Finite Group Databasebeta

← C3×#82542 #11872715

Subgroups — C3×#82542 #11872715

Order 1152.

1005 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#518C211yesmaximal, characteristic, complemented
2C3×#5535C211yesmaximal, characteristic, complemented
3C3×#5217C212yesmaximal, complemented
4C3×#5015C212yesmaximal, complemented
5C3×#5014C212yesmaximal, complemented
6C3×C4×#213C212yesmaximal, complemented
7C3×#5009C212yesmaximal, complemented
8C3×#5003C212yesmaximal, complemented
9C3×#5000C211yesmaximal, characteristic, complemented
10C3×#3122—31nomaximal
11#82542C311yesmaximal, 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×#213C2212yes—
20C2×C3×#213C2212yes—
21C3×#930C2212yes—
22C3×#894—22no—
23C3×#884—22no—
24C3×#874C2211yescharacteristic, complemented
25C3×C4×D12C2212yescomplemented
26C3×#870C2211yescharacteristic, complemented
27C3×#832C2212yes—
28C3×#832C2212yes—
29C3×#830C2212yes—
30C3×#809C2212yescomplemented
31C3×#809C2212yescomplemented
32C3×#808C2212yescomplemented
33C3×#807C2212yescomplemented
34C3×C4⋊(C3⋊C8)C2212yescomplemented
35C3×#803C2211yescharacteristic, complemented
36C3×C4×C3⋊C8C2211yescharacteristic, complemented
37C3×#540—31no—
38C3×#518—21no—
39C3×#518D311yescharacteristic, complemented
40C3×#518C2×C311yescharacteristic, complemented
41#5535C2×C311yescharacteristic, complemented
42C3×#482—32no—
43C3×#478—32no—
44C3×#459—32no—
45C3×#447—32no—
46C3×#442—32no—
47C3×C4×D8—32no—
48C3×#433—31no—
49#5217C2×C312yescomplemented
50#5015C2×C312yescomplemented
51#5014C2×C312yescomplemented
52C4×#213C2×C312yescomplemented
53#5009C2×C312yescomplemented
54#5003C2×C312yescomplemented
55#5000C2×C311yescharacteristic, complemented
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×#67—22no—
64C2×C3×D12—22no—
65C2×C3×D12C2312yes—
66C2×C3×C4×D3—22no—
67C32×C4⋊C4D412yes—
68C32×C4⋊C4C2312yes—
69C32×C22⋊C4—21no—
70C32×C22⋊C4—22no—
71C32×C22⋊C4—22no—
72C32×C22⋊C4D412yes—
73C32×C42—21no—
74C32×C42C2311yescharacteristic
75C32×C42C2311yescharacteristic
76C3×#213—24no—
77C3×#213—24no—
78C3×(C2×D3)⋊C4—22no—
79C3×(C2×D3)⋊C4—22no—
80C3×C4⋊Dic3C2312yes—
81C3×Dic3⋊C4—22no—
82C2×C3×C3⋊C8C2312yes—
83C2×C3×C3⋊C8C2312yes—
84#3122—31noSylow
85C22×C3×D4—21no—
86C22×C3×D4C2×D311yescharacteristic
87C22×C3×D4C22×C311yescharacteristic
88C2×C3×D8—32no—
89C2×C3×D8—32no—
90C3×#127—31no—
91C3×#125—31no—
92C3×#123—62no—
93C3×#121—32no—
94C3×#121—62no—
95C3×C4×D4—24no—
96C3×C4×D4—22no—
97C3×C4×D4—22no—
98C3×C4×D4—22no—
99C3×C4×D4—22no—
100C3×C4×D4—32no—
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×#213C22×C312yes—
115C2×#213C22×C312yes—
116#930C22×C312yes—
117#894—22no—
118#884—22no—
119#874C22×C311yescharacteristic, complemented
120C4×D12C22×C312yescomplemented
