Finite Group Databasebeta

← C3×#79831 #11860796

Subgroups — C3×#79831 #11860796

Order 1152.

966 conjugacy classes of subgroups.

The subgroup lattice has 467 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×Q16C211yesmaximal, characteristic
2C3×#5572C212yesmaximal
3C32×#441C211yesmaximal, characteristic, complemented
4C3×#5184C211yesmaximal, characteristic, complemented
5C3×C4×#216C212yesmaximal, complemented
6C3×#4860C211yesmaximal, characteristic
7C3×#4853C211yesmaximal, characteristic, complemented
8C3×#4802C212yesmaximal
9C3×#4790C212yesmaximal, complemented
10C3×#4716C211yesmaximal, characteristic, complemented
11C3×#4708C211yesmaximal, characteristic
12C3×#2950—31nomaximal
13#79831C311yesmaximal, characteristic, direct product factor
14C2×C3×D3×Q8C2212yes—
15C2×C32×Q16C2211yescharacteristic
16C32×C4×Q8C2212yes—
17C3×Q8×Dic3C2212yes—
18C2×C3×#216C2212yes—
19C3×D3×Q16C418yescomplemented
20C2×C3×Dic12C2211yescharacteristic
21C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
22C2×C3×D3×C8C2211yescharacteristic
23C3×#892—22no—
24C3×#892C2212yes—
25C3×#887—22no—
26C3×#887C2212yes—
27C3×#872—22no—
28C3×#872C2211yescharacteristic
29C3×C4×Dic6—22no—
30C3×C4×Dic6C2212yes—
31C32×#106C2211yescharacteristic
32C32×#103C2212yes—
33C32×#97C2211yescharacteristic
34C3×#835C2212yes—
35C3×#817C2211yescharacteristic
36C3×#816C2212yes—
37C3×#815C2211yescharacteristic
38C3×C8×Dic3C2211yescharacteristic
39C3×#810C2212yes—
40C3×#807C2212yes—
41C3×C4×C3⋊C8C2211yescharacteristic
42C22×C3×Q16—31no—
43C3×#519—32no—
44C2×D3×Q16C2×C311yescharacteristic
45#5572C2×C312yes—
46C3×#441—21no—
47C3×#441—31no—
48C3×#441—31no—
49C3×#441—31no—
50C3×#441D311yescharacteristic, complemented
51C3×#441C2×C311yescharacteristic, complemented
52C3×C4×Q16—32no—
53C3×C4×Q16—32no—
54C3×#427—31no—
55C3×#419—32no—
56C3×#405—31no—
57#5184C2×C311yescharacteristic, complemented
58C4×#216C2×C312yescomplemented
59#4860C2×C311yescharacteristic
60#4853C2×C311yescharacteristic, complemented
61#4802C2×C312yes—
62#4790C2×C312yescomplemented
63#4716C2×C311yescharacteristic, complemented
64#4708C2×C311yescharacteristic
65C2×C32×Q8C2312yes—
66C3×D3×Q8—24no—
67C3×D3×Q8C2×C418yes—
68C2×C3×C4×D3—22no—
69C2×C3×C4×D3C2311yescharacteristic
70C2×C3×Dic6—22no—
71C2×C3×Dic6C2312yes—
72C32×Q16C2×C414yes—
73C2×C32×C8C2311yescharacteristic
74C2×C32×C8C2311yescharacteristic
75C32×C4⋊C4—22no—
76C32×C4⋊C4C2312yes—
77C32×C42—22no—
78C32×C42C2311yescharacteristic
79C3×#216C2×C418yes—
80C3×(C2×D3)⋊C4—22no—
81C3×(C2×D3)⋊C4D412yes—
82C3×C4⋊Dic3—22no—
83C3×C4⋊Dic3C2312yes—
84C3×Dic3⋊C4—22no—
85C3×Dic3⋊C4—22no—
86C3×Dic3⋊C4D412yes—
87C3×C4×Dic3—22no—
88C3×C4×Dic3—22no—
89C3×C4×Dic3—22no—
90C3×C4×Dic3—22no—
91C3×C4×Dic3C2311yescharacteristic
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94C3×Dic12C2×C414yes—
95C3×ΓL(1,𝔽25)—22no—
96C3×D3×C8C2×C414yes—
97#2950—31noSylow
