Finite Group Databasebeta

← C3×#81560 #11876973

Subgroups — C3×#81560 #11876973

Order 1152.

951 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5725C211yesmaximal, characteristic, complemented
2C3×#5716C211yesmaximal, characteristic, complemented
3C32×#486C211yesmaximal, characteristic, complemented
4C3×#5080C211yesmaximal, characteristic, complemented
5C3×#5073C211yesmaximal, characteristic, complemented
6C3×#4785C214yesmaximal, complemented
7C3×#4782C214yesmaximal, complemented
8C3×#4694C211yesmaximal, characteristic, complemented
9C3×C4×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
10C3×#3184—31nomaximal
11#81560C311yesmaximal, characteristic, direct product factor
12C2×C3×#239—21no—
13C2×C3×#237—21no—
14C32×C4⋊Q8C2211yescharacteristic
15C32×#127C2211yescharacteristic
16C3×#947—21no—
17C3×#938—21no—
18C3×#938C2212yes—
19C3×#936—21no—
20C3×D4×Dic3—21no—
21C3×D4×Dic3C2212yes—
22C2×C3×#213C2214yes—
23C2×C3×ΓL(1,𝔽25)C2212yes—
24C3×#895—21no—
25C3×#895C2212yes—
26C3×#893—21no—
27C3×#893C2212yes—
28C3×#874C2211yescharacteristic
29C3×C42×D3C2211yescharacteristic
30C3×#869C2211yescharacteristic
31C32×#102C2214yes—
32C32×C4×C8C2211yescharacteristic
33C3×#821C2214yes—
34C3×#815C2212yes—
35C3×#808C2214yes—
36C3×C4×C3⋊C8C2211yescharacteristic
37C3×#532—31no—
38C3×#532—31no—
39#5725C2×C311yescharacteristic, complemented
40#5716C2×C311yescharacteristic, complemented
41C3×#498—31no—
42C3×#493—31no—
43C3×#486—21no—
44C3×#486—31no—
45C3×#486D311yescharacteristic, complemented
46C3×#486C2×C311yescharacteristic, complemented
47C3×#469—34no—
48C3×#442—34no—
49C3×C4×M16—31no—
50#5080C2×C311yescharacteristic, complemented
51#5073C2×C311yescharacteristic, complemented
52#4785C2×C314yescomplemented
53#4782C2×C314yescomplemented
54#4694C2×C311yescharacteristic, complemented
55C4×ΓL(1,𝔽25)C2×C311yescharacteristic, complemented
56C2×C32×Q8—21no—
57C2×C32×D4—21no—
58C2×C32×D4—21no—
59C2×C32×D4C2312yes—
60C2×C3×#67—22no—
61C22×C3×Dic3—22no—
62C3×#239—44no—
63C3×#237—44no—
64C2×C3×D12—22no—
65C2×C3×D12—21no—
66C2×C3×D12—21no—
67C2×C3×D12C2312yes—
68C2×C3×C4×D3—22no—
69C2×C3×C4×D3D411yescharacteristic
70C2×C3×C4×D3D411yescharacteristic
71C2×C3×C4×D3C2311yescharacteristic
72C2×C3×Dic6—21no—
73C2×C32×C8C2312yes—
74C32×C4⋊C4—21no—
75C32×C4⋊C4C2312yes—
76C32×C42C2311yescharacteristic
77C3×#217—22no—
78C3×#217—22no—
79C3×#213—28no—
80C3×(C2×D3)⋊C4—22no—
81C3×(C2×D3)⋊C4—22no—
82C3×C4⋊Dic3—21no—
83C3×C4⋊Dic3C2312yes—
84C3×C4×Dic3D411yescharacteristic
85C3×C4×Dic3D411yescharacteristic
86C3×C4×Dic3C2311yescharacteristic
87C2×C3×C3⋊C8C2312yes—
88C3×ΓL(1,𝔽25)—24no—
89#3184—31noSylow
90C2×C3×#41—61no—
91C2×C3×#41—61no—
92C2×#239—21no—
93C2×#237—21no—
94C2×C3×D8—34no—
95C2×C3×M16—32no—
96C3×C4⋊Q8—21no—
97C3×C4⋊Q8—31no—
98C3×C4⋊Q8C2×D311yescharacteristic
99C3×C4⋊Q8C22×C311yescharacteristic
100C3×#127—21no—
101C3×#127—31no—
102C3×#127C2×D311yescharacteristic
103C3×#127C22×C311yescharacteristic
104C3×#124—61no—
105C3×#124—61no—
106C3×#121—32no—
107C3×#121—32no—
108C3×#121—61no—
109C3×#121—61no—
110C3×C4×D4—32no—
111C3×C4×D4—32no—
112C3×C4×D4—61no—
113C3×C4×D4—61no—
114C2×C3×C42—31no—
115#947—21no—
116#938—21no—
117#938C22×C312yes—
118#936—21no—
119D4×Dic3—21no—
120D4×Dic3C22×C312yes—
121C2×#213C22×C314yes—
122C2×ΓL(1,𝔽25)C22×C312yes—
123#895—21no—
124#895C22×C312yes—
125#893—21no—
126#893C22×C312yes—
127#874C22×C311yescharacteristic
128C42×D3C22×C311yescharacteristic
129#869C22×C311yescharacteristic
130C3×#106—34no—
131C3×#102—24no—
132C3×#102—34no—
133C3×#102C2×D314yes—
134C3×#102C22×C314yes—
135C3×#97—32no—
136C3×C4×C8—21no—
137C3×C4×C8—31no—
138C3×C4×C8C2×D311yescharacteristic
139C3×C4×C8C22×C311yescharacteristic
140#821C22×C314yes—
141#815C22×C312yes—
142#808C22×C314yes—
