Finite Group Databasebeta

← C3×#69496 #11788227

Subgroups — C3×#69496 #11788227

Order 1152.

1449 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#953C211yesmaximal, characteristic
2C22×C3×#217C211yesmaximal, characteristic, complemented
3C32×#379C211yesmaximal, characteristic, complemented
4C2×C3×#806C212yesmaximal, complemented
5C3×#4527C212yesmaximal, complemented
6C3×#1898—31nomaximal
7#69496C311yesmaximal, characteristic, direct product factor
8C25×C32C2211yescharacteristic
9C22×C3×#67C412yescomplemented
10C22×C3×#67C2211yescharacteristic
11C23×C3×Dic3—21no—
12C2×C32×C22⋊C4—22no—
13C2×C32×C22⋊C4C2212yes—
14C3×#953—21no—
15C3×#953—22no—
16C3×#953—21no—
17C2×C3×#217—24no—
18C2×C3×#217—21no—
19C2×C3×#217C412yescomplemented
20C2×C3×#217C2211yescharacteristic
21C2×C3×#217C2212yes—
22C3×#806—24no—
23C2×C3×#120—31no—
24C22×C3×C22⋊C4—31no—
25C2×#953C2×C311yescharacteristic
26C22×#217C2×C311yescharacteristic, complemented
27C2×C3×#99—32no—
28C3×#379—21no—
29C3×#379D311yescharacteristic, complemented
30C3×#379C2×C311yescharacteristic, complemented
31C2×#806C2×C312yescomplemented
32C3×#342—32no—
33#4527C2×C312yescomplemented
34C24×C32—22no—
35C24×C32—22no—
36C24×C32—44no—
37C24×C32C2×C412yes—
38C24×C32D411yescharacteristic
39C24×C32D412yes—
40C24×C32D411yescharacteristic
41C24×C32C2311yescharacteristic
42C23×C3×D3C2×C411yescharacteristic, complemented
43C22×C32×C4—22no—
44C2×C3×#67—22no—
45C2×C3×#67—22no—
46C2×C3×#67—21no—
47C2×C3×#67—21no—
48C2×C3×#67—22no—
49C2×C3×#67—22no—
50C2×C3×#67—44no—
51C22×C3×Dic3—24no—
52C22×C3×Dic3—22no—
53C22×C3×Dic3—44no—
54C22×C3×Dic3C2×C411yescharacteristic, complemented
55C22×C3×Dic3C2×C412yescomplemented
56C32×C22⋊C4—22no—
57C32×C22⋊C4—22no—
58C32×C22⋊C4—44no—
59C3×#217—24no—
60C3×#217—22no—
61C3×#217—22no—
62C3×#217—22no—
63C3×#217—21no—
64C3×#217—21no—
65C3×#217D414yescomplemented
66#1898—31noSylow
67C25×C3—21no—
68C25×C3C2×D311yescharacteristic
69C25×C3C22×C311yescharacteristic
70C22×C3×D4—31no—
71C22×C3×D4—32no—
72C23×C3×C4—61no—
73C22×#67C3×C412yescomplemented
74C22×#67C22×C311yescharacteristic
75C23×Dic3—21no—
76C3×#120—61no—
77C3×#120—61no—
78C3×#120—62no—
79C2×C3×C22⋊C4—24no—
80C2×C3×C22⋊C4—22no—
81C2×C3×C22⋊C4—22no—
82C2×C3×C22⋊C4—22no—
83C2×C3×C22⋊C4—32no—
84C2×C3×C22⋊C4—32no—
85C2×C3×C22⋊C4—31no—
86C2×C3×C22⋊C4—64no—
87C2×C3×C22⋊C4—61no—
88C2×C3×C22⋊C4C2×D312yes—
89C2×C3×C22⋊C4C22×C312yes—
90#953—21no—
91#953—21no—
92#953—22no—
93C2×#217—21no—
94C2×#217—24no—
95C2×#217C3×C412yescomplemented
96C2×#217C22×C311yescharacteristic
97C2×#217C22×C312yes—
98C3×#99—64no—
99#806—24no—
100C23×C32—24no—
