Finite Group Databasebeta

← C3×#81586 #11895738

Subgroups — C3×#81586 #11895738

Order 1152.

851 conjugacy classes of subgroups.

The subgroup lattice has 561 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5730C211yesmaximal, characteristic, complemented
2C3×#5718C211yesmaximal, characteristic, complemented
3C32×#486C211yesmaximal, characteristic, complemented
4C3×#5084C211yesmaximal, characteristic, complemented
5C3×#5072C211yesmaximal, characteristic, complemented
6C3×#4786C212yesmaximal, complemented
7C3×#4785C212yesmaximal, complemented
8C3×#4766C212yesmaximal, complemented
9C3×#4764C212yesmaximal, complemented
10C3×C4×D24C211yesmaximal, characteristic, complemented
11C3×#4679C211yesmaximal, characteristic, complemented
12C3×#3366—31nomaximal
13#81586C311yesmaximal, characteristic, direct product factor
14C2×C3×#237—21no—
15C32×C4⋊Q8C2211yescharacteristic
16C32×#127C2211yescharacteristic
17C3×#946—22no—
18C3×#940C2212yes—
19C3×#939—22no—
20C3×#938—21no—
21C3×D4×Dic3C2212yes—
22C2×C3×#213C2212yes—
23C2×C3×D24C2211yescharacteristic
24C3×#897—21no—
25C3×#893C2212yes—
26C3×D3×C4⋊C4—21no—
27C3×#890C2212yes—
28C3×C4×D12C2211yescharacteristic
29C3×C4×D12C2211yescharacteristic
30C3×C4×Dic6C2211yescharacteristic
31C32×#102C2212yes—
32C32×#102C2212yes—
33C32×C4×C8C2211yescharacteristic
34C3×#832C2212yes—
35C3×#821C2211yescharacteristic
36C3×#821C2211yescharacteristic
37C3×#818C2211yescharacteristic
38C3×#815C2212yes—
39C3×Dic3⋊C8C2212yes—
40C3×#809C2212yes—
41C3×#808C2212yes—
42C3×C4⋊(C3⋊C8)C2211yescharacteristic
43C3×#554—31no—
44C3×#550—31no—
45#5730C2×C311yescharacteristic, complemented
46#5718C2×C311yescharacteristic, complemented
47C3×#490—32no—
48C3×#486—21no—
49C3×#486D311yescharacteristic, complemented
50C3×#486C2×C311yescharacteristic, complemented
51C3×#478—32no—
52C3×#476—31no—
53C3×#459—31no—
54C3×#459—32no—
55C3×#446—31no—
56C3×#442—32no—
57C3×C4×D8—31no—
58#5084C2×C311yescharacteristic, complemented
59#5072C2×C311yescharacteristic, complemented
60#4786C2×C312yescomplemented
61#4785C2×C312yescomplemented
62#4766C2×C312yescomplemented
63#4764C2×C312yescomplemented
64C4×D24C2×C311yescharacteristic, complemented
65#4679C2×C311yescharacteristic, complemented
66C2×C32×Q8—21no—
67C2×C32×D4—21no—
68C2×C32×D4—21no—
69C2×C32×D4C2312yes—
70C2×C3×#67—22no—
71C2×C3×#67—22no—
72C22×C3×Dic3—22no—
73C3×#237—44no—
74C2×C3×D12C2311yescharacteristic
75C2×C3×D12C2311yescharacteristic
76C2×C3×C4×D3—21no—
77C2×C3×C4×D3—21no—
78C2×C3×C4×D3—22no—
79C2×C3×Dic6D411yescharacteristic
80C2×C32×C8C2311yescharacteristic
81C2×C32×C8C2311yescharacteristic
82C32×C4⋊C4—21no—
83C32×C4⋊C4C2312yes—
84C32×C42C2311yescharacteristic
85C3×#217—22no—
86C3×#213—24no—
87C3×(C2×D3)⋊C4—21no—
88C3×(C2×D3)⋊C4—21no—
89C3×(C2×D3)⋊C4—22no—
90C3×C4⋊Dic3—22no—
91C3×C4⋊Dic3D411yescharacteristic
92C3×C4⋊Dic3C2311yescharacteristic
93C3×C4⋊Dic3C2311yescharacteristic
94C3×Dic3⋊C4—22no—
95C3×Dic3⋊C4D412yes—
96C3×C4×Dic3C2312yes—
97C2×C3×C3⋊C8C2312yes—
98C3×D24—22no—
99#3366—31noSylow
100C2×C3×#41—61no—
101C2×#237—21no—
