Finite Group Databasebeta

← C3×#80893 #11877014

Subgroups — C3×#80893 #11877014

Order 1152.

771 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5622C212yesmaximal
2C32×#470C211yesmaximal, characteristic
3C3×#5184C211yesmaximal, characteristic, complemented
4C3×#5183C211yesmaximal, characteristic, complemented
5C3×#5137C211yesmaximal, characteristic
6C3×Dic3×M16C211yesmaximal, characteristic
7C3×#5052C212yesmaximal
8C3×#4855C211yesmaximal, characteristic, complemented
9C3×#4853C211yesmaximal, characteristic, complemented
10C3×#4792C212yesmaximal, complemented
11C3×#4789C212yesmaximal, complemented
12C3×#3185—31nomaximal
13#80893C311yesmaximal, characteristic, direct product factor
14C2×C32×Q16C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16C32×C22⋊Q8C2212yes—
17C3×Q8×Dic3C2212yes—
18C3×#944C2212yes—
19C2×C3×#216C2212yes—
20C3×#924C2212yes—
21C2×C3×C4×Dic3C2211yescharacteristic
22C2×C3×#208C2211yescharacteristic
23C2×C3×Dic12C2211yescharacteristic
24C3×#889—22no—
25C3×#888C2212yes—
26C3×#887—22no—
27C3×#887C2212yes—
28C3×#878—22no—
29C3×#877—22no—
30C32×#106C2211yescharacteristic
31C32×#103C2212yes—
32C3×#835C2212yes—
33C3×#817C2211yescharacteristic
34C3×#816C2212yes—
35C3×#815C2211yescharacteristic
36C3×#815C2211yescharacteristic
37C3×C8×Dic3C2211yescharacteristic
38C3×C8×Dic3C2211yescharacteristic
39C3×#810C2212yes—
40C3×#808C2212yes—
41C3×#533—32no—
42#5622C2×C312yes—
43C3×#498—31no—
44C3×#494—31no—
45C3×#487—32no—
46C3×#470—21no—
47C3×#470—31no—
48C3×#470—32no—
49C3×#470D311yescharacteristic
50C3×#470C2×C311yescharacteristic
51C3×#441—31no—
52C3×#441—31no—
53C3×#441—32no—
54C3×C4×M16—31no—
55#5184C2×C311yescharacteristic, complemented
56#5183C2×C311yescharacteristic, complemented
57#5137C2×C311yescharacteristic
58Dic3×M16C2×C311yescharacteristic
59#5052C2×C312yes—
60#4855C2×C311yescharacteristic, complemented
61#4853C2×C311yescharacteristic, complemented
62#4792C2×C312yescomplemented
63#4789C2×C312yescomplemented
64C2×C32×Q8C2312yes—
65C22×C32×C4C2311yescharacteristic
66C22×C3×Dic3D412yes—
67C2×C3×Dic6—22no—
68C2×C3×Dic6C2312yes—
69C32×Q16—22no—
70C32×M16—22no—
71C2×C32×C8C2311yescharacteristic
72C2×C32×C8C2311yescharacteristic
73C32×C4⋊C4—22no—
74C32×C4⋊C4C2312yes—
75C32×C22⋊C4—22no—
76C3×#217—22no—
77C3×#216—24no—
78C3×C4⋊Dic3—22no—
79C3×C4⋊Dic3C2312yes—
80C3×Dic3⋊C4—22no—
81C3×Dic3⋊C4—22no—
82C3×Dic3⋊C4—22no—
83C3×Dic3⋊C4—22no—
84C3×Dic3⋊C4—22no—
85C3×C4×Dic3—22no—
86C3×C4×Dic3—22no—
87C3×C4×Dic3D412yes—
88C3×C4×Dic3C2311yescharacteristic
89C3×C4×Dic3C2311yescharacteristic
90C3×#208—22no—
91C2×C3×C3⋊C8C2311yescharacteristic
92C2×C3×C3⋊C8C2311yescharacteristic
93C3×Dic12—22no—
94#3185—31noSylow
95C2×C3×Q16—21no—
