Finite Group Databasebeta

← C3×#82547 #11860579

Subgroups — C3×#82547 #11860579

Order 1152.

1073 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#519C211yesmaximal, characteristic, complemented
2C2×C3×#942C211yesmaximal, characteristic
3C3×#5523C211yesmaximal, characteristic
4C2×C3×#835C211yesmaximal, characteristic, complemented
5C3×#5030C212yesmaximal, complemented
6C3×C4×#216C212yesmaximal, complemented
7C3×#5026C212yesmaximal, complemented
8C3×C4×#215C212yesmaximal, complemented
9C3×#5002C211yesmaximal, characteristic
10C3×#4997C211yesmaximal, characteristic, complemented
11C3×#4995C211yesmaximal, characteristic, complemented
12C3×#2947—31nomaximal
13#82547C311yesmaximal, characteristic, direct product factor
14C22×C32×Q8C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C32×C4×Q8—21no—
17C32×C4×Q8—21no—
18C32×C4×Q8C2212yes—
19C32×C4×Q8C2212yes—
20C32×#117—22no—
21C32×#117C2211yescharacteristic
22C32×#117C2211yescharacteristic
23C2×C3×#216C2212yes—
24C3×#942C418yescomplemented
25C2×C3×#215C2212yes—
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×#208C2211yescharacteristic
28C22×C3×C3⋊C8C2211yescharacteristic
29C3×#892—21no—
30C3×D3×C4⋊C4—21no—
31C3×#67⋊C4—22no—
32C3×C4×D12C2212yes—
33C3×C4×Dic6C2212yes—
34C3×#835C2212yes—
35C3×#835C2212yes—
36C3×#810C2211yescharacteristic
37C3×#810C2211yescharacteristic
38C3×#809C2211yescharacteristic
39C3×#809C2211yescharacteristic
40C3×#808C2212yes—
41C3×#807C2212yes—
42C3×#803C2212yes—
43C3×C4×C3⋊C8C2212yes—
44C2×C3×#137—31no—
45C3×#520—31no—
46C3×#519—21no—
47C3×#519D311yescharacteristic, complemented
48C3×#519C2×C311yescharacteristic, complemented
49C2×#942C2×C311yescharacteristic
50#5523C2×C311yescharacteristic
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—
59C2×#835C2×C311yescharacteristic, complemented
60#5030C2×C312yescomplemented
61C4×#216C2×C312yescomplemented
62#5026C2×C312yescomplemented
63C4×#215C2×C312yescomplemented
64#5002C2×C311yescharacteristic
65#4997C2×C311yescharacteristic, complemented
66#4995C2×C311yescharacteristic, complemented
67C2×C32×Q8—21no—
68C2×C32×Q8—22no—
69C2×C32×Q8C2×C414yescomplemented
70C2×C32×Q8C2312yes—
71C22×C32×C4—21no—
72C22×C32×C4C2311yescharacteristic
73C2×C3×#67—21no—
74C22×C3×Dic3—21no—
75C3×#235—22no—
76C3×#235C2×C414yes—
77C2×C3×D12C2311yescharacteristic
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3—22no—
80C2×C3×Dic6C2311yescharacteristic
81C32×C4⋊C4—22no—
82C32×C4⋊C4—22no—
83C32×C4⋊C4D411yescharacteristic
84C32×C4⋊C4D411yescharacteristic
85C32×C4⋊C4C2311yescharacteristic
86C32×C4⋊C4C2311yescharacteristic
87C32×C22⋊C4—21no—
88C32×C22⋊C4D412yes—
89C32×C42—22no—
90C32×C42—22no—
91C32×C42—21no—
92C32×C42C2312yes—
93C3×#216C2×C418yescomplemented
94C3×#215C2×C418yescomplemented
95C3×(C2×D3)⋊C4—22no—
96C3×C4⋊Dic3—21no—
97C3×C4⋊Dic3C2312yes—
98C3×Dic3⋊C4—22no—
99C3×C4×Dic3—22no—
100C3×#208C2×C414yescomplemented
101C2×C3×C3⋊C8—22no—
102C2×C3×C3⋊C8C2311yescharacteristic
103C2×C3×C3⋊C8C2311yescharacteristic
104C2×C3×C3⋊C8C2312yes—
105#2947—31noSylow
106C2×C3×#41—31no—
107C22×C3×Q8—21no—
108C22×C3×Q8C2×D311yescharacteristic
109C22×C3×Q8C22×C311yescharacteristic
110C2×#235C22×C311yescharacteristic
111C3×#137—38no—
112C2×C3×Q16—32no—
