Finite Group Databasebeta

← C3×#82538 #11860669

Subgroups — C3×#82538 #11860669

Order 1152.

1225 conjugacy classes of subgroups.

The subgroup lattice has 487 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#518C211yesmaximal, characteristic, complemented
2C22×C3×#213C211yesmaximal, characteristic
3C3×#5521C211yesmaximal, characteristic, complemented
4C3×#5215C211yesmaximal, characteristic, complemented
5C3×#5014C214yesmaximal, complemented
6C3×C4×#213C214yesmaximal, complemented
7C3×#5001C211yesmaximal, characteristic, complemented
8C3×#4998C211yesmaximal, characteristic, complemented
9C3×#4997C211yesmaximal, characteristic, complemented
10C3×#2948—31nomaximal
11#82538C311yesmaximal, characteristic, direct product factor
12C22×C32×D4C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C32×C4×D4—22no—
15C32×C4×D4C2214yescomplemented
16C32×#117C2211yescharacteristic
17C32×#117C2211yescharacteristic
18C2×C32×C22⋊C4—22no—
19C2×C3×#213C418yescomplemented
20C2×C3×#213C2212yes—
21C2×C3×#213C2212yes—
22C3×#926C2211yescharacteristic
23C2×C3×#208C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C3×#893—22no—
26C3×D3×C22⋊C4—22no—
27C3×C4×D12C2214yescomplemented
28C3×#832C2214yescomplemented
29C3×#809C2214yescomplemented
30C3×#808C2212yescomplemented
31C3×#807C2212yescomplemented
32C3×#803C2212yescomplemented
33C3×C4×C3⋊C8C2212yescomplemented
34C22×C3×D8—31no—
35C3×#518—21no—
36C3×#518—31no—
37C3×#518D311yescharacteristic, complemented
38C3×#518C2×C311yescharacteristic, complemented
39C22×#213C2×C311yescharacteristic
40#5521C2×C311yescharacteristic, complemented
41C3×#442—34no—
42C3×C4×D8—34no—
43C3×#427—31no—
44C3×#418—31no—
45C3×#418—31no—
46C3×#405—31no—
47#5215C2×C311yescharacteristic, complemented
48#5014C2×C314yescomplemented
49C4×#213C2×C314yescomplemented
50#5001C2×C311yescharacteristic, complemented
51#4998C2×C311yescharacteristic, complemented
52#4997C2×C311yescharacteristic, complemented
53C24×C32—21no—
54C23×C3×D3—21no—
55C2×C32×D4—21no—
56C2×C32×D4—22no—
57C2×C32×D4C2×C414yescomplemented
58C2×C32×D4C2312yes—
59C22×C32×C4—24no—
60C22×C32×C4C2311yescharacteristic
61C2×C3×D12—21no—
62C2×C3×D12—22no—
63C2×C3×D12C2×C414yescomplemented
64C2×C3×D12C2312yes—
65C2×C3×C4×D3—24no—
66C32×C4⋊C4D412yes—
67C32×C4⋊C4C2312yes—
68C32×C22⋊C4—21no—
69C32×C22⋊C4—24no—
70C32×C22⋊C4D412yes—
71C32×C42—21no—
72C32×C42C2312yes—
73C3×#217—21no—
74C3×#213C2×C418yescomplemented
75C3×#213C2×C418yescomplemented
76C3×(C2×D3)⋊C4—24no—
77C3×C4⋊Dic3C2312yes—
78C3×C4×Dic3—21no—
79C3×#208—22no—
80C2×C3×C3⋊C8C2×C414yescomplemented
81C2×C3×C3⋊C8C2312yes—
82C2×C3×C3⋊C8C2311yescharacteristic
83C2×C3×C3⋊C8C2311yescharacteristic
84#2948—31noSylow
85C22×C3×D4—21no—
86C22×C3×D4—31no—
87C22×C3×D4C2×D311yescharacteristic
88C22×C3×D4C22×C311yescharacteristic
