Finite Group Databasebeta

← C3×#78945 #11866318

Subgroups — C3×#78945 #11866318

Order 1152.

1075 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5805C211yesmaximal, characteristic
2C22×C3×#214C211yesmaximal, characteristic, complemented
3C2×C3×#909C211yesmaximal, characteristic, complemented
4C3×#5516C211yesmaximal, characteristic, complemented
5C32×#418C211yesmaximal, characteristic, complemented
6C3×#5119C211yesmaximal, characteristic, complemented
7C3×#5002C211yesmaximal, characteristic, complemented
8C3×#4767C214yesmaximal, complemented
9C3×#4762C214yesmaximal, complemented
10C3×#3043—31nomaximal
11#78945C311yesmaximal, characteristic, direct product factor
12C22×C32×D4C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16C32×#117C2211yescharacteristic
17C3×#953—22no—
18C3×#940C2212yes—
19C3×#938—22no—
20C3×#936C2212yes—
21C2×C3×#214—24no—
22C2×C3×#214C2214yes—
23C3×#926C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C3×#909—24no—
26C2×C3×Dic12C2212yescomplemented
27C2×C3×#204C2212yescomplemented
28C3×#887C2214yescomplemented
29C3×#877—22no—
30C3×C4×Dic6—22no—
31C32×#102C2214yes—
32C3×Dic3⋊C8C2214yescomplemented
33C3×#810C2212yescomplemented
34C3×#809C2212yescomplemented
35C2×C3×#137—31no—
36C22×C3×SD16—31no—
37C3×#535—31no—
38C3×#519—31no—
39#5805C2×C311yescharacteristic
40C22×#214C2×C311yescharacteristic, complemented
41C2×#909C2×C311yescharacteristic, complemented
42#5516C2×C311yescharacteristic, complemented
43C3×#464—34no—
44C3×#460—34no—
45C3×#424—31no—
46C3×#418—21no—
47C3×#418D311yescharacteristic, complemented
48C3×#418C2×C311yescharacteristic, complemented
49C3×#416—31no—
50#5119C2×C311yescharacteristic, complemented
51#5002C2×C311yescharacteristic, complemented
52#4767C2×C314yescomplemented
53#4762C2×C314yescomplemented
54C24×C32—21no—
55C2×C32×D4—22no—
56C2×C32×D4—21no—
57C2×C32×D4—22no—
58C2×C32×D4C2312yes—
59C22×C32×C4C2311yescharacteristic
60C2×C3×#67—21no—
61C2×C3×#67—24no—
62C22×C3×Dic3—21no—
63C3×#235—22no—
64C3×#235—22no—
65C2×C3×D12C2311yescharacteristic
66C2×C3×C4×D3—21no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6—22no—
69C2×C3×Dic6D414yescomplemented
70C2×C3×Dic6C2311yescharacteristic
71C2×C3×Dic6C2312yes—
72C32×M16—22no—
73C2×C32×C8C2312yes—
74C32×C4⋊C4C2312yes—
75C32×C22⋊C4—21no—
76C32×C42—21no—
77C3×#217—24no—
78C3×#217D412yes—
79C3×#214—28no—
80C3×C4⋊Dic3D412yes—
81C3×Dic3⋊C4—24no—
82C3×C4×Dic3—24no—
83C3×C4×Dic3C2312yes—
84C2×C3×C3⋊C8—22no—
85C2×C3×C3⋊C8C2312yes—
86C3×Dic12—24no—
87C3×#204—24no—
88#3043—31noSylow
89C2×C3×#41—31no—
90C22×C3×Q8—31no—
91C22×C3×D4—21no—
92C22×C3×D4C2×D311yescharacteristic
93C22×C3×D4C22×C311yescharacteristic
94C2×#235C22×C311yescharacteristic
95C22×Dic6C22×C311yescharacteristic
96C3×#137—64no—
97C2×C3×Q16—32no—
98C2×C3×SD16—34no—
99C2×C3×SD16—32no—
100C2×C3×SD16—64no—
101C2×C3×M16—21no—
102C2×C3×M16C2×D311yescharacteristic
103C2×C3×M16C22×C311yescharacteristic
104C22×C3×C8—31no—
105C3×#127—32no—
106C3×#124—32no—
107C3×#121—62no—
108C3×#120—62no—
109C3×C4×Q8—34no—
110C3×C4×Q8—62no—
111C3×#117—21no—
112C3×#117—31no—
113C3×#117—62no—
114C3×#117C2×D311yescharacteristic
115C3×#117C22×C311yescharacteristic
116#953—22no—
117#940C22×C312yes—
118#938—22no—
119#936C22×C312yes—
120C2×#214—24no—
121C2×#214C22×C314yes—
122#926C22×C311yescharacteristic
123C22×C3⋊C8C22×C311yescharacteristic
124#909—24no—
125C2×Dic12C22×C312yescomplemented
126C2×#204C22×C312yescomplemented
127#887C22×C314yescomplemented
128#877—22no—
129C4×Dic6—22no—
130C3×C4⋊C8—34no—
131C3×#103—32no—
132C3×#102—24no—
133C3×#102—32no—
