Finite Group Databasebeta

← C3×#70213 #11787563

Subgroups — C3×#70213 #11787563

Order 1152.

849 conjugacy classes of subgroups.

The subgroup lattice has 601 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#214C211yesmaximal, characteristic
2C2×C3×#887C211yesmaximal, characteristic, complemented
3C2×C32×#102C211yesmaximal, characteristic
4C3×#5221C211yesmaximal, characteristic
5C2×C3×#816C211yesmaximal, characteristic, complemented
6C3×#4550C211yesmaximal, characteristic, complemented
7C3×#4529C211yesmaximal, characteristic, complemented
8C3×#1880—31nomaximal
9#70213C311yesmaximal, characteristic, direct product factor
10C22×C32×D4C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C3×#217—21no—
15C2×C3×#217—21no—
16C2×C3×#214—22no—
17C2×C3×#214—22no—
18C2×C3×#214C414yescomplemented
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×Dic3⋊C4—21no—
21C2×C3×C4×Dic3—21no—
22C2×C3×C4×Dic3C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C3×#887—22no—
25C3×#887—22no—
26C32×#102—22no—
27C3×#816—22no—
28C22×C3×SD16—31no—
29C2×C3×C4×Q8—31no—
30C22×#214C2×C311yescharacteristic
31C2×#887C2×C311yescharacteristic, complemented
32C2×C3×#103—31no—
33C2×C3×#102—21no—
34C2×C3×#102D311yescharacteristic
35C2×C3×#102C2×C311yescharacteristic
36C3×#390—31no—
37#5221C2×C311yescharacteristic
38C2×#816C2×C311yescharacteristic, complemented
39C3×#340—31no—
40C3×#336—31no—
41#4550C2×C311yescharacteristic, complemented
42#4529C2×C311yescharacteristic, complemented
43C24×C32—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4—21no—
49C2×C32×D4C2×C412yes—
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
52C22×C3×Dic3—21no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3D411yescharacteristic
55C22×C3×Dic3D411yescharacteristic
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×C8—21no—
65C32×C4⋊C4—21no—
66C32×C4⋊C4D412yes—
67C3×#217—42no—
68C3×#217—42no—
69C3×#214—28no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3—21no—
72C3×Dic3⋊C4—24no—
73C3×C4×Dic3—24no—
74C3×C4×Dic3—21no—
75C3×C4×Dic3—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8C2×C412yes—
79#1880—31noSylow
80C22×C3×Q8—31no—
81C22×C3×D4—21no—
82C22×C3×D4C2×D311yescharacteristic
83C22×C3×D4C22×C311yescharacteristic
84C22×Dic6C22×C311yescharacteristic
85C2×C3×SD16—34no—
86C2×C3×SD16—62no—
87C2×C3×SD16—62no—
88C22×C3×C8—21no—
89C22×C3×C8—31no—
90C22×C3×C8C2×D311yescharacteristic
91C22×C3×C8C22×C311yescharacteristic
92C3×C4×Q8—62no—
93C3×C4×Q8—62no—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4—31no—
96C2×C3×C4⋊C4—61no—
97C2×C3×C4⋊C4C2×D311yescharacteristic
98C2×C3×C4⋊C4C22×C311yescharacteristic
99C2×C3×C22⋊C4—61no—
100C2×C3×C22⋊C4—61no—
101C2×C3×C42—31no—
