Finite Group Databasebeta

← C3×#83934 #11866177

Subgroups — C3×#83934 #11866177

Order 1152.

1201 conjugacy classes of subgroups.

The subgroup lattice has 549 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2C3×#5830C211yesmaximal, characteristic, complemented
3C3×#5798C211yesmaximal, characteristic, complemented
4C22×C3×#213C211yesmaximal, characteristic, complemented
5C3×#5233C211yesmaximal, characteristic, complemented
6C3×#5165C214yesmaximal, complemented
7C3×#5150C214yesmaximal, complemented
8C3×#5131C211yesmaximal, characteristic, complemented
9C3×#5119C211yesmaximal, characteristic, complemented
10C3×#3041—31nomaximal
11#83934C311yesmaximal, characteristic, direct product factor
12C2×C32×#41C2211yescharacteristic
13C22×C32×D4C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C32×AGL(1,ℤ/8)—24no—
16C2×C32×SD16C2212yescomplemented
17C2×C32×D8C2212yescomplemented
18C2×C32×M16C2211yescharacteristic
19C2×C3×#217—22no—
20C3×#947C2212yescomplemented
21C3×#940C2212yescomplemented
22C3×#937—22no—
23C3×D4×Dic3—22no—
24C3×D4×Dic3C2214yescomplemented
25C2×C3×#213—24no—
26C2×C3×#213C2214yes—
27C3×#930—22no—
28C3×#926C2211yescharacteristic
29C3×#926C2211yescharacteristic
30C22×C3×C3⋊C8C2211yescharacteristic
31C3×#835C2212yescomplemented
32C3×#832C2212yescomplemented
33C3×#821C2214yescomplemented
34C3×Dic3⋊C8C2214yescomplemented
35C2×C3×AGL(1,ℤ/8)—21no—
36C2×C3×AGL(1,ℤ/8)D311yescharacteristic, complemented
37C2×C3×AGL(1,ℤ/8)C2×C311yescharacteristic, complemented
38C22×C3×D8—31no—
39C3×#535—31no—
40C3×#518—31no—
41#5830C2×C311yescharacteristic, complemented
42#5798C2×C311yescharacteristic, complemented
43C22×#213C2×C311yescharacteristic, complemented
44C3×#463—34no—
45C3×#459—34no—
46C3×#424—31no—
47C3×#418—31no—
48C3×#416—31no—
49#5233C2×C311yescharacteristic, complemented
50#5165C2×C314yescomplemented
51#5150C2×C314yescomplemented
52#5131C2×C311yescharacteristic, complemented
53#5119C2×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—21no—
61C2×C32×D4—22no—
62C2×C32×D4D414yescomplemented
63C2×C32×D4C2311yescharacteristic
64C2×C32×D4C2312yes—
65C22×C32×C4—21no—
66C22×C32×C4C2311yescharacteristic
67C2×C3×#67—24no—
68C22×C3×Dic3—24no—
69C2×C3×D12—22no—
70C2×C3×D12—22no—
71C2×C3×D12—21no—
72C2×C3×D12C2312yes—
73C32×SD16—24no—
74C32×D8—24no—
75C32×M16—22no—
76C2×C32×C8C2312yes—
77C3×#217—21no—
78C3×#217—24no—
79C3×#217D412yes—
80C3×#213—28no—
81C3×(C2×D3)⋊C4—24no—
82C3×C4⋊Dic3D412yes—
83C3×C4⋊Dic3C2312yes—
84C3×C4×Dic3—21no—
85C3×C4×Dic3C2312yes—
86C2×C3×C3⋊C8—22no—
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)—28no—
98C3×AGL(1,ℤ/8)—24no—