113C2×C3×SD16—32no—
114C2×C3×M16—31no—
115C22×C3×C8—31no—
116C3×C4×Q8—22no—
117C3×C4×Q8—22no—
118C3×C4×Q8—21no—
119C3×C4×Q8—21no—
120C3×C4×Q8—21no—
121C3×C4×Q8—21no—
122C3×C4×Q8—22no—
123C3×C4×Q8—22no—
124C3×C4×Q8—32no—
125C3×C4×Q8C2×D312yes—
126C3×C4×Q8C2×D312yes—
127C3×C4×Q8C22×C312yes—
128C3×C4×Q8C22×C312yes—
129C3×C4×D4—32no—
130C3×C4×D4—62no—
131C3×#117—24no—
132C3×#117—22no—
133C3×#117—22no—
134C3×#117—21no—
135C3×#117—21no—
136C3×#117—61no—
137C3×#117C2×D311yescharacteristic
138C3×#117C2×D311yescharacteristic
139C3×#117C22×C311yescharacteristic
140C3×#117C22×C311yescharacteristic
141C2×C3×C4⋊C4—31no—
142C2×C3×C4⋊C4—61no—
143C2×#216C22×C312yes—
144#942C3×C418yescomplemented
145C2×#215C22×C312yes—
146C2×C4⋊Dic3C22×C311yescharacteristic
147C2×#208C22×C311yescharacteristic
148C22×C3⋊C8C22×C311yescharacteristic
149#892—21no—
150D3×C4⋊C4—21no—
151#67⋊C4—22no—
152C4×D12C22×C312yes—
153C4×Dic6C22×C312yes—
154C3×#107—32no—
155C3×#106—32no—
156C3×#103—32no—
157C3×#103—32no—
158C3×#103—31no—
159C3×#103—31no—
160C3×#102—31no—
161C3×#102—31no—
162C3×#97—32no—
163C3×C4×C8—32no—
164#835C22×C312yes—
165#835C22×C312yes—
166#810C22×C311yescharacteristic
167#810C22×C311yescharacteristic
168#809C22×C311yescharacteristic
169#809C22×C311yescharacteristic
170#808C22×C312yes—
171#807C22×C312yes—
172#803C22×C312yes—
173C4×C3⋊C8C22×C312yes—
174C23×C32C2×D411yescharacteristic
175C22×C3×D3—21no—
176C32×Q8—24no—
177C32×Q8—22no—
178C32×Q8C22×C414yes—
179C2×C32×C4—24no—
180C2×C32×C4—22no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4C22×C412yes—
184C2×C32×C4C2×D412yes—
185C2×C32×C4C2×D412yes—
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4#4112yes—
188C2×C32×C4C2411yescharacteristic
189C3×#67—24no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—81no—
193C3×D12—21no—
194C3×D12C22×C412yes—
195C3×C4×D3—24no—
196C3×C4×D3—82no—
197C3×Dic6—21no—
198C3×Dic6C22×C412yes—
199C3×C3⋊C8—21no—
200C3×C3⋊C8—21no—
201C3×C3⋊C8C22×C414yes—
202C2×#137—31no—
203#520—31no—
204#519C3×D311yescharacteristic, complemented
205#441—32no—
206#440—32no—
207C4×Q16—32no—
208C4×SD16—32no—
209#428—31no—
210#416—31no—
211C2×#103—31no—
212#405—31no—
213C3×#41—34no—
214C3×#41—62no—
215C2×C3×Q8—22no—
216C2×C3×Q8—24no—
217C2×C3×Q8—22no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—22no—
221C2×C3×Q8—24no—
222C2×C3×Q8—22no—
223C2×C3×Q8—31no—
224C2×C3×Q8C4×D314yescomplemented
225C2×C3×Q8C2×C3×C414yescomplemented
226C2×C3×Q8C22×D312yes—
227C2×C3×Q8C23×C312yes—
228C2×C3×D4—31no—
229C2×C3×D4—61no—
230C22×C3×C4—22no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—61no—
235C22×C3×C4—61no—
236C22×C3×C4—62no—
237C22×C3×C4C22×D311yescharacteristic
238C22×C3×C4C23×C311yescharacteristic
239C2×#67—21no—
240C22×Dic3—21no—
241#235—22no—
242#235C2×C3×C414yes—
243C2×D12C23×C311yescharacteristic
244C2×C4×D3—21no—
245C2×C4×D3—22no—
246C2×Dic6C23×C311yescharacteristic
247C3×Q16—38no—
248C3×SD16—38no—
249C3×M16—34no—
250C2×C3×C8—32no—
251C2×C3×C8—31no—
252C2×C3×C8—31no—
253C2×C3×C8—62no—
254C3×C4⋊C4—24no—
255C3×C4⋊C4—24no—
256C3×C4⋊C4—22no—
257C3×C4⋊C4—22no—
258C3×C4⋊C4—22no—
259C3×C4⋊C4—22no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—21no—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—32no—
