Finite Group Databasebeta

← C3×#68909 #11787575

Subgroups — C3×#68909 #11787575

Order 1152.

805 conjugacy classes of subgroups.

The subgroup lattice has 581 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#204C211yesmaximal, characteristic
2C2×C3×#887C211yesmaximal, characteristic, complemented
3C3×#4988C211yesmaximal, characteristic
4C2×C3×#810C211yesmaximal, characteristic, complemented
5C2×C3×#809C211yesmaximal, characteristic
6C32×#340C211yesmaximal, characteristic, complemented
7C3×#4550C211yesmaximal, characteristic, complemented
8C3×#1880—31nomaximal
9#68909C311yesmaximal, characteristic, direct product factor
10C22×C3×D12C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×C3×(C2×D3)⋊C4—21no—
16C2×C3×(C2×D3)⋊C4—21no—
17C2×C3×Dic3⋊C4—21no—
18C2×C3×C4×Dic3—21no—
19C2×C3×C4×Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C2×C3×#204—22no—
22C2×C3×#204—22no—
23C2×C3×#204C414yescomplemented
24C3×#887—22no—
25C3×#887—22no—
26C3×#810—22no—
27C3×#809—22no—
28C22×C3×SD16—31no—
29C2×C3×C4×Q8—31no—
30C22×#204C2×C311yescharacteristic
31C2×#887C2×C311yescharacteristic, complemented
32C2×C3×#103—31no—
33C2×C3×#102—31no—
34C3×#390—31no—
35#4988C2×C311yescharacteristic
36C2×#810C2×C311yescharacteristic, complemented
37C2×#809C2×C311yescharacteristic
38C3×#340—21no—
39C3×#340D311yescharacteristic, complemented
40C3×#340C2×C311yescharacteristic, complemented
41C3×#336—31no—
42#4550C2×C311yescharacteristic, complemented
43C23×C3×D3—21no—
44C22×C32×C4—21no—
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3×Dic3—21no—
48C22×C3×Dic3D411yescharacteristic
49C22×C3×Dic3D411yescharacteristic
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12C2×C412yes—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6C2×C412yes—
60C2×C3×Dic6D412yes—
61C2×C3×Dic6D412yes—
62C2×C32×C8—21no—
63C2×C32×C8—21no—
64C2×C32×C8C2×C412yes—
65C32×C4⋊C4—21no—
66C32×C4⋊C4—21no—
67C32×C4⋊C4—21no—
68C32×C4⋊C4D412yes—
69C3×(C2×D3)⋊C4—42no—
70C3×(C2×D3)⋊C4—42no—
71C3×Dic3⋊C4—24no—
72C3×C4×Dic3—24no—
73C3×C4×Dic3—21no—
74C3×C4×Dic3—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78C3×#204—28no—
79#1880—31noSylow
80C22×C3×Q8—31no—
81C22×C3×D4—31no—
82C22×D12C22×C311yescharacteristic
83C22×Dic6C22×C311yescharacteristic
84C2×C3×SD16—34no—
85C2×C3×SD16—62no—
86C2×C3×SD16—62no—
87C22×C3×C8—21no—
88C22×C3×C8—31no—
89C22×C3×C8C2×D311yescharacteristic
90C22×C3×C8C22×C311yescharacteristic
91C3×C4×Q8—62no—
92C3×C4×Q8—62no—
93C2×C3×C4⋊C4—21no—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4—61no—
96C2×C3×C4⋊C4C2×D311yescharacteristic
97C2×C3×C4⋊C4C2×D311yescharacteristic
98C2×C3×C4⋊C4C22×C311yescharacteristic
99C2×C3×C4⋊C4C22×C311yescharacteristic
