Finite Group Databasebeta

← C3×Dic3×#120 #11801982

Subgroups — C3×Dic3×#120 #11801982

Order 1152.

2779 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C3×Dic3C211yesmaximal, characteristic, complemented
2C2×C32×#120C211yesmaximal, characteristic
3C2×C3×D4×Dic3C213yesmaximal, complemented
4C3×#5247C211yesmaximal, characteristic, complemented
5C3×#5220C213yesmaximal, complemented
6C3×#4950C213yesmaximal, complemented
7C3×Dic3×C22⋊C4C213yesmaximal, complemented
8C3×C4×#120—31nomaximal
9Dic3×#120C311yesmaximal, characteristic, direct product factor
10C25×C32C2211yescharacteristic
11C22×C32×D4C2213yes—
12C23×C3×Dic3—212no—
13C23×C3×Dic3C2213yes—
14C23×C3×Dic3C2213yes—
15C23×C3×Dic3C2211yescharacteristic, complemented
16C32×#120C418yescomplemented
17C2×C32×C22⋊C4C2213yes—
18C2×C3×#217C2213yes—
19C2×C3×#217C2213yes—
20C2×C3×#217C2213yescomplemented
21C3×D4×Dic3—212no—
22C2×C3×C4⋊Dic3C2213yescomplemented
23C2×C3×C4×Dic3C2213yescomplemented
24C3×C3⋊#95C2216yescomplemented
25C24×C3×C4—31no—
26C24×Dic3C2×C311yescharacteristic, complemented
27C2×C3×#120—21no—
28C2×C3×#120D311yescharacteristic
29C2×C3×#120C2×C311yescharacteristic
30C2×C3×C4×D4—33no—
31C2×D4×Dic3C2×C313yescomplemented
32C3×#386—33no—
33C3×#385—33no—
34C3×#379—31no—
35C3×C4×C22⋊C4—33no—
36#5247C2×C311yescharacteristic, complemented
37#5220C2×C313yescomplemented
38#4950C2×C313yescomplemented
39Dic3×C22⋊C4C2×C313yescomplemented
40C24×C32—26no—
41C24×C32—26no—
42C24×C32C2×C414yescomplemented
43C24×C32C2311yescharacteristic
44C24×C32C2313yes—
45C2×C32×D4—26no—
46C2×C32×D4—26no—
47C2×C32×D4C2×C4112yescomplemented
48C22×C32×C4C2313yes—
49C22×C3×Dic3—232no—
50C22×C3×Dic3—26no—
51C22×C3×Dic3—212no—
52C22×C3×Dic3—212no—
53C22×C3×Dic3—26no—
54C22×C3×Dic3D4112yescomplemented
55C22×C3×Dic3C2313yes—
56C22×C3×Dic3C2311yescharacteristic
57C22×C3×Dic3C2313yes—
58C22×C3×Dic3C2311yescharacteristic
59C32×C22⋊C4C2×C4112yescomplemented
60C3×#217—26no—
61C3×#217—26no—
62C3×#217—26no—
63C3×C4⋊Dic3—26no—
64C3×C4×Dic3—26no—
65C4×#120—31noSylow
66C25×C3—21no—
67C25×C3C2×D311yescharacteristic
68C25×C3C22×C311yescharacteristic
69C22×C3×D4—23no—
70C22×C3×D4C2×D313yes—
71C22×C3×D4C22×C313yes—
72C23×C3×C4—33no—
73C23×C3×C4—33no—
74C23×C3×C4—31no—
75C23×C3×C4—612no—
76C23×Dic3—212no—
77C23×Dic3C22×C313yes—
78C23×Dic3C22×C313yes—
79C23×Dic3C22×C311yescharacteristic, complemented
80C3×#120—28no—
81C3×#120Dic318yesdirect product factor
82C3×#120C3×C418yescomplemented
83C3×C4×D4—612no—