89C22×D12C22×C311yescharacteristic
90C2×C3×D8—38no—
91C2×C3×D8—32no—
92C2×C3×D8—32no—
93C2×C3×M16—31no—
94C22×C3×C8—31no—
95C3×C4×D4—24no—
96C3×C4×D4—22no—
97C3×C4×D4—22no—
98C3×C4×D4—24no—
99C3×C4×D4—34no—
100C3×C4×D4—62no—
101C3×C4×D4C2×D314yescomplemented
102C3×C4×D4C22×C314yescomplemented
103C3×#117—21no—
104C3×#117—21no—
105C3×#117—31no—
106C3×#117C2×D311yescharacteristic
107C3×#117C2×D311yescharacteristic
108C3×#117C22×C311yescharacteristic
109C3×#117C22×C311yescharacteristic
110C2×C3×C22⋊C4—24no—
111C2×C3×C22⋊C4—22no—
112C2×C3×C22⋊C4—22no—
113C2×C3×C22⋊C4—62no—
114C2×#213C3×C418yescomplemented
115C2×#213C22×C312yes—
116C2×#213C22×C312yes—
117#926C22×C311yescharacteristic
118C2×#208C22×C311yescharacteristic
119C22×C3⋊C8C22×C311yescharacteristic
120#893—22no—
121D3×C22⋊C4—22no—
122C4×D12C22×C314yescomplemented
123C3×#107—32no—
124C3×#106—32no—
125C3×#102—34no—
126C3×#102—34no—
127C3×#97—32no—
128C3×C4×C8—32no—
129#832C22×C314yescomplemented
130#809C22×C314yescomplemented
131#808C22×C312yescomplemented
132#807C22×C312yescomplemented
133#803C22×C312yescomplemented
134C4×C3⋊C8C22×C312yescomplemented
135C23×C32—22no—
136C23×C32—24no—
137C23×C32—82no—
138C23×C32C2×D411yescharacteristic
139C22×C3×D3—22no—
140C22×C3×D3—24no—
141C22×C3×D3—82no—
142C32×D4—24no—
143C32×D4—22no—
144C32×D4C22×C414yes—
145C2×C32×C4—22no—
146C2×C32×C4—84no—
147C2×C32×C4C22×C412yes—
148C2×C32×C4C2×D414yes—
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4#4112yes—
151C2×C32×C4C2411yescharacteristic
152C2×C3×Dic3—22no—
153C3×D12—24no—
154C3×D12—22no—
155C3×D12C22×C414yes—
156C3×C4×D3—84no—
157C3×C3⋊C8—22no—
158C3×C3⋊C8C22×C412yes—
159C3×C3⋊C8C22×C412yes—
160C22×D8—31no—
161#518—31no—
162#518C3×D311yescharacteristic, complemented
163#442—34no—
164C4×D8—34no—
165#427—31no—
166#418—31no—
167#418—31no—
168#405—31no—
169C24×C3—22no—
170C24×C3—21no—
171C24×C3—21no—
172C24×C3—61no—
173C23×D3—21no—
174C2×C3×D4—22no—
175C2×C3×D4—24no—
176C2×C3×D4—22no—
177C2×C3×D4—21no—
178C2×C3×D4—21no—
179C2×C3×D4—22no—
180C2×C3×D4—24no—
181C2×C3×D4—22no—
182C2×C3×D4—34no—
183C2×C3×D4—32no—
184C2×C3×D4—62no—
185C2×C3×D4—61no—
186C2×C3×D4C4×D314yescomplemented
187C2×C3×D4C2×C3×C414yescomplemented
188C2×C3×D4C22×D312yes—
189C2×C3×D4C23×C312yes—
190C22×C3×C4—28no—
191C22×C3×C4—24no—
192C22×C3×C4—24no—
193C22×C3×C4—21no—
194C22×C3×C4—64no—
195C22×C3×C4C22×D311yescharacteristic
196C22×C3×C4C23×C311yescharacteristic
197C2×D12—21no—
198C2×D12—22no—
199C2×D12C2×C3×C414yescomplemented
200C2×D12C23×C312yes—
201C2×C4×D3—24no—
202C3×D8—38no—
203C3×D8—38no—
204C3×M16—62no—
205C2×C3×C8—34no—
206C2×C3×C8—31no—
207C2×C3×C8—31no—
208C2×C3×C8—32no—
209C3×C4⋊C4—22no—
210C3×C4⋊C4—22no—
211C3×C4⋊C4—32no—
212C3×C4⋊C4#6712yes—
213C3×C4⋊C4C3×D412yes—
214C3×C4⋊C4C22×D312yes—
215C3×C4⋊C4C23×C312yes—
216C3×C22⋊C4—22no—