101C23×C32—24no—
102C23×C32—21no—
103C23×C32—21no—
104C23×C32—24no—
105C23×C32—24no—
106C23×C32—21no—
107C23×C32—24no—
108C23×C32—21no—
109C23×C32—42no—
110C23×C32—42no—
111C23×C32—42no—
112C23×C32—42no—
113C23×C32—48no—
114C23×C32—48no—
115C23×C32C22⋊C412yes—
116C23×C32C22⋊C412yes—
117C23×C32C22×C411yescharacteristic
118C23×C32C2×D411yescharacteristic
119C23×C32C2×D412yes—
120C23×C32C2×D411yescharacteristic
121C23×C32#4112yes—
122C22×C3×D3—21no—
123C22×C3×D3—22no—
124C22×C3×D3—42no—
125C2×C32×C4—44no—
126C2×C32×C4—42no—
127C3×#67—44no—
128C3×#67—44no—
129C3×#67—41no—
130C3×#67—42no—
131C3×#67—41no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—24no—
136C2×C3×Dic3—48no—
137C2×C3×Dic3—44no—
138C2×C3×Dic3—42no—
139C2×#120—31no—
140C22×C22⋊C4—31no—
141C2×#99—32no—
142#379C3×D311yescharacteristic, complemented
143#342—32no—
144C24×C3—22no—
145C24×C3—22no—
146C24×C3—22no—
147C24×C3—22no—
148C24×C3—22no—
149C24×C3—21no—
150C24×C3—21no—
151C24×C3—22no—
152C24×C3—21no—
153C24×C3—31no—
154C24×C3—42no—
155C24×C3—42no—
156C24×C3—44no—
157C24×C3—44no—
158C24×C3—48no—
159C24×C3C4×D312yes—
160C24×C3D1211yescharacteristic
161C24×C3D1211yescharacteristic
162C24×C3#6712yes—
163C24×C3C2×C3×C412yes—
164C24×C3C3×D411yescharacteristic
165C24×C3C3×D411yescharacteristic
166C24×C3C3×D412yes—
167C24×C3C22×D311yescharacteristic
168C24×C3C23×C311yescharacteristic
169C23×D3C2×C3×C411yescharacteristic, complemented
170C2×C3×D4—62no—
171C2×C3×D4—62no—
172C2×C3×D4—61no—
173C2×C3×D4—62no—
174C2×C3×D4—62no—
175C2×C3×D4—61no—
176C2×C3×D4—124no—
177C22×C3×C4—24no—
178C22×C3×C4—22no—
179C22×C3×C4—22no—
180C22×C3×C4—31no—
181C22×C3×C4—32no—
182C22×C3×C4—64no—
183C22×C3×C4—62no—
184C22×C3×C4—124no—
185C2×#67—22no—
186C2×#67—22no—
187C2×#67—22no—
188C2×#67—21no—
189C2×#67—21no—
190C2×#67—22no—
191C2×#67—44no—
192C22×Dic3—24no—
193C22×Dic3—22no—
194C22×Dic3—44no—
195C22×Dic3C2×C3×C411yescharacteristic, complemented
196C22×Dic3C2×C3×C412yescomplemented
197C3×C22⋊C4—22no—
198C3×C22⋊C4—22no—
199C3×C22⋊C4—22no—
200C3×C22⋊C4—22no—
201C3×C22⋊C4—34no—
202C3×C22⋊C4—42no—
203C3×C22⋊C4—42no—
204C3×C22⋊C4—48no—
205C3×C22⋊C4—44no—
206C3×C22⋊C4—44no—
207C3×C22⋊C4—64no—
208C3×C22⋊C4—62no—
209C3×C22⋊C4—62no—
210C3×C22⋊C4—61no—
211C3×C22⋊C4—62no—
212C3×C22⋊C4—61no—
213#217—24no—
214#217—22no—
215#217—22no—
216#217—22no—
217#217—21no—
218#217—21no—
219#217C3×D414yescomplemented
220C22×C32—22no—
221C22×C32—22no—
222C22×C32—24no—
223C22×C32—24no—
224C22×C32—22no—
225C22×C32—22no—
226C22×C32—22no—
227C22×C32—22no—
228C22×C32—22no—
229C22×C32—22no—
230C22×C32—42no—
231C22×C32—42no—
232C22×C32—48no—
