Finite Group Databasebeta

← C3×#81598 #11873479

Subgroups — C3×#81598 #11873479

Order 1152.

849 conjugacy classes of subgroups.

The subgroup lattice has 479 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5728C211yesmaximal, characteristic, complemented
2C3×#5725C211yesmaximal, characteristic
3C32×#487C211yesmaximal, characteristic, complemented
4C3×#5088C211yesmaximal, characteristic, complemented
5C3×#5079C211yesmaximal, characteristic, complemented
6C3×#4804C214yesmaximal, complemented
7C3×#4800C214yesmaximal, complemented
8C3×#4694C211yesmaximal, characteristic, complemented
9C3×C4×D3×C8C211yesmaximal, characteristic, complemented
10C3×#3131—31nomaximal
11#81598C311yesmaximal, characteristic, direct product factor
12C2×C3×#239C2212yes—
13C32×C4⋊Q8C2211yescharacteristic
14C32×C4⋊Q8C2211yescharacteristic
15C3×#947C2212yes—
16C3×#946—21no—
17C3×Q8×Dic3—21no—
18C2×C3×D3×C8C2212yes—
19C3×#897—21no—
20C3×#895—21no—
21C3×#895—21no—
22C3×#893—21no—
23C3×#893—21no—
24C3×#892C2212yes—
25C3×#890C2212yes—
26C3×#887—21no—
27C3×#874C2211yescharacteristic
28C3×C42×D3C2211yescharacteristic
29C3×#869C2211yescharacteristic
30C32×#103C2214yes—
31C32×C4×C8C2211yescharacteristic
32C3×#835C2214yes—
33C3×#821C2214yes—
34C3×C8×Dic3C2212yes—
35C3×#809C2214yes—
36C3×C4×C3⋊C8C2211yescharacteristic
37C3×#533—31no—
38C3×#532—31no—
39#5728C2×C311yescharacteristic, complemented
40#5725C2×C311yescharacteristic
41C3×#488—34no—
42C3×#487—21no—
43C3×#487—31no—
44C3×#487D311yescharacteristic, complemented
45C3×#487C2×C311yescharacteristic, complemented
46C3×#486—31no—
47C3×#486—31no—
48C3×#416—34no—
49C2×C3×C4×C8—31no—
50#5088C2×C311yescharacteristic, complemented
51#5079C2×C311yescharacteristic, complemented
52#4804C2×C314yescomplemented
53#4800C2×C314yescomplemented
54#4694C2×C311yescharacteristic, complemented
55C4×D3×C8C2×C311yescharacteristic, complemented
56C2×C32×Q8—21no—
57C2×C32×Q8C2312yes—
58C3×#239—28no—
59C2×C3×D12—22no—
60C2×C3×D12—21no—
61C2×C3×D12—21no—
62C2×C3×D12C2312yes—
63C2×C3×C4×D3—22no—
64C2×C3×C4×D3D411yescharacteristic
65C2×C3×C4×D3D411yescharacteristic
66C2×C3×C4×D3C2311yescharacteristic
67C2×C3×Dic6—21no—
68C2×C32×C8C2312yes—
69C32×C4⋊C4—21no—
70C32×C4⋊C4—21no—
71C32×C4⋊C4—21no—
72C32×C4⋊C4C2312yes—
73C32×C42C2311yescharacteristic
74C3×(C2×D3)⋊C4—22no—
75C3×(C2×D3)⋊C4—22no—
76C3×(C2×D3)⋊C4—22no—
77C3×C4⋊Dic3—21no—
78C3×C4⋊Dic3—22no—
79C3×C4⋊Dic3C2312yes—
80C3×Dic3⋊C4—22no—
81C3×C4×Dic3—22no—
82C3×C4×Dic3D411yescharacteristic
83C3×C4×Dic3D411yescharacteristic
84C3×C4×Dic3C2311yescharacteristic
85C2×C3×C3⋊C8C2312yes—
86C3×D3×C8—24no—
87#3131—31noSylow
88C2×C3×#41—32no—
89C2×#239C22×C312yes—
90C22×C3×C8—32no—
91C3×C4⋊Q8—21no—
92C3×C4⋊Q8—21no—
93C3×C4⋊Q8—31no—
94C3×C4⋊Q8C2×D311yescharacteristic
95C3×C4⋊Q8C2×D311yescharacteristic
96C3×C4⋊Q8C22×C311yescharacteristic
