Finite Group Databasebeta

← C3×#82545 #11872801

Subgroups — C3×#82545 #11872801

Order 1152.

957 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#518C211yesmaximal, characteristic
2C3×#5518C211yesmaximal, characteristic, complemented
3C3×#5218C212yesmaximal
4C3×#5019C212yesmaximal, complemented
5C3×#5018C212yesmaximal, complemented
6C3×C4×#214C212yesmaximal, complemented
7C3×#5009C212yesmaximal, complemented
8C3×#5000C211yesmaximal, characteristic, complemented
9C3×#4996C212yesmaximal, complemented
10C3×#3123—31nomaximal
11#82545C311yesmaximal, characteristic, direct product factor
12C22×C32×D4C2211yescharacteristic
13C32×C4×D4—22no—
14C32×C4×D4C2212yes—
15C32×C4×D4C2212yes—
16C32×#117C2211yescharacteristic
17C32×#117C2211yescharacteristic
18C2×C32×C22⋊C4—22no—
19C2×C3×#214C2212yes—
20C2×C3×#214C2212yes—
21C3×#924C2212yes—
22C3×#889—22no—
23C3×#879—22no—
24C3×#870C2211yescharacteristic, complemented
25C3×#869C2211yescharacteristic, complemented
26C3×C4×Dic6C2212yescomplemented
27C3×#832C2212yes—
28C3×#832C2212yes—
29C3×#830C2212yes—
30C3×#810C2212yescomplemented
31C3×#810C2212yescomplemented
32C3×#808C2212yescomplemented
33C3×#807C2212yescomplemented
34C3×C4⋊(C3⋊C8)C2212yescomplemented
35C3×#803C2211yescharacteristic, complemented
36C3×C4×C3⋊C8C2211yescharacteristic, complemented
37C3×#541—31no—
38C3×#518—21no—
39C3×#518D311yescharacteristic
40C3×#518C2×C311yescharacteristic
41#5518C2×C311yescharacteristic, complemented
42C3×#485—32no—
43C3×#478—32no—
44C3×#461—32no—
45C3×#450—32no—
46C3×#440—32no—
47C3×C4×SD16—32no—
48C3×#433—31no—
49#5218C2×C312yes—
50#5019C2×C312yescomplemented
51#5018C2×C312yescomplemented
52C4×#214C2×C312yescomplemented
53#5009C2×C312yescomplemented
54#5000C2×C311yescharacteristic, complemented
55#4996C2×C312yescomplemented
56C24×C32—21no—
57C2×C32×D4—24no—
58C2×C32×D4—21no—
59C2×C32×D4C2312yes—
60C22×C32×C4—22no—
61C22×C32×C4—22no—
62C22×C32×C4C2311yescharacteristic
63C2×C3×Dic6C2312yes—
64C32×C4⋊C4D412yes—
65C32×C4⋊C4C2312yes—
66C32×C22⋊C4—21no—
67C32×C22⋊C4—22no—
68C32×C22⋊C4—22no—
69C32×C22⋊C4D412yes—
70C32×C42—21no—
71C32×C42C2311yescharacteristic
72C32×C42C2311yescharacteristic
73C3×#217—22no—
74C3×#214—24no—
75C3×#214—24no—
76C3×C4⋊Dic3—22no—
77C3×C4⋊Dic3C2312yes—
78C3×Dic3⋊C4—22no—
79C3×Dic3⋊C4—22no—
80C3×Dic3⋊C4—22no—
81C3×C4×Dic3—22no—
82C2×C3×C3⋊C8C2312yes—
83C2×C3×C3⋊C8C2312yes—
84#3123—31noSylow
85C22×C3×D4—21no—
86C22×C3×D4C2×D311yescharacteristic
87C22×C3×D4C22×C311yescharacteristic
88C2×C3×SD16—32no—
89C2×C3×SD16—32no—
90C3×C4⋊Q8—31no—
91C3×#126—62no—
92C3×#125—31no—
93C3×#125—62no—
94C3×C22⋊Q8—32no—
95C3×C4×Q8—32no—
96C3×C4×D4—24no—
97C3×C4×D4—22no—
98C3×C4×D4—22no—
99C3×C4×D4—22no—
100C3×C4×D4—22no—
101C3×C4×D4C2×D312yes—
102C3×C4×D4C2×D312yes—
103C3×C4×D4C22×C312yes—
104C3×C4×D4C22×C312yes—
