Finite Group Databasebeta

← C3×#81454 #11871318

Subgroups — C3×#81454 #11871318

Order 1152.

940 conjugacy classes of subgroups.

The subgroup lattice has 587 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5622C211yesmaximal, characteristic, complemented
2C2×C3×#893C211yesmaximal, characteristic
3C32×#484C211yesmaximal, characteristic, complemented
4C3×#5046C211yesmaximal, characteristic
5C3×#4970C211yesmaximal, characteristic, complemented
6C3×#4890C212yesmaximal, complemented
7C3×#4889C212yesmaximal, complemented
8C3×#4818C212yesmaximal, complemented
9C3×#4817C212yesmaximal, complemented
10C3×#4731C211yesmaximal, characteristic
11C3×#4719C211yesmaximal, characteristic, complemented
12C3×#3110—31nomaximal
13#81454C311yesmaximal, characteristic, direct product factor
14C22×C3×D12C2211yescharacteristic
15C22×C3×C4×D3—21no—
16C32×C22⋊Q8C2211yescharacteristic
17C2×C32×C4⋊C4C2211yescharacteristic
18C3×Q8×Dic3C2211yescharacteristic, complemented
19C3×#944C2211yescharacteristic, complemented
20C2×C3×#215C2212yes—
21C2×C3×(C2×D3)⋊C4—21no—
22C3×#924C2211yescharacteristic
23C2×C3×C4×Dic3C2211yescharacteristic
24C2×C3×#204C2212yes—
25C3×#893—21no—
26C3×#893—21no—
27C3×#893C2212yes—
28C3×#893C2212yes—
29C3×#889—21no—
30C3×#888C2211yescharacteristic, complemented
31C3×#887—21no—
32C3×#887C2211yescharacteristic, complemented
33C3×#878—21no—
34C3×#877—21no—
35C32×#107C2212yescomplemented
36C32×#103C2212yescomplemented
37C32×C22⋊C8C2211yescharacteristic
38C3×#830C2211yescharacteristic
39C3×#821C2212yes—
40C3×#815C2212yescomplemented
41C3×Dic3⋊C8C2212yescomplemented
42C3×#810C2212yescomplemented
43C3×#809C2212yes—
44C3×#807C2212yescomplemented
45C3×#533—31no—
46C2×C3×C4×D4—31no—
47#5622C2×C311yescharacteristic, complemented
48C2×#893C2×C311yescharacteristic
49C3×#484—21no—
50C3×#484—31no—
51C3×#484D311yescharacteristic, complemented
52C3×#484C2×C311yescharacteristic, complemented
53C3×#474—32no—
54C3×#461—32no—
55C3×#450—31no—
56C3×#450—31no—
57C3×#440—32no—
58C3×#440—32no—
59C3×#432—31no—
60#5046C2×C311yescharacteristic
61#4970C2×C311yescharacteristic, complemented
62#4890C2×C312yescomplemented
63#4889C2×C312yescomplemented
64#4818C2×C312yescomplemented
65#4817C2×C312yescomplemented
66#4731C2×C311yescharacteristic
67#4719C2×C311yescharacteristic, complemented
68C23×C3×D3—21no—
69C2×C32×Q8C2311yescharacteristic
70C22×C32×C4—21no—
71C22×C32×C4C2311yescharacteristic
72C22×C3×Dic3D411yescharacteristic
73C22×C3×Dic3D411yescharacteristic
74C2×C3×D12—21no—
75C2×C3×D12—24no—
76C2×C3×D12C2312yes—
77C2×C3×C4×D3—22no—
78C2×C3×C4×D3—22no—
79C2×C3×C4×D3—44no—
80C2×C3×Dic6—21no—
81C2×C3×Dic6C2311yescharacteristic
82C2×C32×C8C2312yes—
83C32×C4⋊C4—21no—
84C32×C4⋊C4—21no—
85C32×C4⋊C4C2311yescharacteristic
86C32×C4⋊C4C2312yes—
87C32×C22⋊C4—21no—
88C3×#217—21no—
89C3×#215—24no—
