Finite Group Databasebeta

← C3×#80133 #11870853

Subgroups — C3×#80133 #11870853

Order 1152.

1002 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
2C3×#5624C211yesmaximal, characteristic, complemented
3C32×#450C211yesmaximal, characteristic, complemented
4C3×#5217C211yesmaximal, characteristic
5C3×#5165C212yesmaximal, complemented
6C3×Dic3×SD16C212yesmaximal, complemented
7C3×#5044C211yesmaximal, characteristic, complemented
8C3×#4763C212yesmaximal, complemented
9C3×#4756C212yesmaximal, complemented
10C3×#4735C211yesmaximal, characteristic, complemented
11C3×#4718C211yesmaximal, characteristic, complemented
12C3×#3105—31nomaximal
13#80133C311yesmaximal, characteristic, direct product factor
14C22×C32×D4C2211yescharacteristic
15C23×C3×Dic3—21no—
16C2×C32×SD16C2212yes—
17C32×C22⋊Q8C2211yescharacteristic
18C2×C3×#217—21no—
19C3×#947C2211yescharacteristic, complemented
20C3×Q8×Dic3C2211yescharacteristic, complemented
21C3×D4×Dic3—21no—
22C3×D4×Dic3—21no—
23C3×D4×Dic3C2212yes—
24C3×D4×Dic3C2212yes—
25C2×C3×#213C2212yes—
26C3×#930C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C3×#898—21no—
30C3×#893C2211yescharacteristic, complemented
31C3×#892—21no—
32C3×#890C2211yescharacteristic, complemented
33C3×#886—21no—
34C3×#67⋊C4—21no—
35C32×#102C2212yes—
36C32×C22⋊C8C2211yescharacteristic
37C3×#835C2212yescomplemented
38C3×#832C2212yes—
39C3×#830C2211yescharacteristic
40C3×#821C2212yescomplemented
41C3×#817C2212yescomplemented
42C3×Dic3⋊C8C2212yescomplemented
43C3×C8×Dic3C2212yescomplemented
44C3×#807C2212yescomplemented
45C3×#529—31no—
46C2×C3×C4×D4—31no—
47C2×D4×Dic3C2×C311yescharacteristic, complemented
48#5624C2×C311yescharacteristic, complemented
49C3×#484—31no—
50C3×#481—31no—
51C3×#478—32no—
52C3×#463—32no—
53C3×#450—21no—
54C3×#450D311yescharacteristic, complemented
55C3×#450C2×C311yescharacteristic, complemented
56C3×#447—31no—
57C3×C4×SD16—32no—
58C3×C4×D8—32no—
59C3×#431—31no—
60#5217C2×C311yescharacteristic
61#5165C2×C312yescomplemented
62Dic3×SD16C2×C312yescomplemented
63#5044C2×C311yescharacteristic, complemented
64#4763C2×C312yescomplemented
65#4756C2×C312yescomplemented
66#4735C2×C311yescharacteristic, complemented
67#4718C2×C311yescharacteristic, complemented
68C24×C32—21no—
69C2×C32×Q8C2311yescharacteristic
70C2×C32×D4—24no—
71C2×C32×D4—21no—
72C2×C32×D4C2312yes—
73C22×C32×C4C2311yescharacteristic
74C2×C3×#67—21no—
75C22×C3×Dic3—21no—
76C22×C3×Dic3—22no—
77C22×C3×Dic3—22no—
78C22×C3×Dic3—44no—
79C22×C3×Dic3D411yescharacteristic
80C22×C3×Dic3D411yescharacteristic
81C2×C3×D12C2311yescharacteristic
82C2×C3×C4×D3—21no—
83C32×SD16—24no—
84C2×C32×C8C2312yes—
85C32×C4⋊C4—21no—
86C32×C4⋊C4C2311yescharacteristic
87C32×C22⋊C4—21no—
88C3×#217—22no—
89C3×#217—22no—
90C3×#213—24no—
91C3×(C2×D3)⋊C4—21no—
92C3×(C2×D3)⋊C4—21no—
93C3×(C2×D3)⋊C4—21no—
94C3×(C2×D3)⋊C4—21no—
95C3×C4⋊Dic3—21no—
96C3×C4⋊Dic3—21no—
97C3×C4⋊Dic3—21no—
98C3×C4⋊Dic3C2311yescharacteristic
99C3×C4⋊Dic3C2312yes—
100C3×Dic3⋊C4—21no—