96C2×C3×Q16—32no—
97C2×C3×Q16—31no—
98C2×C3×Q16C2×D311yescharacteristic
99C2×C3×Q16C22×C311yescharacteristic
100C2×C3×M16—21no—
101C2×C3×M16—31no—
102C2×C3×M16C2×D311yescharacteristic
103C2×C3×M16C22×C311yescharacteristic
104C3×C4⋊Q8—32no—
105C3×C4⋊Q8—32no—
106C3×#125—62no—
107C3×C22⋊Q8—22no—
108C3×C22⋊Q8—32no—
109C3×C22⋊Q8—62no—
110C3×C22⋊Q8C2×D312yes—
111C3×C22⋊Q8C22×C312yes—
112C3×C4×Q8—32no—
113C3×C4×Q8—32no—
114C3×C4×Q8—62no—
115C3×#117—62no—
116C2×C3×C42—31no—
117Q8×Dic3C22×C312yes—
118#944C22×C312yes—
119C2×#216C22×C312yes—
120#924C22×C312yes—
121C2×C4×Dic3C22×C311yescharacteristic
122C2×#208C22×C311yescharacteristic
123C2×Dic12C22×C311yescharacteristic
124#889—22no—
125#888C22×C312yes—
126#887—22no—
127#887C22×C312yes—
128#878—22no—
129#877—22no—
130C3×#106—21no—
131C3×#106—31no—
132C3×#106—32no—
133C3×#106C2×D311yescharacteristic
134C3×#106C22×C311yescharacteristic
135C3×#103—22no—
136C3×#103—32no—
137C3×#103—32no—
138C3×#103—32no—
139C3×#103C2×D312yes—
140C3×#103C22×C312yes—
141C3×#97—31no—
142C3×#97—31no—
143C3×C4×C8—31no—
144C3×C4×C8—31no—
145#835C22×C312yes—
146#817C22×C311yescharacteristic
147#816C22×C312yes—
148#815C22×C311yescharacteristic
149#815C22×C311yescharacteristic
150C8×Dic3C22×C311yescharacteristic
151C8×Dic3C22×C311yescharacteristic
152#810C22×C312yes—
153#808C22×C312yes—
154C23×C32C2×D411yescharacteristic
155C32×Q8—22no—
156C32×Q8—22no—
157C2×C32×C4—21no—
158C2×C32×C4—21no—
159C2×C32×C4—22no—
160C2×C32×C4—22no—
161C2×C32×C4C2×D411yescharacteristic
162C2×C32×C4C2411yescharacteristic
163C2×C3×Dic3—24no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3C2×D412yes—
167C2×C3×Dic3C2×D412yes—
168C3×Dic6—22no—
169C3×Dic6—22no—
170C3×Dic6—44no—
171C32×C8—21no—
172C32×C8#4112yes—
173C3×C3⋊C8—21no—
174C3×C3⋊C8#4112yes—
175#533—32no—
176#498—31no—
177#494—31no—
178#487—32no—
179#470—31no—
180#470—32no—
181#470C3×D311yescharacteristic
182#441—31no—
183#441—31no—
184#441—32no—
185C4×M16—31no—
186C2×C3×Q8—22no—
187C2×C3×Q8—32no—
188C2×C3×Q8—62no—
189C2×C3×Q8C22×D312yes—
190C2×C3×Q8C23×C312yes—
191C22×C3×C4—21no—
192C22×C3×C4—32no—
193C22×C3×C4C22×D311yescharacteristic
194C22×C3×C4C23×C311yescharacteristic
195C22×Dic3C3×D412yes—
196C2×Dic6—22no—
197C2×Dic6C23×C312yes—
198C3×Q16—22no—
199C3×Q16—22no—
200C3×Q16—42no—
201C3×Q16—64no—
202C3×Q16—62no—
203C3×M16—22no—
204C3×M16—22no—
205C3×M16—42no—
206C3×M16—62no—
207C2×C3×C8—21no—
208C2×C3×C8—21no—
209C2×C3×C8—31no—
210C2×C3×C8—31no—
211C2×C3×C8C22×D311yescharacteristic
212C2×C3×C8C22×D311yescharacteristic
213C2×C3×C8C23×C311yescharacteristic
214C2×C3×C8C23×C311yescharacteristic
215C3×C4⋊C4—22no—
216C3×C4⋊C4—22no—
217C3×C4⋊C4—22no—
218C3×C4⋊C4—32no—
219C3×C4⋊C4—42no—
220C3×C4⋊C4—62no—
