Finite Group Databasebeta

← C3×#80134 #11871312

Subgroups — C3×#80134 #11871312

Order 1152.

982 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×Dic3C211yesmaximal, characteristic
2C3×#5622C211yesmaximal, characteristic, complemented
3C32×#450C211yesmaximal, characteristic
4C3×#5218C211yesmaximal, characteristic
5C3×#5164C212yesmaximal, complemented
6C3×#5162C212yesmaximal, complemented
7C3×#5044C211yesmaximal, characteristic, complemented
8C3×#4759C212yesmaximal, complemented
9C3×#4757C212yesmaximal, complemented
10C3×#4722C211yesmaximal, characteristic, complemented
11C3×#4719C211yesmaximal, characteristic, complemented
12C3×#3110—31nomaximal
13#80134C311yesmaximal, characteristic, direct product factor
14C22×C32×D4C2211yescharacteristic
15C23×C3×Dic3—21no—
16C2×C32×SD16C2212yes—
17C32×C22⋊Q8C2211yescharacteristic
18C2×C3×#217—21no—
19C3×Q8×Dic3C2211yescharacteristic, complemented
20C3×#944C2211yescharacteristic, complemented
21C3×D4×Dic3—21no—
22C3×D4×Dic3—21no—
23C3×D4×Dic3C2212yes—
24C3×D4×Dic3C2212yes—
25C2×C3×#214C2212yes—
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C3×#924C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C3×#889—21no—
30C3×#888C2211yescharacteristic, complemented
31C3×#887—21no—
32C3×#887C2211yescharacteristic, complemented
33C3×#878—21no—
34C3×#877—21no—
35C32×#102C2212yes—
36C32×C22⋊C8C2211yescharacteristic
37C3×#835C2212yescomplemented
38C3×#832C2212yes—
39C3×#830C2211yescharacteristic
40C3×#818C2212yescomplemented
41C3×#816C2212yescomplemented
42C3×#815C2212yescomplemented
43C3×Dic3⋊C8C2212yescomplemented
44C3×#807C2212yescomplemented
45C3×#533—31no—
46C2×C3×C4×D4—31no—
47C2×D4×Dic3C2×C311yescharacteristic
48#5622C2×C311yescharacteristic, complemented
49C3×#484—31no—
50C3×#484—31no—
51C3×#474—32no—
52C3×#461—32no—
53C3×#450—21no—
54C3×#450—31no—
55C3×#450D311yescharacteristic
56C3×#450C2×C311yescharacteristic
57C3×#440—32no—
58C3×#440—32no—
59C3×#432—31no—
60#5218C2×C311yescharacteristic
61#5164C2×C312yescomplemented
62#5162C2×C312yescomplemented
63#5044C2×C311yescharacteristic, complemented
64#4759C2×C312yescomplemented
65#4757C2×C312yescomplemented
66#4722C2×C311yescharacteristic, complemented
67#4719C2×C311yescharacteristic, complemented
68C24×C32—21no—
69C2×C32×Q8C2311yescharacteristic
70C2×C32×D4—24no—
71C2×C32×D4—21no—
72C2×C32×D4C2312yes—
73C22×C32×C4C2311yescharacteristic
74C22×C3×Dic3—21no—
75C22×C3×Dic3—22no—
76C22×C3×Dic3—22no—
77C22×C3×Dic3—44no—
78C22×C3×Dic3D411yescharacteristic
79C22×C3×Dic3D411yescharacteristic
80C2×C3×Dic6—21no—
81C2×C3×Dic6C2311yescharacteristic
82C32×SD16—24no—
83C2×C32×C8C2312yes—
84C32×C4⋊C4—21no—
85C32×C4⋊C4C2311yescharacteristic
86C32×C22⋊C4—21no—
87C3×#217—21no—
88C3×#217—22no—
89C3×#217—22no—
