Finite Group Databasebeta

← C3×#83384 #11866159

Subgroups — C3×#83384 #11866159

Order 1152.

1219 conjugacy classes of subgroups.

The subgroup lattice has 553 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#535C211yesmaximal, characteristic, complemented
2C2×C3×#949C211yesmaximal, characteristic, complemented
3C22×C3×#213C211yesmaximal, characteristic, complemented
4C3×#5521C211yesmaximal, characteristic, complemented
5C3×#5233C211yesmaximal, characteristic, complemented
6C3×#5215C211yesmaximal, characteristic, complemented
7C3×#5072C214yesmaximal, complemented
8C3×#5057C214yesmaximal, complemented
9C3×#4999C211yesmaximal, characteristic, complemented
10C3×#3041—31nomaximal
11#83384C311yesmaximal, characteristic, direct product factor
12C2×C32×#41C2211yescharacteristic
13C22×C32×D4C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C32×#127C2212yescomplemented
16C32×#124C2212yescomplemented
17C32×#121—22no—
18C32×#120—22no—
19C32×#117C2211yescharacteristic
20C3×#949—24no—
21C2×C3×#215C2212yescomplemented
22C2×C3×#213—24no—
23C2×C3×#213C2214yes—
24C2×C3×#213C2212yescomplemented
25C3×#926C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27C22×C3×C3⋊C8C2211yescharacteristic
28C3×#893—22no—
29C3×D3×C22⋊C4—22no—
30C3×C4×D12C2214yescomplemented
31C3×#835C2212yescomplemented
32C3×#832C2214yescomplemented
33C3×#832C2212yescomplemented
34C3×C4⋊(C3⋊C8)C2214yescomplemented
35C2×C3×AGL(1,ℤ/8)—31no—
36C22×C3×D8—31no—
37C3×#535—21no—
38C3×#535D311yescharacteristic, complemented
39C3×#535C2×C311yescharacteristic, complemented
40C3×#518—31no—
41C2×#949C2×C311yescharacteristic, complemented
42C22×#213C2×C311yescharacteristic, complemented
43#5521C2×C311yescharacteristic, complemented
44C3×#463—34no—
45C3×#459—34no—
46C3×#424—31no—
47C3×#418—31no—
48C3×#416—31no—
49#5233C2×C311yescharacteristic, complemented
50#5215C2×C311yescharacteristic, complemented
51#5072C2×C314yescomplemented
52#5057C2×C314yescomplemented
53#4999C2×C311yescharacteristic, complemented
54C24×C32—21no—
55C23×C3×D3—21no—
56C32×#41—22no—
57C32×#41—22no—
58C2×C32×Q8C2311yescharacteristic
59C2×C32×D4—21no—
60C2×C32×D4—22no—
61C2×C32×D4—21no—
62C2×C32×D4—24no—
63C2×C32×D4—22no—
64C2×C32×D4C2312yes—
65C2×C32×D4C2311yescharacteristic
66C22×C32×C4—21no—
67C22×C32×C4C2311yescharacteristic
68C2×C3×D12—21no—
69C2×C3×D12—22no—
70C2×C3×D12D414yescomplemented
71C2×C3×D12C2312yes—
72C2×C3×C4×D3—24no—
73C32×C4⋊C4D412yes—
74C32×C22⋊C4—24no—
75C32×C22⋊C4D412yes—
76C32×C42C2312yes—
77C3×#217—21no—
78C3×#215—24no—
79C3×#213—28no—
80C3×#213—24no—
81C3×(C2×D3)⋊C4—24no—
82C3×C4⋊Dic3C2312yes—
83C3×C4×Dic3—21no—
84C3×#208—22no—
85C2×C3×C3⋊C8—22no—
86C2×C3×C3⋊C8C2312yes—
87C2×C3×C3⋊C8C2312yes—
88#3041—31noSylow
89C2×C3×#41—21no—
90C2×C3×#41C2×D311yescharacteristic
91C2×C3×#41C22×C311yescharacteristic
92C22×C3×D4—21no—
93C22×C3×D4—31no—
94C22×C3×D4C2×D311yescharacteristic
95C22×C3×D4C22×C311yescharacteristic
96C22×D12C22×C311yescharacteristic
97C3×AGL(1,ℤ/8)—64no—
