Finite Group Databasebeta

← C3×#68972 #11783771

Subgroups — C3×#68972 #11783771

Order 1152.

769 conjugacy classes of subgroups.

The subgroup lattice has 375 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#893C211yesmaximal, characteristic
2C2×C3×#823C212yesmaximal
3C3×Dic3×M16C212yesmaximal, complemented
4C32×#343C211yesmaximal, characteristic, complemented
5C3×#4530C211yesmaximal, characteristic, complemented
6C3×C4×#100—31nomaximal
7#68972C311yesmaximal, characteristic, direct product factor
8C22×C3×D12C2211yescharacteristic
9C22×C3×C4×D3C412yes—
10C2×C32×M16C2212yes—
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C3×(C2×D3)⋊C4C412yes—
13C2×C3×C4×Dic3C2211yescharacteristic
14C2×C3×#208C2212yes—
15C3×#893—22no—
16C3×#893—22no—
17C3×#823C418yescomplemented
18C3×#815—22no—
19C3×C8×Dic3—22no—
20C2×C3×C4×D4—31no—
21C2×#893C2×C311yescharacteristic
22C2×C3×#100—32no—
23C3×C4×M16—32no—
24C2×#823C2×C312yes—
25Dic3×M16C2×C312yescomplemented
26C3×#343—21no—
27C3×#343—31no—
28C3×#343D311yescharacteristic, complemented
29C3×#343C2×C311yescharacteristic, complemented
30#4530C2×C311yescharacteristic, complemented
31C23×C3×D3C2×C412yes—
32C22×C32×C4C2×C412yes—
33C22×C32×C4C2311yescharacteristic
34C22×C3×Dic3C2×C411yescharacteristic
35C22×C3×Dic3C2×C411yescharacteristic
36C2×C3×D12—22no—
37C2×C3×D12—21no—
38C2×C3×D12—21no—
39C2×C3×D12C2×C414yes—
40C2×C3×C4×D3—22no—
41C2×C3×C4×D3—22no—
42C2×C3×C4×D3—44no—
43C32×M16—22no—
44C32×M16C2×C414yescomplemented
45C2×C32×C8—22no—
46C32×C4⋊C4—22no—
47C3×(C2×D3)⋊C4—24no—
48C3×C4×Dic3D412yes—
49C3×C4×Dic3D412yes—
50C3×#208—22no—
51C3×#208C2×C414yescomplemented
52C2×C3×C3⋊C8—22no—
53C4×#100—31noSylow
54C22×C3×D4—31no—
55C23×C3×C4—32no—
56C22×D12C22×C311yescharacteristic
57C22×C4×D3C3×C412yes—
58C2×C3×M16—22no—
59C2×C3×M16—32no—
60C2×C3×M16C2×D312yes—
61C2×C3×M16C22×C312yes—
62C3×C4×D4—62no—
63C3×C4×D4—62no—
64C2×C3×C4⋊C4—21no—
65C2×C3×C4⋊C4C2×D311yescharacteristic
66C2×C3×C4⋊C4C22×C311yescharacteristic
67C2×C3×C22⋊C4—32no—
68C2×C3×C42—31no—
69C2×(C2×D3)⋊C4C3×C412yes—
70C2×C4×Dic3C22×C311yescharacteristic
71C2×#208C22×C312yes—
72#893—22no—
73#893—22no—
74C3×#100—38no—
75C3×#97—62no—
76C3×C4×C8—62no—
77#823C3×C418yescomplemented
78#815—22no—
79C8×Dic3—22no—
80C23×C32C22×C411yescharacteristic
81C22×C3×D3—22no—
82C22×C3×D3—22no—
83C22×C3×D3—42no—
84C22×C3×D3—42no—
85C22×C3×D3C4214yes—
86C2×C32×C4—22no—
87C2×C32×C4—42no—
88C2×C32×C4C22×C412yes—
89C2×C32×C4C2×D412yes—
90C2×C32×C4#4111yescharacteristic
91C2×C32×C4#4111yescharacteristic
92C2×C3×Dic3—22no—
93C2×C3×Dic3—41no—
94C2×C3×Dic3C22⋊C412yes—
95C2×C3×Dic3C22⋊C411yescharacteristic
96C2×C3×Dic3C22⋊C411yescharacteristic
97C3×D12—24no—
98C3×D12—24no—
99C3×C4×D3—44no—
100C3×C4×D3—44no—
101C32×C8—24no—
102C3×C3⋊C8—24no—
103C2×C4×D4—31no—
104C2×#100—32no—
105C4×M16—32no—
106#343—31no—
107#343C3×D311yescharacteristic, complemented
108C24×C3—32no—
109C23×D3C2×C3×C412yes—
110C2×C3×D4—34no—
111C2×C3×D4—62no—
112C2×C3×D4—61no—
113C2×C3×D4—61no—
114C22×C3×C4—22no—
115C22×C3×C4—21no—
116C22×C3×C4—31no—
117C22×C3×C4—31no—
118C22×C3×C4—62no—
119C22×C3×C4—62no—
