Finite Group Databasebeta

← C2×C3×#4808 #11863769

Subgroups — C2×C3×#4808 #11863769

Order 1152.

1601 conjugacy classes of subgroups.

The subgroup lattice has 587 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#239C211yesmaximal, characteristic
2C22×C3×#216C211yesmaximal, characteristic, complemented
3C22×C3×#204C211yesmaximal, characteristic, complemented
4C2×C3×#897C211yesmaximal, characteristic, complemented
5C2×C32×#103C211yesmaximal, characteristic, complemented
6C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
7C2×C3×#809C211yesmaximal, characteristic, complemented
8C3×#4808C218yesmaximal, direct product factor
9C2×C3×#452—31nomaximal
10C2×#4808C311yesmaximal, characteristic, direct product factor
11C22×C32×Q8C2211yescharacteristic
12C2×C3×#239—24no—
13C2×C3×#239—24no—
14C2×C3×#239—22no—
15C2×C3×#239C2214yes—
16C22×C3×D12—21no—
17C22×C3×D12C2211yescharacteristic
18C22×C3×C4×D3—21no—
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C22×C32×C8C2211yescharacteristic
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×C3×#216—24no—
24C2×C3×#216C2214yescomplemented
25C2×C3×(C2×D3)⋊C4—21no—
26C2×C3×C4⋊Dic3—21no—
27C22×C3×C3⋊C8C2211yescharacteristic
28C2×C3×#204—24no—
29C2×C3×#204C2214yescomplemented
30C3×#897—22no—
31C3×#897C2214yescomplemented
32C32×#103C2214yescomplemented
33C3×(C2×D3)⋊C8C2214yescomplemented
34C3×#809C2214yescomplemented
35C22×C3×#41—31no—
36C22×#239C2×C311yescharacteristic
37C22×C3×Q16—31no—
38C22×C3×SD16—31no—
39C2×C3×C22⋊Q8—31no—
40C22×#216C2×C311yescharacteristic, complemented
41C22×#204C2×C311yescharacteristic, complemented
42C2×#897C2×C311yescharacteristic, complemented
43C3×#452—38no—
44C2×C3×#103—21no—
45C2×C3×#103D311yescharacteristic, complemented
46C2×C3×#103C2×C311yescharacteristic, complemented
47C2×C3×#102—31no—
48C2×C3×C22⋊C8—31no—
49C2×(C2×D3)⋊C8C2×C311yescharacteristic, complemented
50C2×#809C2×C311yescharacteristic, complemented
51#4808C2×C318yesdirect product factor
52C23×C3×D3—21no—
53C23×C3×D3D411yescharacteristic
54C2×C32×Q8—22no—
55C2×C32×Q8—21no—
56C2×C32×Q8D414yes—
57C2×C32×Q8C2312yes—
58C22×C32×C4—21no—
59C22×C32×C4—21no—
60C22×C32×C4C2311yescharacteristic
61C22×C3×Dic3—21no—
62C22×C3×Dic3D411yescharacteristic
63C3×#239—216no—
64C3×#239—28no—
65C3×#239—28no—
66C2×C3×D12—28no—
67C2×C3×D12—24no—
68C2×C3×D12—21no—
69C2×C3×D12—22no—
70C2×C3×D12D414yes—
71C2×C3×D12C2312yes—
72C2×C3×C4×D3—28no—
73C2×C3×C4×D3—22no—
74C2×C3×C4×D3—22no—
75C2×C3×C4×D3—24no—
76C2×C3×C4×D3D412yes—
77C2×C3×C4×D3C2312yes—
78C2×C3×Dic6—22no—
79C2×C3×Dic6—22no—
80C2×C3×Dic6—21no—
81C2×C3×Dic6C2312yes—
82C2×C32×C8—22no—
83C2×C32×C8C2312yes—
84C32×C4⋊C4—21no—
85C32×C4⋊C4C2312yes—
86C3×#216—28no—
87C3×(C2×D3)⋊C4—24no—
88C3×C4⋊Dic3—24no—
89C2×C3×C3⋊C8—22no—
90C2×C3×C3⋊C8C2312yes—
91C3×#204—28no—
92C2×#452—31noSylow
93C2×C3×#41—34no—
