Finite Group Databasebeta

← C2×C3×#4991 #11808144

Subgroups — C2×C3×#4991 #11808144

Order 1152.

2713 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×D12C211yesmaximal, characteristic
2C22×C32×C4⋊C4C211yesmaximal, characteristic, complemented
3C22×C3×(C2×D3)⋊C4C212yesmaximal, complemented
4C22×C3×(C2×D3)⋊C4C212yesmaximal, complemented
5C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
6C3×#4991C218yesmaximal, direct product factor
7C2×C3×#394—31nomaximal
8C2×#4991C311yesmaximal, characteristic, direct product factor
9C24×C3×D3C2212yes—
10C23×C32×C4C2211yescharacteristic
11C23×C32×C4C2211yescharacteristic
12C23×C32×C4C2211yescharacteristic
13C23×C3×Dic3C2212yes—
14C22×C3×D12—24no—
15C22×C3×D12—28no—
16C22×C3×D12C2214yes—
17C2×C32×C4⋊C4—24no—
18C2×C32×C4⋊C4C2214yescomplemented
19C2×C3×(C2×D3)⋊C4—28no—
20C2×C3×(C2×D3)⋊C4—28no—
21C2×C3×(C2×D3)⋊C4C2218yescomplemented
22C2×C3×(C2×D3)⋊C4C2218yescomplemented
23C3×C3⋊#95C2214yescomplemented
24C23×C3×D4—31no—
25C23×D12C2×C311yescharacteristic
26C22×C3×C4⋊C4—21no—
27C22×C3×C4⋊C4D311yescharacteristic, complemented
28C22×C3×C4⋊C4C2×C311yescharacteristic, complemented
29C22×C3×C22⋊C4—32no—
30C22×C3×C22⋊C4—32no—
31C22×(C2×D3)⋊C4C2×C312yescomplemented
32C22×(C2×D3)⋊C4C2×C312yescomplemented
33C3×#394—38no—
34C2×C3×#95—31no—
35C2×C3⋊#95C2×C311yescharacteristic, complemented
36#4991C2×C318yesdirect product factor
37C24×C32C2311yescharacteristic
38C23×C3×D3—24no—
39C23×C3×D3—24no—
40C23×C3×D3—24no—
41C23×C3×D3—24no—
42C23×C3×D3—24no—
43C23×C3×D3—24no—
44C23×C3×D3D418yes—
45C23×C3×D3C2314yes—
46C22×C32×C4—22no—
47C22×C32×C4—24no—
48C22×C32×C4—22no—
49C22×C32×C4—22no—
50C22×C32×C4—24no—
51C22×C32×C4D414yes—
52C22×C32×C4D414yescomplemented
53C22×C32×C4C2312yes—
54C22×C32×C4C2312yes—
55C22×C32×C4C2312yes—
56C22×C3×Dic3—24no—
57C22×C3×Dic3—24no—
58C22×C3×Dic3—24no—
59C22×C3×Dic3C2314yes—
60C2×C3×D12—232no—
61C2×C3×D12—216no—
62C2×C3×D12—28no—
63C32×C4⋊C4—28no—
64C3×(C2×D3)⋊C4—216no—
65C3×(C2×D3)⋊C4—216no—
66C2×#394—31noSylow
67C25×C3—32no—
68C24×D3C22×C312yes—
69C22×C3×D4—34no—
70C22×C3×D4—68no—
71C22×C3×D4—64no—
72C23×C3×C4—21no—
73C23×C3×C4—21no—
74C23×C3×C4—21no—
75C23×C3×C4—32no—
76C23×C3×C4C2×D311yescharacteristic
77C23×C3×C4C2×D311yescharacteristic
78C23×C3×C4C2×D311yescharacteristic
79C23×C3×C4C22×C311yescharacteristic
80C23×C3×C4C22×C311yescharacteristic
81C23×C3×C4C22×C311yescharacteristic
82C23×Dic3C22×C312yes—
83C22×D12—28no—
84C22×D12—24no—
85C22×D12C22×C314yes—
86C2×C3×C4⋊C4—28no—
87C2×C3×C4⋊C4—24no—
88C2×C3×C4⋊C4—24no—
89C2×C3×C4⋊C4—24no—
90C2×C3×C4⋊C4C2×D314yescomplemented
