Finite Group Databasebeta

← C3×#84062 #11802677

Subgroups — C3×#84062 #11802677

Order 1152.

1993 conjugacy classes of subgroups.

The subgroup lattice has 274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C32×Q8C211yesmaximal, characteristic
2C2×C3×#926C212yesmaximal
3C3×#5229C218yesmaximal, complemented
4C3×#5211C214yesmaximal
5C3×#2310—31nomaximal
6#84062C311yesmaximal, characteristic, direct product factor
7C22×C32×Q8—28no—
8C22×C32×Q8C418yescomplemented
9C22×C32×Q8C2214yes—
10C23×C32×C4C2212yes—
11C23×C32×C4C2211yescharacteristic
12C2×C3×#217C2214yes—
13C3×#926—28no—
14C2×C3×C4⋊Dic3C2214yes—
15C2×C3×C4×Dic3C2214yes—
16C3×C3⋊#95C22116yes—
17C23×C3×Q8—21no—
18C23×C3×Q8D311yescharacteristic
19C23×C3×Q8C2×C311yescharacteristic
20C2×C3×#117—32no—
21C2×#926C2×C312yes—
22C3×#391—38no—
23C3×#381—34no—
24#5229C2×C318yescomplemented
25#5211C2×C314yes—
26C24×C32C2311yescharacteristic
27C2×C32×Q8—232no—
28C2×C32×Q8—28no—
29C2×C32×Q8—28no—
30C2×C32×Q8C2×C4116yes—
31C22×C32×C4—28no—
32C22×C32×C4C2×C418yes—
33C22×C32×C4C2×C414yes—
34C22×C32×C4D418yes—
35C22×C32×C4C2314yes—
36C22×C32×C4C2312yes—
37C22×C3×Dic3C2318yes—
38C3×#217—28no—
39C3×C4⋊Dic3—28no—
40C3×C4×Dic3—28no—
41#2310—31noSylow
42C22×C3×Q8—216no—
43C22×C3×Q8—28no—
44C22×C3×Q8—28no—
45C22×C3×Q8—28no—
46C22×C3×Q8—24no—
47C22×C3×Q8Dic318yescomplemented
48C22×C3×Q8C3×C418yescomplemented
49C22×C3×Q8C2×D314yes—
50C22×C3×Q8C22×C314yes—
51C23×C3×C4—22no—
52C23×C3×C4—21no—
53C23×C3×C4C2×D312yes—
54C23×C3×C4C2×D311yescharacteristic
55C23×C3×C4C22×C312yes—
56C23×C3×C4C22×C311yescharacteristic
57C3×#117—68no—
58C2×C3×C4⋊C4—34no—
59C2×C3×C22⋊C4—34no—
60C2×C3×C42—34no—
61C2×#217C22×C314yes—
62#926—28no—
63C2×C4⋊Dic3C22×C314yes—
64C2×C4×Dic3C22×C314yes—
65C3×#95—316no—
66C3⋊#95C22×C3116yes—
67C23×C32—24no—
68C23×C32C22×C412yes—
69C23×C32C2×D414yes—
70C23×C32C2411yescharacteristic
71C32×Q8—232no—
72C2×C32×C4—216no—
73C2×C32×C4—28no—
74C2×C32×C4C22⋊C4116yes—
75C2×C32×C4C22×C418yes—
76C2×C32×C4C22×C414yes—
77C2×C32×C4C2×D414yes—
78C2×C32×C4C2×D414yes—
79C2×C3×Dic3—28no—
80C2×C3×Dic3—216no—
81C23×Q8C3×D311yescharacteristic
82C2×#117—32no—
83#391—38no—
84#381—34no—
85C24×C3—21no—
86C24×C3C22×D311yescharacteristic
87C24×C3C23×C311yescharacteristic
88C2×C3×Q8—264no—
89C2×C3×Q8—216no—
90C2×C3×Q8—216no—
91C2×C3×Q8—232no—
92C2×C3×Q8—232no—
93C2×C3×Q8—28no—
94C2×C3×Q8—28no—
95C2×C3×Q8—28no—
96C2×C3×Q8—28no—
97C2×C3×Q8—216no—
98C2×C3×Q8C2×Dic3116yes—
99C2×C3×Q8C2×C3×C4116yes—
100C22×C3×C4—216no—
101C22×C3×C4—28no—
102C22×C3×C4—28no—
103C22×C3×C4—28no—
104C22×C3×C4—24no—
105C22×C3×C4—28no—
106C22×C3×C4—24no—
107C22×C3×C4—22no—
108C22×C3×C4—38no—
109C22×C3×C4C2×Dic318yes—
110C22×C3×C4C2×Dic314yes—
111C22×C3×C4#6718yes—
112C22×C3×C4C2×C3×C418yes—
113C22×C3×C4C2×C3×C414yes—
114C22×C3×C4C3×D418yes—
115C22×C3×C4C22×D314yes—
116C22×C3×C4C22×D312yes—
117C22×C3×C4C23×C314yes—
118C22×C3×C4C23×C312yes—
119C22×Dic3C23×C318yes—
120C3×C4⋊C4—68no—
121C3×C22⋊C4—68no—
122C3×C42—68no—
123#217—28no—
124C4⋊Dic3—28no—
125C4×Dic3—28no—
126C22×C32—24no—
127C22×C32—28no—
128C22×C32C2×C22⋊C414yes—
129C22×C32C23×C411yescharacteristic
130C22×C32C22×D412yes—
131C22×C322−1+414yes—
132C32×C4—28no—
133C32×C4C2×C22⋊C418yes—
134C3×Dic3—48no—
135C22×Q8—28no—
136C22×Q8C3×Dic318yescomplemented
137C22×Q8C2×C3×D314yes—
138C23×C4C2×C3×D312yes—
139C23×C4C2×C3×D311yescharacteristic
140#117—68no—
141C2×C4⋊C4—34no—
142C2×C22⋊C4—34no—
143C2×C42—34no—
144#95—316no—
145C23×C3—28no—