94C2×C3×#41—62no—
95C2×C3×#41—64no—
96C2×C3×#41—64no—
97C22×C3×Q8—21no—
98C22×C3×Q8—31no—
99C22×C3×Q8C2×D311yescharacteristic
100C22×C3×Q8C22×C311yescharacteristic
101C22×C3×D4—31no—
102C22×C3×D4—61no—
103C23×C3×C4—31no—
104C23×C3×C4—61no—
105C2×#239—24no—
106C2×#239—24no—
107C2×#239—22no—
108C2×#239C22×C314yes—
109C22×D12—21no—
110C22×D12C22×C311yescharacteristic
111C22×C4×D3—21no—
112C22×C4×D3C22×C311yescharacteristic
113C22×Dic6C22×C311yescharacteristic
114C2×C3×Q16—34no—
115C2×C3×Q16—64no—
116C2×C3×SD16—34no—
117C2×C3×SD16—64no—
118C22×C3×C8—21no—
119C22×C3×C8—31no—
120C22×C3×C8C2×D311yescharacteristic
121C22×C3×C8C22×C311yescharacteristic
122C3×C22⋊Q8—34no—
123C3×C22⋊Q8—62no—
124C2×C3×C4⋊C4—21no—
125C2×C3×C4⋊C4—61no—
126C2×C3×C4⋊C4C2×D311yescharacteristic
127C2×C3×C4⋊C4C22×C311yescharacteristic
128C2×C3×C22⋊C4—61no—
129C2×#216—24no—
130C2×#216C22×C314yescomplemented
131C2×(C2×D3)⋊C4—21no—
132C2×C4⋊Dic3—21no—
133C22×C3⋊C8C22×C311yescharacteristic
134C2×#204—24no—
135C2×#204C22×C314yescomplemented
136#897—22no—
137#897C22×C314yescomplemented
138C3×#103—24no—
139C3×#103C2×D314yescomplemented
140C3×#103C22×C314yescomplemented
141C3×#102—34no—
142C3×C22⋊C8—34no—
143(C2×D3)⋊C8C22×C314yescomplemented
144#809C22×C314yescomplemented
145C23×C32C2×D411yescharacteristic
146C22×C3×D3—24no—
147C22×C3×D3—22no—
148C22×C3×D3—22no—
149C22×C3×D3—22no—
150C22×C3×D3—22no—
151C22×C3×D3—42no—
152C22×C3×D3—42no—
153C22×C3×D3C2×D412yes—
154C32×Q8—24no—
155C32×Q8—22no—
156C32×Q8C2×D414yes—
157C2×C32×C4—24no—
158C2×C32×C4—22no—
159C2×C32×C4—22no—
160C2×C32×C4—42no—
161C2×C32×C4C2×D412yes—
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4C2×D412yes—
164C2×C32×C4C2411yescharacteristic
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—42no—
168C2×C3×Dic3C2×D412yes—
169C3×D12—216no—
170C3×D12—24no—
171C3×D12—22no—
172C3×D12C2×D414yes—
173C3×C4×D3—216no—
174C3×C4×D3—24no—
175C3×C4×D3—22no—
176C3×C4×D3—22no—
177C3×Dic6—22no—
178C3×Dic6—22no—
179C3×Dic6—42no—
180C32×C8—22no—
181C3×C3⋊C8—22no—
182C22×#41—31no—
183C22×Q16—31no—
184C22×SD16—31no—
185C2×C22⋊Q8—31no—
186#452—38no—
187C2×#103C3×D311yescharacteristic, complemented
188C2×#102—31no—
189C2×C22⋊C8—31no—
190C24×C3—31no—
191C24×C3—61no—
192C23×D3—21no—
193C23×D3C3×D411yescharacteristic
194C3×#41—68no—
195C3×#41—616no—
196C3×#41—68no—
197C2×C3×Q8—22no—
198C2×C3×Q8—21no—
199C2×C3×Q8—22no—
200C2×C3×Q8—21no—
201C2×C3×Q8—24no—
202C2×C3×Q8—22no—
203C2×C3×Q8—32no—
204C2×C3×Q8—41no—
205C2×C3×Q8—42no—
206C2×C3×Q8—61no—
207C2×C3×Q8—62no—
208C2×C3×Q8—62no—
209C2×C3×Q8D1214yes—
210C2×C3×Q8C3×D414yes—
211C2×C3×Q8C22×D312yes—
212C2×C3×Q8C23×C312yes—
213C2×C3×D4—34no—
214C2×C3×D4—32no—
215C2×C3×D4—64no—
216C2×C3×D4—68no—
217C2×C3×D4—62no—
218C2×C3×D4—61no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—31no—
225C22×C3×C4—32no—
