Finite Group Databasebeta

← C2×C3×#4774 #11869328

Subgroups — C2×C3×#4774 #11869328

Order 1152.

1125 conjugacy classes of subgroups.

The subgroup lattice has 517 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#938C211yesmaximal, characteristic
2C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×C32×#102C211yesmaximal, characteristic, complemented
4C2×C3×#832C211yesmaximal, characteristic, complemented
5C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
6C2×C3×#818C211yesmaximal, characteristic, complemented
7C2×C3×#807C211yesmaximal, characteristic, complemented
8C3×#4774C218yesmaximal, direct product factor
9C2×C3×#480—31nomaximal
10C2×#4774C311yesmaximal, characteristic, direct product factor
11C22×C32×D4C2211yescharacteristic
12C22×C3×#67—21no—
13C22×C3×C4×D3—21no—
14C22×C3×C4×D3C2211yescharacteristic
15C22×C32×C8C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×C3×#217—21no—
18C3×#938—22no—
19C3×#938C2214yes—
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×Dic3⋊C4—21no—
23C22×C3×C3⋊C8C2211yescharacteristic
24C3×D3×C4⋊C4—22no—
25C3×D3×C4⋊C4C2214yescomplemented
26C32×#102C2214yescomplemented
27C3×#832C2214yescomplemented
28C3×(C2×D3)⋊C8C2214yescomplemented
29C3×#818C2214yescomplemented
30C3×#807C2214yescomplemented
31C2×C3×#121—31no—
32C22×C3×C4⋊C4—31no—
33C2×#938C2×C311yescharacteristic
34C2×D3×C4⋊C4C2×C311yescharacteristic, complemented
35C3×#480—38no—
36C2×C3×#107—31no—
37C2×C3×#107—31no—
38C2×C3×#102—21no—
39C2×C3×#102—31no—
40C2×C3×#102D311yescharacteristic, complemented
41C2×C3×#102C2×C311yescharacteristic, complemented
42C2×C3×C22⋊C8—31no—
43C2×#832C2×C311yescharacteristic, complemented
44C2×(C2×D3)⋊C8C2×C311yescharacteristic, complemented
45C2×#818C2×C311yescharacteristic, complemented
46C2×#807C2×C311yescharacteristic, complemented
47#4774C2×C318yesdirect product factor
48C24×C32—21no—
49C23×C3×D3D411yescharacteristic
50C2×C32×D4—21no—
51C2×C32×D4—22no—
52C2×C32×D4—22no—
53C2×C32×D4C2312yes—
54C22×C32×C4—21no—
55C22×C32×C4C2311yescharacteristic
56C2×C3×#67—24no—
57C2×C3×#67—44no—
58C22×C3×Dic3—21no—
59C22×C3×Dic3—21no—
60C22×C3×Dic3D411yescharacteristic
61C2×C3×C4×D3—22no—
62C2×C3×C4×D3—22no—
63C2×C3×C4×D3—24no—
64C2×C3×C4×D3—44no—
65C2×C3×C4×D3D412yes—
66C2×C3×C4×D3C2312yes—
67C2×C32×C8—22no—
68C2×C32×C8C2312yes—
69C32×C4⋊C4—21no—
70C32×C4⋊C4C2312yes—
71C3×#217—24no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3C2312yes—
75C3×C4⋊Dic3C2312yes—
76C3×Dic3⋊C4—24no—
77C2×C3×C3⋊C8—22no—
78C2×C3×C3⋊C8C2312yes—
79C2×#480—31noSylow
80C22×C3×D4—21no—
81C22×C3×D4—61no—
82C22×C3×D4C2×D311yescharacteristic
