Finite Group Databasebeta

← C3×#78862 #11866180

Subgroups — C3×#78862 #11866180

Order 1152.

1131 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5830C211yesmaximal, characteristic, complemented
2C2×C3×#949C211yesmaximal, characteristic, complemented
3C22×C3×D24C211yesmaximal, characteristic, complemented
4C3×#5521C211yesmaximal, characteristic, complemented
5C32×#416C211yesmaximal, characteristic, complemented
6C3×#5102C211yesmaximal, characteristic, complemented
7C3×#5001C211yesmaximal, characteristic, complemented
8C3×#4819C214yesmaximal, complemented
9C3×#4786C214yesmaximal, complemented
10C3×#3041—31nomaximal
11#78862C311yesmaximal, characteristic, direct product factor
12C2×C32×#41C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C22×C32×C8C2211yescharacteristic
16C32×#117C2211yescharacteristic
17C3×#949—24no—
18C3×#947C2212yescomplemented
19C2×C3×#215C2212yescomplemented
20C3×#940C2212yescomplemented
21C3×#937—22no—
22C2×C3×#213C2212yescomplemented
23C3×#930—22no—
24C3×#926C2211yescharacteristic
25C2×C3×#208C2211yescharacteristic
26C2×C3×D24—24no—
27C2×C3×D24C2214yes—
28C3×#893C2214yescomplemented
29C3×D3×C22⋊C4—22no—
30C3×C4×D12—22no—
31C32×#103C2212yescomplemented
32C32×#102C2212yescomplemented
33C3×Dic3⋊C8C2214yescomplemented
34C3×#809C2214yescomplemented
35C2×C3×AGL(1,ℤ/8)—31no—
36C22×C3×D8—31no—
37C3×#535—31no—
38C3×#518—31no—
39#5830C2×C311yescharacteristic, complemented
40C2×#949C2×C311yescharacteristic, complemented
41C22×D24C2×C311yescharacteristic, complemented
42#5521C2×C311yescharacteristic, complemented
43C3×#463—34no—
44C3×#459—34no—
45C3×#424—31no—
46C3×#418—31no—
47C3×#416—21no—
48C3×#416D311yescharacteristic, complemented
49C3×#416C2×C311yescharacteristic, complemented
50#5102C2×C311yescharacteristic, complemented
51#5001C2×C311yescharacteristic, complemented
52#4819C2×C314yescomplemented
53#4786C2×C314yescomplemented
54C23×C3×D3—21no—
55C23×C3×D3—21no—
56C32×#41—22no—
57C32×#41—22no—
58C2×C32×Q8C2311yescharacteristic
59C2×C32×D4—21no—
60C2×C32×D4C2311yescharacteristic
61C22×C32×C4—21no—
62C22×C32×C4C2311yescharacteristic
63C2×C3×#67—24no—
64C2×C3×D12—21no—
65C2×C3×D12—22no—
66C2×C3×D12—22no—
67C2×C3×D12—22no—
68C2×C3×D12—21no—
69C2×C3×D12D414yescomplemented
70C2×C3×D12C2312yes—
71C2×C3×D12C2312yes—
72C2×C3×C4×D3—24no—
73C2×C32×C8—22no—
74C2×C32×C8C2312yes—
75C32×C4⋊C4C2312yes—
76C32×C22⋊C4—21no—
77C32×C42—21no—
78C3×#217D412yes—
79C3×#215—24no—
80C3×#213—24no—
81C3×(C2×D3)⋊C4—24no—
82C3×(C2×D3)⋊C4—24no—
83C3×C4⋊Dic3D412yes—
84C3×C4×Dic3C2312yes—
85C3×#208—22no—
86C2×C3×C3⋊C8C2312yes—
87C3×D24—28no—
88#3041—31noSylow
89C2×C3×#41—21no—
90C2×C3×#41C2×D311yescharacteristic
91C2×C3×#41C22×C311yescharacteristic
92C22×C3×D4—31no—
93C22×C3×D4—31no—
94C22×D12C22×C311yescharacteristic
95C22×D12C22×C311yescharacteristic
96C3×AGL(1,ℤ/8)—64no—
97C2×C3×SD16—32no—
98C2×C3×D8—32no—
99C2×C3×D8—34no—
