Finite Group Databasebeta

← C3×#81090 #11895409

Subgroups — C3×#81090 #11895409

Order 1152.

838 conjugacy classes of subgroups.

The subgroup lattice has 545 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5722C211yesmaximal, characteristic, complemented
2C3×#5553C211yesmaximal, characteristic
3C32×#476C211yesmaximal, characteristic, complemented
4C3×#5088C211yesmaximal, characteristic, complemented
5C3×C4×#214C211yesmaximal, characteristic, complemented
6C3×#4870C212yesmaximal, complemented
7C3×#4852C212yesmaximal, complemented
8C3×#4848C211yesmaximal, characteristic, complemented
9C3×#4830C211yesmaximal, characteristic, complemented
10C3×#4762C212yesmaximal, complemented
11C3×#4760C212yesmaximal, complemented
12C3×#3362—31nomaximal
13#81090C311yesmaximal, characteristic, direct product factor
14C2×C3×#235—21no—
15C32×C4⋊Q8C2211yescharacteristic
16C32×C4×D4C2211yescharacteristic
17C3×#944—22no—
18C3×#940C2212yes—
19C2×C3×#214C2211yescharacteristic
20C3×#930—21no—
21C2×C3×#204C2212yes—
22C3×#893C2212yes—
23C3×#888—21no—
24C3×#888C2212yes—
25C3×#887—21no—
26C3×#887C2212yes—
27C3×#884—22no—
28C3×#874C2211yescharacteristic
29C3×C4×Dic6C2211yescharacteristic
30C3×C4×Dic6C2211yescharacteristic
31C32×#106C2212yes—
32C32×C4⋊C8C2211yescharacteristic
33C32×#102C2212yes—
34C3×#832C2211yescharacteristic
35C3×#821C2212yes—
36C3×Dic3⋊C8C2212yes—
37C3×C8×Dic3C2212yes—
38C3×#810C2211yescharacteristic
39C3×#809C2212yes—
40C3×#809C2212yes—
41C3×#808C2211yescharacteristic
42C3×C4×C3⋊C8C2211yescharacteristic
43C3×Q82—31no—
44C3×#550—31no—
45#5722C2×C311yescharacteristic, complemented
46#5553C2×C311yescharacteristic
47C3×#486—31no—
48C3×#486—32no—
49C3×#476—21no—
50C3×#476—32no—
51C3×#476D311yescharacteristic, complemented
52C3×#476C2×C311yescharacteristic, complemented
53C3×#460—31no—
54C3×#460—32no—
55C3×C8×Q8—31no—
56C3×C4×SD16—31no—
57C3×C4×SD16—32no—
58#5088C2×C311yescharacteristic, complemented
59C4×#214C2×C311yescharacteristic, complemented
60#4870C2×C312yescomplemented
61#4852C2×C312yescomplemented
62#4848C2×C311yescharacteristic, complemented
63#4830C2×C311yescharacteristic, complemented
64#4762C2×C312yescomplemented
65#4760C2×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×C4×D3—22no—
76C2×C3×Dic6—22no—
77C2×C3×Dic6D411yescharacteristic
78C2×C3×Dic6C2311yescharacteristic
79C2×C32×C8C2312yes—
80C32×C4⋊C4—21no—
81C32×C4⋊C4C2312yes—
82C32×C4⋊C4C2311yescharacteristic
83C32×C22⋊C4—21no—
84C32×C42C2311yescharacteristic
85C3×#214—22no—
86C3×(C2×D3)⋊C4—22no—
