Finite Group Databasebeta

← C2×C4×#41⋊C9 #11919679

Subgroups — C2×C4×#41⋊C9 #11919679

Order 1152.

765 conjugacy classes of subgroups; only the 189 normal subgroups are shown.

normal subgroups only

This group has 765 conjugacy classes of subgroups — too many to draw. Only its 189 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
2C4×#41⋊C9C214yesmaximal, direct product factor
3C2×C4×Q8⋊C9C212yesmaximal, complemented
4C2×C3×C4×#41C311yesmaximal, characteristic
5C2×#41⋊C9C414yesdirect product factor
6C2×#41⋊C9C2212yes—
7C22×Q8⋊C9C2211yescharacteristic
8C2×C42×C9—41nomaximal
9C4×Q8⋊C9C2214yescomplemented
10C22×C3×#41C2×C311yescharacteristic
11C3×C4×#41—34no—
12C3×C4×#41C2×C314yes—
13C2×C3×C4×Q8C2×C312yes—
14C2×C3×C4×D4—32no—
15C2×C3×#117—31no—
16C22×C3×C42—31no—
17C22×C4×C9—41no—
18C22×C4×C9—42no—
19#41⋊C9C2×C414yesdirect product factor
20C2×Q8⋊C9C2×C412yescomplemented
21C2×Q8⋊C9C2311yescharacteristic
22C42×C9—44no—
23C2×C4×#41C911yescharacteristic, 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×C22⋊C4—32no—
40C2×C3×C42—31no—
41C2×C3×C42—32no—
42C2×C3×C42—34no—
43C2×C3×C42—34no—
44C2×C3×C42A411yescharacteristic
45C23×C9—41no—
46C2×C4×C9—44no—
47C2×C4×C9—48no—
48C2×C4×C9—44no—
49C2×C4×C9—42no—
50Q8⋊C9C22×C411yescharacteristic, complemented
51C22×#41C2×C911yescharacteristic
52C4×#41—34no—
53C4×#41C2×C914yescomplemented
54C2×C4×Q8C2×C912yes—
55C2×C4×D4—32no—
56C2×#117—31no—
57C22×C42—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—68no—
79C22×C3×C4C2×A411yescharacteristic
80C22×C3×C4C2×A412yes—
81C3×C4⋊C4—34no—
82C3×C4⋊C4—34no—
83C3×C22⋊C4—38no—
84C3×C42—34no—
85C3×C42—34no—
86C3×C42—34no—
87C3×C42C2×A414yes—
88C22×C9—42no—
89C22×C9—44no—
90C22×C9—41no—
91C4×C9—44no—
92C4×C9—48no—
93C2×#41—32no—
94C2×#41—34no—
95C2×#41C4×C914yescomplemented
96C2×#41C22×C912yes—
97C22×Q8C22×C911yescharacteristic
98C22×D4—31no—
99C23×C4—31no—
100C23×C4—32no—
101C4×Q8—34no—
102C4×Q8C22×C914yes—
103C4×D4—38no—
104C4×D4—38no—
105#117—34no—
106#117—34no—
107C2×C4⋊C4—32no—
108C2×C22⋊C4—32no—
109C2×C42—31no—
110C2×C42—32no—
111C2×C42—34no—
112C2×C42—34no—
113C2×C42C22⋊C911yescharacteristic
114C23×C3—34no—
115C23×C3—32no—
116C23×C3—64no—
117C23×C3C22×A411yescharacteristic
118C3×Q8—32no—
119C3×Q8—31no—
120C3×Q8—32no—
121C3×Q8C22×C3×C411yescharacteristic
122C3×D4—34no—
123C3×D4—34no—
124C3×D4—38no—
125C2×C3×C4—32no—
126C2×C3×C4—32no—
127C2×C3×C4—31no—
128C2×C3×C4—31no—
129C2×C3×C4—34no—
130C2×C3×C4—38no—
131C2×C3×C4—34no—
132C2×C3×C4—34no—
133C2×C3×C4—64no—
134C2×C3×C4—616no—
135C2×C3×C4C4×A414yes—
136C2×C3×C4#41⋊C318yes—
137C2×C3×C4C22×A412yes—
