Finite Group Databasebeta

← C3×C4×#806 #11783749

Subgroups — C3×C4×#806 #11783749

Order 1152.

953 conjugacy classes of subgroups.

The subgroup lattice has 599 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×#67C211yesmaximal, characteristic
2C32×C4×C22⋊C4C211yesmaximal, characteristic, complemented
3C3×C4×#217C211yesmaximal, characteristic, complemented
4C2×C3×#806C212yesmaximal
5C3×#4527C212yesmaximal, complemented
6C3×C4×#99—31nomaximal
7C4×#806C311yesmaximal, characteristic, direct product factor
8C23×C32×C4C2211yescharacteristic
9C22×C3×#67C2211yescharacteristic
10C22×C3×C4×D3C411yescharacteristic, complemented
11C2×C32×C22⋊C4C2212yes—
12C2×C32×C42—21no—
13C2×C3×#217C2211yescharacteristic
14C2×C3×#217C2212yes—
15C3×C4×#67—21no—
16C3×C4×#67—21no—
17C3×C4×#67—21no—
18C3×C4×#67—21no—
19C2×C3×(C2×D3)⋊C4C411yescharacteristic, complemented
20C2×C3×Dic3⋊C4C411yescharacteristic, complemented
21C2×C3×C4×Dic3—21no—
22C2×C3×C4×Dic3C411yescharacteristic, complemented
23C32×#95—21no—
24C3×C3⋊#95—21no—
25C3×#806C418yesdirect product factor
26C2×C3×C4×D4—31no—
27C2×C4×#67C2×C311yescharacteristic
28C2×C3×#99—32no—
29C3×C4×C22⋊C4—21no—
30C3×C4×C22⋊C4—31no—
31C3×C4×C22⋊C4D311yescharacteristic, complemented
32C3×C4×C22⋊C4C2×C311yescharacteristic, complemented
33C4×#217C2×C311yescharacteristic, complemented
34C2×#806C2×C312yes—
35C3×#342—32no—
36#4527C2×C312yescomplemented
37C24×C32C2311yescharacteristic
38C23×C3×D3C2×C411yescharacteristic
39C22×C32×C4—22no—
40C22×C32×C4—42no—
41C22×C32×C4C2×C411yescharacteristic
42C22×C32×C4C2×C411yescharacteristic
43C22×C32×C4D411yescharacteristic
44C22×C32×C4D411yescharacteristic
45C22×C32×C4D411yescharacteristic
46C22×C32×C4D411yescharacteristic
47C2×C3×#67—21no—
48C2×C3×#67—21no—
49C2×C3×#67—22no—
50C2×C3×#67C2×C414yes—
51C22×C3×Dic3—22no—
52C22×C3×Dic3C2×C411yescharacteristic
53C22×C3×Dic3C2×C411yescharacteristic
54C22×C3×Dic3C2×C411yescharacteristic
55C2×C3×C4×D3—21no—
56C2×C3×C4×D3—21no—
57C2×C3×C4×D3—42no—
58C32×C22⋊C4—22no—
59C32×C22⋊C4C2×C414yescomplemented
60C32×C42—42no—
61C3×#217—21no—
62C3×#217—21no—
63C3×#217—22no—
64C3×#217C2×C414yescomplemented
65C3×(C2×D3)⋊C4—21no—
66C3×(C2×D3)⋊C4—21no—
67C3×Dic3⋊C4—21no—
68C3×Dic3⋊C4—21no—
69C3×C4×Dic3—21no—
70C3×C4×Dic3—21no—
71C3×C4×Dic3—42no—
72C4×#99—31noSylow
73C22×C3×D4—31no—
74C23×C3×C4—21no—
75C23×C3×C4—31no—
76C23×C3×C4C2×D311yescharacteristic
77C23×C3×C4C22×C311yescharacteristic
78C22×#67C22×C311yescharacteristic
79C22×C4×D3C3×C411yescharacteristic, complemented
80C3×C4×D4—61no—
81C3×C4×D4—61no—
82C3×C4×D4—61no—
83C3×C4×D4—61no—
84C2×C3×C4⋊C4—31no—
85C2×C3×C22⋊C4—22no—
86C2×C3×C22⋊C4—32no—
87C2×C3×C22⋊C4—31no—
88C2×C3×C22⋊C4—31no—
89C2×C3×C22⋊C4C2×D312yes—
90C2×C3×C22⋊C4C22×C312yes—
91C2×C3×C42—22no—
92C2×C3×C42—21no—
93C2×C3×C42—21no—
94C2×C3×C42—31no—
95C2×C3×C42—61no—
96C2×#217C22×C311yescharacteristic
97C2×#217C22×C312yes—
