Finite Group Databasebeta

← C3×#81590 #11895940

Subgroups — C3×#81590 #11895940

Order 1152.

823 conjugacy classes of subgroups.

The subgroup lattice has 541 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5721C211yesmaximal, characteristic, complemented
2C3×#5718C211yesmaximal, characteristic
3C32×#486C211yesmaximal, characteristic, complemented
4C3×#5087C211yesmaximal, characteristic, complemented
5C3×#5075C211yesmaximal, characteristic, complemented
6C3×#4764C212yesmaximal, complemented
7C3×#4763C212yesmaximal, complemented
8C3×#4762C212yesmaximal, complemented
9C3×#4757C212yesmaximal, complemented
10C3×C4×#204C211yesmaximal, characteristic, complemented
11C3×#4679C211yesmaximal, characteristic, complemented
12C3×#3368—31nomaximal
13#81590C311yesmaximal, characteristic, direct product factor
14C2×C3×#237—21no—
15C32×C4⋊Q8C2211yescharacteristic
16C32×#127C2211yescharacteristic
17C3×Q8×Dic3—21no—
18C3×#944—21no—
19C3×#940C2212yes—
20C3×#939—22no—
21C3×#938—21no—
22C3×D4×Dic3C2212yes—
23C2×C3×#214C2212yes—
24C2×C3×#204C2211yescharacteristic
25C3×#890C2212yes—
26C3×#889—22no—
27C3×#887C2212yes—
28C3×C4×D12C2211yescharacteristic
29C3×C4×Dic6C2211yescharacteristic
30C3×C4×Dic6C2211yescharacteristic
31C32×#102C2212yes—
32C32×#102C2212yes—
33C32×C4×C8C2211yescharacteristic
34C3×#832C2212yes—
35C3×#821C2211yescharacteristic
36C3×#817C2211yescharacteristic
37C3×#816C2211yescharacteristic
38C3×#815C2212yes—
39C3×Dic3⋊C8C2212yes—
40C3×#809C2212yes—
41C3×#807C2212yes—
42C3×C4⋊(C3⋊C8)C2211yescharacteristic
43C3×#557—31no—
44C3×#550—31no—
45#5721C2×C311yescharacteristic, complemented
46#5718C2×C311yescharacteristic
47C3×#490—32no—
48C3×#486—21no—
49C3×#486D311yescharacteristic, complemented
50C3×#486C2×C311yescharacteristic, complemented
51C3×#478—32no—
52C3×#474—31no—
53C3×#460—31no—
54C3×#460—32no—
55C3×#446—31no—
56C3×#440—32no—
57C3×C4×SD16—31no—
58#5087C2×C311yescharacteristic, complemented
59#5075C2×C311yescharacteristic, complemented
60#4764C2×C312yescomplemented
61#4763C2×C312yescomplemented
62#4762C2×C312yescomplemented
63#4757C2×C312yescomplemented
64C4×#204C2×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×C4×D3—21no—
76C2×C3×Dic6D411yescharacteristic
77C2×C3×Dic6C2311yescharacteristic
78C2×C32×C8C2311yescharacteristic
79C2×C32×C8C2311yescharacteristic
80C32×C4⋊C4—21no—
81C32×C4⋊C4C2312yes—
82C32×C42C2311yescharacteristic
83C3×#217—22no—
84C3×#214—24no—
85C3×(C2×D3)⋊C4—21no—
86C3×C4⋊Dic3—22no—
87C3×C4⋊Dic3D411yescharacteristic
88C3×C4⋊Dic3C2311yescharacteristic
89C3×C4⋊Dic3C2311yescharacteristic
90C3×Dic3⋊C4—21no—
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4—22no—
93C3×Dic3⋊C4D412yes—
94C3×C4×Dic3—21no—
95C3×C4×Dic3—22no—
96C3×C4×Dic3C2312yes—
97C2×C3×C3⋊C8C2312yes—
98C3×#204—22no—
99#3368—31noSylow
100C2×C3×#41—61no—
101C2×#237—21no—
102C2×C3×SD16—32no—
103C2×C3×SD16—31no—
104C3×C4⋊Q8—21no—
105C3×C4⋊Q8—61no—
106C3×C4⋊Q8C2×D311yescharacteristic
107C3×C4⋊Q8C22×C311yescharacteristic
108C3×#127—21no—
109C3×#127—32no—
110C3×#127C2×D311yescharacteristic
