Finite Group Databasebeta

← C2×C3×#4667 #11800981

Subgroups — C2×C3×#4667 #11800981

Order 1152.

2629 conjugacy classes of subgroups.

The subgroup lattice has 468 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
3C22×C3×Dic3⋊C4C212yesmaximal, complemented
4C2×C32×#95C211yesmaximal, characteristic, complemented
5C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
6C3×#4667C218yesmaximal, direct product factor
7C2×C3×#380—31nomaximal
8C2×#4667C311yesmaximal, 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—
19C2×C3×Dic3⋊C4—28no—
20C2×C3×Dic3⋊C4C2218yescomplemented
21C32×#95C2214yescomplemented
22C3×C3⋊#95C2214yescomplemented
23C24×C3×C4—31no—
24C23×C4×D3C2×C311yescharacteristic
25C22×C3×C4⋊C4—32no—
26C22×C3×C22⋊C4—32no—
27C22×(C2×D3)⋊C4C2×C312yes—
28C22×Dic3⋊C4C2×C312yescomplemented
29C3×#380—38no—
30C2×C3×#95—21no—
31C2×C3×#95—31no—
32C2×C3×#95D311yescharacteristic, complemented
33C2×C3×#95C2×C311yescharacteristic, complemented
34C2×C3⋊#95C2×C311yescharacteristic, complemented
35#4667C2×C318yesdirect product factor
36C24×C32C2311yescharacteristic
37C23×C3×D3—24no—
38C23×C3×D3—24no—
39C23×C3×D3C2×C414yes—
40C23×C3×D3D414yes—
41C23×C3×D3Q814yes—
42C23×C3×D3C2312yes—
43C22×C32×C4—24no—
44C22×C32×C4—24no—
45C22×C32×C4—24no—
46C22×C32×C4—24no—
47C22×C32×C4C2×C414yes—
48C22×C32×C4C2314yes—
49C22×C32×C4C2312yes—
50C22×C3×Dic3—24no—
51C22×C3×Dic3—24no—
52C22×C3×Dic3—24no—
53C22×C3×Dic3C2×C414yes—
54C22×C3×Dic3D418yes—
55C22×C3×Dic3C2314yes—
56C22×C3×Dic3C2312yes—
57C2×C3×C4×D3—232no—
58C2×C3×C4×D3—216no—
59C2×C3×C4×D3C2×C4116yescomplemented
60C3×(C2×D3)⋊C4—216no—
61C3×Dic3⋊C4—216no—
62C2×#380—31noSylow
63C25×C3—31no—
64C24×D3C22×C311yescharacteristic
65C23×C3×C4—22no—
66C23×C3×C4—21no—
67C23×C3×C4—31no—
68C23×C3×C4—38no—
69C23×C3×C4—34no—
70C23×C3×C4—32no—
71C23×C3×C4—68no—
72C23×C3×C4C2×D312yes—
73C23×C3×C4C2×D311yescharacteristic
74C23×C3×C4C22×C312yes—
75C23×C3×C4C22×C311yescharacteristic
76C23×Dic3C22×C312yes—
77C23×Dic3C22×C311yescharacteristic
78C22×C4×D3—28no—
79C22×C4×D3C3×C418yescomplemented
80C22×C4×D3C22×C314yes—
81C2×C3×C4⋊C4—38no—
82C2×C3×C4⋊C4—68no—
83C2×C3×C22⋊C4—38no—
84C2×C3×C22⋊C4—68no—
85C2×(C2×D3)⋊C4—28no—
86C2×(C2×D3)⋊C4C22×C318yes—
87C2×Dic3⋊C4—28no—
88C2×Dic3⋊C4C22×C318yescomplemented
89C3×#95—24no—
90C3×#95—34no—
91C3×#95C2×D314yescomplemented
