Finite Group Databasebeta

← C3×#81453 #11870859

Subgroups — C3×#81453 #11870859

Order 1152.

960 conjugacy classes of subgroups.

The subgroup lattice has 603 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5624C211yesmaximal, characteristic, complemented
2C2×C3×#893C211yesmaximal, characteristic, complemented
3C32×#484C211yesmaximal, characteristic, complemented
4C3×#5046C211yesmaximal, characteristic, complemented
5C3×#4968C211yesmaximal, characteristic, complemented
6C3×#4891C212yesmaximal, complemented
7C3×#4872C212yesmaximal, complemented
8C3×#4819C212yesmaximal, complemented
9C3×#4788C212yesmaximal, complemented
10C3×#4732C211yesmaximal, characteristic
11C3×#4718C211yesmaximal, characteristic, complemented
12C3×#3105—31nomaximal
13#81453C311yesmaximal, characteristic, direct product factor
14C22×C3×D12C2211yescharacteristic
15C22×C3×C4×D3—21no—
16C32×C22⋊Q8C2211yescharacteristic
17C2×C32×C4⋊C4C2211yescharacteristic
18C3×#947C2211yescharacteristic, complemented
19C3×Q8×Dic3C2211yescharacteristic, complemented
20C2×C3×#215C2212yes—
21C3×#930C2211yescharacteristic
22C2×C3×(C2×D3)⋊C4—21no—
23C2×C3×C4×Dic3C2211yescharacteristic
24C2×C3×D24C2212yes—
25C3×#898—21no—
26C3×#893—21no—
27C3×#893—21no—
28C3×#893C2212yes—
29C3×#893C2212yes—
30C3×#893C2211yescharacteristic, complemented
31C3×#892—21no—
32C3×#890C2211yescharacteristic, complemented
33C3×#886—21no—
34C3×#67⋊C4—21no—
35C32×#107C2212yescomplemented
36C32×#103C2212yescomplemented
37C32×C22⋊C8C2211yescharacteristic
38C3×#830C2211yescharacteristic
39C3×#821C2212yes—
40C3×Dic3⋊C8C2212yescomplemented
41C3×C8×Dic3C2212yescomplemented
42C3×#809C2212yes—
43C3×#809C2212yescomplemented
44C3×#808C2212yescomplemented
45C3×#529—31no—
46C2×C3×C4×D4—31no—
47#5624C2×C311yescharacteristic, complemented
48C2×#893C2×C311yescharacteristic, complemented
49C3×#484—21no—
50C3×#484D311yescharacteristic, complemented
51C3×#484C2×C311yescharacteristic, complemented
52C3×#481—31no—
53C3×#478—32no—
54C3×#463—32no—
55C3×#450—31no—
56C3×#447—31no—
57C3×C4×SD16—32no—
58C3×C4×D8—32no—
59C3×#431—31no—
60#5046C2×C311yescharacteristic, complemented
61#4968C2×C311yescharacteristic, complemented
62#4891C2×C312yescomplemented
63#4872C2×C312yescomplemented
64#4819C2×C312yescomplemented
65#4788C2×C312yescomplemented
66#4732C2×C311yescharacteristic
67#4718C2×C311yescharacteristic, complemented
68C23×C3×D3—21no—
69C2×C32×Q8C2311yescharacteristic
70C22×C32×C4—21no—
71C22×C32×C4C2311yescharacteristic
72C2×C3×#67—21no—
73C22×C3×Dic3D411yescharacteristic
74C22×C3×Dic3D411yescharacteristic
75C2×C3×D12—21no—
76C2×C3×D12—24no—
77C2×C3×D12C2311yescharacteristic
78C2×C3×D12C2312yes—
79C2×C3×C4×D3—21no—
80C2×C3×C4×D3—22no—
81C2×C3×C4×D3—22no—
82C2×C3×C4×D3—44no—
83C2×C32×C8C2312yes—
84C32×C4⋊C4—21no—
85C32×C4⋊C4—21no—
86C32×C4⋊C4C2311yescharacteristic
87C32×C4⋊C4C2312yes—
88C32×C22⋊C4—21no—
89C3×#215—24no—
90C3×(C2×D3)⋊C4—21no—
91C3×(C2×D3)⋊C4—21no—
92C3×(C2×D3)⋊C4—21no—
93C3×(C2×D3)⋊C4—21no—
94C3×(C2×D3)⋊C4—22no—
95C3×(C2×D3)⋊C4—22no—
96C3×C4⋊Dic3—21no—
97C3×C4⋊Dic3—21no—
98C3×C4⋊Dic3C2311yescharacteristic
99C3×Dic3⋊C4—21no—
100C3×C4×Dic3—21no—
101C3×C4×Dic3D411yescharacteristic
102C3×C4×Dic3D411yescharacteristic
103C3×C4×Dic3C2311yescharacteristic
104C3×C4×Dic3C2311yescharacteristic
105C2×C3×C3⋊C8C2312yes—
106C3×D24—24no—
107#3105—31noSylow
108C22×C3×D4—31no—
109C23×C3×C4—61no—
