Finite Group Databasebeta

← C32×#1463 #11768512

Subgroups — C32×#1463 #11768512

Order 1152.

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

normal subgroups only

This group has 936 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×C4⋊C4C211yesmaximal, characteristic
2C32×#407C212yesmaximal
3C32×#324C214yesmaximal, complemented
4C3×#1463C314yesmaximal, direct product factor
5C23×C32×C4C411yescharacteristic
6C23×C32×C4C411yescharacteristic
7C23×C32×C4C2211yescharacteristic
8C2×C32×M16—22no—
9C2×C32×C4⋊C4—22no—
10C2×C32×C4⋊C4—22no—
11C2×C32×C4⋊C4C412yes—
12C2×C32×C4⋊C4C2212yes—
13C32×C22⋊C8—22no—
14C32×C22⋊C8C2214yes—
15C22×C3×C4⋊C4C2×C314yes—
16C3×#407C2×C318yes—
17C3×#324C2×C3116yescomplemented
18C24×C32C2×C411yescharacteristic
19C22×C32×C4—21no—
20C22×C32×C4—21no—
21C22×C32×C4—24no—
22C22×C32×C4—21no—
23C22×C32×C4—21no—
24C22×C32×C4—42no—
25C22×C32×C4—42no—
26C22×C32×C4C2×C412yes—
27C22×C32×C4C2×C412yes—
28C22×C32×C4C2×C411yescharacteristic
29C22×C32×C4D412yes—
30C22×C32×C4D412yes—
31C22×C32×C4C2311yescharacteristic
32C32×M16—44no—
33C2×C32×C8—24no—
34C32×C4⋊C4—24no—
35C32×C4⋊C4—24no—
36#1463C3211yescharacteristic, direct product factor, Sylow
37C23×C3×C4C3×C414yes—
38C23×C3×C4C3×C414yes—
39C23×C3×C4C22×C314yes—
40C2×C3×M16—28no—
41C2×C3×C4⋊C4—28no—
42C2×C3×C4⋊C4—28no—
43C2×C3×C4⋊C4C3×C418yes—
44C2×C3×C4⋊C4C22×C318yes—
45C3×C22⋊C8—28no—
46C3×C22⋊C8C22×C3116yes—
47C23×C32—22no—
48C23×C32—22no—
49C23×C32—22no—
50C23×C32C22⋊C411yescharacteristic
51C23×C32C22⋊C411yescharacteristic
52C23×C32C22×C411yescharacteristic
53C2×C32×C4—24no—
54C2×C32×C4—24no—
55C2×C32×C4—24no—
56C2×C32×C4—22no—
57C2×C32×C4—22no—
58C2×C32×C4—22no—
59C2×C32×C4—41no—
60C2×C32×C4—42no—
61C2×C32×C4—41no—
62C2×C32×C4—42no—
63C2×C32×C4—42no—
64C2×C32×C4—42no—
65C2×C32×C4C22⋊C412yes—
66C2×C32×C4M1614yescomplemented
67C2×C32×C4C2×D412yes—
68C32×C8—44no—
69C22×C4⋊C4C2×C3211yescharacteristic
70#407C2×C3212yes—
71#324C2×C3214yescomplemented
72C24×C3C2×C3×C414yes—
73C22×C3×C4—24no—
74C22×C3×C4—24no—
75C22×C3×C4—216no—
76C22×C3×C4—24no—
77C22×C3×C4—24no—
78C22×C3×C4—48no—
79C22×C3×C4—48no—
80C22×C3×C4C2×C3×C418yes—
81C22×C3×C4C2×C3×C418yes—
82C22×C3×C4C2×C3×C414yes—
83C22×C3×C4C3×D418yes—
84C22×C3×C4C3×D418yes—
85C22×C3×C4C23×C314yes—
86C3×M16—416no—
87C2×C3×C8—216no—
88C3×C4⋊C4—216no—
89C3×C4⋊C4—216no—
90C22×C32—28no—
91C22×C32—21no—
92C22×C32—21no—
93C22×C32—21no—
94C22×C32—21no—
95C22×C32—21no—
96C22×C32—21no—
97C22×C32#9912yes—
98C22×C32#10112yes—
99C22×C32C2×C22⋊C411yescharacteristic
100C22×C32C2×M1612yes—
101C32×C4—24no—
102C32×C4—22no—
103C32×C4—22no—
104C32×C4—42no—
105C23×C4C32×C411yescharacteristic
106C23×C4C32×C411yescharacteristic
107C23×C4C22×C3211yescharacteristic
108C2×M16—22no—
109C2×C4⋊C4—22no—
110C2×C4⋊C4—22no—
111C2×C4⋊C4C32×C412yes—