99C3×AGL(1,ℤ/8)—24no—
100C2×C3×SD16—22no—
101C2×C3×SD16C2×D312yescomplemented
102C2×C3×SD16C22×C312yescomplemented
103C2×C3×D8—22no—
104C2×C3×D8—34no—
105C2×C3×D8—64no—
106C2×C3×D8C2×D312yescomplemented
107C2×C3×D8C22×C312yescomplemented
108C2×C3×M16—21no—
109C2×C3×M16C2×D311yescharacteristic
110C2×C3×M16C22×C311yescharacteristic
111C22×C3×C8—31no—
112C3×#127—32no—
113C3×#124—32no—
114C3×#121—62no—
115C3×#120—62no—
116C3×C4×D4—34no—
117C3×C4×D4—62no—
118C3×#117—31no—
119C3×#117—31no—
120C2×C3×C22⋊C4—62no—
121C2×#217—22no—
122#947C22×C312yescomplemented
123#940C22×C312yescomplemented
124#937—22no—
125D4×Dic3—22no—
126D4×Dic3C22×C314yescomplemented
127C2×#213—24no—
128C2×#213C22×C314yes—
129#930—22no—
130#926C22×C311yescharacteristic
131#926C22×C311yescharacteristic
132C22×C3⋊C8C22×C311yescharacteristic
133C3×C4⋊C8—34no—
134C3×#103—32no—
135C3×#102—32no—
136C3×#102—34no—
137#835C22×C312yescomplemented
138#832C22×C312yescomplemented
139#821C22×C314yescomplemented
140Dic3⋊C8C22×C314yescomplemented
141C23×C32—22no—
142C23×C32—24no—
143C23×C32—21no—
144C23×C32—82no—
145C23×C32C2×D411yescharacteristic
146C22×C3×D3—22no—
147C22×C3×D3—42no—
148C22×C3×D3—82no—
149C32×Q8—21no—
150C32×Q8—21no—
151C32×D4—21no—
152C32×D4—24no—
153C32×D4—22no—
154C32×D4—21no—
155C32×D4—42no—
156C32×D4C2×D414yes—
157C2×C32×C4—21no—
158C2×C32×C4—42no—
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4C2×D412yes—
161C2×C32×C4#4112yes—
162C2×C32×C4C2411yescharacteristic
163C3×#67—84no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—84no—
166C2×C3×Dic3C2×D414yes—
167C3×D12—22no—
168C3×D12—22no—
169C3×D12—42no—
170C32×C8—22no—
171C3×C3⋊C8—22no—
172C2×AGL(1,ℤ/8)C3×D311yescharacteristic, complemented
173C22×D8—31no—
174#535—31no—
175#518—31no—
176#463—34no—
177#459—34no—
178#424—31no—
179#418—31no—
180#416—31no—
181C24×C3—21no—
182C24×C3—21no—
183C24×C3—41no—
184C24×C3—61no—
185C23×D3—21no—
186C3×#41—24no—
187C3×#41—22no—
188C3×#41—22no—
189C3×#41—22no—
190C3×#41—22no—
191C3×#41—42no—
192C2×C3×Q8—21no—
193C2×C3×Q8C22×D311yescharacteristic
194C2×C3×Q8C23×C311yescharacteristic
195C2×C3×D4—21no—
196C2×C3×D4—21no—
197C2×C3×D4—21no—
198C2×C3×D4—22no—
199C2×C3×D4—21no—
200C2×C3×D4—22no—
201C2×C3×D4—24no—
202C2×C3×D4—21no—
203C2×C3×D4—22no—
204C2×C3×D4—32no—
205C2×C3×D4—41no—
206C2×C3×D4—42no—
207C2×C3×D4—41no—
208C2×C3×D4—64no—
209C2×C3×D4—61no—
210C2×C3×D4—62no—
211C2×C3×D4—62no—
212C2×C3×D4#6714yescomplemented
213C2×C3×D4C3×D414yescomplemented
214C2×C3×D4C22×D311yescharacteristic
215C2×C3×D4C22×D312yes—
216C2×C3×D4C23×C311yescharacteristic