90C3×#214—24no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3C2311yescharacteristic
94C3×C4⋊Dic3C2312yes—
95C3×Dic3⋊C4—21no—
96C3×Dic3⋊C4—21no—
97C3×Dic3⋊C4—21no—
98C3×Dic3⋊C4—21no—
99C3×Dic3⋊C4—21no—
100C3×C4×Dic3—21no—
101C3×C4×Dic3—21no—
102C3×C4×Dic3D411yescharacteristic
103C3×C4×Dic3D411yescharacteristic
104C3×C4×Dic3C2311yescharacteristic
105C3×C4×Dic3C2311yescharacteristic
106C2×C3×C3⋊C8C2312yes—
107#3110—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×SD16—32no—
115C2×C3×SD16C2×D312yes—
116C2×C3×SD16C22×C312yes—
117C3×C4⋊Q8—31no—
118C3×C4⋊Q8—31no—
119C3×#125—61no—
120C3×C22⋊Q8—21no—
121C3×C22⋊Q8—31no—
122C3×C22⋊Q8—61no—
123C3×C22⋊Q8C2×D311yescharacteristic
124C3×C22⋊Q8C22×C311yescharacteristic
125C3×C4×Q8—31no—
126C3×C4×Q8—31no—
127C3×C4×Q8—61no—
128C3×C4×D4—32no—
129C3×C4×D4—32no—
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—
137Q8×Dic3C22×C311yescharacteristic, complemented
138#944C22×C311yescharacteristic, complemented
139D4×Dic3—21no—
140D4×Dic3—21no—
141D4×Dic3C22×C312yes—
142D4×Dic3C22×C312yes—
143C2×#214C22×C312yes—
144C2×C4⋊Dic3C22×C311yescharacteristic
145#924C22×C311yescharacteristic
146C2×C4×Dic3C22×C311yescharacteristic
147#889—21no—
148#888C22×C311yescharacteristic, complemented
149#887—21no—
150#887C22×C311yescharacteristic, complemented
151#878—21no—
152#877—21no—
153C3×#107—32no—
154C3×#107—32no—
155C3×C4⋊C8—32no—
156C3×#103—32no—
157C3×#103—32no—
158C3×#102—22no—
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×#97—32no—
167#835C22×C312yescomplemented
168#832C22×C312yes—
169#830C22×C311yescharacteristic
170#818C22×C312yescomplemented
171#816C22×C312yescomplemented
172#815C22×C312yescomplemented
173Dic3⋊C8C22×C312yescomplemented
174#807C22×C312yescomplemented
175C23×C32—24no—
176C23×C32—22no—
177C23×C32—42no—
178C23×C32—42no—
179C23×C32C2×D411yescharacteristic
180C32×Q8—22no—
181C32×D4—24no—
182C32×D4—22no—
183C32×D4#4114yes—
184C2×C32×C4—22no—
185C2×C32×C4—21no—
186C2×C32×C4—21no—
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2411yescharacteristic
189C2×C3×Dic3—22no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—44no—
195C2×C3×Dic3—42no—
196C2×C3×Dic3—44no—
197C2×C3×Dic3C2×D411yescharacteristic
198C2×C3×Dic3C2×D411yescharacteristic
199C2×C3×Dic3C2×D411yescharacteristic
200C2×C3×Dic3C2×D411yescharacteristic
201C3×Dic6—22no—
202C3×Dic6—42no—
203C32×C8—22no—
204C3×C3⋊C8—22no—
205#533—31no—
206C2×C4×D4—31no—
207#484—31no—
208#484—31no—
209#474—32no—
210#461—32no—
211#450—31no—
212#450C3×D311yescharacteristic
213#440—32no—
214#440—32no—
215#432—31no—
216C24×C3—21no—
217C24×C3—21no—
218C24×C3—41no—
219C2×C3×Q8—21no—
220C2×C3×Q8—31no—
221C2×C3×Q8—61no—
222C2×C3×Q8C22×D311yescharacteristic
223C2×C3×Q8C23×C311yescharacteristic
224C2×C3×D4—24no—
