Finite Group Databasebeta

← C3×#78947 #11860718

Subgroups — C3×#78947 #11860718

Order 1152.

1059 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5812C211yesmaximal, characteristic, complemented
2C22×C3×#215C211yesmaximal, characteristic
3C3×#5521C211yesmaximal, characteristic
4C32×#419C211yesmaximal, characteristic, complemented
5C3×#5131C211yesmaximal, characteristic
6C3×#5122C211yesmaximal, characteristic, complemented
7C3×#4998C211yesmaximal, characteristic, complemented
8C3×#4817C214yesmaximal, complemented
9C3×#4788C214yesmaximal, complemented
10C3×#2949—31nomaximal
11#78947C311yesmaximal, characteristic, direct product factor
12C22×C32×Q8C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15C32×#117C2211yescharacteristic
16C3×Q8×Dic3—22no—
17C3×Q8×Dic3C2214yescomplemented
18C2×C3×#215C418yescomplemented
19C2×C3×#215C2212yes—
20C2×C3×#215C2212yes—
21C3×#926—22no—
22C3×#926C2211yescharacteristic
23C3×#926C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C3×#893C2214yes—
26C3×D3×C22⋊C4—22no—
27C3×C4×D12—22no—
28C32×#103C2214yescomplemented
29C3×#821C2214yes—
30C3×#815C2212yescomplemented
31C3×C8×Dic3C2212yescomplemented
32C3×#808C2212yescomplemented
33C3×#807C2212yescomplemented
34C22×C3×SD16—31no—
35C3×#519—31no—
36C3×#518—31no—
37#5812C2×C311yescharacteristic, complemented
38C22×#215C2×C311yescharacteristic
39#5521C2×C311yescharacteristic
40C3×#440—34no—
41C3×C4×SD16—34no—
42C3×#427—31no—
43C3×#419—21no—
44C3×#419D311yescharacteristic, complemented
45C3×#419C2×C311yescharacteristic, complemented
46C3×#418—31no—
47C3×#405—31no—
48#5131C2×C311yescharacteristic
49#5122C2×C311yescharacteristic, complemented
50#4998C2×C311yescharacteristic, complemented
51#4817C2×C314yescomplemented
52#4788C2×C314yescomplemented
53C23×C3×D3—21no—
54C2×C32×Q8—21no—
55C2×C32×Q8—22no—
56C2×C32×Q8C2×C414yescomplemented
57C2×C32×Q8C2312yes—
58C22×C32×C4—21no—
59C22×C32×C4C2311yescharacteristic
60C2×C3×D12—21no—
61C2×C3×D12—22no—
62C2×C3×D12C2×C414yes—
63C2×C3×D12C2312yes—
64C2×C3×C4×D3—24no—
65C32×M16—22no—
66C2×C32×C8C2312yes—
67C32×C4⋊C4C2312yes—
68C32×C22⋊C4—21no—
69C32×C42—21no—
70C3×#217—21no—
71C3×#217D412yes—
72C3×#215C2×C418yescomplemented
73C3×#215C2×C418yescomplemented
74C3×(C2×D3)⋊C4—24no—
75C3×C4⋊Dic3—24no—
76C3×C4⋊Dic3D412yes—
77C3×C4⋊Dic3C2312yes—
78C3×C4×Dic3—21no—
79C3×C4×Dic3—24no—
80C3×C4×Dic3C2312yes—
81C2×C3×C3⋊C8C2×C414yescomplemented
82C2×C3×C3⋊C8C2311yescharacteristic
83C2×C3×C3⋊C8C2311yescharacteristic
84#2949—31noSylow
85C22×C3×Q8—21no—
86C22×C3×Q8C2×D311yescharacteristic
87C22×C3×Q8C22×C311yescharacteristic
88C22×C3×D4—31no—
89C22×D12C22×C311yescharacteristic
90C2×C3×SD16—38no—
91C2×C3×SD16—32no—
92C2×C3×SD16—32no—
93C2×C3×M16—21no—
94C2×C3×M16C2×D311yescharacteristic
95C2×C3×M16C22×C311yescharacteristic
96C22×C3×C8—31no—
97C3×C4×Q8—34no—
98C3×C4×Q8—62no—
99C3×C4×D4—34no—
100C3×C4×D4—62no—
101C3×#117—21no—
102C3×#117—31no—
103C3×#117—31no—
104C3×#117—62no—