84C2×C3×C4⋊C4—33no—
85C2×C3×C22⋊C4—23no—
86C2×C3×C22⋊C4—33no—
87C2×C3×C22⋊C4—33no—
88C2×C3×C22⋊C4—33no—
89C2×C3×C22⋊C4C2×D313yes—
90C2×C3×C22⋊C4C22×C313yes—
91C2×C3×C42—33no—
92C2×#217C22×C313yes—
93C2×#217C22×C313yes—
94C2×#217C22×C313yescomplemented
95D4×Dic3—212no—
96C2×C4⋊Dic3C22×C313yescomplemented
97C2×C4×Dic3C22×C313yescomplemented
98C3×#95—36no—
99C3⋊#95C22×C316yescomplemented
100C23×C32—224no—
101C23×C32—28no—
102C23×C32—224no—
103C23×C32—26no—
104C23×C32—26no—
105C23×C32—23no—
106C23×C32—23no—
107C23×C32C22×C416yes—
108C23×C32C22×C412yescomplemented
109C23×C32C2×D416yes—
110C23×C32#4116yes—
111C23×C32C2411yescharacteristic
112C32×D4—224no—
113C2×C32×C4—23no—
114C2×C32×C4—23no—
115C2×C32×C4C22×C416yescomplemented
116C2×C3×Dic3—224no—
117C2×C3×Dic3—26no—
118C2×C3×Dic3—224no—
119C2×C3×Dic3—23no—
120C2×C3×Dic3—23no—
121C2×C3×Dic3—26no—
122C2×C3×Dic3—44no—
123C2×C3×Dic3C2×D416yes—
124C2×C3×Dic3C2×D416yes—
125C24×C4—31no—
126C2×#120C3×D311yescharacteristic
127C2×C4×D4—33no—
128#386—33no—
129#385—33no—
130#379—31no—
131C4×C22⋊C4—33no—
132C24×C3—26no—
133C24×C3—26no—
134C24×C3—26no—
135C24×C3—26no—
136C24×C3—24no—
137C24×C3—23no—
138C24×C3—21no—
139C24×C3—46no—
140C24×C3—46no—
141C24×C3C2×Dic314yescomplemented
142C24×C3C2×C3×C414yescomplemented
143C24×C3C22×D311yescharacteristic
144C24×C3C22×D313yes—
145C24×C3C23×C311yescharacteristic
146C24×C3C23×C313yes—
147C2×C3×D4—26no—
148C2×C3×D4—26no—
149C2×C3×D4—26no—
150C2×C3×D4—26no—
151C2×C3×D4—212no—
152C2×C3×D4—46no—
153C2×C3×D4—46no—
154C2×C3×D4C2×Dic3112yescomplemented
155C2×C3×D4C2×C3×C4112yescomplemented
156C22×C3×C4—23no—
157C22×C3×C4—31no—
158C22×C3×C4—312no—
159C22×C3×C4—33no—
160C22×C3×C4—33no—
161C22×C3×C4—31no—
162C22×C3×C4—612no—
163C22×C3×C4—612no—
164C22×C3×C4—66no—
165C22×C3×C4—632no—
166C22×C3×C4—66no—
167C22×C3×C4C22×D313yes—
168C22×C3×C4C23×C313yes—
169C22×Dic3—232no—
170C22×Dic3—26no—
171C22×Dic3—212no—
172C22×Dic3—212no—
173C22×Dic3—26no—
174C22×Dic3C3×D4112yescomplemented
175C22×Dic3C23×C313yes—
176C22×Dic3C23×C311yescharacteristic
177C22×Dic3C23×C313yes—
178C22×Dic3C23×C311yescharacteristic
179C3×C4⋊C4—66no—
180C3×C22⋊C4—212no—
181C3×C22⋊C4—66no—
182C3×C22⋊C4—66no—
183C3×C22⋊C4—66no—
184C3×C22⋊C4C2×Dic3112yescomplemented
185C3×C22⋊C4C2×C3×C4112yescomplemented
186C3×C42—66no—
187#217—26no—
188#217—26no—
189#217—26no—
190C4⋊Dic3—26no—
191C4×Dic3—26no—
192C22×C32—232no—
193C22×C32—212no—
194C22×C32—26no—
195C22×C32—26no—
196C22×C32—212no—