92C3×#95C22×C314yescomplemented
93C3⋊#95C22×C314yescomplemented
94C23×C32C22×C412yes—
95C23×C32C2×D414yes—
96C23×C32C2×D412yes—
97C23×C32C2×Q812yes—
98C23×C32#4114yes—
99C23×C32C2411yescharacteristic
100C22×C3×D3—28no—
101C22×C3×D3—28no—
102C22×C3×D3—216no—
103C22×C3×D3—216no—
104C22×C3×D3—24no—
105C22×C3×D3—24no—
106C22×C3×D3C4⋊C4116yescomplemented
107C22×C3×D3C22×C414yes—
108C22×C3×D3C2×D414yes—
109C22×C3×D3C2×Q814yes—
110C2×C32×C4—24no—
111C2×C32×C4—28no—
112C2×C32×C4—24no—
113C2×C32×C4—24no—
114C2×C32×C4—24no—
115C2×C32×C4—48no—
116C2×C32×C4C22×C414yes—
117C2×C3×Dic3—24no—
118C2×C3×Dic3—24no—
119C2×C3×Dic3—24no—
120C2×C3×Dic3—48no—
121C2×C3×Dic3C22⋊C4116yescomplemented
122C2×C3×Dic3C22×C414yes—
123C2×C3×Dic3C2×D418yes—
124C3×C4×D3—232no—
125C24×C4—31no—
126C22×C4⋊C4—32no—
127C22×C22⋊C4—32no—
128#380—38no—
129C2×#95—31no—
130C2×#95C3×D311yescharacteristic, complemented
131C24×C3—21no—
132C24×C3—34no—
133C24×C3—34no—
134C24×C3—34no—
135C24×C3—32no—
136C24×C3—64no—
137C24×C3—64no—
138C24×C3C22×D311yescharacteristic
139C24×C3C23×C311yescharacteristic
140C23×D3—24no—
141C23×D3—24no—
142C23×D3C2×C3×C414yes—
143C23×D3C3×D414yes—
144C23×D3C3×Q814yes—
145C23×D3C23×C312yes—
146C22×C3×C4—24no—
147C22×C3×C4—24no—
148C22×C3×C4—28no—
149C22×C3×C4—24no—
150C22×C3×C4—24no—
151C22×C3×C4—24no—
152C22×C3×C4—24no—
153C22×C3×C4—24no—
154C22×C3×C4—24no—
155C22×C3×C4—24no—
156C22×C3×C4—24no—
157C22×C3×C4—22no—
158C22×C3×C4—34no—
159C22×C3×C4—38no—
160C22×C3×C4—32no—
161C22×C3×C4—316no—
162C22×C3×C4—34no—
163C22×C3×C4—44no—
164C22×C3×C4—44no—
165C22×C3×C4—44no—
166C22×C3×C4—632no—
167C22×C3×C4—616no—
168C22×C3×C4—64no—
169C22×C3×C4—64no—
170C22×C3×C4—64no—
171C22×C3×C4C4×D314yes—
172C22×C3×C4C2×C3×C414yes—
173C22×C3×C4C22×D314yes—
174C22×C3×C4C22×D312yes—
175C22×C3×C4C23×C314yes—
176C22×C3×C4C23×C312yes—
177C22×Dic3—24no—
178C22×Dic3—24no—
179C22×Dic3—24no—
180C22×Dic3C2×C3×C414yes—
181C22×Dic3C3×D418yes—
182C22×Dic3C23×C314yes—
183C22×Dic3C23×C312yes—
184C2×C4×D3—232no—
185C2×C4×D3—216no—
186C2×C4×D3C2×C3×C4116yescomplemented
187C3×C4⋊C4—616no—
188C3×C22⋊C4—616no—
189(C2×D3)⋊C4—216no—
190Dic3⋊C4—216no—
191C22×C32C2×C22⋊C414yes—
192C22×C32C2×C4⋊C414yes—
193C22×C32#11714yes—
194C22×C32#12118yes—
195C22×C32C22⋊Q818yes—
196C22×C32C23×C411yescharacteristic
197C22×C32C22×D412yes—
198C22×C32C22×D411yescharacteristic