97C3×C4⋊Q8C22×C311yescharacteristic
98C3×#127—31no—
99C3×#125—32no—
100C3×#124—32no—
101C3×C22⋊Q8—61no—
102C3×C22⋊Q8—61no—
103C3×#121—61no—
104C3×#121—61no—
105C3×C4×Q8—61no—
106C3×C4×Q8—61no—
107C3×C4×D4—61no—
108C3×C4×D4—61no—
109C3×#117—32no—
110C2×C3×C42—31no—
111#947C22×C312yes—
112#946—21no—
113Q8×Dic3—21no—
114C2×D3×C8C22×C312yes—
115#897—21no—
116#895—21no—
117#895—21no—
118#893—21no—
119#893—21no—
120#892C22×C312yes—
121#890C22×C312yes—
122#887—21no—
123#874C22×C311yescharacteristic
124C42×D3C22×C311yescharacteristic
125#869C22×C311yescharacteristic
126C3×#103—24no—
127C3×#103—34no—
128C3×#103C2×D314yes—
129C3×#103C22×C314yes—
130C3×#102—34no—
131C3×#102—34no—
132C3×C4×C8—21no—
133C3×C4×C8—32no—
134C3×C4×C8—31no—
135C3×C4×C8C2×D311yescharacteristic
136C3×C4×C8C22×C311yescharacteristic
137#835C22×C314yes—
138#821C22×C314yes—
139C8×Dic3C22×C312yes—
140#809C22×C314yes—
141C4×C3⋊C8C22×C311yescharacteristic
142C22×C3×D3—22no—
143C22×C3×D3C2×D411yescharacteristic
144C32×Q8—24no—
145C32×Q8—42no—
146C2×C32×C4—22no—
147C2×C32×C4—22no—
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2411yescharacteristic
151C2×C3×Dic3—22no—
152C2×C3×Dic3C2×D411yescharacteristic
153C2×C3×Dic3C2×D411yescharacteristic
154C2×C3×Dic3C2×D411yescharacteristic
155C3×D12—24no—
156C3×D12—44no—
157C3×D12—42no—
158C3×D12—42no—
159C3×C4×D3—22no—
160C3×C4×D3—22no—
161C3×C4×D3—44no—
162C3×C4×D3#4114yes—
163C3×Dic6—42no—
164C32×C8—22no—
165C3×C3⋊C8—22no—
166#533—31no—
167#532—31no—
168#488—34no—
169#487—31no—
170#487C3×D311yescharacteristic, complemented
171#486—31no—
172#486—31no—
173#416—34no—
174C2×C4×C8—31no—
175C3×#41—68no—
176C2×C3×Q8—21no—
177C2×C3×Q8—21no—
178C2×C3×Q8—22no—
179C2×C3×Q8—41no—
180C2×C3×Q8—61no—
181C2×C3×Q8C22×D312yes—
182C2×C3×Q8C23×C312yes—
183C2×C3×D4—32no—
184C2×C3×D4—62no—
185C2×C3×D4—61no—
186C2×C3×D4—61no—
187C22×C3×C4—31no—
188C22×C3×C4—31no—
189C22×C3×C4—31no—
190C22×C3×C4—62no—
191#239—28no—
192C2×D12—22no—
193C2×D12—21no—
194C2×D12—21no—
195C2×D12C23×C312yes—
196C2×C4×D3—22no—
197C2×C4×D3C3×D411yescharacteristic
198C2×C4×D3C3×D411yescharacteristic
199C2×C4×D3C23×C311yescharacteristic
200C2×Dic6—21no—
201C2×C3×C8—22no—
202C2×C3×C8—32no—
203C2×C3×C8—64no—
204C2×C3×C8C22×D312yes—
205C2×C3×C8C23×C312yes—
206C3×C4⋊C4—21no—
207C3×C4⋊C4—21no—
208C3×C4⋊C4—21no—
209C3×C4⋊C4—21no—
210C3×C4⋊C4—21no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—22no—
213C3×C4⋊C4—32no—
214C3×C4⋊C4—41no—
215C3×C4⋊C4—41no—
216C3×C4⋊C4—41no—
217C3×C4⋊C4—62no—
218C3×C4⋊C4—62no—
219C3×C4⋊C4—61no—
220C3×C4⋊C4C22×D312yes—
221C3×C4⋊C4C23×C312yes—
222C3×C22⋊C4—62no—
223C3×C22⋊C4—62no—
224C3×C22⋊C4—62no—
225C3×C42—21no—
226C3×C42—31no—
227C3×C42—31no—
228C3×C42—31no—
229C3×C42—62no—
230C3×C42C22×D311yescharacteristic
231C3×C42C23×C311yescharacteristic
232(C2×D3)⋊C4—22no—
233(C2×D3)⋊C4—22no—
234(C2×D3)⋊C4—22no—
