Finite Group Databasebeta

← C3×#68866 #11783250

Subgroups — C3×#68866 #11783250

Order 1152.

905 conjugacy classes of subgroups.

The subgroup lattice has 365 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×C8C211yesmaximal, characteristic
2C2×C3×#892C212yesmaximal
3C32×#340C211yesmaximal, characteristic, complemented
4C3×#4551C211yesmaximal, characteristic, complemented
5C3×#4529C212yesmaximal, complemented
6C3×#1735—31nomaximal
7#68866C311yesmaximal, characteristic, direct product factor
8C22×C3×C4×D3C2211yescharacteristic
9C22×C32×C8C2211yescharacteristic
10C2×C32×C4⋊C4C2212yes—
11C2×C3×(C2×D3)⋊C4—22no—
12C2×C3×C4⋊Dic3C2212yes—
13C2×C3×C4×Dic3—22no—
14C22×C3×C3⋊C8C2211yescharacteristic
15C2×C3×D3×C8—24no—
16C2×C3×D3×C8C414yescomplemented
17C3×#892—24no—
18C3×#892C418yescomplemented
19C23×C3×C8—31no—
20C2×C3×#117—32no—
21C22×D3×C8C2×C311yescharacteristic
22C2×#892C2×C312yes—
23C3×#340—21no—
24C3×#340—31no—
25C3×#340—32no—
26C3×#340D311yescharacteristic, complemented
27C3×#340C2×C311yescharacteristic, complemented
28#4551C2×C311yescharacteristic, complemented
29#4529C2×C312yescomplemented
30C23×C3×D3D411yescharacteristic
31C22×C32×C4—22no—
32C22×C32×C4C2311yescharacteristic
33C22×C3×Dic3—22no—
34C22×C3×Dic3D411yescharacteristic
35C2×C3×C4×D3C2×C412yes—
36C2×C3×C4×D3C2×C414yes—
37C2×C3×C4×D3D414yes—
38C2×C3×C4×D3Q812yes—
39C2×C32×C8—22no—
40C2×C32×C8C2×C412yes—
41C32×C4⋊C4—22no—
42C32×C4⋊C4C2×C414yes—
43C3×(C2×D3)⋊C4—28no—
44C3×C4⋊Dic3—22no—
45C3×C4⋊Dic3C2×C414yes—
46C3×C4×Dic3—28no—
47C2×C3×C3⋊C8—22no—
48C2×C3×C3⋊C8C2×C412yes—
49C3×D3×C8—28no—
50#1735—31noSylow
51C23×C3×C4—31no—
52C22×C4×D3C22×C311yescharacteristic
53C22×C3×C8—21no—
54C22×C3×C8—31no—
55C22×C3×C8—34no—
56C22×C3×C8—64no—
57C22×C3×C8C2×D311yescharacteristic
58C22×C3×C8C22×C311yescharacteristic
59C3×#117—38no—
60C3×#117—64no—
61C2×C3×C4⋊C4—22no—
62C2×C3×C4⋊C4—32no—
63C2×C3×C4⋊C4C2×D312yes—
64C2×C3×C4⋊C4C22×C312yes—
65C2×C3×C22⋊C4—62no—
66C2×C3×C42—62no—
67C2×(C2×D3)⋊C4—22no—
68C2×C4⋊Dic3C22×C312yes—
69C2×C4×Dic3—22no—
70C22×C3⋊C8C22×C311yescharacteristic
71C2×D3×C8—24no—
72C2×D3×C8C3×C414yescomplemented
73#892—24no—
74#892C3×C418yescomplemented
75C23×C32C2×D411yescharacteristic
76C22×C3×D3—21no—
77C22×C3×D3—22no—
78C22×C3×D3—21no—
79C22×C3×D3C22⋊C414yes—
80C22×C3×D3C4⋊C412yes—
81C2×C32×C4—24no—
82C2×C32×C4—42no—
83C2×C32×C4—42no—
84C2×C32×C4C22×C411yescharacteristic
85C2×C32×C4C22×C412yes—
86C2×C32×C4C2×D412yes—
87C2×C32×C4C2×Q811yescharacteristic
88C2×C3×Dic3—24no—
89C2×C3×Dic3—42no—
90C2×C3×Dic3—42no—
91C2×C3×Dic3C22⋊C414yes—
92C2×C3×Dic3C4⋊C412yes—
93C3×C4×D3C4214yes—
94C3×C4×D3C22⋊C414yes—
95C3×C4×D3C4⋊C418yes—
96C32×C8—22no—
97C3×C3⋊C8—22no—
98C23×C8—31no—
99C2×#117—32no—
100#340—31no—
101#340—32no—
102#340C3×D311yescharacteristic, complemented
103C24×C3—31no—
104C23×D3C3×D411yescharacteristic
105C22×C3×C4—22no—
106C22×C3×C4—22no—
107C22×C3×C4—21no—
108C22×C3×C4—31no—
109C22×C3×C4—34no—
110C22×C3×C4—32no—
111C22×C3×C4—34no—
112C22×C3×C4—32no—
113C22×C3×C4—42no—
114C22×C3×C4—62no—
115C22×C3×C4C22×D311yescharacteristic
116C22×C3×C4C23×C311yescharacteristic
