Finite Group Databasebeta

← C3×#83969 #11866327

Subgroups — C3×#83969 #11866327

Order 1152.

1109 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#137C211yesmaximal, characteristic, complemented
2C3×#5830C211yesmaximal, characteristic
3C3×#5812C211yesmaximal, characteristic, complemented
4C22×C3×#215C211yesmaximal, characteristic, complemented
5C3×#5233C211yesmaximal, characteristic, complemented
6C3×#5185C214yesmaximal, complemented
7C3×#5163C214yesmaximal, complemented
8C3×#5131C211yesmaximal, characteristic, complemented
9C3×#5119C211yesmaximal, characteristic, complemented
10C3×#3043—31nomaximal
11#83969C311yesmaximal, characteristic, direct product factor
12C2×C32×#41C2211yescharacteristic
13C22×C32×Q8C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C32×#137—24no—
16C2×C32×Q16C2212yescomplemented
17C2×C32×SD16C2212yescomplemented
18C2×C32×M16C2211yescharacteristic
19C3×#947C2212yes—
20C3×Q8×Dic3—22no—
21C3×Q8×Dic3C2214yescomplemented
22C2×C3×#215—24no—
23C2×C3×#215C2214yes—
24C3×#940C2212yes—
25C3×#937—22no—
26C3×#930—22no—
27C3×#926—22no—
28C3×#926C2211yescharacteristic
29C3×#926C2211yescharacteristic
30C22×C3×C3⋊C8C2211yescharacteristic
31C3×#835C2212yescomplemented
32C3×#832C2212yescomplemented
33C3×#821C2214yes—
34C3×Dic3⋊C8C2214yescomplemented
35C2×C3×#137—21no—
36C2×C3×#137D311yescharacteristic, complemented
37C2×C3×#137C2×C311yescharacteristic, complemented
38C22×C3×SD16—31no—
39C3×#535—31no—
40C3×#519—31no—
41#5830C2×C311yescharacteristic
42#5812C2×C311yescharacteristic, complemented
43C22×#215C2×C311yescharacteristic, complemented
44C3×#464—34no—
45C3×#460—34no—
46C3×#424—31no—
47C3×#418—31no—
48C3×#416—31no—
49#5233C2×C311yescharacteristic, complemented
50#5185C2×C314yescomplemented
51#5163C2×C314yescomplemented
52#5131C2×C311yescharacteristic, complemented
53#5119C2×C311yescharacteristic, complemented
54C23×C3×D3—21no—
55C32×#41—22no—
56C32×#41—22no—
57C2×C32×Q8—21no—
58C2×C32×Q8—22no—
59C2×C32×Q8D414yescomplemented
60C2×C32×Q8C2311yescharacteristic
61C2×C32×Q8C2312yes—
62C2×C32×D4—21no—
63C2×C32×D4C2311yescharacteristic
64C22×C32×C4—21no—
65C22×C32×C4—21no—
66C22×C32×C4C2311yescharacteristic
67C2×C3×#67—24no—
68C2×C3×D12—22no—
69C2×C3×D12—22no—
70C2×C3×D12—21no—
71C2×C3×D12C2312yes—
72C32×Q16—24no—
73C32×SD16—24no—
74C32×M16—22no—
75C2×C32×C8C2312yes—
76C3×#217—21no—
77C3×#217D412yes—
78C3×#215—28no—
79C3×(C2×D3)⋊C4—24no—
80C3×C4⋊Dic3—24no—
81C3×C4⋊Dic3D412yes—
82C3×C4⋊Dic3C2312yes—
83C3×C4×Dic3—21no—
84C3×C4×Dic3—24no—
85C3×C4×Dic3C2312yes—