121#870C22×C311yescharacteristic, complemented
122C3×#107—32no—
123C3×#106—32no—
124C3×C4⋊C8—32no—
125C3×#102—32no—
126C3×#102—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#809C22×C312yescomplemented
136#809C22×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
146C22×C3×D3—22no—
147C32×D4—24no—
148C32×D4—22no—
149C32×D4#4114yes—
150C2×C32×C4—22no—
151C2×C32×C4—22no—
152C2×C32×C4—82no—
153C2×C32×C4—82no—
154C2×C32×C4C2×D412yes—
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4C2×D412yes—
157C2×C32×C4C2411yescharacteristic
158C3×#67—82no—
159C2×C3×Dic3—22no—
160C3×D12—22no—
161C3×D12—22no—
162C3×D12—82no—
163C3×C4×D3—82no—
164C3×C3⋊C8—22no—
165C3×C3⋊C8—22no—
166#540—31no—
167#518C3×D311yescharacteristic, complemented
168#482—32no—
169#478—32no—
170#459—32no—
171#447—32no—
172#442—32no—
173C4×D8—32no—
174#433—31no—
175C24×C3—22no—
176C24×C3—21no—
177C24×C3—21no—
178C2×C3×D4—22no—
179C2×C3×D4—28no—
180C2×C3×D4—24no—
181C2×C3×D4—24no—
182C2×C3×D4—21no—
183C2×C3×D4—21no—
184C2×C3×D4—22no—
185C2×C3×D4—32no—
186C2×C3×D4—62no—
187C2×C3×D4—62no—
188C2×C3×D4C22×D312yes—
189C2×C3×D4C23×C312yes—
190C22×C3×C4—24no—
191C22×C3×C4—24no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—21no—
197C22×C3×C4—62no—
198C22×C3×C4C22×D311yescharacteristic
199C22×C3×C4C23×C311yescharacteristic
200C2×#67—22no—
201C2×D12—22no—
202C2×D12C23×C312yes—
203C2×C4×D3—22no—
204C3×D8—64no—
205C3×D8—64no—
206C2×C3×C8—32no—
207C2×C3×C8—32no—
208C3×C4⋊C4—22no—
209C3×C4⋊C4—22no—
210C3×C4⋊C4—32no—
211C3×C4⋊C4—62no—
212C3×C4⋊C4#6712yes—
213C3×C4⋊C4C3×D412yes—
214C3×C4⋊C4C22×D312yes—
215C3×C4⋊C4C23×C312yes—
216C3×C22⋊C4—22no—
217C3×C22⋊C4—24no—
218C3×C22⋊C4—24no—
219C3×C22⋊C4—21no—
220C3×C22⋊C4—21no—
221C3×C22⋊C4—22no—
222C3×C22⋊C4—22no—
223C3×C22⋊C4—22no—
224C3×C22⋊C4—22no—
225C3×C22⋊C4—22no—
226C3×C22⋊C4—62no—
227C3×C22⋊C4—62no—
228C3×C22⋊C4#6712yes—
229C3×C22⋊C4C3×D412yes—
230C3×C42—22no—
231C3×C42—21no—
232C3×C42—21no—
233C3×C42—21no—
234C3×C42—21no—
235C3×C42C22×D311yescharacteristic
236C3×C42C22×D311yescharacteristic
237C3×C42C23×C311yescharacteristic
238C3×C42C23×C311yescharacteristic
239#213—24no—
240#213—24no—
241(C2×D3)⋊C4—22no—
242(C2×D3)⋊C4—22no—
243C4⋊Dic3C23×C312yes—
244Dic3⋊C4—22no—
245C2×C3⋊C8C23×C312yes—
246C2×C3⋊C8C23×C312yes—
247C22×C32—21no—
248C22×C32—24no—
249C22×C32—22no—
250C22×C32—42no—
251C22×C32—42no—
252C22×C32—84no—
253C22×C32C22×D411yescharacteristic
254C2×C3×D3—42no—
255C2×C3×D3—42no—
256C2×C3×D3—42no—
257C32×C4—21no—
258C32×C4—22no—
259C32×C4—22no—
260C32×C4—42no—
261C32×C4C2×#4112yes—
262C3×Dic3—42no—
263C22×D4C2×C3×D311yescharacteristic
264C2×D8—32no—
265C2×D8—32no—
266#127—31no—
267#125—31no—
268#123—62no—
269#121—32no—
270#121—62no—
271C4×D4—22no—
272C4×D4—32no—
273C4×D4C2×C3×D312yes—