117C22×Dic3—22no—
118C22×Dic3C3×D411yescharacteristic
119C2×C4×D3C2×C3×C412yes—
120C2×C4×D3C2×C3×C414yes—
121C2×C4×D3C3×D414yes—
122C2×C4×D3C3×Q812yes—
123C2×C3×C8—22no—
124C2×C3×C8—22no—
125C2×C3×C8—22no—
126C2×C3×C8—32no—
127C2×C3×C8—42no—
128C2×C3×C8—68no—
129C2×C3×C8—62no—
130C2×C3×C8C4×D312yes—
131C2×C3×C8C2×C3×C412yes—
132C3×C4⋊C4—22no—
133C3×C4⋊C4—22no—
134C3×C4⋊C4—24no—
135C3×C4⋊C4—34no—
136C3×C4⋊C4—42no—
137C3×C4⋊C4—62no—
138C3×C4⋊C4C4×D314yes—
139C3×C4⋊C4C2×C3×C414yes—
140C3×C22⋊C4—68no—
141C3×C42—68no—
142(C2×D3)⋊C4—28no—
143C4⋊Dic3—22no—
144C4⋊Dic3C2×C3×C414yes—
145C4×Dic3—28no—
146C2×C3⋊C8—22no—
147C2×C3⋊C8C2×C3×C412yes—
148D3×C8—28no—
149C22×C32C2×C22⋊C412yes—
150C22×C32C2×C4⋊C411yescharacteristic
151C22×C32#13511yescharacteristic
152C22×C32#13512yes—
153C22×C32#13511yescharacteristic
154C2×C3×D3—24no—
155C2×C3×D3—24no—
156C2×C3×D3—22no—
157C2×C3×D3—22no—
158C2×C3×D3#9514yes—
159C32×C4—44no—
160C32×C4C2×C4211yescharacteristic
161C32×C4C2×C22⋊C411yescharacteristic
162C32×C4C2×C4⋊C412yes—
163C3×Dic3—44no—
164C3×Dic3#9514yes—
165C23×C4—31no—
166C22×C8—31no—
167C22×C8—34no—
168C22×C8—64no—
169C22×C8C2×C3×D311yescharacteristic
170#117—38no—
171#117—64no—
172C2×C4⋊C4—32no—
173C2×C4⋊C4C2×C3×D312yes—
174C2×C22⋊C4—62no—
175C2×C42—62no—
176C23×C3—21no—
177C23×C3—34no—
178C23×C3—32no—
179C23×C3—61no—
180C23×C3—62no—
181C23×C3—61no—
182C23×C3D3×D411yescharacteristic
183C23×C3C2×C3×D411yescharacteristic
184C22×D3—21no—
185C22×D3—22no—
186C22×D3—21no—
187C22×D3C3×C22⋊C414yes—
188C22×D3C3×C4⋊C412yes—
189C2×C3×C4—24no—
190C2×C3×C4—24no—
191C2×C3×C4—22no—
192C2×C3×C4—21no—
193C2×C3×C4—22no—
194C2×C3×C4—21no—
195C2×C3×C4—34no—
196C2×C3×C4—32no—
197C2×C3×C4—34no—
198C2×C3×C4—34no—
199C2×C3×C4—38no—
200C2×C3×C4—44no—
201C2×C3×C4—42no—
202C2×C3×C4—42no—
203C2×C3×C4—42no—
204C2×C3×C4—42no—
205C2×C3×C4—64no—
206C2×C3×C4—82no—
207C2×C3×C4—82no—
208C2×C3×C4—122no—
209C2×C3×C4—122no—
210C2×C3×C4C2×C4×D311yescharacteristic
211C2×C3×C4C2×C4×D312yes—
212C2×C3×C4D3×D412yes—
213C2×C3×C4D3×Q811yescharacteristic
214C2×C3×C4C22×C3×C411yescharacteristic
215C2×C3×C4C22×C3×C412yes—
216C2×C3×C4C2×C3×D412yes—
217C2×C3×C4C2×C3×Q811yescharacteristic
218C2×Dic3—24no—
219C2×Dic3—42no—
220C2×Dic3—42no—
221C2×Dic3C3×C22⋊C414yes—
222C2×Dic3C3×C4⋊C412yes—
223C4×D3C3×C4214yes—
224C4×D3C3×C22⋊C414yes—
225C4×D3C3×C4⋊C418yes—
226C3×C8—22no—
227C3×C8—22no—
228C3×C8—42no—
229C3×C8—62no—
230C3⋊C8—22no—
231C2×C32C2×#9511yescharacteristic
232C2×C32#41612yes—
233C2×C32#41612yes—
234C2×C32#42711yescharacteristic
235C2×C32#42711yescharacteristic
236C3×D3—24no—
237C24—31no—
238C22×C4—22no—
239C22×C4—31no—
240C22×C4—34no—
241C22×C4—32no—
242C22×C4—34no—
243C22×C4—32no—
244C22×C4—62no—
245C22×C4C22×C3×D311yescharacteristic
246C2×C8—22no—
247C2×C8—32no—
248C2×C8—68no—
249C2×C8—62no—
250C2×C8C3×C4×D312yes—
251C4⋊C4—22no—
252C4⋊C4—34no—
253C4⋊C4—62no—
254C4⋊C4C3×C4×D314yes—
255C22⋊C4—68no—
256C42—68no—
257C22×C3—22no—
258C22×C3—21no—
259C22×C3—21no—
260C22×C3—22no—
261C22×C3—21no—
262C22×C3—34no—
263C22×C3—62no—
264C22×C3—64no—
265C22×C3—64no—
266C22×C3—62no—
267C22×C3D3×C22⋊C412yes—