226C22×C3×C4—32no—
227C22×C3×C4—41no—
228C22×C3×C4—41no—
229C22×C3×C4—64no—
230C22×C3×C4—68no—
231C22×C3×C4—62no—
232C22×C3×C4—62no—
233C22×C3×C4—61no—
234C22×C3×C4C22×D311yescharacteristic
235C22×C3×C4C23×C311yescharacteristic
236C22×Dic3—21no—
237C22×Dic3C3×D411yescharacteristic
238#239—216no—
239#239—28no—
240#239—28no—
241C2×D12—28no—
242C2×D12—24no—
243C2×D12—22no—
244C2×D12—21no—
245C2×D12C3×D414yes—
246C2×D12C23×C312yes—
247C2×C4×D3—28no—
248C2×C4×D3—22no—
249C2×C4×D3—22no—
250C2×C4×D3—24no—
251C2×C4×D3C3×D412yes—
252C2×C4×D3C23×C312yes—
253C2×Dic6—22no—
254C2×Dic6—22no—
255C2×Dic6—21no—
256C2×Dic6C23×C312yes—
257C3×Q16—68no—
258C3×SD16—68no—
259C2×C3×C8—22no—
260C2×C3×C8—22no—
261C2×C3×C8—22no—
262C2×C3×C8—32no—
263C2×C3×C8—42no—
264C2×C3×C8—62no—
265C2×C3×C8C22×D312yes—
266C2×C3×C8C23×C312yes—
267C3×C4⋊C4—21no—
268C3×C4⋊C4—21no—
269C3×C4⋊C4—22no—
270C3×C4⋊C4—41no—
271C3×C4⋊C4—64no—
272C3×C4⋊C4C22×D312yes—
273C3×C4⋊C4C23×C312yes—
274C3×C22⋊C4—64no—
275#216—28no—
276(C2×D3)⋊C4—24no—
277C4⋊Dic3—24no—
278C2×C3⋊C8—22no—
279C2×C3⋊C8C23×C312yes—
280#204—28no—
281C22×C32#12012yes—
282C22×C32#13512yes—
283C22×C32#13712yes—
284C22×C32C22×D411yescharacteristic
285C2×C3×D3—22no—
286C2×C3×D3—24no—
287C2×C3×D3—22no—
288C2×C3×D3—22no—
289C2×C3×D3—42no—
290C2×C3×D3—42no—
291C2×C3×D3—44no—
292C2×C3×D3—48no—
293C32×C4—24no—
294C32×C4—42no—
295C32×C4#12012yes—
296C32×C4C22×D411yescharacteristic
297C32×C4C22×D411yescharacteristic
298C3×Dic3—22no—
299C3×Dic3—42no—
300C2×#41—34no—
301C2×#41—62no—
302C2×#41—64no—
303C2×#41—64no—
304C22×Q8—31no—
305C22×Q8C2×C3×D311yescharacteristic
306C22×D4—31no—
307C22×D4—61no—
308C23×C4—31no—
309C23×C4—61no—
310C2×Q16—34no—
311C2×Q16—64no—
312C2×SD16—34no—
313C2×SD16—64no—
314C22×C8—31no—
315C22×C8C2×C3×D311yescharacteristic
316C22⋊Q8—34no—
317C22⋊Q8—62no—
318C2×C4⋊C4—61no—
319C2×C4⋊C4C2×C3×D311yescharacteristic
320C2×C22⋊C4—61no—
321#103C2×C3×D314yescomplemented
322#102—34no—
323C22⋊C8—34no—
324C23×C3—21no—
325C23×C3—32no—
326C23×C3—64no—
327C23×C3—62no—
328C23×C3—62no—
329C23×C3—62no—
330C23×C3—62no—
331C23×C3—122no—
332C23×C3—122no—
333C23×C3D3×D411yescharacteristic
334C23×C3C2×C3×D411yescharacteristic
335C22×D3—22no—
336C22×D3—24no—
337C22×D3—22no—
338C22×D3—22no—
339C22×D3—22no—
340C22×D3—42no—
341C22×D3—42no—
342C22×D3C2×C3×D412yes—
343C3×Q8—24no—
344C3×Q8—24no—
345C3×Q8—22no—
346C3×Q8—22no—
347C3×Q8—24no—
348C3×Q8—44no—
349C3×Q8—42no—
350C3×Q8—62no—
351C3×Q8—62no—
352C3×Q8—122no—
353C3×Q8C2×D1214yes—
354C3×Q8C2×C3×D414yes—
355C3×D4—34no—
356C3×D4—616no—
357C3×D4—64no—
358C3×D4—62no—
359C2×C3×C4—24no—
360C2×C3×C4—24no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—21no—
366C2×C3×C4—22no—
367C2×C3×C4—21no—
368C2×C3×C4—22no—
369C2×C3×C4—32no—
370C2×C3×C4—44no—
371C2×C3×C4—42no—
372C2×C3×C4—42no—
373C2×C3×C4—42no—
374C2×C3×C4—42no—