235C4⋊Dic3—21no—
236C4⋊Dic3—22no—
237C4⋊Dic3C23×C312yes—
238Dic3⋊C4—22no—
239C4×Dic3—22no—
240C4×Dic3C3×D411yescharacteristic
241C4×Dic3C3×D411yescharacteristic
242C4×Dic3C23×C311yescharacteristic
243C2×C3⋊C8C23×C312yes—
244D3×C8—24no—
245C22×C32C22×D411yescharacteristic
246C2×C3×D3—21no—
247C2×C3×D3—21no—
248C2×C3×D3—42no—
249C2×C3×D3—42no—
250C2×C3×D3—42no—
251C2×C3×D3#12412yes—
252C32×C4—42no—
253C32×C4—42no—
254C32×C4#13512yes—
255C32×C4#13512yes—
256C32×C4C2×#4112yes—
257C3×Dic3—21no—
258C3×Dic3—21no—
259C3×Dic3—42no—
260C3×Dic3#12412yes—
261C2×#41—32no—
262C22×C8—32no—
263C4⋊Q8—31no—
264C4⋊Q8C2×C3×D311yescharacteristic
265C4⋊Q8C2×C3×D311yescharacteristic
266#127—31no—
267#125—32no—
268#124—32no—
269C22⋊Q8—61no—
270C22⋊Q8—61no—
271#121—61no—
272#121—61no—
273C4×Q8—61no—
274C4×Q8—61no—
275C4×D4—61no—
276C4×D4—61no—
277#117—32no—
278C2×C42—31no—
279#103—34no—
280#103C2×C3×D314yes—
281#102—34no—
282#102—34no—
283C4×C8—32no—
284C4×C8—31no—
285C4×C8C2×C3×D311yescharacteristic
286C23×C3—31no—
287C23×C3—62no—
288C22×D3—22no—
289C22×D3C2×C3×D411yescharacteristic
290C3×Q8—24no—
291C3×Q8—24no—
292C3×Q8—44no—
293C3×Q8—42no—
294C3×Q8—42no—
295C3×Q8—82no—
296C3×Q8—122no—
297C3×D4—64no—
298C3×D4—124no—
299C3×D4—122no—
300C3×D4—122no—
301C2×C3×C4—22no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—31no—
309C2×C3×C4—34no—
310C2×C3×C4—31no—
311C2×C3×C4—31no—
312C2×C3×C4—42no—
313C2×C3×C4—42no—
314C2×C3×C4—62no—
315C2×C3×C4—62no—
316C2×C3×C4—62no—
317C2×C3×C4—124no—
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4D3×D411yescharacteristic
320C2×C3×C4C2×C3×D411yescharacteristic
321C2×C3×C4C2×C3×D411yescharacteristic
322C2×C3×C4C23×D311yescharacteristic
323C2×C3×C4C24×C311yescharacteristic
324C2×Dic3—22no—
325C2×Dic3C2×C3×D411yescharacteristic
326C2×Dic3C2×C3×D411yescharacteristic
327C2×Dic3C2×C3×D411yescharacteristic
328D12—24no—
329D12—44no—
330D12—42no—
331D12—42no—
332C4×D3—22no—
333C4×D3—22no—
334C4×D3—44no—
335C4×D3C3×#4114yes—
336Dic6—42no—
337C3×C8—22no—
338C3×C8—22no—
339C3×C8—42no—
340C3×C8—62no—
341C3⋊C8—22no—
342C2×C32C2×#12411yescharacteristic
343C2×C32C2×#13511yescharacteristic
344C2×C32C2×#13511yescharacteristic
345C3×D3—22no—
346C3×D3—82no—
347#41—68no—
348C2×Q8—21no—
349C2×Q8—61no—
350C2×Q8C22×C3×D312yes—
351C2×D4—32no—
352C2×D4—62no—
353C2×D4—61no—
354C2×D4—61no—
355C22×C4—31no—
356C22×C4—31no—
357C22×C4—31no—
358C22×C4—62no—
359C2×C8—32no—
360C2×C8—64no—
361C2×C8C22×C3×D312yes—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—32no—
366C4⋊C4—62no—
367C4⋊C4—62no—
368C4⋊C4—61no—
369C4⋊C4C22×C3×D312yes—
370C22⋊C4—62no—
371C22⋊C4—62no—
372C22⋊C4—62no—
373C42—31no—
374C42—31no—
375C42—31no—
376C42—62no—
377C42C22×C3×D311yescharacteristic
378C22×C3—21no—
379C22×C3—32no—
380C22×C3—61no—
381C22×C3—61no—
382C22×C3—122no—
383C22×C3—122no—
384C22×C3—122no—
385C22×C3C2×D3×D411yescharacteristic