83C22×C3×D4C22×C311yescharacteristic
84C23×C3×C4—31no—
85C23×C3×C4—61no—
86C22×#67—21no—
87C22×C4×D3—21no—
88C22×C4×D3C22×C311yescharacteristic
89C22×C3×C8—21no—
90C22×C3×C8—31no—
91C22×C3×C8C2×D311yescharacteristic
92C22×C3×C8C22×C311yescharacteristic
93C3×#121—34no—
94C3×#121—62no—
95C2×C3×C4⋊C4—21no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C4⋊C4—31no—
98C2×C3×C4⋊C4—34no—
99C2×C3×C4⋊C4—62no—
100C2×C3×C4⋊C4—61no—
101C2×C3×C4⋊C4C2×D311yescharacteristic
102C2×C3×C4⋊C4C22×C311yescharacteristic
103C2×C3×C22⋊C4—61no—
104C2×#217—21no—
105#938—22no—
106#938C22×C314yes—
107C2×C4⋊Dic3C22×C311yescharacteristic
108C2×C4⋊Dic3C22×C311yescharacteristic
109C2×Dic3⋊C4—21no—
110C22×C3⋊C8C22×C311yescharacteristic
111D3×C4⋊C4—22no—
112D3×C4⋊C4C22×C314yescomplemented
113C3×#107—34no—
114C3×#107—34no—
115C3×#102—24no—
116C3×#102—34no—
117C3×#102C2×D314yescomplemented
118C3×#102C22×C314yescomplemented
119C3×C22⋊C8—34no—
120#832C22×C314yescomplemented
121(C2×D3)⋊C8C22×C314yescomplemented
122#818C22×C314yescomplemented
123#807C22×C314yescomplemented
124C23×C32—22no—
125C23×C32—42no—
126C23×C32—42no—
127C23×C32—42no—
128C23×C32C2×D411yescharacteristic
129C22×C3×D3—22no—
130C22×C3×D3—22no—
131C22×C3×D3D814yes—
132C22×C3×D3C2×D412yes—
133C32×D4—22no—
134C32×D4—22no—
135C32×D4—42no—
136C2×C32×C4—22no—
137C2×C32×C4—42no—
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4#4112yes—
140C2×C32×C4#4112yes—
141C2×C32×C4C2411yescharacteristic
142C3×#67—48no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—42no—
147C2×C3×Dic3—42no—
148C2×C3×Dic3C2×D412yes—
149C3×C4×D3—24no—
150C3×C4×D3—22no—
151C3×C4×D3—22no—
152C3×C4×D3—48no—
153C32×C8—22no—
154C3×C3⋊C8—22no—
155C2×#121—31no—
156C22×C4⋊C4—31no—
157#480—38no—
158C2×#107—31no—
159C2×#107—31no—
160C2×#102—31no—
161C2×#102C3×D311yescharacteristic, complemented
162C2×C22⋊C8—31no—
163C24×C3—21no—
164C24×C3—21no—
165C24×C3—31no—
166C24×C3—41no—
167C23×D3C3×D411yescharacteristic
168C2×C3×D4—24no—
169C2×C3×D4—22no—
170C2×C3×D4—21no—
171C2×C3×D4—22no—
172C2×C3×D4—21no—
173C2×C3×D4—22no—
174C2×C3×D4—22no—
175C2×C3×D4—22no—
176C2×C3×D4—41no—
177C2×C3×D4—42no—
178C2×C3×D4—64no—
179C2×C3×D4—124no—
180C2×C3×D4C22×D312yes—
181C2×C3×D4C23×C312yes—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—31no—
186C22×C3×C4—32no—
187C22×C3×C4—32no—
188C22×C3×C4—41no—
189C22×C3×C4—64no—
190C22×C3×C4—62no—
191C22×C3×C4—62no—
192C22×C3×C4—61no—
193C22×C3×C4—61no—
194C22×C3×C4—124no—
195C22×C3×C4C22×D311yescharacteristic
196C22×C3×C4C23×C311yescharacteristic
197C2×#67—24no—
198C2×#67—44no—
199C22×Dic3—21no—
200C22×Dic3—21no—
