Finite Group Databasebeta

← C3×#70240 #11787566

Subgroups — C3×#70240 #11787566

Order 1152.

829 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×Q8×Dic3C211yesmaximal, characteristic, complemented
2C22×C3×#215C211yesmaximal, characteristic
3C2×C32×#103C211yesmaximal, characteristic, complemented
4C2×C3×#821C211yesmaximal, characteristic
5C3×#4988C211yesmaximal, characteristic
6C3×#4550C211yesmaximal, characteristic, complemented
7C3×#4529C211yesmaximal, characteristic, complemented
8C3×#1880—31nomaximal
9#70240C311yesmaximal, characteristic, direct product factor
10C22×C32×Q8C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C3×Q8×Dic3—22no—
15C3×Q8×Dic3—22no—
16C2×C3×#215—22no—
17C2×C3×#215—22no—
18C2×C3×#215C414yescomplemented
19C2×C3×(C2×D3)⋊C4—21no—
20C2×C3×(C2×D3)⋊C4—21no—
21C2×C3×C4⋊Dic3—21no—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4×Dic3—21no—
24C2×C3×C4×Dic3C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C32×#103—22no—
27C3×#821—22no—
28C22×C3×SD16—31no—
29C2×C3×C4×Q8—31no—
30C2×Q8×Dic3C2×C311yescharacteristic, complemented
31C22×#215C2×C311yescharacteristic
32C2×C3×#103—21no—
33C2×C3×#103D311yescharacteristic, complemented
34C2×C3×#103C2×C311yescharacteristic, complemented
35C2×C3×#102—31no—
36C3×#390—31no—
37C2×#821C2×C311yescharacteristic
38#4988C2×C311yescharacteristic
39C3×#340—31no—
40C3×#336—31no—
41#4550C2×C311yescharacteristic, complemented
42#4529C2×C311yescharacteristic, complemented
43C23×C3×D3—21no—
44C2×C32×Q8—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8C2×C412yes—
48C2×C32×Q8D412yes—
49C2×C32×Q8D412yes—
50C22×C32×C4—21no—
51C22×C32×C4—21no—
52C22×C32×C4C2311yescharacteristic
53C22×C3×Dic3—21no—
54C22×C3×Dic3D411yescharacteristic
55C22×C3×Dic3D411yescharacteristic
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12C2×C412yes—
62C2×C32×C8—21no—
63C2×C32×C8—21no—
64C2×C32×C8—21no—
65C32×C4⋊C4—21no—
66C32×C4⋊C4—21no—
67C3×#215—28no—
68C3×(C2×D3)⋊C4—42no—
69C3×(C2×D3)⋊C4—42no—
70C3×C4⋊Dic3—24no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3D412yes—
73C3×C4×Dic3—24no—
74C3×C4×Dic3—21no—
75C3×C4×Dic3—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8C2×C412yes—
79#1880—31noSylow
80C22×C3×Q8—21no—
81C22×C3×Q8C2×D311yescharacteristic
82C22×C3×Q8C22×C311yescharacteristic
83C22×C3×D4—31no—
84C22×D12C22×C311yescharacteristic
85C2×C3×SD16—34no—
86C2×C3×SD16—62no—
87C2×C3×SD16—62no—
88C22×C3×C8—21no—
89C22×C3×C8—31no—
90C22×C3×C8C2×D311yescharacteristic
91C22×C3×C8C22×C311yescharacteristic
92C3×C4×Q8—62no—
93C3×C4×Q8—62no—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4—31no—
96C2×C3×C4⋊C4—61no—
97C2×C3×C4⋊C4C2×D311yescharacteristic
98C2×C3×C4⋊C4C22×C311yescharacteristic
99C2×C3×C22⋊C4—61no—
100C2×C3×C22⋊C4—61no—
