Finite Group Databasebeta

← C3×#81037 #11895152

Subgroups — C3×#81037 #11895152

Order 1152.

788 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×#5727C211yesmaximal, characteristic
2C3×#5567C211yesmaximal, characteristic, complemented
3C32×#475C211yesmaximal, characteristic, complemented
4C3×#5093C211yesmaximal, characteristic, complemented
5C3×C4×#215C211yesmaximal, characteristic
6C3×#4854C212yesmaximal, complemented
7C3×#4852C212yesmaximal
8C3×#4841C211yesmaximal, characteristic
9C3×#4830C211yesmaximal, characteristic, complemented
10C3×#4818C212yesmaximal
11C3×#4792C212yesmaximal, complemented
12C3×#3359—31nomaximal
13#81037C311yesmaximal, characteristic, direct product factor
14C2×C3×D3×Q8—21no—
15C32×C4⋊Q8C2211yescharacteristic
16C32×C4×Q8C2211yescharacteristic
17C3×#946—21no—
18C3×#944C2212yes—
19C2×C3×#215C2211yescharacteristic
20C2×C3×#204C2212yes—
21C3×#896—22no—
22C3×#893C2212yes—
23C3×#889—22no—
24C3×#888C2212yes—
25C3×#887C2212yes—
26C3×C4×D12C2211yescharacteristic
27C3×#870—21no—
28C3×#869C2211yescharacteristic
29C3×C4×Dic6—21no—
30C3×C4×Dic6C2211yescharacteristic
31C32×#106C2212yes—
32C32×C4⋊C8C2211yescharacteristic
33C32×#103C2212yes—
34C3×#835C2211yescharacteristic
35C3×#816C2212yes—
36C3×Dic3⋊C8C2212yes—
37C3×C8×Dic3C2212yes—
38C3×#810C2212yes—
39C3×#810C2212yes—
40C3×#809C2211yescharacteristic
41C3×#808C2211yescharacteristic
42C3×C4×C3⋊C8C2211yescharacteristic
43C3×#557—31no—
44C3×D4×Q8—31no—
45#5727C2×C311yescharacteristic
46#5567C2×C311yescharacteristic, complemented
47C3×#487—31no—
48C3×#487—32no—
49C3×#475—21no—
50C3×#475—32no—
51C3×#475D311yescharacteristic, complemented
52C3×#475C2×C311yescharacteristic, complemented
53C3×#461—31no—
54C3×#461—32no—
55C3×C8×Q8—31no—
56C3×C4×SD16—31no—
57C3×C4×SD16—32no—
58#5093C2×C311yescharacteristic, complemented
59C4×#215C2×C311yescharacteristic
60#4854C2×C312yescomplemented
61#4852C2×C312yes—
62#4841C2×C311yescharacteristic
63#4830C2×C311yescharacteristic, complemented
64#4818C2×C312yes—
65#4792C2×C312yescomplemented
66C2×C32×Q8—21no—
67C2×C32×Q8C2311yescharacteristic
68C3×D3×Q8—44no—
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×C4×D3—22no—
72C2×C3×Dic6—22no—
73C2×C3×Dic6D411yescharacteristic
74C2×C3×Dic6C2312yes—
75C2×C32×C8C2312yes—
76C32×C4⋊C4—21no—
77C32×C4⋊C4—21no—
78C32×C4⋊C4C2311yescharacteristic
79C32×C4⋊C4C2312yes—
80C32×C42—21no—
81C32×C42C2311yescharacteristic
82C3×#215—22no—
83C3×(C2×D3)⋊C4—21no—
84C3×(C2×D3)⋊C4—22no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3D411yescharacteristic
88C3×C4⋊Dic3C2311yescharacteristic
89C3×Dic3⋊C4—22no—
90C3×Dic3⋊C4—22no—
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4—22no—
93C3×Dic3⋊C4D412yes—
94C3×C4×Dic3—22no—
95C3×C4×Dic3C2312yes—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98C3×#204—24no—
99#3359—31noSylow
100C22×C3×Q8—61no—
101C2×D3×Q8—21no—
102C2×C3×SD16—31no—
103C2×C3×SD16—32no—
104C3×C4⋊Q8—21no—
105C3×C4⋊Q8—32no—
106C3×C4⋊Q8—32no—
107C3×C4⋊Q8—31no—
108C3×C4⋊Q8C2×D311yescharacteristic