86C2×C3×C3⋊C8—22no—
87C2×C3×C3⋊C8C2312yes—
88#3043—31noSylow
89C2×C3×#41—21no—
90C2×C3×#41C2×D311yescharacteristic
91C2×C3×#41C22×C311yescharacteristic
92C22×C3×Q8—21no—
93C22×C3×Q8C2×D311yescharacteristic
94C22×C3×Q8C22×C311yescharacteristic
95C22×C3×D4—31no—
96C22×D12C22×C311yescharacteristic
97C3×#137—28no—
98C3×#137—24no—
99C3×#137—24no—
100C2×C3×Q16—22no—
101C2×C3×Q16C2×D312yescomplemented
102C2×C3×Q16C22×C312yescomplemented
103C2×C3×SD16—22no—
104C2×C3×SD16—34no—
105C2×C3×SD16—64no—
106C2×C3×SD16C2×D312yescomplemented
107C2×C3×SD16C22×C312yescomplemented
108C2×C3×M16—21no—
109C2×C3×M16C2×D311yescharacteristic
110C2×C3×M16C22×C311yescharacteristic
111C22×C3×C8—31no—
112C3×#127—32no—
113C3×#124—32no—
114C3×#121—62no—
115C3×#120—62no—
116C3×C4×Q8—34no—
117C3×C4×Q8—62no—
118C3×#117—31no—
119C3×#117—31no—
120C3×#117—62no—
121#947C22×C312yes—
122Q8×Dic3—22no—
123Q8×Dic3C22×C314yescomplemented
124C2×#215—24no—
125C2×#215C22×C314yes—
126#940C22×C312yes—
127#937—22no—
128#930—22no—
129#926—22no—
130#926C22×C311yescharacteristic
131#926C22×C311yescharacteristic
132C22×C3⋊C8C22×C311yescharacteristic
133C3×C4⋊C8—34no—
134C3×#103—32no—
135C3×#102—32no—
136C3×#102—34no—
137#835C22×C312yescomplemented
138#832C22×C312yescomplemented
139#821C22×C314yes—
140Dic3⋊C8C22×C314yescomplemented
141C23×C32—21no—
142C23×C32C2×D411yescharacteristic
143C22×C3×D3—22no—
144C22×C3×D3—42no—
145C22×C3×D3—82no—
146C32×Q8—21no—
147C32×Q8—24no—
148C32×Q8—22no—
149C32×Q8—21no—
150C32×Q8C2×D414yes—
151C32×D4—21no—
152C32×D4—21no—
153C32×D4—42no—
154C2×C32×C4—24no—
155C2×C32×C4—22no—
156C2×C32×C4—21no—
157C2×C32×C4—42no—
158C2×C32×C4C2×D411yescharacteristic
159C2×C32×C4C2×D412yes—
160C2×C32×C4#4112yes—
161C2×C32×C4C2411yescharacteristic
162C3×#67—84no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3C2×D414yes—
165C3×D12—22no—
166C3×D12—22no—
167C3×D12—42no—
168C32×C8—22no—
169C3×C3⋊C8—22no—
170C2×#137C3×D311yescharacteristic, complemented
171C22×SD16—31no—
172#535—31no—
173#519—31no—
174#464—34no—
175#460—34no—
176#424—31no—
177#418—31no—
178#416—31no—
179C24×C3—61no—
180C23×D3—21no—
181C3×#41—24no—
182C3×#41—22no—
183C3×#41—22no—
184C3×#41—22no—
185C3×#41—22no—
186C3×#41—42no—
187C2×C3×Q8—21no—
188C2×C3×Q8—22no—
189C2×C3×Q8—21no—
190C2×C3×Q8—22no—
191C2×C3×Q8—24no—
192C2×C3×Q8—22no—
193C2×C3×Q8—21no—
194C2×C3×Q8—41no—
195C2×C3×Q8—42no—
196C2×C3×Q8#6714yescomplemented
197C2×C3×Q8C3×D414yescomplemented
198C2×C3×Q8C22×D311yescharacteristic
199C2×C3×Q8C22×D312yes—
200C2×C3×Q8C23×C311yescharacteristic
