Finite Group Databasebeta

← C2×C3×#4657 #11808340

Subgroups — C2×C3×#4657 #11808340

Order 1152.

1549 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4⋊Dic3C211yesmaximal, characteristic
2C22×C3×Dic3⋊C4C211yesmaximal, characteristic
3C22×C3×Dic3⋊C4C211yesmaximal, characteristic
4C22×C3×Dic3⋊C4C211yesmaximal, characteristic
5C2×C32×#95C211yesmaximal, characteristic
6C2×C3×C3⋊#95C211yesmaximal, characteristic
7C2×C3×C3⋊#95C211yesmaximal, characteristic
8C3×#4657C218yesmaximal, direct product factor
9C2×C3×#398—31nomaximal
10C2×#4657C311yesmaximal, characteristic, direct product factor
11C23×C32×C4C2211yescharacteristic
12C23×C32×C4C2211yescharacteristic
13C23×C32×C4C2211yescharacteristic
14C23×C3×Dic3C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3—24no—
19C2×C3×C4⋊Dic3C2214yes—
20C2×C3×Dic3⋊C4—24no—
21C2×C3×Dic3⋊C4—24no—
22C2×C3×Dic3⋊C4—24no—
23C2×C3×Dic3⋊C4C2214yes—
24C2×C3×Dic3⋊C4C2214yes—
25C2×C3×Dic3⋊C4C2214yes—
26C32×#95C2214yes—
27C3×C3⋊#95C2214yes—
28C3×C3⋊#95C2214yes—
29C22×C3×C4⋊C4—31no—
30C22×C3×C4⋊C4—31no—
31C22×C3×C4⋊C4—31no—
32C22×C3×C4⋊C4—31no—
33C22×C4⋊Dic3C2×C311yescharacteristic
34C22×Dic3⋊C4C2×C311yescharacteristic
35C22×Dic3⋊C4C2×C311yescharacteristic
36C22×Dic3⋊C4C2×C311yescharacteristic
37C3×#398—38no—
38C2×C3×#95—21no—
39C2×C3×#95—31no—
40C2×C3×#95—31no—
41C2×C3×#95D311yescharacteristic
42C2×C3×#95C2×C311yescharacteristic
43C2×C3⋊#95C2×C311yescharacteristic
44C2×C3⋊#95C2×C311yescharacteristic
45#4657C2×C318yesdirect product factor
46C24×C32C2311yescharacteristic
47C22×C32×C4—22no—
48C22×C32×C4—22no—
49C22×C32×C4—22no—
50C22×C32×C4—22no—
51C22×C32×C4—22no—
52C22×C32×C4—22no—
53C22×C32×C4—22no—
54C22×C32×C4—22no—
55C22×C32×C4Q814yes—
56C22×C32×C4C2312yes—
57C22×C32×C4C2312yes—
58C22×C32×C4C2312yes—
59C22×C3×Dic3—22no—
60C22×C3×Dic3—22no—
61C22×C3×Dic3—22no—
62C22×C3×Dic3—22no—
63C22×C3×Dic3—22no—
64C22×C3×Dic3—22no—
65C22×C3×Dic3—22no—
66C22×C3×Dic3—22no—
67C22×C3×Dic3—22no—
68C22×C3×Dic3D414yes—
69C22×C3×Dic3D414yes—
70C22×C3×Dic3Q814yes—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C3×C4⋊Dic3—28no—
76C3×Dic3⋊C4—28no—
77C3×Dic3⋊C4—28no—
78C3×Dic3⋊C4—28no—
79C2×#398—31noSylow
80C23×C3×C4—21no—
81C23×C3×C4—21no—
82C23×C3×C4—21no—
83C23×C3×C4—31no—
84C23×C3×C4—31no—
85C23×C3×C4—31no—
86C23×C3×C4—31no—
87C23×C3×C4C2×D311yescharacteristic
88C23×C3×C4C2×D311yescharacteristic
89C23×C3×C4C2×D311yescharacteristic
90C23×C3×C4C22×C311yescharacteristic
91C23×C3×C4C22×C311yescharacteristic
92C23×C3×C4C22×C311yescharacteristic
93C23×Dic3C22×C311yescharacteristic
94C23×Dic3C22×C311yescharacteristic
