Finite Group Databasebeta

← C3×#78944 #11866168

Subgroups — C3×#78944 #11866168

Order 1152.

1147 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5805C211yesmaximal, characteristic, complemented
2C22×C3×#213C211yesmaximal, characteristic, complemented
3C2×C3×#908C211yesmaximal, characteristic, complemented
4C3×#5521C211yesmaximal, characteristic, complemented
5C32×#418C211yesmaximal, characteristic, complemented
6C3×#5119C211yesmaximal, characteristic, complemented
7C3×#5002C211yesmaximal, characteristic, complemented
8C3×#4787C214yesmaximal, complemented
9C3×#4786C214yesmaximal, complemented
10C3×#3041—31nomaximal
11#78944C311yesmaximal, characteristic, direct product factor
12C22×C32×D4C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16C32×#117C2211yescharacteristic
17C3×#953—22no—
18C3×#940C2212yescomplemented
19C3×#938—22no—
20C3×#936C2212yescomplemented
21C2×C3×#213—24no—
22C2×C3×#213C2214yes—
23C3×#926C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C3×#908—24no—
26C2×C3×D24C2212yescomplemented
27C2×C3×#204C2212yescomplemented
28C3×#893C2214yescomplemented
29C3×D3×C22⋊C4—22no—
30C3×C4×D12—22no—
31C32×#102C2214yescomplemented
32C3×Dic3⋊C8C2214yescomplemented
33C3×#810C2212yescomplemented
34C3×#809C2212yescomplemented
35C2×C3×AGL(1,ℤ/8)—31no—
36C22×C3×D8—31no—
37C3×#535—31no—
38C3×#518—31no—
39#5805C2×C311yescharacteristic, complemented
40C22×#213C2×C311yescharacteristic, complemented
41C2×#908C2×C311yescharacteristic, complemented
42#5521C2×C311yescharacteristic, complemented
43C3×#463—34no—
44C3×#459—34no—
45C3×#424—31no—
46C3×#418—21no—
47C3×#418D311yescharacteristic, complemented
48C3×#418C2×C311yescharacteristic, complemented
49C3×#416—31no—
50#5119C2×C311yescharacteristic, complemented
51#5002C2×C311yescharacteristic, complemented
52#4787C2×C314yescomplemented
53#4786C2×C314yescomplemented
54C24×C32—21no—
55C23×C3×D3—21no—
56C2×C32×D4—22no—
57C2×C32×D4—21no—
58C2×C32×D4—22no—
59C2×C32×D4C2312yes—
60C22×C32×C4C2311yescharacteristic
61C2×C3×#67—21no—
62C2×C3×#67—24no—
63C3×#235—22no—
64C3×#235—22no—
65C2×C3×D12—21no—
66C2×C3×D12—22no—
67C2×C3×D12D414yescomplemented
68C2×C3×D12C2311yescharacteristic
69C2×C3×D12C2312yes—
70C2×C3×C4×D3—21no—
71C2×C3×C4×D3—24no—
72C2×C3×Dic6C2311yescharacteristic
73C32×M16—22no—
74C2×C32×C8C2312yes—
75C32×C4⋊C4C2312yes—
76C32×C22⋊C4—21no—
77C32×C42—21no—
78C3×#217—24no—
79C3×#217D412yes—
80C3×#213—28no—
81C3×(C2×D3)⋊C4—24no—
82C3×C4⋊Dic3D412yes—
83C3×C4×Dic3C2312yes—
84C2×C3×C3⋊C8—22no—
85C2×C3×C3⋊C8C2312yes—
86C3×D24—24no—
87C3×#204—24no—
88#3041—31noSylow
89C2×C3×#41—31no—
90C22×C3×D4—21no—
91C22×C3×D4—31no—
92C22×C3×D4C2×D311yescharacteristic
93C22×C3×D4C22×C311yescharacteristic
94C2×#235C22×C311yescharacteristic
95C22×D12C22×C311yescharacteristic
96C3×AGL(1,ℤ/8)—64no—
