Finite Group Databasebeta

← C2×C3×#4966 #11857894

Subgroups — C2×C3×#4966 #11857894

Order 1152.

1841 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic
2C22×C32×C4⋊C4C211yesmaximal, characteristic, complemented
3C22×C3×#208C211yesmaximal, characteristic, complemented
4C2×C3×#810C212yesmaximal, complemented
5C3×#4966C218yesmaximal, direct product factor
6C2×C3×#809C212yesmaximal, complemented
7C2×C3×#417—31nomaximal
8C2×#4966C311yesmaximal, characteristic, direct product factor
9C23×C32×C4—21no—
10C23×C32×C4C2211yescharacteristic
11C22×C3×#67—21no—
12C2×C3×#235—24no—
13C2×C3×#235—22no—
14C2×C3×#235C418yescomplemented
15C2×C3×#235C2214yes—
16C22×C3×D12C2211yescharacteristic
17C22×C3×C4×D3—21no—
18C22×C3×Dic6C2211yescharacteristic
19C2×C32×C4⋊C4—22no—
20C2×C32×C4⋊C4—21no—
21C2×C32×C4⋊C4C2212yes—
22C2×C32×C4⋊C4C2214yescomplemented
23C2×C3×#208—24no—
24C2×C3×#208C2214yescomplemented
25C22×C3×C3⋊C8C2212yes—
26C3×#810C2218yescomplemented
27C3×#809C2218yescomplemented
28C22×C3×#41—31no—
29C22×#235C2×C311yescharacteristic
30C22×C3×M16—31no—
31C22×C3×C4⋊C4—21no—
32C22×C3×C4⋊C4D311yescharacteristic, complemented
33C22×C3×C4⋊C4C2×C311yescharacteristic, complemented
34C22×#208C2×C311yescharacteristic, complemented
35C3×#417—38no—
36C2×C3×#103—32no—
37C2×C3×#102—32no—
38C2×#810C2×C312yescomplemented
39#4966C2×C318yesdirect product factor
40C2×#809C2×C312yescomplemented
41C24×C32D411yescharacteristic
42C23×C3×D3—21no—
43C22×C32×C4—22no—
44C22×C32×C4—24no—
45C22×C32×C4—44no—
46C22×C32×C4C2×C414yes—
47C22×C32×C4D411yescharacteristic
48C22×C32×C4D412yes—
49C22×C32×C4D414yes—
50C22×C32×C4C2311yescharacteristic
51C22×C32×C4C2312yes—
52C2×C3×#67—28no—
53C2×C3×#67—24no—
54C22×C3×Dic3—21no—
55C3×#235—216no—
56C3×#235—28no—
57C3×#235C2×C4116yescomplemented
58C2×C3×D12—21no—
59C2×C3×D12—22no—
60C2×C3×D12C2×C414yescomplemented
61C2×C3×D12C2312yes—
62C2×C3×C4×D3—28no—
63C2×C3×C4×D3—24no—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—22no—
66C2×C3×Dic6C2×C414yescomplemented
67C2×C3×Dic6C2312yes—
68C32×C4⋊C4—22no—
69C32×C4⋊C4—24no—
70C32×C4⋊C4C2314yes—
71C3×#208—28no—
72C2×C3×C3⋊C8—24no—
73C2×C3×C3⋊C8C2314yes—
74C2×#417—31noSylow
75C2×C3×#41—38no—
76C2×C3×#41—34no—
77C2×C3×#41—64no—
78C2×C3×#41—62no—
79C22×C3×Q8—31no—
80C22×C3×D4—31no—
81C22×C3×D4—61no—
82C23×C3×C4—22no—
83C23×C3×C4—21no—
84C23×C3×C4—21no—
85C23×C3×C4—21no—
86C23×C3×C4—61no—
87C23×C3×C4C2×D311yescharacteristic
88C23×C3×C4C22×C311yescharacteristic
89C22×#67—21no—
90C2×#235—24no—
91C2×#235—22no—
92C2×#235C3×C418yescomplemented
93C2×#235C22×C314yes—
94C22×D12C22×C311yescharacteristic
95C22×C4×D3—21no—
96C22×Dic6C22×C311yescharacteristic
97C2×C3×M16—34no—
98C2×C3×M16—64no—
