Finite Group Databasebeta

← C3×#82307 #11865845

Subgroups — C3×#82307 #11865845

Order 1152.

1309 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic, complemented
2C2×C3×#932C212yesmaximal, complemented
3C3×#5477C211yesmaximal, characteristic, complemented
4C3×#5019C212yesmaximal, complemented
5C3×#5016C214yesmaximal, complemented
6C3×#5015C212yesmaximal, complemented
7C3×#4966C212yesmaximal, complemented
8C3×#4924C211yesmaximal, characteristic, complemented
9C3×#3036—31nomaximal
10#82307C311yesmaximal, characteristic, direct product factor
11C22×C32×D4C2211yescharacteristic
12C23×C32×C4—21no—
13C2×C3×#235C2212yes—
14C32×C4×D4—21no—
15C32×C4×D4—21no—
16C32×C4×D4C2212yes—
17C32×C4×D4C2212yes—
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×C32×C22⋊C4—21no—
20C2×C32×C42C2211yescharacteristic
21C2×C3×#214C2214yes—
22C3×#932—28no—
23C2×C3×#213C2214yes—
24C3×#930—21no—
25C3×#930—21no—
26C2×C3×#208C2212yes—
27C3×#875C2212yescomplemented
28C3×#874C2211yescharacteristic, complemented
29C3×C4×D12—21no—
30C3×C4×D12—21no—
31C3×#869C2211yescharacteristic, complemented
32C3×#810C2214yescomplemented
33C3×#809C2214yescomplemented
34C3×C4⋊(C3⋊C8)C2212yescomplemented
35C3×C4⋊(C3⋊C8)C2212yescomplemented
36C2×C3×AGL(1,ℤ/8)—32no—
37C3×#532—31no—
38C2×C3×C4×D4—21no—
39C2×C3×C4×D4D311yescharacteristic, complemented
40C2×C3×C4×D4C2×C311yescharacteristic, complemented
41C2×#932C2×C312yescomplemented
42#5477C2×C311yescharacteristic, complemented
43C3×#463—34no—
44C3×#461—32no—
45C3×#459—32no—
46C3×#423—31no—
47C3×#417—32no—
48#5019C2×C312yescomplemented
49#5016C2×C314yescomplemented
50#5015C2×C312yescomplemented
51#4966C2×C312yescomplemented
52#4924C2×C311yescharacteristic, complemented
53C24×C32—21no—
54C2×C32×D4—21no—
55C2×C32×D4—22no—
56C2×C32×D4D414yescomplemented
57C2×C32×D4C2312yes—
58C22×C32×C4—21no—
59C22×C32×C4—22no—
60C22×C32×C4—22no—
61C22×C32×C4—44no—
62C22×C32×C4D411yescharacteristic
63C22×C32×C4D411yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C2×C3×#67—22no—
66C3×#235—24no—
67C3×#235—24no—
68C2×C3×D12—21no—
69C2×C3×D12—21no—
70C2×C3×D12C2312yes—
71C2×C3×C4×D3—22no—
72C2×C3×Dic6C2312yes—
73C32×C4⋊C4—21no—
74C32×C4⋊C4C2312yes—
75C32×C22⋊C4—22no—
76C32×C22⋊C4—22no—
77C32×C42D411yescharacteristic
78C32×C42D411yescharacteristic
79C32×C42C2311yescharacteristic
80C32×C42C2311yescharacteristic
81C3×#214—28no—
82C3×#213—28no—
83C3×(C2×D3)⋊C4—22no—
84C3×(C2×D3)⋊C4—22no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3—21no—
87C3×#208—24no—
88C2×C3×C3⋊C8C2314yes—
89#3036—31noSylow
90C2×C3×#41—32no—
91C22×C3×D4—21no—
92C22×C3×D4C2×D311yescharacteristic
93C22×C3×D4C22×C311yescharacteristic
94C23×C3×C4—22no—
95C23×C3×C4—21no—
96C23×C3×C4—21no—
97C2×#235C22×C312yes—
98C3×AGL(1,ℤ/8)—68no—
99C2×C3×SD16—34no—
100C2×C3×D8—34no—
