Finite Group Databasebeta

← C2×C3×#4733 #11863766

Subgroups — C2×C3×#4733 #11863766

Order 1152.

1621 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic
2C2×C3×#924C211yesmaximal, characteristic, complemented
3C22×C3×Dic12C211yesmaximal, characteristic, complemented
4C22×C3×#204C211yesmaximal, characteristic, complemented
5C2×C32×C22⋊C8C211yesmaximal, characteristic, complemented
6C2×C3×#821C211yesmaximal, characteristic, complemented
7C2×C3×#816C211yesmaximal, characteristic, complemented
8C3×#4733C218yesmaximal, direct product factor
9C2×C3×#452—31nomaximal
10C2×#4733C311yesmaximal, characteristic, direct product factor
11C23×C32×C4C2211yescharacteristic
12C22×C3×#67—21no—
13C2×C3×#235—22no—
14C2×C3×#235—24no—
15C2×C3×#235—24no—
16C2×C3×#235C2214yes—
17C22×C3×D12C2211yescharacteristic
18C22×C3×C4×D3—21no—
19C22×C3×Dic6C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C22×C32×C8C2211yescharacteristic
22C22×C32×C8C2211yescharacteristic
23C2×C3×#217—21no—
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C3×#924—22no—
26C3×#924C2214yescomplemented
27C2×C3×Dic3⋊C4—21no—
28C2×C3×Dic12—24no—
29C2×C3×Dic12C2214yescomplemented
30C2×C3×#204—24no—
31C2×C3×#204C2214yescomplemented
32C32×C22⋊C8C2214yescomplemented
33C3×#821C2214yescomplemented
34C3×#816C2214yescomplemented
35C22×C3×#41—31no—
36C22×#235C2×C311yescharacteristic
37C22×C3×Q16—31no—
38C22×C3×SD16—31no—
39C2×C3×C22⋊Q8—31no—
40C2×#924C2×C311yescharacteristic, complemented
41C22×Dic12C2×C311yescharacteristic, complemented
42C22×#204C2×C311yescharacteristic, complemented
43C3×#452—38no—
44C2×C3×#103—31no—
45C2×C3×#102—31no—
46C2×C3×C22⋊C8—21no—
47C2×C3×C22⋊C8D311yescharacteristic, complemented
48C2×C3×C22⋊C8C2×C311yescharacteristic, complemented
49C2×#821C2×C311yescharacteristic, complemented
50C2×#816C2×C311yescharacteristic, complemented
51#4733C2×C318yesdirect product factor
52C24×C32D411yescharacteristic
53C23×C3×D3—21no—
54C22×C32×C4—22no—
55C22×C32×C4—22no—
56C22×C32×C4D411yescharacteristic
57C22×C32×C4D412yes—
58C22×C32×C4C2312yes—
59C22×C32×C4C2311yescharacteristic
60C2×C3×#67—28no—
61C2×C3×#67—24no—
62C22×C3×Dic3—21no—
63C22×C3×Dic3—21no—
64C22×C3×Dic3—21no—
65C3×#235—216no—
66C3×#235—28no—
67C3×#235—28no—
68C2×C3×D12—21no—
69C2×C3×D12—22no—
70C2×C3×D12D414yes—
71C2×C3×D12C2312yes—
72C2×C3×C4×D3—28no—
73C2×C3×C4×D3—24no—
74C2×C3×Dic6—21no—
75C2×C3×Dic6—22no—
76C2×C3×Dic6—22no—
77C2×C3×Dic6—22no—
78C2×C3×Dic6—21no—
79C2×C3×Dic6D414yes—
80C2×C3×Dic6C2312yes—
81C2×C3×Dic6C2312yes—
82C2×C32×C8—22no—
83C2×C32×C8—22no—
84C2×C32×C8C2312yes—
85C2×C32×C8C2312yes—
86C3×#217—24no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3C2312yes—
89C3×Dic3⋊C4—24no—
90C3×Dic12—28no—
91C3×#204—28no—
92C2×#452—31noSylow
93C2×C3×#41—34no—
94C2×C3×#41—64no—
95C2×C3×#41—64no—
96C2×C3×#41—62no—
97C22×C3×Q8—31no—
