Finite Group Databasebeta

← C3×#68991 #11785737

Subgroups — C3×#68991 #11785737

Order 1152.

593 conjugacy classes of subgroups.

The subgroup lattice has 339 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#892C211yesmaximal, characteristic
2C3×#5126C212yesmaximal
3C32×#343C211yesmaximal, characteristic, complemented
4C3×#4554C212yesmaximal, complemented
5C3×#4530C211yesmaximal, characteristic, complemented
6C3×#1822—31nomaximal
7#68991C311yesmaximal, characteristic, direct product factor
8C22×C3×C4×D3C2211yescharacteristic
9C2×C32×M16C2212yes—
10C2×C32×C4⋊C4C2211yescharacteristic
11C2×C3×(C2×D3)⋊C4C412yes—
12C2×C3×C4⋊Dic3C2211yescharacteristic
13C2×C3×C4×Dic3C412yes—
14C2×C3×#208C2212yes—
15C3×#892—24no—
16C3×(C2×D3)⋊C8—24no—
17C2×C3×#117—31no—
18C2×#892C2×C311yescharacteristic
19C3×#407—32no—
20#5126C2×C312yes—
21C3×#343—21no—
22C3×#343—32no—
23C3×#343—31no—
24C3×#343D311yescharacteristic, complemented
25C3×#343C2×C311yescharacteristic, complemented
26#4554C2×C312yescomplemented
27#4530C2×C311yescharacteristic, complemented
28C23×C3×D3C2×C411yescharacteristic
29C22×C32×C4C2×C412yes—
30C22×C32×C4C2311yescharacteristic
31C22×C3×Dic3C2×C411yescharacteristic
32C22×C3×Dic3C2×C412yes—
33C2×C3×C4×D3—22no—
34C2×C3×C4×D3—21no—
35C2×C3×C4×D3—21no—
36C2×C3×C4×D3D414yes—
37C32×M16—22no—
38C32×M16—22no—
39C2×C32×C8—22no—
40C32×C4⋊C4—22no—
41C3×(C2×D3)⋊C4—24no—
42C3×C4⋊Dic3—22no—
43C3×C4×Dic3—24no—
44C3×#208—22no—
45C3×#208—22no—
46C2×C3×C3⋊C8—22no—
47#1822—31noSylow
48C23×C3×C4—31no—
49C22×C4×D3C22×C311yescharacteristic
50C2×C3×M16—22no—
51C2×C3×M16—32no—
52C2×C3×M16C2×D312yes—
53C2×C3×M16C22×C312yes—
54C3×#117—64no—
55C2×C3×C4⋊C4—21no—
56C2×C3×C4⋊C4—31no—
57C2×C3×C4⋊C4C2×D311yescharacteristic
58C2×C3×C4⋊C4C22×C311yescharacteristic
59C2×C3×C22⋊C4—32no—
60C2×C3×C42—32no—
61C2×(C2×D3)⋊C4C3×C412yes—
62C2×C4⋊Dic3C22×C311yescharacteristic
63C2×C4×Dic3C3×C412yes—
64C2×#208C22×C312yes—
65#892—24no—
66C3×C22⋊C8—64no—
67(C2×D3)⋊C8—24no—
68C23×C32C22×C411yescharacteristic
69C22×C3×D3—21no—
70C22×C3×D3—21no—
71C22×C3×D3—41no—
72C22×C3×D3—41no—
73C22×C3×D3C22⋊C412yes—
74C2×C32×C4—22no—
75C2×C32×C4—42no—
76C2×C32×C4C2×D412yes—
77C2×C32×C4#4112yes—
78C2×C32×C4#4111yescharacteristic
79C2×C32×C4#4111yescharacteristic
80C2×C3×Dic3—21no—
81C2×C3×Dic3—21no—
82C2×C3×Dic3—22no—
83C2×C3×Dic3—42no—
84C2×C3×Dic3C22⋊C412yes—
85C3×C4×D3—24no—
86C3×C4×D3—24no—
87C32×C8—42no—
88C3×C3⋊C8—42no—
89C2×#117—31no—
90#407—32no—
91#343—32no—
92#343—31no—
93#343C3×D311yescharacteristic, complemented
94C24×C3—31no—
95C23×D3C2×C3×C411yescharacteristic
96C22×C3×C4—22no—
97C22×C3×C4—21no—
98C22×C3×C4—31no—
99C22×C3×C4—34no—
100C22×C3×C4—32no—
101C22×C3×C4—62no—
102C22×C3×C4—61no—
103C22×C3×C4—61no—
104C22×C3×C4C4×D312yes—
