Finite Group Databasebeta

← C3×#81134 #11895308

Subgroups — C3×#81134 #11895308

Order 1152.

772 conjugacy classes of subgroups.

The subgroup lattice has 529 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5730C211yesmaximal, characteristic, complemented
2C3×#5585C211yesmaximal, characteristic, complemented
3C32×#477C211yesmaximal, characteristic, complemented
4C3×#5088C211yesmaximal, characteristic, complemented
5C3×C4×#215C211yesmaximal, characteristic, complemented
6C3×#4891C212yesmaximal, complemented
7C3×#4872C212yesmaximal, complemented
8C3×#4843C211yesmaximal, characteristic
9C3×#4830C211yesmaximal, characteristic, complemented
10C3×#4819C212yesmaximal, complemented
11C3×#4800C212yesmaximal, complemented
12C3×#3361—31nomaximal
13#81134C311yesmaximal, characteristic, direct product factor
14C32×C4⋊Q8C2211yescharacteristic
15C32×C4×Q8C2211yescharacteristic
16C3×#947C2212yes—
17C3×#946—22no—
18C2×C3×#215C2211yescharacteristic
19C2×C3×D24C2212yes—
20C3×#897—21no—
21C3×#894—22no—
22C3×#893C2212yes—
23C3×#893C2212yes—
24C3×D3×C4⋊C4—21no—
25C3×#890C2212yes—
26C3×#875—21no—
27C3×#874C2211yescharacteristic
28C3×C4×D12—21no—
29C3×C4×D12C2211yescharacteristic
30C3×C4×Dic6C2211yescharacteristic
31C32×#107C2212yes—
32C32×C4⋊C8C2211yescharacteristic
33C32×#103C2212yes—
34C3×#835C2211yescharacteristic
35C3×#821C2212yes—
36C3×Dic3⋊C8C2212yes—
37C3×C8×Dic3C2212yes—
38C3×#809C2211yescharacteristic
39C3×#809C2212yes—
40C3×#809C2212yes—
41C3×#808C2211yescharacteristic
42C3×C4×C3⋊C8C2211yescharacteristic
43C3×#559—31no—
44C3×#554—31no—
45#5730C2×C311yescharacteristic, complemented
46#5585C2×C311yescharacteristic, complemented
47C3×#488—32no—
48C3×#486—31no—
49C3×#478—32no—
50C3×#477—21no—
51C3×#477D311yescharacteristic, complemented
52C3×#477C2×C311yescharacteristic, complemented
53C3×#463—32no—
54C3×#459—31no—
55C3×C8×Q8—31no—
56C3×C4×SD16—31no—
57C3×C4×D8—32no—
58#5088C2×C311yescharacteristic, complemented
59C4×#215C2×C311yescharacteristic, complemented
60#4891C2×C312yescomplemented
61#4872C2×C312yescomplemented
62#4843C2×C311yescharacteristic
63#4830C2×C311yescharacteristic, complemented
64#4819C2×C312yescomplemented
65#4800C2×C312yescomplemented
66C2×C32×Q8—21no—
67C2×C32×Q8C2311yescharacteristic
68C2×C3×D12—21no—
69C2×C3×D12—21no—
70C2×C3×D12C2312yes—
71C2×C3×D12C2311yescharacteristic
72C2×C3×C4×D3—21no—
73C2×C3×C4×D3—22no—
74C2×C3×C4×D3—22no—
75C2×C3×Dic6D411yescharacteristic
76C2×C32×C8C2312yes—
77C32×C4⋊C4—21no—
78C32×C4⋊C4—21no—
79C32×C4⋊C4C2312yes—
80C32×C4⋊C4C2311yescharacteristic
81C32×C42—21no—
82C32×C42C2311yescharacteristic
83C3×#215—22no—
84C3×(C2×D3)⋊C4—21no—
85C3×(C2×D3)⋊C4—22no—
86C3×(C2×D3)⋊C4—22no—
87C3×(C2×D3)⋊C4—22no—
88C3×(C2×D3)⋊C4—22no—
89C3×C4⋊Dic3—22no—
90C3×C4⋊Dic3D411yescharacteristic
91C3×C4⋊Dic3C2311yescharacteristic
92C3×Dic3⋊C4—22no—
93C3×Dic3⋊C4D412yes—
94C3×C4×Dic3C2312yes—
95C2×C3×C3⋊C8C2311yescharacteristic
96C2×C3×C3⋊C8C2311yescharacteristic
97C3×D24—24no—
98#3361—31noSylow
99C2×C3×SD16—31no—
100C2×C3×D8—32no—
101C3×C4⋊Q8—21no—
102C3×C4⋊Q8C2×D311yescharacteristic
103C3×C4⋊Q8C22×C311yescharacteristic
104C3×#127—31no—
105C3×#125—32no—
106C3×#124—32no—
107C3×#124—61no—
108C3×#123—62no—
109C3×C22⋊Q8—61no—
110C3×C22⋊Q8—62no—
111C3×C4×Q8—21no—
112C3×C4×Q8—31no—
113C3×C4×Q8C2×D311yescharacteristic
114C3×C4×Q8C22×C311yescharacteristic
115C3×C4×D4—32no—
116C3×C4×D4—32no—
117C3×C4×D4—31no—
118C3×C4×D4—61no—
119C2×C3×C4⋊C4—61no—
120#947C22×C312yes—
121#946—22no—
122C2×#215C22×C311yescharacteristic
123C2×D24C22×C312yes—
124#897—21no—
125#894—22no—
126#893C22×C312yes—
127#893C22×C312yes—
128D3×C4⋊C4—21no—
129#890C22×C312yes—
130#875—21no—
131#874C22×C311yescharacteristic
132C4×D12—21no—
133C4×D12C22×C311yescharacteristic
134C4×Dic6C22×C311yescharacteristic
135C3×#107—22no—
136C3×#107C2×D312yes—
137C3×#107C22×C312yes—
