Finite Group Databasebeta

← C3×#78916 #11860739

Subgroups — C3×#78916 #11860739

Order 1152.

1079 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5798C211yesmaximal, characteristic
2C22×C3×#214C211yesmaximal, characteristic
3C3×#5516C211yesmaximal, characteristic, complemented
4C32×#418C211yesmaximal, characteristic
5C3×#5122C211yesmaximal, characteristic, complemented
6C3×#5120C211yesmaximal, characteristic, complemented
7C3×#4998C211yesmaximal, characteristic, complemented
8C3×#4758C214yesmaximal, complemented
9C3×#4757C214yesmaximal, complemented
10C3×#2949—31nomaximal
11#78916C311yesmaximal, characteristic, direct product factor
12C22×C32×D4C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15C32×#117C2211yescharacteristic
16C2×C3×#217—22no—
17C3×D4×Dic3—22no—
18C3×D4×Dic3C2214yes—
19C2×C3×#214C418yescomplemented
20C2×C3×#214C2212yes—
21C2×C3×#214C2212yes—
22C3×#926C2211yescharacteristic
23C3×#926C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C3×#887C2214yescomplemented
26C3×#877—22no—
27C3×C4×Dic6—22no—
28C32×#102C2214yes—
29C3×#816C2214yescomplemented
30C3×#815C2212yescomplemented
31C3×C8×Dic3C2212yescomplemented
32C3×#808C2212yescomplemented
33C3×#807C2212yescomplemented
34C22×C3×SD16—31no—
35C3×#519—31no—
36C3×#518—31no—
37#5798C2×C311yescharacteristic
38C22×#214C2×C311yescharacteristic
39#5516C2×C311yescharacteristic, complemented
40C3×#440—34no—
41C3×C4×SD16—34no—
42C3×#427—31no—
43C3×#419—31no—
44C3×#418—21no—
45C3×#418D311yescharacteristic
46C3×#418C2×C311yescharacteristic
47C3×#405—31no—
48#5122C2×C311yescharacteristic, complemented
49#5120C2×C311yescharacteristic, complemented
50#4998C2×C311yescharacteristic, complemented
51#4758C2×C314yescomplemented
52#4757C2×C314yescomplemented
53C24×C32—21no—
54C2×C32×D4—21no—
55C2×C32×D4—22no—
56C2×C32×D4C2×C414yes—
57C2×C32×D4C2312yes—
58C22×C32×C4C2311yescharacteristic
59C22×C3×Dic3—21no—
60C22×C3×Dic3—24no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6—22no—
63C2×C3×Dic6C2×C414yescomplemented
64C2×C3×Dic6C2312yes—
65C32×M16—22no—
66C2×C32×C8C2312yes—
67C32×C4⋊C4C2312yes—
68C32×C22⋊C4—21no—
69C32×C42—21no—
70C3×#217—21no—
71C3×#217—24no—
72C3×#217D412yes—
73C3×#214C2×C418yescomplemented
74C3×#214C2×C418yescomplemented
75C3×C4⋊Dic3D412yes—
76C3×C4⋊Dic3C2312yes—
77C3×Dic3⋊C4—24no—
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—31no—
86C22×C3×D4—21no—
87C22×C3×D4C2×D311yescharacteristic
88C22×C3×D4C22×C311yescharacteristic
89C22×Dic6C22×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—
108C2×#217—22no—
109D4×Dic3—22no—
110D4×Dic3C22×C314yes—
111C2×#214C3×C418yescomplemented
112C2×#214C22×C312yes—
113C2×#214C22×C312yes—
114#926C22×C311yescharacteristic
115#926C22×C311yescharacteristic
116C22×C3⋊C8C22×C311yescharacteristic
117#887C22×C314yescomplemented
118#877—22no—
119C4×Dic6—22no—
120C3×#107—32no—
121C3×#106—32no—
122C3×#103—34no—
123C3×#102—24no—
124C3×#102C2×D314yes—
125C3×#102C22×C314yes—
126C3×#97—32no—
127C3×C4×C8—32no—
128#816C22×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
137C32×D4—24no—
138C32×D4—22no—
139C32×D4C22×C414yes—
140C2×C32×C4—22no—
141C2×C32×C4C22×C412yes—
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4#4112yes—
144C2×C32×C4C2411yescharacteristic
145C2×C3×Dic3—24no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—84no—
