×C4C2×C22⋊C911yescharacteristic
172C4⋊C4—32no—
173C4⋊C4—32no—
174C4⋊C4C2×C22⋊C914yes—
175C22⋊C4—38no—
176C42—32no—
177C42—32no—
178C22×C3—64no—
179C22×C3—64no—
180C22×C3—64no—
181C22×C3—128no—
182C22×C3D4×A412yes—
183C22×C3C2×#41⋊C312yes—
184C22×C3#99412yes—
185C22×C3C23×A411yescharacteristic
186C3×C4—24no—
187C3×C4—31no—
188C3×C4—32no—
189C3×C4—31no—
190C3×C4—62no—
191C3×C4C2×#41⋊C314yes—
192C9—41noSylow
193C23—34no—
194C23—64no—
195C23—64no—
196C23—64no—
197C23C22×C22⋊C911yescharacteristic
198Q8—32no—
199Q8—31no—
200Q8—32no—
201Q8C2×D4×C911yescharacteristic
202D4—64no—
203D4—64no—
204D4—68no—
205D4—68no—
206D4—128no—
207C2×C4—24no—
208C2×C4—31no—
209C2×C4—31no—
210C2×C4—32no—
211C2×C4—32no—
212C2×C4—32no—
213C2×C4—64no—
214C2×C4—64no—
215C2×C4—68no—
216C2×C4—62no—
217C2×C4#41⋊C914yescomplemented
218C2×C4C22×C22⋊C914yes—
219C2×C4C22×C22⋊C912yes—
220C2×C3—124no—
221C2×C3C4⋊(#41⋊C3)14yes—
222C2×C3C2×D4×A411yescharacteristic
223C2×C3C22×#41⋊C311yescharacteristic
224C2×C3C2×#99411yescharacteristic
225C22—64no—
226C22—64no—
227C22—64no—
228C22—128no—
229C22D4×C22⋊C912yes—
230C22C2×#41⋊C912yes—
231C22#6370012yes—
232C22C23×C22⋊C911yescharacteristic
233C4—24no—
234C4—31no—
235C4—31no—
236C4—32no—
237C4—62no—
238C4C2×#41⋊C914yescomplemented
239C3C2×C4⋊(#41⋊C3)11yescharacteristic
240C2—124no—
241C2C4⋊(#41⋊C9)14yesdirect product factor
242C2C2×D4×C22⋊C911yescharacteristic
243C2C22×#41⋊C911yescharacteristic
244C2C2×#6370011yescharacteristic
subgroupG/H
center, socleC23×C3C22×A4
commutatorC2×Q8C23×C9
FrattiniC22×C3C23×A4
Fitting, prime radicalC2×C3×#550C3
cosocleC2×C3×Q8C23×C3
hypercenterC2×C3×C4⋊C4A4
hypocenterQ8C2×D4×C9
LCSG ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C23×C3 ◁ C2×C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#41⋊C9C2semidirect
2. C4⋊(#41⋊C9)C2direct (N × H)
3. C2×C4×Q8⋊C9C2semidirect
6. C2×#41⋊C9C22semidirect
9. C4×Q8⋊C9C22semidirect
20. C2×Q8⋊C9D4semidirect
23. C2×#550C9semidirect
50. Q8⋊C9C2×D4semidirect
53. #550C2×C9semidirect
217. C2×C4#41⋊C9semidirect
238. C4C2×#41⋊C9semidirect
241. C2C4⋊(#41⋊C9)direct (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
C4⋊(#41⋊C9)2
C2×C4×Q8⋊C92
C2×C3×#5503
C2×C9×C4⋊C44