Finite Group Databasebeta

← C2×C3×#4652 #11801340

Subgroups — C2×C3×#4652 #11801340

Order 1152.

1589 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×Dic3⋊C4C211yesmaximal, characteristic
2C22×C3×Dic3⋊C4C211yesmaximal, characteristic
3C22×C3×C4×Dic3C211yesmaximal, characteristic
4C2×C32×#95C211yesmaximal, characteristic
5C2×C3×C3⋊#95C211yesmaximal, characteristic
6C2×C3×C3⋊#95C211yesmaximal, characteristic
7C2×C3×C3⋊#95C211yesmaximal, characteristic
8C3×#4652C218yesmaximal, direct product factor
9C2×C3×#387—31nomaximal
10C2×#4652C311yesmaximal, 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×Dic3⋊C4—24no—
19C2×C3×Dic3⋊C4C418yescomplemented
20C2×C3×Dic3⋊C4C2214yes—
21C2×C3×Dic3⋊C4C2214yes—
22C2×C3×C4×Dic3—24no—
23C2×C3×C4×Dic3C2214yes—
24C32×#95C2214yes—
25C3×C3⋊#95C2214yes—
26C3×C3⋊#95C2214yes—
27C3×C3⋊#95C2214yes—
28C22×C3×C4⋊C4—31no—
29C22×C3×C4⋊C4—31no—
30C22×C3×C42—31no—
31C22×Dic3⋊C4C2×C311yescharacteristic
32C22×Dic3⋊C4C2×C311yescharacteristic
33C22×C4×Dic3C2×C311yescharacteristic
34C3×#387—38no—
35C2×C3×#95—21no—
36C2×C3×#95—31no—
37C2×C3×#95—31no—
38C2×C3×#95—31no—
39C2×C3×#95D311yescharacteristic
40C2×C3×#95C2×C311yescharacteristic
41C2×C3⋊#95C2×C311yescharacteristic
42C2×C3⋊#95C2×C311yescharacteristic
43C2×C3⋊#95C2×C311yescharacteristic
44#4652C2×C318yesdirect product factor
45C24×C32C2311yescharacteristic
46C22×C32×C4—22no—
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×C4C2×C414yes—
55C22×C32×C4C2312yes—
56C22×C32×C4C2312yes—
57C22×C32×C4C2312yes—
58C22×C3×Dic3—22no—
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×Dic3C2×C414yes—
67C22×C3×Dic3C2×C414yes—
68C22×C3×Dic3D414yes—
69C22×C3×Dic3Q814yes—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C3×Dic3⋊C4—28no—
75C3×Dic3⋊C4C2×C4116yescomplemented
76C3×C4×Dic3—28no—
77C2×#387—31noSylow
78C23×C3×C4—21no—
79C23×C3×C4—21no—
80C23×C3×C4—21no—
81C23×C3×C4—31no—
82C23×C3×C4—31no—
83C23×C3×C4—31no—
84C23×C3×C4—31no—
85C23×C3×C4C2×D311yescharacteristic
86C23×C3×C4C2×D311yescharacteristic
87C23×C3×C4C2×D311yescharacteristic
88C23×C3×C4C22×C311yescharacteristic
89C23×C3×C4C22×C311yescharacteristic
90C23×C3×C4C22×C311yescharacteristic
91C23×Dic3C22×C311yescharacteristic
92C23×Dic3C22×C311yescharacteristic
93C23×Dic3C22×C311yescharacteristic
94C23×Dic3C22×C311yescharacteristic
95C2×C3×C4⋊C4—38no—
96C2×C3×C4⋊C4—34no—
97C2×C3×C4⋊C4—34no—
98C2×C3×C4⋊C4—64no—
99C2×C3×C42—34no—
100C2×C3×C42—64no—
101C2×Dic3⋊C4—24no—
102C2×Dic3⋊C4C3×C418yescomplemented
103C2×Dic3⋊C4C22×C314yes—