274C4×D4C2×C3×D312yes—
275#117C2×C3×D311yescharacteristic
276#117C2×C3×D311yescharacteristic
277C2×C22⋊C4—22no—
278#107—32no—
279#106—32no—
280C4⋊C8—32no—
281#102—32no—
282#102—32no—
283#102—32no—
284#102—32no—
285C22⋊C8—32no—
286#97—31no—
287C4×C8—31no—
288C23×C3—24no—
289C23×C3—28no—
290C23×C3—24no—
291C23×C3—24no—
292C23×C3—22no—
293C23×C3—22no—
294C23×C3—21no—
295C23×C3—62no—
296C23×C3—82no—
297C23×C3—82no—
298C23×C3—84no—
299C23×C3C2×#6711yescharacteristic
300C23×C3C2×C3×D411yescharacteristic
301C22×D3—22no—
302C3×D4—28no—
303C3×D4—24no—
304C3×D4—24no—
305C3×D4—24no—
306C3×D4—22no—
307C3×D4—22no—
308C3×D4—24no—
309C3×D4—62no—
310C3×D4—62no—
311C3×D4—242no—
312C3×D4—242no—
313C3×D4#23514yes—
314C3×D4C3×#4114yes—
315C2×C3×C4—24no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—24no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—62no—
326C2×C3×C4—82no—
327C2×C3×C4—82no—
328C2×C3×C4—82no—
329C2×C3×C4—82no—
330C2×C3×C4—84no—
331C2×C3×C4—84no—
332C2×C3×C4—242no—
333C2×C3×C4C2×#6711yescharacteristic
334C2×C3×C4C2×#6712yes—
335C2×C3×C4C2×#6712yes—
336C2×C3×C4C2×C3×D412yes—
337C2×C3×C4C2×C3×D411yescharacteristic
338C2×C3×C4C2×C3×D412yes—
339C2×C3×C4C23×D311yescharacteristic
340C2×C3×C4C24×C311yescharacteristic
341#67—82no—
342C2×Dic3—22no—
343D12—22no—
344D12—22no—
345D12—82no—
346C4×D3—82no—
347C3×C8—62no—
348C3×C8—62no—
349C3⋊C8—22no—
350C3⋊C8—22no—
351C2×C32—41no—
352C2×C32—44no—
353C2×C32#52511yescharacteristic
354C2×C32#57612yes—
355C3×D3—82no—
356C24—21no—
357C2×D4—24no—
358C2×D4—21no—
359C2×D4—32no—
360C2×D4—62no—
361C2×D4—62no—
362C2×D4C22×C3×D312yes—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—62no—
366C22×C4C22×C3×D311yescharacteristic
367D8—64no—
368D8—64no—
369C2×C8—32no—
370C2×C8—32no—
371C4⋊C4—32no—
372C4⋊C4—62no—
373C4⋊C4C3×#6712yes—
374C4⋊C4C22×C3×D312yes—
375C22⋊C4—21no—
376C22⋊C4—22no—
377C22⋊C4—22no—
378C22⋊C4—62no—
379C22⋊C4—62no—
380C22⋊C4C3×#6712yes—
381C42—21no—
382C42C22×C3×D311yescharacteristic
383C42C22×C3×D311yescharacteristic
384C22×C3—22no—
385C22×C3—28no—
386C22×C3—22no—
387C22×C3—21no—
388C22×C3—24no—
389C22×C3—22no—
390C22×C3—21no—
391C22×C3—24no—
392C22×C3—21no—
393C22×C3—42no—
394C22×C3—44no—
395C22×C3—44no—
396C22×C3—42no—
397C22×C3—42no—
398C22×C3—42no—
399C22×C3—42no—
400C22×C3—88no—
401C22×C3—84no—
402C22×C3—84no—
403C22×C3—122no—
404C22×C3—122no—
405C22×C3—122no—
406C22×C3C22×#6711yescharacteristic
407C22×C3C22×C3×D411yescharacteristic
408C2×D3—42no—
409C2×D3—42no—
410C2×D3—42no—
411C3×C4—22no—
412C3×C4—22no—
413C3×C4—22no—
414C3×C4—21no—
415C3×C4—22no—
416C3×C4—22no—
417C3×C4—21no—
418C3×C4—22no—
419C3×C4—42no—
420C3×C4—42no—
421C3×C4—44no—
422C3×C4—42no—
423C3×C4—42no—
424C3×C4—122no—
425C3×C4C2×#23512yes—
