Finite Group Databasebeta

← C3×#84033 #11856255

Subgroups — C3×#84033 #11856255

Order 1152.

2885 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
1C24×C32×C4C211yesmaximal, characteristic, complemented
2C2×C3×#953C211yesmaximal, characteristic
3C2×C3×#929C212yesmaximal, complemented
4C3×#5247C211yesmaximal, characteristic, complemented
5C3×#5213C214yesmaximal, complemented
6C3×#5211C212yesmaximal, complemented
7C3×#5210C214yesmaximal, complemented
8C3×#2849—31nomaximal
9#84033C311yesmaximal, characteristic, direct product factor
10C25×C32C2211yescharacteristic
11C23×C32×C4—28no—
12C23×C32×C4—24no—
13C23×C32×C4C2214yes—
14C23×C32×C4C2212yes—
15C22×C3×#67C2211yescharacteristic
16C22×C3×#67C2212yes—
17C3×#953—24no—
18C2×C3×#217C2212yes—
19C2×C3×#217C2212yes—
20C2×C3×#217C2214yes—
21C2×C3×#217C2211yescharacteristic
22C3×#929—28no—
23C2×C3×(C2×D3)⋊C4C2214yescomplemented
24C2×C3×Dic3⋊C4C2214yescomplemented
25C3×C3⋊#95C2218yescomplemented
26C24×C3×C4—21no—
27C24×C3×C4D311yescharacteristic, complemented
28C24×C3×C4C2×C311yescharacteristic, complemented
29C2×C3×#123—32no—
30C2×C3×#120—31no—
31C2×#953C2×C311yescharacteristic
32C2×#929C2×C312yescomplemented
33C3×#386—34no—
34C3×#385—34no—
35C3×#381—32no—
36C3×#379—31no—
37#5247C2×C311yescharacteristic, complemented
38#5213C2×C314yescomplemented
39#5211C2×C312yescomplemented
40#5210C2×C314yescomplemented
41C24×C32—24no—
42C24×C32—28no—
43C24×C32D414yes—
44C24×C32C2311yescharacteristic
45C24×C32C2312yes—
46C23×C3×D3C2311yescharacteristic
47C22×C32×C4—232no—
48C22×C32×C4—28no—
49C22×C32×C4—24no—
50C22×C32×C4—24no—
51C22×C32×C4—216no—
52C22×C32×C4D418yescomplemented
53C22×C32×C4C2314yes—
54C2×C3×#67—24no—
55C2×C3×#67—22no—
56C2×C3×#67—24no—
57C2×C3×#67—28no—
58C22×C3×Dic3C2311yescharacteristic
59C22×C3×Dic3C2314yes—
60C22×C3×Dic3C2312yes—
61C3×#217—24no—
62C3×#217—22no—
63C3×#217—24no—
64C3×#217—28no—
65C3×(C2×D3)⋊C4—28no—
66C3×Dic3⋊C4—28no—
67#2849—31noSylow
68C25×C3—21no—
69C25×C3C2×D311yescharacteristic
70C25×C3C22×C311yescharacteristic
71C22×C3×D4—32no—
72C22×C3×D4—31no—
73C23×C3×C4—28no—
74C23×C3×C4—216no—
75C23×C3×C4—24no—
76C23×C3×C4—24no—
77C23×C3×C4—28no—
78C23×C3×C4—28no—
79C23×C3×C4—24no—
80C23×C3×C4—22no—
81C23×C3×C4C2×D314yes—
82C23×C3×C4C2×D312yes—
83C23×C3×C4C22×C314yes—
84C23×C3×C4C22×C312yes—
85C22×#67C22×C312yes—
86C22×#67C22×C311yescharacteristic
87C3×#123—68no—
88C3×#120—64no—
89C2×C3×C4⋊C4—34no—
90C2×C3×C22⋊C4—32no—
91C2×C3×C22⋊C4—34no—
92C2×C3×C22⋊C4—31no—
93C2×C3×C22⋊C4—32no—
94C2×C3×C22⋊C4—34no—
95#953—24no—
96C2×#217C22×C312yes—
97C2×#217C22×C314yes—
98C2×#217C22×C311yescharacteristic
99C2×#217C22×C312yes—
100#929—28no—
101C2×(C2×D3)⋊C4C22×C314yescomplemented
102C2×Dic3⋊C4C22×C314yescomplemented
103C3×#95—38no—
104C3⋊#95C22×C318yescomplemented
105C23×C32—232no—
106C23×C32—28no—
107C23×C32—216no—
108C23×C32—24no—
109C23×C32—24no—
110C23×C32—24no—
111C23×C32C2×D414yes—
112C23×C32C2×D412yes—
113C23×C32C2×D414yes—
114C23×C32#4118yes—
115C23×C32C2411yescharacteristic
116C22×C3×D3—22no—
117C22×C3×D3—21no—
118C22×C3×D3—24no—
119C2×C32×C4—232no—
120C2×C32×C4—216no—
121C2×C32×C4—24no—
122C2×C32×C4—24no—
123C2×C32×C4C2×D418yes—
124C3×#67—44no—
125C3×#67—48no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—24no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—28no—