100C2×C3×C22⋊C4—61no—
101C2×C3×C22⋊C4—61no—
102C2×C3×C42—31no—
103C2×C3×C42—61no—
104C2×(C2×D3)⋊C4—21no—
105C2×(C2×D3)⋊C4—21no—
106C2×Dic3⋊C4—21no—
107C2×C4×Dic3—21no—
108C2×C4×Dic3C22×C311yescharacteristic
109C22×C3⋊C8C22×C311yescharacteristic
110C2×#204—22no—
111C2×#204—22no—
112C2×#204C3×C414yescomplemented
113#887—22no—
114#887—22no—
115C3×#103—62no—
116C3×#102—62no—
117#810—22no—
118#809—22no—
119C23×C32C2×D411yescharacteristic
120C22×C3×D3—22no—
121C22×C3×D3—41no—
122C22×C3×D3—41no—
123C22×C3×D3—41no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C22×C3×D3—41no—
127C2×C32×C4—22no—
128C2×C32×C4—41no—
129C2×C32×C4—41no—
130C2×C32×C4—41no—
131C2×C32×C4—41no—
132C2×C32×C4—41no—
133C2×C32×C4C22×C411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4#4111yescharacteristic
138C2×C32×C4#4111yescharacteristic
139C2×C3×Dic3—22no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3SD1612yescomplemented
148C3×D12—22no—
149C3×D12—22no—
150C3×D12—41no—
151C3×D12—41no—
152C3×Dic6—22no—
153C3×Dic6—22no—
154C3×Dic6—22no—
155C3×Dic6C22⋊C414yescomplemented
156C32×C8—22no—
157C3×C3⋊C8—41no—
158C22×SD16—31no—
159C2×C4×Q8—31no—
160C2×#103—31no—
161C2×#102—31no—
162#390—31no—
163#340C3×D311yescharacteristic, complemented
164#336—31no—
165C24×C3—61no—
166C23×D3—21no—
167C2×C3×Q8—32no—
168C2×C3×Q8—32no—
169C2×C3×Q8—32no—
170C2×C3×Q8—61no—
171C2×C3×Q8—61no—
172C2×C3×Q8—61no—
173C2×C3×D4—32no—
174C2×C3×D4—61no—
175C2×C3×D4—61no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C2×C3×D4—61no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—31no—
185C22×C3×C4—31no—
186C22×C3×C4—41no—
187C22×C3×C4—41no—
188C22×C3×C4—61no—
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C23×C311yescharacteristic
191C22×Dic3—21no—
192C22×Dic3C3×D411yescharacteristic
193C22×Dic3C3×D411yescharacteristic
194C2×D12—21no—
195C2×D12—21no—
196C2×D12—21no—
197C2×D12—21no—
198C2×D12—21no—
199C2×D12C2×C3×C412yes—
200C2×Dic6—21no—
201C2×Dic6—21no—
202C2×Dic6—21no—
203C2×Dic6C2×C3×C412yes—
204C2×Dic6C3×D412yes—
205C2×Dic6C3×D412yes—
206C3×SD16—68no—
207C2×C3×C8—21no—
208C2×C3×C8—21no—
209C2×C3×C8—21no—
210C2×C3×C8—21no—
211C2×C3×C8—22no—
212C2×C3×C8—41no—
213C2×C3×C8—41no—
214C2×C3×C8—61no—
215C2×C3×C8—61no—
216C2×C3×C8—61no—
217C2×C3×C8C4×D312yes—
218C2×C3×C8C2×C3×C412yes—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—22no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—22no—
227C3×C4⋊C4—41no—
228C3×C4⋊C4—41no—
229C3×C4⋊C4—64no—
230C3×C4⋊C4D1212yes—
231C3×C4⋊C4C3×D412yes—
232C3×C22⋊C4—122no—
233C3×C22⋊C4—122no—
234C3×C42—64no—
235C3×C42—61no—
236C3×C42—61no—
237(C2×D3)⋊C4—42no—
238(C2×D3)⋊C4—42no—
239Dic3⋊C4—24no—
240C4×Dic3—24no—
241C4×Dic3—21no—
242C4×Dic3—21no—
