Finite Group Databasebeta

← C3×#81088 #11895720

Subgroups — C3×#81088 #11895720

Order 1152.

846 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×#5553C211yesmaximal, characteristic, complemented
3C32×#476C211yesmaximal, characteristic, complemented
4C3×#5088C211yesmaximal, characteristic, complemented
5C3×C4×#213C211yesmaximal, characteristic, complemented
6C3×#4871C212yesmaximal, complemented
7C3×#4869C212yesmaximal, complemented
8C3×#4843C211yesmaximal, characteristic, complemented
9C3×#4831C211yesmaximal, characteristic, complemented
10C3×#4786C212yesmaximal, complemented
11C3×#4764C212yesmaximal, complemented
12C3×#3366—31nomaximal
13#81088C311yesmaximal, characteristic, direct product factor
14C2×C3×#235—21no—
15C32×C4⋊Q8C2211yescharacteristic
16C32×C4×D4C2211yescharacteristic
17C3×#946—22no—
18C3×#940C2212yes—
19C2×C3×#213C2211yescharacteristic
20C3×#930—21no—
21C2×C3×D24C2212yes—
22C3×#897—21no—
23C3×#893C2212yes—
24C3×#893C2212yes—
25C3×D3×C4⋊C4—21no—
26C3×#890C2212yes—
27C3×#884—22no—
28C3×#874C2211yescharacteristic
29C3×C4×D12C2211yescharacteristic
30C3×C4×Dic6C2211yescharacteristic
31C32×#106C2212yes—
32C32×C4⋊C8C2211yescharacteristic
33C32×#102C2212yes—
34C3×#832C2211yescharacteristic
35C3×#821C2212yes—
36C3×#815C2212yes—
37C3×Dic3⋊C8C2212yes—
38C3×#809C2211yescharacteristic
39C3×#809C2212yes—
40C3×#809C2212yes—
41C3×#807C2211yescharacteristic
42C3×C4×C3⋊C8C2211yescharacteristic
43C3×#554—31no—
44C3×#550—31no—
45#5730C2×C311yescharacteristic, complemented
46#5553C2×C311yescharacteristic, complemented
47C3×#490—32no—
48C3×#486—31no—
49C3×#478—32no—
50C3×#476—21no—
51C3×#476D311yescharacteristic, complemented
52C3×#476C2×C311yescharacteristic, complemented
53C3×#459—31no—
54C3×#459—32no—
55C3×#446—31no—
56C3×#442—32no—
57C3×C4×D8—31no—
58#5088C2×C311yescharacteristic, complemented
59C4×#213C2×C311yescharacteristic, complemented
60#4871C2×C312yescomplemented
61#4869C2×C312yescomplemented
62#4843C2×C311yescharacteristic, complemented
63#4831C2×C311yescharacteristic, complemented
64#4786C2×C312yescomplemented
65#4764C2×C312yescomplemented
66C2×C32×Q8—21no—
67C2×C32×D4C2311yescharacteristic
68C22×C32×C4—21no—
69C2×C3×#67—22no—
70C2×C3×#67—22no—
71C3×#235—44no—
72C2×C3×D12—21no—
73C2×C3×D12—21no—
74C2×C3×D12C2312yes—
75C2×C3×D12C2311yescharacteristic
76C2×C3×C4×D3—21no—
77C2×C3×C4×D3—22no—
78C2×C3×C4×D3—22no—
79C2×C3×Dic6D411yescharacteristic
80C2×C32×C8C2312yes—
81C32×C4⋊C4—21no—
82C32×C4⋊C4C2312yes—
83C32×C4⋊C4C2311yescharacteristic
84C32×C22⋊C4—21no—
85C32×C42C2311yescharacteristic
86C3×#213—22no—
87C3×(C2×D3)⋊C4—21no—
88C3×(C2×D3)⋊C4—22no—
89C3×(C2×D3)⋊C4—22no—
90C3×C4⋊Dic3—22no—
91C3×C4⋊Dic3D411yescharacteristic
92C3×C4⋊Dic3C2311yescharacteristic
93C3×Dic3⋊C4—22no—
94C3×Dic3⋊C4D412yes—
95C3×C4×Dic3C2312yes—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98C3×D24—24no—
99#3366—31noSylow
100C2×C3×#41—61no—
101C2×#235—21no—
102C2×C3×D8—31no—
103C2×C3×D8—32no—
104C3×C4⋊Q8—21no—
105C3×C4⋊Q8C2×D311yescharacteristic
106C3×C4⋊Q8C22×C311yescharacteristic
107C3×#127—32no—
108C3×#127—31no—
109C3×#125—32no—
110C3×C22⋊Q8—61no—
111C3×C22⋊Q8—62no—
112C3×#121—62no—
113C3×#121—61no—
114C3×C4×Q8—31no—
115C3×C4×D4—21no—
116C3×C4×D4—32no—
117C3×C4×D4—32no—
118C3×C4×D4—31no—
119C3×C4×D4C2×D311yescharacteristic
120C3×C4×D4C22×C311yescharacteristic
121C2×C3×C4⋊C4—61no—
122#946—22no—
123#940C22×C312yes—
124C2×#213C22×C311yescharacteristic
125#930—21no—
126C2×D24C22×C312yes—
127#897—21no—
128#893C22×C312yes—
129#893C22×C312yes—
130D3×C4⋊C4—21no—
131#890C22×C312yes—
132#884—22no—
133#874C22×C311yescharacteristic
134C4×D12C22×C311yescharacteristic
135C4×Dic6C22×C311yescharacteristic
136C3×#107—31no—
137C3×#106—22no—
138C3×#106C2×D312yes—
139C3×#106C22×C312yes—
140C3×C4⋊C8—21no—
141C3×C4⋊C8—32no—
142C3×C4⋊C8C2×D311yescharacteristic
143C3×C4⋊C8C22×C311yescharacteristic
144C3×#102—22no—
145C3×#102—31no—
146C3×#102—32no—