101C2×C3×C42—31no—
102C2×C3×C42—61no—
103Q8×Dic3—22no—
104Q8×Dic3—22no—
105C2×#215—22no—
106C2×#215—22no—
107C2×#215C3×C414yescomplemented
108C2×(C2×D3)⋊C4—21no—
109C2×(C2×D3)⋊C4—21no—
110C2×C4⋊Dic3—21no—
111C2×C4⋊Dic3C22×C311yescharacteristic
112C2×C4×Dic3—21no—
113C2×C4×Dic3C22×C311yescharacteristic
114C22×C3⋊C8C22×C311yescharacteristic
115C3×#103—24no—
116C3×#103—22no—
117C3×#103—22no—
118C3×#102—62no—
119#821—22no—
120C23×C32C2×D411yescharacteristic
121C22×C3×D3—22no—
122C22×C3×D3—41no—
123C22×C3×D3—41no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C22×C3×D3—41no—
127C22×C3×D3—41no—
128C32×Q8—22no—
129C32×Q8—22no—
130C32×Q8—22no—
131C32×Q8C22⋊C414yescomplemented
132C2×C32×C4—22no—
133C2×C32×C4—22no—
134C2×C32×C4—22no—
135C2×C32×C4—41no—
136C2×C32×C4—41no—
137C2×C32×C4—41no—
138C2×C32×C4C22×C411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C2×C32×C4#4111yescharacteristic
144C2×C3×Dic3—21no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—21no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3SD1612yescomplemented
153C3×D12—22no—
154C3×D12—22no—
155C3×D12—41no—
156C3×D12—41no—
157C32×C8—41no—
158C3×C3⋊C8—22no—
159C22×SD16—31no—
160C2×C4×Q8—31no—
161C2×#103C3×D311yescharacteristic, complemented
162C2×#102—31no—
163#390—31no—
164#340—31no—
165#336—31no—
166C24×C3—61no—
167C23×D3—21no—
168C2×C3×Q8—21no—
169C2×C3×Q8—21no—
170C2×C3×Q8—21no—
171C2×C3×Q8—21no—
172C2×C3×Q8—21no—
173C2×C3×Q8—21no—
174C2×C3×Q8—22no—
175C2×C3×Q8—22no—
176C2×C3×Q8—22no—
177C2×C3×Q8—41no—
178C2×C3×Q8—41no—
179C2×C3×Q8—41no—
180C2×C3×Q8C4×D312yes—
181C2×C3×Q8D1212yes—
182C2×C3×Q8#6712yes—
183C2×C3×Q8C2×C3×C412yes—
184C2×C3×Q8C3×D412yes—
185C2×C3×Q8C3×D412yes—
186C2×C3×D4—32no—
187C2×C3×D4—61no—
188C2×C3×D4—61no—
189C2×C3×D4—61no—
190C2×C3×D4—61no—
191C2×C3×D4—61no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—31no—
198C22×C3×C4—31no—
199C22×C3×C4—41no—
200C22×C3×C4—41no—
201C22×C3×C4—61no—
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C23×C311yescharacteristic
204C22×Dic3—21no—
205C22×Dic3C3×D411yescharacteristic
206C22×Dic3C3×D411yescharacteristic
207C2×D12—21no—
208C2×D12—21no—
209C2×D12—21no—
210C2×D12—21no—
211C2×D12—21no—
212C2×D12C2×C3×C412yes—
213C3×SD16—68no—
214C2×C3×C8—22no—
215C2×C3×C8—21no—
216C2×C3×C8—21no—
217C2×C3×C8—21no—
218C2×C3×C8—21no—
219C2×C3×C8—21no—
220C2×C3×C8—21no—
221C2×C3×C8—32no—
222C2×C3×C8—41no—
223C2×C3×C8—41no—
224C2×C3×C8—61no—
225C2×C3×C8—61no—
226C3×C4⋊C4—22no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—32no—
232C3×C4⋊C4—41no—
233C3×C4⋊C4—64no—
234C3×C4⋊C4—61no—
235C3×C22⋊C4—122no—
236C3×C22⋊C4—122no—
237C3×C42—64no—
238C3×C42—61no—
239C3×C42—61no—
240#215—28no—
241(C2×D3)⋊C4—42no—
242(C2×D3)⋊C4—42no—
243C4⋊Dic3—24no—
244C4⋊Dic3—21no—