201C2×C3×Q8C23×C312yes—
202C2×C3×D4—21no—
203C2×C3×D4—21no—
204C2×C3×D4—21no—
205C2×C3×D4—32no—
206C2×C3×D4—41no—
207C2×C3×D4—64no—
208C2×C3×D4—61no—
209C2×C3×D4—62no—
210C2×C3×D4—62no—
211C2×C3×D4C22×D311yescharacteristic
212C2×C3×D4C23×C311yescharacteristic
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—41no—
219C22×C3×C4—41no—
220C22×C3×C4C22×D311yescharacteristic
221C22×C3×C4C23×C311yescharacteristic
222C2×#67—24no—
223C2×D12—22no—
224C2×D12—22no—
225C2×D12—21no—
226C2×D12C23×C312yes—
227C3×Q16—28no—
228C3×Q16—24no—
229C3×Q16—24no—
230C3×SD16—28no—
231C3×SD16—24no—
232C3×SD16—24no—
233C3×SD16—68no—
234C3×M16—24no—
235C3×M16—22no—
236C3×M16—22no—
237C2×C3×C8—22no—
238C2×C3×C8—32no—
239C2×C3×C8—62no—
240C2×C3×C8C22×D312yes—
241C2×C3×C8C23×C312yes—
242C3×C4⋊C4—32no—
243C3×C4⋊C4—32no—
244C3×C4⋊C4—64no—
245C3×C22⋊C4—32no—
246C3×C22⋊C4—64no—
247C3×C22⋊C4—61no—
248C3×C42—32no—
249C3×C42—64no—
250C3×C42—61no—
251#217—21no—
252#217C3×D412yes—
253#215—28no—
254(C2×D3)⋊C4—24no—
255C4⋊Dic3—24no—
256C4⋊Dic3C3×D412yes—
257C4⋊Dic3C23×C312yes—
258C4×Dic3—21no—
259C4×Dic3—24no—
260C4×Dic3C23×C312yes—
261C2×C3⋊C8—22no—
262C2×C3⋊C8C23×C312yes—
263C22×C32—22no—
264C22×C32—41no—
265C22×C32—42no—
266C22×C32#12112yes—
267C22×C32C22×D411yescharacteristic
268C2×C3×D3—42no—
269C2×C3×D3—44no—
270C2×C3×D3—84no—
271C32×C4—24no—
272C32×C4—41no—
273C32×C4#12112yes—
274C32×C4C22×D411yescharacteristic
275C32×C4C2×#4111yescharacteristic
276C3×Dic3—24no—
277C3×Dic3—42no—
278C2×#41C2×C3×D311yescharacteristic
279C22×Q8C2×C3×D311yescharacteristic
280C22×D4—31no—
281#137—24no—
282C2×Q16C2×C3×D312yescomplemented
283C2×SD16—34no—
284C2×SD16—64no—
285C2×SD16C2×C3×D312yescomplemented
286C2×M16C2×C3×D311yescharacteristic
287C22×C8—31no—
288#127—32no—
289#124—32no—
290#121—62no—
291#120—62no—
292C4×Q8—34no—
293C4×Q8—62no—
294#117—31no—
295#117—31no—
296#117—62no—
297C4⋊C8—34no—
298#103—32no—
299#102—32no—
300#102—34no—
301C23×C3—21no—
302C23×C3—21no—
303C23×C3—21no—
304C23×C3—41no—
305C23×C3—62no—
306C23×C3—122no—
307C23×C3—242no—
308C23×C3D3×D411yescharacteristic
309C23×C3C2×C3×D411yescharacteristic
310C22×D3—22no—
311C22×D3—42no—
312C22×D3—82no—
313C3×Q8—24no—
314C3×Q8—24no—
315C3×Q8—22no—
316C3×Q8—22no—
317C3×Q8—22no—
318C3×Q8—21no—
319C3×Q8—21no—
320C3×Q8—21no—
321C3×Q8—21no—
322C3×Q8—24no—
323C3×Q8—44no—
324C3×Q8—42no—
325C3×Q8—41no—
326C3×Q8C2×#6714yes—
327C3×Q8C2×C3×D414yes—
328C3×D4—22no—
329C3×D4—21no—
330C3×D4—21no—
331C3×D4—21no—
332C3×D4—21no—
333C3×D4—41no—
334C3×D4—44no—
335C3×D4—42no—
336C3×D4—42no—