98C2×C3×SD16—32no—
99C2×C3×D8—34no—
100C2×C3×D8—32no—
101C2×C3×D8—64no—
102C2×C3×M16—31no—
103C22×C3×C8—31no—
104C3×#127—22no—
105C3×#127C2×D312yescomplemented
106C3×#127C22×C312yescomplemented
107C3×#124—22no—
108C3×#124C2×D312yescomplemented
109C3×#124C22×C312yescomplemented
110C3×#121—24no—
111C3×#121—22no—
112C3×#121—22no—
113C3×#120—24no—
114C3×#120—22no—
115C3×#120—22no—
116C3×C4×D4—34no—
117C3×C4×D4—62no—
118C3×#117—21no—
119C3×#117—31no—
120C3×#117C2×D311yescharacteristic
121C3×#117C22×C311yescharacteristic
122C2×C3×C22⋊C4—62no—
123#949—24no—
124C2×#215C22×C312yescomplemented
125C2×#213—24no—
126C2×#213C22×C314yes—
127C2×#213C22×C312yescomplemented
128#926C22×C311yescharacteristic
129C2×#208C22×C311yescharacteristic
130C22×C3⋊C8C22×C311yescharacteristic
131#893—22no—
132D3×C22⋊C4—22no—
133C4×D12C22×C314yescomplemented
134C3×C4⋊C8—34no—
135C3×#103—32no—
136C3×#102—32no—
137C3×#102—34no—
138#835C22×C312yescomplemented
139#832C22×C314yescomplemented
140#832C22×C312yescomplemented
141C4⋊(C3⋊C8)C22×C314yescomplemented
142C23×C32—22no—
143C23×C32—21no—
144C23×C32—42no—
145C23×C32—82no—
146C23×C32C2×D411yescharacteristic
147C22×C3×D3—22no—
148C22×C3×D3—24no—
149C22×C3×D3—82no—
150C32×Q8—21no—
151C32×Q8—21no—
152C32×D4—22no—
153C32×D4—21no—
154C32×D4—22no—
155C32×D4—21no—
156C32×D4—42no—
157C32×D4—42no—
158C32×D4—84no—
159C2×C32×C4—21no—
160C2×C32×C4—42no—
161C2×C32×C4C2×D412yes—
162C2×C32×C4C2×D414yes—
163C2×C32×C4C2×D411yescharacteristic
164C2×C32×C4#4112yes—
165C2×C32×C4C2411yescharacteristic
166C2×C3×Dic3—22no—
167C3×D12—24no—
168C3×D12—22no—
169C3×D12C2×D414yes—
170C3×C4×D3—84no—
171C3×C3⋊C8—22no—
172C3×C3⋊C8—22no—
173C2×AGL(1,ℤ/8)—31no—
174C22×D8—31no—
175#535C3×D311yescharacteristic, complemented
176#518—31no—
177#463—34no—
178#459—34no—
179#424—31no—
180#418—31no—
181#416—31no—
182C24×C3—22no—
183C24×C3—21no—
184C24×C3—21no—
185C24×C3—61no—
186C23×D3—21no—
187C3×#41—22no—
188C3×#41—22no—
189C3×#41—22no—
190C3×#41—22no—
191C3×#41—42no—
192C3×#41—42no—
193C2×C3×Q8—21no—
194C2×C3×Q8C22×D311yescharacteristic
195C2×C3×Q8C23×C311yescharacteristic
196C2×C3×D4—22no—
197C2×C3×D4—22no—
198C2×C3×D4—21no—
199C2×C3×D4—21no—
200C2×C3×D4—28no—
201C2×C3×D4—22no—
202C2×C3×D4—22no—
203C2×C3×D4—21no—
204C2×C3×D4—24no—
205C2×C3×D4—22no—
206C2×C3×D4—21no—
207C2×C3×D4—24no—
208C2×C3×D4—22no—
209C2×C3×D4—22no—
210C2×C3×D4—21no—
211C2×C3×D4—34no—
212C2×C3×D4—32no—
213C2×C3×D4—42no—
214C2×C3×D4—42no—
215C2×C3×D4—62no—
216C2×C3×D4—61no—
217C2×C3×D4C22×D312yes—
218C2×C3×D4C22×D311yescharacteristic
219C2×C3×D4C23×C312yes—
220C2×C3×D4C23×C311yescharacteristic
221C22×C3×C4—22no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—64no—
226C22×C3×C4C22×D311yescharacteristic
227C22×C3×C4C23×C311yescharacteristic
228C2×D12—21no—
229C2×D12—22no—
230C2×D12C3×D414yescomplemented
231C2×D12C23×C312yes—
232C2×C4×D3—24no—
233C3×SD16—64no—
234C3×D8—68no—
235C3×D8—64no—
236C3×M16—62no—
237C2×C3×C8—32no—
238C2×C3×C8—32no—
239C2×C3×C8—62no—
240C3×C4⋊C4—22no—
