Finite Group Databasebeta

← C3×#82543 #11860724

Subgroups — C3×#82543 #11860724

Order 1152.

1153 conjugacy classes of subgroups.

The subgroup lattice has 467 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#518C211yesmaximal, characteristic
2C22×C3×#214C211yesmaximal, characteristic
3C3×#5516C211yesmaximal, characteristic, complemented
4C3×#5215C211yesmaximal, characteristic
5C3×#5018C214yesmaximal, complemented
6C3×C4×#214C214yesmaximal, complemented
7C3×#5004C211yesmaximal, characteristic, complemented
8C3×#4998C211yesmaximal, characteristic, complemented
9C3×#4997C211yesmaximal, characteristic, complemented
10C3×#2949—31nomaximal
11#82543C311yesmaximal, characteristic, direct product factor
12C22×C32×D4C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C32×C4×D4—22no—
15C32×C4×D4C2214yes—
16C32×#117C2211yescharacteristic
17C32×#117C2211yescharacteristic
18C2×C32×C22⋊C4—22no—
19C2×C3×#214C418yescomplemented
20C2×C3×#214C2212yes—
21C2×C3×#214C2212yes—
22C3×#926C2211yescharacteristic
23C2×C3×#208C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C3×#887—22no—
26C3×#877—22no—
27C3×C4×Dic6C2214yescomplemented
28C3×#832C2214yes—
29C3×#810C2214yescomplemented
30C3×#808C2212yescomplemented
31C3×#807C2212yescomplemented
32C3×#803C2212yescomplemented
33C3×C4×C3⋊C8C2212yescomplemented
34C22×C3×SD16—31no—
35C3×#519—31no—
36C3×#518—21no—
37C3×#518D311yescharacteristic
38C3×#518C2×C311yescharacteristic
39C22×#214C2×C311yescharacteristic
40#5516C2×C311yescharacteristic, complemented
41C3×#440—34no—
42C3×C4×SD16—34no—
43C3×#427—31no—
44C3×#419—31no—
45C3×#418—31no—
46C3×#405—31no—
47#5215C2×C311yescharacteristic
48#5018C2×C314yescomplemented
49C4×#214C2×C314yescomplemented
50#5004C2×C311yescharacteristic, complemented
51#4998C2×C311yescharacteristic, complemented
52#4997C2×C311yescharacteristic, complemented
53C24×C32—21no—
54C2×C32×D4—21no—
55C2×C32×D4—22no—
56C2×C32×D4C2×C414yes—
57C2×C32×D4C2312yes—
58C22×C32×C4—24no—
59C22×C32×C4C2311yescharacteristic
60C22×C3×Dic3—21no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6—22no—
63C2×C3×Dic6C2×C414yescomplemented
64C2×C3×Dic6C2312yes—
65C32×C4⋊C4D412yes—
66C32×C4⋊C4C2312yes—
67C32×C22⋊C4—21no—
68C32×C22⋊C4—24no—
69C32×C22⋊C4D412yes—
70C32×C42—21no—
71C32×C42C2312yes—
72C3×#217—21no—
73C3×#214C2×C418yescomplemented
74C3×#214C2×C418yescomplemented
75C3×C4⋊Dic3C2312yes—
76C3×Dic3⋊C4—24no—
77C3×C4×Dic3—24no—
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#2949—31noSylow
85C22×C3×Q8—31no—
86C22×C3×D4—21no—
87C22×C3×D4C2×D311yescharacteristic
88C22×C3×D4C22×C311yescharacteristic
89C22×Dic6C22×C311yescharacteristic
90C2×C3×SD16—38no—
91C2×C3×SD16—32no—
92C2×C3×SD16—32no—
93C2×C3×M16—31no—
94C22×C3×C8—31no—
95C3×C4×Q8—34no—
96C3×C4×Q8—62no—
97C3×C4×D4—24no—
98C3×C4×D4—22no—
99C3×C4×D4—22no—
100C3×C4×D4—24no—
101C3×C4×D4C2×D314yes—
102C3×C4×D4C22×C314yes—
103C3×#117—21no—
