Finite Group Databasebeta

← C3×#78863 #11866255

Subgroups — C3×#78863 #11866255

Order 1152.

1067 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5825C211yesmaximal, characteristic, complemented
2C2×C3×#949C211yesmaximal, characteristic
3C22×C3×#204C211yesmaximal, characteristic, complemented
4C3×#5521C211yesmaximal, characteristic, complemented
5C32×#416C211yesmaximal, characteristic, complemented
6C3×#5102C211yesmaximal, characteristic, complemented
7C3×#5004C211yesmaximal, characteristic, complemented
8C3×#4818C214yesmaximal, complemented
9C3×#4787C214yesmaximal, complemented
10C3×#3042—31nomaximal
11#78863C311yesmaximal, characteristic, direct product factor
12C2×C32×#41C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C22×C32×C8C2211yescharacteristic
16C32×#117C2211yescharacteristic
17C3×#949—24no—
18C3×#944C2212yescomplemented
19C2×C3×#215C2212yes—
20C3×#936C2212yescomplemented
21C3×#935—22no—
22C2×C3×#213C2212yes—
23C3×#926C2211yescharacteristic
24C3×#924—22no—
25C2×C3×#208C2211yescharacteristic
26C2×C3×#204—24no—
27C2×C3×#204C2214yes—
28C3×#893C2214yes—
29C3×D3×C22⋊C4—22no—
30C3×C4×D12—22no—
31C32×#103C2212yescomplemented
32C32×#102C2212yescomplemented
33C3×Dic3⋊C8C2214yescomplemented
34C3×#810C2214yescomplemented
35C2×C3×AGL(1,ℤ/8)—31no—
36C22×C3×SD16—31no—
37C3×#536—31no—
38C3×#518—31no—
39#5825C2×C311yescharacteristic, complemented
40C2×#949C2×C311yescharacteristic
41C22×#204C2×C311yescharacteristic, complemented
42#5521C2×C311yescharacteristic, complemented
43C3×#463—34no—
44C3×#461—34no—
45C3×#424—31no—
46C3×#419—31no—
47C3×#416—21no—
48C3×#416D311yescharacteristic, complemented
49C3×#416C2×C311yescharacteristic, complemented
50#5102C2×C311yescharacteristic, complemented
51#5004C2×C311yescharacteristic, complemented
52#4818C2×C314yescomplemented
53#4787C2×C314yescomplemented
54C23×C3×D3—21no—
55C32×#41—22no—
56C32×#41—22no—
57C2×C32×Q8C2311yescharacteristic
58C2×C32×D4—21no—
59C2×C32×D4C2311yescharacteristic
60C22×C32×C4—21no—
61C22×C32×C4C2311yescharacteristic
62C22×C3×Dic3—21no—
63C2×C3×D12—21no—
64C2×C3×D12—22no—
65C2×C3×D12D414yes—
66C2×C3×D12C2312yes—
67C2×C3×C4×D3—24no—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—22no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6C2312yes—
72C2×C32×C8—22no—
73C2×C32×C8C2312yes—
74C32×C4⋊C4C2312yes—
75C32×C22⋊C4—21no—
76C32×C42—21no—
77C3×#217—24no—
78C3×#217D412yes—
79C3×#215—24no—
80C3×#213—24no—
81C3×(C2×D3)⋊C4—24no—
82C3×C4⋊Dic3D412yes—
83C3×Dic3⋊C4—24no—
84C3×C4×Dic3C2312yes—
85C3×#208—22no—
86C2×C3×C3⋊C8C2312yes—
87C3×#204—28no—
88#3042—31noSylow
89C2×C3×#41—21no—
90C2×C3×#41C2×D311yescharacteristic
91C2×C3×#41C22×C311yescharacteristic
92C22×C3×Q8—31no—
93C22×C3×D4—31no—
94C22×D12C22×C311yescharacteristic
95C22×Dic6C22×C311yescharacteristic
96C3×AGL(1,ℤ/8)—64no—