99C22×C3×C8—32no—
100C2×C3×C4⋊C4—24no—
101C2×C3×C4⋊C4—22no—
102C2×C3×C4⋊C4—22no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4—22no—
105C2×C3×C4⋊C4—21no—
106C2×C3×C4⋊C4—22no—
107C2×C3×C4⋊C4—24no—
108C2×C3×C4⋊C4C2×D312yes—
109C2×C3×C4⋊C4C2×D314yescomplemented
110C2×C3×C4⋊C4C22×C312yes—
111C2×C3×C4⋊C4C22×C314yescomplemented
112C2×#208—24no—
113C2×#208C22×C314yescomplemented
114C22×C3⋊C8C22×C312yes—
115C3×#103—38no—
116C3×#102—38no—
117#810C22×C318yescomplemented
118#809C22×C318yescomplemented
119C23×C32—22no—
120C23×C32—22no—
121C23×C32C22⋊C414yes—
122C23×C32C2×D412yes—
123C23×C32C2×D411yescharacteristic
124C22×C3×D3—24no—
125C22×C3×D3—22no—
126C22×C3×D3—42no—
127C22×C3×D3—42no—
128C2×C32×C4—24no—
129C2×C32×C4—48no—
130C2×C32×C4—44no—
131C2×C32×C4C22⋊C414yes—
132C2×C32×C4C22⋊C418yes—
133C2×C32×C4C22×C412yes—
134C2×C32×C4C22×C414yes—
135C2×C32×C4C2×D412yes—
136C2×C32×C4C2×D414yes—
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D412yes—
139C2×C32×C4C2411yescharacteristic
140C3×#67—216no—
141C2×C3×Dic3—24no—
142C2×C3×Dic3—22no—
143C3×D12—24no—
144C3×D12—22no—
145C3×D12C22×C414yescomplemented
146C3×C4×D3—216no—
147C3×Dic6—24no—
148C3×Dic6—22no—
149C3×Dic6C22×C414yescomplemented
150C3×C3⋊C8—24no—
151C22×#41—31no—
152C22×M16—31no—
153C22×C4⋊C4C3×D311yescharacteristic, complemented
154#417—38no—
155C2×#103—32no—
156C2×#102—32no—
157C24×C3—21no—
158C24×C3—61no—
159C24×C3#6711yescharacteristic
160C24×C3C3×D411yescharacteristic
161C23×D3—21no—
162C3×#41—316no—
163C3×#41—616no—
164C3×#41—68no—
165C2×C3×Q8—34no—
166C2×C3×Q8—32no—
167C2×C3×Q8—62no—
168C2×C3×Q8—61no—
169C2×C3×D4—34no—
170C2×C3×D4—32no—
171C2×C3×D4—68no—
172C2×C3×D4—64no—
173C2×C3×D4—62no—
174C2×C3×D4—61no—
175C22×C3×C4—24no—
176C22×C3×C4—28no—
177C22×C3×C4—24no—
178C22×C3×C4—22no—
179C22×C3×C4—22no—
180C22×C3×C4—24no—
181C22×C3×C4—24no—
182C22×C3×C4—24no—
183C22×C3×C4—21no—
184C22×C3×C4—22no—
185C22×C3×C4—21no—
186C22×C3×C4—22no—
187C22×C3×C4—48no—
188C22×C3×C4—44no—
189C22×C3×C4—44no—
190C22×C3×C4—61no—
191C22×C3×C4—68no—
192C22×C3×C4—64no—
193C22×C3×C4C4×D314yes—
194C22×C3×C4D1214yes—
195C22×C3×C4#6712yes—
196C22×C3×C4#6711yescharacteristic
197C22×C3×C4C2×C3×C414yes—
198C22×C3×C4C3×D414yes—
199C22×C3×C4C3×D411yescharacteristic
200C22×C3×C4C3×D412yes—
201C22×C3×C4C22×D312yes—
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C23×C311yescharacteristic
204C22×C3×C4C23×C312yes—
205C2×#67—28no—
206C2×#67—24no—
207C22×Dic3—21no—
208#235—216no—
209#235—28no—
210#235C2×C3×C4116yescomplemented
211C2×D12—22no—
212C2×D12—21no—
213C2×D12C2×C3×C414yescomplemented
214C2×D12C23×C312yes—
215C2×C4×D3—28no—
216C2×C4×D3—24no—
217C2×Dic6—22no—
218C2×Dic6—21no—
