Finite Group Databasebeta

← C3×#86297 #11904956

Subgroups — C3×#86297 #11904956

Order 1152.

2277 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#534C211yesmaximal, characteristic
2C3×#5798C212yesmaximal, complemented
3C2×C3×#935C212yesmaximal, complemented
4C3×#5650C218yesmaximal, complemented
5C3×#5602C214yesmaximal, complemented
6C3×#5600C214yesmaximal, complemented
7C3×#5587C218yesmaximal, complemented
8C3×#5483C211yesmaximal, characteristic, complemented
9C2×C3×#877C211yesmaximal, characteristic, complemented
10C3×#3491—31nomaximal
11#86297C311yesmaximal, characteristic, direct product factor
12C22×C32×D4C2212yes—
13C23×C3×Dic3C2211yescharacteristic
14C32×#123C2214yes—
15C32×#121C2214yes—
16C32×#120C2214yes—
17C2×C32×C22⋊C4C2211yescharacteristic
18C2×C3×#217C2212yes—
19C2×C3×#217C2211yescharacteristic
20C2×C3×#217C2214yescomplemented
21C2×C3×#217C2214yescomplemented
22C3×#936C2214yescomplemented
23C3×#935C2218yes—
24C3×#935C2214yescomplemented
25C3×#935C2214yescomplemented
26C3×#935C2218yescomplemented
27C3×D4×Dic3C2218yes—
28C3×D4×Dic3C2218yescomplemented
29C3×D4×Dic3C2214yescomplemented
30C3×#926C2214yescomplemented
31C3×#924C2214yescomplemented
32C2×C3×Dic3⋊C4C2214yescomplemented
33C2×C3×Dic3⋊C4C2212yescomplemented
34C2×C3×C4×Dic3C2212yescomplemented
35C3×#890C2214yescomplemented
36C3×#889C2218yescomplemented
37C3×#887C2214yescomplemented
38C3×#879C2218yescomplemented
39C3×#879C2218yescomplemented
40C3×#878C2218yescomplemented
41C3×#878C2218yescomplemented
42C3×#877C2218yescomplemented
43C3×#877C2218yescomplemented
44C3×#552—38no—
45C3×#551—38no—
46C3×#543—31no—
47C3×#539—34no—
48C3×#534—21no—
49C3×#534D311yescharacteristic
50C3×#534C2×C311yescharacteristic
51C3×#529—34no—
52C2×C3×#123—32no—
53C3×#518—32no—
54C2×C3×#117—31no—
55#5798C2×C312yescomplemented
56C2×#935C2×C312yescomplemented
57#5650C2×C318yescomplemented
58#5602C2×C314yescomplemented
59#5600C2×C314yescomplemented
60#5587C2×C318yescomplemented
61#5483C2×C311yescharacteristic, complemented
62C2×#877C2×C311yescharacteristic, complemented
63C24×C32C2312yes—
64C24×C32C2311yescharacteristic
65C2×C32×D4—28no—
66C2×C32×D4C2314yes—
67C2×C32×D4C2314yes—
68C2×C32×D4C2314yes—
69C22×C32×C4C2312yes—
70C22×C32×C4C2312yes—
71C22×C3×Dic3—24no—
72C22×C3×Dic3C2314yes—
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2311yescharacteristic
75C22×C3×Dic3C2318yes—
76C22×C3×Dic3C2314yes—
77C22×C3×Dic3C2312yes—
78C2×C3×Dic6C2314yes—
79C32×C4⋊C4C2314yes—
80C32×C22⋊C4C2314yes—
81C32×C22⋊C4C2318yes—
82C3×#217C2314yes—
83C3×#217C2318yes—
84C3×#217C2314yes—
85C3×#217C2318yes—
86C3×#217C2318yes—
87C3×#217C2314yes—
88C3×C4⋊Dic3C2314yes—
89C3×C4⋊Dic3C2318yes—
90C3×Dic3⋊C4C2318yes—
91C3×Dic3⋊C4C2318yes—
92C3×Dic3⋊C4C2318yes—
93C3×Dic3⋊C4C2318yes—
94C3×C4×Dic3C2314yes—
95C3×C4×Dic3C2314yes—
96C3×C4×Dic3C2318yes—
97#3491—31noSylow
98C22×C3×D4—22no—
99C22×C3×D4C2×D312yes—
100C22×C3×D4C22×C312yes—
101C23×C3×C4—31no—
102C23×Dic3C22×C311yescharacteristic
