Finite Group Databasebeta

← C3×#81041 #11895619

Subgroups — C3×#81041 #11895619

Order 1152.

744 conjugacy classes of subgroups.

The subgroup lattice has 509 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5721C211yesmaximal, characteristic, complemented
2C3×#5585C211yesmaximal, characteristic
3C32×#475C211yesmaximal, characteristic, complemented
4C3×#5088C211yesmaximal, characteristic
5C3×C4×#216C211yesmaximal, characteristic, complemented
6C3×#4871C212yesmaximal, complemented
7C3×#4852C212yesmaximal, complemented
8C3×#4848C211yesmaximal, characteristic
9C3×#4830C211yesmaximal, characteristic, complemented
10C3×#4800C212yesmaximal, complemented
11C3×#4798C212yesmaximal, complemented
12C3×#3365—31nomaximal
13#81041C311yesmaximal, characteristic, direct product factor
14C32×C4⋊Q8C2211yescharacteristic
15C32×C4×Q8C2211yescharacteristic
16C3×#947C2212yes—
17C3×Q8×Dic3—21no—
18C3×#944—21no—
19C2×C3×#216C2211yescharacteristic
20C2×C3×#204C2212yes—
21C3×#894—22no—
22C3×#893C2212yes—
23C3×#890C2212yes—
24C3×#889—22no—
25C3×#887C2212yes—
26C3×#875—21no—
27C3×#874C2211yescharacteristic
28C3×C4×D12—21no—
29C3×C4×Dic6C2211yescharacteristic
30C3×C4×Dic6C2211yescharacteristic
31C32×#106C2212yes—
32C32×C4⋊C8C2211yescharacteristic
33C32×#103C2212yes—
34C3×#835C2211yescharacteristic
35C3×#821C2212yes—
36C3×Dic3⋊C8C2212yes—
37C3×C8×Dic3C2212yes—
38C3×#810C2211yescharacteristic
39C3×#809C2212yes—
40C3×#809C2212yes—
41C3×#807C2211yescharacteristic
42C3×C4×C3⋊C8C2211yescharacteristic
43C3×#559—31no—
44C3×#557—31no—
45#5721C2×C311yescharacteristic, complemented
46#5585C2×C311yescharacteristic
47C3×#488—32no—
48C3×#486—31no—
49C3×#478—32no—
50C3×#475—21no—
51C3×#475D311yescharacteristic, complemented
52C3×#475C2×C311yescharacteristic, complemented
53C3×#464—32no—
54C3×#460—31no—
55C3×C8×Q8—31no—
56C3×C4×Q16—31no—
57C3×C4×SD16—32no—
58#5088C2×C311yescharacteristic
59C4×#216C2×C311yescharacteristic, complemented
60#4871C2×C312yescomplemented
61#4852C2×C312yescomplemented
62#4848C2×C311yescharacteristic
63#4830C2×C311yescharacteristic, complemented
64#4800C2×C312yescomplemented
65#4798C2×C312yescomplemented
66C2×C32×Q8—21no—
67C2×C32×Q8C2311yescharacteristic
68C2×C3×D12—21no—
69C2×C3×D12—21no—
70C2×C3×D12C2312yes—
71C2×C3×C4×D3—22no—
72C2×C3×Dic6D411yescharacteristic
73C2×C3×Dic6C2311yescharacteristic
74C2×C32×C8C2312yes—
75C32×C4⋊C4—21no—
76C32×C4⋊C4—21no—
77C32×C4⋊C4C2312yes—
78C32×C4⋊C4C2311yescharacteristic
79C32×C42—21no—
80C32×C42C2311yescharacteristic
81C3×#216—22no—
82C3×(C2×D3)⋊C4—22no—
83C3×(C2×D3)⋊C4—22no—
84C3×(C2×D3)⋊C4—22no—
85C3×C4⋊Dic3—22no—
86C3×C4⋊Dic3D411yescharacteristic
87C3×C4⋊Dic3C2311yescharacteristic
88C3×Dic3⋊C4—21no—
89C3×Dic3⋊C4—22no—
90C3×Dic3⋊C4—22no—
91C3×Dic3⋊C4D412yes—
92C3×C4×Dic3—21no—
93C3×C4×Dic3—22no—
94C3×C4×Dic3C2312yes—
95C2×C3×C3⋊C8C2311yescharacteristic
96C2×C3×C3⋊C8C2311yescharacteristic
97C3×#204—24no—
