Finite Group Databasebeta

← C3×#78637 #11863933

Subgroups — C3×#78637 #11863933

Order 1152.

2083 conjugacy classes of subgroups.

The subgroup lattice has 511 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×D12C211yesmaximal, characteristic, complemented
2C3×#5791C211yesmaximal, characteristic, complemented
3C2×C3×#908C212yesmaximal, complemented
4C32×#407C211yesmaximal, characteristic, complemented
5C3×#5131C212yesmaximal, complemented
6C3×#4732C214yesmaximal, complemented
7C3×#4731C214yesmaximal, complemented
8C3×#3003—31nomaximal
9#78637C311yesmaximal, characteristic, direct product factor
10C24×C3×D3—21no—
11C23×C32×C4C2211yescharacteristic
12C2×C3×#235C2211yescharacteristic, complemented
13C22×C3×D12—22no—
14C22×C3×D12—21no—
15C22×C3×D12—28no—
16C22×C3×D12C2214yes—
17C22×C3×D12C2212yes—
18C2×C32×M16C2212yescomplemented
19C3×#953—21no—
20C3×#930C2212yescomplemented
21C3×#929—21no—
22C3×C4×#67—22no—
23C3×#926C2211yescharacteristic, complemented
24C3×#924C2212yescomplemented
25C3×#908—28no—
26C2×C3×D24C2214yescomplemented
27C2×C3×#204C2214yescomplemented
28C32×C22⋊C8C2214yescomplemented
29C3×#821C2218yescomplemented
30C23×C3×D4—31no—
31C23×D12C2×C311yescharacteristic, complemented
32C2×C3×AGL(1,ℤ/8)—32no—
33C3×#525—31no—
34#5791C2×C311yescharacteristic, complemented
35C2×#908C2×C312yescomplemented
36C3×#450—34no—
37C3×#447—34no—
38C3×#418—32no—
39C3×#407—21no—
40C3×#407D311yescharacteristic, complemented
41C3×#407C2×C311yescharacteristic, complemented
42#5131C2×C312yescomplemented
43#4732C2×C314yescomplemented
44#4731C2×C314yescomplemented
45C24×C32D411yescharacteristic
46C23×C3×D3—28no—
47C23×C3×D3—24no—
48C23×C3×D3—22no—
49C23×C3×D3—48no—
50C22×C32×C4—24no—
51C22×C32×C4D412yes—
52C22×C32×C4D411yescharacteristic
53C22×C32×C4C2312yes—
54C22×C32×C4C2311yescharacteristic
55C2×C3×#67—22no—
56C2×C3×#67—21no—
57C3×#235—24no—
58C2×C3×D12—28no—
59C2×C3×D12—216no—
60C2×C3×D12—24no—
61C2×C3×D12—22no—
62C2×C3×D12—24no—
63C2×C3×D12—216no—
64C2×C3×D12D418yescomplemented
65C2×C3×D12C2314yes—
66C2×C3×D12C2311yescharacteristic, complemented
67C2×C3×C4×D3—21no—
68C2×C3×Dic6C2311yescharacteristic, complemented
69C32×M16—24no—
70C2×C32×C8C2314yescomplemented
71C3×#217—22no—
72C3×#217—21no—
73C3×(C2×D3)⋊C4—22no—
74C3×C4⋊Dic3C2312yescomplemented
75C3×Dic3⋊C4—22no—
76C3×C4×Dic3—21no—
77C3×D24—28no—
78C3×#204—28no—
79#3003—31noSylow
80C25×C3—61no—
81C24×D3—21no—
82C2×C3×#41—31no—
83C22×C3×D4—32no—
84C22×C3×D4—34no—
85C22×C3×D4—68no—
86C22×C3×D4—62no—
87C22×C3×D4—61no—
88C23×C3×C4—21no—
89C23×C3×C4C2×D311yescharacteristic
90C23×C3×C4C22×C311yescharacteristic
91C2×#235C22×C311yescharacteristic, complemented
92C22×D12—22no—
93C22×D12—21no—
94C22×D12—28no—
95C22×D12C22×C314yes—
96C22×D12C22×C312yes—
97C3×AGL(1,ℤ/8)—68no—