101C3×C4×Dic3—21no—
102C3×C4×Dic3D411yescharacteristic
103C3×C4×Dic3D411yescharacteristic
104C3×C4×Dic3C2311yescharacteristic
105C3×C4×Dic3C2311yescharacteristic
106C2×C3×C3⋊C8C2312yes—
107#3105—31noSylow
108C22×C3×D4—21no—
109C22×C3×D4C2×D311yescharacteristic
110C22×C3×D4C22×C311yescharacteristic
111C23×C3×C4—61no—
112C23×Dic3—21no—
113C2×C3×SD16—22no—
114C2×C3×SD16C2×D312yes—
115C2×C3×SD16C22×C312yes—
116C2×C3×D8—32no—
117C3×#126—61no—
118C3×#125—31no—
119C3×#124—31no—
120C3×#123—61no—
121C3×C22⋊Q8—21no—
122C3×C22⋊Q8C2×D311yescharacteristic
123C3×C22⋊Q8C22×C311yescharacteristic
124C3×#121—31no—
125C3×C4×Q8—31no—
126C3×C4×D4—32no—
127C3×C4×D4—32no—
128C3×C4×D4—31no—
129C3×C4×D4—61no—
130C3×C4×D4—61no—
131C3×C4×D4—61no—
132C3×#117—61no—
133C2×C3×C4⋊C4—31no—
134C2×C3×C22⋊C4—61no—
135C2×C3×C42—31no—
136C2×#217—21no—
137#947C22×C311yescharacteristic, complemented
138Q8×Dic3C22×C311yescharacteristic, complemented
139D4×Dic3—21no—
140D4×Dic3—21no—
141D4×Dic3C22×C312yes—
142D4×Dic3C22×C312yes—
143C2×#213C22×C312yes—
144#930C22×C311yescharacteristic
145C2×C4⋊Dic3C22×C311yescharacteristic
146C2×C4×Dic3C22×C311yescharacteristic
147#898—21no—
148#893C22×C311yescharacteristic, complemented
149#892—21no—
150#890C22×C311yescharacteristic, complemented
151#886—21no—
152#67⋊C4—21no—
153C3×#107—32no—
154C3×#106—32no—
155C3×C4⋊C8—32no—
156C3×#103—32no—
157C3×#102—22no—
158C3×#102—32no—
159C3×#102—32no—
160C3×#102C2×D312yes—
161C3×#102C22×C312yes—
162C3×C22⋊C8—21no—
163C3×C22⋊C8—31no—
164C3×C22⋊C8C2×D311yescharacteristic
165C3×C22⋊C8C22×C311yescharacteristic
166C3×C4×C8—32no—
167#835C22×C312yescomplemented
168#832C22×C312yes—
169#830C22×C311yescharacteristic
170#821C22×C312yescomplemented
171#817C22×C312yescomplemented
172Dic3⋊C8C22×C312yescomplemented
173C8×Dic3C22×C312yescomplemented
174#807C22×C312yescomplemented
175C23×C32—24no—
176C23×C32—22no—
177C23×C32—42no—
178C23×C32—42no—
179C23×C32C2×D411yescharacteristic
180C22×C3×D3—21no—
181C32×Q8—22no—
182C32×D4—24no—
183C32×D4—22no—
184C32×D4#4114yes—
185C2×C32×C4—22no—
186C2×C32×C4—21no—
187C2×C32×C4—21no—
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4C2411yescharacteristic
190C3×#67—42no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—44no—
196C2×C3×Dic3—42no—
197C2×C3×Dic3—44no—
198C2×C3×Dic3C2×D411yescharacteristic
199C2×C3×Dic3C2×D411yescharacteristic
200C2×C3×Dic3C2×D411yescharacteristic
201C2×C3×Dic3C2×D411yescharacteristic
202C3×D12—22no—
203C3×C4×D3—42no—
204C32×C8—22no—
205C3×C3⋊C8—22no—
206#529—31no—
207C2×C4×D4—31no—
208#484—31no—
209#481—31no—
210#478—32no—
211#463—32no—
212#450C3×D311yescharacteristic, complemented
213#447—31no—
214C4×SD16—32no—
215C4×D8—32no—
216#431—31no—
217C24×C3—21no—
218C24×C3—21no—
219C24×C3—41no—
220C2×C3×Q8—21no—
221C2×C3×Q8C22×D311yescharacteristic
222C2×C3×Q8C23×C311yescharacteristic
223C2×C3×D4—24no—
224C2×C3×D4—24no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—22no—
228C2×C3×D4—31no—
229C2×C3×D4—41no—
230C2×C3×D4—44no—