110C22×D12C22×C311yescharacteristic
111C22×C4×D3—21no—
112C2×C3×SD16—32no—
113C2×C3×D8—32no—
114C3×#126—61no—
115C3×#125—31no—
116C3×#124—31no—
117C3×#123—61no—
118C3×C22⋊Q8—21no—
119C3×C22⋊Q8C2×D311yescharacteristic
120C3×C22⋊Q8C22×C311yescharacteristic
121C3×#121—31no—
122C3×C4×Q8—31no—
123C3×C4×D4—32no—
124C3×C4×D4—32no—
125C3×C4×D4—31no—
126C3×C4×D4—61no—
127C3×C4×D4—61no—
128C3×C4×D4—61no—
129C3×#117—61no—
130C2×C3×C4⋊C4—21no—
131C2×C3×C4⋊C4C2×D311yescharacteristic
132C2×C3×C4⋊C4C22×C311yescharacteristic
133C2×C3×C22⋊C4—61no—
134C2×C3×C42—31no—
135#947C22×C311yescharacteristic, complemented
136Q8×Dic3C22×C311yescharacteristic, complemented
137C2×#215C22×C312yes—
138#930C22×C311yescharacteristic
139C2×(C2×D3)⋊C4—21no—
140C2×C4×Dic3C22×C311yescharacteristic
141C2×D24C22×C312yes—
142#898—21no—
143#893—21no—
144#893—21no—
145#893C22×C312yes—
146#893C22×C312yes—
147#893C22×C311yescharacteristic, complemented
148#892—21no—
149#890C22×C311yescharacteristic, complemented
150#886—21no—
151#67⋊C4—21no—
152C3×#107—22no—
153C3×#107C2×D312yescomplemented
154C3×#107C22×C312yescomplemented
155C3×#106—32no—
156C3×C4⋊C8—32no—
157C3×#103—22no—
158C3×#103C2×D312yescomplemented
159C3×#103C22×C312yescomplemented
160C3×#102—32no—
161C3×#102—32no—
162C3×#102—32no—
163C3×C22⋊C8—21no—
164C3×C22⋊C8—31no—
165C3×C22⋊C8C2×D311yescharacteristic
166C3×C22⋊C8C22×C311yescharacteristic
167C3×C4×C8—32no—
168#830C22×C311yescharacteristic
169#821C22×C312yes—
170Dic3⋊C8C22×C312yescomplemented
171C8×Dic3C22×C312yescomplemented
172#809C22×C312yes—
173#809C22×C312yescomplemented
174#808C22×C312yescomplemented
175C23×C32C2×D411yescharacteristic
176C22×C3×D3—24no—
177C22×C3×D3—22no—
178C22×C3×D3—21no—
179C22×C3×D3—42no—
180C22×C3×D3—42no—
181C32×Q8—22no—
182C2×C32×C4—22no—
183C2×C32×C4—21no—
184C2×C32×C4—21no—
185C2×C32×C4—22no—
186C2×C32×C4—42no—
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2411yescharacteristic
189C3×#67—42no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3C2×D411yescharacteristic
194C2×C3×Dic3C2×D411yescharacteristic
195C2×C3×Dic3C2×D411yescharacteristic
196C2×C3×Dic3C2×D411yescharacteristic
197C3×D12—24no—
198C3×D12—22no—
199C3×D12—22no—
200C3×D12#4114yes—
201C3×C4×D3—44no—
202C3×C4×D3—42no—
203C3×C4×D3—44no—
204C32×C8—22no—
205C3×C3⋊C8—22no—
206#529—31no—
207C2×C4×D4—31no—
208#484C3×D311yescharacteristic, complemented
209#481—31no—
210#478—32no—
211#463—32no—
212#450—31no—
213#447—31no—
214C4×SD16—32no—
215C4×D8—32no—
216#431—31no—
217C24×C3—61no—
218C23×D3—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8C22×D311yescharacteristic
221C2×C3×Q8C23×C311yescharacteristic
222C2×C3×D4—32no—
223C2×C3×D4—31no—
224C2×C3×D4—64no—
225C2×C3×D4—61no—
226C2×C3×D4—61no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—31no—
231C22×C3×C4—31no—
232C22×C3×C4—41no—
233C22×C3×C4—61no—
234C22×C3×C4—62no—
235C22×C3×C4—62no—
236C22×C3×C4—124no—
237C22×C3×C4C22×D311yescharacteristic
238C22×C3×C4C23×C311yescharacteristic
239C2×#67—21no—
240C22×Dic3C3×D411yescharacteristic
241C22×Dic3C3×D411yescharacteristic
242C2×D12—21no—
243C2×D12—24no—
244C2×D12C23×C311yescharacteristic
245C2×D12C23×C312yes—
246C2×C4×D3—21no—
247C2×C4×D3—22no—
248C2×C4×D3—22no—
249C2×C4×D3—44no—
250C3×SD16—64no—
251C3×D8—64no—
252C2×C3×C8—22no—
253C2×C3×C8—32no—
254C2×C3×C8C22×D312yes—
255C2×C3×C8C23×C312yes—
256C3×C4⋊C4—21no—
257C3×C4⋊C4—21no—
