Finite Group Databasebeta

← C3×#81765 #11878749

Subgroups — C3×#81765 #11878749

Order 1152.

947 conjugacy classes of subgroups.

The subgroup lattice has 521 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5725C211yesmaximal, characteristic, complemented
2C3×#5716C211yesmaximal, characteristic, complemented
3C32×#492C211yesmaximal, characteristic, complemented
4C3×#5172C214yesmaximal, complemented
5C3×#5165C214yesmaximal, complemented
6C3×#5079C211yesmaximal, characteristic, complemented
7C3×#5073C211yesmaximal, characteristic, complemented
8C3×#4694C211yesmaximal, characteristic, complemented
9C3×#4685C211yesmaximal, characteristic, complemented
10C3×#3207—31nomaximal
11#81765C311yesmaximal, characteristic, direct product factor
12C2×C3×#239C2212yes—
13C2×C3×#237—21no—
14C2×C32×SD16C2214yes—
15C32×C4⋊Q8C2211yescharacteristic
16C32×#127C2211yescharacteristic
17C3×#947C2212yes—
18C3×#938—21no—
19C3×#938C2212yes—
20C3×#936—21no—
21C3×D4×Dic3—21no—
22C3×D4×Dic3C2212yes—
23C2×C3×#213C2214yes—
24C3×#895—21no—
25C3×#895—21no—
26C3×#893—21no—
27C3×#893—21no—
28C3×#874C2211yescharacteristic
29C3×C42×D3C2211yescharacteristic
30C3×#869C2211yescharacteristic
31C32×C4×C8C2211yescharacteristic
32C3×#835C2214yes—
33C3×#821C2214yes—
34C3×(C2×D3)⋊C8C2212yes—
35C3×Dic3⋊C8C2212yes—
36C3×C4×C3⋊C8C2211yescharacteristic
37C3×#532—31no—
38C3×#532—31no—
39#5725C2×C311yescharacteristic, complemented
40#5716C2×C311yescharacteristic, complemented
41C3×#493—31no—
42C3×#492—21no—
43C3×#492D311yescharacteristic, complemented
44C3×#492C2×C311yescharacteristic, complemented
45C3×#487—31no—
46C3×#486—31no—
47C3×#463—34no—
48C3×#449—34no—
49C3×#431—31no—
50#5172C2×C314yescomplemented
51#5165C2×C314yescomplemented
52#5079C2×C311yescharacteristic, complemented
53#5073C2×C311yescharacteristic, complemented
54#4694C2×C311yescharacteristic, complemented
55#4685C2×C311yescharacteristic, complemented
56C2×C32×Q8C2312yes—
57C2×C32×D4—21no—
58C2×C32×D4—21no—
59C2×C32×D4C2312yes—
60C2×C3×#67—22no—
61C22×C3×Dic3—22no—
62C3×#239—44no—
63C3×#237—44no—
64C2×C3×D12—22no—
65C2×C3×D12—21no—
66C2×C3×D12—21no—
67C2×C3×D12C2312yes—
68C2×C3×C4×D3—22no—
69C2×C3×C4×D3D411yescharacteristic
70C2×C3×C4×D3D411yescharacteristic
71C2×C3×C4×D3C2311yescharacteristic
72C2×C3×Dic6—21no—
73C32×SD16—44no—
74C2×C32×C8C2312yes—
75C32×C4⋊C4—21no—
76C32×C4⋊C4—21no—
77C32×C42C2311yescharacteristic
78C3×#217—22no—
79C3×#217—22no—
80C3×#213—44no—
81C3×(C2×D3)⋊C4—22no—
82C3×(C2×D3)⋊C4—22no—
83C3×C4⋊Dic3—21no—
84C3×C4⋊Dic3C2312yes—
85C3×C4×Dic3D411yescharacteristic
86C3×C4×Dic3D411yescharacteristic
87C3×C4×Dic3C2311yescharacteristic
88C2×C3×C3⋊C8C2312yes—
89#3207—31noSylow
90C2×C3×#41—32no—
91C2×C3×#41—61no—
92C2×#239C22×C312yes—
93C2×#237—21no—
94C2×C3×SD16—24no—
95C2×C3×SD16C2×D314yes—
96C2×C3×SD16C22×C314yes—
97C2×C3×D8—34no—
98C3×C4⋊Q8—21no—
99C3×C4⋊Q8—31no—
100C3×C4⋊Q8C2×D311yescharacteristic
101C3×C4⋊Q8C22×C311yescharacteristic
102C3×#127—21no—
103C3×#127—31no—
104C3×#127C2×D311yescharacteristic