225C2×C3×D4—24no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—22no—
229C2×C3×D4—41no—
230C2×C3×D4—44no—
231C2×C3×D4C22×D312yes—
232C2×C3×D4C23×C312yes—
233C22×C3×C4—21no—
234C22×C3×C4—31no—
235C22×C3×C4—31no—
236C22×C3×C4—62no—
237C22×C3×C4—62no—
238C22×C3×C4—61no—
239C22×C3×C4—124no—
240C22×C3×C4C22×D311yescharacteristic
241C22×C3×C4C23×C311yescharacteristic
242C22×Dic3—21no—
243C22×Dic3—22no—
244C22×Dic3—22no—
245C22×Dic3—44no—
246C22×Dic3C3×D411yescharacteristic
247C22×Dic3C3×D411yescharacteristic
248C2×Dic6—21no—
249C2×Dic6C23×C311yescharacteristic
250C3×SD16—24no—
251C3×SD16—24no—
252C3×SD16—44no—
253C3×SD16—64no—
254C2×C3×C8—22no—
255C2×C3×C8—32no—
256C2×C3×C8C22×D312yes—
257C2×C3×C8C23×C312yes—
258C3×C4⋊C4—21no—
259C3×C4⋊C4—21no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—31no—
262C3×C4⋊C4—32no—
263C3×C4⋊C4—41no—
264C3×C4⋊C4—61no—
265C3×C4⋊C4—61no—
266C3×C4⋊C4—61no—
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—62no—
277C3×C22⋊C4—62no—
278C3×C22⋊C4—61no—
279C3×C42—31no—
280C3×C42—31no—
281C3×C42—31no—
282C3×C42—31no—
283C3×C42—61no—
284C3×C42—61no—
285#217—21no—
286#217—22no—
287#217—22no—
288#214—24no—
289C4⋊Dic3—21no—
290C4⋊Dic3—21no—
291C4⋊Dic3C23×C312yes—
292C4⋊Dic3C23×C311yescharacteristic
293Dic3⋊C4—21no—
294Dic3⋊C4—21no—
295Dic3⋊C4—21no—
296Dic3⋊C4—21no—
297Dic3⋊C4—21no—
298C4×Dic3—21no—
299C4×Dic3—21no—
300C4×Dic3C3×D411yescharacteristic
301C4×Dic3C3×D411yescharacteristic
302C4×Dic3C23×C311yescharacteristic
303C4×Dic3C23×C311yescharacteristic
304C2×C3⋊C8C23×C312yes—
305C22×C32—21no—
306C22×C32—21no—
307C22×C32—24no—
308C22×C32—48no—
309C22×C32—42no—
310C22×C32—42no—
311C22×C32#13712yes—
312C22×C32C22×D411yescharacteristic
313C32×C4—21no—
314C32×C4—41no—
315C32×C4—41no—
316C32×C4C2×#4112yes—
317C3×Dic3—21no—
318C3×Dic3—21no—
319C3×Dic3—21no—
320C3×Dic3—41no—
321C3×Dic3—41no—
322C3×Dic3—42no—
323C3×Dic3AGL(1,ℤ/8)12yes—
324C22×D4C2×C3×D311yescharacteristic
325C23×C4—61no—
326C2×SD16—32no—
327C2×SD16C2×C3×D312yes—
328C4⋊Q8—31no—
329C4⋊Q8—31no—
330#125—61no—
331C22⋊Q8—31no—
332C22⋊Q8—61no—
333C22⋊Q8C2×C3×D311yescharacteristic
334C4×Q8—31no—
335C4×Q8—31no—
336C4×Q8—61no—
337C4×D4—32no—
338C4×D4—32no—
339C4×D4—61no—
340C4×D4—61no—
341#117—61no—
342C2×C4⋊C4—31no—
343C2×C22⋊C4—61no—
344C2×C42—31no—
345#107—32no—
346#107—32no—
347C4⋊C8—32no—
348#103—32no—
349#103—32no—
350#102—32no—
351#102C2×C3×D312yes—
352C22⋊C8—31no—
353C22⋊C8C2×C3×D311yescharacteristic
354#97—32no—
355C23×C3—24no—
356C23×C3—24no—
357C23×C3—22no—
358C23×C3—22no—
359C23×C3—21no—
360C23×C3—42no—
361C23×C3—44no—
362C23×C3—42no—
363C23×C3—42no—
364C23×C3—42no—
365C23×C3—42no—
366C23×C3—82no—
367C23×C3—82no—
368C23×C3D3×D411yescharacteristic
369C23×C3C2×C3×D411yescharacteristic
370C3×Q8—22no—
371C3×Q8—22no—
372C3×Q8—42no—