258C3×C4⋊C4—21no—
259C3×C4⋊C4—21no—
260C3×C4⋊C4—22no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—31no—
263C3×C4⋊C4—41no—
264C3×C4⋊C4—41no—
265C3×C4⋊C4—61no—
266C3×C4⋊C4—61no—
267C3×C4⋊C4—61no—
268C3×C4⋊C4C22×D311yescharacteristic
269C3×C4⋊C4C22×D312yes—
270C3×C4⋊C4C23×C312yes—
271C3×C4⋊C4C23×C311yescharacteristic
272C3×C22⋊C4—21no—
273C3×C22⋊C4—21no—
274C3×C22⋊C4—41no—
275C3×C22⋊C4—62no—
276C3×C22⋊C4—62no—
277C3×C22⋊C4—61no—
278C3×C22⋊C4—61no—
279C3×C22⋊C4—61no—
280C3×C22⋊C4—61no—
281C3×C42—31no—
282C3×C42—31no—
283C3×C42—31no—
284C3×C42—31no—
285C3×C42—61no—
286#215—24no—
287(C2×D3)⋊C4—21no—
288(C2×D3)⋊C4—21no—
289(C2×D3)⋊C4—21no—
290(C2×D3)⋊C4—21no—
291(C2×D3)⋊C4—22no—
292(C2×D3)⋊C4—22no—
293C4⋊Dic3—21no—
294C4⋊Dic3—21no—
295C4⋊Dic3C23×C311yescharacteristic
296Dic3⋊C4—21no—
297C4×Dic3—21no—
298C4×Dic3C3×D411yescharacteristic
299C4×Dic3C3×D411yescharacteristic
300C4×Dic3C23×C311yescharacteristic
301C4×Dic3C23×C311yescharacteristic
302C2×C3⋊C8C23×C312yes—
303D24—24no—
304C22×C32—21no—
305C22×C32—21no—
306C22×C32#13512yes—
307C22×C32C22×D411yescharacteristic
308C2×C3×D3—24no—
309C2×C3×D3—48no—
310C2×C3×D3—42no—
311C2×C3×D3—42no—
312C2×C3×D3—41no—
313C2×C3×D3—41no—
314C2×C3×D3—41no—
315C32×C4—21no—
316C32×C4—41no—
317C32×C4—42no—
318C32×C4—41no—
319C32×C4C2×#4112yes—
320C3×Dic3—21no—
321C3×Dic3—21no—
322C3×Dic3—21no—
323C3×Dic3—41no—
324C3×Dic3AGL(1,ℤ/8)12yes—
325C22×D4—31no—
326C23×C4—61no—
327C2×SD16—32no—
328C2×D8—32no—
329#126—61no—
330#125—31no—
331#124—31no—
332#123—61no—
333C22⋊Q8C2×C3×D311yescharacteristic
334#121—31no—
335C4×Q8—31no—
336C4×D4—32no—
337C4×D4—32no—
338C4×D4—31no—
339C4×D4—61no—
340C4×D4—61no—
341C4×D4—61no—
342#117—61no—
343C2×C4⋊C4C2×C3×D311yescharacteristic
344C2×C22⋊C4—61no—
345C2×C42—31no—
346#107C2×C3×D312yescomplemented
347#106—32no—
348C4⋊C8—32no—
349#103C2×C3×D312yescomplemented
350#102—32no—
351#102—32no—
352#102—32no—
353C22⋊C8—31no—
354C22⋊C8C2×C3×D311yescharacteristic
355C4×C8—32no—
356C23×C3—21no—
357C23×C3—64no—
358C23×C3—62no—
359C23×C3—61no—
360C23×C3—122no—
361C23×C3—122no—
362C23×C3D3×D411yescharacteristic
363C23×C3C2×C3×D411yescharacteristic
364C22×D3—24no—
365C22×D3—22no—
366C22×D3—21no—
367C22×D3—42no—
368C22×D3—42no—
369C3×Q8—22no—
370C3×Q8—22no—
371C3×Q8—42no—
372C3×D4—34no—
373C3×D4—64no—
374C3×D4—62no—
375C3×D4—62no—
376C3×D4—122no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—22no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—22no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—31no—
388C2×C3×C4—31no—
389C2×C3×C4—31no—
390C2×C3×C4—31no—
391C2×C3×C4—42no—
392C2×C3×C4—41no—
393C2×C3×C4—41no—
394C2×C3×C4—42no—
395C2×C3×C4—42no—
396C2×C3×C4—42no—
397C2×C3×C4—62no—
398C2×C3×C4—62no—
399C2×C3×C4—61no—
400C2×C3×C4—82no—
401C2×C3×C4—122no—
402C2×C3×C4—124no—
403C2×C3×C4—124no—
404C2×C3×C4D3×D411yescharacteristic
405C2×C3×C4C2×C3×D411yescharacteristic
406C2×C3×C4C23×D311yescharacteristic
407C2×C3×C4C24×C311yescharacteristic
408#67—42no—
409C2×Dic3—22no—
410C2×Dic3—22no—
411C2×Dic3—21no—
412C2×Dic3C2×C3×D411yescharacteristic
413C2×Dic3C2×C3×D411yescharacteristic
414C2×Dic3C2×C3×D411yescharacteristic
415C2×Dic3C2×C3×D411yescharacteristic
416D12—24no—
417D12—22no—
418D12—22no—
419D12C3×#4114yes—
420C4×D3—44no—
421C4×D3—42no—
422C4×D3—44no—
423C3×C8—22no—
424C3×C8—22no—
425C3×C8—42no—
426C3×C8—62no—
427C3⋊C8—22no—
428C2×C32—22no—
