Finite Group Databasebeta

← C3×#78915 #11860663

Subgroups — C3×#78915 #11860663

Order 1152.

1151 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5798C211yesmaximal, characteristic, complemented
2C22×C3×#213C211yesmaximal, characteristic
3C3×#5521C211yesmaximal, characteristic, complemented
4C32×#418C211yesmaximal, characteristic, complemented
5C3×#5131C211yesmaximal, characteristic, complemented
6C3×#5122C211yesmaximal, characteristic, complemented
7C3×#4998C211yesmaximal, characteristic, complemented
8C3×#4785C214yesmaximal, complemented
9C3×#4756C214yesmaximal, complemented
10C3×#2948—31nomaximal
11#78915C311yesmaximal, characteristic, direct product factor
12C22×C32×D4C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15C32×#117C2211yescharacteristic
16C2×C3×#217—22no—
17C3×D4×Dic3—22no—
18C3×D4×Dic3C2214yescomplemented
19C2×C3×#213C418yescomplemented
20C2×C3×#213C2212yes—
21C2×C3×#213C2212yes—
22C3×#926C2211yescharacteristic
23C3×#926C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C3×#893C2214yescomplemented
26C3×D3×C22⋊C4—22no—
27C3×C4×D12—22no—
28C32×#102C2214yescomplemented
29C3×#821C2214yescomplemented
30C3×#815C2212yescomplemented
31C3×C8×Dic3C2212yescomplemented
32C3×#808C2212yescomplemented
33C3×#807C2212yescomplemented
34C22×C3×D8—31no—
35C3×#518—31no—
36C3×#518—31no—
37#5798C2×C311yescharacteristic, complemented
38C22×#213C2×C311yescharacteristic
39#5521C2×C311yescharacteristic, complemented
40C3×#442—34no—
41C3×C4×D8—34no—
42C3×#427—31no—
43C3×#418—21no—
44C3×#418—31no—
45C3×#418D311yescharacteristic, complemented
46C3×#418C2×C311yescharacteristic, complemented
47C3×#405—31no—
48#5131C2×C311yescharacteristic, complemented
49#5122C2×C311yescharacteristic, complemented
50#4998C2×C311yescharacteristic, complemented
51#4785C2×C314yescomplemented
52#4756C2×C314yescomplemented
53C24×C32—21no—
54C23×C3×D3—21no—
55C2×C32×D4—21no—
56C2×C32×D4—22no—
57C2×C32×D4C2×C414yescomplemented
58C2×C32×D4C2312yes—
59C22×C32×C4C2311yescharacteristic
60C22×C3×Dic3—24no—
61C2×C3×D12—21no—
62C2×C3×D12—22no—
63C2×C3×D12C2×C414yescomplemented
64C2×C3×D12C2312yes—
65C2×C3×C4×D3—24no—
66C32×M16—22no—
67C2×C32×C8C2312yes—
68C32×C4⋊C4C2312yes—
69C32×C22⋊C4—21no—
70C32×C42—21no—
71C3×#217—21no—
72C3×#217—24no—
73C3×#217D412yes—
74C3×#213C2×C418yescomplemented
75C3×#213C2×C418yescomplemented
76C3×(C2×D3)⋊C4—24no—
77C3×C4⋊Dic3D412yes—
78C3×C4⋊Dic3C2312yes—
79C3×C4×Dic3—21no—
80C3×C4×Dic3C2312yes—
81C2×C3×C3⋊C8C2×C414yescomplemented
82C2×C3×C3⋊C8C2311yescharacteristic
