Finite Group Databasebeta

← C2×C3×#4664 #11801014

Subgroups — C2×C3×#4664 #11801014

Order 1152.

2453 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
1C23×C3×C4×D3C211yesmaximal, characteristic
2C22×C3×(C2×D3)⋊C4C212yesmaximal
3C2×C32×#95C211yesmaximal, characteristic, complemented
4C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
5C2×C3×C3⋊#95C212yesmaximal, complemented
6C3×#4664C218yesmaximal, direct product factor
7C2×C3×#381—31nomaximal
8C2×#4664C311yesmaximal, characteristic, direct product factor
9C24×C3×D3C2211yescharacteristic
10C23×C32×C4C2212yes—
11C23×C32×C4C2211yescharacteristic
12C23×C3×Dic3C2212yes—
13C23×C3×Dic3C2211yescharacteristic
14C22×C3×C4×D3—28no—
15C22×C3×C4×D3C418yescomplemented
16C22×C3×C4×D3C2214yes—
17C2×C3×(C2×D3)⋊C4—28no—
18C2×C3×(C2×D3)⋊C4C2218yes—
19C32×#95C2214yescomplemented
20C3×C3⋊#95C2214yescomplemented
21C3×C3⋊#95C2218yescomplemented
22C24×C3×C4—31no—
23C23×C4×D3C2×C311yescharacteristic
24C22×C3×C22⋊C4—32no—
25C22×(C2×D3)⋊C4C2×C312yes—
26C3×#381—38no—
27C2×C3×#95—21no—
28C2×C3×#95—32no—
29C2×C3×#95—31no—
30C2×C3×#95D311yescharacteristic, complemented
31C2×C3×#95C2×C311yescharacteristic, complemented
32C2×C3⋊#95C2×C311yescharacteristic, complemented
33C2×C3⋊#95C2×C312yescomplemented
34#4664C2×C318yesdirect product factor
35C24×C32C2311yescharacteristic
36C23×C3×D3—24no—
37C23×C3×D3—22no—
38C23×C3×D3—22no—
39C23×C3×D3C2×C414yes—
40C23×C3×D3D418yes—
41C23×C3×D3C2312yes—
42C22×C32×C4—24no—
43C22×C32×C4—24no—
44C22×C32×C4—24no—
45C22×C32×C4—24no—
46C22×C32×C4C2×C414yes—
47C22×C32×C4C2314yes—
48C22×C32×C4C2312yes—
49C22×C3×Dic3—24no—
50C22×C3×Dic3—24no—
51C22×C3×Dic3—24no—
52C22×C3×Dic3—24no—
53C22×C3×Dic3C2×C414yes—
54C22×C3×Dic3C2314yes—
55C22×C3×Dic3C2312yes—
56C2×C3×C4×D3—232no—
57C2×C3×C4×D3—216no—
58C2×C3×C4×D3C2×C4116yescomplemented
59C3×(C2×D3)⋊C4—216no—
60C2×#381—31noSylow
61C25×C3—31no—
62C24×D3C22×C311yescharacteristic
63C23×C3×C4—22no—
64C23×C3×C4—21no—
65C23×C3×C4—31no—
66C23×C3×C4—38no—
67C23×C3×C4—34no—
68C23×C3×C4—32no—
69C23×C3×C4—68no—
70C23×C3×C4C2×D312yes—
71C23×C3×C4C2×D311yescharacteristic
72C23×C3×C4C22×C312yes—
73C23×C3×C4C22×C311yescharacteristic
74C23×Dic3C22×C312yes—
75C23×Dic3C22×C311yescharacteristic
76C22×C4×D3—28no—
77C22×C4×D3C3×C418yescomplemented
78C22×C4×D3C22×C314yes—
79C2×C3×C22⋊C4—38no—
80C2×C3×C22⋊C4—68no—
81C2×(C2×D3)⋊C4—28no—
82C2×(C2×D3)⋊C4C22×C318yes—
83C3×#95—24no—
84C3×#95—38no—
85C3×#95—34no—
86C3×#95C2×D314yescomplemented
87C3×#95C22×C314yescomplemented
88C3⋊#95C22×C314yescomplemented
89C3⋊#95C22×C318yescomplemented
90C23×C32C22×C412yes—
91C23×C32C2×D414yes—
92C23×C32#4114yes—
93C23×C32#4112yes—
94C23×C32#4112yes—
95C23×C32C2411yescharacteristic
96C22×C3×D3—28no—
97C22×C3×D3—28no—
98C22×C3×D3—216no—
99C22×C3×D3—216no—
100C22×C3×D3—24no—
101C22×C3×D3—22no—
102C22×C3×D3—22no—
103C22×C3×D3C22⋊C4116yes—
104C22×C3×D3C22×C414yes—
105C22×C3×D3C2×D418yes—
106C2×C32×C4—24no—
107C2×C32×C4—28no—
108C2×C32×C4—24no—
109C2×C32×C4—24no—
110C2×C32×C4—24no—
111C2×C32×C4—48no—
112C2×C32×C4C22×C414yes—
113C2×C3×Dic3—28no—
114C2×C3×Dic3—24no—
115C2×C3×Dic3—24no—
116C2×C3×Dic3—24no—
117C2×C3×Dic3—24no—
118C2×C3×Dic3—48no—
119C2×C3×Dic3C22×C414yes—
120C3×C4×D3—232no—
121C24×C4—31no—
122C22×C22⋊C4—32no—
123#381—38no—
124C2×#95—32no—
125C2×#95—31no—
126C2×#95C3×D311yescharacteristic, complemented
127C24×C3—21no—
128C24×C3—34no—
129C24×C3—38no—
130C24×C3—32no—
131C24×C3—64no—
132C24×C3—62no—
133C24×C3—62no—
134C24×C3C22×D311yescharacteristic