233C22×C32—48no—
234C22×C32—42no—
235C22×C32—42no—
236C22×C32#9914yescomplemented
237C22×C32C2×C22⋊C411yescharacteristic
238C22×C32C4×D412yes—
239C22×C32#12011yescharacteristic
240C22×C32#12112yes—
241C22×C32#12311yescharacteristic
242C2×C3×D3—41no—
243C2×C3×D3—42no—
244C2×C3×D3—82no—
245C32×C4—82no—
246C3×Dic3—44no—
247C3×Dic3—41no—
248C3×Dic3—42no—
249C25C2×C3×D311yescharacteristic
250C22×D4—31no—
251C22×D4—32no—
252C23×C4—61no—
253#120—61no—
254#120—61no—
255#120—62no—
256C2×C22⋊C4—22no—
257C2×C22⋊C4—32no—
258C2×C22⋊C4—32no—
259C2×C22⋊C4—31no—
260C2×C22⋊C4—64no—
261C2×C22⋊C4—61no—
262C2×C22⋊C4C2×C3×D312yes—
263#99—64no—
264C23×C3—24no—
265C23×C3—24no—
266C23×C3—21no—
267C23×C3—21no—
268C23×C3—21no—
269C23×C3—21no—
270C23×C3—28no—
271C23×C3—24no—
272C23×C3—24no—
273C23×C3—24no—
274C23×C3—24no—
275C23×C3—24no—
276C23×C3—21no—
277C23×C3—21no—
278C23×C3—24no—
279C23×C3—24no—
280C23×C3—21no—
281C23×C3—24no—
282C23×C3—21no—
283C23×C3—22no—
284C23×C3—22no—
285C23×C3—21no—
286C23×C3—21no—
287C23×C3—22no—
288C23×C3—22no—
289C23×C3—21no—
290C23×C3—41no—
291C23×C3—41no—
292C23×C3—44no—
293C23×C3—44no—
294C23×C3—41no—
295C23×C3—41no—
296C23×C3—44no—
297C23×C3—44no—
298C23×C3—42no—
299C23×C3—42no—
300C23×C3—42no—
301C23×C3—42no—
302C23×C3—42no—
303C23×C3—42no—
304C23×C3—42no—
305C23×C3—42no—
306C23×C3—44no—
307C23×C3—44no—
308C23×C3—44no—
309C23×C3—44no—
310C23×C3—48no—
311C23×C3—48no—
312C23×C3—48no—
313C23×C3—48no—
314C23×C3—416no—
315C23×C3—416no—
316C23×C3—61no—
317C23×C3—62no—
318C23×C3—122no—
319C23×C3(C2×D3)⋊C412yes—
320C23×C3(C2×D3)⋊C412yes—
321C23×C3C3×C22⋊C412yes—
322C23×C3C3×C22⋊C412yes—
323C23×C3C2×C4×D311yescharacteristic
324C23×C3C2×D1211yescharacteristic
325C23×C3D3×D412yes—
326C23×C3#23712yes—
327C23×C3C2×#6711yescharacteristic
328C23×C3C22×C3×C411yescharacteristic
329C23×C3C2×C3×D411yescharacteristic
330C23×C3C2×C3×D412yes—
331C23×C3C2×C3×D411yescharacteristic
332C23×C3C3×#4112yes—
333C22×D3—21no—
334C22×D3—22no—
335C22×D3—42no—
336C3×D4—124no—
337C3×D4—124no—
338C3×D4—121no—
339C3×D4—121no—
340C3×D4—122no—
341C2×C3×C4—48no—
342C2×C3×C4—44no—
343C2×C3×C4—44no—
344C2×C3×C4—44no—
345C2×C3×C4—42no—
346C2×C3×C4—42no—
347C2×C3×C4—62no—
348C2×C3×C4—64no—
349C2×C3×C4—62no—
350C2×C3×C4—61no—
351C2×C3×C4—128no—
352C2×C3×C4—124no—
353C2×C3×C4—122no—
354#67—44no—
355#67—44no—
356#67—41no—
357#67—42no—
358#67—41no—
359C2×Dic3—21no—
360C2×Dic3—22no—
361C2×Dic3—22no—
362C2×Dic3—24no—
363C2×Dic3—48no—
364C2×Dic3—44no—
365C2×Dic3—42no—
366C2×C32—22no—
367C2×C32—21no—
368C2×C32—22no—
369C2×C32—24no—
370C2×C32—21no—
371C2×C32—42no—
