Finite Group Databasebeta

← C3×#83297 #11865833

Subgroups — C3×#83297 #11865833

Order 1152.

1251 conjugacy classes of subgroups.

The subgroup lattice has 591 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#532C211yesmaximal, characteristic, complemented
2C2×C3×#949C212yesmaximal, complemented
3C2×C3×C4×D12C211yesmaximal, characteristic, complemented
4C3×#5232C212yesmaximal, complemented
5C3×#5083C212yesmaximal, complemented
6C3×#5072C212yesmaximal, complemented
7C3×#5057C214yesmaximal, complemented
8C3×#4924C211yesmaximal, characteristic, complemented
9C3×#3036—31nomaximal
10#83297C311yesmaximal, characteristic, direct product factor
11C2×C32×#41C2212yes—
12C22×C3×D12C2211yescharacteristic
13C22×C3×C4×D3—21no—
14C32×C4⋊Q8C2211yescharacteristic, complemented
15C32×#127C2211yescharacteristic, complemented
16C32×#124C2212yescomplemented
17C32×#121—21no—
18C32×#121—21no—
19C32×C4×D4—21no—
20C32×C4×D4—21no—
21C2×C32×C42C2211yescharacteristic
22C3×#949—28no—
23C2×C3×#215C2214yes—
24C2×C3×#213C2214yes—
25C2×C3×(C2×D3)⋊C4—21no—
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×#208C2212yes—
28C3×C4×D12—21no—
29C3×C4×D12—21no—
30C3×C4×D12C2212yes—
31C3×C4×D12C2212yes—
32C3×#835C2214yescomplemented
33C3×#832C2214yescomplemented
34C3×C4⋊(C3⋊C8)C2212yescomplemented
35C3×C4⋊(C3⋊C8)C2212yescomplemented
36C2×C3×AGL(1,ℤ/8)—32no—
37C3×#532—21no—
38C3×#532D311yescharacteristic, complemented
39C3×#532C2×C311yescharacteristic, complemented
40C2×C3×C4×D4—31no—
41C2×#949C2×C312yescomplemented
42C2×C4×D12C2×C311yescharacteristic, complemented
43C3×#463—34no—
44C3×#461—32no—
45C3×#459—32no—
46C3×#423—31no—
47C3×#417—32no—
48#5232C2×C312yescomplemented
49#5083C2×C312yescomplemented
50#5072C2×C312yescomplemented
51#5057C2×C314yescomplemented
52#4924C2×C311yescharacteristic, complemented
53C23×C3×D3—21no—
54C32×#41—24no—
55C32×#41—24no—
56C2×C32×Q8C2312yes—
57C2×C32×D4—22no—
58C2×C32×D4—21no—
59C2×C32×D4—21no—
60C2×C32×D4C2312yes—
61C22×C32×C4—22no—
62C22×C32×C4D411yescharacteristic
63C22×C32×C4D411yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C3×Dic3—21no—
66C2×C3×D12—21no—
67C2×C3×D12—22no—
68C2×C3×D12D414yescomplemented
69C2×C3×D12C2312yes—
70C2×C3×C4×D3—22no—
71C2×C3×C4×D3—22no—
72C2×C3×C4×D3—44no—
73C32×C4⋊C4—21no—
74C32×C4⋊C4—21no—
75C32×C22⋊C4—22no—
76C32×C22⋊C4—22no—
77C32×C42D411yescharacteristic
78C32×C42D411yescharacteristic
79C32×C42C2311yescharacteristic
80C32×C42C2311yescharacteristic
81C3×#215—28no—
82C3×#213—28no—
83C3×(C2×D3)⋊C4—22no—
84C3×(C2×D3)⋊C4—22no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3C2312yes—
87C3×#208—24no—
88C2×C3×C3⋊C8C2314yes—
89#3036—31noSylow
90C2×C3×#41—22no—
91C2×C3×#41C2×D312yes—
92C2×C3×#41C22×C312yes—
93C22×C3×D4—31no—
94C23×C3×C4—61no—
95C22×D12C22×C311yescharacteristic
96C22×C4×D3—21no—
97C3×AGL(1,ℤ/8)—68no—
98C2×C3×SD16—34no—
99C2×C3×D8—34no—
100C2×C3×M16—32no—
101C3×C4⋊Q8—21no—
102C3×C4⋊Q8C2×D311yescharacteristic, complemented
103C3×C4⋊Q8C22×C311yescharacteristic, complemented
104C3×#127—21no—
105C3×#127C2×D311yescharacteristic, complemented
106C3×#127C22×C311yescharacteristic, complemented
107C3×#124—22no—
108C3×#124C2×D312yescomplemented
109C3×#124C22×C312yescomplemented
110C3×#121—22no—
111C3×#121—22no—
112C3×#121—21no—
113C3×#121—21no—
114C3×#121—21no—