138C3×#106—31no—
139C3×C4⋊C8—21no—
140C3×C4⋊C8—32no—
141C3×C4⋊C8C2×D311yescharacteristic
142C3×C4⋊C8C22×C311yescharacteristic
143C3×#103—22no—
144C3×#103—31no—
145C3×#103C2×D312yes—
146C3×#103C22×C312yes—
147C3×#102—32no—
148C3×#102—31no—
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#809C22×C311yescharacteristic
158#809C22×C312yes—
159#809C22×C312yes—
160#808C22×C311yescharacteristic
161C4×C3⋊C8C22×C311yescharacteristic
162C22×C3×D3—21no—
163C22×C3×D3—22no—
164C32×Q8—21no—
165C32×Q8—21no—
166C32×Q8—81no—
167C2×C32×C4—22no—
168C2×C32×C4—21no—
169C2×C32×C4—21no—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2411yescharacteristic
173C2×C3×Dic3—21no—
174C2×C3×Dic3C2×D412yes—
175C2×C3×Dic3C2×D412yes—
176C3×D12—22no—
177C3×D12—21no—
178C3×D12—22no—
179C3×D12—42no—
180C3×D12—81no—
181C3×D12#4112yes—
182C3×C4×D3—42no—
183C3×C4×D3—82no—
184C3×C4×D3—82no—
185C3×Dic6—22no—
186C32×C8—22no—
187C3×C3⋊C8—21no—
188C3×C3⋊C8—21no—
189#559—31no—
190#554—31no—
191#488—32no—
192#486—31no—
193#478—32no—
194#477C3×D311yescharacteristic, complemented
195#463—32no—
196#459—31no—
197C8×Q8—31no—
198C4×SD16—31no—
199C4×D8—32no—
200C2×C3×Q8—21no—
201C2×C3×Q8—21no—
202C2×C3×Q8—21no—
203C2×C3×Q8—31no—
204C2×C3×Q8—41no—
205C2×C3×Q8C22×D311yescharacteristic
206C2×C3×Q8C23×C311yescharacteristic
207C2×C3×D4—31no—
208C2×C3×D4—32no—
209C2×C3×D4—61no—
210C2×C3×D4—61no—
211C22×C3×C4—62no—
212C22×C3×C4—62no—
213C22×C3×C4—61no—
214C2×D12—21no—
215C2×D12—21no—
216C2×D12C23×C312yes—
217C2×D12C23×C311yescharacteristic
218C2×C4×D3—21no—
219C2×C4×D3—22no—
220C2×C4×D3—22no—
221C2×Dic6C3×D411yescharacteristic
222C3×SD16—62no—
223C3×D8—64no—
224C2×C3×C8—22no—
225C2×C3×C8—31no—
226C2×C3×C8—31no—
227C2×C3×C8C22×D312yes—
228C2×C3×C8C23×C312yes—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—22no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—32no—
236C3×C4⋊C4—31no—
237C3×C4⋊C4—31no—
238C3×C4⋊C4—41no—
239C3×C4⋊C4—41no—
240C3×C4⋊C4—62no—
241C3×C4⋊C4—62no—
242C3×C4⋊C4C22×D312yes—
243C3×C4⋊C4C22×D311yescharacteristic
244C3×C4⋊C4C23×C311yescharacteristic
245C3×C4⋊C4C23×C312yes—
246C3×C22⋊C4—62no—
247C3×C22⋊C4—62no—
248C3×C22⋊C4—62no—
249C3×C22⋊C4—62no—
250C3×C22⋊C4—61no—
251C3×C42—21no—
252C3×C42—21no—
253C3×C42—21no—
254C3×C42—32no—
255C3×C42—41no—
256C3×C42C22×D311yescharacteristic
257C3×C42C23×C311yescharacteristic
258#215—22no—
259(C2×D3)⋊C4—21no—
260(C2×D3)⋊C4—22no—
261(C2×D3)⋊C4—22no—
262(C2×D3)⋊C4—22no—
263(C2×D3)⋊C4—22no—
264C4⋊Dic3—22no—
265C4⋊Dic3C3×D411yescharacteristic
266C4⋊Dic3C23×C311yescharacteristic
267Dic3⋊C4—22no—
268Dic3⋊C4C3×D412yes—
269C4×Dic3C23×C312yes—
270C2×C3⋊C8C23×C311yescharacteristic
271C2×C3⋊C8C23×C311yescharacteristic
272D24—24no—
273C22×C32C22×D411yescharacteristic
274C2×C3×D3—22no—
275C2×C3×D3—41no—
276C2×C3×D3—41no—
277C2×C3×D3—42no—
278C2×C3×D3—42no—
279C2×C3×D3—42no—
280C32×C4—21no—
281C32×C4—41no—
282C32×C4—41no—
283C32×C4—42no—
284C32×C4#13512yes—
285C32×C4C2×#4111yescharacteristic
286C32×C42−1+411yescharacteristic
287C3×Dic3—22no—
288C3×Dic3—22no—
289C3×Dic3—41no—
290C2×SD16—31no—
291C2×D8—32no—
292C4⋊Q8C2×C3×D311yescharacteristic
293#127—31no—
294#125—32no—
295#124—32no—
296#124—61no—
297#123—62no—
298C22⋊Q8—61no—
299C22⋊Q8—62no—
300C4×Q8—31no—
301C4×Q8C2×C3×D311yescharacteristic
302C4×D4—32no—
303C4×D4—32no—
304C4×D4—31no—
305C4×D4—61no—
306C2×C4⋊C4—61no—
307#107C2×C3×D312yes—
308#106—31no—
309C4⋊C8—32no—
310C4⋊C8C2×C3×D311yescharacteristic
311#103—31no—
312#103C2×C3×D312yes—
313#102—32no—
314#102—31no—
315#102—32no—
316#102—32no—
317C4×C8—32no—
318C4×C8—31no—
319C23×C3—61no—
320C23×C3—62no—
321C22×D3—21no—
322C22×D3—22no—
323C3×Q8—22no—
324C3×Q8—21no—
325C3×Q8—21no—
326C3×Q8—21no—
327C3×Q8—21no—
328C3×Q8—41no—
329C3×Q8—62no—
330C3×Q8—81no—
331C3×Q8—81no—
332C3×Q8—82no—
333C3×D4—32no—
334C3×D4—61no—
335C3×D4—62no—
