Finite Group Databasebeta

← C3×#81767 #11878932

Subgroups — C3×#81767 #11878932

Order 1152.

859 conjugacy classes of subgroups.

The subgroup lattice has 489 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5728C211yesmaximal, characteristic, complemented
2C3×#5716C211yesmaximal, characteristic
3C32×#492C211yesmaximal, characteristic, complemented
4C3×#5173C214yesmaximal, complemented
5C3×#5166C214yesmaximal, complemented
6C3×#5092C211yesmaximal, characteristic, complemented
7C3×#5070C211yesmaximal, characteristic, complemented
8C3×#4685C211yesmaximal, characteristic, complemented
9C3×#4681C211yesmaximal, characteristic, complemented
10C3×#3210—31nomaximal
11#81767C311yesmaximal, characteristic, direct product factor
12C2×C3×#237C2212yes—
13C2×C32×SD16C2214yes—
14C32×C4⋊Q8C2211yescharacteristic
15C32×#127C2211yescharacteristic
16C3×#946C2212yes—
17C3×Q8×Dic3C2212yes—
18C2×C3×#216C2214yes—
19C3×#938—21no—
20C3×#938—21no—
21C3×#936C2212yes—
22C3×D4×Dic3—21no—
23C3×D4×Dic3—21no—
24C3×#897—21no—
25C3×#892—21no—
26C3×#890—21no—
27C3×#887—21no—
28C3×C42×D3C2211yescharacteristic
29C3×#869C2211yescharacteristic
30C3×#869C2211yescharacteristic
31C32×C4×C8C2211yescharacteristic
32C3×#832C2214yes—
33C3×(C2×D3)⋊C8C2212yes—
34C3×#816C2214yes—
35C3×Dic3⋊C8C2212yes—
36C3×C4×C3⋊C8C2211yescharacteristic
37C3×#533—31no—
38C3×#532—31no—
39#5728C2×C311yescharacteristic, complemented
40#5716C2×C311yescharacteristic
41C3×#494—31no—
42C3×#492—21no—
43C3×#492D311yescharacteristic, complemented
44C3×#492C2×C311yescharacteristic, complemented
45C3×#487—31no—
46C3×#486—31no—
47C3×#464—34no—
48C3×#452—34no—
49C3×#431—31no—
50#5173C2×C314yescomplemented
51#5166C2×C314yescomplemented
52#5092C2×C311yescharacteristic, complemented
53#5070C2×C311yescharacteristic, complemented
54#4685C2×C311yescharacteristic, complemented
55#4681C2×C311yescharacteristic, complemented
56C2×C32×Q8C2312yes—
57C2×C32×D4—21no—
58C2×C32×D4—21no—
59C2×C32×D4C2312yes—
60C2×C3×#67—22no—
61C22×C3×Dic3—22no—
62C3×#237—44no—
63C2×C3×C4×D3D411yescharacteristic
64C2×C3×C4×D3D411yescharacteristic
65C2×C3×C4×D3C2311yescharacteristic
66C2×C3×Dic6—21no—
67C2×C3×Dic6C2312yes—
68C32×SD16—44no—
69C2×C32×C8C2312yes—
70C32×C4⋊C4—21no—
71C32×C4⋊C4—21no—
72C32×C42C2311yescharacteristic
73C3×#217—22no—
74C3×#217—22no—
75C3×#216—44no—
76C3×(C2×D3)⋊C4—22no—
77C3×C4⋊Dic3—21no—
78C3×C4⋊Dic3—21no—
79C3×C4⋊Dic3—21no—
80C3×C4⋊Dic3—22no—
81C3×C4⋊Dic3C2312yes—
82C3×Dic3⋊C4—22no—
83C3×C4×Dic3—22no—
84C3×C4×Dic3D411yescharacteristic
85C3×C4×Dic3D411yescharacteristic
86C3×C4×Dic3C2311yescharacteristic
87C2×C3×C3⋊C8C2312yes—
88#3210—31noSylow
89C2×C3×#41—32no—
90C2×#237C22×C312yes—
91C2×C3×Q16—34no—
92C2×C3×SD16—24no—
93C2×C3×SD16C2×D314yes—
94C2×C3×SD16C22×C314yes—
95C3×C4⋊Q8—21no—
96C3×C4⋊Q8—31no—
97C3×C4⋊Q8—31no—
98C3×C4⋊Q8C2×D311yescharacteristic
99C3×C4⋊Q8C22×C311yescharacteristic
