Finite Group Databasebeta

← C3×#81087 #11895207

Subgroups — C3×#81087 #11895207

Order 1152.

754 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5730C211yesmaximal, characteristic, complemented
2C3×#5542C211yesmaximal, characteristic, complemented
3C32×#476C211yesmaximal, characteristic, complemented
4C3×#5093C211yesmaximal, characteristic, complemented
5C3×C4×#213C211yesmaximal, characteristic
6C3×#4857C212yesmaximal, complemented
7C3×#4852C212yesmaximal, complemented
8C3×#4841C211yesmaximal, characteristic, complemented
9C3×#4830C211yesmaximal, characteristic, complemented
10C3×#4787C212yesmaximal
11C3×#4768C212yesmaximal, complemented
12C3×#3360—31nomaximal
13#81087C311yesmaximal, characteristic, direct product factor
14C32×C4⋊Q8C2211yescharacteristic
15C32×C4×D4C2211yescharacteristic
16C3×#946—22no—
17C3×#936C2212yes—
18C2×C3×#213C2211yescharacteristic
19C3×#926—21no—
20C3×#924—21no—
21C2×C3×#204C2212yes—
22C3×#897—21no—
23C3×#893C2212yes—
24C3×D3×C4⋊C4—21no—
25C3×#890C2212yes—
26C3×#887C2212yes—
27C3×#879—22no—
28C3×C4×D12C2211yescharacteristic
29C3×#869C2211yescharacteristic
30C3×C4×Dic6C2211yescharacteristic
31C32×#106C2212yes—
32C32×C4⋊C8C2211yescharacteristic
33C32×#102C2212yes—
34C3×#832C2211yescharacteristic
35C3×#816C2212yes—
36C3×Dic3⋊C8C2212yes—
37C3×C8×Dic3C2212yes—
38C3×#810C2212yes—
39C3×#810C2212yes—
40C3×#809C2211yescharacteristic
41C3×#807C2211yescharacteristic
42C3×C4×C3⋊C8C2211yescharacteristic
43C3×#556—31no—
44C3×#554—31no—
45#5730C2×C311yescharacteristic, complemented
46#5542C2×C311yescharacteristic, complemented
47C3×#488—32no—
48C3×#487—31no—
49C3×#479—32no—
50C3×#476—21no—
51C3×#476D311yescharacteristic, complemented
52C3×#476C2×C311yescharacteristic, complemented
53C3×#463—32no—
54C3×#461—31no—
55C3×C8×Q8—31no—
56C3×C4×SD16—32no—
57C3×C4×D8—31no—
58#5093C2×C311yescharacteristic, complemented
59C4×#213C2×C311yescharacteristic
60#4857C2×C312yescomplemented
61#4852C2×C312yescomplemented
62#4841C2×C311yescharacteristic, complemented
63#4830C2×C311yescharacteristic, complemented
64#4787C2×C312yes—
65#4768C2×C312yescomplemented
66C2×C32×Q8—21no—
67C2×C32×D4C2311yescharacteristic
68C22×C32×C4—21no—
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×C4×D3—22no—
72C2×C3×Dic6D411yescharacteristic
73C2×C3×Dic6C2312yes—
74C2×C32×C8C2312yes—
75C32×C4⋊C4—21no—
76C32×C4⋊C4C2311yescharacteristic
77C32×C4⋊C4C2312yes—
78C32×C22⋊C4—21no—
79C32×C42C2311yescharacteristic
80C3×#217—22no—
81C3×#217—22no—
82C3×#213—22no—
83C3×(C2×D3)⋊C4—21no—
84C3×(C2×D3)⋊C4—22no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3—22no—
88C3×C4⋊Dic3D411yescharacteristic
89C3×C4⋊Dic3C2311yescharacteristic
90C3×Dic3⋊C4—22no—
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4D412yes—
93C3×C4×Dic3—22no—
94C3×C4×Dic3C2312yes—
95C2×C3×C3⋊C8C2311yescharacteristic
96C2×C3×C3⋊C8C2311yescharacteristic
97C3×#204—24no—
98#3360—31noSylow
99C2×C3×SD16—32no—
100C2×C3×D8—31no—
101C3×C4⋊Q8—21no—
102C3×C4⋊Q8—31no—