375C2×C3×C4—616no—
376C2×C3×C4—62no—
377C2×C3×C4—64no—
378C2×C3×C4—62no—
379C2×C3×C4—62no—
380C2×C3×C4—62no—
381C2×C3×C4—82no—
382C2×C3×C4—122no—
383C2×C3×C4C2×D1212yes—
384C2×C3×C4D3×D411yescharacteristic
385C2×C3×C4D3×D412yes—
386C2×C3×C4C2×C3×D412yes—
387C2×C3×C4C2×C3×D411yescharacteristic
388C2×C3×C4C2×C3×D412yes—
389C2×C3×C4C23×D311yescharacteristic
390C2×C3×C4C24×C311yescharacteristic
391C2×Dic3—22no—
392C2×Dic3—22no—
393C2×Dic3—42no—
394C2×Dic3C2×C3×D412yes—
395D12—216no—
396D12—24no—
397D12—22no—
398D12C2×C3×D414yes—
399C4×D3—216no—
400C4×D3—24no—
401C4×D3—22no—
402C4×D3—22no—
403Dic6—22no—
404Dic6—22no—
405Dic6—42no—
406C3×C8—22no—
407C3×C8—22no—
408C3×C8—42no—
409C3×C8—62no—
410C3⋊C8—22no—
411C2×C32#45214yescomplemented
412C2×C32C2×#12011yescharacteristic
413C2×C32C2×#13511yescharacteristic
414C2×C32C2×#13711yescharacteristic
415C3×D3—42no—
416C3×D3—44no—
417C24—31no—
418C24—61no—
419#41—68no—
420#41—616no—
421#41—68no—
422C2×Q8—22no—
423C2×Q8—21no—
424C2×Q8—32no—
425C2×Q8—61no—
426C2×Q8—62no—
427C2×Q8—62no—
428C2×Q8C3×D1214yes—
429C2×Q8C22×C3×D312yes—
430C2×D4—32no—
431C2×D4—34no—
432C2×D4—64no—
433C2×D4—68no—
434C2×D4—62no—
435C2×D4—61no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—31no—
439C22×C4—32no—
440C22×C4—32no—
441C22×C4—64no—
442C22×C4—68no—
443C22×C4—62no—
444C22×C4—62no—
445C22×C4—61no—
446C22×C4C22×C3×D311yescharacteristic
447Q16—68no—
448SD16—68no—
449C2×C8—22no—
450C2×C8—32no—
451C2×C8—62no—
452C2×C8C22×C3×D312yes—
453C4⋊C4—21no—
454C4⋊C4—64no—
455C4⋊C4C22×C3×D312yes—
456C22⋊C4—64no—
457C22×C3—22no—
458C22×C3—22no—
459C22×C3—22no—
460C22×C3—21no—
461C22×C3—64no—
462C22×C3—62no—
463C22×C3—62no—
464C22×C3—62no—
465C22×C3—122no—
466C22×C3—122no—
467C22×C3—124no—
468C22×C3—128no—
469C22×C3#88212yes—
470C22×C3#91612yes—
471C22×C3#91812yes—
472C22×C3C3×#12012yes—
473C22×C3C3×#13512yes—
474C22×C3C3×#13712yes—
475C22×C3C2×D3×D411yescharacteristic
476C22×C3C22×C3×D411yescharacteristic
477C2×D3—22no—
478C2×D3—22no—
479C2×D3—22no—
480C2×D3—24no—
481C2×D3—42no—
482C2×D3—42no—
483C2×D3—44no—
484C2×D3—48no—
485C3×C4—24no—
486C3×C4—24no—
487C3×C4—22no—
488C3×C4—21no—
489C3×C4—21no—
490C3×C4—44no—
491C3×C4—42no—
492C3×C4—42no—
493C3×C4—62no—
494C3×C4—82no—
495C3×C4—122no—
496C3×C4#88212yes—
497C3×C4C3×#12012yes—
498C3×C4C22×D1211yescharacteristic
499C3×C4C2×D3×D411yescharacteristic
500C3×C4C22×C3×D411yescharacteristic
501C3×C4C22×C3×D411yescharacteristic
502Dic3—22no—
503Dic3—42no—
504C32C2×#45211yescharacteristic, complemented, Sylow
505C23—32no—
506C23—64no—
507C23—62no—
508C23—62no—
509C23—62no—
510C23—62no—
511C23—122no—
512C23—122no—
513C23C3×D3×D411yescharacteristic
514Q8—24no—
515Q8—22no—
516Q8—62no—
517Q8—62no—
518Q8—122no—
519Q8C2×C3×D1214yes—
520D4—34no—
521D4—616no—
522D4—64no—
523D4—62no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—32no—
