Finite Group Databasebeta

← C2×C3×D3×#103 #11857741

Subgroups — C2×C3×D3×#103 #11857741

Order 1152.

1713 conjugacy classes of subgroups.

The subgroup lattice has 543 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×Q8C211yesmaximal, characteristic
2C22×C3×D3×C8C211yesmaximal, characteristic
3C2×C3×D3×C4⋊C4C211yesmaximal, characteristic
4C2×C32×#103C211yesmaximal, characteristic, complemented
5C2×C3×#835C211yesmaximal, characteristic, complemented
6C2×C3×#816C211yesmaximal, characteristic, complemented
7C2×C3×#810C211yesmaximal, characteristic, complemented
8C3×D3×#103C218yesmaximal, direct product factor
9C22×C3×#103—31nomaximal
10C2×D3×#103C311yesmaximal, characteristic, direct product factor
11C22×C32×Q8C2211yescharacteristic
12C2×C3×D3×Q8—24no—
13C2×C3×D3×Q8—22no—
14C2×C3×D3×Q8C418yescomplemented
15C2×C3×D3×Q8C2214yes—
16C22×C3×C4×D3—21no—
17C22×C3×C4×D3—21no—
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×Dic6—21no—
20C22×C3×Dic6C2211yescharacteristic
21C22×C32×C8C2211yescharacteristic
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×Dic3⋊C4—21no—
25C22×C3×C3⋊C8C2211yescharacteristic
26C2×C3×D3×C8—24no—
27C2×C3×D3×C8C2214yes—
28C3×D3×C4⋊C4—22no—
29C3×D3×C4⋊C4C2214yes—
30C32×#103C2214yescomplemented
31C3×#835C2214yescomplemented
32C3×#816C2214yescomplemented
33C3×#810C2214yescomplemented
34C23×C3×Q8—31no—
35C22×D3×Q8C2×C311yescharacteristic
36C23×C3×C8—31no—
37C22×C3×C4⋊C4—31no—
38C22×D3×C8C2×C311yescharacteristic
39C2×D3×C4⋊C4C2×C311yescharacteristic
40C2×C3×#103—21no—
41C2×C3×#103—31no—
42C2×C3×#103—31no—
43C2×C3×#103—31no—
44C2×C3×#103—38no—
45C2×C3×#103D311yescharacteristic, direct product factor
46C2×C3×#103C2×C311yescharacteristic, complemented
47C2×#835C2×C311yescharacteristic, complemented
48C2×#816C2×C311yescharacteristic, complemented
49C2×#810C2×C311yescharacteristic, complemented
50D3×#103C2×C318yesdirect product factor
51C23×C3×D3D411yescharacteristic
52C2×C32×Q8—22no—
53C2×C32×Q8—21no—
54C2×C32×Q8C2×C414yescomplemented
55C2×C32×Q8C2312yes—
56C22×C32×C4—21no—
57C22×C32×C4—21no—
58C22×C32×C4C2311yescharacteristic
59C22×C3×Dic3—21no—
60C22×C3×Dic3—21no—
61C22×C3×Dic3D411yescharacteristic
62C3×D3×Q8—216no—
63C3×D3×Q8—28no—
64C3×D3×Q8C2×C4116yescomplemented
65C2×C3×C4×D3—28no—
66C2×C3×C4×D3—24no—
67C2×C3×C4×D3—24no—
68C2×C3×C4×D3—44no—
69C2×C3×C4×D3C2×C414yes—
70C2×C3×C4×D3D412yes—
71C2×C3×C4×D3D414yes—
72C2×C3×C4×D3C2312yes—
73C2×C3×Dic6—21no—
