Finite Group Databasebeta

← C2×C3×#4960 #11808086

Subgroups — C2×C3×#4960 #11808086

Order 1152.

3961 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×#67C212yesmaximal, complemented
2C23×C3×D12C211yesmaximal, characteristic, complemented
3C22×C32×C22⋊C4C211yesmaximal, characteristic, complemented
4C22×C3×(C2×D3)⋊C4C212yesmaximal, complemented
5C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
6C3×#4960C218yesmaximal, direct product factor
7C2×C3×#392—31nomaximal
8C2×#4960C311yesmaximal, characteristic, direct product factor
9C25×C32C2211yescharacteristic
10C24×C3×D3C2212yes—
11C23×C32×C4C2211yescharacteristic
12C23×C32×C4C2211yescharacteristic
13C22×C3×#67—28no—
14C22×C3×#67—28no—
15C22×C3×#67—28no—
16C22×C3×#67C2218yescomplemented
17C23×C3×Dic3C2212yes—
18C22×C3×D12—24no—
19C22×C3×D12—28no—
20C22×C3×D12C2214yescomplemented
21C2×C32×C22⋊C4—24no—
22C2×C32×C22⋊C4C2214yescomplemented
23C2×C3×(C2×D3)⋊C4—28no—
24C2×C3×(C2×D3)⋊C4C2218yescomplemented
25C3×C3⋊#95C2214yescomplemented
26C23×C3×D4—31no—
27C23×C3×D4—32no—
28C23×#67C2×C312yescomplemented
29C23×D12C2×C311yescharacteristic, complemented
30C22×C3×C22⋊C4—21no—
31C22×C3×C22⋊C4—32no—
32C22×C3×C22⋊C4D311yescharacteristic, complemented
33C22×C3×C22⋊C4C2×C311yescharacteristic, complemented
34C22×(C2×D3)⋊C4C2×C312yescomplemented
35C3×#392—38no—
36C2×C3×#95—31no—
37C2×C3⋊#95C2×C311yescharacteristic, complemented
38#4960C2×C318yesdirect product factor
39C24×C32—22no—
40C24×C32—24no—
41C24×C32—24no—
42C24×C32—22no—
43C24×C32D414yescomplemented
44C24×C32C2312yes—
45C24×C32C2311yescharacteristic
46C23×C3×D3—24no—
47C23×C3×D3—24no—
48C23×C3×D3—24no—
49C23×C3×D3—24no—
50C23×C3×D3—24no—
51C23×C3×D3—24no—
52C23×C3×D3D418yescomplemented
53C23×C3×D3C2314yes—
54C22×C32×C4—24no—
55C22×C32×C4—22no—
56C22×C32×C4—24no—
57C22×C32×C4D414yescomplemented
58C22×C32×C4C2312yes—
59C22×C32×C4C2312yes—
60C2×C3×#67—264no—
61C2×C3×#67—216no—
62C2×C3×#67—216no—
63C2×C3×#67—216no—
64C22×C3×Dic3—24no—
65C22×C3×Dic3—24no—
66C22×C3×Dic3D418yescomplemented
67C22×C3×Dic3C2314yes—
68C2×C3×D12—232no—
69C2×C3×D12—216no—
70C2×C3×D12—28no—
71C32×C22⋊C4—28no—
72C3×(C2×D3)⋊C4—216no—
73C2×#392—31noSylow
74C25×C3—21no—
75C25×C3—32no—
76C25×C3C2×D311yescharacteristic
77C25×C3C22×C311yescharacteristic
78C24×D3C22×C312yes—
79C22×C3×D4—38no—
80C22×C3×D4—34no—
81C22×C3×D4—68no—
82C22×C3×D4—68no—
83C22×C3×D4—68no—
84C22×C3×D4—68no—
85C22×C3×D4—64no—
86C23×C3×C4—21no—
87C23×C3×C4—21no—
88C23×C3×C4—32no—
89C23×C3×C4C2×D311yescharacteristic