98C22×C3×Q8—31no—
99C22×C3×D4—31no—
100C22×C3×D4—61no—
101C23×C3×C4—21no—
102C23×C3×C4—61no—
103C23×C3×C4C2×D311yescharacteristic
104C23×C3×C4C22×C311yescharacteristic
105C22×#67—21no—
106C2×#235—22no—
107C2×#235—24no—
108C2×#235—24no—
109C2×#235C22×C314yes—
110C22×D12C22×C311yescharacteristic
111C22×C4×D3—21no—
112C22×Dic6C22×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—21no—
120C22×C3×C8C2×D311yescharacteristic
121C22×C3×C8C2×D311yescharacteristic
122C22×C3×C8C22×C311yescharacteristic
123C22×C3×C8C22×C311yescharacteristic
124C3×C22⋊Q8—34no—
125C3×C22⋊Q8—62no—
126C2×C3×C4⋊C4—31no—
127C2×C3×C4⋊C4—61no—
128C2×C3×C22⋊C4—61no—
129C2×#217—21no—
130C2×C4⋊Dic3C22×C311yescharacteristic
131#924—22no—
132#924C22×C314yescomplemented
133C2×Dic3⋊C4—21no—
134C2×Dic12—24no—
135C2×Dic12C22×C314yescomplemented
136C2×#204—24no—
137C2×#204C22×C314yescomplemented
138C3×#103—34no—
139C3×#102—34no—
140C3×C22⋊C8—24no—
141C3×C22⋊C8C2×D314yescomplemented
142C3×C22⋊C8C22×C314yescomplemented
143#821C22×C314yescomplemented
144#816C22×C314yescomplemented
145C23×C32—22no—
146C23×C32—22no—
147C23×C32—22no—
148C23×C32C2×D412yes—
149C23×C32C2×D411yescharacteristic
150C22×C3×D3—24no—
151C22×C3×D3—22no—
152C22×C3×D3—42no—
153C22×C3×D3—42no—
154C2×C32×C4—22no—
155C2×C32×C4—24no—
156C2×C32×C4—22no—
157C2×C32×C4—22no—
158C2×C32×C4C2×D412yes—
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4C2×D412yes—
161C2×C32×C4C2×D412yes—
162C2×C32×C4C2411yescharacteristic
163C3×#67—216no—
164C2×C3×Dic3—24no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—42no—
169C2×C3×Dic3—42no—
170C3×D12—24no—
171C3×D12—22no—
172C3×D12C2×D414yes—
173C3×C4×D3—216no—
174C3×Dic6—24no—
175C3×Dic6—22no—
176C3×Dic6—22no—
177C3×Dic6—22no—
178C3×Dic6—42no—
179C3×Dic6C2×D414yes—
180C32×C8—22no—
181C32×C8—22no—
182C22×#41—31no—
183C22×Q16—31no—
184C22×SD16—31no—
185C2×C22⋊Q8—31no—
186#452—38no—
187C2×#103—31no—
188C2×#102—31no—
189C2×C22⋊C8C3×D311yescharacteristic, complemented
190C24×C3—21no—
191C24×C3—61no—
192C24×C3D1211yescharacteristic
193C24×C3C3×D411yescharacteristic
194C23×D3—21no—
195C3×#41—68no—
196C3×#41—68no—
197C3×#41—616no—
198C2×C3×Q8—34no—
199C2×C3×Q8—32no—
200C2×C3×Q8—32no—
201C2×C3×Q8—61no—
202C2×C3×Q8—61no—
203C2×C3×Q8—62no—
204C2×C3×Q8—62no—
205C2×C3×Q8—62no—
206C2×C3×D4—34no—
207C2×C3×D4—32no—
208C2×C3×D4—68no—
209C2×C3×D4—64no—
210C2×C3×D4—61no—
211C2×C3×D4—62no—
212C22×C3×C4—22no—
213C22×C3×C4—22no—
214C22×C3×C4—22no—
215C22×C3×C4—22no—
216C22×C3×C4—21no—
217C22×C3×C4—22no—
218C22×C3×C4—21no—
219C22×C3×C4—22no—
220C22×C3×C4—42no—
221C22×C3×C4—42no—
222C22×C3×C4—68no—
223C22×C3×C4—61no—
224C22×C3×C4—64no—
225C22×C3×C4—61no—
226C22×C3×C4—61no—
227C22×C3×C4D1212yes—
228C22×C3×C4D1211yescharacteristic
229C22×C3×C4C3×D411yescharacteristic
230C22×C3×C4C3×D412yes—
231C22×C3×C4C22×D312yes—