100C2×C3×D8—64no—
101C2×C3×M16—31no—
102C22×C3×C8—21no—
103C22×C3×C8C2×D311yescharacteristic
104C22×C3×C8C22×C311yescharacteristic
105C3×#127—32no—
106C3×#124—32no—
107C3×#121—62no—
108C3×#120—62no—
109C3×C4×D4—34no—
110C3×C4×D4—62no—
111C3×#117—21no—
112C3×#117—31no—
113C3×#117C2×D311yescharacteristic
114C3×#117C22×C311yescharacteristic
115C2×C3×C22⋊C4—62no—
116#949—24no—
117#947C22×C312yescomplemented
118C2×#215C22×C312yescomplemented
119#940C22×C312yescomplemented
120#937—22no—
121C2×#213C22×C312yescomplemented
122#930—22no—
123#926C22×C311yescharacteristic
124C2×#208C22×C311yescharacteristic
125C2×D24—24no—
126C2×D24C22×C314yes—
127#893C22×C314yescomplemented
128D3×C22⋊C4—22no—
129C4×D12—22no—
130C3×C4⋊C8—34no—
131C3×#103—22no—
132C3×#103C2×D312yescomplemented
133C3×#103C22×C312yescomplemented
134C3×#102—22no—
135C3×#102—34no—
136C3×#102C2×D312yescomplemented
137C3×#102C22×C312yescomplemented
138Dic3⋊C8C22×C314yescomplemented
139#809C22×C314yescomplemented
140C23×C32—21no—
141C23×C32C2×D411yescharacteristic
142C22×C3×D3—22no—
143C22×C3×D3—24no—
144C22×C3×D3—22no—
145C22×C3×D3—42no—
146C22×C3×D3—82no—
147C22×C3×D3—82no—
148C32×Q8—21no—
149C32×Q8—21no—
150C32×D4—21no—
151C32×D4—21no—
152C32×D4—42no—
153C2×C32×C4—21no—
154C2×C32×C4—22no—
155C2×C32×C4—42no—
156C2×C32×C4C2×D411yescharacteristic
157C2×C32×C4C2×D412yes—
158C2×C32×C4#4112yes—
159C2×C32×C4C2411yescharacteristic
160C3×#67—84no—
161C2×C3×Dic3C2×D414yes—
162C3×D12—24no—
163C3×D12—22no—
164C3×D12—22no—
165C3×D12—22no—
166C3×D12—42no—
167C3×D12C2×D414yes—
168C3×C4×D3—84no—
169C32×C8—22no—
170C3×C3⋊C8—22no—
171C2×AGL(1,ℤ/8)—31no—
172C22×D8—31no—
173#535—31no—
174#518—31no—
175#463—34no—
176#459—34no—
177#424—31no—
178#418—31no—
179#416C3×D311yescharacteristic, complemented
180C24×C3—61no—
181C24×C3—61no—
182C23×D3—21no—
183C23×D3—21no—
184C3×#41—24no—
185C3×#41—22no—
186C3×#41—22no—
187C3×#41—22no—
188C3×#41—22no—
189C3×#41—42no—
190C2×C3×Q8—21no—
191C2×C3×Q8C22×D311yescharacteristic
192C2×C3×Q8C23×C311yescharacteristic
193C2×C3×D4—21no—
194C2×C3×D4—21no—
195C2×C3×D4—21no—
196C2×C3×D4—34no—
197C2×C3×D4—32no—
198C2×C3×D4—32no—
199C2×C3×D4—41no—
200C2×C3×D4—64no—
201C2×C3×D4—62no—
202C2×C3×D4—62no—
203C2×C3×D4—61no—
204C2×C3×D4—62no—
205C2×C3×D4—61no—
206C2×C3×D4C22×D311yescharacteristic
207C2×C3×D4C23×C311yescharacteristic
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—41no—
212C22×C3×C4—64no—
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C23×C311yescharacteristic
215C2×#67—24no—
216C2×D12—21no—
217C2×D12—22no—
218C2×D12—22no—
219C2×D12—22no—
220C2×D12—21no—
221C2×D12C3×D414yescomplemented
222C2×D12C23×C312yes—
223C2×D12C23×C312yes—
224C2×C4×D3—24no—
225C3×SD16—64no—
226C3×D8—68no—
227C3×D8—64no—
228C3×M16—62no—
229C2×C3×C8—22no—
230C2×C3×C8—22no—
231C2×C3×C8—22no—
232C2×C3×C8—32no—
233C2×C3×C8—42no—
234C2×C3×C8C22×D312yes—
235C2×C3×C8C23×C312yes—