103C3×#126—38no—
104C3×#126—38no—
105C3×#125—38no—
106C3×#125—34no—
107C3×#124—34no—
108C3×#123—24no—
109C3×#123—38no—
110C3×#123—34no—
111C3×#123—34no—
112C3×#123—38no—
113C3×#123C2×D314yes—
114C3×#123C22×C314yes—
115C3×C22⋊Q8—34no—
116C3×C22⋊Q8—38no—
117C3×C22⋊Q8—38no—
118C3×#121—24no—
119C3×#121C2×D314yes—
120C3×#121C22×C314yes—
121C3×#120—24no—
122C3×#120C2×D314yes—
123C3×#120C22×C314yes—
124C3×C4×Q8—34no—
125C3×C4×D4—38no—
126C3×C4×D4—38no—
127C3×C4×D4—34no—
128C3×#117—34no—
129C3×#117—38no—
130C3×#117—38no—
131C2×C3×C4⋊C4—32no—
132C2×C3×C4⋊C4—34no—
133C2×C3×C22⋊C4—21no—
134C2×C3×C22⋊C4—31no—
135C2×C3×C22⋊C4—32no—
136C2×C3×C22⋊C4—34no—
137C2×C3×C22⋊C4—34no—
138C2×C3×C22⋊C4C2×D311yescharacteristic
139C2×C3×C22⋊C4C22×C311yescharacteristic
140C2×C3×C42—32no—
141C2×#217C22×C311yescharacteristic
142C2×#217C22×C312yes—
143C2×#217C22×C314yescomplemented
144C2×#217C22×C314yescomplemented
145#936C22×C314yescomplemented
146#935C22×C318yes—
147#935C22×C314yescomplemented
148#935C22×C314yescomplemented
149#935C22×C318yescomplemented
150D4×Dic3C22×C318yes—
151D4×Dic3C22×C318yescomplemented
152D4×Dic3C22×C314yescomplemented
153#926C22×C314yescomplemented
154#924C22×C314yescomplemented
155C2×Dic3⋊C4C22×C314yescomplemented
156C2×Dic3⋊C4C22×C312yescomplemented
157C2×C4×Dic3C22×C312yescomplemented
158#890C22×C314yescomplemented
159#889C22×C318yescomplemented
160#887C22×C314yescomplemented
161#879C22×C318yescomplemented
162#879C22×C318yescomplemented
163#878C22×C318yescomplemented
164#878C22×C318yescomplemented
165#877C22×C318yescomplemented
166#877C22×C318yescomplemented
167C23×C32—24no—
168C23×C32—42no—
169C23×C32—44no—
170C23×C32#4114yes—
171C23×C32C2414yes—
172C23×C32C2412yes—
173C23×C32C2411yescharacteristic
174C32×D4—28no—
175C32×D4—28no—
176C32×D4—44no—
177C2×C32×C4—24no—
178C2×C32×C4—42no—
179C2×C32×C4C2414yes—
180C2×C32×C4C2414yes—
181C2×C3×Dic3—28no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—44no—
185C2×C3×Dic3—48no—
186C2×C3×Dic3—42no—
187C2×C3×Dic3C2412yes—
188C2×C3×Dic3C2414yes—
189C2×C3×Dic3C2418yes—
190C2×C3×Dic3C2412yes—
191C3×Dic6—44no—
192#552—38no—
193#551—38no—
194#543—31no—
195#539—34no—
196#534C3×D311yescharacteristic
197#529—34no—
198C2×#123—32no—
199#518—32no—
200C2×#117—31no—
201C24×C3—21no—
202C24×C3—22no—
203C24×C3C22×D312yes—
204C24×C3C22×D311yescharacteristic
205C24×C3C23×C312yes—
206C24×C3C23×C311yescharacteristic
207C2×C3×Q8—34no—
208C2×C3×D4—28no—
209C2×C3×D4—28no—
210C2×C3×D4—24no—
211C2×C3×D4—24no—
212C2×C3×D4—24no—
213C2×C3×D4—48no—
214C2×C3×D4C22×D314yes—
215C2×C3×D4C22×D314yes—
216C2×C3×D4C22×D314yes—
217C2×C3×D4C23×C314yes—
218C2×C3×D4C23×C314yes—
219C2×C3×D4C23×C314yes—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—31no—
223C22×C3×C4—34no—
224C22×C3×C4—31no—
225C22×C3×C4—32no—
226C22×C3×C4—34no—
227C22×C3×C4—38no—
228C22×C3×C4—64no—
229C22×C3×C4C22×D312yes—
230C22×C3×C4C22×D312yes—
231C22×C3×C4C23×C312yes—
232C22×C3×C4C23×C312yes—
