Finite Group Databasebeta

← C3×#78976 #11866243

Subgroups — C3×#78976 #11866243

Order 1152.

1063 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5816C211yesmaximal, characteristic, complemented
2C22×C3×#215C211yesmaximal, characteristic, complemented
3C2×C3×#908C211yesmaximal, characteristic
4C3×#5521C211yesmaximal, characteristic, complemented
5C32×#419C211yesmaximal, characteristic, complemented
6C3×#5119C211yesmaximal, characteristic, complemented
7C3×#5002C211yesmaximal, characteristic, complemented
8C3×#4819C214yesmaximal, complemented
9C3×#4818C214yesmaximal, complemented
10C3×#3042—31nomaximal
11#78976C311yesmaximal, characteristic, direct product factor
12C22×C32×Q8C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16C32×#117C2211yescharacteristic
17C3×#947C2212yescomplemented
18C3×#946—22no—
19C3×#944C2212yescomplemented
20C2×C3×#215—24no—
21C2×C3×#215C2214yes—
22C3×#929—22no—
23C3×#926C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C3×#908—24no—
26C2×C3×D24C2212yes—
27C2×C3×#204C2212yes—
28C3×#893C2214yes—
29C3×D3×C22⋊C4—22no—
30C3×C4×D12—22no—
31C32×#103C2214yescomplemented
32C3×Dic3⋊C8C2214yescomplemented
33C3×#810C2212yescomplemented
34C3×#809C2212yescomplemented
35C2×C3×AGL(1,ℤ/8)—31no—
36C22×C3×SD16—31no—
37C3×#536—31no—
38C3×#518—31no—
39#5816C2×C311yescharacteristic, complemented
40C22×#215C2×C311yescharacteristic, complemented
41C2×#908C2×C311yescharacteristic
42#5521C2×C311yescharacteristic, complemented
43C3×#463—34no—
44C3×#461—34no—
45C3×#424—31no—
46C3×#419—21no—
47C3×#419D311yescharacteristic, complemented
48C3×#419C2×C311yescharacteristic, complemented
49C3×#416—31no—
50#5119C2×C311yescharacteristic, complemented
51#5002C2×C311yescharacteristic, complemented
52#4819C2×C314yescomplemented
53#4818C2×C314yescomplemented
54C23×C3×D3—21no—
55C2×C32×Q8—21no—
56C2×C32×Q8—22no—
57C2×C32×Q8—22no—
58C2×C32×Q8C2312yes—
59C22×C32×C4—21no—
60C22×C32×C4C2311yescharacteristic
61C2×C3×#67—21no—
62C3×#235—22no—
63C3×#235—22no—
64C2×C3×D12—21no—
65C2×C3×D12—22no—
66C2×C3×D12D414yes—
67C2×C3×D12C2311yescharacteristic
68C2×C3×D12C2312yes—
69C2×C3×C4×D3—21no—
70C2×C3×C4×D3—24no—
71C2×C3×Dic6C2311yescharacteristic
72C32×M16—22no—
73C2×C32×C8C2312yes—
74C32×C4⋊C4C2312yes—
75C32×C22⋊C4—21no—
76C32×C42—21no—
77C3×#217D412yes—
78C3×#215—28no—
79C3×(C2×D3)⋊C4—24no—
80C3×(C2×D3)⋊C4—24no—
81C3×C4⋊Dic3D412yes—
82C3×Dic3⋊C4—24no—
83C3×C4×Dic3C2312yes—
84C2×C3×C3⋊C8—22no—
85C2×C3×C3⋊C8C2312yes—
86C3×D24—24no—
87C3×#204—24no—
88#3042—31noSylow
89C2×C3×#41—31no—
90C22×C3×Q8—21no—
91C22×C3×Q8C2×D311yescharacteristic
92C22×C3×Q8C22×C311yescharacteristic
93C22×C3×D4—31no—
94C2×#235C22×C311yescharacteristic
95C22×D12C22×C311yescharacteristic
96C3×AGL(1,ℤ/8)—64no—
97C2×C3×SD16—34no—
98C2×C3×SD16—32no—
99C2×C3×SD16—64no—
100C2×C3×D8—32no—
101C2×C3×M16—21no—
102C2×C3×M16C2×D311yescharacteristic
103C2×C3×M16C22×C311yescharacteristic
104C22×C3×C8—31no—
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#947C22×C312yescomplemented
117#946—22no—
118#944C22×C312yescomplemented
119C2×#215—24no—
120C2×#215C22×C314yes—
121#929—22no—
122#926C22×C311yescharacteristic
123C22×C3⋊C8C22×C311yescharacteristic
124#908—24no—
125C2×D24C22×C312yes—
126C2×#204C22×C312yes—
127#893C22×C314yes—
128D3×C22⋊C4—22no—
129C4×D12—22no—
130C3×C4⋊C8—34no—
131C3×#103—24no—
132C3×#103—32no—
133C3×#103C2×D314yescomplemented
134C3×#103C22×C314yescomplemented
135C3×#102—32no—
136Dic3⋊C8C22×C314yescomplemented
137#810C22×C312yescomplemented
138#809C22×C312yescomplemented
139C23×C32C2×D411yescharacteristic
140C22×C3×D3—22no—