104C3×#117—21no—
105C3×#117—31no—
106C3×#117—62no—
107C3×#117C2×D311yescharacteristic
108C3×#117C2×D311yescharacteristic
109C3×#117C22×C311yescharacteristic
110C3×#117C22×C311yescharacteristic
111C2×C3×C22⋊C4—24no—
112C2×C3×C22⋊C4—22no—
113C2×C3×C22⋊C4—22no—
114C2×#214C3×C418yescomplemented
115C2×#214C22×C312yes—
116C2×#214C22×C312yes—
117#926C22×C311yescharacteristic
118C2×#208C22×C311yescharacteristic
119C22×C3⋊C8C22×C311yescharacteristic
120#887—22no—
121#877—22no—
122C4×Dic6C22×C314yescomplemented
123C3×#107—32no—
124C3×#106—32no—
125C3×#103—34no—
126C3×#102—34no—
127C3×#97—32no—
128C3×C4×C8—32no—
129#832C22×C314yes—
130#810C22×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
139C32×D4—24no—
140C32×D4—22no—
141C32×D4C22×C414yes—
142C2×C32×C4—22no—
143C2×C32×C4—84no—
144C2×C32×C4C22×C412yes—
145C2×C32×C4C2×D414yes—
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4#4112yes—
148C2×C32×C4C2411yescharacteristic
149C2×C3×Dic3—24no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C3×Dic6—24no—
153C3×Dic6—22no—
154C3×Dic6C22×C414yes—
155C3×C3⋊C8—22no—
156C3×C3⋊C8C22×C412yes—
157C3×C3⋊C8C22×C412yes—
158C22×SD16—31no—
159#519—31no—
160#518C3×D311yescharacteristic
161#440—34no—
162C4×SD16—34no—
163#427—31no—
164#419—31no—
165#418—31no—
166#405—31no—
167C24×C3—22no—
168C24×C3—21no—
169C24×C3—21no—
170C2×C3×Q8—34no—
171C2×C3×Q8—32no—
172C2×C3×Q8—62no—
173C2×C3×Q8—61no—
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×D4C4×D314yes—
183C2×C3×D4C2×C3×C414yes—
184C2×C3×D4C22×D312yes—
185C2×C3×D4C23×C312yes—
186C22×C3×C4—28no—
187C22×C3×C4—24no—
188C22×C3×C4—24no—
189C22×C3×C4—21no—
190C22×C3×C4—61no—
191C22×C3×C4C22×D311yescharacteristic
192C22×C3×C4C23×C311yescharacteristic
193C22×Dic3—21no—
194C2×Dic6—21no—
195C2×Dic6—22no—
196C2×Dic6C2×C3×C414yescomplemented
197C2×Dic6C23×C312yes—
198C3×SD16—38no—
199C3×SD16—38no—
200C3×M16—62no—
201C2×C3×C8—34no—
202C2×C3×C8—31no—
203C2×C3×C8—31no—
204C2×C3×C8—32no—
205C3×C4⋊C4—22no—
206C3×C4⋊C4—22no—
207C3×C4⋊C4—32no—
208C3×C4⋊C4—64no—
209C3×C4⋊C4#6712yes—
210C3×C4⋊C4C3×D412yes—
211C3×C4⋊C4C22×D312yes—
212C3×C4⋊C4C23×C312yes—
213C3×C22⋊C4—22no—
214C3×C22⋊C4—28no—
215C3×C22⋊C4—21no—
216C3×C22⋊C4—21no—
217C3×C22⋊C4—24no—
218C3×C22⋊C4—24no—
219C3×C22⋊C4—22no—
220C3×C22⋊C4—61no—
221C3×C22⋊C4#6712yes—
222C3×C22⋊C4C3×D412yes—
223C3×C42—22no—
224C3×C42—21no—
225C3×C42—21no—
226C3×C42—22no—
227C3×C42—61no—
228C3×C42—64no—
229C3×C42C22×D312yes—
230C3×C42C23×C312yes—
231#217—21no—
232#214C2×C3×C418yescomplemented
233#214C2×C3×C418yescomplemented
234C4⋊Dic3C23×C312yes—
235Dic3⋊C4—24no—
236C4×Dic3—24no—
237C4×Dic3—21no—
238#208—22no—
239C2×C3⋊C8C2×C3×C414yescomplemented
240C2×C3⋊C8C23×C312yes—
241C2×C3⋊C8C23×C311yescharacteristic
242C2×C3⋊C8C23×C311yescharacteristic
243C22×C32—24no—
244C22×C32—22no—
245C22×C32—44no—
246C22×C32—84no—
247C22×C32C4×D412yes—
248C22×C32C22×D411yescharacteristic
