Finite Group Databasebeta

← C3×#86959 #11904234

Subgroups — C3×#86959 #11904234

Order 1152.

2522 conjugacy classes of subgroups.

The subgroup lattice has 609 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#555C211yesmaximal, characteristic, complemented
2C3×#5725C211yesmaximal, characteristic, complemented
3C3×#5722C211yesmaximal, characteristic, complemented
4C3×#5670C214yesmaximal, complemented
5C3×#5668C214yesmaximal, complemented
6C3×#5599C214yesmaximal, complemented
7C3×#5596C214yesmaximal, complemented
8C3×#5553C212yesmaximal, complemented
9C3×C4×#237C212yesmaximal, complemented
10C3×#5532C214yesmaximal, complemented
11C3×#5522C214yesmaximal, complemented
12C3×#3483—31nomaximal
13#86959C311yesmaximal, characteristic, direct product factor
14C2×C3×#239C2212yes—
15C2×C3×#237C2212yes—
16C2×C3×#237C2214yes—
17C2×C3×#235C2214yes—
18C32×C4⋊Q8C2211yescharacteristic
19C32×#124C2214yes—
20C32×#121C2214yes—
21C32×C4×D4C2212yes—
22C32×#117C2214yes—
23C3×#947C2212yes—
24C3×#944C2214yes—
25C3×#940C2214yes—
26C3×#940C2214yes—
27C3×#939C2218yes—
28C3×D4×Dic3C2212yes—
29C3×#930C2214yes—
30C3×C4×#67C2214yes—
31C2×C3×C4×Dic3C2214yes—
32C3×#895C2214yes—
33C3×#893C2214yes—
34C3×#893C2214yes—
35C3×#892C2212yes—
36C3×#888C2214yes—
37C3×#887C2212yes—
38C3×#887C2214yes—
39C3×#885C2218yes—
40C3×#884C2218yes—
41C3×#884C2218yes—
42C3×#67⋊C4C2218yes—
43C3×#67⋊C4C2218yes—
44C3×#67⋊C4C2214yes—
45C3×#877C2214yes—
46C3×#875C2214yes—
47C3×#874C2211yescharacteristic
48C3×#872C2218yes—
49C3×C42×D3C2214yes—
50C3×C42×D3C2211yescharacteristic
51C3×C4×Dic6C2212yes—
52C3×Q82—31no—
53C3×#555—21no—
54C3×#555—34no—
55C3×#555—34no—
56C3×#555D311yescharacteristic, complemented
57C3×#555C2×C311yescharacteristic, complemented
58C3×#550—34no—
59C3×#550—32no—
60C3×#532—31no—
61C3×#532—34no—
62C3×#532—34no—
63C3×C4×#41—32no—
64C3×C4×#41—34no—
65#5725C2×C311yescharacteristic, complemented
66#5722C2×C311yescharacteristic, complemented
67#5670C2×C314yescomplemented
68#5668C2×C314yescomplemented
69#5599C2×C314yescomplemented
70#5596C2×C314yescomplemented
71#5553C2×C312yescomplemented
72C4×#237C2×C312yescomplemented
73#5532C2×C314yescomplemented
74#5522C2×C314yescomplemented
75C2×C32×Q8C2312yes—
76C2×C32×D4C2312yes—
77C2×C32×D4C2314yes—
78C22×C32×C4C2314yes—
79C2×C3×#67C2318yes—
80C2×C3×#67C2314yes—
81C2×C3×#67C2318yes—
82C22×C3×Dic3C2314yes—
83C22×C3×Dic3C2314yes—
84C3×#239—44no—
85C3×#237—28no—
86C3×#237—48no—
87C3×#235—216no—
88C2×C3×D12C2314yes—
89C2×C3×D12C2312yes—
90C2×C3×D12C2314yes—
91C2×C3×C4×D3C2311yescharacteristic
92C2×C3×C4×D3C2314yes—
93C2×C3×C4×D3C2318yes—
94C2×C3×C4×D3C2312yes—
95C2×C3×Dic6C2314yes—
96C2×C3×Dic6C2312yes—
97C32×C4⋊C4C2314yes—
98C32×C4⋊C4C2312yes—
99C32×C22⋊C4C2314yes—
100C32×C22⋊C4C2318yes—
101C32×C42C2314yes—
102C32×C42C2311yescharacteristic
103C3×#217C2314yes—
104C3×(C2×D3)⋊C4C2314yes—
105C3×(C2×D3)⋊C4C2318yes—
106C3×(C2×D3)⋊C4C2318yes—
107C3×C4⋊Dic3C2312yes—
108C3×Dic3⋊C4C2314yes—
109C3×Dic3⋊C4C2314yes—
110C3×Dic3⋊C4C2318yes—
111C3×C4×Dic3C2311yescharacteristic
112C3×C4×Dic3C2314yes—
113C3×C4×Dic3C2314yes—
114C3×C4×Dic3C2314yes—
115C3×C4×Dic3C2314yes—
116C3×C4×Dic3C2312yes—
117#3483—31noSylow
118C2×C3×#41—32no—