197C22×C32—26no—
198C22×C32—41no—
199C22×C32—43no—
200C22×C32C4×D4112yescomplemented
201C22×C32C23×C411yescharacteristic
202C22×C32C22×D413yes—
203C22×C32C2×#4113yes—
204C32×C4—26no—
205C3×Dic3—26no—
206C3×Dic3—41no—
207C3×Dic3—43no—
208C3×Dic3#12014yesdirect product factor
209C25C2×C3×D311yescharacteristic
210C22×D4C2×C3×D313yes—
211C23×C4—33no—
212C23×C4—31no—
213C23×C4—33no—
214C23×C4—612no—
215#120C3×Dic318yesdirect product factor
216C4×D4—612no—
217C2×C4⋊C4—33no—
218C2×C22⋊C4—33no—
219C2×C22⋊C4—33no—
220C2×C22⋊C4—33no—
221C2×C22⋊C4C2×C3×D313yes—
222C2×C42—33no—
223#95—36no—
224C23×C3—28no—
225C23×C3—28no—
226C23×C3—224no—
227C23×C3—224no—
228C23×C3—224no—
229C23×C3—224no—
230C23×C3—26no—
231C23×C3—26no—
232C23×C3—26no—
233C23×C3—26no—
234C23×C3—23no—
235C23×C3—23no—
236C23×C3—23no—
237C23×C3—23no—
238C23×C3—21no—
239C23×C3—26no—
240C23×C3—26no—
241C23×C3—26no—
242C23×C3—22no—
243C23×C3—424no—
244C23×C3—46no—
245C23×C3—46no—
246C23×C3—43no—
247C23×C3—43no—
248C23×C3—48no—
249C23×C3—424no—
250C23×C3D3×D416yes—
251C23×C3#23716yes—
252C23×C3C22×Dic316yes—
253C23×C3C22×Dic312yescomplemented
254C23×C3C22×C3×C416yes—
255C23×C3C22×C3×C412yescomplemented
256C23×C3C2×C3×D416yes—
257C23×C3C3×#4116yes—
258C23×C3C23×D311yescharacteristic
259C23×C3C24×C311yescharacteristic
260C3×D4—224no—
261C3×D4—224no—
262C3×D4—424no—
263C2×C3×C4—23no—
264C2×C3×C4—23no—
265C2×C3×C4—23no—
266C2×C3×C4—23no—
267C2×C3×C4—26no—
268C2×C3×C4—36no—
269C2×C3×C4—36no—
270C2×C3×C4—43no—
271C2×C3×C4—43no—
272C2×C3×C4—624no—
273C2×C3×C4—624no—
274C2×C3×C4—66no—
275C2×C3×C4—63no—
276C2×C3×C4—63no—
277C2×C3×C4—66no—
278C2×C3×C4—124no—
279C2×C3×C4C22×Dic316yescomplemented
280C2×C3×C4C22×C3×C416yescomplemented
281C2×Dic3—224no—
282C2×Dic3—26no—
283C2×Dic3—224no—
284C2×Dic3—23no—
285C2×Dic3—23no—
286C2×Dic3—26no—
287C2×Dic3—44no—
288C2×Dic3C2×C3×D416yes—
289C2×Dic3C2×C3×D416yes—
290C2×C32—212no—
291C2×C32—42no—
292C2×C32C2×C4×D413yes—
293C2×C32C2×#12011yescharacteristic
294C2×C32#52513yes—
295C24—26no—
296C24—26no—
297C24C2×C3×Dic314yescomplemented
298C24C22×C3×D311yescharacteristic
299C24C22×C3×D313yes—
300C2×D4—26no—
301C2×D4—26no—
302C2×D4C2×C3×Dic3112yescomplemented
303C22×C4—31no—
304C22×C4—33no—
305C22×C4—312no—
306C22×C4—33no—
307C22×C4—31no—
308C22×C4—612no—
309C22×C4—612no—
310C22×C4—66no—
311C22×C4—632no—
312C22×C4—66no—
313C22×C4C22×C3×D313yes—
314C4⋊C4—66no—
315C22⋊C4—66no—
316C22⋊C4—66no—
317C22⋊C4—66no—
318C22⋊C4C2×C3×Dic3112yescomplemented
