Finite Group Databasebeta

← C3×#81588 #11895403

Subgroups — C3×#81588 #11895403

Order 1152.

843 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×#5718C211yesmaximal, characteristic
3C32×#486C211yesmaximal, characteristic, complemented
4C3×#5084C211yesmaximal, characteristic, complemented
5C3×#5075C211yesmaximal, characteristic, complemented
6C3×#4762C212yesmaximal, complemented
7C3×#4761C212yesmaximal, complemented
8C3×#4760C212yesmaximal, complemented
9C3×#4758C212yesmaximal, complemented
10C3×C4×#204C211yesmaximal, characteristic, complemented
11C3×C8×Dic6C211yesmaximal, characteristic, complemented
12C3×#3362—31nomaximal
13#81588C311yesmaximal, characteristic, direct product factor
14C2×C3×#237—21no—
15C32×C4⋊Q8C2211yescharacteristic
16C32×#127C2211yescharacteristic
17C3×#944—22no—
18C3×#940C2212yes—
19C3×#939—22no—
20C3×#938—21no—
21C3×D4×Dic3C2212yes—
22C2×C3×#214C2212yes—
23C2×C3×#204C2211yescharacteristic
24C3×#888—21no—
25C3×#888C2212yes—
26C3×#887—21no—
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×Dic3⋊C8C2212yes—
39C3×C8×Dic3C2212yes—
40C3×#809C2212yes—
41C3×#808C2212yes—
42C3×C4⋊(C3⋊C8)C2211yescharacteristic
43C3×Q82—31no—
44C3×#550—31no—
45#5722C2×C311yescharacteristic, complemented
46#5718C2×C311yescharacteristic
47C3×#486—21no—
48C3×#486—32no—
49C3×#486D311yescharacteristic, complemented
50C3×#486C2×C311yescharacteristic, complemented
51C3×#476—31no—
52C3×#476—32no—
53C3×#460—31no—
54C3×#460—32no—
55C3×C8×Q8—31no—
56C3×C4×SD16—32no—
57C3×C4×SD16—31no—
58#5084C2×C311yescharacteristic, complemented
59#5075C2×C311yescharacteristic, complemented
60#4762C2×C312yescomplemented
61#4761C2×C312yescomplemented
62#4760C2×C312yescomplemented
63#4758C2×C312yescomplemented
64C4×#204C2×C311yescharacteristic, complemented
65C8×Dic6C2×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×Dic6—22no—
77C2×C3×Dic6D411yescharacteristic
78C2×C3×Dic6C2311yescharacteristic
79C2×C32×C8C2311yescharacteristic
80C2×C32×C8C2311yescharacteristic
81C32×C4⋊C4—21no—
82C32×C4⋊C4C2312yes—
83C32×C42C2311yescharacteristic
84C3×#217—22no—
85C3×#214—24no—
86C3×(C2×D3)⋊C4—21no—
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#3362—31noSylow
100C2×C3×#41—61no—
101C2×#237—21no—
102C2×C3×SD16—32no—
103C2×C3×SD16—31no—
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—21no—
111C3×#127—32no—
112C3×#127C2×D311yescharacteristic
113C3×#127C22×C311yescharacteristic
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—
122#944—22no—
123#940C22×C312yes—
124#939—22no—
125#938—21no—
126D4×Dic3C22×C312yes—
127C2×#214C22×C312yes—
128C2×#204C22×C311yescharacteristic
129#888—21no—
130#888C22×C312yes—
131#887—21no—
132#887C22×C312yes—
133C4×D12C22×C311yescharacteristic