528C2×C4—42no—
529C2×C4—616no—
530C2×C4—62no—
531C2×C4—64no—
532C2×C4—62no—
533C2×C4—62no—
534C2×C4—62no—
535C2×C4—122no—
536C2×C4C2×C3×D1212yes—
537C2×C4C3×D3×D411yescharacteristic
538C2×C4C3×D3×D412yes—
539C2×C4C23×C3×D311yescharacteristic
540C8—22no—
541C8—62no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—24no—
546C2×C3—122no—
547C2×C3—124no—
548C2×C3#480814yesdirect product factor
549C2×C3C3×#45214yescomplemented
550C2×C3C2×#88211yescharacteristic
551C2×C3C2×#91611yescharacteristic
552C2×C3C2×#91811yescharacteristic
553C2×C3C2×C3×#12011yescharacteristic
554C2×C3C2×C3×#13511yescharacteristic
555C2×C3C2×C3×#13711yescharacteristic
556D3—42no—
557D3—44no—
558C22—64no—
559C22—62no—
560C22—62no—
561C22—62no—
562C22—122no—
563C22—122no—
564C22—124no—
565C22—128no—
566C22C3×#88212yes—
567C22C3×#91612yes—
568C22C3×#91812yes—
569C22C2×C3×D3×D411yescharacteristic
570C4—24no—
571C4—42no—
572C4—62no—
573C4—122no—
574C4C3×#88212yes—
575C4C22×C3×D1211yescharacteristic
576C4C2×C3×D3×D411yescharacteristic
577C3—21no—
578C3C2×#480811yescharacteristic, direct product factor
579C3C2×C3×#45211yescharacteristic, complemented
580C2—122no—
581C2—124no—
582C2C3×#480814yesdirect product factor
583C2C2×C3×#88211yescharacteristic
584C2C2×C3×#91611yescharacteristic
585C2C2×C3×#91811yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#103C2
socleC23×C32C2×D4
prime radicalC22×C3×#239C2
hypercenterC2×C3×#103D3
hypocenterC3C2×C3×#452
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×#103

Complements

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

NH ≅ G/Ntype
2. C22×C3×#216C2semidirect
3. C22×C3×#204C2semidirect
4. C2×C3×#897C2semidirect
5. C2×C32×#103C2semidirect
6. C2×C3×(C2×D3)⋊C8C2semidirect
7. C2×C3×#809C2semidirect
8. C3×#4808C2direct (N × H)
10. C2×#4808C3direct (N × H)
24. C2×C3×#216C22semidirect
29. C2×C3×#204C22semidirect
31. C3×#897C22semidirect
32. C32×#103C22semidirect
33. C3×(C2×D3)⋊C8C22semidirect
34. C3×#809C22semidirect
40. C22×#216C2×C3semidirect
41. C22×#204C2×C3semidirect
42. C2×#897C2×C3semidirect
45. C2×C3×#103D3semidirect
46. C2×C3×#103C2×C3semidirect
49. C2×(C2×D3)⋊C8C2×C3semidirect
50. C2×#809C2×C3semidirect
51. #4808C2×C3direct (N × H)
130. C2×#216C22×C3semidirect
135. C2×#204C22×C3semidirect
137. #897C22×C3semidirect
139. C3×#103C2×D3semidirect
140. C3×#103C22×C3semidirect
143. (C2×D3)⋊C8C22×C3semidirect
144. #809C22×C3semidirect
187. C2×#103C3×D3semidirect
321. #103C2×C3×D3semidirect
411. C2×C32#452semidirect
504. C32C2×#452semidirect
548. C2×C3#4808direct (N × H)
549. C2×C3C3×#452semidirect
578. C3C2×#4808direct (N × H)
579. C3C2×C3×#452semidirect
582. C2C3×#4808direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2392
C22×C3×#2162
C22×C3×#2042
C2×C3×#8972
C2×C32×#1032
C2×C3×(C2×D3)⋊C82
C2×C3×#8092
C3×#48082
C2×C3×#4523
C2×#48083