98C22×C3×Q8—32no—
99C2×D3×Q8C22×C312yes—
100C2×C3×Q16—21no—
101C2×C3×Q16—32no—
102C2×C3×Q16—38no—
103C2×C3×Q16—31no—
104C2×C3×Q16C2×D311yescharacteristic
105C2×C3×Q16C22×C311yescharacteristic
106C2×C3×M16—31no—
107C22×C3×C8—31no—
108C3×C4×Q8—22no—
109C3×C4×Q8—32no—
110C3×C4×Q8—32no—
111C3×C4×Q8—32no—
112C3×C4×Q8—62no—
113C3×C4×Q8—62no—
114C3×C4×Q8C2×D312yes—
115C3×C4×Q8C22×C312yes—
116C3×#117—31no—
117C3×#117—32no—
118C3×#117—62no—
119C3×#117—62no—
120Q8×Dic3C22×C312yes—
121C2×#216C22×C312yes—
122D3×Q16C3×C418yescomplemented
123C2×Dic12C22×C311yescharacteristic
124C2×ΓL(1,𝔽25)C22×C311yescharacteristic
125C2×D3×C8C22×C311yescharacteristic
126#892—22no—
127#892C22×C312yes—
128#887—22no—
129#887C22×C312yes—
130#872—22no—
131#872C22×C311yescharacteristic
132C4×Dic6—22no—
133C4×Dic6C22×C312yes—
134C3×#107—32no—
135C3×#106—21no—
136C3×#106—31no—
137C3×#106C2×D311yescharacteristic
138C3×#106C22×C311yescharacteristic
139C3×#103—22no—
140C3×#103—32no—
141C3×#103—32no—
142C3×#103—32no—
143C3×#103C2×D312yes—
144C3×#103C22×C312yes—
145C3×#97—21no—
146C3×#97—31no—
147C3×#97C2×D311yescharacteristic
148C3×#97C22×C311yescharacteristic
149C3×C4×C8—31no—
150C3×C4×C8—31no—
151#835C22×C312yes—
152#817C22×C311yescharacteristic
153#816C22×C312yes—
154#815C22×C311yescharacteristic
155C8×Dic3C22×C311yescharacteristic
156#810C22×C312yes—
157#807C22×C312yes—
158C4×C3⋊C8C22×C311yescharacteristic
159C22×C3×D3C2×D411yescharacteristic
160C32×Q8—22no—
161C32×Q8C22×C414yes—
162C2×C32×C4—22no—
163C2×C32×C4—22no—
164C2×C32×C4C2×D412yes—
165C2×C32×C4C2411yescharacteristic
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3C2×D412yes—
169C2×C3×Dic3C2×D411yescharacteristic
170C3×C4×D3—28no—
171C3×C4×D3C22×C412yes—
172C3×C4×D3#4112yes—
173C3×Dic6—22no—
174C3×Dic6—28no—
175C3×Dic6C22×C414yes—
176C32×C8—21no—
177C32×C8C22×C412yes—
178C3×C3⋊C8—21no—
179C3×C3⋊C8C22×C412yes—
180C22×Q16—31no—
181#519—32no—
182#441—31no—
183#441—31no—
184#441—31no—
185#441C3×D311yescharacteristic, complemented
186C4×Q16—32no—
187C4×Q16—32no—
188#427—31no—
189#419—32no—
190#405—31no—
191C2×C3×Q8—22no—
192C2×C3×Q8—38no—
193C2×C3×Q8—32no—
194C2×C3×Q8—62no—
195C2×C3×Q8—64no—
196C2×C3×Q8C22×D312yes—
197C2×C3×Q8C23×C312yes—
198C22×C3×C4—31no—
199C22×C3×C4—62no—
200D3×Q8—24no—
201D3×Q8C2×C3×C418yes—
202C2×C4×D3—22no—
203C2×C4×D3C23×C311yescharacteristic
204C2×Dic6—22no—
205C2×Dic6C23×C312yes—
206C3×Q16—24no—
207C3×Q16—38no—
208C3×Q16—34no—
209C3×Q16C4×D314yes—
210C3×Q16C2×C3×C414yes—
211C3×M16—62no—
212C2×C3×C8—21no—
213C2×C3×C8—21no—
214C2×C3×C8—31no—
215C2×C3×C8—34no—
216C2×C3×C8—31no—
217C2×C3×C8C22×D311yescharacteristic
218C2×C3×C8C22×D311yescharacteristic
219C2×C3×C8C23×C311yescharacteristic
220C2×C3×C8C23×C311yescharacteristic
221C3×C4⋊C4—22no—
222C3×C4⋊C4—22no—
223C3×C4⋊C4—22no—
224C3×C4⋊C4—32no—
225C3×C4⋊C4—32no—
226C3×C4⋊C4—42no—
227C3×C4⋊C4—62no—
