Finite Group Databasebeta

← C3×#81637 #11873470

Subgroups — C3×#81637 #11873470

Order 1152.

848 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5688C211yesmaximal, characteristic, complemented
2C3×#5668C211yesmaximal, characteristic
3C32×#488C211yesmaximal, characteristic, complemented
4C3×#5068C211yesmaximal, characteristic, complemented
5C3×#5056C211yesmaximal, characteristic, complemented
6C3×#4804C212yesmaximal, complemented
7C3×#4792C212yesmaximal, complemented
8C3×#4772C212yesmaximal, complemented
9C3×#4760C212yesmaximal, complemented
10C3×#4697C211yesmaximal, characteristic, complemented
11C3×C4×D3×C8C211yesmaximal, characteristic, complemented
12C3×#3131—31nomaximal
13#81637C311yesmaximal, characteristic, direct product factor
14C2×C3×#239C2211yescharacteristic
15C2×C3×#237C2211yescharacteristic
16C32×#125C2211yescharacteristic
17C32×#124C2211yescharacteristic
18C3×#944C2211yescharacteristic
19C3×#940C2211yescharacteristic
20C2×C3×D3×C8C2212yes—
21C3×#896—22no—
22C3×#892C2212yes—
23C3×#888C2212yes—
24C3×#887—22no—
25C3×#884—22no—
26C3×#67⋊C4—22no—
27C3×#875C2211yescharacteristic
28C3×C42×D3C2211yescharacteristic
29C3×#870C2211yescharacteristic
30C32×#103C2212yes—
31C32×#102C2212yes—
32C32×C4×C8C2211yescharacteristic
33C3×#835C2212yes—
34C3×#832C2212yes—
35C3×#821C2212yes—
36C3×#816C2212yes—
37C3×C8×Dic3C2212yes—
38C3×#810C2212yes—
39C3×#809C2212yes—
40C3×C4×C3⋊C8C2211yescharacteristic
41C3×#533—31no—
42C3×#532—31no—
43#5688C2×C311yescharacteristic, complemented
44#5668C2×C311yescharacteristic
45C3×#488—21no—
46C3×#488—31no—
47C3×#488—31no—
48C3×#488—31no—
49C3×#488D311yescharacteristic, complemented
50C3×#488C2×C311yescharacteristic, complemented
51C3×#487—32no—
52C3×#486—32no—
53C3×#416—32no—
54C3×#416—32no—
55C2×C3×C4×C8—31no—
56#5068C2×C311yescharacteristic, complemented
57#5056C2×C311yescharacteristic, complemented
58#4804C2×C312yescomplemented
59#4792C2×C312yescomplemented
60#4772C2×C312yescomplemented
61#4760C2×C312yescomplemented
62#4697C2×C311yescharacteristic, complemented
63C4×D3×C8C2×C311yescharacteristic, complemented
64C2×C32×Q8C2311yescharacteristic
65C2×C32×D4C2311yescharacteristic
66C2×C3×#67—21no—
67C2×C3×#67—22no—
68C22×C3×Dic3—21no—
69C3×#239—24no—
70C3×#237—24no—
71C2×C3×D12—21no—
72C2×C3×D12C2311yescharacteristic
73C2×C3×C4×D3—21no—
74C2×C3×C4×D3D412yes—
75C2×C3×C4×D3C2311yescharacteristic
76C2×C3×Dic6—22no—
77C2×C3×Dic6C2311yescharacteristic
78C2×C32×C8C2312yes—
79C32×C4⋊C4—22no—
80C32×C4⋊C4C2312yes—
81C32×C22⋊C4—22no—
82C32×C42C2311yescharacteristic
83C3×(C2×D3)⋊C4—22no—
84C3×(C2×D3)⋊C4—22no—
85C3×C4⋊Dic3C2312yes—
86C3×Dic3⋊C4—22no—
87C3×Dic3⋊C4—22no—
88C3×Dic3⋊C4—22no—
89C3×C4×Dic3—22no—
90C3×C4×Dic3D412yes—
91C3×C4×Dic3C2311yescharacteristic
92C2×C3×C3⋊C8C2312yes—
93C3×D3×C8—24no—
94#3131—31noSylow
95C2×C3×#41—31no—
96C2×C3×#41—31no—
97C2×#239C22×C311yescharacteristic
98C2×#237C22×C311yescharacteristic
99C22×C3×C8—32no—
100C3×C4⋊Q8—32no—
101C3×C4⋊Q8—31no—
102C3×#127—31no—
103C3×#125—21no—
104C3×#125—31no—
105C3×#125C2×D311yescharacteristic
106C3×#125C22×C311yescharacteristic
107C3×#124—21no—
108C3×#124—31no—
109C3×#124C2×D311yescharacteristic
110C3×#124C22×C311yescharacteristic
111C3×C22⋊Q8—62no—
112C3×#121—62no—
113C3×C4×Q8—62no—
114C3×C4×D4—62no—
115C3×#117—32no—
116C2×C3×C42—31no—
117#944C22×C311yescharacteristic
118#940C22×C311yescharacteristic
119C2×D3×C8C22×C312yes—
120#896—22no—
121#892C22×C312yes—
122#888C22×C312yes—
123#887—22no—
124#884—22no—
125#67⋊C4—22no—
126#875C22×C311yescharacteristic
127C42×D3C22×C311yescharacteristic