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—31no—
106C3×#125—32no—
107C3×#125—62no—
108C3×#124—32no—
109C3×#124—61no—
110C3×#123—62no—
111C3×C4×Q8—21no—
112C3×C4×Q8—31no—
113C3×C4×Q8—32no—
114C3×C4×Q8—31no—
115C3×C4×Q8—61no—
116C3×C4×Q8C2×D311yescharacteristic
117C3×C4×Q8C22×C311yescharacteristic
118C3×C4×D4—32no—
119C3×C4×D4—61no—
120#947C22×C312yes—
121Q8×Dic3—21no—
122#944—21no—
123C2×#216C22×C311yescharacteristic
124C2×#204C22×C312yes—
125#894—22no—
126#893C22×C312yes—
127#890C22×C312yes—
128#889—22no—
129#887C22×C312yes—
130#875—21no—
131#874C22×C311yescharacteristic
132C4×D12—21no—
133C4×Dic6C22×C311yescharacteristic
134C4×Dic6C22×C311yescharacteristic
135C3×#107—31no—
136C3×#106—22no—
137C3×#106C2×D312yes—
138C3×#106C22×C312yes—
139C3×C4⋊C8—21no—
140C3×C4⋊C8—32no—
141C3×C4⋊C8C2×D311yescharacteristic
142C3×C4⋊C8C22×C311yescharacteristic
143C3×#103—22no—
144C3×#103—31no—
145C3×#103—31no—
146C3×#103C2×D312yes—
147C3×#103C22×C312yes—
148C3×#102—32no—
149C3×#102—32no—
150C3×#102—32no—
151C3×C4×C8—32no—
152C3×C4×C8—31no—
153#835C22×C311yescharacteristic
154#821C22×C312yes—
155Dic3⋊C8C22×C312yes—
156C8×Dic3C22×C312yes—
157#810C22×C311yescharacteristic
158#809C22×C312yes—
159#809C22×C312yes—
160#807C22×C311yescharacteristic
161C4×C3⋊C8C22×C311yescharacteristic
162C22×C3×D3—22no—
163C32×Q8—21no—
164C32×Q8—21no—
165C32×Q8—42no—
166C2×C32×C4—22no—
167C2×C32×C4—21no—
168C2×C32×C4—21no—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2411yescharacteristic
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3C2×D412yes—
175C2×C3×Dic3C2×D412yes—
176C3×D12—22no—
177C3×D12—22no—
178C3×D12—42no—
179C3×D12—81no—
180C3×C4×D3—82no—
181C3×Dic6—22no—
182C3×Dic6—21no—
183C3×Dic6#4112yes—
184C32×C8—22no—
185C3×C3⋊C8—21no—
186C3×C3⋊C8—21no—
187#559—31no—
188#557—31no—
189#488—32no—
190#486—31no—
191#478—32no—
192#475C3×D311yescharacteristic, complemented
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—21no—
201C2×C3×Q8—31no—
202C2×C3×Q8—31no—
203C2×C3×Q8—41no—
204C2×C3×Q8C22×D311yescharacteristic
205C2×C3×Q8C23×C311yescharacteristic
206C2×C3×D4—32no—
207C2×C3×D4—61no—
208C2×C3×D4—61no—
209C22×C3×C4—62no—
210C2×D12—21no—
211C2×D12—21no—
212C2×D12C23×C312yes—
213C2×C4×D3—22no—
214C2×Dic6C3×D411yescharacteristic
215C2×Dic6C23×C311yescharacteristic
216C3×Q16—62no—
217C3×SD16—64no—
218C2×C3×C8—22no—
219C2×C3×C8—31no—
220C2×C3×C8—31no—
221C2×C3×C8C22×D312yes—
222C2×C3×C8C23×C312yes—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—22no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—32no—
230C3×C4⋊C4—31no—
231C3×C4⋊C4—31no—
232C3×C4⋊C4—41no—
233C3×C4⋊C4—41no—
234C3×C4⋊C4—62no—
235C3×C4⋊C4—62no—
236C3×C4⋊C4—62no—
237C3×C4⋊C4—61no—
238C3×C4⋊C4C22×D312yes—
239C3×C4⋊C4C22×D311yescharacteristic
240C3×C4⋊C4C23×C311yescharacteristic
241C3×C4⋊C4C23×C312yes—
242C3×C22⋊C4—62no—
243C3×C22⋊C4—62no—
244C3×C22⋊C4—62no—
245C3×C42—21no—
246C3×C42—21no—
247C3×C42—21no—
248C3×C42—32no—
