Finite Group Databasebeta

← C3×#81562 #11873464

Subgroups — C3×#81562 #11873464

Order 1152.

859 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5728C211yesmaximal, characteristic, complemented
2C3×#5716C211yesmaximal, characteristic
3C32×#486C211yesmaximal, characteristic, complemented
4C3×#5093C211yesmaximal, characteristic, complemented
5C3×#5070C211yesmaximal, characteristic, complemented
6C3×#4772C214yesmaximal, complemented
7C3×#4768C214yesmaximal, complemented
8C3×C4×D3×C8C211yesmaximal, characteristic, complemented
9C3×#4681C211yesmaximal, characteristic, complemented
10C3×#3131—31nomaximal
11#81562C311yesmaximal, characteristic, direct product factor
12C2×C3×#237C2212yes—
13C32×C4⋊Q8C2211yescharacteristic
14C32×#127C2211yescharacteristic
15C3×#946—21no—
16C3×Q8×Dic3—21no—
17C3×#938—21no—
18C3×#938—21no—
19C3×#936C2212yes—
20C3×D4×Dic3—21no—
21C3×D4×Dic3—21no—
22C2×C3×D3×C8C2212yes—
23C3×#897—21no—
24C3×#892C2212yes—
25C3×#890C2212yes—
26C3×#887—21no—
27C3×C42×D3C2211yescharacteristic
28C3×#869C2211yescharacteristic
29C3×#869C2211yescharacteristic
30C32×#102C2214yes—
31C32×C4×C8C2211yescharacteristic
32C3×#832C2214yes—
33C3×#816C2214yes—
34C3×C8×Dic3C2212yes—
35C3×#810C2214yes—
36C3×C4×C3⋊C8C2211yescharacteristic
37C3×#533—31no—
38C3×#532—31no—
39#5728C2×C311yescharacteristic, complemented
40#5716C2×C311yescharacteristic
41C3×#488—34no—
42C3×#487—31no—
43C3×#487—31no—
44C3×#486—21no—
45C3×#486—31no—
46C3×#486D311yescharacteristic, complemented
47C3×#486C2×C311yescharacteristic, complemented
48C3×#416—34no—
49C2×C3×C4×C8—31no—
50#5093C2×C311yescharacteristic, complemented
51#5070C2×C311yescharacteristic, complemented
52#4772C2×C314yescomplemented
53#4768C2×C314yescomplemented
54C4×D3×C8C2×C311yescharacteristic, complemented
55#4681C2×C311yescharacteristic, complemented
56C2×C32×Q8—21no—
57C2×C32×D4—21no—
58C2×C32×D4—21no—
59C2×C32×D4C2312yes—
60C2×C3×#67—22no—
61C22×C3×Dic3—22no—
62C3×#237—28no—
63C2×C3×C4×D3D411yescharacteristic
64C2×C3×C4×D3D411yescharacteristic
65C2×C3×C4×D3C2311yescharacteristic
66C2×C3×Dic6—21no—
67C2×C3×Dic6C2312yes—
68C2×C32×C8C2312yes—
69C32×C4⋊C4—21no—
70C32×C4⋊C4C2312yes—
71C32×C42C2311yescharacteristic
72C3×#217—22no—
73C3×#217—22no—
74C3×(C2×D3)⋊C4—22no—
75C3×C4⋊Dic3—21no—
76C3×C4⋊Dic3—21no—
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×#237C22×C312yes—
90C22×C3×C8—32no—
91C3×C4⋊Q8—21no—
92C3×C4⋊Q8—31no—
93C3×C4⋊Q8—31no—
94C3×C4⋊Q8C2×D311yescharacteristic
95C3×C4⋊Q8C22×C311yescharacteristic
96C3×#127—21no—
97C3×#127C2×D311yescharacteristic
98C3×#127C22×C311yescharacteristic
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#946—21no—