337C3×D4—62no—
338C3×D4—62no—
339C3×D4—122no—
340C3×D4—244no—
341C2×C3×C4—24no—
342C2×C3×C4—24no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—22no—
350C2×C3×C4—22no—
351C2×C3×C4—34no—
352C2×C3×C4—41no—
353C2×C3×C4—44no—
354C2×C3×C4—42no—
355C2×C3×C4—44no—
356C2×C3×C4—42no—
357C2×C3×C4—42no—
358C2×C3×C4—62no—
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4#23712yes—
361C2×C3×C4C2×#6712yes—
362C2×C3×C4C2×C3×D411yescharacteristic
363C2×C3×C4C2×C3×D412yes—
364C2×C3×C4C3×#4112yes—
365C2×C3×C4C23×D311yescharacteristic
366C2×C3×C4C24×C311yescharacteristic
367#67—84no—
368C2×Dic3—22no—
369C2×Dic3C2×C3×D414yes—
370D12—22no—
371D12—22no—
372D12—42no—
373C3×C8—24no—
374C3×C8—22no—
375C3×C8—22no—
376C3×C8—62no—
377C3⋊C8—22no—
378C2×C32—22no—
379C2×C32—81no—
380C2×C32C2×#12111yescharacteristic
381C2×C32#57712yes—
382C3×D3—82no—
383C24—61no—
384#41—22no—
385#41—22no—
386C2×Q8—21no—
387C2×Q8—22no—
388C2×Q8C3×#6714yescomplemented
389C2×Q8C22×C3×D311yescharacteristic
390C2×Q8C22×C3×D312yes—
391C2×D4—21no—
392C2×D4—32no—
393C2×D4—64no—
394C2×D4—61no—
395C2×D4—62no—
396C2×D4—62no—
397C2×D4C22×C3×D311yescharacteristic
398C22×C4—21no—
399C22×C4—21no—
400C22×C4C22×C3×D311yescharacteristic
401Q16—24no—
402SD16—24no—
403SD16—68no—
404M16—22no—
405C2×C8—32no—
406C2×C8—62no—
407C2×C8C22×C3×D312yes—
408C4⋊C4—32no—
409C4⋊C4—32no—
410C4⋊C4—64no—
411C22⋊C4—32no—
412C22⋊C4—64no—
413C22⋊C4—61no—
414C42—32no—
415C42—64no—
416C42—61no—
417C22×C3—22no—
418C22×C3—22no—
419C22×C3—22no—
420C22×C3—21no—
421C22×C3—42no—
422C22×C3—42no—
423C22×C3—42no—
424C22×C3—42no—
425C22×C3—41no—
426C22×C3—41no—
427C22×C3—82no—
428C22×C3—124no—
429C22×C3—122no—
430C22×C3—244no—
431C22×C3#93912yes—
432C22×C3C3×#12112yes—
433C22×C3C2×D3×D411yescharacteristic
434C22×C3C22×C3×D411yescharacteristic
435C2×D3—44no—
436C2×D3—42no—
437C2×D3—84no—
438C3×C4—24no—
439C3×C4—24no—
440C3×C4—22no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—44no—
444C3×C4—42no—
445C3×C4—41no—
446C3×C4—41no—
447C3×C4—64no—
448C3×C4—122no—
449C3×C4#93912yes—
450C3×C4C3×#12112yes—
451C3×C4C2×#23711yescharacteristic
452C3×C4C22×#6711yescharacteristic
453C3×C4C22×C3×D411yescharacteristic
454C3×C4C2×C3×#4111yescharacteristic
455Dic3—24no—
456Dic3—42no—
457C32#304311yescharacteristic, complemented, Sylow
458C23—21no—
459C23—62no—
460C23—122no—
461C23—242no—
462C23C3×D3×D411yescharacteristic
463Q8—24no—
464Q8—22no—
465Q8—21no—
466Q8—21no—
467Q8C2×C3×#6714yes—
468D4—21no—
469D4—21no—
470D4—42no—
471D4—62no—
472D4—62no—
473D4—122no—
474D4—244no—
475C2×C4—24no—