101C2×C3×M16—32no—
102C3×C4⋊Q8—31no—
103C3×#127—31no—
104C3×#124—32no—
105C3×#121—61no—
106C3×#121—61no—
107C3×C4×D4—22no—
108C3×C4×D4—22no—
109C3×C4×D4—21no—
110C3×C4×D4—21no—
111C3×C4×D4—21no—
112C3×C4×D4—21no—
113C3×C4×D4—22no—
114C3×C4×D4—22no—
115C3×C4×D4—61no—
116C3×C4×D4—61no—
117C3×C4×D4C2×D312yes—
118C3×C4×D4C2×D312yes—
119C3×C4×D4C22×C312yes—
120C3×C4×D4C22×C312yes—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4C2×D311yescharacteristic
123C2×C3×C4⋊C4C22×C311yescharacteristic
124C2×C3×C22⋊C4—22no—
125C2×C3×C22⋊C4—21no—
126C2×C3×C22⋊C4—21no—
127C2×C3×C42—21no—
128C2×C3×C42C2×D311yescharacteristic
129C2×C3×C42C22×C311yescharacteristic
130C2×#214C22×C314yes—
131#932—28no—
132C2×#213C22×C314yes—
133#930—21no—
134#930—21no—
135C2×#208C22×C312yes—
136#875C22×C312yescomplemented
137#874C22×C311yescharacteristic, complemented
138C4×D12—21no—
139C4×D12—21no—
140#869C22×C311yescharacteristic, complemented
141C3×C4⋊C8—32no—
142C3×C4⋊C8—32no—
143C3×#103—34no—
144C3×#102—34no—
145#810C22×C314yescomplemented
146#809C22×C314yescomplemented
147C4⋊(C3⋊C8)C22×C312yescomplemented
148C4⋊(C3⋊C8)C22×C312yescomplemented
149C23×C32—24no—
150C23×C32—22no—
151C23×C32—42no—
152C23×C32—42no—
153C23×C32C2×D411yescharacteristic
154C22×C3×D3—22no—
155C32×D4—24no—
156C32×D4—22no—
157C32×D4C2×D414yes—
158C2×C32×C4—22no—
159C2×C32×C4—22no—
160C2×C32×C4—41no—
161C2×C32×C4—44no—
162C2×C32×C4—42no—
163C2×C32×C4—44no—
164C2×C32×C4C2×D412yes—
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4#4112yes—
171C2×C32×C4C2411yescharacteristic
172C3×#67—44no—
173C2×C3×Dic3—22no—
174C3×D12—22no—
175C3×D12—22no—
176C3×D12—42no—
177C3×D12—42no—
178C3×C4×D3—44no—
179C3×Dic6—22no—
180C3×Dic6—22no—
181C3×C3⋊C8—24no—
182C2×AGL(1,ℤ/8)—32no—
183#532—31no—
184C2×C4×D4C3×D311yescharacteristic, complemented
185#463—34no—
186#461—32no—
187#459—32no—
188#423—31no—
189#417—32no—
190C24×C3—22no—
191C24×C3—21no—
192C24×C3—21no—
193C3×#41—64no—
194C3×#41—64no—
195C2×C3×Q8—32no—
196C2×C3×D4—22no—
197C2×C3×D4—24no—
198C2×C3×D4—22no—
199C2×C3×D4—21no—
200C2×C3×D4—21no—
201C2×C3×D4—22no—
202C2×C3×D4—24no—
203C2×C3×D4—22no—
204C2×C3×D4—32no—
205C2×C3×D4—62no—
206C2×C3×D4—61no—
207C2×C3×D4—61no—
208C2×C3×D4D1214yescomplemented
209C2×C3×D4C3×D414yescomplemented
210C2×C3×D4C22×D312yes—
211C2×C3×D4C23×C312yes—
212C22×C3×C4—22no—
213C22×C3×C4—24no—
214C22×C3×C4—24no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—22no—
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—22no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—48no—
225C22×C3×C4—44no—
226C22×C3×C4—44no—
227C22×C3×C4—62no—
228C22×C3×C4#6711yescharacteristic
229C22×C3×C4#6711yescharacteristic
230C22×C3×C4C3×D411yescharacteristic
231C22×C3×C4C3×D411yescharacteristic
232C22×C3×C4C22×D311yescharacteristic