87C3×C4⋊Dic3D411yescharacteristic
88C3×C4⋊Dic3C2311yescharacteristic
89C3×Dic3⋊C4—21no—
90C3×Dic3⋊C4—22no—
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4D412yes—
93C3×C4×Dic3—21no—
94C3×C4×Dic3—22no—
95C3×C4×Dic3C2312yes—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98C3×#204—24no—
99#3362—31noSylow
100C2×C3×#41—61no—
101C2×#235—21no—
102C2×C3×SD16—31no—
103C2×C3×SD16—32no—
104C3×C4⋊Q8—21no—
105C3×C4⋊Q8—32no—
106C3×C4⋊Q8—61no—
107C3×C4⋊Q8—62no—
108C3×C4⋊Q8C2×D311yescharacteristic
109C3×C4⋊Q8C22×C311yescharacteristic
110C3×#127—32no—
111C3×#127—31no—
112C3×#121—62no—
113C3×#121—61no—
114C3×C4×Q8—31no—
115C3×C4×Q8—32no—
116C3×C4×Q8—31no—
117C3×C4×Q8—61no—
118C3×C4×D4—21no—
119C3×C4×D4—32no—
120C3×C4×D4C2×D311yescharacteristic
121C3×C4×D4C22×C311yescharacteristic
122#944—22no—
123#940C22×C312yes—
124C2×#214C22×C311yescharacteristic
125#930—21no—
126C2×#204C22×C312yes—
127#893C22×C312yes—
128#888—21no—
129#888C22×C312yes—
130#887—21no—
131#887C22×C312yes—
132#884—22no—
133#874C22×C311yescharacteristic
134C4×Dic6C22×C311yescharacteristic
135C4×Dic6C22×C311yescharacteristic
136C3×#106—22no—
137C3×#106—31no—
138C3×#106C2×D312yes—
139C3×#106C22×C312yes—
140C3×C4⋊C8—21no—
141C3×C4⋊C8—32no—
142C3×C4⋊C8C2×D311yescharacteristic
143C3×C4⋊C8C22×C311yescharacteristic
144C3×#103—31no—
145C3×#102—22no—
146C3×#102—31no—
147C3×#102—32no—
148C3×#102—32no—
149C3×#102—32no—
150C3×#102C2×D312yes—
151C3×#102C22×C312yes—
152C3×C4×C8—32no—
153C3×C4×C8—31no—
154#832C22×C311yescharacteristic
155#821C22×C312yes—
156Dic3⋊C8C22×C312yes—
157C8×Dic3C22×C312yes—
158#810C22×C311yescharacteristic
159#809C22×C312yes—
160#809C22×C312yes—
161#808C22×C311yescharacteristic
162C4×C3⋊C8C22×C311yescharacteristic
163C23×C32—21no—
164C22×C3×D3—22no—
165C32×Q8—81no—
166C32×D4—21no—
167C32×D4—21no—
168C2×C32×C4—22no—
169C2×C32×C4—21no—
170C2×C32×C4—42no—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2411yescharacteristic
174C3×#67—44no—
175C3×#67—82no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3C2×D412yes—
179C2×C3×Dic3C2×D412yes—
180C3×D12—22no—
181C3×D12—22no—
182C3×D12—42no—
183C3×D12—81no—
184C3×C4×D3—44no—
185C3×Dic6—21no—
186C3×Dic6—82no—
187C3×Dic6SD1614yescomplemented
188C3×Dic6#4112yescomplemented
189C32×C8—22no—
190C3×C3⋊C8—21no—
191C3×C3⋊C8—21no—
192Q82—31no—
193#550—31no—
194#486—31no—
195#486—32no—
196#476—32no—
197#476C3×D311yescharacteristic, complemented
198#460—31no—
199#460—32no—
200C8×Q8—31no—
201C4×SD16—31no—
202C4×SD16—32no—
203C3×#41—124no—
204C2×C3×Q8—21no—
205C2×C3×Q8—21no—