112Q8×Dic3—21no—
113#938—21no—
114#938—21no—
115#936C22×C312yes—
116D4×Dic3—21no—
117D4×Dic3—21no—
118C2×D3×C8C22×C312yes—
119#897—21no—
120#892C22×C312yes—
121#890C22×C312yes—
122#887—21no—
123C42×D3C22×C311yescharacteristic
124#869C22×C311yescharacteristic
125#869C22×C311yescharacteristic
126C3×#103—34no—
127C3×#103—34no—
128C3×#102—24no—
129C3×#102—34no—
130C3×#102C2×D314yes—
131C3×#102C22×C314yes—
132C3×C4×C8—21no—
133C3×C4×C8—32no—
134C3×C4×C8—31no—
135C3×C4×C8C2×D311yescharacteristic
136C3×C4×C8C22×C311yescharacteristic
137#832C22×C314yes—
138#816C22×C314yes—
139C8×Dic3C22×C312yes—
140#810C22×C314yes—
141C4×C3⋊C8C22×C311yescharacteristic
142C23×C32—22no—
143C22×C3×D3C2×D411yescharacteristic
144C32×Q8—42no—
145C32×D4—24no—
146C32×D4—42no—
147C32×D4—42no—
148C2×C32×C4—22no—
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2411yescharacteristic
152C3×#67—44no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—44no—
156C2×C3×Dic3C2×D411yescharacteristic
157C2×C3×Dic3C2×D411yescharacteristic
158C2×C3×Dic3C2×D411yescharacteristic
159C3×C4×D3—22no—
160C3×C4×D3—22no—
161C3×C4×D3#4114yes—
162C3×Dic6—24no—
163C3×Dic6—42no—
164C32×C8—22no—
165C3×C3⋊C8—22no—
166#533—31no—
167#532—31no—
168#488—34no—
169#487—31no—
170#487—31no—
171#486—31no—
172#486C3×D311yescharacteristic, complemented
173#416—34no—
174C2×C4×C8—31no—
175C3×#41—68no—
176C2×C3×Q8—21no—
177C2×C3×Q8—21no—
178C2×C3×Q8—32no—
179C2×C3×Q8—41no—
180C2×C3×Q8—61no—
181C2×C3×D4—21no—
182C2×C3×D4—21no—
183C2×C3×D4—21no—
184C2×C3×D4—21no—
185C2×C3×D4—22no—
186C2×C3×D4—41no—
187C2×C3×D4—41no—
188C2×C3×D4—62no—
189C2×C3×D4C22×D312yes—
190C2×C3×D4C23×C312yes—
191C22×C3×C4—31no—
192C22×C3×C4—31no—
193C22×C3×C4—31no—
194C22×C3×C4—62no—
195C2×#67—22no—
196C22×Dic3—22no—
197#237—28no—
198C2×C4×D3C3×D411yescharacteristic
199C2×C4×D3C3×D411yescharacteristic
200C2×C4×D3C23×C311yescharacteristic
201C2×Dic6—21no—
202C2×Dic6C23×C312yes—
203C2×C3×C8—22no—
204C2×C3×C8—32no—
205C2×C3×C8—64no—
206C2×C3×C8C22×D312yes—
207C2×C3×C8C23×C312yes—
208C3×C4⋊C4—21no—
209C3×C4⋊C4—21no—
210C3×C4⋊C4—22no—
211C3×C4⋊C4—32no—
212C3×C4⋊C4—41no—
213C3×C4⋊C4—62no—
214C3×C4⋊C4—62no—
215C3×C4⋊C4—61no—
216C3×C4⋊C4—61no—
217C3×C4⋊C4—61no—
218C3×C4⋊C4C22×D312yes—
219C3×C4⋊C4C23×C312yes—
220C3×C22⋊C4—62no—
221C3×C22⋊C4—62no—
222C3×C22⋊C4—62no—
223C3×C42—21no—
224C3×C42—31no—
225C3×C42—31no—
226C3×C42—31no—
227C3×C42—62no—
228C3×C42C22×D311yescharacteristic
229C3×C42C23×C311yescharacteristic
230#217—22no—
231#217—22no—
232(C2×D3)⋊C4—22no—
233C4⋊Dic3—21no—
234C4⋊Dic3—21no—
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×C32—42no—
