Finite Group Databasebeta

← C3×#80996 #11870717

Subgroups — C3×#80996 #11870717

Order 1152.

904 conjugacy classes of subgroups.

The subgroup lattice has 601 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5725C211yesmaximal, characteristic
2C3×C4×D3×Q8C211yesmaximal, characteristic, complemented
3C32×#475C211yesmaximal, characteristic, complemented
4C3×#5094C211yesmaximal, characteristic, complemented
5C3×#5027C211yesmaximal, characteristic, complemented
6C3×#4863C212yesmaximal, complemented
7C3×#4852C212yesmaximal, complemented
8C3×#4848C211yesmaximal, characteristic, complemented
9C3×#4833C211yesmaximal, characteristic, complemented
10C3×#4806C212yesmaximal, complemented
11C3×#4788C212yesmaximal, complemented
12C3×#3103—31nomaximal
13#80996C311yesmaximal, characteristic, direct product factor
14C2×C3×#239—21no—
15C2×C3×D3×Q8C2211yescharacteristic
16C32×C4⋊Q8C2211yescharacteristic
17C32×C4×Q8C2211yescharacteristic
18C3×#947—21no—
19C3×Q8×Dic3C2211yescharacteristic
20C2×C3×#215C2212yes—
21C2×C3×#204C2212yes—
22C3×#895—21no—
23C3×#895C2212yes—
24C3×#893—21no—
25C3×#893C2212yes—
26C3×D3×C4⋊C4—21no—
27C3×D3×C4⋊C4C2211yescharacteristic
28C3×#887—21no—
29C3×#887C2211yescharacteristic
30C3×#874C2211yescharacteristic
31C3×C42×D3—21no—
32C3×C42×D3C2211yescharacteristic
33C3×C4×Dic6—21no—
34C3×C4×Dic6C2211yescharacteristic
35C32×#106C2212yes—
36C32×C4⋊C8C2211yescharacteristic
37C32×#103C2212yes—
38C3×#821C2212yes—
39C3×(C2×D3)⋊C8C2212yes—
40C3×C8×Dic3C2212yes—
41C3×#810C2212yes—
42C3×#809C2212yes—
43C3×#808C2212yes—
44C3×C4⋊(C3⋊C8)C2211yescharacteristic
45C3×#532—31no—
46C2×C3×C4×Q8—31no—
47#5725C2×C311yescharacteristic
48C4×D3×Q8C2×C311yescharacteristic, complemented
49C3×#481—32no—
50C3×#475—21no—
51C3×#475—31no—
52C3×#475D311yescharacteristic, complemented
53C3×#475C2×C311yescharacteristic, complemented
54C3×#460—31no—
55C3×#460—31no—
56C3×#448—32no—
57C3×C4×SD16—32no—
58C3×C4×SD16—32no—
59C3×#431—31no—
60#5094C2×C311yescharacteristic, complemented
61#5027C2×C311yescharacteristic, complemented
62#4863C2×C312yescomplemented
63#4852C2×C312yescomplemented
64#4848C2×C311yescharacteristic, complemented
65#4833C2×C311yescharacteristic, complemented
66#4806C2×C312yescomplemented
67#4788C2×C312yescomplemented
68C2×C32×Q8—21no—
69C2×C32×Q8C2311yescharacteristic
70C3×#239—44no—
71C3×D3×Q8—22no—
72C3×D3×Q8—22no—
73C2×C3×D12—22no—
74C2×C3×D12—21no—
75C2×C3×D12—21no—
76C2×C3×D12C2312yes—
77C2×C3×C4×D3—21no—
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3—22no—
80C2×C3×C4×D3D411yescharacteristic
81C2×C3×C4×D3D411yescharacteristic
82C2×C3×C4×D3C2311yescharacteristic
83C2×C3×Dic6—21no—
84C2×C3×Dic6C2311yescharacteristic
85C2×C32×C8C2312yes—
86C32×C4⋊C4—21no—
87C32×C4⋊C4—21no—
88C32×C4⋊C4C2311yescharacteristic
89C32×C4⋊C4C2312yes—
90C32×C42—21no—
91C32×C42C2311yescharacteristic
92C3×#215—24no—
93C3×(C2×D3)⋊C4—22no—
94C3×(C2×D3)⋊C4—22no—
95C3×C4⋊Dic3—21no—
96C3×C4⋊Dic3C2311yescharacteristic
97C3×Dic3⋊C4—21no—
98C3×Dic3⋊C4—21no—
99C3×Dic3⋊C4—21no—
100C3×C4×Dic3—21no—
101C3×C4×Dic3—21no—
102C3×C4×Dic3—21no—
103C3×C4×Dic3D411yescharacteristic
104C3×C4×Dic3D411yescharacteristic
105C3×C4×Dic3C2311yescharacteristic
106C2×C3×C3⋊C8C2312yes—
107C3×#204—24no—
108#3103—31noSylow
109C2×C3×#41—61no—
110C22×C3×Q8—31no—
111C2×#239—21no—
112C2×D3×Q8C22×C311yescharacteristic