115C3×#121—21no—
116C3×C4×D4—22no—
117C3×C4×D4—22no—
118C3×C4×D4—21no—
119C3×C4×D4—21no—
120C3×C4×D4—21no—
121C3×C4×D4—21no—
122C3×C4×D4—32no—
123C3×C4×D4—32no—
124C3×C4×D4—61no—
125C3×C4×D4—61no—
126C2×C3×C4⋊C4—31no—
127C2×C3×C22⋊C4—61no—
128C2×C3×C42—21no—
129C2×C3×C42C2×D311yescharacteristic
130C2×C3×C42C22×C311yescharacteristic
131#949—28no—
132C2×#215C22×C314yes—
133C2×#213C22×C314yes—
134C2×(C2×D3)⋊C4—21no—
135C2×C4⋊Dic3C22×C311yescharacteristic
136C2×#208C22×C312yes—
137C4×D12—21no—
138C4×D12—21no—
139C4×D12C22×C312yes—
140C4×D12C22×C312yes—
141C3×C4⋊C8—32no—
142C3×C4⋊C8—32no—
143C3×#103—34no—
144C3×#102—34no—
145#835C22×C314yescomplemented
146#832C22×C314yescomplemented
147C4⋊(C3⋊C8)C22×C312yescomplemented
148C4⋊(C3⋊C8)C22×C312yescomplemented
149C23×C32—22no—
150C23×C32C2×D411yescharacteristic
151C22×C3×D3—24no—
152C22×C3×D3—22no—
153C22×C3×D3—42no—
154C22×C3×D3—42no—
155C32×Q8—22no—
156C32×Q8—22no—
157C32×D4—22no—
158C32×D4—22no—
159C32×D4—42no—
160C32×D4—44no—
161C32×D4—42no—
162C2×C32×C4—22no—
163C2×C32×C4—22no—
164C2×C32×C4—41no—
165C2×C32×C4—44no—
166C2×C32×C4C2×D412yes—
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4#4112yes—
173C2×C32×C4C2411yescharacteristic
174C2×C3×Dic3—22no—
175C2×C3×Dic3—42no—
176C3×D12—24no—
177C3×D12—22no—
178C3×D12C2×D414yes—
179C3×C4×D3—44no—
180C3×C4×D3—44no—
181C3×C3⋊C8—24no—
182C2×AGL(1,ℤ/8)—32no—
183#532C3×D311yescharacteristic, complemented
184C2×C4×D4—31no—
185#463—34no—
186#461—32no—
187#459—32no—
188#423—31no—
189#417—32no—
190C24×C3—61no—
191C23×D3—21no—
192C3×#41—24no—
193C3×#41—24no—
194C3×#41—24no—
195C3×#41—24no—
196C3×#41—44no—
197C3×#41—44no—
198C2×C3×Q8—22no—
199C2×C3×Q8C22×D312yes—
200C2×C3×Q8C23×C312yes—
201C2×C3×D4—22no—
202C2×C3×D4—22no—
203C2×C3×D4—24no—
204C2×C3×D4—22no—
205C2×C3×D4—22no—
206C2×C3×D4—21no—
207C2×C3×D4—21no—
208C2×C3×D4—21no—
209C2×C3×D4—21no—
210C2×C3×D4—22no—
211C2×C3×D4—34no—
212C2×C3×D4—32no—
213C2×C3×D4—62no—
214C2×C3×D4—61no—
215C2×C3×D4C22×D312yes—
216C2×C3×D4C23×C312yes—
217C22×C3×C4—24no—
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—61no—
224C22×C3×C4—62no—
225C22×C3×C4—62no—
226C22×C3×C4—124no—
227C22×C3×C4#6711yescharacteristic
228C22×C3×C4#6711yescharacteristic
229C22×C3×C4C3×D411yescharacteristic
230C22×C3×C4C3×D411yescharacteristic
231C22×C3×C4C22×D311yescharacteristic
232C22×C3×C4C23×C311yescharacteristic
233C22×Dic3—21no—
234C2×D12—21no—
235C2×D12—22no—
236C2×D12C3×D414yescomplemented
237C2×D12C23×C312yes—
238C2×C4×D3—22no—
239C2×C4×D3—22no—
240C2×C4×D3—44no—
241C3×SD16—68no—
242C3×D8—68no—
243C3×M16—64no—
244C2×C3×C8—34no—
245C3×C4⋊C4—22no—
246C3×C4⋊C4—22no—
247C3×C4⋊C4—21no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—21no—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—32no—
252C3×C4⋊C4—61no—
253C3×C22⋊C4—24no—
254C3×C22⋊C4—24no—
255C3×C22⋊C4—22no—
256C3×C22⋊C4—22no—
257C3×C22⋊C4—22no—
258C3×C22⋊C4—22no—
259C3×C22⋊C4—62no—
260C3×C22⋊C4—62no—
261C3×C42—21no—
262C3×C42—21no—
263C3×C42—21no—
264C3×C42—21no—
265C3×C42#6711yescharacteristic
266C3×C42#6711yescharacteristic
267C3×C42C3×D411yescharacteristic
268C3×C42C3×D411yescharacteristic
269C3×C42C22×D311yescharacteristic
270C3×C42C22×D311yescharacteristic
271C3×C42C23×C311yescharacteristic
272C3×C42C23×C311yescharacteristic