386C22×C3C22×C3×D411yescharacteristic
387C2×D3—21no—
388C2×D3—21no—
389C2×D3—42no—
390C2×D3—42no—
391C2×D3—42no—
392C2×D3C3×#12412yes—
393C3×C4—22no—
394C3×C4—22no—
395C3×C4—22no—
396C3×C4—32no—
397C3×C4—42no—
398C3×C4—42no—
399C3×C4—42no—
400C3×C4—42no—
401C3×C4—61no—
402C3×C4—61no—
403C3×C4—82no—
404C3×C4—82no—
405C3×C4—122no—
406C3×C4#91612yes—
407C3×C4#91912yes—
408C3×C4C3×#13512yes—
409C3×C4C3×#13512yes—
410C3×C4D3×#4112yes—
411C3×C4C2×C3×#4112yes—
412Dic3—21no—
413Dic3—21no—
414Dic3—42no—
415Dic3C3×#12412yes—
416C32#313111yescharacteristic, complemented, Sylow
417C23—31no—
418C23—62no—
419Q8—24no—
420Q8—42no—
421Q8—122no—
422D4—64no—
423D4—124no—
424D4—122no—
425D4—122no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—31no—
429C2×C4—34no—
430C2×C4—31no—
431C2×C4—31no—
432C2×C4—62no—
433C2×C4—62no—
434C2×C4—62no—
435C2×C4—124no—
436C2×C4C3×D3×D411yescharacteristic
437C2×C4C3×D3×D411yescharacteristic
438C2×C4C23×C3×D311yescharacteristic
439C8—22no—
440C8—62no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—62no—
445C2×C3—242no—
446C2×C3D3×#12411yescharacteristic
447C2×C3C2×#91611yescharacteristic
448C2×C3C2×#91911yescharacteristic
449C2×C3C2×C3×#12411yescharacteristic
450C2×C3C2×C3×#13511yescharacteristic
451C2×C3C2×C3×#13511yescharacteristic
452D3—22no—
453D3—82no—
454C22—32no—
455C22—61no—
456C22—61no—
457C22—122no—
458C22—122no—
459C22—122no—
460C22C2×C3×D3×D411yescharacteristic
461C4—32no—
462C4—42no—
463C4—42no—
464C4—61no—
465C4—61no—
466C4—122no—
467C4C3×#91612yes—
468C4C3×#91912yes—
469C4C3×D3×#4112yes—
470C3—21no—
471C3#8159811yescharacteristic, direct product factor
472C3C3×#313111yescharacteristic, complemented
473C2—62no—
474C2—242no—
475C2C3×D3×#12411yescharacteristic
476C2C2×C3×#91611yescharacteristic
477C2C2×C3×#91911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#487C2
socleC22×C32C22×D4
prime radicalC3×#5725C2
hypercenterC3×#487D3
hypocenterC3C3×#3131
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#487

Complements

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

NH ≅ G/Ntype
1. C3×#5728C2semidirect
3. C32×#487C2semidirect
4. C3×#5088C2semidirect
5. C3×#5079C2semidirect
6. C3×#4804C2semidirect
7. C3×#4800C2semidirect
8. C3×#4694C2semidirect
9. C3×C4×D3×C8C2semidirect
11. #81598C3direct (N × H)
39. #5728C2×C3semidirect
44. C3×#487D3semidirect
45. C3×#487C2×C3semidirect
50. #5088C2×C3semidirect
51. #5079C2×C3semidirect
52. #4804C2×C3semidirect
53. #4800C2×C3semidirect
54. #4694C2×C3semidirect
55. C4×D3×C8C2×C3semidirect
170. #487C3×D3semidirect
416. C32#3131semidirect
471. C3#81598direct (N × H)
472. C3C3×#3131semidirect

Maximal subgroups

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

subgroupindex
C3×#57282
C3×#57252
C32×#4872
C3×#50882
C3×#50792
C3×#48042
C3×#48002
C3×#46942
C3×C4×D3×C82
C3×#31313
#815983