103C3×C4⋊Q8C2×D311yescharacteristic
104C3×C4⋊Q8C22×C311yescharacteristic
105C3×#126—62no—
106C3×#125—32no—
107C3×#124—32no—
108C3×C22⋊Q8—61no—
109C3×C22⋊Q8—62no—
110C3×C22⋊Q8—61no—
111C3×C4×Q8—31no—
112C3×C4×Q8—32no—
113C3×C4×D4—21no—
114C3×C4×D4—32no—
115C3×C4×D4—31no—
116C3×C4×D4C2×D311yescharacteristic
117C3×C4×D4C22×C311yescharacteristic
118C3×#117—61no—
119C2×C3×C4⋊C4—61no—
120#946—22no—
121#936C22×C312yes—
122C2×#213C22×C311yescharacteristic
123#926—21no—
124#924—21no—
125C2×#204C22×C312yes—
126#897—21no—
127#893C22×C312yes—
128D3×C4⋊C4—21no—
129#890C22×C312yes—
130#887C22×C312yes—
131#879—22no—
132C4×D12C22×C311yescharacteristic
133#869C22×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—32no—
144C3×#103—32no—
145C3×#103—32no—
146C3×#102—22no—
147C3×#102—31no—
148C3×#102—31no—
149C3×#102C2×D312yes—
150C3×#102C22×C312yes—
151C3×C4×C8—32no—
152C3×C4×C8—31no—
153#832C22×C311yescharacteristic
154#816C22×C312yes—
155Dic3⋊C8C22×C312yes—
156C8×Dic3C22×C312yes—
157#810C22×C312yes—
158#810C22×C312yes—
159#809C22×C311yescharacteristic
160#807C22×C311yescharacteristic
161C4×C3⋊C8C22×C311yescharacteristic
162C23×C32—21no—
163C22×C3×D3—21no—
164C32×Q8—81no—
165C32×D4—21no—
166C32×D4—21no—
167C2×C32×C4—21no—
168C2×C32×C4—22no—
169C2×C32×C4—42no—
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—82no—
181C3×Dic6—22no—
182C3×Dic6—22no—
183C3×Dic6—22no—
184C32×C8—22no—
185C3×C3⋊C8—21no—
186C3×C3⋊C8—21no—
187#556—31no—
188#554—31no—
189#488—32no—
190#487—31no—
191#479—32no—
192#476C3×D311yescharacteristic, complemented
193#463—32no—
194#461—31no—
195C8×Q8—31no—
196C4×SD16—32no—
197C4×D8—31no—
198C2×C3×Q8—21no—
199C2×C3×Q8—21no—
200C2×C3×Q8—31no—
201C2×C3×Q8—32no—
202C2×C3×Q8—41no—
203C2×C3×D4—21no—
204C2×C3×D4—31no—
205C2×C3×D4C22×D311yescharacteristic
206C2×C3×D4C23×C311yescharacteristic
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—41no—
210C22×C3×C4—62no—
211C22×C3×C4—61no—
212C2×D12C23×C311yescharacteristic
213C2×C4×D3—21no—
214C2×C4×D3—22no—
215C2×Dic6C3×D411yescharacteristic
216C2×Dic6C23×C312yes—
217C3×SD16—64no—
218C3×D8—62no—
219C2×C3×C8—22no—
220C2×C3×C8—31no—
221C2×C3×C8—31no—
222C2×C3×C8C22×D312yes—
223C2×C3×C8C23×C312yes—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—22no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—32no—
229C3×C4⋊C4—31no—
230C3×C4⋊C4—31no—
231C3×C4⋊C4—41no—
232C3×C4⋊C4—62no—
233C3×C4⋊C4—62no—
234C3×C4⋊C4—62no—
235C3×C4⋊C4—61no—
236C3×C4⋊C4—61no—
237C3×C4⋊C4C22×D311yescharacteristic
238C3×C4⋊C4C22×D312yes—
239C3×C4⋊C4C23×C311yescharacteristic
240C3×C4⋊C4C23×C312yes—
241C3×C22⋊C4—21no—
242C3×C22⋊C4—21no—
243C3×C22⋊C4—41no—
244C3×C22⋊C4—62no—
245C3×C22⋊C4—62no—
246C3×C22⋊C4—62no—
247C3×C22⋊C4—61no—
248C3×C42—21no—
249C3×C42—32no—
250C3×C42—62no—
251C3×C42C22×D311yescharacteristic
252C3×C42C23×C311yescharacteristic
253#217—22no—
254#217—22no—
255#213—22no—
256(C2×D3)⋊C4—21no—
257(C2×D3)⋊C4—22no—
258C4⋊Dic3—21no—
259C4⋊Dic3—21no—
260C4⋊Dic3—22no—
261C4⋊Dic3C3×D411yescharacteristic