336C3×D4—62no—
337C3×D4—122no—
338C3×D4—241no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—32no—
349C2×C3×C4—32no—
350C2×C3×C4—41no—
351C2×C3×C4—41no—
352C2×C3×C4—42no—
353C2×C3×C4—61no—
354C2×C3×C4—122no—
355C2×C3×C4—242no—
356C2×C3×C4—242no—
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4C2×C3×D411yescharacteristic
360C2×C3×C4C2×C3×D411yescharacteristic
361C2×C3×C4C23×D311yescharacteristic
362C2×C3×C4C24×C311yescharacteristic
363C2×Dic3—21no—
364C2×Dic3C2×C3×D412yes—
365C2×Dic3C2×C3×D412yes—
366D12—22no—
367D12—21no—
368D12—22no—
369D12—42no—
370D12—81no—
371D12C3×#4112yes—
372C4×D3—42no—
373C4×D3—82no—
374C4×D3—82no—
375Dic6—22no—
376C3×C8—22no—
377C3×C8—22no—
378C3×C8—42no—
379C3×C8—61no—
380C3×C8—61no—
381C3⋊C8—21no—
382C3⋊C8—21no—
383C2×C32#54811yescharacteristic
384C2×C32C2×#13511yescharacteristic
385C2×C32#57611yescharacteristic
386C3×D3—42no—
387C3×D3—82no—
388C2×Q8—21no—
389C2×Q8—31no—
390C2×Q8C22×C3×D311yescharacteristic
391C2×D4—31no—
392C2×D4—32no—
393C2×D4—61no—
394C2×D4—61no—
395C22×C4—62no—
396C22×C4—62no—
397C22×C4—61no—
398SD16—62no—
399D8—64no—
400C2×C8—31no—
401C2×C8—31no—
402C2×C8C22×C3×D312yes—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—31no—
406C4⋊C4—32no—
407C4⋊C4—31no—
408C4⋊C4—62no—
409C4⋊C4—62no—
410C4⋊C4C22×C3×D312yes—
411C4⋊C4C22×C3×D311yescharacteristic
412C22⋊C4—62no—
413C22⋊C4—62no—
414C22⋊C4—62no—
415C22⋊C4—62no—
416C22⋊C4—61no—
417C42—21no—
418C42—32no—
419C42C22×C3×D311yescharacteristic
420C22×C3—21no—
421C22×C3—62no—
422C22×C3—121no—
423C22×C3—121no—
424C22×C3—122no—
425C22×C3—122no—
426C22×C3—122no—
427C22×C3C2×D3×D411yescharacteristic
428C22×C3C22×C3×D411yescharacteristic
429C2×D3—22no—
430C2×D3—41no—
431C2×D3—41no—
432C2×D3—42no—
433C2×D3—42no—
434C2×D3—42no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—22no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—41no—
441C3×C4—42no—
442C3×C4—41no—
443C3×C4—41no—
444C3×C4—42no—
445C3×C4—41no—
446C3×C4—42no—
447C3×C4—41no—
448C3×C4—62no—
449C3×C4—62no—
450C3×C4—82no—
451C3×C4—81no—
452C3×C4—121no—
453C3×C4#91912yes—
454C3×C4C3×#13512yes—
455C3×C4#100711yescharacteristic
456C3×C4D3×#4111yescharacteristic
457C3×C4C2×C3×#4111yescharacteristic
458C3×C4C3×2−1+411yescharacteristic
459Dic3—22no—
460Dic3—22no—
461Dic3—41no—
462C32#336111yescharacteristic, complemented, Sylow
463C23—61no—
464C23—62no—
465Q8—21no—
466Q8—21no—
467Q8—62no—
468Q8—81no—
469D4—32no—
470D4—61no—
471D4—62no—
472D4—62no—
473D4—122no—
474D4—241no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—22no—
478C2×C4—32no—
479C2×C4—32no—
480C2×C4—61no—
481C2×C4—122no—
482C2×C4—242no—
483C2×C4—242no—
484C2×C4C3×D3×D411yescharacteristic
485C2×C4C3×D3×D411yescharacteristic
486C2×C4C23×C3×D311yescharacteristic
487C8—22no—
488C8—61no—
489C8—61no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—122no—
494C2×C3—242no—
495C2×C3#563311yescharacteristic
496C2×C3C2×#91911yescharacteristic
497C2×C3#577411yescharacteristic
498C2×C3C3×#54811yescharacteristic
499C2×C3C2×C3×#13511yescharacteristic
500C2×C3C3×#57611yescharacteristic
501D3—42no—
502D3—82no—
503C22—62no—
504C22—121no—
505C22—121no—
506C22—122no—
507C22—122no—
508C22—122no—
509C22C2×C3×D3×D411yescharacteristic
510C4—21no—
511C4—41no—
512C4—42no—
513C4—41no—
514C4—62no—
515C4—62no—
516C4—121no—
517C4C3×#91912yes—
518C4C3×#100711yescharacteristic
519C4C3×D3×#4111yescharacteristic
520C3—21no—
521C3#8113411yescharacteristic, direct product factor
522C3C3×#336111yescharacteristic, complemented
523C2—122no—
524C2—242no—
525C2C3×#563311yescharacteristic
526C2C2×C3×#91911yescharacteristic
527C2C3×#577411yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#477C2
socleC22×C32C22×D4
prime radicalC3×#4843C2
hypercenterC3×#477D3
hypocenterC3C3×#3361
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#477