232C22×C3×C4C22×D311yescharacteristic
233C22×C3×C4C23×C312yes—
234C22×C3×C4C23×C311yescharacteristic
235C2×#67—28no—
236C2×#67—24no—
237C22×Dic3—21no—
238C22×Dic3—21no—
239C22×Dic3—21no—
240#235—216no—
241#235—28no—
242#235—28no—
243C2×D12—21no—
244C2×D12—22no—
245C2×D12C3×D414yes—
246C2×D12C23×C312yes—
247C2×C4×D3—28no—
248C2×C4×D3—24no—
249C2×Dic6—21no—
250C2×Dic6—22no—
251C2×Dic6—22no—
252C2×Dic6—22no—
253C2×Dic6—21no—
254C2×Dic6C3×D414yes—
255C2×Dic6C23×C312yes—
256C2×Dic6C23×C312yes—
257C3×Q16—68no—
258C3×SD16—68no—
259C2×C3×C8—22no—
260C2×C3×C8—22no—
261C2×C3×C8—22no—
262C2×C3×C8—22no—
263C2×C3×C8—22no—
264C2×C3×C8—22no—
265C2×C3×C8—42no—
266C2×C3×C8—42no—
267C2×C3×C8C22×D312yes—
268C2×C3×C8C22×D312yes—
269C2×C3×C8C23×C312yes—
270C2×C3×C8C23×C312yes—
271C3×C4⋊C4—32no—
272C3×C4⋊C4—64no—
273C3×C4⋊C4—61no—
274C3×C22⋊C4—64no—
275#217—24no—
276C4⋊Dic3—21no—
277C4⋊Dic3C23×C312yes—
278Dic3⋊C4—24no—
279Dic12—28no—
280#204—28no—
281C22×C32—22no—
282C22×C32—22no—
283C22×C32—22no—
284C22×C32—44no—
285C22×C32#12012yes—
286C22×C32#13512yes—
287C22×C32#13712yes—
288C22×C32C22×D411yescharacteristic
289C2×C3×D3—24no—
290C2×C3×D3—42no—
291C2×C3×D3—42no—
292C2×C3×D3—48no—
293C32×C4—22no—
294C32×C4#12012yes—
295C32×C4C22×D411yescharacteristic
296C32×C4C22×D411yescharacteristic
297C3×Dic3—24no—
298C3×Dic3—42no—
299C3×Dic3—42no—
300C2×#41—34no—
301C2×#41—64no—
302C2×#41—64no—
303C2×#41—62no—
304C22×Q8—31no—
305C22×Q8—31no—
306C22×D4—31no—
307C22×D4—61no—
308C23×C4—61no—
309C23×C4C2×C3×D311yescharacteristic
310C2×Q16—34no—
311C2×Q16—64no—
312C2×SD16—34no—
313C2×SD16—64no—
314C22×C8C2×C3×D311yescharacteristic
315C22×C8C2×C3×D311yescharacteristic
316C22⋊Q8—34no—
317C22⋊Q8—62no—
318C2×C4⋊C4—31no—
319C2×C4⋊C4—61no—
320C2×C22⋊C4—61no—
321#103—34no—
322#102—34no—
323C22⋊C8C2×C3×D314yescomplemented
324C23×C3—24no—
325C23×C3—22no—
326C23×C3—22no—
327C23×C3—22no—
328C23×C3—22no—
329C23×C3—22no—
330C23×C3—22no—
331C23×C3—21no—
332C23×C3—22no—
333C23×C3—42no—
334C23×C3—42no—
335C23×C3—64no—
336C23×C3—62no—
337C23×C3—122no—
338C23×C3—122no—
339C23×C3C2×D1212yes—
340C23×C3C2×D1211yescharacteristic
341C23×C3C2×C3×D412yes—
342C23×C3C2×C3×D411yescharacteristic
343C22×D3—24no—
344C22×D3—22no—
345C22×D3—42no—
346C22×D3—42no—
347C3×Q8—34no—
348C3×Q8—64no—
349C3×Q8—62no—
350C3×Q8—62no—
351C3×Q8—62no—
352C3×Q8—122no—
353C3×D4—34no—
354C3×D4—616no—
355C3×D4—64no—
356C3×D4—62no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
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—21no—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—44no—
371C2×C3×C4—42no—
372C2×C3×C4—42no—
373C2×C3×C4—42no—
374C2×C3×C4—616no—
375C2×C3×C4—64no—
376C2×C3×C4—62no—
377C2×C3×C4—62no—
378C2×C3×C4—62no—
379C2×C3×C4—122no—
380C2×C3×C4—122no—
381C2×C3×C4C2×D1212yes—
382C2×C3×C4C2×D1211yescharacteristic
383C2×C3×C4D3×D412yes—