201C22×Dic3C3×D411yescharacteristic
202C2×C4×D3—22no—
203C2×C4×D3—22no—
204C2×C4×D3—24no—
205C2×C4×D3—44no—
206C2×C4×D3C3×D412yes—
207C2×C4×D3C23×C312yes—
208C2×C3×C8—22no—
209C2×C3×C8—22no—
210C2×C3×C8—22no—
211C2×C3×C8—32no—
212C2×C3×C8—42no—
213C2×C3×C8—62no—
214C2×C3×C8C22×D312yes—
215C2×C3×C8C23×C312yes—
216C3×C4⋊C4—21no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—22no—
219C3×C4⋊C4—32no—
220C3×C4⋊C4—32no—
221C3×C4⋊C4—41no—
222C3×C4⋊C4—64no—
223C3×C4⋊C4—61no—
224C3×C4⋊C4—61no—
225C3×C4⋊C4C22×D312yes—
226C3×C4⋊C4C23×C312yes—
227C3×C22⋊C4—64no—
228#217—24no—
229C4⋊Dic3—21no—
230C4⋊Dic3—21no—
231C4⋊Dic3C23×C312yes—
232C4⋊Dic3C23×C312yes—
233Dic3⋊C4—24no—
234C2×C3⋊C8—22no—
235C2×C3⋊C8C23×C312yes—
236C22×C32—42no—
237C22×C32—42no—
238C22×C32—42no—
239C22×C32—84no—
240C22×C32#12312yes—
241C22×C32C2×D812yes—
242C22×C32#13712yes—
243C22×C32C22×D411yescharacteristic
244C2×C3×D3—22no—
245C2×C3×D3—22no—
246C2×C3×D3—28no—
247C2×C3×D3C2×D814yes—
248C32×C4—42no—
249C32×C4#12312yes—
250C32×C4C2×#4111yescharacteristic
251C32×C4C2×#4111yescharacteristic
252C3×Dic3—22no—
253C3×Dic3—42no—
254C3×Dic3—42no—
255C22×D4—61no—
256C22×D4C2×C3×D311yescharacteristic
257C23×C4—31no—
258C23×C4—61no—
259C22×C8—31no—
260C22×C8C2×C3×D311yescharacteristic
261#121—34no—
262#121—62no—
263C2×C4⋊C4—31no—
264C2×C4⋊C4—31no—
265C2×C4⋊C4—34no—
266C2×C4⋊C4—62no—
267C2×C4⋊C4—61no—
268C2×C4⋊C4C2×C3×D311yescharacteristic
269C2×C22⋊C4—61no—
270#107—34no—
271#107—34no—
272#102—34no—
273#102C2×C3×D314yescomplemented
274C22⋊C8—34no—
275C23×C3—22no—
276C23×C3—22no—
277C23×C3—21no—
278C23×C3—34no—
279C23×C3—32no—
280C23×C3—42no—
281C23×C3—44no—
282C23×C3—42no—
283C23×C3—42no—
284C23×C3—42no—
285C23×C3—42no—
286C23×C3—42no—
287C23×C3—42no—
288C23×C3—62no—
289C23×C3—62no—
290C23×C3—82no—
291C23×C3—82no—
292C23×C3D3×D411yescharacteristic
293C23×C3C2×C3×D411yescharacteristic
294C22×D3—22no—
295C22×D3—22no—
296C22×D3C3×D814yes—
297C22×D3C2×C3×D412yes—
298C3×D4—24no—
299C3×D4—22no—
300C3×D4—22no—
301C3×D4—22no—
302C3×D4—22no—
303C3×D4—42no—
304C3×D4—44no—
305C3×D4—42no—
306C3×D4—42no—
307C3×D4—128no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—21no—
311C2×C3×C4—22no—
312C2×C3×C4—21no—
313C2×C3×C4—22no—
314C2×C3×C4—32no—
315C2×C3×C4—42no—
316C2×C3×C4—42no—
317C2×C3×C4—42no—
318C2×C3×C4—62no—
319C2×C3×C4—64no—
320C2×C3×C4—62no—
321C2×C3×C4—62no—
322C2×C3×C4—62no—
323C2×C3×C4—62no—
324C2×C3×C4—82no—
325C2×C3×C4—128no—
326C2×C3×C4—122no—
327C2×C3×C4—122no—
328C2×C3×C4#23512yes—
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4#23712yes—
331C2×C3×C4C2×C3×D411yescharacteristic
