Finite Group Databasebeta

← C2×C3×#4844 #11865525

Subgroups — C2×C3×#4844 #11865525

Order 1152.

1197 conjugacy classes of subgroups.

The subgroup lattice has 535 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D24C211yesmaximal, characteristic
2C22×C3×#204C211yesmaximal, characteristic, complemented
3C2×C3×#875C211yesmaximal, characteristic, complemented
4C2×C3×C4×D12C211yesmaximal, characteristic, complemented
5C2×C32×C4⋊C8C211yesmaximal, characteristic, complemented
6C2×C3×#821C211yesmaximal, characteristic, complemented
7C2×C3×#816C211yesmaximal, characteristic, complemented
8C3×#4844C218yesmaximal, direct product factor
9C2×C3×#463—31nomaximal
10C2×#4844C311yesmaximal, characteristic, direct product factor
11C22×C3×D12C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×C4×D3—21no—
14C22×C3×Dic6C2211yescharacteristic
15C22×C32×C8C2211yescharacteristic
16C22×C32×C8C2211yescharacteristic
17C2×C32×C42C2211yescharacteristic
18C2×C3×(C2×D3)⋊C4—21no—
19C2×C3×(C2×D3)⋊C4—21no—
20C2×C3×(C2×D3)⋊C4—21no—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×D24—24no—
23C2×C3×D24C2214yes—
24C2×C3×#204—24no—
25C2×C3×#204C2214yescomplemented
26C3×#875—22no—
27C3×#875C2214yescomplemented
28C3×C4×D12—22no—
29C3×C4×D12C2214yescomplemented
30C32×C4⋊C8C2214yescomplemented
31C3×#821C2214yescomplemented
32C3×#816C2214yescomplemented
33C22×C3×SD16—31no—
34C22×C3×D8—31no—
35C2×C3×#124—31no—
36C2×C3×C4×D4—31no—
37C22×D24C2×C311yescharacteristic
38C22×#204C2×C311yescharacteristic, complemented
39C2×#875C2×C311yescharacteristic, complemented
40C2×C4×D12C2×C311yescharacteristic, complemented
41C3×#463—38no—
42C2×C3×C4⋊C8—21no—
43C2×C3×C4⋊C8D311yescharacteristic, complemented
44C2×C3×C4⋊C8C2×C311yescharacteristic, complemented
45C2×C3×#103—31no—
46C2×C3×#102—31no—
47C2×#821C2×C311yescharacteristic, complemented
48C2×#816C2×C311yescharacteristic, complemented
49#4844C2×C318yesdirect product factor
50C23×C3×D3—21no—
51C23×C3×D3—21no—
52C22×C32×C4D411yescharacteristic
53C22×C32×C4D411yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C22×C3×Dic3—21no—
56C22×C3×Dic3—21no—
57C2×C3×D12—21no—
58C2×C3×D12—22no—
59C2×C3×D12—22no—
60C2×C3×D12—22no—
61C2×C3×D12—21no—
62C2×C3×D12D414yes—
63C2×C3×D12C2312yes—
64C2×C3×D12C2312yes—
65C2×C3×C4×D3—24no—
66C2×C3×C4×D3—44no—
67C2×C3×Dic6—22no—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6C2312yes—
71C2×C32×C8—22no—
72C2×C32×C8—22no—
73C2×C32×C8C2312yes—
74C2×C32×C8C2312yes—
75C32×C42D412yes—
76C32×C42C2312yes—
77C3×(C2×D3)⋊C4—24no—
78C3×(C2×D3)⋊C4—24no—
79C3×(C2×D3)⋊C4—24no—
80C3×C4⋊Dic3—21no—
81C3×C4⋊Dic3C2312yes—
82C3×D24—28no—
83C3×#204—28no—
84C2×#463—31noSylow
85C22×C3×Q8—31no—