97C2×C3×SD16—32no—
98C2×C3×SD16—34no—
99C2×C3×SD16—64no—
100C2×C3×D8—32no—
101C2×C3×M16—31no—
102C22×C3×C8—21no—
103C22×C3×C8C2×D311yescharacteristic
104C22×C3×C8C22×C311yescharacteristic
105C3×C4⋊Q8—32no—
106C3×#124—32no—
107C3×#123—62no—
108C3×C22⋊Q8—62no—
109C3×C4×D4—34no—
110C3×C4×D4—62no—
111C3×#117—21no—
112C3×#117—31no—
113C3×#117C2×D311yescharacteristic
114C3×#117C22×C311yescharacteristic
115C2×C3×C22⋊C4—62no—
116#949—24no—
117#944C22×C312yescomplemented
118C2×#215C22×C312yes—
119#936C22×C312yescomplemented
120#935—22no—
121C2×#213C22×C312yes—
122#926C22×C311yescharacteristic
123#924—22no—
124C2×#208C22×C311yescharacteristic
125C2×#204—24no—
126C2×#204C22×C314yes—
127#893C22×C314yes—
128D3×C22⋊C4—22no—
129C4×D12—22no—
130C3×C4⋊C8—34no—
131C3×#103—22no—
132C3×#103—34no—
133C3×#103C2×D312yescomplemented
134C3×#103C22×C312yescomplemented
135C3×#102—22no—
136C3×#102C2×D312yescomplemented
137C3×#102C22×C312yescomplemented
138Dic3⋊C8C22×C314yescomplemented
139#810C22×C314yescomplemented
140C23×C32—21no—
141C23×C32C2×D411yescharacteristic
142C22×C3×D3—22no—
143C22×C3×D3—24no—
144C22×C3×D3—82no—
145C32×Q8—21no—
146C32×Q8—21no—
147C32×D4—21no—
148C32×D4—21no—
149C32×D4—42no—
150C2×C32×C4—21no—
151C2×C32×C4—22no—
152C2×C32×C4—42no—
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×D412yes—
155C2×C32×C4#4112yes—
156C2×C32×C4C2411yescharacteristic
157C2×C3×Dic3—22no—
158C2×C3×Dic3—42no—
159C2×C3×Dic3C2×D414yes—
160C3×D12—24no—
161C3×D12—22no—
162C3×D12C2×D414yes—
163C3×C4×D3—84no—
164C3×Dic6—22no—
165C3×Dic6—22no—
166C3×Dic6—42no—
167C32×C8—22no—
168C3×C3⋊C8—22no—
169C2×AGL(1,ℤ/8)—31no—
170C22×SD16—31no—
171#536—31no—
172#518—31no—
173#463—34no—
174#461—34no—
175#424—31no—
176#419—31no—
177#416C3×D311yescharacteristic, complemented
178C24×C3—61no—
179C23×D3—21no—
180C3×#41—24no—
181C3×#41—22no—
182C3×#41—22no—
183C3×#41—22no—
184C3×#41—22no—
185C3×#41—42no—
186C2×C3×Q8—21no—
187C2×C3×Q8—32no—
188C2×C3×Q8—61no—
189C2×C3×Q8—62no—
190C2×C3×Q8—62no—
191C2×C3×Q8C22×D311yescharacteristic
192C2×C3×Q8C23×C311yescharacteristic
193C2×C3×D4—21no—
194C2×C3×D4—21no—
195C2×C3×D4—21no—
196C2×C3×D4—34no—
197C2×C3×D4—32no—
198C2×C3×D4—41no—
199C2×C3×D4—62no—
200C2×C3×D4—61no—
201C2×C3×D4C22×D311yescharacteristic
202C2×C3×D4C23×C311yescharacteristic
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—41no—
207C22×C3×C4—64no—
208C22×C3×C4—61no—
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C23×C311yescharacteristic
211C22×Dic3—21no—
212C2×D12—21no—
213C2×D12—22no—
214C2×D12C3×D414yes—
215C2×D12C23×C312yes—
216C2×C4×D3—24no—
217C2×Dic6—22no—
218C2×Dic6—22no—
219C2×Dic6—21no—
220C2×Dic6C23×C312yes—
221C3×SD16—68no—
222C3×SD16—64no—
223C3×D8—64no—
224C3×M16—62no—
225C2×C3×C8—22no—
226C2×C3×C8—22no—
227C2×C3×C8—22no—
228C2×C3×C8—32no—
229C2×C3×C8—42no—