102C2×C3×D8—32no—
103C2×C3×D8—31no—
104C3×C4⋊Q8—21no—
105C3×C4⋊Q8C2×D311yescharacteristic
106C3×C4⋊Q8C22×C311yescharacteristic
107C3×#127—21no—
108C3×#127—32no—
109C3×#127C2×D311yescharacteristic
110C3×#127C22×C311yescharacteristic
111C3×#125—32no—
112C3×C22⋊Q8—61no—
113C3×C22⋊Q8—62no—
114C3×#121—61no—
115C3×#121—62no—
116C3×C4×Q8—31no—
117C3×C4×D4—32no—
118C3×C4×D4—32no—
119C3×C4×D4—31no—
120C3×C4×D4—31no—
121C2×C3×C4⋊C4—61no—
122#946—22no—
123#940C22×C312yes—
124#939—22no—
125#938—21no—
126D4×Dic3C22×C312yes—
127C2×#213C22×C312yes—
128C2×D24C22×C311yescharacteristic
129#897—21no—
130#893C22×C312yes—
131D3×C4⋊C4—21no—
132#890C22×C312yes—
133C4×D12C22×C311yescharacteristic
134C4×D12C22×C311yescharacteristic
135C4×Dic6C22×C311yescharacteristic
136C3×#107—31no—
137C3×#106—32no—
138C3×C4⋊C8—32no—
139C3×C4⋊C8—31no—
140C3×#102—22no—
141C3×#102—22no—
142C3×#102—32no—
143C3×#102—31no—
144C3×#102—31no—
145C3×#102—32no—
146C3×#102C2×D312yes—
147C3×#102C2×D312yes—
148C3×#102C22×C312yes—
149C3×#102C22×C312yes—
150C3×#97—32no—
151C3×C4×C8—21no—
152C3×C4×C8C2×D311yescharacteristic
153C3×C4×C8C22×C311yescharacteristic
154#832C22×C312yes—
155#821C22×C311yescharacteristic
156#821C22×C311yescharacteristic
157#818C22×C311yescharacteristic
158#815C22×C312yes—
159Dic3⋊C8C22×C312yes—
160#809C22×C312yes—
161#808C22×C312yes—
162C4⋊(C3⋊C8)C22×C311yescharacteristic
163C23×C32—22no—
164C22×C3×D3—21no—
165C22×C3×D3—21no—
166C32×Q8—81no—
167C32×D4—22no—
168C32×D4—22no—
169C32×D4—42no—
170C32×D4—81no—
171C2×C32×C4—22no—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2411yescharacteristic
175C3×#67—44no—
176C3×#67—82no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—44no—
180C2×C3×Dic3C2×D412yes—
181C2×C3×Dic3C2×D412yes—
182C3×D12—21no—
183C3×D12—21no—
184C3×D12—21no—
185C3×D12#4112yescomplemented
186C3×C4×D3—42no—
187C3×C4×D3—42no—
188C3×C4×D3—82no—
189C3×Dic6—22no—
190C32×C8—21no—
191C32×C8—21no—
192C3×C3⋊C8—22no—
193#554—31no—
194#550—31no—
195#490—32no—
196#486C3×D311yescharacteristic, complemented
197#478—32no—
198#476—31no—
199#459—31no—
200#459—32no—
201#446—31no—
202#442—32no—
203C4×D8—31no—
204C3×#41—124no—
205C2×C3×Q8—21no—
206C2×C3×Q8—21no—
207C2×C3×Q8—31no—
208C2×C3×Q8—41no—
209C2×C3×D4—21no—
210C2×C3×D4—21no—
211C2×C3×D4—21no—
212C2×C3×D4—21no—
213C2×C3×D4—22no—
214C2×C3×D4—31no—
215C2×C3×D4—31no—
216C2×C3×D4—41no—
217C2×C3×D4—41no—
218C2×C3×D4—62no—
219C2×C3×D4—62no—
220C2×C3×D4C22×D312yes—
221C2×C3×D4C23×C312yes—
222C22×C3×C4—62no—
223C22×C3×C4—62no—
224C22×C3×C4—61no—
225C22×C3×C4—61no—
226C2×#67—22no—
227C2×#67—22no—
228C22×Dic3—22no—
229#237—44no—
230C2×D12C23×C311yescharacteristic
231C2×D12C23×C311yescharacteristic
232C2×C4×D3—21no—
233C2×C4×D3—21no—
234C2×C4×D3—22no—
235C2×Dic6C3×D411yescharacteristic
236C3×D8—62no—
237C3×D8—64no—
238C2×C3×C8—21no—
239C2×C3×C8—21no—
240C2×C3×C8—32no—
241C2×C3×C8C22×D311yescharacteristic
242C2×C3×C8C22×D311yescharacteristic
243C2×C3×C8C23×C311yescharacteristic
244C2×C3×C8C23×C311yescharacteristic
245C3×C4⋊C4—21no—
246C3×C4⋊C4—21no—
247C3×C4⋊C4—22no—
248C3×C4⋊C4—32no—