373C3×Q8—62no—
374C3×Q8—122no—
375C3×D4—24no—
376C3×D4—24no—
377C3×D4—22no—
378C3×D4—22no—
379C3×D4—24no—
380C3×D4—42no—
381C3×D4—44no—
382C3×D4#23714yes—
383C3×D4C3×#4114yes—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—31no—
393C2×C3×C4—31no—
394C2×C3×C4—31no—
395C2×C3×C4—31no—
396C2×C3×C4—42no—
397C2×C3×C4—41no—
398C2×C3×C4—41no—
399C2×C3×C4—62no—
400C2×C3×C4—62no—
401C2×C3×C4—61no—
402C2×C3×C4—61no—
403C2×C3×C4—62no—
404C2×C3×C4—124no—
405C2×C3×C4—124no—
406C2×C3×C4—122no—
407C2×C3×C4D3×D411yescharacteristic
408C2×C3×C4C2×C3×D411yescharacteristic
409C2×C3×C4C23×D311yescharacteristic
410C2×C3×C4C24×C311yescharacteristic
411C2×Dic3—22no—
412C2×Dic3—22no—
413C2×Dic3—21no—
414C2×Dic3—21no—
415C2×Dic3—22no—
416C2×Dic3—44no—
417C2×Dic3—42no—
418C2×Dic3—44no—
419C2×Dic3C2×C3×D411yescharacteristic
420C2×Dic3C2×C3×D411yescharacteristic
421C2×Dic3C2×C3×D411yescharacteristic
422C2×Dic3C2×C3×D411yescharacteristic
423Dic6—22no—
424Dic6—42no—
425C3×C8—22no—
426C3×C8—22no—
427C3×C8—42no—
428C3×C8—62no—
429C3⋊C8—22no—
430C2×C32—22no—
431C2×C32—44no—
432C2×C32#52511yescharacteristic
433C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
434C2×C32C2×#13711yescharacteristic
435C24—21no—
436C2×Q8—31no—
437C2×Q8—61no—
438C2×Q8C22×C3×D311yescharacteristic
439C2×D4—24no—
440C2×D4—21no—
441C2×D4C22×C3×D312yes—
442C22×C4—31no—
443C22×C4—31no—
444C22×C4—62no—
445C22×C4—62no—
446C22×C4—61no—
447C22×C4—124no—
448C22×C4C22×C3×D311yescharacteristic
449SD16—24no—
450SD16—64no—
451C2×C8—32no—
452C2×C8C22×C3×D312yes—
453C4⋊C4—21no—
454C4⋊C4—31no—
455C4⋊C4—32no—
456C4⋊C4—61no—
457C4⋊C4—61no—
458C4⋊C4—61no—
459C4⋊C4—61no—
460C4⋊C4—61no—
461C4⋊C4—61no—
462C4⋊C4—61no—
463C4⋊C4C22×C3×D311yescharacteristic
464C22⋊C4—21no—
465C22⋊C4—62no—
466C22⋊C4—62no—
467C22⋊C4—61no—
468C42—31no—
469C42—31no—
470C42—31no—
471C42—31no—
472C42—61no—
473C42—61no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—24no—
479C22×C3—24no—
480C22×C3—22no—
481C22×C3—21no—
482C22×C3—41no—
483C22×C3—41no—
484C22×C3—44no—
485C22×C3—48no—
486C22×C3—48no—
487C22×C3—42no—
488C22×C3—42no—
489C22×C3—42no—
490C22×C3—42no—
491C22×C3—82no—
492C22×C3—82no—
493C22×C3—88no—
494C22×C3#91512yes—
495C22×C3C3×#13712yes—
496C22×C3C2×D3×D411yescharacteristic
497C22×C3C22×C3×D411yescharacteristic
498C3×C4—21no—
499C3×C4—21no—
500C3×C4—22no—
501C3×C4—32no—
502C3×C4—41no—
503C3×C4—41no—
504C3×C4—41no—
505C3×C4—41no—
506C3×C4—41no—
507C3×C4—61no—
508C3×C4—61no—
509C3×C4—61no—
510C3×C4—81no—
511C3×C4—81no—
512C3×C4—122no—
513C3×C4—121no—
514C3×C4—121no—
515C3×C4C2×#23712yes—
516C3×C4C2×C3×#4112yes—
517Dic3—21no—
518Dic3—21no—
519Dic3—21no—
520Dic3—41no—
521Dic3—42no—
522Dic3—41no—
523Dic3C3×AGL(1,ℤ/8)12yes—
524C32#311011yescharacteristic, complemented, Sylow
525C23—24no—