74C2×C3×Dic6—22no—
75C2×C3×Dic6—28no—
76C2×C3×Dic6—24no—
77C2×C3×Dic6C2×C414yescomplemented
78C2×C3×Dic6C2312yes—
79C2×C32×C8—22no—
80C2×C32×C8C2312yes—
81C32×C4⋊C4—21no—
82C32×C4⋊C4C2312yes—
83C3×C4⋊Dic3—21no—
84C3×C4⋊Dic3C2312yes—
85C3×Dic3⋊C4—24no—
86C2×C3×C3⋊C8—22no—
87C2×C3×C3⋊C8C2312yes—
88C3×D3×C8—28no—
89C22×#103—31noSylow
90C22×C3×Q8—21no—
91C22×C3×Q8—38no—
92C22×C3×Q8—34no—
93C22×C3×Q8—31no—
94C22×C3×Q8—61no—
95C22×C3×Q8—62no—
96C22×C3×Q8—64no—
97C22×C3×Q8C2×D311yescharacteristic
98C22×C3×Q8C22×C311yescharacteristic
99C23×C3×C4—31no—
100C23×C3×C4—61no—
101C23×C3×C4—61no—
102C2×D3×Q8—24no—
103C2×D3×Q8—22no—
104C2×D3×Q8C3×C418yescomplemented
105C2×D3×Q8C22×C314yes—
106C22×C4×D3—21no—
107C22×C4×D3—21no—
108C22×C4×D3C22×C311yescharacteristic
109C22×Dic6—21no—
110C22×Dic6C22×C311yescharacteristic
111C22×C3×C8—21no—
112C22×C3×C8—31no—
113C22×C3×C8—34no—
114C22×C3×C8—64no—
115C22×C3×C8C2×D311yescharacteristic
116C22×C3×C8C22×C311yescharacteristic
117C2×C3×C4⋊C4—21no—
118C2×C3×C4⋊C4—31no—
119C2×C3×C4⋊C4—34no—
120C2×C3×C4⋊C4—62no—
121C2×C3×C4⋊C4—61no—
122C2×C3×C4⋊C4C2×D311yescharacteristic
123C2×C3×C4⋊C4C22×C311yescharacteristic
124C2×C4⋊Dic3C22×C311yescharacteristic
125C2×Dic3⋊C4—21no—
126C22×C3⋊C8C22×C311yescharacteristic
127C2×D3×C8—24no—
128C2×D3×C8C22×C314yes—
129D3×C4⋊C4—22no—
130D3×C4⋊C4C22×C314yes—
131C3×#103—24no—
132C3×#103—34no—
133C3×#103—34no—
134C3×#103—34no—
135C3×#103C2×D314yesdirect product factor
136C3×#103C22×C314yescomplemented
137#835C22×C314yescomplemented
138#816C22×C314yescomplemented
139#810C22×C314yescomplemented
140C23×C32C2×D411yescharacteristic
141C22×C3×D3C22⋊C414yes—
142C22×C3×D3SD1614yes—
143C22×C3×D3Q1614yes—
144C22×C3×D3C2×D412yes—
145C32×Q8—24no—
146C32×Q8—22no—
147C32×Q8C22×C414yescomplemented
148C2×C32×C4—24no—
149C2×C32×C4—22no—
150C2×C32×C4—22no—
151C2×C32×C4—42no—
152C2×C32×C4C22×C412yes—
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×D412yes—
155C2×C32×C4C2411yescharacteristic
156C2×C3×Dic3—24no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—42no—
160C2×C3×Dic3C22⋊C414yes—
161C2×C3×Dic3C2×D412yes—
162C3×C4×D3—216no—
163C3×C4×D3—48no—
164C3×C4×D3C22⋊C418yes—
165C3×C4×D3C22×C414yes—
166C3×C4×D3C2×D414yes—
167C3×Dic6—24no—
168C3×Dic6—22no—
169C3×Dic6—216no—
170C3×Dic6C22×C414yescomplemented
171C32×C8—22no—
172C3×C3⋊C8—22no—
173C23×Q8—31no—
174C23×C8—31no—
175C22×C4⋊C4—31no—
176C2×#103—31no—
177C2×#103—31no—