86C22×C3×D4—31no—
87C22×C3×D4—31no—
88C23×C3×C4—61no—
89C22×D12C22×C311yescharacteristic
90C22×D12C22×C311yescharacteristic
91C22×C4×D3—21no—
92C22×Dic6C22×C311yescharacteristic
93C2×C3×SD16—34no—
94C2×C3×SD16—64no—
95C2×C3×D8—34no—
96C2×C3×D8—64no—
97C22×C3×C8—21no—
98C22×C3×C8—21no—
99C22×C3×C8C2×D311yescharacteristic
100C22×C3×C8C2×D311yescharacteristic
101C22×C3×C8C22×C311yescharacteristic
102C22×C3×C8C22×C311yescharacteristic
103C3×#124—34no—
104C3×#124—62no—
105C3×C4×D4—34no—
106C3×C4×D4—62no—
107C2×C3×C4⋊C4—31no—
108C2×C3×C22⋊C4—61no—
109C2×C3×C22⋊C4—61no—
110C2×C3×C22⋊C4—61no—
111C2×C3×C42—21no—
112C2×C3×C42C2×D311yescharacteristic
113C2×C3×C42C22×C311yescharacteristic
114C2×(C2×D3)⋊C4—21no—
115C2×(C2×D3)⋊C4—21no—
116C2×(C2×D3)⋊C4—21no—
117C2×C4⋊Dic3C22×C311yescharacteristic
118C2×D24—24no—
119C2×D24C22×C314yes—
120C2×#204—24no—
121C2×#204C22×C314yescomplemented
122#875—22no—
123#875C22×C314yescomplemented
124C4×D12—22no—
125C4×D12C22×C314yescomplemented
126C3×C4⋊C8—24no—
127C3×C4⋊C8C2×D314yescomplemented
128C3×C4⋊C8C22×C314yescomplemented
129C3×#103—34no—
130C3×#102—34no—
131#821C22×C314yescomplemented
132#816C22×C314yescomplemented
133C23×C32C2×D411yescharacteristic
134C22×C3×D3—24no—
135C22×C3×D3—22no—
136C22×C3×D3—22no—
137C22×C3×D3—42no—
138C22×C3×D3—42no—
139C22×C3×D3—42no—
140C22×C3×D3—42no—
141C22×C3×D3—42no—
142C2×C32×C4—22no—
143C2×C32×C4—22no—
144C2×C32×C4C2×D412yes—
145C2×C32×C4C2×D412yes—
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D412yes—
148C2×C32×C4#4112yes—
149C2×C32×C4C2411yescharacteristic
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—42no—
153C2×C3×Dic3—42no—
154C3×D12—24no—
155C3×D12—22no—
156C3×D12—22no—
157C3×D12—22no—
158C3×D12—42no—
159C3×D12C2×D414yes—
160C3×C4×D3—48no—
161C3×Dic6—22no—
162C3×Dic6—22no—
163C3×Dic6—42no—
164C32×C8—22no—
165C32×C8—22no—
166C22×SD16—31no—
167C22×D8—31no—
168C2×#124—31no—
169C2×C4×D4—31no—
170#463—38no—
171C2×C4⋊C8C3×D311yescharacteristic, complemented
172C2×#103—31no—
173C2×#102—31no—
174C24×C3—61no—
175C24×C3—61no—
176C23×D3—21no—
177C23×D3—21no—
178C2×C3×Q8—32no—
179C2×C3×Q8—61no—
180C2×C3×Q8—62no—
181C2×C3×Q8—62no—
182C2×C3×D4—34no—
183C2×C3×D4—32no—
184C2×C3×D4—32no—
185C2×C3×D4—61no—
186C2×C3×D4—61no—
187C2×C3×D4—62no—
188C2×C3×D4—62no—
189C2×C3×D4—62no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—61no—
194C22×C3×C4—61no—
195C22×C3×C4—64no—
196C22×C3×C4—124no—
197C22×C3×C4D1211yescharacteristic
198C22×C3×C4D1211yescharacteristic
199C22×C3×C4C3×D411yescharacteristic
200C22×C3×C4C3×D411yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C23×C311yescharacteristic
203C22×Dic3—21no—
204C22×Dic3—21no—
205C2×D12—21no—