Complements

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

NH ≅ G/Ntype
1. C3×#5730C2semidirect
2. C3×#5585C2semidirect
3. C32×#477C2semidirect
4. C3×#5088C2semidirect
5. C3×C4×#215C2semidirect
6. C3×#4891C2semidirect
7. C3×#4872C2semidirect
9. C3×#4830C2semidirect
10. C3×#4819C2semidirect
11. C3×#4800C2semidirect
13. #81134C3direct (N × H)
45. #5730C2×C3semidirect
46. #5585C2×C3semidirect
51. C3×#477D3semidirect
52. C3×#477C2×C3semidirect
58. #5088C2×C3semidirect
59. C4×#215C2×C3semidirect
60. #4891C2×C3semidirect
61. #4872C2×C3semidirect
63. #4830C2×C3semidirect
64. #4819C2×C3semidirect
65. #4800C2×C3semidirect
194. #477C3×D3semidirect
462. C32#3361semidirect
521. C3#81134direct (N × H)
522. C3C3×#3361semidirect

Maximal subgroups

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

subgroupindex
C3×#57302
C3×#55852
C32×#4772
C3×#50882
C3×C4×#2152
C3×#48912
C3×#48722
C3×#48432
C3×#48302
C3×#48192
C3×#48002
C3×#33613
#811343