Finite Group Databasebeta

← C3×#73388 #11803806

Subgroups — C3×#73388 #11803806

Order 1152.

1121 conjugacy classes of subgroups.

The subgroup lattice has 303 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#869C211yesmaximal, characteristic
2C2×C3×C4×Dic6C212yesmaximal
3C32×#376C211yesmaximal, characteristic
4C3×#4936C211yesmaximal, characteristic
5C3×#4929C212yesmaximal
6C3×#4653C218yesmaximal
7C3×#2327—31nomaximal
8#73388C311yesmaximal, characteristic, direct product factor
9C22×C3×Dic6C2212yes—
10C2×C32×C42C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C2×C3×C4⋊Dic3C2212yes—
14C2×C3×C4⋊Dic3C2214yes—
15C2×C3×Dic3⋊C4C2214yes—
16C2×C3×C4×Dic3C2214yes—
17C3×#869C418yescomplemented
18C3×C4×Dic6—28no—
19C32×#95C2214yes—
20C3×C3⋊#95C2218yes—
21C3×C3⋊#95C2214yes—
22C2×C3×C4⋊Q8—31no—
23C2×C3×C4×Q8—32no—
24C2×#869C2×C311yescharacteristic
25C2×C4×Dic6C2×C312yes—
26C3×#391—32no—
27C3×#387—38no—
28C3×#382—31no—
29C3×#376—21no—
30C3×#376D311yescharacteristic
31C3×#376C2×C311yescharacteristic
32#4936C2×C311yescharacteristic
33#4929C2×C312yes—
34#4653C2×C318yes—
35C22×C32×C4C2312yes—
36C22×C32×C4C2312yes—
37C22×C32×C4C2312yes—
38C22×C32×C4C2311yescharacteristic
39C22×C3×Dic3C2314yes—
40C22×C3×Dic3C2314yes—
41C2×C3×Dic6—24no—
42C2×C3×Dic6—24no—
43C2×C3×Dic6C2×C418yes—
44C32×C42—22no—
45C32×C42C2×C414yes—
46C32×C42D414yes—
47C3×C4⋊Dic3—24no—
48C3×C4⋊Dic3C2×C4116yes—
49C3×Dic3⋊C4—28no—
50C3×C4×Dic3—28no—
51#2327—31noSylow
52C22×C3×Q8—32no—
53C22×Dic6C22×C312yes—
54C3×C4⋊Q8—38no—
55C3×C4×Q8—68no—
56C2×C3×C4⋊C4—34no—
57C2×C3×C4⋊C4—34no—
58C2×C3×C4⋊C4—32no—
59C2×C3×C42—21no—
60C2×C3×C42—21no—
61C2×C3×C42—21no—
62C2×C3×C42—34no—
63C2×C3×C42C2×D311yescharacteristic
64C2×C3×C42C2×D311yescharacteristic
65C2×C3×C42C2×D311yescharacteristic
66C2×C3×C42C22×C311yescharacteristic
67C2×C3×C42C22×C311yescharacteristic
68C2×C3×C42C22×C311yescharacteristic
69C2×C4⋊Dic3C22×C312yes—
70C2×C4⋊Dic3C22×C314yes—
71C2×Dic3⋊C4C22×C314yes—
72C2×C4×Dic3C22×C314yes—
73#869C3×C418yescomplemented
74C4×Dic6—28no—
75C3×#95—24no—
76C3×#95—34no—
77C3×#95—38no—
78C3×#95C2×D314yes—
79C3×#95C22×C314yes—
80C3⋊#95C22×C318yes—
81C3⋊#95C22×C314yes—
82C23×C32C2411yescharacteristic
83C2×C32×C4—22no—
84C2×C32×C4—24no—
85C2×C32×C4—24no—
86C2×C32×C4—24no—
87C2×C32×C4C22×C414yes—
88C2×C32×C4C22×C412yes—
89C2×C32×C4C2×D414yes—
90C2×C32×C4C2×D412yes—
91C2×C32×C4#4112yes—
92C2×C3×Dic3—24no—
93C2×C3×Dic3—24no—
94C2×C3×Dic3—24no—
95C2×C3×Dic3—28no—
96C2×C3×Dic3C22×C418yes—
