Finite Group Databasebeta

← C3×#73301 #11801928

Subgroups — C3×#73301 #11801928

Order 1152.

1177 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#872C211yesmaximal, characteristic
2C32×C43C211yesmaximal, characteristic, complemented
3C3×#4940C214yesmaximal
4C3×C4×(C2×D3)⋊C4C212yesmaximal
5C3×#4933C214yesmaximal, complemented
6C3×#4932C211yesmaximal, characteristic, complemented
7C3×C4×Dic3⋊C4C212yesmaximal, complemented
8C3×#2298—31nomaximal
9#73301C311yesmaximal, characteristic, direct product factor
10C22×C3×C4×D3C2211yescharacteristic
11C2×C32×C42C2212yes—
12C2×C32×C42C2214yes—
13C2×C32×C42C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4C2214yes—
15C2×C3×(C2×D3)⋊C4C2212yes—
16C2×C3×Dic3⋊C4C2214yes—
17C2×C3×Dic3⋊C4C2212yes—
18C2×C3×C4×Dic3C2212yes—
19C2×C3×C4×Dic3C2211yescharacteristic
20C3×#872C418yescomplemented
21C3×C3⋊#95C2214yes—
22C3×C3⋊#95C2214yes—
23C3×C3⋊#95C2214yes—
24C2×C3×#117—31no—
25C2×#872C2×C311yescharacteristic
26C3×#388—34no—
27C3×#387—34no—
28C3×C4×C4⋊C4—32no—
29C3×C4×C22⋊C4—32no—
30C3×#376—31no—
31C3×C43—21no—
32C3×C43D311yescharacteristic, complemented
33C3×C43C2×C311yescharacteristic, complemented
34#4940C2×C314yes—
35C4×(C2×D3)⋊C4C2×C312yes—
36#4933C2×C314yescomplemented
37#4932C2×C311yescharacteristic, complemented
38C4×Dic3⋊C4C2×C312yescomplemented
39C23×C3×D3C2311yescharacteristic
40C22×C32×C4C2312yes—
41C22×C32×C4C2314yes—
42C22×C32×C4C2311yescharacteristic
43C22×C3×Dic3C2314yes—
44C22×C3×Dic3C2312yes—
45C22×C3×Dic3C2311yescharacteristic
46C2×C3×C4×D3—24no—
47C2×C3×C4×D3C2×C414yes—
48C32×C42—28no—
49C32×C42—24no—
50C32×C42C2×C414yes—
51C3×(C2×D3)⋊C4—28no—
52C3×(C2×D3)⋊C4C2×C418yes—
53C3×Dic3⋊C4—28no—
54C3×Dic3⋊C4C2×C418yes—
55C3×C4×Dic3—24no—
56C3×C4×Dic3C2×C414yes—
57#2298—31noSylow
58C23×C3×C4—31no—
59C22×C4×D3C22×C311yescharacteristic
60C3×#117—38no—
61C2×C3×C4⋊C4—32no—
62C2×C3×C4⋊C4—34no—
63C2×C3×C22⋊C4—32no—
64C2×C3×C22⋊C4—34no—
65C2×C3×C42—22no—
66C2×C3×C42—24no—
67C2×C3×C42—21no—
68C2×C3×C42—31no—
69C2×C3×C42—32no—
70C2×C3×C42C2×D314yes—
71C2×C3×C42C2×D312yes—
72C2×C3×C42C2×D311yescharacteristic
73C2×C3×C42C22×C312yes—
74C2×C3×C42C22×C314yes—
75C2×C3×C42C22×C311yescharacteristic
76C2×(C2×D3)⋊C4C22×C314yes—
77C2×(C2×D3)⋊C4C22×C312yes—
78C2×Dic3⋊C4C22×C314yes—
79C2×Dic3⋊C4C22×C312yes—
80C2×C4×Dic3C22×C312yes—
81C2×C4×Dic3C22×C311yescharacteristic
82#872C3×C418yescomplemented
83C3×#95—34no—
84C3×#95—34no—
85C3×#95—34no—
86C3⋊#95C22×C314yes—
87C3⋊#95C22×C314yes—
88C3⋊#95C22×C314yes—
89C23×C32C2411yescharacteristic
90C22×C3×D3—24no—
91C22×C3×D3—22no—
92C22×C3×D3C22×C412yes—
93C2×C32×C4—24no—
94C2×C32×C4—24no—
95C2×C32×C4—24no—
96C2×C32×C4C22×C414yes—
97C2×C32×C4C22×C412yes—
98C2×C32×C4#4118yes—
99C2×C32×C4#4114yes—
100C2×C3×Dic3—24no—