90C23×C3×C4C2×D311yescharacteristic
91C23×C3×C4C22×C311yescharacteristic
92C23×C3×C4C22×C311yescharacteristic
93C22×#67—28no—
94C22×#67—28no—
95C22×#67—28no—
96C22×#67C22×C318yescomplemented
97C23×Dic3C22×C312yes—
98C22×D12—28no—
99C22×D12—24no—
100C22×D12C22×C314yescomplemented
101C2×C3×C22⋊C4—28no—
102C2×C3×C22⋊C4—24no—
103C2×C3×C22⋊C4—24no—
104C2×C3×C22⋊C4—24no—
105C2×C3×C22⋊C4—38no—
106C2×C3×C22⋊C4—68no—
107C2×C3×C22⋊C4C2×D314yescomplemented
108C2×C3×C22⋊C4C22×C314yescomplemented
109C2×(C2×D3)⋊C4—28no—
110C2×(C2×D3)⋊C4C22×C318yescomplemented
111C3×#95—34no—
112C3⋊#95C22×C314yescomplemented
113C23×C32—28no—
114C23×C32—22no—
115C23×C32—22no—
116C23×C32—216no—
117C23×C32—24no—
118C23×C32—24no—
119C23×C32—44no—
120C23×C32—48no—
121C23×C32—44no—
122C23×C32C2×D412yes—
123C23×C32C2×D414yes—
124C23×C32C2×D414yes—
125C23×C32C2×D412yes—
126C23×C32C2×D414yescomplemented
127C23×C32#4112yes—
128C23×C32C2411yescharacteristic
129C22×C3×D3—216no—
130C22×C3×D3—216no—
131C22×C3×D3—216no—
132C22×C3×D3—24no—
133C22×C3×D3—24no—
134C22×C3×D3—24no—
135C22×C3×D3—24no—
136C22×C3×D3—24no—
137C22×C3×D3—24no—
138C22×C3×D3—48no—
139C22×C3×D3—48no—
140C22×C3×D3—48no—
141C22×C3×D3—48no—
142C22×C3×D3C2×D418yescomplemented
143C2×C32×C4—22no—
144C2×C32×C4—28no—
145C2×C32×C4—24no—
146C2×C32×C4—24no—
147C2×C32×C4—44no—
148C2×C32×C4C2×D414yescomplemented
149C3×#67—264no—
150C2×C3×Dic3—216no—
151C2×C3×Dic3—24no—
152C2×C3×Dic3—24no—
153C2×C3×Dic3C2×D418yescomplemented
154C3×D12—232no—
155C23×D4—32no—
156C23×D4—31no—
157C22×C22⋊C4—32no—
158C22×C22⋊C4C3×D311yescharacteristic, complemented
159#392—38no—
160C2×#95—31no—
161C24×C3—24no—
162C24×C3—24no—
163C24×C3—22no—
164C24×C3—24no—
165C24×C3—24no—
166C24×C3—22no—
167C24×C3—22no—
168C24×C3—24no—
169C24×C3—24no—
170C24×C3—22no—
171C24×C3—24no—
172C24×C3—21no—
173C24×C3—22no—
174C24×C3—38no—
175C24×C3—34no—
176C24×C3—44no—
177C24×C3—44no—
178C24×C3—64no—
179C24×C3—64no—
180C24×C3—64no—
181C24×C3—64no—
182C24×C3—64no—
183C24×C3—64no—
184C24×C3D1214yescomplemented
185C24×C3C3×D414yescomplemented
186C24×C3C22×D312yes—
187C24×C3C22×D311yescharacteristic
188C24×C3C23×C312yes—
189C24×C3C23×C311yescharacteristic
190C23×D3—24no—
191C23×D3—24no—
192C23×D3—24no—
193C23×D3—24no—
194C23×D3—24no—
195C23×D3—24no—
196C23×D3C3×D418yescomplemented
197C23×D3C23×C314yes—
198C2×C3×D4—616no—
199C2×C3×D4—632no—
200C2×C3×D4—616no—
201C2×C3×D4—616no—
202C2×C3×D4—664no—
203C2×C3×D4—616no—
204C2×C3×D4—68no—
205C22×C3×C4—24no—
206C22×C3×C4—24no—
207C22×C3×C4—24no—