199C22×C32C22×Q811yescharacteristic
200C22×C32C2×#4112yes—
201C2×C3×D3—24no—
202C2×C3×D3—24no—
203C2×C3×D3—28no—
204C2×C3×D3—28no—
205C2×C3×D3—232no—
206C2×C3×D3C2×C4⋊C418yescomplemented
207C32×C4—24no—
208C32×C4—44no—
209C3×Dic3—44no—
210C3×Dic3C2×C22⋊C418yescomplemented
211C25—31no—
212C23×C4—31no—
213C23×C4—38no—
214C23×C4—34no—
215C23×C4—32no—
216C23×C4—68no—
217C23×C4C2×C3×D312yes—
218C23×C4C2×C3×D311yescharacteristic
219C2×C4⋊C4—38no—
220C2×C4⋊C4—68no—
221C2×C22⋊C4—38no—
222C2×C22⋊C4—68no—
223#95—34no—
224#95C2×C3×D314yescomplemented
225C23×C3—21no—
226C23×C3—22no—
227C23×C3—24no—
228C23×C3—24no—
229C23×C3—22no—
230C23×C3—22no—
231C23×C3—316no—
232C23×C3—34no—
233C23×C3—34no—
234C23×C3—34no—
235C23×C3—68no—
236C23×C3—68no—
237C23×C3—616no—
238C23×C3—616no—
239C23×C3—64no—
240C23×C3—64no—
241C23×C3C2×C4×D312yes—
242C23×C3#23514yes—
243C23×C3D3×D414yes—
244C23×C3D3×D412yes—
245C23×C3D3×Q812yes—
246C23×C3C22×C3×C412yes—
247C23×C3C2×C3×D414yes—
248C23×C3C2×C3×D412yes—
249C23×C3C2×C3×Q812yes—
250C23×C3C3×#4114yes—
251C23×C3C23×D311yescharacteristic
252C23×C3C24×C311yescharacteristic
253C22×D3—28no—
254C22×D3—28no—
255C22×D3—216no—
256C22×D3—216no—
257C22×D3—24no—
258C22×D3—24no—
259C22×D3C3×C4⋊C4116yescomplemented
260C22×D3C22×C3×C414yes—
261C22×D3C2×C3×D414yes—
262C22×D3C2×C3×Q814yes—
263C2×C3×C4—28no—
264C2×C3×C4—28no—
265C2×C3×C4—24no—
266C2×C3×C4—24no—
267C2×C3×C4—28no—
268C2×C3×C4—24no—
269C2×C3×C4—24no—
270C2×C3×C4—24no—
271C2×C3×C4—24no—
272C2×C3×C4—24no—
273C2×C3×C4—24no—
274C2×C3×C4—24no—
275C2×C3×C4—316no—
276C2×C3×C4—34no—
277C2×C3×C4—38no—
278C2×C3×C4—48no—
279C2×C3×C4—44no—
280C2×C3×C4—44no—
281C2×C3×C4—44no—
282C2×C3×C4—416no—
283C2×C3×C4—48no—
284C2×C3×C4—48no—
285C2×C3×C4—632no—
286C2×C3×C4—64no—
287C2×C3×C4—64no—
288C2×C3×C4—64no—
289C2×C3×C4—128no—
290C2×C3×C4C2×C4×D314yes—
291C2×C3×C4C22×C3×C414yes—
292C2×Dic3—24no—
293C2×Dic3—24no—
294C2×Dic3—24no—
295C2×Dic3—48no—
296C2×Dic3C3×C22⋊C4116yescomplemented
297C2×Dic3C22×C3×C414yes—
298C2×Dic3C2×C3×D418yes—
299C4×D3—232no—
300C2×C32#38018yescomplemented
301C2×C32C22×C22⋊C411yescharacteristic
302C2×C32C22×C4⋊C411yescharacteristic
303C2×C32C2×#11711yescharacteristic
304C2×C32C2×#12112yes—
305C2×C32C2×C22⋊Q812yes—
306C3×D3—28no—
307C24—32no—
308C24—34no—
309C24—34no—
310C24—34no—
311C24—64no—