105C3×#127C22×C311yescharacteristic
106C3×#124—32no—
107C3×#124—61no—
108C3×#121—32no—
109C3×#121—61no—
110C3×#121—61no—
111C3×#121—61no—
112C3×C4×D4—32no—
113C3×C4×D4—61no—
114C3×C4×D4—61no—
115C3×C4×D4—61no—
116C2×C3×C42—31no—
117#947C22×C312yes—
118#938—21no—
119#938C22×C312yes—
120#936—21no—
121D4×Dic3—21no—
122D4×Dic3C22×C312yes—
123C2×#213C22×C314yes—
124#895—21no—
125#895—21no—
126#893—21no—
127#893—21no—
128#874C22×C311yescharacteristic
129C42×D3C22×C311yescharacteristic
130#869C22×C311yescharacteristic
131C3×C4⋊C8—32no—
132C3×#103—34no—
133C3×#102—34no—
134C3×C22⋊C8—32no—
135C3×C4×C8—21no—
136C3×C4×C8—31no—
137C3×C4×C8C2×D311yescharacteristic
138C3×C4×C8C22×C311yescharacteristic
139#835C22×C314yes—
140#821C22×C314yes—
141(C2×D3)⋊C8C22×C312yes—
142Dic3⋊C8C22×C312yes—
143C4×C3⋊C8C22×C311yescharacteristic
144C23×C32—22no—
145C22×C3×D3—22no—
146C22×C3×D3C2×D411yescharacteristic
147C32×Q8—24no—
148C32×D4—24no—
149C32×D4—42no—
150C32×D4—42no—
151C2×C32×C4—22no—
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2411yescharacteristic
155C3×#67—44no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—44no—
158C2×C3×Dic3C2×D411yescharacteristic
159C2×C3×Dic3C2×D411yescharacteristic
160C2×C3×Dic3C2×D411yescharacteristic
161C3×D12—24no—
162C3×D12—44no—
163C3×D12—42no—
164C3×D12—42no—
165C3×C4×D3—22no—
166C3×C4×D3—22no—
167C3×C4×D3—22no—
168C3×C4×D3—44no—
169C3×Dic6—42no—
170C32×C8—22no—
171C3×C3⋊C8—22no—
172#532—31no—
173#532—31no—
174#493—31no—
175#492C3×D311yescharacteristic, complemented
176#487—31no—
177#486—31no—
178#463—34no—
179#449—34no—
180#431—31no—
181C3×#41—124no—
182C3×#41—124no—
183C2×C3×Q8—22no—
184C2×C3×Q8—61no—
185C2×C3×Q8C22×D312yes—
186C2×C3×Q8C23×C312yes—
187C2×C3×D4—21no—
188C2×C3×D4—21no—
189C2×C3×D4—21no—
190C2×C3×D4—21no—
191C2×C3×D4—22no—
192C2×C3×D4—32no—
193C2×C3×D4—41no—
194C2×C3×D4—41no—
195C2×C3×D4—62no—
196C2×C3×D4—62no—
197C2×C3×D4—61no—
198C2×C3×D4—61no—
199C2×C3×D4C22×D312yes—
200C2×C3×D4C23×C312yes—
201C22×C3×C4—31no—
202C22×C3×C4—31no—
203C22×C3×C4—31no—
204C22×C3×C4—62no—
205C22×C3×C4—62no—
206C2×#67—22no—
207C22×Dic3—22no—
208#239—44no—
209#237—44no—
210C2×D12—22no—
211C2×D12—21no—
212C2×D12—21no—
213C2×D12C23×C312yes—
214C2×C4×D3—22no—
215C2×C4×D3C3×D411yescharacteristic
216C2×C4×D3C3×D411yescharacteristic
217C2×C4×D3C23×C311yescharacteristic
218C2×Dic6—21no—
219C3×SD16—44no—
220C3×SD16—44no—
221C3×SD16—48no—
222C3×D8—124no—
223C2×C3×C8—22no—
224C2×C3×C8—32no—
225C2×C3×C8C22×D312yes—
226C2×C3×C8C23×C312yes—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—32no—
232C3×C4⋊C4—41no—
233C3×C4⋊C4—41no—
234C3×C4⋊C4—61no—
235C3×C22⋊C4—62no—
236C3×C22⋊C4—62no—
237C3×C22⋊C4—62no—
238C3×C22⋊C4—62no—
239C3×C42—21no—
240C3×C42—31no—
241C3×C42—31no—
242C3×C42—31no—
243C3×C42C22×D311yescharacteristic
244C3×C42C23×C311yescharacteristic
245#217—22no—
246#217—22no—
247#213—44no—
248(C2×D3)⋊C4—22no—
249(C2×D3)⋊C4—22no—
250C4⋊Dic3—21no—
251C4⋊Dic3C23×C312yes—
252C4×Dic3C3×D411yescharacteristic
253C4×Dic3C3×D411yescharacteristic