83C2×C3×C3⋊C8C2311yescharacteristic
84#2948—31noSylow
85C22×C3×D4—21no—
86C22×C3×D4—31no—
87C22×C3×D4C2×D311yescharacteristic
88C22×C3×D4C22×C311yescharacteristic
89C22×D12C22×C311yescharacteristic
90C2×C3×D8—38no—
91C2×C3×D8—32no—
92C2×C3×D8—32no—
93C2×C3×M16—21no—
94C2×C3×M16C2×D311yescharacteristic
95C2×C3×M16C22×C311yescharacteristic
96C22×C3×C8—31no—
97C3×C4×D4—34no—
98C3×C4×D4—34no—
99C3×C4×D4—62no—
100C3×C4×D4—62no—
101C3×#117—21no—
102C3×#117—31no—
103C3×#117—31no—
104C3×#117C2×D311yescharacteristic
105C3×#117C22×C311yescharacteristic
106C2×C3×C22⋊C4—62no—
107C2×C3×C22⋊C4—62no—
108C2×#217—22no—
109D4×Dic3—22no—
110D4×Dic3C22×C314yescomplemented
111C2×#213C3×C418yescomplemented
112C2×#213C22×C312yes—
113C2×#213C22×C312yes—
114#926C22×C311yescharacteristic
115#926C22×C311yescharacteristic
116C22×C3⋊C8C22×C311yescharacteristic
117#893C22×C314yescomplemented
118D3×C22⋊C4—22no—
119C4×D12—22no—
120C3×#107—32no—
121C3×#106—32no—
122C3×#102—24no—
123C3×#102—34no—
124C3×#102C2×D314yescomplemented
125C3×#102C22×C314yescomplemented
126C3×#97—32no—
127C3×C4×C8—32no—
128#821C22×C314yescomplemented
129#815C22×C312yescomplemented
130C8×Dic3C22×C312yescomplemented
131#808C22×C312yescomplemented
132#807C22×C312yescomplemented
133C23×C32—22no—
134C23×C32—24no—
135C23×C32—82no—
136C23×C32C2×D411yescharacteristic
137C22×C3×D3—22no—
138C22×C3×D3—24no—
139C22×C3×D3—82no—
140C32×D4—24no—
141C32×D4—22no—
142C32×D4C22×C414yes—
143C2×C32×C4—22no—
144C2×C32×C4C22×C412yes—
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4#4112yes—
147C2×C32×C4C2411yescharacteristic
148C2×C3×Dic3—22no—
149C2×C3×Dic3—84no—
150C2×C3×Dic3C2×D414yes—
151C3×D12—24no—
152C3×D12—22no—
153C3×D12C22×C414yes—
154C3×C4×D3—84no—
155C32×C8—22no—
156C3×C3⋊C8C22×C412yes—
157C3×C3⋊C8C22×C412yes—
158C22×D8—31no—
159#518—31no—
160#518—31no—
161#442—34no—
162C4×D8—34no—
163#427—31no—
164#418—31no—
165#418C3×D311yescharacteristic, complemented
166#405—31no—
167C24×C3—21no—
168C24×C3—21no—
169C24×C3—41no—
170C24×C3—61no—
171C23×D3—21no—
172C2×C3×D4—21no—
173C2×C3×D4—22no—
174C2×C3×D4—21no—
175C2×C3×D4—22no—
176C2×C3×D4—24no—
177C2×C3×D4—22no—
178C2×C3×D4—34no—
179C2×C3×D4—32no—
180C2×C3×D4—41no—
181C2×C3×D4—42no—
182C2×C3×D4—61no—
183C2×C3×D4—62no—
184C2×C3×D4C4×D314yescomplemented
185C2×C3×D4C2×C3×C414yescomplemented
186C2×C3×D4C22×D312yes—
187C2×C3×D4C23×C312yes—
188C22×C3×C4—21no—
189C22×C3×C4—64no—
190C22×C3×C4—64no—
191C22×C3×C4C22×D311yescharacteristic
192C22×C3×C4C23×C311yescharacteristic