113C2×C3×SD16—32no—
114C2×C3×SD16—32no—
115C3×C4⋊Q8—21no—
116C3×C4⋊Q8C2×D311yescharacteristic
117C3×C4⋊Q8C22×C311yescharacteristic
118C3×#127—31no—
119C3×#124—61no—
120C3×#121—32no—
121C3×#121—61no—
122C3×C4×Q8—21no—
123C3×C4×Q8—31no—
124C3×C4×Q8—31no—
125C3×C4×Q8—31no—
126C3×C4×Q8—61no—
127C3×C4×Q8—61no—
128C3×C4×Q8C2×D311yescharacteristic
129C3×C4×Q8C22×C311yescharacteristic
130C3×C4×D4—32no—
131C3×C4×D4—61no—
132C2×C3×C4⋊C4—31no—
133C2×C3×C4⋊C4—61no—
134C2×C3×C42—31no—
135C2×C3×C42—61no—
136#947—21no—
137Q8×Dic3C22×C311yescharacteristic
138C2×#215C22×C312yes—
139C2×#204C22×C312yes—
140#895—21no—
141#895C22×C312yes—
142#893—21no—
143#893C22×C312yes—
144D3×C4⋊C4—21no—
145D3×C4⋊C4C22×C311yescharacteristic
146#887—21no—
147#887C22×C311yescharacteristic
148#874C22×C311yescharacteristic
149C42×D3—21no—
150C42×D3C22×C311yescharacteristic
151C4×Dic6—21no—
152C4×Dic6C22×C311yescharacteristic
153C3×#106—22no—
154C3×#106—32no—
155C3×#106C2×D312yes—
156C3×#106C22×C312yes—
157C3×C4⋊C8—21no—
158C3×C4⋊C8—31no—
159C3×C4⋊C8C2×D311yescharacteristic
160C3×C4⋊C8C22×C311yescharacteristic
161C3×#103—22no—
162C3×#103—32no—
163C3×#103C2×D312yes—
164C3×#103C22×C312yes—
165C3×#102—32no—
166C3×#102—32no—
167C3×C22⋊C8—32no—
168C3×C4×C8—32no—
169#821C22×C312yes—
170(C2×D3)⋊C8C22×C312yes—
171C8×Dic3C22×C312yes—
172#810C22×C312yes—
173#809C22×C312yes—
174#808C22×C312yes—
175C4⋊(C3⋊C8)C22×C311yescharacteristic
176C22×C3×D3—22no—
177C22×C3×D3C2×D411yescharacteristic
178C32×Q8—21no—
179C32×Q8—42no—
180C32×Q8#4112yescomplemented
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—22no—
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2411yescharacteristic
187C2×C3×Dic3—21no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3C2×D411yescharacteristic
190C2×C3×Dic3C2×D411yescharacteristic
191C2×C3×Dic3C2×D411yescharacteristic
192C3×D12—22no—
193C3×D12—22no—
194C3×D12—42no—
195C3×D12—44no—
196C3×D12—42no—
197C3×C4×D3—24no—
198C3×C4×D3—21no—
199C3×C4×D3—21no—
200C3×C4×D3—41no—
201C3×C4×D3—42no—
202C3×C4×D3—44no—
203C3×C4×D3SD1614yescomplemented
204C3×Dic6—24no—
205C3×Dic6—21no—
206C3×Dic6#4112yescomplemented
207C32×C8—22no—
208C3×C3⋊C8—22no—
209#532—31no—
210C2×C4×Q8—31no—
211#481—32no—
212#475—31no—
213#475C3×D311yescharacteristic, complemented
214#460—31no—
215#460—31no—
216#448—32no—
217C4×SD16—32no—
218C4×SD16—32no—
219#431—31no—
220C3×#41—124no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—31no—
225C2×C3×Q8—41no—
226C2×C3×Q8—61no—
227C2×C3×Q8—62no—
228C2×C3×Q8—62no—
229C2×C3×Q8C22×D311yescharacteristic
230C2×C3×Q8C23×C311yescharacteristic
231C2×C3×D4—32no—
232C2×C3×D4—62no—
233C2×C3×D4—61no—
234C2×C3×D4—61no—
235C22×C3×C4—31no—
236C22×C3×C4—31no—
237C22×C3×C4—31no—
238C22×C3×C4—62no—
239C22×C3×C4—61no—
240C22×C3×C4—61no—
241#239—44no—
242D3×Q8—22no—
243D3×Q8—22no—
244C2×D12—22no—
245C2×D12—21no—
246C2×D12—21no—
247C2×D12C23×C312yes—
248C2×C4×D3—21no—
249C2×C4×D3—21no—
250C2×C4×D3—22no—
251C2×C4×D3C3×D411yescharacteristic
252C2×C4×D3C3×D411yescharacteristic
253C2×C4×D3C23×C311yescharacteristic
254C2×Dic6—21no—
255C2×Dic6C23×C311yescharacteristic
256C3×SD16—64no—
257C3×SD16—64no—
258C2×C3×C8—22no—
259C2×C3×C8—32no—
260C2×C3×C8C22×D312yes—
261C2×C3×C8C23×C312yes—
262C3×C4⋊C4—21no—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—21no—
266C3×C4⋊C4—22no—
267C3×C4⋊C4—21no—
