Finite Group Databasebeta

← C22×C3×#818 #11858399

Subgroups — C22×C3×#818 #11858399

Order 1152.

1369 conjugacy classes of subgroups.

The subgroup lattice has 226 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C32×C8C211yesmaximal, characteristic
2C22×C3×C4⋊Dic3C212yesmaximal
3C2×C3×#818C2112yesmaximal, direct product factor
4C22×C3×#107—31nomaximal
5C22×#818C311yesmaximal, characteristic, direct product factor
6C23×C32×C4C2211yescharacteristic
7C23×C3×Dic3—22no—
8C22×C32×C8C418yescomplemented
9C22×C32×C8C2216yes—
10C2×C3×C4⋊Dic3—26no—
11C2×C3×C4⋊Dic3C22112yes—
12C3×#818C22116yesdirect product factor
13C23×C3×C8—21no—
14C23×C3×C8D311yescharacteristic
15C23×C3×C8C2×C311yescharacteristic
16C22×C3×C4⋊C4—32no—
17C22×C4⋊Dic3C2×C312yes—
18C2×C3×#107—312no—
19C2×#818C2×C3112yesdirect product factor
20C24×C32D411yescharacteristic
21C22×C32×C4C2×C414yes—
22C22×C32×C4D413yes—
23C22×C32×C4Q814yes—
24C22×C32×C4C2313yes—
25C22×C3×Dic3—212no—
26C22×C3×Dic3—48no—
27C2×C32×C8C2×C4124yescomplemented
28C2×C32×C8C2314yes—
29C3×C4⋊Dic3—212no—
30C3×C4⋊Dic3C2318yes—
31C22×#107—31noSylow
32C23×C3×C4—21no—
33C23×C3×C4—62no—
34C23×C3×C4C2×D311yescharacteristic
35C23×C3×C4C22×C311yescharacteristic
36C23×Dic3—22no—
37C22×C3×C8—28no—
38C22×C3×C8—26no—
39C22×C3×C8Dic318yescomplemented
40C22×C3×C8C3×C418yescomplemented
41C22×C3×C8C2×D316yes—
42C22×C3×C8C22×C316yes—
43C2×C3×C4⋊C4—312no—
44C2×C3×C4⋊C4—66no—
45C2×C4⋊Dic3—26no—
46C2×C4⋊Dic3C22×C3112yes—
47C3×#107—316no—
48#818C22×C3116yesdirect product factor
49C23×C32C4⋊C414yes—
50C23×C32D814yes—
51C23×C32Q1614yes—
52C23×C32C2×D413yes—
53C2×C32×C4C4⋊C4112yes—
54C2×C32×C4C22×C416yes—
55C2×C32×C4C2×D413yes—
56C2×C32×C4C2×Q816yes—
57C2×C32×C4C2411yescharacteristic
58C2×C3×Dic3—28no—
59C2×C3×Dic3—424no—
60C32×C8C22×C418yescomplemented
61C23×C8C3×D311yescharacteristic
62C22×C4⋊C4—32no—
63C2×#107—312no—
64C24×C3—21no—
65C24×C3D1211yescharacteristic
66C24×C3C3×D411yescharacteristic
67C22×C3×C4—24no—
68C22×C3×C4—23no—
69C22×C3×C4—24no—
70C22×C3×C4—23no—
71C22×C3×C4—612no—
72C22×C3×C4—128no—
73C22×C3×C4Dic614yes—
74C22×C3×C4D1213yes—
75C22×C3×C4C2×Dic314yes—
76C22×C3×C4C2×C3×C414yes—
77C22×C3×C4C3×D413yes—
78C22×C3×C4C3×Q814yes—
79C22×C3×C4C22×D313yes—
80C22×C3×C4C23×C313yes—
81C22×Dic3—212no—
82C22×Dic3—48no—
83C2×C3×C8—224no—
84C2×C3×C8—24no—
85C2×C3×C8C2×Dic3124yescomplemented
86C2×C3×C8C2×C3×C4124yescomplemented
87C2×C3×C8C22×D314yes—
88C2×C3×C8C23×C314yes—
89C3×C4⋊C4—38no—
90C3×C4⋊C4—612no—
91C4⋊Dic3—212no—
92C4⋊Dic3C23×C318yes—
93C22×C32#107116yescomplemented
94C22×C32C2×C4⋊C416yes—
95C22×C32C2×D816yes—
96C22×C32C2×Q1616yes—
97C22×C32C22×D411yescharacteristic
98C32×C4C2×C4⋊C416yes—
99C32×C4C23×C411yescharacteristic
100C32×C4C22×Q811yescharacteristic
101C3×Dic3—48no—
102C23×C4—62no—
103C23×C4C2×C3×D311yescharacteristic
104C22×C8C3×Dic318yescomplemented
105C22×C8C2×C3×D316yes—
106C2×C4⋊C4—312no—
107C2×C4⋊C4—66no—
108#107—316no—
109C23×C3—24no—
110C23×C3—24no—
111C23×C3—24no—
112C23×C3—23no—
113C23×C3D2414yes—
114C23×C3Dic1214yes—
115C23×C3C4⋊Dic314yes—
116C23×C3C3×C4⋊C414yes—
117C23×C3C3×D814yes—
118C23×C3C3×Q1614yes—
119C23×C3C2×D1213yes—