147C3×#102—31no—
148C3×#102—32no—
149C3×#102—32no—
150C3×#102C2×D312yes—
151C3×#102C22×C312yes—
152C3×#97—32no—
153C3×C4×C8—31no—
154#832C22×C311yescharacteristic
155#821C22×C312yes—
156#815C22×C312yes—
157Dic3⋊C8C22×C312yes—
158#809C22×C311yescharacteristic
159#809C22×C312yes—
160#809C22×C312yes—
161#807C22×C311yescharacteristic
162C4×C3⋊C8C22×C311yescharacteristic
163C23×C32—21no—
164C22×C3×D3—21no—
165C22×C3×D3—22no—
166C32×Q8—81no—
167C32×D4—21no—
168C32×D4—21no—
169C2×C32×C4—22no—
170C2×C32×C4—21no—
171C2×C32×C4—42no—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2411yescharacteristic
175C3×#67—44no—
176C3×#67—82no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3C2×D412yes—
179C2×C3×Dic3C2×D412yes—
180C3×D12—22no—
181C3×D12—21no—
182C3×D12—22no—
183C3×D12—42no—
184C3×D12—81no—
185C3×D12#4112yescomplemented
186C3×C4×D3—44no—
187C3×C4×D3—42no—
188C3×C4×D3—82no—
189C3×Dic6—22no—
190C32×C8—22no—
191C3×C3⋊C8—21no—
192C3×C3⋊C8—21no—
193#554—31no—
194#550—31no—
195#490—32no—
196#486—31no—
197#478—32no—
198#476C3×D311yescharacteristic, complemented
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—31no—
211C2×C3×D4—32no—
212C2×C3×D4—62no—
213C2×C3×D4—62no—
214C2×C3×D4—61no—
215C2×C3×D4—61no—
216C2×C3×D4C22×D311yescharacteristic
217C2×C3×D4C23×C311yescharacteristic
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—41no—
221C22×C3×C4—62no—
222C22×C3×C4—62no—
223C22×C3×C4—61no—
224C2×#67—22no—
225C2×#67—22no—
226#235—44no—
227C2×D12—21no—
228C2×D12—21no—
229C2×D12C23×C312yes—
230C2×D12C23×C311yescharacteristic
231C2×C4×D3—21no—
232C2×C4×D3—22no—
233C2×C4×D3—22no—
234C2×Dic6C3×D411yescharacteristic
235C3×D8—64no—
236C3×D8—62no—
237C2×C3×C8—22no—
238C2×C3×C8—31no—
239C2×C3×C8—31no—
240C2×C3×C8C22×D312yes—
241C2×C3×C8C23×C312yes—
242C3×C4⋊C4—21no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—22no—
245C3×C4⋊C4—21no—
246C3×C4⋊C4—32no—
247C3×C4⋊C4—31no—
248C3×C4⋊C4—31no—
249C3×C4⋊C4—41no—
250C3×C4⋊C4—62no—
251C3×C4⋊C4—62no—
252C3×C4⋊C4C22×D312yes—
253C3×C4⋊C4C22×D311yescharacteristic
254C3×C4⋊C4C23×C311yescharacteristic
255C3×C4⋊C4C23×C312yes—
256C3×C22⋊C4—21no—
257C3×C22⋊C4—21no—
258C3×C22⋊C4—41no—
259C3×C22⋊C4—62no—
260C3×C22⋊C4—62no—
261C3×C22⋊C4—61no—
262C3×C42—21no—
263C3×C42—32no—
264C3×C42C22×D311yescharacteristic
265C3×C42C23×C311yescharacteristic
266#213—22no—
267(C2×D3)⋊C4—21no—
268(C2×D3)⋊C4—22no—
269(C2×D3)⋊C4—22no—
270C4⋊Dic3—22no—
271C4⋊Dic3C3×D411yescharacteristic
272C4⋊Dic3C23×C311yescharacteristic
273Dic3⋊C4—22no—
274Dic3⋊C4C3×D412yes—
275C4×Dic3C23×C312yes—
276C2×C3⋊C8C23×C311yescharacteristic
277C2×C3⋊C8C23×C311yescharacteristic
278D24—24no—
279C22×C32—41no—
280C22×C32—41no—
281C22×C32—41no—
282C22×C32C22×D411yescharacteristic
283C2×C3×D3—22no—
284C2×C3×D3—41no—
285C2×C3×D3—41no—
286C2×C3×D3—42no—
287C2×C3×D3—42no—
288C2×C3×D3—42no—
289C32×C4—21no—
290C32×C4—41no—
291C32×C4—42no—
292C32×C4AGL(1,ℤ/8)12yes—
293C32×C4C2×#4111yescharacteristic
294C32×C42−1+411yescharacteristic
295C3×Dic3—22no—
296C3×Dic3—22no—
297C3×Dic3—41no—
298C2×#41—61no—
299C2×D8—31no—
300C2×D8—32no—
301C4⋊Q8C2×C3×D311yescharacteristic
302#127—32no—
303#127—31no—
304#125—32no—
305C22⋊Q8—61no—
306C22⋊Q8—62no—
307#121—62no—
308#121—61no—
309C4×Q8—31no—
310C4×D4—32no—
311C4×D4—32no—
312C4×D4—31no—
313C4×D4C2×C3×D311yescharacteristic
314C2×C4⋊C4—61no—
315#107—31no—
316#106C2×C3×D312yes—
317C4⋊C8—32no—
318C4⋊C8C2×C3×D311yescharacteristic
319#102—31no—
320#102—32no—
321#102—31no—
322#102—32no—
323#102—32no—
324#102C2×C3×D312yes—
325#97—32no—
326C4×C8—31no—
327C23×C3—21no—
328C23×C3—21no—
329C23×C3—41no—
330C23×C3—61no—
331C23×C3—62no—
332C22×D3—21no—
333C22×D3—22no—
334C3×Q8—62no—
335C3×Q8—81no—
336C3×Q8—81no—
337C3×Q8—82no—
338C3×D4—22no—
339C3×D4—21no—
340C3×D4—21no—
341C3×D4—21no—
342C3×D4—21no—
343C3×D4—32no—
344C3×D4—41no—
345C3×D4—61no—
346C3×D4—62no—
347C3×D4—62no—
348C3×D4—124no—
349C3×D4—122no—
350C3×D4—241no—