243C2×C3⋊C8—21no—
244C2×C3⋊C8—21no—
245C2×C3⋊C8—21no—
246#204—28no—
247C22×C32C4×D411yescharacteristic
248C22×C32#12011yescharacteristic
249C22×C32#12111yescharacteristic
250C22×C32C2×SD1611yescharacteristic
251C22×C32#13511yescharacteristic
252C22×C32AGL(1,ℤ/8)11yescharacteristic
253C22×C32#13711yescharacteristic
254C2×C3×D3—42no—
255C2×C3×D3—42no—
256C2×C3×D3—42no—
257C2×C3×D3—81no—
258C2×C3×D3—81no—
259C2×C3×D3—81no—
260C2×C3×D3—81no—
261C32×C4—42no—
262C32×C4—81no—
263C32×C4C2×C22⋊C411yescharacteristic
264C32×C4C4×D411yescharacteristic
265C32×C4#12111yescharacteristic
266C32×C4#12311yescharacteristic
267C3×Dic3—24no—
268C3×Dic3—22no—
269C3×Dic3—41no—
270C22×Q8—31no—
271C22×D4—31no—
272C2×SD16—34no—
273C2×SD16—62no—
274C2×SD16—62no—
275C22×C8—31no—
276C22×C8C2×C3×D311yescharacteristic
277C4×Q8—62no—
278C4×Q8—62no—
279C2×C4⋊C4—61no—
280C2×C4⋊C4C2×C3×D311yescharacteristic
281C2×C4⋊C4C2×C3×D311yescharacteristic
282C2×C22⋊C4—61no—
283C2×C22⋊C4—61no—
284C2×C42—31no—
285C2×C42—61no—
286#103—62no—
287#102—62no—
288C23×C3—21no—
289C23×C3—62no—
290C23×C3—121no—
291C23×C3—121no—
292C23×C3—121no—
293C23×C3—121no—
294C23×C3—121no—
295C23×C3—121no—
296C23×C3D3×D411yescharacteristic
297C23×C3C2×C3×D411yescharacteristic
298C22×D3—22no—
299C22×D3—41no—
300C22×D3—41no—
301C22×D3—41no—
302C22×D3—41no—
303C22×D3—41no—
304C22×D3—41no—
305C3×Q8—34no—
306C3×Q8—62no—
307C3×Q8—62no—
308C3×Q8—62no—
309C3×D4—62no—
310C3×D4—62no—
311C3×D4—121no—
312C3×D4—121no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—32no—
322C2×C3×C4—42no—
323C2×C3×C4—41no—
324C2×C3×C4—41no—
325C2×C3×C4—41no—
326C2×C3×C4—41no—
327C2×C3×C4—42no—
328C2×C3×C4—41no—
329C2×C3×C4—41no—
330C2×C3×C4—41no—
331C2×C3×C4—41no—
332C2×C3×C4—41no—
333C2×C3×C4—41no—
334C2×C3×C4—61no—
335C2×C3×C4—62no—
336C2×C3×C4—62no—
337C2×C3×C4—62no—
338C2×C3×C4—61no—
339C2×C3×C4—61no—
340C2×C3×C4—61no—
341C2×C3×C4—61no—
342C2×C3×C4—81no—
343C2×C3×C4—81no—
344C2×C3×C4—81no—
345C2×C3×C4—81no—
346C2×C3×C4C2×C4×D311yescharacteristic
347C2×C3×C4C2×D1211yescharacteristic
348C2×C3×C4#23511yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4#23911yescharacteristic
352C2×C3×C4C22×C3×C411yescharacteristic
353C2×C3×C4C2×C3×D411yescharacteristic
354C2×C3×C4C2×C3×D411yescharacteristic
355C2×C3×C4C2×C3×D411yescharacteristic
356C2×C3×C4C3×#4111yescharacteristic
357C2×C3×C4C3×#4111yescharacteristic
358C2×Dic3—22no—
359C2×Dic3—21no—
360C2×Dic3—22no—
361C2×Dic3—22no—
362C2×Dic3—21no—
363C2×Dic3—21no—
364C2×Dic3—21no—
365C2×Dic3—21no—
366C2×Dic3C3×SD1612yescomplemented
367D12—22no—
368D12—22no—
369D12—41no—
370D12—41no—
371Dic6—22no—
372Dic6—22no—
373Dic6—22no—
374Dic6C3×C22⋊C414yescomplemented
375C3×C8—22no—
376C3×C8—22no—
