Finite Group Databasebeta

← C3×#71560 #11787309

Subgroups — C3×#71560 #11787309

Order 1152.

1121 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×C3×#930C211yesmaximal, characteristic
3C2×C3×#830C211yesmaximal, characteristic, complemented
4C2×C3×#809C212yesmaximal, complemented
5C3×#4529C212yesmaximal, complemented
6C3×#1874—31nomaximal
7#71560C311yesmaximal, characteristic, direct product factor
8C23×C32×C4—21no—
9C23×C32×C4C2211yescharacteristic
10C22×C3×#67—21no—
11C22×C3×D12C2211yescharacteristic
12C2×C32×C4⋊C4—21no—
13C2×C32×C4⋊C4—24no—
14C2×C32×C4⋊C4C2212yes—
15C3×#930—22no—
16C3×#930C414yescomplemented
17C2×C3×(C2×D3)⋊C4—21no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2212yes—
20C3×#830—22no—
21C3×#809—24no—
22C2×C3×#121—31no—
23C22×C3×C4⋊C4—21no—
24C22×C3×C4⋊C4D311yescharacteristic, complemented
25C22×C3×C4⋊C4C2×C311yescharacteristic, complemented
26C2×#930C2×C311yescharacteristic
27C2×C3×#102—32no—
28C2×C3×C22⋊C8—31no—
29C2×#830C2×C311yescharacteristic, complemented
30C2×#809C2×C312yescomplemented
31C3×#340—32no—
32#4529C2×C312yescomplemented
33C24×C32D411yescharacteristic
34C23×C3×D3—21no—
35C22×C32×C4—22no—
36C22×C32×C4—22no—
37C22×C32×C4—24no—
38C22×C32×C4—22no—
39C22×C32×C4—42no—
40C22×C32×C4—42no—
41C22×C32×C4C2×C412yes—
42C22×C32×C4D411yescharacteristic
43C22×C32×C4D412yes—
44C22×C32×C4C2311yescharacteristic
45C2×C3×#67—24no—
46C2×C3×#67—42no—
47C2×C3×#67—42no—
48C22×C3×Dic3—21no—
49C2×C3×D12—22no—
50C2×C3×D12—22no—
51C2×C3×D12—21no—
52C2×C3×D12C2×C412yescomplemented
53C32×C4⋊C4—24no—
54C32×C4⋊C4—22no—
55C32×C4⋊C4D414yescomplemented
56C3×(C2×D3)⋊C4—24no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3C2×C412yescomplemented
59C2×C3×C3⋊C8—22no—
60C2×C3×C3⋊C8—22no—
61C2×C3×C3⋊C8—22no—
62#1874—31noSylow
63C22×C3×D4—31no—
64C22×C3×D4—61no—
65C23×C3×C4—22no—
66C23×C3×C4—21no—
67C23×C3×C4—21no—
68C23×C3×C4—21no—
69C23×C3×C4C2×D311yescharacteristic
70C23×C3×C4C22×C311yescharacteristic
71C22×#67—21no—
72C22×D12C22×C311yescharacteristic
73C22×C3×C8—32no—
74C3×#121—34no—
75C3×#121—62no—
76C2×C3×C4⋊C4—22no—
77C2×C3×C4⋊C4—28no—
78C2×C3×C4⋊C4—21no—
79C2×C3×C4⋊C4—21no—
80C2×C3×C4⋊C4—24no—
81C2×C3×C4⋊C4—24no—
82C2×C3×C4⋊C4—22no—
83C2×C3×C4⋊C4—31no—
84C2×C3×C4⋊C4C2×D312yes—
85C2×C3×C4⋊C4C22×C312yes—
86C2×C3×C22⋊C4—61no—
87#930—22no—
88#930C3×C414yescomplemented
89C2×(C2×D3)⋊C4—21no—
90C2×C4⋊Dic3C22×C311yescharacteristic
91C22×C3⋊C8C22×C312yes—
92C3×#102—64no—
93C3×C22⋊C8—62no—
94#830—22no—
95#809—24no—
96C23×C32—21no—
97C23×C32—21no—
98C23×C32—21no—
99C23×C32—21no—
100C23×C32C22⋊C412yes—
101C23×C32D812yes—
102C23×C32SD1612yes—