351C3×D4—242no—
352C2×C3×C4—21no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—32no—
360C2×C3×C4—32no—
361C2×C3×C4—41no—
362C2×C3×C4—42no—
363C2×C3×C4—42no—
364C2×C3×C4—42no—
365C2×C3×C4—61no—
366C2×C3×C4—82no—
367C2×C3×C4—124no—
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×Dic3C2×C3×D412yes—
380C2×Dic3C2×C3×D412yes—
381D12—22no—
382D12—21no—
383D12—22no—
384D12—42no—
385D12—81no—
386D12C3×#4112yescomplemented
387C4×D3—44no—
388C4×D3—42no—
389C4×D3—82no—
390Dic6—22no—
391C3×C8—22no—
392C3×C8—22no—
393C3×C8—42no—
394C3×C8—61no—
395C3×C8—61no—
396C3⋊C8—21no—
397C3⋊C8—21no—
398C2×C32—81no—
399C2×C32#54811yescharacteristic
400C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
401C2×C32#57611yescharacteristic
402C3×D3—42no—
403C3×D3—82no—
404#41—124no—
405C2×Q8—21no—
406C2×Q8—31no—
407C2×D4—31no—
408C2×D4—32no—
409C2×D4—62no—
410C2×D4—62no—
411C2×D4—61no—
412C2×D4—61no—
413C2×D4C22×C3×D311yescharacteristic
414C22×C4—21no—
415C22×C4—62no—
416C22×C4—62no—
417C22×C4—61no—
418D8—64no—
419D8—62no—
420C2×C8—31no—
421C2×C8—31no—
422C2×C8C22×C3×D312yes—
423C4⋊C4—21no—
424C4⋊C4—31no—
425C4⋊C4—32no—
426C4⋊C4—31no—
427C4⋊C4—62no—
428C4⋊C4—62no—
429C4⋊C4C22×C3×D312yes—
430C4⋊C4C22×C3×D311yescharacteristic
431C22⋊C4—21no—
432C22⋊C4—62no—
433C22⋊C4—62no—
434C22⋊C4—61no—
435C42—32no—
436C42C22×C3×D311yescharacteristic
437C22×C3—21no—
438C22×C3—42no—
439C22×C3—41no—
440C22×C3—41no—
441C22×C3—41no—
442C22×C3—41no—
443C22×C3—41no—
444C22×C3—41no—
445C22×C3—62no—
446C22×C3—81no—
447C22×C3—81no—
448C22×C3—121no—
449C22×C3—121no—
450C22×C3—122no—
451C22×C3—122no—
452C22×C3—122no—
453C22×C3C2×D3×D411yescharacteristic
454C22×C3C22×C3×D411yescharacteristic
455C2×D3—22no—
456C2×D3—41no—
457C2×D3—41no—
458C2×D3—42no—
459C2×D3—42no—
460C2×D3—42no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—22no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—41no—
467C3×C4—41no—
468C3×C4—42no—
469C3×C4—41no—
470C3×C4—42no—
471C3×C4—62no—
472C3×C4—62no—
473C3×C4—81no—
474C3×C4—82no—
475C3×C4—121no—
476C3×C4#91412yes—
477C3×C4C3×AGL(1,ℤ/8)12yes—
478C3×C4#100711yescharacteristic
479C3×C4D3×#4111yescharacteristic
480C3×C4C2×C3×#4111yescharacteristic
481C3×C4C3×2−1+411yescharacteristic
482Dic3—22no—
483Dic3—22no—
484Dic3—41no—
485C32#336611yescharacteristic, complemented, Sylow
486C23—21no—
487C23—61no—
488C23—62no—
489Q8—62no—
490Q8—81no—
491D4—21no—
492D4—21no—
493D4—32no—
494D4—61no—
495D4—62no—
496D4—62no—
497D4—124no—
498D4—122no—
499D4—241no—
500D4—242no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—32no—
504C2×C4—32no—
505C2×C4—42no—
506C2×C4—61no—
507C2×C4—124no—
508C2×C4—122no—
509C2×C4—242no—
510C2×C4C3×D3×D411yescharacteristic
511C2×C4C3×D3×D411yescharacteristic
512C2×C4C23×C3×D311yescharacteristic
513C8—22no—
514C8—61no—
515C8—61no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—82no—
520C2×C3—81no—
521C2×C3—81no—
522C2×C3—122no—
523C2×C3—242no—
524C2×C3#563311yescharacteristic
525C2×C3C2×#91411yescharacteristic
526C2×C3#577411yescharacteristic
527C2×C3C3×#54811yescharacteristic
528C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
529C2×C3C3×#57611yescharacteristic
530D3—42no—
531D3—82no—
532C22—41no—
533C22—41no—
534C22—41no—
535C22—62no—
536C22—121no—
537C22—121no—
538C22—122no—
539C22—122no—
540C22—122no—
541C22C2×C3×D3×D411yescharacteristic
542C4—21no—
543C4—41no—
544C4—42no—
545C4—62no—
546C4—62no—
547C4—121no—
548C4C3×#91412yes—
549C4C3×#100711yescharacteristic
550C4C3×D3×#4111yescharacteristic
551C3—21no—
552C3#8108811yescharacteristic, direct product factor
553C3C3×#336611yescharacteristic, complemented
554C2—81no—
555C2—122no—
556C2—242no—
557C2C3×#563311yescharacteristic
558C2C2×C3×#91411yescharacteristic
559C2C3×#577411yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#476C2
socleC22×C32C22×D4
hypercenterC3×#476D3
hypocenterC3C3×#3366
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#476