249C3×C42—41no—
250C3×C42—62no—
251C3×C42—61no—
252C3×C42C22×D311yescharacteristic
253C3×C42C23×C311yescharacteristic
254#216—22no—
255(C2×D3)⋊C4—22no—
256(C2×D3)⋊C4—22no—
257(C2×D3)⋊C4—22no—
258C4⋊Dic3—22no—
259C4⋊Dic3C3×D411yescharacteristic
260C4⋊Dic3C23×C311yescharacteristic
261Dic3⋊C4—21no—
262Dic3⋊C4—22no—
263Dic3⋊C4—22no—
264Dic3⋊C4C3×D412yes—
265C4×Dic3—21no—
266C4×Dic3—22no—
267C4×Dic3C23×C312yes—
268C2×C3⋊C8C23×C311yescharacteristic
269C2×C3⋊C8C23×C311yescharacteristic
270#204—24no—
271C22×C32C22×D411yescharacteristic
272C2×C3×D3—42no—
273C2×C3×D3—42no—
274C2×C3×D3—42no—
275C32×C4—21no—
276C32×C4—41no—
277C32×C4—42no—
278C32×C4—41no—
279C32×C4#13512yes—
280C32×C4C2×#4111yescharacteristic
281C32×C42−1+411yescharacteristic
282C3×Dic3—22no—
283C3×Dic3—22no—
284C3×Dic3—22no—
285C3×Dic3—41no—
286C2×Q16—31no—
287C2×SD16—32no—
288C4⋊Q8—61no—
289C4⋊Q8C2×C3×D311yescharacteristic
290#127—31no—
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—61no—
300C4×Q8C2×C3×D311yescharacteristic
301C4×D4—32no—
302C4×D4—61no—
303#107—31no—
304#106C2×C3×D312yes—
305C4⋊C8—32no—
306C4⋊C8C2×C3×D311yescharacteristic
307#103—31no—
308#103—31no—
309#103C2×C3×D312yes—
310#102—32no—
311#102—32no—
312#102—32no—
313C4×C8—32no—
314C4×C8—31no—
315C23×C3—62no—
316C22×D3—22no—
317C3×Q8—22no—
318C3×Q8—21no—
319C3×Q8—21no—
320C3×Q8—21no—
321C3×Q8—21no—
322C3×Q8—32no—
323C3×Q8—41no—
324C3×Q8—42no—
325C3×Q8—42no—
326C3×Q8—62no—
327C3×Q8—61no—
328C3×Q8—82no—
329C3×D4—62no—
330C3×D4—62no—
331C3×D4—122no—
332C3×D4—241no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—32no—
343C2×C3×C4—32no—
344C2×C3×C4—41no—
345C2×C3×C4—41no—
346C2×C3×C4—42no—
347C2×C3×C4—61no—
348C2×C3×C4—61no—
349C2×C3×C4—242no—
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4C2×C3×D411yescharacteristic
353C2×C3×C4C2×C3×D411yescharacteristic
354C2×C3×C4C23×D311yescharacteristic
355C2×C3×C4C24×C311yescharacteristic
356C2×Dic3—21no—
357C2×Dic3—21no—
358C2×Dic3C2×C3×D412yes—
359C2×Dic3C2×C3×D412yes—
360D12—22no—
361D12—22no—
362D12—42no—
363D12—81no—
364C4×D3—82no—
365Dic6—22no—
366Dic6—21no—
367Dic6C3×#4112yes—
368C3×C8—22no—
369C3×C8—22no—
370C3×C8—42no—
371C3×C8—61no—
372C3×C8—61no—
373C3⋊C8—21no—
374C3⋊C8—21no—
375C2×C32#54811yescharacteristic
376C2×C32C2×#13511yescharacteristic
377C2×C32#57711yescharacteristic
378C3×D3—82no—
379C2×Q8—21no—
380C2×Q8—31no—
381C2×Q8—31no—
382C2×Q8C22×C3×D311yescharacteristic
383C2×D4—32no—
384C2×D4—61no—
385C2×D4—61no—
386C22×C4—62no—
387Q16—62no—
388SD16—64no—
389C2×C8—31no—
390C2×C8—31no—
391C2×C8C22×C3×D312yes—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—31no—
395C4⋊C4—32no—
396C4⋊C4—31no—
397C4⋊C4—62no—
398C4⋊C4—62no—
399C4⋊C4—62no—
400C4⋊C4—61no—
401C4⋊C4C22×C3×D312yes—
402C4⋊C4C22×C3×D311yescharacteristic
403C22⋊C4—62no—
404C22⋊C4—62no—
405C22⋊C4—62no—
406C42—21no—
407C42—32no—
408C42—62no—
409C42—61no—
410C42C22×C3×D311yescharacteristic
411C22×C3—21no—