109C3×C4⋊Q8C22×C311yescharacteristic
110C3×#125—61no—
111C3×#125—62no—
112C3×C22⋊Q8—62no—
113C3×C22⋊Q8—61no—
114C3×C4×Q8—21no—
115C3×C4×Q8—31no—
116C3×C4×Q8—32no—
117C3×C4×Q8—61no—
118C3×C4×Q8C2×D311yescharacteristic
119C3×C4×Q8C22×C311yescharacteristic
120C3×C4×D4—32no—
121C3×C4×D4—31no—
122#946—21no—
123#944C22×C312yes—
124C2×#215C22×C311yescharacteristic
125C2×#204C22×C312yes—
126#896—22no—
127#893C22×C312yes—
128#889—22no—
129#888C22×C312yes—
130#887C22×C312yes—
131C4×D12C22×C311yescharacteristic
132#870—21no—
133#869C22×C311yescharacteristic
134C4×Dic6—21no—
135C4×Dic6C22×C311yescharacteristic
136C3×#106—22no—
137C3×#106—31no—
138C3×#106C2×D312yes—
139C3×#106C22×C312yes—
140C3×C4⋊C8—21no—
141C3×C4⋊C8—32no—
142C3×C4⋊C8C2×D311yescharacteristic
143C3×C4⋊C8C22×C311yescharacteristic
144C3×#103—22no—
145C3×#103—31no—
146C3×#103—32no—
147C3×#103—32no—
148C3×#103—32no—
149C3×#103C2×D312yes—
150C3×#103C22×C312yes—
151C3×#102—31no—
152C3×C4×C8—32no—
153C3×C4×C8—31no—
154#835C22×C311yescharacteristic
155#816C22×C312yes—
156Dic3⋊C8C22×C312yes—
157C8×Dic3C22×C312yes—
158#810C22×C312yes—
159#810C22×C312yes—
160#809C22×C311yescharacteristic
161#808C22×C311yescharacteristic
162C4×C3⋊C8C22×C311yescharacteristic
163C22×C3×D3—21no—
164C32×Q8—21no—
165C32×Q8—21no—
166C32×Q8—42no—
167C2×C32×C4—21no—
168C2×C32×C4—21no—
169C2×C32×C4—22no—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2411yescharacteristic
173C2×C3×Dic3—22no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3C2×D412yes—
176C2×C3×Dic3C2×D412yes—
177C3×D12—21no—
178C3×D12#4112yes—
179C3×C4×D3—42no—
180C3×C4×D3—44no—
181C3×Dic6—22no—
182C3×Dic6—22no—
183C3×Dic6—44no—
184C3×Dic6SD1614yescomplemented
185C32×C8—22no—
186C3×C3⋊C8—21no—
187C3×C3⋊C8—21no—
188#557—31no—
189D4×Q8—31no—
190#487—31no—
191#487—32no—
192#475—32no—
193#475C3×D311yescharacteristic, complemented
194#461—31no—
195#461—32no—
196C8×Q8—31no—
197C4×SD16—31no—
198C4×SD16—32no—
199C2×C3×Q8—21no—
200C2×C3×Q8—21no—
201C2×C3×Q8—21no—
202C2×C3×Q8—31no—
203C2×C3×Q8—32no—
204C2×C3×Q8—41no—
205C2×C3×Q8—62no—
206C2×C3×Q8—124no—
207C2×C3×Q8C22×D311yescharacteristic
208C2×C3×Q8C23×C311yescharacteristic
209C2×C3×D4—31no—
210C22×C3×C4—62no—
211C22×C3×C4—61no—
212D3×Q8—44no—
213C2×D12C23×C311yescharacteristic
214C2×C4×D3—21no—
215C2×C4×D3—22no—
216C2×Dic6—22no—
217C2×Dic6C3×D411yescharacteristic
218C2×Dic6C23×C312yes—
219C3×SD16—64no—
220C3×SD16—62no—
221C2×C3×C8—22no—
222C2×C3×C8—31no—
223C2×C3×C8—31no—
224C2×C3×C8C22×D312yes—
225C2×C3×C8C23×C312yes—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—22no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—32no—
233C3×C4⋊C4—31no—
234C3×C4⋊C4—31no—
235C3×C4⋊C4—41no—
236C3×C4⋊C4—41no—
237C3×C4⋊C4—62no—
238C3×C4⋊C4—62no—
239C3×C4⋊C4—62no—
240C3×C4⋊C4—62no—
241C3×C4⋊C4—61no—
242C3×C4⋊C4—61no—
243C3×C4⋊C4C22×D311yescharacteristic
244C3×C4⋊C4C22×D312yes—
245C3×C4⋊C4C23×C311yescharacteristic
246C3×C4⋊C4C23×C312yes—
247C3×C22⋊C4—62no—
248C3×C22⋊C4—61no—
249C3×C42—21no—
250C3×C42—21no—
251C3×C42—21no—