112C2×C4⋊C4C22×C3212yes—
113C22⋊C8—22no—
114C22⋊C8C22×C3214yes—
115C23×C3—28no—
116C23×C3—28no—
117C23×C3—28no—
118C23×C3C3×C22⋊C414yes—
119C23×C3C3×C22⋊C414yes—
120C23×C3C22×C3×C414yes—
121C2×C3×C4—216no—
122C2×C3×C4—216no—
123C2×C3×C4—216no—
124C2×C3×C4—28no—
125C2×C3×C4—28no—
126C2×C3×C4—28no—
127C2×C3×C4—44no—
128C2×C3×C4—48no—
129C2×C3×C4—44no—
130C2×C3×C4—48no—
131C2×C3×C4—48no—
132C2×C3×C4—48no—
133C2×C3×C4C3×C22⋊C418yes—
134C2×C3×C4C3×M16116yescomplemented
135C2×C3×C4C2×C3×D418yes—
136C3×C8—416no—
137C2×C32—22no—
138C2×C32—22no—
139C2×C32—22no—
140C2×C32#40711yescharacteristic
141C2×C32C2×#9911yescharacteristic
142C2×C32C2×#10111yescharacteristic
143C24C2×C32×C411yescharacteristic
144C22×C4—21no—
145C22×C4—21no—
146C22×C4—24no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—42no—
150C22×C4—42no—
151C22×C4C2×C32×C412yes—
152C22×C4C2×C32×C412yes—
153C22×C4C2×C32×C411yescharacteristic
154C22×C4C32×D412yes—
155C22×C4C32×D412yes—
156C22×C4C23×C3211yescharacteristic
157M16—44no—
158C2×C8—24no—
159C4⋊C4—24no—
160C4⋊C4—24no—
161C22×C3—232no—
162C22×C3—24no—
163C22×C3—24no—
164C22×C3—24no—
165C22×C3—24no—
166C22×C3—24no—
167C22×C3—24no—
168C22×C3C3×#9918yes—
169C22×C3C3×#10118yes—
170C22×C3C2×C3×C22⋊C414yes—
171C22×C3C2×C3×M1618yes—
172C3×C4—216no—
173C3×C4—28no—
174C3×C4—28no—
175C3×C4—48no—
176C32#146311yescharacteristic, direct product factor, Sylow
177C23—22no—
178C23—22no—
179C23—22no—
180C23C32×C22⋊C411yescharacteristic
181C23C32×C22⋊C411yescharacteristic
182C23C22×C32×C411yescharacteristic
183C2×C4—24no—
184C2×C4—24no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—24no—
188C2×C4—22no—
189C2×C4—41no—
190C2×C4—42no—
191C2×C4—41no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4C32×C22⋊C412yes—
196C2×C4C32×M1614yescomplemented
197C2×C4C2×C32×D412yes—
198C8—44no—
199C2×C3—28no—
200C2×C3—28no—
201C2×C3—28no—
202C2×C3C3×#40714yes—
203C2×C3C2×C3×#9914yes—
204C2×C3C2×C3×#10114yes—
205C22—28no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22C32×#9912yes—
213C22C32×#10112yes—
214C22C2×C32×C22⋊C411yescharacteristic
215C22C2×C32×M1612yes—
216C4—24no—
217C4—22no—
218C4—22no—
219C4—42no—
220C3C3×#146314yesdirect product factor
221C2—22no—
222C2—22no—
223C2—22no—
224C2C32×#40711yescharacteristic
225C2C2×C32×#9911yescharacteristic
226C2C2×C32×#10111yescharacteristic
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 ◁ C23×C32×C4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C32×#324C2semidirect
4. C3×#1463C3direct (N × H)
17. C3×#324C2×C3semidirect
36. #1463C32direct (N × H)
66. C2×C32×C4M16semidirect
71. #324C2×C32semidirect
134. C2×C3×C4C3×M16semidirect
176. C32#1463direct (N × H)
196. C2×C4C32×M16semidirect
220. C3C3×#1463direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C32×C4⋊C42
C32×#4072
C32×#3242
C3×#14633