Finite Group Databasebeta

← C2×C3×#4739 #11863654

Subgroups — C2×C3×#4739 #11863654

Order 1152.

1581 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×Dic6C211yesmaximal, characteristic
2C2×C3×#924C211yesmaximal, characteristic
3C22×C3×Dic12C212yesmaximal, complemented
4C2×C32×C22⋊C8C211yesmaximal, characteristic
5C2×C3×#816C212yesmaximal, complemented
6C3×#4739C218yesmaximal, direct product factor
7C2×C3×#451—31nomaximal
8C2×#4739C311yesmaximal, characteristic, direct product factor
9C23×C32×C4C2211yescharacteristic
10C23×C3×Dic3—21no—
11C22×C3×Dic6—21no—
12C22×C3×Dic6—22no—
13C22×C3×Dic6—28no—
14C22×C3×Dic6C2211yescharacteristic
15C22×C3×Dic6C2214yes—
16C22×C3×Dic6C2212yes—
17C22×C32×C8C2212yes—
18C2×C3×#217—21no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C3×#924—22no—
21C3×#924C2214yes—
22C2×C3×Dic3⋊C4—21no—
23C2×C3×Dic12—28no—
24C2×C3×Dic12C2218yescomplemented
25C32×C22⋊C8C2214yes—
26C3×#816C2218yescomplemented
27C23×C3×Q8—31no—
28C23×Dic6C2×C311yescharacteristic
29C22×C3×Q16—32no—
30C2×C3×C22⋊Q8—31no—
31C2×#924C2×C311yescharacteristic
32C22×Dic12C2×C312yescomplemented
33C3×#451—38no—
34C2×C3×#103—32no—
35C2×C3×C22⋊C8—21no—
36C2×C3×C22⋊C8D311yescharacteristic
37C2×C3×C22⋊C8C2×C311yescharacteristic
38C2×#816C2×C312yescomplemented
39#4739C2×C318yesdirect product factor
40C24×C32D411yescharacteristic
41C22×C32×C4—24no—
42C22×C32×C4D411yescharacteristic
43C22×C32×C4D412yes—
44C22×C32×C4C2312yes—
45C22×C32×C4C2311yescharacteristic
46C22×C3×Dic3—28no—
47C22×C3×Dic3—24no—
48C22×C3×Dic3—22no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3—21no—
51C2×C3×Dic6—28no—
52C2×C3×Dic6—216no—
53C2×C3×Dic6—24no—
54C2×C3×Dic6—22no—
55C2×C3×Dic6—24no—
56C2×C3×Dic6—216no—
57C2×C3×Dic6—24no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6D418yes—
60C2×C3×Dic6C2312yes—
61C2×C3×Dic6C2314yes—
62C2×C32×C8—24no—
63C2×C32×C8C2314yes—
64C3×#217—24no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3C2312yes—
67C3×Dic3⋊C4—24no—
68C3×Dic12—216no—
69C2×#451—31noSylow
70C22×C3×Q8—32no—
71C22×C3×Q8—31no—
72C22×C3×Q8—34no—
73C22×C3×Q8—68no—
74C22×C3×Q8—62no—
75C22×C3×Q8—61no—
76C23×C3×C4—21no—
77C23×C3×C4—61no—
78C23×C3×C4C2×D311yescharacteristic
79C23×C3×C4C22×C311yescharacteristic
80C23×Dic3—21no—
81C22×Dic6—21no—
82C22×Dic6—22no—
83C22×Dic6—28no—
84C22×Dic6C22×C314yes—
85C22×Dic6C22×C311yescharacteristic
86C22×Dic6C22×C312yes—
87C2×C3×Q16—38no—
88C2×C3×Q16—68no—
89C22×C3×C8—22no—
90C22×C3×C8C2×D312yes—
91C22×C3×C8C22×C312yes—
92C3×C22⋊Q8—34no—
93C3×C22⋊Q8—62no—
94C2×C3×C4⋊C4—31no—
95C2×C3×C4⋊C4—61no—
96C2×C3×C22⋊C4—61no—
97C2×#217—21no—
98C2×C4⋊Dic3C22×C311yescharacteristic
99#924—22no—
100#924C22×C314yes—
101C2×Dic3⋊C4—21no—
102C2×Dic12—28no—
103C2×Dic12C22×C318yescomplemented
