Finite Group Databasebeta

← C3×#83965 #11860582

Subgroups — C3×#83965 #11860582

Order 1152.

1069 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#137C211yesmaximal, characteristic
2C3×#5827C211yesmaximal, characteristic
3C3×#5812C211yesmaximal, characteristic, complemented
4C3×#5233C211yesmaximal, characteristic
5C2×C3×#835C211yesmaximal, characteristic, complemented
6C3×#5184C212yesmaximal, complemented
7C3×Dic3×Q16C212yesmaximal, complemented
8C3×#5164C212yesmaximal, complemented
9C3×Dic3×SD16C212yesmaximal, complemented
10C3×#5122C211yesmaximal, characteristic, complemented
11C3×#5121C211yesmaximal, characteristic, complemented
12C3×#2947—31nomaximal
13#83965C311yesmaximal, characteristic, direct product factor
14C2×C32×#41C2211yescharacteristic
15C22×C32×Q8C2211yescharacteristic
16C32×#137C418yescomplemented
17C2×C32×Q16C2212yes—
18C2×C32×SD16C2212yes—
19C2×C32×M16C2211yescharacteristic
20C3×Q8×Dic3—21no—
21C3×Q8×Dic3—21no—
22C3×Q8×Dic3C2212yes—
23C3×Q8×Dic3C2212yes—
24C3×Q8×Dic3C2212yes—
25C3×D4×Dic3—22no—
26C3×D4×Dic3C2212yes—
27C3×#926—22no—
28C3×#926—21no—
29C3×#926C2211yescharacteristic
30C3×#926C2211yescharacteristic
31C2×C3×C4⋊Dic3—21no—
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C22×C3×C3⋊C8C2211yescharacteristic
34C3×#835C2212yes—
35C3×#835C2212yes—
36C3×#835C2211yescharacteristic
37C3×#835C2211yescharacteristic
38C3×#832C2211yescharacteristic
39C3×#832C2211yescharacteristic
40C3×#818C2212yes—
41C3×#817C2212yes—
42C3×#815C2212yes—
43C3×C8×Dic3C2212yes—
44C2×C3×#137—21no—
45C2×C3×#137D311yescharacteristic
46C2×C3×#137C2×C311yescharacteristic
47C3×#520—31no—
48C3×#519—31no—
49#5827C2×C311yescharacteristic
50#5812C2×C311yescharacteristic, complemented
51C3×#441—32no—
52C3×#440—32no—
53C3×C4×Q16—32no—
54C3×C4×SD16—32no—
55C3×#428—31no—
56C3×#416—31no—
57C2×C3×#103—31no—
58C3×#405—31no—
59#5233C2×C311yescharacteristic
60C2×#835C2×C311yescharacteristic, complemented
61#5184C2×C312yescomplemented
62Dic3×Q16C2×C312yescomplemented
63#5164C2×C312yescomplemented
64Dic3×SD16C2×C312yescomplemented
65#5122C2×C311yescharacteristic, complemented
66#5121C2×C311yescharacteristic, complemented
67C32×#41—22no—
68C32×#41C2×C414yes—
69C2×C32×Q8—21no—
70C2×C32×Q8—22no—
71C2×C32×Q8C2×C414yescomplemented
72C2×C32×Q8C2312yes—
73C2×C32×Q8C2311yescharacteristic
74C2×C32×D4—21no—
75C2×C32×D4C2311yescharacteristic
76C22×C32×C4—21no—
77C22×C32×C4—21no—
78C22×C32×C4C2311yescharacteristic
79C22×C3×Dic3—21no—
80C22×C3×Dic3—22no—
81C32×Q16C2×C418yescomplemented
82C32×SD16C2×C418yescomplemented
83C32×M16C2×C414yescomplemented
84C2×C32×C8C2312yes—
85C3×#217—21no—
86C3×#217—22no—
87C3×#217D412yes—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3—22no—
90C3×C4⋊Dic3—22no—
91C3×C4⋊Dic3—22no—
92C3×C4⋊Dic3D411yescharacteristic
93C3×C4⋊Dic3D411yescharacteristic
94C3×C4⋊Dic3C2312yes—
95C3×C4⋊Dic3C2311yescharacteristic
96C3×C4⋊Dic3C2311yescharacteristic