231C2×C3×D4—61no—
232C2×C3×D4C22×D312yes—
233C2×C3×D4C23×C312yes—
234C22×C3×C4—21no—
235C22×C3×C4—31no—
236C22×C3×C4—31no—
237C22×C3×C4—61no—
238C22×C3×C4—62no—
239C22×C3×C4—62no—
240C22×C3×C4—61no—
241C22×C3×C4—124no—
242C22×C3×C4C22×D311yescharacteristic
243C22×C3×C4C23×C311yescharacteristic
244C2×#67—21no—
245C22×Dic3—21no—
246C22×Dic3—22no—
247C22×Dic3—22no—
248C22×Dic3—44no—
249C22×Dic3C3×D411yescharacteristic
250C22×Dic3C3×D411yescharacteristic
251C2×D12C23×C311yescharacteristic
252C2×C4×D3—21no—
253C3×SD16—24no—
254C3×SD16—24no—
255C3×SD16—44no—
256C3×D8—64no—
257C2×C3×C8—22no—
258C2×C3×C8—32no—
259C2×C3×C8C22×D312yes—
260C2×C3×C8C23×C312yes—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—21no—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—31no—
265C3×C4⋊C4—32no—
266C3×C4⋊C4—41no—
267C3×C4⋊C4—61no—
268C3×C4⋊C4—61no—
269C3×C4⋊C4—61no—
270C3×C4⋊C4—61no—
271C3×C4⋊C4C22×D311yescharacteristic
272C3×C4⋊C4C23×C311yescharacteristic
273C3×C22⋊C4—21no—
274C3×C22⋊C4—21no—
275C3×C22⋊C4—41no—
276C3×C22⋊C4—61no—
277C3×C22⋊C4—61no—
278C3×C22⋊C4—61no—
279C3×C22⋊C4—62no—
280C3×C22⋊C4—62no—
281C3×C22⋊C4—61no—
282C3×C42—31no—
283C3×C42—31no—
284C3×C42—31no—
285C3×C42—31no—
286C3×C42—61no—
287#217—22no—
288#217—22no—
289#213—24no—
290(C2×D3)⋊C4—21no—
291(C2×D3)⋊C4—21no—
292(C2×D3)⋊C4—21no—
293(C2×D3)⋊C4—21no—
294C4⋊Dic3—21no—
295C4⋊Dic3—21no—
296C4⋊Dic3—21no—
297C4⋊Dic3C23×C312yes—
298C4⋊Dic3C23×C311yescharacteristic
299Dic3⋊C4—21no—
300C4×Dic3—21no—
301C4×Dic3C3×D411yescharacteristic
302C4×Dic3C3×D411yescharacteristic
303C4×Dic3C23×C311yescharacteristic
304C4×Dic3C23×C311yescharacteristic
305C2×C3⋊C8C23×C312yes—
306C22×C32—21no—
307C22×C32—21no—
308C22×C32—24no—
309C22×C32—48no—
310C22×C32—42no—
311C22×C32—42no—
312C22×C32#13512yes—
313C22×C32C22×D411yescharacteristic
314C2×C3×D3—41no—
315C2×C3×D3—41no—
316C2×C3×D3—41no—
317C32×C4—21no—
318C32×C4—41no—
319C32×C4—41no—
320C32×C4C2×#4112yes—
321C3×Dic3—21no—
322C3×Dic3—21no—
323C3×Dic3—21no—
324C3×Dic3—41no—
325C3×Dic3—42no—
326C3×Dic3AGL(1,ℤ/8)12yes—
327C22×D4C2×C3×D311yescharacteristic
328C23×C4—61no—
329C2×SD16C2×C3×D312yes—
330C2×D8—32no—
331#126—61no—
332#125—31no—
333#124—31no—
334#123—61no—
335C22⋊Q8C2×C3×D311yescharacteristic
336#121—31no—
337C4×Q8—31no—
338C4×D4—32no—
339C4×D4—32no—
340C4×D4—31no—
341C4×D4—61no—
342C4×D4—61no—
343C4×D4—61no—
344#117—61no—
345C2×C4⋊C4—31no—
346C2×C22⋊C4—61no—
347C2×C42—31no—
348#107—32no—
349#106—32no—
350C4⋊C8—32no—
351#103—32no—
352#102—32no—
353#102—32no—
354#102C2×C3×D312yes—
355C22⋊C8—31no—
356C22⋊C8C2×C3×D311yescharacteristic
357C4×C8—32no—
358C23×C3—24no—
359C23×C3—24no—
360C23×C3—22no—
361C23×C3—22no—
362C23×C3—21no—
363C23×C3—42no—
364C23×C3—44no—
365C23×C3—42no—
366C23×C3—42no—
367C23×C3—42no—
368C23×C3—42no—
369C23×C3—61no—
370C23×C3—82no—
371C23×C3—82no—
372C23×C3D3×D411yescharacteristic
373C23×C3C2×C3×D411yescharacteristic
374C22×D3—21no—
375C3×Q8—22no—
376C3×Q8—22no—
377C3×Q8—42no—
378C3×D4—24no—
379C3×D4—24no—