101C2×C3×Dic3—22no—
102C2×C3×Dic3—24no—
103C2×C3×Dic3—24no—
104C2×C3×Dic3—24no—
105C2×C3×Dic3C22×C414yes—
106C2×C3×Dic3C22×C412yes—
107C3×C4×D3—28no—
108C2×#117—31no—
109#388—34no—
110#387—34no—
111C4×C4⋊C4—32no—
112C4×C22⋊C4—32no—
113#376—31no—
114C43C3×D311yescharacteristic, complemented
115C24×C3—31no—
116C23×D3C23×C311yescharacteristic
117C22×C3×C4—22no—
118C22×C3×C4—24no—
119C22×C3×C4—21no—
120C22×C3×C4—31no—
121C22×C3×C4—32no—
122C22×C3×C4—34no—
123C22×C3×C4—34no—
124C22×C3×C4—64no—
125C22×C3×C4C22×D312yes—
126C22×C3×C4C22×D314yes—
127C22×C3×C4C22×D311yescharacteristic
128C22×C3×C4C23×C312yes—
129C22×C3×C4C23×C314yes—
130C22×C3×C4C23×C311yescharacteristic
131C22×Dic3C23×C314yes—
132C22×Dic3C23×C311yescharacteristic
133C22×Dic3C23×C312yes—
134C2×C4×D3—24no—
135C2×C4×D3C2×C3×C414yes—
136C3×C4⋊C4—38no—
137C3×C4⋊C4—68no—
138C3×C22⋊C4—38no—
139C3×C22⋊C4—68no—
140C3×C42—216no—
141C3×C42—28no—
142C3×C42—28no—
143C3×C42—24no—
144C3×C42—28no—
145C3×C42—24no—
146C3×C42—24no—
147C3×C42—34no—
148C3×C42—64no—
149C3×C42C4×D314yes—
150C3×C42C2×C3×C414yes—
151(C2×D3)⋊C4—28no—
152(C2×D3)⋊C4C2×C3×C418yes—
153Dic3⋊C4—28no—
154Dic3⋊C4C2×C3×C418yes—
155C4×Dic3—24no—
156C4×Dic3C2×C3×C414yes—
157C22×C32C23×C411yescharacteristic
158C22×C32C2×#4112yes—
159C22×C32C2×#4114yes—
160C2×C3×D3—22no—
161C2×C3×D3—24no—
162C2×C3×D3—44no—
163C32×C4—24no—
164C32×C4—28no—
165C32×C4#11714yes—
166C3×Dic3—22no—
167C3×Dic3—24no—
168C3×Dic3—44no—
169C23×C4—31no—
170#117—38no—
171C2×C4⋊C4—32no—
172C2×C4⋊C4—34no—
173C2×C22⋊C4—32no—
174C2×C22⋊C4—34no—
175C2×C42—31no—
176C2×C42—32no—
177C2×C42C2×C3×D312yes—
178C2×C42C2×C3×D314yes—
179C2×C42C2×C3×D311yescharacteristic
180#95—34no—
181#95—34no—
182#95—34no—
183C23×C3—21no—
184C23×C3—32no—
185C23×C3—64no—
186C23×C3—62no—
187C23×C3C23×D311yescharacteristic
188C23×C3C24×C311yescharacteristic
189C22×D3—24no—
190C22×D3—22no—
191C22×D3C22×C3×C412yes—
192C2×C3×C4—28no—
193C2×C3×C4—28no—
194C2×C3×C4—28no—
195C2×C3×C4—24no—
196C2×C3×C4—24no—
197C2×C3×C4—24no—
198C2×C3×C4—24no—
199C2×C3×C4—24no—
200C2×C3×C4—24no—
201C2×C3×C4—24no—
202C2×C3×C4—22no—
203C2×C3×C4—28no—
204C2×C3×C4—24no—
205C2×C3×C4—34no—
206C2×C3×C4—32no—
207C2×C3×C4—64no—
208C2×C3×C4—62no—
209C2×C3×C4—68no—
210C2×C3×C4—64no—
211C2×C3×C4—64no—
212C2×C3×C4—64no—
213C2×C3×C4C2×C4×D314yes—
214C2×C3×C4C2×C4×D312yes—
215C2×C3×C4#23518yes—
216C2×C3×C4#23514yes—
217C2×C3×C4C22×C3×C414yes—
218C2×C3×C4C22×C3×C412yes—
219C2×C3×C4C3×#4118yes—
220C2×C3×C4C3×#4114yes—
221C2×Dic3—24no—
222C2×Dic3—22no—
223C2×Dic3—24no—
224C2×Dic3—24no—
225C2×Dic3—24no—
226C2×Dic3C22×C3×C414yes—
227C2×Dic3C22×C3×C412yes—
228C4×D3—28no—
229C2×C32C2×#11711yescharacteristic
230C2×C32C4×#4112yes—
231C2×C32#52914yes—
232C3×D3—42no—
233C24—31no—
234C22×C4—31no—