90C3×(C2×D3)⋊C4—22no—
91C3×(C2×D3)⋊C4—22no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3C2311yescharacteristic
94C3×Dic3⋊C4—21no—
95C3×Dic3⋊C4—21no—
96C3×Dic3⋊C4—21no—
97C3×Dic3⋊C4—21no—
98C3×Dic3⋊C4—21no—
99C3×C4×Dic3—21no—
100C3×C4×Dic3—21no—
101C3×C4×Dic3D411yescharacteristic
102C3×C4×Dic3D411yescharacteristic
103C3×C4×Dic3C2311yescharacteristic
104C3×C4×Dic3C2311yescharacteristic
105C2×C3×C3⋊C8C2312yes—
106C3×#204—24no—
107#3110—31noSylow
108C22×C3×D4—31no—
109C23×C3×C4—61no—
110C22×D12C22×C311yescharacteristic
111C22×C4×D3—21no—
112C2×C3×SD16—32no—
113C2×C3×SD16—32no—
114C3×C4⋊Q8—31no—
115C3×C4⋊Q8—31no—
116C3×#125—61no—
117C3×C22⋊Q8—21no—
118C3×C22⋊Q8—31no—
119C3×C22⋊Q8—61no—
120C3×C22⋊Q8C2×D311yescharacteristic
121C3×C22⋊Q8C22×C311yescharacteristic
122C3×C4×Q8—31no—
123C3×C4×Q8—31no—
124C3×C4×Q8—61no—
125C3×C4×D4—32no—
126C3×C4×D4—32no—
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—
135Q8×Dic3C22×C311yescharacteristic, complemented
136#944C22×C311yescharacteristic, complemented
137C2×#215C22×C312yes—
138C2×(C2×D3)⋊C4—21no—
139#924C22×C311yescharacteristic
140C2×C4×Dic3C22×C311yescharacteristic
141C2×#204C22×C312yes—
142#893—21no—
143#893—21no—
144#893C22×C312yes—
145#893C22×C312yes—
146#889—21no—
147#888C22×C311yescharacteristic, complemented
148#887—21no—
149#887C22×C311yescharacteristic, complemented
150#878—21no—
151#877—21no—
152C3×#107—22no—
153C3×#107—32no—
154C3×#107C2×D312yescomplemented
155C3×#107C22×C312yescomplemented
156C3×C4⋊C8—32no—
157C3×#103—22no—
158C3×#103—32no—
159C3×#103C2×D312yescomplemented
160C3×#103C22×C312yescomplemented
161C3×#102—32no—
162C3×#102—32no—
163C3×C22⋊C8—21no—
164C3×C22⋊C8—31no—
165C3×C22⋊C8C2×D311yescharacteristic
166C3×C22⋊C8C22×C311yescharacteristic
167C3×#97—32no—
168#830C22×C311yescharacteristic
169#821C22×C312yes—
170#815C22×C312yescomplemented
171Dic3⋊C8C22×C312yescomplemented
172#810C22×C312yescomplemented
173#809C22×C312yes—
174#807C22×C312yescomplemented
175C23×C32C2×D411yescharacteristic
176C22×C3×D3—24no—
177C22×C3×D3—22no—
178C22×C3×D3—42no—
179C22×C3×D3—42no—
180C32×Q8—22no—
181C2×C32×C4—22no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4—22no—
185C2×C32×C4—42no—
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2411yescharacteristic
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3C2×D411yescharacteristic
193C2×C3×Dic3C2×D411yescharacteristic
194C2×C3×Dic3C2×D411yescharacteristic
195C2×C3×Dic3C2×D411yescharacteristic
196C3×D12—24no—
197C3×D12—22no—
198C3×D12#4114yes—
199C3×C4×D3—44no—
200C3×C4×D3—44no—
201C3×Dic6—22no—
202C3×Dic6—42no—
203C32×C8—22no—
204C3×C3⋊C8—22no—
205#533—31no—
206C2×C4×D4—31no—
207#484—31no—
208#484C3×D311yescharacteristic, complemented
209#474—32no—
210#461—32no—
211#450—31no—
212#450—31no—
213#440—32no—
214#440—32no—
215#432—31no—
216C24×C3—61no—