97C2×C3×SD16—32no—
98C2×C3×D8—34no—
99C2×C3×D8—32no—
100C2×C3×D8—64no—
101C2×C3×M16—21no—
102C2×C3×M16C2×D311yescharacteristic
103C2×C3×M16C22×C311yescharacteristic
104C22×C3×C8—31no—
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#953—22no—
117#940C22×C312yescomplemented
118#938—22no—
119#936C22×C312yescomplemented
120C2×#213—24no—
121C2×#213C22×C314yes—
122#926C22×C311yescharacteristic
123C22×C3⋊C8C22×C311yescharacteristic
124#908—24no—
125C2×D24C22×C312yescomplemented
126C2×#204C22×C312yescomplemented
127#893C22×C314yescomplemented
128D3×C22⋊C4—22no—
129C4×D12—22no—
130C3×C4⋊C8—34no—
131C3×#103—32no—
132C3×#102—24no—
133C3×#102—32no—
134C3×#102C2×D314yescomplemented
135C3×#102C22×C314yescomplemented
136Dic3⋊C8C22×C314yescomplemented
137#810C22×C312yescomplemented
138#809C22×C312yescomplemented
139C23×C32—22no—
140C23×C32—42no—
141C23×C32—82no—
142C23×C32C2×D411yescharacteristic
143C22×C3×D3—22no—
144C22×C3×D3—24no—
145C22×C3×D3—21no—
146C22×C3×D3—82no—
147C32×D4—22no—
148C32×D4—22no—
149C32×D4—42no—
150C2×C32×C4—22no—
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D412yes—
153C2×C32×C4#4112yes—
154C2×C32×C4C2411yescharacteristic
155C3×#67—42no—
156C3×#67—84no—
157C2×C3×Dic3—21no—
158C2×C3×Dic3C2×D414yes—
159C3×D12—24no—
160C3×D12—21no—
161C3×D12—22no—
162C3×D12—21no—
163C3×D12C2×D414yes—
164C3×C4×D3—42no—
165C3×C4×D3—84no—
166C3×Dic6—21no—
167C3×Dic6—21no—
168C32×C8—22no—
169C3×C3⋊C8—22no—
170C2×AGL(1,ℤ/8)—31no—
171C22×D8—31no—
172#535—31no—
173#518—31no—
174#463—34no—
175#459—34no—
176#424—31no—
177#418C3×D311yescharacteristic, complemented
178#416—31no—
179C24×C3—21no—
180C24×C3—21no—
181C24×C3—41no—
182C24×C3—61no—
183C23×D3—21no—
184C3×#41—62no—
185C3×#41—62no—
186C2×C3×Q8—31no—
187C2×C3×D4—24no—
188C2×C3×D4—22no—
189C2×C3×D4—22no—
190C2×C3×D4—21no—
191C2×C3×D4—22no—
192C2×C3×D4—21no—
193C2×C3×D4—22no—
194C2×C3×D4—22no—
195C2×C3×D4—34no—
196C2×C3×D4—32no—
197C2×C3×D4—31no—
198C2×C3×D4—42no—
199C2×C3×D4—41no—
200C2×C3×D4—64no—
201C2×C3×D4—61no—
202C2×C3×D4—62no—
203C2×C3×D4—61no—
204C2×C3×D4C22×D312yes—
205C2×C3×D4C23×C312yes—
206C22×C3×C4—21no—
207C22×C3×C4—64no—
208C22×C3×C4—61no—
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C23×C311yescharacteristic
211C2×#67—21no—
212C2×#67—24no—
213#235—22no—
214#235—22no—
215C2×D12—21no—
216C2×D12—22no—
217C2×D12C3×D414yescomplemented
218C2×D12C23×C311yescharacteristic
219C2×D12C23×C312yes—
220C2×C4×D3—21no—
221C2×C4×D3—24no—
222C2×Dic6C23×C311yescharacteristic
223C3×SD16—64no—
224C3×D8—64no—
225C3×D8—68no—
226C3×M16—22no—
227C3×M16—22no—
228C3×M16—42no—
229C2×C3×C8—22no—
230C2×C3×C8—32no—
231C2×C3×C8—62no—
232C2×C3×C8C22×D312yes—
233C2×C3×C8C23×C312yes—
234C3×C4⋊C4—22no—
235C3×C4⋊C4—32no—
236C3×C4⋊C4C22×D312yes—
237C3×C4⋊C4C23×C312yes—
238C3×C22⋊C4—21no—
