Finite Group Databasebeta

← C3×#80421 #11898347

Subgroups — C3×#80421 #11898347

Order 1152.

780 conjugacy classes of subgroups.

The subgroup lattice has 539 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5732C211yesmaximal, characteristic, complemented
2C3×#5542C211yesmaximal, characteristic, complemented
3C32×#461C211yesmaximal, characteristic, complemented
4C3×#5168C212yesmaximal
5C3×#5166C212yesmaximal, complemented
6C3×#5092C211yesmaximal, characteristic, complemented
7C3×C4×#213C211yesmaximal, characteristic
8C3×#4841C211yesmaximal, characteristic, complemented
9C3×#4830C211yesmaximal, characteristic, complemented
10C3×#4798C212yesmaximal, complemented
11C3×#4790C212yesmaximal, complemented
12C3×#3393—31nomaximal
13#80421C311yesmaximal, characteristic, direct product factor
14C2×C32×SD16C2212yes—
15C32×C4⋊Q8C2211yescharacteristic
16C32×C4×D4C2211yescharacteristic
17C3×#947C2212yes—
18C3×Q8×Dic3C2212yes—
19C2×C3×#216C2212yes—
20C2×C3×#216C2212yes—
21C3×#936C2212yes—
22C2×C3×#213C2211yescharacteristic
23C3×#926—21no—
24C3×#924—21no—
25C2×C3×#204C2212yes—
26C3×#898—22no—
27C3×#897—21no—
28C3×#892—21no—
29C3×#887C2212yes—
30C3×#879—22no—
31C3×C4×D12C2211yescharacteristic
32C3×#869C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic
34C32×C4⋊C8C2211yescharacteristic
35C32×#103C2212yes—
36C3×#832C2211yescharacteristic
37C3×#816C2212yes—
38C3×Dic3⋊C8C2212yes—
39C3×C8×Dic3C2212yes—
40C3×#809C2211yescharacteristic
41C3×#807C2211yescharacteristic
42C3×C4×C3⋊C8C2211yescharacteristic
43C3×#556—31no—
44C3×#556—31no—
45#5732C2×C311yescharacteristic, complemented
46#5542C2×C311yescharacteristic, complemented
47C3×#495—32no—
48C3×#494—31no—
49C3×#464—32no—
50C3×#464—32no—
51C3×#461—21no—
52C3×#461—31no—
53C3×#461D311yescharacteristic, complemented
54C3×#461C2×C311yescharacteristic, complemented
55C3×C8×Q8—31no—
56C3×C4×Q16—32no—
57C3×C4×D8—31no—
58#5168C2×C312yes—
59#5166C2×C312yescomplemented
60#5092C2×C311yescharacteristic, complemented
61C4×#213C2×C311yescharacteristic
62#4841C2×C311yescharacteristic, complemented
63#4830C2×C311yescharacteristic, complemented
64#4798C2×C312yescomplemented
65#4790C2×C312yescomplemented
66C2×C32×Q8C2312yes—
67C2×C32×D4C2311yescharacteristic
68C22×C32×C4—21no—
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×Dic6D411yescharacteristic
72C2×C3×Dic6C2312yes—
73C32×SD16—42no—
74C2×C32×C8C2312yes—
75C32×C4⋊C4—21no—
76C32×C4⋊C4—21no—
77C32×C4⋊C4C2311yescharacteristic
78C32×C22⋊C4—21no—
79C32×C42C2311yescharacteristic