312C24—64no—
313C24C22×C3×D311yescharacteristic
314C22×C4—24no—
315C22×C4—24no—
316C22×C4—24no—
317C22×C4—24no—
318C22×C4—32no—
319C22×C4—34no—
320C22×C4—38no—
321C22×C4—316no—
322C22×C4—34no—
323C22×C4—632no—
324C22×C4—616no—
325C22×C4—64no—
326C22×C4—64no—
327C22×C4—64no—
328C22×C4C3×C4×D314yes—
329C22×C4C22×C3×D314yes—
330C22×C4C22×C3×D312yes—
331C4⋊C4—616no—
332C22⋊C4—616no—
333C22×C3—24no—
334C22×C3—28no—
335C22×C3—24no—
336C22×C3—28no—
337C22×C3—21no—
338C22×C3—22no—
339C22×C3—21no—
340C22×C3—22no—
341C22×C3—21no—
342C22×C3—24no—
343C22×C3—38no—
344C22×C3—632no—
345C22×C3—64no—
346C22×C3—64no—
347C22×C3—68no—
348C22×C3—68no—
349C22×C3#87214yes—
350C22×C3D3×C22⋊C414yes—
351C22×C3#88418yes—
352C22×C3D3×C4⋊C414yes—
353C22×C3#89618yes—
354C22×C3C2×C3×C22⋊C414yes—
355C22×C3C2×C3×C4⋊C414yes—
356C22×C3C3×#11714yes—
357C22×C3C3×#12118yes—
358C22×C3C3×C22⋊Q818yes—
359C22×C3C22×C4×D311yescharacteristic
360C22×C3C2×#23512yes—
361C22×C3C2×D3×D412yes—
362C22×C3C2×D3×D411yescharacteristic
363C22×C3C2×D3×Q811yescharacteristic
364C22×C3C23×C3×C411yescharacteristic
365C22×C3C22×C3×D412yes—
366C22×C3C22×C3×D411yescharacteristic
367C22×C3C22×C3×Q811yescharacteristic
368C22×C3C2×C3×#4112yes—
369C2×D3—232no—
370C2×D3—24no—
371C2×D3—24no—
372C2×D3—28no—
373C2×D3—28no—
374C2×D3C2×C3×C4⋊C418yescomplemented
375C3×C4—24no—
376C3×C4—24no—
377C3×C4—38no—
378C3×C4—44no—
379C3×C4—48no—
380C3×C4—44no—
381C3×C4—44no—
382C3×C4—124no—
383Dic3—44no—
384Dic3C2×C3×C22⋊C418yescomplemented
385C32C2×#38011yescharacteristic, complemented, Sylow
386C23—316no—
387C23—34no—
388C23—34no—
389C23—34no—
390C23—68no—
391C23—616no—
392C23—616no—
393C23—64no—
394C23—64no—
395C23—68no—
396C23C2×C3×C4×D312yes—
397C23C3×#23514yes—
398C23C3×D3×D414yes—
399C23C3×D3×D412yes—
400C23C3×D3×Q812yes—
401C23C23×C3×D311yescharacteristic
402C2×C4—28no—
403C2×C4—24no—
404C2×C4—24no—
405C2×C4—24no—
406C2×C4—24no—
407C2×C4—316no—
408C2×C4—34no—
409C2×C4—38no—
410C2×C4—48no—
411C2×C4—632no—
412C2×C4—64no—
413C2×C4—64no—
414C2×C4—64no—
415C2×C4—128no—
416C2×C4C2×C3×C4×D314yes—
417C2×C3—22no—
418C2×C3—21no—
419C2×C3—28no—
420C2×C3—22no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—68no—
424C2×C3#466718yesdirect product factor
425C2×C3C3×#38018yescomplemented
426C2×C3C2×#87211yescharacteristic
427C2×C3C2×D3×C22⋊C411yescharacteristic