412C22×C3—122no—
413C22×C3—122no—
414C22×C3—122no—
415C22×C3C2×D3×D411yescharacteristic
416C22×C3C22×C3×D411yescharacteristic
417C2×D3—42no—
418C2×D3—42no—
419C2×D3—42no—
420C3×C4—21no—
421C3×C4—21no—
422C3×C4—22no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—41no—
426C3×C4—42no—
427C3×C4—41no—
428C3×C4—42no—
429C3×C4—41no—
430C3×C4—42no—
431C3×C4—41no—
432C3×C4—41no—
433C3×C4—62no—
434C3×C4—62no—
435C3×C4—62no—
436C3×C4—82no—
437C3×C4—81no—
438C3×C4—121no—
439C3×C4#91612yes—
440C3×C4C3×#13512yes—
441C3×C4#100711yescharacteristic
442C3×C4D3×#4111yescharacteristic
443C3×C4C2×C3×#4111yescharacteristic
444C3×C4C3×2−1+411yescharacteristic
445Dic3—22no—
446Dic3—22no—
447Dic3—22no—
448Dic3—41no—
449C32#336511yescharacteristic, complemented, Sylow
450C23—62no—
451Q8—21no—
452Q8—21no—
453Q8—32no—
454Q8—42no—
455Q8—62no—
456Q8—61no—
457D4—62no—
458D4—62no—
459D4—122no—
460D4—241no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—22no—
464C2×C4—32no—
465C2×C4—32no—
466C2×C4—61no—
467C2×C4—61no—
468C2×C4—242no—
469C2×C4C3×D3×D411yescharacteristic
470C2×C4C3×D3×D411yescharacteristic
471C2×C4C23×C3×D311yescharacteristic
472C8—22no—
473C8—61no—
474C8—61no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—242no—
479C2×C3#563311yescharacteristic
480C2×C3C2×#91611yescharacteristic
481C2×C3#577811yescharacteristic
482C2×C3C3×#54811yescharacteristic
483C2×C3C2×C3×#13511yescharacteristic
484C2×C3C3×#57711yescharacteristic
485D3—82no—
486C22—122no—
487C22—122no—
488C22—122no—
489C22C2×C3×D3×D411yescharacteristic
490C4—21no—
491C4—42no—
492C4—41no—
493C4—41no—
494C4—62no—
495C4—62no—
496C4—62no—
497C4—121no—
498C4C3×#91612yes—
499C4C3×#100711yescharacteristic
500C4C3×D3×#4111yescharacteristic
501C3—21no—
502C3#8104111yescharacteristic, direct product factor
503C3C3×#336511yescharacteristic, complemented
504C2—242no—
505C2C3×#563311yescharacteristic
506C2C2×C3×#91611yescharacteristic
507C2C3×#577811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#475C2
socleC22×C32C22×D4
prime radicalC3×#874C22
hypercenterC3×#475D3
hypocenterC3C3×#3365
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#475

Complements

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

NH ≅ G/Ntype
1. C3×#5721C2semidirect
3. C32×#475C2semidirect
5. C3×C4×#216C2semidirect
6. C3×#4871C2semidirect
7. C3×#4852C2semidirect
9. C3×#4830C2semidirect
10. C3×#4800C2semidirect
11. C3×#4798C2semidirect
13. #81041C3direct (N × H)
45. #5721C2×C3semidirect
51. C3×#475D3semidirect
52. C3×#475C2×C3semidirect
59. C4×#216C2×C3semidirect
60. #4871C2×C3semidirect
61. #4852C2×C3semidirect
63. #4830C2×C3semidirect
64. #4800C2×C3semidirect
65. #4798C2×C3semidirect
192. #475C3×D3semidirect
449. C32#3365semidirect
502. C3#81041direct (N × H)
503. 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×#55852
C32×#4752
C3×#50882
C3×C4×#2162
C3×#48712
C3×#48522
C3×#48482
C3×#48302
C3×#48002
C3×#47982
C3×#33653
#810413