91C2×C3×C4⋊C4C22×C314yescomplemented
92C2×C3×C22⋊C4—38no—
93C2×C3×C22⋊C4—38no—
94C2×C3×C22⋊C4—68no—
95C2×C3×C22⋊C4—68no—
96C2×(C2×D3)⋊C4—28no—
97C2×(C2×D3)⋊C4—28no—
98C2×(C2×D3)⋊C4C22×C318yescomplemented
99C2×(C2×D3)⋊C4C22×C318yescomplemented
100C3×#95—34no—
101C3⋊#95C22×C314yescomplemented
102C23×C32C2×D412yes—
103C23×C32C2×D414yes—
104C23×C32C2×D412yes—
105C23×C32#4112yes—
106C23×C32#4114yes—
107C23×C32C2411yescharacteristic
108C22×C3×D3—216no—
109C22×C3×D3—216no—
110C22×C3×D3—216no—
111C22×C3×D3—24no—
112C22×C3×D3—24no—
113C22×C3×D3—24no—
114C22×C3×D3—24no—
115C22×C3×D3—24no—
116C22×C3×D3—24no—
117C22×C3×D3—48no—
118C22×C3×D3—48no—
119C22×C3×D3—48no—
120C22×C3×D3—48no—
121C22×C3×D3C2×D418yes—
122C2×C32×C4—28no—
123C2×C32×C4—22no—
124C2×C32×C4—22no—
125C2×C32×C4—22no—
126C2×C32×C4—28no—
127C2×C32×C4—24no—
128C2×C32×C4—24no—
129C2×C32×C4—44no—
130C2×C32×C4C2×D414yes—
131C2×C32×C4C2×D414yescomplemented
132C2×C3×Dic3—24no—
133C2×C3×Dic3—24no—
134C2×C3×Dic3—24no—
135C2×C3×Dic3—48no—
136C3×D12—232no—
137C23×D4—31no—
138C22×C4⋊C4C3×D311yescharacteristic, complemented
139C22×C22⋊C4—32no—
140C22×C22⋊C4—32no—
141#394—38no—
142C2×#95—31no—
143C24×C3—21no—
144C24×C3—38no—
145C24×C3—34no—
146C24×C3—64no—
147C24×C3—64no—
148C24×C3—64no—
149C24×C3—64no—
150C24×C3—64no—
151C24×C3—64no—
152C24×C3C22×D311yescharacteristic
153C24×C3C23×C311yescharacteristic
154C23×D3—24no—
155C23×D3—24no—
156C23×D3—24no—
157C23×D3—24no—
158C23×D3—24no—
159C23×D3—24no—
160C23×D3C3×D418yes—
161C23×D3C23×C314yes—
162C2×C3×D4—616no—
163C2×C3×D4—632no—
164C2×C3×D4—68no—
165C22×C3×C4—24no—
166C22×C3×C4—24no—
167C22×C3×C4—22no—
168C22×C3×C4—24no—
169C22×C3×C4—22no—
170C22×C3×C4—22no—
171C22×C3×C4—24no—
172C22×C3×C4—22no—
173C22×C3×C4—24no—
174C22×C3×C4—24no—
175C22×C3×C4—22no—
176C22×C3×C4—24no—
177C22×C3×C4—22no—
178C22×C3×C4—24no—
179C22×C3×C4—24no—
180C22×C3×C4—22no—
181C22×C3×C4—22no—
182C22×C3×C4—22no—
183C22×C3×C4—34no—
184C22×C3×C4—44no—
185C22×C3×C4—44no—
186C22×C3×C4—64no—
187C22×C3×C4—64no—
188C22×C3×C4—64no—
189C22×C3×C4D1214yescomplemented
190C22×C3×C4#6714yes—
191C22×C3×C4C3×D414yes—
192C22×C3×C4C3×D414yescomplemented
193C22×C3×C4C22×D312yes—
194C22×C3×C4C22×D312yes—
195C22×C3×C4C22×D312yes—
196C22×C3×C4C23×C312yes—
197C22×C3×C4C23×C312yes—
198C22×C3×C4C23×C312yes—
199C22×Dic3—24no—
200C22×Dic3—24no—
201C22×Dic3—24no—
202C22×Dic3C23×C314yes—
203C2×D12—232no—
204C2×D12—216no—
205C2×D12—28no—
206C3×C4⋊C4—216no—
207C3×C4⋊C4—28no—
208C3×C4⋊C4—28no—
209C3×C22⋊C4—616no—
210C3×C22⋊C4—616no—
211(C2×D3)⋊C4—216no—
212(C2×D3)⋊C4—216no—
213C22×C32#12014yes—