219C2×Dic6C2×C3×C414yescomplemented
220C2×Dic6C23×C312yes—
221C3×M16—68no—
222C2×C3×C8—34no—
223C2×C3×C8—64no—
224C3×C4⋊C4—24no—
225C3×C4⋊C4—28no—
226C3×C4⋊C4—22no—
227C3×C4⋊C4—24no—
228C3×C4⋊C4—22no—
229C3×C4⋊C4—24no—
230C3×C4⋊C4—24no—
231C3×C4⋊C4C22×D314yes—
232C3×C4⋊C4C23×C314yes—
233#208—28no—
234C2×C3⋊C8—24no—
235C2×C3⋊C8C23×C314yes—
236C22×C32—22no—
237C22×C32—22no—
238C22×C32—28no—
239C22×C32C2×C22⋊C414yes—
240C22×C32C2×C22⋊C412yes—
241C22×C32AGL(1,ℤ/8)12yes—
242C22×C32#13712yes—
243C22×C32C22×D411yescharacteristic
244C2×C3×D3—24no—
245C2×C3×D3—42no—
246C2×C3×D3—42no—
247C2×C3×D3—48no—
248C32×C4—44no—
249C32×C4C2×C22⋊C412yes—
250C32×C4C2×C22⋊C414yes—
251C32×C4C23×C411yescharacteristic
252C32×C4C22×D411yescharacteristic
253C3×Dic3—24no—
254C2×#41—38no—
255C2×#41—34no—
256C2×#41—64no—
257C2×#41—62no—
258C22×Q8—31no—
259C22×D4—31no—
260C22×D4—61no—
261C23×C4—21no—
262C23×C4—61no—
263C23×C4C2×C3×D311yescharacteristic
264C2×M16—34no—
265C2×M16—64no—
266C22×C8—32no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4C2×C3×D312yes—
270C2×C4⋊C4C2×C3×D314yescomplemented
271#103—38no—
272#102—38no—
273C23×C3—24no—
274C23×C3—24no—
275C23×C3—22no—
276C23×C3—22no—
277C23×C3—22no—
278C23×C3—22no—
279C23×C3—24no—
280C23×C3—22no—
281C23×C3—21no—
282C23×C3—64no—
283C23×C3—62no—
284C23×C3—122no—
285C23×C3—122no—
286C23×C3(C2×D3)⋊C414yes—
287C23×C3C3×C22⋊C414yes—
288C23×C3C2×#6712yes—
289C23×C3C2×#6711yescharacteristic
290C23×C3C2×C3×D412yes—
291C23×C3C2×C3×D411yescharacteristic
292C22×D3—24no—
293C22×D3—22no—
294C22×D3—42no—
295C22×D3—42no—
296C3×Q8—34no—
297C3×Q8—64no—
298C3×Q8—62no—
299C3×D4—34no—
300C3×D4—616no—
301C3×D4—64no—
302C3×D4—62no—
303C2×C3×C4—28no—
304C2×C3×C4—24no—
305C2×C3×C4—24no—
306C2×C3×C4—21no—
307C2×C3×C4—24no—
308C2×C3×C4—28no—
309C2×C3×C4—22no—
310C2×C3×C4—24no—
311C2×C3×C4—22no—
312C2×C3×C4—24no—
313C2×C3×C4—22no—
314C2×C3×C4—21no—
315C2×C3×C4—416no—
316C2×C3×C4—48no—
317C2×C3×C4—48no—
318C2×C3×C4—48no—
319C2×C3×C4—44no—
320C2×C3×C4—44no—
321C2×C3×C4—64no—
322C2×C3×C4—62no—
323C2×C3×C4—616no—
324C2×C3×C4(C2×D3)⋊C414yes—
325C2×C3×C4(C2×D3)⋊C418yes—
326C2×C3×C4C3×C22⋊C414yes—
327C2×C3×C4C3×C22⋊C418yes—
328C2×C3×C4C2×C4×D312yes—
329C2×C3×C4C2×C4×D314yes—
330C2×C3×C4C2×D1212yes—
331C2×C3×C4C2×D1214yes—
332C2×C3×C4C2×#6712yes—
333C2×C3×C4C2×#6711yescharacteristic
334C2×C3×C4C22×C3×C412yes—
335C2×C3×C4C22×C3×C414yes—
336C2×C3×C4C2×C3×D412yes—
337C2×C3×C4C2×C3×D414yes—
338C2×C3×C4C2×C3×D411yescharacteristic
339C2×C3×C4C2×C3×D412yes—
340C2×C3×C4C23×D311yescharacteristic
341C2×C3×C4C24×C311yescharacteristic
342#67—216no—
343C2×Dic3—24no—
344C2×Dic3—22no—
345D12—24no—
346D12—22no—
347D12C22×C3×C414yescomplemented
348C4×D3—216no—