319C42—66no—
320C22×C3—232no—
321C22×C3—232no—
322C22×C3—212no—
323C22×C3—26no—
324C22×C3—212no—
325C22×C3—26no—
326C22×C3—212no—
327C22×C3—26no—
328C22×C3—26no—
329C22×C3—212no—
330C22×C3—26no—
331C22×C3—26no—
332C22×C3—212no—
333C22×C3—23no—
334C22×C3—23no—
335C22×C3—21no—
336C22×C3—412no—
337C22×C3—46no—
338C22×C3—412no—
339C22×C3—46no—
340C22×C3—46no—
341C22×C3—432no—
342C22×C3—43no—
343C22×C3—41no—
344C22×C3—41no—
345C22×C3—43no—
346C22×C3—83no—
347C22×C3—81no—
348C22×C3D4×Dic3112yescomplemented
349C22×C3C3×C4×D4112yescomplemented
350C22×C3C2×D3×D413yes—
351C22×C3C2×#23713yes—
352C22×C3C23×Dic311yescharacteristic
353C22×C3C23×C3×C411yescharacteristic
354C22×C3C22×C3×D413yes—
355C22×C3C2×C3×#4113yes—
356C3×C4—26no—
357C3×C4—26no—
358C3×C4—34no—
359C3×C4—46no—
360C3×C4—66no—
361C3×C4—123no—
362C3×C4—121no—
363Dic3—26no—
364Dic3—41no—
365Dic3—43no—
366Dic3C3×#12014yesdirect product factor
367C32C4×#12011yescharacteristic, complemented, Sylow
368C23—28no—
369C23—224no—
370C23—224no—
371C23—26no—
372C23—26no—
373C23—23no—
374C23—23no—
375C23C3×D3×D416yes—
376C23C3×#23716yes—
377C23C22×C3×Dic316yes—
378C23C22×C3×Dic312yescomplemented
379C23C23×C3×D311yescharacteristic
380D4—224no—
381C2×C4—23no—
382C2×C4—23no—
383C2×C4—36no—
384C2×C4—36no—
385C2×C4—624no—
386C2×C4—624no—
387C2×C4—66no—
388C2×C4—63no—
389C2×C4—63no—
390C2×C4—66no—
391C2×C4—124no—
392C2×C4C22×C3×Dic316yescomplemented
393C2×C3—212no—
394C2×C3—212no—
395C2×C3—23no—
396C2×C3—23no—
397C2×C3—21no—
398C2×C3—412no—
399C2×C3—42no—
400C2×C3—42no—
401C2×C3—82no—
402C2×C3#558613yes—
403C2×C3D3×#12011yescharacteristic
404C2×C3C2×D4×Dic313yes—
405C2×C3C2×C3×C4×D413yes—
406C2×C3C2×C3×#12011yescharacteristic
407C2×C3C3×#52513yes—
408C22—232no—
409C22—212no—
410C22—26no—
411C22—212no—
412C22—26no—
413C22—26no—
414C22—43no—
415C22—41no—
416C22C3×D4×Dic3112yescomplemented
417C22C2×C3×D3×D413yes—
418C22C2×C3×#23713yes—
419C22C23×C3×Dic311yescharacteristic
420C4—26no—
421C4—34no—
422C4—66no—
423C4—123no—
424C4—121no—
425C3—21no—
426C3Dic3×#12011yescharacteristic, direct product factor
427C3C3×C4×#12011yescharacteristic, complemented
428C2—212no—
429C2—42no—
430C2C3×#558613yes—
431C2C3×D3×#12011yescharacteristic
432C2C2×C3×D4×Dic313yes—
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
Fitting, prime radicalC2×C32×#120C2
socleC23×C32C24
cosocleC23×C3C24×C3
hypercenterC2×C3×#120D3
hypocenterC3C3×C4×#120
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#120

