Finite Group Databasebeta

← C2×C3×#4541 #11796341

Subgroups — C2×C3×#4541 #11796341

Order 1152.

733 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#124C211yesmaximal, characteristic
2C2×C3×#834C212yesmaximal
3C3×#4541C214yesmaximal, direct product factor
4C2×C3×#354—31nomaximal
5C2×#4541C311yesmaximal, characteristic, direct product factor
6C22×C32×Q8C411yescharacteristic, complemented
7C22×C32×D4C2211yescharacteristic
8C32×#124—22no—
9C32×#124C412yescomplemented
10C32×#124C2212yes—
11C2×C32×C22⋊C4—22no—
12C2×C32×C42C411yescharacteristic, complemented
13C2×C3×#217—22no—
14C3×#834—22no—
15C3×#834C2214yes—
16C2×C3×#124—21no—
17C2×C3×#124D311yescharacteristic
18C2×C3×#124C2×C311yescharacteristic
19C2×C3×#99—32no—
20C2×#834C2×C312yes—
21C3×#354—34no—
22#4541C2×C314yesdirect product factor
23C24×C32D412yes—
24C2×C32×Q8—21no—
25C2×C32×Q8—41no—
26C2×C32×Q8—41no—
27C2×C32×Q8C2×C412yescomplemented
28C2×C32×D4—41no—
29C2×C32×D4—41no—
30C2×C32×D4C2×C411yescharacteristic
31C2×C32×D4D412yes—
32C2×C32×D4C2311yescharacteristic
33C22×C32×C4—21no—
34C22×C32×C4—21no—
35C22×C32×C4C2×C411yescharacteristic
36C22×C3×Dic3—42no—
37C32×C22⋊C4—24no—
38C32×C22⋊C4—24no—
39C32×C42—21no—
40C32×C42C2×C412yescomplemented
41C3×#217—24no—
42C3×#217—42no—
43C2×#354—31noSylow
44C22×C3×Q8—21no—
45C22×C3×Q8Dic311yescharacteristic, complemented
46C22×C3×Q8C3×C411yescharacteristic, complemented
47C22×C3×D4—21no—
48C22×C3×D4C2×D311yescharacteristic
49C22×C3×D4C22×C311yescharacteristic
50C3×#124—24no—
51C3×#124—22no—
52C3×#124—22no—
53C3×#124—22no—
54C3×#124—22no—
55C3×#124Dic312yescomplemented
56C3×#124C3×C412yescomplemented
57C3×#124C2×D312yes—
58C3×#124C22×C312yes—
59C2×C3×C22⋊C4—24no—
60C2×C3×C22⋊C4—22no—
61C2×C3×C22⋊C4—22no—
62C2×C3×C22⋊C4—62no—
63C2×C3×C42—21no—
64C2×C3×C42Dic311yescharacteristic, complemented
65C2×C3×C42C3×C411yescharacteristic, complemented
66C2×#217—22no—
67C3×#99—34no—
68C3×#99—62no—
69#834—22no—
70#834C22×C314yes—
71C23×C32—22no—
72C23×C32—22no—
73C23×C32—44no—
74C23×C32C22⋊C412yes—
75C23×C32C22⋊C411yescharacteristic
76C23×C32C2×D412yes—
77C32×Q8—42no—
78C32×Q8—42no—
79C32×D4—41no—
80C32×D4—42no—
81C32×D4—41no—
82C2×C32×C4—21no—
83C2×C32×C4—21no—
84C2×C32×C4—22no—
85C2×C32×C4—22no—
86C2×C32×C4—42no—
87C2×C32×C4—41no—
88C2×C32×C4—41no—
89C2×C32×C4C22⋊C411yescharacteristic
90C2×C32×C4C22×C411yescharacteristic
91C2×C3×Dic3—44no—
92C2×C3×Dic3—84no—
93C2×#124C3×D311yescharacteristic
94C2×#99—32no—
95#354—34no—
96C24×C3—22no—
97C24×C3#6712yes—
98C24×C3C3×D412yes—
99C2×C3×Q8—22no—
100C2×C3×Q8—21no—
101C2×C3×Q8—21no—
102C2×C3×Q8—22no—
103C2×C3×Q8—42no—
104C2×C3×Q8—42no—
105C2×C3×Q8—41no—
106C2×C3×Q8—41no—
107C2×C3×Q8—41no—
108C2×C3×Q8—41no—
109C2×C3×Q8C2×Dic312yescomplemented
110C2×C3×Q8C2×C3×C412yescomplemented
111C2×C3×D4—21no—
112C2×C3×D4—22no—
113C2×C3×D4—21no—
114C2×C3×D4—41no—
115C2×C3×D4—41no—
116C2×C3×D4—41no—
117C2×C3×D4—41no—
118C2×C3×D4—42no—
119C2×C3×D4—42no—
120C2×C3×D4C2×Dic311yescharacteristic
121C2×C3×D4#6712yes—
122C2×C3×D4C2×C3×C411yescharacteristic
123C2×C3×D4C3×D412yes—
124C2×C3×D4C22×D311yescharacteristic
125C2×C3×D4C23×C311yescharacteristic
126C22×C3×C4—22no—
127C22×C3×C4—22no—
128C22×C3×C4—21no—
129C22×C3×C4—21no—
130C22×C3×C4—21no—
131C22×C3×C4—21no—
132C22×C3×C4—21no—
133C22×C3×C4—122no—
134C22×C3×C4C2×Dic311yescharacteristic
135C22×C3×C4C2×C3×C411yescharacteristic
136C22×Dic3—42no—
137C3×C22⋊C4—28no—
138C3×C22⋊C4—28no—
139C3×C22⋊C4—24no—
140C3×C22⋊C4—24no—
141C3×C22⋊C4—24no—
142C3×C22⋊C4—24no—
143C3×C22⋊C4—64no—
144C3×C22⋊C4—122no—
145C3×C42—22no—
146C3×C42—21no—
147C3×C42—21no—
148C3×C42—22no—
149C3×C42C2×Dic312yescomplemented
150C3×C42C2×C3×C412yescomplemented
151#217—24no—
152#217—42no—
153C22×C32—22no—
154C22×C32—22no—
155C22×C32—22no—
156C22×C32—42no—
157C22×C32—42no—
158C22×C32—44no—
159C22×C32—82no—
160C22×C32#9911yescharacteristic
161C22×C32#9911yescharacteristic
162C22×C32C2×C22⋊C411yescharacteristic
163C32×C4—21no—
164C32×C4—21no—
165C32×C4—42no—
166C32×C4—42no—
167C3×Dic3—84no—
168C22×Q8C3×Dic311yescharacteristic, complemented
169C22×D4C2×C3×D311yescharacteristic
170#124—22no—
171#124C3×Dic312yescomplemented
172#124C2×C3×D312yes—
173C2×C22⋊C4—22no—