135C24×C3C23×C311yescharacteristic
136C23×D3—24no—
137C23×D3—22no—
138C23×D3—22no—
139C23×D3C2×C3×C414yes—
140C23×D3C3×D418yes—
141C23×D3C23×C312yes—
142C22×C3×C4—24no—
143C22×C3×C4—24no—
144C22×C3×C4—28no—
145C22×C3×C4—24no—
146C22×C3×C4—24no—
147C22×C3×C4—24no—
148C22×C3×C4—24no—
149C22×C3×C4—24no—
150C22×C3×C4—24no—
151C22×C3×C4—24no—
152C22×C3×C4—24no—
153C22×C3×C4—22no—
154C22×C3×C4—34no—
155C22×C3×C4—32no—
156C22×C3×C4—316no—
157C22×C3×C4—34no—
158C22×C3×C4—44no—
159C22×C3×C4—44no—
160C22×C3×C4—44no—
161C22×C3×C4—632no—
162C22×C3×C4—616no—
163C22×C3×C4—64no—
164C22×C3×C4—64no—
165C22×C3×C4—64no—
166C22×C3×C4—64no—
167C22×C3×C4C4×D314yes—
168C22×C3×C4C2×C3×C414yes—
169C22×C3×C4C22×D314yes—
170C22×C3×C4C22×D312yes—
171C22×C3×C4C23×C314yes—
172C22×C3×C4C23×C312yes—
173C22×Dic3—24no—
174C22×Dic3—24no—
175C22×Dic3—24no—
176C22×Dic3—24no—
177C22×Dic3C2×C3×C414yes—
178C22×Dic3C23×C314yes—
179C22×Dic3C23×C312yes—
180C2×C4×D3—232no—
181C2×C4×D3—216no—
182C2×C4×D3C2×C3×C4116yescomplemented
183C3×C22⋊C4—616no—
184(C2×D3)⋊C4—216no—
185C22×C32C2×C22⋊C414yes—
186C22×C32#11714yes—
187C22×C32#11714yes—
188C22×C32#12318yes—
189C22×C32#12318yes—
190C22×C32C23×C411yescharacteristic
191C22×C32C22×D412yes—
192C22×C32C2×#4112yes—
193C22×C32C2×#4111yescharacteristic
194C22×C32C2×#4111yescharacteristic
195C2×C3×D3—24no—
196C2×C3×D3—24no—
197C2×C3×D3—28no—
198C2×C3×D3—28no—
199C2×C3×D3—232no—
200C2×C3×D3C2×C22⋊C418yes—
201C32×C4—24no—
202C32×C4—44no—
203C3×Dic3—24no—
204C3×Dic3—44no—
205C25—31no—
206C23×C4—31no—
207C23×C4—38no—
208C23×C4—34no—
209C23×C4—32no—
210C23×C4—68no—
211C23×C4C2×C3×D312yes—
212C23×C4C2×C3×D311yescharacteristic
213C2×C22⋊C4—38no—
214C2×C22⋊C4—68no—
215#95—38no—
216#95—34no—
217#95C2×C3×D314yescomplemented
218C23×C3—21no—
219C23×C3—22no—
220C23×C3—24no—
221C23×C3—24no—
222C23×C3—22no—
223C23×C3—22no—
224C23×C3—316no—
225C23×C3—34no—
226C23×C3—38no—
227C23×C3—68no—
228C23×C3—616no—
229C23×C3—68no—
230C23×C3—616no—
231C23×C3—64no—
232C23×C3—62no—
233C23×C3—62no—
234C23×C3C2×C4×D312yes—
235C23×C3#23514yes—
236C23×C3D3×D414yes—
237C23×C3#23712yes—
238C23×C3#23912yes—
239C23×C3C22×C3×C412yes—
240C23×C3C2×C3×D414yes—
241C23×C3C3×#4114yes—
242C23×C3C3×#4112yes—
243C23×C3C3×#4112yes—
244C23×C3C23×D311yescharacteristic
245C23×C3C24×C311yescharacteristic
246C22×D3—28no—
247C22×D3—28no—
248C22×D3—216no—
249C22×D3—216no—
250C22×D3—24no—
251C22×D3—22no—
252C22×D3—22no—
253C22×D3C3×C22⋊C4116yes—
254C22×D3C22×C3×C414yes—
255C22×D3C2×C3×D418yes—
256C2×C3×C4—28no—
257C2×C3×C4—28no—
258C2×C3×C4—24no—
259C2×C3×C4—24no—
260C2×C3×C4—28no—
261C2×C3×C4—24no—
262C2×C3×C4—24no—
263C2×C3×C4—24no—
264C2×C3×C4—24no—
265C2×C3×C4—24no—
266C2×C3×C4—24no—
267C2×C3×C4—24no—
268C2×C3×C4—34no—
269C2×C3×C4—48no—
270C2×C3×C4—44no—
271C2×C3×C4—44no—
272C2×C3×C4—44no—
273C2×C3×C4—416no—
274C2×C3×C4—48no—
275C2×C3×C4—48no—
276C2×C3×C4—632no—
277C2×C3×C4—68no—
278C2×C3×C4—64no—
279C2×C3×C4—64no—
280C2×C3×C4—64no—
281C2×C3×C4—64no—
282C2×C3×C4—128no—
283C2×C3×C4C2×C4×D314yes—
284C2×C3×C4C22×C3×C414yes—
285C2×Dic3—28no—
286C2×Dic3—24no—
287C2×Dic3—24no—
288C2×Dic3—24no—
289C2×Dic3—24no—
290C2×Dic3—48no—
291C2×Dic3C22×C3×C414yes—
292C4×D3—232no—
293C2×C32#38118yescomplemented
294C2×C32C22×C22⋊C411yescharacteristic
295C2×C32C2×#11711yescharacteristic
296C2×C32C2×#11711yescharacteristic
297C2×C32C2×#12312yes—
298C2×C32C2×#12312yes—
299C3×D3—28no—
300C24—32no—
301C24—34no—
302C24—38no—
303C24—64no—
304C24—62no—
305C24—62no—
306C24C22×C3×D311yescharacteristic