138C2×C3×C4C22×A414yes—
139C2×C9—41no—
140C2×C9—42no—
141C2×C9—44no—
142C24—31no—
143#41—38no—
144#41—38no—
145#41—34no—
146#41C2×C4×C914yescomplemented
147C2×Q8—31no—
148C2×Q8—32no—
149C2×Q8C2×C4×C912yes—
150C2×Q8C23×C911yescharacteristic
151C2×D4—32no—
152C2×D4—34no—
153C2×D4—32no—
154C2×D4—34no—
155C22×C4—31no—
156C22×C4—34no—
157C22×C4—34no—
158C22×C4—32no—
159C22×C4—32no—
160C22×C4—32no—
161C22×C4—38no—
162C22×C4—68no—
163C22×C4C2×C22⋊C911yescharacteristic
164C22×C4C2×C22⋊C912yes—
165C4⋊C4—34no—
166C4⋊C4—34no—
167C22⋊C4—38no—
168C42—34no—
169C42—34no—
170C42—34no—
171C42C2×C22⋊C914yes—
172C22×C3—34no—
173C22×C3—64no—
174C22×C3—68no—
175C22×C3C2×C4×A412yes—
176C22×C3C2×#41⋊C314yes—
177C22×C3C23×A411yescharacteristic
178C3×C4—31no—
179C3×C4—32no—
180C3×C4—31no—
181C3×C4—64no—
182C3×C4C2×C4×A414yes—
183C3×C4C2×#41⋊C318yes—
184C9—41noSylow
185C23—32no—
186C23—34no—
187C23—64no—
188C23C22×C22⋊C911yescharacteristic
189Q8—32no—
190Q8—31no—
191Q8—32no—
192Q8C22×C4×C911yescharacteristic
193D4—34no—
194D4—34no—
195D4—38no—
196C2×C4—31no—
197C2×C4—31no—
198C2×C4—32no—
199C2×C4—32no—
200C2×C4—34no—
201C2×C4—38no—
202C2×C4—34no—
203C2×C4—34no—
204C2×C4—64no—
205C2×C4—616no—
206C2×C4C4×C22⋊C914yes—
207C2×C4#41⋊C918yesdirect product factor
208C2×C4C22×C22⋊C912yes—
209C2×C4C22×C22⋊C914yes—
210C2×C3—64no—
211C2×C3C4×#41⋊C314yes—
212C2×C3C22×C4×A411yescharacteristic
213C2×C3C22×#41⋊C312yes—
214C22—34no—
215C22—64no—
216C22—68no—
217C22C2×C4×C22⋊C912yes—
218C22C2×#41⋊C914yes—
219C22C23×C22⋊C911yescharacteristic
220C4—31no—
221C4—31no—
222C4—32no—
223C4—64no—
224C4C2×C4×C22⋊C914yes—
225C4C2×#41⋊C918yesdirect product factor
226C3C2×C4×#41⋊C311yescharacteristic
227C2—64no—
228C2C4×#41⋊C914yesdirect product factor
229C2C22×C4×C22⋊C911yescharacteristic
230C2C22×#41⋊C912yes—
subgroupG/H
center, hypercenterC2×C3×C42A4
commutator, hypocenterQ8C22×C4×C9
FrattiniC22×C3C23×A4
FittingC2×C3×C4×#41C3
socleC23×C3C22×A4
prime radicalC22×C3×#41C2×C3
cosocleC2×C3×Q8C23×C3
LCSG ▷ Q8
UCSC1 ◁ C2×C3×C42

Complements

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

NH ≅ G/Ntype
2. C4×#41⋊C9C2direct (N × H)
3. C2×C4×Q8⋊C9C2semidirect
5. C2×#41⋊C9C4direct (N × H)
9. C4×Q8⋊C9C22semidirect
19. #41⋊C9C2×C4direct (N × H)
20. C2×Q8⋊C9C2×C4semidirect
23. C2×C4×#41C9semidirect
50. Q8⋊C9C22×C4semidirect
53. C4×#41C2×C9semidirect
95. C2×#41C4×C9semidirect
146. #41C2×C4×C9semidirect
207. C2×C4#41⋊C9direct (N × H)
225. C4C2×#41⋊C9direct (N × H)
228. C2C4×#41⋊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
C4×#41⋊C92
C2×C4×Q8⋊C92
C2×C3×C4×#413
C2×C42×C94