104C3×#103—38no—
105C3×C22⋊C8—24no—
106C3×C22⋊C8C2×D314yes—
107C3×C22⋊C8C22×C314yes—
108#816C22×C318yescomplemented
109C23×C32—22no—
110C23×C32—22no—
111C23×C32Q1614yescomplemented
112C23×C32C2×D412yes—
113C23×C32C2×D411yescharacteristic
114C2×C32×C4—22no—
115C2×C32×C4—24no—
116C2×C32×C4—24no—
117C2×C32×C4C2×D412yes—
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D414yes—
120C2×C32×C4C2411yescharacteristic
121C2×C3×Dic3—216no—
122C2×C3×Dic3—28no—
123C2×C3×Dic3—24no—
124C2×C3×Dic3—22no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—42no—
127C2×C3×Dic3—42no—
128C3×Dic6—216no—
129C3×Dic6—28no—
130C3×Dic6—24no—
131C3×Dic6—24no—
132C3×Dic6—42no—
133C3×Dic6C2×D418yes—
134C32×C8—24no—
135C23×Q8—31no—
136C22×Q16—32no—
137C2×C22⋊Q8—31no—
138#451—38no—
139C2×#103—32no—
140C2×C22⋊C8C3×D311yescharacteristic
141C24×C3—21no—
142C24×C3D1211yescharacteristic
143C24×C3C3×D411yescharacteristic
144C2×C3×Q8—38no—
145C2×C3×Q8—34no—
146C2×C3×Q8—32no—
147C2×C3×Q8—616no—
148C2×C3×Q8—68no—
149C2×C3×Q8—616no—
150C2×C3×Q8—64no—
151C2×C3×Q8—62no—
152C2×C3×Q8—61no—
153C2×C3×Q8—64no—
154C2×C3×Q8—64no—
155C22×C3×C4—24no—
156C22×C3×C4—24no—
157C22×C3×C4—21no—
158C22×C3×C4—22no—
159C22×C3×C4—21no—
160C22×C3×C4—22no—
161C22×C3×C4—44no—
162C22×C3×C4—68no—
163C22×C3×C4—64no—
164C22×C3×C4—62no—
165C22×C3×C4—61no—
166C22×C3×C4—61no—
167C22×C3×C4D1212yes—
168C22×C3×C4D1211yescharacteristic
169C22×C3×C4C3×D411yescharacteristic
170C22×C3×C4C3×D412yes—
171C22×C3×C4C22×D312yes—
172C22×C3×C4C22×D311yescharacteristic
173C22×C3×C4C23×C312yes—
174C22×C3×C4C23×C311yescharacteristic
175C22×Dic3—28no—
176C22×Dic3—24no—
177C22×Dic3—22no—
178C22×Dic3—21no—
179C22×Dic3—21no—
180C2×Dic6—28no—
181C2×Dic6—216no—
182C2×Dic6—24no—
183C2×Dic6—22no—
184C2×Dic6—24no—
185C2×Dic6—216no—
186C2×Dic6—24no—
187C2×Dic6—21no—
188C2×Dic6C3×D418yes—
189C2×Dic6C23×C312yes—
190C2×Dic6C23×C314yes—
191C3×Q16—616no—
192C2×C3×C8—24no—
193C2×C3×C8—24no—
194C2×C3×C8—24no—
195C2×C3×C8—44no—
196C2×C3×C8C22×D314yes—
197C2×C3×C8C23×C314yes—
198C3×C4⋊C4—32no—
199C3×C4⋊C4—64no—
200C3×C4⋊C4—61no—
201C3×C22⋊C4—64no—
202#217—24no—
203C4⋊Dic3—21no—
204C4⋊Dic3C23×C312yes—
205Dic3⋊C4—24no—
206Dic12—216no—
207C22×C32—22no—
208C22×C32—22no—
209C22×C32—28no—
210C22×C32#12012yes—
211C22×C32C2×Q1612yes—
212C22×C32C2×Q1614yescomplemented
213C22×C32#13712yes—
214C22×C32C22×D411yescharacteristic
215C32×C4—22no—
216C32×C4#12012yes—
217C32×C4C22×D412yes—
218C3×Dic3—28no—
219C3×Dic3—42no—
220C3×Dic3—42no—
221C22×Q8—32no—
222C22×Q8—31no—
223C22×Q8—34no—
224C22×Q8—68no—
225C22×Q8—61no—
226C22×Q8—62no—
227C23×C4—61no—
228C23×C4C2×C3×D311yescharacteristic
229C2×Q16—38no—
230C2×Q16—68no—
231C22×C8C2×C3×D312yes—
232C22⋊Q8—34no—
233C22⋊Q8—62no—
234C2×C4⋊C4—31no—