206C2×D12—22no—
207C2×D12—22no—
208C2×D12—22no—
209C2×D12—21no—
210C2×D12C3×D414yes—
211C2×D12C23×C312yes—
212C2×D12C23×C312yes—
213C2×C4×D3—24no—
214C2×C4×D3—44no—
215C2×Dic6—22no—
216C2×Dic6—22no—
217C2×Dic6—21no—
218C2×Dic6C23×C312yes—
219C3×SD16—68no—
220C3×D8—68no—
221C2×C3×C8—22no—
222C2×C3×C8—22no—
223C2×C3×C8—22no—
224C2×C3×C8—22no—
225C2×C3×C8—22no—
226C2×C3×C8—22no—
227C2×C3×C8—42no—
228C2×C3×C8—42no—
229C2×C3×C8C22×D312yes—
230C2×C3×C8C22×D312yes—
231C2×C3×C8C23×C312yes—
232C2×C3×C8C23×C312yes—
233C3×C4⋊C4—32no—
234C3×C4⋊C4—61no—
235C3×C22⋊C4—64no—
236C3×C22⋊C4—64no—
237C3×C22⋊C4—64no—
238C3×C42—22no—
239C3×C42—22no—
240C3×C42D1212yes—
241C3×C42C3×D412yes—
242C3×C42C22×D312yes—
243C3×C42C23×C312yes—
244(C2×D3)⋊C4—24no—
245(C2×D3)⋊C4—24no—
246(C2×D3)⋊C4—24no—
247C4⋊Dic3—21no—
248C4⋊Dic3C23×C312yes—
249D24—28no—
250#204—28no—
251C22×C32#12112yes—
252C22×C32#13512yes—
253C22×C32AGL(1,ℤ/8)12yes—
254C22×C32C22×D411yescharacteristic
255C2×C3×D3—24no—
256C2×C3×D3—42no—
257C2×C3×D3—42no—
258C2×C3×D3—48no—
259C2×C3×D3—42no—
260C2×C3×D3—42no—
261C2×C3×D3—42no—
262C2×C3×D3—84no—
263C32×C4—22no—
264C32×C4—22no—
265C32×C4#12112yes—
266C32×C4C22×D411yescharacteristic
267C32×C4C2×#4111yescharacteristic
268C3×Dic3—42no—
269C3×Dic3—42no—
270C22×Q8—31no—
271C22×D4—31no—
272C22×D4—31no—
273C23×C4—61no—
274C2×SD16—34no—
275C2×SD16—64no—
276C2×D8—34no—
277C2×D8—64no—
278C22×C8C2×C3×D311yescharacteristic
279C22×C8C2×C3×D311yescharacteristic
280#124—34no—
281#124—62no—
282C4×D4—34no—
283C4×D4—62no—
284C2×C4⋊C4—31no—
285C2×C22⋊C4—61no—
286C2×C22⋊C4—61no—
287C2×C22⋊C4—61no—
288C2×C42C2×C3×D311yescharacteristic
289C4⋊C8C2×C3×D314yescomplemented
290#103—34no—
291#102—34no—
292C23×C3—21no—
293C23×C3—64no—
294C23×C3—62no—
295C23×C3—62no—
296C23×C3—122no—
297C23×C3—122no—
298C23×C3—122no—
299C23×C3—122no—
300C23×C3—122no—
301C23×C3C2×D1211yescharacteristic
302C23×C3C2×C3×D411yescharacteristic
303C22×D3—24no—
304C22×D3—22no—
305C22×D3—22no—
306C22×D3—42no—
307C22×D3—42no—
308C22×D3—42no—
309C22×D3—42no—
310C22×D3—42no—
311C3×Q8—62no—
312C3×Q8—62no—
313C3×Q8—122no—
314C3×D4—34no—
315C3×D4—64no—
316C3×D4—62no—
317C3×D4—62no—
318C3×D4—62no—
319C3×D4—122no—
320C2×C3×C4—24no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—21no—
326C2×C3×C4—22no—
327C2×C3×C4—21no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—42no—
332C2×C3×C4—62no—
333C2×C3×C4—62no—
334C2×C3×C4—128no—
335C2×C3×C4—122no—
336C2×C3×C4—122no—
337C2×C3×C4C2×D1212yes—
338C2×C3×C4C2×D1212yes—
339C2×C3×C4C2×D1211yescharacteristic
340C2×C3×C4D3×D412yes—
341C2×C3×C4#23912yes—
342C2×C3×C4C2×C3×D412yes—
343C2×C3×C4C2×C3×D412yes—
344C2×C3×C4C2×C3×D411yescharacteristic