230C2×C3×C8C22×D312yes—
231C2×C3×C8C23×C312yes—
232C3×C4⋊C4—22no—
233C3×C4⋊C4—32no—
234C3×C4⋊C4—64no—
235C3×C4⋊C4C22×D312yes—
236C3×C4⋊C4C23×C312yes—
237C3×C22⋊C4—21no—
238C3×C22⋊C4—21no—
239C3×C22⋊C4—32no—
240C3×C22⋊C4—41no—
241C3×C22⋊C4—64no—
242C3×C22⋊C4—64no—
243C3×C42—21no—
244C3×C42—21no—
245C3×C42—32no—
246C3×C42—41no—
247#217—24no—
248#217C3×D412yes—
249#215—24no—
250#213—24no—
251(C2×D3)⋊C4—24no—
252C4⋊Dic3C3×D412yes—
253Dic3⋊C4—24no—
254C4×Dic3C23×C312yes—
255#208—22no—
256C2×C3⋊C8C23×C312yes—
257#204—28no—
258C22×C32—22no—
259C22×C32—41no—
260C22×C32—42no—
261C22×C32#12112yes—
262C22×C32C22×D411yescharacteristic
263C2×C3×D3—24no—
264C2×C3×D3—44no—
265C2×C3×D3—84no—
266C32×C4—41no—
267C32×C4—42no—
268C32×C4#12112yes—
269C32×C4C22×D411yescharacteristic
270C32×C4C2×#4111yescharacteristic
271C3×Dic3—24no—
272C3×Dic3—42no—
273C2×#41C2×C3×D311yescharacteristic
274C22×Q8—31no—
275C22×D4—31no—
276AGL(1,ℤ/8)—64no—
277C2×SD16—32no—
278C2×SD16—34no—
279C2×SD16—64no—
280C2×D8—32no—
281C2×M16—31no—
282C22×C8C2×C3×D311yescharacteristic
283C4⋊Q8—32no—
284#124—32no—
285#123—62no—
286C22⋊Q8—62no—
287C4×D4—34no—
288C4×D4—62no—
289#117—31no—
290#117C2×C3×D311yescharacteristic
291C2×C22⋊C4—62no—
292C4⋊C8—34no—
293#103—34no—
294#103C2×C3×D312yescomplemented
295#102C2×C3×D312yescomplemented
296C23×C3—21no—
297C23×C3—21no—
298C23×C3—21no—
299C23×C3—41no—
300C23×C3—62no—
301C23×C3—64no—
302C23×C3—242no—
303C23×C3D3×D411yescharacteristic
304C23×C3C2×C3×D411yescharacteristic
305C22×D3—22no—
306C22×D3—24no—
307C22×D3—82no—
308C3×Q8—22no—
309C3×Q8—21no—
310C3×Q8—21no—
311C3×Q8—21no—
312C3×Q8—21no—
313C3×Q8—41no—
314C3×Q8—62no—
315C3×Q8—62no—
316C3×Q8—122no—
317C3×D4—22no—
318C3×D4—21no—
319C3×D4—21no—
320C3×D4—21no—
321C3×D4—21no—
322C3×D4—34no—
323C3×D4—41no—
324C3×D4—44no—
325C3×D4—42no—
326C3×D4—42no—
327C3×D4—64no—
328C3×D4—62no—
329C2×C3×C4—22no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—22no—
333C2×C3×C4—21no—
334C2×C3×C4—22no—
335C2×C3×C4—21no—
336C2×C3×C4—22no—
337C2×C3×C4—34no—
338C2×C3×C4—41no—
339C2×C3×C4—42no—
340C2×C3×C4—44no—
341C2×C3×C4—42no—
342C2×C3×C4—42no—
343C2×C3×C4—62no—
344C2×C3×C4—122no—
345C2×C3×C4—244no—
346C2×C3×C4#23512yes—
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4D3×D412yes—
349C2×C3×C4C2×C3×D411yescharacteristic
350C2×C3×C4C2×C3×D412yes—
351C2×C3×C4C3×#4112yes—
352C2×C3×C4C23×D311yescharacteristic
353C2×C3×C4C24×C311yescharacteristic
354C2×Dic3—22no—
355C2×Dic3—42no—
356C2×Dic3C2×C3×D414yes—
357D12—24no—
358D12—22no—
359D12C2×C3×D414yes—
360C4×D3—84no—
361Dic6—22no—
362Dic6—22no—
363Dic6—42no—
364C3×C8—22no—
365C3×C8—22no—
366C3×C8—42no—
367C3×C8—62no—
368C3⋊C8—22no—
369C2×C32—22no—
370C2×C32—81no—
371C2×C32C2×#12111yescharacteristic
372C2×C32#57712yes—
373C3×D3—44no—
374C24—61no—
375#41—22no—
376#41—22no—
