Finite Group Databasebeta

← C3×#80993 #11895821

Subgroups — C3×#80993 #11895821

Order 1152.

798 conjugacy classes of subgroups.

The subgroup lattice has 533 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5727C211yesmaximal, characteristic, complemented
2C3×#5542C211yesmaximal, characteristic, complemented
3C32×#474C211yesmaximal, characteristic, complemented
4C3×#5093C211yesmaximal, characteristic, complemented
5C3×C4×#213C211yesmaximal, characteristic
6C3×#4889C212yesmaximal, complemented
7C3×#4875C212yesmaximal, complemented
8C3×#4841C211yesmaximal, characteristic, complemented
9C3×#4831C211yesmaximal, characteristic, complemented
10C3×#4787C212yesmaximal
11C3×#4765C212yesmaximal, complemented
12C3×#3367—31nomaximal
13#80993C311yesmaximal, characteristic, direct product factor
14C2×C3×D3×Q8—21no—
15C32×C4⋊Q8C2211yescharacteristic
16C32×C4×D4C2211yescharacteristic
17C3×#946—21no—
18C3×#936C2212yes—
19C2×C3×#213C2211yescharacteristic
20C3×#926—21no—
21C3×#924—21no—
22C2×C3×#204C2212yes—
23C3×#896—22no—
24C3×#893C2212yes—
25C3×#888C2212yes—
26C3×#887C2212yes—
27C3×#879—22no—
28C3×C4×D12C2211yescharacteristic
29C3×#869C2211yescharacteristic
30C3×C4×Dic6C2211yescharacteristic
31C32×#107C2212yes—
32C32×C4⋊C8C2211yescharacteristic
33C32×#102C2212yes—
34C3×#832C2211yescharacteristic
35C3×#816C2212yes—
36C3×#815C2212yes—
37C3×Dic3⋊C8C2212yes—
38C3×#810C2212yes—
39C3×#810C2212yes—
40C3×#809C2211yescharacteristic
41C3×#807C2211yescharacteristic
42C3×C4×C3⋊C8C2211yescharacteristic
43C3×#556—31no—
44C3×D4×Q8—31no—
45#5727C2×C311yescharacteristic, complemented
46#5542C2×C311yescharacteristic, complemented
47C3×#489—32no—
48C3×#487—31no—
49C3×#477—32no—
50C3×#474—21no—
51C3×#474D311yescharacteristic, complemented
52C3×#474C2×C311yescharacteristic, complemented
53C3×#463—32no—
54C3×#461—31no—
55C3×#446—31no—
56C3×#440—32no—
57C3×C4×D8—31no—
58#5093C2×C311yescharacteristic, complemented
59C4×#213C2×C311yescharacteristic
60#4889C2×C312yescomplemented
61#4875C2×C312yescomplemented
62#4841C2×C311yescharacteristic, complemented
63#4831C2×C311yescharacteristic, complemented
64#4787C2×C312yes—
65#4765C2×C312yescomplemented
66C2×C32×Q8—21no—
67C2×C32×D4C2311yescharacteristic
68C22×C32×C4—21no—
69C3×D3×Q8—44no—
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×C4×D3—22no—
73C2×C3×Dic6—22no—
74C2×C3×Dic6D411yescharacteristic
75C2×C3×Dic6C2312yes—
76C2×C32×C8C2312yes—
77C32×C4⋊C4—21no—
78C32×C4⋊C4C2311yescharacteristic
79C32×C4⋊C4C2312yes—
80C32×C22⋊C4—21no—
81C32×C42C2311yescharacteristic
82C3×#217—22no—
83C3×#217—22no—
84C3×#213—22no—
85C3×(C2×D3)⋊C4—21no—
86C3×(C2×D3)⋊C4—22no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3D411yescharacteristic
90C3×C4⋊Dic3C2311yescharacteristic
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4—22no—
93C3×Dic3⋊C4D412yes—
94C3×C4×Dic3—22no—
95C3×C4×Dic3C2312yes—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98C3×#204—24no—
99#3367—31noSylow
100C22×C3×Q8—61no—
101C2×D3×Q8—21no—
102C2×C3×SD16—32no—
103C2×C3×D8—31no—
104C3×C4⋊Q8—21no—
105C3×C4⋊Q8—32no—
106C3×C4⋊Q8—31no—
107C3×C4⋊Q8C2×D311yescharacteristic