236C3×C4⋊C4—22no—
237C3×C4⋊C4—32no—
238C3×C4⋊C4C22×D312yes—
239C3×C4⋊C4C23×C312yes—
240C3×C22⋊C4—21no—
241C3×C22⋊C4—21no—
242C3×C22⋊C4—32no—
243C3×C22⋊C4—41no—
244C3×C22⋊C4—64no—
245C3×C22⋊C4—64no—
246C3×C42—21no—
247C3×C42—21no—
248C3×C42—32no—
249C3×C42—41no—
250#217C3×D412yes—
251#215—24no—
252#213—24no—
253(C2×D3)⋊C4—24no—
254(C2×D3)⋊C4—24no—
255C4⋊Dic3C3×D412yes—
256C4×Dic3C23×C312yes—
257#208—22no—
258C2×C3⋊C8C23×C312yes—
259D24—28no—
260C22×C32—22no—
261C22×C32—41no—
262C22×C32—42no—
263C22×C32#12112yes—
264C22×C32C22×D411yescharacteristic
265C2×C3×D3—24no—
266C2×C3×D3—44no—
267C2×C3×D3—42no—
268C2×C3×D3—44no—
269C2×C3×D3—84no—
270C2×C3×D3—84no—
271C32×C4—41no—
272C32×C4—42no—
273C32×C4#12112yes—
274C32×C4C22×D411yescharacteristic
275C32×C4C2×#4111yescharacteristic
276C3×Dic3—24no—
277C2×#41C2×C3×D311yescharacteristic
278C22×D4—31no—
279C22×D4—31no—
280AGL(1,ℤ/8)—64no—
281C2×SD16—32no—
282C2×D8—32no—
283C2×D8—34no—
284C2×D8—64no—
285C2×M16—31no—
286C22×C8C2×C3×D311yescharacteristic
287#127—32no—
288#124—32no—
289#121—62no—
290#120—62no—
291C4×D4—34no—
292C4×D4—62no—
293#117—31no—
294#117C2×C3×D311yescharacteristic
295C2×C22⋊C4—62no—
296C4⋊C8—34no—
297#103C2×C3×D312yescomplemented
298#102—34no—
299#102C2×C3×D312yescomplemented
300C23×C3—21no—
301C23×C3—21no—
302C23×C3—21no—
303C23×C3—41no—
304C23×C3—62no—
305C23×C3—64no—
306C23×C3—62no—
307C23×C3—122no—
308C23×C3—242no—
309C23×C3—242no—
310C23×C3D3×D411yescharacteristic
311C23×C3C2×C3×D411yescharacteristic
312C22×D3—22no—
313C22×D3—24no—
314C22×D3—22no—
315C22×D3—42no—
316C22×D3—82no—
317C22×D3—82no—
318C3×Q8—22no—
319C3×Q8—21no—
320C3×Q8—21no—
321C3×Q8—21no—
322C3×Q8—21no—
323C3×Q8—41no—
324C3×D4—22no—
325C3×D4—21no—
326C3×D4—21no—
327C3×D4—21no—
328C3×D4—21no—
329C3×D4—34no—
330C3×D4—41no—
331C3×D4—44no—
332C3×D4—42no—
333C3×D4—42no—
334C3×D4—64no—
335C3×D4—62no—
336C3×D4—62no—
337C3×D4—62no—
338C3×D4—122no—
339C3×D4—244no—
340C2×C3×C4—22no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—22no—
344C2×C3×C4—21no—
345C2×C3×C4—22no—
346C2×C3×C4—21no—
347C2×C3×C4—22no—
348C2×C3×C4—34no—
349C2×C3×C4—41no—
350C2×C3×C4—42no—
351C2×C3×C4—44no—
352C2×C3×C4—42no—
353C2×C3×C4—42no—
354C2×C3×C4—244no—
355C2×C3×C4#23512yes—
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D412yes—
358C2×C3×C4C2×C3×D411yescharacteristic
359C2×C3×C4C2×C3×D412yes—
360C2×C3×C4C3×#4112yes—
361C2×C3×C4C23×D311yescharacteristic
362C2×C3×C4C24×C311yescharacteristic
363#67—84no—
364C2×Dic3C2×C3×D414yes—
365D12—24no—
366D12—22no—
367D12—22no—
368D12—22no—
369D12—42no—
370D12C2×C3×D414yes—
371C4×D3—84no—
372C3×C8—22no—
373C3×C8—22no—
374C3×C8—42no—
375C3×C8—62no—
376C3⋊C8—22no—
377C2×C32—22no—
378C2×C32—81no—
379C2×C32C2×#12111yescharacteristic
380C2×C32#57612yes—
381C3×D3—44no—
382C3×D3—82no—
383C24—61no—
384C24—61no—
385#41—22no—
386#41—22no—
387C2×Q8C22×C3×D311yescharacteristic
388C2×D4—21no—