134C3×#102C2×D314yes—
135C3×#102C22×C314yes—
136Dic3⋊C8C22×C314yescomplemented
137#810C22×C312yescomplemented
138#809C22×C312yescomplemented
139C23×C32—22no—
140C23×C32—42no—
141C23×C32—82no—
142C23×C32C2×D411yescharacteristic
143C22×C3×D3—21no—
144C32×D4—22no—
145C32×D4—22no—
146C32×D4—42no—
147C2×C32×C4—22no—
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D412yes—
150C2×C32×C4#4112yes—
151C2×C32×C4C2411yescharacteristic
152C3×#67—42no—
153C3×#67—84no—
154C2×C3×Dic3—24no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—21no—
157C2×C3×Dic3C2×D414yes—
158C3×D12—21no—
159C3×D12—21no—
160C3×C4×D3—42no—
161C3×Dic6—24no—
162C3×Dic6—22no—
163C3×Dic6—21no—
164C3×Dic6—21no—
165C3×Dic6C2×D414yes—
166C32×C8—22no—
167C3×C3⋊C8—22no—
168C2×#137—31no—
169C22×SD16—31no—
170#535—31no—
171#519—31no—
172#464—34no—
173#460—34no—
174#424—31no—
175#418C3×D311yescharacteristic, complemented
176#416—31no—
177C24×C3—21no—
178C24×C3—21no—
179C24×C3—41no—
180C3×#41—62no—
181C3×#41—62no—
182C2×C3×Q8—34no—
183C2×C3×Q8—32no—
184C2×C3×Q8—31no—
185C2×C3×Q8—62no—
186C2×C3×Q8—61no—
187C2×C3×D4—24no—
188C2×C3×D4—22no—
189C2×C3×D4—22no—
190C2×C3×D4—21no—
191C2×C3×D4—22no—
192C2×C3×D4—21no—
193C2×C3×D4—22no—
194C2×C3×D4—22no—
195C2×C3×D4—31no—
196C2×C3×D4—42no—
197C2×C3×D4—41no—
198C2×C3×D4—64no—
199C2×C3×D4—61no—
200C2×C3×D4C22×D312yes—
201C2×C3×D4C23×C312yes—
202C22×C3×C4—21no—
203C22×C3×C4—61no—
204C22×C3×C4—61no—
205C22×C3×C4C22×D311yescharacteristic
206C22×C3×C4C23×C311yescharacteristic
207C2×#67—21no—
208C2×#67—24no—
209C22×Dic3—21no—
210#235—22no—
211#235—22no—
212C2×D12C23×C311yescharacteristic
213C2×C4×D3—21no—
214C2×Dic6—21no—
215C2×Dic6—22no—
216C2×Dic6C3×D414yescomplemented
217C2×Dic6C23×C311yescharacteristic
218C2×Dic6C23×C312yes—
219C3×Q16—64no—
220C3×SD16—64no—
221C3×SD16—68no—
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×C42—21no—
241C3×C42—21no—
242C3×C42—32no—
243C3×C42—41no—
244C3×C42—64no—
245#217—24no—
246#217C3×D412yes—
247#214—28no—
248C4⋊Dic3C3×D412yes—
249Dic3⋊C4—24no—
250C4×Dic3—24no—
251C4×Dic3C23×C312yes—
252C2×C3⋊C8—22no—
253C2×C3⋊C8C23×C312yes—
254Dic12—24no—
255#204—24no—
256C22×C32—22no—
257C22×C32—42no—
258C22×C32—44no—
259C22×C32—84no—
260C22×C32#12112yes—
261C22×C32C22×D411yescharacteristic
262C2×C3×D3—41no—
263C2×C3×D3—42no—
264C32×C4—42no—
265C32×C4#12112yes—
266C32×C4C22×D411yescharacteristic
267C32×C4C2×#4111yescharacteristic
268C3×Dic3—24no—
269C3×Dic3—24no—
270C3×Dic3—41no—
271C2×#41—31no—
272C22×Q8—31no—
273C22×D4C2×C3×D311yescharacteristic
274#137—64no—
275C2×Q16—32no—
276C2×SD16—34no—
277C2×SD16—32no—
278C2×SD16—64no—
279C2×M16C2×C3×D311yescharacteristic
280C22×C8—31no—
281#127—32no—
282#124—32no—
283#121—62no—
284#120—62no—
285C4×Q8—34no—
286C4×Q8—62no—
287#117—31no—
288#117—62no—
289#117C2×C3×D311yescharacteristic
290C4⋊C8—34no—
291#103—32no—
292#102—32no—
293#102C2×C3×D314yes—
294C23×C3—22no—
295C23×C3—22no—
296C23×C3—21no—
297C23×C3—42no—
298C23×C3—44no—
299C23×C3—42no—
300C23×C3—42no—
301C23×C3—61no—
302C23×C3—82no—
303C23×C3—82no—
304C23×C3—84no—
305C23×C3D3×D411yescharacteristic
306C23×C3C2×C3×D411yescharacteristic
307C22×D3—21no—
308C3×Q8—34no—
309C3×Q8—64no—
310C3×Q8—62no—
311C3×Q8—61no—
312C3×Q8—61no—
313C3×D4—24no—
314C3×D4—22no—
315C3×D4—22no—
316C3×D4—22no—
317C3×D4—22no—
318C3×D4—42no—
319C3×D4—44no—
320C3×D4—42no—
321C3×D4—42no—
322C3×D4—61no—
323C3×D4—61no—
324C3×D4—122no—
325C3×D4—244no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—21no—
329C2×C3×C4—22no—
330C2×C3×C4—21no—
331C2×C3×C4—22no—
332C2×C3×C4—34no—
333C2×C3×C4—42no—