249C3×C4⋊C4—31no—
250C3×C4⋊C4—31no—
251C3×C4⋊C4—31no—
252C3×C4⋊C4—41no—
253C3×C4⋊C4—62no—
254C3×C4⋊C4—62no—
255C3×C4⋊C4C22×D312yes—
256C3×C4⋊C4C23×C312yes—
257C3×C22⋊C4—62no—
258C3×C22⋊C4—62no—
259C3×C22⋊C4—61no—
260C3×C22⋊C4—61no—
261C3×C42—21no—
262C3×C42—32no—
263C3×C42C22×D311yescharacteristic
264C3×C42C23×C311yescharacteristic
265#217—22no—
266#213—24no—
267(C2×D3)⋊C4—21no—
268(C2×D3)⋊C4—21no—
269(C2×D3)⋊C4—22no—
270C4⋊Dic3—22no—
271C4⋊Dic3C3×D411yescharacteristic
272C4⋊Dic3C23×C311yescharacteristic
273C4⋊Dic3C23×C311yescharacteristic
274Dic3⋊C4—22no—
275Dic3⋊C4C3×D412yes—
276C4×Dic3C23×C312yes—
277C2×C3⋊C8C23×C312yes—
278D24—22no—
279C22×C32—42no—
280C22×C32—42no—
281C22×C32—42no—
282C22×C32C22×D411yescharacteristic
283C2×C3×D3—22no—
284C2×C3×D3—41no—
285C2×C3×D3—41no—
286C2×C3×D3—41no—
287C2×C3×D3—41no—
288C2×C3×D3—41no—
289C32×C4—21no—
290C32×C4—42no—
291C32×C4AGL(1,ℤ/8)12yes—
292C32×C4C2×#4111yescharacteristic
293C32×C42−1+411yescharacteristic
294C3×Dic3—22no—
295C3×Dic3—22no—
296C3×Dic3—41no—
297C3×Dic3—41no—
298C2×#41—61no—
299C2×D8—32no—
300C2×D8—31no—
301C4⋊Q8C2×C3×D311yescharacteristic
302#127—32no—
303#127C2×C3×D311yescharacteristic
304#125—32no—
305C22⋊Q8—61no—
306C22⋊Q8—62no—
307#121—61no—
308#121—62no—
309C4×Q8—31no—
310C4×D4—32no—
311C4×D4—32no—
312C4×D4—31no—
313C4×D4—31no—
314C2×C4⋊C4—61no—
315#107—31no—
316#106—32no—
317C4⋊C8—32no—
318C4⋊C8—31no—
319#102—32no—
320#102—31no—
321#102—31no—
322#102—32no—
323#102C2×C3×D312yes—
324#102C2×C3×D312yes—
325#97—32no—
326C4×C8C2×C3×D311yescharacteristic
327C23×C3—22no—
328C23×C3—22no—
329C23×C3—42no—
330C23×C3—61no—
331C23×C3—61no—
332C22×D3—21no—
333C22×D3—21no—
334C3×Q8—62no—
335C3×Q8—81no—
336C3×Q8—81no—
337C3×Q8—82no—
338C3×D4—22no—
339C3×D4—22no—
340C3×D4—22no—
341C3×D4—22no—
342C3×D4—32no—
343C3×D4—42no—
344C3×D4—42no—
345C3×D4—42no—
346C3×D4—42no—
347C3×D4—61no—
348C3×D4—61no—
349C3×D4—61no—
350C3×D4—82no—
351C3×D4—81no—
352C3×D4—81no—
353C3×D4—82no—
354C3×D4—124no—
355C3×D4—242no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—32no—
362C2×C3×C4—32no—
363C2×C3×C4—42no—
364C2×C3×C4—61no—
365C2×C3×C4—61no—
366C2×C3×C4—124no—
367C2×C3×C4—122no—
368C2×C3×C4—122no—
369C2×C3×C4—242no—
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4D3×D411yescharacteristic
372C2×C3×C4C2×C3×D411yescharacteristic
373C2×C3×C4C2×C3×D411yescharacteristic
374C2×C3×C4C23×D311yescharacteristic
375C2×C3×C4C24×C311yescharacteristic
376#67—44no—
377#67—82no—
378C2×Dic3—21no—
379C2×Dic3—21no—
380C2×Dic3—44no—
381C2×Dic3C2×C3×D412yes—
382C2×Dic3C2×C3×D412yes—
383D12—21no—
384D12—21no—
385D12—21no—
386D12C3×#4112yescomplemented
387C4×D3—42no—
388C4×D3—42no—
389C4×D3—82no—
390Dic6—22no—
391C3×C8—21no—
392C3×C8—21no—
393C3×C8—21no—
394C3×C8—21no—
395C3×C8—41no—
396C3×C8—41no—
397C3×C8—62no—
398C3⋊C8—22no—
399C2×C32—82no—
400C2×C32#54811yescharacteristic
401C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
402C2×C32#57611yescharacteristic
403C3×D3—42no—
404C3×D3—81no—
405#41—124no—
406C2×Q8—21no—
407C2×Q8—31no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—31no—
