Finite Group Databasebeta

← C3×#67683 #11771092

Subgroups — C3×#67683 #11771092

Order 1152.

587 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 587 conjugacy classes of subgroups — too many to draw. Only its 130 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
1C32×#407C211yesmaximal, characteristic
2C3×C4×#217C212yesmaximal
3C3×#1297—31nomaximal
4#67683C311yesmaximal, characteristic, direct product factor
5C23×C32×C4C2211yescharacteristic
6C2×C32×M16C412yescomplemented
7C2×C3×#217—22no—
8C2×C3×C4×Dic3—22no—
9C32×C22⋊C8—22no—
10C3×C3⋊#95C414yescomplemented
11C3×#407—21no—
12C3×#407D311yescharacteristic
13C3×#407C2×C311yescharacteristic
14C3×C4×C22⋊C4—32no—
15C4×#217C2×C312yes—
16C24×C32D411yescharacteristic
17C22×C32×C4—42no—
18C22×C32×C4C2×C411yescharacteristic
19C22×C32×C4C2×C412yes—
20C22×C32×C4D412yes—
21C22×C32×C4Q811yescharacteristic
22C22×C3×Dic3—24no—
23C32×M16—42no—
24C2×C32×C8—22no—
25C3×#217—28no—
26C3×C4×Dic3—44no—
27#1297—31noSylow
28C23×C3×C4—21no—
29C23×C3×C4C2×D311yescharacteristic
30C23×C3×C4C22×C311yescharacteristic
31C2×C3×M16—22no—
32C2×C3×M16Dic312yescomplemented
33C2×C3×M16C3×C412yescomplemented
34C2×C3×C22⋊C4—62no—
35C2×C3×C42—62no—
36C2×#217—22no—
37C2×C4×Dic3—22no—
38C3×C22⋊C8—24no—
39C3×C22⋊C8—22no—
40C3×C22⋊C8—22no—
41C3×#95—34no—
42C3⋊#95C3×C414yescomplemented
43C23×C32—24no—
44C23×C32—41no—
45C23×C32C22⋊C412yes—
46C23×C32C4⋊C411yescharacteristic
47C2×C32×C4—22no—
48C2×C32×C4—24no—
49C2×C32×C4—42no—
50C2×C32×C4—41no—
51C2×C32×C4C4211yescharacteristic
52C2×C32×C4C22⋊C411yescharacteristic
53C2×C32×C4C4⋊C412yes—
54C2×C3×Dic3—28no—
55C2×C3×Dic3—44no—
56C2×C3×Dic3—44no—
57C32×C8—42no—
58#407C3×D311yescharacteristic
59C4×C22⋊C4—32no—
60C24×C3—21no—
61C24×C3D1211yescharacteristic
62C24×C3C3×D411yescharacteristic
63C22×C3×C4—21no—
64C22×C3×C4—22no—
65C22×C3×C4—21no—
66C22×C3×C4—22no—
67C22×C3×C4—42no—
68C22×C3×C4—42no—
69C22×C3×C4—44no—
70C22×C3×C4—64no—
71C22×C3×C4Dic611yescharacteristic
72C22×C3×C4C4×D312yes—
73C22×C3×C4C2×Dic311yescharacteristic
74C22×C3×C4#6712yes—
75C22×C3×C4C2×C3×C412yes—
76C22×C3×C4C2×C3×C411yescharacteristic
77C22×C3×C4C3×D412yes—
78C22×C3×C4C3×Q811yescharacteristic
79C22×Dic3—24no—
80C3×M16—44no—
81C3×M16—42no—
82C3×M16—42no—
83C2×C3×C8—24no—
84C2×C3×C8—22no—
85C2×C3×C8—22no—
86C3×C22⋊C4—68no—
87C3×C42—124no—
88#217—28no—
89C4×Dic3—44no—
90C22×C32—21no—
91C22×C32—22no—
92C22×C32—22no—
93C22×C32—22no—
94C22×C32—44no—
95C22×C32#9511yescharacteristic
96C22×C32#10414yes—
97C32×C4—21no—
98C32×C4—22no—
99C32×C4#9912yes—
100C3×Dic3—48no—
101C23×C4C2×C3×D311yescharacteristic
102C2×M16C3×Dic312yescomplemented
103C2×C22⋊C4—62no—
104C2×C42—62no—
105C22⋊C8—22no—
106#95—34no—
107C23×C3—24no—
108C23×C3—24no—
109C23×C3—21no—
110C23×C3—22no—
111C23×C3—44no—
112C23×C3—41no—
113C23×C3—41no—
114C23×C3—42no—
115C23×C3C4⋊Dic311yescharacteristic
116C23×C3(C2×D3)⋊C412yes—
117C23×C3C3×C22⋊C412yes—
118C23×C3C3×C4⋊C411yescharacteristic
119C2×C3×C4—24no—
120C2×C3×C4—24no—
121C2×C3×C4—22no—
122C2×C3×C4—24no—
123C2×C3×C4—22no—
124C2×C3×C4—21no—
125C2×C3×C4—22no—
126C2×C3×C4—21no—