208C22×C3×C4—24no—
209C22×C3×C4—22no—
210C22×C3×C4—24no—
211C22×C3×C4—22no—
212C22×C3×C4—24no—
213C22×C3×C4—22no—
214C22×C3×C4—22no—
215C22×C3×C4—38no—
216C22×C3×C4—34no—
217C22×C3×C4—44no—
218C22×C3×C4—44no—
219C22×C3×C4—64no—
220C22×C3×C4—64no—
221C22×C3×C4#6714yescomplemented
222C22×C3×C4C3×D414yescomplemented
223C22×C3×C4C22×D312yes—
224C22×C3×C4C22×D312yes—
225C22×C3×C4C23×C312yes—
226C22×C3×C4C23×C312yes—
227C2×#67—264no—
228C2×#67—216no—
229C2×#67—216no—
230C2×#67—216no—
231C22×Dic3—24no—
232C22×Dic3—24no—
233C22×Dic3C3×D418yescomplemented
234C22×Dic3C23×C314yes—
235C2×D12—232no—
236C2×D12—216no—
237C2×D12—28no—
238C3×C22⋊C4—216no—
239C3×C22⋊C4—28no—
240C3×C22⋊C4—28no—
241C3×C22⋊C4—616no—
242(C2×D3)⋊C4—216no—
243C22×C32—24no—
244C22×C32—28no—
245C22×C32—42no—
246C22×C32—44no—
247C22×C32—42no—
248C22×C32—416no—
249C22×C32#12018yes—
250C22×C32#12014yes—
251C22×C32#12118yes—
252C22×C32#12114yes—
253C22×C32#12714yes—
254C22×C32C22×D411yescharacteristic
255C22×C32C22×D412yes—
256C22×C32C22×D412yes—
257C22×C32C22×D411yescharacteristic
258C22×C32C2×#4111yescharacteristic
259C2×C3×D3—28no—
260C2×C3×D3—28no—
261C2×C3×D3—28no—
262C2×C3×D3—44no—
263C2×C3×D3—44no—
264C2×C3×D3—44no—
265C2×C3×D3—44no—
266C2×C3×D3—432no—
267C32×C4—24no—
268C32×C4—42no—
269C3×Dic3—28no—
270C25—32no—
271C25C2×C3×D311yescharacteristic
272C22×D4—38no—
273C22×D4—34no—
274C22×D4—68no—
275C22×D4—68no—
276C22×D4—68no—
277C22×D4—68no—
278C22×D4—64no—
279C23×C4—32no—
280C23×C4C2×C3×D311yescharacteristic
281C23×C4C2×C3×D311yescharacteristic
282C2×C22⋊C4—24no—
283C2×C22⋊C4—38no—
284C2×C22⋊C4—68no—
285C2×C22⋊C4C2×C3×D314yescomplemented
286#95—34no—
287C23×C3—24no—
288C23×C3—216no—
289C23×C3—24no—
290C23×C3—216no—
291C23×C3—28no—
292C23×C3—216no—
293C23×C3—28no—
294C23×C3—22no—
295C23×C3—24no—
296C23×C3—24no—
297C23×C3—22no—
298C23×C3—22no—
299C23×C3—24no—
300C23×C3—24no—
301C23×C3—22no—
302C23×C3—21no—
303C23×C3—22no—
304C23×C3—24no—
305C23×C3—22no—
306C23×C3—24no—
307C23×C3—24no—
308C23×C3—22no—
309C23×C3—38no—
310C23×C3—416no—
311C23×C3—44no—
312C23×C3—44no—
313C23×C3—416no—
314C23×C3—48no—
315C23×C3—48no—
316C23×C3—48no—
317C23×C3—44no—
318C23×C3—44no—
319C23×C3—44no—
320C23×C3—48no—
321C23×C3—44no—
322C23×C3—616no—
323C23×C3—616no—
324C23×C3—616no—
325C23×C3—64no—
326C23×C3—64no—
327C23×C3—64no—
328C23×C3—64no—
329C23×C3—64no—
330C23×C3—64no—
331C23×C3—128no—
332C23×C3—128no—
333C23×C3—128no—
334C23×C3—128no—
335C23×C3C2×D1212yes—
336C23×C3C2×D1214yescomplemented
337C23×C3#23512yes—