98C2×C3×SD16—34no—
99C2×C3×D8—34no—
100C2×C3×M16—22no—
101C2×C3×M16C2×D312yescomplemented
102C2×C3×M16C22×C312yescomplemented
103C3×#123—61no—
104C3×C22⋊Q8—32no—
105C3×#121—32no—
106C3×#120—61no—
107C3×C4×D4—62no—
108C3×#117—31no—
109#953—21no—
110#930C22×C312yescomplemented
111#929—21no—
112C4×#67—22no—
113#926C22×C311yescharacteristic, complemented
114#924C22×C312yescomplemented
115#908—28no—
116C2×D24C22×C314yescomplemented
117C2×#204C22×C314yescomplemented
118C3×#102—38no—
119C3×C22⋊C8—24no—
120C3×C22⋊C8C2×D314yescomplemented
121C3×C22⋊C8C22×C314yescomplemented
122#821C22×C318yescomplemented
123C23×C32—22no—
124C23×C32—24no—
125C23×C32C2×D411yescharacteristic
126C23×C32C2×D412yes—
127C22×C3×D3—216no—
128C22×C3×D3—28no—
129C22×C3×D3—24no—
130C22×C3×D3—21no—
131C22×C3×D3—432no—
132C22×C3×D3—48no—
133C22×C3×D3—48no—
134C22×C3×D3—48no—
135C2×C32×C4—22no—
136C2×C32×C4—24no—
137C2×C32×C4—24no—
138C2×C32×C4C2×D412yes—
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D414yes—
141C2×C32×C4C2411yescharacteristic
142C3×#67—42no—
143C3×#67—44no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—21no—
146C3×D12—216no—
147C3×D12—28no—
148C3×D12—24no—
149C3×D12—22no—
150C3×D12C2×D418yes—
151C3×C4×D3—42no—
152C3×Dic6—22no—
153C32×C8—24no—
154C23×D4—31no—
155C2×AGL(1,ℤ/8)—32no—
156#525—31no—
157#450—34no—
158#447—34no—
159#418—32no—
160#407C3×D311yescharacteristic, complemented
161C24×C3—21no—
162C24×C3—68no—
163C24×C3—64no—
164C24×C3—62no—
165C24×C3—128no—
166C24×C3D1211yescharacteristic
167C24×C3C3×D411yescharacteristic
168C23×D3—28no—
169C23×D3—24no—
170C23×D3—22no—
171C23×D3—48no—
172C3×#41—64no—
173C2×C3×Q8—31no—
174C2×C3×D4—38no—
175C2×C3×D4—34no—
176C2×C3×D4—31no—
177C2×C3×D4—616no—
178C2×C3×D4—68no—
179C2×C3×D4—616no—
180C2×C3×D4—62no—
181C2×C3×D4—61no—
182C2×C3×D4—64no—
183C2×C3×D4—62no—
184C2×C3×D4—64no—
185C22×C3×C4—24no—
186C22×C3×C4—24no—
187C22×C3×C4—22no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—22no—
191C22×C3×C4—44no—
192C22×C3×C4—61no—
193C22×C3×C4D1212yes—
194C22×C3×C4D1211yescharacteristic
195C22×C3×C4C3×D412yes—
196C22×C3×C4C3×D411yescharacteristic
197C22×C3×C4C22×D312yes—
198C22×C3×C4C22×D311yescharacteristic
199C22×C3×C4C23×C312yes—
200C22×C3×C4C23×C311yescharacteristic
201C2×#67—22no—
202C2×#67—21no—
203#235—24no—
204C2×D12—28no—
205C2×D12—216no—
206C2×D12—24no—
207C2×D12—22no—
208C2×D12—24no—
209C2×D12—216no—
210C2×D12C3×D418yescomplemented
211C2×D12C23×C314yes—
212C2×D12C23×C311yescharacteristic, complemented
213C2×C4×D3—21no—
214C2×Dic6C23×C311yescharacteristic, complemented
215C3×SD16—68no—
216C3×D8—68no—
217C3×M16—24no—
218C3×M16—24no—
219C3×M16—44no—
220C2×C3×C8—24no—
221C2×C3×C8C22×D314yescomplemented
222C2×C3×C8C23×C314yescomplemented
223C3×C4⋊C4—32no—
224C3×C4⋊C4—62no—