127C2×C3×C4—44no—
128C2×C3×C4—41no—
129C2×C3×C4—42no—
130C2×C3×C4—42no—
131C2×C3×C4—41no—
132C2×C3×C4—44no—
133C2×C3×C4—42no—
134C2×C3×C4—68no—
135C2×C3×C4—124no—
136C2×C3×C4—124no—
137C2×C3×C4C4×Dic311yescharacteristic
138C2×C3×C4Dic3⋊C412yes—
139C2×C3×C4#21711yescharacteristic
140C2×C3×C4C3×C4211yescharacteristic
141C2×C3×C4C3×C22⋊C411yescharacteristic
142C2×C3×C4C3×C4⋊C412yes—
143C2×Dic3—28no—
144C2×Dic3—44no—
145C2×Dic3—44no—
146C3×C8—44no—
147C3×C8—42no—
148C3×C8—42no—
149C2×C32—24no—
150C2×C32—41no—
151C2×C32#33912yes—
152C2×C32#34211yescharacteristic
153C24C3×D1211yescharacteristic
154C22×C4—42no—
155C22×C4—64no—
156C22×C4C3×Dic611yescharacteristic
157C22×C4C3×C4×D312yes—
158C22×C4C2×C3×Dic311yescharacteristic
159C22×C4C3×#6712yes—
160M16—42no—
161C2×C8—22no—
162C22⋊C4—68no—
163C42—124no—
164C22×C3—22no—
165C22×C3—22no—
166C22×C3—22no—
167C22×C3—22no—
168C22×C3—22no—
169C22×C3—21no—
170C22×C3—22no—
171C22×C3—22no—
172C22×C3—21no—
173C22×C3—24no—
174C22×C3—21no—
175C22×C3—42no—
176C22×C3—42no—
177C22×C3—42no—
178C22×C3—44no—
179C22×C3—44no—
180C22×C3—48no—
181C22×C3#82514yes—
182C22×C3C3⋊#9511yescharacteristic
183C22×C3C3×#9511yescharacteristic
184C22×C3C3×#10414yes—
185C3×C4—22no—
186C3×C4—21no—
187C3×C4—22no—
188C3×C4—21no—
189C3×C4—22no—
190C3×C4—22no—
191C3×C4—42no—
192C3×C4—128no—
193C3×C4#83412yes—
194C3×C4C3×#9912yes—
195Dic3—48no—
196C32#129711yescharacteristic, complemented, Sylow
197C23—24no—
198C23—41no—
199C23C3×C4⋊Dic311yescharacteristic
200C23C3×(C2×D3)⋊C412yes—
201C2×C4—24no—
202C2×C4—22no—
203C2×C4—41no—
204C2×C4—42no—
205C2×C4—68no—
206C2×C4—124no—
207C2×C4—124no—
208C2×C4C3×C4×Dic311yescharacteristic
209C2×C4C3×Dic3⋊C412yes—
210C2×C4C3×#21711yescharacteristic
211C8—42no—
212C2×C3—24no—
213C2×C3—24no—
214C2×C3—21no—
215C2×C3—22no—
216C2×C3—44no—
217C2×C3—42no—
218C2×C3—41no—
219C2×C3—41no—
220C2×C3#452611yescharacteristic
221C2×C3#455512yes—
222C2×C3C3×#33912yes—
223C2×C3C3×#34211yescharacteristic
224C22—22no—
225C22—22no—
226C22—21no—
227C22—22no—
228C22—44no—
229C22C3×#82514yes—
230C22C3×C3⋊#9511yescharacteristic
231C4—21no—
232C4—22no—
233C4—128no—
234C4C3×#83412yes—
235C3—21no—
236C3#6768311yescharacteristic, direct product factor
237C3C3×#129711yescharacteristic, complemented
238C2—24no—
239C2—41no—
240C2C3×#452611yescharacteristic
241C2C3×#455512yes—
subgroupG/H
centerC2×C3×C4#217
commutatorC2×C3×C4C3×C42
FrattiniC23×C4C2×C3×D3
FittingC32×#407C2
socleC22×C32#95
prime radicalC24×C32D4
cosocleC23×C3×C4C22×C3
hypercenterC3×#407D3
hypocenterC3C3×#1297
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C23×C3×C4 ◁ C3×#407

Complements

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

NH ≅ G/Ntype
4. #67683C3direct (N × H)
6. C2×C32×M16C4semidirect
10. C3×C3⋊#95C4semidirect
32. C2×C3×M16Dic3semidirect
33. C2×C3×M16C3×C4semidirect
42. C3⋊#95C3×C4semidirect
102. C2×M16C3×Dic3semidirect
196. C32#1297semidirect
236. C3#67683direct (N × H)
237. C3C3×#1297semidirect

Maximal subgroups

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

subgroupindex
C32×#4072
C3×C4×#2172
C3×#12973
#676833