103C23×C32C2×D411yescharacteristic
104C22×C3×D3—22no—
105C22×C3×D3—41no—
106C22×C3×D3—41no—
107C22×C3×D3—41no—
108C22×C3×D3—41no—
109C22×C3×D3—41no—
110C22×C3×D3—41no—
111C2×C32×C4—21no—
112C2×C32×C4—21no—
113C2×C32×C4—24no—
114C2×C32×C4—24no—
115C2×C32×C4—24no—
116C2×C32×C4—48no—
117C2×C32×C4—42no—
118C2×C32×C4—42no—
119C2×C32×C4C22⋊C412yes—
120C2×C32×C4C22×C411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D412yes—
123C2×C32×C4#4112yes—
124C3×#67—48no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—41no—
127C2×C3×Dic3—41no—
128C3×D12—24no—
129C3×D12—42no—
130C3×C3⋊C8—42no—
131C2×#121—31no—
132C22×C4⋊C4C3×D311yescharacteristic, complemented
133C2×#102—32no—
134C2×C22⋊C8—31no—
135#340—32no—
136C24×C3—21no—
137C24×C3—61no—
138C24×C3#6711yescharacteristic
139C24×C3C3×D411yescharacteristic
140C23×D3—21no—
141C2×C3×D4—32no—
142C2×C3×D4—64no—
143C2×C3×D4—61no—
144C2×C3×D4—62no—
145C2×C3×D4—62no—
146C2×C3×D4—122no—
147C2×C3×D4—122no—
148C22×C3×C4—24no—
149C22×C3×C4—24no—
150C22×C3×C4—22no—
151C22×C3×C4—22no—
152C22×C3×C4—22no—
153C22×C3×C4—22no—
154C22×C3×C4—28no—
155C22×C3×C4—24no—
156C22×C3×C4—24no—
157C22×C3×C4—24no—
158C22×C3×C4—22no—
159C22×C3×C4—22no—
160C22×C3×C4—22no—
161C22×C3×C4—22no—
162C22×C3×C4—21no—
163C22×C3×C4—21no—
164C22×C3×C4—44no—
165C22×C3×C4—42no—
166C22×C3×C4—42no—
167C22×C3×C4—44no—
168C22×C3×C4—42no—
169C22×C3×C4—42no—
170C22×C3×C4—61no—
171C22×C3×C4C4×D312yes—
172C22×C3×C4D1212yes—
173C22×C3×C4#6711yescharacteristic
174C22×C3×C4C2×C3×C412yes—
175C22×C3×C4C3×D412yes—
176C22×C3×C4C3×D411yescharacteristic
177C22×C3×C4C22×D311yescharacteristic
178C22×C3×C4C23×C311yescharacteristic
179C2×#67—24no—
180C2×#67—42no—
181C2×#67—42no—
182C22×Dic3—21no—
183C2×D12—22no—
184C2×D12—22no—
185C2×D12—21no—
186C2×D12C2×C3×C412yescomplemented
187C2×C3×C8—62no—
188C2×C3×C8—62no—
189C2×C3×C8—62no—
190C3×C4⋊C4—28no—
191C3×C4⋊C4—24no—
192C3×C4⋊C4—24no—
193C3×C4⋊C4—24no—
194C3×C4⋊C4—22no—
195C3×C4⋊C4—22no—
196C3×C4⋊C4—24no—
197C3×C4⋊C4—32no—
198C3×C4⋊C4—61no—
199C3×C4⋊C4#6714yescomplemented
200C3×C4⋊C4C3×D414yescomplemented
201C3×C22⋊C4—64no—
202(C2×D3)⋊C4—24no—
203C4⋊Dic3—21no—
204C4⋊Dic3C2×C3×C412yescomplemented
205C2×C3⋊C8—22no—
206C2×C3⋊C8—22no—
207C2×C3⋊C8—22no—
208C22×C32—22no—
209C22×C32—22no—
210C22×C32—22no—
211C22×C32—22no—
212C22×C32—22no—
213C22×C32—22no—
214C22×C32#10214yescomplemented
215C22×C32C2×C22⋊C411yescharacteristic
216C22×C32#12011yescharacteristic
217C22×C32#12311yescharacteristic
218C22×C32C2×D811yescharacteristic
219C22×C32C2×SD1611yescharacteristic
220C22×C32AGL(1,ℤ/8)11yescharacteristic
221C22×C32#13711yescharacteristic