268C22×C3D3×C4⋊C411yescharacteristic
269C22×C3#91211yescharacteristic
270C22×C3#91612yes—
271C22×C3#91911yescharacteristic
272C22×C3C2×C3×C22⋊C412yes—
273C22×C3C2×C3×C4⋊C411yescharacteristic
274C22×C3C3×#13511yescharacteristic
275C22×C3C3×#13512yes—
276C22×C3C3×#13511yescharacteristic
277C2×D3—24no—
278C2×D3—24no—
279C2×D3—22no—
280C2×D3—22no—
281C2×D3C3×#9514yes—
282C3×C4—21no—
283C3×C4—22no—
284C3×C4—21no—
285C3×C4—34no—
286C3×C4—44no—
287C3×C4—44no—
288C3×C4—84no—
289C3×C4—124no—
290C3×C4C42×D311yescharacteristic
291C3×C4D3×C22⋊C411yescharacteristic
292C3×C4D3×C4⋊C412yes—
293C3×C4C2×C3×C4211yescharacteristic
294C3×C4C2×C3×C22⋊C411yescharacteristic
295C3×C4C2×C3×C4⋊C412yes—
296Dic3—44no—
297Dic3C3×#9514yes—
298C32#173511yescharacteristic, complemented, Sylow
299C23—34no—
300C23—32no—
301C23—61no—
302C23—62no—
303C23—61no—
304C23C3×D3×D411yescharacteristic
305C2×C4—24no—
306C2×C4—34no—
307C2×C4—32no—
308C2×C4—34no—
309C2×C4—38no—
310C2×C4—34no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—64no—
314C2×C4—122no—
315C2×C4—122no—
316C2×C4C2×C3×C4×D311yescharacteristic
317C2×C4C2×C3×C4×D312yes—
318C2×C4C3×D3×D412yes—
319C2×C4C3×D3×Q811yescharacteristic
320C8—22no—
321C8—62no—
322C2×C3—21no—
323C2×C3—22no—
324C2×C3—22no—
325C2×C3—21no—
326C2×C3—21no—
327C2×C3—64no—
328C2×C3D3×#9511yescharacteristic
329C2×C3#477212yes—
330C2×C3#480412yes—
331C2×C3#486011yescharacteristic
332C2×C3#488011yescharacteristic
333C2×C3C2×C3×#9511yescharacteristic
334C2×C3C3×#41612yes—
335C2×C3C3×#41612yes—
336C2×C3C3×#42711yescharacteristic
337C2×C3C3×#42711yescharacteristic
338D3—24no—
339C22—34no—
340C22—64no—
341C22—64no—
342C22—62no—
343C22—62no—
344C22C3×D3×C22⋊C412yes—
345C22C3×D3×C4⋊C411yescharacteristic
346C22C3×#91211yescharacteristic
347C22C3×#91612yes—
348C22C3×#91911yescharacteristic
349C4—34no—
350C4—44no—
351C4—124no—
352C4C3×C42×D311yescharacteristic
353C4C3×D3×C22⋊C411yescharacteristic
354C4C3×D3×C4⋊C412yes—
355C3—21no—
356C3#6886611yescharacteristic, direct product factor
357C3C3×#173511yescharacteristic, complemented
358C2—64no—
359C2C3×D3×#9511yescharacteristic
360C2C3×#477212yes—
361C2C3×#480412yes—
362C2C3×#486011yescharacteristic
363C2C3×#488011yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutatorC3×C4C2×C3×C42
FrattiniC22×C4C22×C3×D3
FittingC32×#340C2
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
cosocleC22×C3×C4C23×C3
hypercenterC3×#340D3
hypocenterC3C3×#1735
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C3×#340

Complements

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

NH ≅ G/Ntype
3. C32×#340C2semidirect
4. C3×#4551C2semidirect
5. C3×#4529C2semidirect
7. #68866C3direct (N × H)
16. C2×C3×D3×C8C4semidirect
18. C3×#892C4semidirect
26. C3×#340D3semidirect
27. C3×#340C2×C3semidirect
28. #4551C2×C3semidirect
29. #4529C2×C3semidirect
72. C2×D3×C8C3×C4semidirect
74. #892C3×C4semidirect
102. #340C3×D3semidirect
298. C32#1735semidirect
356. C3#68866direct (N × H)
357. C3C3×#1735semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×C82
C2×C3×#8922
C32×#3402
C3×#45512
C3×#45292
C3×#17353
#688663