217C3×C22⋊C4—28no—
218C3×C22⋊C4—21no—
219C3×C22⋊C4—21no—
220C3×C22⋊C4—24no—
221C3×C22⋊C4—24no—
222C3×C22⋊C4—22no—
223C3×C22⋊C4—61no—
224C3×C22⋊C4—64no—
225C3×C22⋊C4#6712yes—
226C3×C22⋊C4C3×D412yes—
227C3×C42—22no—
228C3×C42—21no—
229C3×C42—21no—
230C3×C42—22no—
231C3×C42—61no—
232C3×C42C22×D312yes—
233C3×C42C23×C312yes—
234#217—21no—
235#213C2×C3×C418yescomplemented
236#213C2×C3×C418yescomplemented
237(C2×D3)⋊C4—24no—
238C4⋊Dic3C23×C312yes—
239C4×Dic3—21no—
240#208—22no—
241C2×C3⋊C8C2×C3×C414yescomplemented
242C2×C3⋊C8C23×C312yes—
243C2×C3⋊C8C23×C311yescharacteristic
244C2×C3⋊C8C23×C311yescharacteristic
245C22×C32—24no—
246C22×C32—22no—
247C22×C32—44no—
248C22×C32—84no—
249C22×C32C4×D412yes—
250C22×C32C22×D411yescharacteristic
251C2×C3×D3—24no—
252C2×C3×D3—44no—
253C2×C3×D3—84no—
254C32×C4—24no—
255C32×C4—42no—
256C32×C4C4×D412yes—
257C32×C4C23×C411yescharacteristic
258C32×C4C2×#4111yescharacteristic
259C3×Dic3—42no—
260C22×D4—31no—
261C22×D4C2×C3×D311yescharacteristic
262C2×D8—38no—
263C2×D8—32no—
264C2×D8—32no—
265C2×M16—31no—
266C22×C8—31no—
267C4×D4—22no—
268C4×D4—34no—
269C4×D4—62no—
270C4×D4C2×C3×D314yescomplemented
271#117—31no—
272#117C2×C3×D311yescharacteristic
273#117C2×C3×D311yescharacteristic
274C2×C22⋊C4—22no—
275C2×C22⋊C4—62no—
276#107—32no—
277#106—32no—
278#102—34no—
279#102—34no—
280#97—32no—
281C4×C8—32no—
282C23×C3—24no—
283C23×C3—28no—
284C23×C3—22no—
285C23×C3—22no—
286C23×C3—24no—
287C23×C3—24no—
288C23×C3—21no—
289C23×C3—62no—
290C23×C3—64no—
291C23×C3—82no—
292C23×C3—82no—
293C23×C3—84no—
294C23×C3—242no—
295C23×C3C2×#6711yescharacteristic
296C23×C3C2×C3×D411yescharacteristic
297C22×D3—22no—
298C22×D3—24no—
299C22×D3—82no—
300C3×D4—28no—
301C3×D4—24no—
302C3×D4—24no—
303C3×D4—24no—
304C3×D4—22no—
305C3×D4—22no—
306C3×D4—24no—
307C3×D4—34no—
308C3×D4—64no—
309C3×D4—62no—
310C3×D4C2×C4×D314yes—
311C3×D4C22×C3×C414yes—
312C2×C3×C4—24no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—21no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—21no—
319C2×C3×C4—24no—
320C2×C3×C4—62no—
321C2×C3×C4—84no—
322C2×C3×C4—84no—
323C2×C3×C4—88no—
324C2×C3×C4—244no—
325C2×C3×C4C2×C4×D312yes—
326C2×C3×C4#23512yes—
327C2×C3×C4C2×#6714yes—
328C2×C3×C4C2×#6711yescharacteristic
329C2×C3×C4C22×C3×C412yes—
330C2×C3×C4C2×C3×D414yes—
331C2×C3×C4C2×C3×D411yescharacteristic
332C2×C3×C4C3×#4112yes—
333C2×C3×C4C23×D311yescharacteristic
334C2×C3×C4C24×C311yescharacteristic
335C2×Dic3—22no—
336D12—24no—
337D12—22no—
338D12C22×C3×C414yes—
339C4×D3—84no—
340C3×C8—32no—
341C3×C8—32no—
342C3×C8—62no—
343C3⋊C8—22no—
344C3⋊C8C22×C3×C412yes—
345C3⋊C8C22×C3×C412yes—
346C2×C32—22no—
347C2×C32—44no—
348C2×C32C2×C4×D411yescharacteristic
349C2×C32#57612yes—
350C3×D3—44no—
351C24—21no—
352C24—61no—
353C2×D4—22no—
354C2×D4—21no—
355C2×D4—32no—