95C23×Dic3C22×C311yescharacteristic
96C23×Dic3C22×C311yescharacteristic
97C2×C3×C4⋊C4—34no—
98C2×C3×C4⋊C4—34no—
99C2×C3×C4⋊C4—34no—
100C2×C3×C4⋊C4—34no—
101C2×C3×C4⋊C4—64no—
102C2×C3×C4⋊C4—64no—
103C2×C3×C4⋊C4—64no—
104C2×C3×C4⋊C4—64no—
105C2×C4⋊Dic3—24no—
106C2×C4⋊Dic3C22×C314yes—
107C2×Dic3⋊C4—24no—
108C2×Dic3⋊C4—24no—
109C2×Dic3⋊C4—24no—
110C2×Dic3⋊C4C22×C314yes—
111C2×Dic3⋊C4C22×C314yes—
112C2×Dic3⋊C4C22×C314yes—
113C3×#95—24no—
114C3×#95—34no—
115C3×#95—34no—
116C3×#95C2×D314yes—
117C3×#95C22×C314yes—
118C3⋊#95C22×C314yes—
119C3⋊#95C22×C314yes—
120C23×C32C2×D412yes—
121C23×C32C2×D412yes—
122C23×C32C2×Q812yes—
123C23×C32C2×Q812yes—
124C23×C32#4112yes—
125C23×C32#4112yes—
126C23×C32#4112yes—
127C23×C32C2411yescharacteristic
128C2×C32×C4—22no—
129C2×C32×C4—22no—
130C2×C32×C4—28no—
131C2×C32×C4—22no—
132C2×C32×C4—22no—
133C2×C32×C4—22no—
134C2×C32×C4—22no—
135C2×C32×C4—22no—
136C2×C32×C4—22no—
137C2×C32×C4—44no—
138C2×C32×C4—44no—
139C2×C32×C4C2×Q814yes—
140C2×C3×Dic3—28no—
141C2×C3×Dic3—28no—
142C2×C3×Dic3—28no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—44no—
153C2×C3×Dic3C2×D414yes—
154C2×C3×Dic3C2×D414yes—
155C2×C3×Dic3C2×Q814yes—
156C22×C4⋊C4—31no—
157C22×C4⋊C4—31no—
158C22×C4⋊C4—31no—
159C22×C4⋊C4—31no—
160#398—38no—
161C2×#95—31no—
162C2×#95—31no—
163C2×#95C3×D311yescharacteristic
164C24×C3—21no—
165C24×C3C22×D311yescharacteristic
166C24×C3C23×C311yescharacteristic
167C22×C3×C4—22no—
168C22×C3×C4—22no—
169C22×C3×C4—22no—
170C22×C3×C4—22no—
171C22×C3×C4—24no—
172C22×C3×C4—24no—
173C22×C3×C4—22no—
174C22×C3×C4—22no—
175C22×C3×C4—22no—
176C22×C3×C4—22no—
177C22×C3×C4—22no—
178C22×C3×C4—22no—
179C22×C3×C4—22no—
180C22×C3×C4—22no—
181C22×C3×C4—22no—
182C22×C3×C4—22no—
183C22×C3×C4—22no—
184C22×C3×C4—22no—
185C22×C3×C4—24no—
186C22×C3×C4—22no—
187C22×C3×C4—22no—
188C22×C3×C4—22no—
189C22×C3×C4—34no—
190C22×C3×C4—34no—
191C22×C3×C4—34no—
192C22×C3×C4—32no—
193C22×C3×C4—32no—
194C22×C3×C4—32no—
195C22×C3×C4—32no—
196C22×C3×C4—42no—
197C22×C3×C4—42no—
198C22×C3×C4—42no—
199C22×C3×C4—42no—
200C22×C3×C4—42no—
201C22×C3×C4—42no—
202C22×C3×C4—62no—
203C22×C3×C4—62no—
204C22×C3×C4—62no—
205C22×C3×C4—62no—
206C22×C3×C4—62no—
207C22×C3×C4—62no—
208C22×C3×C4—62no—
209C22×C3×C4—62no—
210C22×C3×C4—62no—
211C22×C3×C4Dic614yes—
212C22×C3×C4C3×Q814yes—
213C22×C3×C4C22×D312yes—
214C22×C3×C4C22×D312yes—
215C22×C3×C4C22×D312yes—
216C22×C3×C4C23×C312yes—
217C22×C3×C4C23×C312yes—
218C22×C3×C4C23×C312yes—
219C22×Dic3—22no—
220C22×Dic3—22no—
221C22×Dic3—22no—
222C22×Dic3—22no—
223C22×Dic3—22no—
224C22×Dic3—22no—