143C4×C3⋊C8C22×C311yescharacteristic
144C23×C32—22no—
145C22×C3×D3—22no—
146C22×C3×D3C2×D411yescharacteristic
147C32×Q8—42no—
148C32×D4—24no—
149C32×D4—42no—
150C32×D4—42no—
151C2×C32×C4—22no—
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2411yescharacteristic
155C3×#67—44no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—44no—
158C2×C3×Dic3C2×D411yescharacteristic
159C2×C3×Dic3C2×D411yescharacteristic
160C2×C3×Dic3C2×D411yescharacteristic
161C3×D12—24no—
162C3×D12—44no—
163C3×D12—42no—
164C3×D12—42no—
165C3×C4×D3—22no—
166C3×C4×D3—22no—
167C3×C4×D3—22no—
168C3×C4×D3—44no—
169C3×Dic6—42no—
170C32×C8—22no—
171C3×C3⋊C8#4114yescomplemented
172#532—31no—
173#532—31no—
174#498—31no—
175#493—31no—
176#486—31no—
177#486C3×D311yescharacteristic, complemented
178#469—34no—
179#442—34no—
180C4×M16—31no—
181C3×#41—124no—
182C3×#41—124no—
183C2×C3×Q8—21no—
184C2×C3×Q8—21no—
185C2×C3×Q8—41no—
186C2×C3×Q8—61no—
187C2×C3×D4—21no—
188C2×C3×D4—21no—
189C2×C3×D4—21no—
190C2×C3×D4—21no—
191C2×C3×D4—22no—
192C2×C3×D4—32no—
193C2×C3×D4—41no—
194C2×C3×D4—41no—
195C2×C3×D4—62no—
196C2×C3×D4—62no—
197C2×C3×D4—61no—
198C2×C3×D4—61no—
199C2×C3×D4C22×D312yes—
200C2×C3×D4C23×C312yes—
201C22×C3×C4—31no—
202C22×C3×C4—31no—
203C22×C3×C4—31no—
204C22×C3×C4—62no—
205C22×C3×C4—62no—
206C2×#67—22no—
207C22×Dic3—22no—
208#239—44no—
209#237—44no—
210C2×D12—22no—
211C2×D12—21no—
212C2×D12—21no—
213C2×D12C23×C312yes—
214C2×C4×D3—22no—
215C2×C4×D3C3×D411yescharacteristic
216C2×C4×D3C3×D411yescharacteristic
217C2×C4×D3C23×C311yescharacteristic
218C2×Dic6—21no—
219C3×D8—68no—
220C3×M16—64no—
221C2×C3×C8—22no—
222C2×C3×C8—32no—
223C2×C3×C8C22×D312yes—
224C2×C3×C8C23×C312yes—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—22no—
228C3×C4⋊C4—32no—
229C3×C4⋊C4—41no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4C22×D312yes—
232C3×C4⋊C4C23×C312yes—
233C3×C22⋊C4—62no—
234C3×C22⋊C4—62no—
235C3×C22⋊C4—62no—
236C3×C22⋊C4—62no—
237C3×C42—21no—
238C3×C42—31no—
239C3×C42—31no—
240C3×C42—31no—
241C3×C42C22×D311yescharacteristic
242C3×C42C23×C311yescharacteristic
243#217—22no—
244#217—22no—
245#213—28no—
246(C2×D3)⋊C4—22no—
247(C2×D3)⋊C4—22no—
248C4⋊Dic3—21no—
249C4⋊Dic3C23×C312yes—
250C4×Dic3C3×D411yescharacteristic
251C4×Dic3C3×D411yescharacteristic
252C4×Dic3C23×C311yescharacteristic
253C2×C3⋊C8C23×C312yes—
254ΓL(1,𝔽25)—24no—
255C22×C32—42no—
256C22×C32—42no—
257C22×C32—42no—
258C22×C32C22×D411yescharacteristic
259C2×C3×D3—21no—
260C2×C3×D3—21no—
261C2×C3×D3—21no—
262C2×C3×D3—42no—
263C2×C3×D3—42no—
264C2×C3×D3—42no—
265C32×C4—42no—
266C32×C4AGL(1,ℤ/8)12yes—
267C32×C4AGL(1,ℤ/8)12yes—
268C32×C4C2×#4112yes—
269C3×Dic3—21no—
270C3×Dic3—21no—
271C3×Dic3—21no—
272C3×Dic3—42no—
273C2×#41—61no—
274C2×#41—61no—
275C2×D8—34no—
276C2×M16—32no—
277C4⋊Q8—31no—
278C4⋊Q8C2×C3×D311yescharacteristic
279#127—31no—
280#127C2×C3×D311yescharacteristic
281#124—61no—
282#124—61no—
283#121—32no—
284#121—32no—
285#121—61no—
286#121—61no—
287C4×D4—32no—
288C4×D4—32no—
289C4×D4—61no—
290C4×D4—61no—
291C2×C42—31no—
292#106—34no—
293#102—34no—
294#102C2×C3×D314yes—
295#97—32no—
296C4×C8—31no—
297C4×C8C2×C3×D311yescharacteristic
298C23×C3—22no—
299C23×C3—22no—
300C23×C3—31no—
301C23×C3—42no—
302C23×C3—62no—
303C22×D3—22no—
304C22×D3C2×C3×D411yescharacteristic
305C3×Q8—42no—
306C3×Q8—42no—
307C3×Q8—82no—
308C3×Q8—122no—
309C3×D4—24no—
310C3×D4—24no—
311C3×D4—44no—
312C3×D4—42no—
313C3×D4—42no—
314C3×D4—42no—
315C3×D4—42no—
316C3×D4—64no—
317C3×D4—82no—
318C3×D4—82no—
319C3×D4—124no—
320C3×D4—124no—
321C3×D4—122no—
322C3×D4—122no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—31no—
329C2×C3×C4—31no—
330C2×C3×C4—31no—
331C2×C3×C4—42no—
332C2×C3×C4—62no—
333C2×C3×C4—62no—
334C2×C3×C4—62no—
335C2×C3×C4—62no—