307C22×C4—24no—
308C22×C4—24no—
309C22×C4—24no—
310C22×C4—24no—
311C22×C4—32no—
312C22×C4—34no—
313C22×C4—316no—
314C22×C4—34no—
315C22×C4—632no—
316C22×C4—616no—
317C22×C4—64no—
318C22×C4—64no—
319C22×C4—64no—
320C22×C4—64no—
321C22×C4C3×C4×D314yes—
322C22×C4C22×C3×D314yes—
323C22×C4C22×C3×D312yes—
324C22⋊C4—616no—
325C22×C3—24no—
326C22×C3—28no—
327C22×C3—24no—
328C22×C3—28no—
329C22×C3—21no—
330C22×C3—22no—
331C22×C3—22no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—24no—
335C22×C3—38no—
336C22×C3—632no—
337C22×C3—64no—
338C22×C3—68no—
339C22×C3—64no—
340C22×C3—68no—
341C22×C3#87214yes—
342C22×C3D3×C22⋊C414yes—
343C22×C3#88318yes—
344C22×C3#89214yes—
345C22×C3#89418yes—
346C22×C3C2×C3×C22⋊C414yes—
347C22×C3C3×#11714yes—
348C22×C3C3×#11714yes—
349C22×C3C3×#12318yes—
350C22×C3C3×#12318yes—
351C22×C3C22×C4×D311yescharacteristic
352C22×C3C2×#23512yes—
353C22×C3C2×D3×D412yes—
354C22×C3C2×#23711yescharacteristic
355C22×C3C2×#23911yescharacteristic
356C22×C3C23×C3×C411yescharacteristic
357C22×C3C22×C3×D412yes—
358C22×C3C2×C3×#4112yes—
359C22×C3C2×C3×#4111yescharacteristic
360C22×C3C2×C3×#4111yescharacteristic
361C2×D3—232no—
362C2×D3—24no—
363C2×D3—24no—
364C2×D3—28no—
365C2×D3—28no—
366C2×D3C2×C3×C22⋊C418yes—
367C3×C4—24no—
368C3×C4—24no—
369C3×C4—44no—
370C3×C4—48no—
371C3×C4—44no—
372C3×C4—44no—
373C3×C4—64no—
374C3×C4—124no—
375Dic3—24no—
376Dic3—44no—
377C32C2×#38111yescharacteristic, complemented, Sylow
378C23—316no—
379C23—34no—
380C23—38no—
381C23—616no—
382C23—68no—
383C23—616no—
384C23—64no—
385C23—62no—
386C23—62no—
387C23—68no—
388C23C2×C3×C4×D312yes—
389C23C3×#23514yes—
390C23C3×D3×D414yes—
391C23C3×#23712yes—
392C23C3×#23912yes—
393C23C23×C3×D311yescharacteristic
394C2×C4—28no—
395C2×C4—24no—
396C2×C4—24no—
397C2×C4—24no—
398C2×C4—24no—
399C2×C4—34no—
400C2×C4—48no—
401C2×C4—632no—
402C2×C4—68no—
403C2×C4—64no—
404C2×C4—64no—
405C2×C4—64no—
406C2×C4—64no—
407C2×C4—128no—
408C2×C4C2×C3×C4×D314yes—
409C2×C3—22no—
410C2×C3—21no—
411C2×C3—28no—
412C2×C3—22no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—68no—
416C2×C3#466418yesdirect product factor
417C2×C3C3×#38118yescomplemented
418C2×C3C2×#87211yescharacteristic
419C2×C3C2×D3×C22⋊C411yescharacteristic
420C2×C3C2×#88312yes—
421C2×C3C2×#89211yescharacteristic
422C2×C3C2×#89412yes—
423C2×C3C22×C3×C22⋊C411yescharacteristic
424C2×C3C2×C3×#11711yescharacteristic
425C2×C3C2×C3×#11711yescharacteristic
426C2×C3C2×C3×#12312yes—
427C2×C3C2×C3×#12312yes—
428D3—28no—
429C22—38no—
430C22—68no—
431C22—64no—
432C22—632no—
433C22—68no—
434C22—64no—
435C22C3×#87214yes—
436C22C3×D3×C22⋊C414yes—
437C22C3×#88318yes—
438C22C3×#89214yes—
439C22C3×#89418yes—
440C22C22×C3×C4×D311yescharacteristic
441C22C2×C3×#23512yes—
442C22C2×C3×D3×D412yes—
443C22C2×C3×#23711yescharacteristic
444C22C2×C3×#23911yescharacteristic
445C4—24no—
446C4—44no—
447C4—64no—
448C4—124no—
449C3—21no—
450C3C2×#466411yescharacteristic, direct product factor
451C3C2×C3×#38111yescharacteristic, complemented
452C2—68no—
453C2C3×#466418yesdirect product factor
454C2C2×C3×#87211yescharacteristic
455C2C2×C3×D3×C22⋊C411yescharacteristic
456C2C2×C3×#88312yes—
457C2C2×C3×#89211yescharacteristic
458C2C2×C3×#89412yes—
subgroupG/H
centerC24×C3C22×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC2×C32×#95C2
socleC24×C32C23
prime radicalC24×C3×D3C22
cosocleC23×C3C24×C3
hypercenterC2×C3×#95D3
hypocenterC3C2×C3×#381
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C24×C3 ◁ C2×C3×#95