356C2×D4—34no—
357C2×D4—62no—
358C2×D4—61no—
359C2×D4C3×C4×D314yescomplemented
360C2×D4C22×C3×D312yes—
361C22×C4—24no—
362C22×C4—64no—
363C22×C4C22×C3×D311yescharacteristic
364D8—38no—
365D8—38no—
366M16—62no—
367C2×C8—31no—
368C2×C8—31no—
369C2×C8—34no—
370C2×C8—32no—
371C4⋊C4—32no—
372C4⋊C4C3×#6712yes—
373C4⋊C4C22×C3×D312yes—
374C22⋊C4—21no—
375C22⋊C4—24no—
376C22⋊C4—61no—
377C22⋊C4—64no—
378C22⋊C4C3×#6712yes—
379C42—21no—
380C42—61no—
381C42C22×C3×D312yes—
382C22×C3—22no—
383C22×C3—22no—
384C22×C3—28no—
385C22×C3—24no—
386C22×C3—24no—
387C22×C3—22no—
388C22×C3—21no—
389C22×C3—42no—
390C22×C3—48no—
391C22×C3—44no—
392C22×C3—44no—
393C22×C3—64no—
394C22×C3—84no—
395C22×C3—84no—
396C22×C3—88no—
397C22×C3—124no—
398C22×C3—244no—
399C22×C3C4×#6712yes—
400C22×C3C3×C4×D412yes—
401C22×C3C22×#6711yescharacteristic
402C22×C3C22×C3×D411yescharacteristic
403C2×D3—24no—
404C2×D3—44no—
405C2×D3—84no—
406C3×C4—24no—
407C3×C4—24no—
408C3×C4—22no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—44no—
412C3×C4—44no—
413C3×C4—42no—
414C3×C4—42no—
415C3×C4—122no—
416C3×C4C4×#6712yes—
417C3×C4C3×C4×D412yes—
418C3×C4C22×C4×D311yescharacteristic
419C3×C4C2×#23511yescharacteristic
420C3×C4C23×C3×C411yescharacteristic
421C3×C4C2×C3×#4111yescharacteristic
422Dic3—42no—
423C32#294811yescharacteristic, complemented, Sylow
424C23—22no—
425C23—24no—
426C23—62no—
427C23—64no—
428C23—82no—
429C23—242no—
430C23C2×C3×#6711yescharacteristic
431D4—24no—
432D4—22no—
433D4—34no—
434D4—64no—
435D4—62no—
436D4C2×C3×C4×D314yes—
437C2×C4—22no—
438C2×C4—62no—
439C2×C4—84no—
440C2×C4—244no—
441C2×C4C2×C3×C4×D312yes—
442C2×C4C3×#23512yes—
443C2×C4C2×C3×#6714yes—
444C2×C4C2×C3×#6711yescharacteristic
445C2×C4C23×C3×D311yescharacteristic
446C8—32no—
447C8—32no—
448C8—62no—
449C2×C3—22no—
450C2×C3—22no—
451C2×C3—21no—
452C2×C3—22no—
453C2×C3—42no—
454C2×C3—48no—
455C2×C3—44no—
456C2×C3—44no—
457C2×C3—124no—
458C2×C3C2×C4×#6711yescharacteristic
459C2×C3#583512yes—
460C2×C3C2×C3×C4×D411yescharacteristic
461C2×C3C3×#57612yes—
462D3—44no—
463C22—22no—
464C22—24no—
465C22—44no—
466C22—64no—
467C22—84no—
468C22—124no—
469C22—244no—
470C22C3×C4×#6712yes—
471C22C22×C3×#6711yescharacteristic
472C4—24no—
473C4—42no—
474C4—122no—
475C4C3×C4×#6712yes—
476C4C22×C3×C4×D311yescharacteristic
477C4C2×C3×#23511yescharacteristic
478C3—21no—
479C3#8253811yescharacteristic, direct product factor
480C3C3×#294811yescharacteristic, complemented
481C2—22no—
482C2—44no—
483C2—124no—
484C2C2×C3×C4×#6711yescharacteristic
485C2C3×#583512yes—
subgroupG/H
centerC22×C3C22×#67
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC32×#518C2
socleC22×C32C22×D4
prime radicalC22×C3×#213C2
cosocleC2×C3×C4C24×C3
hypercenterC3×#518D3
hypocenterC3C3×#2948
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#117 ◁ C3×#518