245C4⋊Dic3C3×D412yes—
246C4×Dic3—24no—
247C4×Dic3—21no—
248C4×Dic3—21no—
249C2×C3⋊C8—21no—
250C2×C3⋊C8—21no—
251C2×C3⋊C8C2×C3×C412yes—
252C22×C32C4×D411yescharacteristic
253C22×C32#12011yescharacteristic
254C22×C32#12111yescharacteristic
255C22×C32C2×SD1611yescharacteristic
256C22×C32#13511yescharacteristic
257C22×C32AGL(1,ℤ/8)11yescharacteristic
258C22×C32#13711yescharacteristic
259C2×C3×D3—42no—
260C2×C3×D3—42no—
261C2×C3×D3—42no—
262C2×C3×D3—81no—
263C2×C3×D3—81no—
264C2×C3×D3—81no—
265C2×C3×D3—81no—
266C32×C4—24no—
267C32×C4—81no—
268C32×C4C2×C22⋊C411yescharacteristic
269C32×C4C4×D411yescharacteristic
270C32×C4#12111yescharacteristic
271C32×C4#12311yescharacteristic
272C3×Dic3—22no—
273C3×Dic3—41no—
274C3×Dic3—42no—
275C22×Q8C2×C3×D311yescharacteristic
276C22×D4—31no—
277C2×SD16—34no—
278C2×SD16—62no—
279C2×SD16—62no—
280C22×C8—31no—
281C22×C8C2×C3×D311yescharacteristic
282C4×Q8—62no—
283C4×Q8—62no—
284C2×C4⋊C4—31no—
285C2×C4⋊C4—61no—
286C2×C4⋊C4C2×C3×D311yescharacteristic
287C2×C22⋊C4—61no—
288C2×C22⋊C4—61no—
289C2×C42—31no—
290C2×C42—61no—
291#103—22no—
292#102—62no—
293C23×C3—21no—
294C23×C3—62no—
295C23×C3—121no—
296C23×C3—121no—
297C23×C3—121no—
298C23×C3—121no—
299C23×C3—121no—
300C23×C3—121no—
301C23×C3D3×D411yescharacteristic
302C23×C3C2×C3×D411yescharacteristic
303C22×D3—22no—
304C22×D3—41no—
305C22×D3—41no—
306C22×D3—41no—
307C22×D3—41no—
308C22×D3—41no—
309C22×D3—41no—
310C3×Q8—22no—
311C3×Q8—22no—
312C3×Q8—22no—
313C3×Q8—22no—
314C3×Q8—22no—
315C3×Q8—22no—
316C3×Q8—24no—
317C3×Q8—42no—
318C3×Q8—42no—
319C3×Q8—42no—
320C3×Q8(C2×D3)⋊C414yescomplemented
321C3×Q8C3×C22⋊C414yescomplemented
322C3×D4—62no—
323C3×D4—62no—
324C3×D4—121no—
325C3×D4—121no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—32no—
339C2×C3×C4—42no—
340C2×C3×C4—42no—
341C2×C3×C4—42no—
342C2×C3×C4—42no—
343C2×C3×C4—41no—
344C2×C3×C4—41no—
345C2×C3×C4—41no—
346C2×C3×C4—41no—
347C2×C3×C4—41no—
348C2×C3×C4—41no—
349C2×C3×C4—61no—
350C2×C3×C4—61no—
351C2×C3×C4—62no—
352C2×C3×C4—61no—
353C2×C3×C4—61no—
354C2×C3×C4—61no—
355C2×C3×C4—81no—
356C2×C3×C4—81no—
357C2×C3×C4—121no—
358C2×C3×C4—121no—
359C2×C3×C4C2×C4×D311yescharacteristic
360C2×C3×C4C2×D1211yescharacteristic
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4#23711yescharacteristic
363C2×C3×C4#23711yescharacteristic
364C2×C3×C4C2×#6711yescharacteristic
365C2×C3×C4C22×C3×C411yescharacteristic
366C2×C3×C4C2×C3×D411yescharacteristic
367C2×C3×C4C2×C3×D411yescharacteristic
368C2×C3×C4C2×C3×D411yescharacteristic
369C2×C3×C4C3×#4111yescharacteristic
370C2×C3×C4C3×#4111yescharacteristic
371C2×Dic3—21no—
372C2×Dic3—21no—
373C2×Dic3—21no—
374C2×Dic3—22no—
375C2×Dic3—21no—
376C2×Dic3—21no—
377C2×Dic3—41no—
378C2×Dic3—41no—
379C2×Dic3C3×SD1612yescomplemented