233C22×C3×C4C23×C311yescharacteristic
234C2×#67—22no—
235#235—24no—
236#235—24no—
237C2×D12—21no—
238C2×D12—21no—
239C2×D12C23×C312yes—
240C2×C4×D3—22no—
241C2×Dic6C23×C312yes—
242C3×SD16—68no—
243C3×D8—68no—
244C3×M16—64no—
245C2×C3×C8—34no—
246C3×C4⋊C4—22no—
247C3×C4⋊C4—21no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—22no—
250C3×C4⋊C4—61no—
251C3×C4⋊C4—61no—
252C3×C4⋊C4C22×D312yes—
253C3×C4⋊C4C23×C312yes—
254C3×C22⋊C4—24no—
255C3×C22⋊C4—24no—
256C3×C22⋊C4—22no—
257C3×C22⋊C4—22no—
258C3×C22⋊C4—22no—
259C3×C22⋊C4—22no—
260C3×C22⋊C4—62no—
261C3×C22⋊C4—62no—
262C3×C42—21no—
263C3×C42—21no—
264C3×C42—21no—
265C3×C42—21no—
266C3×C42#6711yescharacteristic
267C3×C42#6711yescharacteristic
268C3×C42C3×D411yescharacteristic
269C3×C42C3×D411yescharacteristic
270C3×C42C22×D311yescharacteristic
271C3×C42C22×D311yescharacteristic
272C3×C42C23×C311yescharacteristic
273C3×C42C23×C311yescharacteristic
274#214—28no—
275#213—28no—
276(C2×D3)⋊C4—22no—
277(C2×D3)⋊C4—22no—
278C4⋊Dic3—21no—
279C4⋊Dic3—21no—
280#208—24no—
281C2×C3⋊C8C23×C314yes—
282C22×C32—21no—
283C22×C32—21no—
284C22×C32—24no—
285C22×C32—48no—
286C22×C32—42no—
287C22×C32—42no—
288C22×C32#12112yes—
289C22×C32C22×D411yescharacteristic
290C2×C3×D3—42no—
291C2×C3×D3—42no—
292C2×C3×D3—42no—
293C32×C4—21no—
294C32×C4—21no—
295C32×C4—21no—
296C32×C4—42no—
297C32×C4#12112yes—
298C32×C4AGL(1,ℤ/8)12yescomplemented
299C32×C4C22×D411yescharacteristic
300C32×C4C2×#4111yescharacteristic
301C3×Dic3—42no—
302C2×#41—32no—
303C22×D4C2×C3×D311yescharacteristic
304C23×C4—21no—
305AGL(1,ℤ/8)—68no—
306C2×SD16—34no—
307C2×D8—34no—
308C2×M16—32no—
309C4⋊Q8—31no—
310#127—31no—
311#124—32no—
312#121—61no—
313#121—61no—
314C4×D4—21no—
315C4×D4—21no—
316C4×D4—61no—
317C4×D4—61no—
318C4×D4C2×C3×D312yes—
319C4×D4C2×C3×D312yes—
320C2×C4⋊C4C2×C3×D311yescharacteristic
321C2×C22⋊C4—21no—
322C2×C42C2×C3×D311yescharacteristic
323C4⋊C8—32no—
324C4⋊C8—32no—
325#103—34no—
326#102—34no—
327C23×C3—24no—
328C23×C3—28no—
329C23×C3—24no—
330C23×C3—24no—
331C23×C3—22no—
332C23×C3—22no—
333C23×C3—21no—
334C23×C3—44no—
335C23×C3—42no—
336C23×C3—42no—
337C23×C3—44no—
338C23×C3—42no—
339C23×C3—42no—
340C23×C3—62no—
341C23×C3C2×#6711yescharacteristic
342C23×C3C2×C3×D411yescharacteristic
343C22×D3—22no—
344C3×Q8—62no—
345C3×Q8—62no—
346C3×D4—28no—
347C3×D4—24no—
348C3×D4—24no—
349C3×D4—24no—
350C3×D4—22no—
351C3×D4—22no—
352C3×D4—24no—
353C3×D4—62no—
354C3×D4—62no—
355C3×D4—122no—
356C3×D4—124no—
357C3×D4—122no—
358C3×D4C2×D1214yes—
359C3×D4C2×C3×D414yes—
360C2×C3×C4—24no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—24no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—21no—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—41no—
375C2×C3×C4—41no—
376C2×C3×C4—48no—
377C2×C3×C4—44no—