119C2×C3×#41—32no—
120C2×C3×#41—34no—
121C2×C3×#41—34no—
122C2×#239C22×C312yes—
123C2×#237C22×C312yes—
124C2×#237C22×C314yes—
125C2×#235C22×C314yes—
126C3×C4⋊Q8—21no—
127C3×C4⋊Q8—34no—
128C3×C4⋊Q8—34no—
129C3×C4⋊Q8C2×D311yescharacteristic
130C3×C4⋊Q8C22×C311yescharacteristic
131C3×#127—34no—
132C3×#127—34no—
133C3×#127—31no—
134C3×#124—24no—
135C3×#124—32no—
136C3×#124—38no—
137C3×#124—34no—
138C3×#124C2×D314yes—
139C3×#124C22×C314yes—
140C3×#121—24no—
141C3×#121—38no—
142C3×#121—34no—
143C3×#121—34no—
144C3×#121—38no—
145C3×#121—38no—
146C3×#121C2×D314yes—
147C3×#121C22×C314yes—
148C3×C4×Q8—34no—
149C3×C4×Q8—32no—
150C3×C4×Q8—32no—
151C3×C4×D4—22no—
152C3×C4×D4—32no—
153C3×C4×D4—34no—
154C3×C4×D4—34no—
155C3×C4×D4—34no—
156C3×C4×D4—34no—
157C3×C4×D4—38no—
158C3×C4×D4—38no—
159C3×C4×D4C2×D312yes—
160C3×C4×D4C22×C312yes—
161C3×#117—24no—
162C3×#117—32no—
163C3×#117—34no—
164C3×#117—38no—
165C3×#117C2×D314yes—
166C3×#117C22×C314yes—
167C2×C3×C42—34no—
168C2×C3×C42—31no—
169C2×C3×C42—34no—
170#947C22×C312yes—
171#944C22×C314yes—
172#940C22×C314yes—
173#940C22×C314yes—
174#939C22×C318yes—
175D4×Dic3C22×C312yes—
176#930C22×C314yes—
177C4×#67C22×C314yes—
178C2×C4×Dic3C22×C314yes—
179#895C22×C314yes—
180#893C22×C314yes—
181#893C22×C314yes—
182#892C22×C312yes—
183#888C22×C314yes—
184#887C22×C314yes—
185#887C22×C312yes—
186#885C22×C318yes—
187#884C22×C318yes—
188#884C22×C318yes—
189#67⋊C4C22×C314yes—
190#67⋊C4C22×C318yes—
191#67⋊C4C22×C318yes—
192#877C22×C314yes—
193#875C22×C314yes—
194#874C22×C311yescharacteristic
195#872C22×C318yes—
196C42×D3C22×C314yes—
197C42×D3C22×C311yescharacteristic
198C4×Dic6C22×C312yes—
199C23×C32C2414yes—
200C22×C3×D3C2414yes—
201C22×C3×D3C2411yescharacteristic
202C32×Q8—42no—
203C32×D4—24no—
204C32×D4—44no—
205C2×C32×C4—28no—
206C2×C32×C4C2414yes—
207C2×C32×C4C2411yescharacteristic
208C2×C32×C4C2414yes—
209C2×C32×C4C2412yes—
210C3×#67—216no—
211C3×#67—28no—
212C3×#67—48no—
213C2×C3×Dic3—28no—
214C2×C3×Dic3—28no—
215C2×C3×Dic3C2412yes—
216C2×C3×Dic3C2414yes—
217C2×C3×Dic3C2414yes—
218C2×C3×Dic3C2411yescharacteristic
219C3×D12—28no—
220C3×D12—44no—
221C3×D12—42no—
222C3×C4×D3—24no—
223C3×C4×D3—216no—
224C3×C4×D3—28no—
225C3×C4×D3—22no—
226C3×Dic6—44no—
227C3×Dic6#4118yescomplemented
228Q82—31no—
229#555—34no—
230#555—34no—
231#555C3×D311yescharacteristic, complemented
232#550—34no—
233#550—32no—
234#532—31no—
235#532—34no—
236#532—34no—
237C4×#41—32no—
238C4×#41—34no—
239C3×#41—616no—
240C3×#41—68no—
241C3×#41—128no—
242C3×#41—124no—
243C2×C3×Q8—22no—
244C2×C3×Q8—32no—
245C2×C3×Q8—34no—
246C2×C3×Q8C22×D312yes—
247C2×C3×Q8C23×C312yes—
248C2×C3×D4—22no—
249C2×C3×D4—24no—
250C2×C3×D4—34no—
251C2×C3×D4—38no—
252C2×C3×D4—38no—
253C2×C3×D4—34no—
254C2×C3×D4—34no—
255C2×C3×D4—32no—
256C2×C3×D4C22×D312yes—
257C2×C3×D4C22×D314yes—
258C2×C3×D4C23×C312yes—
259C2×C3×D4C23×C314yes—
260C22×C3×C4—24no—
261C22×C3×C4—34no—
262C22×C3×C4—34no—
263C22×C3×C4—38no—
264C22×C3×C4—32no—
265C22×C3×C4—34no—
266C22×C3×C4—31no—
267C22×C3×C4C22×D314yes—
268C22×C3×C4C23×C314yes—
269C2×#67C23×C318yes—
270C2×#67C23×C314yes—
271C2×#67C23×C318yes—
272C22×Dic3C23×C314yes—
273C22×Dic3C23×C314yes—
274#239—44no—
275#237—28no—