104C2×Dic3⋊C4C22×C314yes—
105C2×C4×Dic3—24no—
106C2×C4×Dic3C22×C314yes—
107C3×#95—24no—
108C3×#95—34no—
109C3×#95—34no—
110C3×#95—34no—
111C3×#95C2×D314yes—
112C3×#95C22×C314yes—
113C3⋊#95C22×C314yes—
114C3⋊#95C22×C314yes—
115C3⋊#95C22×C314yes—
116C23×C32C22×C412yes—
117C23×C32C2×D412yes—
118C23×C32C2×Q812yes—
119C23×C32#4112yes—
120C23×C32#4112yes—
121C23×C32#4112yes—
122C23×C32#4112yes—
123C23×C32C2411yescharacteristic
124C2×C32×C4—22no—
125C2×C32×C4—22no—
126C2×C32×C4—28no—
127C2×C32×C4—22no—
128C2×C32×C4—22no—
129C2×C32×C4—22no—
130C2×C32×C4—22no—
131C2×C32×C4—22no—
132C2×C32×C4—22no—
133C2×C32×C4—44no—
134C2×C32×C4—44no—
135C2×C32×C4C22×C414yes—
136C2×C3×Dic3—28no—
137C2×C3×Dic3—28no—
138C2×C3×Dic3—28no—
139C2×C3×Dic3—28no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3C22×C414yes—
149C2×C3×Dic3C22×C414yes—
150C2×C3×Dic3C2×D414yes—
151C2×C3×Dic3C2×Q814yes—
152C22×C4⋊C4—31no—
153C22×C4⋊C4—31no—
154C22×C42—31no—
155#387—38no—
156C2×#95—31no—
157C2×#95—31no—
158C2×#95—31no—
159C2×#95C3×D311yescharacteristic
160C24×C3—21no—
161C24×C3C22×D311yescharacteristic
162C24×C3C23×C311yescharacteristic
163C22×C3×C4—22no—
164C22×C3×C4—22no—
165C22×C3×C4—22no—
166C22×C3×C4—22no—
167C22×C3×C4—24no—
168C22×C3×C4—24no—
169C22×C3×C4—22no—
170C22×C3×C4—22no—
171C22×C3×C4—22no—
172C22×C3×C4—22no—
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—24no—
182C22×C3×C4—22no—
183C22×C3×C4—22no—
184C22×C3×C4—22no—
185C22×C3×C4—34no—
186C22×C3×C4—34no—
187C22×C3×C4—34no—
188C22×C3×C4—34no—
189C22×C3×C4—32no—
190C22×C3×C4—32no—
191C22×C3×C4—32no—
192C22×C3×C4—32no—
193C22×C3×C4—42no—
194C22×C3×C4—42no—
195C22×C3×C4—42no—
196C22×C3×C4—42no—
197C22×C3×C4—42no—
198C22×C3×C4—42no—
199C22×C3×C4—62no—
200C22×C3×C4—62no—
201C22×C3×C4—62no—
202C22×C3×C4—62no—
203C22×C3×C4—62no—
204C22×C3×C4—62no—
205C22×C3×C4—62no—
206C22×C3×C4—62no—
207C22×C3×C4C4×D314yes—
208C22×C3×C4C2×C3×C414yes—
209C22×C3×C4C22×D312yes—
210C22×C3×C4C22×D312yes—
211C22×C3×C4C22×D312yes—
212C22×C3×C4C23×C312yes—
213C22×C3×C4C23×C312yes—
214C22×C3×C4C23×C312yes—
215C22×Dic3—22no—
216C22×Dic3—22no—
217C22×Dic3—22no—
218C22×Dic3—22no—
219C22×Dic3—22no—
220C22×Dic3—22no—
221C22×Dic3—22no—
222C22×Dic3—22no—
223C22×Dic3C2×C3×C414yes—
224C22×Dic3C2×C3×C414yes—
225C22×Dic3C3×D414yes—
226C22×Dic3C3×Q814yes—
227C22×Dic3C23×C312yes—
228C22×Dic3C23×C312yes—
229C22×Dic3C23×C312yes—
230C22×Dic3C23×C312yes—
231C3×C4⋊C4—316no—
232C3×C4⋊C4—68no—
233C3×C42—68no—
234Dic3⋊C4—28no—
235Dic3⋊C4C2×C3×C4116yescomplemented
236C4×Dic3—28no—