80C3×#217—22no—
81C3×#217—22no—
82C3×#216—24no—
83C3×#216—42no—
84C3×#213—22no—
85C3×(C2×D3)⋊C4—21no—
86C3×(C2×D3)⋊C4—22no—
87C3×(C2×D3)⋊C4—22no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3—22no—
91C3×C4⋊Dic3D411yescharacteristic
92C3×C4⋊Dic3C2311yescharacteristic
93C3×Dic3⋊C4—22no—
94C3×Dic3⋊C4D412yes—
95C3×C4×Dic3—22no—
96C3×C4×Dic3—22no—
97C3×C4×Dic3C2312yes—
98C2×C3×C3⋊C8C2311yescharacteristic
99C2×C3×C3⋊C8C2311yescharacteristic
100C3×#204—42no—
101#3393—31noSylow
102C2×C3×Q16—32no—
103C2×C3×Q16—32no—
104C2×C3×SD16—22no—
105C2×C3×SD16—32no—
106C2×C3×SD16C2×D312yes—
107C2×C3×SD16C22×C312yes—
108C2×C3×D8—31no—
109C3×C4⋊Q8—21no—
110C3×C4⋊Q8—31no—
111C3×C4⋊Q8C2×D311yescharacteristic
112C3×C4⋊Q8C22×C311yescharacteristic
113C3×#126—62no—
114C3×#126—62no—
115C3×#124—32no—
116C3×#124—32no—
117C3×C22⋊Q8—61no—
118C3×C22⋊Q8—61no—
119C3×C4×Q8—31no—
120C3×C4×Q8—32no—
121C3×C4×Q8—32no—
122C3×C4×D4—21no—
123C3×C4×D4—31no—
124C3×C4×D4C2×D311yescharacteristic
125C3×C4×D4C22×C311yescharacteristic
126C3×#117—61no—
127C3×#117—61no—
128#947C22×C312yes—
129Q8×Dic3C22×C312yes—
130C2×#216C22×C312yes—
131C2×#216C22×C312yes—
132#936C22×C312yes—
133C2×#213C22×C311yescharacteristic
134#926—21no—
135#924—21no—
136C2×#204C22×C312yes—
137#898—22no—
138#897—21no—
139#892—21no—
140#887C22×C312yes—
141#879—22no—
142C4×D12C22×C311yescharacteristic
143#869C22×C311yescharacteristic
144C4×Dic6C22×C311yescharacteristic
145C3×#107—31no—
146C3×C4⋊C8—21no—
147C3×C4⋊C8—32no—
148C3×C4⋊C8C2×D311yescharacteristic
149C3×C4⋊C8C22×C311yescharacteristic
150C3×#103—22no—
151C3×#103—32no—
152C3×#103C2×D312yes—
153C3×#103C22×C312yes—
154C3×#102—31no—
155C3×#102—31no—
156C3×C4×C8—32no—
157C3×C4×C8—31no—
158#832C22×C311yescharacteristic
159#816C22×C312yes—
160Dic3⋊C8C22×C312yes—
161C8×Dic3C22×C312yes—
162#809C22×C311yescharacteristic
163#807C22×C311yescharacteristic
164C4×C3⋊C8C22×C311yescharacteristic
165C23×C32—21no—
166C22×C3×D3—21no—
167C32×Q8—22no—
168C32×Q8—22no—
169C32×D4—21no—
170C32×D4—21no—
171C2×C32×C4—21no—
172C2×C32×C4—22no—
173C2×C32×C4—42no—
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2411yescharacteristic
177C2×C3×Dic3—21no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3C2×D412yes—
180C2×C3×Dic3C2×D412yes—
181C3×D12—21no—
182C3×D12—21no—
183C3×C4×D3—42no—
184C3×Dic6—22no—
185C3×Dic6—22no—
186C3×Dic6—22no—
187C32×C8—22no—
188C3×C3⋊C8—21no—
189C3×C3⋊C8#4112yes—
190#556—31no—
191#556—31no—
192#495—32no—
193#494—31no—
194#464—32no—
195#464—32no—
196#461—31no—