111C3×#127C22×C311yescharacteristic
112C3×#125—32no—
113C3×#125—62no—
114C3×#121—61no—
115C3×#121—62no—
116C3×C4×Q8—31no—
117C3×C4×Q8—32no—
118C3×C4×Q8—31no—
119C3×C4×Q8—61no—
120C3×C4×D4—32no—
121C3×C4×D4—31no—
122Q8×Dic3—21no—
123#944—21no—
124#940C22×C312yes—
125#939—22no—
126#938—21no—
127D4×Dic3C22×C312yes—
128C2×#214C22×C312yes—
129C2×#204C22×C311yescharacteristic
130#890C22×C312yes—
131#889—22no—
132#887C22×C312yes—
133C4×D12C22×C311yescharacteristic
134C4×Dic6C22×C311yescharacteristic
135C4×Dic6C22×C311yescharacteristic
136C3×#107—32no—
137C3×#106—31no—
138C3×C4⋊C8—32no—
139C3×C4⋊C8—31no—
140C3×#103—31no—
141C3×#102—22no—
142C3×#102—22no—
143C3×#102—32no—
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#817C22×C311yescharacteristic
157#816C22×C311yescharacteristic
158#815C22×C312yes—
159Dic3⋊C8C22×C312yes—
160#809C22×C312yes—
161#807C22×C312yes—
162C4⋊(C3⋊C8)C22×C311yescharacteristic
163C23×C32—22no—
164C22×C3×D3—21no—
165C32×Q8—42no—
166C32×D4—22no—
167C32×D4—22no—
168C32×D4—42no—
169C32×D4—81no—
170C2×C32×C4—22no—
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×Dic3—21no—
179C2×C3×Dic3—44no—
180C2×C3×Dic3C2×D412yes—
181C2×C3×Dic3C2×D412yes—
182C3×D12—21no—
183C3×D12—21no—
184C3×C4×D3—42no—
185C3×Dic6—22no—
186C3×Dic6—21no—
187C3×Dic6#4112yescomplemented
188C32×C8—21no—
189C32×C8—21no—
190C3×C3⋊C8—22no—
191#557—31no—
192#550—31no—
193#490—32no—
194#486C3×D311yescharacteristic, complemented
195#478—32no—
196#474—31no—
197#460—31no—
198#460—32no—
199#446—31no—
200#440—32no—
201C4×SD16—31no—
202C3×#41—124no—
203C2×C3×Q8—21no—
204C2×C3×Q8—21no—
205C2×C3×Q8—31no—
206C2×C3×Q8—31no—
207C2×C3×Q8—41no—
208C2×C3×D4—21no—
209C2×C3×D4—21no—
210C2×C3×D4—21no—
211C2×C3×D4—21no—
212C2×C3×D4—22no—
213C2×C3×D4—31no—
214C2×C3×D4—41no—
215C2×C3×D4—41no—
216C2×C3×D4—62no—
217C2×C3×D4—62no—
218C2×C3×D4C22×D312yes—
219C2×C3×D4C23×C312yes—
220C22×C3×C4—62no—
221C22×C3×C4—61no—
222C2×#67—22no—
223C2×#67—22no—
224C22×Dic3—22no—
225#237—44no—
226C2×D12C23×C311yescharacteristic
227C2×C4×D3—21no—
228C2×Dic6C3×D411yescharacteristic
229C2×Dic6C23×C311yescharacteristic
230C3×SD16—62no—
231C3×SD16—64no—
232C2×C3×C8—21no—
233C2×C3×C8—21no—
234C2×C3×C8—32no—
235C2×C3×C8C22×D311yescharacteristic
236C2×C3×C8C22×D311yescharacteristic
237C2×C3×C8C23×C311yescharacteristic
238C2×C3×C8C23×C311yescharacteristic
239C3×C4⋊C4—21no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—22no—
242C3×C4⋊C4—32no—
243C3×C4⋊C4—31no—
244C3×C4⋊C4—31no—
245C3×C4⋊C4—31no—
246C3×C4⋊C4—41no—
247C3×C4⋊C4—62no—
248C3×C4⋊C4—62no—
249C3×C4⋊C4—62no—
250C3×C4⋊C4—61no—
251C3×C4⋊C4C22×D312yes—
252C3×C4⋊C4C23×C312yes—
253C3×C22⋊C4—62no—
254C3×C22⋊C4—61no—
255C3×C42—21no—
256C3×C42—32no—
257C3×C42—62no—
258C3×C42—61no—
259C3×C42C22×D311yescharacteristic
260C3×C42C23×C311yescharacteristic
261#217—22no—
262#214—24no—
263(C2×D3)⋊C4—21no—
264C4⋊Dic3—22no—
265C4⋊Dic3C3×D411yescharacteristic
266C4⋊Dic3C23×C311yescharacteristic
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×C312yes—
276#204—22no—