332C2×C3×C4C3×#4112yes—
333C2×C3×C4C3×#4112yes—
334C2×C3×C4C23×D311yescharacteristic
335C2×C3×C4C24×C311yescharacteristic
336#67—48no—
337C2×Dic3—22no—
338C2×Dic3—22no—
339C2×Dic3—22no—
340C2×Dic3—42no—
341C2×Dic3—42no—
342C2×Dic3C2×C3×D412yes—
343C4×D3—24no—
344C4×D3—22no—
345C4×D3—22no—
346C4×D3—48no—
347C3×C8—22no—
348C3×C8—22no—
349C3×C8—42no—
350C3×C8—62no—
351C3⋊C8—22no—
352C2×C32—82no—
353C2×C32#48014yescomplemented
354C2×C32C2×#12311yescharacteristic
355C2×C32C22×D811yescharacteristic
356C2×C32C2×#13711yescharacteristic
357C3×D3—24no—
358C24—21no—
359C24—31no—
360C2×D4—22no—
361C2×D4—21no—
362C2×D4—22no—
363C2×D4—64no—
364C2×D4—124no—
365C2×D4C22×C3×D312yes—
366C22×C4—21no—
367C22×C4—31no—
368C22×C4—32no—
369C22×C4—32no—
370C22×C4—64no—
371C22×C4—62no—
372C22×C4—62no—
373C22×C4—61no—
374C22×C4—61no—
375C22×C4—124no—
376C22×C4C22×C3×D311yescharacteristic
377C2×C8—22no—
378C2×C8—32no—
379C2×C8—62no—
380C2×C8C22×C3×D312yes—
381C4⋊C4—21no—
382C4⋊C4—32no—
383C4⋊C4—32no—
384C4⋊C4—64no—
385C4⋊C4—61no—
386C4⋊C4—61no—
387C4⋊C4C22×C3×D312yes—
388C22⋊C4—64no—
389C22×C3—22no—
390C22×C3—22no—
391C22×C3—22no—
392C22×C3—21no—
393C22×C3—34no—
394C22×C3—44no—
395C22×C3—42no—
396C22×C3—42no—
397C22×C3—42no—
398C22×C3—42no—
399C22×C3—42no—
400C22×C3—42no—
401C22×C3—62no—
402C22×C3—62no—
403C22×C3—68no—
404C22×C3—82no—
405C22×C3—82no—
406C22×C3—88no—
407C22×C3—84no—
408C22×C3—84no—
409C22×C3#88312yes—
410C22×C3D3×D812yes—
411C22×C3#91512yes—
412C22×C3C3×#12312yes—
413C22×C3C2×C3×D812yes—
414C22×C3C3×#13712yes—
415C22×C3C2×D3×D411yescharacteristic
416C22×C3C22×C3×D411yescharacteristic
417C2×D3—22no—
418C2×D3—22no—
419C2×D3—28no—
420C2×D3C2×C3×D814yes—
421C3×C4—22no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—42no—
425C3×C4—42no—
426C3×C4—62no—
427C3×C4—82no—
428C3×C4—122no—
429C3×C4—122no—
430C3×C4#88312yes—
431C3×C4C3×#12312yes—
432C3×C4C2×#23511yescharacteristic
433C3×C4C2×#23711yescharacteristic
434C3×C4C2×C3×#4111yescharacteristic
435C3×C4C2×C3×#4111yescharacteristic
436Dic3—22no—
437Dic3—42no—
438Dic3—42no—
439C32C2×#48011yescharacteristic, complemented, Sylow
440C23—22no—
441C23—34no—
442C23—32no—
443C23—42no—
444C23—42no—
445C23—42no—
446C23—62no—
447C23—62no—
448C23C3×D3×D411yescharacteristic
449D4—22no—
450D4—22no—
451D4—42no—
452D4—128no—
453C2×C4—22no—
454C2×C4—32no—
455C2×C4—42no—
456C2×C4—62no—
457C2×C4—64no—
458C2×C4—62no—
459C2×C4—62no—
460C2×C4—62no—
461C2×C4—62no—
462C2×C4—128no—
463C2×C4—122no—
464C2×C4—122no—
465C2×C4C3×#23512yes—
466C2×C4C3×D3×D411yescharacteristic
467C2×C4C3×#23712yes—
468C2×C4C23×C3×D311yescharacteristic