222C2×C3×D3—42no—
223C2×C3×D3—42no—
224C2×C3×D3—42no—
225C2×C3×D3—81no—
226C2×C3×D3—81no—
227C2×C3×D3—81no—
228C2×C3×D3—81no—
229C32×C4—22no—
230C32×C4—44no—
231C32×C4C4×D412yes—
232C32×C4#12112yes—
233C3×Dic3—42no—
234C22×D4—31no—
235C22×D4—61no—
236C23×C4—21no—
237C23×C4C2×C3×D311yescharacteristic
238C22×C8—32no—
239#121—34no—
240#121—62no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—24no—
243C2×C4⋊C4—31no—
244C2×C4⋊C4C2×C3×D312yes—
245C2×C22⋊C4—61no—
246#102—64no—
247C22⋊C8—62no—
248C23×C3—22no—
249C23×C3—22no—
250C23×C3—22no—
251C23×C3—22no—
252C23×C3—21no—
253C23×C3—21no—
254C23×C3—21no—
255C23×C3—21no—
256C23×C3—21no—
257C23×C3—21no—
258C23×C3—21no—
259C23×C3—21no—
260C23×C3—22no—
261C23×C3—22no—
262C23×C3—22no—
263C23×C3—21no—
264C23×C3—62no—
265C23×C3—121no—
266C23×C3—121no—
267C23×C3—121no—
268C23×C3—121no—
269C23×C3—121no—
270C23×C3—121no—
271C23×C3(C2×D3)⋊C412yes—
272C23×C3#21312yes—
273C23×C3#21512yes—
274C23×C3C3×C22⋊C412yes—
275C23×C3C3×D812yes—
276C23×C3C3×SD1612yes—
277C23×C3C2×#6711yescharacteristic
278C23×C3C2×C3×D411yescharacteristic
279C22×D3—22no—
280C22×D3—41no—
281C22×D3—41no—
282C22×D3—41no—
283C22×D3—41no—
284C22×D3—41no—
285C22×D3—41no—
286C3×D4—64no—
287C3×D4—128no—
288C3×D4—122no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—28no—
292C2×C3×C4—28no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—24no—
298C2×C3×C4—24no—
299C2×C3×C4—24no—
300C2×C3×C4—24no—
301C2×C3×C4—28no—
302C2×C3×C4—24no—
303C2×C3×C4—24no—
304C2×C3×C4—22no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—416no—
310C2×C3×C4—48no—
311C2×C3×C4—48no—
312C2×C3×C4—44no—
313C2×C3×C4—44no—
314C2×C3×C4—42no—
315C2×C3×C4—42no—
316C2×C3×C4—42no—
317C2×C3×C4—42no—
318C2×C3×C4—62no—
319C2×C3×C4—121no—
320C2×C3×C4—121no—
321C2×C3×C4(C2×D3)⋊C412yes—
322C2×C3×C4C3×C22⋊C412yes—
323C2×C3×C4C2×C4×D311yescharacteristic
324C2×C3×C4C2×D1211yescharacteristic
325C2×C3×C4#23512yes—
326C2×C3×C4C2×#6712yes—
327C2×C3×C4C22×C3×C411yescharacteristic
328C2×C3×C4C2×C3×D411yescharacteristic
329C2×C3×C4C2×C3×D412yes—
330C2×C3×C4C3×#4112yes—
331#67—48no—
332C2×Dic3—22no—
333C2×Dic3—41no—
334C2×Dic3—41no—
335D12—24no—
336D12—42no—
337C3×C8—122no—
338C3⋊C8—42no—
339C2×C32—24no—
340C2×C32#38611yescharacteristic
341C2×C32C2×#10211yescharacteristic
342C2×C32#41711yescharacteristic
343C2×C32#44711yescharacteristic
344C2×C32#44811yescharacteristic
345C2×C32#48011yescharacteristic
346C2×C32#48111yescharacteristic
347C3×D3—82no—
348C24—61no—
349C24C3×#6711yescharacteristic
350C2×D4—32no—
351C2×D4—64no—
352C2×D4—61no—
353C2×D4—62no—
354C2×D4—62no—
355C2×D4—122no—