221C3×C4⋊C4—62no—
222C3×C4⋊C4—62no—
223C3×C4⋊C4—62no—
224C3×C4⋊C4—62no—
225C3×C4⋊C4—62no—
226C3×C4⋊C4C22×D312yes—
227C3×C4⋊C4C23×C312yes—
228C3×C22⋊C4—22no—
229C3×C22⋊C4—22no—
230C3×C22⋊C4—42no—
231C3×C22⋊C4—62no—
232C3×C42—32no—
233C3×C42—31no—
234C3×C42—31no—
235C3×C42—62no—
236C3×C42—62no—
237#217—22no—
238#216—24no—
239C4⋊Dic3—22no—
240C4⋊Dic3C23×C312yes—
241Dic3⋊C4—22no—
242Dic3⋊C4—22no—
243Dic3⋊C4—22no—
244Dic3⋊C4—22no—
245Dic3⋊C4—22no—
246C4×Dic3—22no—
247C4×Dic3—22no—
248C4×Dic3C3×D412yes—
249C4×Dic3C23×C311yescharacteristic
250C4×Dic3C23×C311yescharacteristic
251#208—22no—
252C2×C3⋊C8C23×C311yescharacteristic
253C2×C3⋊C8C23×C311yescharacteristic
254Dic12—22no—
255C22×C32—21no—
256C22×C32—22no—
257C22×C32C22×D411yescharacteristic
258C32×C4—21no—
259C32×C4—42no—
260C32×C4—42no—
261C32×C4C2×#4111yescharacteristic
262C32×C4C2×#4111yescharacteristic
263C3×Dic3—22no—
264C3×Dic3—42no—
265C3×Dic3—42no—
266C3×Dic3#13714yes—
267C2×Q16—32no—
268C2×Q16—31no—
269C2×Q16C2×C3×D311yescharacteristic
270C2×M16—31no—
271C2×M16C2×C3×D311yescharacteristic
272C4⋊Q8—32no—
273C4⋊Q8—32no—
274#125—62no—
275C22⋊Q8—32no—
276C22⋊Q8—62no—
277C22⋊Q8C2×C3×D312yes—
278C4×Q8—32no—
279C4×Q8—32no—
280C4×Q8—62no—
281#117—62no—
282C2×C42—31no—
283#106—31no—
284#106—32no—
285#106C2×C3×D311yescharacteristic
286#103—32no—
287#103—32no—
288#103—32no—
289#103C2×C3×D312yes—
290#97—31no—
291#97—31no—
292C4×C8—31no—
293C4×C8—31no—
294C23×C3—21no—
295C23×C3D3×D411yescharacteristic
296C23×C3C2×C3×D411yescharacteristic
297C3×Q8—22no—
298C3×Q8—22no—
299C3×Q8—22no—
300C3×Q8—22no—
301C3×Q8—42no—
302C3×Q8—42no—
303C3×Q8—62no—
304C3×Q8—62no—
305C3×Q8—124no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—32no—
317C2×C3×C4—32no—
318C2×C3×C4—41no—
319C2×C3×C4—41no—
320C2×C3×C4—42no—
321C2×C3×C4—42no—
322C2×C3×C4—64no—
323C2×C3×C4—62no—
324C2×C3×C4—62no—
325C2×C3×C4D3×D411yescharacteristic
326C2×C3×C4C2×C3×D411yescharacteristic
327C2×C3×C4C23×D311yescharacteristic
328C2×C3×C4C24×C311yescharacteristic
329C2×Dic3—24no—
330C2×Dic3—22no—
331C2×Dic3—22no—
332C2×Dic3C2×C3×D412yes—
333C2×Dic3C2×C3×D412yes—
334Dic6—22no—
335Dic6—22no—
336Dic6—44no—
337C3×C8—21no—
338C3×C8—21no—
339C3×C8—22no—
340C3×C8—32no—
341C3×C8—41no—
342C3×C8—61no—
343C3×C8#23712yes—
344C3×C8C3×#4112yes—
345C3⋊C8—21no—
346C3⋊C8C3×#4112yes—
347C2×C32—41no—
348C2×C32#53211yescharacteristic
349C2×C32C2×#13712yes—
350C2×Q8—32no—
351C2×Q8—62no—
352C2×Q8C22×C3×D312yes—
353C22×C4—32no—
354C22×C4C22×C3×D311yescharacteristic
355Q16—22no—
356Q16—64no—
357Q16—62no—
358M16—22no—
359M16—62no—
360C2×C8—31no—
361C2×C8—31no—
362C2×C8C22×C3×D311yescharacteristic
363C2×C8C22×C3×D311yescharacteristic
364C4⋊C4—22no—
365C4⋊C4—32no—
366C4⋊C4—62no—