262C4⋊Dic3C23×C311yescharacteristic
263Dic3⋊C4—22no—
264Dic3⋊C4—22no—
265Dic3⋊C4C3×D412yes—
266C4×Dic3—22no—
267C4×Dic3C23×C312yes—
268C2×C3⋊C8C23×C311yescharacteristic
269C2×C3⋊C8C23×C311yescharacteristic
270#204—24no—
271C22×C32—41no—
272C22×C32—41no—
273C22×C32—41no—
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#13512yes—
282C32×C4C2×#4111yescharacteristic
283C32×C42−1+411yescharacteristic
284C3×Dic3—22no—
285C3×Dic3—22no—
286C3×Dic3—42no—
287C3×Dic3—41no—
288C2×SD16—32no—
289C2×D8—31no—
290C4⋊Q8—31no—
291C4⋊Q8C2×C3×D311yescharacteristic
292#126—62no—
293#125—32no—
294#124—32no—
295C22⋊Q8—61no—
296C22⋊Q8—62no—
297C22⋊Q8—61no—
298C4×Q8—31no—
299C4×Q8—32no—
300C4×D4—32no—
301C4×D4—31no—
302C4×D4C2×C3×D311yescharacteristic
303#117—61no—
304C2×C4⋊C4—61no—
305#107—31no—
306#106C2×C3×D312yes—
307C4⋊C8—32no—
308C4⋊C8C2×C3×D311yescharacteristic
309#103—32no—
310#103—32no—
311#103—32no—
312#102—31no—
313#102—31no—
314#102C2×C3×D312yes—
315C4×C8—32no—
316C4×C8—31no—
317C23×C3—21no—
318C23×C3—21no—
319C23×C3—41no—
320C23×C3—61no—
321C22×D3—21no—
322C3×Q8—62no—
323C3×Q8—62no—
324C3×Q8—62no—
325C3×Q8—81no—
326C3×Q8—81no—
327C3×Q8—82no—
328C3×D4—22no—
329C3×D4—21no—
330C3×D4—21no—
331C3×D4—21no—
332C3×D4—21no—
333C3×D4—32no—
334C3×D4—41no—
335C3×D4—61no—
336C2×C3×C4—21no—
337C2×C3×C4—22no—
338C2×C3×C4—21no—
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—41no—
346C2×C3×C4—42no—
347C2×C3×C4—42no—
348C2×C3×C4—42no—
349C2×C3×C4—62no—
350C2×C3×C4—61no—
351C2×C3×C4—82no—
352C2×C3×C4—122no—
353C2×C3×C4—242no—
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4C2×C3×D411yescharacteristic
357C2×C3×C4C2×C3×D411yescharacteristic
358C2×C3×C4C23×D311yescharacteristic
359C2×C3×C4C24×C311yescharacteristic
360C2×Dic3—22no—
361C2×Dic3—21no—
362C2×Dic3C2×C3×D412yes—
363C2×Dic3C2×C3×D412yes—
364D12—21no—
365D12C3×#4112yes—
366C4×D3—42no—
367C4×D3—82no—
368Dic6—22no—
369Dic6—22no—
370Dic6—22no—
371C3×C8—22no—
372C3×C8—22no—
373C3×C8—42no—
374C3×C8—61no—
375C3×C8—61no—
376C3⋊C8—21no—
377C3⋊C8—21no—
378C2×C32—81no—
379C2×C32#54811yescharacteristic
380C2×C32C2×#13511yescharacteristic
381C2×C32#57711yescharacteristic
382C3×D3—42no—
383C2×Q8—21no—
384C2×Q8—31no—
385C2×Q8—32no—
386C2×D4—31no—
387C2×D4C22×C3×D311yescharacteristic
388C22×C4—21no—
389C22×C4—62no—
390C22×C4—61no—
391SD16—64no—
392D8—62no—
393C2×C8—31no—
394C2×C8—31no—
395C2×C8C22×C3×D312yes—
396C4⋊C4—21no—
397C4⋊C4—31no—
398C4⋊C4—32no—
399C4⋊C4—31no—
400C4⋊C4—62no—
401C4⋊C4—62no—
402C4⋊C4—62no—
403C4⋊C4—61no—
404C4⋊C4—61no—
405C4⋊C4C22×C3×D311yescharacteristic
406C4⋊C4C22×C3×D312yes—
407C22⋊C4—21no—
408C22⋊C4—62no—
409C22⋊C4—62no—
410C22⋊C4—62no—
411C22⋊C4—61no—
412C42—32no—
413C42—62no—
414C42C22×C3×D311yescharacteristic
415C22×C3—21no—
416C22×C3—42no—
417C22×C3—41no—
418C22×C3—41no—
419C22×C3—41no—
420C22×C3—41no—
421C22×C3—41no—
422C22×C3—41no—
423C22×C3—62no—
424C22×C3—81no—
425C22×C3—81no—
426C22×C3—121no—
427C22×C3—121no—
428C22×C3C2×D3×D411yescharacteristic