225C22×Dic3—22no—
226C22×Dic3—22no—
227C22×Dic3—22no—
228C22×Dic3C3×D414yes—
229C22×Dic3C3×D414yes—
230C22×Dic3C3×Q814yes—
231C22×Dic3C23×C312yes—
232C22×Dic3C23×C312yes—
233C22×Dic3C23×C312yes—
234C22×Dic3C23×C312yes—
235C3×C4⋊C4—68no—
236C3×C4⋊C4—68no—
237C3×C4⋊C4—68no—
238C3×C4⋊C4—68no—
239C4⋊Dic3—28no—
240Dic3⋊C4—28no—
241Dic3⋊C4—28no—
242Dic3⋊C4—28no—
243C22×C32#12114yes—
244C22×C32C22⋊Q814yes—
245C22×C32C22⋊Q814yes—
246C22×C32#12314yes—
247C22×C32#12514yes—
248C22×C32#12514yes—
249C22×C32C4⋊Q814yes—
250C22×C32C22×D411yescharacteristic
251C22×C32C22×D411yescharacteristic
252C22×C32C22×Q811yescharacteristic
253C22×C32C22×Q811yescharacteristic
254C22×C32C2×#4111yescharacteristic
255C22×C32C2×#4111yescharacteristic
256C22×C32C2×#4111yescharacteristic
257C32×C4—24no—
258C32×C4—42no—
259C32×C4—42no—
260C3×Dic3—24no—
261C3×Dic3—24no—
262C3×Dic3—24no—
263C3×Dic3—42no—
264C23×C4—31no—
265C23×C4—31no—
266C23×C4—31no—
267C23×C4—31no—
268C23×C4C2×C3×D311yescharacteristic
269C23×C4C2×C3×D311yescharacteristic
270C23×C4C2×C3×D311yescharacteristic
271C2×C4⋊C4—34no—
272C2×C4⋊C4—34no—
273C2×C4⋊C4—34no—
274C2×C4⋊C4—34no—
275C2×C4⋊C4—64no—
276C2×C4⋊C4—64no—
277C2×C4⋊C4—64no—
278C2×C4⋊C4—64no—
279#95—34no—
280#95—34no—
281#95C2×C3×D314yes—
282C23×C3—21no—
283C23×C3—22no—
284C23×C3—22no—
285C23×C3—22no—
286C23×C3—22no—
287C23×C3—22no—
288C23×C3—22no—
289C23×C3—22no—
290C23×C3C2×Dic612yes—
291C23×C3#23512yes—
292C23×C3#23512yes—
293C23×C3D3×D412yes—
294C23×C3D3×D412yes—
295C23×C3#23712yes—
296C23×C3D3×Q812yes—
297C23×C3C2×C3×D412yes—
298C23×C3C2×C3×D412yes—
299C23×C3C2×C3×Q812yes—
300C23×C3C2×C3×Q812yes—
301C23×C3C3×#4112yes—
302C23×C3C3×#4112yes—
303C23×C3C3×#4112yes—
304C23×C3C23×D311yescharacteristic
305C23×C3C24×C311yescharacteristic
306C2×C3×C4—28no—
307C2×C3×C4—28no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—24no—
313C2×C3×C4—24no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—24no—
327C2×C3×C4—34no—
328C2×C3×C4—34no—
329C2×C3×C4—34no—
330C2×C3×C4—48no—
331C2×C3×C4—42no—
332C2×C3×C4—42no—
333C2×C3×C4—42no—
334C2×C3×C4—42no—
335C2×C3×C4—42no—
336C2×C3×C4—42no—
337C2×C3×C4—48no—
338C2×C3×C4—48no—
339C2×C3×C4—44no—
340C2×C3×C4—44no—
341C2×C3×C4—44no—
342C2×C3×C4—44no—
343C2×C3×C4—68no—
344C2×C3×C4—68no—
345C2×C3×C4—68no—
346C2×C3×C4—62no—
347C2×C3×C4—62no—
348C2×C3×C4—62no—
349C2×C3×C4—62no—
350C2×C3×C4—62no—
351C2×C3×C4—62no—
352C2×C3×C4—62no—
353C2×C3×C4—62no—
354C2×C3×C4—62no—
355C2×C3×C4—124no—
356C2×C3×C4C2×Dic614yes—
357C2×C3×C4C2×C3×Q814yes—
358C2×Dic3—28no—
359C2×Dic3—28no—
360C2×Dic3—28no—