254C4×Dic3C23×C311yescharacteristic
255C2×C3⋊C8C23×C312yes—
256C22×C32—42no—
257C22×C32—42no—
258C22×C32—42no—
259C22×C32C22×D411yescharacteristic
260C2×C3×D3—21no—
261C2×C3×D3—21no—
262C2×C3×D3—21no—
263C2×C3×D3—42no—
264C2×C3×D3—42no—
265C2×C3×D3—42no—
266C32×C4—42no—
267C32×C4#13512yes—
268C32×C4AGL(1,ℤ/8)12yes—
269C32×C4H(5,𝔽2)12yes—
270C3×Dic3—21no—
271C3×Dic3—21no—
272C3×Dic3—21no—
273C3×Dic3—42no—
274C2×#41—32no—
275C2×#41—61no—
276C2×SD16C2×C3×D314yes—
277C2×D8—34no—
278C4⋊Q8—31no—
279C4⋊Q8C2×C3×D311yescharacteristic
280#127—31no—
281#127C2×C3×D311yescharacteristic
282#124—32no—
283#124—61no—
284#121—32no—
285#121—61no—
286#121—61no—
287#121—61no—
288C4×D4—32no—
289C4×D4—61no—
290C4×D4—61no—
291C4×D4—61no—
292C2×C42—31no—
293C4⋊C8—32no—
294#103—34no—
295#102—34no—
296C22⋊C8—32no—
297C4×C8—31no—
298C4×C8C2×C3×D311yescharacteristic
299C23×C3—22no—
300C23×C3—22no—
301C23×C3—31no—
302C23×C3—42no—
303C23×C3—62no—
304C22×D3—22no—
305C22×D3C2×C3×D411yescharacteristic
306C3×Q8—24no—
307C3×Q8—24no—
308C3×Q8—44no—
309C3×Q8—122no—
310C3×D4—24no—
311C3×D4—24no—
312C3×D4—44no—
313C3×D4—42no—
314C3×D4—42no—
315C3×D4—42no—
316C3×D4—42no—
317C3×D4—64no—
318C3×D4—82no—
319C3×D4—82no—
320C3×D4—124no—
321C3×D4—124no—
322C3×D4—122no—
323C3×D4—122no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—31no—
330C2×C3×C4—31no—
331C2×C3×C4—31no—
332C2×C3×C4—42no—
333C2×C3×C4—62no—
334C2×C3×C4—62no—
335C2×C3×C4—62no—
336C2×C3×C4—62no—
337C2×C3×C4—124no—
338C2×C3×C4—124no—
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4C2×C3×D411yescharacteristic
342C2×C3×C4C2×C3×D411yescharacteristic
343C2×C3×C4C23×D311yescharacteristic
344C2×C3×C4C24×C311yescharacteristic
345#67—44no—
346C2×Dic3—22no—
347C2×Dic3—44no—
348C2×Dic3C2×C3×D411yescharacteristic
349C2×Dic3C2×C3×D411yescharacteristic
350C2×Dic3C2×C3×D411yescharacteristic
351D12—24no—
352D12—44no—
353D12—42no—
354D12—42no—
355C4×D3—22no—
356C4×D3—22no—
357C4×D3—22no—
358C4×D3—44no—
359Dic6—42no—
360C3×C8—24no—
361C3×C8—22no—
362C3×C8—22no—
363C3×C8—62no—
364C3⋊C8—22no—
365C2×C32—82no—
366C2×C32#53511yescharacteristic
367C2×C32C2×#13511yescharacteristic
368C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
369C3×D3—41no—
370C3×D3—82no—
371#41—124no—
372#41—124no—
373C2×Q8—61no—
374C2×Q8C22×C3×D312yes—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—32no—
378C2×D4—62no—
379C2×D4—62no—
380C2×D4—61no—
381C2×D4—61no—
382C2×D4C22×C3×D312yes—
383C22×C4—31no—
384C22×C4—31no—
385C22×C4—31no—
386C22×C4—62no—
387C22×C4—62no—
388SD16—44no—
389D8—124no—
390C2×C8—32no—
391C2×C8C22×C3×D312yes—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—32no—
395C4⋊C4—61no—
396C22⋊C4—62no—
397C22⋊C4—62no—
398C22⋊C4—62no—
399C22⋊C4—62no—
400C42—31no—
401C42—31no—
402C42—31no—
403C42C22×C3×D311yescharacteristic
404C22×C3—21no—
405C22×C3—42no—
406C22×C3—42no—
407C22×C3—42no—
408C22×C3—42no—
409C22×C3—42no—
410C22×C3—42no—
411C22×C3—61no—
412C22×C3—61no—
413C22×C3—61no—
414C22×C3—82no—
415C22×C3—82no—
416C22×C3—82no—
417C22×C3—122no—