380D12—22no—
381D12—22no—
382D12—41no—
383D12—41no—
384C3×C8—42no—
385C3×C8—41no—
386C3×C8—41no—
387C3×C8—62no—
388C3⋊C8—22no—
389C2×C32#38611yescharacteristic
390C2×C32C4×SD1611yescharacteristic
391C2×C32#44011yescharacteristic
392C2×C32#44811yescharacteristic
393C2×C32#44911yescharacteristic
394C2×C32#46011yescharacteristic
395C2×C32#46411yescharacteristic
396C3×D3—82no—
397C24—61no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8C3×C4×D312yes—
402C2×Q8C3×D1212yes—
403C2×Q8C3×#6712yes—
404C2×D4—32no—
405C2×D4—61no—
406C2×D4—61no—
407C2×D4—61no—
408C2×D4—61no—
409C2×D4—61no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—31no—
413C22×C4—31no—
414C22×C4—61no—
415C22×C4C22×C3×D311yescharacteristic
416SD16—68no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—32no—
421C2×C8—61no—
422C2×C8—61no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—32no—
426C4⋊C4—64no—
427C4⋊C4—61no—
428C22⋊C4—122no—
429C22⋊C4—122no—
430C42—64no—
431C42—61no—
432C42—61no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—122no—
441C22×C3—122no—
442C22×C3—122no—
443C22×C3—241no—
444C22×C3—241no—
445C22×C3—241no—
446C22×C3—241no—
447C22×C3#67⋊C411yescharacteristic
448C22×C3#88211yescharacteristic
449C22×C3D3×SD1611yescharacteristic
450C22×C3#91411yescharacteristic
451C22×C3#91811yescharacteristic
452C22×C3#91911yescharacteristic
453C22×C3#93911yescharacteristic
454C22×C3C3×C4×D411yescharacteristic
455C22×C3C3×#12011yescharacteristic
456C22×C3C3×#12111yescharacteristic
457C22×C3C2×C3×SD1611yescharacteristic
458C22×C3C3×#13511yescharacteristic
459C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
460C22×C3C3×#13711yescharacteristic
461C2×D3—42no—
462C2×D3—42no—
463C2×D3—42no—
464C2×D3—81no—
465C2×D3—81no—
466C2×D3—81no—
467C2×D3—81no—
468C3×C4—24no—
469C3×C4—24no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—44no—
475C3×C4—62no—
476C3×C4—82no—
477C3×C4—81no—
478C3×C4—81no—
479C3×C4—121no—
480C3×C4—122no—
481C3×C4#67⋊C411yescharacteristic
482C3×C4#88611yescharacteristic
483C3×C4C2×(C2×D3)⋊C411yescharacteristic
484C3×C4#93911yescharacteristic
485C3×C4C2×C3×C22⋊C411yescharacteristic
486C3×C4C3×C4×D411yescharacteristic
487C3×C4C3×#12111yescharacteristic
488C3×C4C3×#12311yescharacteristic
489Dic3—22no—
490Dic3—41no—
491Dic3—42no—
492C32#188011yescharacteristic, complemented, Sylow
493C23—62no—
494C23—121no—
495C23—121no—
496C23—121no—
497C23—121no—
498C23—121no—
499C23—121no—
500C23C3×D3×D411yescharacteristic
501Q8—22no—
502Q8—22no—
503Q8—22no—
504Q8C3×(C2×D3)⋊C414yescomplemented
505D4—62no—
506D4—62no—
507D4—121no—
508D4—121no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—32no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—61no—
517C2×C4—61no—
518C2×C4—62no—
519C2×C4—61no—
