Finite Group Databasebeta

← C2×C3×#4779 #11869420

Subgroups — C2×C3×#4779 #11869420

Order 1152.

1037 conjugacy classes of subgroups.

The subgroup lattice has 509 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#938C211yesmaximal, characteristic
2C2×C3×#892C211yesmaximal, characteristic, complemented
3C2×C32×#102C211yesmaximal, characteristic, complemented
4C2×C3×#832C211yesmaximal, characteristic, complemented
5C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
6C2×C3×#817C211yesmaximal, characteristic, complemented
7C2×C3×#807C211yesmaximal, characteristic, complemented
8C3×#4779C218yesmaximal, direct product factor
9C2×C3×#482—31nomaximal
10C2×#4779C311yesmaximal, characteristic, direct product factor
11C22×C32×D4C2211yescharacteristic
12C22×C3×#67—21no—
13C22×C3×C4×D3C2211yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C3×#217—21no—
17C3×#938—22no—
18C3×#938C2214yes—
19C2×C3×(C2×D3)⋊C4—21no—
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4×Dic3—21no—
23C22×C3×C3⋊C8C2211yescharacteristic
24C3×#892—22no—
25C3×#892C2214yescomplemented
26C32×#102C2214yescomplemented
27C3×#832C2214yescomplemented
28C3×(C2×D3)⋊C8C2214yescomplemented
29C3×#817C2214yescomplemented
30C3×#807C2214yescomplemented
31C2×C3×#121—31no—
32C2×C3×#117—31no—
33C2×#938C2×C311yescharacteristic
34C2×#892C2×C311yescharacteristic, complemented
35C3×#482—38no—
36C2×C3×#107—31no—
37C2×C3×#106—31no—
38C2×C3×#102—21no—
39C2×C3×#102—31no—
40C2×C3×#102D311yescharacteristic, complemented
41C2×C3×#102C2×C311yescharacteristic, complemented
42C2×C3×C22⋊C8—31no—
43C2×#832C2×C311yescharacteristic, complemented
44C2×(C2×D3)⋊C8C2×C311yescharacteristic, complemented
45C2×#817C2×C311yescharacteristic, complemented
46C2×#807C2×C311yescharacteristic, complemented
47#4779C2×C318yesdirect product factor
48C24×C32—21no—
49C23×C3×D3D411yescharacteristic
50C2×C32×D4—21no—
51C2×C32×D4—22no—
52C2×C32×D4—22no—
53C2×C32×D4C2312yes—
54C22×C32×C4—21no—
55C22×C32×C4C2311yescharacteristic
56C2×C3×#67—24no—
57C2×C3×#67—44no—
58C22×C3×Dic3—21no—
59C22×C3×Dic3—21no—
60C22×C3×Dic3D411yescharacteristic
61C2×C3×C4×D3—22no—
62C2×C3×C4×D3—22no—
63C2×C3×C4×D3D412yes—
64C2×C3×C4×D3C2312yes—
65C2×C32×C8—22no—
66C2×C32×C8C2312yes—
67C32×C4⋊C4—21no—
68C32×C4⋊C4C2312yes—
69C3×#217—24no—
70C3×(C2×D3)⋊C4—24no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3C2312yes—
74C3×C4⋊Dic3C2312yes—
75C3×C4×Dic3—24no—
76C2×C3×C3⋊C8—22no—
77C2×C3×C3⋊C8C2312yes—
78C2×#482—31noSylow
79C22×C3×D4—21no—
80C22×C3×D4—61no—
81C22×C3×D4C2×D311yescharacteristic