120C23×C3C2×C3×D413yes—
121C2×C3×C4—21no—
122C2×C3×C4—212no—
123C2×C3×C4—26no—
124C2×C3×C4—23no—
125C2×C3×C4—26no—
126C2×C3×C4—68no—
127C2×C3×C4—1224no—
128C2×C3×C4C4⋊Dic3112yes—
129C2×C3×C4C3×C4⋊C4112yes—
130C2×C3×C4C2×Dic616yes—
131C2×C3×C4C2×D1213yes—
132C2×C3×C4C22×Dic316yes—
133C2×C3×C4C22×C3×C416yes—
134C2×C3×C4C2×C3×D413yes—
135C2×C3×C4C2×C3×Q816yes—
136C2×C3×C4C23×D311yescharacteristic
137C2×C3×C4C24×C311yescharacteristic
138C2×Dic3—28no—
139C2×Dic3—424no—
140C3×C8—28no—
141C3×C8C22×Dic318yescomplemented
142C3×C8C22×C3×C418yescomplemented
143C2×C32C2×#107112yescomplemented
144C2×C32C22×C4⋊C411yescharacteristic
145C2×C32C22×D811yescharacteristic
146C2×C32C22×Q1611yescharacteristic
147C24C3×D1211yescharacteristic
148C22×C4—612no—
149C22×C4—128no—
150C22×C4C3×Dic614yes—
151C22×C4C3×D1213yes—
152C22×C4C2×C3×Dic314yes—
153C22×C4C22×C3×D313yes—
154C2×C8C2×C3×Dic3124yescomplemented
155C2×C8C22×C3×D314yes—
156C4⋊C4—38no—
157C4⋊C4—612no—
158C22×C3—26no—
159C22×C3—26no—
160C22×C3—26no—
161C22×C3—21no—
162C22×C3—216no—
163C22×C3#818116yesdirect product factor
164C22×C3C3×#107116yescomplemented
165C22×C3C2×D2416yes—
166C22×C3C2×Dic1216yes—
167C22×C3C2×C4⋊Dic316yes—
168C22×C3C2×C3×C4⋊C416yes—
169C22×C3C2×C3×D816yes—
170C22×C3C2×C3×Q1616yes—
171C22×C3C22×D1211yescharacteristic
172C22×C3C22×C3×D411yescharacteristic
173C3×C4—26no—
174C3×C4—21no—
175C3×C4—21no—
176C3×C4—128no—
177C3×C4C2×C4⋊Dic316yes—
178C3×C4C2×C3×C4⋊C416yes—
179C3×C4C22×Dic611yescharacteristic
180C3×C4C23×Dic311yescharacteristic
181C3×C4C23×C3×C411yescharacteristic
182C3×C4C22×C3×Q811yescharacteristic
183Dic3—48no—
184C32C22×#10711yescharacteristic, complemented, Sylow
185C23C3×D2414yes—
186C23C3×Dic1214yes—
187C23C3×C4⋊Dic314yes—
188C23C2×C3×D1213yes—
189C2×C4—68no—
190C2×C4—1224no—
191C2×C4C3×C4⋊Dic3112yes—
192C2×C4C2×C3×Dic616yes—
193C2×C4C2×C3×D1213yes—
194C2×C4C22×C3×Dic316yes—
195C2×C4C23×C3×D311yescharacteristic
196C8C22×C3×Dic318yescomplemented
197C2×C3—21no—
198C2×C3—212no—
199C2×C3—21no—
200C2×C3—21no—
201C2×C3C2×#818112yesdirect product factor
202C2×C3C2×C3×#107112yescomplemented
203C2×C3C22×D2411yescharacteristic
204C2×C3C22×Dic1211yescharacteristic
205C2×C3C22×C4⋊Dic311yescharacteristic
206C2×C3C22×C3×C4⋊C411yescharacteristic
207C2×C3C22×C3×D811yescharacteristic
208C2×C3C22×C3×Q1611yescharacteristic
209C22C3×#818116yesdirect product factor
210C22C2×C3×D2416yes—
211C22C2×C3×Dic1216yes—
212C22C2×C3×C4⋊Dic316yes—
213C22C22×C3×D1211yescharacteristic
214C4—128no—
215C4C2×C3×C4⋊Dic316yes—
216C4C22×C3×Dic611yescharacteristic
217C4C23×C3×Dic311yescharacteristic
218C3—21no—
219C3C22×#81811yescharacteristic, direct product factor
220C3C22×C3×#10711yescharacteristic, complemented
221C2C2×C3×#818112yesdirect product factor
222C2C22×C3×D2411yescharacteristic
223C2C22×C3×Dic1211yescharacteristic
224C2C22×C3×C4⋊Dic311yescharacteristic
subgroupG/H
centerC24×C3D12
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC23×C32×C8C2
socle, prime radicalC24×C32D4
cosocleC2×C3×C4C24×C3
hypercenterC23×C3×C8D3
hypocenterC3C22×C3×#107
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C24×C3 ◁ C23×C3×C4 ◁ C23×C3×C8