361C2×Dic3—22no—
362C2×Dic3—22no—
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—44no—
371C2×Dic3C2×C3×D414yes—
372C2×Dic3C2×C3×D414yes—
373C2×Dic3C2×C3×Q814yes—
374C2×C32#39818yescomplemented
375C2×C32C2×#12111yescharacteristic
376C2×C32C2×C22⋊Q811yescharacteristic
377C2×C32C2×C22⋊Q811yescharacteristic
378C2×C32C2×#12311yescharacteristic
379C2×C32C2×#12511yescharacteristic
380C2×C32C2×#12511yescharacteristic
381C2×C32C2×C4⋊Q811yescharacteristic
382C24C22×C3×D311yescharacteristic
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—32no—
392C22×C4—32no—
393C22×C4—32no—
394C22×C4—34no—
395C22×C4—34no—
396C22×C4—34no—
397C22×C4—32no—
398C22×C4—62no—
399C22×C4—62no—
400C22×C4—62no—
401C22×C4—62no—
402C22×C4—62no—
403C22×C4—62no—
404C22×C4—62no—
405C22×C4—62no—
406C22×C4—62no—
407C22×C4C3×Dic614yes—
408C22×C4C22×C3×D312yes—
409C22×C4C22×C3×D312yes—
410C22×C4C22×C3×D312yes—
411C4⋊C4—68no—
412C4⋊C4—68no—
413C4⋊C4—68no—
414C4⋊C4—68no—
415C22×C3—24no—
416C22×C3—24no—
417C22×C3—24no—
418C22×C3—24no—
419C22×C3—24no—
420C22×C3—24no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—21no—
427C22×C3—21no—
428C22×C3—24no—
429C22×C3#87014yes—
430C22×C3#87814yes—
431C22×C3#88314yes—
432C22×C3#88414yes—
433C22×C3#88814yes—
434C22×C3#88914yes—
435C22×C3#89614yes—
436C22×C3C3×#12114yes—
437C22×C3C3×C22⋊Q814yes—
438C22×C3C3×C22⋊Q814yes—
439C22×C3C3×#12314yes—
440C22×C3C3×#12514yes—
441C22×C3C3×#12514yes—
442C22×C3C3×C4⋊Q814yes—
443C22×C3C22×Dic611yescharacteristic
444C22×C3C2×#23511yescharacteristic
445C22×C3C2×#23511yescharacteristic
446C22×C3C2×D3×D411yescharacteristic
447C22×C3C2×D3×D411yescharacteristic
448C22×C3C2×#23711yescharacteristic
449C22×C3C2×D3×Q811yescharacteristic
450C22×C3C22×C3×D411yescharacteristic
451C22×C3C22×C3×D411yescharacteristic
452C22×C3C22×C3×Q811yescharacteristic
453C22×C3C22×C3×Q811yescharacteristic
454C22×C3C2×C3×#4111yescharacteristic
455C22×C3C2×C3×#4111yescharacteristic
456C22×C3C2×C3×#4111yescharacteristic
457C3×C4—24no—
458C3×C4—24no—
459C3×C4—44no—
460C3×C4—44no—
461C3×C4—44no—
462C3×C4—42no—
463C3×C4—42no—
464C3×C4—42no—
465C3×C4—42no—
466C3×C4—64no—
467C3×C4—64no—
468C3×C4—64no—
469C3×C4—122no—
470Dic3—24no—
471Dic3—24no—
472Dic3—24no—
473Dic3—42no—
474C32C2×#39811yescharacteristic, complemented, Sylow
475C23C2×C3×Dic612yes—
476C23C3×#23512yes—
477C23C3×#23512yes—
478C23C3×D3×D412yes—
479C23C3×D3×D412yes—
480C23C3×#23712yes—
481C23C3×D3×Q812yes—
482C23C23×C3×D311yescharacteristic
483C2×C4—28no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—34no—
493C2×C4—34no—
494C2×C4—34no—
