Finite Group Databasebeta

← C2×C3×#4760 #11873352

Subgroups — C2×C3×#4760 #11873352

Order 1152.

1157 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#940C211yesmaximal, characteristic
2C2×C3×#888C211yesmaximal, characteristic, complemented
3C2×C32×#102C211yesmaximal, characteristic, complemented
4C2×C3×#832C211yesmaximal, characteristic, complemented
5C2×C3×#821C211yesmaximal, characteristic, complemented
6C2×C3×C8×Dic3C211yesmaximal, characteristic, complemented
7C2×C3×#809C211yesmaximal, characteristic, complemented
8C3×#4760C218yesmaximal, direct product factor
9C2×C3×#486—31nomaximal
10C2×#4760C311yesmaximal, characteristic, direct product factor
11C22×C32×D4C2211yescharacteristic
12C22×C3×#67—21no—
13C22×C3×#67—21no—
14C22×C3×D12C2211yescharacteristic
15C22×C3×Dic6—21no—
16C22×C32×C8C2211yescharacteristic
17C2×C32×C4⋊C4C2211yescharacteristic
18C3×#940—22no—
19C3×#940C2214yes—
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×Dic3⋊C4—21no—
22C2×C3×C4×Dic3C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C3×#888—22no—
25C3×#888C2214yescomplemented
26C32×#102C2214yescomplemented
27C3×#832C2214yescomplemented
28C3×#821C2214yescomplemented
29C3×C8×Dic3C2214yescomplemented
30C3×#809C2214yescomplemented
31C2×C3×C4⋊Q8—31no—
32C2×C3×#127—31no—
33C2×#940C2×C311yescharacteristic
34C2×#888C2×C311yescharacteristic, complemented
35C3×#486—38no—
36C2×C3×#102—21no—
37C2×C3×#102—31no—
38C2×C3×#102—31no—
39C2×C3×#102—31no—
40C2×C3×#102D311yescharacteristic, complemented
41C2×C3×#102C2×C311yescharacteristic, complemented
42C2×C3×C4×C8—31no—
43C2×#832C2×C311yescharacteristic, complemented
44C2×#821C2×C311yescharacteristic, complemented
45C2×C8×Dic3C2×C311yescharacteristic, complemented
46C2×#809C2×C311yescharacteristic, complemented
47#4760C2×C318yesdirect product factor
48C24×C32—21no—
49C23×C3×D3—21no—
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—24no—
58C2×C3×#67—44no—
59C2×C3×#67—44no—
60C22×C3×Dic3—21no—
61C22×C3×Dic3D411yescharacteristic
62C22×C3×Dic3D411yescharacteristic
63C2×C3×D12—22no—
64C2×C3×D12—22no—
65C2×C3×D12—21no—
66C2×C3×D12C2312yes—
67C2×C3×Dic6—24no—
68C2×C3×Dic6—44no—
69C2×C32×C8—22no—
70C2×C32×C8C2312yes—
71C32×C4⋊C4—21no—
72C32×C4⋊C4C2312yes—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3C2312yes—
75C3×Dic3⋊C4—24no—
76C3×C4×Dic3D412yes—
77C3×C4×Dic3C2312yes—
78C2×C3×C3⋊C8—22no—
79C2×C3×C3⋊C8C2312yes—
80C2×#486—31noSylow
81C22×C3×Q8—61no—
82C22×C3×D4—21no—
83C22×C3×D4—31no—
84C22×C3×D4—61no—
85C22×C3×D4—61no—
86C22×C3×D4C2×D311yescharacteristic