225C3×C22⋊C4—61no—
226C3×C22⋊C4—62no—
227C3×C22⋊C4—62no—
228C3×C42—61no—
229#217—22no—
230#217—21no—
231(C2×D3)⋊C4—22no—
232C4⋊Dic3C23×C312yescomplemented
233Dic3⋊C4—22no—
234C4×Dic3—21no—
235D24—28no—
236#204—28no—
237C22×C32—28no—
238C22×C32—22no—
239C22×C32—22no—
240C22×C32—22no—
241C22×C32#12012yes—
242C22×C32AGL(1,ℤ/8)14yescomplemented
243C22×C32C22×D411yescharacteristic
244C2×C3×D3—28no—
245C2×C3×D3—416no—
246C2×C3×D3—432no—
247C2×C3×D3—48no—
248C2×C3×D3—41no—
249C2×C3×D3—42no—
250C32×C4—22no—
251C32×C4#12012yes—
252C32×C4C22×D412yes—
253C3×Dic3—41no—
254C3×Dic3—42no—
255C25—61no—
256C2×#41—31no—
257C22×D4—32no—
258C22×D4—34no—
259C22×D4—68no—
260C22×D4—62no—
261C22×D4—61no—
262C23×C4C2×C3×D311yescharacteristic
263AGL(1,ℤ/8)—68no—
264C2×SD16—34no—
265C2×D8—34no—
266C2×M16C2×C3×D312yescomplemented
267#123—61no—
268C22⋊Q8—32no—
269#121—32no—
270#120—61no—
271C4×D4—62no—
272#117—31no—
273#102—38no—
274C22⋊C8C2×C3×D314yescomplemented
275C23×C3—22no—
276C23×C3—24no—
277C23×C3—22no—
278C23×C3—24no—
279C23×C3—21no—
280C23×C3—22no—
281C23×C3—42no—
282C23×C3—44no—
283C23×C3—616no—
284C23×C3—68no—
285C23×C3—64no—
286C23×C3—61no—
287C23×C3—1232no—
288C23×C3—128no—
289C23×C3—128no—
290C23×C3—128no—
291C23×C3C2×D1211yescharacteristic
292C23×C3C2×D1212yes—
293C23×C3C2×C3×D411yescharacteristic
294C23×C3C2×C3×D412yes—
295C22×D3—216no—
296C22×D3—28no—
297C22×D3—24no—
298C22×D3—21no—
299C22×D3—432no—
300C22×D3—48no—
301C22×D3—48no—
302C22×D3—48no—
303C3×Q8—62no—
304C3×D4—38no—
305C3×D4—616no—
306C3×D4—68no—
307C3×D4—64no—
308C3×D4—62no—
309C3×D4—122no—
310C3×D4—124no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—24no—
314C2×C3×C4—24no—
315C2×C3×C4—24no—
316C2×C3×C4—24no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—22no—
320C2×C3×C4—24no—
321C2×C3×C4—44no—
322C2×C3×C4—44no—
323C2×C3×C4—42no—
324C2×C3×C4—62no—
325C2×C3×C4—61no—
326C2×C3×C4—122no—
327C2×C3×C4C2×D1212yes—
328C2×C3×C4C2×D1211yescharacteristic
329C2×C3×C4D3×D414yes—
330C2×C3×C4C2×C3×D412yes—
331C2×C3×C4C2×C3×D411yescharacteristic
332C2×C3×C4C2×C3×D414yes—
333C2×C3×C4C23×D311yescharacteristic
334C2×C3×C4C24×C311yescharacteristic
335#67—42no—
336#67—44no—
337C2×Dic3—22no—
338C2×Dic3—21no—
339D12—216no—
340D12—28no—
341D12—24no—
342D12—22no—
343D12C2×C3×D418yes—
344C4×D3—42no—
345Dic6—22no—
346C3×C8—24no—
347C3×C8—24no—
348C3×C8—44no—
349C2×C32—22no—
350C2×C32—24no—
351C2×C32C2×#12011yescharacteristic
352C2×C32C2×AGL(1,ℤ/8)12yes—
353C3×D3—48no—
354C3×D3—81no—
355C24—68no—
356C24—64no—
357C24—62no—
358C24—128no—
359C24C3×D1211yescharacteristic
360#41—64no—
361C2×Q8—31no—
362C2×D4—34no—
363C2×D4—31no—
364C2×D4—38no—
365C2×D4—616no—
366C2×D4—68no—
367C2×D4—616no—
368C2×D4—62no—
369C2×D4—61no—
370C2×D4—64no—
371C2×D4—62no—
372C2×D4—64no—
373C22×C4—24no—
