Finite Group Databasebeta

← C3×C4×#834 #11783746

Subgroups — C3×C4×#834 #11783746

Order 1152.

1037 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic
2C2×C3×#834C212yesmaximal
3C3×C4×#217C212yesmaximal, complemented
4C3×#4526C212yesmaximal, complemented
5C3×C4×#99—31nomaximal
6C4×#834C311yesmaximal, characteristic, direct product factor
7C22×C32×D4C2211yescharacteristic
8C23×C32×C4C411yescharacteristic, complemented
9C23×C32×C4C2211yescharacteristic
10C32×C4×D4—22no—
11C32×C4×D4—22no—
12C2×C32×C4⋊C4C411yescharacteristic, complemented
13C2×C32×C22⋊C4C411yescharacteristic, complemented
14C2×C32×C22⋊C4C2211yescharacteristic
15C2×C32×C42C411yescharacteristic, complemented
16C2×C3×#217C2214yes—
17C2×C3×C4×Dic3—22no—
18C3×#834C418yesdirect product factor
19C3×C3⋊#95—22no—
20C2×C3×C4×D4—21no—
21C2×C3×C4×D4D311yescharacteristic
22C2×C3×C4×D4C2×C311yescharacteristic
23C2×C3×#99—32no—
24C3×C4×C22⋊C4—32no—
25C2×#834C2×C312yes—
26C4×#217C2×C312yescomplemented
27C3×#342—32no—
28#4526C2×C312yescomplemented
29C24×C32C2×C411yescharacteristic
30C24×C32C2311yescharacteristic
31C2×C32×D4—22no—
32C2×C32×D4—22no—
33C2×C32×D4C2×C414yes—
34C22×C32×C4—21no—
35C22×C32×C4—21no—
36C22×C32×C4—42no—
37C22×C32×C4—42no—
38C22×C32×C4C2×C411yescharacteristic
39C22×C32×C4C2×C411yescharacteristic
40C22×C32×C4C2×C411yescharacteristic
41C22×C32×C4C2×C411yescharacteristic
42C22×C32×C4C2×C411yescharacteristic
43C22×C32×C4D412yes—
44C22×C32×C4D412yes—
45C22×C3×Dic3—24no—
46C32×C4⋊C4—22no—
47C32×C22⋊C4—22no—
48C32×C22⋊C4—22no—
49C32×C42—21no—
50C32×C42—21no—
51C3×#217—24no—
52C3×#217C2×C418yescomplemented
53C3×C4×Dic3—44no—
54C4×#99—31noSylow
55C22×C3×D4—21no—
56C22×C3×D4C2×D311yescharacteristic
57C22×C3×D4C22×C311yescharacteristic
58C23×C3×C4—21no—
59C23×C3×C4—21no—
60C23×C3×C4Dic311yescharacteristic, complemented
61C23×C3×C4C3×C411yescharacteristic, complemented
62C23×C3×C4C2×D311yescharacteristic
63C23×C3×C4C22×C311yescharacteristic
64C3×C4×D4—24no—
65C3×C4×D4—24no—
66C3×C4×D4—22no—
67C3×C4×D4—22no—
68C3×C4×D4—22no—
69C3×C4×D4—22no—
70C2×C3×C4⋊C4—21no—
71C2×C3×C4⋊C4Dic311yescharacteristic, complemented
72C2×C3×C4⋊C4C3×C411yescharacteristic, complemented
73C2×C3×C22⋊C4—21no—
74C2×C3×C22⋊C4—21no—
75C2×C3×C22⋊C4—34no—
76C2×C3×C22⋊C4Dic311yescharacteristic, complemented
77C2×C3×C22⋊C4C3×C411yescharacteristic, complemented
78C2×C3×C22⋊C4C2×D311yescharacteristic
79C2×C3×C22⋊C4C22×C311yescharacteristic
80C2×C3×C42—21no—
81C2×C3×C42—62no—
82C2×C3×C42Dic311yescharacteristic, complemented
83C2×C3×C42C3×C411yescharacteristic, complemented