276#237—48no—
277#235—216no—
278C2×D12C23×C314yes—
279C2×D12C23×C312yes—
280C2×D12C23×C314yes—
281C2×C4×D3C23×C318yes—
282C2×C4×D3C23×C311yescharacteristic
283C2×C4×D3C23×C314yes—
284C2×C4×D3C23×C312yes—
285C2×Dic6C23×C314yes—
286C2×Dic6C23×C312yes—
287C3×C4⋊C4—22no—
288C3×C4⋊C4—24no—
289C3×C4⋊C4—34no—
290C3×C4⋊C4—38no—
291C3×C4⋊C4—34no—
292C3×C4⋊C4—32no—
293C3×C4⋊C4C22×D312yes—
294C3×C4⋊C4C22×D314yes—
295C3×C4⋊C4C23×C314yes—
296C3×C4⋊C4C23×C312yes—
297C3×C22⋊C4—28no—
298C3×C22⋊C4—24no—
299C3×C22⋊C4—34no—
300C3×C22⋊C4—38no—
301C3×C22⋊C4—34no—
302C3×C22⋊C4—38no—
303C3×C22⋊C4C22×D314yes—
304C3×C22⋊C4C22×D318yes—
305C3×C22⋊C4C23×C314yes—
306C3×C22⋊C4C23×C318yes—
307C3×C42—24no—
308C3×C42—21no—
309C3×C42—34no—
310C3×C42—32no—
311C3×C42—31no—
312C3×C42—34no—
313C3×C42—34no—
314C3×C42—34no—
315C3×C42C22×D314yes—
316C3×C42C22×D311yescharacteristic
317C3×C42C23×C311yescharacteristic
318C3×C42C23×C314yes—
319#217C23×C314yes—
320(C2×D3)⋊C4C23×C318yes—
321(C2×D3)⋊C4C23×C318yes—
322(C2×D3)⋊C4C23×C314yes—
323C4⋊Dic3C23×C312yes—
324Dic3⋊C4C23×C314yes—
325Dic3⋊C4C23×C314yes—
326Dic3⋊C4C23×C318yes—
327C4×Dic3C23×C314yes—
328C4×Dic3C23×C314yes—
329C4×Dic3C23×C311yescharacteristic
330C4×Dic3C23×C314yes—
331C4×Dic3C23×C312yes—
332C4×Dic3C23×C314yes—
333C22×C32—24no—
334C22×C32—24no—
335C22×C32—24no—
336C22×C32C2511yescharacteristic
337C2×C3×D3—28no—
338C2×C3×D3—22no—
339C2×C3×D3—21no—
340C2×C3×D3—24no—
341C32×C4—24no—
342C32×C4—24no—
343C32×C4—21no—
344C32×C4C2×#4114yes—
345C3×Dic3—22no—
346C3×Dic3—24no—
347C3×Dic3C2×#4118yes—
348C3×Dic3H(5,𝔽2)12yes—
349C2×#41—32no—
350C2×#41—32no—
351C2×#41—34no—
352C2×#41—34no—
353C4⋊Q8—34no—
354C4⋊Q8—34no—
355C4⋊Q8C2×C3×D311yescharacteristic
356#127—34no—
357#127—34no—
358#127—31no—
359#124—32no—
360#124—38no—
361#124—34no—
362#124C2×C3×D314yes—
363#121—38no—
364#121—34no—
365#121—34no—
366#121—38no—
367#121—38no—
368#121C2×C3×D314yes—
369C4×Q8—32no—
370C4×Q8—34no—
371C4×Q8—32no—
372C4×D4—32no—
373C4×D4—34no—
374C4×D4—34no—
375C4×D4—34no—
376C4×D4—34no—
377C4×D4—38no—
378C4×D4—38no—
379C4×D4C2×C3×D312yes—
380#117—32no—
381#117—34no—
382#117—38no—
383#117C2×C3×D314yes—
384C2×C42—34no—
385C2×C42—31no—
386C2×C42—34no—
387C23×C3—24no—
388C23×C3—31no—
389C23×C3—34no—
390C23×C3C23×D314yes—
391C23×C3C24×C314yes—
392C22×D3C24×C314yes—
393C22×D3C24×C311yescharacteristic
394C3×Q8—38no—
395C3×Q8—42no—
396C3×Q8—42no—
397C3×Q8—82no—
398C3×Q8—124no—
399C3×D4—24no—
400C3×D4—24no—
401C3×D4—44no—
402C3×D4—44no—
403C3×D4—44no—
404C3×D4—616no—
405C3×D4—68no—
406C3×D4—68no—
407C3×D4—84no—
408C3×D4—124no—
409C3×D4—122no—
410C3×D4—128no—
411C2×C3×C4—28no—
412C2×C3×C4—28no—
413C2×C3×C4—22no—
414C2×C3×C4—24no—
415C2×C3×C4—21no—
416C2×C3×C4—24no—
417C2×C3×C4—31no—
418C2×C3×C4—34no—
419C2×C3×C4—32no—
420C2×C3×C4—34no—
421C2×C3×C4—48no—
422C2×C3×C4—616no—
423C2×C3×C4—68no—
424C2×C3×C4—62no—
425C2×C3×C4—68no—
426C2×C3×C4—68no—
427C2×C3×C4—64no—
428C2×C3×C4C23×D314yes—
429C2×C3×C4C23×D314yes—
430C2×C3×C4C23×D311yescharacteristic
431C2×C3×C4C23×D312yes—
432C2×C3×C4C24×C314yes—
433C2×C3×C4C24×C311yescharacteristic
434C2×C3×C4C24×C314yes—
435C2×C3×C4C24×C312yes—
436#67—216no—
437#67—28no—
438#67—48no—
439C2×Dic3—28no—
440C2×Dic3—28no—