526C23—22no—
527C23—42no—
528C23—42no—
529C23C3×D3×D411yescharacteristic
530Q8—22no—
531Q8—62no—
532Q8—122no—
533D4—24no—
534D4—22no—
535D4C3×#23714yes—
536C2×C4—22no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—31no—
540C2×C4—31no—
541C2×C4—31no—
542C2×C4—31no—
543C2×C4—62no—
544C2×C4—62no—
545C2×C4—61no—
546C2×C4—61no—
547C2×C4—62no—
548C2×C4—124no—
549C2×C4—124no—
550C2×C4—122no—
551C2×C4C3×D3×D411yescharacteristic
552C2×C4C23×C3×D311yescharacteristic
553C8—22no—
554C8—62no—
555C2×C3—22no—
556C2×C3—22no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—21no—
560C2×C3—42no—
561C2×C3—44no—
562C2×C3—44no—
563C2×C3—84no—
564C2×C3#558611yescharacteristic
565C2×C3C2×#91511yescharacteristic
566C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
567C2×C3C3×#52511yescharacteristic
568C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
569C2×C3C2×C3×#13711yescharacteristic
570C22—21no—
571C22—21no—
572C22—24no—
573C22—48no—
574C22—42no—
575C22—42no—
576C22C3×#91512yes—
577C22C2×C3×D3×D411yescharacteristic
578C4—21no—
579C4—32no—
580C4—41no—
581C4—41no—
582C4—61no—
583C4—61no—
584C4—61no—
585C4—122no—
586C4—121no—
587C4—121no—
588C4C2×C3×#23712yes—
589C3—21no—
590C3#8013411yescharacteristic, direct product factor
591C3C3×#311011yescharacteristic, complemented
592C2—22no—
593C2—44no—
594C2C3×#558611yescharacteristic
595C2C2×C3×#91511yescharacteristic
596C2C3×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 radicalC22×C32×D4C22
hypercenterC3×#450D3
hypocenterC3C3×#3110
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
2. C3×#5622C2semidirect
5. C3×#5164C2semidirect
6. C3×#5162C2semidirect
7. C3×#5044C2semidirect
8. C3×#4759C2semidirect
9. C3×#4757C2semidirect
10. C3×#4722C2semidirect
11. C3×#4719C2semidirect
13. #80134C3direct (N × H)
19. C3×Q8×Dic3C22semidirect
20. C3×#944C22semidirect
30. C3×#888C22semidirect
32. C3×#887C22semidirect
37. C3×#835C22semidirect
40. C3×#818C22semidirect
41. C3×#816C22semidirect
42. C3×#815C22semidirect
43. C3×Dic3⋊C8C22semidirect
44. C3×#807C22semidirect
48. #5622C2×C3semidirect
61. #5164C2×C3semidirect
62. #5162C2×C3semidirect
63. #5044C2×C3semidirect
64. #4759C2×C3semidirect
65. #4757C2×C3semidirect
66. #4722C2×C3semidirect
67. #4719C2×C3semidirect
137. Q8×Dic3C22×C3semidirect
138. #944C22×C3semidirect
148. #888C22×C3semidirect
150. #887C22×C3semidirect
167. #835C22×C3semidirect
170. #818C22×C3semidirect
171. #816C22×C3semidirect
172. #815C22×C3semidirect
173. Dic3⋊C8C22×C3semidirect
174. #807C22×C3semidirect
524. C32#3110semidirect
590. C3#80134direct (N × H)
591. C3C3×#3110semidirect

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×#56222
C32×#4502
C3×#52182
C3×#51642
C3×#51622
C3×#50442
C3×#47592
C3×#47572
C3×#47222
C3×#47192
C3×#31103
#801343