102C2×C3×C42—61no—
103C2×#217—21no—
104C2×#217—21no—
105C2×#214—22no—
106C2×#214—22no—
107C2×#214C3×C414yescomplemented
108C2×C4⋊Dic3C22×C311yescharacteristic
109C2×Dic3⋊C4—21no—
110C2×C4×Dic3—21no—
111C2×C4×Dic3C22×C311yescharacteristic
112C22×C3⋊C8C22×C311yescharacteristic
113#887—22no—
114#887—22no—
115C3×#103—62no—
116C3×#102—24no—
117C3×#102—22no—
118C3×#102—22no—
119#816—22no—
120C23×C32—22no—
121C23×C32—41no—
122C23×C32—41no—
123C23×C32—41no—
124C23×C32—41no—
125C23×C32—41no—
126C23×C32—41no—
127C23×C32C2×D411yescharacteristic
128C32×D4—22no—
129C32×D4—22no—
130C32×D4—41no—
131C32×D4—41no—
132C2×C32×C4—22no—
133C2×C32×C4—41no—
134C2×C32×C4—41no—
135C2×C32×C4C22×C411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4#4111yescharacteristic
140C2×C32×C4#4111yescharacteristic
141C2×C3×Dic3—22no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3SD1612yescomplemented
153C3×Dic6—22no—
154C3×Dic6—22no—
155C3×Dic6—22no—
156C3×Dic6C22⋊C414yescomplemented
157C32×C8—41no—
158C3×C3⋊C8—22no—
159C22×SD16—31no—
160C2×C4×Q8—31no—
161C2×#103—31no—
162C2×#102C3×D311yescharacteristic
163#390—31no—
164#340—31no—
165#336—31no—
166C24×C3—21no—
167C24×C3—21no—
168C24×C3—41no—
169C2×C3×Q8—32no—
170C2×C3×Q8—32no—
171C2×C3×Q8—32no—
172C2×C3×Q8—61no—
173C2×C3×Q8—61no—
174C2×C3×Q8—61no—
175C2×C3×D4—22no—
176C2×C3×D4—22no—
177C2×C3×D4—21no—
178C2×C3×D4—21no—
179C2×C3×D4—21no—
180C2×C3×D4—21no—
181C2×C3×D4—21no—
182C2×C3×D4—21no—
183C2×C3×D4—21no—
184C2×C3×D4—21no—
185C2×C3×D4—21no—
186C2×C3×D4—21no—
187C2×C3×D4—22no—
188C2×C3×D4—41no—
189C2×C3×D4—41no—
190C2×C3×D4—41no—
191C2×C3×D4C4×D312yes—
192C2×C3×D4C2×C3×C412yes—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—31no—
197C22×C3×C4—31no—
198C22×C3×C4—41no—
199C22×C3×C4—61no—
200C22×C3×C4—61no—
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C23×C311yescharacteristic
203C22×Dic3—21no—
204C22×Dic3—21no—
205C22×Dic3C3×D411yescharacteristic
206C22×Dic3C3×D411yescharacteristic
207C2×Dic6—21no—
208C2×Dic6—21no—
209C2×Dic6—21no—
210C2×Dic6C2×C3×C412yes—
211C2×Dic6C3×D412yes—
212C2×Dic6C3×D412yes—
213C3×SD16—68no—
214C2×C3×C8—22no—
215C2×C3×C8—21no—
216C2×C3×C8—21no—
217C2×C3×C8—21no—
218C2×C3×C8—21no—
219C2×C3×C8—21no—
220C2×C3×C8—21no—
221C2×C3×C8—32no—
222C2×C3×C8—41no—
223C2×C3×C8—41no—
224C2×C3×C8—61no—
225C2×C3×C8—61no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—22no—
229C3×C4⋊C4—41no—
230C3×C4⋊C4—64no—
231C3×C4⋊C4—61no—
232C3×C4⋊C4—61no—
233C3×C4⋊C4#6712yes—
234C3×C4⋊C4C3×D412yes—
235C3×C22⋊C4—122no—
236C3×C22⋊C4—122no—
237C3×C42—64no—
238C3×C42—61no—
239C3×C42—61no—
240#217—42no—
241#217—42no—
242#214—28no—
243C4⋊Dic3—21no—
244C4⋊Dic3—21no—
245Dic3⋊C4—24no—
246C4×Dic3—24no—