241C3×C4⋊C4—32no—
242C3×C4⋊C4#6712yes—
243C3×C4⋊C4C3×D412yes—
244C3×C22⋊C4—28no—
245C3×C22⋊C4—24no—
246C3×C22⋊C4—24no—
247C3×C22⋊C4—22no—
248C3×C22⋊C4—61no—
249C3×C22⋊C4—64no—
250C3×C22⋊C4#6712yes—
251C3×C22⋊C4C3×D412yes—
252C3×C42—22no—
253C3×C42—61no—
254C3×C42C22×D312yes—
255C3×C42C23×C312yes—
256#217—21no—
257#215—24no—
258#213—28no—
259#213—24no—
260(C2×D3)⋊C4—24no—
261C4⋊Dic3C23×C312yes—
262C4×Dic3—21no—
263#208—22no—
264C2×C3⋊C8—22no—
265C2×C3⋊C8C23×C312yes—
266C2×C3⋊C8C23×C312yes—
267C22×C32—22no—
268C22×C32—41no—
269C22×C32—42no—
270C22×C32—42no—
271C22×C32—44no—
272C22×C32—84no—
273C22×C32#12112yes—
274C22×C32C22×D411yescharacteristic
275C2×C3×D3—24no—
276C2×C3×D3—44no—
277C2×C3×D3—84no—
278C32×C4—24no—
279C32×C4—41no—
280C32×C4#12112yes—
281C32×C4C22×D411yescharacteristic
282C32×C4C2×#4111yescharacteristic
283C3×Dic3—42no—
284C2×#41C2×C3×D311yescharacteristic
285C22×D4—31no—
286C22×D4C2×C3×D311yescharacteristic
287AGL(1,ℤ/8)—64no—
288C2×SD16—32no—
289C2×D8—34no—
290C2×D8—32no—
291C2×D8—64no—
292C2×M16—31no—
293C22×C8—31no—
294#127C2×C3×D312yescomplemented
295#124C2×C3×D312yescomplemented
296#121—22no—
297#120—22no—
298C4×D4—34no—
299C4×D4—62no—
300#117—31no—
301#117C2×C3×D311yescharacteristic
302C2×C22⋊C4—62no—
303C4⋊C8—34no—
304#103—32no—
305#102—32no—
306#102—34no—
307C23×C3—24no—
308C23×C3—22no—
309C23×C3—22no—
310C23×C3—21no—
311C23×C3—22no—
312C23×C3—21no—
313C23×C3—21no—
314C23×C3—44no—
315C23×C3—42no—
316C23×C3—42no—
317C23×C3—62no—
318C23×C3—64no—
319C23×C3—82no—
320C23×C3—82no—
321C23×C3—84no—
322C23×C3—242no—
323C23×C3C2×#6711yescharacteristic
324C23×C3C2×C3×D411yescharacteristic
325C22×D3—22no—
326C22×D3—24no—
327C22×D3—82no—
328C3×Q8—21no—
329C3×Q8—21no—
330C3×Q8—21no—
331C3×Q8—21no—
332C3×Q8—41no—
333C3×Q8—41no—
334C3×D4—22no—
335C3×D4—21no—
336C3×D4—22no—
337C3×D4—21no—
338C3×D4—22no—
339C3×D4—21no—
340C3×D4—22no—
341C3×D4—21no—
342C3×D4—34no—
343C3×D4—42no—
344C3×D4—42no—
345C3×D4—41no—
346C3×D4—41no—
347C3×D4—44no—
348C3×D4—44no—
349C3×D4—42no—
350C3×D4—42no—
351C3×D4—42no—
352C3×D4—42no—
353C3×D4—64no—
354C3×D4—62no—
355C3×D4—84no—
356C3×D4—84no—
357C3×D4—88no—
358C2×C3×C4—22no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—21no—
365C2×C3×C4—24no—
366C2×C3×C4—44no—
367C2×C3×C4—42no—
368C2×C3×C4—42no—
369C2×C3×C4—62no—
370C2×C3×C4—244no—
371C2×C3×C4D3×D412yes—
372C2×C3×C4#23712yes—
373C2×C3×C4C2×#6714yes—
374C2×C3×C4C2×#6711yescharacteristic
375C2×C3×C4C2×C3×D412yes—
376C2×C3×C4C2×C3×D414yes—
377C2×C3×C4C2×C3×D411yescharacteristic
378C2×C3×C4C3×#4112yes—
379C2×C3×C4C23×D311yescharacteristic
380C2×C3×C4C24×C311yescharacteristic
381C2×Dic3—22no—
382D12—24no—
383D12—22no—
384D12C2×C3×D414yes—
385C4×D3—84no—
386C3×C8—62no—
387C3×C8—62no—
388C3⋊C8—22no—
389C3⋊C8—22no—
390C2×C32—22no—
391C2×C32—81no—
392C2×C32—82no—
393C2×C32C2×#12111yescharacteristic
394C2×C32#57612yes—
395C3×D3—44no—
396C24—21no—
397C24—61no—
398#41—22no—
399#41—22no—
400C2×Q8C22×C3×D311yescharacteristic