233C22×Dic3—24no—
234C22×Dic3C23×C314yes—
235C22×Dic3C23×C311yescharacteristic
236C22×Dic3C23×C311yescharacteristic
237C22×Dic3C23×C318yes—
238C22×Dic3C23×C314yes—
239C22×Dic3C23×C312yes—
240C2×Dic6C23×C314yes—
241C3×C4⋊C4—24no—
242C3×C4⋊C4—38no—
243C3×C4⋊C4—38no—
244C3×C4⋊C4—38no—
245C3×C4⋊C4—38no—
246C3×C4⋊C4—38no—
247C3×C4⋊C4—34no—
248C3×C4⋊C4C22×D314yes—
249C3×C4⋊C4C23×C314yes—
250C3×C22⋊C4—24no—
251C3×C22⋊C4—28no—
252C3×C22⋊C4—34no—
253C3×C22⋊C4—34no—
254C3×C22⋊C4—38no—
255C3×C22⋊C4—34no—
256C3×C22⋊C4—38no—
257C3×C22⋊C4—38no—
258C3×C22⋊C4C22×D314yes—
259C3×C22⋊C4C22×D318yes—
260C3×C22⋊C4C23×C314yes—
261C3×C22⋊C4C23×C318yes—
262C3×C42—34no—
263C3×C42—34no—
264C3×C42—38no—
265#217C23×C314yes—
266#217C23×C318yes—
267#217C23×C314yes—
268#217C23×C318yes—
269#217C23×C318yes—
270#217C23×C314yes—
271C4⋊Dic3C23×C314yes—
272C4⋊Dic3C23×C318yes—
273Dic3⋊C4C23×C318yes—
274Dic3⋊C4C23×C318yes—
275Dic3⋊C4C23×C318yes—
276Dic3⋊C4C23×C318yes—
277C4×Dic3C23×C314yes—
278C4×Dic3C23×C314yes—
279C4×Dic3C23×C318yes—
280C22×C32—22no—
281C22×C32—24no—
282C22×C32—24no—
283C22×C32—28no—
284C22×C32—44no—
285C22×C32—84no—
286C22×C32C2×#4114yes—
287C22×C32C2×#4112yes—
288C22×C32C2511yescharacteristic
289C32×C4—24no—
290C32×C4—24no—
291C3×Dic3—22no—
292C3×Dic3—22no—
293C3×Dic3—28no—
294C3×Dic3—24no—
295C22×D4C2×C3×D312yes—
296C23×C4—31no—
297#126—38no—
298#126—38no—
299#125—34no—
300#125—38no—
301#124—34no—
302#123—34no—
303#123—34no—
304#123—38no—
305#123—38no—
306#123C2×C3×D314yes—
307C22⋊Q8—34no—
308C22⋊Q8—38no—
309C22⋊Q8—38no—
310#121C2×C3×D314yes—
311#120C2×C3×D314yes—
312C4×Q8—34no—
313C4×D4—38no—
314C4×D4—38no—
315C4×D4—34no—
316#117—34no—
317#117—38no—
318#117—38no—
319C2×C4⋊C4—32no—
320C2×C4⋊C4—34no—
321C2×C22⋊C4—31no—
322C2×C22⋊C4—32no—
323C2×C22⋊C4—34no—
324C2×C22⋊C4—34no—
325C2×C22⋊C4C2×C3×D311yescharacteristic
326C2×C42—32no—
327C23×C3—24no—
328C23×C3—24no—
329C23×C3—22no—
330C23×C3—21no—
331C23×C3—24no—
332C23×C3—24no—
333C23×C3—44no—
334C23×C3—42no—
335C23×C3—42no—
336C23×C3—44no—
337C23×C3—44no—
338C23×C3—82no—
339C23×C3—84no—
340C23×C3#23714yes—
341C23×C3C3×#4114yes—
342C23×C3C23×D314yes—
343C23×C3C23×D312yes—
344C23×C3C23×D311yescharacteristic
345C23×C3C24×C314yes—
346C23×C3C24×C312yes—
347C23×C3C24×C311yescharacteristic
348C3×Q8—124no—
349C3×D4—28no—
350C3×D4—28no—
351C3×D4—28no—
352C3×D4—28no—
353C3×D4—48no—
354C3×D4—48no—
355C3×D4—44no—
356C3×D4—44no—
357C3×D4—84no—
358C2×C3×C4—24no—
359C2×C3×C4—24no—
360C2×C3×C4—24no—
361C2×C3×C4—24no—
362C2×C3×C4—32no—
363C2×C3×C4—34no—
364C2×C3×C4—38no—
365C2×C3×C4—32no—
366C2×C3×C4—44no—
367C2×C3×C4—42no—
368C2×C3×C4—42no—
369C2×C3×C4—68no—
370C2×C3×C4—62no—
371C2×C3×C4—62no—
372C2×C3×C4—82no—
373C2×C3×C4—122no—
374C2×C3×C4—128no—
375C2×C3×C4—124no—
376C2×C3×C4C23×D314yes—
377C2×C3×C4C23×D314yes—
378C2×C3×C4C24×C314yes—
379C2×C3×C4C24×C314yes—
380C2×Dic3—28no—
381C2×Dic3—22no—
382C2×Dic3—22no—
383C2×Dic3—44no—
384C2×Dic3—48no—
385C2×Dic3—42no—