338C23×C3D3×D414yes—
339C23×C3D3×D414yes—
340C23×C3C2×#6712yes—
341C23×C3C2×C3×D412yes—
342C23×C3C2×C3×D414yes—
343C23×C3C2×C3×D414yes—
344C23×C3C2×C3×D412yes—
345C23×C3C2×C3×D414yescomplemented
346C23×C3C3×#4112yes—
347C23×C3C23×D311yescharacteristic
348C23×C3C24×C311yescharacteristic
349C22×D3—216no—
350C22×D3—216no—
351C22×D3—216no—
352C22×D3—24no—
353C22×D3—24no—
354C22×D3—24no—
355C22×D3—24no—
356C22×D3—24no—
357C22×D3—24no—
358C22×D3—48no—
359C22×D3—48no—
360C22×D3—48no—
361C22×D3—48no—
362C22×D3C2×C3×D418yescomplemented
363C3×D4—632no—
364C3×D4—664no—
365C2×C3×C4—28no—
366C2×C3×C4—28no—
367C2×C3×C4—24no—
368C2×C3×C4—24no—
369C2×C3×C4—24no—
370C2×C3×C4—24no—
371C2×C3×C4—22no—
372C2×C3×C4—24no—
373C2×C3×C4—22no—
374C2×C3×C4—24no—
375C2×C3×C4—38no—
376C2×C3×C4—48no—
377C2×C3×C4—44no—
378C2×C3×C4—44no—
379C2×C3×C4—48no—
380C2×C3×C4—44no—
381C2×C3×C4—44no—
382C2×C3×C4—616no—
383C2×C3×C4—64no—
384C2×C3×C4—64no—
385C2×C3×C4C2×#6714yescomplemented
386C2×C3×C4C2×C3×D414yescomplemented
387#67—264no—
388C2×Dic3—216no—
389C2×Dic3—24no—
390C2×Dic3—24no—
391C2×Dic3C2×C3×D418yescomplemented
392D12—232no—
393C2×C32—44no—
394C2×C32#39218yescomplemented
395C2×C32C2×#12012yes—
396C2×C32C2×#12011yescharacteristic
397C2×C32C2×#12112yes—
398C2×C32C2×#12111yescharacteristic
399C2×C32C2×#12711yescharacteristic
400C3×D3—48no—
401C24—22no—
402C24—24no—
403C24—24no—
404C24—22no—
405C24—34no—
406C24—38no—
407C24—64no—
408C24—64no—
409C24—64no—
410C24—64no—
411C24—64no—
412C24—64no—
413C24C3×D1214yescomplemented
414C24C22×C3×D312yes—
415C24C22×C3×D311yescharacteristic
416C2×D4—616no—
417C2×D4—632no—
418C2×D4—616no—
419C2×D4—616no—
420C2×D4—664no—
421C2×D4—616no—
422C2×D4—68no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—22no—
426C22×C4—34no—
427C22×C4—38no—
428C22×C4—64no—
429C22×C4—64no—
430C22×C4C3×#6714yescomplemented
431C22×C4C22×C3×D312yes—
432C22×C4C22×C3×D312yes—
433C22⋊C4—28no—
434C22⋊C4—616no—
435C22×C3—28no—
436C22×C3—28no—
437C22×C3—24no—
438C22×C3—28no—
439C22×C3—24no—
440C22×C3—28no—
441C22×C3—28no—
442C22×C3—24no—
443C22×C3—24no—
444C22×C3—24no—
445C22×C3—21no—
446C22×C3—21no—
447C22×C3—22no—
448C22×C3—22no—
449C22×C3—21no—
450C22×C3—48no—
451C22×C3—48no—
452C22×C3—44no—
453C22×C3—432no—
454C22×C3—44no—
455C22×C3—416no—
456C22×C3—44no—
457C22×C3—416no—
458C22×C3—42no—
459C22×C3—42no—
460C22×C3—42no—
461C22×C3—44no—
462C22×C3—42no—
463C22×C3—68no—
464C22×C3—68no—
465C22×C3—68no—
466C22×C3—1232no—
467C22×C3—124no—
468C22×C3—124no—
469C22×C3—124no—
