Finite Group Databasebeta

← C3×#72133 #11784657

Subgroups — C3×#72133 #11784657

Order 1152.

1553 conjugacy classes of subgroups.

The subgroup lattice has 291 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C32×Q8C211yesmaximal, characteristic
2C2×C3×#836C214yesmaximal, complemented
3C3×#5207C212yesmaximal
4C3×#1784—31nomaximal
5#72133C311yesmaximal, characteristic, direct product factor
6C22×C32×Q8—28no—
7C22×C32×Q8—24no—
8C22×C32×Q8C412yes—
9C22×C32×Q8C2212yes—
10C23×C32×C4C412yes—
11C23×C32×C4C2211yescharacteristic
12C2×C3×#208C2214yes—
13C3×#836—28no—
14C3×#830—24no—
15C23×C3×Q8—21no—
16C23×C3×Q8D311yescharacteristic
17C23×C3×Q8C2×C311yescharacteristic
18C2×C3×#101—34no—
19C3×#407—32no—
20C2×#836C2×C314yescomplemented
21#5207C2×C312yes—
22C24×C32C2×C411yescharacteristic
23C2×C32×Q8—232no—
24C2×C32×Q8—28no—
25C2×C32×Q8—24no—
26C2×C32×Q8—24no—
27C2×C32×Q8—24no—
28C2×C32×Q8D418yes—
29C22×C32×C4—24no—
30C22×C32×C4—28no—
31C22×C32×C4—24no—
32C22×C32×C4C2×C414yes—
33C22×C32×C4C2×C411yescharacteristic
34C22×C32×C4D414yes—
35C22×C32×C4C2311yescharacteristic
36C3×#208—28no—
37C2×C3×C3⋊C8—24no—
38#1784—31noSylow
39C22×C3×Q8—216no—
40C22×C3×Q8—28no—
41C22×C3×Q8—28no—
42C22×C3×Q8—28no—
43C22×C3×Q8—24no—
44C22×C3×Q8—24no—
45C22×C3×Q8—22no—
46C22×C3×Q8—22no—
47C22×C3×Q8Dic312yes—
48C22×C3×Q8C3×C412yes—
49C22×C3×Q8C2×D312yes—
50C22×C3×Q8C22×C312yes—
51C23×C3×C4—22no—
52C23×C3×C4—21no—
53C23×C3×C4Dic312yes—
54C23×C3×C4C3×C412yes—
55C23×C3×C4C2×D311yescharacteristic
56C23×C3×C4C22×C311yescharacteristic
57C2×C3×M16—34no—
58C2×#208C22×C314yes—
59C3×#101—68no—
60C3×C22⋊C8—64no—
61#836—28no—
62#830—24no—
63C23×C32—24no—
64C23×C32—22no—
65C23×C32C22⋊C412yes—
66C23×C32C22×C411yescharacteristic
67C32×Q8—216no—
68C32×Q8—216no—
69C2×C32×C4—216no—
70C2×C32×C4—24no—
71C2×C32×C4—22no—
72C2×C32×C4—24no—
73C2×C32×C4—28no—
74C2×C32×C4C22⋊C418yes—
75C2×C32×C4C22⋊C412yes—
76C2×C32×C4C2×D412yes—
77C2×C32×C4C2×D414yes—
78C3×C3⋊C8—44no—
79C23×Q8C3×D311yescharacteristic
80C2×#101—34no—
81#407—32no—
82C24×C3—21no—
83C24×C3C2×Dic311yescharacteristic
84C24×C3C2×C3×C411yescharacteristic
85C2×C3×Q8—264no—
86C2×C3×Q8—232no—
87C2×C3×Q8—232no—
88C2×C3×Q8—216no—
89C2×C3×Q8—28no—
90C2×C3×Q8—28no—
91C2×C3×Q8—28no—
92C2×C3×Q8—28no—
93C2×C3×Q8—24no—
94C2×C3×Q8—28no—
95C2×C3×Q8—24no—
96C2×C3×Q8—24no—
97C2×C3×Q8—24no—
98C2×C3×Q8—24no—