174C2×C22⋊C4—62no—
175C2×C42C3×Dic311yescharacteristic, complemented
176#99—34no—
177#99—62no—
178C23×C3—22no—
179C23×C3—22no—
180C23×C3—22no—
181C23×C3—22no—
182C23×C3—21no—
183C23×C3—22no—
184C23×C3—22no—
185C23×C3—42no—
186C23×C3—42no—
187C23×C3—44no—
188C23×C3—44no—
189C23×C3—48no—
190C23×C3#21712yes—
191C23×C3#21711yescharacteristic
192C23×C3C3×C22⋊C411yescharacteristic
193C23×C3C3×C22⋊C412yes—
194C23×C3C2×#6712yes—
195C23×C3C2×C3×D412yes—
196C3×Q8—42no—
197C3×Q8—42no—
198C3×Q8—44no—
199C3×Q8—44no—
200C3×Q8—42no—
201C3×Q8—42no—
202C3×D4—41no—
203C3×D4—42no—
204C3×D4—41no—
205C3×D4—42no—
206C3×D4—41no—
207C3×D4—41no—
208C3×D4—42no—
209C3×D4—44no—
210C3×D4—42no—
211C2×C3×C4—22no—
212C2×C3×C4—22no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—24no—
218C2×C3×C4—24no—
219C2×C3×C4—22no—
220C2×C3×C4—22no—
221C2×C3×C4—22no—
222C2×C3×C4—22no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—44no—
226C2×C3×C4—42no—
227C2×C3×C4—42no—
228C2×C3×C4—42no—
229C2×C3×C4—42no—
230C2×C3×C4—41no—
231C2×C3×C4—41no—
232C2×C3×C4—41no—
233C2×C3×C4—41no—
234C2×C3×C4—124no—
235C2×C3×C4—244no—
236C2×C3×C4#21711yescharacteristic
237C2×C3×C4C3×C22⋊C411yescharacteristic
238C2×C3×C4C22×Dic311yescharacteristic
239C2×C3×C4C22×C3×C411yescharacteristic
240C2×Dic3—44no—
241C2×Dic3—84no—
242C2×C32—21no—
243C2×C32—21no—
244C2×C32—42no—
245C2×C32—42no—
246C2×C32#35412yescomplemented
247C2×C32C2×#9911yescharacteristic
248C24C3×#6712yes—
249C2×Q8—21no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8C2×C3×Dic312yescomplemented
253C2×D4—41no—
254C2×D4—41no—
255C2×D4C2×C3×Dic311yescharacteristic
256C2×D4C3×#6712yes—
257C2×D4C22×C3×D311yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—122no—
261C22×C4C2×C3×Dic311yescharacteristic
262C22⋊C4—24no—
263C22⋊C4—24no—
264C22⋊C4—64no—
265C22⋊C4—122no—
266C42—21no—
267C42C2×C3×Dic312yescomplemented
268C22×C3—24no—
269C22×C3—22no—
270C22×C3—22no—
271C22×C3—22no—
272C22×C3—22no—
273C22×C3—22no—
274C22×C3—22no—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3—21no—
278C22×C3—42no—
279C22×C3—42no—
280C22×C3—42no—
281C22×C3—42no—
282C22×C3—42no—
283C22×C3—42no—
284C22×C3—44no—
285C22×C3—44no—
286C22×C3—44no—
287C22×C3—44no—
288C22×C3—84no—
289C22×C3—82no—
290C22×C3—82no—
291C22×C3—84no—
292C22×C3#83411yescharacteristic
293C22×C3#83411yescharacteristic
294C22×C3C3×#9911yescharacteristic
295C22×C3C3×#9911yescharacteristic
296C22×C3C2×#21711yescharacteristic
297C22×C3C2×C3×C22⋊C411yescharacteristic
298C3×C4—22no—
299C3×C4—22no—
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—44no—
305C3×C4—44no—
306C3×C4—42no—
307C3×C4—42no—
308C3×C4—42no—
309C3×C4—42no—
310C3×C4—244no—
311Dic3—84no—
312C32C2×#35411yescharacteristic, complemented, Sylow
313C23—22no—
314C23—22no—
315C23—44no—
316C23C3×#21711yescharacteristic
317C23C3×#21712yes—
318C23C2×C3×#6712yes—
319Q8—42no—
320Q8—42no—
321D4—41no—
322D4—42no—
323D4—41no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—124no—
332C2×C4—244no—
333C2×C4C3×#21711yescharacteristic
334C2×C4C22×C3×Dic311yescharacteristic
335C2×C3—22no—
336C2×C3—22no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—21no—
342C2×C3—22no—
343C2×C3—42no—
344C2×C3—42no—
345C2×C3—42no—
346C2×C3—42no—
347C2×C3—82no—
348C2×C3—82no—
349C2×C3#454112yesdirect product factor
350C2×C3C3×#35412yescomplemented
351C2×C3C2×#83411yescharacteristic
352C2×C3C2×C3×#9911yescharacteristic
353C22—22no—
354C22—22no—
355C22—22no—
356C22—42no—
357C22—42no—
358C22—44no—
359C22—82no—
360C22C3×#83411yescharacteristic
361C22C3×#83411yescharacteristic
362C22C2×C3×#21711yescharacteristic
363C4—21no—
364C4—21no—
365C4—42no—
366C4—42no—
367C4—244no—
368C3—21no—
369C3C2×#454111yescharacteristic, direct product factor
370C3C2×C3×#35411yescharacteristic, complemented
371C2—21no—
372C2—21no—
373C2—42no—
374C2—42no—
375C2C3×#454112yesdirect product factor
376C2C2×C3×#83411yescharacteristic
subgroupG/H
centerC22×C3#834
commutatorC2×C3×C4C22×C3×C4
FrattiniC2×D4C22×C3×D3
FittingC2×C32×#124C2
socleC22×C32#99
prime radicalC22×C32×D4C22
cosocleC2×C3×D4C23×C3
hypercenterC2×C3×#124D3
hypocenterC3C2×C3×#354
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C22×C3×D4 ◁ C2×C3×#124

