Finite Group Databasebeta

← C2×C3×#4862 #11869381

Subgroups — C2×C3×#4862 #11869381

Order 1152.

985 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#897C211yesmaximal, characteristic
2C2×C3×D3×C4⋊C4C211yesmaximal, characteristic
3C2×C32×#106C211yesmaximal, characteristic, complemented
4C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic
5C2×C3×#816C211yesmaximal, characteristic, complemented
6C2×C3×#810C211yesmaximal, characteristic, complemented
7C2×C3×#808C211yesmaximal, characteristic, complemented
8C3×#4862C218yesmaximal, direct product factor
9C2×C3×#483—31nomaximal
10C2×#4862C311yesmaximal, characteristic, direct product factor
11C22×C3×C4×D3—21no—
12C22×C3×C4×D3C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×C3×(C2×D3)⋊C4—21no—
18C2×C3×C4⋊Dic3—21no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×Dic3⋊C4—21no—
21C22×C3×C3⋊C8C2211yescharacteristic
22C3×#897—22no—
23C3×#897C2214yes—
24C3×D3×C4⋊C4—22no—
25C3×D3×C4⋊C4C2214yes—
26C32×#106C2214yescomplemented
27C3×(C2×D3)⋊C8C2214yes—
28C3×#816C2214yescomplemented
29C3×#810C2214yescomplemented
30C3×#808C2214yescomplemented
31C2×C3×C22⋊Q8—31no—
32C22×C3×C4⋊C4—31no—
33C2×#897C2×C311yescharacteristic
34C2×D3×C4⋊C4C2×C311yescharacteristic
35C3×#483—38no—
36C2×C3×#106—21no—
37C2×C3×#106—31no—
38C2×C3×#106D311yescharacteristic, complemented
39C2×C3×#106C2×C311yescharacteristic, complemented
40C2×C3×#103—31no—
41C2×C3×#103—31no—
42C2×C3×C22⋊C8—31no—
43C2×(C2×D3)⋊C8C2×C311yescharacteristic
44C2×#816C2×C311yescharacteristic, complemented
45C2×#810C2×C311yescharacteristic, complemented
46C2×#808C2×C311yescharacteristic, complemented
47#4862C2×C318yesdirect product factor
48C23×C3×D3D411yescharacteristic
49C22×C32×C4—21no—
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
52C22×C3×Dic3—21no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3D411yescharacteristic
55C2×C3×C4×D3—22no—
56C2×C3×C4×D3—22no—
57C2×C3×C4×D3—24no—
58C2×C3×C4×D3—44no—
59C2×C3×C4×D3D412yes—
60C2×C3×C4×D3C2312yes—
61C2×C3×Dic6—22no—
62C2×C3×Dic6—22no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6C2312yes—
65C2×C32×C8—22no—
66C2×C32×C8C2312yes—
67C32×C4⋊C4—21no—
68C32×C4⋊C4—21no—
69C32×C4⋊C4C2312yes—
70C32×C4⋊C4C2312yes—
71C3×(C2×D3)⋊C4—24no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3—24no—
74C3×C4⋊Dic3C2312yes—
75C3×Dic3⋊C4—24no—
76C2×C3×C3⋊C8—22no—
77C2×C3×C3⋊C8C2312yes—
78C2×#483—31noSylow
79C22×C3×Q8—31no—
80C23×C3×C4—31no—
81C23×C3×C4—61no—
82C22×C4×D3—21no—
83C22×C4×D3C22×C311yescharacteristic
84C22×Dic6C22×C311yescharacteristic
85C22×C3×C8—21no—
86C22×C3×C8—31no—
87C22×C3×C8C2×D311yescharacteristic
88C22×C3×C8C22×C311yescharacteristic
89C3×C22⋊Q8—34no—
90C3×C22⋊Q8—62no—
91C2×C3×C4⋊C4—21no—
92C2×C3×C4⋊C4—21no—
93C2×C3×C4⋊C4—31no—
94C2×C3×C4⋊C4—34no—
95C2×C3×C4⋊C4—62no—
96C2×C3×C4⋊C4—61no—
97C2×C3×C4⋊C4—61no—
98C2×C3×C4⋊C4C2×D311yescharacteristic
99C2×C3×C4⋊C4C2×D311yescharacteristic
100C2×C3×C4⋊C4C22×C311yescharacteristic
101C2×C3×C4⋊C4C22×C311yescharacteristic
102C2×C3×C22⋊C4—61no—
103C2×(C2×D3)⋊C4—21no—
104C2×C4⋊Dic3—21no—
105C2×C4⋊Dic3C22×C311yescharacteristic
106C2×Dic3⋊C4—21no—
107C22×C3⋊C8C22×C311yescharacteristic
108#897—22no—
109#897C22×C314yes—
110D3×C4⋊C4—22no—
111D3×C4⋊C4C22×C314yes—
112C3×#106—24no—
113C3×#106—34no—
114C3×#106C2×D314yescomplemented
115C3×#106C22×C314yescomplemented
116C3×#103—34no—
117C3×#103—34no—
118C3×C22⋊C8—34no—
119(C2×D3)⋊C8C22×C314yes—
120#816C22×C314yescomplemented
121#810C22×C314yescomplemented
122#808C22×C314yescomplemented
123C23×C32C2×D411yescharacteristic
124C22×C3×D3—22no—
125C22×C3×D3—22no—
126C22×C3×D3SD1614yes—
127C22×C3×D3C2×D412yes—
128C2×C32×C4—22no—
129C2×C32×C4—22no—