265C3×C4⋊C4—62no—
266C3×C4⋊C4—61no—
267C3×C4⋊C4#6711yescharacteristic
268C3×C4⋊C4#6711yescharacteristic
269C3×C4⋊C4C3×D411yescharacteristic
270C3×C4⋊C4C3×D411yescharacteristic
271C3×C4⋊C4C22×D311yescharacteristic
272C3×C4⋊C4C22×D311yescharacteristic
273C3×C4⋊C4C23×C311yescharacteristic
274C3×C4⋊C4C23×C311yescharacteristic
275C3×C22⋊C4—22no—
276C3×C22⋊C4—21no—
277C3×C22⋊C4—21no—
278C3×C22⋊C4—22no—
279C3×C22⋊C4—62no—
280C3×C22⋊C4#6712yes—
281C3×C22⋊C4C3×D412yes—
282C3×C42—24no—
283C3×C42—24no—
284C3×C42—22no—
285C3×C42—22no—
286C3×C42—22no—
287C3×C42—21no—
288C3×C42—22no—
289C3×C42—22no—
290C3×C42—21no—
291C3×C42—22no—
292C3×C42—62no—
293C3×C42C22×D312yes—
294C3×C42C23×C312yes—
295#216C2×C3×C418yescomplemented
296#215C2×C3×C418yescomplemented
297(C2×D3)⋊C4—22no—
298C4⋊Dic3—21no—
299C4⋊Dic3C23×C312yes—
300Dic3⋊C4—22no—
301C4×Dic3—22no—
302#208C2×C3×C414yescomplemented
303C2×C3⋊C8—22no—
304C2×C3⋊C8C23×C311yescharacteristic
305C2×C3⋊C8C23×C311yescharacteristic
306C2×C3⋊C8C23×C312yes—
307C22×C32—21no—
308C22×C32—21no—
309C22×C32C4×D412yes—
310C22×C32C22×D411yescharacteristic
311C2×C3×D3—22no—
312C2×C3×D3—41no—
313C2×C3×D3—41no—
314C32×C4—24no—
315C32×C4—22no—
316C32×C4—22no—
317C32×C4—41no—
318C32×C4—41no—
319C32×C4C4×D412yes—
320C32×C4C23×C411yescharacteristic
321C32×C4C2×#4111yescharacteristic
322C3×Dic3—22no—
323C3×Dic3—42no—
324C2×#41—31no—
325C22×Q8C2×C3×D311yescharacteristic
326#137—38no—
327C2×Q16—32no—
328C2×SD16—32no—
329C2×M16—31no—
330C22×C8—31no—
331C4×Q8—21no—
332C4×Q8—21no—
333C4×Q8—32no—
334C4×Q8C2×C3×D312yes—
335C4×Q8C2×C3×D312yes—
336C4×D4—32no—
337C4×D4—62no—
338#117—22no—
339#117—61no—
340#117C2×C3×D311yescharacteristic
341#117C2×C3×D311yescharacteristic
342C2×C4⋊C4—31no—
343C2×C4⋊C4—61no—
344#107—32no—
345#106—32no—
346#103—32no—
347#103—32no—
348#103—31no—
349#103—31no—
350#102—31no—
351#102—31no—
352#97—32no—
353C4×C8—32no—
354C23×C3—21no—
355C23×C3—61no—
356C23×C3C2×#6711yescharacteristic
357C23×C3C2×C3×D411yescharacteristic
358C22×D3—21no—
359C3×Q8—28no—
360C3×Q8—24no—
361C3×Q8—24no—
362C3×Q8—24no—
363C3×Q8—22no—
364C3×Q8—22no—
365C3×Q8—24no—
366C3×Q8—32no—
367C3×Q8—61no—
368C3×Q8C2×C4×D314yes—
369C3×Q8C22×C3×C414yes—
370C3×D4—32no—
371C3×D4—64no—
372C3×D4—61no—
373C2×C3×C4—24no—
374C2×C3×C4—28no—
375C2×C3×C4—24no—
376C2×C3×C4—24no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—21no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—61no—
392C2×C3×C4—64no—
393C2×C3×C4—62no—
394C2×C3×C4—242no—
395C2×C3×C4—241no—
396C2×C3×C4C2×C4×D312yes—
397C2×C3×C4#23512yes—
398C2×C3×C4C2×#6712yes—
399C2×C3×C4C2×#6712yes—
400C2×C3×C4C2×#6711yescharacteristic
401C2×C3×C4C22×C3×C412yes—
402C2×C3×C4C2×C3×D412yes—
403C2×C3×C4C2×C3×D412yes—
404C2×C3×C4C2×C3×D411yescharacteristic
405C2×C3×C4C3×#4112yes—
406C2×C3×C4C23×D311yescharacteristic
407C2×C3×C4C24×C311yescharacteristic
408#67—24no—
409C2×Dic3—21no—
410C2×Dic3—22no—
411C2×Dic3—81no—
412D12—21no—
413D12C22×C3×C412yes—
414C4×D3—24no—
415C4×D3—82no—
416Dic6—21no—
417Dic6C22×C3×C412yes—
418C3×C8—34no—
419C3×C8—61no—
420C3×C8—61no—
421C3⋊C8—21no—
422C3⋊C8—21no—
423C3⋊C8C22×C3×C414yes—
424C2×C32—22no—
425C2×C32C2×C4×D411yescharacteristic
426C2×C32#57711yescharacteristic