120C22×C3×C4—124no—
121C22×C3×C4C4×D312yes—
122C22×C3×C4C2×C3×C412yes—
123C22×C3×C4C22×D311yescharacteristic
124C22×C3×C4C23×C311yescharacteristic
125C22×Dic3C2×C3×C411yescharacteristic
126C22×Dic3C2×C3×C411yescharacteristic
127C2×D12—22no—
128C2×D12—21no—
129C2×D12—21no—
130C2×D12C2×C3×C414yes—
131C2×C4×D3—22no—
132C2×C4×D3—22no—
133C2×C4×D3—44no—
134C3×M16—22no—
135C3×M16—22no—
136C3×M16—24no—
137C3×M16—34no—
138C3×M16—42no—
139C3×M16—62no—
140C3×M16C4×D314yescomplemented
141C3×M16C2×C3×C414yescomplemented
142C2×C3×C8—22no—
143C2×C3×C8—22no—
144C2×C3×C8—42no—
145C2×C3×C8—62no—
146C3×C4⋊C4—22no—
147C3×C4⋊C4—22no—
148C3×C4⋊C4—42no—
149C3×C22⋊C4—64no—
150C3×C42—32no—
151C3×C42—32no—
152(C2×D3)⋊C4—24no—
153C4×Dic3C3×D412yes—
154C4×Dic3C3×D412yes—
155#208—22no—
156#208C2×C3×C414yescomplemented
157C2×C3⋊C8—22no—
158C22×C32—21no—
159C22×C32—21no—
160C22×C32C2×C4211yescharacteristic
161C22×C32C2×C22⋊C411yescharacteristic
162C22×C32#11711yescharacteristic
163C2×C3×D3—24no—
164C2×C3×D3—44no—
165C2×C3×D3—42no—
166C2×C3×D3—42no—
167C2×C3×D3—44no—
168C32×C4—42no—
169C32×C4C4×D412yes—
170C32×C4C4×D412yes—
171C3×Dic3—21no—
172C3×Dic3—22no—
173C3×Dic3#10012yescomplemented
174C22×D4—31no—
175C23×C4—32no—
176C2×M16—32no—
177C2×M16C2×C3×D312yes—
178C4×D4—62no—
179C4×D4—62no—
180C2×C4⋊C4C2×C3×D311yescharacteristic
181C2×C22⋊C4—32no—
182C2×C42—31no—
183#100—38no—
184#97—62no—
185C4×C8—62no—
186C23×C3—21no—
187C23×C3—34no—
188C23×C3—62no—
189C23×C3—62no—
190C23×C3—122no—
191C23×C3—122no—
192C23×C3C2×C4×D311yescharacteristic
193C23×C3C22×C3×C411yescharacteristic
194C22×D3—22no—
195C22×D3—22no—
196C22×D3—42no—
197C22×D3—42no—
198C22×D3C3×C4214yes—
199C3×D4—64no—
200C3×D4—64no—
201C2×C3×C4—22no—
202C2×C3×C4—22no—
203C2×C3×C4—22no—
204C2×C3×C4—22no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—31no—
208C2×C3×C4—32no—
209C2×C3×C4—31no—
210C2×C3×C4—42no—
211C2×C3×C4—42no—
212C2×C3×C4—42no—
213C2×C3×C4—62no—
214C2×C3×C4—82no—
215C2×C3×C4—124no—
216C2×C3×C4—124no—
217C2×C3×C4—121no—
218C2×C3×C4C2×C4×D312yes—
219C2×C3×C4D3×D412yes—
220C2×C3×C4#23711yescharacteristic
221C2×C3×C4#23911yescharacteristic
222C2×C3×C4C22×C3×C412yes—
223C2×C3×C4C2×C3×D412yes—
224C2×C3×C4C3×#4111yescharacteristic
225C2×C3×C4C3×#4111yescharacteristic
226C2×Dic3—22no—
227C2×Dic3—41no—
228C2×Dic3C3×C22⋊C412yes—
229C2×Dic3C3×C22⋊C411yescharacteristic
230C2×Dic3C3×C22⋊C411yescharacteristic
231D12—24no—
232D12—24no—
233C4×D3—44no—
234C4×D3—44no—
235C3×C8—24no—
236C3×C8—24no—
237C3×C8—44no—
238C3×C8—64no—
239C3⋊C8—24no—
240C2×C32—21no—
241C2×C32—21no—
242C2×C32C4×C22⋊C411yescharacteristic
243C2×C32C2×#10011yescharacteristic
244C2×C32#41311yescharacteristic
245C3×D3—44no—
246C24—32no—
247C2×D4—34no—
248C2×D4—62no—
249C2×D4—61no—
250C2×D4—61no—
251C22×C4—31no—
252C22×C4—31no—
253C22×C4—62no—
254C22×C4—62no—
255C22×C4—124no—
256C22×C4C3×C4×D312yes—
257C22×C4C22×C3×D311yescharacteristic
258M16—22no—
259M16—34no—
260M16—62no—
261M16C3×C4×D314yescomplemented
262C2×C8—22no—
263C2×C8—62no—
264C4⋊C4—22no—
265C22⋊C4—64no—
266C42—32no—
267C42—32no—
268C22×C3—21no—
269C22×C3—21no—
270C22×C3—21no—
271C22×C3—21no—