277C22×C32—42no—
278C22×C32—42no—
279C22×C32—42no—
280C22×C32C22×D411yescharacteristic
281C2×C3×D3—41no—
282C2×C3×D3—41no—
283C2×C3×D3—41no—
284C32×C4—21no—
285C32×C4—42no—
286C32×C4AGL(1,ℤ/8)12yes—
287C32×C4C2×#4111yescharacteristic
288C32×C42−1+411yescharacteristic
289C3×Dic3—22no—
290C3×Dic3—22no—
291C3×Dic3—22no—
292C3×Dic3—41no—
293C3×Dic3—41no—
294C2×#41—61no—
295C2×SD16—32no—
296C2×SD16—31no—
297C4⋊Q8—61no—
298C4⋊Q8C2×C3×D311yescharacteristic
299#127—32no—
300#127C2×C3×D311yescharacteristic
301#125—32no—
302#125—62no—
303#121—61no—
304#121—62no—
305C4×Q8—31no—
306C4×Q8—32no—
307C4×Q8—31no—
308C4×Q8—61no—
309C4×D4—32no—
310C4×D4—31no—
311#107—32no—
312#106—31no—
313C4⋊C8—32no—
314C4⋊C8—31no—
315#103—31no—
316#102—32no—
317#102—31no—
318#102—32no—
319#102C2×C3×D312yes—
320#102C2×C3×D312yes—
321#97—32no—
322C4×C8C2×C3×D311yescharacteristic
323C23×C3—22no—
324C23×C3—22no—
325C23×C3—42no—
326C23×C3—61no—
327C22×D3—21no—
328C3×Q8—32no—
329C3×Q8—42no—
330C3×Q8—42no—
331C3×Q8—62no—
332C3×Q8—61no—
333C3×Q8—82no—
334C3×D4—22no—
335C3×D4—22no—
336C3×D4—22no—
337C3×D4—22no—
338C3×D4—42no—
339C3×D4—42no—
340C3×D4—42no—
341C3×D4—42no—
342C3×D4—61no—
343C3×D4—61no—
344C3×D4—82no—
345C3×D4—81no—
346C3×D4—81no—
347C3×D4—82no—
348C3×D4—124no—
349C3×D4—242no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—32no—
356C2×C3×C4—32no—
357C2×C3×C4—42no—
358C2×C3×C4—61no—
359C2×C3×C4—61no—
360C2×C3×C4—61no—
361C2×C3×C4—124no—
362C2×C3×C4—122no—
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4C2×C3×D411yescharacteristic
366C2×C3×C4C2×C3×D411yescharacteristic
367C2×C3×C4C23×D311yescharacteristic
368C2×C3×C4C24×C311yescharacteristic
369#67—44no—
370#67—82no—
371C2×Dic3—21no—
372C2×Dic3—21no—
373C2×Dic3—21no—
374C2×Dic3—44no—
375C2×Dic3C2×C3×D412yes—
376C2×Dic3C2×C3×D412yes—
377D12—21no—
378D12—21no—
379C4×D3—42no—
380Dic6—22no—
381Dic6—21no—
382Dic6C3×#4112yescomplemented
383C3×C8—21no—
384C3×C8—21no—
385C3×C8—21no—
386C3×C8—21no—
387C3×C8—41no—
388C3×C8—41no—
389C3×C8—62no—
390C3⋊C8—22no—
391C2×C32—82no—
392C2×C32#54811yescharacteristic
393C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
394C2×C32#57711yescharacteristic
395C3×D3—81no—
396#41—124no—
397C2×Q8—21no—
398C2×Q8—31no—
399C2×Q8—31no—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—31no—
403C2×D4—62no—
404C2×D4—62no—
405C2×D4C22×C3×D312yes—
406C22×C4—62no—
407C22×C4—61no—
408SD16—62no—
409SD16—64no—
410C2×C8—32no—
411C2×C8C22×C3×D311yescharacteristic
412C2×C8C22×C3×D311yescharacteristic
413C4⋊C4—21no—
414C4⋊C4—31no—
415C4⋊C4—32no—
416C4⋊C4—31no—
417C4⋊C4—31no—
418C4⋊C4—62no—
419C4⋊C4—62no—
420C4⋊C4—62no—
421C4⋊C4—61no—
422C4⋊C4C22×C3×D312yes—
423C22⋊C4—62no—
424C22⋊C4—61no—
425C42—32no—
426C42—62no—
427C42—61no—
428C42C22×C3×D311yescharacteristic
429C22×C3—21no—
430C22×C3—42no—
431C22×C3—42no—
432C22×C3—42no—
433C22×C3—42no—
434C22×C3—42no—
435C22×C3—42no—
436C22×C3—82no—
437C22×C3—82no—
438C22×C3—82no—
439C22×C3—121no—
440C22×C3—121no—
441C22×C3—121no—
442C22×C3C2×D3×D411yescharacteristic
443C22×C3C22×C3×D411yescharacteristic