378C2×C3×C4—44no—
379C2×C3×C4—48no—
380C2×C3×C4—42no—
381C2×C3×C4—44no—
382C2×C3×C4—42no—
383C2×C3×C4—42no—
384C2×C3×C4—44no—
385C2×C3×C4—44no—
386C2×C3×C4—62no—
387C2×C3×C4—124no—
388C2×C3×C4C2×D1212yes—
389C2×C3×C4#23512yes—
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
404#67—44no—
405C2×Dic3—22no—
406D12—22no—
407D12—22no—
408D12—42no—
409D12—42no—
410C4×D3—44no—
411Dic6—22no—
412Dic6—22no—
413C3×C8—64no—
414C3⋊C8—24no—
415C2×C32—22no—
416C2×C32—44no—
417C2×C32C2×#12111yescharacteristic
418C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
419C2×C32#57511yescharacteristic
420C3×D3—82no—
421C24—21no—
422#41—64no—
423#41—64no—
424C2×Q8—32no—
425C2×D4—22no—
426C2×D4—21no—
427C2×D4—32no—
428C2×D4—62no—
429C2×D4—61no—
430C2×D4—61no—
431C2×D4C3×D1214yescomplemented
432C2×D4C22×C3×D312yes—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—44no—
437C22×C4—62no—
438C22×C4C3×#6711yescharacteristic
439C22×C4C3×#6711yescharacteristic
440C22×C4C22×C3×D311yescharacteristic
441SD16—68no—
442D8—68no—
443M16—64no—
444C2×C8—34no—
445C4⋊C4—21no—
446C4⋊C4—61no—
447C4⋊C4—61no—
448C4⋊C4C22×C3×D312yes—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—62no—
452C22⋊C4—62no—
453C42C3×#6711yescharacteristic
454C42C3×#6711yescharacteristic
455C42C22×C3×D311yescharacteristic
456C42C22×C3×D311yescharacteristic
457C22×C3—22no—
458C22×C3—22no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—28no—
464C22×C3—24no—
465C22×C3—24no—
466C22×C3—22no—
467C22×C3—21no—
468C22×C3—44no—
469C22×C3—416no—
470C22×C3—48no—
471C22×C3—48no—
472C22×C3—44no—
473C22×C3—42no—
474C22×C3—42no—
475C22×C3—42no—
476C22×C3—42no—
477C22×C3—122no—
478C22×C3—122no—
479C22×C3—122no—
480C22×C3#93012yes—
481C22×C3C3×#12112yes—
482C22×C3C22×#6711yescharacteristic
483C22×C3C22×C3×D411yescharacteristic
484C2×D3—42no—
485C2×D3—42no—
486C2×D3—42no—
487C3×C4—22no—
488C3×C4—21no—
489C3×C4—21no—
490C3×C4—21no—
491C3×C4—21no—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—22no—
495C3×C4—22no—
496C3×C4—21no—
497C3×C4—21no—
498C3×C4—41no—
499C3×C4—41no—
500C3×C4—44no—
501C3×C4—42no—
502C3×C4—42no—
503C3×C4—122no—
504C3×C4#93012yes—
505C3×C4#93212yescomplemented
506C3×C4C3×#12112yes—
507C3×C4C3×AGL(1,ℤ/8)12yescomplemented
508C3×C4C22×D1211yescharacteristic
509C3×C4C2×#23511yescharacteristic
510C3×C4C22×C3×D411yescharacteristic
511C3×C4C2×C3×#4111yescharacteristic
512Dic3—42no—
513C32#303611yescharacteristic, complemented, Sylow
514C23—24no—
515C23—22no—
516C23—42no—
517C23—42no—
518C23—62no—
519C23C2×C3×#6711yescharacteristic
520Q8—62no—
521Q8—62no—
522D4—24no—
523D4—22no—
524D4—62no—
525D4—62no—
526D4—122no—
527D4—124no—
528D4—122no—
529D4C2×C3×D1214yes—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—41no—
533C2×C4—44no—
534C2×C4—42no—
535C2×C4—44no—