197#461C3×D311yescharacteristic, complemented
198C8×Q8—31no—
199C4×Q16—32no—
200C4×D8—31no—
201C2×C3×Q8—22no—
202C2×C3×Q8—31no—
203C2×C3×Q8—32no—
204C2×C3×Q8C22×D312yes—
205C2×C3×Q8C23×C312yes—
206C2×C3×D4—21no—
207C2×C3×D4—31no—
208C2×C3×D4C22×D311yescharacteristic
209C2×C3×D4C23×C311yescharacteristic
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—41no—
213C22×C3×C4—61no—
214C2×D12C23×C311yescharacteristic
215C2×C4×D3—21no—
216C2×Dic6C3×D411yescharacteristic
217C2×Dic6C23×C312yes—
218C3×Q16—64no—
219C3×Q16—122no—
220C3×SD16—42no—
221C3×SD16—42no—
222C3×SD16—44no—
223C3×SD16—122no—
224C3×D8—62no—
225C2×C3×C8—22no—
226C2×C3×C8—31no—
227C2×C3×C8—31no—
228C2×C3×C8C22×D312yes—
229C2×C3×C8C23×C312yes—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—32no—
236C3×C4⋊C4—31no—
237C3×C4⋊C4—31no—
238C3×C4⋊C4—41no—
239C3×C4⋊C4—41no—
240C3×C4⋊C4—62no—
241C3×C4⋊C4—62no—
242C3×C4⋊C4—61no—
243C3×C4⋊C4—61no—
244C3×C4⋊C4C22×D311yescharacteristic
245C3×C4⋊C4C23×C311yescharacteristic
246C3×C22⋊C4—21no—
247C3×C22⋊C4—21no—
248C3×C22⋊C4—41no—
249C3×C22⋊C4—62no—
250C3×C22⋊C4—62no—
251C3×C22⋊C4—62no—
252C3×C22⋊C4—62no—
253C3×C22⋊C4—61no—
254C3×C42—21no—
255C3×C42—32no—
256C3×C42—62no—
257C3×C42—62no—
258C3×C42C22×D311yescharacteristic
259C3×C42C23×C311yescharacteristic
260#217—22no—
261#217—22no—
262#216—24no—
263#216—42no—
264#213—22no—
265(C2×D3)⋊C4—21no—
266(C2×D3)⋊C4—22no—
267(C2×D3)⋊C4—22no—
268C4⋊Dic3—21no—
269C4⋊Dic3—21no—
270C4⋊Dic3—22no—
271C4⋊Dic3C3×D411yescharacteristic
272C4⋊Dic3C23×C311yescharacteristic
273Dic3⋊C4—22no—
274Dic3⋊C4C3×D412yes—
275C4×Dic3—22no—
276C4×Dic3—22no—
277C4×Dic3C23×C312yes—
278C2×C3⋊C8C23×C311yescharacteristic
279C2×C3⋊C8C23×C311yescharacteristic
280#204—42no—
281C22×C32—41no—
282C22×C32—41no—
283C22×C32—41no—
284C22×C32C22×D411yescharacteristic
285C2×C3×D3—41no—
286C2×C3×D3—41no—
287C2×C3×D3—41no—
288C32×C4—21no—
289C32×C4—42no—
290C32×C4—41no—
291C32×C4#13512yes—
292C32×C4C2×#4111yescharacteristic
293C32×C4H(5,𝔽2)11yescharacteristic
294C3×Dic3—22no—
295C3×Dic3—22no—
296C3×Dic3—42no—
297C3×Dic3—41no—
298C2×Q16—32no—
299C2×Q16—32no—
300C2×SD16—32no—
301C2×SD16C2×C3×D312yes—
302C2×D8—31no—
303C4⋊Q8—31no—
304C4⋊Q8C2×C3×D311yescharacteristic
305#126—62no—
306#126—62no—
307#124—32no—
308#124—32no—
309C22⋊Q8—61no—
310C22⋊Q8—61no—
311C4×Q8—31no—
312C4×Q8—32no—
313C4×Q8—32no—
314C4×D4—31no—
315C4×D4C2×C3×D311yescharacteristic
316#117—61no—
317#117—61no—
318#107—31no—
319C4⋊C8—32no—
320C4⋊C8C2×C3×D311yescharacteristic
321#103—32no—
322#103C2×C3×D312yes—
323#102—31no—