87C22×C3×D4C22×C311yescharacteristic
88C22×#67—21no—
89C22×#67—21no—
90C22×D12C22×C311yescharacteristic
91C22×Dic6—21no—
92C22×C3×C8—21no—
93C22×C3×C8—31no—
94C22×C3×C8C2×D311yescharacteristic
95C22×C3×C8C22×C311yescharacteristic
96C3×C4⋊Q8—34no—
97C3×C4⋊Q8—62no—
98C3×#127—34no—
99C3×#127—62no—
100C2×C3×C4⋊C4—21no—
101C2×C3×C4⋊C4—31no—
102C2×C3×C4⋊C4—61no—
103C2×C3×C4⋊C4C2×D311yescharacteristic
104C2×C3×C4⋊C4C22×C311yescharacteristic
105C2×C3×C42—31no—
106#940—22no—
107#940C22×C314yes—
108C2×C4⋊Dic3C22×C311yescharacteristic
109C2×Dic3⋊C4—21no—
110C2×C4×Dic3C22×C311yescharacteristic
111C22×C3⋊C8C22×C311yescharacteristic
112#888—22no—
113#888C22×C314yescomplemented
114C3×#102—24no—
115C3×#102—34no—
116C3×#102—34no—
117C3×#102—34no—
118C3×#102C2×D314yescomplemented
119C3×#102C22×C314yescomplemented
120C3×C4×C8—34no—
121#832C22×C314yescomplemented
122#821C22×C314yescomplemented
123C8×Dic3C22×C314yescomplemented
124#809C22×C314yescomplemented
125C23×C32—22no—
126C23×C32—42no—
127C23×C32—42no—
128C23×C32—42no—
129C23×C32C2×D411yescharacteristic
130C22×C3×D3—22no—
131C22×C3×D3—42no—
132C22×C3×D3—42no—
133C22×C3×D3—42no—
134C32×D4—22no—
135C32×D4—22no—
136C32×D4—42no—
137C2×C32×C4—22no—
138C2×C32×C4—42no—
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4#4112yes—
141C2×C32×C4#4112yes—
142C2×C32×C4C2411yescharacteristic
143C3×#67—48no—
144C3×#67—48no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—42no—
147C2×C3×Dic3D814yes—
148C2×C3×Dic3SD1614yes—
149C2×C3×Dic3C2×D412yes—
150C2×C3×Dic3C2×D412yes—
151C3×D12—22no—
152C3×D12—22no—
153C3×D12—42no—
154C3×Dic6—48no—
155C32×C8—22no—
156C3×C3⋊C8—22no—
157C2×C4⋊Q8—31no—
158C2×#127—31no—
159#486—38no—
160C2×#102—31no—
161C2×#102—31no—
162C2×#102—31no—
163C2×#102C3×D311yescharacteristic, complemented
164C2×C4×C8—31no—
165C24×C3—21no—
166C24×C3—21no—
167C24×C3—41no—
168C24×C3—61no—
169C23×D3—21no—
170C2×C3×Q8—64no—
171C2×C3×Q8—124no—
172C2×C3×D4—24no—
173C2×C3×D4—22no—
174C2×C3×D4—21no—
175C2×C3×D4—22no—
176C2×C3×D4—21no—
177C2×C3×D4—22no—
178C2×C3×D4—22no—
179C2×C3×D4—22no—
180C2×C3×D4—32no—
181C2×C3×D4—41no—
182C2×C3×D4—42no—
183C2×C3×D4—64no—
184C2×C3×D4—64no—
185C2×C3×D4—62no—
186C2×C3×D4—61no—
187C2×C3×D4—62no—
188C2×C3×D4—124no—
189C2×C3×D4—124no—
190C2×C3×D4C22×D312yes—
191C2×C3×D4C23×C312yes—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—31no—
196C22×C3×C4—31no—
197C22×C3×C4—41no—
198C22×C3×C4—61no—
199C22×C3×C4C22×D311yescharacteristic
200C22×C3×C4C23×C311yescharacteristic
201C2×#67—24no—
202C2×#67—24no—
203C2×#67—44no—
204C2×#67—44no—
205C22×Dic3—21no—
