Finite Group Databasebeta

← C3×#81589 #11895637

Subgroups — C3×#81589 #11895637

Order 1152.

755 conjugacy classes of subgroups.

The subgroup lattice has 513 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5721C211yesmaximal, characteristic, complemented
2C3×#5713C211yesmaximal, characteristic
3C32×#486C211yesmaximal, characteristic
4C3×#5094C211yesmaximal, characteristic, complemented
5C3×#5075C211yesmaximal, characteristic
6C3×#4768C212yesmaximal, complemented
7C3×#4767C212yesmaximal, complemented
8C3×#4766C212yesmaximal, complemented
9C3×#4758C212yesmaximal, complemented
10C3×C4×Dic12C211yesmaximal, characteristic, complemented
11C3×C8×Dic6C211yesmaximal, characteristic, complemented
12C3×#3365—31nomaximal
13#81589C311yesmaximal, characteristic, direct product factor
14C32×C4⋊Q8C2211yescharacteristic
15C32×#127C2211yescharacteristic
16C3×Q8×Dic3—21no—
17C3×#944—21no—
18C3×#936—21no—
19C3×#936C2212yes—
20C3×#935—22no—
21C3×D4×Dic3—21no—
22C3×D4×Dic3C2212yes—
23C2×C3×#214C2212yes—
24C2×C3×Dic12C2211yescharacteristic
25C3×#890C2212yes—
26C3×#889—22no—
27C3×#887C2212yes—
28C3×C4×Dic6C2211yescharacteristic
29C3×C4×Dic6C2211yescharacteristic
30C3×C4×Dic6C2211yescharacteristic
31C32×#102C2212yes—
32C32×#102C2212yes—
33C32×C4×C8C2211yescharacteristic
34C3×#832C2212yes—
35C3×#818C2211yescharacteristic
36C3×#816C2211yescharacteristic
37C3×#816C2211yescharacteristic
38C3×Dic3⋊C8C2212yes—
39C3×C8×Dic3C2212yes—
40C3×#810C2212yes—
41C3×#808C2212yes—
42C3×C4⋊(C3⋊C8)C2211yescharacteristic
43C3×#559—31no—
44C3×#557—31no—
45#5721C2×C311yescharacteristic, complemented
46#5713C2×C311yescharacteristic
47C3×#488—32no—
48C3×#486—21no—
49C3×#486D311yescharacteristic
50C3×#486C2×C311yescharacteristic
51C3×#478—32no—
52C3×#475—31no—
53C3×#464—32no—
54C3×#460—31no—
55C3×C8×Q8—31no—
56C3×C4×Q16—31no—
57C3×C4×SD16—32no—
58#5094C2×C311yescharacteristic, complemented
59#5075C2×C311yescharacteristic
60#4768C2×C312yescomplemented
61#4767C2×C312yescomplemented
62#4766C2×C312yescomplemented
63#4758C2×C312yescomplemented
64C4×Dic12C2×C311yescharacteristic, complemented
65C8×Dic6C2×C311yescharacteristic, complemented
66C2×C32×Q8—21no—
67C2×C32×D4—21no—
68C2×C32×D4—21no—
69C2×C32×D4C2312yes—
70C22×C3×Dic3—22no—
71C2×C3×Dic6D411yescharacteristic
72C2×C3×Dic6C2311yescharacteristic
73C2×C3×Dic6C2311yescharacteristic
74C2×C32×C8C2311yescharacteristic
75C2×C32×C8C2311yescharacteristic
76C32×C4⋊C4—21no—
77C32×C4⋊C4C2312yes—
78C32×C42C2311yescharacteristic
79C3×#217—22no—
80C3×#217—22no—
81C3×#217—22no—
82C3×#214—24no—
83C3×C4⋊Dic3—22no—
84C3×C4⋊Dic3D411yescharacteristic
85C3×C4⋊Dic3C2311yescharacteristic
86C3×C4⋊Dic3C2311yescharacteristic
87C3×Dic3⋊C4—21no—
88C3×Dic3⋊C4—21no—
89C3×Dic3⋊C4—22no—
90C3×Dic3⋊C4—22no—
91C3×Dic3⋊C4D412yes—
92C3×C4×Dic3—21no—
93C3×C4×Dic3—21no—
94C3×C4×Dic3—22no—
95C3×C4×Dic3C2312yes—
96C2×C3×C3⋊C8C2312yes—
97C3×Dic12—22no—
98#3365—31noSylow
99C2×C3×Q16—31no—
100C2×C3×SD16—32no—
101C3×C4⋊Q8—21no—
102C3×C4⋊Q8—61no—