217C2×C3×D4C23×C312yes—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—41no—
222C22×C3×C4—64no—
223C22×C3×C4C22×D311yescharacteristic
224C22×C3×C4C23×C311yescharacteristic
225C2×#67—24no—
226C22×Dic3—24no—
227C2×D12—22no—
228C2×D12—22no—
229C2×D12—21no—
230C2×D12C23×C312yes—
231C3×SD16—28no—
232C3×SD16—24no—
233C3×SD16—24no—
234C3×D8—28no—
235C3×D8—24no—
236C3×D8—24no—
237C3×D8—68no—
238C3×M16—24no—
239C3×M16—22no—
240C3×M16—22no—
241C2×C3×C8—22no—
242C2×C3×C8—32no—
243C2×C3×C8—62no—
244C2×C3×C8C22×D312yes—
245C2×C3×C8C23×C312yes—
246C3×C4⋊C4—32no—
247C3×C4⋊C4—32no—
248C3×C22⋊C4—32no—
249C3×C22⋊C4—64no—
250C3×C22⋊C4—64no—
251C3×C22⋊C4—61no—
252C3×C42—32no—
253C3×C42—61no—
254#217—21no—
255#217—24no—
256#217C3×D412yes—
257#213—28no—
258(C2×D3)⋊C4—24no—
259C4⋊Dic3C3×D412yes—
260C4⋊Dic3C23×C312yes—
261C4×Dic3—21no—
262C4×Dic3C23×C312yes—
263C2×C3⋊C8—22no—
264C2×C3⋊C8C23×C312yes—
265C22×C32—22no—
266C22×C32—24no—
267C22×C32—41no—
268C22×C32—44no—
269C22×C32—42no—
270C22×C32—84no—
271C22×C32#12112yes—
272C22×C32C22×D411yescharacteristic
273C2×C3×D3—42no—
274C2×C3×D3—44no—
275C2×C3×D3—84no—
276C32×C4—41no—
277C32×C4#12112yes—
278C32×C4C22×D411yescharacteristic
279C32×C4C2×#4111yescharacteristic
280C3×Dic3—24no—
281C3×Dic3—42no—
282C2×#41C2×C3×D311yescharacteristic
283C22×D4—31no—
284C22×D4C2×C3×D311yescharacteristic
285AGL(1,ℤ/8)—24no—
286C2×SD16C2×C3×D312yescomplemented
287C2×D8—34no—
288C2×D8—64no—
289C2×D8C2×C3×D312yescomplemented
290C2×M16C2×C3×D311yescharacteristic
291C22×C8—31no—
292#127—32no—
293#124—32no—
294#121—62no—
295#120—62no—
296C4×D4—34no—
297C4×D4—62no—
298#117—31no—
299#117—31no—
300C2×C22⋊C4—62no—
301C4⋊C8—34no—
302#103—32no—
303#102—32no—
304#102—34no—
305C23×C3—22no—
306C23×C3—22no—
307C23×C3—24no—
308C23×C3—24no—
309C23×C3—21no—
310C23×C3—21no—
311C23×C3—21no—
312C23×C3—41no—
313C23×C3—42no—
314C23×C3—44no—
315C23×C3—62no—
316C23×C3—82no—
317C23×C3—82no—
318C23×C3—84no—
319C23×C3—122no—
320C23×C3—242no—
321C23×C3D3×D411yescharacteristic
322C23×C3C2×C3×D411yescharacteristic
323C22×D3—22no—
324C22×D3—42no—
325C22×D3—82no—
326C3×Q8—22no—
327C3×Q8—21no—
328C3×Q8—21no—
329C3×Q8—21no—
330C3×Q8—21no—
331C3×Q8—41no—
332C3×D4—22no—
333C3×D4—24no—
334C3×D4—24no—
335C3×D4—22no—
336C3×D4—21no—
337C3×D4—21no—
338C3×D4—21no—
339C3×D4—22no—
340C3×D4—21no—
341C3×D4—24no—
342C3×D4—44no—
343C3×D4—42no—
344C3×D4—41no—
345C3×D4—44no—
346C3×D4—42no—
347C3×D4—42no—
348C3×D4—62no—
349C3×D4—62no—
350C3×D4—122no—
351C3×D4—244no—
352C3×D4C2×#6714yes—
353C3×D4C2×C3×D414yes—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—34no—
361C2×C3×C4—41no—
362C2×C3×C4—44no—
363C2×C3×C4—42no—