380C3×D4—22no—
381C3×D4—22no—
382C3×D4—24no—
383C3×D4—42no—
384C3×D4—44no—
385C3×D4—62no—
386C3×D4—122no—
387C3×D4#23714yes—
388C3×D4C3×#4114yes—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—31no—
398C2×C3×C4—31no—
399C2×C3×C4—31no—
400C2×C3×C4—31no—
401C2×C3×C4—42no—
402C2×C3×C4—41no—
403C2×C3×C4—41no—
404C2×C3×C4—62no—
405C2×C3×C4—62no—
406C2×C3×C4—61no—
407C2×C3×C4—62no—
408C2×C3×C4—122no—
409C2×C3×C4—124no—
410C2×C3×C4—124no—
411C2×C3×C4—122no—
412C2×C3×C4D3×D411yescharacteristic
413C2×C3×C4C2×C3×D411yescharacteristic
414C2×C3×C4C23×D311yescharacteristic
415C2×C3×C4C24×C311yescharacteristic
416#67—42no—
417C2×Dic3—22no—
418C2×Dic3—22no—
419C2×Dic3—21no—
420C2×Dic3—22no—
421C2×Dic3—44no—
422C2×Dic3—42no—
423C2×Dic3—44no—
424C2×Dic3C2×C3×D411yescharacteristic
425C2×Dic3C2×C3×D411yescharacteristic
426C2×Dic3C2×C3×D411yescharacteristic
427C2×Dic3C2×C3×D411yescharacteristic
428D12—22no—
429C4×D3—42no—
430C3×C8—22no—
431C3×C8—22no—
432C3×C8—42no—
433C3×C8—62no—
434C3⋊C8—22no—
435C2×C32—22no—
436C2×C32—44no—
437C2×C32#52511yescharacteristic
438C2×C32C2×#13511yescharacteristic
439C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
440C3×D3—81no—
441C24—21no—
442C2×Q8C22×C3×D311yescharacteristic
443C2×D4—24no—
444C2×D4—21no—
445C2×D4—31no—
446C2×D4—61no—
447C2×D4C22×C3×D312yes—
448C22×C4—31no—
449C22×C4—31no—
450C22×C4—61no—
451C22×C4—62no—
452C22×C4—62no—
453C22×C4—61no—
454C22×C4—124no—
455C22×C4C22×C3×D311yescharacteristic
456SD16—24no—
457D8—64no—
458C2×C8—32no—
459C2×C8C22×C3×D312yes—
460C4⋊C4—21no—
461C4⋊C4—31no—
462C4⋊C4—32no—
463C4⋊C4—61no—
464C4⋊C4—61no—
465C4⋊C4—61no—
466C4⋊C4—61no—
467C4⋊C4C22×C3×D311yescharacteristic
468C22⋊C4—21no—
469C22⋊C4—61no—
470C22⋊C4—61no—
471C22⋊C4—61no—
472C22⋊C4—62no—
473C22⋊C4—62no—
474C22⋊C4—61no—
475C42—31no—
476C42—31no—
477C42—31no—
478C42—31no—
479C42—61no—
480C22×C3—21no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—24no—
485C22×C3—24no—
486C22×C3—22no—
487C22×C3—21no—
488C22×C3—41no—
489C22×C3—41no—
490C22×C3—44no—
491C22×C3—48no—
492C22×C3—48no—
493C22×C3—42no—
494C22×C3—42no—
495C22×C3—42no—
496C22×C3—42no—
497C22×C3—82no—
498C22×C3—82no—
499C22×C3—88no—
500C22×C3—121no—
501C22×C3—121no—
502C22×C3—121no—
503C22×C3#91612yes—
504C22×C3C3×#13512yes—
505C22×C3C2×D3×D411yescharacteristic
506C22×C3C22×C3×D411yescharacteristic
507C2×D3—41no—
508C2×D3—41no—
509C2×D3—41no—
510C3×C4—21no—
511C3×C4—21no—
512C3×C4—22no—
513C3×C4—32no—
514C3×C4—41no—
515C3×C4—41no—
516C3×C4—41no—
517C3×C4—41no—
518C3×C4—41no—
519C3×C4—61no—
520C3×C4—61no—
521C3×C4—61no—
522C3×C4—81no—
523C3×C4—81no—
524C3×C4—121no—
525C3×C4—122no—
526C3×C4C2×#23712yes—
527C3×C4C2×C3×#4112yes—
528Dic3—21no—
529Dic3—21no—
530Dic3—21no—
531Dic3—41no—
532Dic3—42no—
533Dic3C3×AGL(1,ℤ/8)12yes—
534C32#310511yescharacteristic, complemented, Sylow
535C23—24no—
536C23—22no—
537C23—42no—
538C23—42no—
539C23—61no—
540C23C3×D3×D411yescharacteristic
541Q8—22no—
542D4—24no—
543D4—22no—
544D4—62no—
545D4—122no—