372C2×C32#38611yescharacteristic
373C2×C32C2×#9912yes—
374C3×D3—81no—
375C24—22no—
376C24—22no—
377C24—31no—
378C24—44no—
379C24C3×C4×D312yes—
380C24C3×D1211yescharacteristic
381C24C3×D1211yescharacteristic
382C24C3×#6712yes—
383C24C22×C3×D311yescharacteristic
384C2×D4—62no—
385C2×D4—62no—
386C2×D4—61no—
387C2×D4—62no—
388C2×D4—62no—
389C2×D4—61no—
390C2×D4—124no—
391C22×C4—22no—
392C22×C4—31no—
393C22×C4—32no—
394C22×C4—64no—
395C22×C4—62no—
396C22×C4—124no—
397C22⋊C4—22no—
398C22⋊C4—22no—
399C22⋊C4—34no—
400C22⋊C4—44no—
401C22⋊C4—64no—
402C22⋊C4—62no—
403C22⋊C4—62no—
404C22⋊C4—61no—
405C22⋊C4—62no—
406C22⋊C4—61no—
407C22×C3—24no—
408C22×C3—24no—
409C22×C3—24no—
410C22×C3—24no—
411C22×C3—24no—
412C22×C3—22no—
413C22×C3—22no—
414C22×C3—22no—
415C22×C3—22no—
416C22×C3—22no—
417C22×C3—22no—
418C22×C3—22no—
419C22×C3—22no—
420C22×C3—22no—
421C22×C3—22no—
422C22×C3—24no—
423C22×C3—22no—
424C22×C3—22no—
425C22×C3—22no—
426C22×C3—22no—
427C22×C3—22no—
428C22×C3—22no—
429C22×C3—22no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—22no—
434C22×C3—24no—
435C22×C3—42no—
436C22×C3—42no—
437C22×C3—42no—
438C22×C3—42no—
439C22×C3—42no—
440C22×C3—42no—
441C22×C3—44no—
442C22×C3—44no—
443C22×C3—42no—
444C22×C3—42no—
445C22×C3—42no—
446C22×C3—42no—
447C22×C3—48no—
448C22×C3—48no—
449C22×C3—48no—
450C22×C3—48no—
451C22×C3—44no—
452C22×C3—44no—
453C22×C3—416no—
454C22×C3—42no—
455C22×C3—42no—
456C22×C3—42no—
457C22×C3—42no—
458C22×C3—416no—
459C22×C3—44no—
460C22×C3—44no—
461C22×C3—122no—
462C22×C3—121no—
463C22×C3—242no—
464C22×C3#80614yescomplemented
465C22×C3C3×#9914yescomplemented
466C22×C3#67⋊C412yes—
467C22×C3#88211yescharacteristic
468C22×C3#88611yescharacteristic
469C22×C3C2×(C2×D3)⋊C411yescharacteristic
470C22×C3#93912yes—
471C22×C3C2×C3×C22⋊C411yescharacteristic
472C22×C3C3×C4×D412yes—
473C22×C3C3×#12011yescharacteristic
474C22×C3C3×#12112yes—
475C22×C3C3×#12311yescharacteristic
476C2×D3—41no—
477C2×D3—42no—
478C2×D3—82no—
479C3×C4—84no—
480C3×C4—82no—
481C3×C4—82no—
482C3×C4—124no—
483C3×C4—122no—
484C3×C4—121no—
485Dic3—44no—
486Dic3—41no—
487Dic3—42no—
488C32#189811yescharacteristic, complemented, Sylow
489C23—21no—
490C23—21no—
491C23—24no—
492C23—24no—
493C23—21no—
494C23—21no—
495C23—24no—
496C23—24no—
497C23—24no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—48no—
503C23—48no—
504C23—61no—
505C23—62no—
506C23—122no—
507C23C3×(C2×D3)⋊C412yes—
508C23C3×(C2×D3)⋊C412yes—
509C23C2×C3×C4×D311yescharacteristic
510C23C2×C3×D1211yescharacteristic
511C23C3×D3×D412yes—
512C23C3×#23712yes—
513C23C2×C3×#6711yescharacteristic
514D4—124no—
515D4—121no—
516D4—121no—