349Dic6—24no—
350Dic6—22no—
351Dic6C22×C3×C414yescomplemented
352C3×C8—64no—
353C3⋊C8—24no—
354C2×C32—24no—
355C2×C32#41714yescomplemented
356C2×C32C22×C22⋊C411yescharacteristic
357C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
358C2×C32C2×#13711yescharacteristic
359C3×D3—44no—
360C24—61no—
361C24C3×#6711yescharacteristic
362#41—316no—
363#41—616no—
364#41—68no—
365C2×Q8—32no—
366C2×Q8—34no—
367C2×Q8—62no—
368C2×Q8—61no—
369C2×D4—32no—
370C2×D4—34no—
371C2×D4—68no—
372C2×D4—64no—
373C2×D4—62no—
374C2×D4—61no—
375C22×C4—22no—
376C22×C4—24no—
377C22×C4—44no—
378C22×C4—61no—
379C22×C4—68no—
380C22×C4—64no—
381C22×C4C3×C4×D314yes—
382C22×C4C3×D1214yes—
383C22×C4C3×#6711yescharacteristic
384C22×C4C3×#6712yes—
385C22×C4C22×C3×D311yescharacteristic
386C22×C4C22×C3×D312yes—
387M16—68no—
388C2×C8—34no—
389C2×C8—64no—
390C4⋊C4—22no—
391C4⋊C4—24no—
392C4⋊C4C22×C3×D314yes—
393C22×C3—24no—
394C22×C3—216no—
395C22×C3—24no—
396C22×C3—22no—
397C22×C3—22no—
398C22×C3—28no—
399C22×C3—22no—
400C22×C3—28no—
401C22×C3—22no—
402C22×C3—24no—
403C22×C3—22no—
404C22×C3—22no—
405C22×C3—22no—
406C22×C3—21no—
407C22×C3—64no—
408C22×C3—128no—
409C22×C3—122no—
410C22×C3—122no—
411C22×C3C2×(C2×D3)⋊C414yes—
412C22×C3C2×(C2×D3)⋊C412yes—
413C22×C3#93212yes—
414C22×C3#94212yes—
415C22×C3C2×C3×C22⋊C414yes—
416C22×C3C2×C3×C22⋊C412yes—
417C22×C3C3×AGL(1,ℤ/8)12yes—
418C22×C3C3×#13712yes—
419C22×C3C22×#6711yescharacteristic
420C22×C3C22×C3×D411yescharacteristic
421C2×D3—24no—
422C2×D3—42no—
423C2×D3—42no—
424C2×D3—48no—
425C3×C4—24no—
426C3×C4—22no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—48no—
430C3×C4—44no—
431C3×C4—44no—
432C3×C4—64no—
433C3×C4C2×(C2×D3)⋊C414yes—
434C3×C4C2×(C2×D3)⋊C412yes—
435C3×C4C2×C3×C22⋊C412yes—
436C3×C4C2×C3×C22⋊C414yes—
437C3×C4C22×C4×D311yescharacteristic
438C3×C4C22×D1211yescharacteristic
439C3×C4C23×C3×C411yescharacteristic
440C3×C4C22×C3×D411yescharacteristic
441Dic3—24no—
442C32C2×#41711yescharacteristic, complemented, Sylow
443C23—22no—
444C23—22no—
445C23—64no—
446C23—62no—
447C23—122no—
448C23—122no—
449C23C3×(C2×D3)⋊C414yes—
450C23C2×C3×#6712yes—
451C23C2×C3×#6711yescharacteristic
452Q8—34no—
453Q8—64no—
454Q8—62no—
455D4—34no—
456D4—616no—
457D4—64no—
458D4—62no—
459C2×C4—24no—
460C2×C4—48no—
461C2×C4—44no—
462C2×C4—64no—
463C2×C4—62no—
464C2×C4—616no—
465C2×C4C3×(C2×D3)⋊C414yes—
466C2×C4C3×(C2×D3)⋊C418yes—
467C2×C4C2×C3×C4×D312yes—
468C2×C4C2×C3×C4×D314yes—
469C2×C4C2×C3×D1212yes—
470C2×C4C2×C3×D1214yes—
471C2×C4C2×C3×#6712yes—
472C2×C4C2×C3×#6711yescharacteristic
473C2×C4C23×C3×D311yescharacteristic
474C8—64no—
475C2×C3—28no—
476C2×C3—24no—
477C2×C3—24no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—24no—