427C2×C32#57811yescharacteristic
428C3×D3—42no—
429#41—34no—
430#41—62no—
431C2×Q8—22no—
432C2×Q8—21no—
433C2×Q8—31no—
434C2×Q8C3×C4×D314yescomplemented
435C2×Q8C22×C3×D312yes—
436C2×D4—31no—
437C2×D4—61no—
438C22×C4—21no—
439C22×C4—61no—
440C22×C4—61no—
441C22×C4—62no—
442C22×C4C22×C3×D311yescharacteristic
443Q16—38no—
444SD16—38no—
445M16—34no—
446C2×C8—32no—
447C2×C8—31no—
448C2×C8—31no—
449C2×C8—62no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—32no—
453C4⋊C4—61no—
454C4⋊C4—62no—
455C4⋊C4C3×#6711yescharacteristic
456C4⋊C4C3×#6711yescharacteristic
457C4⋊C4C22×C3×D311yescharacteristic
458C4⋊C4C22×C3×D311yescharacteristic
459C22⋊C4—21no—
460C22⋊C4—62no—
461C22⋊C4C3×#6712yes—
462C42—22no—
463C42—22no—
464C42—21no—
465C42—62no—
466C42C22×C3×D312yes—
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—62no—
476C22×C3—121no—
477C22×C3—121no—
478C22×C3C4×#6712yes—
479C22×C3C3×C4×D412yes—
480C22×C3C22×#6711yescharacteristic
481C22×C3C22×C3×D411yescharacteristic
482C2×D3—22no—
483C2×D3—41no—
484C2×D3—41no—
485C3×C4—28no—
486C3×C4—22no—
487C3×C4—22no—
488C3×C4—24no—
489C3×C4—22no—
490C3×C4—22no—
491C3×C4—24no—
492C3×C4—22no—
493C3×C4—21no—
494C3×C4—21no—
495C3×C4—42no—
496C3×C4—42no—
497C3×C4—42no—
498C3×C4—42no—
499C3×C4—41no—
500C3×C4—41no—
501C3×C4—41no—
502C3×C4—41no—
503C3×C4—62no—
504C3×C4—122no—
505C3×C4C4×#6712yes—
506C3×C4C3×C4×D412yes—
507C3×C4C22×C4×D311yescharacteristic
508C3×C4C2×#23511yescharacteristic
509C3×C4C23×C3×C411yescharacteristic
510C3×C4C2×C3×#4111yescharacteristic
511Dic3—22no—
512Dic3—42no—
513C32#294711yescharacteristic, complemented, Sylow
514C23—61no—
515C23C2×C3×#6711yescharacteristic
516Q8—24no—
517Q8—22no—
518Q8—32no—
519Q8—61no—
520Q8C2×C3×C4×D314yes—
521D4—32no—
522D4—64no—
523D4—61no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—61no—
529C2×C4—64no—
530C2×C4—62no—
531C2×C4—242no—
532C2×C4—241no—
533C2×C4C2×C3×C4×D312yes—
534C2×C4C3×#23512yes—
535C2×C4C2×C3×#6712yes—
536C2×C4C2×C3×#6712yes—
537C2×C4C2×C3×#6711yescharacteristic
538C2×C4C23×C3×D311yescharacteristic
539C8—34no—
540C8—61no—
541C8—61no—
542C2×C3—22no—
543C2×C3—22no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—42no—
548C2×C3—122no—
549C2×C3C2×C4×#6711yescharacteristic
550C2×C3#583711yescharacteristic
551C2×C3#583811yescharacteristic
552C2×C3C2×C3×C4×D411yescharacteristic
553C2×C3C3×#57711yescharacteristic
554C2×C3C3×#57811yescharacteristic
555D3—42no—
556C22—21no—
557C22—21no—
558C22—62no—
559C22—121no—
560C22—121no—
561C22C3×C4×#6712yes—
562C22C22×C3×#6711yescharacteristic
563C4—24no—
564C4—22no—
565C4—22no—
566C4—41no—
567C4—41no—
568C4—62no—
569C4—122no—
570C4C3×C4×#6712yes—
571C4C22×C3×C4×D311yescharacteristic
572C4C2×C3×#23511yescharacteristic
573C3—21no—
574C3#8254711yescharacteristic, direct product factor
575C3C3×#294711yescharacteristic, complemented
576C2—22no—
577C2—122no—
578C2C2×C3×C4×#6711yescharacteristic
579C2C3×#583711yescharacteristic
580C2C3×#583811yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC32×#519C2
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
cosocleC2×C3×C4C24×C3
hypercenterC3×#519D3
hypocenterC3C3×#2947
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#117 ◁ C3×#519