495C2×C4—44no—
496C2×C4—44no—
497C2×C4—68no—
498C2×C4—68no—
499C2×C4—68no—
500C2×C4—62no—
501C2×C4—62no—
502C2×C4—62no—
503C2×C4—62no—
504C2×C4—62no—
505C2×C4—62no—
506C2×C4—62no—
507C2×C4—62no—
508C2×C4—62no—
509C2×C4—124no—
510C2×C4C2×C3×Dic614yes—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—28no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3#465718yesdirect product factor
520C2×C3C3×#39818yescomplemented
521C2×C3C2×#87011yescharacteristic
522C2×C3C2×#87811yescharacteristic
523C2×C3C2×#88311yescharacteristic
524C2×C3C2×#88411yescharacteristic
525C2×C3C2×#88811yescharacteristic
526C2×C3C2×#88911yescharacteristic
527C2×C3C2×#89611yescharacteristic
528C2×C3C2×C3×#12111yescharacteristic
529C2×C3C2×C3×C22⋊Q811yescharacteristic
530C2×C3C2×C3×C22⋊Q811yescharacteristic
531C2×C3C2×C3×#12311yescharacteristic
532C2×C3C2×C3×#12511yescharacteristic
533C2×C3C2×C3×#12511yescharacteristic
534C2×C3C2×C3×C4⋊Q811yescharacteristic
535C22C3×#87014yes—
536C22C3×#87814yes—
537C22C3×#88314yes—
538C22C3×#88414yes—
539C22C3×#88814yes—
540C22C3×#88914yes—
541C22C3×#89614yes—
542C22C22×C3×Dic611yescharacteristic
543C22C2×C3×#23511yescharacteristic
544C22C2×C3×#23511yescharacteristic
545C22C2×C3×D3×D411yescharacteristic
546C22C2×C3×D3×D411yescharacteristic
547C22C2×C3×#23711yescharacteristic
548C22C2×C3×D3×Q811yescharacteristic
549C4—24no—
550C4—42no—
551C4—42no—
552C4—64no—
553C4—64no—
554C4—64no—
555C4—122no—
556C3—21no—
557C3C2×#465711yescharacteristic, direct product factor
558C3C2×C3×#39811yescharacteristic, complemented
559C2C3×#465718yesdirect product factor
560C2C2×C3×#87011yescharacteristic
561C2C2×C3×#87811yescharacteristic
562C2C2×C3×#88311yescharacteristic
563C2C2×C3×#88411yescharacteristic
564C2C2×C3×#88811yescharacteristic
565C2C2×C3×#88911yescharacteristic
566C2C2×C3×#89611yescharacteristic
subgroupG/H
centerC24×C3C22×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC2×C32×#95C2
socle, prime radicalC24×C32C23
hypercenterC2×C3×#95D3
hypocenterC3C2×C3×#398
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24×C3 ◁ C2×C3×#95

Complements

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

NH ≅ G/Ntype
8. C3×#4657C2direct (N × H)
10. C2×#4657C3direct (N × H)
45. #4657C2×C3direct (N × H)
374. C2×C32#398semidirect
474. C32C2×#398semidirect
519. C2×C3#4657direct (N × H)
520. C2×C3C3×#398semidirect
557. C3C2×#4657direct (N × H)
558. C3C2×C3×#398semidirect
559. C2C3×#4657direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C4⋊Dic32
C22×C3×Dic3⋊C42
C2×C32×#952
C2×C3×C3⋊#952
C3×#46572
C2×C3×#3983
C2×#46573