134C4×Dic6C22×C311yescharacteristic
135C4×Dic6C22×C311yescharacteristic
136C3×#106—31no—
137C3×#106—32no—
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×C4×C8—21no—
151C3×C4×C8—32no—
152C3×C4×C8C2×D311yescharacteristic
153C3×C4×C8C22×C311yescharacteristic
154#832C22×C312yes—
155#821C22×C311yescharacteristic
156#817C22×C311yescharacteristic
157#816C22×C311yescharacteristic
158Dic3⋊C8C22×C312yes—
159C8×Dic3C22×C312yes—
160#809C22×C312yes—
161#808C22×C312yes—
162C4⋊(C3⋊C8)C22×C311yescharacteristic
163C23×C32—22no—
164C22×C3×D3—21no—
165C32×Q8—81no—
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—21no—
186C3×Dic6—82no—
187C3×Dic6SD1614yescomplemented
188C3×Dic6#4112yescomplemented
189C32×C8—21no—
190C32×C8—21no—
191C3×C3⋊C8—22no—
192Q82—31no—
193#550—31no—
194#486—32no—
195#486C3×D311yescharacteristic, complemented
196#476—31no—
197#476—32no—
198#460—31no—
199#460—32no—
200C8×Q8—31no—
201C4×SD16—32no—
202C4×SD16—31no—
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—21no—
212C2×C3×D4—21no—
213C2×C3×D4—21no—
214C2×C3×D4—22no—
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—61no—
224C2×#67—22no—
225C2×#67—22no—
226C22×Dic3—22no—
227#237—44no—
228C2×D12C23×C311yescharacteristic
229C2×C4×D3—21no—
230C2×Dic6—22no—
231C2×Dic6C3×D411yescharacteristic
232C2×Dic6C23×C311yescharacteristic
233C3×SD16—62no—
234C3×SD16—64no—
235C2×C3×C8—21no—
236C2×C3×C8—21no—
237C2×C3×C8—32no—
238C2×C3×C8C22×D311yescharacteristic
239C2×C3×C8C22×D311yescharacteristic
240C2×C3×C8C23×C311yescharacteristic
241C2×C3×C8C23×C311yescharacteristic
242C3×C4⋊C4—21no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—22no—
245C3×C4⋊C4—32no—
246C3×C4⋊C4—31no—
247C3×C4⋊C4—31no—
248C3×C4⋊C4—31no—
249C3×C4⋊C4—41no—
250C3×C4⋊C4—62no—
251C3×C4⋊C4—62no—
252C3×C4⋊C4—61no—
253C3×C4⋊C4C22×D312yes—
254C3×C4⋊C4C23×C312yes—
255C3×C22⋊C4—62no—
256C3×C22⋊C4—61no—
257C3×C42—21no—
258C3×C42—32no—
259C3×C42—62no—
260C3×C42—61no—
261C3×C42C22×D311yescharacteristic
262C3×C42C23×C311yescharacteristic
263#217—22no—
264#214—24no—
265(C2×D3)⋊C4—21no—
266C4⋊Dic3C3×D411yescharacteristic
267C4⋊Dic3C23×C311yescharacteristic
268C4⋊Dic3C23×C311yescharacteristic
269Dic3⋊C4—21no—
270Dic3⋊C4—22no—
271Dic3⋊C4—22no—
272Dic3⋊C4C3×D412yes—
273C4×Dic3—21no—
274C4×Dic3—22no—
275C4×Dic3C23×C312yes—
276C2×C3⋊C8C23×C312yes—
277#204—22no—
278C22×C32—42no—
279C22×C32—42no—
280C22×C32—42no—
281C22×C32C22×D411yescharacteristic
282C2×C3×D3—41no—
283C2×C3×D3—41no—
284C2×C3×D3—41no—
285C32×C4—21no—
286C32×C4—42no—
287C32×C4C2×SD1612yes—
288C32×C4C2×#4111yescharacteristic
289C32×C42−1+411yescharacteristic
290C3×Dic3—22no—
291C3×Dic3—22no—
292C3×Dic3—41no—
293C3×Dic3—41no—
294C3×Dic3C2×SD1614yes—