246C22×C32—42no—
247C22×C32—42no—
248C22×C32C22×D411yescharacteristic
249C2×C3×D3—21no—
250C2×C3×D3—21no—
251C2×C3×D3#12412yes—
252C32×C4—42no—
253C32×C4#13512yes—
254C32×C4#13512yes—
255C32×C4C2×#4112yes—
256C3×Dic3—21no—
257C3×Dic3—21no—
258C3×Dic3—42no—
259C3×Dic3—42no—
260C3×Dic3#12412yes—
261C2×#41—32no—
262C22×C8—32no—
263C4⋊Q8—31no—
264C4⋊Q8—31no—
265C4⋊Q8C2×C3×D311yescharacteristic
266#127C2×C3×D311yescharacteristic
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#103—34no—
281#102—34no—
282#102C2×C3×D314yes—
283C4×C8—32no—
284C4×C8—31no—
285C4×C8C2×C3×D311yescharacteristic
286C23×C3—22no—
287C23×C3—22no—
288C23×C3—31no—
289C23×C3—42no—
290C22×D3C2×C3×D411yescharacteristic
291C3×Q8—42no—
292C3×Q8—42no—
293C3×Q8—64no—
294C3×Q8—82no—
295C3×Q8—122no—
296C3×D4—24no—
297C3×D4—24no—
298C3×D4—44no—
299C3×D4—42no—
300C3×D4—42no—
301C3×D4—42no—
302C3×D4—42no—
303C3×D4—82no—
304C3×D4—82no—
305C3×D4—124no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—31no—
312C2×C3×C4—34no—
313C2×C3×C4—31no—
314C2×C3×C4—31no—
315C2×C3×C4—42no—
316C2×C3×C4—62no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4—62no—
320C2×C3×C4—124no—
321C2×C3×C4D3×D411yescharacteristic
322C2×C3×C4D3×D411yescharacteristic
323C2×C3×C4C2×C3×D411yescharacteristic
324C2×C3×C4C2×C3×D411yescharacteristic
325C2×C3×C4C23×D311yescharacteristic
326C2×C3×C4C24×C311yescharacteristic
327#67—44no—
328C2×Dic3—22no—
329C2×Dic3—22no—
330C2×Dic3—44no—
331C2×Dic3C2×C3×D411yescharacteristic
332C2×Dic3C2×C3×D411yescharacteristic
333C2×Dic3C2×C3×D411yescharacteristic
334C4×D3—22no—
335C4×D3—22no—
336C4×D3C3×#4114yes—
337Dic6—24no—
338Dic6—42no—
339C3×C8—22no—
340C3×C8—22no—
341C3×C8—42no—
342C3×C8—62no—
343C3⋊C8—22no—
344C2×C32—82no—
345C2×C32C2×#12411yescharacteristic
346C2×C32C2×#13511yescharacteristic
347C2×C32C2×#13511yescharacteristic
348C3×D3—22no—
349#41—68no—
350C2×Q8—21no—
351C2×Q8—32no—
352C2×Q8—61no—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—62no—
356C2×D4C22×C3×D312yes—
357C22×C4—31no—
358C22×C4—31no—
359C22×C4—31no—
360C22×C4—62no—
361C2×C8—32no—
362C2×C8—64no—
363C2×C8C22×C3×D312yes—
364C4⋊C4—21no—
365C4⋊C4—32no—
366C4⋊C4—62no—
367C4⋊C4—62no—
368C4⋊C4—61no—
369C4⋊C4—61no—
370C4⋊C4—61no—
371C4⋊C4C22×C3×D312yes—
372C22⋊C4—62no—
373C22⋊C4—62no—
374C22⋊C4—62no—
375C42—31no—
376C42—31no—
377C42—31no—
378C42—62no—
379C42C22×C3×D311yescharacteristic
380C22×C3—21no—
381C22×C3—32no—
382C22×C3—42no—
383C22×C3—42no—
384C22×C3—42no—
385C22×C3—42no—
386C22×C3—42no—
387C22×C3—42no—
388C22×C3—61no—
389C22×C3—61no—
390C22×C3—82no—
391C22×C3—82no—
392C22×C3—82no—
393C22×C3C2×D3×D411yescharacteristic