384C2×C3×C4D3×D412yes—
385C2×C3×C4C2×C3×D412yes—
386C2×C3×C4C2×C3×D411yescharacteristic
387C2×C3×C4C2×C3×D412yes—
388C2×C3×C4C2×C3×D412yes—
389C2×C3×C4C23×D311yescharacteristic
390C2×C3×C4C24×C311yescharacteristic
391#67—216no—
392C2×Dic3—24no—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—42no—
397C2×Dic3—42no—
398D12—24no—
399D12—22no—
400D12C2×C3×D414yes—
401C4×D3—216no—
402Dic6—24no—
403Dic6—22no—
404Dic6—22no—
405Dic6—22no—
406Dic6—42no—
407Dic6C2×C3×D414yes—
408C3×C8—22no—
409C3×C8—22no—
410C3×C8—22no—
411C3×C8—22no—
412C3×C8—42no—
413C3×C8—42no—
414C2×C32—42no—
415C2×C32#45214yescomplemented
416C2×C32C2×#12011yescharacteristic
417C2×C32C2×#13511yescharacteristic
418C2×C32C2×#13711yescharacteristic
419C3×D3—44no—
420C24—61no—
421C24C3×D1211yescharacteristic
422#41—68no—
423#41—68no—
424#41—616no—
425C2×Q8—32no—
426C2×Q8—32no—
427C2×Q8—34no—
428C2×Q8—61no—
429C2×Q8—61no—
430C2×Q8—62no—
431C2×Q8—62no—
432C2×Q8—62no—
433C2×D4—32no—
434C2×D4—34no—
435C2×D4—68no—
436C2×D4—64no—
437C2×D4—61no—
438C2×D4—62no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—68no—
442C22×C4—61no—
443C22×C4—64no—
444C22×C4—61no—
445C22×C4—61no—
446C22×C4C3×D1211yescharacteristic
447C22×C4C3×D1212yes—
448C22×C4C22×C3×D312yes—
449C22×C4C22×C3×D311yescharacteristic
450Q16—68no—
451SD16—68no—
452C2×C8—22no—
453C2×C8—22no—
454C2×C8C22×C3×D312yes—
455C2×C8C22×C3×D312yes—
456C4⋊C4—32no—
457C4⋊C4—61no—
458C4⋊C4—64no—
459C22⋊C4—64no—
460C22×C3—24no—
461C22×C3—22no—
462C22×C3—22no—
463C22×C3—22no—
464C22×C3—22no—
465C22×C3—22no—
466C22×C3—22no—
467C22×C3—22no—
468C22×C3—22no—
469C22×C3—22no—
470C22×C3—21no—
471C22×C3—42no—
472C22×C3—42no—
473C22×C3—48no—
474C22×C3—44no—
475C22×C3—44no—
476C22×C3—64no—
477C22×C3—122no—
478C22×C3—122no—
479C22×C3—128no—
480C22×C3#88212yes—
481C22×C3#90412yes—
482C22×C3#90912yes—
483C22×C3C3×#12012yes—
484C22×C3C3×#13512yes—
485C22×C3C3×#13712yes—
486C22×C3C22×D1211yescharacteristic
487C22×C3C22×C3×D411yescharacteristic
488C2×D3—24no—
489C2×D3—42no—
490C2×D3—42no—
491C2×D3—48no—
492C3×C4—22no—
493C3×C4—22no—
494C3×C4—22no—
495C3×C4—21no—
496C3×C4—21no—
497C3×C4—42no—
498C3×C4—64no—
499C3×C4—122no—
500C3×C4—122no—
501C3×C4#88212yes—
502C3×C4C3×#12012yes—
503C3×C4C2×D3×D411yescharacteristic
504C3×C4C2×D3×D411yescharacteristic
505C3×C4C22×C3×D411yescharacteristic
506C3×C4C22×C3×D411yescharacteristic
507Dic3—24no—
508Dic3—42no—
509Dic3—42no—
510C32C2×#45211yescharacteristic, complemented, Sylow
511C23—22no—
512C23—22no—
513C23—22no—
514C23—64no—
515C23—62no—
516C23—122no—
517C23—122no—
518C23C2×C3×D1212yes—
519C23C2×C3×D1211yescharacteristic
520Q8—34no—
521Q8—64no—
522Q8—62no—
523Q8—62no—
524Q8—62no—
525Q8—122no—
526D4—34no—
527D4—616no—
528D4—64no—
529D4—62no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—616no—
535C2×C4—64no—
536C2×C4—62no—
537C2×C4—62no—