97C3×C4×Dic3—21no—
98C3×C4×Dic3—22no—
99C3×C4×Dic3—22no—
100C3×C4×Dic3—22no—
101C3×C4×Dic3C2312yes—
102C2×C3×C3⋊C8—22no—
103C2×C3×C3⋊C8C2311yescharacteristic
104C2×C3×C3⋊C8C2311yescharacteristic
105#2947—31noSylow
106C2×C3×#41—21no—
107C2×C3×#41C2×D311yescharacteristic
108C2×C3×#41C22×C311yescharacteristic
109C22×C3×Q8—21no—
110C22×C3×Q8C2×D311yescharacteristic
111C22×C3×Q8C22×C311yescharacteristic
112C3×#137—28no—
113C3×#137Dic318yescomplemented
114C3×#137C3×C418yescomplemented
115C2×C3×Q16—22no—
116C2×C3×Q16C2×D312yes—
117C2×C3×Q16C22×C312yes—
118C2×C3×SD16—22no—
119C2×C3×SD16C2×D312yes—
120C2×C3×SD16C22×C312yes—
121C2×C3×M16—21no—
122C2×C3×M16C2×D311yescharacteristic
123C2×C3×M16C22×C311yescharacteristic
124C22×C3×C8—31no—
125C3×C4×Q8—32no—
126C3×C4×Q8—32no—
127C3×C4×Q8—32no—
128C3×C4×Q8—61no—
129C3×C4×Q8—61no—
130C3×C4×D4—32no—
131C3×C4×D4—62no—
132C3×#117—31no—
133C3×#117—31no—
134C3×#117—62no—
135C3×#117—61no—
136C2×C3×C4⋊C4—31no—
137C2×C3×C4⋊C4—61no—
138Q8×Dic3—21no—
139Q8×Dic3—21no—
140Q8×Dic3C22×C312yes—
141Q8×Dic3C22×C312yes—
142Q8×Dic3C22×C312yes—
143D4×Dic3—22no—
144D4×Dic3C22×C312yes—
145#926—22no—
146#926—21no—
147#926C22×C311yescharacteristic
148#926C22×C311yescharacteristic
149C2×C4⋊Dic3—21no—
150C2×C4⋊Dic3C22×C311yescharacteristic
151C22×C3⋊C8C22×C311yescharacteristic
152C3×#107—32no—
153C3×#106—32no—
154C3×#103—32no—
155C3×#103—32no—
156C3×#103—31no—
157C3×#103—31no—
158C3×#102—31no—
159C3×#102—31no—
160C3×#97—32no—
161C3×C4×C8—32no—
162#835C22×C312yes—
163#835C22×C312yes—
164#835C22×C311yescharacteristic
165#835C22×C311yescharacteristic
166#832C22×C311yescharacteristic
167#832C22×C311yescharacteristic
168#818C22×C312yes—
169#817C22×C312yes—
170#815C22×C312yes—
171C8×Dic3C22×C312yes—
172C23×C32—21no—
173C23×C32C2×D411yescharacteristic
174C32×Q8—24no—
175C32×Q8—22no—
176C32×Q8—21no—
177C32×Q8C22×C414yes—
178C32×Q8C22×C412yes—
179C32×D4—24no—
180C32×D4—21no—
181C32×D4C22×C412yes—
182C2×C32×C4—24no—
183C2×C32×C4—21no—
184C2×C32×C4—22no—
185C2×C32×C4—24no—
186C2×C32×C4C22×C412yes—
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4#4112yes—
189C2×C32×C4C2411yescharacteristic
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—82no—
194C2×C3×Dic3—81no—
195C2×C3×Dic3C2×D412yes—
196C2×C3×Dic3C2×D412yes—
197C32×C8C22×C414yes—
198C3×C3⋊C8—21no—
199C3×C3⋊C8—21no—
200C2×#137C3×D311yescharacteristic
201#520—31no—
202#519—31no—
203#441—32no—
204#440—32no—
205C4×Q16—32no—
206C4×SD16—32no—
207#428—31no—
208#416—31no—
209C2×#103—31no—
210#405—31no—
211C3×#41—22no—
212C3×#41—22no—
213C3×#41—24no—
214C3×#41—42no—
215C3×#41C2×Dic314yes—
216C3×#41C2×C3×C414yes—
217C2×C3×Q8—21no—
218C2×C3×Q8—22no—
219C2×C3×Q8—21no—
220C2×C3×Q8—22no—
221C2×C3×Q8—24no—
222C2×C3×Q8—22no—
223C2×C3×Q8—21no—
224C2×C3×Q8—41no—
225C2×C3×Q8—42no—
226C2×C3×Q8C2×Dic314yescomplemented
227C2×C3×Q8C2×C3×C414yescomplemented
228C2×C3×Q8C22×D312yes—