377C2×Q8—32no—
378C2×Q8—61no—
379C2×Q8—62no—
380C2×Q8—62no—
381C2×Q8C22×C3×D311yescharacteristic
382C2×D4—21no—
383C2×D4—32no—
384C2×D4—34no—
385C2×D4—62no—
386C2×D4—61no—
387C2×D4C22×C3×D311yescharacteristic
388C22×C4—21no—
389C22×C4—64no—
390C22×C4—61no—
391C22×C4C22×C3×D311yescharacteristic
392SD16—68no—
393SD16—64no—
394D8—64no—
395M16—62no—
396C2×C8—22no—
397C2×C8—32no—
398C2×C8C22×C3×D312yes—
399C4⋊C4—32no—
400C4⋊C4—64no—
401C4⋊C4C22×C3×D312yes—
402C22⋊C4—21no—
403C22⋊C4—32no—
404C22⋊C4—64no—
405C22⋊C4—64no—
406C42—21no—
407C42—32no—
408C22×C3—22no—
409C22×C3—22no—
410C22×C3—22no—
411C22×C3—21no—
412C22×C3—42no—
413C22×C3—42no—
414C22×C3—42no—
415C22×C3—41no—
416C22×C3—42no—
417C22×C3—41no—
418C22×C3—64no—
419C22×C3—82no—
420C22×C3—124no—
421C22×C3—244no—
422C22×C3#88412yes—
423C22×C3C3×#12112yes—
424C22×C3C2×D3×D411yescharacteristic
425C22×C3C22×C3×D411yescharacteristic
426C2×D3—24no—
427C2×D3—44no—
428C2×D3—84no—
429C3×C4—22no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—42no—
433C3×C4—42no—
434C3×C4—41no—
435C3×C4—42no—
436C3×C4—41no—
437C3×C4—64no—
438C3×C4—82no—
439C3×C4—122no—
440C3×C4#88412yes—
441C3×C4C3×#12112yes—
442C3×C4C2×#23511yescharacteristic
443C3×C4C2×D3×D411yescharacteristic
444C3×C4C22×C3×D411yescharacteristic
445C3×C4C2×C3×#4111yescharacteristic
446Dic3—24no—
447Dic3—42no—
448C32#304211yescharacteristic, complemented, Sylow
449C23—21no—
450C23—62no—
451C23—64no—
452C23—242no—
453C23C3×D3×D411yescharacteristic
454Q8—21no—
455Q8—21no—
456Q8—62no—
457Q8—62no—
458Q8—122no—
459D4—21no—
460D4—21no—
461D4—34no—
462D4—42no—
463D4—64no—
464D4—62no—
465C2×C4—22no—
466C2×C4—21no—
467C2×C4—34no—
468C2×C4—42no—
469C2×C4—62no—
470C2×C4—122no—
471C2×C4—244no—
472C2×C4C3×#23512yes—
473C2×C4C3×D3×D411yescharacteristic
474C2×C4C3×D3×D412yes—
475C2×C4C23×C3×D311yescharacteristic
476C8—22no—
477C8—62no—
478C2×C3—22no—
479C2×C3—22no—
480C2×C3—21no—
481C2×C3—22no—
482C2×C3—42no—
483C2×C3—82no—
484C2×C3—81no—
485C2×C3—81no—
486C2×C3—124no—
487C2×C3C2×#88411yescharacteristic
488C2×C3#577012yes—
489C2×C3C2×C3×#12111yescharacteristic
490C2×C3C3×#57712yes—
491D3—44no—
492C22—22no—
493C22—41no—
494C22—42no—
495C22—64no—
496C22—124no—
497C22—244no—
498C22C3×#88412yes—
499C22C2×C3×D3×D411yescharacteristic
500C4—41no—
501C4—42no—
502C4—64no—
503C4—122no—
504C4C3×#88412yes—
505C4C2×C3×#23511yescharacteristic
506C4C2×C3×D3×D411yescharacteristic
507C3—21no—
508C3#7886311yescharacteristic, direct product factor
509C3C3×#304211yescharacteristic, complemented
510C2—22no—
511C2—81no—
512C2—124no—
513C2C2×C3×#88411yescharacteristic
514C2C3×#577012yes—
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#416C2
socleC22×C32C22×D4
prime radicalC2×C3×#949C2
hypercenterC3×#416D3
hypocenterC3C3×#3042
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#416