206C2×C3×Q8—31no—
207C2×C3×Q8—31no—
208C2×C3×Q8—41no—
209C2×C3×Q8—62no—
210C2×C3×D4—21no—
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—
222C2×#67—22no—
223C2×#67—22no—
224#235—44no—
225C2×D12—21no—
226C2×D12—21no—
227C2×D12C23×C312yes—
228C2×C4×D3—22no—
229C2×Dic6—22no—
230C2×Dic6C3×D411yescharacteristic
231C2×Dic6C23×C311yescharacteristic
232C3×SD16—64no—
233C3×SD16—62no—
234C2×C3×C8—22no—
235C2×C3×C8—31no—
236C2×C3×C8—31no—
237C2×C3×C8C22×D312yes—
238C2×C3×C8C23×C312yes—
239C3×C4⋊C4—21no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—22no—
242C3×C4⋊C4—21no—
243C3×C4⋊C4—32no—
244C3×C4⋊C4—31no—
245C3×C4⋊C4—31no—
246C3×C4⋊C4—41no—
247C3×C4⋊C4—62no—
248C3×C4⋊C4—62no—
249C3×C4⋊C4—61no—
250C3×C4⋊C4C22×D312yes—
251C3×C4⋊C4C22×D311yescharacteristic
252C3×C4⋊C4C23×C311yescharacteristic
253C3×C4⋊C4C23×C312yes—
254C3×C22⋊C4—21no—
255C3×C22⋊C4—21no—
256C3×C22⋊C4—41no—
257C3×C22⋊C4—62no—
258C3×C42—21no—
259C3×C42—32no—
260C3×C42—62no—
261C3×C42—61no—
262C3×C42C22×D311yescharacteristic
263C3×C42C23×C311yescharacteristic
264#214—22no—
265(C2×D3)⋊C4—22no—
266C4⋊Dic3C3×D411yescharacteristic
267C4⋊Dic3C23×C311yescharacteristic
268Dic3⋊C4—21no—
269Dic3⋊C4—22no—
270Dic3⋊C4—22no—
271Dic3⋊C4C3×D412yes—
272C4×Dic3—21no—
273C4×Dic3—22no—
274C4×Dic3C23×C312yes—
275C2×C3⋊C8C23×C311yescharacteristic
276C2×C3⋊C8C23×C311yescharacteristic
277#204—24no—
278C22×C32—41no—
279C22×C32—41no—
280C22×C32—41no—
281C22×C32C22×D411yescharacteristic
282C2×C3×D3—42no—
283C2×C3×D3—42no—
284C2×C3×D3—42no—
285C32×C4—21no—
286C32×C4—41no—
287C32×C4—42no—
288C32×C4C2×SD1612yes—
289C32×C4C2×#4111yescharacteristic
290C32×C42−1+411yescharacteristic
291C3×Dic3—22no—
292C3×Dic3—22no—
293C3×Dic3—41no—
294C3×Dic3C2×SD1614yes—
295C2×#41—61no—
296C2×SD16—31no—
297C2×SD16—32no—
298C4⋊Q8—32no—
299C4⋊Q8—61no—
300C4⋊Q8—62no—
301C4⋊Q8C2×C3×D311yescharacteristic
302#127—32no—
303#127—31no—
304#121—62no—
305#121—61no—
306C4×Q8—31no—
307C4×Q8—32no—
308C4×Q8—31no—
309C4×Q8—61no—
310C4×D4—32no—
311C4×D4C2×C3×D311yescharacteristic
312#106—31no—
313#106C2×C3×D312yes—
314C4⋊C8—32no—
315C4⋊C8C2×C3×D311yescharacteristic
316#103—31no—
317#102—31no—
318#102—32no—
319#102—32no—
320#102—32no—
321#102C2×C3×D312yes—
322C4×C8—32no—
323C4×C8—31no—
324C23×C3—21no—
325C23×C3—21no—
326C23×C3—41no—
327C23×C3—62no—
328C22×D3—22no—
329C3×Q8—34no—
330C3×Q8—32no—
331C3×Q8—61no—
332C3×Q8—81no—
333C3×Q8—81no—
334C3×Q8—82no—
335C3×Q8—242no—
336C3×D4—22no—
337C3×D4—21no—
338C3×D4—21no—
339C3×D4—21no—
340C3×D4—21no—
341C3×D4—41no—
342C3×D4—62no—