252C3×C42—32no—
253C3×C42—41no—
254C3×C42—62no—
255C3×C42C22×D311yescharacteristic
256C3×C42C23×C311yescharacteristic
257#215—22no—
258(C2×D3)⋊C4—21no—
259(C2×D3)⋊C4—22no—
260C4⋊Dic3—21no—
261C4⋊Dic3—21no—
262C4⋊Dic3C3×D411yescharacteristic
263C4⋊Dic3C23×C311yescharacteristic
264Dic3⋊C4—22no—
265Dic3⋊C4—22no—
266Dic3⋊C4—22no—
267Dic3⋊C4—22no—
268Dic3⋊C4C3×D412yes—
269C4×Dic3—22no—
270C4×Dic3C23×C312yes—
271C2×C3⋊C8C23×C311yescharacteristic
272C2×C3⋊C8C23×C311yescharacteristic
273#204—24no—
274C22×C32C22×D411yescharacteristic
275C2×C3×D3—22no—
276C2×C3×D3—41no—
277C2×C3×D3—41no—
278C32×C4—21no—
279C32×C4—41no—
280C32×C4—42no—
281C32×C4—41no—
282C32×C4C2×SD1612yes—
283C32×C4C2×#4111yescharacteristic
284C32×C42−1+411yescharacteristic
285C3×Dic3—22no—
286C3×Dic3—42no—
287C3×Dic3—41no—
288C3×Dic3C2×SD1614yes—
289C22×Q8—61no—
290C2×SD16—31no—
291C2×SD16—32no—
292C4⋊Q8—32no—
293C4⋊Q8—32no—
294C4⋊Q8—31no—
295C4⋊Q8C2×C3×D311yescharacteristic
296#125—61no—
297#125—62no—
298C22⋊Q8—62no—
299C22⋊Q8—61no—
300C4×Q8—31no—
301C4×Q8—32no—
302C4×Q8—61no—
303C4×Q8C2×C3×D311yescharacteristic
304C4×D4—32no—
305C4×D4—31no—
306#106—31no—
307#106C2×C3×D312yes—
308C4⋊C8—32no—
309C4⋊C8C2×C3×D311yescharacteristic
310#103—31no—
311#103—32no—
312#103—32no—
313#103—32no—
314#103C2×C3×D312yes—
315#102—31no—
316C4×C8—32no—
317C4×C8—31no—
318C23×C3—61no—
319C22×D3—21no—
320C3×Q8—22no—
321C3×Q8—21no—
322C3×Q8—21no—
323C3×Q8—21no—
324C3×Q8—21no—
325C3×Q8—34no—
326C3×Q8—41no—
327C3×Q8—42no—
328C3×Q8—42no—
329C3×Q8—62no—
330C3×Q8—62no—
331C3×Q8—82no—
332C3×Q8—124no—
333C3×D4—32no—
334C3×D4—61no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—22no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—22no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—32no—
345C2×C3×C4—32no—
346C2×C3×C4—41no—
347C2×C3×C4—41no—
348C2×C3×C4—42no—
349C2×C3×C4—62no—
350C2×C3×C4—61no—
351C2×C3×C4—124no—
352C2×C3×C4—122no—
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4C2×C3×D411yescharacteristic
356C2×C3×C4C2×C3×D411yescharacteristic
357C2×C3×C4C23×D311yescharacteristic
358C2×C3×C4C24×C311yescharacteristic
359C2×Dic3—22no—
360C2×Dic3—21no—
361C2×Dic3C2×C3×D412yes—
362C2×Dic3C2×C3×D412yes—
363D12—21no—
364D12C3×#4112yes—
365C4×D3—42no—
366C4×D3—44no—
367Dic6—22no—
368Dic6—22no—
369Dic6—44no—
370Dic6C3×SD1614yescomplemented
371C3×C8—22no—
372C3×C8—22no—
373C3×C8—42no—
374C3×C8—61no—
375C3×C8—61no—
376C3⋊C8—21no—
377C3⋊C8—21no—
378C2×C32#54811yescharacteristic
379C2×C32C22×SD1611yescharacteristic
380C2×C32#57811yescharacteristic
381C3×D3—42no—
382C2×Q8—21no—
383C2×Q8—31no—
384C2×Q8—32no—
385C2×Q8—62no—
386C2×Q8—124no—
387C2×Q8C22×C3×D311yescharacteristic
388C2×D4—31no—
389C22×C4—62no—
390C22×C4—61no—
391SD16—64no—
392SD16—62no—
393C2×C8—31no—
394C2×C8—31no—
395C2×C8C22×C3×D312yes—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—32no—
399C4⋊C4—31no—
400C4⋊C4—31no—
401C4⋊C4—62no—
402C4⋊C4—62no—
403C4⋊C4—62no—
404C4⋊C4—62no—
405C4⋊C4—61no—
406C4⋊C4—61no—
407C4⋊C4C22×C3×D311yescharacteristic