149C2×C3×Dic3C2×D414yes—
150C3×Dic6—24no—
151C3×Dic6—22no—
152C3×Dic6C22×C414yes—
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#419—31no—
163#418C3×D311yescharacteristic
164#405—31no—
165C24×C3—21no—
166C24×C3—21no—
167C24×C3—41no—
168C2×C3×Q8—34no—
169C2×C3×Q8—32no—
170C2×C3×Q8—61no—
171C2×C3×Q8—62no—
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—41no—
179C2×C3×D4—42no—
180C2×C3×D4C4×D314yes—
181C2×C3×D4C2×C3×C414yes—
182C2×C3×D4C22×D312yes—
183C2×C3×D4C23×C312yes—
184C22×C3×C4—21no—
185C22×C3×C4—64no—
186C22×C3×C4—61no—
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C23×C311yescharacteristic
189C22×Dic3—21no—
190C22×Dic3—24no—
191C2×Dic6—21no—
192C2×Dic6—22no—
193C2×Dic6C2×C3×C414yescomplemented
194C2×Dic6C23×C312yes—
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#217—24no—
226#217C3×D412yes—
227#214C2×C3×C418yescomplemented
228#214C2×C3×C418yescomplemented
229C4⋊Dic3C3×D412yes—
230C4⋊Dic3C23×C312yes—
231Dic3⋊C4—24no—
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×C32—24no—
240C22×C32—44no—
241C22×C32—84no—
242C22×C32C4×D412yes—
243C22×C32C22×D411yescharacteristic
244C32×C4—42no—
245C32×C4C4×D412yes—
246C32×C4C23×C411yescharacteristic
247C32×C4C2×#4111yescharacteristic
248C3×Dic3—24no—
249C3×Dic3—24no—
250C3×Dic3—42no—
251C22×Q8—31no—
252C22×D4C2×C3×D311yescharacteristic
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#103—34no—
270#102C2×C3×D314yes—
271#97—32no—
272C4×C8—32no—
273C23×C3—22no—
274C23×C3—22no—
275C23×C3—24no—
276C23×C3—24no—
277C23×C3—21no—
278C23×C3—42no—
279C23×C3—44no—
280C23×C3—82no—
281C23×C3—82no—
282C23×C3—84no—
283C23×C3D3×D411yescharacteristic
284C23×C3C2×C3×D411yescharacteristic
285C3×Q8—34no—
286C3×Q8—64no—
287C3×Q8—62no—
288C3×D4—24no—
289C3×D4—24no—
290C3×D4—22no—
291C3×D4—22no—
292C3×D4—24no—
293C3×D4—44no—
294C3×D4—42no—
295C3×D4C2×C4×D314yes—
296C3×D4C22×C3×C414yes—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—21no—
300C2×C3×C4—22no—
301C2×C3×C4—21no—
302C2×C3×C4—22no—
303C2×C3×C4—34no—
304C2×C3×C4—42no—
305C2×C3×C4—64no—
306C2×C3×C4—62no—
307C2×C3×C4—62no—
308C2×C3×C4—244no—
309C2×C3×C4C2×C4×D312yes—
310C2×C3×C4D3×D411yescharacteristic
311C2×C3×C4#23712yes—
312C2×C3×C4C22×C3×C412yes—
313C2×C3×C4C2×C3×D411yescharacteristic
314C2×C3×C4C3×#4112yes—
315C2×C3×C4C23×D311yescharacteristic
316C2×C3×C4C24×C311yescharacteristic
317C2×Dic3—24no—
318C2×Dic3—22no—
319C2×Dic3—22no—
320C2×Dic3—84no—
321C2×Dic3C2×C3×D414yes—
322Dic6—24no—
323Dic6—22no—
324Dic6C22×C3×C414yes—
325C3×C8—22no—
326C3×C8—22no—
327C3×C8—32no—
328C3×C8—32no—
329C3×C8—42no—
330C3⋊C8C22×C3×C412yes—
331C3⋊C8C22×C3×C412yes—
332C2×C32—22no—
333C2×C32—44no—
334C2×C32C2×C4×D411yescharacteristic
335C2×C32#57712yes—
336C24—21no—
337C2×Q8—32no—
338C2×Q8—34no—
339C2×Q8—61no—
340C2×Q8—62no—
341C2×D4—21no—
342C2×D4—22no—
343C2×D4C3×C4×D314yes—
344C2×D4C22×C3×D312yes—
345C22×C4—64no—
346C22×C4—61no—
347C22×C4C22×C3×D311yescharacteristic
348SD16—38no—
349SD16—38no—
350M16—22no—
351C2×C8—31no—
352C2×C8—31no—
353C2×C8—34no—
354C2×C8C22×C3×D312yes—
355C4⋊C4—32no—
356C4⋊C4—32no—
357C4⋊C4—64no—
358C4⋊C4C22×C3×D312yes—
359C22⋊C4—21no—
360C22⋊C4—32no—
361C22⋊C4—64no—
362C22⋊C4—61no—
363C42—21no—
364C42—32no—
365C42—64no—
366C42—61no—
367C22×C3—22no—
368C22×C3—22no—