249C32×C4—24no—
250C32×C4—42no—
251C32×C4C4×D412yes—
252C32×C4C23×C411yescharacteristic
253C32×C4C2×#4111yescharacteristic
254C3×Dic3—24no—
255C3×Dic3—42no—
256C22×Q8—31no—
257C22×D4C2×C3×D311yescharacteristic
258C2×SD16—38no—
259C2×SD16—32no—
260C2×SD16—32no—
261C2×M16—31no—
262C22×C8—31no—
263C4×Q8—34no—
264C4×Q8—62no—
265C4×D4—22no—
266C4×D4C2×C3×D314yes—
267#117—31no—
268#117—62no—
269#117C2×C3×D311yescharacteristic
270#117C2×C3×D311yescharacteristic
271C2×C22⋊C4—22no—
272#107—32no—
273#106—32no—
274#103—34no—
275#102—34no—
276#97—32no—
277C4×C8—32no—
278C23×C3—24no—
279C23×C3—28no—
280C23×C3—22no—
281C23×C3—22no—
282C23×C3—24no—
283C23×C3—24no—
284C23×C3—21no—
285C23×C3—82no—
286C23×C3—82no—
287C23×C3—84no—
288C23×C3C2×#6711yescharacteristic
289C23×C3C2×C3×D411yescharacteristic
290C3×Q8—34no—
291C3×Q8—64no—
292C3×Q8—62no—
293C3×D4—28no—
294C3×D4—24no—
295C3×D4—24no—
296C3×D4—24no—
297C3×D4—22no—
298C3×D4—22no—
299C3×D4—24no—
300C3×D4C2×C4×D314yes—
301C3×D4C22×C3×C414yes—
302C2×C3×C4—24no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—21no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—21no—
309C2×C3×C4—24no—
310C2×C3×C4—64no—
311C2×C3×C4—62no—
312C2×C3×C4—62no—
313C2×C3×C4—84no—
314C2×C3×C4—84no—
315C2×C3×C4—88no—
316C2×C3×C4C2×C4×D312yes—
317C2×C3×C4#23512yes—
318C2×C3×C4C2×#6714yes—
319C2×C3×C4C2×#6711yescharacteristic
320C2×C3×C4C22×C3×C412yes—
321C2×C3×C4C2×C3×D414yes—
322C2×C3×C4C2×C3×D411yescharacteristic
323C2×C3×C4C3×#4112yes—
324C2×C3×C4C23×D311yescharacteristic
325C2×C3×C4C24×C311yescharacteristic
326C2×Dic3—24no—
327C2×Dic3—22no—
328C2×Dic3—22no—
329Dic6—24no—
330Dic6—22no—
331Dic6C22×C3×C414yes—
332C3×C8—32no—
333C3×C8—32no—
334C3×C8—62no—
335C3⋊C8—22no—
336C3⋊C8C22×C3×C412yes—
337C3⋊C8C22×C3×C412yes—
338C2×C32—22no—
339C2×C32—44no—
340C2×C32C2×C4×D411yescharacteristic
341C2×C32#57712yes—
342C24—21no—
343C2×Q8—32no—
344C2×Q8—34no—
345C2×Q8—62no—
346C2×Q8—61no—
347C2×D4—22no—
348C2×D4—21no—
349C2×D4C3×C4×D314yes—
350C2×D4C22×C3×D312yes—
351C22×C4—24no—
352C22×C4—61no—
353C22×C4C22×C3×D311yescharacteristic
354SD16—38no—
355SD16—38no—
356M16—62no—
357C2×C8—31no—
358C2×C8—31no—
359C2×C8—34no—
360C2×C8—32no—
361C4⋊C4—32no—
362C4⋊C4—64no—
363C4⋊C4C3×#6712yes—
364C4⋊C4C22×C3×D312yes—
365C22⋊C4—21no—
366C22⋊C4—24no—
367C22⋊C4—61no—
368C22⋊C4C3×#6712yes—
369C42—21no—
370C42—61no—
371C42—64no—
372C42C22×C3×D312yes—
373C22×C3—22no—
374C22×C3—22no—
375C22×C3—28no—
376C22×C3—24no—
377C22×C3—24no—
378C22×C3—22no—
379C22×C3—21no—
380C22×C3—42no—
381C22×C3—48no—
382C22×C3—44no—
383C22×C3—44no—
384C22×C3—84no—
385C22×C3—84no—
386C22×C3—88no—
387C22×C3C4×#6712yes—
388C22×C3C3×C4×D412yes—
389C22×C3C22×#6711yescharacteristic
390C22×C3C22×C3×D411yescharacteristic
391C3×C4—24no—
392C3×C4—24no—
393C3×C4—22no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—44no—
397C3×C4—44no—
398C3×C4—42no—
399C3×C4—42no—