374C22×C4—61no—
375C22×C4C3×D1212yes—
376C22×C4C3×D1211yescharacteristic
377C22×C4C22×C3×D312yes—
378C22×C4C22×C3×D311yescharacteristic
379SD16—68no—
380D8—68no—
381M16—24no—
382C2×C8C22×C3×D314yescomplemented
383C4⋊C4—32no—
384C4⋊C4—62no—
385C22⋊C4—61no—
386C22⋊C4—62no—
387C22⋊C4—62no—
388C42—61no—
389C22×C3—28no—
390C22×C3—28no—
391C22×C3—22no—
392C22×C3—22no—
393C22×C3—22no—
394C22×C3—22no—
395C22×C3—22no—
396C22×C3—22no—
397C22×C3—22no—
398C22×C3—24no—
399C22×C3—21no—
400C22×C3—42no—
401C22×C3—42no—
402C22×C3—42no—
403C22×C3—48no—
404C22×C3—68no—
405C22×C3—1216no—
406C22×C3—1232no—
407C22×C3—128no—
408C22×C3—121no—
409C22×C3—122no—
410C22×C3#88212yes—
411C22×C3#90814yescomplemented
412C22×C3C3×#12012yes—
413C22×C3C3×AGL(1,ℤ/8)14yescomplemented
414C22×C3C22×D1211yescharacteristic
415C22×C3C22×C3×D411yescharacteristic
416C2×D3—28no—
417C2×D3—416no—
418C2×D3—432no—
419C2×D3—48no—
420C2×D3—42no—
421C2×D3—41no—
422C3×C4—22no—
423C3×C4—22no—
424C3×C4—22no—
425C3×C4—22no—
426C3×C4—42no—
427C3×C4—121no—
428C3×C4—122no—
429C3×C4#88212yes—
430C3×C4C3×#12012yes—
431C3×C4C2×D3×D412yes—
432C3×C4C22×C3×D412yes—
433Dic3—42no—
434Dic3—41no—
435C32#300311yescharacteristic, complemented, Sylow
436C23—22no—
437C23—24no—
438C23—616no—
439C23—68no—
440C23—64no—
441C23—61no—
442C23—1232no—
443C23—128no—
444C23—128no—
445C23—128no—
446C23C2×C3×D1211yescharacteristic
447C23C2×C3×D1212yes—
448Q8—62no—
449D4—38no—
450D4—616no—
451D4—68no—
452D4—64no—
453D4—62no—
454D4—122no—
455D4—124no—
456C2×C4—22no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—62no—
460C2×C4—61no—
461C2×C4—122no—
462C2×C4C2×C3×D1212yes—
463C2×C4C2×C3×D1211yescharacteristic
464C2×C4C3×D3×D414yes—
465C2×C4C23×C3×D311yescharacteristic
466C8—24no—
467C2×C3—22no—
468C2×C3—24no—
469C2×C3—22no—
470C2×C3—24no—
471C2×C3—21no—
472C2×C3—22no—
473C2×C3—42no—
474C2×C3—44no—
475C2×C3—128no—
476C2×C3—241no—
477C2×C3C2×#88211yescharacteristic
478C2×C3C2×#90812yes—
479C2×C3C2×C3×#12011yescharacteristic
480C2×C3C2×C3×AGL(1,ℤ/8)12yes—
481D3—48no—
482D3—81no—
483C22—28no—
484C22—22no—
485C22—22no—
486C22—22no—
487C22—68no—
488C22—1216no—
489C22—1232no—
490C22—128no—
491C22—121no—
492C22—122no—
493C22C3×#88212yes—
494C22C3×#90814yescomplemented
495C22C22×C3×D1211yescharacteristic
496C4—22no—
497C4—121no—
498C4—122no—
499C4C3×#88212yes—
500C4C2×C3×D3×D412yes—
501C3—21no—
502C3#7863711yescharacteristic, direct product factor
503C3C3×#300311yescharacteristic, complemented
504C2—22no—
505C2—24no—
506C2—128no—
507C2—241no—
508C2C2×C3×#88211yescharacteristic
509C2C2×C3×#90812yes—
subgroupG/H
centerC22×C3C22×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#407C2
socleC22×C32C22×D4
hypercenterC3×#407D3
hypocenterC3C3×#3003
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C3×#407