428C2×C3C2×#88412yes—
429C2×C3C2×D3×C4⋊C411yescharacteristic
430C2×C3C2×#89612yes—
431C2×C3C22×C3×C22⋊C411yescharacteristic
432C2×C3C22×C3×C4⋊C411yescharacteristic
433C2×C3C2×C3×#11711yescharacteristic
434C2×C3C2×C3×#12112yes—
435C2×C3C2×C3×C22⋊Q812yes—
436D3—28no—
437C22—38no—
438C22—68no—
439C22—632no—
440C22—68no—
441C22—64no—
442C22—64no—
443C22C3×#87214yes—
444C22C3×D3×C22⋊C414yes—
445C22C3×#88418yes—
446C22C3×D3×C4⋊C414yes—
447C22C3×#89618yes—
448C22C22×C3×C4×D311yescharacteristic
449C22C2×C3×#23512yes—
450C22C2×C3×D3×D411yescharacteristic
451C22C2×C3×D3×D412yes—
452C22C2×C3×D3×Q811yescharacteristic
453C4—24no—
454C4—38no—
455C4—44no—
456C4—124no—
457C3—21no—
458C3C2×#466711yescharacteristic, direct product factor
459C3C2×C3×#38011yescharacteristic, complemented
460C2—68no—
461C2C3×#466718yesdirect product factor
462C2C2×C3×#87211yescharacteristic
463C2C2×C3×D3×C22⋊C411yescharacteristic
464C2C2×C3×#88412yes—
465C2C2×C3×D3×C4⋊C411yescharacteristic
466C2C2×C3×#89612yes—
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×#380
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. C22×C3×Dic3⋊C4C2semidirect
4. C2×C32×#95C2semidirect
5. C2×C3×C3⋊#95C2semidirect
6. C3×#4667C2direct (N × H)
8. C2×#4667C3direct (N × H)
15. C22×C3×C4×D3C4semidirect
20. C2×C3×Dic3⋊C4C22semidirect
21. C32×#95C22semidirect
22. C3×C3⋊#95C22semidirect
28. C22×Dic3⋊C4C2×C3semidirect
32. C2×C3×#95D3semidirect
33. C2×C3×#95C2×C3semidirect
34. C2×C3⋊#95C2×C3semidirect
35. #4667C2×C3direct (N × H)
59. C2×C3×C4×D3C2×C4semidirect
79. C22×C4×D3C3×C4semidirect
88. C2×Dic3⋊C4C22×C3semidirect
91. C3×#95C2×D3semidirect
92. C3×#95C22×C3semidirect
93. C3⋊#95C22×C3semidirect
106. C22×C3×D3C4⋊C4semidirect
121. C2×C3×Dic3C22⋊C4semidirect
130. C2×#95C3×D3semidirect
186. C2×C4×D3C2×C3×C4semidirect
206. C2×C3×D3C2×C4⋊C4semidirect
210. C3×Dic3C2×C22⋊C4semidirect
224. #95C2×C3×D3semidirect
259. C22×D3C3×C4⋊C4semidirect
296. C2×Dic3C3×C22⋊C4semidirect
300. C2×C32#380semidirect
374. C2×D3C2×C3×C4⋊C4semidirect
384. Dic3C2×C3×C22⋊C4semidirect
385. C32C2×#380semidirect
424. C2×C3#4667direct (N × H)
425. C2×C3C3×#380semidirect
458. C3C2×#4667direct (N × H)
459. C3C2×C3×#380semidirect
461. C2C3×#4667direct (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
C22×C3×Dic3⋊C42
C2×C32×#952
C2×C3×C3⋊#952
C3×#46672
C2×C3×#3803
C2×#46673