Finite Group Databasebeta

← C32×#1462 #11768511

Subgroups — C32×#1462 #11768511

Order 1152.

1320 conjugacy classes of subgroups; only the 312 normal subgroups are shown.

normal subgroups only

This group has 1320 conjugacy classes of subgroups — too many to draw. Only its 312 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×C32×C22⋊C4C211yesmaximal, characteristic
2C32×#407C212yesmaximal, complemented
3C32×#323C214yesmaximal, complemented
4C3×#1462C314yesmaximal, direct product factor
5C25×C32C411yescharacteristic
6C23×C32×C4C411yescharacteristic
7C23×C32×C4C2211yescharacteristic
8C2×C32×M16—22no—
9C2×C32×C22⋊C4—22no—
10C2×C32×C22⋊C4—22no—
11C2×C32×C22⋊C4C412yes—
12C2×C32×C22⋊C4C2212yes—
13C32×C22⋊C8—22no—
14C32×C22⋊C8C2214yescomplemented
15C22×C3×C22⋊C4C2×C314yes—
16C3×#407C2×C318yescomplemented
17C3×#323C2×C3116yescomplemented
18C24×C32—21no—
19C24×C32—21no—
20C24×C32—24no—
21C24×C32—42no—
22C24×C32—42no—
23C24×C32C2×C411yescharacteristic
24C24×C32C2×C412yes—
25C22×C32×C4—21no—
26C22×C32×C4—21no—
27C22×C32×C4—42no—
28C22×C32×C4—42no—
29C22×C32×C4C2×C412yes—
30C22×C32×C4C2×C411yescharacteristic
31C22×C32×C4D412yes—
32C22×C32×C4D412yes—
33C22×C32×C4C2311yescharacteristic
34C32×M16—44no—
35C2×C32×C8—24no—
36C32×C22⋊C4—24no—
37C32×C22⋊C4—24no—
38#1462C3211yescharacteristic, direct product factor, Sylow
39C25×C3C3×C414yes—
40C23×C3×C4C3×C414yes—
41C23×C3×C4C22×C314yes—
42C2×C3×M16—28no—
43C2×C3×C22⋊C4—28no—
44C2×C3×C22⋊C4—28no—
45C2×C3×C22⋊C4C3×C418yes—
46C2×C3×C22⋊C4C22×C318yes—
47C3×C22⋊C8—28no—
48C3×C22⋊C8C22×C3116yescomplemented
49C23×C32—22no—
50C23×C32—22no—
51C23×C32—22no—
52C23×C32—24no—
53C23×C32—24no—
54C23×C32—22no—
55C23×C32—22no—
56C23×C32—42no—
57C23×C32—42no—
58C23×C32—416no—
59C23×C32—42no—
60C23×C32—42no—
61C23×C32—42no—
62C23×C32—42no—
63C23×C32C22⋊C411yescharacteristic
64C23×C32C22⋊C411yescharacteristic
65C23×C32M1614yescomplemented
66C23×C32C22×C411yescharacteristic
67C2×C32×C4—24no—
68C2×C32×C4—22no—
69C2×C32×C4—41no—
70C2×C32×C4—42no—
71C2×C32×C4—41no—
72C2×C32×C4—42no—
73C2×C32×C4—42no—
74C2×C32×C4—42no—
75C2×C32×C4C22⋊C412yes—
76C2×C32×C4C2×D412yes—
77C32×C8—44no—
78C22×C22⋊C4C2×C3211yescharacteristic
79#407C2×C3212yescomplemented
80#323C2×C3214yescomplemented
81C24×C3—24no—
82C24×C3—24no—
83C24×C3—216no—
84C24×C3—48no—
85C24×C3—48no—
86C24×C3C2×C3×C414yes—
87C24×C3C2×C3×C418yes—
88C22×C3×C4—24no—
89C22×C3×C4—24no—
90C22×C3×C4—48no—
91C22×C3×C4—48no—
92C22×C3×C4C2×C3×C418yes—
93C22×C3×C4C2×C3×C414yes—
94C22×C3×C4C3×D418yes—
95C22×C3×C4C3×D418yes—
96C22×C3×C4C23×C314yes—
97C3×M16—416no—
98C2×C3×C8—216no—
99C3×C22⋊C4—216no—
100C3×C22⋊C4—216no—
101C22×C32—28no—
102C22×C32—21no—
103C22×C32—21no—
104C22×C32—21no—
105C22×C32—21no—
106C22×C32—21no—
107C22×C32—21no—
108C22×C32—24no—
109C22×C32—44no—
110C22×C32—48no—
111C22×C32—48no—
112C22×C32—44no—
113C22×C32—42no—
114C22×C32—42no—
115C22×C32#9912yes—
116C22×C32#10012yes—
117C22×C32C2×C22⋊C411yescharacteristic
118C22×C32C2×M1612yes—
119C32×C4—22no—
120C32×C4—22no—
121C32×C4—42no—
122C25C32×C411yescharacteristic
123C23×C4C32×C411yescharacteristic
124C23×C4C22×C3211yescharacteristic
125C2×M16—22no—
126C2×C22⋊C4—22no—
127C2×C22⋊C4—22no—
128C2×C22⋊C4C32×C412yes—
129C2×C22⋊C4C22×C3212yes—
130C22⋊C8—22no—
131C22⋊C8C22×C3214yescomplemented
132C23×C3—28no—
133C23×C3—28no—
134C23×C3—28no—
135C23×C3—216no—
136C23×C3—216no—
137C23×C3—28no—