411C2×D4—31no—
412C2×D4—62no—
413C2×D4—62no—
414C2×D4C22×C3×D312yes—
415C22×C4—62no—
416C22×C4—62no—
417C22×C4—61no—
418C22×C4—61no—
419D8—62no—
420D8—64no—
421C2×C8—32no—
422C2×C8C22×C3×D311yescharacteristic
423C2×C8C22×C3×D311yescharacteristic
424C4⋊C4—21no—
425C4⋊C4—31no—
426C4⋊C4—32no—
427C4⋊C4—31no—
428C4⋊C4—31no—
429C4⋊C4—62no—
430C4⋊C4—62no—
431C4⋊C4C22×C3×D312yes—
432C22⋊C4—62no—
433C22⋊C4—62no—
434C22⋊C4—61no—
435C22⋊C4—61no—
436C42—32no—
437C42C22×C3×D311yescharacteristic
438C22×C3—21no—
439C22×C3—42no—
440C22×C3—42no—
441C22×C3—42no—
442C22×C3—42no—
443C22×C3—42no—
444C22×C3—42no—
445C22×C3—62no—
446C22×C3—82no—
447C22×C3—82no—
448C22×C3—82no—
449C22×C3—121no—
450C22×C3—121no—
451C22×C3—121no—
452C22×C3—121no—
453C22×C3—121no—
454C22×C3C2×D3×D411yescharacteristic
455C22×C3C22×C3×D411yescharacteristic
456C2×D3—22no—
457C2×D3—41no—
458C2×D3—41no—
459C2×D3—41no—
460C2×D3—41no—
461C2×D3—41no—
462C3×C4—22no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—22no—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—42no—
469C3×C4—42no—
470C3×C4—62no—
471C3×C4—62no—
472C3×C4—82no—
473C3×C4—121no—
474C3×C4—121no—
475C3×C4#91412yes—
476C3×C4C3×AGL(1,ℤ/8)12yes—
477C3×C4D3×#4111yescharacteristic
478C3×C4#101011yescharacteristic
479C3×C4C2×C3×#4111yescharacteristic
480C3×C4C3×2−1+411yescharacteristic
481Dic3—22no—
482Dic3—22no—
483Dic3—41no—
484Dic3—41no—
485C32#336611yescharacteristic, complemented, Sylow
486C23—22no—
487C23—61no—
488C23—61no—
489Q8—62no—
490Q8—81no—
491D4—22no—
492D4—22no—
493D4—32no—
494D4—42no—
495D4—61no—
496D4—61no—
497D4—61no—
498D4—81no—
499D4—124no—
500D4—242no—
501C2×C4—22no—
502C2×C4—32no—
503C2×C4—32no—
504C2×C4—61no—
505C2×C4—61no—
506C2×C4—124no—
507C2×C4—122no—
508C2×C4—122no—
509C2×C4—242no—
510C2×C4C3×D3×D411yescharacteristic
511C2×C4C3×D3×D411yescharacteristic
512C2×C4C23×C3×D311yescharacteristic
513C8—21no—
514C8—21no—
515C8—62no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—82no—
520C2×C3—82no—
521C2×C3—122no—
522C2×C3—162no—
523C2×C3—241no—
524C2×C3#567711yescharacteristic
525C2×C3#575711yescharacteristic
526C2×C3C2×#91411yescharacteristic
527C2×C3C3×#54811yescharacteristic
528C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
529C2×C3C3×#57611yescharacteristic
530D3—42no—
531D3—81no—
532C22—42no—
533C22—42no—
534C22—42no—
535C22—62no—
536C22—121no—
537C22—121no—
538C22—121no—
539C22—121no—
540C22—121no—
541C22C2×C3×D3×D411yescharacteristic
542C4—21no—
543C4—42no—
544C4—62no—
545C4—62no—
546C4—121no—
547C4—121no—
548C4C3×#91412yes—
549C4C3×D3×#4111yescharacteristic
550C4C3×#101011yescharacteristic
551C3—21no—
552C3#8158611yescharacteristic, direct product factor
553C3C3×#336611yescharacteristic, complemented
554C2—82no—
555C2—122no—
556C2—241no—
557C2C3×#567711yescharacteristic
558C2C3×#575711yescharacteristic
559C2C2×C3×#91411yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#486C2
socleC22×C32C22×D4
hypercenterC3×#486D3
hypocenterC3C3×#3366
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#486