295C2×#41—61no—
296C2×SD16—32no—
297C2×SD16—31no—
298C4⋊Q8—32no—
299C4⋊Q8—61no—
300C4⋊Q8—62no—
301C4⋊Q8C2×C3×D311yescharacteristic
302#127—32no—
303#127C2×C3×D311yescharacteristic
304#121—61no—
305#121—62no—
306C4×Q8—31no—
307C4×Q8—32no—
308C4×Q8—31no—
309C4×Q8—61no—
310C4×D4—32no—
311C4×D4—31no—
312#106—31no—
313#106—32no—
314C4⋊C8—32no—
315C4⋊C8—31no—
316#103—31no—
317#102—32no—
318#102—31no—
319#102—32no—
320#102C2×C3×D312yes—
321#102C2×C3×D312yes—
322C4×C8—32no—
323C4×C8C2×C3×D311yescharacteristic
324C23×C3—22no—
325C23×C3—22no—
326C23×C3—42no—
327C23×C3—61no—
328C22×D3—21no—
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—22no—
338C3×D4—22no—
339C3×D4—22no—
340C3×D4—42no—
341C3×D4—42no—
342C3×D4—42no—
343C3×D4—42no—
344C3×D4—61no—
345C3×D4—61no—
346C3×D4—82no—
347C3×D4—81no—
348C3×D4—81no—
349C3×D4—82no—
350C3×D4—124no—
351C3×D4—242no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—32no—
358C2×C3×C4—32no—
359C2×C3×C4—42no—
360C2×C3×C4—61no—
361C2×C3×C4—61no—
362C2×C3×C4—61no—
363C2×C3×C4—124no—
364C2×C3×C4—122no—
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×Dic3—21no—
376C2×Dic3—44no—
377C2×Dic3C2×C3×D412yes—
378C2×Dic3C2×C3×D412yes—
379D12—21no—
380D12—21no—
381C4×D3—42no—
382Dic6—21no—
383Dic6—82no—
384Dic6C3×SD1614yescomplemented
385Dic6C3×#4112yescomplemented
386C3×C8—21no—
387C3×C8—21no—
388C3×C8—21no—
389C3×C8—21no—
390C3×C8—41no—
391C3×C8—41no—
392C3×C8—62no—
393C3⋊C8—22no—
394C2×C32—82no—
395C2×C32#54811yescharacteristic
396C2×C32C22×SD1611yescharacteristic
397C2×C32#57611yescharacteristic
398C3×D3—81no—
399#41—124no—
400C2×Q8—21no—
401C2×Q8—31no—
402C2×Q8—31no—
403C2×Q8—62no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—31no—
407C2×D4—62no—
408C2×D4—62no—
409C2×D4C22×C3×D312yes—
410C22×C4—62no—
411C22×C4—61no—
412SD16—62no—
413SD16—64no—
414C2×C8—32no—
415C2×C8C22×C3×D311yescharacteristic
416C2×C8C22×C3×D311yescharacteristic
417C4⋊C4—21no—
418C4⋊C4—32no—
419C4⋊C4—31no—
420C4⋊C4—31no—
421C4⋊C4—31no—
422C4⋊C4—62no—
423C4⋊C4—62no—
424C4⋊C4—61no—
425C4⋊C4C22×C3×D312yes—
426C22⋊C4—62no—
427C22⋊C4—61no—
428C42—32no—
429C42—62no—
430C42—61no—
431C42C22×C3×D311yescharacteristic
432C22×C3—21no—
433C22×C3—42no—
434C22×C3—42no—
435C22×C3—42no—
436C22×C3—42no—
437C22×C3—42no—
438C22×C3—42no—
439C22×C3—82no—
440C22×C3—82no—
441C22×C3—82no—
442C22×C3—121no—
443C22×C3—121no—
444C22×C3—121no—
445C22×C3C2×D3×D411yescharacteristic
446C22×C3C22×C3×D411yescharacteristic
447C2×D3—41no—
448C2×D3—41no—
449C2×D3—41no—
450C3×C4—22no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—22no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—34no—
457C3×C4—42no—
458C3×C4—42no—
459C3×C4—62no—
460C3×C4—62no—
461C3×C4—82no—