141C22×C3×D3—24no—
142C22×C3×D3—21no—
143C22×C3×D3—82no—
144C32×Q8—22no—
145C32×Q8—22no—
146C32×Q8—42no—
147C2×C32×C4—22no—
148C2×C32×C4—22no—
149C2×C32×C4—42no—
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D412yes—
152C2×C32×C4#4112yes—
153C2×C32×C4C2411yescharacteristic
154C3×#67—42no—
155C2×C3×Dic3—21no—
156C2×C3×Dic3C2×D414yes—
157C3×D12—24no—
158C3×D12—21no—
159C3×D12—22no—
160C3×D12—21no—
161C3×D12C2×D414yes—
162C3×C4×D3—42no—
163C3×C4×D3—84no—
164C3×Dic6—21no—
165C3×Dic6—21no—
166C32×C8—22no—
167C3×C3⋊C8—22no—
168C2×AGL(1,ℤ/8)—31no—
169C22×SD16—31no—
170#536—31no—
171#518—31no—
172#463—34no—
173#461—34no—
174#424—31no—
175#419C3×D311yescharacteristic, complemented
176#416—31no—
177C24×C3—61no—
178C23×D3—21no—
179C3×#41—62no—
180C3×#41—62no—
181C2×C3×Q8—21no—
182C2×C3×Q8—21no—
183C2×C3×Q8—24no—
184C2×C3×Q8—22no—
185C2×C3×Q8—22no—
186C2×C3×Q8—22no—
187C2×C3×Q8—22no—
188C2×C3×Q8—22no—
189C2×C3×Q8—31no—
190C2×C3×Q8—41no—
191C2×C3×Q8—42no—
192C2×C3×Q8C22×D312yes—
193C2×C3×Q8C23×C312yes—
194C2×C3×D4—34no—
195C2×C3×D4—32no—
196C2×C3×D4—31no—
197C2×C3×D4—61no—
198C2×C3×D4—62no—
199C2×C3×D4—61no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—41no—
204C22×C3×C4—64no—
205C22×C3×C4—61no—
206C22×C3×C4C22×D311yescharacteristic
207C22×C3×C4C23×C311yescharacteristic
208C2×#67—21no—
209#235—22no—
210#235—22no—
211C2×D12—21no—
212C2×D12—22no—
213C2×D12C3×D414yes—
214C2×D12C23×C311yescharacteristic
215C2×D12C23×C312yes—
216C2×C4×D3—21no—
217C2×C4×D3—24no—
218C2×Dic6C23×C311yescharacteristic
219C3×SD16—64no—
220C3×SD16—68no—
221C3×D8—64no—
222C3×M16—22no—
223C3×M16—22no—
224C3×M16—42no—
225C2×C3×C8—22no—
226C2×C3×C8—32no—
227C2×C3×C8—62no—
228C2×C3×C8C22×D312yes—
229C2×C3×C8C23×C312yes—
230C3×C4⋊C4—22no—
231C3×C4⋊C4—32no—
232C3×C4⋊C4—64no—
233C3×C4⋊C4C22×D312yes—
234C3×C4⋊C4C23×C312yes—
235C3×C22⋊C4—21no—
236C3×C22⋊C4—21no—
237C3×C22⋊C4—32no—
238C3×C22⋊C4—41no—
239C3×C22⋊C4—64no—
240C3×C22⋊C4—64no—
241C3×C42—21no—
242C3×C42—21no—
243C3×C42—32no—
244C3×C42—41no—
245#217C3×D412yes—
246#215—28no—
247(C2×D3)⋊C4—24no—
248(C2×D3)⋊C4—24no—
249C4⋊Dic3C3×D412yes—
250Dic3⋊C4—24no—
251C4×Dic3C23×C312yes—
252C2×C3⋊C8—22no—
253C2×C3⋊C8C23×C312yes—
254D24—24no—
255#204—24no—
256C22×C32—22no—
257C22×C32#12112yes—
258C22×C32C22×D411yescharacteristic
259C2×C3×D3—24no—
260C2×C3×D3—44no—
261C2×C3×D3—41no—
262C2×C3×D3—42no—
263C2×C3×D3—84no—
264C32×C4—42no—
265C32×C4—42no—
266C32×C4#12112yes—
267C32×C4C22×D411yescharacteristic
268C32×C4C2×#4111yescharacteristic
269C3×Dic3—24no—
270C3×Dic3—41no—
271C2×#41—31no—
272C22×Q8C2×C3×D311yescharacteristic
273C22×D4—31no—
274AGL(1,ℤ/8)—64no—
275C2×SD16—34no—
276C2×SD16—32no—
277C2×SD16—64no—
278C2×D8—32no—
279C2×M16C2×C3×D311yescharacteristic
280C22×C8—31no—
281C4⋊Q8—32no—
282#124—32no—
283#123—62no—
284C22⋊Q8—62no—
285C4×D4—34no—
286C4×D4—62no—
287#117—31no—
288#117C2×C3×D311yescharacteristic
289C2×C22⋊C4—62no—
290C4⋊C8—34no—
291#103—32no—
292#103C2×C3×D314yescomplemented
293#102—32no—
294C23×C3—21no—
295C23×C3—62no—
296C23×C3—64no—
297C23×C3—61no—
298C23×C3—242no—
299C23×C3D3×D411yescharacteristic
300C23×C3C2×C3×D411yescharacteristic
301C22×D3—22no—
302C22×D3—24no—
303C22×D3—21no—
304C22×D3—82no—
305C3×Q8—24no—
306C3×Q8—22no—
307C3×Q8—22no—
308C3×Q8—22no—
309C3×Q8—22no—
310C3×Q8—42no—
311C3×Q8—44no—
312C3×Q8—42no—
313C3×Q8—42no—
314C3×Q8—61no—
315C3×Q8—61no—
316C3×D4—34no—
317C3×D4—64no—
318C3×D4—62no—
319C3×D4—61no—
320C3×D4—61no—
321C3×D4—122no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—21no—
327C2×C3×C4—22no—
328C2×C3×C4—21no—
329C2×C3×C4—22no—