98C4×#67—21no—
99C4×#67—21no—
100C4×#67—21no—
101C4×#67—21no—
102C2×(C2×D3)⋊C4C3×C411yescharacteristic, complemented
103C2×Dic3⋊C4C3×C411yescharacteristic, complemented
104C2×C4×Dic3—21no—
105C2×C4×Dic3C3×C411yescharacteristic, complemented
106C3×#99—38no—
107C3×#95—22no—
108C3×#95—21no—
109C3×#95—21no—
110C3×#95—61no—
111C3⋊#95—21no—
112#806C3×C418yesdirect product factor
113C23×C32—41no—
114C23×C32—41no—
115C23×C32C22×C411yescharacteristic
116C23×C32C22×C412yes—
117C23×C32C2×D411yescharacteristic
118C23×C32C2×D411yescharacteristic
119C23×C32#4112yes—
120C22×C3×D3—21no—
121C22×C3×D3—21no—
122C22×C3×D3—41no—
123C22×C3×D3—41no—
124C22×C3×D3C4212yescomplemented
125C2×C32×C4—22no—
126C2×C32×C4—24no—
127C2×C32×C4—22no—
128C2×C32×C4—22no—
129C2×C32×C4—41no—
130C2×C32×C4—41no—
131C2×C32×C4—41no—
132C2×C32×C4—42no—
133C2×C32×C4—42no—
134C2×C32×C4C22⋊C411yescharacteristic
135C2×C32×C4C22⋊C411yescharacteristic
136C2×C32×C4C22⋊C411yescharacteristic
137C2×C32×C4C22⋊C411yescharacteristic
138C3×#67—24no—
139C3×#67—24no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—24no—
145C2×C3×Dic3—42no—
146C2×C3×Dic3—42no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3C4212yescomplemented
150C3×C4×D3—42no—
151C3×C4×D3—42no—
152C2×C4×D4—31no—
153C2×#99—32no—
154C4×C22⋊C4—31no—
155C4×C22⋊C4C3×D311yescharacteristic, complemented
156#342—32no—
157C24×C3—21no—
158C24×C3—31no—
159C24×C3C22×D311yescharacteristic
160C24×C3C23×C311yescharacteristic
161C23×D3C2×C3×C411yescharacteristic
162C2×C3×D4—34no—
163C2×C3×D4—61no—
164C2×C3×D4—62no—
165C2×C3×D4—61no—
166C22×C3×C4—24no—
167C22×C3×C4—22no—
168C22×C3×C4—22no—
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—31no—
176C22×C3×C4—31no—
177C22×C3×C4—31no—
178C22×C3×C4—42no—
179C22×C3×C4—42no—
180C22×C3×C4—44no—
181C22×C3×C4—62no—
182C22×C3×C4—61no—
183C22×C3×C4—61no—
184C22×C3×C4—122no—
185C22×C3×C4C4×D311yescharacteristic
186C22×C3×C4C4×D311yescharacteristic
187C22×C3×C4D1211yescharacteristic
188C22×C3×C4D1211yescharacteristic
189C22×C3×C4#6711yescharacteristic
190C22×C3×C4#6711yescharacteristic
191C22×C3×C4C2×C3×C411yescharacteristic
192C22×C3×C4C2×C3×C411yescharacteristic
193C22×C3×C4C3×D411yescharacteristic
194C22×C3×C4C3×D411yescharacteristic
195C22×C3×C4C3×D411yescharacteristic
196C22×C3×C4C3×D411yescharacteristic
197C2×#67—21no—
198C2×#67—21no—
199C2×#67—22no—
200C2×#67C2×C3×C414yes—
201C22×Dic3—22no—
202C22×Dic3C2×C3×C411yescharacteristic
203C22×Dic3C2×C3×C411yescharacteristic
204C22×Dic3C2×C3×C411yescharacteristic
205C2×C4×D3—21no—
206C2×C4×D3—21no—
207C2×C4×D3—42no—
208C3×C4⋊C4—61no—
209C3×C4⋊C4—61no—
210C3×C22⋊C4—24no—
211C3×C22⋊C4—22no—
212C3×C22⋊C4—22no—
213C3×C22⋊C4—24no—
214C3×C22⋊C4—34no—
215C3×C22⋊C4—61no—
216C3×C22⋊C4—62no—
217C3×C22⋊C4—61no—
218C3×C22⋊C4—61no—
219C3×C22⋊C4—61no—
220C3×C22⋊C4C4×D314yescomplemented
221C3×C22⋊C4C2×C3×C414yescomplemented
222C3×C42—44no—
223C3×C42—42no—