97C3×Dic6—216no—
98C2×C4⋊Q8—31no—
99C2×C4×Q8—32no—
100#391—32no—
101#387—38no—
102#382—31no—
103#376C3×D311yescharacteristic
104C2×C3×Q8—38no—
105C2×C3×Q8—64no—
106C2×C3×Q8—64no—
107C22×C3×C4—21no—
108C22×C3×C4—22no—
109C22×C3×C4—22no—
110C22×C3×C4—22no—
111C22×C3×C4—34no—
112C22×C3×C4—34no—
113C22×C3×C4C22×D312yes—
114C22×C3×C4C22×D312yes—
115C22×C3×C4C22×D312yes—
116C22×C3×C4C22×D311yescharacteristic
117C22×C3×C4C23×C312yes—
118C22×C3×C4C23×C312yes—
119C22×C3×C4C23×C312yes—
120C22×C3×C4C23×C311yescharacteristic
121C22×Dic3C23×C314yes—
122C22×Dic3C23×C314yes—
123C2×Dic6—24no—
124C2×Dic6—24no—
125C2×Dic6C2×C3×C418yes—
126C3×C4⋊C4—316no—
127C3×C4⋊C4—68no—
128C3×C4⋊C4—64no—
129C3×C42—24no—
130C3×C42—22no—
131C3×C42—22no—
132C3×C42—24no—
133C3×C42—24no—
134C3×C42—68no—
135C3×C42C4×D314yes—
136C3×C42D1214yes—
137C3×C42C2×C3×C414yes—
138C3×C42C3×D414yes—
139C4⋊Dic3—24no—
140C4⋊Dic3C2×C3×C4116yes—
141Dic3⋊C4—28no—
142C4×Dic3—28no—
143C22×C32C23×C411yescharacteristic
144C22×C32C22×D411yescharacteristic
145C22×C32C2×#4111yescharacteristic
146C22×C322−1+414yes—
147C32×C4—24no—
148C32×C4—24no—
149C32×C4—42no—
150C32×C4C4×D414yes—
151C3×Dic3—28no—
152C3×Dic3—44no—
153C22×Q8—32no—
154C4⋊Q8—38no—
155C4×Q8—68no—
156C2×C4⋊C4—34no—
157C2×C4⋊C4—32no—
158C2×C4⋊C4—34no—
159C2×C42—34no—
160C2×C42C2×C3×D311yescharacteristic
161C2×C42C2×C3×D311yescharacteristic
162C2×C42C2×C3×D311yescharacteristic
163#95—34no—
164#95—38no—
165#95C2×C3×D314yes—
166C23×C3—21no—
167C23×C3C23×D311yescharacteristic
168C23×C3C24×C311yescharacteristic
169C3×Q8—616no—
170C2×C3×C4—24no—
171C2×C3×C4—24no—
172C2×C3×C4—24no—
173C2×C3×C4—24no—
174C2×C3×C4—24no—
175C2×C3×C4—22no—
176C2×C3×C4—24no—
177C2×C3×C4—22no—
178C2×C3×C4—24no—
179C2×C3×C4—22no—
180C2×C3×C4—24no—
181C2×C3×C4—22no—
182C2×C3×C4—24no—
183C2×C3×C4—22no—
184C2×C3×C4—38no—
185C2×C3×C4—44no—
186C2×C3×C4—44no—
187C2×C3×C4—44no—
188C2×C3×C4—64no—
189C2×C3×C4—64no—
190C2×C3×C4—64no—
191C2×C3×C4—68no—
192C2×C3×C4C2×C4×D314yes—
193C2×C3×C4C2×C4×D312yes—
194C2×C3×C4C2×D1214yes—
195C2×C3×C4C2×D1212yes—
196C2×C3×C4#23512yes—
197C2×C3×C4C22×C3×C414yes—
198C2×C3×C4C22×C3×C412yes—
199C2×C3×C4C2×C3×D414yes—
200C2×C3×C4C2×C3×D412yes—
201C2×C3×C4C3×#4112yes—
202C2×Dic3—24no—
203C2×Dic3—24no—
204C2×Dic3—24no—
205C2×Dic3—28no—
206C2×Dic3C22×C3×C418yes—
207Dic6—216no—
208C2×C32C2×C4×D411yescharacteristic
209C2×C32#51912yes—
210C2×C32#53612yes—
211C2×C32#54112yes—
212C2×Q8—38no—
213C2×Q8—64no—
214C2×Q8—64no—