247C4×Dic3—21no—
248C4×Dic3—21no—
249C2×C3⋊C8—21no—
250C2×C3⋊C8—21no—
251C2×C3⋊C8C2×C3×C412yes—
252C22×C32—42no—
253C22×C32—42no—
254C22×C32—42no—
255C22×C32—81no—
256C22×C32—81no—
257C22×C32—81no—
258C22×C32—81no—
259C22×C32C4×D411yescharacteristic
260C22×C32#12011yescharacteristic
261C22×C32#12111yescharacteristic
262C22×C32C2×SD1611yescharacteristic
263C22×C32#13511yescharacteristic
264C22×C32AGL(1,ℤ/8)11yescharacteristic
265C22×C32#13711yescharacteristic
266C32×C4—42no—
267C32×C4C2×C22⋊C411yescharacteristic
268C32×C4C4×D411yescharacteristic
269C32×C4#12111yescharacteristic
270C32×C4#12311yescharacteristic
271C3×Dic3—24no—
272C3×Dic3—22no—
273C3×Dic3—41no—
274C3×Dic3—81no—
275C22×Q8—31no—
276C22×D4C2×C3×D311yescharacteristic
277C2×SD16—34no—
278C2×SD16—62no—
279C2×SD16—62no—
280C22×C8—31no—
281C22×C8C2×C3×D311yescharacteristic
282C4×Q8—62no—
283C4×Q8—62no—
284C2×C4⋊C4—31no—
285C2×C4⋊C4—61no—
286C2×C4⋊C4C2×C3×D311yescharacteristic
287C2×C22⋊C4—61no—
288C2×C22⋊C4—61no—
289C2×C42—31no—
290C2×C42—61no—
291#103—62no—
292#102—22no—
293C23×C3—22no—
294C23×C3—22no—
295C23×C3—21no—
296C23×C3—42no—
297C23×C3—42no—
298C23×C3—42no—
299C23×C3—41no—
300C23×C3—41no—
301C23×C3—41no—
302C23×C3—41no—
303C23×C3—41no—
304C23×C3—41no—
305C23×C3—41no—
306C23×C3—41no—
307C23×C3—41no—
308C23×C3—41no—
309C23×C3—41no—
310C23×C3—41no—
311C23×C3—81no—
312C23×C3—81no—
313C23×C3—81no—
314C23×C3—81no—
315C23×C3D3×D411yescharacteristic
316C23×C3C2×C3×D411yescharacteristic
317C3×Q8—34no—
318C3×Q8—62no—
319C3×Q8—62no—
320C3×Q8—62no—
321C3×D4—24no—
322C3×D4—22no—
323C3×D4—22no—
324C3×D4—22no—
325C3×D4—22no—
326C3×D4—42no—
327C3×D4—42no—
328C3×D4—42no—
329C3×D4—41no—
330C3×D4—41no—
331C3×D4—41no—
332C3×D4—41no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—32no—
342C2×C3×C4—42no—
343C2×C3×C4—41no—
344C2×C3×C4—41no—
345C2×C3×C4—41no—
346C2×C3×C4—41no—
347C2×C3×C4—62no—
348C2×C3×C4—62no—
349C2×C3×C4—61no—
350C2×C3×C4—61no—
351C2×C3×C4—62no—
352C2×C3×C4—61no—
353C2×C3×C4—61no—
354C2×C3×C4—61no—
355C2×C3×C4—81no—
356C2×C3×C4—81no—
357C2×C3×C4—121no—
358C2×C3×C4—121no—
359C2×C3×C4—121no—
360C2×C3×C4C2×C4×D311yescharacteristic
361C2×C3×C4#23511yescharacteristic
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4#23711yescharacteristic
365C2×C3×C4C2×#6711yescharacteristic
366C2×C3×C4C22×C3×C411yescharacteristic
367C2×C3×C4C2×C3×D411yescharacteristic
368C2×C3×C4C2×C3×D411yescharacteristic
369C2×C3×C4C2×C3×D411yescharacteristic
370C2×C3×C4C3×#4111yescharacteristic
371C2×C3×C4C3×#4111yescharacteristic
372C2×Dic3—22no—
373C2×Dic3—21no—
374C2×Dic3—22no—
375C2×Dic3—22no—
376C2×Dic3—21no—
377C2×Dic3—21no—
378C2×Dic3—21no—
379C2×Dic3—21no—
380C2×Dic3—41no—
381C2×Dic3—41no—