224C3×C42—42no—
225C3×C42—61no—
226C3×C42—61no—
227C3×C42—122no—
228#217—21no—
229#217—21no—
230#217—22no—
231#217C2×C3×C414yescomplemented
232(C2×D3)⋊C4—21no—
233(C2×D3)⋊C4—21no—
234Dic3⋊C4—21no—
235Dic3⋊C4—21no—
236C4×Dic3—21no—
237C4×Dic3—21no—
238C4×Dic3—42no—
239C22×C32—21no—
240C22×C32—21no—
241C22×C32—21no—
242C22×C32—21no—
243C22×C32—21no—
244C22×C32—21no—
245C22×C32—42no—
246C22×C32—42no—
247C22×C32C2×C4211yescharacteristic
248C22×C32C2×C22⋊C411yescharacteristic
249C22×C32#11711yescharacteristic
250C22×C32C4×D412yes—
251C22×C32C4×D412yes—
252C2×C3×D3—22no—
253C2×C3×D3—42no—
254C2×C3×D3—41no—
255C2×C3×D3—41no—
256C2×C3×D3—42no—
257C32×C4—21no—
258C32×C4—21no—
259C32×C4—21no—
260C32×C4—44no—
261C32×C4#9912yescomplemented
262C3×Dic3—22no—
263C3×Dic3—44no—
264C3×Dic3—41no—
265C3×Dic3—41no—
266C22×D4—31no—
267C23×C4—31no—
268C23×C4C2×C3×D311yescharacteristic
269C4×D4—61no—
270C4×D4—61no—
271C4×D4—61no—
272C4×D4—61no—
273C2×C4⋊C4—31no—
274C2×C22⋊C4—32no—
275C2×C22⋊C4—31no—
276C2×C22⋊C4—31no—
277C2×C22⋊C4C2×C3×D312yes—
278C2×C42—21no—
279C2×C42—31no—
280C2×C42—61no—
281#99—38no—
282#95—21no—
283#95—61no—
284C23×C3—22no—
285C23×C3—21no—
286C23×C3—21no—
287C23×C3—22no—
288C23×C3—21no—
289C23×C3—32no—
290C23×C3—41no—
291C23×C3—41no—
292C23×C3—41no—
293C23×C3—41no—
294C23×C3—42no—
295C23×C3—42no—
296C23×C3—61no—
297C23×C3—61no—
298C23×C3—121no—
299C23×C3—121no—
300C23×C3C2×C4×D311yescharacteristic
301C23×C3C2×C4×D312yes—
302C23×C3C2×D1211yescharacteristic
303C23×C3#23512yes—
304C23×C3C2×#6711yescharacteristic
305C23×C3C22×C3×C411yescharacteristic
306C23×C3C22×C3×C412yes—
307C23×C3C2×C3×D411yescharacteristic
308C23×C3C2×C3×D411yescharacteristic
309C23×C3C3×#4112yes—
310C22×D3—21no—
311C22×D3—21no—
312C22×D3—41no—
313C22×D3—41no—
314C22×D3C3×C4212yescomplemented
315C3×D4—64no—
316C3×D4—64no—
317C2×C3×C4—24no—
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—28no—
325C2×C3×C4—24no—
326C2×C3×C4—24no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—32no—
332C2×C3×C4—42no—
333C2×C3×C4—42no—
334C2×C3×C4—41no—
335C2×C3×C4—41no—
336C2×C3×C4—41no—
337C2×C3×C4—41no—
338C2×C3×C4—41no—
339C2×C3×C4—41no—
340C2×C3×C4—42no—
341C2×C3×C4—42no—
342C2×C3×C4—44no—
343C2×C3×C4—42no—
344C2×C3×C4—42no—
345C2×C3×C4—44no—
346C2×C3×C4—42no—
347C2×C3×C4—42no—
348C2×C3×C4—42no—
349C2×C3×C4—61no—
350C2×C3×C4—61no—
351C2×C3×C4—64no—
352C2×C3×C4—61no—
353C2×C3×C4—61no—
354C2×C3×C4—122no—
355C2×C3×C4—122no—
356C2×C3×C4—122no—
357C2×C3×C4—122no—
358C2×C3×C4—121no—
359C2×C3×C4—121no—
360C2×C3×C4(C2×D3)⋊C411yescharacteristic
361C2×C3×C4(C2×D3)⋊C411yescharacteristic
362C2×C3×C4(C2×D3)⋊C411yescharacteristic
363C2×C3×C4(C2×D3)⋊C411yescharacteristic
364C2×C3×C4C3×C22⋊C411yescharacteristic
365C2×C3×C4C3×C22⋊C411yescharacteristic
366C2×C3×C4C3×C22⋊C411yescharacteristic
367C2×C3×C4C3×C22⋊C411yescharacteristic
368#67—24no—
369#67—24no—
370C2×Dic3—21no—