389C2×D4—32no—
390C2×D4—32no—
391C2×D4—34no—
392C2×D4—64no—
393C2×D4—62no—
394C2×D4—62no—
395C2×D4—61no—
396C2×D4—62no—
397C2×D4—61no—
398C2×D4C22×C3×D311yescharacteristic
399C22×C4—21no—
400C22×C4—64no—
401C22×C4C22×C3×D311yescharacteristic
402SD16—64no—
403D8—68no—
404D8—64no—
405M16—62no—
406C2×C8—22no—
407C2×C8—32no—
408C2×C8C22×C3×D312yes—
409C4⋊C4—32no—
410C4⋊C4C22×C3×D312yes—
411C22⋊C4—21no—
412C22⋊C4—32no—
413C22⋊C4—64no—
414C22⋊C4—64no—
415C42—21no—
416C42—32no—
417C22×C3—22no—
418C22×C3—22no—
419C22×C3—22no—
420C22×C3—21no—
421C22×C3—42no—
422C22×C3—42no—
423C22×C3—42no—
424C22×C3—41no—
425C22×C3—42no—
426C22×C3—41no—
427C22×C3—64no—
428C22×C3—82no—
429C22×C3—124no—
430C22×C3—122no—
431C22×C3—124no—
432C22×C3—244no—
433C22×C3—244no—
434C22×C3#88412yes—
435C22×C3C3×#12112yes—
436C22×C3C2×D3×D411yescharacteristic
437C22×C3C22×C3×D411yescharacteristic
438C2×D3—24no—
439C2×D3—44no—
440C2×D3—44no—
441C2×D3—42no—
442C2×D3—84no—
443C2×D3—84no—
444C3×C4—22no—
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—42no—
448C3×C4—42no—
449C3×C4—41no—
450C3×C4—42no—
451C3×C4—41no—
452C3×C4—64no—
453C3×C4—82no—
454C3×C4#88412yes—
455C3×C4C3×#12112yes—
456C3×C4C2×#23511yescharacteristic
457C3×C4C2×D3×D411yescharacteristic
458C3×C4C22×C3×D411yescharacteristic
459C3×C4C2×C3×#4111yescharacteristic
460Dic3—24no—
461C32#304111yescharacteristic, complemented, Sylow
462C23—21no—
463C23—62no—
464C23—64no—
465C23—62no—
466C23—122no—
467C23—242no—
468C23—242no—
469C23C3×D3×D411yescharacteristic
470Q8—21no—
471Q8—21no—
472D4—21no—
473D4—21no—
474D4—34no—
475D4—42no—
476D4—64no—
477D4—62no—
478D4—62no—
479D4—62no—
480D4—122no—
481D4—244no—
482C2×C4—22no—
483C2×C4—21no—
484C2×C4—34no—
485C2×C4—42no—
486C2×C4—244no—
487C2×C4C3×#23512yes—
488C2×C4C3×D3×D411yescharacteristic
489C2×C4C3×D3×D412yes—
490C2×C4C23×C3×D311yescharacteristic
491C8—22no—
492C8—62no—
493C2×C3—22no—
494C2×C3—22no—
495C2×C3—21no—
496C2×C3—22no—
497C2×C3—42no—
498C2×C3—82no—
499C2×C3—81no—
500C2×C3—81no—
501C2×C3—124no—
502C2×C3—242no—
503C2×C3C2×#88411yescharacteristic
504C2×C3#576912yes—
505C2×C3C2×C3×#12111yescharacteristic
506C2×C3C3×#57612yes—
507D3—44no—
508D3—82no—
509C22—22no—
510C22—41no—
511C22—42no—
512C22—64no—
513C22—124no—
514C22—122no—
515C22—124no—
516C22—244no—
517C22—244no—
518C22C3×#88412yes—
519C22C2×C3×D3×D411yescharacteristic
520C4—41no—
521C4—42no—
522C4—64no—
523C4C3×#88412yes—
524C4C2×C3×#23511yescharacteristic
525C4C2×C3×D3×D411yescharacteristic
526C3—21no—
527C3#7886211yescharacteristic, direct product factor
528C3C3×#304111yescharacteristic, complemented
529C2—22no—
530C2—81no—
531C2—124no—
532C2—242no—
533C2C2×C3×#88411yescharacteristic
534C2C3×#576912yes—
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#416C2
socleC22×C32C22×D4
hypercenterC3×#416D3
hypocenterC3C3×#3041
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#416