546D4C3×#23714yes—
547C2×C4—22no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—31no—
551C2×C4—31no—
552C2×C4—31no—
553C2×C4—31no—
554C2×C4—62no—
555C2×C4—62no—
556C2×C4—61no—
557C2×C4—62no—
558C2×C4—122no—
559C2×C4—124no—
560C2×C4—124no—
561C2×C4—122no—
562C2×C4C3×D3×D411yescharacteristic
563C2×C4C23×C3×D311yescharacteristic
564C8—22no—
565C8—62no—
566C2×C3—22no—
567C2×C3—22no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—42no—
572C2×C3—44no—
573C2×C3—44no—
574C2×C3—84no—
575C2×C3—241no—
576C2×C3#558611yescharacteristic
577C2×C3C2×#91611yescharacteristic
578C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
579C2×C3C3×#52511yescharacteristic
580C2×C3C2×C3×#13511yescharacteristic
581C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
582D3—81no—
583C22—21no—
584C22—21no—
585C22—24no—
586C22—48no—
587C22—42no—
588C22—42no—
589C22—121no—
590C22—121no—
591C22—121no—
592C22C3×#91612yes—
593C22C2×C3×D3×D411yescharacteristic
594C4—21no—
595C4—32no—
596C4—41no—
597C4—41no—
598C4—61no—
599C4—61no—
600C4—61no—
601C4—121no—
602C4—122no—
603C4C2×C3×#23712yes—
604C3—21no—
605C3#8013311yescharacteristic, direct product factor
606C3C3×#310511yescharacteristic, complemented
607C2—22no—
608C2—44no—
609C2—241no—
610C2C3×#558611yescharacteristic
611C2C2×C3×#91611yescharacteristic
612C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#450C2
socleC22×C32C22×D4
prime radicalC3×#5217C2
hypercenterC3×#450D3
hypocenterC3C3×#3105
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#450

Complements

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

NH ≅ G/Ntype
1. C2×C3×D4×Dic3C2semidirect
2. C3×#5624C2semidirect
3. C32×#450C2semidirect
5. C3×#5165C2semidirect
6. C3×Dic3×SD16C2semidirect
7. C3×#5044C2semidirect
8. C3×#4763C2semidirect
9. C3×#4756C2semidirect
10. C3×#4735C2semidirect
11. C3×#4718C2semidirect
13. #80133C3direct (N × H)
19. C3×#947C22semidirect
20. C3×Q8×Dic3C22semidirect
30. C3×#893C22semidirect
32. C3×#890C22semidirect
37. C3×#835C22semidirect
40. C3×#821C22semidirect
41. C3×#817C22semidirect
42. C3×Dic3⋊C8C22semidirect
43. C3×C8×Dic3C22semidirect
44. C3×#807C22semidirect
47. C2×D4×Dic3C2×C3semidirect
48. #5624C2×C3semidirect
54. C3×#450D3semidirect
55. C3×#450C2×C3semidirect
61. #5165C2×C3semidirect
62. Dic3×SD16C2×C3semidirect
63. #5044C2×C3semidirect
64. #4763C2×C3semidirect
65. #4756C2×C3semidirect
66. #4735C2×C3semidirect
67. #4718C2×C3semidirect
137. #947C22×C3semidirect
138. Q8×Dic3C22×C3semidirect
148. #893C22×C3semidirect
150. #890C22×C3semidirect
167. #835C22×C3semidirect
170. #821C22×C3semidirect
171. #817C22×C3semidirect
172. Dic3⋊C8C22×C3semidirect
173. C8×Dic3C22×C3semidirect
174. #807C22×C3semidirect
212. #450C3×D3semidirect
534. C32#3105semidirect
605. C3#80133direct (N × H)
606. C3C3×#3105semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×Dic32
C3×#56242
C32×#4502
C3×#52172
C3×#51652
C3×Dic3×SD162
C3×#50442
C3×#47632
C3×#47562
C3×#47352
C3×#47182
C3×#31053
#801333