330C2×C3×C4—34no—
331C2×C3×C4—42no—
332C2×C3×C4—42no—
333C2×C3×C4—44no—
334C2×C3×C4—42no—
335C2×C3×C4—42no—
336C2×C3×C4—61no—
337C2×C3×C4—122no—
338C2×C3×C4—244no—
339C2×C3×C4#23512yes—
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4D3×D412yes—
342C2×C3×C4C2×C3×D411yescharacteristic
343C2×C3×C4C2×C3×D412yes—
344C2×C3×C4C3×#4112yes—
345C2×C3×C4C23×D311yescharacteristic
346C2×C3×C4C24×C311yescharacteristic
347#67—42no—
348C2×Dic3—21no—
349C2×Dic3C2×C3×D414yes—
350D12—24no—
351D12—21no—
352D12—22no—
353D12—21no—
354D12C2×C3×D414yes—
355C4×D3—42no—
356C4×D3—84no—
357Dic6—21no—
358Dic6—21no—
359C3×C8—22no—
360C3×C8—22no—
361C3×C8—42no—
362C3×C8—62no—
363C3⋊C8—22no—
364C2×C32—22no—
365C2×C32C2×#12111yescharacteristic
366C2×C32#57712yes—
367C3×D3—44no—
368C3×D3—81no—
369C24—61no—
370#41—62no—
371#41—62no—
372C2×Q8—21no—
373C2×Q8—22no—
374C2×Q8—22no—
375C2×Q8—31no—
376C2×Q8C22×C3×D312yes—
377C2×D4—32no—
378C2×D4—31no—
379C2×D4—34no—
380C2×D4—61no—
381C2×D4—62no—
382C2×D4—61no—
383C22×C4—21no—
384C22×C4—64no—
385C22×C4—61no—
386C22×C4C22×C3×D311yescharacteristic
387SD16—64no—
388SD16—68no—
389D8—64no—
390M16—22no—
391C2×C8—32no—
392C2×C8—62no—
393C2×C8C22×C3×D312yes—
394C4⋊C4—32no—
395C4⋊C4—64no—
396C4⋊C4C22×C3×D312yes—
397C22⋊C4—21no—
398C22⋊C4—32no—
399C22⋊C4—64no—
400C22⋊C4—64no—
401C42—21no—
402C42—32no—
403C22×C3—22no—
404C22×C3—22no—
405C22×C3—22no—
406C22×C3—21no—
407C22×C3—42no—
408C22×C3—64no—
409C22×C3—124no—
410C22×C3—121no—
411C22×C3—122no—
412C22×C3—244no—
413C22×C3#88412yes—
414C22×C3C3×#12112yes—
415C22×C3C2×D3×D411yescharacteristic
416C22×C3C22×C3×D411yescharacteristic
417C2×D3—24no—
418C2×D3—44no—
419C2×D3—42no—
420C2×D3—41no—
421C2×D3—84no—
422C3×C4—22no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—44no—
426C3×C4—42no—
427C3×C4—42no—
428C3×C4—42no—
429C3×C4—42no—
430C3×C4—64no—
431C3×C4—82no—
432C3×C4—121no—
433C3×C4#88412yes—
434C3×C4C3×#12112yes—
435C3×C4C2×#23511yescharacteristic
436C3×C4C2×D3×D411yescharacteristic
437C3×C4C22×C3×D411yescharacteristic
438C3×C4C2×C3×#4111yescharacteristic
439Dic3—24no—
440Dic3—41no—
441C32#304211yescharacteristic, complemented, Sylow
442C23—62no—
443C23—64no—
444C23—61no—
445C23—242no—
446C23C3×D3×D411yescharacteristic
447Q8—22no—
448Q8—22no—
449Q8—42no—
450Q8—61no—
451Q8—61no—
452D4—34no—
453D4—64no—
454D4—62no—
455D4—61no—
456D4—61no—
457D4—122no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—34no—
461C2×C4—42no—
462C2×C4—61no—
463C2×C4—122no—
464C2×C4—244no—
465C2×C4C3×#23512yes—
466C2×C4C3×D3×D411yescharacteristic
467C2×C4C3×D3×D412yes—
468C2×C4C23×C3×D311yescharacteristic
469C8—22no—
470C8—62no—
471C2×C3—22no—
472C2×C3—22no—
473C2×C3—21no—
474C2×C3—22no—
475C2×C3—42no—
476C2×C3—124no—
477C2×C3—241no—
478C2×C3C2×#88411yescharacteristic
479C2×C3#577812yes—
480C2×C3C2×C3×#12111yescharacteristic
481C2×C3C3×#57712yes—
482D3—44no—
483D3—81no—
484C22—22no—
485C22—64no—
486C22—124no—
487C22—121no—
488C22—122no—
489C22—244no—
490C22C3×#88412yes—
491C22C2×C3×D3×D411yescharacteristic
492C4—42no—
493C4—42no—
494C4—64no—
495C4—121no—
496C4C3×#88412yes—
497C4C2×C3×#23511yescharacteristic
498C4C2×C3×D3×D411yescharacteristic
499C3—21no—
500C3#7897611yescharacteristic, direct product factor
501C3C3×#304211yescharacteristic, complemented
502C2—22no—
503C2—124no—
504C2—241no—
505C2C2×C3×#88411yescharacteristic
506C2C3×#577812yes—
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#419C2
socleC22×C32C22×D4
prime radicalC2×C3×#908C2
hypercenterC3×#419D3
hypocenterC3C3×#3042
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#419