Complements

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

NH ≅ G/Ntype
1. C3×#5730C2semidirect
2. C3×#5718C2semidirect
3. C32×#486C2semidirect
4. C3×#5084C2semidirect
5. C3×#5072C2semidirect
6. C3×#4786C2semidirect
7. C3×#4785C2semidirect
8. C3×#4766C2semidirect
9. C3×#4764C2semidirect
10. C3×C4×D24C2semidirect
11. C3×#4679C2semidirect
13. #81586C3direct (N × H)
45. #5730C2×C3semidirect
46. #5718C2×C3semidirect
49. C3×#486D3semidirect
50. C3×#486C2×C3semidirect
58. #5084C2×C3semidirect
59. #5072C2×C3semidirect
60. #4786C2×C3semidirect
61. #4785C2×C3semidirect
62. #4766C2×C3semidirect
63. #4764C2×C3semidirect
64. C4×D24C2×C3semidirect
65. #4679C2×C3semidirect
185. C3×D12#41semidirect
196. #486C3×D3semidirect
386. D12C3×#41semidirect
485. C32#3366semidirect
552. C3#81586direct (N × H)
553. C3C3×#3366semidirect

Maximal subgroups

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

subgroupindex
C3×#57302
C3×#57182
C32×#4862
C3×#50842
C3×#50722
C3×#47862
C3×#47852
C3×#47662
C3×#47642
C3×C4×D242
C3×#46792
C3×#33663
#815863