178C2×#103—31no—
179C2×#103—38no—
180C2×#103C3×D311yescharacteristic, direct product factor
181C24×C3—31no—
182C23×D3C3×D411yescharacteristic
183C2×C3×Q8—22no—
184C2×C3×Q8—21no—
185C2×C3×Q8—22no—
186C2×C3×Q8—21no—
187C2×C3×Q8—24no—
188C2×C3×Q8—22no—
189C2×C3×Q8—316no—
190C2×C3×Q8—34no—
191C2×C3×Q8—32no—
192C2×C3×Q8—41no—
193C2×C3×Q8—42no—
194C2×C3×Q8—68no—
195C2×C3×Q8—64no—
196C2×C3×Q8—616no—
197C2×C3×Q8—68no—
198C2×C3×Q8—62no—
199C2×C3×Q8—61no—
200C2×C3×Q8C4×D314yescomplemented
201C2×C3×Q8C2×C3×C414yescomplemented
202C2×C3×Q8C22×D312yes—
203C2×C3×Q8C23×C312yes—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—31no—
210C22×C3×C4—34no—
211C22×C3×C4—32no—
212C22×C3×C4—34no—
213C22×C3×C4—32no—
214C22×C3×C4—41no—
215C22×C3×C4—41no—
216C22×C3×C4—68no—
217C22×C3×C4—64no—
218C22×C3×C4—64no—
219C22×C3×C4—61no—
220C22×C3×C4—61no—
221C22×C3×C4—124no—
222C22×C3×C4C22×D311yescharacteristic
223C22×C3×C4C23×C311yescharacteristic
224C22×Dic3—21no—
225C22×Dic3—21no—
226C22×Dic3C3×D411yescharacteristic
227D3×Q8—216no—
228D3×Q8—28no—
229D3×Q8C2×C3×C4116yescomplemented
230C2×C4×D3—28no—
231C2×C4×D3—24no—
232C2×C4×D3—24no—
233C2×C4×D3—44no—
234C2×C4×D3C2×C3×C414yes—
235C2×C4×D3C3×D412yes—
236C2×C4×D3C3×D414yes—
237C2×C4×D3C23×C312yes—
238C2×Dic6—21no—
239C2×Dic6—22no—
240C2×Dic6—28no—
241C2×Dic6—24no—
242C2×Dic6C2×C3×C414yescomplemented
243C2×Dic6C23×C312yes—
244C2×C3×C8—22no—
245C2×C3×C8—22no—
246C2×C3×C8—22no—
247C2×C3×C8—32no—
248C2×C3×C8—42no—
249C2×C3×C8—68no—
250C2×C3×C8—62no—
251C2×C3×C8C22×D312yes—
252C2×C3×C8C23×C312yes—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—22no—
256C3×C4⋊C4—32no—
257C3×C4⋊C4—41no—
258C3×C4⋊C4—64no—
259C3×C4⋊C4—61no—
260C3×C4⋊C4C22×D312yes—
261C3×C4⋊C4C23×C312yes—
262C4⋊Dic3—21no—
263C4⋊Dic3C23×C312yes—
264Dic3⋊C4—24no—
265C2×C3⋊C8—22no—
266C2×C3⋊C8C23×C312yes—
267D3×C8—28no—
268C22×C32C2×C22⋊C412yes—
269C22×C32C2×SD1612yes—
270C22×C32C2×Q1612yes—
271C22×C32C22×D411yescharacteristic
272C2×C3×D3#103116yesdirect product factor
273C2×C3×D3C2×C22⋊C414yes—
274C2×C3×D3C2×SD1614yes—
275C2×C3×D3C2×Q1614yes—
276C32×C4—24no—
277C32×C4—42no—
278C32×C4C2×C22⋊C412yes—
279C32×C4C23×C411yescharacteristic
280C32×C4C22×D411yescharacteristic
281C3×Dic3—24no—
282C3×Dic3—42no—
283C3×Dic3C2×C22⋊C414yes—
284C22×Q8—38no—
285C22×Q8—34no—
286C22×Q8—31no—
287C22×Q8—61no—
288C22×Q8—62no—
289C22×Q8—64no—
290C22×Q8C2×C3×D311yescharacteristic
291C23×C4—31no—
292C23×C4—61no—