128#870C22×C311yescharacteristic
129C3×#103—22no—
130C3×#103—32no—
131C3×#103—32no—
132C3×#103—32no—
133C3×#103C2×D312yes—
134C3×#103C22×C312yes—
135C3×#102—22no—
136C3×#102—32no—
137C3×#102—32no—
138C3×#102—32no—
139C3×#102C2×D312yes—
140C3×#102C22×C312yes—
141C3×C4×C8—21no—
142C3×C4×C8—32no—
143C3×C4×C8—31no—
144C3×C4×C8C2×D311yescharacteristic
145C3×C4×C8C22×C311yescharacteristic
146#835C22×C312yes—
147#832C22×C312yes—
148#821C22×C312yes—
149#816C22×C312yes—
150C8×Dic3C22×C312yes—
151#810C22×C312yes—
152#809C22×C312yes—
153C4×C3⋊C8C22×C311yescharacteristic
154C23×C32—21no—
155C22×C3×D3—21no—
156C22×C3×D3C2×D411yescharacteristic
157C32×Q8—22no—
158C32×D4—22no—
159C2×C32×C4—22no—
160C2×C32×C4—21no—
161C2×C32×C4C2×D412yes—
162C2×C32×C4C2411yescharacteristic
163C3×#67—42no—
164C3×#67—44no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—21no—
167C2×C3×Dic3—42no—
168C2×C3×Dic3C2×D411yescharacteristic
169C2×C3×Dic3C2×D412yes—
170C3×D12—22no—
171C3×D12—42no—
172C3×C4×D3—24no—
173C3×C4×D3—42no—
174C3×C4×D3#4114yes—
175C3×Dic6—22no—
176C3×Dic6—44no—
177C32×C8—22no—
178C3×C3⋊C8—22no—
179#533—31no—
180#532—31no—
181#488—31no—
182#488—31no—
183#488—31no—
184#488C3×D311yescharacteristic, complemented
185#487—32no—
186#486—32no—
187#416—32no—
188#416—32no—
189C2×C4×C8—31no—
190C3×#41—64no—
191C3×#41—64no—
192C2×C3×Q8—21no—
193C2×C3×Q8—31no—
194C2×C3×Q8—62no—
195C2×C3×Q8C22×D311yescharacteristic
196C2×C3×Q8C23×C311yescharacteristic
197C2×C3×D4—21no—
198C2×C3×D4—31no—
199C2×C3×D4—61no—
200C2×C3×D4—62no—
201C2×C3×D4—61no—
202C2×C3×D4C22×D311yescharacteristic
203C2×C3×D4C23×C311yescharacteristic
204C22×C3×C4—31no—
205C22×C3×C4—32no—
206C22×C3×C4—61no—
207C22×C3×C4—61no—
208C2×#67—21no—
209C2×#67—22no—
210C22×Dic3—21no—
211#239—24no—
212#237—24no—
213C2×D12—21no—
214C2×D12C23×C311yescharacteristic
215C2×C4×D3—21no—
216C2×C4×D3C3×D412yes—
217C2×C4×D3C23×C311yescharacteristic
218C2×Dic6—22no—
219C2×Dic6C23×C311yescharacteristic
220C2×C3×C8—22no—
221C2×C3×C8—32no—
222C2×C3×C8—64no—
223C2×C3×C8C22×D312yes—
224C2×C3×C8C23×C312yes—
225C3×C4⋊C4—22no—
226C3×C4⋊C4—22no—
227C3×C4⋊C4—22no—
228C3×C4⋊C4—32no—
229C3×C4⋊C4—42no—
230C3×C4⋊C4—62no—
231C3×C4⋊C4—62no—
232C3×C4⋊C4—62no—
233C3×C4⋊C4C22×D312yes—
234C3×C4⋊C4C23×C312yes—
235C3×C22⋊C4—22no—
236C3×C22⋊C4—22no—
237C3×C22⋊C4—42no—
238C3×C22⋊C4—62no—
239C3×C22⋊C4—62no—
240C3×C42—21no—
241C3×C42—32no—
242C3×C42—31no—
243C3×C42—62no—
244C3×C42C22×D311yescharacteristic
245C3×C42C23×C311yescharacteristic
246(C2×D3)⋊C4—22no—
247(C2×D3)⋊C4—22no—
248C4⋊Dic3C23×C312yes—
249Dic3⋊C4—22no—
250Dic3⋊C4—22no—
251Dic3⋊C4—22no—
252C4×Dic3—22no—
253C4×Dic3C3×D412yes—
254C4×Dic3C23×C311yescharacteristic
255C2×C3⋊C8C23×C312yes—
256D3×C8—24no—
257C22×C32—41no—
258C22×C32—42no—
259C22×C32C22×D411yescharacteristic
260C2×C3×D3—22no—
261C2×C3×D3—41no—
262C2×C3×D3—42no—
263C2×C3×D3#12412yes—
264C32×C4—22no—
265C32×C4—41no—
266C32×C4—42no—
267C32×C4C2×#4112yes—
268C3×Dic3—41no—
269C3×Dic3—42no—
270C3×Dic3#12412yes—
271C3×Dic3#13514yes—
272C2×#41—31no—
273C2×#41—31no—
274C22×C8—32no—
275C4⋊Q8—32no—
276C4⋊Q8—31no—
277#127—31no—
278#125—31no—
279#125C2×C3×D311yescharacteristic
280#124—31no—
281#124C2×C3×D311yescharacteristic
282C22⋊Q8—62no—
283#121—62no—
284C4×Q8—62no—
285C4×D4—62no—
286#117—32no—
287C2×C42—31no—
288#103—32no—
289#103—32no—
290#103—32no—
291#103C2×C3×D312yes—
292#102—32no—
293#102—32no—
294#102—32no—
295#102C2×C3×D312yes—
296C4×C8—32no—
297C4×C8—31no—
298C4×C8C2×C3×D311yescharacteristic
299C23×C3—21no—
300C23×C3—21no—
301C23×C3—31no—
302C23×C3—41no—
303C23×C3—61no—
304C22×D3—21no—