Complements

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

NH ≅ G/Ntype
3. C2×C3×#818C2direct (N × H)
5. C22×#818C3direct (N × H)
8. C22×C32×C8C4semidirect
12. C3×#818C22direct (N × H)
19. C2×#818C2×C3direct (N × H)
27. C2×C32×C8C2×C4semidirect
39. C22×C3×C8Dic3semidirect
40. C22×C3×C8C3×C4semidirect
48. #818C22×C3direct (N × H)
60. C32×C8C22×C4semidirect
85. C2×C3×C8C2×Dic3semidirect
86. C2×C3×C8C2×C3×C4semidirect
93. C22×C32#107semidirect
104. C22×C8C3×Dic3semidirect
141. C3×C8C22×Dic3semidirect
142. C3×C8C22×C3×C4semidirect
143. C2×C32C2×#107semidirect
154. C2×C8C2×C3×Dic3semidirect
163. C22×C3#818direct (N × H)
164. C22×C3C3×#107semidirect
184. C32C22×#107semidirect
196. C8C22×C3×Dic3semidirect
201. C2×C3C2×#818direct (N × H)
202. C2×C3C2×C3×#107semidirect
209. C22C3×#818direct (N × H)
219. C3C22×#818direct (N × H)
220. C3C22×C3×#107semidirect
221. C2C2×C3×#818direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C32×C82
C22×C3×C4⋊Dic32
C2×C3×#8182
C22×C3×#1073
C22×#8183