105C3×#117—21no—
106C3×#117—21no—
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×#214C22×C312yes—
115C2×#214C22×C312yes—
116#924C22×C312yes—
117#889—22no—
118#879—22no—
119#870C22×C311yescharacteristic, complemented
120#869C22×C311yescharacteristic, complemented
121C4×Dic6C22×C312yescomplemented
122C3×#107—32no—
123C3×#106—32no—
124C3×C4⋊C8—32no—
125C3×#103—32no—
126C3×#103—32no—
127C3×#102—32no—
128C3×#102—32no—
129C3×C22⋊C8—32no—
130C3×#97—31no—
131C3×C4×C8—31no—
132#832C22×C312yes—
133#832C22×C312yes—
134#830C22×C312yes—
135#810C22×C312yescomplemented
136#810C22×C312yescomplemented
137#808C22×C312yescomplemented
138#807C22×C312yescomplemented
139C4⋊(C3⋊C8)C22×C312yescomplemented
140#803C22×C311yescharacteristic, complemented
141C4×C3⋊C8C22×C311yescharacteristic, complemented
142C23×C32—24no—
143C23×C32—22no—
144C23×C32—82no—
145C23×C32C2×D411yescharacteristic
146C32×D4—24no—
147C32×D4—22no—
148C32×D4#4114yes—
149C2×C32×C4—22no—
150C2×C32×C4—22no—
151C2×C32×C4—82no—
152C2×C32×C4—82no—
153C2×C32×C4C2×D412yes—
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2×D412yes—
156C2×C32×C4C2411yescharacteristic
157C2×C3×Dic3—22no—
158C2×C3×Dic3—22no—
159C3×Dic6—22no—
160C3×Dic6—22no—
161C3×C3⋊C8—22no—
162C3×C3⋊C8—22no—
163#541—31no—
164#518C3×D311yescharacteristic
165#485—32no—
166#478—32no—
167#461—32no—
168#450—32no—
169#440—32no—
170C4×SD16—32no—
171#433—31no—
172C24×C3—22no—
173C24×C3—21no—
174C24×C3—21no—
175C2×C3×Q8—32no—
176C2×C3×D4—22no—
177C2×C3×D4—28no—
178C2×C3×D4—24no—
179C2×C3×D4—24no—
180C2×C3×D4—21no—
181C2×C3×D4—21no—
182C2×C3×D4—22no—
183C2×C3×D4C22×D312yes—
184C2×C3×D4C23×C312yes—
185C22×C3×C4—24no—
186C22×C3×C4—24no—
187C22×C3×C4—22no—
188C22×C3×C4—22no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—21no—
192C22×C3×C4C22×D311yescharacteristic
193C22×C3×C4C23×C311yescharacteristic
194C2×Dic6C23×C312yes—
195C3×SD16—64no—
196C3×SD16—64no—
197C2×C3×C8—32no—
198C2×C3×C8—32no—
199C3×C4⋊C4—22no—
200C3×C4⋊C4—22no—
201C3×C4⋊C4—32no—
202C3×C4⋊C4—62no—
203C3×C4⋊C4—62no—
204C3×C4⋊C4—62no—
205C3×C4⋊C4—62no—
206C3×C4⋊C4#6712yes—
207C3×C4⋊C4C3×D412yes—
208C3×C4⋊C4C22×D312yes—
209C3×C4⋊C4C23×C312yes—
210C3×C22⋊C4—22no—
211C3×C22⋊C4—24no—
212C3×C22⋊C4—24no—
213C3×C22⋊C4—21no—
214C3×C22⋊C4—21no—
215C3×C22⋊C4—22no—
216C3×C22⋊C4—22no—
217C3×C22⋊C4—22no—
218C3×C22⋊C4—22no—
219C3×C22⋊C4—22no—
220C3×C22⋊C4—62no—
221C3×C22⋊C4#6712yes—
222C3×C22⋊C4C3×D412yes—
223C3×C42—22no—
224C3×C42—21no—
225C3×C42—21no—
226C3×C42—21no—
227C3×C42—21no—
228C3×C42—62no—
229C3×C42C22×D311yescharacteristic
230C3×C42C22×D311yescharacteristic
231C3×C42C23×C311yescharacteristic
232C3×C42C23×C311yescharacteristic
233#217—22no—
234#214—24no—
235#214—24no—
236C4⋊Dic3—22no—
237C4⋊Dic3C23×C312yes—
238Dic3⋊C4—22no—
239Dic3⋊C4—22no—
240Dic3⋊C4—22no—