105C22×C3×C4C2×C3×C412yes—
106C22×C3×C4C22×D311yescharacteristic
107C22×C3×C4C23×C311yescharacteristic
108C22×Dic3C2×C3×C411yescharacteristic
109C22×Dic3C2×C3×C412yes—
110C2×C4×D3—22no—
111C2×C4×D3—21no—
112C2×C4×D3—21no—
113C2×C4×D3C3×D414yes—
114C3×M16—24no—
115C3×M16—22no—
116C3×M16—22no—
117C3×M16—22no—
118C3×M16—22no—
119C3×M16—42no—
120C3×M16—62no—
121C3×M16—62no—
122C2×C3×C8—22no—
123C2×C3×C8—22no—
124C2×C3×C8—42no—
125C2×C3×C8—62no—
126C3×C4⋊C4—22no—
127C3×C4⋊C4—22no—
128C3×C4⋊C4—42no—
129C3×C4⋊C4—62no—
130C3×C22⋊C4—64no—
131C3×C42—64no—
132(C2×D3)⋊C4—24no—
133C4⋊Dic3—22no—
134C4×Dic3—24no—
135#208—22no—
136#208—22no—
137C2×C3⋊C8—22no—
138C22×C32—21no—
139C22×C32—21no—
140C22×C32C2×C22⋊C411yescharacteristic
141C22×C32#11711yescharacteristic
142C22×C32#11711yescharacteristic
143C2×C3×D3—22no—
144C2×C3×D3—22no—
145C2×C3×D3—22no—
146C2×C3×D3—42no—
147C2×C3×D3—42no—
148C32×C4—42no—
149C32×C4#12312yes—
150C32×C4#12312yes—
151C3×Dic3—22no—
152C3×Dic3—42no—
153C23×C4—31no—
154C2×M16—32no—
155C2×M16C2×C3×D312yes—
156#117—64no—
157C2×C4⋊C4—31no—
158C2×C4⋊C4C2×C3×D311yescharacteristic
159C2×C22⋊C4—32no—
160C2×C42—32no—
161C22⋊C8—64no—
162C23×C3—21no—
163C23×C3—32no—
164C23×C3—61no—
165C23×C3—61no—
166C23×C3—121no—
167C23×C3—121no—
168C23×C3C2×C4×D311yescharacteristic
169C23×C3C22×C3×C411yescharacteristic
170C22×D3—21no—
171C22×D3—21no—
172C22×D3—41no—
173C22×D3—41no—
174C22×D3C3×C22⋊C412yes—
175C2×C3×C4—22no—
176C2×C3×C4—22no—
177C2×C3×C4—22no—
178C2×C3×C4—22no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—32no—
182C2×C3×C4—42no—
183C2×C3×C4—42no—
184C2×C3×C4—42no—
185C2×C3×C4—61no—
186C2×C3×C4—61no—
187C2×C3×C4—64no—
188C2×C3×C4—64no—
189C2×C3×C4—62no—
190C2×C3×C4—82no—
191C2×C3×C4—122no—
192C2×C3×C4#23512yes—
193C2×C3×C4D3×D412yes—
194C2×C3×C4#23711yescharacteristic
195C2×C3×C4#23911yescharacteristic
196C2×C3×C4C2×C3×D412yes—
197C2×C3×C4C3×#4112yes—
198C2×C3×C4C3×#4111yescharacteristic
199C2×C3×C4C3×#4111yescharacteristic
200C2×Dic3—21no—
201C2×Dic3—21no—
202C2×Dic3—22no—
203C2×Dic3—42no—
204C2×Dic3C3×C22⋊C412yes—
205C4×D3—24no—
206C4×D3—24no—
207C3×C8—44no—
208C3×C8—42no—
209C3×C8—42no—
210C3×C8—122no—
211C3⋊C8—42no—
212C2×C32—21no—
213C2×C32—21no—
214C2×C32#38111yescharacteristic
215C2×C32#41311yescharacteristic
216C2×C32#41311yescharacteristic
217C3×D3—42no—
218C24—31no—
219C22×C4—31no—
220C22×C4—34no—
221C22×C4—32no—
222C22×C4—62no—
223C22×C4—61no—
224C22×C4—61no—
225C22×C4C3×C4×D312yes—
226C22×C4C22×C3×D311yescharacteristic
227M16—22no—
228M16—22no—
229M16—62no—
230M16—62no—
231C2×C8—22no—
232C2×C8—62no—
233C4⋊C4—22no—
234C4⋊C4—62no—
235C22⋊C4—64no—
236C42—64no—
237C22×C3—21no—
238C22×C3—21no—
239C22×C3—21no—
240C22×C3—21no—
241C22×C3—21no—
242C22×C3—21no—
243C22×C3—21no—