364C2×C3×C4—42no—
365C2×C3×C4—62no—
366C2×C3×C4—244no—
367C2×C3×C4D3×D411yescharacteristic
368C2×C3×C4#23712yes—
369C2×C3×C4C2×#6712yes—
370C2×C3×C4C2×C3×D411yescharacteristic
371C2×C3×C4C2×C3×D412yes—
372C2×C3×C4C3×#4112yes—
373C2×C3×C4C23×D311yescharacteristic
374C2×C3×C4C24×C311yescharacteristic
375#67—84no—
376C2×Dic3—22no—
377C2×Dic3—84no—
378C2×Dic3C2×C3×D414yes—
379D12—22no—
380D12—22no—
381D12—42no—
382C3×C8—24no—
383C3×C8—22no—
384C3×C8—22no—
385C3×C8—62no—
386C3⋊C8—22no—
387C2×C32—22no—
388C2×C32—44no—
389C2×C32—81no—
390C2×C32C2×#12111yescharacteristic
391C2×C32#57612yes—
392C3×D3—82no—
393C24—21no—
394C24—61no—
395#41—22no—
396#41—22no—
397C2×Q8C22×C3×D311yescharacteristic
398C2×D4—21no—
399C2×D4—21no—
400C2×D4—22no—
401C2×D4—32no—
402C2×D4—64no—
403C2×D4—61no—
404C2×D4—62no—
405C2×D4—62no—
406C2×D4C3×#6714yescomplemented
407C2×D4C22×C3×D311yescharacteristic
408C2×D4C22×C3×D312yes—
409C22×C4—21no—
410C22×C4—64no—
411C22×C4C22×C3×D311yescharacteristic
412SD16—24no—
413D8—24no—
414D8—68no—
415M16—22no—
416C2×C8—32no—
417C2×C8—62no—
418C2×C8C22×C3×D312yes—
419C4⋊C4—32no—
420C4⋊C4—32no—
421C22⋊C4—32no—
422C22⋊C4—64no—
423C22⋊C4—64no—
424C22⋊C4—61no—
425C42—32no—
426C42—61no—
427C22×C3—22no—
428C22×C3—22no—
429C22×C3—24no—
430C22×C3—24no—
431C22×C3—22no—
432C22×C3—21no—
433C22×C3—42no—
434C22×C3—44no—
435C22×C3—42no—
436C22×C3—44no—
437C22×C3—44no—
438C22×C3—42no—
439C22×C3—42no—
440C22×C3—41no—
441C22×C3—41no—
442C22×C3—84no—
443C22×C3—82no—
444C22×C3—84no—
445C22×C3—84no—
446C22×C3—88no—
447C22×C3—124no—
448C22×C3—122no—
449C22×C3—244no—
450C22×C3#93912yes—
451C22×C3C3×#12112yes—
452C22×C3C2×D3×D411yescharacteristic
453C22×C3C22×C3×D411yescharacteristic
454C2×D3—44no—
455C2×D3—42no—
456C2×D3—84no—
457C3×C4—22no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—42no—
461C3×C4—41no—
462C3×C4—41no—
463C3×C4—64no—
464C3×C4—122no—
465C3×C4#93912yes—
466C3×C4C3×#12112yes—
467C3×C4C2×#23711yescharacteristic
468C3×C4C22×#6711yescharacteristic
469C3×C4C22×C3×D411yescharacteristic
470C3×C4C2×C3×#4111yescharacteristic
471Dic3—24no—
472Dic3—42no—
473C32#304111yescharacteristic, complemented, Sylow
474C23—22no—
475C23—24no—
476C23—21no—
477C23—62no—
478C23—82no—
479C23—122no—
480C23—242no—
481C23C3×D3×D411yescharacteristic
482Q8—21no—
483Q8—21no—
484D4—24no—
485D4—22no—
486D4—21no—
487D4—21no—
488D4—42no—
489D4—62no—
490D4—62no—
491D4—122no—
492D4—244no—
493D4C2×C3×#6714yes—
494C2×C4—21no—
495C2×C4—34no—
496C2×C4—42no—
497C2×C4—62no—
498C2×C4—244no—
499C2×C4C3×D3×D411yescharacteristic
500C2×C4C3×#23712yes—
501C2×C4C2×C3×#6712yes—
502C2×C4C23×C3×D311yescharacteristic