237C22×C32#11714yes—
238C22×C32C4×D414yes—
239C22×C32C4×Q814yes—
240C22×C32C22⋊Q814yes—
241C22×C32#12314yes—
242C22×C32#12514yes—
243C22×C32#12614yes—
244C22×C32C23×C411yescharacteristic
245C22×C32C22×D411yescharacteristic
246C22×C32C22×Q811yescharacteristic
247C22×C32C2×#4111yescharacteristic
248C22×C32C2×#4111yescharacteristic
249C22×C32C2×#4111yescharacteristic
250C22×C32C2×#4111yescharacteristic
251C32×C4—24no—
252C32×C4—42no—
253C32×C4—42no—
254C3×Dic3—24no—
255C3×Dic3—24no—
256C3×Dic3—24no—
257C3×Dic3—24no—
258C23×C4—31no—
259C23×C4—31no—
260C23×C4—31no—
261C23×C4—31no—
262C23×C4C2×C3×D311yescharacteristic
263C23×C4C2×C3×D311yescharacteristic
264C23×C4C2×C3×D311yescharacteristic
265C2×C4⋊C4—38no—
266C2×C4⋊C4—34no—
267C2×C4⋊C4—34no—
268C2×C4⋊C4—64no—
269C2×C42—34no—
270C2×C42—64no—
271#95—34no—
272#95—34no—
273#95—34no—
274#95C2×C3×D314yes—
275C23×C3—21no—
276C23×C3—22no—
277C23×C3—22no—
278C23×C3—22no—
279C23×C3—22no—
280C23×C3—22no—
281C23×C3—22no—
282C23×C3—22no—
283C23×C3C2×C4×D312yes—
284C23×C3#23512yes—
285C23×C3#23512yes—
286C23×C3D3×D412yes—
287C23×C3#23712yes—
288C23×C3#23712yes—
289C23×C3D3×Q812yes—
290C23×C3C22×C3×C412yes—
291C23×C3C2×C3×D412yes—
292C23×C3C2×C3×Q812yes—
293C23×C3C3×#4112yes—
294C23×C3C3×#4112yes—
295C23×C3C3×#4112yes—
296C23×C3C3×#4112yes—
297C23×C3C23×D311yescharacteristic
298C23×C3C24×C311yescharacteristic
299C2×C3×C4—28no—
300C2×C3×C4—28no—
301C2×C3×C4—22no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—24no—
306C2×C3×C4—24no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—24no—
320C2×C3×C4—34no—
321C2×C3×C4—34no—
322C2×C3×C4—34no—
323C2×C3×C4—34no—
324C2×C3×C4—48no—
325C2×C3×C4—42no—
326C2×C3×C4—42no—
327C2×C3×C4—42no—
328C2×C3×C4—42no—
329C2×C3×C4—42no—
330C2×C3×C4—42no—
331C2×C3×C4—48no—
332C2×C3×C4—48no—
333C2×C3×C4—44no—
334C2×C3×C4—44no—
335C2×C3×C4—44no—
336C2×C3×C4—44no—
337C2×C3×C4—68no—
338C2×C3×C4—68no—
339C2×C3×C4—68no—
340C2×C3×C4—68no—
341C2×C3×C4—62no—
342C2×C3×C4—62no—
343C2×C3×C4—62no—
344C2×C3×C4—62no—
345C2×C3×C4—62no—
346C2×C3×C4—62no—
347C2×C3×C4—62no—
348C2×C3×C4—62no—
349C2×C3×C4C2×C4×D314yes—
350C2×C3×C4C22×C3×C414yes—
351C2×Dic3—28no—
352C2×Dic3—28no—
353C2×Dic3—28no—
354C2×Dic3—28no—
355C2×Dic3—22no—
356C2×Dic3—22no—
357C2×Dic3—22no—
358C2×Dic3—22no—
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—22no—
362C2×Dic3—22no—
363C2×Dic3C22×C3×C414yes—
364C2×Dic3C22×C3×C414yes—
365C2×Dic3C2×C3×D414yes—
366C2×Dic3C2×C3×Q814yes—
367C2×C32#38718yescomplemented
368C2×C32C2×#11711yescharacteristic