193C22×Dic3—24no—
194C2×D12—21no—
195C2×D12—22no—
196C2×D12C2×C3×C414yescomplemented
197C2×D12C23×C312yes—
198C2×C4×D3—24no—
199C3×D8—38no—
200C3×D8—38no—
201C3×M16—22no—
202C3×M16—22no—
203C3×M16—42no—
204C2×C3×C8—22no—
205C2×C3×C8—34no—
206C2×C3×C8—31no—
207C2×C3×C8—31no—
208C2×C3×C8C22×D312yes—
209C2×C3×C8C23×C312yes—
210C3×C4⋊C4—22no—
211C3×C4⋊C4—32no—
212C3×C4⋊C4—32no—
213C3×C4⋊C4C22×D312yes—
214C3×C4⋊C4C23×C312yes—
215C3×C22⋊C4—21no—
216C3×C22⋊C4—21no—
217C3×C22⋊C4—32no—
218C3×C22⋊C4—41no—
219C3×C22⋊C4—64no—
220C3×C22⋊C4—64no—
221C3×C22⋊C4—61no—
222C3×C42—21no—
223C3×C42—21no—
224C3×C42—32no—
225C3×C42—41no—
226C3×C42—61no—
227#217—21no—
228#217—24no—
229#217C3×D412yes—
230#213C2×C3×C418yescomplemented
231#213C2×C3×C418yescomplemented
232(C2×D3)⋊C4—24no—
233C4⋊Dic3C3×D412yes—
234C4⋊Dic3C23×C312yes—
235C4×Dic3—21no—
236C4×Dic3C23×C312yes—
237C2×C3⋊C8C2×C3×C414yescomplemented
238C2×C3⋊C8C23×C311yescharacteristic
239C2×C3⋊C8C23×C311yescharacteristic
240C22×C32—22no—
241C22×C32—24no—
242C22×C32—44no—
243C22×C32—84no—
244C22×C32C4×D412yes—
245C22×C32C22×D411yescharacteristic
246C2×C3×D3—24no—
247C2×C3×D3—44no—
248C2×C3×D3—84no—
249C32×C4—42no—
250C32×C4C4×D412yes—
251C32×C4C23×C411yescharacteristic
252C32×C4C2×#4111yescharacteristic
253C3×Dic3—24no—
254C3×Dic3—42no—
255C22×D4—31no—
256C22×D4C2×C3×D311yescharacteristic
257C2×D8—38no—
258C2×D8—32no—
259C2×D8—32no—
260C2×M16C2×C3×D311yescharacteristic
261C22×C8—31no—
262C4×D4—34no—
263C4×D4—34no—
264C4×D4—62no—
265C4×D4—62no—
266#117—31no—
267#117—31no—
268#117C2×C3×D311yescharacteristic
269C2×C22⋊C4—62no—
270C2×C22⋊C4—62no—
271#107—32no—
272#106—32no—
273#102—34no—
274#102C2×C3×D314yescomplemented
275#97—32no—
276C4×C8—32no—
277C23×C3—22no—
278C23×C3—22no—
279C23×C3—24no—
280C23×C3—24no—
281C23×C3—21no—
282C23×C3—42no—
283C23×C3—44no—
284C23×C3—62no—
285C23×C3—64no—
286C23×C3—82no—
287C23×C3—82no—
288C23×C3—84no—
289C23×C3—242no—
290C23×C3D3×D411yescharacteristic
291C23×C3C2×C3×D411yescharacteristic
292C22×D3—22no—
293C22×D3—24no—
294C22×D3—82no—
295C3×D4—24no—
296C3×D4—24no—
297C3×D4—22no—
298C3×D4—22no—
299C3×D4—24no—
300C3×D4—34no—
301C3×D4—44no—
302C3×D4—42no—
303C3×D4—64no—
304C3×D4—62no—
305C3×D4C2×C4×D314yes—
306C3×D4C22×C3×C414yes—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—21no—
310C2×C3×C4—22no—
311C2×C3×C4—21no—
312C2×C3×C4—22no—
313C2×C3×C4—34no—
314C2×C3×C4—42no—
315C2×C3×C4—62no—
316C2×C3×C4—244no—
317C2×C3×C4—244no—
318C2×C3×C4C2×C4×D312yes—
319C2×C3×C4D3×D411yescharacteristic