305C22×D3C2×C3×D411yescharacteristic
306C3×Q8—22no—
307C3×Q8—22no—
308C3×Q8—42no—
309C3×Q8—62no—
310C3×Q8—124no—
311C3×D4—22no—
312C3×D4—22no—
313C3×D4—42no—
314C3×D4—62no—
315C3×D4—124no—
316C3×D4—122no—
317C3×D4—122no—
318C2×C3×C4—22no—
319C2×C3×C4—21no—
320C2×C3×C4—22no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—22no—
324C2×C3×C4—31no—
325C2×C3×C4—32no—
326C2×C3×C4—34no—
327C2×C3×C4—41no—
328C2×C3×C4—42no—
329C2×C3×C4—64no—
330C2×C3×C4—62no—
331C2×C3×C4—61no—
332C2×C3×C4—122no—
333C2×C3×C4—122no—
334C2×C3×C4D3×D412yes—
335C2×C3×C4C2×C3×D412yes—
336C2×C3×C4C23×D311yescharacteristic
337C2×C3×C4C24×C311yescharacteristic
338#67—42no—
339#67—44no—
340C2×Dic3—22no—
341C2×Dic3—21no—
342C2×Dic3—42no—
343C2×Dic3C2×C3×D411yescharacteristic
344C2×Dic3C2×C3×D412yes—
345D12—22no—
346D12—42no—
347C4×D3—24no—
348C4×D3—42no—
349C4×D3C3×#4114yes—
350Dic6—22no—
351Dic6—44no—
352C3×C8—22no—
353C3×C8—22no—
354C3×C8—42no—
355C3×C8—62no—
356C3⋊C8—22no—
357C2×C32—81no—
358C2×C32C2×#12411yescharacteristic
359C2×C32C2×#13512yes—
360C3×D3—22no—
361C3×D3—81no—
362#41—64no—
363#41—64no—
364C2×Q8—31no—
365C2×Q8—62no—
366C2×Q8C22×C3×D311yescharacteristic
367C2×D4—31no—
368C2×D4—61no—
369C2×D4—62no—
370C2×D4—61no—
371C2×D4C22×C3×D311yescharacteristic
372C22×C4—31no—
373C22×C4—32no—
374C22×C4—61no—
375C22×C4—61no—
376C2×C8—32no—
377C2×C8—64no—
378C2×C8C22×C3×D312yes—
379C4⋊C4—22no—
380C4⋊C4—32no—
381C4⋊C4—62no—
382C4⋊C4—62no—
383C4⋊C4—62no—
384C4⋊C4C22×C3×D312yes—
385C22⋊C4—22no—
386C22⋊C4—62no—
387C22⋊C4—62no—
388C42—31no—
389C42—32no—
390C42—62no—
391C42C22×C3×D311yescharacteristic
392C22×C3—21no—
393C22×C3—32no—
394C22×C3—42no—
395C22×C3—41no—
396C22×C3—42no—
397C22×C3—41no—
398C22×C3—62no—
399C22×C3—81no—
400C22×C3—82no—
401C22×C3—121no—
402C22×C3—122no—
403C22×C3C2×D3×D411yescharacteristic
404C22×C3C22×C3×D411yescharacteristic
405C2×D3—22no—
406C2×D3—42no—
407C2×D3—41no—
408C2×D3C3×#12412yes—
409C3×C4—22no—
410C3×C4—22no—
411C3×C4—22no—
412C3×C4—32no—
413C3×C4—34no—
414C3×C4—42no—
415C3×C4—42no—
416C3×C4—41no—
417C3×C4—42no—
418C3×C4—41no—
419C3×C4—81no—
420C3×C4—82no—
421C3×C4—121no—
422C3×C4—122no—
423C3×C4D3×#4112yes—
424C3×C4C2×C3×#4112yes—
425Dic3—42no—
426Dic3—41no—
427Dic3C3×#12412yes—
428Dic3C3×#13514yes—
429C32#313111yescharacteristic, complemented, Sylow
430C23—21no—
431C23—31no—
432C23—61no—
433Q8—22no—
434Q8—62no—
435Q8—124no—
436D4—22no—
437D4—62no—
438D4—124no—
439D4—122no—
440D4—122no—
441C2×C4—22no—
442C2×C4—21no—
443C2×C4—31no—
444C2×C4—32no—
445C2×C4—34no—
446C2×C4—64no—
447C2×C4—62no—
448C2×C4—61no—
449C2×C4—122no—
450C2×C4—122no—
451C2×C4C3×D3×D412yes—
452C2×C4C23×C3×D311yescharacteristic
453C8—22no—
454C8—62no—
455C2×C3—22no—
456C2×C3—21no—
457C2×C3—62no—
458C2×C3—81no—
459C2×C3—81no—
460C2×C3—161no—
461C2×C3—241no—
462C2×C3D3×#12411yescharacteristic
463C2×C3D3×#13512yes—
464C2×C3C2×C3×#12411yescharacteristic
465C2×C3C2×C3×#13512yes—
466D3—22no—
467D3—81no—
468C22—32no—
469C22—42no—
470C22—41no—
471C22—62no—
472C22—122no—
473C22—121no—
474C22C2×C3×D3×D411yescharacteristic
475C4—22no—
476C4—34no—
477C4—32no—
478C4—42no—
479C4—41no—
480C4—122no—
481C4—121no—
482C4C3×D3×#4112yes—
483C3—21no—
484C3#8163711yescharacteristic, direct product factor
485C3C3×#313111yescharacteristic, complemented
486C2—62no—
487C2—81no—
488C2—241no—
489C2C3×D3×#12411yescharacteristic
490C2C3×D3×#13512yes—
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#488C2
socleC22×C32C22×D4
prime radicalC3×#5668C2
hypercenterC3×#488D3
hypocenterC3C3×#3131
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#488