235C22×C4—32no—
236C22×C4—34no—
237C22×C4—34no—
238C22×C4—64no—
239C22×C4C22×C3×D312yes—
240C22×C4C22×C3×D314yes—
241C22×C4C22×C3×D311yescharacteristic
242C4⋊C4—38no—
243C4⋊C4—68no—
244C22⋊C4—38no—
245C22⋊C4—68no—
246C42—28no—
247C42—24no—
248C42—34no—
249C42—64no—
250C42C3×C4×D314yes—
251C22×C3—21no—
252C22×C3—22no—
253C22×C3—24no—
254C22×C3—62no—
255C22×C3—64no—
256C22×C3—124no—
257C22×C3C22×C4×D311yescharacteristic
258C22×C3C2×#23512yes—
259C22×C3C2×#23514yes—
260C22×C3C23×C3×C411yescharacteristic
261C22×C3C2×C3×#4112yes—
262C22×C3C2×C3×#4114yes—
263C2×D3—22no—
264C2×D3—24no—
265C2×D3—44no—
266C3×C4—28no—
267C3×C4—216no—
268C3×C4—24no—
269C3×C4—28no—
270C3×C4—24no—
271C3×C4—28no—
272C3×C4—24no—
273C3×C4—62no—
274C3×C4—64no—
275C3×C4—124no—
276C3×C4#87214yes—
277C3×C4C3×#11714yes—
278Dic3—22no—
279Dic3—24no—
280Dic3—44no—
281C32#229811yescharacteristic, complemented, Sylow
282C23—32no—
283C23—64no—
284C23—62no—
285C23C23×C3×D311yescharacteristic
286C2×C4—24no—
287C2×C4—24no—
288C2×C4—24no—
289C2×C4—34no—
290C2×C4—32no—
291C2×C4—64no—
292C2×C4—62no—
293C2×C4—68no—
294C2×C4—64no—
295C2×C4—64no—
296C2×C4—64no—
297C2×C4C2×C3×C4×D314yes—
298C2×C4C2×C3×C4×D312yes—
299C2×C4C3×#23518yes—
300C2×C4C3×#23514yes—
301C2×C3—21no—
302C2×C3—22no—
303C2×C3—24no—
304C2×C3—122no—
305C2×C3C2×#87211yescharacteristic
306C2×C3C4×#23512yes—
307C2×C3#547914yes—
308C2×C3C2×C3×#11711yescharacteristic
309C2×C3C3×C4×#4112yes—
310C2×C3C3×#52914yes—
311D3—42no—
312C22—62no—
313C22—64no—
314C22—124no—
315C22C22×C3×C4×D311yescharacteristic
316C22C2×C3×#23512yes—
317C22C2×C3×#23514yes—
318C4—24no—
319C4—28no—
320C4—62no—
321C4—64no—
322C4—124no—
323C4C3×#87214yes—
324C3—21no—
325C3#7330111yescharacteristic, direct product factor
326C3C3×#229811yescharacteristic, complemented
327C2—122no—
328C2C2×C3×#87211yescharacteristic
329C2C3×C4×#23512yes—
330C2C3×#547914yes—
subgroupG/H
centerC22×C3×C4C22×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×C43C2
socleC23×C32C24
prime radicalC23×C3×D3C23
cosocleC23×C3C24×C3
hypercenterC3×C43D3
hypocenterC3C3×#2298
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C3×C43

Complements

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

NH ≅ G/Ntype
2. C32×C43C2semidirect
5. C3×#4933C2semidirect
6. C3×#4932C2semidirect
7. C3×C4×Dic3⋊C4C2semidirect
9. #73301C3direct (N × H)
20. C3×#872C4semidirect
32. C3×C43D3semidirect
33. C3×C43C2×C3semidirect
36. #4933C2×C3semidirect
37. #4932C2×C3semidirect
38. C4×Dic3⋊C4C2×C3semidirect
82. #872C3×C4semidirect
114. C43C3×D3semidirect
281. C32#2298semidirect
325. C3#73301direct (N × H)
326. C3C3×#2298semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8722
C32×C432
C3×#49402
C3×C4×(C2×D3)⋊C42
C3×#49332
C3×#49322
C3×C4×Dic3⋊C42
C3×#22983
#733013