Complements

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

NH ≅ G/Ntype
3. C2×C32×#95C2semidirect
4. C2×C3×C3⋊#95C2semidirect
5. C2×C3×C3⋊#95C2semidirect
6. C3×#4664C2direct (N × H)
8. C2×#4664C3direct (N × H)
15. C22×C3×C4×D3C4semidirect
19. C32×#95C22semidirect
20. C3×C3⋊#95C22semidirect
21. C3×C3⋊#95C22semidirect
30. C2×C3×#95D3semidirect
31. C2×C3×#95C2×C3semidirect
32. C2×C3⋊#95C2×C3semidirect
33. C2×C3⋊#95C2×C3semidirect
34. #4664C2×C3direct (N × H)
58. C2×C3×C4×D3C2×C4semidirect
77. C22×C4×D3C3×C4semidirect
86. C3×#95C2×D3semidirect
87. C3×#95C22×C3semidirect
88. C3⋊#95C22×C3semidirect
89. C3⋊#95C22×C3semidirect
126. C2×#95C3×D3semidirect
182. C2×C4×D3C2×C3×C4semidirect
217. #95C2×C3×D3semidirect
293. C2×C32#381semidirect
377. C32C2×#381semidirect
416. C2×C3#4664direct (N × H)
417. C2×C3C3×#381semidirect
450. C3C2×#4664direct (N × H)
451. C3C2×C3×#381semidirect
453. C2C3×#4664direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C4×D32
C22×C3×(C2×D3)⋊C42
C2×C32×#952
C2×C3×C3⋊#952
C3×#46642
C2×C3×#3813
C2×#46643