82C22×C3×D4C22×C311yescharacteristic
83C23×C3×C4—31no—
84C22×#67—21no—
85C22×C4×D3C22×C311yescharacteristic
86C22×C3×C8—21no—
87C22×C3×C8—31no—
88C22×C3×C8C2×D311yescharacteristic
89C22×C3×C8C22×C311yescharacteristic
90C3×#121—34no—
91C3×#121—62no—
92C3×#117—34no—
93C3×#117—62no—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4—31no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C4⋊C4C2×D311yescharacteristic
98C2×C3×C4⋊C4C22×C311yescharacteristic
99C2×C3×C22⋊C4—61no—
100C2×C3×C22⋊C4—61no—
101C2×C3×C42—61no—
102C2×#217—21no—
103#938—22no—
104#938C22×C314yes—
105C2×(C2×D3)⋊C4—21no—
106C2×C4⋊Dic3C22×C311yescharacteristic
107C2×C4⋊Dic3C22×C311yescharacteristic
108C2×C4×Dic3—21no—
109C22×C3⋊C8C22×C311yescharacteristic
110#892—22no—
111#892C22×C314yescomplemented
112C3×#107—34no—
113C3×#106—34no—
114C3×#102—24no—
115C3×#102—34no—
116C3×#102C2×D314yescomplemented
117C3×#102C22×C314yescomplemented
118C3×C22⋊C8—34no—
119#832C22×C314yescomplemented
120(C2×D3)⋊C8C22×C314yescomplemented
121#817C22×C314yescomplemented
122#807C22×C314yescomplemented
123C23×C32—22no—
124C23×C32—42no—
125C23×C32—42no—
126C23×C32—42no—
127C23×C32C2×D411yescharacteristic
128C22×C3×D3—22no—
129C22×C3×D3—22no—
130C22×C3×D3—22no—
131C22×C3×D3C2×D412yes—
132C32×D4—22no—
133C32×D4—22no—
134C32×D4—42no—
135C2×C32×C4—22no—
136C2×C32×C4—42no—
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4#4112yes—
139C2×C32×C4#4112yes—
140C2×C32×C4C2411yescharacteristic
141C3×#67—48no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—42no—
146C2×C3×Dic3—42no—
147C2×C3×Dic3C2×D412yes—
148C3×C4×D3—24no—
149C3×C4×D3—22no—
150C3×C4×D3—22no—
151C32×C8—22no—
152C3×C3⋊C8—22no—
153C2×#121—31no—
154C2×#117—31no—
155#482—38no—
156C2×#107—31no—
157C2×#106—31no—
158C2×#102—31no—
159C2×#102C3×D311yescharacteristic, complemented
160C2×C22⋊C8—31no—
161C24×C3—21no—
162C24×C3—21no—
163C24×C3—31no—
164C24×C3—41no—
165C23×D3C3×D411yescharacteristic
166C2×C3×D4—24no—
167C2×C3×D4—22no—
168C2×C3×D4—21no—
169C2×C3×D4—22no—
170C2×C3×D4—21no—
171C2×C3×D4—22no—
172C2×C3×D4—22no—
173C2×C3×D4—22no—
174C2×C3×D4—41no—
175C2×C3×D4—42no—
176C2×C3×D4—64no—
177C2×C3×D4—124no—
178C2×C3×D4C22×D312yes—
179C2×C3×D4C23×C312yes—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—31no—
184C22×C3×C4—32no—
185C22×C3×C4—32no—
186C22×C3×C4—41no—
187C22×C3×C4—62no—
188C22×C3×C4—62no—
189C22×C3×C4—61no—
190C22×C3×C4—61no—
191C22×C3×C4C22×D311yescharacteristic
192C22×C3×C4C23×C311yescharacteristic
193C2×#67—24no—
194C2×#67—44no—
195C22×Dic3—21no—
196C22×Dic3—21no—
197C22×Dic3C3×D411yescharacteristic