371C2×Dic3—21no—
372C2×Dic3—21no—
373C2×Dic3—21no—
374C2×Dic3—24no—
375C2×Dic3—42no—
376C2×Dic3—42no—
377C2×Dic3—41no—
378C2×Dic3—41no—
379C2×Dic3C3×C4212yescomplemented
380C4×D3—42no—
381C4×D3—42no—
382C2×C32—22no—
383C2×C32—22no—
384C2×C32—21no—
385C2×C32—21no—
386C2×C32C4×C22⋊C411yescharacteristic
387C2×C32C2×#9911yescharacteristic
388C2×C32#41011yescharacteristic
389C3×D3—42no—
390C24—31no—
391C24C22×C3×D311yescharacteristic
392C2×D4—34no—
393C2×D4—61no—
394C2×D4—62no—
395C2×D4—61no—
396C22×C4—22no—
397C22×C4—31no—
398C22×C4—31no—
399C22×C4—31no—
400C22×C4—42no—
401C22×C4—62no—
402C22×C4—61no—
403C22×C4—61no—
404C22×C4—122no—
405C22×C4C3×C4×D311yescharacteristic
406C22×C4C3×C4×D311yescharacteristic
407C22×C4C3×D1211yescharacteristic
408C22×C4C3×D1211yescharacteristic
409C22×C4C3×#6711yescharacteristic
410C22×C4C3×#6711yescharacteristic
411C4⋊C4—61no—
412C4⋊C4—61no—
413C22⋊C4—22no—
414C22⋊C4—34no—
415C22⋊C4—61no—
416C22⋊C4—62no—
417C22⋊C4—61no—
418C22⋊C4—61no—
419C22⋊C4—61no—
420C22⋊C4C3×C4×D314yescomplemented
421C42—42no—
422C42—61no—
423C42—61no—
424C42—122no—
425C22×C3—22no—
426C22×C3—22no—
427C22×C3—21no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—22no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—22no—
444C22×C3—41no—
445C22×C3—41no—
446C22×C3—41no—
447C22×C3—41no—
448C22×C3—42no—
449C22×C3—42no—
450C22×C3—42no—
451C22×C3—42no—
452C22×C3—44no—
453C22×C3—44no—
454C22×C3—62no—
455C22×C3—122no—
456C22×C3—122no—
457C22×C3—121no—
458C22×C3—121no—
459C22×C3C42×D311yescharacteristic
460C22×C3#87211yescharacteristic
461C22×C3C4×D1212yes—
462C22×C3C2×(C2×D3)⋊C411yescharacteristic
463C22×C3C4×#6712yes—
464C22×C3C2×C3×C4211yescharacteristic
465C22×C3C2×C3×C22⋊C411yescharacteristic
466C22×C3C3×#11711yescharacteristic
467C22×C3C3×C4×D412yes—
468C22×C3C3×C4×D412yes—
469C2×D3—22no—
470C2×D3—42no—
471C2×D3—41no—
472C2×D3—41no—
473C2×D3—42no—
474C3×C4—22no—
475C3×C4—21no—
476C3×C4—21no—
477C3×C4—21no—
478C3×C4—21no—
479C3×C4—21no—
480C3×C4—21no—
481C3×C4—22no—
482C3×C4—41no—
483C3×C4—41no—
484C3×C4—48no—
485C3×C4—44no—
486C3×C4—44no—
487C3×C4—62no—
488C3×C4—124no—
489C3×C4—121no—
490C3×C4—121no—
491C3×C4#80612yesdirect product factor
492C3×C4C3×#9912yescomplemented
493Dic3—22no—
494Dic3—44no—
495Dic3—41no—
496Dic3—41no—
497C32C4×#9911yescharacteristic, complemented, Sylow
498C23—32no—
499C23—41no—
500C23—41no—
501C23—61no—
502C23—61no—
503C23—121no—
504C23—121no—
505C23C2×C3×C4×D311yescharacteristic
506C23C2×C3×C4×D312yes—
507C23C2×C3×D1211yescharacteristic
508C23C3×#23512yes—
509C23C2×C3×#6711yescharacteristic
510D4—64no—
511D4—64no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—24no—
516C2×C4—32no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—61no—
523C2×C4—61no—
524C2×C4—61no—
525C2×C4—61no—
526C2×C4—64no—
527C2×C4—122no—
528C2×C4—122no—
529C2×C4—122no—
530C2×C4—122no—
531C2×C4—121no—
532C2×C4—121no—