517D4—122no—
518D4—124no—
519C2×C4—44no—
520C2×C4—42no—
521C2×C4—62no—
522C2×C4—64no—
523C2×C4—62no—
524C2×C4—61no—
525C2×C4—128no—
526C2×C4—124no—
527C2×C4—122no—
528C2×C3—24no—
529C2×C3—22no—
530C2×C3—21no—
531C2×C3—24no—
532C2×C3—21no—
533C2×C3—22no—
534C2×C3—21no—
535C2×C3—22no—
536C2×C3—22no—
537C2×C3—24no—
538C2×C3—21no—
539C2×C3—22no—
540C2×C3—21no—
541C2×C3—41no—
542C2×C3—41no—
543C2×C3—44no—
544C2×C3—42no—
545C2×C3—44no—
546C2×C3—42no—
547C2×C3—42no—
548C2×C3—241no—
549C2×C3C2×#80612yes—
550C2×C3#495811yescharacteristic
551C2×C3C3×#38611yescharacteristic
552C2×C3C2×C3×#9912yes—
553D3—81no—
554C22—24no—
555C22—24no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—22no—
564C22—42no—
565C22—42no—
566C22—48no—
567C22—48no—
568C22—42no—
569C22—42no—
570C22—122no—
571C22—121no—
572C22—242no—
573C22C3×#80614yescomplemented
574C22C3×#67⋊C412yes—
575C22C3×#88211yescharacteristic
576C22C3×#88611yescharacteristic
577C22C2×C3×(C2×D3)⋊C411yescharacteristic
578C22C3×#93912yes—
579C4—82no—
580C4—124no—
581C4—122no—
582C4—121no—
583C3—21no—
584C3#6949611yescharacteristic, direct product factor
585C3C3×#189811yescharacteristic, complemented
586C2—22no—
587C2—21no—
588C2—21no—
589C2—24no—
590C2—22no—
591C2—42no—
592C2—241no—
593C2C2×C3×#80612yes—
594C2C3×#495811yescharacteristic
subgroupG/H
centerC22×C3C2×(C2×D3)⋊C4
commutatorC23×C3C22×C3×C4
FrattiniC24C22×C3×D3
FittingC32×#379C2
socleC22×C32C2×C22⋊C4
prime radicalC2×C3×#953C2
cosocleC24×C3C23×C3
hypercenterC3×#379D3
hypocenterC3C3×#1898
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C25×C3 ◁ C3×#379

Complements

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

NH ≅ G/Ntype
2. C22×C3×#217C2semidirect
3. C32×#379C2semidirect
4. C2×C3×#806C2semidirect
5. C3×#4527C2semidirect
7. #69496C3direct (N × H)
9. C22×C3×#67C4semidirect
19. C2×C3×#217C4semidirect
26. C22×#217C2×C3semidirect
29. C3×#379D3semidirect
30. C3×#379C2×C3semidirect
31. C2×#806C2×C3semidirect
33. #4527C2×C3semidirect
42. C23×C3×D3C2×C4semidirect
54. C22×C3×Dic3C2×C4semidirect
55. C22×C3×Dic3C2×C4semidirect
65. C3×#217D4semidirect
73. C22×#67C3×C4semidirect
95. C2×#217C3×C4semidirect
142. #379C3×D3semidirect
169. C23×D3C2×C3×C4semidirect
195. C22×Dic3C2×C3×C4semidirect
196. C22×Dic3C2×C3×C4semidirect
219. #217C3×D4semidirect
236. C22×C32#99semidirect
464. C22×C3#806semidirect
465. C22×C3C3×#99semidirect
488. C32#1898semidirect
573. C22C3×#806semidirect
584. C3#69496direct (N × H)
585. C3C3×#1898semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9532
C22×C3×#2172
C32×#3792
C2×C3×#8062
C3×#45272
C3×#18983
#694963