377C3×C8—42no—
378C3×C8—121no—
379C3⋊C8—41no—
380C2×C32#38611yescharacteristic
381C2×C32C4×SD1611yescharacteristic
382C2×C32#44011yescharacteristic
383C2×C32#44811yescharacteristic
384C2×C32#44911yescharacteristic
385C2×C32#46011yescharacteristic
386C2×C32#46411yescharacteristic
387C3×D3—82no—
388C24—61no—
389C2×Q8—32no—
390C2×Q8—32no—
391C2×Q8—32no—
392C2×Q8—61no—
393C2×Q8—61no—
394C2×Q8—61no—
395C2×D4—32no—
396C2×D4—61no—
397C2×D4—61no—
398C2×D4—61no—
399C2×D4—61no—
400C2×D4—61no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—31no—
404C22×C4—31no—
405C22×C4—61no—
406C22×C4C22×C3×D311yescharacteristic
407SD16—68no—
408C2×C8—21no—
409C2×C8—21no—
410C2×C8—61no—
411C2×C8—61no—
412C2×C8—61no—
413C2×C8C3×C4×D312yes—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—64no—
418C4⋊C4C3×D1212yes—
419C22⋊C4—122no—
420C22⋊C4—122no—
421C42—64no—
422C42—61no—
423C42—61no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—21no—
427C22×C3—21no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—122no—
432C22×C3—122no—
433C22×C3—122no—
434C22×C3—241no—
435C22×C3—241no—
436C22×C3—241no—
437C22×C3—241no—
438C22×C3#88211yescharacteristic
439C22×C3#88411yescharacteristic
440C22×C3#89311yescharacteristic
441C22×C3#91111yescharacteristic
442C22×C3D3×SD1611yescharacteristic
443C22×C3#91611yescharacteristic
444C22×C3#91811yescharacteristic
445C22×C3C3×C4×D411yescharacteristic
446C22×C3C3×#12011yescharacteristic
447C22×C3C3×#12111yescharacteristic
448C22×C3C2×C3×SD1611yescharacteristic
449C22×C3C3×#13511yescharacteristic
450C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
451C22×C3C3×#13711yescharacteristic
452C2×D3—42no—
453C2×D3—42no—
454C2×D3—42no—
455C2×D3—81no—
456C2×D3—81no—
457C2×D3—81no—
458C2×D3—81no—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—42no—
464C3×C4—42no—
465C3×C4—64no—
466C3×C4—62no—
467C3×C4—82no—
468C3×C4—82no—
469C3×C4—81no—
470C3×C4—81no—
471C3×C4—121no—
472C3×C4C4×D1211yescharacteristic
473C3×C4D3×C22⋊C411yescharacteristic
474C3×C4#89411yescharacteristic
475C3×C4#89511yescharacteristic
476C3×C4C2×C3×C22⋊C411yescharacteristic
477C3×C4C3×C4×D411yescharacteristic
478C3×C4C3×#12111yescharacteristic
479C3×C4C3×#12311yescharacteristic
480Dic3—24no—
481Dic3—22no—
482Dic3—41no—
483C32#188011yescharacteristic, complemented, Sylow
484C23—62no—
485C23—121no—
486C23—121no—
487C23—121no—
488C23—121no—
489C23—121no—
490C23—121no—
491C23C3×D3×D411yescharacteristic
492Q8—34no—
493Q8—62no—
494Q8—62no—
495Q8—62no—
496D4—62no—
497D4—62no—
498D4—121no—
499D4—121no—
500C2×C4—22no—
501C2×C4—32no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—61no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—62no—
511C2×C4—61no—