Complements

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

NH ≅ G/Ntype
1. C32×#519C2semidirect
4. C2×C3×#835C2semidirect
5. C3×#5030C2semidirect
6. C3×C4×#216C2semidirect
7. C3×#5026C2semidirect
8. C3×C4×#215C2semidirect
10. C3×#4997C2semidirect
11. C3×#4995C2semidirect
13. #82547C3direct (N × H)
24. C3×#942C4semidirect
47. C3×#519D3semidirect
48. C3×#519C2×C3semidirect
59. C2×#835C2×C3semidirect
60. #5030C2×C3semidirect
61. C4×#216C2×C3semidirect
62. #5026C2×C3semidirect
63. C4×#215C2×C3semidirect
65. #4997C2×C3semidirect
66. #4995C2×C3semidirect
69. C2×C32×Q8C2×C4semidirect
93. C3×#216C2×C4semidirect
94. C3×#215C2×C4semidirect
100. C3×#208C2×C4semidirect
144. #942C3×C4semidirect
204. #519C3×D3semidirect
224. C2×C3×Q8C4×D3semidirect
225. C2×C3×Q8C2×C3×C4semidirect
295. #216C2×C3×C4semidirect
296. #215C2×C3×C4semidirect
302. #208C2×C3×C4semidirect
434. C2×Q8C3×C4×D3semidirect
513. C32#2947semidirect
574. C3#82547direct (N × H)
575. C3C3×#2947semidirect

Maximal subgroups

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

subgroupindex
C32×#5192
C2×C3×#9422
C3×#55232
C2×C3×#8352
C3×#50302
C3×C4×#2162
C3×#50262
C3×C4×#2152
C3×#50022
C3×#49972
C3×#49952
C3×#29473
#825473