239C3×C22⋊C4—21no—
240C3×C22⋊C4—32no—
241C3×C22⋊C4—41no—
242C3×C22⋊C4—64no—
243C3×C22⋊C4—64no—
244C3×C42—21no—
245C3×C42—21no—
246C3×C42—32no—
247C3×C42—41no—
248#217—24no—
249#217C3×D412yes—
250#213—28no—
251(C2×D3)⋊C4—24no—
252C4⋊Dic3C3×D412yes—
253C4×Dic3C23×C312yes—
254C2×C3⋊C8—22no—
255C2×C3⋊C8C23×C312yes—
256D24—24no—
257#204—24no—
258C22×C32—22no—
259C22×C32—42no—
260C22×C32—44no—
261C22×C32—84no—
262C22×C32#12112yes—
263C22×C32C22×D411yescharacteristic
264C2×C3×D3—24no—
265C2×C3×D3—44no—
266C2×C3×D3—41no—
267C2×C3×D3—42no—
268C2×C3×D3—84no—
269C32×C4—42no—
270C32×C4#12112yes—
271C32×C4C22×D411yescharacteristic
272C32×C4C2×#4111yescharacteristic
273C3×Dic3—24no—
274C3×Dic3—41no—
275C2×#41—31no—
276C22×D4—31no—
277C22×D4C2×C3×D311yescharacteristic
278AGL(1,ℤ/8)—64no—
279C2×SD16—32no—
280C2×D8—34no—
281C2×D8—32no—
282C2×D8—64no—
283C2×M16C2×C3×D311yescharacteristic
284C22×C8—31no—
285#127—32no—
286#124—32no—
287#121—62no—
288#120—62no—
289C4×D4—34no—
290C4×D4—62no—
291#117—31no—
292#117C2×C3×D311yescharacteristic
293C2×C22⋊C4—62no—
294C4⋊C8—34no—
295#103—32no—
296#102—32no—
297#102C2×C3×D314yescomplemented
298C23×C3—22no—
299C23×C3—22no—
300C23×C3—21no—
301C23×C3—42no—
302C23×C3—44no—
303C23×C3—42no—
304C23×C3—42no—
305C23×C3—62no—
306C23×C3—64no—
307C23×C3—61no—
308C23×C3—82no—
309C23×C3—82no—
310C23×C3—84no—
311C23×C3—242no—
312C23×C3D3×D411yescharacteristic
313C23×C3C2×C3×D411yescharacteristic
314C22×D3—22no—
315C22×D3—24no—
316C22×D3—21no—
317C22×D3—82no—
318C3×Q8—61no—
319C3×Q8—61no—
320C3×D4—24no—
321C3×D4—22no—
322C3×D4—22no—
323C3×D4—22no—
324C3×D4—22no—
325C3×D4—34no—
326C3×D4—42no—
327C3×D4—44no—
328C3×D4—42no—
329C3×D4—42no—
330C3×D4—64no—
331C3×D4—62no—
332C3×D4—61no—
333C3×D4—61no—
334C3×D4—122no—
335C3×D4—244no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—21no—
339C2×C3×C4—22no—
340C2×C3×C4—21no—
341C2×C3×C4—22no—
342C2×C3×C4—34no—
343C2×C3×C4—42no—
344C2×C3×C4—61no—
345C2×C3×C4—122no—
346C2×C3×C4—244no—
347C2×C3×C4#23512yes—
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4D3×D412yes—
350C2×C3×C4C2×C3×D411yescharacteristic
351C2×C3×C4C2×C3×D412yes—
352C2×C3×C4C3×#4112yes—
353C2×C3×C4C23×D311yescharacteristic
354C2×C3×C4C24×C311yescharacteristic
355#67—42no—
356#67—84no—
357C2×Dic3—21no—
358C2×Dic3C2×C3×D414yes—
359D12—24no—
360D12—21no—
361D12—22no—
362D12—21no—
363D12C2×C3×D414yes—
364C4×D3—42no—
365C4×D3—84no—
366Dic6—21no—
367Dic6—21no—
368C3×C8—22no—
369C3×C8—22no—
370C3×C8—42no—
371C3×C8—62no—
372C3⋊C8—22no—
373C2×C32—22no—
374C2×C32—82no—
375C2×C32C2×#12111yescharacteristic
376C2×C32#57612yes—
377C3×D3—44no—
378C3×D3—81no—
379C24—21no—
380C24—61no—
381#41—62no—
382#41—62no—
383C2×Q8—31no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—21no—
387C2×D4—32no—
388C2×D4—31no—
389C2×D4—34no—