462C3×C4—121no—
463C3×C4—121no—
464C3×C4D3×SD1612yes—
465C3×C4C2×C3×SD1612yes—
466C3×C4D3×#4111yescharacteristic
467C3×C4#101011yescharacteristic
468C3×C4C2×C3×#4111yescharacteristic
469C3×C4C3×2−1+411yescharacteristic
470Dic3—22no—
471Dic3—22no—
472Dic3—41no—
473Dic3—41no—
474Dic3C2×C3×SD1614yes—
475C32#336211yescharacteristic, complemented, Sylow
476C23—22no—
477C23—61no—
478Q8—34no—
479Q8—32no—
480Q8—61no—
481Q8—81no—
482Q8—242no—
483D4—22no—
484D4—22no—
485D4—42no—
486D4—61no—
487D4—61no—
488D4—81no—
489D4—124no—
490D4—242no—
491C2×C4—22no—
492C2×C4—32no—
493C2×C4—32no—
494C2×C4—61no—
495C2×C4—61no—
496C2×C4—61no—
497C2×C4—124no—
498C2×C4—122no—
499C2×C4C3×D3×D411yescharacteristic
500C2×C4C3×D3×D411yescharacteristic
501C2×C4C23×C3×D311yescharacteristic
502C8—21no—
503C8—21no—
504C8—62no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—82no—
509C2×C3—82no—
510C2×C3—162no—
511C2×C3—241no—
512C2×C3#567711yescharacteristic
513C2×C3#575711yescharacteristic
514C2×C3C2×D3×SD1611yescharacteristic
515C2×C3C3×#54811yescharacteristic
516C2×C3C22×C3×SD1611yescharacteristic
517C2×C3C3×#57611yescharacteristic
518D3—81no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—121no—
523C22—121no—
524C22—121no—
525C22C2×C3×D3×D411yescharacteristic
526C4—21no—
527C4—34no—
528C4—42no—
529C4—62no—
530C4—62no—
531C4—121no—
532C4—121no—
533C4C3×D3×SD1612yes—
534C4C3×D3×#4111yescharacteristic
535C4C3×#101011yescharacteristic
536C3—21no—
537C3#8158811yescharacteristic, direct product factor
538C3C3×#336211yescharacteristic, complemented
539C2—82no—
540C2—241no—
541C2C3×#567711yescharacteristic
542C2C3×#575711yescharacteristic
543C2C2×C3×D3×SD1611yescharacteristic
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×#3362
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×#5722C2semidirect
3. C32×#486C2semidirect
4. C3×#5084C2semidirect
5. C3×#5075C2semidirect
6. C3×#4762C2semidirect
7. C3×#4761C2semidirect
8. C3×#4760C2semidirect
9. C3×#4758C2semidirect
10. C3×C4×#204C2semidirect
11. C3×C8×Dic6C2semidirect
13. #81588C3direct (N × H)
45. #5722C2×C3semidirect
49. C3×#486D3semidirect
50. C3×#486C2×C3semidirect
58. #5084C2×C3semidirect
59. #5075C2×C3semidirect
60. #4762C2×C3semidirect
61. #4761C2×C3semidirect
62. #4760C2×C3semidirect
63. #4758C2×C3semidirect
64. C4×#204C2×C3semidirect
65. C8×Dic6C2×C3semidirect
187. C3×Dic6SD16semidirect
188. C3×Dic6#41semidirect
195. #486C3×D3semidirect
384. Dic6C3×SD16semidirect
385. Dic6C3×#41semidirect
475. C32#3362semidirect
537. C3#81588direct (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×#57182
C32×#4862
C3×#50842
C3×#50752
C3×#47622
C3×#47612
C3×#47602
C3×#47582
C3×C4×#2042
C3×C8×Dic62
C3×#33623
#815883