244C22×C3—41no—
245C22×C3—41no—
246C22×C3—62no—
247C22×C3—62no—
248C22×C3—62no—
249C22×C3—122no—
250C22×C3—122no—
251C22×C3#87211yescharacteristic
252C22×C3D3×C22⋊C411yescharacteristic
253C22×C3#89211yescharacteristic
254C22×C3C2×C3×C22⋊C411yescharacteristic
255C22×C3C3×#11711yescharacteristic
256C22×C3C3×#11711yescharacteristic
257C2×D3—22no—
258C2×D3—22no—
259C2×D3—22no—
260C2×D3—42no—
261C2×D3—42no—
262C3×C4—22no—
263C3×C4—22no—
264C3×C4—42no—
265C3×C4—42no—
266C3×C4—62no—
267C3×C4—82no—
268C3×C4—122no—
269C3×C4#88312yes—
270C3×C4#89412yes—
271C3×C4C3×#12312yes—
272C3×C4C3×#12312yes—
273Dic3—22no—
274Dic3—42no—
275C32#182211yescharacteristic, complemented, Sylow
276C23—32no—
277C23—61no—
278C23—61no—
279C23—121no—
280C23—121no—
281C23C2×C3×C4×D311yescharacteristic
282C2×C4—22no—
283C2×C4—32no—
284C2×C4—42no—
285C2×C4—61no—
286C2×C4—61no—
287C2×C4—64no—
288C2×C4—64no—
289C2×C4—62no—
290C2×C4—122no—
291C2×C4C3×#23512yes—
292C2×C4C3×D3×D412yes—
293C2×C4C3×#23711yescharacteristic
294C2×C4C3×#23911yescharacteristic
295C8—42no—
296C8—122no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3—21no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—41no—
305C2×C3—41no—
306C2×C3—122no—
307C2×C3#466411yescharacteristic
308C2×C3#474511yescharacteristic
309C2×C3#475111yescharacteristic
310C2×C3C3×#38111yescharacteristic
311C2×C3C3×#41311yescharacteristic
312C2×C3C3×#41311yescharacteristic
313D3—42no—
314C22—21no—
315C22—21no—
316C22—62no—
317C22—62no—
318C22—62no—
319C22—122no—
320C22—122no—
321C22C3×#87211yescharacteristic
322C22C3×D3×C22⋊C411yescharacteristic
323C22C3×#89211yescharacteristic
324C4—42no—
325C4—62no—
326C4—122no—
327C4C3×#88312yes—
328C4C3×#89412yes—
329C3—21no—
330C3#6899111yescharacteristic, direct product factor
331C3C3×#182211yescharacteristic, complemented
332C2—21no—
333C2—21no—
334C2—122no—
335C2C3×#466411yescharacteristic
336C2C3×#474511yescharacteristic
337C2C3×#475111yescharacteristic
subgroupG/H
centerC22×C3D3×C22⋊C4
commutatorC23×C3C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#343C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C3×D3C2×C4
cosocleC22×C3×C4C23×C3
hypercenterC3×#343D3
hypocenterC3C3×#1822
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#343

Complements

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

NH ≅ G/Ntype
3. C32×#343C2semidirect
4. C3×#4554C2semidirect
5. C3×#4530C2semidirect
7. #68991C3direct (N × H)
24. C3×#343D3semidirect
25. C3×#343C2×C3semidirect
26. #4554C2×C3semidirect
27. #4530C2×C3semidirect
93. #343C3×D3semidirect
275. C32#1822semidirect
330. C3#68991direct (N × H)
331. C3C3×#1822semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8922
C3×#51262
C32×#3432
C3×#45542
C3×#45302
C3×#18223
#689913