401C2×D4—21no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—21no—
405C2×D4—24no—
406C2×D4—32no—
407C2×D4—34no—
408C2×D4—62no—
409C2×D4—61no—
410C2×D4C22×C3×D312yes—
411C2×D4C22×C3×D311yescharacteristic
412C22×C4—21no—
413C22×C4—64no—
414C22×C4C22×C3×D311yescharacteristic
415SD16—64no—
416D8—68no—
417D8—64no—
418M16—62no—
419C2×C8—32no—
420C2×C8—32no—
421C2×C8—62no—
422C4⋊C4—32no—
423C4⋊C4C3×#6712yes—
424C22⋊C4—24no—
425C22⋊C4—61no—
426C22⋊C4—64no—
427C22⋊C4C3×#6712yes—
428C42—61no—
429C42C22×C3×D312yes—
430C22×C3—22no—
431C22×C3—22no—
432C22×C3—22no—
433C22×C3—21no—
434C22×C3—42no—
435C22×C3—42no—
436C22×C3—44no—
437C22×C3—44no—
438C22×C3—48no—
439C22×C3—42no—
440C22×C3—44no—
441C22×C3—41no—
442C22×C3—42no—
443C22×C3—42no—
444C22×C3—44no—
445C22×C3—41no—
446C22×C3—42no—
447C22×C3—64no—
448C22×C3—84no—
449C22×C3—84no—
450C22×C3—88no—
451C22×C3—124no—
452C22×C3—244no—
453C22×C3#93812yes—
454C22×C3C3×#12112yes—
455C22×C3C22×#6711yescharacteristic
456C22×C3C22×C3×D411yescharacteristic
457C2×D3—24no—
458C2×D3—44no—
459C2×D3—84no—
460C3×C4—24no—
461C3×C4—24no—
462C3×C4—22no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—44no—
466C3×C4—42no—
467C3×C4—41no—
468C3×C4—41no—
469C3×C4—122no—
470C3×C4#93812yes—
471C3×C4C3×#12112yes—
472C3×C4C2×D3×D411yescharacteristic
473C3×C4C2×#23711yescharacteristic
474C3×C4C22×C3×D411yescharacteristic
475C3×C4C2×C3×#4111yescharacteristic
476Dic3—42no—
477C32#304111yescharacteristic, complemented, Sylow
478C23—22no—
479C23—21no—
480C23—42no—
481C23—62no—
482C23—64no—
483C23—82no—
484C23—242no—
485C23C2×C3×#6711yescharacteristic
486Q8—21no—
487Q8—21no—
488D4—22no—
489D4—21no—
490D4—22no—
491D4—21no—
492D4—34no—
493D4—42no—
494D4—42no—
495D4—64no—
496D4—62no—
497D4—84no—
498C2×C4—21no—
499C2×C4—42no—
500C2×C4—62no—
501C2×C4—244no—
502C2×C4C3×D3×D412yes—
503C2×C4C3×#23712yes—
504C2×C4C2×C3×#6714yes—
505C2×C4C2×C3×#6711yescharacteristic
506C2×C4C23×C3×D311yescharacteristic
507C8—62no—
508C8—62no—
509C2×C3—22no—
510C2×C3—22no—
511C2×C3—21no—
512C2×C3—22no—
513C2×C3—42no—
514C2×C3—84no—
515C2×C3—82no—
516C2×C3—82no—
517C2×C3—81no—
518C2×C3—82no—
519C2×C3—81no—
520C2×C3—124no—
521C2×C3C2×#93811yescharacteristic
522C2×C3#583512yes—
523C2×C3C2×C3×#12111yescharacteristic
524C2×C3C3×#57612yes—
525D3—44no—
526C22—22no—
527C22—41no—
528C22—42no—
529C22—42no—
530C22—44no—
531C22—64no—
532C22—84no—
533C22—124no—
534C22—244no—
535C22C3×#93812yes—
536C22C22×C3×#6711yescharacteristic
537C4—24no—
538C4—41no—
539C4—122no—
540C4C3×#93812yes—
541C4C2×C3×D3×D411yescharacteristic
542C4C2×C3×#23711yescharacteristic
543C3—21no—
544C3#8338411yescharacteristic, direct product factor
545C3C3×#304111yescharacteristic, complemented
546C2—22no—
547C2—82no—
548C2—81no—
549C2—124no—
550C2C2×C3×#93811yescharacteristic
551C2C3×#583512yes—
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#535C2
socleC22×C32C22×D4
hypercenterC3×#535D3
hypocenterC3C3×#3041
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#117 ◁ C3×#535