470C22×C3—124no—
471C22×C3#88218yes—
472C22×C3#88418yes—
473C22×C3#93014yes—
474C22×C3#93714yes—
475C22×C3#94014yes—
476C22×C3C3×#12018yes—
477C22×C3C3×#12014yes—
478C22×C3C3×#12118yes—
479C22×C3C3×#12114yes—
480C22×C3C3×#12714yes—
481C22×C3C22×D1211yescharacteristic
482C22×C3C2×#23511yescharacteristic
483C22×C3C2×D3×D412yes—
484C22×C3C2×D3×D412yes—
485C22×C3C22×#6711yescharacteristic
486C22×C3C22×C3×D411yescharacteristic
487C22×C3C22×C3×D412yes—
488C22×C3C22×C3×D412yes—
489C22×C3C22×C3×D411yescharacteristic
490C22×C3C2×C3×#4111yescharacteristic
491C2×D3—28no—
492C2×D3—28no—
493C2×D3—28no—
494C2×D3—432no—
495C2×D3—44no—
496C2×D3—44no—
497C2×D3—44no—
498C2×D3—44no—
499C3×C4—24no—
500C3×C4—24no—
501C3×C4—44no—
502C3×C4—44no—
503C3×C4—42no—
504C3×C4—42no—
505C3×C4—68no—
506Dic3—28no—
507C32C2×#39211yescharacteristic, complemented, Sylow
508C23—216no—
509C23—28no—
510C23—22no—
511C23—24no—
512C23—24no—
513C23—22no—
514C23—38no—
515C23—48no—
516C23—44no—
517C23—44no—
518C23—616no—
519C23—616no—
520C23—616no—
521C23—64no—
522C23—64no—
523C23—64no—
524C23—64no—
525C23—64no—
526C23—64no—
527C23—128no—
528C23—128no—
529C23—128no—
530C23—128no—
531C23C2×C3×D1212yes—
532C23C2×C3×D1214yescomplemented
533C23C3×#23512yes—
534C23C3×D3×D414yes—
535C23C3×D3×D414yes—
536C23C2×C3×#6712yes—
537C23C23×C3×D311yescharacteristic
538D4—632no—
539D4—664no—
540C2×C4—28no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—38no—
545C2×C4—44no—
546C2×C4—616no—
547C2×C4—64no—
548C2×C4—64no—
549C2×C4C2×C3×#6714yescomplemented
550C2×C3—22no—
551C2×C3—22no—
552C2×C3—21no—
553C2×C3—21no—
554C2×C3—28no—
555C2×C3—21no—
556C2×C3—48no—
557C2×C3—44no—
558C2×C3—44no—
559C2×C3—128no—
560C2×C3#496018yesdirect product factor
561C2×C3C3×#39218yescomplemented
562C2×C3C2×#88212yes—
563C2×C3C2×#88412yes—
564C2×C3C2×#93011yescharacteristic
565C2×C3C2×#93711yescharacteristic
566C2×C3C2×#94011yescharacteristic
567C2×C3C2×C3×#12012yes—
568C2×C3C2×C3×#12011yescharacteristic
569C2×C3C2×C3×#12112yes—
570C2×C3C2×C3×#12111yescharacteristic
571C2×C3C2×C3×#12711yescharacteristic
572D3—48no—
573C22—28no—
574C22—24no—
575C22—44no—
576C22—42no—
577C22—416no—
578C22—42no—
579C22—68no—
580C22—68no—
581C22—68no—
582C22—124no—
583C22—124no—
584C22—124no—
585C22—1232no—
586C22—124no—
587C22C3×#88218yes—
588C22C3×#88418yes—
589C22C3×#93014yes—
590C22C3×#93714yes—
591C22C3×#94014yes—
592C22C22×C3×D1211yescharacteristic
593C22C2×C3×#23511yescharacteristic
594C22C2×C3×D3×D412yes—
595C22C2×C3×D3×D412yes—