241C4×Dic3—22no—
242C2×C3⋊C8C23×C312yes—
243C2×C3⋊C8C23×C312yes—
244C22×C32—21no—
245C22×C32—24no—
246C22×C32—22no—
247C22×C32—42no—
248C22×C32—42no—
249C22×C32—84no—
250C22×C32C22×D411yescharacteristic
251C32×C4—21no—
252C32×C4—22no—
253C32×C4—22no—
254C32×C4—42no—
255C32×C4C2×#4112yes—
256C3×Dic3—42no—
257C3×Dic3—42no—
258C22×D4C2×C3×D311yescharacteristic
259C2×SD16—32no—
260C2×SD16—32no—
261C4⋊Q8—31no—
262#126—62no—
263#125—31no—
264#125—62no—
265C22⋊Q8—32no—
266C4×Q8—32no—
267C4×D4—22no—
268C4×D4C2×C3×D312yes—
269C4×D4C2×C3×D312yes—
270#117C2×C3×D311yescharacteristic
271#117C2×C3×D311yescharacteristic
272C2×C22⋊C4—22no—
273#107—32no—
274#106—32no—
275C4⋊C8—32no—
276#103—32no—
277#103—32no—
278#102—32no—
279#102—32no—
280C22⋊C8—32no—
281#97—31no—
282C4×C8—31no—
283C23×C3—24no—
284C23×C3—28no—
285C23×C3—24no—
286C23×C3—24no—
287C23×C3—22no—
288C23×C3—22no—
289C23×C3—21no—
290C23×C3—82no—
291C23×C3—82no—
292C23×C3—84no—
293C23×C3C2×#6711yescharacteristic
294C23×C3C2×C3×D411yescharacteristic
295C3×Q8—62no—
296C3×Q8—62no—
297C3×D4—28no—
298C3×D4—24no—
299C3×D4—24no—
300C3×D4—24no—
301C3×D4—22no—
302C3×D4—22no—
303C3×D4—24no—
304C3×D4#23514yes—
305C3×D4C3×#4114yes—
306C2×C3×C4—24no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—24no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—62no—
317C2×C3×C4—62no—
318C2×C3×C4—82no—
319C2×C3×C4—82no—
320C2×C3×C4—82no—
321C2×C3×C4—82no—
322C2×C3×C4—84no—
323C2×C3×C4—84no—
324C2×C3×C4C2×#6711yescharacteristic
325C2×C3×C4C2×#6712yes—
326C2×C3×C4C2×#6712yes—
327C2×C3×C4C2×C3×D412yes—
328C2×C3×C4C2×C3×D411yescharacteristic
329C2×C3×C4C2×C3×D412yes—
330C2×C3×C4C23×D311yescharacteristic
331C2×C3×C4C24×C311yescharacteristic
332C2×Dic3—22no—
333C2×Dic3—22no—
334Dic6—22no—
335Dic6—22no—
336C3×C8—62no—
337C3×C8—62no—
338C3⋊C8—22no—
339C3⋊C8—22no—
340C2×C32—41no—
341C2×C32—44no—
342C2×C32#52511yescharacteristic
343C2×C32#57712yes—
344C24—21no—
345C2×Q8—32no—
346C2×D4—24no—
347C2×D4—21no—
348C2×D4C22×C3×D312yes—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4C22×C3×D311yescharacteristic
352SD16—64no—
353SD16—64no—
354C2×C8—32no—
355C2×C8—32no—
356C4⋊C4—32no—
357C4⋊C4—62no—
358C4⋊C4—62no—
359C4⋊C4—62no—
360C4⋊C4—62no—
361C4⋊C4C3×#6712yes—
362C4⋊C4C22×C3×D312yes—
363C22⋊C4—21no—
364C22⋊C4—22no—
365C22⋊C4—22no—
366C22⋊C4—62no—
367C22⋊C4C3×#6712yes—
368C42—21no—
369C42—62no—
370C42C22×C3×D311yescharacteristic
371C42C22×C3×D311yescharacteristic
372C22×C3—22no—
373C22×C3—28no—
374C22×C3—22no—
375C22×C3—21no—
376C22×C3—24no—
377C22×C3—22no—
378C22×C3—21no—
379C22×C3—24no—
380C22×C3—21no—
381C22×C3—42no—
382C22×C3—44no—
383C22×C3—44no—
384C22×C3—42no—
385C22×C3—42no—
386C22×C3—42no—
387C22×C3—42no—
388C22×C3—88no—
389C22×C3—84no—
390C22×C3—84no—
391C22×C3C22×#6711yescharacteristic
392C22×C3C22×C3×D411yescharacteristic