103C3×C4⋊Q8C2×D311yescharacteristic
104C3×C4⋊Q8C22×C311yescharacteristic
105C3×#127—21no—
106C3×#127C2×D311yescharacteristic
107C3×#127C22×C311yescharacteristic
108C3×#125—32no—
109C3×#125—62no—
110C3×#124—32no—
111C3×#124—61no—
112C3×#123—62no—
113C3×C4×Q8—31no—
114C3×C4×Q8—32no—
115C3×C4×Q8—31no—
116C3×C4×Q8—31no—
117C3×C4×Q8—61no—
118C3×C4×D4—32no—
119C3×C4×D4—61no—
120Q8×Dic3—21no—
121#944—21no—
122#936—21no—
123#936C22×C312yes—
124#935—22no—
125D4×Dic3—21no—
126D4×Dic3C22×C312yes—
127C2×#214C22×C312yes—
128C2×Dic12C22×C311yescharacteristic
129#890C22×C312yes—
130#889—22no—
131#887C22×C312yes—
132C4×Dic6C22×C311yescharacteristic
133C4×Dic6C22×C311yescharacteristic
134C4×Dic6C22×C311yescharacteristic
135C3×#107—31no—
136C3×#106—32no—
137C3×C4⋊C8—32no—
138C3×C4⋊C8—31no—
139C3×#103—31no—
140C3×#103—31no—
141C3×#103—32no—
142C3×#102—22no—
143C3×#102—22no—
144C3×#102—32no—
145C3×#102C2×D312yes—
146C3×#102C2×D312yes—
147C3×#102C22×C312yes—
148C3×#102C22×C312yes—
149C3×C4×C8—21no—
150C3×C4×C8—32no—
151C3×C4×C8C2×D311yescharacteristic
152C3×C4×C8C22×C311yescharacteristic
153#832C22×C312yes—
154#818C22×C311yescharacteristic
155#816C22×C311yescharacteristic
156#816C22×C311yescharacteristic
157Dic3⋊C8C22×C312yes—
158C8×Dic3C22×C312yes—
159#810C22×C312yes—
160#808C22×C312yes—
161C4⋊(C3⋊C8)C22×C311yescharacteristic
162C23×C32—22no—
163C32×Q8—42no—
164C32×D4—22no—
165C32×D4—22no—
166C32×D4—42no—
167C32×D4—81no—
168C2×C32×C4—22no—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2411yescharacteristic
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—82no—
177C2×C3×Dic3C2×D412yes—
178C2×C3×Dic3C2×D412yes—
179C3×Dic6—22no—
180C3×Dic6—21no—
181C3×Dic6—21no—
182C3×Dic6—21no—
183C3×Dic6#4112yes—
184C32×C8—21no—
185C32×C8—21no—
186C3×C3⋊C8—22no—
187#559—31no—
188#557—31no—
189#488—32no—
190#486C3×D311yescharacteristic
191#478—32no—
192#475—31no—
193#464—32no—
194#460—31no—
195C8×Q8—31no—
196C4×Q16—31no—
197C4×SD16—32no—
198C2×C3×Q8—21no—
199C2×C3×Q8—21no—
200C2×C3×Q8—31no—
201C2×C3×Q8—31no—
202C2×C3×Q8—31no—
203C2×C3×Q8—41no—
204C2×C3×D4—21no—
205C2×C3×D4—21no—
206C2×C3×D4—21no—
207C2×C3×D4—21no—
208C2×C3×D4—22no—
209C2×C3×D4—41no—
210C2×C3×D4—41no—
211C2×C3×D4C22×D312yes—
212C2×C3×D4C23×C312yes—
213C22×C3×C4—62no—
214C22×Dic3—22no—
215C2×Dic6C3×D411yescharacteristic
216C2×Dic6C23×C311yescharacteristic
217C2×Dic6C23×C311yescharacteristic
218C3×Q16—62no—
219C3×SD16—64no—
220C2×C3×C8—21no—
221C2×C3×C8—21no—
222C2×C3×C8—32no—
223C2×C3×C8C22×D311yescharacteristic
224C2×C3×C8C22×D311yescharacteristic
225C2×C3×C8C23×C311yescharacteristic
226C2×C3×C8C23×C311yescharacteristic
227C3×C4⋊C4—21no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—22no—
230C3×C4⋊C4—32no—
231C3×C4⋊C4—31no—
232C3×C4⋊C4—31no—
233C3×C4⋊C4—31no—
234C3×C4⋊C4—41no—
235C3×C4⋊C4—62no—
236C3×C4⋊C4—62no—
237C3×C4⋊C4—62no—
238C3×C4⋊C4—61no—
239C3×C4⋊C4—61no—
240C3×C4⋊C4C22×D312yes—
241C3×C4⋊C4C23×C312yes—
242C3×C22⋊C4—62no—
243C3×C22⋊C4—62no—
244C3×C22⋊C4—62no—
245C3×C42—21no—
246C3×C42—32no—