229C2×C3×Q8C22×D311yescharacteristic
230C2×C3×Q8C23×C312yes—
231C2×C3×Q8C23×C311yescharacteristic
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—41no—
236C2×C3×D4C22×D311yescharacteristic
237C2×C3×D4C23×C311yescharacteristic
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—41no—
244C22×C3×C4—41no—
245C22×C3×C4—62no—
246C22×C3×C4—61no—
247C22×C3×C4C22×D311yescharacteristic
248C22×C3×C4C23×C311yescharacteristic
249C22×Dic3—21no—
250C22×Dic3—22no—
251C3×Q16—28no—
252C3×Q16C2×Dic318yescomplemented
253C3×Q16C2×C3×C418yescomplemented
254C3×SD16—28no—
255C3×SD16C2×Dic318yescomplemented
256C3×SD16C2×C3×C418yescomplemented
257C3×M16—24no—
258C3×M16C2×Dic314yescomplemented
259C3×M16C2×C3×C414yescomplemented
260C2×C3×C8—22no—
261C2×C3×C8—31no—
262C2×C3×C8—31no—
263C2×C3×C8—62no—
264C2×C3×C8C22×D312yes—
265C2×C3×C8C23×C312yes—
266C3×C4⋊C4—31no—
267C3×C4⋊C4—31no—
268C3×C4⋊C4—31no—
269C3×C4⋊C4—31no—
270C3×C4⋊C4—32no—
271C3×C4⋊C4—62no—
272C3×C4⋊C4—62no—
273C3×C4⋊C4—62no—
274C3×C4⋊C4—61no—
275C3×C22⋊C4—32no—
276C3×C22⋊C4—62no—
277C3×C22⋊C4—61no—
278C3×C42—32no—
279C3×C42—62no—
280C3×C42—62no—
281C3×C42—62no—
282C3×C42—61no—
283#217—21no—
284#217—22no—
285#217C3×D412yes—
286C4⋊Dic3—21no—
287C4⋊Dic3—22no—
288C4⋊Dic3—22no—
289C4⋊Dic3—22no—
290C4⋊Dic3C3×D411yescharacteristic
291C4⋊Dic3C3×D411yescharacteristic
292C4⋊Dic3C23×C311yescharacteristic
293C4⋊Dic3C23×C312yes—
294C4⋊Dic3C23×C311yescharacteristic
295C4×Dic3—21no—
296C4×Dic3—22no—
297C4×Dic3—22no—
298C4×Dic3—22no—
299C4×Dic3C23×C312yes—
300C2×C3⋊C8—22no—
301C2×C3⋊C8C23×C311yescharacteristic
302C2×C3⋊C8C23×C311yescharacteristic
303C22×C32—21no—
304C22×C32—21no—
305C22×C32—22no—
306C22×C32—41no—
307C22×C32—41no—
308C22×C32C4×D412yes—
309C22×C32C22×D411yescharacteristic
310C32×C4—22no—
311C32×C4—24no—
312C32×C4C4×D412yes—
313C32×C4C23×C411yescharacteristic
314C32×C4C2×#4111yescharacteristic
315C3×Dic3—22no—
316C3×Dic3—22no—
317C3×Dic3—41no—
318C3×Dic3—42no—
319C3×Dic3—41no—
320C2×#41C2×C3×D311yescharacteristic
321C22×Q8C2×C3×D311yescharacteristic
322#137C3×Dic318yescomplemented
323C2×Q16C2×C3×D312yes—
324C2×SD16C2×C3×D312yes—
325C2×M16C2×C3×D311yescharacteristic
326C22×C8—31no—
327C4×Q8—32no—
328C4×Q8—32no—
329C4×Q8—32no—
330C4×Q8—61no—
331C4×Q8—61no—
332C4×D4—32no—
333C4×D4—62no—
334#117—31no—
335#117—31no—
336#117—62no—
337#117—61no—
338C2×C4⋊C4—31no—
339C2×C4⋊C4—61no—
340#107—32no—
341#106—32no—
342#103—32no—
343#103—32no—
344#103—31no—
345#103—31no—
346#102—31no—
347#102—31no—
348#97—32no—
349C4×C8—32no—
350C23×C3—21no—
351C23×C3—21no—
352C23×C3—21no—
353C23×C3—41no—
354C23×C3D3×D411yescharacteristic
355C23×C3C2×C3×D411yescharacteristic
356C3×Q8—24no—
357C3×Q8—24no—
358C3×Q8—22no—
359C3×Q8—21no—
360C3×Q8—22no—
361C3×Q8—21no—
362C3×Q8—24no—
363C3×Q8—22no—
364C3×Q8—44no—
365C3×Q8—42no—
366C3×Q8—41no—
367C3×Q8C22×Dic314yes—
368C3×Q8C22×Dic312yes—
369C3×Q8C22×C3×C414yes—
370C3×Q8C22×C3×C412yes—
371C3×D4—24no—
