Finite Group Databasebeta

← C32×#1464 #11768513

Subgroups — C32×#1464 #11768513

Order 1152.

756 conjugacy classes of subgroups.

The subgroup lattice has 255 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#117C211yesmaximal, characteristic
2C32×#432C212yesmaximal, complemented
3C32×#324C212yesmaximal, complemented
4C32×#323C212yesmaximal
5C3×#1464C314yesmaximal, direct product factor
6C23×C32×C4C411yescharacteristic
7C32×#117—22no—
8C32×#117—22no—
9C2×C32×C4⋊C4C411yescharacteristic
10C2×C32×C4⋊C4C2211yescharacteristic
11C2×C32×C22⋊C4C411yescharacteristic
12C2×C32×C22⋊C4C2211yescharacteristic
13C2×C32×C42C411yescharacteristic
14C2×C32×C42C2211yescharacteristic
15C32×C4⋊C8—22no—
16C32×C22⋊C8C2214yes—
17C32×#97—22no—
18C2×C3×#117C2×C314yes—
19C3×#432C2×C318yescomplemented
20C3×#324C2×C318yescomplemented
21C3×#323C2×C318yes—
22C24×C32C2×C411yescharacteristic
23C22×C32×C4—22no—
24C22×C32×C4—21no—
25C22×C32×C4—21no—
26C22×C32×C4—22no—
27C22×C32×C4C2×C411yescharacteristic
28C22×C32×C4C2×C411yescharacteristic
29C22×C32×C4C2×C411yescharacteristic
30C22×C32×C4C2×C411yescharacteristic
31C22×C32×C4C2×C411yescharacteristic
32C22×C32×C4C2311yescharacteristic
33C2×C32×C8—24no—
34C32×C4⋊C4—22no—
35C32×C4⋊C4—22no—
36C32×C22⋊C4—22no—
37C32×C22⋊C4—22no—
38C32×C42—21no—
39C32×C42—21no—
40C32×C42D412yes—
41C32×C42D412yes—
42#1464C3211yescharacteristic, direct product factor, Sylow
43C23×C3×C4C3×C414yes—
44C3×#117—28no—
45C3×#117—28no—
46C2×C3×C4⋊C4C3×C414yes—
47C2×C3×C4⋊C4C22×C314yes—
48C2×C3×C22⋊C4C3×C414yes—
49C2×C3×C22⋊C4C22×C314yes—
50C2×C3×C42C3×C414yes—
51C2×C3×C42C22×C314yes—
52C3×C4⋊C8—28no—
53C3×C22⋊C8C22×C3116yes—
54C3×#97—28no—
55C23×C32—21no—
56C23×C32—21no—
57C23×C32—41no—
58C23×C32—41no—
59C23×C32M1612yes—
60C23×C32C22×C411yescharacteristic
61C2×C32×C4—24no—
62C2×C32×C4—24no—
63C2×C32×C4—21no—
64C2×C32×C4—21no—
65C2×C32×C4—21no—
66C2×C32×C4—21no—
67C2×C32×C4—21no—
68C2×C32×C4—21no—
69C2×C32×C4—41no—
70C2×C32×C4—41no—
71C2×C32×C4—41no—
72C2×C32×C4—41no—
73C2×C32×C4C22⋊C411yescharacteristic
74C2×C32×C4C22⋊C411yescharacteristic
75C2×C32×C4C22⋊C412yes—
76C2×C32×C4M1612yes—
77C2×C32×C4C2×D412yes—
78C32×C8—44no—
79C2×#117C2×C3211yescharacteristic
80#432C2×C3212yescomplemented
81#324C2×C3212yescomplemented
82#323C2×C3212yes—
83C24×C3C2×C3×C414yes—
84C22×C3×C4—28no—
85C22×C3×C4—24no—
86C22×C3×C4—24no—
87C22×C3×C4—28no—
88C22×C3×C4C2×C3×C414yes—
89C22×C3×C4C2×C3×C414yes—
90C22×C3×C4C2×C3×C414yes—
91C22×C3×C4C2×C3×C414yes—
92C22×C3×C4C2×C3×C414yes—
93C22×C3×C4C23×C314yes—
94C2×C3×C8—216no—
95C3×C4⋊C4—28no—
96C3×C4⋊C4—28no—
97C3×C22⋊C4—28no—
98C3×C22⋊C4—28no—
99C3×C42—24no—
100C3×C42—24no—
101C3×C42C3×D418yes—
102C3×C42C3×D418yes—
103C22×C32—21no—
104C22×C32—21no—
105C22×C32—22no—
106C22×C32—42no—
107C22×C32—42no—
108C22×C32—41no—
109C22×C32—41no—
110C22×C32C2×C22⋊C411yescharacteristic
111C22×C32C2×M1611yescharacteristic
112C22×C32C2×M1611yescharacteristic
113C32×C4—21no—
114C32×C4—21no—
115C32×C4—22no—
116C32×C4—22no—
117C32×C4—22no—
118C32×C4—41no—
119C32×C4—41no—
120C23×C4C32×C411yescharacteristic
121#117—22no—
122#117—22no—
123C2×C4⋊C4C32×C411yescharacteristic
124C2×C4⋊C4C22×C3211yescharacteristic
125C2×C22⋊C4C32×C411yescharacteristic