Complements

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

NH ≅ G/Ntype
1. C3×#5830C2semidirect
2. C2×C3×#949C2semidirect
3. C22×C3×D24C2semidirect
4. C3×#5521C2semidirect
5. C32×#416C2semidirect
6. C3×#5102C2semidirect
7. C3×#5001C2semidirect
8. C3×#4819C2semidirect
9. C3×#4786C2semidirect
11. #78862C3direct (N × H)
18. C3×#947C22semidirect
19. C2×C3×#215C22semidirect
20. C3×#940C22semidirect
22. C2×C3×#213C22semidirect
28. C3×#893C22semidirect
31. C32×#103C22semidirect
32. C32×#102C22semidirect
33. C3×Dic3⋊C8C22semidirect
34. C3×#809C22semidirect
39. #5830C2×C3semidirect
40. C2×#949C2×C3semidirect
41. C22×D24C2×C3semidirect
42. #5521C2×C3semidirect
48. C3×#416D3semidirect
49. C3×#416C2×C3semidirect
50. #5102C2×C3semidirect
51. #5001C2×C3semidirect
52. #4819C2×C3semidirect
53. #4786C2×C3semidirect
69. C2×C3×D12D4semidirect
117. #947C22×C3semidirect
118. C2×#215C22×C3semidirect
119. #940C22×C3semidirect
121. C2×#213C22×C3semidirect
127. #893C22×C3semidirect
132. C3×#103C2×D3semidirect
133. C3×#103C22×C3semidirect
136. C3×#102C2×D3semidirect
137. C3×#102C22×C3semidirect
138. Dic3⋊C8C22×C3semidirect
139. #809C22×C3semidirect
179. #416C3×D3semidirect
221. C2×D12C3×D4semidirect
297. #103C2×C3×D3semidirect
299. #102C2×C3×D3semidirect
461. C32#3041semidirect
527. C3#78862direct (N × H)
528. C3C3×#3041semidirect

Maximal subgroups

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

subgroupindex
C3×#58302
C2×C3×#9492
C22×C3×D242
C3×#55212
C32×#4162
C3×#51022
C3×#50012
C3×#48192
C3×#47862
C3×#30413
#788623