390C2×D4—64no—
391C2×D4—61no—
392C2×D4—62no—
393C2×D4—61no—
394C2×D4C22×C3×D312yes—
395C22×C4—64no—
396C22×C4—61no—
397C22×C4C22×C3×D311yescharacteristic
398SD16—64no—
399D8—64no—
400D8—68no—
401M16—22no—
402C2×C8—32no—
403C2×C8—62no—
404C2×C8C22×C3×D312yes—
405C4⋊C4—32no—
406C4⋊C4C22×C3×D312yes—
407C22⋊C4—21no—
408C22⋊C4—32no—
409C22⋊C4—64no—
410C22⋊C4—64no—
411C42—21no—
412C42—32no—
413C22×C3—22no—
414C22×C3—22no—
415C22×C3—22no—
416C22×C3—21no—
417C22×C3—42no—
418C22×C3—44no—
419C22×C3—44no—
420C22×C3—42no—
421C22×C3—44no—
422C22×C3—42no—
423C22×C3—64no—
424C22×C3—84no—
425C22×C3—84no—
426C22×C3—84no—
427C22×C3—88no—
428C22×C3—124no—
429C22×C3—121no—
430C22×C3—122no—
431C22×C3—244no—
432C22×C3#88412yes—
433C22×C3C3×#12112yes—
434C22×C3C2×D3×D411yescharacteristic
435C22×C3C22×C3×D411yescharacteristic
436C2×D3—24no—
437C2×D3—44no—
438C2×D3—42no—
439C2×D3—41no—
440C2×D3—84no—
441C3×C4—22no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—42no—
445C3×C4—42no—
446C3×C4—64no—
447C3×C4—82no—
448C3×C4—121no—
449C3×C4#88412yes—
450C3×C4C3×#12112yes—
451C3×C4C2×#23511yescharacteristic
452C3×C4C2×D3×D411yescharacteristic
453C3×C4C22×C3×D411yescharacteristic
454C3×C4C2×C3×#4111yescharacteristic
455Dic3—24no—
456Dic3—41no—
457C32#304111yescharacteristic, complemented, Sylow
458C23—22no—
459C23—42no—
460C23—62no—
461C23—64no—
462C23—61no—
463C23—82no—
464C23—242no—
465C23C3×D3×D411yescharacteristic
466Q8—61no—
467Q8—61no—
468D4—22no—
469D4—22no—
470D4—34no—
471D4—42no—
472D4—64no—
473D4—62no—
474D4—61no—
475D4—61no—
476D4—122no—
477D4—244no—
478C2×C4—22no—
479C2×C4—34no—
480C2×C4—61no—
481C2×C4—122no—
482C2×C4—244no—
483C2×C4C3×#23512yes—
484C2×C4C3×D3×D411yescharacteristic
485C2×C4C3×D3×D412yes—
486C2×C4C23×C3×D311yescharacteristic
487C8—22no—
488C8—62no—
489C2×C3—22no—
490C2×C3—22no—
491C2×C3—21no—
492C2×C3—22no—
493C2×C3—42no—
494C2×C3—84no—
495C2×C3—82no—
496C2×C3—82no—
497C2×C3—124no—
498C2×C3—241no—
499C2×C3C2×#88411yescharacteristic
500C2×C3#577412yes—
501C2×C3C2×C3×#12111yescharacteristic
502C2×C3C3×#57612yes—
503D3—44no—
504D3—81no—
505C22—22no—
506C22—42no—
507C22—44no—
508C22—64no—
509C22—84no—
510C22—124no—
511C22—121no—
512C22—122no—
513C22—244no—
514C22C3×#88412yes—
515C22C2×C3×D3×D411yescharacteristic
516C4—42no—
517C4—64no—
518C4—121no—
519C4C3×#88412yes—
520C4C2×C3×#23511yescharacteristic
521C4C2×C3×D3×D411yescharacteristic
522C3—21no—
523C3#7894411yescharacteristic, direct product factor
524C3C3×#304111yescharacteristic, complemented
525C2—22no—
526C2—82no—
527C2—124no—
528C2—241no—
529C2C2×C3×#88411yescharacteristic
530C2C3×#577412yes—
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#418C2
socleC22×C32C22×D4
hypercenterC3×#418D3
hypocenterC3C3×#3041
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#418