206C22×Dic3C3×D411yescharacteristic
207C22×Dic3C3×D411yescharacteristic
208C2×D12—22no—
209C2×D12—22no—
210C2×D12—21no—
211C2×D12C23×C312yes—
212C2×Dic6—24no—
213C2×Dic6—44no—
214C2×C3×C8—22no—
215C2×C3×C8—22no—
216C2×C3×C8—22no—
217C2×C3×C8—32no—
218C2×C3×C8—42no—
219C2×C3×C8—62no—
220C2×C3×C8C22×D312yes—
221C2×C3×C8C23×C312yes—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—22no—
225C3×C4⋊C4—32no—
226C3×C4⋊C4—41no—
227C3×C4⋊C4—64no—
228C3×C4⋊C4—61no—
229C3×C4⋊C4C22×D312yes—
230C3×C4⋊C4C23×C312yes—
231C3×C42—32no—
232C3×C42—32no—
233C4⋊Dic3—21no—
234C4⋊Dic3C23×C312yes—
235Dic3⋊C4—24no—
236C4×Dic3C3×D412yes—
237C4×Dic3C23×C312yes—
238C2×C3⋊C8—22no—
239C2×C3⋊C8C23×C312yes—
240C22×C32—42no—
241C22×C32—42no—
242C22×C32—42no—
243C22×C32—84no—
244C22×C32#12412yes—
245C22×C32C2×D812yes—
246C22×C32C2×SD1612yes—
247C22×C32C22×D411yescharacteristic
248C2×C3×D3—42no—
249C2×C3×D3—42no—
250C2×C3×D3—42no—
251C2×C3×D3—84no—
252C32×C4—42no—
253C32×C4#12412yes—
254C32×C4C2×#4111yescharacteristic
255C32×C4C2×#4111yescharacteristic
256C3×Dic3—42no—
257C3×Dic3C2×D814yes—
258C3×Dic3C2×SD1614yes—
259C22×Q8—61no—
260C22×D4—31no—
261C22×D4—61no—
262C22×D4—61no—
263C22×D4C2×C3×D311yescharacteristic
264C22×C8—31no—
265C22×C8C2×C3×D311yescharacteristic
266C4⋊Q8—34no—
267C4⋊Q8—62no—
268#127—34no—
269#127—62no—
270C2×C4⋊C4—31no—
271C2×C4⋊C4—61no—
272C2×C4⋊C4C2×C3×D311yescharacteristic
273C2×C42—31no—
274#102—34no—
275#102—34no—
276#102—34no—
277#102C2×C3×D314yescomplemented
278C4×C8—34no—
279C23×C3—22no—
280C23×C3—22no—
281C23×C3—21no—
282C23×C3—42no—
283C23×C3—44no—
284C23×C3—42no—
285C23×C3—42no—
286C23×C3—42no—
287C23×C3—42no—
288C23×C3—42no—
289C23×C3—42no—
290C23×C3—62no—
291C23×C3—82no—
292C23×C3—82no—
293C23×C3—122no—
294C23×C3—122no—
295C23×C3—122no—
296C23×C3D3×D411yescharacteristic
297C23×C3C2×C3×D411yescharacteristic
298C22×D3—22no—
299C22×D3—42no—
300C22×D3—42no—
301C22×D3—42no—
302C3×Q8—128no—
303C3×D4—24no—
304C3×D4—22no—
305C3×D4—22no—
306C3×D4—22no—
307C3×D4—22no—
308C3×D4—42no—
309C3×D4—44no—
310C3×D4—42no—
311C3×D4—42no—
312C3×D4—62no—
313C3×D4—62no—
314C3×D4—128no—
315C3×D4—128no—
316C3×D4—122no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—21no—
320C2×C3×C4—22no—
321C2×C3×C4—21no—
322C2×C3×C4—22no—
323C2×C3×C4—34no—
324C2×C3×C4—34no—
325C2×C3×C4—32no—
326C2×C3×C4—32no—
327C2×C3×C4—42no—
328C2×C3×C4—42no—
329C2×C3×C4—42no—
330C2×C3×C4—62no—
331C2×C3×C4—82no—
332C2×C3×C4—122no—
333C2×C3×C4#23512yes—
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4#23712yes—
336C2×C3×C4C2×C3×D411yescharacteristic