345C2×C3×C4C2×C3×D412yes—
346C2×C3×C4C3×#4112yes—
347C2×C3×C4C23×D311yescharacteristic
348C2×C3×C4C24×C311yescharacteristic
349C2×Dic3—22no—
350C2×Dic3—22no—
351C2×Dic3—42no—
352C2×Dic3—42no—
353D12—24no—
354D12—22no—
355D12—22no—
356D12—22no—
357D12—42no—
358D12C2×C3×D414yes—
359C4×D3—48no—
360Dic6—22no—
361Dic6—22no—
362Dic6—42no—
363C3×C8—22no—
364C3×C8—22no—
365C3×C8—22no—
366C3×C8—22no—
367C3×C8—42no—
368C3×C8—42no—
369C2×C32#46314yescomplemented
370C2×C32C2×#12111yescharacteristic
371C2×C32C2×#13511yescharacteristic
372C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
373C3×D3—44no—
374C3×D3—82no—
375C24—61no—
376C24—61no—
377C2×Q8—32no—
378C2×Q8—61no—
379C2×Q8—62no—
380C2×Q8—62no—
381C2×D4—32no—
382C2×D4—32no—
383C2×D4—34no—
384C2×D4—61no—
385C2×D4—61no—
386C2×D4—62no—
387C2×D4—62no—
388C2×D4—62no—
389C22×C4—61no—
390C22×C4—61no—
391C22×C4—64no—
392C22×C4—124no—
393C22×C4C3×D1211yescharacteristic
394C22×C4C3×D1211yescharacteristic
395C22×C4C22×C3×D311yescharacteristic
396SD16—68no—
397D8—68no—
398C2×C8—22no—
399C2×C8—22no—
400C2×C8C22×C3×D312yes—
401C2×C8C22×C3×D312yes—
402C4⋊C4—32no—
403C4⋊C4—61no—
404C22⋊C4—64no—
405C22⋊C4—64no—
406C22⋊C4—64no—
407C42C3×D1212yes—
408C42C22×C3×D312yes—
409C22×C3—22no—
410C22×C3—22no—
411C22×C3—22no—
412C22×C3—21no—
413C22×C3—64no—
414C22×C3—122no—
415C22×C3—122no—
416C22×C3—128no—
417C22×C3—122no—
418C22×C3—122no—
419C22×C3—122no—
420C22×C3—244no—
421C22×C3#89512yes—
422C22×C3#90412yes—
423C22×C3#90812yes—
424C22×C3C3×#12112yes—
425C22×C3C3×#13512yes—
426C22×C3C3×AGL(1,ℤ/8)12yes—
427C22×C3C22×D1211yescharacteristic
428C22×C3C22×C3×D411yescharacteristic
429C2×D3—24no—
430C2×D3—42no—
431C2×D3—42no—
432C2×D3—48no—
433C2×D3—42no—
434C2×D3—42no—
435C2×D3—42no—
436C2×D3—84no—
437C3×C4—24no—
438C3×C4—22no—
439C3×C4—22no—
440C3×C4—22no—
441C3×C4—22no—
442C3×C4—22no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—42no—
446C3×C4—122no—
447C3×C4—122no—
448C3×C4#89512yes—
449C3×C4C3×#12112yes—
450C3×C4C2×D3×D411yescharacteristic
451C3×C4C2×#23911yescharacteristic
452C3×C4C22×C3×D411yescharacteristic
453C3×C4C2×C3×#4111yescharacteristic
454Dic3—42no—
455Dic3—42no—
456C32C2×#46311yescharacteristic, complemented, Sylow
457C23—64no—
458C23—62no—
459C23—62no—
460C23—122no—
461C23—122no—
462C23—122no—
463C23—122no—
464C23—122no—
465C23C2×C3×D1211yescharacteristic
466Q8—62no—
467Q8—62no—
468Q8—122no—
469D4—34no—
470D4—64no—
471D4—62no—
472D4—62no—
473D4—62no—
474D4—122no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—62no—
478C2×C4—62no—
479C2×C4—128no—
480C2×C4—122no—
481C2×C4—122no—
482C2×C4C2×C3×D1212yes—
483C2×C4C2×C3×D1212yes—
484C2×C4C2×C3×D1211yescharacteristic
485C2×C4C3×D3×D412yes—