99C2×C3×Q8—24no—
100C2×C3×Q8—28no—
101C2×C3×Q8#6718yes—
102C2×C3×Q8C3×D418yes—
103C22×C3×C4—28no—
104C22×C3×C4—216no—
105C22×C3×C4—28no—
106C22×C3×C4—24no—
107C22×C3×C4—24no—
108C22×C3×C4—28no—
109C22×C3×C4—28no—
110C22×C3×C4—24no—
111C22×C3×C4—24no—
112C22×C3×C4—24no—
113C22×C3×C4—21no—
114C22×C3×C4—24no—
115C22×C3×C4—21no—
116C22×C3×C4C2×Dic314yes—
117C22×C3×C4C2×Dic311yescharacteristic
118C22×C3×C4#6714yes—
119C22×C3×C4C2×C3×C414yes—
120C22×C3×C4C2×C3×C411yescharacteristic
121C22×C3×C4C3×D414yes—
122C22×C3×C4C22×D311yescharacteristic
123C22×C3×C4C23×C311yescharacteristic
124C3×M16—68no—
125C2×C3×C8—64no—
126#208—28no—
127C2×C3⋊C8—24no—
128C22×C32—28no—
129C22×C32—22no—
130C22×C32—22no—
131C22×C32—22no—
132C22×C32#10114yescomplemented
133C22×C32C2×C22⋊C412yes—
134C22×C32C2×C22⋊C411yescharacteristic
135C32×C4—28no—
136C32×C4—22no—
137C32×C4#12014yes—
138C22×Q8—28no—
139C22×Q8—24no—
140C22×Q8C3×Dic312yes—
141C22×Q8C2×C3×D312yes—
142C23×C4C3×Dic312yes—
143C23×C4C2×C3×D311yescharacteristic
144C2×M16—34no—
145#101—68no—
146C22⋊C8—64no—
147C23×C3—24no—
148C23×C3—28no—
149C23×C3—24no—
150C23×C3—24no—
151C23×C3—22no—
152C23×C3—22no—
153C23×C3—22no—
154C23×C3—21no—
155C23×C3#21712yes—
156C23×C3C3×C22⋊C412yes—
157C23×C3C22×Dic311yescharacteristic
158C23×C3C22×C3×C411yescharacteristic
159C3×Q8—232no—
160C3×Q8—216no—
161C3×Q8—216no—
162C3×Q8—232no—
163C3×Q8—216no—
164C3×Q8—216no—
165C2×C3×C4—232no—
166C2×C3×C4—216no—
167C2×C3×C4—216no—
168C2×C3×C4—28no—
169C2×C3×C4—24no—
170C2×C3×C4—28no—
171C2×C3×C4—216no—
172C2×C3×C4—24no—
173C2×C3×C4—22no—
174C2×C3×C4—24no—
175C2×C3×C4—24no—
176C2×C3×C4—22no—
177C2×C3×C4—24no—
178C2×C3×C4—28no—
179C2×C3×C4—28no—
180C2×C3×C4—28no—
181C2×C3×C4—22no—
182C2×C3×C4—22no—
183C2×C3×C4—24no—
184C2×C3×C4#21718yes—
185C2×C3×C4#21712yes—
186C2×C3×C4C3×C22⋊C418yes—
187C2×C3×C4C3×C22⋊C412yes—
188C2×C3×C4C2×#6714yes—
189C2×C3×C4C2×#6712yes—
190C2×C3×C4C2×C3×D412yes—
191C2×C3×C4C2×C3×D414yes—
192C3×C8—124no—
193C3⋊C8—44no—
194C2×C32—24no—
195C2×C32—22no—
196C2×C32#37911yescharacteristic
197C2×C32C2×#10112yes—
198C24C2×C3×Dic311yescharacteristic
199C2×Q8—232no—
200C2×Q8—28no—
201C2×Q8—24no—
202C2×Q8—24no—
203C2×Q8—24no—
204C2×Q8C3×#6718yes—
205C22×C4—24no—
206C22×C4—28no—
207C22×C4—24no—
208C22×C4C2×C3×Dic314yes—
209C22×C4C2×C3×Dic311yescharacteristic
210C22×C4C3×#6714yes—