441C2×Dic3C24×C312yes—
442C2×Dic3C24×C314yes—
443C2×Dic3C24×C314yes—
444C2×Dic3C24×C311yescharacteristic
445D12—28no—
446D12—44no—
447D12—42no—
448C4×D3—24no—
449C4×D3—216no—
450C4×D3—28no—
451C4×D3—22no—
452Dic6—44no—
453Dic6C3×#4118yescomplemented
454C2×C32—44no—
455C2×C32C22×#4112yes—
456C2×C32C2×H(5,𝔽2)11yescharacteristic
457C3×D3—44no—
458C3×D3—41no—
459#41—616no—
460#41—68no—
461#41—128no—
462#41—124no—
463C2×Q8—32no—
464C2×Q8—34no—
465C2×Q8C22×C3×D312yes—
466C2×D4—34no—
467C2×D4—38no—
468C2×D4—38no—
469C2×D4—34no—
470C2×D4—34no—
471C2×D4—32no—
472C2×D4C22×C3×D312yes—
473C2×D4C22×C3×D314yes—
474C22×C4—34no—
475C22×C4—34no—
476C22×C4—38no—
477C22×C4—32no—
478C22×C4—34no—
479C22×C4—31no—
480C22×C4C22×C3×D314yes—
481C4⋊C4—34no—
482C4⋊C4—38no—
483C4⋊C4—34no—
484C4⋊C4—32no—
485C4⋊C4C22×C3×D312yes—
486C4⋊C4C22×C3×D314yes—
487C22⋊C4—34no—
488C22⋊C4—38no—
489C22⋊C4—34no—
490C22⋊C4—38no—
491C22⋊C4C22×C3×D314yes—
492C22⋊C4C22×C3×D318yes—
493C42—34no—
494C42—32no—
495C42—31no—
496C42—34no—
497C42—34no—
498C42—34no—
499C42C22×C3×D314yes—
500C42C22×C3×D311yescharacteristic
501C22×C3—24no—
502C22×C3—24no—
503C22×C3—24no—
504C22×C3—24no—
505C22×C3—24no—
506C22×C3—24no—
507C22×C3—21no—
508C22×C3—44no—
509C22×C3—44no—
510C22×C3—44no—
511C22×C3—68no—
512C22×C3—62no—
513C22×C3—61no—
514C22×C3—64no—
515C22×C3C24×D311yescharacteristic
516C22×C3C25×C311yescharacteristic
517C2×D3—28no—
518C2×D3—22no—
519C2×D3—21no—
520C2×D3—24no—
521C3×C4—24no—
522C3×C4—24no—
523C3×C4—21no—
524C3×C4—24no—
525C3×C4—24no—
526C3×C4—21no—
527C3×C4—24no—
528C3×C4—38no—
529C3×C4—32no—
530C3×C4—44no—
531C3×C4—44no—
532C3×C4—41no—
533C3×C4—62no—
534C3×C4—64no—
535C3×C4D3×#4114yes—
536C3×C4C2×C3×#4114yes—
537Dic3—22no—
538Dic3—24no—
539Dic3C2×C3×#4118yes—
540Dic3C3×H(5,𝔽2)12yes—
541C32#348311yescharacteristic, complemented, Sylow
542C23—31no—
543C23—34no—
544C23C23×C3×D314yes—
545Q8—38no—
546Q8—42no—
547Q8—124no—
548D4—24no—
549D4—44no—
550D4—616no—
551D4—68no—
552D4—68no—
553D4—124no—
554D4—122no—
555D4—128no—
556C2×C4—28no—
557C2×C4—31no—
558C2×C4—34no—
559C2×C4—32no—
560C2×C4—34no—
561C2×C4—616no—
562C2×C4—68no—
563C2×C4—62no—
564C2×C4—68no—
565C2×C4—68no—
566C2×C4—64no—
567C2×C4C23×C3×D314yes—
568C2×C4C23×C3×D314yes—
569C2×C4C23×C3×D311yescharacteristic
570C2×C4C23×C3×D312yes—
571C2×C3—22no—
572C2×C3—21no—
573C2×C3—44no—
574C2×C3—44no—
575C2×C3—84no—
576C2×C3—124no—
577C2×C3—121no—
578C2×C3C2×D3×#4112yes—
579C2×C3D3×H(5,𝔽2)11yescharacteristic
580C2×C3C22×C3×#4112yes—
581C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
582D3—44no—
583D3—41no—
584C22—24no—
585C22—24no—
586C22—24no—
587C22—68no—
588C22—62no—
589C22—61no—
590C22—64no—
591C22C24×C3×D311yescharacteristic
592C4—24no—
593C4—24no—
594C4—21no—
595C4—38no—
596C4—32no—
597C4—62no—
598C4—64no—
599C4C3×D3×#4114yes—
600C3—21no—
601C3#8695911yescharacteristic, direct product factor
602C3C3×#348311yescharacteristic, complemented
603C2—44no—
604C2—124no—
605C2—121no—
606C2C2×C3×D3×#4112yes—
607C2C3×D3×H(5,𝔽2)11yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×#555C2
socleC22×C32C25
hypercenterC3×#555D3
hypocenterC3C3×#3483
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#555