408C4⋊C4C22×C3×D312yes—
409C22⋊C4—62no—
410C22⋊C4—61no—
411C42—21no—
412C42—32no—
413C42—62no—
414C42C22×C3×D311yescharacteristic
415C22×C3—21no—
416C22×C3—62no—
417C22×C3—121no—
418C22×C3—121no—
419C22×C3C2×D3×D411yescharacteristic
420C22×C3C22×C3×D411yescharacteristic
421C2×D3—22no—
422C2×D3—41no—
423C2×D3—41no—
424C3×C4—21no—
425C3×C4—21no—
426C3×C4—22no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—34no—
430C3×C4—41no—
431C3×C4—42no—
432C3×C4—41no—
433C3×C4—42no—
434C3×C4—41no—
435C3×C4—42no—
436C3×C4—41no—
437C3×C4—41no—
438C3×C4—62no—
439C3×C4—82no—
440C3×C4—81no—
441C3×C4—122no—
442C3×C4—121no—
443C3×C4D3×SD1612yes—
444C3×C4C2×C3×SD1612yes—
445C3×C4#100711yescharacteristic
446C3×C4D3×#4111yescharacteristic
447C3×C4C2×C3×#4111yescharacteristic
448C3×C4C3×2−1+411yescharacteristic
449Dic3—22no—
450Dic3—41no—
451Dic3—42no—
452Dic3C2×C3×SD1614yes—
453C32#335911yescharacteristic, complemented, Sylow
454C23—61no—
455Q8—21no—
456Q8—21no—
457Q8—34no—
458Q8—42no—
459Q8—62no—
460Q8—62no—
461Q8—124no—
462D4—32no—
463D4—61no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—32no—
468C2×C4—32no—
469C2×C4—62no—
470C2×C4—61no—
471C2×C4—124no—
472C2×C4—122no—
473C2×C4C3×D3×D411yescharacteristic
474C2×C4C3×D3×D411yescharacteristic
475C2×C4C23×C3×D311yescharacteristic
476C8—22no—
477C8—61no—
478C8—61no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—122no—
483C2×C3#563311yescharacteristic
484C2×C3C2×D3×SD1611yescharacteristic
485C2×C3#577911yescharacteristic
486C2×C3C3×#54811yescharacteristic
487C2×C3C22×C3×SD1611yescharacteristic
488C2×C3C3×#57811yescharacteristic
489D3—42no—
490C22—62no—
491C22—121no—
492C22—121no—
493C22C2×C3×D3×D411yescharacteristic
494C4—21no—
495C4—34no—
496C4—42no—
497C4—41no—
498C4—41no—
499C4—62no—
500C4—121no—
501C4—122no—
502C4C3×D3×SD1612yes—
503C4C3×#100711yescharacteristic
504C4C3×D3×#4111yescharacteristic
505C3—21no—
506C3#8103711yescharacteristic, direct product factor
507C3C3×#335911yescharacteristic, complemented
508C2—122no—
509C2C3×#563311yescharacteristic
510C2C2×C3×D3×SD1611yescharacteristic
511C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#475C2
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenterC3×#475D3
hypocenterC3C3×#3359
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
2. C3×#5567C2semidirect
3. C32×#475C2semidirect
4. C3×#5093C2semidirect
6. C3×#4854C2semidirect
9. C3×#4830C2semidirect
11. C3×#4792C2semidirect
13. #81037C3direct (N × H)
46. #5567C2×C3semidirect
51. C3×#475D3semidirect
52. C3×#475C2×C3semidirect
58. #5093C2×C3semidirect
60. #4854C2×C3semidirect
63. #4830C2×C3semidirect
65. #4792C2×C3semidirect
184. C3×Dic6SD16semidirect
193. #475C3×D3semidirect
370. Dic6C3×SD16semidirect
453. C32#3359semidirect
506. C3#81037direct (N × H)
507. C3C3×#3359semidirect

Maximal subgroups

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

subgroupindex
C3×#57272
C3×#55672
C32×#4752
C3×#50932
C3×C4×#2152
C3×#48542
C3×#48522
C3×#48412
C3×#48302
C3×#48182
C3×#47922
C3×#33593
#810373