198C2×C4×D3—22no—
199C2×C4×D3—22no—
200C2×C4×D3C3×D412yes—
201C2×C4×D3C23×C312yes—
202C2×C3×C8—22no—
203C2×C3×C8—22no—
204C2×C3×C8—22no—
205C2×C3×C8—32no—
206C2×C3×C8—42no—
207C2×C3×C8—62no—
208C2×C3×C8C22×D312yes—
209C2×C3×C8C23×C312yes—
210C3×C4⋊C4—21no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—22no—
213C3×C4⋊C4—32no—
214C3×C4⋊C4—32no—
215C3×C4⋊C4—41no—
216C3×C4⋊C4—61no—
217C3×C4⋊C4—61no—
218C3×C4⋊C4C22×D312yes—
219C3×C4⋊C4C23×C312yes—
220C3×C22⋊C4—64no—
221C3×C22⋊C4—64no—
222C3×C42—64no—
223#217—24no—
224(C2×D3)⋊C4—24no—
225C4⋊Dic3—21no—
226C4⋊Dic3—21no—
227C4⋊Dic3C23×C312yes—
228C4⋊Dic3C23×C312yes—
229C4×Dic3—24no—
230C2×C3⋊C8—22no—
231C2×C3⋊C8C23×C312yes—
232C22×C32—42no—
233C22×C32—42no—
234C22×C32—42no—
235C22×C32—84no—
236C22×C32#12312yes—
237C22×C32#13512yes—
238C22×C32AGL(1,ℤ/8)12yes—
239C22×C32C22×D411yescharacteristic
240C2×C3×D3—22no—
241C2×C3×D3—22no—
242C2×C3×D3—22no—
243C2×C3×D3—44no—
244C32×C4—42no—
245C32×C4#12312yes—
246C32×C4C2×#4111yescharacteristic
247C32×C4C2×#4111yescharacteristic
248C3×Dic3—22no—
249C3×Dic3—42no—
250C3×Dic3—42no—
251C22×D4—61no—
252C22×D4C2×C3×D311yescharacteristic
253C23×C4—31no—
254C22×C8—31no—
255C22×C8C2×C3×D311yescharacteristic
256#121—34no—
257#121—62no—
258#117—34no—
259#117—62no—
260C2×C4⋊C4—31no—
261C2×C4⋊C4—31no—
262C2×C4⋊C4C2×C3×D311yescharacteristic
263C2×C22⋊C4—61no—
264C2×C22⋊C4—61no—
265C2×C42—61no—
266#107—34no—
267#106—34no—
268#102—34no—
269#102C2×C3×D314yescomplemented
270C22⋊C8—34no—
271C23×C3—22no—
272C23×C3—22no—
273C23×C3—21no—
274C23×C3—32no—
275C23×C3—42no—
276C23×C3—44no—
277C23×C3—42no—
278C23×C3—42no—
279C23×C3—42no—
280C23×C3—42no—
281C23×C3—42no—
282C23×C3—42no—
283C23×C3—62no—
284C23×C3—62no—
285C23×C3—62no—
286C23×C3—82no—
287C23×C3—82no—
288C23×C3D3×D411yescharacteristic
289C23×C3C2×C3×D411yescharacteristic
290C22×D3—22no—
291C22×D3—22no—
292C22×D3—22no—
293C22×D3C2×C3×D412yes—
294C3×D4—24no—
295C3×D4—22no—
296C3×D4—22no—
297C3×D4—22no—
298C3×D4—22no—
299C3×D4—42no—
300C3×D4—44no—
301C3×D4—42no—
302C3×D4—42no—
303C3×D4—128no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—21no—
307C2×C3×C4—22no—
308C2×C3×C4—21no—
309C2×C3×C4—22no—
310C2×C3×C4—32no—
311C2×C3×C4—42no—
312C2×C3×C4—42no—
313C2×C3×C4—42no—
314C2×C3×C4—62no—
315C2×C3×C4—64no—
316C2×C3×C4—62no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4—62no—
320C2×C3×C4—82no—
321C2×C3×C4—122no—
322C2×C3×C4—122no—
323C2×C3×C4#23512yes—
324C2×C3×C4D3×D411yescharacteristic
325C2×C3×C4#23712yes—
326C2×C3×C4C2×C3×D411yescharacteristic
327C2×C3×C4C3×#4112yes—