356C2×D4—122no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—24no—
360C22×C4—22no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—61no—
364C22×C4C3×C4×D312yes—
365C22×C4C3×D1212yes—
366C22×C4C3×#6711yescharacteristic
367C22×C4C22×C3×D311yescharacteristic
368C2×C8—62no—
369C2×C8—62no—
370C2×C8—62no—
371C4⋊C4—24no—
372C4⋊C4—22no—
373C4⋊C4—32no—
374C4⋊C4—61no—
375C4⋊C4C3×#6714yescomplemented
376C22⋊C4—64no—
377C22×C3—24no—
378C22×C3—24no—
379C22×C3—24no—
380C22×C3—24no—
381C22×C3—24no—
382C22×C3—24no—
383C22×C3—22no—
384C22×C3—22no—
385C22×C3—22no—
386C22×C3—22no—
387C22×C3—22no—
388C22×C3—22no—
389C22×C3—22no—
390C22×C3—22no—
391C22×C3—22no—
392C22×C3—22no—
393C22×C3—22no—
394C22×C3—22no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—24no—
403C22×C3—122no—
404C22×C3—122no—
405C22×C3—122no—
406C22×C3—241no—
407C22×C3—241no—
408C22×C3—241no—
409C22×C3—241no—
410C22×C3#80914yescomplemented
411C22×C3C3×#10214yescomplemented
412C22×C3C2×(C2×D3)⋊C411yescharacteristic
413C22×C3#92911yescharacteristic
414C22×C3C2×#21311yescharacteristic
415C22×C3#93211yescharacteristic
416C22×C3C2×#21511yescharacteristic
417C22×C3#94211yescharacteristic
418C22×C3#95311yescharacteristic
419C22×C3C2×C3×C22⋊C411yescharacteristic
420C22×C3C3×#12011yescharacteristic
421C22×C3C3×#12311yescharacteristic
422C22×C3C2×C3×D811yescharacteristic
423C22×C3C2×C3×SD1611yescharacteristic
424C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
425C22×C3C3×#13711yescharacteristic
426C2×D3—42no—
427C2×D3—42no—
428C2×D3—42no—
429C2×D3—81no—
430C2×D3—81no—
431C2×D3—81no—
432C2×D3—81no—
433C3×C4—24no—
434C3×C4—22no—
435C3×C4—22no—
436C3×C4—22no—
437C3×C4—22no—
438C3×C4—48no—
439C3×C4—44no—
440C3×C4—44no—
441C3×C4—122no—
442C3×C4C4×#6712yes—
443C3×C4#93012yes—
444C3×C4C3×C4×D412yes—
445C3×C4C3×#12112yes—
446Dic3—42no—
447C32#187411yescharacteristic, complemented, Sylow
448C23—21no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—62no—
453C23—121no—
454C23—121no—
455C23—121no—
456C23—121no—
457C23—121no—
458C23—121no—
459C23C3×(C2×D3)⋊C412yes—
460C23C3×#21312yes—
461C23C3×#21512yes—
462C23C2×C3×#6711yescharacteristic
463D4—64no—
464D4—128no—
465D4—122no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—48no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—62no—
475C2×C4—121no—
476C2×C4—121no—
477C2×C4C3×(C2×D3)⋊C412yes—
478C2×C4C2×C3×C4×D311yescharacteristic
479C2×C4C2×C3×D1211yescharacteristic
480C2×C4C3×#23512yes—
481C2×C4C2×C3×#6712yes—
482C8—122no—
483C2×C3—28no—
484C2×C3—24no—
485C2×C3—24no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—242no—