Complements

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

NH ≅ G/Ntype
1. C3×#5825C2semidirect
3. C22×C3×#204C2semidirect
4. C3×#5521C2semidirect
5. C32×#416C2semidirect
6. C3×#5102C2semidirect
7. C3×#5004C2semidirect
8. C3×#4818C2semidirect
9. C3×#4787C2semidirect
11. #78863C3direct (N × H)
18. C3×#944C22semidirect
20. C3×#936C22semidirect
31. C32×#103C22semidirect
32. C32×#102C22semidirect
33. C3×Dic3⋊C8C22semidirect
34. C3×#810C22semidirect
39. #5825C2×C3semidirect
41. C22×#204C2×C3semidirect
42. #5521C2×C3semidirect
48. C3×#416D3semidirect
49. C3×#416C2×C3semidirect
50. #5102C2×C3semidirect
51. #5004C2×C3semidirect
52. #4818C2×C3semidirect
53. #4787C2×C3semidirect
117. #944C22×C3semidirect
119. #936C22×C3semidirect
133. C3×#103C2×D3semidirect
134. C3×#103C22×C3semidirect
136. C3×#102C2×D3semidirect
137. C3×#102C22×C3semidirect
138. Dic3⋊C8C22×C3semidirect
139. #810C22×C3semidirect
177. #416C3×D3semidirect
294. #103C2×C3×D3semidirect
295. #102C2×C3×D3semidirect
448. C32#3042semidirect
508. C3#78863direct (N × H)
509. C3C3×#3042semidirect

Maximal subgroups

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

subgroupindex
C3×#58252
C2×C3×#9492
C22×C3×#2042
C3×#55212
C32×#4162
C3×#51022
C3×#50042
C3×#48182
C3×#47872
C3×#30423
#788633