486C2×C4C3×#23912yes—
487C2×C4C23×C3×D311yescharacteristic
488C8—22no—
489C8—22no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—24no—
493C2×C3—21no—
494C2×C3—124no—
495C2×C3—242no—
496C2×C3#484414yesdirect product factor
497C2×C3C3×#46314yescomplemented
498C2×C3C2×#89511yescharacteristic
499C2×C3C2×#90411yescharacteristic
500C2×C3C2×#90811yescharacteristic
501C2×C3C2×C3×#12111yescharacteristic
502C2×C3C2×C3×#13511yescharacteristic
503C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
504D3—44no—
505D3—82no—
506C22—64no—
507C22—122no—
508C22—128no—
509C22—122no—
510C22—122no—
511C22—122no—
512C22—122no—
513C22—244no—
514C22C3×#89512yes—
515C22C3×#90412yes—
516C22C3×#90812yes—
517C22C22×C3×D1211yescharacteristic
518C4—22no—
519C4—22no—
520C4—122no—
521C4—122no—
522C4C3×#89512yes—
523C4C2×C3×D3×D411yescharacteristic
524C4C2×C3×#23911yescharacteristic
525C3—21no—
526C3C2×#484411yescharacteristic, direct product factor
527C3C2×C3×#46311yescharacteristic, complemented
528C2—124no—
529C2—242no—
530C2C3×#484414yesdirect product factor
531C2C2×C3×#89511yescharacteristic
532C2C2×C3×#90411yescharacteristic
533C2C2×C3×#90811yescharacteristic
subgroupG/H
centerC23×C3C2×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×C4⋊C8C2
socleC23×C32C2×D4
prime radicalC22×C3×D24C2
hypercenterC2×C3×C4⋊C8D3
hypocenterC3C2×C3×#463
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ C2×C3×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C22×C3×#204C2semidirect
3. C2×C3×#875C2semidirect
4. C2×C3×C4×D12C2semidirect
5. C2×C32×C4⋊C8C2semidirect
6. C2×C3×#821C2semidirect
7. C2×C3×#816C2semidirect
8. C3×#4844C2direct (N × H)
10. C2×#4844C3direct (N × H)
25. C2×C3×#204C22semidirect
27. C3×#875C22semidirect
29. C3×C4×D12C22semidirect
30. C32×C4⋊C8C22semidirect
31. C3×#821C22semidirect
32. C3×#816C22semidirect
38. C22×#204C2×C3semidirect
39. C2×#875C2×C3semidirect
40. C2×C4×D12C2×C3semidirect
43. C2×C3×C4⋊C8D3semidirect
44. C2×C3×C4⋊C8C2×C3semidirect
47. C2×#821C2×C3semidirect
48. C2×#816C2×C3semidirect
49. #4844C2×C3direct (N × H)
121. C2×#204C22×C3semidirect
123. #875C22×C3semidirect
125. C4×D12C22×C3semidirect
127. C3×C4⋊C8C2×D3semidirect
128. C3×C4⋊C8C22×C3semidirect
131. #821C22×C3semidirect
132. #816C22×C3semidirect
171. C2×C4⋊C8C3×D3semidirect
289. C4⋊C8C2×C3×D3semidirect
369. C2×C32#463semidirect
456. C32C2×#463semidirect
496. C2×C3#4844direct (N × H)
497. C2×C3C3×#463semidirect
526. C3C2×#4844direct (N × H)
527. C3C2×C3×#463semidirect
530. C2C3×#4844direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D242
C22×C3×#2042
C2×C3×#8752
C2×C3×C4×D122
C2×C32×C4⋊C82
C2×C3×#8212
C2×C3×#8162
C3×#48442
C2×C3×#4633
C2×#48443