596C22C22×C3×#6711yescharacteristic
597C4—24no—
598C4—42no—
599C4—68no—
600C3—21no—
601C3C2×#496011yescharacteristic, direct product factor
602C3C2×C3×#39211yescharacteristic, complemented
603C2—44no—
604C2—128no—
605C2C3×#496018yesdirect product factor
606C2C2×C3×#88212yes—
607C2C2×C3×#88412yes—
608C2C2×C3×#93011yescharacteristic
609C2C2×C3×#93711yescharacteristic
610C2C2×C3×#94011yescharacteristic
subgroupG/H
centerC24×C3C22×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC22×C32×C22⋊C4C2
socleC24×C32C23
hypercenterC22×C3×C22⋊C4D3
hypocenterC3C2×C3×#392
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24×C3 ◁ C22×C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×C3×#67C2semidirect
2. C23×C3×D12C2semidirect
3. C22×C32×C22⋊C4C2semidirect
4. C22×C3×(C2×D3)⋊C4C2semidirect
5. C2×C3×C3⋊#95C2semidirect
6. C3×#4960C2direct (N × H)
8. C2×#4960C3direct (N × H)
16. C22×C3×#67C22semidirect
20. C22×C3×D12C22semidirect
22. C2×C32×C22⋊C4C22semidirect
24. C2×C3×(C2×D3)⋊C4C22semidirect
25. C3×C3⋊#95C22semidirect
28. C23×#67C2×C3semidirect
29. C23×D12C2×C3semidirect
32. C22×C3×C22⋊C4D3semidirect
33. C22×C3×C22⋊C4C2×C3semidirect
34. C22×(C2×D3)⋊C4C2×C3semidirect
37. C2×C3⋊#95C2×C3semidirect
38. #4960C2×C3direct (N × H)
43. C24×C32D4semidirect
52. C23×C3×D3D4semidirect
57. C22×C32×C4D4semidirect
66. C22×C3×Dic3D4semidirect
96. C22×#67C22×C3semidirect
100. C22×D12C22×C3semidirect
107. C2×C3×C22⋊C4C2×D3semidirect
108. C2×C3×C22⋊C4C22×C3semidirect
110. C2×(C2×D3)⋊C4C22×C3semidirect
112. C3⋊#95C22×C3semidirect
126. C23×C32C2×D4semidirect
142. C22×C3×D3C2×D4semidirect
148. C2×C32×C4C2×D4semidirect
153. C2×C3×Dic3C2×D4semidirect
158. C22×C22⋊C4C3×D3semidirect
184. C24×C3D12semidirect
185. C24×C3C3×D4semidirect
196. C23×D3C3×D4semidirect
221. C22×C3×C4#67semidirect
222. C22×C3×C4C3×D4semidirect
233. C22×Dic3C3×D4semidirect
285. C2×C22⋊C4C2×C3×D3semidirect
336. C23×C3C2×D12semidirect
345. C23×C3C2×C3×D4semidirect
362. C22×D3C2×C3×D4semidirect
385. C2×C3×C4C2×#67semidirect
386. C2×C3×C4C2×C3×D4semidirect
391. C2×Dic3C2×C3×D4semidirect
394. C2×C32#392semidirect
413. C24C3×D12semidirect
430. C22×C4C3×#67semidirect
507. C32C2×#392semidirect
532. C23C2×C3×D12semidirect
549. C2×C4C2×C3×#67semidirect
560. C2×C3#4960direct (N × H)
561. C2×C3C3×#392semidirect
601. C3C2×#4960direct (N × H)
602. C3C2×C3×#392semidirect
605. C2C3×#4960direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×#672
C23×C3×D122
C22×C32×C22⋊C42
C22×C3×(C2×D3)⋊C42
C2×C3×C3⋊#952
C3×#49602
C2×C3×#3923
C2×#49603