273#215—28no—
274#213—28no—
275(C2×D3)⋊C4—22no—
276(C2×D3)⋊C4—22no—
277C4⋊Dic3—21no—
278C4⋊Dic3C23×C312yes—
279#208—24no—
280C2×C3⋊C8C23×C314yes—
281C22×C32—21no—
282C22×C32—21no—
283C22×C32—42no—
284C22×C32—42no—
285C22×C32—42no—
286C22×C32#12112yes—
287C22×C32C22×D411yescharacteristic
288C2×C3×D3—24no—
289C2×C3×D3—48no—
290C2×C3×D3—42no—
291C2×C3×D3—42no—
292C32×C4—21no—
293C32×C4—21no—
294C32×C4—21no—
295C32×C4—42no—
296C32×C4#12112yes—
297C32×C4AGL(1,ℤ/8)12yescomplemented
298C32×C4C22×D411yescharacteristic
299C32×C4C2×#4111yescharacteristic
300C3×Dic3—42no—
301C2×#41C2×C3×D312yes—
302C22×D4—31no—
303C23×C4—61no—
304AGL(1,ℤ/8)—68no—
305C2×SD16—34no—
306C2×D8—34no—
307C2×M16—32no—
308C4⋊Q8C2×C3×D311yescharacteristic, complemented
309#127C2×C3×D311yescharacteristic, complemented
310#124C2×C3×D312yescomplemented
311#121—21no—
312#121—21no—
313C4×D4—21no—
314C4×D4—21no—
315C4×D4—32no—
316C4×D4—32no—
317C4×D4—61no—
318C4×D4—61no—
319C2×C4⋊C4—31no—
320C2×C22⋊C4—61no—
321C2×C42C2×C3×D311yescharacteristic
322C4⋊C8—32no—
323C4⋊C8—32no—
324#103—34no—
325#102—34no—
326C23×C3—24no—
327C23×C3—22no—
328C23×C3—22no—
329C23×C3—21no—
330C23×C3—64no—
331C23×C3—62no—
332C23×C3—122no—
333C23×C3—122no—
334C23×C3C2×#6711yescharacteristic
335C23×C3C2×C3×D411yescharacteristic
336C22×D3—24no—
337C22×D3—22no—
338C22×D3—42no—
339C22×D3—42no—
340C3×Q8—22no—
341C3×Q8—22no—
342C3×Q8—22no—
343C3×Q8—22no—
344C3×Q8—42no—
345C3×Q8—42no—
346C3×D4—22no—
347C3×D4—22no—
348C3×D4—22no—
349C3×D4—22no—
350C3×D4—34no—
351C3×D4—42no—
352C3×D4—42no—
353C3×D4—44no—
354C3×D4—42no—
355C3×D4—42no—
356C3×D4—44no—
357C3×D4—48no—
358C3×D4—44no—
359C3×D4—44no—
360C3×D4—42no—
361C3×D4—42no—
362C3×D4—64no—
363C3×D4—62no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—24no—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—21no—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—42no—
378C2×C3×C4—41no—
379C2×C3×C4—41no—
380C2×C3×C4—42no—
381C2×C3×C4—48no—
382C2×C3×C4—44no—
383C2×C3×C4—44no—
384C2×C3×C4—62no—
385C2×C3×C4—124no—
386C2×C3×C4—122no—
387C2×C3×C4—124no—
388C2×C3×C4D3×D412yes—
389C2×C3×C4#23712yes—
390C2×C3×C4C2×#6711yescharacteristic
391C2×C3×C4C2×#6711yescharacteristic
392C2×C3×C4C2×#6711yescharacteristic
393C2×C3×C4C2×#6711yescharacteristic
394C2×C3×C4C2×#6711yescharacteristic
395C2×C3×C4C2×C3×D412yes—
396C2×C3×C4C2×C3×D411yescharacteristic
397C2×C3×C4C2×C3×D411yescharacteristic
398C2×C3×C4C2×C3×D411yescharacteristic
399C2×C3×C4C2×C3×D411yescharacteristic
400C2×C3×C4C2×C3×D411yescharacteristic
401C2×C3×C4C3×#4112yes—
402C2×C3×C4C23×D311yescharacteristic
403C2×C3×C4C24×C311yescharacteristic
404C2×Dic3—22no—
405C2×Dic3—42no—
406D12—24no—
407D12—22no—
408D12C2×C3×D414yes—
409C4×D3—44no—
410C4×D3—44no—
411C3×C8—64no—
412C3⋊C8—24no—
413C2×C32—22no—
414C2×C32—82no—
415C2×C32C2×#12111yescharacteristic
416C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
417C2×C32#57511yescharacteristic
418C3×D3—44no—
419C24—61no—
420#41—24no—
421#41—24no—
422C2×Q8C22×C3×D312yes—
423C2×D4—22no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—32no—
427C2×D4—34no—
428C2×D4—62no—
429C2×D4—61no—
430C2×D4C22×C3×D312yes—
431C22×C4—22no—
432C22×C4—61no—
433C22×C4—62no—
434C22×C4—62no—
435C22×C4—124no—
436C22×C4C3×#6711yescharacteristic
437C22×C4C3×#6711yescharacteristic