146C23×C3—24no—
147C23×C3—24no—
148C23×C3—21no—
149C23×C3—22no—
150C23×C3—24no—
151C23×C3C22×Dic312yes—
152C23×C3C2×#6714yes—
153C23×C3C22×C3×C412yes—
154C23×C3C2×C3×D414yes—
155C23×C3C23×D311yescharacteristic
156C23×C3C24×C311yescharacteristic
157C3×Q8—264no—
158C3×Q8—232no—
159C3×Q8—232no—
160C2×C3×C4—232no—
161C2×C3×C4—216no—
162C2×C3×C4—216no—
163C2×C3×C4—216no—
164C2×C3×C4—28no—
165C2×C3×C4—28no—
166C2×C3×C4—216no—
167C2×C3×C4—28no—
168C2×C3×C4—24no—
169C2×C3×C4—24no—
170C2×C3×C4—24no—
171C2×C3×C4—616no—
172C2×C3×C4—68no—
173C2×C3×C4#217116yes—
174C2×C3×C4C3×C22⋊C4116yes—
175C2×C3×C4C22×Dic318yes—
176C2×C3×C4C22×Dic314yes—
177C2×C3×C4C2×#6714yes—
178C2×C3×C4C2×#6714yes—
179C2×C3×C4C22×C3×C418yes—
180C2×C3×C4C22×C3×C414yes—
181C2×C3×C4C2×C3×D414yes—
182C2×C3×C4C2×C3×D414yes—
183C2×Dic3—28no—
184C2×Dic3—216no—
185C2×C32—24no—
186C2×C32C22×C22⋊C411yescharacteristic
187C2×C32#51912yes—
188C2×C32#53614yes—
189C24C22×C3×D311yescharacteristic
190C2×Q8—232no—
191C2×Q8—28no—
192C2×Q8—28no—
193C2×Q8C2×C3×Dic3116yes—
194C22×C4—28no—
195C22×C4—38no—
196C22×C4C2×C3×Dic318yes—
197C22×C4C2×C3×Dic314yes—
198C22×C4C3×#6718yes—
199C22×C4C22×C3×D314yes—
200C22×C4C22×C3×D312yes—
201C4⋊C4—68no—
202C22⋊C4—68no—
203C42—68no—
204C22×C3—28no—
205C22×C3—216no—
206C22×C3—24no—
207C22×C3—28no—
208C22×C3—24no—
209C22×C3—28no—
210C22×C3—24no—
211C22×C3—24no—
212C22×C3—21no—
213C22×C3—22no—
214C22×C3C2×#21714yes—
215C22×C3C2×C3×C22⋊C414yes—
216C22×C3#100714yes—
217C22×C3C23×Dic311yescharacteristic
218C22×C3C22×#6712yes—
219C22×C3C23×C3×C411yescharacteristic
220C22×C3C22×C3×D412yes—
221C22×C3C3×2−1+414yes—
222C3×C4—216no—
223C3×C4—28no—
224C3×C4—28no—
225C3×C4—28no—
226C3×C4—128no—
227C3×C4C2×#21718yes—
228C3×C4C2×C3×C22⋊C418yes—
229Dic3—48no—
230C32#231011yescharacteristic, complemented, Sylow
231C23—24no—
232C23C22×C3×Dic312yes—
233C23C2×C3×#6714yes—
234C23C23×C3×D311yescharacteristic
235Q8—232no—
236C2×C4—216no—
237C2×C4—28no—
238C2×C4—616no—
239C2×C4—68no—
240C2×C4C3×#217116yes—
241C2×C4C22×C3×Dic318yes—
242C2×C4C22×C3×Dic314yes—
243C2×C4C2×C3×#6714yes—
244C2×C4C2×C3×#6714yes—
245C2×C3—28no—
246C2×C3—24no—
247C2×C3—24no—
248C2×C3—22no—
249C2×C3—24no—
250C2×C3—21no—
251C2×C3#581212yes—
252C2×C3#581614yes—
253C2×C3C22×#21711yescharacteristic
254C2×C3C22×C3×C22⋊C411yescharacteristic
255C2×C3C3×#51912yes—
256C2×C3C3×#53614yes—
257C22—24no—
258C22—28no—
259C22C2×C3×#21714yes—
260C22C3×#100714yes—
261C22C23×C3×Dic311yescharacteristic
262C22C22×C3×#6712yes—
263C4—28no—
264C4—128no—
265C4C2×C3×#21718yes—
266C3—21no—
267C3#8406211yescharacteristic, direct product factor
268C3C3×#231011yescharacteristic, complemented
269C2—24no—
270C2C3×#581212yes—
271C2C3×#581614yes—
272C2C22×C3×#21711yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC23×C32×Q8C2
socleC23×C32C24
prime radicalC24×C32C23
cosocleC23×C3C24×C3
hypercenterC23×C3×Q8D3
hypocenterC3C3×#2310
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C23×C3×Q8

Complements

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

NH ≅ G/Ntype
3. C3×#5229C2semidirect
6. #84062C3direct (N × H)
8. C22×C32×Q8C4semidirect
24. #5229C2×C3semidirect
47. C22×C3×Q8Dic3semidirect
48. C22×C3×Q8C3×C4semidirect
136. C22×Q8C3×Dic3semidirect
230. C32#2310semidirect
267. C3#84062direct (N × H)
268. C3C3×#2310semidirect

Maximal subgroups

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

subgroupindex
C23×C32×Q82
C2×C3×#9262
C3×#52292
C3×#52112
C3×#23103
#840623