217C23×D3—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—31no—
220C2×C3×Q8—61no—
221C2×C3×Q8C22×D311yescharacteristic
222C2×C3×Q8C23×C311yescharacteristic
223C2×C3×D4—32no—
224C2×C3×D4—64no—
225C2×C3×D4—61no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—31no—
230C22×C3×C4—31no—
231C22×C3×C4—41no—
232C22×C3×C4—62no—
233C22×C3×C4—62no—
234C22×C3×C4—124no—
235C22×C3×C4C22×D311yescharacteristic
236C22×C3×C4C23×C311yescharacteristic
237C22×Dic3C3×D411yescharacteristic
238C22×Dic3C3×D411yescharacteristic
239C2×D12—21no—
240C2×D12—24no—
241C2×D12C23×C312yes—
242C2×C4×D3—22no—
243C2×C4×D3—22no—
244C2×C4×D3—44no—
245C2×Dic6—21no—
246C2×Dic6C23×C311yescharacteristic
247C3×SD16—64no—
248C3×SD16—64no—
249C2×C3×C8—22no—
250C2×C3×C8—32no—
251C2×C3×C8C22×D312yes—
252C2×C3×C8C23×C312yes—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—21no—
256C3×C4⋊C4—21no—
257C3×C4⋊C4—22no—
258C3×C4⋊C4—21no—
259C3×C4⋊C4—31no—
260C3×C4⋊C4—41no—
261C3×C4⋊C4—41no—
262C3×C4⋊C4—61no—
263C3×C4⋊C4—61no—
264C3×C4⋊C4—61no—
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×C42—31no—
279C3×C42—31no—
280C3×C42—31no—
281C3×C42—31no—
282C3×C42—61no—
283C3×C42—61no—
284#217—21no—
285#215—24no—
286(C2×D3)⋊C4—22no—
287(C2×D3)⋊C4—22no—
288C4⋊Dic3—21no—
289C4⋊Dic3C23×C311yescharacteristic
290Dic3⋊C4—21no—
291Dic3⋊C4—21no—
292Dic3⋊C4—21no—
293Dic3⋊C4—21no—
294Dic3⋊C4—21no—
295C4×Dic3—21no—
296C4×Dic3—21no—
297C4×Dic3C3×D411yescharacteristic
298C4×Dic3C3×D411yescharacteristic
299C4×Dic3C23×C311yescharacteristic
300C4×Dic3C23×C311yescharacteristic
301C2×C3⋊C8C23×C312yes—
302#204—24no—
303C22×C32—21no—
304C22×C32—21no—
305C22×C32#13712yes—
306C22×C32C22×D411yescharacteristic
307C2×C3×D3—24no—
308C2×C3×D3—48no—
309C2×C3×D3—42no—
310C2×C3×D3—42no—
311C32×C4—21no—
312C32×C4—41no—
313C32×C4—41no—
314C32×C4—42no—
315C32×C4C2×#4112yes—
316C3×Dic3—21no—
317C3×Dic3—21no—
318C3×Dic3—21no—
319C3×Dic3—41no—
320C3×Dic3—41no—
321C3×Dic3AGL(1,ℤ/8)12yes—
322C22×D4—31no—
323C23×C4—61no—
324C2×SD16—32no—
325C2×SD16—32no—
326C4⋊Q8—31no—
327C4⋊Q8—31no—
328#125—61no—
329C22⋊Q8—31no—
330C22⋊Q8—61no—
331C22⋊Q8C2×C3×D311yescharacteristic
332C4×Q8—31no—
333C4×Q8—31no—
334C4×Q8—61no—
335C4×D4—32no—
336C4×D4—32no—
337C4×D4—61no—
338C4×D4—61no—
339#117—61no—
340C2×C4⋊C4C2×C3×D311yescharacteristic
341C2×C22⋊C4—61no—
342C2×C42—31no—
343#107—32no—
344#107C2×C3×D312yescomplemented
345C4⋊C8—32no—
346#103—32no—
347#103C2×C3×D312yescomplemented
348#102—32no—
349#102—32no—
350C22⋊C8—31no—
351C22⋊C8C2×C3×D311yescharacteristic
352#97—32no—
353C23×C3—21no—
354C23×C3—64no—
355C23×C3—62no—
356C23×C3—122no—
357C23×C3—122no—
358C23×C3D3×D411yescharacteristic
359C23×C3C2×C3×D411yescharacteristic
360C22×D3—24no—
361C22×D3—22no—
362C22×D3—42no—
363C22×D3—42no—
364C3×Q8—22no—
365C3×Q8—22no—
366C3×Q8—42no—
367C3×Q8—62no—
368C3×Q8—122no—
369C3×D4—34no—