476C2×C4—22no—
477C2×C4—21no—
478C2×C4—34no—
479C2×C4—42no—
480C2×C4—62no—
481C2×C4C3×D3×D411yescharacteristic
482C2×C4C3×#23712yes—
483C2×C4C2×C3×#6712yes—
484C2×C4C23×C3×D311yescharacteristic
485C8—22no—
486C8—62no—
487C2×C3—22no—
488C2×C3—22no—
489C2×C3—22no—
490C2×C3—21no—
491C2×C3—42no—
492C2×C3—82no—
493C2×C3—81no—
494C2×C3—81no—
495C2×C3—242no—
496C2×C3#577812yes—
497C2×C3C2×#93911yescharacteristic
498C2×C3C2×C3×#12111yescharacteristic
499C2×C3C3×#57712yes—
500D3—82no—
501C22—22no—
502C22—42no—
503C22—41no—
504C22—124no—
505C22—122no—
506C22—244no—
507C22C3×#93912yes—
508C22C2×C3×D3×D411yescharacteristic
509C4—24no—
510C4—41no—
511C4—64no—
512C4—122no—
513C4C3×#93912yes—
514C4C2×C3×#23711yescharacteristic
515C4C22×C3×#6711yescharacteristic
516C3—21no—
517C3#8396911yescharacteristic, direct product factor
518C3C3×#304311yescharacteristic, complemented
519C2—22no—
520C2—81no—
521C2—242no—
522C2C3×#577812yes—
523C2C2×C3×#93911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#137C2
socleC22×C32C22×D4
prime radicalC3×#5830C2
hypercenterC2×C3×#137D3
hypocenterC3C3×#3043
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#137

Complements

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

NH ≅ G/Ntype
1. C2×C32×#137C2semidirect
3. C3×#5812C2semidirect
4. C22×C3×#215C2semidirect
5. C3×#5233C2semidirect
6. C3×#5185C2semidirect
7. C3×#5163C2semidirect
8. C3×#5131C2semidirect
9. C3×#5119C2semidirect
11. #83969C3direct (N × H)
16. C2×C32×Q16C22semidirect
17. C2×C32×SD16C22semidirect
21. C3×Q8×Dic3C22semidirect
31. C3×#835C22semidirect
32. C3×#832C22semidirect
34. C3×Dic3⋊C8C22semidirect
36. C2×C3×#137D3semidirect
37. C2×C3×#137C2×C3semidirect
42. #5812C2×C3semidirect
43. C22×#215C2×C3semidirect
49. #5233C2×C3semidirect
50. #5185C2×C3semidirect
51. #5163C2×C3semidirect
52. #5131C2×C3semidirect
53. #5119C2×C3semidirect
59. C2×C32×Q8D4semidirect
101. C2×C3×Q16C2×D3semidirect
102. C2×C3×Q16C22×C3semidirect
106. C2×C3×SD16C2×D3semidirect
107. C2×C3×SD16C22×C3semidirect
123. Q8×Dic3C22×C3semidirect
137. #835C22×C3semidirect
138. #832C22×C3semidirect
140. Dic3⋊C8C22×C3semidirect
170. C2×#137C3×D3semidirect
196. C2×C3×Q8#67semidirect
197. C2×C3×Q8C3×D4semidirect
282. C2×Q16C2×C3×D3semidirect
285. C2×SD16C2×C3×D3semidirect
388. C2×Q8C3×#67semidirect
457. C32#3043semidirect
517. C3#83969direct (N × H)
518. C3C3×#3043semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1372
C3×#58302
C3×#58122
C22×C3×#2152
C3×#52332
C3×#51852
C3×#51632
C3×#51312
C3×#51192
C3×#30433
#839693