214C22×C32#12118yes—
215C22×C32#12114yes—
216C22×C32#12318yes—
217C22×C32#12414yes—
218C22×C32C22×D411yescharacteristic
219C22×C32C22×D412yes—
220C22×C32C22×D411yescharacteristic
221C22×C32C2×#4111yescharacteristic
222C22×C32C2×#4112yes—
223C2×C3×D3—28no—
224C2×C3×D3—28no—
225C2×C3×D3—28no—
226C2×C3×D3—44no—
227C2×C3×D3—44no—
228C2×C3×D3—44no—
229C2×C3×D3—44no—
230C2×C3×D3—432no—
231C32×C4—24no—
232C32×C4—24no—
233C32×C4—42no—
234C3×Dic3—44no—
235C25—32no—
236C22×D4—34no—
237C22×D4—68no—
238C22×D4—64no—
239C23×C4—32no—
240C23×C4C2×C3×D311yescharacteristic
241C23×C4C2×C3×D311yescharacteristic
242C23×C4C2×C3×D311yescharacteristic
243C2×C4⋊C4—24no—
244C2×C4⋊C4C2×C3×D314yescomplemented
245C2×C22⋊C4—38no—
246C2×C22⋊C4—38no—
247C2×C22⋊C4—68no—
248C2×C22⋊C4—68no—
249#95—34no—
250C23×C3—21no—
251C23×C3—22no—
252C23×C3—22no—
253C23×C3—24no—
254C23×C3—24no—
255C23×C3—22no—
256C23×C3—38no—
257C23×C3—616no—
258C23×C3—616no—
259C23×C3—616no—
260C23×C3—64no—
261C23×C3—64no—
262C23×C3—64no—
263C23×C3—64no—
264C23×C3—64no—
265C23×C3—64no—
266C23×C3—128no—
267C23×C3—128no—
268C23×C3—128no—
269C23×C3—128no—
270C23×C3C2×D1212yes—
271C23×C3#23512yes—
272C23×C3D3×D414yes—
273C23×C3#23914yes—
274C23×C3C2×#6712yes—
275C23×C3C2×C3×D412yes—
276C23×C3C2×C3×D414yes—
277C23×C3C2×C3×D412yes—
278C23×C3C3×#4112yes—
279C23×C3C3×#4114yes—
280C23×C3C23×D311yescharacteristic
281C23×C3C24×C311yescharacteristic
282C22×D3—216no—
283C22×D3—216no—
284C22×D3—216no—
285C22×D3—24no—
286C22×D3—24no—
287C22×D3—24no—
288C22×D3—24no—
289C22×D3—24no—
290C22×D3—24no—
291C22×D3—48no—
292C22×D3—48no—
293C22×D3—48no—
294C22×D3—48no—
295C22×D3C2×C3×D418yes—
296C3×D4—632no—
297C2×C3×C4—24no—
298C2×C3×C4—216no—
299C2×C3×C4—24no—
300C2×C3×C4—28no—
301C2×C3×C4—28no—
302C2×C3×C4—28no—
303C2×C3×C4—28no—
304C2×C3×C4—22no—
305C2×C3×C4—24no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—24no—
309C2×C3×C4—22no—
310C2×C3×C4—24no—
311C2×C3×C4—24no—
312C2×C3×C4—22no—
313C2×C3×C4—24no—
314C2×C3×C4—22no—
315C2×C3×C4—24no—
316C2×C3×C4—24no—
317C2×C3×C4—48no—
318C2×C3×C4—44no—
319C2×C3×C4—44no—
320C2×C3×C4—48no—
321C2×C3×C4—44no—
322C2×C3×C4—44no—
323C2×C3×C4—64no—
324C2×C3×C4—64no—
325C2×C3×C4—64no—
326C2×C3×C4—128no—
327C2×C3×C4C2×D1214yescomplemented
328C2×C3×C4C2×#6714yes—
329C2×C3×C4C2×C3×D414yes—
330C2×C3×C4C2×C3×D414yescomplemented
331C2×Dic3—24no—
332C2×Dic3—24no—
333C2×Dic3—24no—
334C2×Dic3—48no—
335D12—232no—
336C2×C32#39418yescomplemented
337C2×C32C2×#12011yescharacteristic
338C2×C32C2×#12112yes—
339C2×C32C2×#12111yescharacteristic
340C2×C32C2×#12312yes—