418C22×C3—122no—
419C22×C3—122no—
420C22×C3C2×D3×D411yescharacteristic
421C22×C3C22×C3×D411yescharacteristic
422C2×D3—21no—
423C2×D3—21no—
424C2×D3—21no—
425C2×D3—42no—
426C2×D3—42no—
427C2×D3—42no—
428C3×C4—22no—
429C3×C4—22no—
430C3×C4—22no—
431C3×C4—42no—
432C3×C4—42no—
433C3×C4—61no—
434C3×C4—61no—
435C3×C4—61no—
436C3×C4—82no—
437C3×C4—122no—
438C3×C4#91412yes—
439C3×C4#91612yes—
440C3×C4C3×#13512yes—
441C3×C4C3×AGL(1,ℤ/8)12yes—
442C3×C4#100412yes—
443C3×C4C3×H(5,𝔽2)12yes—
444Dic3—21no—
445Dic3—21no—
446Dic3—21no—
447Dic3—42no—
448C32#320711yescharacteristic, complemented, Sylow
449C23—22no—
450C23—31no—
451C23—62no—
452Q8—24no—
453Q8—122no—
454D4—24no—
455D4—42no—
456D4—42no—
457D4—64no—
458D4—124no—
459D4—124no—
460D4—122no—
461D4—122no—
462C2×C4—22no—
463C2×C4—31no—
464C2×C4—31no—
465C2×C4—31no—
466C2×C4—62no—
467C2×C4—62no—
468C2×C4—62no—
469C2×C4—62no—
470C2×C4—124no—
471C2×C4—124no—
472C2×C4C3×D3×D411yescharacteristic
473C2×C4C3×D3×D411yescharacteristic
474C2×C4C23×C3×D311yescharacteristic
475C8—22no—
476C8—62no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—82no—
481C2×C3—82no—
482C2×C3—121no—
483C2×C3—162no—
484C2×C3—242no—
485C2×C3#571511yescharacteristic
486C2×C3C2×#91411yescharacteristic
487C2×C3C2×#91611yescharacteristic
488C2×C3C3×#53511yescharacteristic
489C2×C3C2×C3×#13511yescharacteristic
490C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
491D3—41no—
492D3—82no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—61no—
497C22—61no—
498C22—61no—
499C22—122no—
500C22—122no—
501C22—122no—
502C22C2×C3×D3×D411yescharacteristic
503C4—42no—
504C4—61no—
505C4—61no—
506C4—61no—
507C4—122no—
508C4C3×#91412yes—
509C4C3×#91612yes—
510C4C3×#100412yes—
511C3—21no—
512C3#8176511yescharacteristic, direct product factor
513C3C3×#320711yescharacteristic, complemented
514C2—82no—
515C2—121no—
516C2—242no—
517C2C3×#571511yescharacteristic
518C2C2×C3×#91411yescharacteristic
519C2C2×C3×#91611yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#492C2
socleC22×C32C22×D4
hypercenterC3×#492D3
hypocenterC3C3×#3207
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#492

Complements

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

NH ≅ G/Ntype
1. C3×#5725C2semidirect
2. C3×#5716C2semidirect
3. C32×#492C2semidirect
4. C3×#5172C2semidirect
5. C3×#5165C2semidirect
6. C3×#5079C2semidirect
7. C3×#5073C2semidirect
8. C3×#4694C2semidirect
9. C3×#4685C2semidirect
11. #81765C3direct (N × H)
39. #5725C2×C3semidirect
40. #5716C2×C3semidirect
43. C3×#492D3semidirect
44. C3×#492C2×C3semidirect
50. #5172C2×C3semidirect
51. #5165C2×C3semidirect
52. #5079C2×C3semidirect
53. #5073C2×C3semidirect
54. #4694C2×C3semidirect
55. #4685C2×C3semidirect
175. #492C3×D3semidirect
448. C32#3207semidirect
512. C3#81765direct (N × H)
513. C3C3×#3207semidirect

Maximal subgroups

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

subgroupindex
C3×#57252
C3×#57162
C32×#4922
C3×#51722
C3×#51652
C3×#50792
C3×#50732
C3×#46942
C3×#46852
C3×#32073
#817653