Complements

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

NH ≅ G/Ntype
1. C3×#5688C2semidirect
3. C32×#488C2semidirect
4. C3×#5068C2semidirect
5. C3×#5056C2semidirect
6. C3×#4804C2semidirect
7. C3×#4792C2semidirect
8. C3×#4772C2semidirect
9. C3×#4760C2semidirect
10. C3×#4697C2semidirect
11. C3×C4×D3×C8C2semidirect
13. #81637C3direct (N × H)
43. #5688C2×C3semidirect
49. C3×#488D3semidirect
50. C3×#488C2×C3semidirect
56. #5068C2×C3semidirect
57. #5056C2×C3semidirect
58. #4804C2×C3semidirect
59. #4792C2×C3semidirect
60. #4772C2×C3semidirect
61. #4760C2×C3semidirect
62. #4697C2×C3semidirect
63. C4×D3×C8C2×C3semidirect
184. #488C3×D3semidirect
429. C32#3131semidirect
484. C3#81637direct (N × H)
485. C3C3×#3131semidirect

Maximal subgroups

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

subgroupindex
C3×#56882
C3×#56682
C32×#4882
C3×#50682
C3×#50562
C3×#48042
C3×#47922
C3×#47722
C3×#47602
C3×#46972
C3×C4×D3×C82
C3×#31313
#816373