438C22×C4C22×C3×D311yescharacteristic
439SD16—68no—
440D8—68no—
441M16—64no—
442C2×C8—34no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—32no—
446C4⋊C4—61no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—62no—
450C22⋊C4—62no—
451C42C3×#6711yescharacteristic
452C42C3×#6711yescharacteristic
453C42C22×C3×D311yescharacteristic
454C42C22×C3×D311yescharacteristic
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—22no—
460C22×C3—21no—
461C22×C3—41no—
462C22×C3—41no—
463C22×C3—44no—
464C22×C3—44no—
465C22×C3—44no—
466C22×C3—42no—
467C22×C3—42no—
468C22×C3—42no—
469C22×C3—42no—
470C22×C3—42no—
471C22×C3—42no—
472C22×C3—64no—
473C22×C3—128no—
474C22×C3—122no—
475C22×C3—122no—
476C22×C3#93812yes—
477C22×C3C3×#12112yes—
478C22×C3C22×#6711yescharacteristic
479C22×C3C22×C3×D411yescharacteristic
480C2×D3—24no—
481C2×D3—48no—
482C2×D3—42no—
483C2×D3—42no—
484C3×C4—22no—
485C3×C4—21no—
486C3×C4—21no—
487C3×C4—21no—
488C3×C4—21no—
489C3×C4—21no—
490C3×C4—21no—
491C3×C4—22no—
492C3×C4—22no—
493C3×C4—21no—
494C3×C4—21no—
495C3×C4—41no—
496C3×C4—41no—
497C3×C4—44no—
498C3×C4—42no—
499C3×C4—42no—
500C3×C4—122no—
501C3×C4#93812yes—
502C3×C4#94912yescomplemented
503C3×C4C3×#12112yes—
504C3×C4C3×AGL(1,ℤ/8)12yescomplemented
505C3×C4C2×D3×D411yescharacteristic
506C3×C4C2×#23711yescharacteristic
507C3×C4C22×C3×D411yescharacteristic
508C3×C4C2×C3×#4111yescharacteristic
509Dic3—42no—
510C32#303611yescharacteristic, complemented, Sylow
511C23—22no—
512C23—64no—
513C23—62no—
514C23—122no—
515C23—122no—
516C23C2×C3×#6711yescharacteristic
517Q8—22no—
518Q8—22no—
519D4—22no—
520D4—22no—
521D4—34no—
522D4—42no—
523D4—44no—
524D4—42no—
525D4—64no—
526D4—62no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—41no—
530C2×C4—44no—
531C2×C4—62no—
532C2×C4—124no—
533C2×C4—122no—
534C2×C4—124no—
535C2×C4C3×D3×D412yes—
536C2×C4C3×#23712yes—
537C2×C4C2×C3×#6711yescharacteristic
538C2×C4C2×C3×#6711yescharacteristic
539C2×C4C2×C3×#6711yescharacteristic
540C2×C4C2×C3×#6711yescharacteristic
541C2×C4C2×C3×#6711yescharacteristic
542C2×C4C23×C3×D311yescharacteristic
543C8—64no—
544C2×C3—22no—
545C2×C3—22no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—42no—
550C2×C3—84no—
551C2×C3—82no—
552C2×C3—82no—
553C2×C3—124no—
554C2×C3C2×#93811yescharacteristic
555C2×C3C2×#94911yescharacteristic
556C2×C3#582211yescharacteristic
557C2×C3C2×C3×#12111yescharacteristic
558C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
559C2×C3C3×#57511yescharacteristic
560D3—44no—
561C22—21no—
562C22—21no—
563C22—42no—
564C22—42no—
565C22—42no—
566C22—64no—
567C22—128no—
568C22—122no—
569C22—122no—
570C22C3×#93812yes—
571C22C22×C3×#6711yescharacteristic
572C4—21no—
573C4—21no—
574C4—21no—
575C4—42no—
576C4—122no—
577C4C3×#93812yes—
578C4C3×#94912yescomplemented
579C4C2×C3×D3×D411yescharacteristic
580C4C2×C3×#23711yescharacteristic
581C3—21no—
582C3#8329711yescharacteristic, direct product factor
583C3C3×#303611yescharacteristic, complemented
584C2—22no—
585C2—82no—
586C2—124no—
587C2C2×C3×#93811yescharacteristic
588C2C2×C3×#94911yescharacteristic
589C2C3×#582211yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#532C2
socleC22×C32C22×D4
hypercenterC3×#532D3
hypocenterC3C3×#3036
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ C3×#532