130C2×C32×C4—42no—
131C2×C32×C4—42no—
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4#4112yes—
134C2×C32×C4#4112yes—
135C2×C32×C4C2411yescharacteristic
136C2×C3×Dic3—22no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—42no—
140C2×C3×Dic3—42no—
141C2×C3×Dic3C2×D412yes—
142C3×C4×D3—24no—
143C3×C4×D3—22no—
144C3×C4×D3—22no—
145C3×C4×D3—48no—
146C3×Dic6—22no—
147C3×Dic6—22no—
148C3×Dic6—42no—
149C32×C8—22no—
150C3×C3⋊C8—22no—
151C2×C22⋊Q8—31no—
152C22×C4⋊C4—31no—
153#483—38no—
154C2×#106—31no—
155C2×#106C3×D311yescharacteristic, complemented
156C2×#103—31no—
157C2×#103—31no—
158C2×C22⋊C8—31no—
159C24×C3—31no—
160C23×D3C3×D411yescharacteristic
161C2×C3×Q8—32no—
162C2×C3×Q8—61no—
163C2×C3×Q8—62no—
164C2×C3×Q8—62no—
165C22×C3×C4—21no—
166C22×C3×C4—21no—
167C22×C3×C4—21no—
168C22×C3×C4—21no—
169C22×C3×C4—21no—
170C22×C3×C4—31no—
171C22×C3×C4—32no—
172C22×C3×C4—32no—
173C22×C3×C4—41no—
174C22×C3×C4—41no—
175C22×C3×C4—64no—
176C22×C3×C4—62no—
177C22×C3×C4—62no—
178C22×C3×C4—61no—
179C22×C3×C4—61no—
180C22×C3×C4—124no—
181C22×C3×C4C22×D311yescharacteristic
182C22×C3×C4C23×C311yescharacteristic
183C22×Dic3—21no—
184C22×Dic3—21no—
185C22×Dic3C3×D411yescharacteristic
186C2×C4×D3—22no—
187C2×C4×D3—22no—
188C2×C4×D3—24no—
189C2×C4×D3—44no—
190C2×C4×D3C3×D412yes—
191C2×C4×D3C23×C312yes—
192C2×Dic6—22no—
193C2×Dic6—22no—
194C2×Dic6—21no—
195C2×Dic6C23×C312yes—
196C2×C3×C8—24no—
197C2×C3×C8—22no—
198C2×C3×C8—22no—
199C2×C3×C8—22no—
200C2×C3×C8—32no—
201C2×C3×C8—62no—
202C2×C3×C8C22×D312yes—
203C2×C3×C8C23×C312yes—
204C3×C4⋊C4—21no—
205C3×C4⋊C4—21no—
206C3×C4⋊C4—21no—
207C3×C4⋊C4—21no—
208C3×C4⋊C4—22no—
209C3×C4⋊C4—22no—
210C3×C4⋊C4—32no—
211C3×C4⋊C4—41no—
212C3×C4⋊C4—41no—
213C3×C4⋊C4—64no—
214C3×C4⋊C4—64no—
215C3×C4⋊C4—61no—
216C3×C4⋊C4C22×D312yes—
217C3×C4⋊C4C22×D312yes—
218C3×C4⋊C4C23×C312yes—
219C3×C4⋊C4C23×C312yes—
220C3×C22⋊C4—64no—
221(C2×D3)⋊C4—24no—
222C4⋊Dic3—21no—
223C4⋊Dic3—24no—
224C4⋊Dic3C23×C312yes—
225Dic3⋊C4—24no—
226C2×C3⋊C8—22no—
227C2×C3⋊C8C23×C312yes—
228C22×C32#12312yes—
229C22×C32C2×SD1612yes—
230C22×C32#13712yes—
231C22×C32C22×D411yescharacteristic
232C2×C3×D3—22no—
233C2×C3×D3—22no—
234C2×C3×D3—28no—
235C2×C3×D3C2×SD1614yes—
236C32×C4—42no—
237C32×C4—42no—
238C32×C4#12312yes—
239C32×C4C2×#4111yescharacteristic
240C32×C4C2×#4111yescharacteristic
241C3×Dic3—22no—
242C3×Dic3—42no—
243C3×Dic3—42no—
244C22×Q8—31no—
245C23×C4—31no—
246C23×C4—61no—
247C22×C8—31no—
248C22×C8C2×C3×D311yescharacteristic
249C22⋊Q8—34no—
250C22⋊Q8—62no—
251C2×C4⋊C4—31no—
252C2×C4⋊C4—34no—
253C2×C4⋊C4—62no—
254C2×C4⋊C4—61no—
255C2×C4⋊C4—61no—
256C2×C4⋊C4C2×C3×D311yescharacteristic
257C2×C4⋊C4C2×C3×D311yescharacteristic
258C2×C22⋊C4—61no—
259#106—34no—
260#106C2×C3×D314yescomplemented
261#103—34no—
262#103—34no—
263C22⋊C8—34no—
264C23×C3—21no—
265C23×C3—34no—
266C23×C3—32no—
267C23×C3—62no—
268C23×C3—62no—
269C23×C3D3×D411yescharacteristic
270C23×C3C2×C3×D411yescharacteristic
271C22×D3—22no—
272C22×D3—22no—
273C22×D3C3×SD1614yes—
274C22×D3C2×C3×D412yes—
275C3×Q8—62no—
276C3×Q8—62no—
277C3×Q8—122no—
278C2×C3×C4—22no—
279C2×C3×C4—22no—
280C2×C3×C4—22no—
281C2×C3×C4—22no—
282C2×C3×C4—21no—
283C2×C3×C4—22no—
284C2×C3×C4—21no—
285C2×C3×C4—22no—
286C2×C3×C4—32no—
287C2×C3×C4—42no—
288C2×C3×C4—42no—
289C2×C3×C4—42no—
290C2×C3×C4—42no—
291C2×C3×C4—42no—
292C2×C3×C4—42no—
293C2×C3×C4—62no—
294C2×C3×C4—64no—
295C2×C3×C4—62no—
296C2×C3×C4—62no—
297C2×C3×C4—62no—
298C2×C3×C4—62no—
299C2×C3×C4—82no—
300C2×C3×C4—82no—
301C2×C3×C4—128no—
302C2×C3×C4—122no—
303C2×C3×C4—122no—
304C2×C3×C4#23512yes—
305C2×C3×C4D3×D411yescharacteristic
306C2×C3×C4#23912yes—
307C2×C3×C4C2×C3×D411yescharacteristic