84C2×#217C22×C314yes—
85C2×C4×Dic3—22no—
86C3×#99—38no—
87C3×#95—62no—
88#834C3×C418yesdirect product factor
89C3⋊#95—22no—
90C23×C32—21no—
91C23×C32—21no—
92C23×C32—41no—
93C23×C32—41no—
94C23×C32—41no—
95C23×C32—41no—
96C23×C32C4212yescomplemented
97C23×C32C22×C412yes—
98C23×C32C22×C411yescharacteristic
99C23×C32C2×D412yes—
100C23×C32#4112yes—
101C32×D4—28no—
102C2×C32×C4—21no—
103C2×C32×C4—21no—
104C2×C32×C4—22no—
105C2×C32×C4—21no—
106C2×C32×C4—21no—
107C2×C32×C4—24no—
108C2×C32×C4—41no—
109C2×C32×C4—42no—
110C2×C32×C4—42no—
111C2×C32×C4—42no—
112C2×C32×C4—41no—
113C2×C32×C4—41no—
114C2×C32×C4C4212yescomplemented
115C2×C32×C4C22⋊C411yescharacteristic
116C2×C32×C4C22⋊C412yes—
117C2×C32×C4C22⋊C411yescharacteristic
118C2×C3×Dic3—28no—
119C2×C3×Dic3—44no—
120C2×C3×Dic3—44no—
121C2×C4×D4C3×D311yescharacteristic
122C2×#99—32no—
123C4×C22⋊C4—32no—
124#342—32no—
125C24×C3—21no—
126C24×C3—21no—
127C24×C3C2×Dic311yescharacteristic
128C24×C3C2×C3×C411yescharacteristic
129C24×C3C22×D311yescharacteristic
130C24×C3C23×C311yescharacteristic
131C2×C3×D4—24no—
132C2×C3×D4—24no—
133C2×C3×D4—22no—
134C2×C3×D4—22no—
135C2×C3×D4—22no—
136C2×C3×D4—22no—
137C2×C3×D4—24no—
138C2×C3×D4C4×D314yes—
139C2×C3×D4C2×C3×C414yes—
140C22×C3×C4—22no—
141C22×C3×C4—22no—
142C22×C3×C4—21no—
143C22×C3×C4—21no—
144C22×C3×C4—21no—
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4—21no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—22no—
152C22×C3×C4—22no—
153C22×C3×C4—42no—
154C22×C3×C4—42no—
155C22×C3×C4—44no—
156C22×C3×C4—44no—
157C22×C3×C4—42no—
158C22×C3×C4—42no—
159C22×C3×C4—64no—
160C22×C3×C4C2×Dic311yescharacteristic
161C22×C3×C4C2×Dic311yescharacteristic
162C22×C3×C4C2×Dic311yescharacteristic
163C22×C3×C4C2×Dic311yescharacteristic
164C22×C3×C4C2×Dic311yescharacteristic
165C22×C3×C4#6712yes—
166C22×C3×C4#6712yes—
167C22×C3×C4C2×C3×C411yescharacteristic
168C22×C3×C4C2×C3×C411yescharacteristic
169C22×C3×C4C2×C3×C411yescharacteristic
170C22×C3×C4C2×C3×C411yescharacteristic
171C22×C3×C4C2×C3×C411yescharacteristic
172C22×C3×C4C3×D412yes—
173C22×C3×C4C3×D412yes—
174C22×Dic3—24no—
175C3×C4⋊C4—24no—
176C3×C4⋊C4—22no—
177C3×C4⋊C4—22no—
178C3×C22⋊C4—24no—
179C3×C22⋊C4—24no—
180C3×C22⋊C4—22no—
181C3×C22⋊C4—22no—
182C3×C22⋊C4—22no—
183C3×C22⋊C4—22no—
184C3×C22⋊C4—38no—
185C3×C22⋊C4—64no—
186C3×C42—22no—
187C3×C42—22no—
188C3×C42—21no—
189C3×C42—21no—
190C3×C42—21no—
191C3×C42—21no—
192C3×C42—124no—
193#217—24no—
194#217C2×C3×C418yescomplemented
195C4×Dic3—44no—
196C22×C32—21no—
197C22×C32—21no—
198C22×C32—22no—
199C22×C32—22no—
200C22×C32—22no—