Complements

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

NH ≅ G/Ntype
1. C23×C3×D12C2semidirect
2. C3×#5791C2semidirect
3. C2×C3×#908C2semidirect
4. C32×#407C2semidirect
5. C3×#5131C2semidirect
6. C3×#4732C2semidirect
7. C3×#4731C2semidirect
9. #78637C3direct (N × H)
12. C2×C3×#235C22semidirect
18. C2×C32×M16C22semidirect
20. C3×#930C22semidirect
23. C3×#926C22semidirect
24. C3×#924C22semidirect
26. C2×C3×D24C22semidirect
27. C2×C3×#204C22semidirect
28. C32×C22⋊C8C22semidirect
29. C3×#821C22semidirect
31. C23×D12C2×C3semidirect
34. #5791C2×C3semidirect
35. C2×#908C2×C3semidirect
40. C3×#407D3semidirect
41. C3×#407C2×C3semidirect
42. #5131C2×C3semidirect
43. #4732C2×C3semidirect
44. #4731C2×C3semidirect
64. C2×C3×D12D4semidirect
66. C2×C3×D12C23semidirect
68. C2×C3×Dic6C23semidirect
70. C2×C32×C8C23semidirect
74. C3×C4⋊Dic3C23semidirect
91. C2×#235C22×C3semidirect
101. C2×C3×M16C2×D3semidirect
102. C2×C3×M16C22×C3semidirect
110. #930C22×C3semidirect
113. #926C22×C3semidirect
114. #924C22×C3semidirect
116. C2×D24C22×C3semidirect
117. C2×#204C22×C3semidirect
120. C3×C22⋊C8C2×D3semidirect
121. C3×C22⋊C8C22×C3semidirect
122. #821C22×C3semidirect
160. #407C3×D3semidirect
210. C2×D12C3×D4semidirect
212. C2×D12C23×C3semidirect
214. C2×Dic6C23×C3semidirect
221. C2×C3×C8C22×D3semidirect
222. C2×C3×C8C23×C3semidirect
232. C4⋊Dic3C23×C3semidirect
242. C22×C32AGL(1,ℤ/8)semidirect
266. C2×M16C2×C3×D3semidirect
274. C22⋊C8C2×C3×D3semidirect
382. C2×C8C22×C3×D3semidirect
411. C22×C3#908semidirect
413. C22×C3C3×AGL(1,ℤ/8)semidirect
435. C32#3003semidirect
494. C22C3×#908semidirect
502. C3#78637direct (N × H)
503. C3C3×#3003semidirect

Maximal subgroups

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

subgroupindex
C23×C3×D122
C3×#57912
C2×C3×#9082
C32×#4072
C3×#51312
C3×#47322
C3×#47312
C3×#30033
#786373