131C2×C3×Dic3—24no—
132C24×C4C3×D311yescharacteristic, complemented
133C2×#123—32no—
134C2×#120—31no—
135#386—34no—
136#385—34no—
137#381—32no—
138#379—31no—
139C24×C3—216no—
140C24×C3—28no—
141C24×C3—28no—
142C24×C3—24no—
143C24×C3—24no—
144C24×C3—28no—
145C24×C3—24no—
146C24×C3—22no—
147C24×C3—21no—
148C24×C3—31no—
149C24×C3#6714yes—
150C24×C3C3×D414yes—
151C24×C3C22×D312yes—
152C24×C3C22×D311yescharacteristic
153C24×C3C23×C311yescharacteristic
154C24×C3C23×C312yes—
155C23×D3C23×C311yescharacteristic
156C2×C3×D4—68no—
157C2×C3×D4—64no—
158C2×C3×D4—62no—
159C2×C3×D4—64no—
160C22×C3×C4—264no—
161C22×C3×C4—232no—
162C22×C3×C4—232no—
163C22×C3×C4—216no—
164C22×C3×C4—28no—
165C22×C3×C4—28no—
166C22×C3×C4—232no—
167C22×C3×C4—28no—
168C22×C3×C4—24no—
169C22×C3×C4—24no—
170C22×C3×C4—28no—
171C22×C3×C4—24no—
172C22×C3×C4—24no—
173C22×C3×C4—216no—
174C22×C3×C4—216no—
175C22×C3×C4—28no—
176C22×C3×C4—24no—
177C22×C3×C4—32no—
178C22×C3×C4—34no—
179C22×C3×C4—31no—
180C22×C3×C4#6718yescomplemented
181C22×C3×C4C3×D418yescomplemented
182C22×C3×C4C22×D314yes—
183C22×C3×C4C23×C314yes—
184C2×#67—24no—
185C2×#67—22no—
186C2×#67—24no—
187C2×#67—28no—
188C22×Dic3C23×C312yes—
189C22×Dic3C23×C314yes—
190C22×Dic3C23×C311yescharacteristic
191C3×C4⋊C4—68no—
192C3×C22⋊C4—68no—
193C3×C22⋊C4—64no—
194C3×C22⋊C4—62no—
195C3×C22⋊C4—64no—
196C3×C22⋊C4—68no—
197#217—24no—
198#217—22no—
199#217—24no—
200#217—28no—
201(C2×D3)⋊C4—28no—
202Dic3⋊C4—28no—
203C22×C32—232no—
204C22×C32—24no—
205C22×C32—24no—
206C22×C32—24no—
207C22×C32—28no—
208C22×C32—216no—
209C22×C32#12014yes—
210C22×C32#12318yescomplemented
211C22×C32C22×D411yescharacteristic
212C22×C32C22×D412yes—
213C22×C32C2×#4114yes—
214C2×C3×D3—41no—
215C2×C3×D3—42no—
216C2×C3×D3—44no—
217C32×C4—28no—
218C3×Dic3—41no—
219C3×Dic3—42no—
220C3×Dic3—44no—
221C25C2×C3×D311yescharacteristic
222C22×D4—31no—
223C22×D4—32no—
224C23×C4—24no—
225C23×C4—28no—
226C23×C4C2×C3×D314yes—
227C23×C4C2×C3×D312yes—
228#123—68no—
229#120—64no—
230C2×C4⋊C4—34no—
231C2×C22⋊C4—31no—
232C2×C22⋊C4—32no—
233C2×C22⋊C4—32no—
234C2×C22⋊C4—34no—
235C2×C22⋊C4—34no—
236#95—38no—
237C23×C3—216no—
238C23×C3—28no—
239C23×C3—264no—
240C23×C3—232no—
241C23×C3—232no—
242C23×C3—232no—
243C23×C3—28no—
244C23×C3—28no—
245C23×C3—216no—
246C23×C3—28no—
247C23×C3—28no—
248C23×C3—216no—
249C23×C3—24no—
250C23×C3—24no—
251C23×C3—24no—
252C23×C3—24no—
253C23×C3—24no—
254C23×C3—24no—
255C23×C3—21no—
256C23×C3—28no—
257C23×C3—24no—
258C23×C3—22no—
259C23×C3—24no—
260C23×C3—64no—
261C23×C3—62no—
262C23×C3—61no—
263C23×C3#23518yes—
264C23×C3C2×#6714yes—
265C23×C3C2×#6712yes—
266C23×C3C2×#6714yes—
267C23×C3C2×C3×D412yes—
268C23×C3C2×C3×D414yes—
269C23×C3C2×C3×D414yes—
270C23×C3C3×#4118yes—
271C23×C3C23×D311yescharacteristic
272C23×C3C24×C311yescharacteristic
273C22×D3—22no—
274C22×D3—21no—
275C22×D3—24no—
276C3×D4—128no—
277C3×D4—124no—
278C2×C3×C4—264no—
279C2×C3×C4—232no—
280C2×C3×C4—232no—
281C2×C3×C4—232no—
282C2×C3×C4—28no—
283C2×C3×C4—28no—
284C2×C3×C4—216no—
285C2×C3×C4—216no—
286C2×C3×C4—24no—
287C2×C3×C4—24no—
288C2×C3×C4—24no—
289C2×C3×C4—24no—
290C2×C3×C4—28no—
291C2×C3×C4—68no—
292C2×C3×C4—64no—
293C2×C3×C4—64no—
294C2×C3×C4—62no—
295C2×C3×C4—61no—