235C2×C4⋊C4—61no—
236C2×C22⋊C4—61no—
237#103—38no—
238C22⋊C8C2×C3×D314yes—
239C23×C3—22no—
240C23×C3—22no—
241C23×C3—22no—
242C23×C3—22no—
243C23×C3—24no—
244C23×C3—21no—
245C23×C3—22no—
246C23×C3—42no—
247C23×C3—42no—
248C23×C3Dic1214yescomplemented
249C23×C3C3×Q1614yescomplemented
250C23×C3C2×D1212yes—
251C23×C3C2×D1211yescharacteristic
252C23×C3C2×C3×D412yes—
253C23×C3C2×C3×D411yescharacteristic
254C3×Q8—38no—
255C3×Q8—616no—
256C3×Q8—68no—
257C3×Q8—64no—
258C3×Q8—64no—
259C3×Q8—122no—
260C2×C3×C4—22no—
261C2×C3×C4—22no—
262C2×C3×C4—24no—
263C2×C3×C4—24no—
264C2×C3×C4—24no—
265C2×C3×C4—24no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—22no—
269C2×C3×C4—24no—
270C2×C3×C4—44no—
271C2×C3×C4—44no—
272C2×C3×C4—42no—
273C2×C3×C4—616no—
274C2×C3×C4—68no—
275C2×C3×C4—64no—
276C2×C3×C4—62no—
277C2×C3×C4—62no—
278C2×C3×C4—122no—
279C2×C3×C4—122no—
280C2×C3×C4C2×D1212yes—
281C2×C3×C4C2×D1211yescharacteristic
282C2×C3×C4D3×D414yes—
283C2×C3×C4C2×C3×D412yes—
284C2×C3×C4C2×C3×D411yescharacteristic
285C2×C3×C4C2×C3×D414yes—
286C2×C3×C4C23×D311yescharacteristic
287C2×C3×C4C24×C311yescharacteristic
288C2×Dic3—216no—
289C2×Dic3—28no—
290C2×Dic3—24no—
291C2×Dic3—22no—
292C2×Dic3—22no—
293C2×Dic3—42no—
294C2×Dic3—42no—
295Dic6—216no—
296Dic6—28no—
297Dic6—24no—
298Dic6—24no—
299Dic6—42no—
300Dic6C2×C3×D418yes—
301C3×C8—24no—
302C3×C8—24no—
303C3×C8—44no—
304C2×C32—24no—
305C2×C32#45114yescomplemented
306C2×C32C2×#12011yescharacteristic
307C2×C32C22×Q1611yescharacteristic
308C2×C32C2×#13711yescharacteristic
309C24C3×D1211yescharacteristic
310C2×Q8—34no—
311C2×Q8—32no—
312C2×Q8—38no—
313C2×Q8—616no—
314C2×Q8—68no—
315C2×Q8—616no—
316C2×Q8—64no—
317C2×Q8—62no—
318C2×Q8—61no—
319C2×Q8—64no—
320C2×Q8—64no—
321C22×C4—24no—
322C22×C4—68no—
323C22×C4—64no—
324C22×C4—62no—
325C22×C4—61no—
326C22×C4—61no—
327C22×C4C3×D1211yescharacteristic
328C22×C4C3×D1212yes—
329C22×C4C22×C3×D312yes—
330C22×C4C22×C3×D311yescharacteristic
331Q16—616no—
332C2×C8—24no—
333C2×C8C22×C3×D314yes—
334C4⋊C4—32no—
335C4⋊C4—61no—
336C4⋊C4—64no—
337C22⋊C4—64no—
338C22×C3—22no—
339C22×C3—22no—
340C22×C3—22no—
341C22×C3—28no—
342C22×C3—28no—
343C22×C3—22no—
344C22×C3—22no—
345C22×C3—22no—
346C22×C3—24no—
347C22×C3—22no—
348C22×C3—21no—
349C22×C3—42no—
350C22×C3—42no—
351C22×C3—48no—
352C22×C3#88212yes—
353C22×C3C2×Dic1212yes—
354C22×C3C2×Dic1214yescomplemented
355C22×C3#90912yes—
356C22×C3C3×#12012yes—
357C22×C3C2×C3×Q1612yes—
358C22×C3C2×C3×Q1614yescomplemented
359C22×C3C3×#13712yes—
360C22×C3C22×D1211yescharacteristic
361C22×C3C22×C3×D411yescharacteristic
362C3×C4—22no—
363C3×C4—22no—
364C3×C4—22no—
365C3×C4—22no—
366C3×C4—42no—
367C3×C4—68no—
368C3×C4—122no—
369C3×C4—122no—
370C3×C4#88212yes—
371C3×C4C3×#12012yes—
372C3×C4C2×D3×D412yes—