382C2×Dic3—41no—
383C2×Dic3C3×SD1612yescomplemented
384Dic6—22no—
385Dic6—22no—
386Dic6—22no—
387Dic6C3×C22⋊C414yescomplemented
388C3×C8—42no—
389C3×C8—41no—
390C3×C8—41no—
391C3×C8—62no—
392C3⋊C8—22no—
393C2×C32—82no—
394C2×C32#38611yescharacteristic
395C2×C32C4×SD1611yescharacteristic
396C2×C32#44011yescharacteristic
397C2×C32#44811yescharacteristic
398C2×C32#44911yescharacteristic
399C2×C32#46011yescharacteristic
400C2×C32#46411yescharacteristic
401C24—21no—
402C2×Q8—32no—
403C2×Q8—32no—
404C2×Q8—32no—
405C2×Q8—61no—
406C2×Q8—61no—
407C2×Q8—61no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4C3×C4×D312yes—
414C22×C4—21no—
415C22×C4—31no—
416C22×C4—31no—
417C22×C4—61no—
418C22×C4—61no—
419C22×C4C22×C3×D311yescharacteristic
420SD16—68no—
421C2×C8—21no—
422C2×C8—21no—
423C2×C8—21no—
424C2×C8—32no—
425C2×C8—61no—
426C2×C8—61no—
427C4⋊C4—21no—
428C4⋊C4—64no—
429C4⋊C4—61no—
430C4⋊C4—61no—
431C4⋊C4C3×#6712yes—
432C22⋊C4—122no—
433C22⋊C4—122no—
434C42—64no—
435C42—61no—
436C42—61no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—44no—
445C22×C3—42no—
446C22×C3—42no—
447C22×C3—42no—
448C22×C3—42no—
449C22×C3—42no—
450C22×C3—42no—
451C22×C3—82no—
452C22×C3—82no—
453C22×C3—82no—
454C22×C3—82no—
455C22×C3—82no—
456C22×C3—82no—
457C22×C3—81no—
458C22×C3—81no—
459C22×C3—81no—
460C22×C3—81no—
461C22×C3—81no—
462C22×C3—81no—
463C22×C3—81no—
464C22×C3—81no—
465C22×C3#67⋊C411yescharacteristic
466C22×C3#88411yescharacteristic
467C22×C3#91111yescharacteristic
468C22×C3#91211yescharacteristic
469C22×C3D3×SD1611yescharacteristic
470C22×C3#91511yescharacteristic
471C22×C3#93711yescharacteristic
472C22×C3C3×C4×D411yescharacteristic
473C22×C3C3×#12011yescharacteristic
474C22×C3C3×#12111yescharacteristic
475C22×C3C2×C3×SD1611yescharacteristic
476C22×C3C3×#13511yescharacteristic
477C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
478C22×C3C3×#13711yescharacteristic
479C3×C4—21no—
480C3×C4—21no—
481C3×C4—21no—
482C3×C4—21no—
483C3×C4—42no—
484C3×C4—42no—
485C3×C4—62no—
486C3×C4—64no—
487C3×C4—82no—
488C3×C4—121no—
489C3×C4—241no—
490C3×C4D3×C22⋊C411yescharacteristic
491C3×C4#88311yescharacteristic
492C3×C4C4×#6711yescharacteristic
493C3×C4#93811yescharacteristic
494C3×C4C2×C3×C22⋊C411yescharacteristic
495C3×C4C3×C4×D411yescharacteristic
496C3×C4C3×#12111yescharacteristic
497C3×C4C3×#12311yescharacteristic
498Dic3—24no—
499Dic3—22no—
500Dic3—41no—
501Dic3—81no—
502C32#188011yescharacteristic, complemented, Sylow
503C23—22no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23C3×D3×D411yescharacteristic
511Q8—34no—
512Q8—62no—
513Q8—62no—
514Q8—62no—
515D4—22no—
516D4—22no—
517D4—41no—
518D4—41no—
519C2×C4—22no—