370C3×D4—64no—
371C3×D4—62no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—22no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—22no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—31no—
383C2×C3×C4—31no—
384C2×C3×C4—31no—
385C2×C3×C4—31no—
386C2×C3×C4—42no—
387C2×C3×C4—41no—
388C2×C3×C4—41no—
389C2×C3×C4—42no—
390C2×C3×C4—42no—
391C2×C3×C4—42no—
392C2×C3×C4—62no—
393C2×C3×C4—62no—
394C2×C3×C4—61no—
395C2×C3×C4—61no—
396C2×C3×C4—82no—
397C2×C3×C4—124no—
398C2×C3×C4—124no—
399C2×C3×C4D3×D411yescharacteristic
400C2×C3×C4C2×C3×D411yescharacteristic
401C2×C3×C4C23×D311yescharacteristic
402C2×C3×C4C24×C311yescharacteristic
403C2×Dic3—22no—
404C2×Dic3—22no—
405C2×Dic3—21no—
406C2×Dic3—21no—
407C2×Dic3C2×C3×D411yescharacteristic
408C2×Dic3C2×C3×D411yescharacteristic
409C2×Dic3C2×C3×D411yescharacteristic
410C2×Dic3C2×C3×D411yescharacteristic
411D12—24no—
412D12—22no—
413D12C3×#4114yes—
414C4×D3—44no—
415C4×D3—44no—
416Dic6—22no—
417Dic6—42no—
418C3×C8—22no—
419C3×C8—22no—
420C3×C8—42no—
421C3×C8—62no—
422C3⋊C8—22no—
423C2×C32—22no—
424C2×C32#52511yescharacteristic
425C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
426C2×C32C2×#13711yescharacteristic
427C3×D3—44no—
428C24—61no—
429C2×Q8—31no—
430C2×Q8—61no—
431C2×Q8C22×C3×D311yescharacteristic
432C2×D4—32no—
433C2×D4—64no—
434C2×D4—61no—
435C22×C4—21no—
436C22×C4—31no—
437C22×C4—31no—
438C22×C4—62no—
439C22×C4—62no—
440C22×C4—124no—
441C22×C4C22×C3×D311yescharacteristic
442SD16—64no—
443SD16—64no—
444C2×C8—32no—
445C2×C8C22×C3×D312yes—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—31no—
449C4⋊C4—61no—
450C4⋊C4—61no—
451C4⋊C4—61no—
452C4⋊C4—61no—
453C4⋊C4—61no—
454C4⋊C4—61no—
455C4⋊C4C22×C3×D311yescharacteristic
456C4⋊C4C22×C3×D312yes—
457C22⋊C4—21no—
458C22⋊C4—62no—
459C22⋊C4—62no—
460C22⋊C4—61no—
461C42—31no—
462C42—31no—
463C42—31no—
464C42—31no—
465C42—61no—
466C42—61no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—22no—
472C22×C3—21no—
473C22×C3—41no—
474C22×C3—41no—
475C22×C3—64no—
476C22×C3—128no—
477C22×C3—122no—
478C22×C3—122no—
479C22×C3#91812yes—
480C22×C3C3×#13712yes—
481C22×C3C2×D3×D411yescharacteristic
482C22×C3C22×C3×D411yescharacteristic
483C2×D3—24no—
484C2×D3—48no—
485C2×D3—42no—
486C2×D3—42no—
487C3×C4—21no—
488C3×C4—21no—
489C3×C4—22no—
490C3×C4—32no—
491C3×C4—41no—
492C3×C4—41no—
493C3×C4—42no—
494C3×C4—41no—
495C3×C4—42no—
496C3×C4—41no—
497C3×C4—41no—
498C3×C4—61no—
499C3×C4—61no—
500C3×C4—61no—
501C3×C4—82no—
502C3×C4—81no—
503C3×C4—81no—
504C3×C4—121no—
505C3×C4—121no—
506C3×C4D3×#4112yes—
507C3×C4C2×C3×#4112yes—
508Dic3—21no—
509Dic3—21no—
510Dic3—21no—
511Dic3—41no—
512Dic3—41no—
513Dic3C3×AGL(1,ℤ/8)12yes—
514C32#311011yescharacteristic, complemented, Sylow
515C23—64no—
516C23—62no—
517C23—122no—
518C23—122no—
519C23C3×D3×D411yescharacteristic
520Q8—22no—