520C2×C4—61no—
521C2×C4—61no—
522C2×C4—121no—
523C2×C4—121no—
524C2×C4C2×C3×C4×D311yescharacteristic
525C2×C4C2×C3×D1211yescharacteristic
526C2×C4C3×D3×D411yescharacteristic
527C2×C4C3×#23711yescharacteristic
528C2×C4C3×#23711yescharacteristic
529C2×C4C2×C3×#6711yescharacteristic
530C8—41no—
531C8—62no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—242no—
540C2×C3#478811yescharacteristic
541C2×C3#480611yescharacteristic
542C2×C3#481011yescharacteristic
543C2×C3#481711yescharacteristic
544C2×C3#495811yescharacteristic
545C2×C3#516311yescharacteristic
546C2×C3#518511yescharacteristic
547C2×C3C3×#38611yescharacteristic
548C2×C3C3×C4×SD1611yescharacteristic
549C2×C3C3×#44011yescharacteristic
550C2×C3C3×#44811yescharacteristic
551C2×C3C3×#44911yescharacteristic
552C2×C3C3×#46011yescharacteristic
553C2×C3C3×#46411yescharacteristic
554D3—82no—
555C22—122no—
556C22—122no—
557C22—122no—
558C22—241no—
559C22—241no—
560C22—241no—
561C22—241no—
562C22C3×#67⋊C411yescharacteristic
563C22C3×#88211yescharacteristic
564C22C3×D3×SD1611yescharacteristic
565C22C3×#91411yescharacteristic
566C22C3×#91811yescharacteristic
567C22C3×#91911yescharacteristic
568C22C3×#93911yescharacteristic
569C4—24no—
570C4—62no—
571C4—81no—
572C4—121no—
573C4—122no—
574C4C3×#67⋊C411yescharacteristic
575C4C3×#88611yescharacteristic
576C4C2×C3×(C2×D3)⋊C411yescharacteristic
577C4C3×#93911yescharacteristic
578C3—21no—
579C3#7024011yescharacteristic, direct product factor
580C3C3×#188011yescharacteristic, complemented
581C2—242no—
582C2C3×#478811yescharacteristic
583C2C3×#480611yescharacteristic
584C2C3×#481011yescharacteristic
585C2C3×#481711yescharacteristic
586C2C3×#495811yescharacteristic
587C2C3×#516311yescharacteristic
588C2C3×#518511yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#103C2
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×#103D3
hypocenterC3C3×#1880
LCSG ▷ C2×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
1. C2×C3×Q8×Dic3C2semidirect
3. C2×C32×#103C2semidirect
6. C3×#4550C2semidirect
7. C3×#4529C2semidirect
9. #70240C3direct (N × H)
18. C2×C3×#215C4semidirect
30. C2×Q8×Dic3C2×C3semidirect
33. C2×C3×#103D3semidirect
34. C2×C3×#103C2×C3semidirect
41. #4550C2×C3semidirect
42. #4529C2×C3semidirect
107. C2×#215C3×C4semidirect
131. C32×Q8C22⋊C4semidirect
152. C2×C3×Dic3SD16semidirect
161. C2×#103C3×D3semidirect
320. C3×Q8(C2×D3)⋊C4semidirect
321. C3×Q8C3×C22⋊C4semidirect
379. C2×Dic3C3×SD16semidirect
492. C32#1880semidirect
504. Q8C3×(C2×D3)⋊C4semidirect
579. C3#70240direct (N × H)
580. C3C3×#1880semidirect

Maximal subgroups

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

subgroupindex
C2×C3×Q8×Dic32
C22×C3×#2152
C2×C32×#1032
C2×C3×#8212
C3×#49882
C3×#45502
C3×#45292
C3×#18803
#702403