293C23×C4—61no—
294C22×C8—31no—
295C22×C8—34no—
296C22×C8—64no—
297C22×C8C2×C3×D311yescharacteristic
298C2×C4⋊C4—31no—
299C2×C4⋊C4—34no—
300C2×C4⋊C4—62no—
301C2×C4⋊C4—61no—
302C2×C4⋊C4C2×C3×D311yescharacteristic
303#103—34no—
304#103—34no—
305#103—34no—
306#103C2×C3×D314yesdirect product factor
307C23×C3—21no—
308C23×C3—34no—
309C23×C3—34no—
310C23×C3—34no—
311C23×C3—32no—
312C23×C3D3×D411yescharacteristic
313C23×C3C2×C3×D411yescharacteristic
314C22×D3C3×C22⋊C414yes—
315C22×D3C3×SD1614yes—
316C22×D3C3×Q1614yes—
317C22×D3C2×C3×D412yes—
318C3×Q8—24no—
319C3×Q8—24no—
320C3×Q8—22no—
321C3×Q8—22no—
322C3×Q8—24no—
323C3×Q8—34no—
324C3×Q8—44no—
325C3×Q8—42no—
326C3×Q8—616no—
327C3×Q8—64no—
328C3×Q8—62no—
329C3×Q8C2×C4×D314yescomplemented
330C3×Q8C22×C3×C414yescomplemented
331C2×C3×C4—24no—
332C2×C3×C4—24no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—21no—
338C2×C3×C4—22no—
339C2×C3×C4—21no—
340C2×C3×C4—22no—
341C2×C3×C4—34no—
342C2×C3×C4—32no—
343C2×C3×C4—38no—
344C2×C3×C4—34no—
345C2×C3×C4—34no—
346C2×C3×C4—44no—
347C2×C3×C4—42no—
348C2×C3×C4—42no—
349C2×C3×C4—42no—
350C2×C3×C4—42no—
351C2×C3×C4—616no—
352C2×C3×C4—64no—
353C2×C3×C4—62no—
354C2×C3×C4—62no—
355C2×C3×C4—82no—
356C2×C3×C4—128no—
357C2×C3×C4—122no—
358C2×C3×C4C2×C4×D312yes—
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4D3×D412yes—
361C2×C3×C4C22×C3×C412yes—
362C2×C3×C4C2×C3×D411yescharacteristic
363C2×C3×C4C2×C3×D412yes—
364C2×C3×C4C23×D311yescharacteristic
365C2×C3×C4C24×C311yescharacteristic
366C2×Dic3—24no—
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3—42no—
370C2×Dic3C3×C22⋊C414yes—
371C2×Dic3C2×C3×D412yes—
372C4×D3—216no—
373C4×D3—48no—
374C4×D3C3×C22⋊C418yes—
375C4×D3C22×C3×C414yes—
376C4×D3C2×C3×D414yes—
377Dic6—24no—
378Dic6—22no—
379Dic6—216no—
380Dic6C22×C3×C414yescomplemented
381C3×C8—22no—
382C3×C8—22no—
383C3×C8—42no—
384C3×C8—62no—
385C3⋊C8—22no—
386C2×C32C2×#10314yescomplemented
387C2×C32C22×C22⋊C411yescharacteristic
388C2×C32C22×SD1611yescharacteristic
389C2×C32C22×Q1611yescharacteristic
390C3×D3C2×#10318yesdirect product factor
391C24—31no—
392C2×Q8—22no—
393C2×Q8—21no—
394C2×Q8—316no—
395C2×Q8—32no—
396C2×Q8—34no—
397C2×Q8—68no—
398C2×Q8—64no—
399C2×Q8—616no—
400C2×Q8—68no—
401C2×Q8—62no—
402C2×Q8—61no—
403C2×Q8C3×C4×D314yescomplemented
404C2×Q8C22×C3×D312yes—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—31no—
408C22×C4—32no—
409C22×C4—34no—
410C22×C4—32no—
411C22×C4—34no—