343C3×D4—62no—
344C3×D4—124no—
345C3×D4—122no—
346C3×D4—241no—
347C3×D4—242no—
348C2×C3×C4—22no—
349C2×C3×C4—21no—
350C2×C3×C4—22no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—32no—
356C2×C3×C4—32no—
357C2×C3×C4—41no—
358C2×C3×C4—42no—
359C2×C3×C4—42no—
360C2×C3×C4—42no—
361C2×C3×C4—61no—
362C2×C3×C4—61no—
363C2×C3×C4—82no—
364C2×C3×C4—124no—
365C2×C3×C4D3×D411yescharacteristic
366C2×C3×C4D3×D411yescharacteristic
367C2×C3×C4C2×C3×D411yescharacteristic
368C2×C3×C4C2×C3×D411yescharacteristic
369C2×C3×C4C23×D311yescharacteristic
370C2×C3×C4C24×C311yescharacteristic
371#67—44no—
372#67—82no—
373C2×Dic3—21no—
374C2×Dic3—21no—
375C2×Dic3C2×C3×D412yes—
376C2×Dic3C2×C3×D412yes—
377D12—22no—
378D12—22no—
379D12—42no—
380D12—81no—
381C4×D3—44no—
382Dic6—21no—
383Dic6—82no—
384Dic6C3×SD1614yescomplemented
385Dic6C3×#4112yescomplemented
386C3×C8—22no—
387C3×C8—22no—
388C3×C8—42no—
389C3×C8—61no—
390C3×C8—61no—
391C3⋊C8—21no—
392C3⋊C8—21no—
393C2×C32—81no—
394C2×C32#54811yescharacteristic
395C2×C32C22×SD1611yescharacteristic
396C2×C32#57611yescharacteristic
397C3×D3—82no—
398#41—124no—
399C2×Q8—21no—
400C2×Q8—31no—
401C2×Q8—31no—
402C2×Q8—62no—
403C2×D4—32no—
404C2×D4—62no—
405C2×D4—62no—
406C2×D4—61no—
407C2×D4—61no—
408C2×D4C22×C3×D311yescharacteristic
409C22×C4—21no—
410C22×C4—62no—
411SD16—64no—
412SD16—62no—
413C2×C8—31no—
414C2×C8—31no—
415C2×C8C22×C3×D312yes—
416C4⋊C4—21no—
417C4⋊C4—32no—
418C4⋊C4—31no—
419C4⋊C4—31no—
420C4⋊C4—62no—
421C4⋊C4—62no—
422C4⋊C4—61no—
423C4⋊C4C22×C3×D312yes—
424C4⋊C4C22×C3×D311yescharacteristic
425C22⋊C4—21no—
426C22⋊C4—62no—
427C42—32no—
428C42—62no—
429C42—61no—
430C42C22×C3×D311yescharacteristic
431C22×C3—21no—
432C22×C3—42no—
433C22×C3—41no—
434C22×C3—41no—
435C22×C3—41no—
436C22×C3—41no—
437C22×C3—41no—
438C22×C3—41no—
439C22×C3—81no—
440C22×C3—81no—
441C22×C3—122no—
442C22×C3—122no—
443C22×C3—122no—
444C22×C3C2×D3×D411yescharacteristic
445C22×C3C22×C3×D411yescharacteristic
446C2×D3—42no—
447C2×D3—42no—
448C2×D3—42no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—22no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—34no—
455C3×C4—41no—
456C3×C4—41no—
457C3×C4—42no—
458C3×C4—41no—
459C3×C4—42no—
460C3×C4—62no—
461C3×C4—62no—
462C3×C4—81no—
463C3×C4—82no—
464C3×C4—121no—
465C3×C4D3×SD1612yes—
466C3×C4C2×C3×SD1612yes—
467C3×C4#100711yescharacteristic
468C3×C4D3×#4111yescharacteristic
469C3×C4C2×C3×#4111yescharacteristic
470C3×C4C3×2−1+411yescharacteristic
471Dic3—22no—
472Dic3—22no—
473Dic3—41no—
474Dic3C2×C3×SD1614yes—