126C2×C22⋊C4C22×C3211yescharacteristic
127C2×C42C32×C411yescharacteristic
128C2×C42C22×C3211yescharacteristic
129C4⋊C8—22no—
130C22⋊C8C22×C3214yes—
131#97—22no—
132C23×C3—24no—
133C23×C3—24no—
134C23×C3—44no—
135C23×C3—44no—
136C23×C3C3×M1618yes—
137C23×C3C22×C3×C414yes—
138C2×C3×C4—216no—
139C2×C3×C4—216no—
140C2×C3×C4—24no—
141C2×C3×C4—24no—
142C2×C3×C4—24no—
143C2×C3×C4—24no—
144C2×C3×C4—24no—
145C2×C3×C4—24no—
146C2×C3×C4—44no—
147C2×C3×C4—44no—
148C2×C3×C4—44no—
149C2×C3×C4—44no—
150C2×C3×C4C3×C22⋊C414yes—
151C2×C3×C4C3×C22⋊C414yes—
152C2×C3×C4C3×C22⋊C418yes—
153C2×C3×C4C3×M1618yes—
154C2×C3×C4C2×C3×D418yes—
155C3×C8—416no—
156C2×C32—21no—
157C2×C32—21no—
158C2×C32—42no—
159C2×C32#40711yescharacteristic
160C2×C32#41011yescharacteristic
161C2×C32#41311yescharacteristic
162C24C2×C32×C411yescharacteristic
163C22×C4—22no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—22no—
167C22×C4C2×C32×C411yescharacteristic
168C22×C4C2×C32×C411yescharacteristic
169C22×C4C2×C32×C411yescharacteristic
170C22×C4C2×C32×C411yescharacteristic
171C22×C4C2×C32×C411yescharacteristic
172C22×C4C23×C3211yescharacteristic
173C2×C8—24no—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C22⋊C4—22no—
177C22⋊C4—22no—
178C42—21no—
179C42—21no—
180C42C32×D412yes—
181C42C32×D412yes—
182C22×C3—24no—
183C22×C3—24no—
184C22×C3—28no—
185C22×C3—48no—
186C22×C3—48no—
187C22×C3—44no—
188C22×C3—44no—
189C22×C3C2×C3×C22⋊C414yes—
190C22×C3C2×C3×M1614yes—
191C22×C3C2×C3×M1614yes—
192C3×C4—24no—
193C3×C4—24no—
194C3×C4—28no—
195C3×C4—28no—
196C3×C4—28no—
197C3×C4—44no—
198C3×C4—44no—
199C32#146411yescharacteristic, direct product factor, Sylow
200C23—21no—
201C23—21no—
202C23—41no—
203C23—41no—
204C23C32×M1612yes—
205C23C22×C32×C411yescharacteristic
206C2×C4—24no—
207C2×C4—24no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4C32×C22⋊C411yescharacteristic
219C2×C4C32×C22⋊C411yescharacteristic
220C2×C4C32×C22⋊C412yes—
221C2×C4C32×M1612yes—
222C2×C4C2×C32×D412yes—
223C8—44no—
224C2×C3—24no—
225C2×C3—24no—
226C2×C3—48no—
227C2×C3C3×#40714yes—
228C2×C3C3×#41014yes—
229C2×C3C3×#41314yes—
230C22—21no—
231C22—21no—
232C22—22no—
233C22—42no—
234C22—42no—
235C22—41no—
236C22—41no—
237C22C2×C32×C22⋊C411yescharacteristic
238C22C2×C32×M1611yescharacteristic
239C22C2×C32×M1611yescharacteristic
240C4—21no—
241C4—21no—
242C4—22no—
243C4—22no—
244C4—22no—
245C4—41no—
246C4—41no—
247C3C3×#146414yesdirect product factor
248C2—21no—
249C2—21no—
250C2—42no—
251C2C32×#40711yescharacteristic
252C2C32×#41011yescharacteristic
253C2C32×#41311yescharacteristic
subgroupG/H
center, socleC22×C32C2×C22⋊C4
commutatorC23C22×C32×C4
Frattini, cosocleC22×C4C23×C32
prime radicalC24×C32C2×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C32 ◁ C2×C32×C42 ◁ G

Complements

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

NH ≅ G/Ntype
2. C32×#432C2semidirect
3. C32×#324C2semidirect
5. C3×#1464C3direct (N × H)
19. C3×#432C2×C3semidirect
20. C3×#324C2×C3semidirect
42. #1464C32direct (N × H)
80. #432C2×C32semidirect
81. #324C2×C32semidirect
199. C32#1464direct (N × H)
247. C3C3×#1464direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1172
C32×#4322
C32×#3242
C32×#3232
C3×#14643