Complements

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

NH ≅ G/Ntype
1. C3×#5816C2semidirect
2. C22×C3×#215C2semidirect
4. C3×#5521C2semidirect
5. C32×#419C2semidirect
6. C3×#5119C2semidirect
7. C3×#5002C2semidirect
8. C3×#4819C2semidirect
9. C3×#4818C2semidirect
11. #78976C3direct (N × H)
17. C3×#947C22semidirect
19. C3×#944C22semidirect
31. C32×#103C22semidirect
32. C3×Dic3⋊C8C22semidirect
33. C3×#810C22semidirect
34. C3×#809C22semidirect
39. #5816C2×C3semidirect
40. C22×#215C2×C3semidirect
42. #5521C2×C3semidirect
47. C3×#419D3semidirect
48. C3×#419C2×C3semidirect
50. #5119C2×C3semidirect
51. #5002C2×C3semidirect
52. #4819C2×C3semidirect
53. #4818C2×C3semidirect
116. #947C22×C3semidirect
118. #944C22×C3semidirect
133. C3×#103C2×D3semidirect
134. C3×#103C22×C3semidirect
136. Dic3⋊C8C22×C3semidirect
137. #810C22×C3semidirect
138. #809C22×C3semidirect
175. #419C3×D3semidirect
292. #103C2×C3×D3semidirect
441. C32#3042semidirect
500. C3#78976direct (N × H)
501. C3C3×#3042semidirect

Maximal subgroups

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

subgroupindex
C3×#58162
C22×C3×#2152
C2×C3×#9082
C3×#55212
C32×#4192
C3×#51192
C3×#50022
C3×#48192
C3×#48182
C3×#30423
#789763