296C2×C3×C4—62no—
297C2×C3×C4C2×#6718yes—
298C2×C3×C4C2×C3×D418yes—
299#67—44no—
300#67—48no—
301C2×Dic3—22no—
302C2×Dic3—24no—
303C2×Dic3—21no—
304C2×Dic3—22no—
305C2×Dic3—28no—
306C2×Dic3—24no—
307C2×C32—24no—
308C2×C32—28no—
309C2×C32C2×#12011yescharacteristic
310C2×C32C2×#12312yes—
311C2×C32#52514yes—
312C3×D3—81no—
313C24—28no—
314C24—24no—
315C24—31no—
316C24C3×#6714yes—
317C24C22×C3×D312yes—
318C24C22×C3×D311yescharacteristic
319C2×D4—68no—
320C2×D4—64no—
321C2×D4—62no—
322C2×D4—64no—
323C22×C4—232no—
324C22×C4—28no—
325C22×C4—24no—
326C22×C4—24no—
327C22×C4—216no—
328C22×C4—32no—
329C22×C4—34no—
330C22×C4—31no—
331C22×C4C3×#6718yescomplemented
332C22×C4C22×C3×D314yes—
333C4⋊C4—68no—
334C22⋊C4—68no—
335C22⋊C4—64no—
336C22⋊C4—62no—
337C22⋊C4—64no—
338C22⋊C4—68no—
339C22×C3—28no—
340C22×C3—264no—
341C22×C3—232no—
342C22×C3—232no—
343C22×C3—28no—
344C22×C3—28no—
345C22×C3—232no—
346C22×C3—216no—
347C22×C3—24no—
348C22×C3—24no—
349C22×C3—216no—
350C22×C3—28no—
351C22×C3—24no—
352C22×C3—24no—
353C22×C3—24no—
354C22×C3—24no—
355C22×C3—28no—
356C22×C3—216no—
357C22×C3—28no—
358C22×C3—24no—
359C22×C3—24no—
360C22×C3—21no—
361C22×C3—22no—
362C22×C3—122no—
363C22×C3—124no—
364C22×C3—121no—
365C22×C3#92918yescomplemented
366C22×C3#95314yes—
367C22×C3C3×#12014yes—
368C22×C3C3×#12318yescomplemented
369C22×C3C2×#23514yes—
370C22×C3C22×#6711yescharacteristic
371C22×C3C22×#6712yes—
372C22×C3C22×C3×D411yescharacteristic
373C22×C3C22×C3×D412yes—
374C22×C3C2×C3×#4114yes—
375C2×D3—41no—
376C2×D3—42no—
377C2×D3—44no—
378C3×C4—216no—
379C3×C4—28no—
380C3×C4—28no—
381C3×C4—122no—
382C3×C4—124no—
383C3×C4—121no—
384Dic3—41no—
385Dic3—42no—
386Dic3—44no—
387C32#284911yescharacteristic, complemented, Sylow
388C23—232no—
389C23—216no—
390C23—28no—
391C23—24no—
392C23—24no—
393C23—24no—
394C23—64no—
395C23—62no—
396C23—61no—
397C23C3×#23518yes—
398C23C2×C3×#6714yes—
399C23C2×C3×#6712yes—
400C23C2×C3×#6714yes—
401C23C23×C3×D311yescharacteristic
402D4—128no—
403D4—124no—
404C2×C4—232no—
405C2×C4—216no—
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—68no—
409C2×C4—64no—
410C2×C4—64no—
411C2×C4—62no—
412C2×C4—61no—
413C2×C4—62no—
414C2×C4C2×C3×#6718yes—
415C2×C3—216no—
416C2×C3—28no—
417C2×C3—28no—
418C2×C3—24no—
419C2×C3—24no—
420C2×C3—28no—
421C2×C3—22no—
422C2×C3—24no—
423C2×C3—21no—
424C2×C3—241no—
425C2×C3C2×#92912yes—
426C2×C3#579114yes—
427C2×C3C2×#95311yescharacteristic
428C2×C3C2×C3×#12011yescharacteristic
429C2×C3C2×C3×#12312yes—
430C2×C3C3×#52514yes—
431D3—81no—
432C22—232no—
433C22—24no—
434C22—24no—
435C22—216no—
436C22—28no—
437C22—24no—
438C22—122no—
439C22—124no—
440C22—121no—
441C22C3×#92918yescomplemented
442C22C3×#95314yes—
443C22C2×C3×#23514yes—
444C22C22×C3×#6711yescharacteristic
445C22C22×C3×#6712yes—
446C4—28no—
447C4—122no—
448C4—124no—
449C4—121no—
450C3—21no—
451C3#8403311yescharacteristic, direct product factor
452C3C3×#284911yescharacteristic, complemented
453C2—28no—
454C2—24no—
455C2—241no—
456C2C2×C3×#92912yes—
457C2C3×#579114yes—
458C2C2×C3×#95311yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC24×C32×C4C2
socleC23×C32C24
prime radicalC2×C3×#953C2
hypercenterC24×C3×C4D3
hypocenterC3C3×#2849
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C24×C3×C4