337C2×C3×C4C3×#4112yes—
338C2×C3×C4C3×#4112yes—
339C2×C3×C4C23×D311yescharacteristic
340C2×C3×C4C24×C311yescharacteristic
341#67—48no—
342#67—48no—
343C2×Dic3—22no—
344C2×Dic3—42no—
345C2×Dic3C3×D814yes—
346C2×Dic3C3×SD1614yes—
347C2×Dic3C2×C3×D412yes—
348C2×Dic3C2×C3×D412yes—
349D12—22no—
350D12—22no—
351D12—42no—
352Dic6—48no—
353C3×C8—22no—
354C3×C8—22no—
355C3×C8—42no—
356C3×C8—62no—
357C3⋊C8—22no—
358C2×C32—82no—
359C2×C32#48614yescomplemented
360C2×C32C2×#12411yescharacteristic
361C2×C32C22×D811yescharacteristic
362C2×C32C22×SD1611yescharacteristic
363C3×D3—82no—
364C24—21no—
365C24—61no—
366C2×Q8—64no—
367C2×Q8—124no—
368C2×D4—22no—
369C2×D4—21no—
370C2×D4—22no—
371C2×D4—32no—
372C2×D4—64no—
373C2×D4—64no—
374C2×D4—62no—
375C2×D4—61no—
376C2×D4—62no—
377C2×D4—124no—
378C2×D4—124no—
379C2×D4C22×C3×D312yes—
380C22×C4—21no—
381C22×C4—31no—
382C22×C4—31no—
383C22×C4—61no—
384C22×C4C22×C3×D311yescharacteristic
385C2×C8—22no—
386C2×C8—32no—
387C2×C8—62no—
388C2×C8C22×C3×D312yes—
389C4⋊C4—21no—
390C4⋊C4—32no—
391C4⋊C4—64no—
392C4⋊C4—61no—
393C4⋊C4C22×C3×D312yes—
394C42—32no—
395C42—32no—
396C22×C3—22no—
397C22×C3—22no—
398C22×C3—22no—
399C22×C3—21no—
400C22×C3—44no—
401C22×C3—42no—
402C22×C3—42no—
403C22×C3—42no—
404C22×C3—42no—
405C22×C3—42no—
406C22×C3—42no—
407C22×C3—82no—
408C22×C3—82no—
409C22×C3—88no—
410C22×C3—84no—
411C22×C3—84no—
412C22×C3—122no—
413C22×C3—122no—
414C22×C3—122no—
415C22×C3—244no—
416C22×C3#88512yes—
417C22×C3D3×D812yes—
418C22×C3D3×SD1612yes—
419C22×C3C3×#12412yes—
420C22×C3C2×C3×D812yes—
421C22×C3C2×C3×SD1612yes—
422C22×C3C2×D3×D411yescharacteristic
423C22×C3C22×C3×D411yescharacteristic
424C2×D3—42no—
425C2×D3—42no—
426C2×D3—42no—
427C2×D3—84no—
428C3×C4—22no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—34no—
432C3×C4—34no—
433C3×C4—42no—
434C3×C4—42no—
435C3×C4—82no—
436C3×C4—122no—
437C3×C4#88512yes—
438C3×C4C3×#12412yes—
439C3×C4C2×#23511yescharacteristic
440C3×C4C2×#23711yescharacteristic
441C3×C4C2×C3×#4111yescharacteristic
442C3×C4C2×C3×#4111yescharacteristic
443Dic3—42no—
444Dic3C2×C3×D814yes—
445Dic3C2×C3×SD1614yes—
446C32C2×#48611yescharacteristic, complemented, Sylow
447C23—22no—
448C23—42no—
449C23—42no—
450C23—42no—
451C23—62no—
452C23—122no—
453C23—122no—
454C23—122no—
455C23C3×D3×D411yescharacteristic
456Q8—128no—
457D4—22no—
458D4—22no—
459D4—42no—
460D4—62no—
461D4—62no—
462D4—128no—
463D4—128no—
464D4—122no—
465C2×C4—22no—
466C2×C4—34no—
467C2×C4—34no—
468C2×C4—32no—
469C2×C4—32no—
470C2×C4—42no—
471C2×C4—62no—
472C2×C4—122no—
473C2×C4C3×#23512yes—