341C2×C32C2×#12411yescharacteristic
342C3×D3—48no—
343C24—34no—
344C24—38no—
345C24—64no—
346C24—64no—
347C24—64no—
348C24—64no—
349C24—64no—
350C24—64no—
351C24C22×C3×D311yescharacteristic
352C2×D4—616no—
353C2×D4—632no—
354C2×D4—68no—
355C22×C4—22no—
356C22×C4—24no—
357C22×C4—22no—
358C22×C4—24no—
359C22×C4—22no—
360C22×C4—34no—
361C22×C4—64no—
362C22×C4—64no—
363C22×C4—64no—
364C22×C4C3×D1214yescomplemented
365C22×C4C3×#6714yes—
366C22×C4C22×C3×D312yes—
367C22×C4C22×C3×D312yes—
368C22×C4C22×C3×D312yes—
369C4⋊C4—28no—
370C22⋊C4—616no—
371C22⋊C4—616no—
372C22×C3—28no—
373C22×C3—28no—
374C22×C3—24no—
375C22×C3—24no—
376C22×C3—24no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—22no—
380C22×C3—22no—
381C22×C3—21no—
382C22×C3—68no—
383C22×C3—68no—
384C22×C3—68no—
385C22×C3—1232no—
386C22×C3—124no—
387C22×C3—124no—
388C22×C3—124no—
389C22×C3—124no—
390C22×C3#89418yes—
391C22×C3#89518yes—
392C22×C3#93014yes—
393C22×C3#93714yes—
394C22×C3#94714yes—
395C22×C3C3×#12014yes—
396C22×C3C3×#12118yes—
397C22×C3C3×#12114yes—
398C22×C3C3×#12318yes—
399C22×C3C3×#12414yes—
400C22×C3C22×D1211yescharacteristic
401C22×C3C2×#23511yescharacteristic
402C22×C3C2×D3×D412yes—
403C22×C3C2×#23912yes—
404C22×C3C22×#6711yescharacteristic
405C22×C3C22×C3×D411yescharacteristic
406C22×C3C22×C3×D412yes—
407C22×C3C22×C3×D411yescharacteristic
408C22×C3C2×C3×#4111yescharacteristic
409C22×C3C2×C3×#4112yes—
410C2×D3—28no—
411C2×D3—28no—
412C2×D3—28no—
413C2×D3—432no—
414C2×D3—44no—
415C2×D3—44no—
416C2×D3—44no—
417C2×D3—44no—
418C3×C4—28no—
419C3×C4—24no—
420C3×C4—24no—
421C3×C4—24no—
422C3×C4—24no—
423C3×C4—44no—
424C3×C4—44no—
425C3×C4—42no—
426C3×C4—42no—
427C3×C4—124no—
428Dic3—44no—
429C32C2×#39411yescharacteristic, complemented, Sylow
430C23—38no—
431C23—616no—
432C23—616no—
433C23—616no—
434C23—64no—
435C23—64no—
436C23—64no—
437C23—64no—
438C23—64no—
439C23—64no—
440C23—128no—
441C23—128no—
442C23—128no—
443C23—128no—
444C23C2×C3×D1212yes—
445C23C3×#23512yes—
446C23C3×D3×D414yes—
447C23C3×#23914yes—
448C23C2×C3×#6712yes—
449C23C23×C3×D311yescharacteristic
450D4—632no—
451C2×C4—28no—
452C2×C4—28no—
453C2×C4—22no—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—24no—
457C2×C4—22no—
458C2×C4—44no—
459C2×C4—64no—
460C2×C4—64no—
461C2×C4—64no—
462C2×C4—128no—
463C2×C4C2×C3×D1214yescomplemented
464C2×C4C2×C3×#6714yes—
465C2×C3—22no—
466C2×C3—22no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—28no—
471C2×C3—128no—
472C2×C3#499118yesdirect product factor
473C2×C3C3×#39418yescomplemented
474C2×C3C2×#89412yes—
475C2×C3C2×#89512yes—
476C2×C3C2×#93011yescharacteristic