328C2×C3×C4C3×#4112yes—
329C2×C3×C4C23×D311yescharacteristic
330C2×C3×C4C24×C311yescharacteristic
331#67—48no—
332C2×Dic3—22no—
333C2×Dic3—22no—
334C2×Dic3—22no—
335C2×Dic3—42no—
336C2×Dic3—42no—
337C2×Dic3C2×C3×D412yes—
338C4×D3—24no—
339C4×D3—22no—
340C4×D3—22no—
341C3×C8—22no—
342C3×C8—22no—
343C3×C8—42no—
344C3×C8—62no—
345C3⋊C8—22no—
346C2×C32—82no—
347C2×C32#48214yescomplemented
348C2×C32C2×#12311yescharacteristic
349C2×C32C2×#13511yescharacteristic
350C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
351C3×D3—42no—
352C24—21no—
353C24—31no—
354C2×D4—22no—
355C2×D4—21no—
356C2×D4—22no—
357C2×D4—64no—
358C2×D4—124no—
359C2×D4C22×C3×D312yes—
360C22×C4—21no—
361C22×C4—31no—
362C22×C4—32no—
363C22×C4—32no—
364C22×C4—62no—
365C22×C4—62no—
366C22×C4—61no—
367C22×C4—61no—
368C22×C4C22×C3×D311yescharacteristic
369C2×C8—22no—
370C2×C8—32no—
371C2×C8—62no—
372C2×C8C22×C3×D312yes—
373C4⋊C4—21no—
374C4⋊C4—32no—
375C4⋊C4—32no—
376C4⋊C4—61no—
377C4⋊C4—61no—
378C4⋊C4C22×C3×D312yes—
379C22⋊C4—64no—
380C22⋊C4—64no—
381C42—64no—
382C22×C3—22no—
383C22×C3—22no—
384C22×C3—22no—
385C22×C3—21no—
386C22×C3—44no—
387C22×C3—42no—
388C22×C3—42no—
389C22×C3—42no—
390C22×C3—42no—
391C22×C3—42no—
392C22×C3—42no—
393C22×C3—62no—
394C22×C3—62no—
395C22×C3—62no—
396C22×C3—82no—
397C22×C3—82no—
398C22×C3—88no—
399C22×C3—84no—
400C22×C3—84no—
401C22×C3—124no—
402C22×C3#88312yes—
403C22×C3#91112yes—
404C22×C3#91612yes—
405C22×C3C3×#12312yes—
406C22×C3C3×#13512yes—
407C22×C3C3×AGL(1,ℤ/8)12yes—
408C22×C3C2×D3×D411yescharacteristic
409C22×C3C22×C3×D411yescharacteristic
410C2×D3—22no—
411C2×D3—22no—
412C2×D3—22no—
413C2×D3—44no—
414C3×C4—22no—
415C3×C4—21no—
416C3×C4—21no—
417C3×C4—42no—
418C3×C4—42no—
419C3×C4—62no—
420C3×C4—82no—
421C3×C4—122no—
422C3×C4—122no—
423C3×C4#88312yes—
424C3×C4C3×#12312yes—
425C3×C4C2×#23511yescharacteristic
426C3×C4C2×#23711yescharacteristic
427C3×C4C2×C3×#4111yescharacteristic
428C3×C4C2×C3×#4111yescharacteristic
429Dic3—22no—
430Dic3—42no—
431Dic3—42no—
432C32C2×#48211yescharacteristic, complemented, Sylow
433C23—22no—
434C23—32no—
435C23—42no—
436C23—42no—
437C23—42no—
438C23—62no—
439C23—62no—
440C23—62no—
441C23C3×D3×D411yescharacteristic
442D4—22no—
443D4—22no—
444D4—42no—
445D4—128no—
446C2×C4—22no—
447C2×C4—32no—
448C2×C4—42no—
449C2×C4—62no—
450C2×C4—64no—
451C2×C4—62no—
452C2×C4—62no—
453C2×C4—62no—
454C2×C4—62no—
455C2×C4—122no—
456C2×C4—122no—
457C2×C4C3×#23512yes—
458C2×C4C3×D3×D411yescharacteristic
459C2×C4C3×#23712yes—
460C2×C4C23×C3×D311yescharacteristic
461C8—22no—