481C2×C3—21no—
482C2×C3—124no—
483C2×C3#496614yesdirect product factor
484C2×C3C3×#41714yescomplemented
485C2×C3C22×(C2×D3)⋊C411yescharacteristic
486C2×C3C2×#93211yescharacteristic
487C2×C3C2×#94211yescharacteristic
488C2×C3C22×C3×C22⋊C411yescharacteristic
489C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
490C2×C3C2×C3×#13711yescharacteristic
491D3—44no—
492C22—22no—
493C22—28no—
494C22—22no—
495C22—64no—
496C22—122no—
497C22—128no—
498C22—122no—
499C22C2×C3×(C2×D3)⋊C414yes—
500C22C2×C3×(C2×D3)⋊C412yes—
501C22C3×#93212yes—
502C22C3×#94212yes—
503C22C22×C3×#6711yescharacteristic
504C4—44no—
505C4—64no—
506C4C2×C3×(C2×D3)⋊C414yes—
507C4C2×C3×(C2×D3)⋊C412yes—
508C4C22×C3×C4×D311yescharacteristic
509C4C22×C3×D1211yescharacteristic
510C3—21no—
511C3C2×#496611yescharacteristic, direct product factor
512C3C2×C3×#41711yescharacteristic, complemented
513C2—24no—
514C2—124no—
515C2C3×#496614yesdirect product factor
516C2C22×C3×(C2×D3)⋊C411yescharacteristic
517C2C2×C3×#93211yescharacteristic
518C2C2×C3×#94211yescharacteristic
subgroupG/H
centerC23×C3C2×#67
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC22×C32×C4⋊C4C2
socleC23×C32C2×D4
prime radicalC22×C3×#235C2
cosocleC2×C3×C4C24×C3
hypercenterC22×C3×C4⋊C4D3
hypocenterC3C2×C3×#417
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C23×C3×C4 ◁ 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×#208C2semidirect
4. C2×C3×#810C2semidirect
5. C3×#4966C2direct (N × H)
6. C2×C3×#809C2semidirect
8. C2×#4966C3direct (N × H)
14. C2×C3×#235C4semidirect
22. C2×C32×C4⋊C4C22semidirect
24. C2×C3×#208C22semidirect
26. C3×#810C22semidirect
27. C3×#809C22semidirect
32. C22×C3×C4⋊C4D3semidirect
33. C22×C3×C4⋊C4C2×C3semidirect
34. C22×#208C2×C3semidirect
38. C2×#810C2×C3semidirect
39. #4966C2×C3direct (N × H)
40. C2×#809C2×C3semidirect
57. C3×#235C2×C4semidirect
60. C2×C3×D12C2×C4semidirect
66. C2×C3×Dic6C2×C4semidirect
92. C2×#235C3×C4semidirect
109. C2×C3×C4⋊C4C2×D3semidirect
111. C2×C3×C4⋊C4C22×C3semidirect
113. C2×#208C22×C3semidirect
117. #810C22×C3semidirect
118. #809C22×C3semidirect
145. C3×D12C22×C4semidirect
149. C3×Dic6C22×C4semidirect
153. C22×C4⋊C4C3×D3semidirect
210. #235C2×C3×C4semidirect
213. C2×D12C2×C3×C4semidirect
219. C2×Dic6C2×C3×C4semidirect
270. C2×C4⋊C4C2×C3×D3semidirect
347. D12C22×C3×C4semidirect
351. Dic6C22×C3×C4semidirect
355. C2×C32#417semidirect
442. C32C2×#417semidirect
483. C2×C3#4966direct (N × H)
484. C2×C3C3×#417semidirect
511. C3C2×#4966direct (N × H)
512. C3C2×C3×#417semidirect
515. C2C3×#4966direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C22×C32×C4⋊C42
C22×C3×#2082
C2×C3×#8102
C3×#49662
C2×C3×#8092
C2×C3×#4173
C2×#49663