108C3×C4⋊Q8C22×C311yescharacteristic
109C3×#126—62no—
110C3×#124—32no—
111C3×C22⋊Q8—62no—
112C3×C22⋊Q8—61no—
113C3×C22⋊Q8—61no—
114C3×C4×Q8—31no—
115C3×C4×Q8—32no—
116C3×C4×D4—21no—
117C3×C4×D4—32no—
118C3×C4×D4—31no—
119C3×C4×D4C2×D311yescharacteristic
120C3×C4×D4C22×C311yescharacteristic
121C3×#117—61no—
122#946—21no—
123#936C22×C312yes—
124C2×#213C22×C311yescharacteristic
125#926—21no—
126#924—21no—
127C2×#204C22×C312yes—
128#896—22no—
129#893C22×C312yes—
130#888C22×C312yes—
131#887C22×C312yes—
132#879—22no—
133C4×D12C22×C311yescharacteristic
134#869C22×C311yescharacteristic
135C4×Dic6C22×C311yescharacteristic
136C3×#107—22no—
137C3×#107—31no—
138C3×#107C2×D312yes—
139C3×#107C22×C312yes—
140C3×C4⋊C8—21no—
141C3×C4⋊C8—32no—
142C3×C4⋊C8C2×D311yescharacteristic
143C3×C4⋊C8C22×C311yescharacteristic
144C3×#103—32no—
145C3×#103—32no—
146C3×#103—32no—
147C3×#102—22no—
148C3×#102—31no—
149C3×#102—31no—
150C3×#102C2×D312yes—
151C3×#102C22×C312yes—
152C3×#97—32no—
153C3×C4×C8—31no—
154#832C22×C311yescharacteristic
155#816C22×C312yes—
156#815C22×C312yes—
157Dic3⋊C8C22×C312yes—
158#810C22×C312yes—
159#810C22×C312yes—
160#809C22×C311yescharacteristic
161#807C22×C311yescharacteristic
162C4×C3⋊C8C22×C311yescharacteristic
163C23×C32—21no—
164C22×C3×D3—21no—
165C32×Q8—42no—
166C32×D4—21no—
167C32×D4—21no—
168C2×C32×C4—21no—
169C2×C32×C4—22no—
170C2×C32×C4—42no—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2411yescharacteristic
174C2×C3×Dic3—22no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3C2×D412yes—
177C2×C3×Dic3C2×D412yes—
178C3×D12—21no—
179C3×D12#4112yes—
180C3×C4×D3—44no—
181C3×C4×D3—42no—
182C3×Dic6—22no—
183C3×Dic6—22no—
184C3×Dic6—22no—
185C3×Dic6—44no—
186C32×C8—22no—
187C3×C3⋊C8—21no—
188C3×C3⋊C8—21no—
189#556—31no—
190D4×Q8—31no—
191#489—32no—
192#487—31no—
193#477—32no—
194#474C3×D311yescharacteristic, complemented
195#463—32no—
196#461—31no—
197#446—31no—
198#440—32no—
199C4×D8—31no—
200C2×C3×Q8—21no—
201C2×C3×Q8—21no—
202C2×C3×Q8—31no—
203C2×C3×Q8—32no—
204C2×C3×Q8—41no—
205C2×C3×Q8—62no—
206C2×C3×Q8—124no—
207C2×C3×D4—21no—
208C2×C3×D4—31no—
209C2×C3×D4C22×D311yescharacteristic
210C2×C3×D4C23×C311yescharacteristic
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—41no—
214C22×C3×C4—62no—
215C22×C3×C4—61no—
216D3×Q8—44no—
217C2×D12C23×C311yescharacteristic
218C2×C4×D3—21no—
219C2×C4×D3—22no—
220C2×Dic6—22no—
221C2×Dic6C3×D411yescharacteristic
222C2×Dic6C23×C312yes—
223C3×SD16—64no—
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—22no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—32no—
235C3×C4⋊C4—31no—
236C3×C4⋊C4—31no—
237C3×C4⋊C4—41no—
238C3×C4⋊C4—62no—
239C3×C4⋊C4—62no—
240C3×C4⋊C4—61no—
241C3×C4⋊C4—61no—
242C3×C4⋊C4C22×D311yescharacteristic
243C3×C4⋊C4C22×D312yes—
244C3×C4⋊C4C23×C311yescharacteristic
245C3×C4⋊C4C23×C312yes—
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—61no—
253C3×C42—21no—
254C3×C42—32no—
255C3×C42—62no—
256C3×C42C22×D311yescharacteristic
257C3×C42C23×C311yescharacteristic
258#217—22no—
259#217—22no—
260#213—22no—
261(C2×D3)⋊C4—21no—
262(C2×D3)⋊C4—22no—
263C4⋊Dic3—21no—
264C4⋊Dic3—21no—
265C4⋊Dic3C3×D411yescharacteristic