412C22×C4—68no—
413C22×C4—64no—
414C22×C4—64no—
415C22×C4—61no—
416C22×C4—61no—
417C22×C4—124no—
418C22×C4C22×C3×D311yescharacteristic
419C2×C8—22no—
420C2×C8—32no—
421C2×C8—68no—
422C2×C8—62no—
423C2×C8C22×C3×D312yes—
424C4⋊C4—21no—
425C4⋊C4—32no—
426C4⋊C4—64no—
427C4⋊C4—61no—
428C4⋊C4C22×C3×D312yes—
429C22×C3—22no—
430C22×C3—22no—
431C22×C3—22no—
432C22×C3—21no—
433C22×C3—34no—
434C22×C3—34no—
435C22×C3—34no—
436C22×C3—316no—
437C22×C3D3×C22⋊C412yes—
438C22×C3D3×SD1612yes—
439C22×C3D3×Q1612yes—
440C22×C3C2×C3×C22⋊C412yes—
441C22×C3C2×C3×SD1612yes—
442C22×C3C2×C3×Q1612yes—
443C22×C3C2×D3×D411yescharacteristic
444C22×C3C22×C3×D411yescharacteristic
445C2×D3C3×#103116yesdirect product factor
446C2×D3C2×C3×C22⋊C414yes—
447C2×D3C2×C3×SD1614yes—
448C2×D3C2×C3×Q1614yes—
449C3×C4—24no—
450C3×C4—24no—
451C3×C4—22no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—34no—
455C3×C4—44no—
456C3×C4—42no—
457C3×C4—42no—
458C3×C4—64no—
459C3×C4—82no—
460C3×C4—122no—
461C3×C4D3×C22⋊C412yes—
462C3×C4C2×C3×C22⋊C412yes—
463C3×C4C22×C4×D311yescharacteristic
464C3×C4C2×D3×D411yescharacteristic
465C3×C4C23×C3×C411yescharacteristic
466C3×C4C22×C3×D411yescharacteristic
467Dic3—24no—
468Dic3—42no—
469Dic3C2×C3×C22⋊C414yes—
470C32C22×#10311yescharacteristic, complemented, Sylow
471C23—34no—
472C23—34no—
473C23—34no—
474C23—32no—
475C23C3×D3×D411yescharacteristic
476Q8—24no—
477Q8—22no—
478Q8—34no—
479Q8—616no—
480Q8—64no—
481Q8—62no—
482Q8C2×C3×C4×D314yescomplemented
483C2×C4—24no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—34no—
487C2×C4—32no—
488C2×C4—38no—
489C2×C4—34no—
490C2×C4—34no—
491C2×C4—42no—
492C2×C4—616no—
493C2×C4—64no—
494C2×C4—62no—
495C2×C4—62no—
496C2×C4—128no—
497C2×C4—122no—
498C2×C4C2×C3×C4×D312yes—
499C2×C4C3×D3×D411yescharacteristic
500C2×C4C3×D3×D412yes—
501C2×C4C23×C3×D311yescharacteristic
502C8—22no—
503C8—62no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—24no—
507C2×C3—21no—
508C2×C3—38no—
509C2×C3D3×#10314yesdirect product factor
510C2×C3C2×C3×#10314yescomplemented
511C2×C3C2×D3×C22⋊C411yescharacteristic
512C2×C3C2×D3×SD1611yescharacteristic
513C2×C3C2×D3×Q1611yescharacteristic
514C2×C3C22×C3×C22⋊C411yescharacteristic
515C2×C3C22×C3×SD1611yescharacteristic
516C2×C3C22×C3×Q1611yescharacteristic
517D3C2×C3×#10318yesdirect product factor
518C22—34no—
519C22—34no—
520C22—316no—
521C22—34no—
522C22C3×D3×C22⋊C412yes—
523C22C3×D3×SD1612yes—
524C22C3×D3×Q1612yes—