215C22×C4—34no—
216C22×C4—34no—
217C22×C4C22×C3×D312yes—
218C22×C4C22×C3×D312yes—
219C22×C4C22×C3×D312yes—
220C22×C4C22×C3×D311yescharacteristic
221C4⋊C4—316no—
222C4⋊C4—68no—
223C4⋊C4—64no—
224C42—22no—
225C42—68no—
226C42C3×C4×D314yes—
227C42C3×D1214yes—
228C22×C3—21no—
229C22×C3—21no—
230C22×C3—21no—
231C22×C3—24no—
232C22×C3C22×C4×D311yescharacteristic
233C22×C3C22×D1211yescharacteristic
234C22×C3C2×#23511yescharacteristic
235C22×C3#101014yes—
236C22×C3C23×C3×C411yescharacteristic
237C22×C3C22×C3×D411yescharacteristic
238C22×C3C2×C3×#4111yescharacteristic
239C22×C3C3×2−1+414yes—
240C3×C4—24no—
241C3×C4—24no—
242C3×C4—24no—
243C3×C4—24no—
244C3×C4—24no—
245C3×C4—44no—
246C3×C4—44no—
247C3×C4—44no—
248C3×C4—42no—
249C3×C4—42no—
250C3×C4—68no—
251C3×C4—124no—
252C3×C4C4×D1214yes—
253C3×C4C3×C4×D414yes—
254Dic3—28no—
255Dic3—44no—
256C32#232711yescharacteristic, complemented, Sylow
257C23C23×C3×D311yescharacteristic
258Q8—616no—
259C2×C4—24no—
260C2×C4—24no—
261C2×C4—22no—
262C2×C4—24no—
263C2×C4—38no—
264C2×C4—64no—
265C2×C4—64no—
266C2×C4—64no—
267C2×C4—68no—
268C2×C4C2×C3×C4×D314yes—
269C2×C4C2×C3×C4×D312yes—
270C2×C4C2×C3×D1214yes—
271C2×C4C2×C3×D1212yes—
272C2×C4C3×#23512yes—
273C2×C3—22no—
274C2×C3—22no—
275C2×C3—22no—
276C2×C3—21no—
277C2×C3C2×C4×D1211yescharacteristic
278C2×C3#551612yes—
279C2×C3#551812yes—
280C2×C3#552612yes—
281C2×C3C2×C3×C4×D411yescharacteristic
282C2×C3C3×#51912yes—
283C2×C3C3×#53612yes—
284C2×C3C3×#54112yes—
285C22C22×C3×C4×D311yescharacteristic
286C22C22×C3×D1211yescharacteristic
287C22C2×C3×#23511yescharacteristic
288C22C3×#101014yes—
289C4—24no—
290C4—24no—
291C4—42no—
292C4—68no—
293C4—124no—
294C4C3×C4×D1214yes—
295C3—21no—
296C3#7338811yescharacteristic, direct product factor
297C3C3×#232711yescharacteristic, complemented
298C2C2×C3×C4×D1211yescharacteristic
299C2C3×#551612yes—
300C2C3×#551812yes—
301C2C3×#552612yes—
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#376C2
socle, prime radicalC23×C32C24
cosocleC23×C3C24×C3
hypercenterC3×#376D3
hypocenterC3C3×#2327
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#376

Complements

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

NH ≅ G/Ntype
8. #73388C3direct (N × H)
17. C3×#869C4semidirect
73. #869C3×C4semidirect
256. C32#2327semidirect
296. C3#73388direct (N × H)
297. C3C3×#2327semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8692
C2×C3×C4×Dic62
C32×#3762
C3×#49362
C3×#49292
C3×#46532
C3×#23273
#733883