474C2×C4C3×D3×D411yescharacteristic
475C2×C4C3×#23712yes—
476C2×C4C23×C3×D311yescharacteristic
477C8—22no—
478C8—62no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—24no—
483C2×C3—84no—
484C2×C3—82no—
485C2×C3—82no—
486C2×C3—242no—
487C2×C3#476014yesdirect product factor
488C2×C3C3×#48614yescomplemented
489C2×C3C2×#88511yescharacteristic
490C2×C3C2×D3×D811yescharacteristic
491C2×C3C2×D3×SD1611yescharacteristic
492C2×C3C2×C3×#12411yescharacteristic
493C2×C3C22×C3×D811yescharacteristic
494C2×C3C22×C3×SD1611yescharacteristic
495D3—82no—
496C22—42no—
497C22—42no—
498C22—42no—
499C22—84no—
500C22—122no—
501C22—122no—
502C22—122no—
503C22—244no—
504C22C3×#88512yes—
505C22C3×D3×D812yes—
506C22C3×D3×SD1612yes—
507C22C2×C3×D3×D411yescharacteristic
508C4—34no—
509C4—34no—
510C4—42no—
511C4—122no—
512C4C3×#88512yes—
513C4C2×C3×#23511yescharacteristic
514C4C2×C3×#23711yescharacteristic
515C3—21no—
516C3C2×#476011yescharacteristic, direct product factor
517C3C2×C3×#48611yescharacteristic, complemented
518C2—82no—
519C2—242no—
520C2C3×#476014yesdirect product factor
521C2C2×C3×#88511yescharacteristic
522C2C2×C3×D3×D811yescharacteristic
523C2C2×C3×D3×SD1611yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#102C2
socleC23×C32C2×D4
prime radicalC2×C3×#940C2
hypercenterC2×C3×#102D3
hypocenterC3C2×C3×#486
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×#888C2semidirect
3. C2×C32×#102C2semidirect
4. C2×C3×#832C2semidirect
5. C2×C3×#821C2semidirect
6. C2×C3×C8×Dic3C2semidirect
7. C2×C3×#809C2semidirect
8. C3×#4760C2direct (N × H)
10. C2×#4760C3direct (N × H)
25. C3×#888C22semidirect
26. C32×#102C22semidirect
27. C3×#832C22semidirect
28. C3×#821C22semidirect
29. C3×C8×Dic3C22semidirect
30. C3×#809C22semidirect
34. C2×#888C2×C3semidirect
40. C2×C3×#102D3semidirect
41. C2×C3×#102C2×C3semidirect
43. C2×#832C2×C3semidirect
44. C2×#821C2×C3semidirect
45. C2×C8×Dic3C2×C3semidirect
46. C2×#809C2×C3semidirect
47. #4760C2×C3direct (N × H)
113. #888C22×C3semidirect
118. C3×#102C2×D3semidirect
119. C3×#102C22×C3semidirect
121. #832C22×C3semidirect
122. #821C22×C3semidirect
123. C8×Dic3C22×C3semidirect
124. #809C22×C3semidirect
163. C2×#102C3×D3semidirect
277. #102C2×C3×D3semidirect
359. C2×C32#486semidirect
446. C32C2×#486semidirect
487. C2×C3#4760direct (N × H)
488. C2×C3C3×#486semidirect
516. C3C2×#4760direct (N × H)
517. C3C2×C3×#486semidirect
520. C2C3×#4760direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9402
C2×C3×#8882
C2×C32×#1022
C2×C3×#8322
C2×C3×#8212
C2×C3×C8×Dic32
C2×C3×#8092
C3×#47602
C2×C3×#4863
C2×#47603