400C3×C4—64no—
401C3×C4—122no—
402C3×C4C4×#6712yes—
403C3×C4C3×C4×D412yes—
404C3×C4C22×C4×D311yescharacteristic
405C3×C4C2×#23511yescharacteristic
406C3×C4C23×C3×C411yescharacteristic
407C3×C4C2×C3×#4111yescharacteristic
408Dic3—24no—
409Dic3—42no—
410C32#294911yescharacteristic, complemented, Sylow
411C23—22no—
412C23—24no—
413C23—82no—
414C23C2×C3×#6711yescharacteristic
415Q8—34no—
416Q8—64no—
417Q8—62no—
418D4—24no—
419D4—22no—
420D4C2×C3×C4×D314yes—
421C2×C4—22no—
422C2×C4—64no—
423C2×C4—62no—
424C2×C4—62no—
425C2×C4—84no—
426C2×C4C2×C3×C4×D312yes—
427C2×C4C3×#23512yes—
428C2×C4C2×C3×#6714yes—
429C2×C4C2×C3×#6711yescharacteristic
430C2×C4C23×C3×D311yescharacteristic
431C8—32no—
432C8—32no—
433C8—62no—
434C2×C3—22no—
435C2×C3—22no—
436C2×C3—21no—
437C2×C3—22no—
438C2×C3—42no—
439C2×C3—48no—
440C2×C3—44no—
441C2×C3—44no—
442C2×C3C2×C4×#6711yescharacteristic
443C2×C3#583612yes—
444C2×C3C2×C3×C4×D411yescharacteristic
445C2×C3C3×#57712yes—
446C22—22no—
447C22—24no—
448C22—44no—
449C22—84no—
450C22C3×C4×#6712yes—
451C22C22×C3×#6711yescharacteristic
452C4—24no—
453C4—42no—
454C4—64no—
455C4—122no—
456C4C3×C4×#6712yes—
457C4C22×C3×C4×D311yescharacteristic
458C4C2×C3×#23511yescharacteristic
459C3—21no—
460C3#8254311yescharacteristic, direct product factor
461C3C3×#294911yescharacteristic, complemented
462C2—22no—
463C2—44no—
464C2C2×C3×C4×#6711yescharacteristic
465C2C3×#583612yes—
subgroupG/H
centerC22×C3C22×#67
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC32×#518C2
socleC22×C32C22×D4
prime radicalC22×C32×D4C22
cosocleC2×C3×C4C24×C3
hypercenterC3×#518D3
hypocenterC3C3×#2949
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
3. C3×#5516C2semidirect
5. C3×#5018C2semidirect
6. C3×C4×#214C2semidirect
7. C3×#5004C2semidirect
8. C3×#4998C2semidirect
9. C3×#4997C2semidirect
11. #82543C3direct (N × H)
19. C2×C3×#214C4semidirect
27. C3×C4×Dic6C22semidirect
29. C3×#810C22semidirect
30. C3×#808C22semidirect
31. C3×#807C22semidirect
32. C3×#803C22semidirect
33. C3×C4×C3⋊C8C22semidirect
40. #5516C2×C3semidirect
48. #5018C2×C3semidirect
49. C4×#214C2×C3semidirect
50. #5004C2×C3semidirect
51. #4998C2×C3semidirect
52. #4997C2×C3semidirect
63. C2×C3×Dic6C2×C4semidirect
73. C3×#214C2×C4semidirect
74. C3×#214C2×C4semidirect
80. C2×C3×C3⋊C8C2×C4semidirect
114. C2×#214C3×C4semidirect
122. C4×Dic6C22×C3semidirect
130. #810C22×C3semidirect
131. #808C22×C3semidirect
132. #807C22×C3semidirect
133. #803C22×C3semidirect
134. C4×C3⋊C8C22×C3semidirect
196. C2×Dic6C2×C3×C4semidirect
232. #214C2×C3×C4semidirect
233. #214C2×C3×C4semidirect
239. C2×C3⋊C8C2×C3×C4semidirect
410. C32#2949semidirect
460. C3#82543direct (N × H)
461. C3C3×#2949semidirect

Maximal subgroups

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

subgroupindex
C32×#5182
C22×C3×#2142
C3×#55162
C3×#52152
C3×#50182
C3×C4×#2142
C3×#50042
C3×#49982
C3×#49972
C3×#29493
#825433