105C3×#117C2×D311yescharacteristic
106C3×#117C22×C311yescharacteristic
107C2×C3×C22⋊C4—62no—
108Q8×Dic3—22no—
109Q8×Dic3C22×C314yescomplemented
110C2×#215C3×C418yescomplemented
111C2×#215C22×C312yes—
112C2×#215C22×C312yes—
113#926—22no—
114#926C22×C311yescharacteristic
115#926C22×C311yescharacteristic
116C22×C3⋊C8C22×C311yescharacteristic
117#893C22×C314yes—
118D3×C22⋊C4—22no—
119C4×D12—22no—
120C3×#107—32no—
121C3×#106—32no—
122C3×#103—24no—
123C3×#103C2×D314yescomplemented
124C3×#103C22×C314yescomplemented
125C3×#102—34no—
126C3×#97—32no—
127C3×C4×C8—32no—
128#821C22×C314yes—
129#815C22×C312yescomplemented
130C8×Dic3C22×C312yescomplemented
131#808C22×C312yescomplemented
132#807C22×C312yescomplemented
133C23×C32C2×D411yescharacteristic
134C22×C3×D3—22no—
135C22×C3×D3—24no—
136C22×C3×D3—82no—
137C32×Q8—24no—
138C32×Q8—22no—
139C32×Q8C22×C414yes—
140C2×C32×C4—24no—
141C2×C32×C4—22no—
142C2×C32×C4—22no—
143C2×C32×C4C22×C412yes—
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4#4112yes—
146C2×C32×C4C2411yescharacteristic
147C2×C3×Dic3—22no—
148C2×C3×Dic3C2×D414yes—
149C3×D12—24no—
150C3×D12—22no—
151C3×D12C22×C414yes—
152C3×C4×D3—84no—
153C32×C8—22no—
154C3×C3⋊C8C22×C412yes—
155C3×C3⋊C8C22×C412yes—
156C22×SD16—31no—
157#519—31no—
158#518—31no—
159#440—34no—
160C4×SD16—34no—
161#427—31no—
162#419C3×D311yescharacteristic, complemented
163#418—31no—
164#405—31no—
165C24×C3—61no—
166C23×D3—21no—
167C2×C3×Q8—21no—
168C2×C3×Q8—22no—
169C2×C3×Q8—21no—
170C2×C3×Q8—22no—
171C2×C3×Q8—24no—
172C2×C3×Q8—22no—
173C2×C3×Q8—41no—
174C2×C3×Q8—42no—
175C2×C3×Q8C4×D314yescomplemented
176C2×C3×Q8C2×C3×C414yescomplemented
177C2×C3×Q8C22×D312yes—
178C2×C3×Q8C23×C312yes—
179C2×C3×D4—34no—
180C2×C3×D4—32no—
181C2×C3×D4—61no—
182C2×C3×D4—62no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—41no—
187C22×C3×C4—64no—
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C23×C311yescharacteristic
190C2×D12—21no—
191C2×D12—22no—
192C2×D12C2×C3×C414yes—
193C2×D12C23×C312yes—
194C2×C4×D3—24no—
195C3×SD16—38no—
196C3×SD16—38no—
197C3×M16—22no—
198C3×M16—22no—
199C3×M16—42no—
200C2×C3×C8—22no—
201C2×C3×C8—34no—
202C2×C3×C8—31no—
203C2×C3×C8—31no—
204C2×C3×C8C22×D312yes—
205C2×C3×C8C23×C312yes—
206C3×C4⋊C4—22no—
207C3×C4⋊C4—32no—
208C3×C4⋊C4—32no—
209C3×C4⋊C4—64no—
210C3×C4⋊C4C22×D312yes—
211C3×C4⋊C4C23×C312yes—
212C3×C22⋊C4—21no—
213C3×C22⋊C4—21no—
214C3×C22⋊C4—32no—
215C3×C22⋊C4—41no—
216C3×C22⋊C4—64no—
217C3×C22⋊C4—61no—
218C3×C42—21no—
219C3×C42—21no—
220C3×C42—32no—
221C3×C42—41no—
222C3×C42—64no—
223C3×C42—61no—
224#217—21no—
225#217C3×D412yes—
226#215C2×C3×C418yescomplemented
227#215C2×C3×C418yescomplemented
228(C2×D3)⋊C4—24no—
229C4⋊Dic3—24no—
230C4⋊Dic3C3×D412yes—
231C4⋊Dic3C23×C312yes—
232C4×Dic3—21no—
233C4×Dic3—24no—
234C4×Dic3C23×C312yes—
235C2×C3⋊C8C2×C3×C414yescomplemented
236C2×C3⋊C8C23×C311yescharacteristic
237C2×C3⋊C8C23×C311yescharacteristic
238C22×C32—22no—
239C22×C32C4×D412yes—