475C32#336211yescharacteristic, complemented, Sylow
476C23—21no—
477C23—62no—
478Q8—34no—
479Q8—32no—
480Q8—61no—
481Q8—81no—
482Q8—242no—
483D4—21no—
484D4—21no—
485D4—62no—
486D4—62no—
487D4—124no—
488D4—122no—
489D4—241no—
490D4—242no—
491C2×C4—22no—
492C2×C4—21no—
493C2×C4—32no—
494C2×C4—32no—
495C2×C4—42no—
496C2×C4—61no—
497C2×C4—61no—
498C2×C4—124no—
499C2×C4C3×D3×D411yescharacteristic
500C2×C4C3×D3×D411yescharacteristic
501C2×C4C23×C3×D311yescharacteristic
502C8—22no—
503C8—61no—
504C8—61no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—82no—
509C2×C3—81no—
510C2×C3—81no—
511C2×C3—242no—
512C2×C3#563311yescharacteristic
513C2×C3C2×D3×SD1611yescharacteristic
514C2×C3#577411yescharacteristic
515C2×C3C3×#54811yescharacteristic
516C2×C3C22×C3×SD1611yescharacteristic
517C2×C3C3×#57611yescharacteristic
518D3—82no—
519C22—41no—
520C22—41no—
521C22—41no—
522C22—122no—
523C22—122no—
524C22—122no—
525C22C2×C3×D3×D411yescharacteristic
526C4—21no—
527C4—34no—
528C4—41no—
529C4—42no—
530C4—62no—
531C4—62no—
532C4—121no—
533C4C3×D3×SD1612yes—
534C4C3×#100711yescharacteristic
535C4C3×D3×#4111yescharacteristic
536C3—21no—
537C3#8109011yescharacteristic, direct product factor
538C3C3×#336211yescharacteristic, complemented
539C2—81no—
540C2—242no—
541C2C3×#563311yescharacteristic
542C2C2×C3×D3×SD1611yescharacteristic
543C2C3×#577411yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#476C2
socleC22×C32C22×D4
prime radicalC3×#5553C2
hypercenterC3×#476D3
hypocenterC3C3×#3362
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×#5722C2semidirect
3. C32×#476C2semidirect
4. C3×#5088C2semidirect
5. C3×C4×#214C2semidirect
6. C3×#4870C2semidirect
7. C3×#4852C2semidirect
8. C3×#4848C2semidirect
9. C3×#4830C2semidirect
10. C3×#4762C2semidirect
11. C3×#4760C2semidirect
13. #81090C3direct (N × H)
45. #5722C2×C3semidirect
51. C3×#476D3semidirect
52. C3×#476C2×C3semidirect
58. #5088C2×C3semidirect
59. C4×#214C2×C3semidirect
60. #4870C2×C3semidirect
61. #4852C2×C3semidirect
62. #4848C2×C3semidirect
63. #4830C2×C3semidirect
64. #4762C2×C3semidirect
65. #4760C2×C3semidirect
187. C3×Dic6SD16semidirect
188. C3×Dic6#41semidirect
197. #476C3×D3semidirect
384. Dic6C3×SD16semidirect
385. Dic6C3×#41semidirect
475. C32#3362semidirect
537. C3#81090direct (N × H)
538. C3C3×#3362semidirect

Maximal subgroups

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

subgroupindex
C3×#57222
C3×#55532
C32×#4762
C3×#50882
C3×C4×#2142
C3×#48702
C3×#48522
C3×#48482
C3×#48302
C3×#47622
C3×#47602
C3×#33623
#810903