Complements

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

NH ≅ G/Ntype
3. C3×#4541C2direct (N × H)
5. C2×#4541C3direct (N × H)
6. C22×C32×Q8C4semidirect
9. C32×#124C4semidirect
12. C2×C32×C42C4semidirect
22. #4541C2×C3direct (N × H)
27. C2×C32×Q8C2×C4semidirect
40. C32×C42C2×C4semidirect
45. C22×C3×Q8Dic3semidirect
46. C22×C3×Q8C3×C4semidirect
55. C3×#124Dic3semidirect
56. C3×#124C3×C4semidirect
64. C2×C3×C42Dic3semidirect
65. C2×C3×C42C3×C4semidirect
109. C2×C3×Q8C2×Dic3semidirect
110. C2×C3×Q8C2×C3×C4semidirect
149. C3×C42C2×Dic3semidirect
150. C3×C42C2×C3×C4semidirect
168. C22×Q8C3×Dic3semidirect
171. #124C3×Dic3semidirect
175. C2×C42C3×Dic3semidirect
246. C2×C32#354semidirect
252. C2×Q8C2×C3×Dic3semidirect
267. C42C2×C3×Dic3semidirect
312. C32C2×#354semidirect
349. C2×C3#4541direct (N × H)
350. C2×C3C3×#354semidirect
369. C3C2×#4541direct (N × H)
370. C3C2×C3×#354semidirect
375. C2C3×#4541direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1242
C2×C3×#8342
C3×#45412
C2×C3×#3543
C2×#45413