Complements

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

NH ≅ G/Ntype
1. C3×#5805C2semidirect
2. C22×C3×#213C2semidirect
3. C2×C3×#908C2semidirect
4. C3×#5521C2semidirect
5. C32×#418C2semidirect
6. C3×#5119C2semidirect
7. C3×#5002C2semidirect
8. C3×#4787C2semidirect
9. C3×#4786C2semidirect
11. #78944C3direct (N × H)
18. C3×#940C22semidirect
20. C3×#936C22semidirect
26. C2×C3×D24C22semidirect
27. C2×C3×#204C22semidirect
28. C3×#893C22semidirect
31. C32×#102C22semidirect
32. C3×Dic3⋊C8C22semidirect
33. C3×#810C22semidirect
34. C3×#809C22semidirect
39. #5805C2×C3semidirect
40. C22×#213C2×C3semidirect
41. C2×#908C2×C3semidirect
42. #5521C2×C3semidirect
47. C3×#418D3semidirect
48. C3×#418C2×C3semidirect
50. #5119C2×C3semidirect
51. #5002C2×C3semidirect
52. #4787C2×C3semidirect
53. #4786C2×C3semidirect
67. C2×C3×D12D4semidirect
117. #940C22×C3semidirect
119. #936C22×C3semidirect
125. C2×D24C22×C3semidirect
126. C2×#204C22×C3semidirect
127. #893C22×C3semidirect
134. C3×#102C2×D3semidirect
135. C3×#102C22×C3semidirect
136. Dic3⋊C8C22×C3semidirect
137. #810C22×C3semidirect
138. #809C22×C3semidirect
177. #418C3×D3semidirect
217. C2×D12C3×D4semidirect
297. #102C2×C3×D3semidirect
457. C32#3041semidirect
523. C3#78944direct (N × H)
524. C3C3×#3041semidirect

Maximal subgroups

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

subgroupindex
C3×#58052
C22×C3×#2132
C2×C3×#9082
C3×#55212
C32×#4182
C3×#51192
C3×#50022
C3×#47872
C3×#47862
C3×#30413
#789443