367C4⋊C4—62no—
368C4⋊C4—62no—
369C4⋊C4—62no—
370C4⋊C4—62no—
371C4⋊C4—62no—
372C4⋊C4C22×C3×D312yes—
373C22⋊C4—22no—
374C22⋊C4—62no—
375C42—31no—
376C42—31no—
377C42—32no—
378C42—62no—
379C42—62no—
380C22×C3—22no—
381C22×C3—22no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—41no—
386C22×C3—42no—
387C22×C3C2×D3×D411yescharacteristic
388C22×C3C22×C3×D411yescharacteristic
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—34no—
394C3×C4—41no—
395C3×C4—42no—
396C3×C4—42no—
397C3×C4—42no—
398C3×C4—42no—
399C3×C4—62no—
400C3×C4—82no—
401C3×C4—82no—
402C3×C4—122no—
403C3×C4—122no—
404C3×C4C2×#23711yescharacteristic
405C3×C4D3×#4111yescharacteristic
406C3×C4C2×C3×#4111yescharacteristic
407C3×C4C2×C3×#4111yescharacteristic
408Dic3—22no—
409Dic3—42no—
410Dic3—42no—
411Dic3C3×#13714yes—
412C32#318511yescharacteristic, complemented, Sylow
413C23C3×D3×D411yescharacteristic
414Q8—22no—
415Q8—22no—
416Q8—62no—
417Q8—62no—
418Q8—124no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—32no—
424C2×C4—32no—
425C2×C4—64no—
426C2×C4—62no—
427C2×C4—62no—
428C2×C4C3×D3×D411yescharacteristic
429C2×C4C23×C3×D311yescharacteristic
430C8—21no—
431C8—32no—
432C8—61no—
433C8C3×#23712yes—
434C2×C3—22no—
435C2×C3—21no—
436C2×C3—41no—
437C2×C3—41no—
438C2×C3—81no—
439C2×C3#559611yescharacteristic
440C2×C3D3×#13712yes—
441C2×C3C3×#53211yescharacteristic
442C2×C3C2×C3×#13712yes—
443C22—22no—
444C22—21no—
445C22C2×C3×D3×D411yescharacteristic
446C4—21no—
447C4—34no—
448C4—42no—
449C4—42no—
450C4—62no—
451C4—122no—
452C4—122no—
453C4C2×C3×#23711yescharacteristic
454C4C3×D3×#4111yescharacteristic
455C3—21no—
456C3#8089311yescharacteristic, direct product factor
457C3C3×#318511yescharacteristic, complemented
458C2—41no—
459C2C3×#559611yescharacteristic
460C2C3×D3×#13712yes—
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#470C2
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenterC3×#470D3
hypocenterC3C3×#3185
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#470

Complements

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

NH ≅ G/Ntype
3. C3×#5184C2semidirect
4. C3×#5183C2semidirect
8. C3×#4855C2semidirect
9. C3×#4853C2semidirect
10. C3×#4792C2semidirect
11. C3×#4789C2semidirect
13. #80893C3direct (N × H)
55. #5184C2×C3semidirect
56. #5183C2×C3semidirect
60. #4855C2×C3semidirect
61. #4853C2×C3semidirect
62. #4792C2×C3semidirect
63. #4789C2×C3semidirect
412. C32#3185semidirect
456. C3#80893direct (N × H)
457. C3C3×#3185semidirect

Maximal subgroups

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

subgroupindex
C3×#56222
C32×#4702
C3×#51842
C3×#51832
C3×#51372
C3×Dic3×M162
C3×#50522
C3×#48552
C3×#48532
C3×#47922
C3×#47892
C3×#31853
#808933