240C22×C32C22×D411yescharacteristic
241C2×C3×D3—24no—
242C2×C3×D3—44no—
243C2×C3×D3—84no—
244C32×C4—24no—
245C32×C4—42no—
246C32×C4C4×D412yes—
247C32×C4C23×C411yescharacteristic
248C32×C4C2×#4111yescharacteristic
249C3×Dic3—24no—
250C3×Dic3—42no—
251C22×Q8C2×C3×D311yescharacteristic
252C22×D4—31no—
253C2×SD16—38no—
254C2×SD16—32no—
255C2×SD16—32no—
256C2×M16C2×C3×D311yescharacteristic
257C22×C8—31no—
258C4×Q8—34no—
259C4×Q8—62no—
260C4×D4—34no—
261C4×D4—62no—
262#117—31no—
263#117—31no—
264#117—62no—
265#117C2×C3×D311yescharacteristic
266C2×C22⋊C4—62no—
267#107—32no—
268#106—32no—
269#103C2×C3×D314yescomplemented
270#102—34no—
271#97—32no—
272C4×C8—32no—
273C23×C3—21no—
274C23×C3—62no—
275C23×C3—64no—
276C23×C3—242no—
277C23×C3D3×D411yescharacteristic
278C23×C3C2×C3×D411yescharacteristic
279C22×D3—22no—
280C22×D3—24no—
281C22×D3—82no—
282C3×Q8—24no—
283C3×Q8—24no—
284C3×Q8—22no—
285C3×Q8—22no—
286C3×Q8—24no—
287C3×Q8—44no—
288C3×Q8—42no—
289C3×Q8C2×C4×D314yes—
290C3×Q8C22×C3×C414yes—
291C3×D4—34no—
292C3×D4—64no—
293C3×D4—62no—
294C2×C3×C4—24no—
295C2×C3×C4—24no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—21no—
301C2×C3×C4—22no—
302C2×C3×C4—21no—
303C2×C3×C4—22no—
304C2×C3×C4—34no—
305C2×C3×C4—44no—
306C2×C3×C4—42no—
307C2×C3×C4—42no—
308C2×C3×C4—62no—
309C2×C3×C4—244no—
310C2×C3×C4C2×C4×D312yes—
311C2×C3×C4D3×D411yescharacteristic
312C2×C3×C4#23712yes—
313C2×C3×C4C22×C3×C412yes—
314C2×C3×C4C2×C3×D411yescharacteristic
315C2×C3×C4C3×#4112yes—
316C2×C3×C4C23×D311yescharacteristic
317C2×C3×C4C24×C311yescharacteristic
318C2×Dic3—22no—
319C2×Dic3C2×C3×D414yes—
320D12—24no—
321D12—22no—
322D12C22×C3×C414yes—
323C4×D3—84no—
324C3×C8—22no—
325C3×C8—22no—
326C3×C8—32no—
327C3×C8—32no—
328C3×C8—42no—
329C3⋊C8C22×C3×C412yes—
330C3⋊C8C22×C3×C412yes—
331C2×C32—22no—
332C2×C32C2×C4×D411yescharacteristic
333C2×C32#57712yes—
334C3×D3—44no—
335C24—61no—
336C2×Q8—21no—
337C2×Q8—22no—
338C2×Q8C3×C4×D314yescomplemented
339C2×Q8C22×C3×D312yes—
340C2×D4—32no—
341C2×D4—34no—
342C2×D4—61no—
343C2×D4—62no—
344C22×C4—21no—
345C22×C4—64no—
346C22×C4C22×C3×D311yescharacteristic
347SD16—38no—
348SD16—38no—
349M16—22no—
350C2×C8—31no—
351C2×C8—31no—
352C2×C8—34no—
353C2×C8C22×C3×D312yes—
354C4⋊C4—32no—
355C4⋊C4—32no—
356C4⋊C4—64no—
357C4⋊C4C22×C3×D312yes—
358C22⋊C4—21no—
359C22⋊C4—32no—
360C22⋊C4—64no—
361C22⋊C4—61no—
362C42—21no—
363C42—32no—
364C42—64no—
365C42—61no—
366C22×C3—22no—
367C22×C3—22no—
368C22×C3—22no—
369C22×C3—21no—
370C22×C3—42no—
371C22×C3—64no—
372C22×C3—124no—
373C22×C3—244no—
374C22×C3#67⋊C412yes—
375C22×C3C3×C4×D412yes—
376C22×C3C2×D3×D411yescharacteristic
377C22×C3C22×C3×D411yescharacteristic
378C2×D3—24no—
379C2×D3—44no—
380C2×D3—84no—
381C3×C4—24no—
382C3×C4—24no—
383C3×C4—22no—
384C3×C4—21no—
385C3×C4—21no—
386C3×C4—44no—
387C3×C4—42no—
388C3×C4—42no—
389C3×C4—64no—
390C3×C4—82no—
391C3×C4—122no—
392C3×C4#67⋊C412yes—
393C3×C4C3×C4×D412yes—
394C3×C4C22×C4×D311yescharacteristic