268C3×C4⋊C4—31no—
269C3×C4⋊C4—41no—
270C3×C4⋊C4—41no—
271C3×C4⋊C4—61no—
272C3×C4⋊C4—61no—
273C3×C4⋊C4—61no—
274C3×C4⋊C4—61no—
275C3×C4⋊C4C22×D311yescharacteristic
276C3×C4⋊C4C22×D312yes—
277C3×C4⋊C4C23×C312yes—
278C3×C4⋊C4C23×C311yescharacteristic
279C3×C22⋊C4—62no—
280C3×C22⋊C4—62no—
281C3×C42—21no—
282C3×C42—21no—
283C3×C42—21no—
284C3×C42—31no—
285C3×C42—31no—
286C3×C42—31no—
287C3×C42—41no—
288C3×C42—61no—
289C3×C42—61no—
290C3×C42—61no—
291C3×C42C22×D311yescharacteristic
292C3×C42C23×C311yescharacteristic
293#215—24no—
294(C2×D3)⋊C4—22no—
295(C2×D3)⋊C4—22no—
296C4⋊Dic3—21no—
297C4⋊Dic3C23×C311yescharacteristic
298Dic3⋊C4—21no—
299Dic3⋊C4—21no—
300Dic3⋊C4—21no—
301C4×Dic3—21no—
302C4×Dic3—21no—
303C4×Dic3—21no—
304C4×Dic3C3×D411yescharacteristic
305C4×Dic3C3×D411yescharacteristic
306C4×Dic3C23×C311yescharacteristic
307C2×C3⋊C8C23×C312yes—
308#204—24no—
309C22×C32C22×D411yescharacteristic
310C2×C3×D3—21no—
311C2×C3×D3—21no—
312C2×C3×D3—42no—
313C2×C3×D3—42no—
314C2×C3×D3—42no—
315C2×C3×D3C2×SD1612yes—
316C32×C4—22no—
317C32×C4—21no—
318C32×C4—42no—
319C32×C4—41no—
320C32×C4C2×SD1612yes—
321C32×C4C2×#4111yescharacteristic
322C32×C4C2×#4111yescharacteristic
323C3×Dic3—21no—
324C3×Dic3—22no—
325C3×Dic3—21no—
326C3×Dic3—41no—
327C3×Dic3C2×SD1612yes—
328C2×#41—61no—
329C22×Q8—31no—
330C2×SD16—32no—
331C2×SD16—32no—
332C4⋊Q8C2×C3×D311yescharacteristic
333#127—31no—
334#124—61no—
335#121—32no—
336#121—61no—
337C4×Q8—31no—
338C4×Q8—31no—
339C4×Q8—31no—
340C4×Q8—61no—
341C4×Q8—61no—
342C4×Q8C2×C3×D311yescharacteristic
343C4×D4—32no—
344C4×D4—61no—
345C2×C4⋊C4—31no—
346C2×C4⋊C4—61no—
347C2×C42—31no—
348C2×C42—61no—
349#106—32no—
350#106C2×C3×D312yes—
351C4⋊C8—31no—
352C4⋊C8C2×C3×D311yescharacteristic
353#103—32no—
354#103C2×C3×D312yes—
355#102—32no—
356#102—32no—
357C22⋊C8—32no—
358C4×C8—32no—
359C23×C3—31no—
360C23×C3—62no—
361C22×D3—22no—
362C22×D3C2×C3×D411yescharacteristic
363C3×Q8—21no—
364C3×Q8—21no—
365C3×Q8—22no—
366C3×Q8—32no—
367C3×Q8—41no—
368C3×Q8—42no—
369C3×Q8—42no—
370C3×Q8—64no—
371C3×Q8—61no—
372C3×Q8—82no—
373C3×Q8#23912yescomplemented
374C3×Q8C3×#4112yescomplemented
375C3×D4—62no—
376C3×D4—62no—
377C3×D4—122no—
378C3×D4—124no—
379C3×D4—122no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—22no—
384C2×C3×C4—21no—
385C2×C3×C4—22no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—31no—
390C2×C3×C4—34no—
391C2×C3×C4—31no—
392C2×C3×C4—31no—
393C2×C3×C4—41no—
394C2×C3×C4—41no—
395C2×C3×C4—42no—
396C2×C3×C4—64no—
397C2×C3×C4—61no—
398C2×C3×C4—61no—
399C2×C3×C4—61no—
400C2×C3×C4—61no—
401C2×C3×C4—121no—
402C2×C3×C4—124no—
403C2×C3×C4—122no—
404C2×C3×C4D3×D411yescharacteristic
405C2×C3×C4D3×D411yescharacteristic
406C2×C3×C4C2×C3×D411yescharacteristic
407C2×C3×C4C2×C3×D411yescharacteristic
408C2×C3×C4C23×D311yescharacteristic
409C2×C3×C4C24×C311yescharacteristic
410C2×Dic3—21no—
411C2×Dic3—21no—
412C2×Dic3C2×C3×D411yescharacteristic
413C2×Dic3C2×C3×D411yescharacteristic
414C2×Dic3C2×C3×D411yescharacteristic
415D12—22no—
416D12—22no—
417D12—42no—
418D12—44no—
419D12—42no—
420C4×D3—24no—
421C4×D3—21no—
422C4×D3—21no—
423C4×D3—41no—
424C4×D3—42no—
425C4×D3—44no—
426C4×D3C3×SD1614yescomplemented
427Dic6—24no—
428Dic6—21no—
429Dic6C3×#4112yescomplemented
430C3×C8—22no—
431C3×C8—22no—
432C3×C8—42no—
433C3×C8—62no—
434C3⋊C8—22no—
435C2×C32#52511yescharacteristic