100C3×#127—21no—
101C3×#127C2×D311yescharacteristic
102C3×#127C22×C311yescharacteristic
103C3×#125—61no—
104C3×#124—32no—
105C3×C22⋊Q8—32no—
106C3×C22⋊Q8—61no—
107C3×#121—61no—
108C3×#121—61no—
109C3×C4×Q8—32no—
110C3×C4×Q8—61no—
111C3×C4×D4—61no—
112C3×C4×D4—61no—
113C3×#117—61no—
114C2×C3×C42—31no—
115#946C22×C312yes—
116Q8×Dic3C22×C312yes—
117C2×#216C22×C314yes—
118#938—21no—
119#938—21no—
120#936C22×C312yes—
121D4×Dic3—21no—
122D4×Dic3—21no—
123#897—21no—
124#892—21no—
125#890—21no—
126#887—21no—
127C42×D3C22×C311yescharacteristic
128#869C22×C311yescharacteristic
129#869C22×C311yescharacteristic
130C3×C4⋊C8—32no—
131C3×#103—34no—
132C3×#102—34no—
133C3×C22⋊C8—32no—
134C3×C4×C8—21no—
135C3×C4×C8—31no—
136C3×C4×C8C2×D311yescharacteristic
137C3×C4×C8C22×C311yescharacteristic
138#832C22×C314yes—
139(C2×D3)⋊C8C22×C312yes—
140#816C22×C314yes—
141Dic3⋊C8C22×C312yes—
142C4×C3⋊C8C22×C311yescharacteristic
143C23×C32—22no—
144C22×C3×D3C2×D411yescharacteristic
145C32×Q8—24no—
146C32×D4—24no—
147C32×D4—42no—
148C32×D4—42no—
149C2×C32×C4—22no—
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2411yescharacteristic
153C3×#67—44no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—44no—
157C2×C3×Dic3C2×D411yescharacteristic
158C2×C3×Dic3C2×D411yescharacteristic
159C2×C3×Dic3C2×D411yescharacteristic
160C3×C4×D3—22no—
161C3×C4×D3—22no—
162C3×C4×D3—22no—
163C3×Dic6—24no—
164C3×Dic6—42no—
165C32×C8—22no—
166C3×C3⋊C8—22no—
167#533—31no—
168#532—31no—
169#494—31no—
170#492C3×D311yescharacteristic, complemented
171#487—31no—
172#486—31no—
173#464—34no—
174#452—34no—
175#431—31no—
176C3×#41—124no—
177C2×C3×Q8—22no—
178C2×C3×Q8—32no—
179C2×C3×Q8—61no—
180C2×C3×Q8C22×D312yes—
181C2×C3×Q8C23×C312yes—
182C2×C3×D4—21no—
183C2×C3×D4—21no—
184C2×C3×D4—21no—
185C2×C3×D4—21no—
186C2×C3×D4—22no—
187C2×C3×D4—41no—
188C2×C3×D4—41no—
189C2×C3×D4—62no—
190C2×C3×D4C22×D312yes—
191C2×C3×D4C23×C312yes—
192C22×C3×C4—31no—
193C22×C3×C4—31no—
194C22×C3×C4—31no—
195C22×C3×C4—62no—
196C2×#67—22no—
197C22×Dic3—22no—
198#237—44no—
199C2×C4×D3C3×D411yescharacteristic
200C2×C4×D3C3×D411yescharacteristic
201C2×C4×D3C23×C311yescharacteristic
202C2×Dic6—21no—
203C2×Dic6C23×C312yes—
204C3×Q16—124no—
205C3×SD16—44no—
206C3×SD16—44no—
207C3×SD16—48no—
208C2×C3×C8—22no—
209C2×C3×C8—32no—
210C2×C3×C8C22×D312yes—
211C2×C3×C8C23×C312yes—
212C3×C4⋊C4—21no—
213C3×C4⋊C4—21no—
214C3×C4⋊C4—21no—
215C3×C4⋊C4—21no—
216C3×C4⋊C4—32no—
217C3×C4⋊C4—41no—
218C3×C4⋊C4—41no—
219C3×C4⋊C4—62no—
220C3×C4⋊C4—62no—
221C3×C4⋊C4—61no—
222C3×C4⋊C4—61no—
223C3×C4⋊C4—61no—
224C3×C22⋊C4—62no—
225C3×C22⋊C4—62no—
226C3×C22⋊C4—62no—
227C3×C42—21no—
228C3×C42—31no—
229C3×C42—31no—
230C3×C42—31no—
231C3×C42—62no—
232C3×C42C22×D311yescharacteristic
233C3×C42C23×C311yescharacteristic
234#217—22no—
235#217—22no—
236#216—44no—
237(C2×D3)⋊C4—22no—
238C4⋊Dic3—21no—
239C4⋊Dic3—21no—
240C4⋊Dic3—21no—