494C2×C3C2×#80911yescharacteristic
495C2×C3#496611yescharacteristic
496C2×C3#496711yescharacteristic
497C2×C3#496811yescharacteristic
498C2×C3#521311yescharacteristic
499C2×C3#521711yescharacteristic
500C2×C3#522711yescharacteristic
501C2×C3C3×#38611yescharacteristic
502C2×C3C2×C3×#10211yescharacteristic
503C2×C3C3×#41711yescharacteristic
504C2×C3C3×#44711yescharacteristic
505C2×C3C3×#44811yescharacteristic
506C2×C3C3×#48011yescharacteristic
507C2×C3C3×#48111yescharacteristic
508D3—82no—
509C22—22no—
510C22—22no—
511C22—22no—
512C22—22no—
513C22—22no—
514C22—22no—
515C22—122no—
516C22—122no—
517C22—122no—
518C22—241no—
519C22—241no—
520C22—241no—
521C22—241no—
522C22C3×#80914yescomplemented
523C22C2×C3×(C2×D3)⋊C411yescharacteristic
524C22C3×#92911yescharacteristic
525C22C2×C3×#21311yescharacteristic
526C22C3×#93211yescharacteristic
527C22C2×C3×#21511yescharacteristic
528C22C3×#94211yescharacteristic
529C22C3×#95311yescharacteristic
530C4—22no—
531C4—44no—
532C4—122no—
533C4C3×C4×#6712yes—
534C4C3×#93012yes—
535C3—21no—
536C3#7156011yescharacteristic, direct product factor
537C3C3×#187411yescharacteristic, complemented
538C2—24no—
539C2—242no—
540C2C2×C3×#80911yescharacteristic
541C2C3×#496611yescharacteristic
542C2C3×#496711yescharacteristic
543C2C3×#496811yescharacteristic
544C2C3×#521311yescharacteristic
545C2C3×#521711yescharacteristic
546C2C3×#522711yescharacteristic
subgroupG/H
centerC23×C3C2×#67
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC22×C32×C4⋊C4C2
socleC23×C32C2×D4
prime radicalC2×C3×#930C2
cosocleC22×C3×C4C23×C3
hypercenterC22×C3×C4⋊C4D3
hypocenterC3C3×#1874
LCSG ▷ C2×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
1. C22×C32×C4⋊C4C2semidirect
3. C2×C3×#830C2semidirect
4. C2×C3×#809C2semidirect
5. C3×#4529C2semidirect
7. #71560C3direct (N × H)
16. C3×#930C4semidirect
24. C22×C3×C4⋊C4D3semidirect
25. C22×C3×C4⋊C4C2×C3semidirect
29. C2×#830C2×C3semidirect
30. C2×#809C2×C3semidirect
32. #4529C2×C3semidirect
52. C2×C3×D12C2×C4semidirect
55. C32×C4⋊C4D4semidirect
58. C3×C4⋊Dic3C2×C4semidirect
88. #930C3×C4semidirect
132. C22×C4⋊C4C3×D3semidirect
186. C2×D12C2×C3×C4semidirect
199. C3×C4⋊C4#67semidirect
200. C3×C4⋊C4C3×D4semidirect
204. C4⋊Dic3C2×C3×C4semidirect
214. C22×C32#102semidirect
375. C4⋊C4C3×#67semidirect
410. C22×C3#809semidirect
411. C22×C3C3×#102semidirect
447. C32#1874semidirect
522. C22C3×#809semidirect
536. C3#71560direct (N × H)
537. C3C3×#1874semidirect

Maximal subgroups

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

subgroupindex
C22×C32×C4⋊C42
C2×C3×#9302
C2×C3×#8302
C2×C3×#8092
C3×#45292
C3×#18743
#715603