429C2×C32#52511yescharacteristic
430C2×C32C2×#13511yescharacteristic
431C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
432C3×D3—44no—
433C3×D3—81no—
434C24—61no—
435C2×Q8C22×C3×D311yescharacteristic
436C2×D4—32no—
437C2×D4—31no—
438C2×D4—64no—
439C2×D4—61no—
440C2×D4—61no—
441C22×C4—21no—
442C22×C4—31no—
443C22×C4—31no—
444C22×C4—61no—
445C22×C4—62no—
446C22×C4—62no—
447C22×C4—124no—
448C22×C4C22×C3×D311yescharacteristic
449SD16—64no—
450D8—64no—
451C2×C8—32no—
452C2×C8C22×C3×D312yes—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—31no—
456C4⋊C4—61no—
457C4⋊C4—61no—
458C4⋊C4—61no—
459C4⋊C4C22×C3×D311yescharacteristic
460C4⋊C4C22×C3×D312yes—
461C22⋊C4—21no—
462C22⋊C4—62no—
463C22⋊C4—62no—
464C22⋊C4—61no—
465C22⋊C4—61no—
466C22⋊C4—61no—
467C22⋊C4—61no—
468C42—31no—
469C42—31no—
470C42—31no—
471C42—31no—
472C42—61no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—22no—
478C22×C3—21no—
479C22×C3—41no—
480C22×C3—41no—
481C22×C3—64no—
482C22×C3—128no—
483C22×C3—122no—
484C22×C3—122no—
485C22×C3—121no—
486C22×C3—121no—
487C22×C3—121no—
488C22×C3#91912yes—
489C22×C3C3×#13512yes—
490C22×C3C2×D3×D411yescharacteristic
491C22×C3C22×C3×D411yescharacteristic
492C2×D3—24no—
493C2×D3—48no—
494C2×D3—42no—
495C2×D3—42no—
496C2×D3—41no—
497C2×D3—41no—
498C2×D3—41no—
499C3×C4—21no—
500C3×C4—21no—
501C3×C4—22no—
502C3×C4—32no—
503C3×C4—41no—
504C3×C4—42no—
505C3×C4—41no—
506C3×C4—41no—
507C3×C4—42no—
508C3×C4—41no—
509C3×C4—41no—
510C3×C4—61no—
511C3×C4—61no—
512C3×C4—61no—
513C3×C4—82no—
514C3×C4—81no—
515C3×C4—81no—
516C3×C4—121no—
517C3×C4D3×#4112yes—
518C3×C4C2×C3×#4112yes—
519Dic3—21no—
520Dic3—21no—
521Dic3—21no—
522Dic3—41no—
523Dic3C3×AGL(1,ℤ/8)12yes—
524C32#310511yescharacteristic, complemented, Sylow
525C23—64no—
526C23—62no—
527C23—61no—
528C23—122no—
529C23—122no—
530C23C3×D3×D411yescharacteristic
531Q8—22no—
532D4—34no—
533D4—64no—
534D4—62no—
535D4—62no—
536D4—122no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—31no—
542C2×C4—31no—
543C2×C4—31no—
544C2×C4—31no—
545C2×C4—42no—
546C2×C4—62no—
547C2×C4—62no—
548C2×C4—61no—
549C2×C4—124no—
550C2×C4—122no—
551C2×C4—124no—
552C2×C4C3×D3×D411yescharacteristic
553C2×C4C23×C3×D311yescharacteristic
554C8—22no—
555C8—62no—
556C2×C3—22no—
557C2×C3—22no—
558C2×C3—21no—
559C2×C3—21no—
560C2×C3—21no—
561C2×C3—42no—
562C2×C3—124no—
563C2×C3—241no—
564C2×C3#565611yescharacteristic
565C2×C3C2×#91911yescharacteristic
566C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
567C2×C3C3×#52511yescharacteristic
568C2×C3C2×C3×#13511yescharacteristic
569C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
570D3—44no—
571D3—81no—
572C22—21no—
573C22—21no—
574C22—64no—
575C22—128no—
576C22—122no—
577C22—122no—
578C22—121no—
579C22—121no—
580C22—121no—
581C22C3×#91912yes—
582C22C2×C3×D3×D411yescharacteristic
583C4—21no—
584C4—32no—
585C4—42no—
586C4—41no—
587C4—41no—
588C4—61no—
589C4—61no—
590C4—61no—
591C4—121no—
592C4C3×D3×#4112yes—
593C3—21no—
594C3#8145311yescharacteristic, direct product factor
595C3C3×#310511yescharacteristic, complemented
596C2—22no—
597C2—124no—
598C2—241no—
599C2C3×#565611yescharacteristic
600C2C2×C3×#91911yescharacteristic
601C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#484C2
socleC22×C32C22×D4
prime radicalC3×#4732C2
hypercenterC3×#484D3
hypocenterC3C3×#3105
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#484