228C3×C4⋊C4—62no—
229C3×C4⋊C4—62no—
230C3×C4⋊C4C22×D312yes—
231C3×C4⋊C4C23×C312yes—
232C3×C22⋊C4—32no—
233C3×C22⋊C4—62no—
234C3×C42—22no—
235C3×C42—22no—
236C3×C42—21no—
237C3×C42—31no—
238C3×C42—42no—
239C3×C42—62no—
240C3×C42—62no—
241C3×C42—62no—
242C3×C42—62no—
243C3×C42C22×D311yescharacteristic
244C3×C42C23×C311yescharacteristic
245#216C2×C3×C418yes—
246(C2×D3)⋊C4—22no—
247(C2×D3)⋊C4C3×D412yes—
248C4⋊Dic3—22no—
249C4⋊Dic3C23×C312yes—
250Dic3⋊C4—22no—
251Dic3⋊C4—22no—
252Dic3⋊C4C3×D412yes—
253C4×Dic3—22no—
254C4×Dic3—22no—
255C4×Dic3—22no—
256C4×Dic3—22no—
257C4×Dic3C23×C311yescharacteristic
258C2×C3⋊C8C23×C311yescharacteristic
259C2×C3⋊C8C23×C311yescharacteristic
260Dic12C2×C3×C414yes—
261ΓL(1,𝔽25)—22no—
262D3×C8C2×C3×C414yes—
263C22×C32C22×D411yescharacteristic
264C2×C3×D3—22no—
265C2×C3×D3C4×D412yes—
266C32×C4—24no—
267C32×C4—22no—
268C32×C4—42no—
269C32×C4C23×C411yescharacteristic
270C32×C4C2×#4111yescharacteristic
271C3×Dic3—24no—
272C3×Dic3—22no—
273C3×Dic3—42no—
274C3×Dic3C4×D412yes—
275C22×Q8—32no—
276C2×Q16—32no—
277C2×Q16—38no—
278C2×Q16—31no—
279C2×Q16C2×C3×D311yescharacteristic
280C2×M16—31no—
281C22×C8—31no—
282C4×Q8—32no—
283C4×Q8—32no—
284C4×Q8—32no—
285C4×Q8—62no—
286C4×Q8—62no—
287C4×Q8C2×C3×D312yes—
288#117—31no—
289#117—32no—
290#117—62no—
291#117—62no—
292#107—32no—
293#106—31no—
294#106C2×C3×D311yescharacteristic
295#103—32no—
296#103—32no—
297#103—32no—
298#103C2×C3×D312yes—
299#97—31no—
300#97C2×C3×D311yescharacteristic
301C4×C8—31no—
302C4×C8—31no—
303C23×C3—31no—
304C22×D3C2×C3×D411yescharacteristic
305C3×Q8—22no—
306C3×Q8—22no—
307C3×Q8—24no—
308C3×Q8—34no—
309C3×Q8—42no—
310C3×Q8—68no—
311C3×Q8—62no—
312C3×Q8C2×C4×D314yes—
313C3×Q8C22×C3×C414yes—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—21no—
319C2×C3×C4—22no—
320C2×C3×C4—31no—
321C2×C3×C4—32no—
322C2×C3×C4—32no—
323C2×C3×C4—32no—
324C2×C3×C4—42no—
325C2×C3×C4—42no—
326C2×C3×C4—68no—
327C2×C3×C4—62no—
328C2×C3×C4—62no—
329C2×C3×C4D3×D412yes—
330C2×C3×C4C2×C3×D412yes—
331C2×C3×C4C23×D311yescharacteristic
332C2×C3×C4C24×C311yescharacteristic
333C2×Dic3—22no—
334C2×Dic3—22no—
335C2×Dic3C2×C3×D412yes—
336C2×Dic3C2×C3×D411yescharacteristic
337C4×D3—28no—
338C4×D3C22×C3×C412yes—
339C4×D3C3×#4112yes—
340Dic6—22no—
341Dic6—28no—
342Dic6C22×C3×C414yes—
343C3×C8—21no—
344C3×C8—21no—
345C3×C8—22no—
346C3×C8—32no—
347C3×C8—41no—
348C3×C8—61no—
349C3×C8C2×C4×D312yes—
350C3×C8C22×C3×C412yes—
351C3⋊C8—21no—
352C3⋊C8C22×C3×C412yes—
353C2×C32C2×C4×D411yescharacteristic
354C2×C32#57812yes—
355C3×D3—22no—
356C2×Q8—38no—
357C2×Q8—32no—
358C2×Q8—62no—
359C2×Q8—64no—
360C2×Q8C22×C3×D312yes—
361C22×C4—31no—
362C22×C4—62no—
363Q16—38no—
364Q16—34no—
365Q16C3×C4×D314yes—
366M16—62no—
367C2×C8—31no—
368C2×C8—34no—
369C2×C8—31no—
370C2×C8C22×C3×D311yescharacteristic
371C2×C8C22×C3×D311yescharacteristic
372C4⋊C4—22no—
373C4⋊C4—32no—