272C22×C3—21no—
273C22×C3—21no—
274C22×C3—21no—
275C22×C3—41no—
276C22×C3—41no—
277C22×C3—64no—
278C22×C3—124no—
279C22×C3—124no—
280C22×C3—122no—
281C22×C3—122no—
282C22×C3C42×D311yescharacteristic
283C22×C3D3×C22⋊C411yescharacteristic
284C22×C3#89211yescharacteristic
285C22×C3C2×C3×C4211yescharacteristic
286C22×C3C2×C3×C22⋊C411yescharacteristic
287C22×C3C3×#11711yescharacteristic
288C2×D3—24no—
289C2×D3—44no—
290C2×D3—42no—
291C2×D3—42no—
292C2×D3—44no—
293C3×C4—22no—
294C3×C4—22no—
295C3×C4—32no—
296C3×C4—42no—
297C3×C4—42no—
298C3×C4—61no—
299C3×C4—62no—
300C3×C4—82no—
301C3×C4#67⋊C412yes—
302C3×C4#89312yes—
303C3×C4C3×C4×D412yes—
304C3×C4C3×C4×D412yes—
305Dic3—21no—
306Dic3—22no—
307Dic3C3×#10012yescomplemented
308C32C4×#10011yescharacteristic, complemented, Sylow
309C23—34no—
310C23—62no—
311C23—62no—
312C23—122no—
313C23—122no—
314C23C2×C3×C4×D311yescharacteristic
315D4—64no—
316D4—64no—
317C2×C4—22no—
318C2×C4—31no—
319C2×C4—32no—
320C2×C4—31no—
321C2×C4—42no—
322C2×C4—62no—
323C2×C4—124no—
324C2×C4—124no—
325C2×C4—121no—
326C2×C4C2×C3×C4×D312yes—
327C2×C4C3×D3×D412yes—
328C2×C4C3×#23711yescharacteristic
329C2×C4C3×#23911yescharacteristic
330C8—24no—
331C8—64no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—21no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3—41no—
340C2×C3—41no—
341C2×C3—124no—
342C2×C3#466611yescharacteristic
343C2×C3D3×#10011yescharacteristic
344C2×C3#475111yescharacteristic
345C2×C3C3×C4×C22⋊C411yescharacteristic
346C2×C3C2×C3×#10011yescharacteristic
347C2×C3C3×#41311yescharacteristic
348D3—44no—
349C22—21no—
350C22—21no—
351C22—64no—
352C22—124no—
353C22—124no—
354C22—122no—
355C22—122no—
356C22C3×C42×D311yescharacteristic
357C22C3×D3×C22⋊C411yescharacteristic
358C22C3×#89211yescharacteristic
359C4—32no—
360C4—42no—
361C4—61no—
362C4—62no—
363C4C3×#67⋊C412yes—
364C4C3×#89312yes—
365C3—21no—
366C3#6897211yescharacteristic, direct product factor
367C3C3×C4×#10011yescharacteristic, complemented
368C2—21no—
369C2—21no—
370C2—124no—
371C2C3×#466611yescharacteristic
372C2C3×D3×#10011yescharacteristic
373C2C3×#475111yescharacteristic
subgroupG/H
centerC22×C3D3×C22⋊C4
commutatorC22×C3C2×C3×C42
FrattiniC22×C4C22×C3×D3
FittingC32×#343C2
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×D12C22
cosocleC22×C3×C4C23×C3
hypercenterC3×#343D3
hypocenterC3C3×C4×#100
LCSG ▷ C22×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. C3×Dic3×M16C2semidirect
4. C32×#343C2semidirect
5. C3×#4530C2semidirect
7. #68972C3direct (N × H)
17. C3×#823C4semidirect
25. Dic3×M16C2×C3semidirect
28. C3×#343D3semidirect
29. C3×#343C2×C3semidirect
30. #4530C2×C3semidirect
44. C32×M16C2×C4semidirect
51. C3×#208C2×C4semidirect
77. #823C3×C4semidirect
107. #343C3×D3semidirect
140. C3×M16C4×D3semidirect
141. C3×M16C2×C3×C4semidirect
156. #208C2×C3×C4semidirect
173. C3×Dic3#100semidirect
261. M16C3×C4×D3semidirect
307. Dic3C3×#100semidirect
308. C32C4×#100semidirect
366. C3#68972direct (N × H)
367. C3C3×C4×#100semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8932
C2×C3×#8232
C3×Dic3×M162
C32×#3432
C3×#45302
C3×C4×#1003
#689723