308C2×C3×C4C3×#4112yes—
309C2×C3×C4C3×#4112yes—
310C2×C3×C4C23×D311yescharacteristic
311C2×C3×C4C24×C311yescharacteristic
312C2×Dic3—22no—
313C2×Dic3—22no—
314C2×Dic3—22no—
315C2×Dic3—42no—
316C2×Dic3—42no—
317C2×Dic3C2×C3×D412yes—
318C4×D3—24no—
319C4×D3—22no—
320C4×D3—22no—
321C4×D3—48no—
322Dic6—22no—
323Dic6—22no—
324Dic6—42no—
325C3×C8—24no—
326C3×C8—22no—
327C3×C8—22no—
328C3×C8—62no—
329C3⋊C8—22no—
330C2×C32#48314yescomplemented
331C2×C32C2×#12311yescharacteristic
332C2×C32C22×SD1611yescharacteristic
333C2×C32C2×#13711yescharacteristic
334C3×D3—24no—
335C24—31no—
336C2×Q8—32no—
337C2×Q8—61no—
338C2×Q8—62no—
339C2×Q8—62no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—31no—
343C22×C4—32no—
344C22×C4—32no—
345C22×C4—64no—
346C22×C4—62no—
347C22×C4—62no—
348C22×C4—61no—
349C22×C4—61no—
350C22×C4—124no—
351C22×C4C22×C3×D311yescharacteristic
352C2×C8—22no—
353C2×C8—32no—
354C2×C8—62no—
355C2×C8C22×C3×D312yes—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—32no—
359C4⋊C4—64no—
360C4⋊C4—64no—
361C4⋊C4—61no—
362C4⋊C4C22×C3×D312yes—
363C4⋊C4C22×C3×D312yes—
364C22⋊C4—64no—
365C22×C3—22no—
366C22×C3—22no—
367C22×C3—22no—
368C22×C3—21no—
369C22×C3—34no—
370C22×C3—62no—
371C22×C3—62no—
372C22×C3—68no—
373C22×C3#89412yes—
374C22×C3D3×SD1612yes—
375C22×C3#91512yes—
376C22×C3C3×#12312yes—
377C22×C3C2×C3×SD1612yes—
378C22×C3C3×#13712yes—
379C22×C3C2×D3×D411yescharacteristic
380C22×C3C22×C3×D411yescharacteristic
381C2×D3—22no—
382C2×D3—22no—
383C2×D3—28no—
384C2×D3C2×C3×SD1614yes—
385C3×C4—22no—
386C3×C4—21no—
387C3×C4—21no—
388C3×C4—42no—
389C3×C4—42no—
390C3×C4—42no—
391C3×C4—42no—
392C3×C4—62no—
393C3×C4—82no—
394C3×C4—82no—
395C3×C4—122no—
396C3×C4—122no—
397C3×C4#89412yes—
398C3×C4C3×#12312yes—
399C3×C4C2×#23511yescharacteristic
400C3×C4C2×#23911yescharacteristic
401C3×C4C2×C3×#4111yescharacteristic
402C3×C4C2×C3×#4111yescharacteristic
403Dic3—22no—
404Dic3—42no—
405Dic3—42no—
406C32C2×#48311yescharacteristic, complemented, Sylow
407C23—34no—
408C23—32no—
409C23—62no—
410C23—62no—
411C23C3×D3×D411yescharacteristic
412Q8—62no—
413Q8—62no—
414Q8—122no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—32no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—62no—
421C2×C4—64no—
422C2×C4—62no—
423C2×C4—62no—
424C2×C4—62no—
425C2×C4—62no—
426C2×C4—128no—
427C2×C4—122no—
428C2×C4—122no—
429C2×C4C3×#23512yes—
430C2×C4C3×D3×D411yescharacteristic
431C2×C4C3×#23912yes—
432C2×C4C23×C3×D311yescharacteristic
433C8—22no—
434C8—62no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—24no—
439C2×C3—64no—
440C2×C3#486214yesdirect product factor
441C2×C3C3×#48314yescomplemented
442C2×C3C2×#89411yescharacteristic
443C2×C3C2×D3×SD1611yescharacteristic
444C2×C3C2×#91511yescharacteristic
445C2×C3C2×C3×#12311yescharacteristic
446C2×C3C22×C3×SD1611yescharacteristic
447C2×C3C2×C3×#13711yescharacteristic
448D3—24no—
449C22—34no—
450C22—62no—
451C22—62no—
452C22—68no—
453C22C3×#89412yes—
454C22C3×D3×SD1612yes—
455C22C3×#91512yes—
456C22C2×C3×D3×D411yescharacteristic
457C4—42no—
458C4—42no—
459C4—62no—
460C4—122no—
461C4—122no—
462C4C3×#89412yes—
463C4C2×C3×#23511yescharacteristic
464C4C2×C3×#23911yescharacteristic
465C3—21no—
466C3C2×#486211yescharacteristic, direct product factor
467C3C2×C3×#48311yescharacteristic, complemented
468C2—64no—
469C2C3×#486214yesdirect product factor
470C2C2×C3×#89411yescharacteristic
471C2C2×C3×D3×SD1611yescharacteristic
472C2C2×C3×#91511yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#106C2
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
hypercenterC2×C3×#106D3
hypocenterC3C2×C3×#483
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×#106