395C3×C4C2×#23711yescharacteristic
396C3×C4C23×C3×C411yescharacteristic
397C3×C4C2×C3×#4111yescharacteristic
398Dic3—24no—
399Dic3—42no—
400C32#294911yescharacteristic, complemented, Sylow
401C23—62no—
402C23—64no—
403C23—242no—
404C23C3×D3×D411yescharacteristic
405Q8—24no—
406Q8—22no—
407Q8C2×C3×C4×D314yes—
408D4—34no—
409D4—64no—
410D4—62no—
411C2×C4—24no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—34no—
415C2×C4—62no—
416C2×C4—244no—
417C2×C4C2×C3×C4×D312yes—
418C2×C4C3×D3×D411yescharacteristic
419C2×C4C3×#23712yes—
420C2×C4C23×C3×D311yescharacteristic
421C8—22no—
422C8—32no—
423C8—32no—
424C2×C3—22no—
425C2×C3—22no—
426C2×C3—22no—
427C2×C3—21no—
428C2×C3—42no—
429C2×C3—124no—
430C2×C3C2×#67⋊C411yescharacteristic
431C2×C3#577812yes—
432C2×C3C2×C3×C4×D411yescharacteristic
433C2×C3C3×#57712yes—
434D3—44no—
435C22—22no—
436C22—64no—
437C22—124no—
438C22—244no—
439C22C3×#67⋊C412yes—
440C22C2×C3×D3×D411yescharacteristic
441C4—24no—
442C4—42no—
443C4—64no—
444C4—122no—
445C4C3×#67⋊C412yes—
446C4C22×C3×C4×D311yescharacteristic
447C4C2×C3×#23711yescharacteristic
448C3—21no—
449C3#7894711yescharacteristic, direct product factor
450C3C3×#294911yescharacteristic, complemented
451C2—22no—
452C2—124no—
453C2C2×C3×#67⋊C411yescharacteristic
454C2C3×#577812yes—
subgroupG/H
centerC22×C3C2×D3×D4
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC32×#419C2
socleC22×C32C22×D4
prime radicalC22×C3×D12C22
cosocleC2×C3×C4C24×C3
hypercenterC3×#419D3
hypocenterC3C3×#2949
LCSG ▷ 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×#5812C2semidirect
4. C32×#419C2semidirect
6. C3×#5122C2semidirect
7. C3×#4998C2semidirect
8. C3×#4817C2semidirect
9. C3×#4788C2semidirect
11. #78947C3direct (N × H)
17. C3×Q8×Dic3C22semidirect
18. C2×C3×#215C4semidirect
28. C32×#103C22semidirect
30. C3×#815C22semidirect
31. C3×C8×Dic3C22semidirect
32. C3×#808C22semidirect
33. C3×#807C22semidirect
37. #5812C2×C3semidirect
44. C3×#419D3semidirect
45. C3×#419C2×C3semidirect
49. #5122C2×C3semidirect
50. #4998C2×C3semidirect
51. #4817C2×C3semidirect
52. #4788C2×C3semidirect
56. C2×C32×Q8C2×C4semidirect
72. C3×#215C2×C4semidirect
73. C3×#215C2×C4semidirect
81. C2×C3×C3⋊C8C2×C4semidirect
109. Q8×Dic3C22×C3semidirect
110. C2×#215C3×C4semidirect
123. C3×#103C2×D3semidirect
124. C3×#103C22×C3semidirect
129. #815C22×C3semidirect
130. C8×Dic3C22×C3semidirect
131. #808C22×C3semidirect
132. #807C22×C3semidirect
162. #419C3×D3semidirect
175. C2×C3×Q8C4×D3semidirect
176. C2×C3×Q8C2×C3×C4semidirect
226. #215C2×C3×C4semidirect
227. #215C2×C3×C4semidirect
235. C2×C3⋊C8C2×C3×C4semidirect
269. #103C2×C3×D3semidirect
338. C2×Q8C3×C4×D3semidirect
400. C32#2949semidirect
449. C3#78947direct (N × H)
450. C3C3×#2949semidirect

Maximal subgroups

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

subgroupindex
C3×#58122
C22×C3×#2152
C3×#55212
C32×#4192
C3×#51312
C3×#51222
C3×#49982
C3×#48172
C3×#47882
C3×#29493
#789473