429C22×C3C22×C3×D411yescharacteristic
430C2×D3—22no—
431C2×D3—41no—
432C2×D3—41no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—22no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—41no—
439C3×C4—41no—
440C3×C4—42no—
441C3×C4—41no—
442C3×C4—42no—
443C3×C4—62no—
444C3×C4—62no—
445C3×C4—81no—
446C3×C4—82no—
447C3×C4—122no—
448C3×C4—121no—
449C3×C4#91612yes—
450C3×C4C3×#13512yes—
451C3×C4#100711yescharacteristic
452C3×C4D3×#4111yescharacteristic
453C3×C4C2×C3×#4111yescharacteristic
454C3×C4C3×2−1+411yescharacteristic
455Dic3—22no—
456Dic3—22no—
457Dic3—41no—
458Dic3—42no—
459C32#336011yescharacteristic, complemented, Sylow
460C23—21no—
461C23—61no—
462Q8—62no—
463Q8—62no—
464Q8—62no—
465Q8—81no—
466D4—21no—
467D4—21no—
468D4—32no—
469D4—61no—
470C2×C4—21no—
471C2×C4—22no—
472C2×C4—32no—
473C2×C4—32no—
474C2×C4—42no—
475C2×C4—62no—
476C2×C4—61no—
477C2×C4—122no—
478C2×C4—242no—
479C2×C4C3×D3×D411yescharacteristic
480C2×C4C3×D3×D411yescharacteristic
481C2×C4C23×C3×D311yescharacteristic
482C8—22no—
483C8—61no—
484C8—61no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—82no—
489C2×C3—81no—
490C2×C3—81no—
491C2×C3—122no—
492C2×C3#563311yescharacteristic
493C2×C3C2×#91611yescharacteristic
494C2×C3#577511yescharacteristic
495C2×C3C3×#54811yescharacteristic
496C2×C3C2×C3×#13511yescharacteristic
497C2×C3C3×#57711yescharacteristic
498D3—42no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—62no—
503C22—121no—
504C22—121no—
505C22C2×C3×D3×D411yescharacteristic
506C4—21no—
507C4—41no—
508C4—42no—
509C4—62no—
510C4—62no—
511C4—121no—
512C4—122no—
513C4C3×#91612yes—
514C4C3×#100711yescharacteristic
515C4C3×D3×#4111yescharacteristic
516C3—21no—
517C3#8108711yescharacteristic, direct product factor
518C3C3×#336011yescharacteristic, complemented
519C2—81no—
520C2—122no—
521C2C3×#563311yescharacteristic
522C2C2×C3×#91611yescharacteristic
523C2C3×#577511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#476C2
socleC22×C32C22×D4
prime radicalC2×C3×#213C22
hypercenterC3×#476D3
hypocenterC3C3×#3360
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#476

Complements

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

NH ≅ G/Ntype
1. C3×#5730C2semidirect
2. C3×#5542C2semidirect
3. C32×#476C2semidirect
4. C3×#5093C2semidirect
6. C3×#4857C2semidirect
7. C3×#4852C2semidirect
8. C3×#4841C2semidirect
9. C3×#4830C2semidirect
11. C3×#4768C2semidirect
13. #81087C3direct (N × H)
45. #5730C2×C3semidirect
46. #5542C2×C3semidirect
51. C3×#476D3semidirect
52. C3×#476C2×C3semidirect
58. #5093C2×C3semidirect
60. #4857C2×C3semidirect
61. #4852C2×C3semidirect
62. #4841C2×C3semidirect
63. #4830C2×C3semidirect
65. #4768C2×C3semidirect
192. #476C3×D3semidirect
459. C32#3360semidirect
517. C3#81087direct (N × H)
518. C3C3×#3360semidirect

Maximal subgroups

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

subgroupindex
C3×#57302
C3×#55422
C32×#4762
C3×#50932
C3×C4×#2132
C3×#48572
C3×#48522
C3×#48412
C3×#48302
C3×#47872
C3×#47682
C3×#33603
#810873