Complements

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

NH ≅ G/Ntype
1. C32×#535C2semidirect
2. C2×C3×#949C2semidirect
3. C22×C3×#213C2semidirect
4. C3×#5521C2semidirect
5. C3×#5233C2semidirect
6. C3×#5215C2semidirect
7. C3×#5072C2semidirect
8. C3×#5057C2semidirect
9. C3×#4999C2semidirect
11. #83384C3direct (N × H)
15. C32×#127C22semidirect
16. C32×#124C22semidirect
21. C2×C3×#215C22semidirect
24. C2×C3×#213C22semidirect
30. C3×C4×D12C22semidirect
31. C3×#835C22semidirect
32. C3×#832C22semidirect
33. C3×#832C22semidirect
34. C3×C4⋊(C3⋊C8)C22semidirect
38. C3×#535D3semidirect
39. C3×#535C2×C3semidirect
41. C2×#949C2×C3semidirect
42. C22×#213C2×C3semidirect
43. #5521C2×C3semidirect
49. #5233C2×C3semidirect
50. #5215C2×C3semidirect
51. #5072C2×C3semidirect
52. #5057C2×C3semidirect
53. #4999C2×C3semidirect
70. C2×C3×D12D4semidirect
105. C3×#127C2×D3semidirect
106. C3×#127C22×C3semidirect
108. C3×#124C2×D3semidirect
109. C3×#124C22×C3semidirect
124. C2×#215C22×C3semidirect
127. C2×#213C22×C3semidirect
133. C4×D12C22×C3semidirect
138. #835C22×C3semidirect
139. #832C22×C3semidirect
140. #832C22×C3semidirect
141. C4⋊(C3⋊C8)C22×C3semidirect
175. #535C3×D3semidirect
230. C2×D12C3×D4semidirect
294. #127C2×C3×D3semidirect
295. #124C2×C3×D3semidirect
477. C32#3041semidirect
544. C3#83384direct (N × H)
545. C3C3×#3041semidirect

Maximal subgroups

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

subgroupindex
C32×#5352
C2×C3×#9492
C22×C3×#2132
C3×#55212
C3×#52332
C3×#52152
C3×#50722
C3×#50572
C3×#49992
C3×#30413
#833843