241C4⋊Dic3—22no—
242C4⋊Dic3C23×C312yes—
243Dic3⋊C4—22no—
244C4×Dic3—22no—
245C4×Dic3C3×D411yescharacteristic
246C4×Dic3C3×D411yescharacteristic
247C4×Dic3C23×C311yescharacteristic
248C2×C3⋊C8C23×C312yes—
249C22×C32—42no—
250C22×C32—42no—
251C22×C32—42no—
252C22×C32C22×D411yescharacteristic
253C2×C3×D3—21no—
254C2×C3×D3—21no—
255C2×C3×D3—21no—
256C32×C4—42no—
257C32×C4#13512yes—
258C32×C4#13712yes—
259C32×C4H(5,𝔽2)12yes—
260C3×Dic3—21no—
261C3×Dic3—21no—
262C3×Dic3—21no—
263C3×Dic3—42no—
264C3×Dic3—42no—
265C2×#41—32no—
266C2×Q16—34no—
267C2×SD16C2×C3×D314yes—
268C4⋊Q8—31no—
269C4⋊Q8—31no—
270C4⋊Q8C2×C3×D311yescharacteristic
271#127C2×C3×D311yescharacteristic
272#125—61no—
273#124—32no—
274C22⋊Q8—32no—
275C22⋊Q8—61no—
276#121—61no—
277#121—61no—
278C4×Q8—32no—
279C4×Q8—61no—
280C4×D4—61no—
281C4×D4—61no—
282#117—61no—
283C2×C42—31no—
284C4⋊C8—32no—
285#103—34no—
286#102—34no—
287C22⋊C8—32no—
288C4×C8—31no—
289C4×C8C2×C3×D311yescharacteristic
290C23×C3—22no—
291C23×C3—22no—
292C23×C3—31no—
293C23×C3—42no—
294C22×D3C2×C3×D411yescharacteristic
295C3×Q8—24no—
296C3×Q8—24no—
297C3×Q8—44no—
298C3×Q8—64no—
299C3×Q8—122no—
300C3×D4—24no—
301C3×D4—24no—
302C3×D4—44no—
303C3×D4—42no—
304C3×D4—42no—
305C3×D4—42no—
306C3×D4—42no—
307C3×D4—82no—
308C3×D4—82no—
309C3×D4—124no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—31no—
316C2×C3×C4—31no—
317C2×C3×C4—31no—
318C2×C3×C4—42no—
319C2×C3×C4—62no—
320C2×C3×C4—62no—
321C2×C3×C4—62no—
322C2×C3×C4—62no—
323C2×C3×C4—62no—
324C2×C3×C4—124no—
325C2×C3×C4D3×D411yescharacteristic
326C2×C3×C4D3×D411yescharacteristic
327C2×C3×C4C2×C3×D411yescharacteristic
328C2×C3×C4C2×C3×D411yescharacteristic
329C2×C3×C4C23×D311yescharacteristic
330C2×C3×C4C24×C311yescharacteristic
331#67—44no—
332C2×Dic3—22no—
333C2×Dic3—22no—
334C2×Dic3—44no—
335C2×Dic3C2×C3×D411yescharacteristic
336C2×Dic3C2×C3×D411yescharacteristic
337C2×Dic3C2×C3×D411yescharacteristic
338C4×D3—22no—
339C4×D3—22no—
340C4×D3—22no—
341Dic6—24no—
342Dic6—42no—
343C3×C8—24no—
344C3×C8—22no—
345C3×C8—22no—
346C3×C8—62no—
347C3⋊C8—22no—
348C2×C32—82no—
349C2×C32#53511yescharacteristic
350C2×C32C2×#13511yescharacteristic
351C2×C32C2×#13711yescharacteristic
352C3×D3—41no—
353#41—124no—
354C2×Q8—32no—
355C2×Q8—61no—
356C2×Q8C22×C3×D312yes—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—62no—
360C2×D4C22×C3×D312yes—
361C22×C4—31no—
362C22×C4—31no—
363C22×C4—31no—
364C22×C4—62no—
365Q16—124no—
366SD16—44no—
367C2×C8—32no—
368C2×C8C22×C3×D312yes—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—32no—
372C4⋊C4—62no—
373C4⋊C4—62no—
374C4⋊C4—61no—
375C4⋊C4—61no—
376C4⋊C4—61no—
377C22⋊C4—62no—
378C22⋊C4—62no—
379C22⋊C4—62no—
380C42—31no—
381C42—31no—
382C42—31no—
383C42—62no—
384C42C22×C3×D311yescharacteristic
385C22×C3—21no—
386C22×C3—42no—
387C22×C3—42no—
388C22×C3—42no—
389C22×C3—42no—
390C22×C3—42no—
391C22×C3—42no—