393C3×C4—22no—
394C3×C4—22no—
395C3×C4—22no—
396C3×C4—21no—
397C3×C4—22no—
398C3×C4—22no—
399C3×C4—21no—
400C3×C4—22no—
401C3×C4—42no—
402C3×C4—42no—
403C3×C4—44no—
404C3×C4—42no—
405C3×C4—42no—
406C3×C4—122no—
407C3×C4—122no—
408C3×C4C2×#23512yes—
409C3×C4C2×C3×#4112yes—
410Dic3—42no—
411Dic3—42no—
412C32#312311yescharacteristic, complemented, Sylow
413C23—24no—
414C23—22no—
415C23—82no—
416C23C2×C3×#6711yescharacteristic
417Q8—62no—
418Q8—62no—
419D4—24no—
420D4—22no—
421D4C3×#23514yes—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—62no—
425C2×C4—62no—
426C2×C4—82no—
427C2×C4—82no—
428C2×C4C2×C3×#6711yescharacteristic
429C2×C4C2×C3×#6712yes—
430C2×C4C2×C3×#6712yes—
431C2×C4C23×C3×D311yescharacteristic
432C8—62no—
433C8—62no—
434C2×C3—21no—
435C2×C3—22no—
436C2×C3—42no—
437C2×C3—48no—
438C2×C3—41no—
439C2×C3—44no—
440C2×C3—41no—
441C2×C3—44no—
442C2×C3#579111yescharacteristic
443C2×C3#583612yes—
444C2×C3C3×#52511yescharacteristic
445C2×C3C3×#57712yes—
446C22—21no—
447C22—24no—
448C22—22no—
449C22—42no—
450C22—42no—
451C22—84no—
452C22C22×C3×#6711yescharacteristic
453C4—21no—
454C4—22no—
455C4—22no—
456C4—42no—
457C4—122no—
458C4—122no—
459C4C2×C3×#23512yes—
460C3—21no—
461C3#8254511yescharacteristic, direct product factor
462C3C3×#312311yescharacteristic, complemented
463C2—41no—
464C2—44no—
465C2C3×#579111yescharacteristic
466C2C3×#583612yes—
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#518C2
socleC22×C32C22×D4
prime radicalC22×C32×D4C22
hypercenterC3×#518D3
hypocenterC3C3×#3123
LCSG ▷ C2×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
2. C3×#5518C2semidirect
4. C3×#5019C2semidirect
5. C3×#5018C2semidirect
6. C3×C4×#214C2semidirect
7. C3×#5009C2semidirect
8. C3×#5000C2semidirect
9. C3×#4996C2semidirect
11. #82545C3direct (N × H)
24. C3×#870C22semidirect
25. C3×#869C22semidirect
26. C3×C4×Dic6C22semidirect
30. C3×#810C22semidirect
31. C3×#810C22semidirect
32. C3×#808C22semidirect
33. C3×#807C22semidirect
34. C3×C4⋊(C3⋊C8)C22semidirect
35. C3×#803C22semidirect
36. C3×C4×C3⋊C8C22semidirect
41. #5518C2×C3semidirect
50. #5019C2×C3semidirect
51. #5018C2×C3semidirect
52. C4×#214C2×C3semidirect
53. #5009C2×C3semidirect
54. #5000C2×C3semidirect
55. #4996C2×C3semidirect
119. #870C22×C3semidirect
120. #869C22×C3semidirect
121. C4×Dic6C22×C3semidirect
135. #810C22×C3semidirect
136. #810C22×C3semidirect
137. #808C22×C3semidirect
138. #807C22×C3semidirect
139. C4⋊(C3⋊C8)C22×C3semidirect
140. #803C22×C3semidirect
141. C4×C3⋊C8C22×C3semidirect
412. C32#3123semidirect
461. C3#82545direct (N × H)
462. C3C3×#3123semidirect

Maximal subgroups

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

subgroupindex
C32×#5182
C3×#55182
C3×#52182
C3×#50192
C3×#50182
C3×C4×#2142
C3×#50092
C3×#50002
C3×#49962
C3×#31233
#825453