538C2×C4—62no—
539C2×C4—122no—
540C2×C4—122no—
541C2×C4C2×C3×D1212yes—
542C2×C4C2×C3×D1211yescharacteristic
543C2×C4C3×D3×D412yes—
544C2×C4C3×D3×D412yes—
545C2×C4C23×C3×D311yescharacteristic
546C8—22no—
547C8—22no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—24no—
551C2×C3—21no—
552C2×C3—44no—
553C2×C3—42no—
554C2×C3—42no—
555C2×C3—124no—
556C2×C3#473314yesdirect product factor
557C2×C3C3×#45214yescomplemented
558C2×C3C2×#88211yescharacteristic
559C2×C3C2×#90411yescharacteristic
560C2×C3C2×#90911yescharacteristic
561C2×C3C2×C3×#12011yescharacteristic
562C2×C3C2×C3×#13511yescharacteristic
563C2×C3C2×C3×#13711yescharacteristic
564D3—44no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—44no—
569C22—64no—
570C22—122no—
571C22—128no—
572C22—122no—
573C22C3×#88212yes—
574C22C3×#90412yes—
575C22C3×#90912yes—
576C22C22×C3×D1211yescharacteristic
577C4—22no—
578C4—64no—
579C4—122no—
580C4—122no—
581C4C3×#88212yes—
582C4C2×C3×D3×D411yescharacteristic
583C4C2×C3×D3×D411yescharacteristic
584C3—21no—
585C3C2×#473311yescharacteristic, direct product factor
586C3C2×C3×#45211yescharacteristic, complemented
587C2—42no—
588C2—124no—
589C2C3×#473314yesdirect product factor
590C2C2×C3×#88211yescharacteristic
591C2C2×C3×#90411yescharacteristic
592C2C2×C3×#90911yescharacteristic
subgroupG/H
centerC23×C3C2×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×C22⋊C8C2
socleC23×C32C2×D4
prime radicalC22×C3×#235C2
hypercenterC2×C3×C22⋊C8D3
hypocenterC3C2×C3×#452
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C23×C3×C4 ◁ C2×C3×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×C3×#924C2semidirect
3. C22×C3×Dic12C2semidirect
4. C22×C3×#204C2semidirect
5. C2×C32×C22⋊C8C2semidirect
6. C2×C3×#821C2semidirect
7. C2×C3×#816C2semidirect
8. C3×#4733C2direct (N × H)
10. C2×#4733C3direct (N × H)
26. C3×#924C22semidirect
29. C2×C3×Dic12C22semidirect
31. C2×C3×#204C22semidirect
32. C32×C22⋊C8C22semidirect
33. C3×#821C22semidirect
34. C3×#816C22semidirect
40. C2×#924C2×C3semidirect
41. C22×Dic12C2×C3semidirect
42. C22×#204C2×C3semidirect
47. C2×C3×C22⋊C8D3semidirect
48. C2×C3×C22⋊C8C2×C3semidirect
49. C2×#821C2×C3semidirect
50. C2×#816C2×C3semidirect
51. #4733C2×C3direct (N × H)
132. #924C22×C3semidirect
135. C2×Dic12C22×C3semidirect
137. C2×#204C22×C3semidirect
141. C3×C22⋊C8C2×D3semidirect
142. C3×C22⋊C8C22×C3semidirect
143. #821C22×C3semidirect
144. #816C22×C3semidirect
189. C2×C22⋊C8C3×D3semidirect
323. C22⋊C8C2×C3×D3semidirect
415. C2×C32#452semidirect
510. C32C2×#452semidirect
556. C2×C3#4733direct (N × H)
557. C2×C3C3×#452semidirect
585. C3C2×#4733direct (N × H)
586. C3C2×C3×#452semidirect
589. C2C3×#4733direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C2×C3×#9242
C22×C3×Dic122
C22×C3×#2042
C2×C32×C22⋊C82
C2×C3×#8212
C2×C3×#8162
C3×#47332
C2×C3×#4523
C2×#47333