436C2×C32C22×SD1611yescharacteristic
437C2×C32#57511yescharacteristic
438C3×D3—22no—
439C3×D3—82no—
440#41—124no—
441C2×Q8—21no—
442C2×Q8—31no—
443C2×Q8—61no—
444C2×Q8—62no—
445C2×Q8—62no—
446C2×Q8C22×C3×D311yescharacteristic
447C2×D4—32no—
448C2×D4—62no—
449C2×D4—61no—
450C2×D4—61no—
451C22×C4—31no—
452C22×C4—31no—
453C22×C4—31no—
454C22×C4—62no—
455C22×C4—61no—
456C22×C4—61no—
457SD16—64no—
458SD16—64no—
459C2×C8—32no—
460C2×C8C22×C3×D312yes—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—31no—
464C4⋊C4—61no—
465C4⋊C4—61no—
466C4⋊C4—61no—
467C4⋊C4—61no—
468C4⋊C4C22×C3×D311yescharacteristic
469C4⋊C4C22×C3×D312yes—
470C22⋊C4—62no—
471C22⋊C4—62no—
472C42—21no—
473C42—31no—
474C42—31no—
475C42—31no—
476C42—61no—
477C42—61no—
478C42—61no—
479C42C22×C3×D311yescharacteristic
480C22×C3—21no—
481C22×C3—32no—
482C22×C3—61no—
483C22×C3—61no—
484C22×C3—122no—
485C22×C3—122no—
486C22×C3—122no—
487C22×C3C2×D3×D411yescharacteristic
488C22×C3C22×C3×D411yescharacteristic
489C2×D3—21no—
490C2×D3—21no—
491C2×D3—42no—
492C2×D3—42no—
493C2×D3—42no—
494C2×D3C2×C3×SD1612yes—
495C3×C4—21no—
496C3×C4—21no—
497C3×C4—22no—
498C3×C4—22no—
499C3×C4—22no—
500C3×C4—21no—
501C3×C4—21no—
502C3×C4—32no—
503C3×C4—41no—
504C3×C4—42no—
505C3×C4—42no—
506C3×C4—41no—
507C3×C4—42no—
508C3×C4—41no—
509C3×C4—61no—
510C3×C4—61no—
511C3×C4—62no—
512C3×C4—82no—
513C3×C4—81no—
514C3×C4—121no—
515C3×C4D3×SD1612yes—
516C3×C4C2×C3×SD1612yes—
517C3×C4C2×#23911yescharacteristic
518C3×C4D3×#4111yescharacteristic
519C3×C4C2×C3×#4111yescharacteristic
520C3×C4C2×C3×#4111yescharacteristic
521Dic3—21no—
522Dic3—21no—
523Dic3—22no—
524Dic3—41no—
525Dic3C2×C3×SD1612yes—
526C32#310311yescharacteristic, complemented, Sylow
527C23—31no—
528C23—62no—
529Q8—21no—
530Q8—32no—
531Q8—42no—
532Q8—64no—
533Q8—61no—
534Q8C3×#23912yescomplemented
535D4—62no—
536D4—62no—
537D4—122no—
538D4—124no—
539D4—122no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—22no—
543C2×C4—31no—
544C2×C4—34no—
545C2×C4—31no—
546C2×C4—31no—
547C2×C4—64no—
548C2×C4—61no—
549C2×C4—61no—
550C2×C4—61no—
551C2×C4—61no—
552C2×C4—121no—
553C2×C4—124no—
554C2×C4—122no—
555C2×C4C3×D3×D411yescharacteristic
556C2×C4C3×D3×D411yescharacteristic
557C2×C4C23×C3×D311yescharacteristic
558C8—22no—
559C8—62no—
560C2×C3—21no—
561C2×C3—21no—
562C2×C3—21no—
563C2×C3—62no—
564C2×C3—242no—
565C2×C3#562711yescharacteristic
566C2×C3C2×D3×SD1611yescharacteristic
567C2×C3#577711yescharacteristic
568C2×C3C3×#52511yescharacteristic
569C2×C3C22×C3×SD1611yescharacteristic
570C2×C3C3×#57511yescharacteristic
571D3—22no—
572D3—82no—
573C22—32no—
574C22—61no—
575C22—61no—
576C22—122no—
577C22—122no—
578C22—122no—
579C22C2×C3×D3×D411yescharacteristic
580C4—21no—
581C4—22no—
582C4—32no—
583C4—42no—
584C4—41no—
585C4—61no—
586C4—61no—
587C4—62no—
588C4—121no—
589C4C3×D3×SD1612yes—
590C4C2×C3×#23911yescharacteristic
591C4C3×D3×#4111yescharacteristic
592C3—21no—
593C3#8099611yescharacteristic, direct product factor
594C3C3×#310311yescharacteristic, complemented
595C2—62no—
596C2—242no—
597C2C3×#562711yescharacteristic
598C2C2×C3×D3×SD1611yescharacteristic
599C2C3×#577711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#475C2
socleC22×C32C22×D4
prime radicalC3×#5725C2
hypercenterC3×#475D3
hypocenterC3C3×#3103
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#475