336C2×C3×C4—124no—
337C2×C3×C4—124no—
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4C2×C3×D411yescharacteristic
341C2×C3×C4C2×C3×D411yescharacteristic
342C2×C3×C4C23×D311yescharacteristic
343C2×C3×C4C24×C311yescharacteristic
344#67—44no—
345C2×Dic3—22no—
346C2×Dic3—44no—
347C2×Dic3C2×C3×D411yescharacteristic
348C2×Dic3C2×C3×D411yescharacteristic
349C2×Dic3C2×C3×D411yescharacteristic
350D12—24no—
351D12—44no—
352D12—42no—
353D12—42no—
354C4×D3—22no—
355C4×D3—22no—
356C4×D3—22no—
357C4×D3—44no—
358Dic6—42no—
359C3×C8—22no—
360C3×C8—22no—
361C3×C8—34no—
362C3×C8—42no—
363C3⋊C8C3×#4114yescomplemented
364C2×C32—82no—
365C2×C32#53211yescharacteristic
366C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
367C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
368C3×D3—41no—
369C3×D3—82no—
370#41—124no—
371#41—124no—
372C2×Q8—21no—
373C2×Q8—61no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4—32no—
377C2×D4—62no—
378C2×D4—62no—
379C2×D4—61no—
380C2×D4—61no—
381C2×D4C22×C3×D312yes—
382C22×C4—31no—
383C22×C4—31no—
384C22×C4—31no—
385C22×C4—62no—
386C22×C4—62no—
387D8—68no—
388M16—64no—
389C2×C8—32no—
390C2×C8C22×C3×D312yes—
391C4⋊C4—21no—
392C4⋊C4—32no—
393C4⋊C4—61no—
394C4⋊C4C22×C3×D312yes—
395C22⋊C4—62no—
396C22⋊C4—62no—
397C22⋊C4—62no—
398C22⋊C4—62no—
399C42—31no—
400C42—31no—
401C42—31no—
402C42C22×C3×D311yescharacteristic
403C22×C3—21no—
404C22×C3—42no—
405C22×C3—42no—
406C22×C3—42no—
407C22×C3—42no—
408C22×C3—42no—
409C22×C3—42no—
410C22×C3—61no—
411C22×C3—61no—
412C22×C3—61no—
413C22×C3—82no—
414C22×C3—82no—
415C22×C3—82no—
416C22×C3—122no—
417C22×C3—122no—
418C22×C3—122no—
419C22×C3C2×D3×D411yescharacteristic
420C22×C3C22×C3×D411yescharacteristic
421C2×D3—21no—
422C2×D3—21no—
423C2×D3—21no—
424C2×D3—42no—
425C2×D3—42no—
426C2×D3—42no—
427C3×C4—22no—
428C3×C4—22no—
429C3×C4—22no—
430C3×C4—42no—
431C3×C4—42no—
432C3×C4—61no—
433C3×C4—61no—
434C3×C4—61no—
435C3×C4—82no—
436C3×C4—122no—
437C3×C4#91112yes—
438C3×C4#91412yes—
439C3×C4C3×AGL(1,ℤ/8)12yes—
440C3×C4C3×AGL(1,ℤ/8)12yes—
441C3×C4D3×#4112yes—
442C3×C4C2×C3×#4112yes—
443Dic3—21no—
444Dic3—21no—
445Dic3—21no—
446Dic3—42no—
447C32#318411yescharacteristic, complemented, Sylow
448C23—22no—
449C23—31no—
450C23—62no—
451Q8—42no—
452Q8—122no—
453D4—24no—
454D4—42no—
455D4—42no—
456D4—64no—
457D4—124no—
458D4—124no—
459D4—122no—
460D4—122no—
461C2×C4—22no—
462C2×C4—31no—
463C2×C4—31no—
464C2×C4—31no—
465C2×C4—62no—
466C2×C4—62no—
467C2×C4—62no—
468C2×C4—62no—
469C2×C4—124no—
470C2×C4—124no—
471C2×C4C3×D3×D411yescharacteristic
472C2×C4C3×D3×D411yescharacteristic
473C2×C4C23×C3×D311yescharacteristic
474C8—22no—
475C8—34no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—82no—
480C2×C3—82no—
481C2×C3—121no—
482C2×C3—162no—
483C2×C3—242no—
484C2×C3#566811yescharacteristic
485C2×C3C2×#91111yescharacteristic
486C2×C3C2×#91411yescharacteristic
487C2×C3C3×#53211yescharacteristic
488C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
489C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
490D3—41no—
491D3—82no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—61no—
496C22—61no—
497C22—61no—
498C22—122no—
499C22—122no—
500C22—122no—
501C22C2×C3×D3×D411yescharacteristic
502C4—42no—
503C4—61no—
504C4—61no—
505C4—61no—
506C4—122no—
507C4C3×#91112yes—
508C4C3×#91412yes—
509C4C3×D3×#4112yes—
510C3—21no—
511C3#8156011yescharacteristic, direct product factor
512C3C3×#318411yescharacteristic, complemented
513C2—82no—
514C2—121no—
515C2—242no—
516C2C3×#566811yescharacteristic
517C2C2×C3×#91111yescharacteristic
518C2C2×C3×#91411yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#486C2
socleC22×C32C22×D4
hypercenterC3×#486D3
hypocenterC3C3×#3184
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#486