512C2×C4—61no—
513C2×C4—61no—
514C2×C4—61no—
515C2×C4C2×C3×C4×D311yescharacteristic
516C2×C4C2×C3×D1211yescharacteristic
517C2×C4C3×#23511yescharacteristic
518C2×C4C3×D3×D411yescharacteristic
519C2×C4C3×D3×D411yescharacteristic
520C2×C4C3×#23911yescharacteristic
521C8—22no—
522C8—121no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—242no—
531C2×C3#466511yescharacteristic
532C2×C3#476211yescharacteristic
533C2×C3#478111yescharacteristic
534C2×C3#479811yescharacteristic
535C2×C3#480611yescharacteristic
536C2×C3#485211yescharacteristic
537C2×C3#488911yescharacteristic
538C2×C3C3×#38611yescharacteristic
539C2×C3C3×C4×SD1611yescharacteristic
540C2×C3C3×#44011yescharacteristic
541C2×C3C3×#44811yescharacteristic
542C2×C3C3×#44911yescharacteristic
543C2×C3C3×#46011yescharacteristic
544C2×C3C3×#46411yescharacteristic
545D3—82no—
546C22—122no—
547C22—122no—
548C22—122no—
549C22—241no—
550C22—241no—
551C22—241no—
552C22—241no—
553C22C3×#88211yescharacteristic
554C22C3×#88411yescharacteristic
555C22C3×#89311yescharacteristic
556C22C3×#91111yescharacteristic
557C22C3×D3×SD1611yescharacteristic
558C22C3×#91611yescharacteristic
559C22C3×#91811yescharacteristic
560C4—42no—
561C4—64no—
562C4—62no—
563C4—81no—
564C4—121no—
565C4C3×C4×D1211yescharacteristic
566C4C3×D3×C22⋊C411yescharacteristic
567C4C3×#89411yescharacteristic
568C4C3×#89511yescharacteristic
569C3—21no—
570C3#6890911yescharacteristic, direct product factor
571C3C3×#188011yescharacteristic, complemented
572C2—242no—
573C2C3×#466511yescharacteristic
574C2C3×#476211yescharacteristic
575C2C3×#478111yescharacteristic
576C2C3×#479811yescharacteristic
577C2C3×#480611yescharacteristic
578C2C3×#485211yescharacteristic
579C2C3×#488911yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#340C2
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C3×C4C23×C3
hypercenterC3×#340D3
hypocenterC3C3×#1880
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C3×#340

Complements

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

NH ≅ G/Ntype
2. C2×C3×#887C2semidirect
4. C2×C3×#810C2semidirect
6. C32×#340C2semidirect
7. C3×#4550C2semidirect
9. #68909C3direct (N × H)
23. C2×C3×#204C4semidirect
31. C2×#887C2×C3semidirect
36. C2×#810C2×C3semidirect
39. C3×#340D3semidirect
40. C3×#340C2×C3semidirect
42. #4550C2×C3semidirect
112. C2×#204C3×C4semidirect
147. C2×C3×Dic3SD16semidirect
155. C3×Dic6C22⋊C4semidirect
163. #340C3×D3semidirect
366. C2×Dic3C3×SD16semidirect
374. Dic6C3×C22⋊C4semidirect
483. C32#1880semidirect
570. C3#68909direct (N × H)
571. C3C3×#1880semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2042
C2×C3×#8872
C3×#49882
C2×C3×#8102
C2×C3×#8092
C32×#3402
C3×#45502
C3×#18803
#689093