266C4⋊Dic3C23×C311yescharacteristic
267Dic3⋊C4—22no—
268Dic3⋊C4—22no—
269Dic3⋊C4C3×D412yes—
270C4×Dic3—22no—
271C4×Dic3C23×C312yes—
272C2×C3⋊C8C23×C311yescharacteristic
273C2×C3⋊C8C23×C311yescharacteristic
274#204—24no—
275C22×C32—41no—
276C22×C32—41no—
277C22×C32—41no—
278C22×C32C22×D411yescharacteristic
279C2×C3×D3—22no—
280C2×C3×D3—41no—
281C2×C3×D3—41no—
282C32×C4—21no—
283C32×C4—42no—
284C32×C4—41no—
285C32×C4AGL(1,ℤ/8)12yes—
286C32×C4C2×#4111yescharacteristic
287C32×C42−1+411yescharacteristic
288C3×Dic3—22no—
289C3×Dic3—22no—
290C3×Dic3—42no—
291C3×Dic3—41no—
292C22×Q8—61no—
293C2×SD16—32no—
294C2×D8—31no—
295C4⋊Q8—32no—
296C4⋊Q8—31no—
297C4⋊Q8C2×C3×D311yescharacteristic
298#126—62no—
299#124—32no—
300C22⋊Q8—62no—
301C22⋊Q8—61no—
302C22⋊Q8—61no—
303C4×Q8—31no—
304C4×Q8—32no—
305C4×D4—32no—
306C4×D4—31no—
307C4×D4C2×C3×D311yescharacteristic
308#117—61no—
309#107—31no—
310#107C2×C3×D312yes—
311C4⋊C8—32no—
312C4⋊C8C2×C3×D311yescharacteristic
313#103—32no—
314#103—32no—
315#103—32no—
316#102—31no—
317#102—31no—
318#102C2×C3×D312yes—
319#97—32no—
320C4×C8—31no—
321C23×C3—21no—
322C23×C3—21no—
323C23×C3—41no—
324C23×C3—61no—
325C22×D3—21no—
326C3×Q8—42no—
327C3×Q8—42no—
328C3×Q8—62no—
329C3×Q8—62no—
330C3×Q8—62no—
331C3×Q8—82no—
332C3×Q8—124no—
333C3×D4—22no—
334C3×D4—21no—
335C3×D4—21no—
336C3×D4—21no—
337C3×D4—21no—
338C3×D4—32no—
339C3×D4—41no—
340C3×D4—61no—
341C2×C3×C4—21no—
342C2×C3×C4—22no—
343C2×C3×C4—21no—
344C2×C3×C4—22no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—32no—
349C2×C3×C4—32no—
350C2×C3×C4—41no—
351C2×C3×C4—42no—
352C2×C3×C4—42no—
353C2×C3×C4—42no—
354C2×C3×C4—62no—
355C2×C3×C4—61no—
356C2×C3×C4—82no—
357C2×C3×C4—124no—
358C2×C3×C4—122no—
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4D3×D411yescharacteristic
361C2×C3×C4C2×C3×D411yescharacteristic
362C2×C3×C4C2×C3×D411yescharacteristic
363C2×C3×C4C23×D311yescharacteristic
364C2×C3×C4C24×C311yescharacteristic
365C2×Dic3—22no—
366C2×Dic3—21no—
367C2×Dic3C2×C3×D412yes—
368C2×Dic3C2×C3×D412yes—
369D12—21no—
370D12C3×#4112yes—
371C4×D3—44no—
372C4×D3—42no—
373Dic6—22no—
374Dic6—22no—
375Dic6—22no—
376Dic6—44no—
377C3×C8—22no—
378C3×C8—22no—
379C3×C8—42no—
380C3×C8—61no—
381C3×C8—61no—
382C3⋊C8—21no—
383C3⋊C8—21no—
384C2×C32—81no—
385C2×C32#54811yescharacteristic
386C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
387C2×C32#57811yescharacteristic
388C3×D3—42no—
389C2×Q8—21no—
390C2×Q8—31no—
391C2×Q8—32no—
392C2×Q8—62no—
393C2×Q8—124no—
394C2×D4—31no—
395C2×D4C22×C3×D311yescharacteristic
396C22×C4—21no—
397C22×C4—62no—
398C22×C4—61no—
399SD16—64no—
400D8—62no—
401C2×C8—31no—
402C2×C8—31no—
403C2×C8C22×C3×D312yes—
404C4⋊C4—21no—
405C4⋊C4—31no—
406C4⋊C4—32no—
407C4⋊C4—31no—
408C4⋊C4—62no—
409C4⋊C4—62no—
410C4⋊C4—61no—
411C4⋊C4—61no—
412C4⋊C4C22×C3×D311yescharacteristic
413C4⋊C4C22×C3×D312yes—
414C22⋊C4—21no—
415C22⋊C4—62no—
416C22⋊C4—62no—
417C22⋊C4—62no—
418C22⋊C4—61no—
419C42—32no—
420C42—62no—
421C42C22×C3×D311yescharacteristic
422C22×C3—21no—
423C22×C3—42no—
424C22×C3—41no—
425C22×C3—41no—
426C22×C3—41no—
427C22×C3—41no—
428C22×C3—41no—
429C22×C3—41no—
430C22×C3—62no—