426C3×C4C2×C3×#4112yes—
427Dic3—42no—
428C32#312211yescharacteristic, complemented, Sylow
429C23—24no—
430C23—22no—
431C23—62no—
432C23—82no—
433C23C2×C3×#6711yescharacteristic
434D4—24no—
435D4—22no—
436D4—62no—
437D4—62no—
438D4—242no—
439D4—242no—
440D4C3×#23514yes—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—62no—
444C2×C4—82no—
445C2×C4—82no—
446C2×C4—242no—
447C2×C4C2×C3×#6711yescharacteristic
448C2×C4C2×C3×#6712yes—
449C2×C4C2×C3×#6712yes—
450C2×C4C23×C3×D311yescharacteristic
451C8—62no—
452C8—62no—
453C2×C3—21no—
454C2×C3—22no—
455C2×C3—42no—
456C2×C3—48no—
457C2×C3—41no—
458C2×C3—44no—
459C2×C3—41no—
460C2×C3—44no—
461C2×C3—242no—
462C2×C3#579111yescharacteristic
463C2×C3#583512yes—
464C2×C3C3×#52511yescharacteristic
465C2×C3C3×#57612yes—
466D3—82no—
467C22—21no—
468C22—24no—
469C22—22no—
470C22—42no—
471C22—42no—
472C22—84no—
473C22—122no—
474C22—122no—
475C22—122no—
476C22C22×C3×#6711yescharacteristic
477C4—21no—
478C4—22no—
479C4—22no—
480C4—42no—
481C4—122no—
482C4C2×C3×#23512yes—
483C3—21no—
484C3#8254211yescharacteristic, direct product factor
485C3C3×#312211yescharacteristic, complemented
486C2—41no—
487C2—44no—
488C2—242no—
489C2C3×#579111yescharacteristic
490C2C3×#583512yes—
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#518C2
socleC22×C32C22×D4
hypercenterC3×#518D3
hypocenterC3C3×#3122
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
1. C32×#518C2semidirect
2. C3×#5535C2semidirect
3. C3×#5217C2semidirect
4. C3×#5015C2semidirect
5. C3×#5014C2semidirect
6. C3×C4×#213C2semidirect
7. C3×#5009C2semidirect
8. C3×#5003C2semidirect
9. C3×#5000C2semidirect
11. #82542C3direct (N × H)
24. C3×#874C22semidirect
25. C3×C4×D12C22semidirect
26. C3×#870C22semidirect
30. C3×#809C22semidirect
31. C3×#809C22semidirect
32. C3×#808C22semidirect
33. C3×#807C22semidirect
34. C3×C4⋊(C3⋊C8)C22semidirect
35. C3×#803C22semidirect
36. C3×C4×C3⋊C8C22semidirect
39. C3×#518D3semidirect
40. C3×#518C2×C3semidirect
41. #5535C2×C3semidirect
49. #5217C2×C3semidirect
50. #5015C2×C3semidirect
51. #5014C2×C3semidirect
52. C4×#213C2×C3semidirect
53. #5009C2×C3semidirect
54. #5003C2×C3semidirect
55. #5000C2×C3semidirect
119. #874C22×C3semidirect
120. C4×D12C22×C3semidirect
121. #870C22×C3semidirect
135. #809C22×C3semidirect
136. #809C22×C3semidirect
137. #808C22×C3semidirect
138. #807C22×C3semidirect
139. C4⋊(C3⋊C8)C22×C3semidirect
140. #803C22×C3semidirect
141. C4×C3⋊C8C22×C3semidirect
167. #518C3×D3semidirect
428. C32#3122semidirect
484. C3#82542direct (N × H)
485. C3C3×#3122semidirect

Maximal subgroups

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

subgroupindex
C32×#5182
C3×#55352
C3×#52172
C3×#50152
C3×#50142
C3×C4×#2132
C3×#50092
C3×#50032
C3×#50002
C3×#31223
#825423