Complements

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

NH ≅ G/Ntype
1. C3×#5725C2semidirect
2. C3×#5716C2semidirect
3. C32×#486C2semidirect
4. C3×#5080C2semidirect
5. C3×#5073C2semidirect
6. C3×#4785C2semidirect
7. C3×#4782C2semidirect
8. C3×#4694C2semidirect
9. C3×C4×ΓL(1,𝔽25)C2semidirect
11. #81560C3direct (N × H)
39. #5725C2×C3semidirect
40. #5716C2×C3semidirect
45. C3×#486D3semidirect
46. C3×#486C2×C3semidirect
50. #5080C2×C3semidirect
51. #5073C2×C3semidirect
52. #4785C2×C3semidirect
53. #4782C2×C3semidirect
54. #4694C2×C3semidirect
55. C4×ΓL(1,𝔽25)C2×C3semidirect
171. C3×C3⋊C8#41semidirect
177. #486C3×D3semidirect
363. C3⋊C8C3×#41semidirect
447. C32#3184semidirect
511. C3#81560direct (N × H)
512. C3C3×#3184semidirect

Maximal subgroups

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

subgroupindex
C3×#57252
C3×#57162
C32×#4862
C3×#50802
C3×#50732
C3×#47852
C3×#47822
C3×#46942
C3×C4×ΓL(1,𝔽25)2
C3×#31843
#815603