533C2×C4C3×(C2×D3)⋊C411yescharacteristic
534C2×C4C3×(C2×D3)⋊C411yescharacteristic
535C2×C4C3×(C2×D3)⋊C411yescharacteristic
536C2×C4C3×(C2×D3)⋊C411yescharacteristic
537C2×C3—24no—
538C2×C3—22no—
539C2×C3—22no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—22no—
543C2×C3—22no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—42no—
550C2×C3—41no—
551C2×C3—41no—
552C2×C3—122no—
553C2×C3C4×(C2×D3)⋊C411yescharacteristic
554C2×C3C2×#80611yescharacteristic
555C2×C3#500611yescharacteristic
556C2×C3C3×C4×C22⋊C411yescharacteristic
557C2×C3C2×C3×#9911yescharacteristic
558C2×C3C3×#41011yescharacteristic
559D3—42no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—21no—
565C22—21no—
566C22—42no—
567C22—42no—
568C22—62no—
569C22—122no—
570C22—122no—
571C22—121no—
572C22—121no—
573C22C3×C42×D311yescharacteristic
574C22C3×#87211yescharacteristic
575C22C3×C4×D1212yes—
576C22C2×C3×(C2×D3)⋊C411yescharacteristic
577C22C3×C4×#6712yes—
578C4—21no—
579C4—21no—
580C4—21no—
581C4—44no—
582C4—62no—
583C4—124no—
584C4—121no—
585C4—121no—
586C4C3×#80612yesdirect product factor
587C3—21no—
588C3C4×#80611yescharacteristic, direct product factor
589C3C3×C4×#9911yescharacteristic, complemented
590C2—22no—
591C2—22no—
592C2—21no—
593C2—21no—
594C2—122no—
595C2C3×C4×(C2×D3)⋊C411yescharacteristic
596C2C2×C3×#80611yescharacteristic
597C2C3×#500611yescharacteristic
subgroupG/H
centerC2×C3×C4(C2×D3)⋊C4
commutatorC22×C3C2×C3×C42
FrattiniC24C22×C3×D3
FittingC32×C4×C22⋊C4C2
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×#67C22
cosocleC24×C3C23×C3
hypercenterC3×C4×C22⋊C4D3
hypocenterC3C3×C4×#99
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C23×C3×C4 ◁ C3×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C32×C4×C22⋊C4C2semidirect
3. C3×C4×#217C2semidirect
5. C3×#4527C2semidirect
7. C4×#806C3direct (N × H)
10. C22×C3×C4×D3C4semidirect
19. C2×C3×(C2×D3)⋊C4C4semidirect
20. C2×C3×Dic3⋊C4C4semidirect
22. C2×C3×C4×Dic3C4semidirect
25. C3×#806C4direct (N × H)
31. C3×C4×C22⋊C4D3semidirect
32. C3×C4×C22⋊C4C2×C3semidirect
33. C4×#217C2×C3semidirect
36. #4527C2×C3semidirect
59. C32×C22⋊C4C2×C4semidirect
64. C3×#217C2×C4semidirect
79. C22×C4×D3C3×C4semidirect
102. C2×(C2×D3)⋊C4C3×C4semidirect
103. C2×Dic3⋊C4C3×C4semidirect
105. C2×C4×Dic3C3×C4semidirect
112. #806C3×C4direct (N × H)
124. C22×C3×D3C42semidirect
149. C2×C3×Dic3C42semidirect
155. C4×C22⋊C4C3×D3semidirect
220. C3×C22⋊C4C4×D3semidirect
221. C3×C22⋊C4C2×C3×C4semidirect
231. #217C2×C3×C4semidirect
261. C32×C4#99semidirect
314. C22×D3C3×C42semidirect
379. C2×Dic3C3×C42semidirect
420. C22⋊C4C3×C4×D3semidirect
491. C3×C4#806direct (N × H)
492. C3×C4C3×#99semidirect
497. C32C4×#99semidirect
586. C4C3×#806direct (N × H)
588. C3C4×#806direct (N × H)
589. C3C3×C4×#99semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×#672
C32×C4×C22⋊C42
C3×C4×#2172
C2×C3×#8062
C3×#45272
C3×C4×#993
C4×#8063