201C22×C32—42no—
202C22×C32—42no—
203C22×C32—42no—
204C22×C32—42no—
205C22×C32—41no—
206C22×C32—41no—
207C22×C32C2×C4211yescharacteristic
208C22×C32C2×C22⋊C411yescharacteristic
209C22×C32#11711yescharacteristic
210C22×C32C4×D414yes—
211C32×C4—22no—
212C32×C4—21no—
213C32×C4—22no—
214C32×C4—41no—
215C32×C4—41no—
216C32×C4#9912yescomplemented
217C3×Dic3—48no—
218C22×D4C2×C3×D311yescharacteristic
219C23×C4C3×Dic311yescharacteristic, complemented
220C23×C4C2×C3×D311yescharacteristic
221C4×D4—22no—
222C4×D4—22no—
223C2×C4⋊C4C3×Dic311yescharacteristic, complemented
224C2×C22⋊C4—34no—
225C2×C22⋊C4C3×Dic311yescharacteristic, complemented
226C2×C22⋊C4C2×C3×D311yescharacteristic
227C2×C42—62no—
228C2×C42C3×Dic311yescharacteristic, complemented
229#99—38no—
230#95—62no—
231C23×C3—22no—
232C23×C3—22no—
233C23×C3—21no—
234C23×C3—21no—
235C23×C3—21no—
236C23×C3—21no—
237C23×C3—22no—
238C23×C3—22no—
239C23×C3—22no—
240C23×C3—21no—
241C23×C3—22no—
242C23×C3—41no—
243C23×C3—41no—
244C23×C3—41no—
245C23×C3—41no—
246C23×C3—41no—
247C23×C3—41no—
248C23×C3—41no—
249C23×C3—41no—
250C23×C3—42no—
251C23×C3—42no—
252C23×C3—42no—
253C23×C3—42no—
254C23×C3C4×Dic312yescomplemented
255C23×C3C3×C4212yescomplemented
256C23×C3C2×C4×D312yes—
257C23×C3#23512yes—
258C23×C3C22×Dic311yescharacteristic
259C23×C3C2×#6712yes—
260C23×C3C22×C3×C412yes—
261C23×C3C22×C3×C411yescharacteristic
262C23×C3C2×C3×D412yes—
263C23×C3C3×#4112yes—
264C3×D4—216no—
265C3×D4—28no—
266C3×D4—28no—
267C2×C3×C4—22no—
268C2×C3×C4—24no—
269C2×C3×C4—22no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—24no—
275C2×C3×C4—22no—
276C2×C3×C4—24no—
277C2×C3×C4—22no—
278C2×C3×C4—22no—
279C2×C3×C4—22no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—22no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—22no—
288C2×C3×C4—44no—
289C2×C3×C4—41no—
290C2×C3×C4—42no—
291C2×C3×C4—41no—
292C2×C3×C4—42no—
293C2×C3×C4—44no—
294C2×C3×C4—44no—
295C2×C3×C4—42no—
296C2×C3×C4—42no—
297C2×C3×C4—44no—
298C2×C3×C4—42no—
299C2×C3×C4—42no—
300C2×C3×C4—42no—
301C2×C3×C4—42no—
302C2×C3×C4—42no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4—68no—
308C2×C3×C4—124no—
309C2×C3×C4—124no—
310C2×C3×C4C4×Dic312yescomplemented
311C2×C3×C4#21711yescharacteristic
312C2×C3×C4#21712yes—
313C2×C3×C4#21711yescharacteristic
314C2×C3×C4C3×C4212yescomplemented
315C2×C3×C4C3×C22⋊C411yescharacteristic
316C2×C3×C4C3×C22⋊C412yes—
317C2×C3×C4C3×C22⋊C411yescharacteristic
318C2×Dic3—28no—
319C2×Dic3—44no—
320C2×Dic3—44no—
321C2×C32—21no—
322C2×C32—21no—
323C2×C32—24no—
324C2×C32—42no—