369C2×C32C2×C4×D411yescharacteristic
370C2×C32C2×C4×Q811yescharacteristic
371C2×C32C2×C22⋊Q811yescharacteristic
372C2×C32C2×#12311yescharacteristic
373C2×C32C2×#12511yescharacteristic
374C2×C32C2×#12611yescharacteristic
375C24C22×C3×D311yescharacteristic
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—32no—
385C22×C4—32no—
386C22×C4—32no—
387C22×C4—32no—
388C22×C4—34no—
389C22×C4—34no—
390C22×C4—34no—
391C22×C4—34no—
392C22×C4—62no—
393C22×C4—62no—
394C22×C4—62no—
395C22×C4—62no—
396C22×C4—62no—
397C22×C4—62no—
398C22×C4—62no—
399C22×C4—62no—
400C22×C4C3×C4×D314yes—
401C22×C4C22×C3×D312yes—
402C22×C4C22×C3×D312yes—
403C22×C4C22×C3×D312yes—
404C4⋊C4—316no—
405C4⋊C4—68no—
406C42—68no—
407C22×C3—24no—
408C22×C3—24no—
409C22×C3—24no—
410C22×C3—24no—
411C22×C3—24no—
412C22×C3—24no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—21no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—24no—
421C22×C3#87214yes—
422C22×C3#87914yes—
423C22×C3#67⋊C414yes—
424C22×C3#88314yes—
425C22×C3#88714yes—
426C22×C3#88914yes—
427C22×C3#89614yes—
428C22×C3C3×#11714yes—
429C22×C3C3×C4×D414yes—
430C22×C3C3×C4×Q814yes—
431C22×C3C3×C22⋊Q814yes—
432C22×C3C3×#12314yes—
433C22×C3C3×#12514yes—
434C22×C3C3×#12614yes—
435C22×C3C22×C4×D311yescharacteristic
436C22×C3C2×#23511yescharacteristic
437C22×C3C2×#23511yescharacteristic
438C22×C3C2×D3×D411yescharacteristic
439C22×C3C2×#23711yescharacteristic
440C22×C3C2×#23711yescharacteristic
441C22×C3C2×D3×Q811yescharacteristic
442C22×C3C23×C3×C411yescharacteristic
443C22×C3C22×C3×D411yescharacteristic
444C22×C3C22×C3×Q811yescharacteristic
445C22×C3C2×C3×#4111yescharacteristic
446C22×C3C2×C3×#4111yescharacteristic
447C22×C3C2×C3×#4111yescharacteristic
448C22×C3C2×C3×#4111yescharacteristic
449C3×C4—24no—
450C3×C4—24no—
451C3×C4—44no—
452C3×C4—44no—
453C3×C4—44no—
454C3×C4—42no—
455C3×C4—42no—
456C3×C4—42no—
457C3×C4—42no—
458C3×C4—64no—
459C3×C4—64no—
460C3×C4—64no—
461C3×C4—64no—
462Dic3—24no—
463Dic3—24no—
464Dic3—24no—
465Dic3—24no—
466C32C2×#38711yescharacteristic, complemented, Sylow
467C23C2×C3×C4×D312yes—
468C23C3×#23512yes—
469C23C3×#23512yes—
470C23C3×D3×D412yes—
471C23C3×#23712yes—
472C23C3×#23712yes—
473C23C3×D3×Q812yes—
474C23C23×C3×D311yescharacteristic
475C2×C4—28no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—34no—
485C2×C4—34no—
486C2×C4—34no—
487C2×C4—34no—
488C2×C4—44no—
489C2×C4—44no—
490C2×C4—68no—
491C2×C4—68no—
492C2×C4—68no—
493C2×C4—62no—
494C2×C4—62no—
495C2×C4—62no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—62no—