138C23×C3—28no—
139C23×C3—48no—
140C23×C3—48no—
141C23×C3—464no—
142C23×C3—48no—
143C23×C3—48no—
144C23×C3—48no—
145C23×C3—48no—
146C23×C3C3×C22⋊C414yes—
147C23×C3C3×C22⋊C414yes—
148C23×C3C3×M16116yescomplemented
149C23×C3C22×C3×C414yes—
150C2×C3×C4—216no—
151C2×C3×C4—28no—
152C2×C3×C4—44no—
153C2×C3×C4—48no—
154C2×C3×C4—44no—
155C2×C3×C4—48no—
156C2×C3×C4—48no—
157C2×C3×C4—48no—
158C2×C3×C4C3×C22⋊C418yes—
159C2×C3×C4C2×C3×D418yes—
160C3×C8—416no—
161C2×C32—22no—
162C2×C32—22no—
163C2×C32—22no—
164C2×C32—44no—
165C2×C32#40711yescharacteristic
166C2×C32C2×#9911yescharacteristic
167C2×C32C2×#10011yescharacteristic
168C24—21no—
169C24—21no—
170C24—24no—
171C24—42no—
172C24—42no—
173C24C2×C32×C411yescharacteristic
174C24C2×C32×C412yes—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—42no—
178C22×C4—42no—
179C22×C4C2×C32×C412yes—
180C22×C4C2×C32×C411yescharacteristic
181C22×C4C32×D412yes—
182C22×C4C32×D412yes—
183C22×C4C23×C3211yescharacteristic
184M16—44no—
185C2×C8—24no—
186C22⋊C4—24no—
187C22⋊C4—24no—
188C22×C3—232no—
189C22×C3—24no—
190C22×C3—24no—
191C22×C3—24no—
192C22×C3—24no—
193C22×C3—24no—
194C22×C3—24no—
195C22×C3—216no—
196C22×C3—416no—
197C22×C3—432no—
198C22×C3—432no—
199C22×C3—416no—
200C22×C3—48no—
201C22×C3—48no—
202C22×C3C3×#9918yes—
203C22×C3C3×#10018yes—
204C22×C3C2×C3×C22⋊C414yes—
205C22×C3C2×C3×M1618yes—
206C3×C4—28no—
207C3×C4—28no—
208C3×C4—48no—
209C32#146211yescharacteristic, direct product factor, Sylow
210C23—22no—
211C23—22no—
212C23—22no—
213C23—24no—
214C23—24no—
215C23—22no—
216C23—22no—
217C23—42no—
218C23—42no—
219C23—416no—
220C23—42no—
221C23—42no—
222C23—42no—
223C23—42no—
224C23C32×C22⋊C411yescharacteristic
225C23C32×C22⋊C411yescharacteristic
226C23C32×M1614yescomplemented
227C23C22×C32×C411yescharacteristic
228C2×C4—24no—
229C2×C4—22no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—41no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4C32×C22⋊C412yes—
237C2×C4C2×C32×D412yes—
238C8—44no—
239C2×C3—28no—
240C2×C3—28no—
241C2×C3—28no—
242C2×C3—416no—
243C2×C3C3×#40714yes—
244C2×C3C2×C3×#9914yes—
245C2×C3C2×C3×#10014yes—
246C22—28no—
247C22—21no—
248C22—21no—
249C22—21no—
250C22—21no—
251C22—21no—
252C22—21no—
253C22—24no—
254C22—44no—
255C22—44no—
256C22—48no—
257C22—48no—
258C22—42no—
259C22—42no—
260C22C32×#9912yes—
261C22C32×#10012yes—
262C22C2×C32×C22⋊C411yescharacteristic
263C22C2×C32×M1612yes—
264C4—22no—
265C4—22no—
266C4—42no—
267C3C3×#146214yesdirect product factor
268C2—22no—
269C2—22no—
270C2—22no—
271C2—44no—
272C2C32×#40711yescharacteristic
273C2C2×C32×#9911yescharacteristic
274C2C2×C32×#10011yescharacteristic
subgroupG/H
center, socleC22×C32C2×C22⋊C4
commutatorC23C22×C32×C4
Frattini, cosocleC22×C4C23×C32
prime radicalC25×C32C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C32 ◁ C23×C32×C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C32×#407C2semidirect
3. C32×#323C2semidirect
4. C3×#1462C3direct (N × H)
14. C32×C22⋊C8C22semidirect
16. C3×#407C2×C3semidirect
17. C3×#323C2×C3semidirect
38. #1462C32direct (N × H)
48. C3×C22⋊C8C22×C3semidirect
65. C23×C32M16semidirect
79. #407C2×C32semidirect
80. #323C2×C32semidirect
131. C22⋊C8C22×C32semidirect
148. C23×C3C3×M16semidirect
209. C32#1462direct (N × H)
226. C23C32×M16semidirect
267. C3C3×#1462direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C32×C22⋊C42
C32×#4072
C32×#3232
C3×#14623