521Q8—62no—
522Q8—122no—
523D4—34no—
524D4—64no—
525D4—62no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—31no—
531C2×C4—31no—
532C2×C4—31no—
533C2×C4—31no—
534C2×C4—42no—
535C2×C4—62no—
536C2×C4—62no—
537C2×C4—61no—
538C2×C4—61no—
539C2×C4—124no—
540C2×C4—124no—
541C2×C4C3×D3×D411yescharacteristic
542C2×C4C23×C3×D311yescharacteristic
543C8—22no—
544C8—62no—
545C2×C3—22no—
546C2×C3—22no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—42no—
551C2×C3—124no—
552C2×C3#565611yescharacteristic
553C2×C3C2×#91811yescharacteristic
554C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
555C2×C3C3×#52511yescharacteristic
556C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
557C2×C3C2×C3×#13711yescharacteristic
558D3—44no—
559C22—21no—
560C22—21no—
561C22—64no—
562C22—128no—
563C22—122no—
564C22—122no—
565C22C3×#91812yes—
566C22C2×C3×D3×D411yescharacteristic
567C4—21no—
568C4—32no—
569C4—42no—
570C4—41no—
571C4—41no—
572C4—61no—
573C4—61no—
574C4—61no—
575C4—121no—
576C4—121no—
577C4C3×D3×#4112yes—
578C3—21no—
579C3#8145411yescharacteristic, direct product factor
580C3C3×#311011yescharacteristic, complemented
581C2—22no—
582C2—124no—
583C2C3×#565611yescharacteristic
584C2C2×C3×#91811yescharacteristic
585C2C3×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 radicalC22×C3×D12C22
hypercenterC3×#484D3
hypocenterC3C3×#3110
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×#5622C2semidirect
3. C32×#484C2semidirect
5. C3×#4970C2semidirect
6. C3×#4890C2semidirect
7. C3×#4889C2semidirect
8. C3×#4818C2semidirect
9. C3×#4817C2semidirect
11. C3×#4719C2semidirect
13. #81454C3direct (N × H)
18. C3×Q8×Dic3C22semidirect
19. C3×#944C22semidirect
30. C3×#888C22semidirect
32. C3×#887C22semidirect
35. C32×#107C22semidirect
36. C32×#103C22semidirect
40. C3×#815C22semidirect
41. C3×Dic3⋊C8C22semidirect
42. C3×#810C22semidirect
44. C3×#807C22semidirect
47. #5622C2×C3semidirect
51. C3×#484D3semidirect
52. C3×#484C2×C3semidirect
61. #4970C2×C3semidirect
62. #4890C2×C3semidirect
63. #4889C2×C3semidirect
64. #4818C2×C3semidirect
65. #4817C2×C3semidirect
67. #4719C2×C3semidirect
135. Q8×Dic3C22×C3semidirect
136. #944C22×C3semidirect
147. #888C22×C3semidirect
149. #887C22×C3semidirect
154. C3×#107C2×D3semidirect
155. C3×#107C22×C3semidirect
159. C3×#103C2×D3semidirect
160. C3×#103C22×C3semidirect
170. #815C22×C3semidirect
171. Dic3⋊C8C22×C3semidirect
172. #810C22×C3semidirect
174. #807C22×C3semidirect
208. #484C3×D3semidirect
344. #107C2×C3×D3semidirect
347. #103C2×C3×D3semidirect
514. C32#3110semidirect
579. C3#81454direct (N × H)
580. C3C3×#3110semidirect

Maximal subgroups

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

subgroupindex
C3×#56222
C2×C3×#8932
C32×#4842
C3×#50462
C3×#49702
C3×#48902
C3×#48892
C3×#48182
C3×#48172
C3×#47312
C3×#47192
C3×#31103
#814543