525C22C2×C3×D3×D411yescharacteristic
526C4—24no—
527C4—34no—
528C4—42no—
529C4—64no—
530C4—122no—
531C4C3×D3×C22⋊C412yes—
532C4C22×C3×C4×D311yescharacteristic
533C4C2×C3×D3×D411yescharacteristic
534C3—21no—
535C3C2×D3×#10311yescharacteristic, direct product factor
536C3C22×C3×#10311yescharacteristic, complemented
537C2—38no—
538C2C3×D3×#10314yesdirect product factor
539C2C2×C3×D3×C22⋊C411yescharacteristic
540C2C2×C3×D3×SD1611yescharacteristic
541C2C2×C3×D3×Q1611yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#103C2
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
cosocleC2×C3×C4C24×C3
hypercenterC2×C3×#103D3
hypocenterC3C22×C3×#103
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×#103

Complements

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

NH ≅ G/Ntype
4. C2×C32×#103C2semidirect
5. C2×C3×#835C2semidirect
6. C2×C3×#816C2semidirect
7. C2×C3×#810C2semidirect
8. C3×D3×#103C2direct (N × H)
10. C2×D3×#103C3direct (N × H)
14. C2×C3×D3×Q8C4semidirect
30. C32×#103C22semidirect
31. C3×#835C22semidirect
32. C3×#816C22semidirect
33. C3×#810C22semidirect
45. C2×C3×#103D3direct (N × H)
46. C2×C3×#103C2×C3semidirect
47. C2×#835C2×C3semidirect
48. C2×#816C2×C3semidirect
49. C2×#810C2×C3semidirect
50. D3×#103C2×C3direct (N × H)
54. C2×C32×Q8C2×C4semidirect
64. C3×D3×Q8C2×C4semidirect
77. C2×C3×Dic6C2×C4semidirect
104. C2×D3×Q8C3×C4semidirect
135. C3×#103C2×D3direct (N × H)
136. C3×#103C22×C3semidirect
137. #835C22×C3semidirect
138. #816C22×C3semidirect
139. #810C22×C3semidirect
147. C32×Q8C22×C4semidirect
170. C3×Dic6C22×C4semidirect
180. C2×#103C3×D3direct (N × H)
200. C2×C3×Q8C4×D3semidirect
201. C2×C3×Q8C2×C3×C4semidirect
229. D3×Q8C2×C3×C4semidirect
242. C2×Dic6C2×C3×C4semidirect
272. C2×C3×D3#103direct (N × H)
306. #103C2×C3×D3direct (N × H)
329. C3×Q8C2×C4×D3semidirect
330. C3×Q8C22×C3×C4semidirect
380. Dic6C22×C3×C4semidirect
386. C2×C32C2×#103semidirect
390. C3×D3C2×#103direct (N × H)
403. C2×Q8C3×C4×D3semidirect
445. C2×D3C3×#103direct (N × H)
470. C32C22×#103semidirect
482. Q8C2×C3×C4×D3semidirect
509. C2×C3D3×#103direct (N × H)
510. C2×C3C2×C3×#103semidirect
517. D3C2×C3×#103direct (N × H)
535. C3C2×D3×#103direct (N × H)
536. C3C22×C3×#103semidirect
538. C2C3×D3×#103direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D3×Q82
C22×C3×D3×C82
C2×C3×D3×C4⋊C42
C2×C32×#1032
C2×C3×#8352
C2×C3×#8162
C2×C3×#8102
C3×D3×#1032
C22×C3×#1033
C2×D3×#1033