325C2×C32C4×C22⋊C411yescharacteristic
326C2×C32C2×#9911yescharacteristic
327C2×C32#41011yescharacteristic
328C24C2×C3×Dic311yescharacteristic
329C24C22×C3×D311yescharacteristic
330C2×D4—22no—
331C2×D4—22no—
332C2×D4C3×C4×D314yes—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—42no—
336C22×C4—42no—
337C22×C4—64no—
338C22×C4C2×C3×Dic311yescharacteristic
339C22×C4C2×C3×Dic311yescharacteristic
340C22×C4C2×C3×Dic311yescharacteristic
341C22×C4C2×C3×Dic311yescharacteristic
342C22×C4C2×C3×Dic311yescharacteristic
343C22×C4C3×#6712yes—
344C22×C4C3×#6712yes—
345C4⋊C4—22no—
346C22⋊C4—22no—
347C22⋊C4—22no—
348C22⋊C4—38no—
349C22⋊C4—64no—
350C42—21no—
351C42—21no—
352C42—124no—
353C22×C3—22no—
354C22×C3—22no—
355C22×C3—21no—
356C22×C3—22no—
357C22×C3—21no—
358C22×C3—22no—
359C22×C3—22no—
360C22×C3—21no—
361C22×C3—22no—
362C22×C3—21no—
363C22×C3—24no—
364C22×C3—22no—
365C22×C3—22no—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—24no—
369C22×C3—21no—
370C22×C3—42no—
371C22×C3—42no—
372C22×C3—42no—
373C22×C3—42no—
374C22×C3—42no—
375C22×C3—42no—
376C22×C3—42no—
377C22×C3—42no—
378C22×C3—42no—
379C22×C3—44no—
380C22×C3—44no—
381C22×C3—44no—
382C22×C3—44no—
383C22×C3—42no—
384C22×C3—42no—
385C22×C3—42no—
386C22×C3—41no—
387C22×C3—41no—
388C22×C3—41no—
389C22×C3—41no—
390C22×C3C2×C4×Dic311yescharacteristic
391C22×C3#92611yescharacteristic
392C22×C3C4×#6714yes—
393C22×C3C2×#21711yescharacteristic
394C22×C3C2×C3×C4211yescharacteristic
395C22×C3C2×C3×C22⋊C411yescharacteristic
396C22×C3C3×#11711yescharacteristic
397C22×C3C3×C4×D414yes—
398C3×C4—22no—
399C3×C4—24no—
400C3×C4—22no—
401C3×C4—21no—
402C3×C4—22no—
403C3×C4—22no—
404C3×C4—21no—
405C3×C4—22no—
406C3×C4—22no—
407C3×C4—42no—
408C3×C4—42no—
409C3×C4—42no—
410C3×C4—41no—
411C3×C4—41no—
412C3×C4—41no—
413C3×C4—41no—
414C3×C4—128no—
415C3×C4#83412yesdirect product factor
416C3×C4C3×#9912yescomplemented
417Dic3—48no—
418C32C4×#9911yescharacteristic, complemented, Sylow
419C23—21no—
420C23—21no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—41no—
425C23C3×C4×Dic312yescomplemented
426C23C2×C3×C4×D312yes—
427C23C3×#23512yes—
428C23C22×C3×Dic311yescharacteristic
429C23C2×C3×#6712yes—
430D4—28no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—24no—
434C2×C4—22no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—68no—
444C2×C4—124no—
445C2×C4—124no—
446C2×C4C3×C4×Dic312yescomplemented
447C2×C4C3×#21711yescharacteristic
448C2×C4C3×#21712yes—
449C2×C4C3×#21711yescharacteristic
450C2×C3—22no—
451C2×C3—22no—