477C2×C3C2×#93711yescharacteristic
478C2×C3C2×#94711yescharacteristic
479C2×C3C2×C3×#12011yescharacteristic
480C2×C3C2×C3×#12112yes—
481C2×C3C2×C3×#12111yescharacteristic
482C2×C3C2×C3×#12312yes—
483C2×C3C2×C3×#12411yescharacteristic
484D3—48no—
485C22—68no—
486C22—68no—
487C22—68no—
488C22—124no—
489C22—124no—
490C22—124no—
491C22—124no—
492C22—1232no—
493C22C3×#89418yes—
494C22C3×#89518yes—
495C22C3×#93014yes—
496C22C3×#93714yes—
497C22C3×#94714yes—
498C22C22×C3×D1211yescharacteristic
499C22C2×C3×#23511yescharacteristic
500C22C2×C3×D3×D412yes—
501C22C2×C3×#23912yes—
502C22C22×C3×#6711yescharacteristic
503C4—24no—
504C4—24no—
505C4—42no—
506C4—124no—
507C3—21no—
508C3C2×#499111yescharacteristic, direct product factor
509C3C2×C3×#39411yescharacteristic, complemented
510C2—128no—
511C2C3×#499118yesdirect product factor
512C2C2×C3×#89412yes—
513C2C2×C3×#89512yes—
514C2C2×C3×#93011yescharacteristic
515C2C2×C3×#93711yescharacteristic
516C2C2×C3×#94711yescharacteristic
subgroupG/H
centerC24×C3C22×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC22×C32×C4⋊C4C2
socleC24×C32C23
prime radicalC23×C3×D12C2
hypercenterC22×C3×C4⋊C4D3
hypocenterC3C2×C3×#394
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24×C3 ◁ C22×C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C32×C4⋊C4C2semidirect
3. C22×C3×(C2×D3)⋊C4C2semidirect
4. C22×C3×(C2×D3)⋊C4C2semidirect
5. C2×C3×C3⋊#95C2semidirect
6. C3×#4991C2direct (N × H)
8. C2×#4991C3direct (N × H)
18. C2×C32×C4⋊C4C22semidirect
21. C2×C3×(C2×D3)⋊C4C22semidirect
22. C2×C3×(C2×D3)⋊C4C22semidirect
23. C3×C3⋊#95C22semidirect
27. C22×C3×C4⋊C4D3semidirect
28. C22×C3×C4⋊C4C2×C3semidirect
31. C22×(C2×D3)⋊C4C2×C3semidirect
32. C22×(C2×D3)⋊C4C2×C3semidirect
35. C2×C3⋊#95C2×C3semidirect
36. #4991C2×C3direct (N × H)
52. C22×C32×C4D4semidirect
90. C2×C3×C4⋊C4C2×D3semidirect
91. C2×C3×C4⋊C4C22×C3semidirect
98. C2×(C2×D3)⋊C4C22×C3semidirect
99. C2×(C2×D3)⋊C4C22×C3semidirect
101. C3⋊#95C22×C3semidirect
131. C2×C32×C4C2×D4semidirect
138. C22×C4⋊C4C3×D3semidirect
189. C22×C3×C4D12semidirect
192. C22×C3×C4C3×D4semidirect
244. C2×C4⋊C4C2×C3×D3semidirect
327. C2×C3×C4C2×D12semidirect
330. C2×C3×C4C2×C3×D4semidirect
336. C2×C32#394semidirect
364. C22×C4C3×D12semidirect
429. C32C2×#394semidirect
463. C2×C4C2×C3×D12semidirect
472. C2×C3#4991direct (N × H)
473. C2×C3C3×#394semidirect
508. C3C2×#4991direct (N × H)
509. C3C2×C3×#394semidirect
511. C2C3×#4991direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×D122
C22×C32×C4⋊C42
C22×C3×(C2×D3)⋊C42
C2×C3×C3⋊#952
C3×#49912
C2×C3×#3943
C2×#49913