392C22×C3—61no—
393C22×C3—61no—
394C22×C3—61no—
395C22×C3—82no—
396C22×C3—82no—
397C22×C3—82no—
398C22×C3C2×D3×D411yescharacteristic
399C22×C3C22×C3×D411yescharacteristic
400C2×D3—21no—
401C2×D3—21no—
402C2×D3—21no—
403C3×C4—22no—
404C3×C4—22no—
405C3×C4—22no—
406C3×C4—42no—
407C3×C4—42no—
408C3×C4—61no—
409C3×C4—61no—
410C3×C4—61no—
411C3×C4—82no—
412C3×C4—122no—
413C3×C4—122no—
414C3×C4#91512yes—
415C3×C4#91612yes—
416C3×C4C3×#13512yes—
417C3×C4C3×#13712yes—
418C3×C4#100412yes—
419C3×C4C3×H(5,𝔽2)12yes—
420Dic3—21no—
421Dic3—21no—
422Dic3—21no—
423Dic3—42no—
424Dic3—42no—
425C32#321011yescharacteristic, complemented, Sylow
426C23—22no—
427C23—31no—
428Q8—24no—
429Q8—64no—
430Q8—122no—
431D4—24no—
432D4—42no—
433D4—42no—
434D4—124no—
435C2×C4—22no—
436C2×C4—31no—
437C2×C4—31no—
438C2×C4—31no—
439C2×C4—62no—
440C2×C4—62no—
441C2×C4—62no—
442C2×C4—62no—
443C2×C4—62no—
444C2×C4—124no—
445C2×C4C3×D3×D411yescharacteristic
446C2×C4C3×D3×D411yescharacteristic
447C2×C4C23×C3×D311yescharacteristic
448C8—22no—
449C8—62no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—82no—
454C2×C3—82no—
455C2×C3—121no—
456C2×C3—162no—
457C2×C3#571511yescharacteristic
458C2×C3C2×#91511yescharacteristic
459C2×C3C2×#91611yescharacteristic
460C2×C3C3×#53511yescharacteristic
461C2×C3C2×C3×#13511yescharacteristic
462C2×C3C2×C3×#13711yescharacteristic
463D3—41no—
464C22—42no—
465C22—42no—
466C22—42no—
467C22—61no—
468C22—61no—
469C22—61no—
470C22C2×C3×D3×D411yescharacteristic
471C4—42no—
472C4—61no—
473C4—61no—
474C4—61no—
475C4—122no—
476C4—122no—
477C4C3×#91512yes—
478C4C3×#91612yes—
479C4C3×#100412yes—
480C3—21no—
481C3#8176711yescharacteristic, direct product factor
482C3C3×#321011yescharacteristic, complemented
483C2—82no—
484C2—121no—
485C2C3×#571511yescharacteristic
486C2C2×C3×#91511yescharacteristic
487C2C2×C3×#91611yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#492C2
socleC22×C32C22×D4
prime radicalC3×#5716C2
hypercenterC3×#492D3
hypocenterC3C3×#3210
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#492

Complements

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

NH ≅ G/Ntype
1. C3×#5728C2semidirect
3. C32×#492C2semidirect
4. C3×#5173C2semidirect
5. C3×#5166C2semidirect
6. C3×#5092C2semidirect
7. C3×#5070C2semidirect
8. C3×#4685C2semidirect
9. C3×#4681C2semidirect
11. #81767C3direct (N × H)
39. #5728C2×C3semidirect
43. C3×#492D3semidirect
44. C3×#492C2×C3semidirect
50. #5173C2×C3semidirect
51. #5166C2×C3semidirect
52. #5092C2×C3semidirect
53. #5070C2×C3semidirect
54. #4685C2×C3semidirect
55. #4681C2×C3semidirect
170. #492C3×D3semidirect
425. C32#3210semidirect
481. C3#81767direct (N × H)
482. C3C3×#3210semidirect

Maximal subgroups

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

subgroupindex
C3×#57282
C3×#57162
C32×#4922
C3×#51732
C3×#51662
C3×#50922
C3×#50702
C3×#46852
C3×#46812
C3×#32103
#817673