386C2×Dic3C24×C312yes—
387C2×Dic3C24×C314yes—
388C2×Dic3C24×C318yes—
389C2×Dic3C24×C312yes—
390Dic6—44no—
391C2×C32—24no—
392C2×C32—22no—
393C2×C32—44no—
394C2×C32C22×#4111yescharacteristic
395C2×C32#58512yes—
396C24C22×C3×D312yes—
397C24C22×C3×D311yescharacteristic
398C2×Q8—34no—
399C2×D4—28no—
400C2×D4C22×C3×D314yes—
401C2×D4C22×C3×D314yes—
402C2×D4C22×C3×D314yes—
403C22×C4—31no—
404C22×C4—34no—
405C22×C4—31no—
406C22×C4—32no—
407C22×C4—34no—
408C22×C4—38no—
409C22×C4—64no—
410C22×C4C22×C3×D312yes—
411C22×C4C22×C3×D312yes—
412C4⋊C4—38no—
413C4⋊C4—38no—
414C4⋊C4—38no—
415C4⋊C4—38no—
416C4⋊C4—38no—
417C4⋊C4—34no—
418C4⋊C4C22×C3×D314yes—
419C22⋊C4—34no—
420C22⋊C4—34no—
421C22⋊C4—38no—
422C22⋊C4—34no—
423C22⋊C4—38no—
424C22⋊C4—38no—
425C22⋊C4C22×C3×D314yes—
426C22⋊C4C22×C3×D318yes—
427C42—34no—
428C42—34no—
429C42—38no—
430C22×C3—22no—
431C22×C3—24no—
432C22×C3—22no—
433C22×C3—24no—
434C22×C3—24no—
435C22×C3—28no—
436C22×C3—24no—
437C22×C3—28no—
438C22×C3—24no—
439C22×C3—22no—
440C22×C3—21no—
441C22×C3—42no—
442C22×C3—44no—
443C22×C3—44no—
444C22×C3—48no—
445C22×C3—44no—
446C22×C3—44no—
447C22×C3—84no—
448C22×C3—84no—
449C22×C3—84no—
450C22×C3—88no—
451C22×C3C2×#23714yes—
452C22×C3C2×#23712yes—
453C22×C3C2×C3×#4114yes—
454C22×C3C2×C3×#4112yes—
455C22×C3C24×D311yescharacteristic
456C22×C3C25×C311yescharacteristic
457C3×C4—24no—
458C3×C4—24no—
459C3×C4—24no—
460C3×C4—24no—
461C3×C4—44no—
462C3×C4—44no—
463C3×C4—62no—
464C3×C4—62no—
465C3×C4—64no—
466C3×C4—68no—
467Dic3—22no—
468Dic3—22no—
469Dic3—28no—
470Dic3—24no—
471C32#349111yescharacteristic, complemented, Sylow
472C23—24no—
473C23—42no—
474C23—44no—
475C23C3×#23714yes—
476C23C23×C3×D314yes—
477C23C23×C3×D312yes—
478C23C23×C3×D311yescharacteristic
479Q8—124no—
480D4—28no—
481D4—28no—
482D4—44no—
483C2×C4—24no—
484C2×C4—32no—
485C2×C4—34no—
486C2×C4—38no—
487C2×C4—32no—
488C2×C4—42no—
489C2×C4—68no—
490C2×C4—62no—
491C2×C4—62no—
492C2×C4—122no—
493C2×C4—128no—
494C2×C4—124no—
495C2×C4C23×C3×D314yes—
496C2×C4C23×C3×D314yes—
497C2×C3—24no—
498C2×C3—22no—
499C2×C3—24no—
500C2×C3—22no—
501C2×C3—21no—
502C2×C3—22no—
503C2×C3—44no—
504C2×C3—42no—
505C2×C3—44no—
506C2×C3—44no—
507C2×C3—84no—
508C2×C3C22×#23711yescharacteristic
509C2×C3#596612yes—
510C2×C3C22×C3×#4111yescharacteristic
511C2×C3C3×#58512yes—
512C22—22no—
513C22—24no—
514C22—24no—
515C22—28no—
516C22—44no—
517C22—84no—
518C22C2×C3×#23714yes—
519C22C2×C3×#23712yes—
520C22C24×C3×D311yescharacteristic
521C4—24no—
522C4—24no—
523C4—62no—
524C4—62no—
525C4—64no—
526C4—68no—
527C3—21no—
528C3#8629711yescharacteristic, direct product factor
529C3C3×#349111yescharacteristic, complemented
530C2—24no—
531C2—22no—
532C2—44no—
533C2C22×C3×#23711yescharacteristic
534C2C3×#596612yes—
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
Fitting, prime radicalC32×#534C2
socleC22×C32C25
hypercenterC3×#534D3
hypocenterC3C3×#3491
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#534