452C2×C3—24no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—24no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—44no—
462C2×C3—44no—
463C2×C3—42no—
464C2×C3—42no—
465C2×C3C4×#21711yescharacteristic
466C2×C3C2×#83411yescharacteristic
467C2×C3#524011yescharacteristic
468C2×C3C3×C4×C22⋊C411yescharacteristic
469C2×C3C2×C3×#9911yescharacteristic
470C2×C3C3×#41011yescharacteristic
471C22—21no—
472C22—22no—
473C22—21no—
474C22—22no—
475C22—22no—
476C22—42no—
477C22—42no—
478C22—42no—
479C22—42no—
480C22—41no—
481C22—41no—
482C22C2×C3×C4×Dic311yescharacteristic
483C22C3×#92611yescharacteristic
484C22C3×C4×#6714yes—
485C22C2×C3×#21711yescharacteristic
486C4—22no—
487C4—21no—
488C4—22no—
489C4—41no—
490C4—41no—
491C4—128no—
492C4C3×#83412yesdirect product factor
493C3—21no—
494C3C4×#83411yescharacteristic, direct product factor
495C3C3×C4×#9911yescharacteristic, complemented
496C2—24no—
497C2—21no—
498C2—21no—
499C2—42no—
500C2C3×C4×#21711yescharacteristic
501C2C2×C3×#83411yescharacteristic
502C2C3×#524011yescharacteristic
subgroupG/H
centerC2×C3×C4#217
commutatorC22×C3C2×C3×C42
FrattiniC24C22×C3×D3
FittingC2×C32×C4×D4C2
socleC22×C32C2×C22⋊C4
prime radicalC22×C32×D4C22
cosocleC24×C3C23×C3
hypercenterC2×C3×C4×D4D3
hypocenterC3C3×C4×#99
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C23×C3×C4 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
3. C3×C4×#217C2semidirect
4. C3×#4526C2semidirect
6. C4×#834C3direct (N × H)
8. C23×C32×C4C4semidirect
12. C2×C32×C4⋊C4C4semidirect
13. C2×C32×C22⋊C4C4semidirect
15. C2×C32×C42C4semidirect
18. C3×#834C4direct (N × H)
26. C4×#217C2×C3semidirect
28. #4526C2×C3semidirect
52. C3×#217C2×C4semidirect
60. C23×C3×C4Dic3semidirect
61. C23×C3×C4C3×C4semidirect
71. C2×C3×C4⋊C4Dic3semidirect
72. C2×C3×C4⋊C4C3×C4semidirect
76. C2×C3×C22⋊C4Dic3semidirect
77. C2×C3×C22⋊C4C3×C4semidirect
82. C2×C3×C42Dic3semidirect
83. C2×C3×C42C3×C4semidirect
88. #834C3×C4direct (N × H)
96. C23×C32C42semidirect
114. C2×C32×C4C42semidirect
194. #217C2×C3×C4semidirect
216. C32×C4#99semidirect
219. C23×C4C3×Dic3semidirect
223. C2×C4⋊C4C3×Dic3semidirect
225. C2×C22⋊C4C3×Dic3semidirect
228. C2×C42C3×Dic3semidirect
254. C23×C3C4×Dic3semidirect
255. C23×C3C3×C42semidirect
310. C2×C3×C4C4×Dic3semidirect
314. C2×C3×C4C3×C42semidirect
415. C3×C4#834direct (N × H)
416. C3×C4C3×#99semidirect
418. C32C4×#99semidirect
425. C23C3×C4×Dic3semidirect
446. C2×C4C3×C4×Dic3semidirect
492. C4C3×#834direct (N × H)
494. C3C4×#834direct (N × H)
495. C3C3×C4×#99semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C2×C3×#8342
C3×C4×#2172
C3×#45262
C3×C4×#993
C4×#8343