Complements

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

NH ≅ G/Ntype
1. C24×C32×C4C2semidirect
3. C2×C3×#929C2semidirect
4. C3×#5247C2semidirect
5. C3×#5213C2semidirect
6. C3×#5211C2semidirect
7. C3×#5210C2semidirect
9. #84033C3direct (N × H)
23. C2×C3×(C2×D3)⋊C4C22semidirect
24. C2×C3×Dic3⋊C4C22semidirect
25. C3×C3⋊#95C22semidirect
27. C24×C3×C4D3semidirect
28. C24×C3×C4C2×C3semidirect
32. C2×#929C2×C3semidirect
37. #5247C2×C3semidirect
38. #5213C2×C3semidirect
39. #5211C2×C3semidirect
40. #5210C2×C3semidirect
52. C22×C32×C4D4semidirect
101. C2×(C2×D3)⋊C4C22×C3semidirect
102. C2×Dic3⋊C4C22×C3semidirect
104. C3⋊#95C22×C3semidirect
132. C24×C4C3×D3semidirect
180. C22×C3×C4#67semidirect
181. C22×C3×C4C3×D4semidirect
210. C22×C32#123semidirect
331. C22×C4C3×#67semidirect
365. C22×C3#929semidirect
368. C22×C3C3×#123semidirect
387. C32#2849semidirect
441. C22C3×#929semidirect
451. C3#84033direct (N × H)
452. C3C3×#2849semidirect

Maximal subgroups

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

subgroupindex
C24×C32×C42
C2×C3×#9532
C2×C3×#9292
C3×#52472
C3×#52132
C3×#52112
C3×#52102
C3×#28493
#840333