536C2×C4—62no—
537C2×C4—124no—
538C2×C4C2×C3×D1212yes—
539C2×C4C3×#23512yes—
540C2×C4C2×C3×#6711yescharacteristic
541C2×C4C2×C3×#6711yescharacteristic
542C2×C4C2×C3×#6711yescharacteristic
543C2×C4C2×C3×#6711yescharacteristic
544C2×C4C2×C3×#6711yescharacteristic
545C2×C4C23×C3×D311yescharacteristic
546C8—64no—
547C2×C3—24no—
548C2×C3—22no—
549C2×C3—22no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—48no—
554C2×C3—44no—
555C2×C3—44no—
556C2×C3—242no—
557C2×C3C2×#93011yescharacteristic
558C2×C3C2×#93211yescharacteristic
559C2×C3#582211yescharacteristic
560C2×C3C2×C3×#12111yescharacteristic
561C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
562C2×C3C3×#57511yescharacteristic
563D3—82no—
564C22—21no—
565C22—21no—
566C22—24no—
567C22—48no—
568C22—42no—
569C22—42no—
570C22—122no—
571C22—122no—
572C22—122no—
573C22C3×#93012yes—
574C22C22×C3×#6711yescharacteristic
575C4—21no—
576C4—21no—
577C4—21no—
578C4—42no—
579C4—122no—
580C4C3×#93012yes—
581C4C3×#93212yescomplemented
582C4C22×C3×D1211yescharacteristic
583C4C2×C3×#23511yescharacteristic
584C3—21no—
585C3#8230711yescharacteristic, direct product factor
586C3C3×#303611yescharacteristic, complemented
587C2—22no—
588C2—44no—
589C2—242no—
590C2C2×C3×#93011yescharacteristic
591C2C2×C3×#93211yescharacteristic
592C2C3×#582211yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×C4×D4C2
socleC22×C32C22×D4
hypercenterC2×C3×C4×D4D3
hypocenterC3C3×#3036
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×D4C2semidirect
2. C2×C3×#932C2semidirect
3. C3×#5477C2semidirect
4. C3×#5019C2semidirect
5. C3×#5016C2semidirect
6. C3×#5015C2semidirect
7. C3×#4966C2semidirect
8. C3×#4924C2semidirect
10. #82307C3direct (N × H)
27. C3×#875C22semidirect
28. C3×#874C22semidirect
31. C3×#869C22semidirect
32. C3×#810C22semidirect
33. C3×#809C22semidirect
34. C3×C4⋊(C3⋊C8)C22semidirect
35. C3×C4⋊(C3⋊C8)C22semidirect
39. C2×C3×C4×D4D3semidirect
40. C2×C3×C4×D4C2×C3semidirect
41. C2×#932C2×C3semidirect
42. #5477C2×C3semidirect
48. #5019C2×C3semidirect
49. #5016C2×C3semidirect
50. #5015C2×C3semidirect
51. #4966C2×C3semidirect
52. #4924C2×C3semidirect
56. C2×C32×D4D4semidirect
136. #875C22×C3semidirect
137. #874C22×C3semidirect
140. #869C22×C3semidirect
145. #810C22×C3semidirect
146. #809C22×C3semidirect
147. C4⋊(C3⋊C8)C22×C3semidirect
148. C4⋊(C3⋊C8)C22×C3semidirect
184. C2×C4×D4C3×D3semidirect
208. C2×C3×D4D12semidirect
209. C2×C3×D4C3×D4semidirect
298. C32×C4AGL(1,ℤ/8)semidirect
431. C2×D4C3×D12semidirect
505. C3×C4#932semidirect
507. C3×C4C3×AGL(1,ℤ/8)semidirect
513. C32#3036semidirect
581. C4C3×#932semidirect
585. C3#82307direct (N × H)
586. C3C3×#3036semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C2×C3×#9322
C3×#54772
C3×#50192
C3×#50162
C3×#50152
C3×#49662
C3×#49242
C3×#30363
#823073