Complements

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

NH ≅ G/Ntype
1. C3×#5730C2semidirect
2. C3×#5553C2semidirect
3. C32×#476C2semidirect
4. C3×#5088C2semidirect
5. C3×C4×#213C2semidirect
6. C3×#4871C2semidirect
7. C3×#4869C2semidirect
8. C3×#4843C2semidirect
9. C3×#4831C2semidirect
10. C3×#4786C2semidirect
11. C3×#4764C2semidirect
13. #81088C3direct (N × H)
45. #5730C2×C3semidirect
46. #5553C2×C3semidirect
51. C3×#476D3semidirect
52. C3×#476C2×C3semidirect
58. #5088C2×C3semidirect
59. C4×#213C2×C3semidirect
60. #4871C2×C3semidirect
61. #4869C2×C3semidirect
62. #4843C2×C3semidirect
63. #4831C2×C3semidirect
64. #4786C2×C3semidirect
65. #4764C2×C3semidirect
185. C3×D12#41semidirect
198. #476C3×D3semidirect
386. D12C3×#41semidirect
485. C32#3366semidirect
552. C3#81088direct (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×#55532
C32×#4762
C3×#50882
C3×C4×#2132
C3×#48712
C3×#48692
C3×#48432
C3×#48312
C3×#47862
C3×#47642
C3×#33663
#810883