Complements

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

NH ≅ G/Ntype
3. C2×C32×#106C2semidirect
5. C2×C3×#816C2semidirect
6. C2×C3×#810C2semidirect
7. C2×C3×#808C2semidirect
8. C3×#4862C2direct (N × H)
10. C2×#4862C3direct (N × H)
26. C32×#106C22semidirect
28. C3×#816C22semidirect
29. C3×#810C22semidirect
30. C3×#808C22semidirect
38. C2×C3×#106D3semidirect
39. C2×C3×#106C2×C3semidirect
44. C2×#816C2×C3semidirect
45. C2×#810C2×C3semidirect
46. C2×#808C2×C3semidirect
47. #4862C2×C3direct (N × H)
114. C3×#106C2×D3semidirect
115. C3×#106C22×C3semidirect
120. #816C22×C3semidirect
121. #810C22×C3semidirect
122. #808C22×C3semidirect
155. C2×#106C3×D3semidirect
260. #106C2×C3×D3semidirect
330. C2×C32#483semidirect
406. C32C2×#483semidirect
440. C2×C3#4862direct (N × H)
441. C2×C3C3×#483semidirect
466. C3C2×#4862direct (N × H)
467. C3C2×C3×#483semidirect
469. C2C3×#4862direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#8972
C2×C3×D3×C4⋊C42
C2×C32×#1062
C2×C3×(C2×D3)⋊C82
C2×C3×#8162
C2×C3×#8102
C2×C3×#8082
C3×#48622
C2×C3×#4833
C2×#48623