Complements

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

NH ≅ G/Ntype
1. C32×#518C2semidirect
3. C3×#5521C2semidirect
4. C3×#5215C2semidirect
5. C3×#5014C2semidirect
6. C3×C4×#213C2semidirect
7. C3×#5001C2semidirect
8. C3×#4998C2semidirect
9. C3×#4997C2semidirect
11. #82538C3direct (N × H)
15. C32×C4×D4C22semidirect
19. C2×C3×#213C4semidirect
27. C3×C4×D12C22semidirect
28. C3×#832C22semidirect
29. C3×#809C22semidirect
30. C3×#808C22semidirect
31. C3×#807C22semidirect
32. C3×#803C22semidirect
33. C3×C4×C3⋊C8C22semidirect
37. C3×#518D3semidirect
38. C3×#518C2×C3semidirect
40. #5521C2×C3semidirect
47. #5215C2×C3semidirect
48. #5014C2×C3semidirect
49. C4×#213C2×C3semidirect
50. #5001C2×C3semidirect
51. #4998C2×C3semidirect
52. #4997C2×C3semidirect
57. C2×C32×D4C2×C4semidirect
63. C2×C3×D12C2×C4semidirect
74. C3×#213C2×C4semidirect
75. C3×#213C2×C4semidirect
80. C2×C3×C3⋊C8C2×C4semidirect
101. C3×C4×D4C2×D3semidirect
102. C3×C4×D4C22×C3semidirect
114. C2×#213C3×C4semidirect
122. C4×D12C22×C3semidirect
129. #832C22×C3semidirect
130. #809C22×C3semidirect
131. #808C22×C3semidirect
132. #807C22×C3semidirect
133. #803C22×C3semidirect
134. C4×C3⋊C8C22×C3semidirect
162. #518C3×D3semidirect
186. C2×C3×D4C4×D3semidirect
187. C2×C3×D4C2×C3×C4semidirect
199. C2×D12C2×C3×C4semidirect
235. #213C2×C3×C4semidirect
236. #213C2×C3×C4semidirect
241. C2×C3⋊C8C2×C3×C4semidirect
270. C4×D4C2×C3×D3semidirect
359. C2×D4C3×C4×D3semidirect
423. C32#2948semidirect
479. C3#82538direct (N × H)
480. C3C3×#2948semidirect

Maximal subgroups

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

subgroupindex
C32×#5182
C22×C3×#2132
C3×#55212
C3×#52152
C3×#50142
C3×C4×#2132
C3×#50012
C3×#49982
C3×#49972
C3×#29483
#825383