520C2×C4—32no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—61no—
526C2×C4—61no—
527C2×C4—62no—
528C2×C4—61no—
529C2×C4—61no—
530C2×C4—61no—
531C2×C4—121no—
532C2×C4—121no—
533C2×C4—121no—
534C2×C4C2×C3×C4×D311yescharacteristic
535C2×C4C3×#23511yescharacteristic
536C2×C4C3×D3×D411yescharacteristic
537C2×C4C3×D3×D411yescharacteristic
538C2×C4C3×#23711yescharacteristic
539C2×C4C2×C3×#6711yescharacteristic
540C8—41no—
541C8—62no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—84no—
550C2×C3—82no—
551C2×C3—82no—
552C2×C3#475711yescharacteristic
553C2×C3#475811yescharacteristic
554C2×C3#476211yescharacteristic
555C2×C3#476711yescharacteristic
556C2×C3#495611yescharacteristic
557C2×C3#515811yescharacteristic
558C2×C3#517011yescharacteristic
559C2×C3C3×#38611yescharacteristic
560C2×C3C3×C4×SD1611yescharacteristic
561C2×C3C3×#44011yescharacteristic
562C2×C3C3×#44811yescharacteristic
563C2×C3C3×#44911yescharacteristic
564C2×C3C3×#46011yescharacteristic
565C2×C3C3×#46411yescharacteristic
566C22—42no—
567C22—42no—
568C22—42no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22C3×#67⋊C411yescharacteristic
574C22C3×#88411yescharacteristic
575C22C3×#91111yescharacteristic
576C22C3×#91211yescharacteristic
577C22C3×D3×SD1611yescharacteristic
578C22C3×#91511yescharacteristic
579C22C3×#93711yescharacteristic
580C4—42no—
581C4—62no—
582C4—64no—
583C4—121no—
584C4—241no—
585C4C3×D3×C22⋊C411yescharacteristic
586C4C3×#88311yescharacteristic
587C4C3×C4×#6711yescharacteristic
588C4C3×#93811yescharacteristic
589C3—21no—
590C3#7021311yescharacteristic, direct product factor
591C3C3×#188011yescharacteristic, complemented
592C2—82no—
593C2C3×#475711yescharacteristic
594C2C3×#475811yescharacteristic
595C2C3×#476211yescharacteristic
596C2C3×#476711yescharacteristic
597C2C3×#495611yescharacteristic
598C2C3×#515811yescharacteristic
599C2C3×#517011yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#102C2
socleC23×C32C2×D4
prime radicalC22×C32×D4C22
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×#102D3
hypocenterC3C3×#1880
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×#887C2semidirect
5. C2×C3×#816C2semidirect
6. C3×#4550C2semidirect
7. C3×#4529C2semidirect
9. #70213C3direct (N × H)
18. C2×C3×#214C4semidirect
31. C2×#887C2×C3semidirect
38. C2×#816C2×C3semidirect
41. #4550C2×C3semidirect
42. #4529C2×C3semidirect
107. C2×#214C3×C4semidirect
152. C2×C3×Dic3SD16semidirect
156. C3×Dic6C22⋊C4semidirect
383. C2×Dic3C3×SD16semidirect
387. Dic6C3×C22⋊C4semidirect
502. C32#1880semidirect
590. C3#70213direct (N × H)
591. C3C3×#1880semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2142
C2×C3×#8872
C2×C32×#1022
C3×#52212
C2×C3×#8162
C3×#45502
C3×#45292
C3×#18803
#702133