247C3×C42—62no—
248C3×C42—61no—
249C3×C42—61no—
250C3×C42C22×D311yescharacteristic
251C3×C42C23×C311yescharacteristic
252#217—22no—
253#217—22no—
254#217—22no—
255#214—24no—
256C4⋊Dic3—22no—
257C4⋊Dic3C3×D411yescharacteristic
258C4⋊Dic3C23×C311yescharacteristic
259C4⋊Dic3C23×C311yescharacteristic
260Dic3⋊C4—21no—
261Dic3⋊C4—21no—
262Dic3⋊C4—22no—
263Dic3⋊C4—22no—
264Dic3⋊C4C3×D412yes—
265C4×Dic3—21no—
266C4×Dic3—21no—
267C4×Dic3—22no—
268C4×Dic3C23×C312yes—
269C2×C3⋊C8C23×C312yes—
270Dic12—22no—
271C22×C32—42no—
272C22×C32—42no—
273C22×C32—42no—
274C22×C32C22×D411yescharacteristic
275C32×C4—21no—
276C32×C4—42no—
277C32×C4#13512yes—
278C32×C4C2×#4111yescharacteristic
279C32×C42−1+411yescharacteristic
280C3×Dic3—22no—
281C3×Dic3—22no—
282C3×Dic3—22no—
283C3×Dic3—41no—
284C3×Dic3—41no—
285C3×Dic3—41no—
286C2×Q16—31no—
287C2×SD16—32no—
288C4⋊Q8—61no—
289C4⋊Q8C2×C3×D311yescharacteristic
290#127C2×C3×D311yescharacteristic
291#125—32no—
292#125—62no—
293#124—32no—
294#124—61no—
295#123—62no—
296C4×Q8—31no—
297C4×Q8—32no—
298C4×Q8—31no—
299C4×Q8—31no—
300C4×Q8—61no—
301C4×D4—32no—
302C4×D4—61no—
303#107—31no—
304#106—32no—
305C4⋊C8—32no—
306C4⋊C8—31no—
307#103—31no—
308#103—31no—
309#103—32no—
310#102—32no—
311#102C2×C3×D312yes—
312#102C2×C3×D312yes—
313C4×C8—32no—
314C4×C8C2×C3×D311yescharacteristic
315C23×C3—22no—
316C23×C3—22no—
317C23×C3—42no—
318C3×Q8—32no—
319C3×Q8—42no—
320C3×Q8—42no—
321C3×Q8—62no—
322C3×Q8—61no—
323C3×Q8—61no—
324C3×Q8—61no—
325C3×Q8—82no—
326C3×D4—22no—
327C3×D4—22no—
328C3×D4—22no—
329C3×D4—22no—
330C3×D4—42no—
331C3×D4—42no—
332C3×D4—42no—
333C3×D4—42no—
334C3×D4—82no—
335C3×D4—81no—
336C3×D4—81no—
337C3×D4—82no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—32no—
344C2×C3×C4—32no—
345C2×C3×C4—42no—
346C2×C3×C4—61no—
347C2×C3×C4—61no—
348C2×C3×C4—61no—
349C2×C3×C4—61no—
350C2×C3×C4—242no—
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4C2×C3×D411yescharacteristic
354C2×C3×C4C2×C3×D411yescharacteristic
355C2×C3×C4C23×D311yescharacteristic
356C2×C3×C4C24×C311yescharacteristic
357C2×Dic3—21no—
358C2×Dic3—21no—
359C2×Dic3—21no—
360C2×Dic3—21no—
361C2×Dic3—82no—
362C2×Dic3C2×C3×D412yes—
363C2×Dic3C2×C3×D412yes—
364Dic6—22no—
365Dic6—21no—
366Dic6—21no—
367Dic6—21no—
368Dic6C3×#4112yes—
369C3×C8—21no—
370C3×C8—21no—
371C3×C8—21no—
372C3×C8—21no—
373C3×C8—41no—
374C3×C8—41no—
375C3×C8—62no—
376C3⋊C8—22no—
377C2×C32—82no—
378C2×C32#54811yescharacteristic
379C2×C32C2×#13511yescharacteristic
380C2×C32#57711yescharacteristic
381C2×Q8—21no—
382C2×Q8—31no—
383C2×Q8—31no—
384C2×Q8—31no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4C22×C3×D312yes—
388C22×C4—62no—
389Q16—62no—
390SD16—64no—
391C2×C8—32no—
392C2×C8C22×C3×D311yescharacteristic
393C2×C8C22×C3×D311yescharacteristic
394C4⋊C4—21no—
395C4⋊C4—31no—
396C4⋊C4—32no—
397C4⋊C4—31no—
398C4⋊C4—31no—
399C4⋊C4—62no—
400C4⋊C4—62no—
401C4⋊C4—62no—
402C4⋊C4—61no—
403C4⋊C4—61no—
404C4⋊C4C22×C3×D312yes—
405C22⋊C4—62no—
406C22⋊C4—62no—
407C22⋊C4—62no—