320C2×C3×C4#23712yes—
321C2×C3×C4C22×C3×C412yes—
322C2×C3×C4C2×C3×D411yescharacteristic
323C2×C3×C4C3×#4112yes—
324C2×C3×C4C23×D311yescharacteristic
325C2×C3×C4C24×C311yescharacteristic
326C2×Dic3—22no—
327C2×Dic3—84no—
328C2×Dic3C2×C3×D414yes—
329D12—24no—
330D12—22no—
331D12C22×C3×C414yes—
332C4×D3—84no—
333C3×C8—22no—
334C3×C8—22no—
335C3×C8—32no—
336C3×C8—32no—
337C3×C8—42no—
338C3⋊C8C22×C3×C412yes—
339C3⋊C8C22×C3×C412yes—
340C2×C32—22no—
341C2×C32—44no—
342C2×C32C2×C4×D411yescharacteristic
343C2×C32#57612yes—
344C3×D3—44no—
345C24—21no—
346C24—61no—
347C2×D4—21no—
348C2×D4—22no—
349C2×D4—32no—
350C2×D4—34no—
351C2×D4—61no—
352C2×D4—62no—
353C2×D4C3×C4×D314yescomplemented
354C2×D4C22×C3×D312yes—
355C22×C4—64no—
356C22×C4—64no—
357C22×C4C22×C3×D311yescharacteristic
358D8—38no—
359D8—38no—
360M16—22no—
361C2×C8—31no—
362C2×C8—31no—
363C2×C8—34no—
364C2×C8C22×C3×D312yes—
365C4⋊C4—32no—
366C4⋊C4—32no—
367C4⋊C4C22×C3×D312yes—
368C22⋊C4—21no—
369C22⋊C4—32no—
370C22⋊C4—64no—
371C22⋊C4—64no—
372C22⋊C4—61no—
373C42—21no—
374C42—32no—
375C42—61no—
376C22×C3—22no—
377C22×C3—22no—
378C22×C3—24no—
379C22×C3—24no—
380C22×C3—22no—
381C22×C3—21no—
382C22×C3—42no—
383C22×C3—44no—
384C22×C3—44no—
385C22×C3—44no—
386C22×C3—64no—
387C22×C3—84no—
388C22×C3—84no—
389C22×C3—84no—
390C22×C3—88no—
391C22×C3—124no—
392C22×C3—244no—
393C22×C3#67⋊C412yes—
394C22×C3C3×C4×D412yes—
395C22×C3C2×D3×D411yescharacteristic
396C22×C3C22×C3×D411yescharacteristic
397C2×D3—24no—
398C2×D3—44no—
399C2×D3—84no—
400C3×C4—22no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—42no—
404C3×C4—42no—
405C3×C4—64no—
406C3×C4—82no—
407C3×C4—122no—
408C3×C4#67⋊C412yes—
409C3×C4C3×C4×D412yes—
410C3×C4C22×C4×D311yescharacteristic
411C3×C4C2×#23711yescharacteristic
412C3×C4C23×C3×C411yescharacteristic
413C3×C4C2×C3×#4111yescharacteristic
414Dic3—24no—
415Dic3—42no—
416C32#294811yescharacteristic, complemented, Sylow
417C23—22no—
418C23—24no—
419C23—62no—
420C23—64no—
421C23—82no—
422C23—242no—
423C23C3×D3×D411yescharacteristic
424D4—24no—
425D4—22no—
426D4—34no—
427D4—64no—
428D4—62no—
429D4C2×C3×C4×D314yes—
430C2×C4—22no—
431C2×C4—34no—
432C2×C4—62no—
433C2×C4—244no—
434C2×C4—244no—
435C2×C4C2×C3×C4×D312yes—
436C2×C4C3×D3×D411yescharacteristic
437C2×C4C3×#23712yes—
438C2×C4C23×C3×D311yescharacteristic
439C8—22no—
440C8—32no—
441C8—32no—
442C2×C3—22no—
443C2×C3—22no—
444C2×C3—22no—
445C2×C3—21no—
446C2×C3—42no—
447C2×C3—44no—
448C2×C3—44no—
449C2×C3—84no—
450C2×C3—124no—
451C2×C3C2×#67⋊C411yescharacteristic