372C3×D4—24no—
373C3×D4—21no—
374C3×D4—21no—
375C3×D4—22no—
376C3×D4—41no—
377C3×D4—44no—
378C3×D4C22×Dic312yes—
379C3×D4C22×C3×C412yes—
380C2×C3×C4—24no—
381C2×C3×C4—24no—
382C2×C3×C4—21no—
383C2×C3×C4—22no—
384C2×C3×C4—21no—
385C2×C3×C4—22no—
386C2×C3×C4—24no—
387C2×C3×C4—24no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—32no—
393C2×C3×C4—32no—
394C2×C3×C4—44no—
395C2×C3×C4—41no—
396C2×C3×C4—44no—
397C2×C3×C4—42no—
398C2×C3×C4—61no—
399C2×C3×C4—61no—
400C2×C3×C4—62no—
401C2×C3×C4—242no—
402C2×C3×C4—241no—
403C2×C3×C4D3×D411yescharacteristic
404C2×C3×C4#23712yes—
405C2×C3×C4C22×Dic312yes—
406C2×C3×C4C22×C3×C412yes—
407C2×C3×C4C2×C3×D411yescharacteristic
408C2×C3×C4C3×#4112yes—
409C2×C3×C4C23×D311yescharacteristic
410C2×C3×C4C24×C311yescharacteristic
411C2×Dic3—21no—
412C2×Dic3—21no—
413C2×Dic3—22no—
414C2×Dic3—82no—
415C2×Dic3—81no—
416C2×Dic3C2×C3×D412yes—
417C2×Dic3C2×C3×D412yes—
418C3×C8—24no—
419C3×C8—61no—
420C3×C8—61no—
421C3×C8C22×Dic314yes—
422C3×C8C22×C3×C414yes—
423C3⋊C8—21no—
424C3⋊C8—21no—
425C2×C32—22no—
426C2×C32—42no—
427C2×C32C2×C4×D411yescharacteristic
428C2×C32#57711yescharacteristic
429C2×C32#57811yescharacteristic
430#41—22no—
431#41C2×C3×Dic314yes—
432C2×Q8—21no—
433C2×Q8—22no—
434C2×Q8C2×C3×Dic314yescomplemented
435C2×Q8C22×C3×D312yes—
436C2×Q8C22×C3×D311yescharacteristic
437C2×D4—21no—
438C2×D4C22×C3×D311yescharacteristic
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—62no—
442C22×C4—61no—
443C22×C4C22×C3×D311yescharacteristic
444Q16C2×C3×Dic318yescomplemented
445SD16C2×C3×Dic318yescomplemented
446M16C2×C3×Dic314yescomplemented
447C2×C8—31no—
448C2×C8—31no—
449C2×C8—62no—
450C2×C8C22×C3×D312yes—
451C4⋊C4—31no—
452C4⋊C4—31no—
453C4⋊C4—31no—
454C4⋊C4—31no—
455C4⋊C4—32no—
456C4⋊C4—62no—
457C4⋊C4—62no—
458C4⋊C4—62no—
459C4⋊C4—61no—
460C22⋊C4—32no—
461C22⋊C4—62no—
462C22⋊C4—61no—
463C42—32no—
464C42—62no—
465C42—62no—
466C42—62no—
467C42—61no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—22no—
473C22×C3—22no—
474C22×C3—22no—
475C22×C3—21no—
476C22×C3—41no—
477C22×C3—41no—
478C22×C3—42no—
479C22×C3—41no—
480C22×C3—41no—
481C22×C3—41no—
482C22×C3—41no—
483C22×C3—81no—
484C22×C3—81no—
485C22×C3D4×Dic312yes—
486C22×C3C3×C4×D412yes—
487C22×C3C2×D3×D411yescharacteristic
488C22×C3C22×C3×D411yescharacteristic
489C3×C4—22no—
490C3×C4—24no—
491C3×C4—22no—
492C3×C4—24no—
493C3×C4—22no—
494C3×C4—21no—
495C3×C4—21no—
496C3×C4—42no—
497C3×C4—44no—
498C3×C4—62no—
499C3×C4—62no—
500C3×C4—122no—
501C3×C4—121no—
502C3×C4—121no—
503C3×C4D4×Dic312yes—
504C3×C4C3×C4×D412yes—
505C3×C4C2×#23711yescharacteristic
506C3×C4C23×Dic311yescharacteristic
507C3×C4C23×C3×C411yescharacteristic
508C3×C4C2×C3×#4111yescharacteristic
509Dic3—22no—
510Dic3—22no—
511Dic3—42no—
512Dic3—41no—
513Dic3—41no—
514C32#294711yescharacteristic, complemented, Sylow
515C23—21no—
516C23C3×D3×D411yescharacteristic
517Q8—24no—
518Q8—22no—
519Q8—21no—