499C2×C4—62no—
500C2×C4—62no—
501C2×C4—68no—
502C2×C4C2×C3×C4×D314yes—
503C2×C3—21no—
504C2×C3—28no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3#465218yesdirect product factor
512C2×C3C3×#38718yescomplemented
513C2×C3C2×#87211yescharacteristic
514C2×C3C2×#87911yescharacteristic
515C2×C3C2×#67⋊C411yescharacteristic
516C2×C3C2×#88311yescharacteristic
517C2×C3C2×#88711yescharacteristic
518C2×C3C2×#88911yescharacteristic
519C2×C3C2×#89611yescharacteristic
520C2×C3C2×C3×#11711yescharacteristic
521C2×C3C2×C3×C4×D411yescharacteristic
522C2×C3C2×C3×C4×Q811yescharacteristic
523C2×C3C2×C3×C22⋊Q811yescharacteristic
524C2×C3C2×C3×#12311yescharacteristic
525C2×C3C2×C3×#12511yescharacteristic
526C2×C3C2×C3×#12611yescharacteristic
527C22C3×#87214yes—
528C22C3×#87914yes—
529C22C3×#67⋊C414yes—
530C22C3×#88314yes—
531C22C3×#88714yes—
532C22C3×#88914yes—
533C22C3×#89614yes—
534C22C22×C3×C4×D311yescharacteristic
535C22C2×C3×#23511yescharacteristic
536C22C2×C3×#23511yescharacteristic
537C22C2×C3×D3×D411yescharacteristic
538C22C2×C3×#23711yescharacteristic
539C22C2×C3×#23711yescharacteristic
540C22C2×C3×D3×Q811yescharacteristic
541C4—24no—
542C4—42no—
543C4—42no—
544C4—64no—
545C4—64no—
546C4—64no—
547C4—64no—
548C3—21no—
549C3C2×#465211yescharacteristic, direct product factor
550C3C2×C3×#38711yescharacteristic, complemented
551C2C3×#465218yesdirect product factor
552C2C2×C3×#87211yescharacteristic
553C2C2×C3×#87911yescharacteristic
554C2C2×C3×#67⋊C411yescharacteristic
555C2C2×C3×#88311yescharacteristic
556C2C2×C3×#88711yescharacteristic
557C2C2×C3×#88911yescharacteristic
558C2C2×C3×#89611yescharacteristic
subgroupG/H
centerC24×C3C22×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC2×C32×#95C2
socle, prime radicalC24×C32C23
cosocleC23×C3C24×C3
hypercenterC2×C3×#95D3
hypocenterC3C2×C3×#387
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C24×C3 ◁ C2×C3×#95

Complements

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

NH ≅ G/Ntype
8. C3×#4652C2direct (N × H)
10. C2×#4652C3direct (N × H)
19. C2×C3×Dic3⋊C4C4semidirect
44. #4652C2×C3direct (N × H)
75. C3×Dic3⋊C4C2×C4semidirect
102. C2×Dic3⋊C4C3×C4semidirect
235. Dic3⋊C4C2×C3×C4semidirect
367. C2×C32#387semidirect
466. C32C2×#387semidirect
511. C2×C3#4652direct (N × H)
512. C2×C3C3×#387semidirect
549. C3C2×#4652direct (N × H)
550. C3C2×C3×#387semidirect
551. C2C3×#4652direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×Dic3⋊C42
C22×C3×C4×Dic32
C2×C32×#952
C2×C3×C3⋊#952
C3×#46522
C2×C3×#3873
C2×#46523