394C22×C3C22×C3×D411yescharacteristic
395C2×D3—21no—
396C2×D3—21no—
397C2×D3C3×#12412yes—
398C3×C4—22no—
399C3×C4—22no—
400C3×C4—22no—
401C3×C4—32no—
402C3×C4—42no—
403C3×C4—42no—
404C3×C4—61no—
405C3×C4—61no—
406C3×C4—82no—
407C3×C4—122no—
408C3×C4—122no—
409C3×C4#91212yes—
410C3×C4#91612yes—
411C3×C4C3×#13512yes—
412C3×C4C3×#13512yes—
413C3×C4D3×#4112yes—
414C3×C4C2×C3×#4112yes—
415Dic3—21no—
416Dic3—21no—
417Dic3—42no—
418Dic3—42no—
419Dic3C3×#12412yes—
420C32#313111yescharacteristic, complemented, Sylow
421C23—22no—
422C23—31no—
423Q8—42no—
424Q8—64no—
425Q8—122no—
426D4—24no—
427D4—42no—
428D4—42no—
429D4—124no—
430C2×C4—22no—
431C2×C4—31no—
432C2×C4—34no—
433C2×C4—31no—
434C2×C4—31no—
435C2×C4—62no—
436C2×C4—62no—
437C2×C4—62no—
438C2×C4—62no—
439C2×C4—124no—
440C2×C4C3×D3×D411yescharacteristic
441C2×C4C3×D3×D411yescharacteristic
442C2×C4C23×C3×D311yescharacteristic
443C8—22no—
444C8—62no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—62no—
449C2×C3—82no—
450C2×C3—82no—
451C2×C3—162no—
452C2×C3D3×#12411yescharacteristic
453C2×C3C2×#91211yescharacteristic
454C2×C3C2×#91611yescharacteristic
455C2×C3C2×C3×#12411yescharacteristic
456C2×C3C2×C3×#13511yescharacteristic
457C2×C3C2×C3×#13511yescharacteristic
458D3—22no—
459C22—32no—
460C22—42no—
461C22—42no—
462C22—42no—
463C22—61no—
464C22—61no—
465C22C2×C3×D3×D411yescharacteristic
466C4—32no—
467C4—42no—
468C4—61no—
469C4—61no—
470C4—122no—
471C4—122no—
472C4C3×#91212yes—
473C4C3×#91612yes—
474C4C3×D3×#4112yes—
475C3—21no—
476C3#8156211yescharacteristic, direct product factor
477C3C3×#313111yescharacteristic, complemented
478C2—62no—
479C2—82no—
480C2C3×D3×#12411yescharacteristic
481C2C2×C3×#91211yescharacteristic
482C2C2×C3×#91611yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#486C2
socleC22×C32C22×D4
prime radicalC3×#5716C2
hypercenterC3×#486D3
hypocenterC3C3×#3131
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×#5728C2semidirect
3. C32×#486C2semidirect
4. C3×#5093C2semidirect
5. C3×#5070C2semidirect
6. C3×#4772C2semidirect
7. C3×#4768C2semidirect
8. C3×C4×D3×C8C2semidirect
9. C3×#4681C2semidirect
11. #81562C3direct (N × H)
39. #5728C2×C3semidirect
46. C3×#486D3semidirect
47. C3×#486C2×C3semidirect
50. #5093C2×C3semidirect
51. #5070C2×C3semidirect
52. #4772C2×C3semidirect
53. #4768C2×C3semidirect
54. C4×D3×C8C2×C3semidirect
55. #4681C2×C3semidirect
172. #486C3×D3semidirect
420. C32#3131semidirect
476. C3#81562direct (N × H)
477. 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×#57162
C32×#4862
C3×#50932
C3×#50702
C3×#47722
C3×#47682
C3×C4×D3×C82
C3×#46812
C3×#31313
#815623