Complements

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

NH ≅ G/Ntype
2. C3×#5798C2semidirect
3. C2×C3×#935C2semidirect
4. C3×#5650C2semidirect
5. C3×#5602C2semidirect
6. C3×#5600C2semidirect
7. C3×#5587C2semidirect
8. C3×#5483C2semidirect
9. C2×C3×#877C2semidirect
11. #86297C3direct (N × H)
20. C2×C3×#217C22semidirect
21. C2×C3×#217C22semidirect
22. C3×#936C22semidirect
24. C3×#935C22semidirect
25. C3×#935C22semidirect
26. C3×#935C22semidirect
28. C3×D4×Dic3C22semidirect
29. C3×D4×Dic3C22semidirect
30. C3×#926C22semidirect
31. C3×#924C22semidirect
32. C2×C3×Dic3⋊C4C22semidirect
33. C2×C3×Dic3⋊C4C22semidirect
34. C2×C3×C4×Dic3C22semidirect
35. C3×#890C22semidirect
36. C3×#889C22semidirect
37. C3×#887C22semidirect
38. C3×#879C22semidirect
39. C3×#879C22semidirect
40. C3×#878C22semidirect
41. C3×#878C22semidirect
42. C3×#877C22semidirect
43. C3×#877C22semidirect
55. #5798C2×C3semidirect
56. C2×#935C2×C3semidirect
57. #5650C2×C3semidirect
58. #5602C2×C3semidirect
59. #5600C2×C3semidirect
60. #5587C2×C3semidirect
61. #5483C2×C3semidirect
62. C2×#877C2×C3semidirect
143. C2×#217C22×C3semidirect
144. C2×#217C22×C3semidirect
145. #936C22×C3semidirect
147. #935C22×C3semidirect
148. #935C22×C3semidirect
149. #935C22×C3semidirect
151. D4×Dic3C22×C3semidirect
152. D4×Dic3C22×C3semidirect
153. #926C22×C3semidirect
154. #924C22×C3semidirect
155. C2×Dic3⋊C4C22×C3semidirect
156. C2×Dic3⋊C4C22×C3semidirect
157. C2×C4×Dic3C22×C3semidirect
158. #890C22×C3semidirect
159. #889C22×C3semidirect
160. #887C22×C3semidirect
161. #879C22×C3semidirect
162. #879C22×C3semidirect
163. #878C22×C3semidirect
164. #878C22×C3semidirect
165. #877C22×C3semidirect
166. #877C22×C3semidirect
471. C32#3491semidirect
528. C3#86297direct (N × H)
529. C3C3×#3491semidirect

Maximal subgroups

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

subgroupindex
C32×#5342
C3×#57982
C2×C3×#9352
C3×#56502
C3×#56022
C3×#56002
C3×#55872
C3×#54832
C2×C3×#8772
C3×#34913
#862973