Complements

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

NH ≅ G/Ntype
1. C32×#555C2semidirect
2. C3×#5725C2semidirect
3. C3×#5722C2semidirect
4. C3×#5670C2semidirect
5. C3×#5668C2semidirect
6. C3×#5599C2semidirect
7. C3×#5596C2semidirect
8. C3×#5553C2semidirect
9. C3×C4×#237C2semidirect
10. C3×#5532C2semidirect
11. C3×#5522C2semidirect
13. #86959C3direct (N × H)
56. C3×#555D3semidirect
57. C3×#555C2×C3semidirect
65. #5725C2×C3semidirect
66. #5722C2×C3semidirect
67. #5670C2×C3semidirect
68. #5668C2×C3semidirect
69. #5599C2×C3semidirect
70. #5596C2×C3semidirect
71. #5553C2×C3semidirect
72. C4×#237C2×C3semidirect
73. #5532C2×C3semidirect
74. #5522C2×C3semidirect
227. C3×Dic6#41semidirect
231. #555C3×D3semidirect
453. Dic6C3×#41semidirect
541. C32#3483semidirect
601. C3#86959direct (N × H)
602. C3C3×#3483semidirect

Maximal subgroups

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

subgroupindex
C32×#5552
C3×#57252
C3×#57222
C3×#56702
C3×#56682
C3×#55992
C3×#55962
C3×#55532
C3×C4×#2372
C3×#55322
C3×#55222
C3×#34833
#869593