324#102—31no—
325C4×C8—32no—
326C4×C8—31no—
327C23×C3—21no—
328C23×C3—21no—
329C23×C3—41no—
330C23×C3—61no—
331C22×D3—21no—
332C3×Q8—22no—
333C3×Q8—22no—
334C3×Q8—22no—
335C3×Q8—22no—
336C3×Q8—42no—
337C3×Q8—42no—
338C3×Q8—62no—
339C3×Q8—62no—
340C3×Q8—62no—
341C3×D4—22no—
342C3×D4—21no—
343C3×D4—21no—
344C3×D4—21no—
345C3×D4—21no—
346C3×D4—41no—
347C3×D4—61no—
348C3×D4—61no—
349C2×C3×C4—21no—
350C2×C3×C4—22no—
351C2×C3×C4—21no—
352C2×C3×C4—22no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—32no—
357C2×C3×C4—32no—
358C2×C3×C4—41no—
359C2×C3×C4—42no—
360C2×C3×C4—42no—
361C2×C3×C4—42no—
362C2×C3×C4—61no—
363C2×C3×C4—62no—
364C2×C3×C4—82no—
365C2×C3×C4—122no—
366C2×C3×C4D3×D411yescharacteristic
367C2×C3×C4D3×D411yescharacteristic
368C2×C3×C4C2×C3×D411yescharacteristic
369C2×C3×C4C2×C3×D411yescharacteristic
370C2×C3×C4C23×D311yescharacteristic
371C2×C3×C4C24×C311yescharacteristic
372C2×Dic3—21no—
373C2×Dic3—22no—
374C2×Dic3C2×C3×D412yes—
375C2×Dic3C2×C3×D412yes—
376D12—21no—
377D12—21no—
378C4×D3—42no—
379Dic6—22no—
380Dic6—22no—
381Dic6—22no—
382C3×C8—22no—
383C3×C8—22no—
384C3×C8—32no—
385C3×C8—42no—
386C3×C8—61no—
387C3⋊C8—21no—
388C3⋊C8C3×#4112yes—
389C2×C32—81no—
390C2×C32#55011yescharacteristic
391C2×C32C2×#13511yescharacteristic
392C2×C32#57811yescharacteristic
393C3×D3—81no—
394C2×Q8—31no—
395C2×Q8—32no—
396C2×Q8C22×C3×D312yes—
397C2×D4—31no—
398C2×D4C22×C3×D311yescharacteristic
399C22×C4—21no—
400C22×C4—61no—
401Q16—64no—
402Q16—122no—
403SD16—42no—
404SD16—122no—
405D8—62no—
406C2×C8—31no—
407C2×C8—31no—
408C2×C8C22×C3×D312yes—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—31no—
412C4⋊C4—32no—
413C4⋊C4—31no—
414C4⋊C4—62no—
415C4⋊C4—62no—
416C4⋊C4—61no—
417C4⋊C4—61no—
418C4⋊C4C22×C3×D311yescharacteristic
419C22⋊C4—21no—
420C22⋊C4—62no—
421C22⋊C4—62no—
422C22⋊C4—62no—
423C22⋊C4—62no—
424C22⋊C4—61no—
425C42—32no—
426C42—62no—
427C42—62no—
428C42C22×C3×D311yescharacteristic
429C22×C3—21no—
430C22×C3—42no—
431C22×C3—41no—
432C22×C3—41no—
433C22×C3—41no—
434C22×C3—41no—
435C22×C3—41no—
436C22×C3—41no—
437C22×C3—81no—
438C22×C3—81no—
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—21no—
448C3×C4—21no—
449C3×C4—22no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—41no—
453C3×C4—41no—
454C3×C4—41no—
455C3×C4—42no—
456C3×C4—42no—
457C3×C4—62no—
458C3×C4—62no—
459C3×C4—81no—
460C3×C4—82no—
461C3×C4—121no—
462C3×C4—122no—
463C3×C4#91612yes—
464C3×C4C3×#13512yes—
465C3×C4#100411yescharacteristic
466C3×C4D3×#4111yescharacteristic