Complements

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

NH ≅ G/Ntype
2. C3×C4×D3×Q8C2semidirect
3. C32×#475C2semidirect
4. C3×#5094C2semidirect
5. C3×#5027C2semidirect
6. C3×#4863C2semidirect
7. C3×#4852C2semidirect
8. C3×#4848C2semidirect
9. C3×#4833C2semidirect
10. C3×#4806C2semidirect
11. C3×#4788C2semidirect
13. #80996C3direct (N × H)
48. C4×D3×Q8C2×C3semidirect
52. C3×#475D3semidirect
53. C3×#475C2×C3semidirect
60. #5094C2×C3semidirect
61. #5027C2×C3semidirect
62. #4863C2×C3semidirect
63. #4852C2×C3semidirect
64. #4848C2×C3semidirect
65. #4833C2×C3semidirect
66. #4806C2×C3semidirect
67. #4788C2×C3semidirect
180. C32×Q8#41semidirect
203. C3×C4×D3SD16semidirect
206. C3×Dic6#41semidirect
213. #475C3×D3semidirect
373. C3×Q8#239semidirect
374. C3×Q8C3×#41semidirect
426. C4×D3C3×SD16semidirect
429. Dic6C3×#41semidirect
526. C32#3103semidirect
534. Q8C3×#239semidirect
593. C3#80996direct (N × H)
594. C3C3×#3103semidirect

Maximal subgroups

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

subgroupindex
C3×#57252
C3×C4×D3×Q82
C32×#4752
C3×#50942
C3×#50272
C3×#48632
C3×#48522
C3×#48482
C3×#48332
C3×#48062
C3×#47882
C3×#31033
#809963