Complements

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

NH ≅ G/Ntype
1. C32×#532C2semidirect
2. C2×C3×#949C2semidirect
3. C2×C3×C4×D12C2semidirect
4. C3×#5232C2semidirect
5. C3×#5083C2semidirect
6. C3×#5072C2semidirect
7. C3×#5057C2semidirect
8. C3×#4924C2semidirect
10. #83297C3direct (N × H)
14. C32×C4⋊Q8C22semidirect
15. C32×#127C22semidirect
16. C32×#124C22semidirect
32. C3×#835C22semidirect
33. C3×#832C22semidirect
34. C3×C4⋊(C3⋊C8)C22semidirect
35. C3×C4⋊(C3⋊C8)C22semidirect
38. C3×#532D3semidirect
39. C3×#532C2×C3semidirect
41. C2×#949C2×C3semidirect
42. C2×C4×D12C2×C3semidirect
48. #5232C2×C3semidirect
49. #5083C2×C3semidirect
50. #5072C2×C3semidirect
51. #5057C2×C3semidirect
52. #4924C2×C3semidirect
68. C2×C3×D12D4semidirect
102. C3×C4⋊Q8C2×D3semidirect
103. C3×C4⋊Q8C22×C3semidirect
105. C3×#127C2×D3semidirect
106. C3×#127C22×C3semidirect
108. C3×#124C2×D3semidirect
109. C3×#124C22×C3semidirect
145. #835C22×C3semidirect
146. #832C22×C3semidirect
147. C4⋊(C3⋊C8)C22×C3semidirect
148. C4⋊(C3⋊C8)C22×C3semidirect
183. #532C3×D3semidirect
236. C2×D12C3×D4semidirect
297. C32×C4AGL(1,ℤ/8)semidirect
308. C4⋊Q8C2×C3×D3semidirect
309. #127C2×C3×D3semidirect
310. #124C2×C3×D3semidirect
502. C3×C4#949semidirect
504. C3×C4C3×AGL(1,ℤ/8)semidirect
510. C32#3036semidirect
578. C4C3×#949semidirect
582. C3#83297direct (N × H)
583. C3C3×#3036semidirect

Maximal subgroups

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

subgroupindex
C32×#5322
C2×C3×#9492
C2×C3×C4×D122
C3×#52322
C3×#50832
C3×#50722
C3×#50572
C3×#49242
C3×#30363
#832973