374C4⋊C4—32no—
375C4⋊C4—62no—
376C4⋊C4—62no—
377C4⋊C4—62no—
378C4⋊C4C22×C3×D312yes—
379C22⋊C4—32no—
380C22⋊C4—62no—
381C42—22no—
382C42—31no—
383C42—62no—
384C42—62no—
385C42—62no—
386C42—62no—
387C42C22×C3×D311yescharacteristic
388C22×C3—21no—
389C22×C3—32no—
390C22×C3—62no—
391C22×C3C2×D3×D411yescharacteristic
392C22×C3C22×C3×D411yescharacteristic
393C2×D3—22no—
394C2×D3C3×C4×D412yes—
395C3×C4—22no—
396C3×C4—22no—
397C3×C4—24no—
398C3×C4—24no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—32no—
402C3×C4—42no—
403C3×C4—44no—
404C3×C4—42no—
405C3×C4—42no—
406C3×C4—62no—
407C3×C4—64no—
408C3×C4—82no—
409C3×C4—122no—
410C3×C4C22×C4×D311yescharacteristic
411C3×C4D3×#4111yescharacteristic
412C3×C4C23×C3×C411yescharacteristic
413C3×C4C2×C3×#4111yescharacteristic
414Dic3—22no—
415Dic3—24no—
416Dic3—42no—
417Dic3C3×C4×D412yes—
418C32#295011yescharacteristic, complemented, Sylow
419C23—31no—
420Q8—22no—
421Q8—34no—
422Q8—68no—
423Q8—62no—
424Q8C2×C3×C4×D314yes—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—31no—
428C2×C4—32no—
429C2×C4—32no—
430C2×C4—32no—
431C2×C4—68no—
432C2×C4—62no—
433C2×C4—62no—
434C2×C4C3×D3×D412yes—
435C2×C4C23×C3×D311yescharacteristic
436C8—21no—
437C8—32no—
438C8—61no—
439C8C2×C3×C4×D312yes—
440C2×C3—22no—
441C2×C3—21no—
442C2×C3—62no—
443C2×C3C4×D3×D411yescharacteristic
444C2×C3#577912yes—
445C2×C3C2×C3×C4×D411yescharacteristic
446C2×C3C3×#57812yes—
447D3—22no—
448C22—32no—
449C22—62no—
450C22C2×C3×D3×D411yescharacteristic
451C4—22no—
452C4—24no—
453C4—32no—
454C4—42no—
455C4—62no—
456C4—64no—
457C4—122no—
458C4C22×C3×C4×D311yescharacteristic
459C4C3×D3×#4111yescharacteristic
460C3—21no—
461C3#7983111yescharacteristic, direct product factor
462C3C3×#295011yescharacteristic, complemented
463C2—62no—
464C2C3×C4×D3×D411yescharacteristic
465C2C3×#577912yes—
subgroupG/H
centerC22×C3C2×D3×D4
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC32×#441C2
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
cosocleC2×C3×C4C24×C3
hypercenterC3×#441D3
hypocenterC3C3×#2950
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#441

Complements

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

NH ≅ G/Ntype
3. C32×#441C2semidirect
4. C3×#5184C2semidirect
5. C3×C4×#216C2semidirect
7. C3×#4853C2semidirect
9. C3×#4790C2semidirect
10. C3×#4716C2semidirect
13. #79831C3direct (N × H)
19. C3×D3×Q16C4semidirect
50. C3×#441D3semidirect
51. C3×#441C2×C3semidirect
57. #5184C2×C3semidirect
58. C4×#216C2×C3semidirect
60. #4853C2×C3semidirect
62. #4790C2×C3semidirect
63. #4716C2×C3semidirect
122. D3×Q16C3×C4semidirect
185. #441C3×D3semidirect
418. C32#2950semidirect
461. C3#79831direct (N × H)
462. C3C3×#2950semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×Q162
C3×#55722
C32×#4412
C3×#51842
C3×C4×#2162
C3×#48602
C3×#48532
C3×#48022
C3×#47902
C3×#47162
C3×#47082
C3×#29503
#798313