Complements

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

NH ≅ G/Ntype
1. C24×C3×Dic3C2semidirect
3. C2×C3×D4×Dic3C2semidirect
4. C3×#5247C2semidirect
5. C3×#5220C2semidirect
6. C3×#4950C2semidirect
7. C3×Dic3×C22⋊C4C2semidirect
9. Dic3×#120C3direct (N × H)
15. C23×C3×Dic3C22semidirect
16. C32×#120C4semidirect
20. C2×C3×#217C22semidirect
22. C2×C3×C4⋊Dic3C22semidirect
23. C2×C3×C4×Dic3C22semidirect
24. C3×C3⋊#95C22semidirect
26. C24×Dic3C2×C3semidirect
31. C2×D4×Dic3C2×C3semidirect
36. #5247C2×C3semidirect
37. #5220C2×C3semidirect
38. #4950C2×C3semidirect
39. Dic3×C22⋊C4C2×C3semidirect
42. C24×C32C2×C4semidirect
47. C2×C32×D4C2×C4semidirect
54. C22×C3×Dic3D4semidirect
59. C32×C22⋊C4C2×C4semidirect
79. C23×Dic3C22×C3semidirect
81. C3×#120Dic3direct (N × H)
82. C3×#120C3×C4semidirect
94. C2×#217C22×C3semidirect
96. C2×C4⋊Dic3C22×C3semidirect
97. C2×C4×Dic3C22×C3semidirect
99. C3⋊#95C22×C3semidirect
108. C23×C32C22×C4semidirect
115. C2×C32×C4C22×C4semidirect
141. C24×C3C2×Dic3semidirect
142. C24×C3C2×C3×C4semidirect
154. C2×C3×D4C2×Dic3semidirect
155. C2×C3×D4C2×C3×C4semidirect
174. C22×Dic3C3×D4semidirect
184. C3×C22⋊C4C2×Dic3semidirect
185. C3×C22⋊C4C2×C3×C4semidirect
200. C22×C32C4×D4semidirect
208. C3×Dic3#120direct (N × H)
215. #120C3×Dic3direct (N × H)
253. C23×C3C22×Dic3semidirect
255. C23×C3C22×C3×C4semidirect
279. C2×C3×C4C22×Dic3semidirect
280. C2×C3×C4C22×C3×C4semidirect
297. C24C2×C3×Dic3semidirect
302. C2×D4C2×C3×Dic3semidirect
318. C22⋊C4C2×C3×Dic3semidirect
348. C22×C3D4×Dic3semidirect
349. C22×C3C3×C4×D4semidirect
366. Dic3C3×#120direct (N × H)
367. C32C4×#120semidirect
378. C23C22×C3×Dic3semidirect
392. C2×C4C22×C3×Dic3semidirect
416. C22C3×D4×Dic3semidirect
426. C3Dic3×#120direct (N × H)
427. C3C3×C4×#120semidirect

Maximal subgroups

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

subgroupindex
C24×C3×Dic32
C2×C32×#1202
C2×C3×D4×Dic32
C3×#52472
C3×#52202
C3×#49502
C3×Dic3×C22⋊C42
C3×C4×#1203
Dic3×#1203