408C42—32no—
409C42—62no—
410C42—61no—
411C42—61no—
412C42C22×C3×D311yescharacteristic
413C22×C3—21no—
414C22×C3—42no—
415C22×C3—42no—
416C22×C3—42no—
417C22×C3—42no—
418C22×C3—42no—
419C22×C3—42no—
420C22×C3—82no—
421C22×C3—82no—
422C22×C3—82no—
423C22×C3C2×D3×D411yescharacteristic
424C22×C3C22×C3×D411yescharacteristic
425C3×C4—22no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—22no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—42no—
432C3×C4—42no—
433C3×C4—62no—
434C3×C4—62no—
435C3×C4—62no—
436C3×C4—82no—
437C3×C4—121no—
438C3×C4—121no—
439C3×C4—121no—
440C3×C4#91212yes—
441C3×C4C3×#13512yes—
442C3×C4D3×#4111yescharacteristic
443C3×C4#101011yescharacteristic
444C3×C4C2×C3×#4111yescharacteristic
445C3×C4C3×2−1+411yescharacteristic
446Dic3—22no—
447Dic3—22no—
448Dic3—22no—
449Dic3—41no—
450Dic3—41no—
451Dic3—41no—
452C32#336511yescharacteristic, complemented, Sylow
453C23—22no—
454Q8—32no—
455Q8—42no—
456Q8—62no—
457Q8—61no—
458Q8—61no—
459Q8—61no—
460D4—22no—
461D4—22no—
462D4—42no—
463D4—81no—
464C2×C4—22no—
465C2×C4—32no—
466C2×C4—32no—
467C2×C4—61no—
468C2×C4—61no—
469C2×C4—61no—
470C2×C4—61no—
471C2×C4—242no—
472C2×C4C3×D3×D411yescharacteristic
473C2×C4C3×D3×D411yescharacteristic
474C2×C4C23×C3×D311yescharacteristic
475C8—21no—
476C8—21no—
477C8—62no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—82no—
482C2×C3—82no—
483C2×C3—162no—
484C2×C3#567711yescharacteristic
485C2×C3C2×#91211yescharacteristic
486C2×C3#576211yescharacteristic
487C2×C3C3×#54811yescharacteristic
488C2×C3C2×C3×#13511yescharacteristic
489C2×C3C3×#57711yescharacteristic
490C22—42no—
491C22—42no—
492C22—42no—
493C22C2×C3×D3×D411yescharacteristic
494C4—21no—
495C4—42no—
496C4—62no—
497C4—62no—
498C4—62no—
499C4—121no—
500C4—121no—
501C4—121no—
502C4C3×#91212yes—
503C4C3×D3×#4111yescharacteristic
504C4C3×#101011yescharacteristic
505C3—21no—
506C3#8158911yescharacteristic, direct product factor
507C3C3×#336511yescharacteristic, complemented
508C2—82no—
509C2C3×#567711yescharacteristic
510C2C2×C3×#91211yescharacteristic
511C2C3×#576211yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#486C2
socleC22×C32C22×D4
prime radicalC32×#127C22
hypercenterC3×#486D3
hypocenterC3C3×#3365
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×#5721C2semidirect
4. C3×#5094C2semidirect
6. C3×#4768C2semidirect
7. C3×#4767C2semidirect
8. C3×#4766C2semidirect
9. C3×#4758C2semidirect
10. C3×C4×Dic12C2semidirect
11. C3×C8×Dic6C2semidirect
13. #81589C3direct (N × H)
45. #5721C2×C3semidirect
58. #5094C2×C3semidirect
60. #4768C2×C3semidirect
61. #4767C2×C3semidirect
62. #4766C2×C3semidirect
63. #4758C2×C3semidirect
64. C4×Dic12C2×C3semidirect
65. C8×Dic6C2×C3semidirect
452. C32#3365semidirect
506. C3#81589direct (N × H)
507. C3C3×#3365semidirect

Maximal subgroups

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

subgroupindex
C3×#57212
C3×#57132
C32×#4862
C3×#50942
C3×#50752
C3×#47682
C3×#47672
C3×#47662
C3×#47582
C3×C4×Dic122
C3×C8×Dic62
C3×#33653
#815893