Complements

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

NH ≅ G/Ntype
1. C3×#5624C2semidirect
2. C2×C3×#893C2semidirect
3. C32×#484C2semidirect
4. C3×#5046C2semidirect
5. C3×#4968C2semidirect
6. C3×#4891C2semidirect
7. C3×#4872C2semidirect
8. C3×#4819C2semidirect
9. C3×#4788C2semidirect
11. C3×#4718C2semidirect
13. #81453C3direct (N × H)
18. C3×#947C22semidirect
19. C3×Q8×Dic3C22semidirect
30. C3×#893C22semidirect
32. C3×#890C22semidirect
35. C32×#107C22semidirect
36. C32×#103C22semidirect
40. C3×Dic3⋊C8C22semidirect
41. C3×C8×Dic3C22semidirect
43. C3×#809C22semidirect
44. C3×#808C22semidirect
47. #5624C2×C3semidirect
48. C2×#893C2×C3semidirect
50. C3×#484D3semidirect
51. C3×#484C2×C3semidirect
60. #5046C2×C3semidirect
61. #4968C2×C3semidirect
62. #4891C2×C3semidirect
63. #4872C2×C3semidirect
64. #4819C2×C3semidirect
65. #4788C2×C3semidirect
67. #4718C2×C3semidirect
135. #947C22×C3semidirect
136. Q8×Dic3C22×C3semidirect
147. #893C22×C3semidirect
149. #890C22×C3semidirect
153. C3×#107C2×D3semidirect
154. C3×#107C22×C3semidirect
158. C3×#103C2×D3semidirect
159. C3×#103C22×C3semidirect
170. Dic3⋊C8C22×C3semidirect
171. C8×Dic3C22×C3semidirect
173. #809C22×C3semidirect
174. #808C22×C3semidirect
208. #484C3×D3semidirect
346. #107C2×C3×D3semidirect
349. #103C2×C3×D3semidirect
524. C32#3105semidirect
594. C3#81453direct (N × H)
595. C3C3×#3105semidirect

Maximal subgroups

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

subgroupindex
C3×#56242
C2×C3×#8932
C32×#4842
C3×#50462
C3×#49682
C3×#48912
C3×#48722
C3×#48192
C3×#47882
C3×#47322
C3×#47182
C3×#31053
#814533