369C22×C3—24no—
370C22×C3—24no—
371C22×C3—22no—
372C22×C3—21no—
373C22×C3—42no—
374C22×C3—44no—
375C22×C3—44no—
376C22×C3—44no—
377C22×C3—84no—
378C22×C3—84no—
379C22×C3—84no—
380C22×C3—88no—
381C22×C3#67⋊C412yes—
382C22×C3C3×C4×D412yes—
383C22×C3C2×D3×D411yescharacteristic
384C22×C3C22×C3×D411yescharacteristic
385C3×C4—22no—
386C3×C4—21no—
387C3×C4—21no—
388C3×C4—42no—
389C3×C4—42no—
390C3×C4—64no—
391C3×C4—64no—
392C3×C4—82no—
393C3×C4—122no—
394C3×C4#67⋊C412yes—
395C3×C4C3×C4×D412yes—
396C3×C4C22×C4×D311yescharacteristic
397C3×C4C2×#23711yescharacteristic
398C3×C4C23×C3×C411yescharacteristic
399C3×C4C2×C3×#4111yescharacteristic
400Dic3—24no—
401Dic3—24no—
402Dic3—42no—
403C32#294911yescharacteristic, complemented, Sylow
404C23—22no—
405C23—24no—
406C23—82no—
407C23C3×D3×D411yescharacteristic
408Q8—34no—
409Q8—64no—
410Q8—62no—
411D4—24no—
412D4—22no—
413D4C2×C3×C4×D314yes—
414C2×C4—22no—
415C2×C4—34no—
416C2×C4—64no—
417C2×C4—62no—
418C2×C4—62no—
419C2×C4—244no—
420C2×C4C2×C3×C4×D312yes—
421C2×C4C3×D3×D411yescharacteristic
422C2×C4C3×#23712yes—
423C2×C4C23×C3×D311yescharacteristic
424C8—22no—
425C8—32no—
426C8—32no—
427C2×C3—22no—
428C2×C3—22no—
429C2×C3—22no—
430C2×C3—21no—
431C2×C3—42no—
432C2×C3—44no—
433C2×C3—44no—
434C2×C3—84no—
435C2×C3C2×#67⋊C411yescharacteristic
436C2×C3#577512yes—
437C2×C3C2×C3×C4×D411yescharacteristic
438C2×C3C3×#57712yes—
439C22—22no—
440C22—24no—
441C22—44no—
442C22—84no—
443C22C3×#67⋊C412yes—
444C22C2×C3×D3×D411yescharacteristic
445C4—42no—
446C4—64no—
447C4—64no—
448C4—122no—
449C4C3×#67⋊C412yes—
450C4C22×C3×C4×D311yescharacteristic
451C4C2×C3×#23711yescharacteristic
452C3—21no—
453C3#7891611yescharacteristic, direct product factor
454C3C3×#294911yescharacteristic, complemented
455C2—22no—
456C2—44no—
457C2C2×C3×#67⋊C411yescharacteristic
458C2C3×#577512yes—
subgroupG/H
centerC22×C3C2×D3×D4
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC32×#418C2
socleC22×C32C22×D4
prime radicalC22×C32×D4C22
cosocleC2×C3×C4C24×C3
hypercenterC3×#418D3
hypocenterC3C3×#2949
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
3. C3×#5516C2semidirect
5. C3×#5122C2semidirect
6. C3×#5120C2semidirect
7. C3×#4998C2semidirect
8. C3×#4758C2semidirect
9. C3×#4757C2semidirect
11. #78916C3direct (N × H)
19. C2×C3×#214C4semidirect
25. C3×#887C22semidirect
29. C3×#816C22semidirect
30. C3×#815C22semidirect
31. C3×C8×Dic3C22semidirect
32. C3×#808C22semidirect
33. C3×#807C22semidirect
39. #5516C2×C3semidirect
48. #5122C2×C3semidirect
49. #5120C2×C3semidirect
50. #4998C2×C3semidirect
51. #4758C2×C3semidirect
52. #4757C2×C3semidirect
63. C2×C3×Dic6C2×C4semidirect
73. C3×#214C2×C4semidirect
74. C3×#214C2×C4semidirect
81. C2×C3×C3⋊C8C2×C4semidirect
111. C2×#214C3×C4semidirect
117. #887C22×C3semidirect
128. #816C22×C3semidirect
129. #815C22×C3semidirect
130. C8×Dic3C22×C3semidirect
131. #808C22×C3semidirect
132. #807C22×C3semidirect
193. C2×Dic6C2×C3×C4semidirect
227. #214C2×C3×C4semidirect
228. #214C2×C3×C4semidirect
235. C2×C3⋊C8C2×C3×C4semidirect
403. C32#2949semidirect
453. C3#78916direct (N × H)
454. C3C3×#2949semidirect

Maximal subgroups

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

subgroupindex
C3×#57982
C22×C3×#2142
C3×#55162
C32×#4182
C3×#51222
C3×#51202
C3×#49982
C3×#47582
C3×#47572
C3×#29493
#789163