444C2×D3—41no—
445C2×D3—41no—
446C2×D3—41no—
447C3×C4—22no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—22no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—42no—
454C3×C4—42no—
455C3×C4—62no—
456C3×C4—62no—
457C3×C4—62no—
458C3×C4—82no—
459C3×C4—121no—
460C3×C4—121no—
461C3×C4#91112yes—
462C3×C4C3×AGL(1,ℤ/8)12yes—
463C3×C4D3×#4111yescharacteristic
464C3×C4#101011yescharacteristic
465C3×C4C2×C3×#4111yescharacteristic
466C3×C4C3×2−1+411yescharacteristic
467Dic3—22no—
468Dic3—22no—
469Dic3—22no—
470Dic3—41no—
471Dic3—41no—
472C32#336811yescharacteristic, complemented, Sylow
473C23—22no—
474C23—61no—
475Q8—32no—
476Q8—42no—
477Q8—62no—
478Q8—61no—
479D4—22no—
480D4—22no—
481D4—42no—
482D4—61no—
483D4—61no—
484D4—81no—
485D4—124no—
486D4—242no—
487C2×C4—22no—
488C2×C4—32no—
489C2×C4—32no—
490C2×C4—61no—
491C2×C4—61no—
492C2×C4—61no—
493C2×C4—124no—
494C2×C4—122no—
495C2×C4C3×D3×D411yescharacteristic
496C2×C4C3×D3×D411yescharacteristic
497C2×C4C23×C3×D311yescharacteristic
498C8—21no—
499C8—21no—
500C8—62no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—82no—
505C2×C3—82no—
506C2×C3—162no—
507C2×C3—241no—
508C2×C3#567711yescharacteristic
509C2×C3C2×#91111yescharacteristic
510C2×C3#576211yescharacteristic
511C2×C3C3×#54811yescharacteristic
512C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
513C2×C3C3×#57711yescharacteristic
514D3—81no—
515C22—42no—
516C22—42no—
517C22—42no—
518C22—121no—
519C22—121no—
520C22—121no—
521C22C2×C3×D3×D411yescharacteristic
522C4—21no—
523C4—42no—
524C4—62no—
525C4—62no—
526C4—62no—
527C4—121no—
528C4—121no—
529C4C3×#91112yes—
530C4C3×D3×#4111yescharacteristic
531C4C3×#101011yescharacteristic
532C3—21no—
533C3#8159011yescharacteristic, direct product factor
534C3C3×#336811yescharacteristic, complemented
535C2—82no—
536C2—241no—
537C2C3×#567711yescharacteristic
538C2C2×C3×#91111yescharacteristic
539C2C3×#576211yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#486C2
socleC22×C32C22×D4
prime radicalC3×#5718C2
hypercenterC3×#486D3
hypocenterC3C3×#3368
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×#5721C2semidirect
3. C32×#486C2semidirect
4. C3×#5087C2semidirect
5. C3×#5075C2semidirect
6. C3×#4764C2semidirect
7. C3×#4763C2semidirect
8. C3×#4762C2semidirect
9. C3×#4757C2semidirect
10. C3×C4×#204C2semidirect
11. C3×#4679C2semidirect
13. #81590C3direct (N × H)
45. #5721C2×C3semidirect
49. C3×#486D3semidirect
50. C3×#486C2×C3semidirect
58. #5087C2×C3semidirect
59. #5075C2×C3semidirect
60. #4764C2×C3semidirect
61. #4763C2×C3semidirect
62. #4762C2×C3semidirect
63. #4757C2×C3semidirect
64. C4×#204C2×C3semidirect
65. #4679C2×C3semidirect
187. C3×Dic6#41semidirect
194. #486C3×D3semidirect
382. Dic6C3×#41semidirect
472. C32#3368semidirect
533. C3#81590direct (N × H)
534. C3C3×#3368semidirect

Maximal subgroups

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

subgroupindex
C3×#57212
C3×#57182
C32×#4862
C3×#50872
C3×#50752
C3×#47642
C3×#47632
C3×#47622
C3×#47572
C3×C4×#2042
C3×#46792
C3×#33683
#815903