469C8—22no—
470C8—62no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—24no—
475C2×C3—64no—
476C2×C3—84no—
477C2×C3—82no—
478C2×C3—82no—
479C2×C3#477414yesdirect product factor
480C2×C3C3×#48014yescomplemented
481C2×C3C2×#88311yescharacteristic
482C2×C3C2×D3×D811yescharacteristic
483C2×C3C2×#91511yescharacteristic
484C2×C3C2×C3×#12311yescharacteristic
485C2×C3C22×C3×D811yescharacteristic
486C2×C3C2×C3×#13711yescharacteristic
487D3—24no—
488C22—34no—
489C22—42no—
490C22—42no—
491C22—42no—
492C22—62no—
493C22—62no—
494C22—68no—
495C22—84no—
496C22C3×#88312yes—
497C22C3×D3×D812yes—
498C22C3×#91512yes—
499C22C2×C3×D3×D411yescharacteristic
500C4—42no—
501C4—62no—
502C4—122no—
503C4—122no—
504C4C3×#88312yes—
505C4C2×C3×#23511yescharacteristic
506C4C2×C3×#23711yescharacteristic
507C3—21no—
508C3C2×#477411yescharacteristic, direct product factor
509C3C2×C3×#48011yescharacteristic, complemented
510C2—64no—
511C2—82no—
512C2C3×#477414yesdirect product factor
513C2C2×C3×#88311yescharacteristic
514C2C2×C3×D3×D811yescharacteristic
515C2C2×C3×#91511yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#102C2
socleC23×C32C2×D4
prime radicalC2×C3×#938C2
hypercenterC2×C3×#102D3
hypocenterC3C2×C3×#480
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×#102

Complements

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

NH ≅ G/Ntype
2. C2×C3×D3×C4⋊C4C2semidirect
3. C2×C32×#102C2semidirect
4. C2×C3×#832C2semidirect
5. C2×C3×(C2×D3)⋊C8C2semidirect
6. C2×C3×#818C2semidirect
7. C2×C3×#807C2semidirect
8. C3×#4774C2direct (N × H)
10. C2×#4774C3direct (N × H)
25. C3×D3×C4⋊C4C22semidirect
26. C32×#102C22semidirect
27. C3×#832C22semidirect
28. C3×(C2×D3)⋊C8C22semidirect
29. C3×#818C22semidirect
30. C3×#807C22semidirect
34. C2×D3×C4⋊C4C2×C3semidirect
40. C2×C3×#102D3semidirect
41. C2×C3×#102C2×C3semidirect
43. C2×#832C2×C3semidirect
44. C2×(C2×D3)⋊C8C2×C3semidirect
45. C2×#818C2×C3semidirect
46. C2×#807C2×C3semidirect
47. #4774C2×C3direct (N × H)
112. D3×C4⋊C4C22×C3semidirect
117. C3×#102C2×D3semidirect
118. C3×#102C22×C3semidirect
120. #832C22×C3semidirect
121. (C2×D3)⋊C8C22×C3semidirect
122. #818C22×C3semidirect
123. #807C22×C3semidirect
161. C2×#102C3×D3semidirect
273. #102C2×C3×D3semidirect
353. C2×C32#480semidirect
439. C32C2×#480semidirect
479. C2×C3#4774direct (N × H)
480. C2×C3C3×#480semidirect
508. C3C2×#4774direct (N × H)
509. C3C2×C3×#480semidirect
512. C2C3×#4774direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9382
C2×C3×D3×C4⋊C42
C2×C32×#1022
C2×C3×#8322
C2×C3×(C2×D3)⋊C82
C2×C3×#8182
C2×C3×#8072
C3×#47742
C2×C3×#4803
C2×#47743