462C8—62no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—24no—
467C2×C3—84no—
468C2×C3—82no—
469C2×C3—82no—
470C2×C3—122no—
471C2×C3#477914yesdirect product factor
472C2×C3C3×#48214yescomplemented
473C2×C3C2×#88311yescharacteristic
474C2×C3C2×#91111yescharacteristic
475C2×C3C2×#91611yescharacteristic
476C2×C3C2×C3×#12311yescharacteristic
477C2×C3C2×C3×#13511yescharacteristic
478C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
479D3—42no—
480C22—42no—
481C22—42no—
482C22—42no—
483C22—62no—
484C22—62no—
485C22—62no—
486C22—84no—
487C22—124no—
488C22C3×#88312yes—
489C22C3×#91112yes—
490C22C3×#91612yes—
491C22C2×C3×D3×D411yescharacteristic
492C4—42no—
493C4—62no—
494C4—122no—
495C4—122no—
496C4C3×#88312yes—
497C4C2×C3×#23511yescharacteristic
498C4C2×C3×#23711yescharacteristic
499C3—21no—
500C3C2×#477911yescharacteristic, direct product factor
501C3C2×C3×#48211yescharacteristic, complemented
502C2—82no—
503C2—122no—
504C2C3×#477914yesdirect product factor
505C2C2×C3×#88311yescharacteristic
506C2C2×C3×#91111yescharacteristic
507C2C2×C3×#91611yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#102C2
socleC23×C32C2×D4
prime radicalC2×C3×#938C2
hypercenterC2×C3×#102D3
hypocenterC3C2×C3×#482
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×#102

Complements

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

NH ≅ G/Ntype
2. C2×C3×#892C2semidirect
3. C2×C32×#102C2semidirect
4. C2×C3×#832C2semidirect
5. C2×C3×(C2×D3)⋊C8C2semidirect
6. C2×C3×#817C2semidirect
7. C2×C3×#807C2semidirect
8. C3×#4779C2direct (N × H)
10. C2×#4779C3direct (N × H)
25. C3×#892C22semidirect
26. C32×#102C22semidirect
27. C3×#832C22semidirect
28. C3×(C2×D3)⋊C8C22semidirect
29. C3×#817C22semidirect
30. C3×#807C22semidirect
34. C2×#892C2×C3semidirect
40. C2×C3×#102D3semidirect
41. C2×C3×#102C2×C3semidirect
43. C2×#832C2×C3semidirect
44. C2×(C2×D3)⋊C8C2×C3semidirect
45. C2×#817C2×C3semidirect
46. C2×#807C2×C3semidirect
47. #4779C2×C3direct (N × H)
111. #892C22×C3semidirect
116. C3×#102C2×D3semidirect
117. C3×#102C22×C3semidirect
119. #832C22×C3semidirect
120. (C2×D3)⋊C8C22×C3semidirect
121. #817C22×C3semidirect
122. #807C22×C3semidirect
159. C2×#102C3×D3semidirect
269. #102C2×C3×D3semidirect
347. C2×C32#482semidirect
432. C32C2×#482semidirect
471. C2×C3#4779direct (N × H)
472. C2×C3C3×#482semidirect
500. C3C2×#4779direct (N × H)
501. C3C2×C3×#482semidirect
504. C2C3×#4779direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9382
C2×C3×#8922
C2×C32×#1022
C2×C3×#8322
C2×C3×(C2×D3)⋊C82
C2×C3×#8172
C2×C3×#8072
C3×#47792
C2×C3×#4823
C2×#47793