334C2×C3×C4—64no—
335C2×C3×C4—62no—
336C2×C3×C4—61no—
337C2×C3×C4—122no—
338C2×C3×C4#23512yes—
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4D3×D412yes—
341C2×C3×C4C2×C3×D411yescharacteristic
342C2×C3×C4C2×C3×D412yes—
343C2×C3×C4C3×#4112yes—
344C2×C3×C4C23×D311yescharacteristic
345C2×C3×C4C24×C311yescharacteristic
346#67—42no—
347#67—84no—
348C2×Dic3—24no—
349C2×Dic3—22no—
350C2×Dic3—21no—
351C2×Dic3C2×C3×D414yes—
352D12—21no—
353D12—21no—
354C4×D3—42no—
355Dic6—24no—
356Dic6—22no—
357Dic6—21no—
358Dic6—21no—
359Dic6C2×C3×D414yes—
360C3×C8—22no—
361C3×C8—22no—
362C3×C8—42no—
363C3×C8—62no—
364C3⋊C8—22no—
365C2×C32—22no—
366C2×C32—82no—
367C2×C32C2×#12111yescharacteristic
368C2×C32#57712yes—
369C3×D3—81no—
370C24—21no—
371#41—62no—
372#41—62no—
373C2×Q8—32no—
374C2×Q8—31no—
375C2×Q8—34no—
376C2×Q8—62no—
377C2×Q8—61no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—21no—
381C2×D4—31no—
382C2×D4—64no—
383C2×D4—61no—
384C2×D4C22×C3×D312yes—
385C22×C4—61no—
386C22×C4—61no—
387C22×C4C22×C3×D311yescharacteristic
388Q16—64no—
389SD16—64no—
390SD16—68no—
391M16—22no—
392C2×C8—32no—
393C2×C8—62no—
394C2×C8C22×C3×D312yes—
395C4⋊C4—32no—
396C4⋊C4—64no—
397C4⋊C4C22×C3×D312yes—
398C22⋊C4—21no—
399C22⋊C4—32no—
400C22⋊C4—64no—
401C42—21no—
402C42—32no—
403C42—64no—
404C22×C3—22no—
405C22×C3—22no—
406C22×C3—22no—
407C22×C3—21no—
408C22×C3—42no—
409C22×C3—44no—
410C22×C3—44no—
411C22×C3—42no—
412C22×C3—44no—
413C22×C3—42no—
414C22×C3—84no—
415C22×C3—84no—
416C22×C3—84no—
417C22×C3—88no—
418C22×C3—121no—
419C22×C3—122no—
420C22×C3#88412yes—
421C22×C3C3×#12112yes—
422C22×C3C2×D3×D411yescharacteristic
423C22×C3C22×C3×D411yescharacteristic
424C2×D3—42no—
425C2×D3—41no—
426C3×C4—22no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—42no—
430C3×C4—42no—
431C3×C4—64no—
432C3×C4—64no—
433C3×C4—82no—
434C3×C4—121no—
435C3×C4#88412yes—
436C3×C4C3×#12112yes—
437C3×C4C2×#23511yescharacteristic
438C3×C4C2×D3×D411yescharacteristic
439C3×C4C22×C3×D411yescharacteristic
440C3×C4C2×C3×#4111yescharacteristic
441Dic3—24no—
442Dic3—24no—
443Dic3—41no—
444C32#304311yescharacteristic, complemented, Sylow
445C23—22no—
446C23—42no—
447C23—61no—
448C23—82no—
449C23C3×D3×D411yescharacteristic
450Q8—34no—
451Q8—64no—
452Q8—62no—
453Q8—61no—
454Q8—61no—
455D4—22no—
456D4—22no—
457D4—42no—
458D4—61no—
459D4—61no—
460D4—122no—
461D4—244no—
462C2×C4—22no—
463C2×C4—34no—
464C2×C4—64no—
465C2×C4—62no—
466C2×C4—61no—
467C2×C4—122no—
468C2×C4C3×#23512yes—
469C2×C4C3×D3×D411yescharacteristic
470C2×C4C3×D3×D412yes—
471C2×C4C23×C3×D311yescharacteristic
472C8—22no—
473C8—62no—
474C2×C3—22no—
475C2×C3—22no—
476C2×C3—21no—
477C2×C3—22no—
478C2×C3—42no—
479C2×C3—84no—
480C2×C3—82no—
481C2×C3—82no—
482C2×C3—241no—
483C2×C3C2×#88411yescharacteristic
484C2×C3#577512yes—
485C2×C3C2×C3×#12111yescharacteristic
486C2×C3C3×#57712yes—
487D3—81no—
488C22—22no—
489C22—42no—
490C22—44no—
491C22—84no—
492C22—121no—
493C22—122no—
494C22C3×#88412yes—
495C22C2×C3×D3×D411yescharacteristic
496C4—42no—
497C4—64no—
498C4—64no—
499C4—121no—
500C4C3×#88412yes—
501C4C2×C3×#23511yescharacteristic
502C4C2×C3×D3×D411yescharacteristic
503C3—21no—
504C3#7894511yescharacteristic, direct product factor
505C3C3×#304311yescharacteristic, complemented
506C2—22no—
507C2—82no—
508C2—241no—
509C2C2×C3×#88411yescharacteristic
510C2C3×#577512yes—
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#418C2
socleC22×C32C22×D4
prime radicalC3×#5805C2
hypercenterC3×#418D3
hypocenterC3C3×#3043
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#418