467C3×C4C2×C3×#4111yescharacteristic
468C3×C4C3×H(5,𝔽2)11yescharacteristic
469Dic3—22no—
470Dic3—22no—
471Dic3—41no—
472Dic3—42no—
473C32#339311yescharacteristic, complemented, Sylow
474C23—21no—
475C23—61no—
476Q8—22no—
477Q8—22no—
478Q8—62no—
479Q8—62no—
480Q8—62no—
481D4—21no—
482D4—21no—
483D4—61no—
484D4—61no—
485C2×C4—21no—
486C2×C4—22no—
487C2×C4—32no—
488C2×C4—32no—
489C2×C4—42no—
490C2×C4—61no—
491C2×C4—62no—
492C2×C4—122no—
493C2×C4C3×D3×D411yescharacteristic
494C2×C4C3×D3×D411yescharacteristic
495C2×C4C23×C3×D311yescharacteristic
496C8—22no—
497C8—32no—
498C8—61no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—82no—
503C2×C3—81no—
504C2×C3—81no—
505C2×C3—241no—
506C2×C3#559911yescharacteristic
507C2×C3C2×#91611yescharacteristic
508C2×C3#577911yescharacteristic
509C2×C3C3×#55011yescharacteristic
510C2×C3C2×C3×#13511yescharacteristic
511C2×C3C3×#57811yescharacteristic
512D3—81no—
513C22—41no—
514C22—41no—
515C22—41no—
516C22—121no—
517C22—121no—
518C22—121no—
519C22C2×C3×D3×D411yescharacteristic
520C4—21no—
521C4—41no—
522C4—42no—
523C4—62no—
524C4—62no—
525C4—121no—
526C4—122no—
527C4C3×#91612yes—
528C4C3×#100411yescharacteristic
529C4C3×D3×#4111yescharacteristic
530C3—21no—
531C3#8042111yescharacteristic, direct product factor
532C3C3×#339311yescharacteristic, complemented
533C2—81no—
534C2—241no—
535C2C3×#559911yescharacteristic
536C2C2×C3×#91611yescharacteristic
537C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#461C2
socleC22×C32C22×D4
prime radicalC2×C3×#213C22
hypercenterC3×#461D3
hypocenterC3C3×#3393
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#461

Complements

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

NH ≅ G/Ntype
1. C3×#5732C2semidirect
2. C3×#5542C2semidirect
3. C32×#461C2semidirect
5. C3×#5166C2semidirect
6. C3×#5092C2semidirect
8. C3×#4841C2semidirect
9. C3×#4830C2semidirect
10. C3×#4798C2semidirect
11. C3×#4790C2semidirect
13. #80421C3direct (N × H)
45. #5732C2×C3semidirect
46. #5542C2×C3semidirect
53. C3×#461D3semidirect
54. C3×#461C2×C3semidirect
59. #5166C2×C3semidirect
60. #5092C2×C3semidirect
62. #4841C2×C3semidirect
63. #4830C2×C3semidirect
64. #4798C2×C3semidirect
65. #4790C2×C3semidirect
197. #461C3×D3semidirect
473. C32#3393semidirect
531. C3#80421direct (N × H)
532. C3C3×#3393semidirect

Maximal subgroups

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

subgroupindex
C3×#57322
C3×#55422
C32×#4612
C3×#51682
C3×#51662
C3×#50922
C3×C4×#2132
C3×#48412
C3×#48302
C3×#47982
C3×#47902
C3×#33933
#804213