452C2×C3#577412yes—
453C2×C3C2×C3×C4×D411yescharacteristic
454C2×C3C3×#57612yes—
455D3—44no—
456C22—22no—
457C22—24no—
458C22—44no—
459C22—64no—
460C22—84no—
461C22—124no—
462C22—244no—
463C22C3×#67⋊C412yes—
464C22C2×C3×D3×D411yescharacteristic
465C4—42no—
466C4—64no—
467C4—122no—
468C4C3×#67⋊C412yes—
469C4C22×C3×C4×D311yescharacteristic
470C4C2×C3×#23711yescharacteristic
471C3—21no—
472C3#7891511yescharacteristic, direct product factor
473C3C3×#294811yescharacteristic, complemented
474C2—22no—
475C2—44no—
476C2—124no—
477C2C2×C3×#67⋊C411yescharacteristic
478C2C3×#577412yes—
subgroupG/H
centerC22×C3C2×D3×D4
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC32×#418C2
socleC22×C32C22×D4
prime radicalC22×C3×#213C2
cosocleC2×C3×C4C24×C3
hypercenterC3×#418D3
hypocenterC3C3×#2948
LCSG ▷ 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
1. C3×#5798C2semidirect
3. C3×#5521C2semidirect
4. C32×#418C2semidirect
5. C3×#5131C2semidirect
6. C3×#5122C2semidirect
7. C3×#4998C2semidirect
8. C3×#4785C2semidirect
9. C3×#4756C2semidirect
11. #78915C3direct (N × H)
18. C3×D4×Dic3C22semidirect
19. C2×C3×#213C4semidirect
25. C3×#893C22semidirect
28. C32×#102C22semidirect
29. C3×#821C22semidirect
30. C3×#815C22semidirect
31. C3×C8×Dic3C22semidirect
32. C3×#808C22semidirect
33. C3×#807C22semidirect
37. #5798C2×C3semidirect
39. #5521C2×C3semidirect
45. C3×#418D3semidirect
46. C3×#418C2×C3semidirect
48. #5131C2×C3semidirect
49. #5122C2×C3semidirect
50. #4998C2×C3semidirect
51. #4785C2×C3semidirect
52. #4756C2×C3semidirect
57. C2×C32×D4C2×C4semidirect
63. C2×C3×D12C2×C4semidirect
74. C3×#213C2×C4semidirect
75. C3×#213C2×C4semidirect
81. C2×C3×C3⋊C8C2×C4semidirect
110. D4×Dic3C22×C3semidirect
111. C2×#213C3×C4semidirect
117. #893C22×C3semidirect
124. C3×#102C2×D3semidirect
125. C3×#102C22×C3semidirect
128. #821C22×C3semidirect
129. #815C22×C3semidirect
130. C8×Dic3C22×C3semidirect
131. #808C22×C3semidirect
132. #807C22×C3semidirect
165. #418C3×D3semidirect
184. C2×C3×D4C4×D3semidirect
185. C2×C3×D4C2×C3×C4semidirect
196. C2×D12C2×C3×C4semidirect
230. #213C2×C3×C4semidirect
231. #213C2×C3×C4semidirect
237. C2×C3⋊C8C2×C3×C4semidirect
274. #102C2×C3×D3semidirect
353. C2×D4C3×C4×D3semidirect
416. C32#2948semidirect
472. C3#78915direct (N × H)
473. C3C3×#2948semidirect

Maximal subgroups

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

subgroupindex
C3×#57982
C22×C3×#2132
C3×#55212
C32×#4182
C3×#51312
C3×#51222
C3×#49982
C3×#47852
C3×#47562
C3×#29483
#789153