431C22×C3—81no—
432C22×C3—81no—
433C22×C3—121no—
434C22×C3—121no—
435C22×C3C2×D3×D411yescharacteristic
436C22×C3C22×C3×D411yescharacteristic
437C2×D3—22no—
438C2×D3—41no—
439C2×D3—41no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—22no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—41no—
446C3×C4—42no—
447C3×C4—41no—
448C3×C4—41no—
449C3×C4—42no—
450C3×C4—62no—
451C3×C4—62no—
452C3×C4—81no—
453C3×C4—82no—
454C3×C4—122no—
455C3×C4—121no—
456C3×C4#91112yes—
457C3×C4C3×AGL(1,ℤ/8)12yes—
458C3×C4#100711yescharacteristic
459C3×C4D3×#4111yescharacteristic
460C3×C4C2×C3×#4111yescharacteristic
461C3×C4C3×2−1+411yescharacteristic
462Dic3—22no—
463Dic3—22no—
464Dic3—41no—
465Dic3—42no—
466C32#336711yescharacteristic, complemented, Sylow
467C23—21no—
468C23—61no—
469Q8—42no—
470Q8—62no—
471Q8—62no—
472Q8—62no—
473Q8—124no—
474D4—21no—
475D4—21no—
476D4—32no—
477D4—61no—
478C2×C4—21no—
479C2×C4—22no—
480C2×C4—32no—
481C2×C4—32no—
482C2×C4—42no—
483C2×C4—62no—
484C2×C4—61no—
485C2×C4—124no—
486C2×C4—122no—
487C2×C4C3×D3×D411yescharacteristic
488C2×C4C3×D3×D411yescharacteristic
489C2×C4C23×C3×D311yescharacteristic
490C8—22no—
491C8—61no—
492C8—61no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—82no—
497C2×C3—81no—
498C2×C3—81no—
499C2×C3—122no—
500C2×C3#563311yescharacteristic
501C2×C3C2×#91111yescharacteristic
502C2×C3#577911yescharacteristic
503C2×C3C3×#54811yescharacteristic
504C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
505C2×C3C3×#57811yescharacteristic
506D3—42no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—62no—
511C22—121no—
512C22—121no—
513C22C2×C3×D3×D411yescharacteristic
514C4—21no—
515C4—41no—
516C4—42no—
517C4—62no—
518C4—62no—
519C4—121no—
520C4—122no—
521C4C3×#91112yes—
522C4C3×#100711yescharacteristic
523C4C3×D3×#4111yescharacteristic
524C3—21no—
525C3#8099311yescharacteristic, direct product factor
526C3C3×#336711yescharacteristic, complemented
527C2—81no—
528C2—122no—
529C2C3×#563311yescharacteristic
530C2C2×C3×#91111yescharacteristic
531C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#474C2
socleC22×C32C22×D4
prime radicalC2×C3×#213C22
hypercenterC3×#474D3
hypocenterC3C3×#3367
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#474

Complements

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

NH ≅ G/Ntype
1. C3×#5727C2semidirect
2. C3×#5542C2semidirect
3. C32×#474C2semidirect
4. C3×#5093C2semidirect
6. C3×#4889C2semidirect
7. C3×#4875C2semidirect
8. C3×#4841C2semidirect
9. C3×#4831C2semidirect
11. C3×#4765C2semidirect
13. #80993C3direct (N × H)
45. #5727C2×C3semidirect
46. #5542C2×C3semidirect
51. C3×#474D3semidirect
52. C3×#474C2×C3semidirect
58. #5093C2×C3semidirect
60. #4889C2×C3semidirect
61. #4875C2×C3semidirect
62. #4841C2×C3semidirect
63. #4831C2×C3semidirect
65. #4765C2×C3semidirect
194. #474C3×D3semidirect
466. C32#3367semidirect
525. C3#80993direct (N × H)
526. C3C3×#3367semidirect

Maximal subgroups

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

subgroupindex
C3×#57272
C3×#55422
C32×#4742
C3×#50932
C3×C4×#2132
C3×#48892
C3×#48752
C3×#48412
C3×#48312
C3×#47872
C3×#47652
C3×#33673
#809933