520Q8C22×C3×Dic314yes—
521Q8C22×C3×Dic312yes—
522D4—24no—
523D4—21no—
524D4C22×C3×Dic312yes—
525C2×C4—24no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—32no—
530C2×C4—32no—
531C2×C4—61no—
532C2×C4—61no—
533C2×C4—62no—
534C2×C4—242no—
535C2×C4—241no—
536C2×C4C3×D3×D411yescharacteristic
537C2×C4C3×#23712yes—
538C2×C4C22×C3×Dic312yes—
539C2×C4C23×C3×D311yescharacteristic
540C8—61no—
541C8—61no—
542C8C22×C3×Dic314yes—
543C2×C3—22no—
544C2×C3—22no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—42no—
549C2×C3—42no—
550C2×C3—42no—
551C2×C3—82no—
552C2×C3#577811yescharacteristic
553C2×C3#577911yescharacteristic
554C2×C3C2×D4×Dic311yescharacteristic
555C2×C3C2×C3×C4×D411yescharacteristic
556C2×C3C3×#57711yescharacteristic
557C2×C3C3×#57811yescharacteristic
558C22—21no—
559C22—21no—
560C22—22no—
561C22—41no—
562C22—41no—
563C22C3×D4×Dic312yes—
564C22C2×C3×D3×D411yescharacteristic
565C4—22no—
566C4—24no—
567C4—62no—
568C4—62no—
569C4—122no—
570C4—121no—
571C4—121no—
572C4C3×D4×Dic312yes—
573C4C2×C3×#23711yescharacteristic
574C4C23×C3×Dic311yescharacteristic
575C3—21no—
576C3#8396511yescharacteristic, direct product factor
577C3C3×#294711yescharacteristic, complemented
578C2—22no—
579C2—42no—
580C2C3×#577811yescharacteristic
581C2C3×#577911yescharacteristic
582C2C2×C3×D4×Dic311yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#137C2
socleC22×C32C22×D4
prime radicalC2×C32×#41C22
cosocleC2×C3×C4C24×C3
hypercenterC2×C3×#137D3
hypocenterC3C3×#2947
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#137

Complements

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

NH ≅ G/Ntype
3. C3×#5812C2semidirect
5. C2×C3×#835C2semidirect
6. C3×#5184C2semidirect
7. C3×Dic3×Q16C2semidirect
8. C3×#5164C2semidirect
9. C3×Dic3×SD16C2semidirect
10. C3×#5122C2semidirect
11. C3×#5121C2semidirect
13. #83965C3direct (N × H)
16. C32×#137C4semidirect
50. #5812C2×C3semidirect
60. C2×#835C2×C3semidirect
61. #5184C2×C3semidirect
62. Dic3×Q16C2×C3semidirect
63. #5164C2×C3semidirect
64. Dic3×SD16C2×C3semidirect
65. #5122C2×C3semidirect
66. #5121C2×C3semidirect
71. C2×C32×Q8C2×C4semidirect
81. C32×Q16C2×C4semidirect
82. C32×SD16C2×C4semidirect
83. C32×M16C2×C4semidirect
113. C3×#137Dic3semidirect
114. C3×#137C3×C4semidirect
226. C2×C3×Q8C2×Dic3semidirect
227. C2×C3×Q8C2×C3×C4semidirect
252. C3×Q16C2×Dic3semidirect
253. C3×Q16C2×C3×C4semidirect
255. C3×SD16C2×Dic3semidirect
256. C3×SD16C2×C3×C4semidirect
258. C3×M16C2×Dic3semidirect
259. C3×M16C2×C3×C4semidirect
322. #137C3×Dic3semidirect
434. C2×Q8C2×C3×Dic3semidirect
444. Q16C2×C3×Dic3semidirect
445. SD16C2×C3×Dic3semidirect
446. M16C2×C3×Dic3semidirect
514. C32#2947semidirect
576. C3#83965direct (N × H)
577. C3C3×#2947semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1372
C3×#58272
C3×#58122
C3×#52332
C2×C3×#8352
C3×#51842
C3×Dic3×Q162
C3×#51642
C3×Dic3×SD162
C3×#51222
C3×#51212
C3×#29473
#839653