211C22×C4C22×C3×D311yescharacteristic
212M16—68no—
213C2×C8—64no—
214C22×C3—24no—
215C22×C3—216no—
216C22×C3—28no—
217C22×C3—28no—
218C22×C3—24no—
219C22×C3—24no—
220C22×C3—22no—
221C22×C3—22no—
222C22×C3—22no—
223C22×C3—22no—
224C22×C3—22no—
225C22×C3—22no—
226C22×C3—22no—
227C22×C3—21no—
228C22×C3—24no—
229C22×C3#83614yescomplemented
230C22×C3C3×#10114yescomplemented
231C22×C3C2×#21712yes—
232C22×C3C2×#21711yescharacteristic
233C22×C3C2×C3×C22⋊C412yes—
234C22×C3C2×C3×C22⋊C411yescharacteristic
235C3×C4—216no—
236C3×C4—24no—
237C3×C4—28no—
238C3×C4—22no—
239C3×C4—28no—
240C3×C4—22no—
241C3×C4—24no—
242C3×C4#95314yes—
243C3×C4C3×#12014yes—
244C32#178411yescharacteristic, complemented, Sylow
245C23—22no—
246C23—24no—
247C23C3×#21712yes—
248C23C22×C3×Dic311yescharacteristic
249Q8—216no—
250Q8—216no—
251C2×C4—216no—
252C2×C4—24no—
253C2×C4—22no—
254C2×C4—24no—
255C2×C4—28no—
256C2×C4C3×#21718yes—
257C2×C4C3×#21712yes—
258C2×C4C2×C3×#6712yes—
259C2×C4C2×C3×#6714yes—
260C8—124no—
261C2×C3—24no—
262C2×C3—28no—
263C2×C3—24no—
264C2×C3—22no—
265C2×C3—24no—
266C2×C3—22no—
267C2×C3—22no—
268C2×C3—21no—
269C2×C3C2×#83612yes—
270C2×C3#524711yescharacteristic
271C2×C3C3×#37911yescharacteristic
272C2×C3C2×C3×#10112yes—
273C22—28no—
274C22—22no—
275C22—22no—
276C22—22no—
277C22C3×#83614yescomplemented
278C22C2×C3×#21712yes—
279C22C2×C3×#21711yescharacteristic
280C4—28no—
281C4—22no—
282C4C3×#95314yes—
283C3—21no—
284C3#7213311yescharacteristic, direct product factor
285C3C3×#178411yescharacteristic, complemented
286C2—22no—
287C2—24no—
288C2C2×C3×#83612yes—
289C2C3×#524711yescharacteristic
subgroupG/H
centerC22×C3C2×#217
commutatorC23×C3C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC23×C32×Q8C2
socleC22×C32C2×C22⋊C4
prime radicalC24×C32C2×C4
cosocleC22×C3×C4C23×C3
hypercenterC23×C3×Q8D3
hypocenterC3C3×#1784
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C23×C3×Q8

Complements

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

NH ≅ G/Ntype
2. C2×C3×#836C2semidirect
5. #72133C3direct (N × H)
20. C2×#836C2×C3semidirect
132. C22×C32#101semidirect
229. C22×C3#836semidirect
230. C22×C3C3×#101semidirect
244. C32#1784semidirect
277. C22C3×#836semidirect
284. C3#72133direct (N × H)
285. C3C3×#1784semidirect

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×#8362
C3×#52072
C3×#17843
#721333