373C3×C4C22×C3×D412yes—
374Dic3—28no—
375Dic3—42no—
376Dic3—42no—
377C32C2×#45111yescharacteristic, complemented, Sylow
378C23—22no—
379C23—22no—
380C23C3×Dic1214yescomplemented
381C23C2×C3×D1212yes—
382C23C2×C3×D1211yescharacteristic
383Q8—38no—
384Q8—616no—
385Q8—68no—
386Q8—64no—
387Q8—64no—
388Q8—122no—
389C2×C4—22no—
390C2×C4—24no—
391C2×C4—24no—
392C2×C4—616no—
393C2×C4—68no—
394C2×C4—64no—
395C2×C4—62no—
396C2×C4—62no—
397C2×C4—122no—
398C2×C4—122no—
399C2×C4C2×C3×D1212yes—
400C2×C4C2×C3×D1211yescharacteristic
401C2×C4C3×D3×D414yes—
402C2×C4C23×C3×D311yescharacteristic
403C8—24no—
404C2×C3—24no—
405C2×C3—24no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—24no—
409C2×C3—21no—
410C2×C3—44no—
411C2×C3#473914yesdirect product factor
412C2×C3C3×#45114yescomplemented
413C2×C3C2×#88211yescharacteristic
414C2×C3C22×Dic1211yescharacteristic
415C2×C3C2×#90911yescharacteristic
416C2×C3C2×C3×#12011yescharacteristic
417C2×C3C22×C3×Q1611yescharacteristic
418C2×C3C2×C3×#13711yescharacteristic
419C22—22no—
420C22—22no—
421C22—28no—
422C22C3×#88212yes—
423C22C2×C3×Dic1212yes—
424C22C2×C3×Dic1214yescomplemented
425C22C3×#90912yes—
426C22C22×C3×D1211yescharacteristic
427C4—22no—
428C4—68no—
429C4—122no—
430C4—122no—
431C4C3×#88212yes—
432C4C2×C3×D3×D412yes—
433C3—21no—
434C3C2×#473911yescharacteristic, direct product factor
435C3C2×C3×#45111yescharacteristic, complemented
436C2—24no—
437C2C3×#473914yesdirect product factor
438C2C2×C3×#88211yescharacteristic
439C2C22×C3×Dic1211yescharacteristic
440C2C2×C3×#90911yescharacteristic
subgroupG/H
centerC23×C3C2×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×C22⋊C8C2
socleC23×C32C2×D4
prime radicalC24×C32D4
hypercenterC2×C3×C22⋊C8D3
hypocenterC3C2×C3×#451
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C23×C3×C4 ◁ C2×C3×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. C22×C3×Dic12C2semidirect
5. C2×C3×#816C2semidirect
6. C3×#4739C2direct (N × H)
8. C2×#4739C3direct (N × H)
24. C2×C3×Dic12C22semidirect
26. C3×#816C22semidirect
32. C22×Dic12C2×C3semidirect
38. C2×#816C2×C3semidirect
39. #4739C2×C3direct (N × H)
103. C2×Dic12C22×C3semidirect
108. #816C22×C3semidirect
111. C23×C32Q16semidirect
212. C22×C32C2×Q16semidirect
248. C23×C3Dic12semidirect
249. C23×C3C3×Q16semidirect
305. C2×C32#451semidirect
354. C22×C3C2×Dic12semidirect
358. C22×C3C2×C3×Q16semidirect
377. C32C2×#451semidirect
380. C23C3×Dic12semidirect
411. C2×C3#4739direct (N × H)
412. C2×C3C3×#451semidirect
424. C22C2×C3×Dic12semidirect
434. C3C2×#4739direct (N × H)
435. C3C2×C3×#451semidirect
437. C2C3×#4739direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×Dic62
C2×C3×#9242
C22×C3×Dic122
C2×C32×C22⋊C82
C2×C3×#8162
C3×#47392
C2×C3×#4513
C2×#47393