503C8—22no—
504C8—62no—
505C2×C3—22no—
506C2×C3—22no—
507C2×C3—22no—
508C2×C3—21no—
509C2×C3—42no—
510C2×C3—44no—
511C2×C3—44no—
512C2×C3—84no—
513C2×C3—82no—
514C2×C3—81no—
515C2×C3—81no—
516C2×C3—242no—
517C2×C3#577412yes—
518C2×C3C2×#93911yescharacteristic
519C2×C3C2×C3×#12111yescharacteristic
520C2×C3C3×#57612yes—
521D3—82no—
522C22—22no—
523C22—24no—
524C22—44no—
525C22—42no—
526C22—41no—
527C22—84no—
528C22—124no—
529C22—122no—
530C22—244no—
531C22C3×#93912yes—
532C22C2×C3×D3×D411yescharacteristic
533C4—41no—
534C4—64no—
535C4—122no—
536C4C3×#93912yes—
537C4C2×C3×#23711yescharacteristic
538C4C22×C3×#6711yescharacteristic
539C3—21no—
540C3#8393411yescharacteristic, direct product factor
541C3C3×#304111yescharacteristic, complemented
542C2—22no—
543C2—44no—
544C2—81no—
545C2—242no—
546C2C3×#577412yes—
547C2C2×C3×#93911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×AGL(1,ℤ/8)C2
socleC22×C32C22×D4
hypercenterC2×C3×AGL(1,ℤ/8)D3
hypocenterC3C3×#3041
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×C32×AGL(1,ℤ/8)C2semidirect
2. C3×#5830C2semidirect
3. C3×#5798C2semidirect
4. C22×C3×#213C2semidirect
5. C3×#5233C2semidirect
6. C3×#5165C2semidirect
7. C3×#5150C2semidirect
8. C3×#5131C2semidirect
9. C3×#5119C2semidirect
11. #83934C3direct (N × H)
16. C2×C32×SD16C22semidirect
17. C2×C32×D8C22semidirect
20. C3×#947C22semidirect
21. C3×#940C22semidirect
24. C3×D4×Dic3C22semidirect
31. C3×#835C22semidirect
32. C3×#832C22semidirect
33. C3×#821C22semidirect
34. C3×Dic3⋊C8C22semidirect
36. C2×C3×AGL(1,ℤ/8)D3semidirect
37. C2×C3×AGL(1,ℤ/8)C2×C3semidirect
41. #5830C2×C3semidirect
42. #5798C2×C3semidirect
43. C22×#213C2×C3semidirect
49. #5233C2×C3semidirect
50. #5165C2×C3semidirect
51. #5150C2×C3semidirect
52. #5131C2×C3semidirect
53. #5119C2×C3semidirect
62. C2×C32×D4D4semidirect
101. C2×C3×SD16C2×D3semidirect
102. C2×C3×SD16C22×C3semidirect
106. C2×C3×D8C2×D3semidirect
107. C2×C3×D8C22×C3semidirect
122. #947C22×C3semidirect
123. #940C22×C3semidirect
126. D4×Dic3C22×C3semidirect
137. #835C22×C3semidirect
138. #832C22×C3semidirect
139. #821C22×C3semidirect
140. Dic3⋊C8C22×C3semidirect
172. C2×AGL(1,ℤ/8)C3×D3semidirect
212. C2×C3×D4#67semidirect
213. C2×C3×D4C3×D4semidirect
286. C2×SD16C2×C3×D3semidirect
289. C2×D8C2×C3×D3semidirect
406. C2×D4C3×#67semidirect
473. C32#3041semidirect
540. C3#83934direct (N × H)
541. C3C3×#3041semidirect

Maximal subgroups

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

subgroupindex
C2×C32×AGL(1,ℤ/8)2
C3×#58302
C3×#57982
C22×C3×#2132
C3×#52332
C3×#51652
C3×#51502
C3×#51312
C3×#51192
C3×#30413
#839343