Complements

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

NH ≅ G/Ntype
2. C22×C3×#214C2semidirect
3. C2×C3×#909C2semidirect
4. C3×#5516C2semidirect
5. C32×#418C2semidirect
6. C3×#5119C2semidirect
7. C3×#5002C2semidirect
8. C3×#4767C2semidirect
9. C3×#4762C2semidirect
11. #78945C3direct (N × H)
26. C2×C3×Dic12C22semidirect
27. C2×C3×#204C22semidirect
28. C3×#887C22semidirect
32. C3×Dic3⋊C8C22semidirect
33. C3×#810C22semidirect
34. C3×#809C22semidirect
40. C22×#214C2×C3semidirect
41. C2×#909C2×C3semidirect
42. #5516C2×C3semidirect
47. C3×#418D3semidirect
48. C3×#418C2×C3semidirect
50. #5119C2×C3semidirect
51. #5002C2×C3semidirect
52. #4767C2×C3semidirect
53. #4762C2×C3semidirect
69. C2×C3×Dic6D4semidirect
125. C2×Dic12C22×C3semidirect
126. C2×#204C22×C3semidirect
127. #887C22×C3semidirect
136. Dic3⋊C8C22×C3semidirect
137. #810C22×C3semidirect
138. #809C22×C3semidirect
175. #418C3×D3semidirect
216. C2×Dic6C3×D4semidirect
444. C32#3043semidirect
504. C3#78945direct (N × H)
505. C3C3×#3043semidirect

Maximal subgroups

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

subgroupindex
C3×#58052
C22×C3×#2142
C2×C3×#9092
C3×#55162
C32×#4182
C3×#51192
C3×#50022
C3×#47672
C3×#47622
C3×#30433
#789453