Finite Group Databasebeta

← C3×#79989 #11870835

Subgroups — C3×#79989 #11870835

Order 1152.

1007 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
2C3×#5600C211yesmaximal, characteristic, complemented
3C32×#447C211yesmaximal, characteristic
4C3×#5218C211yesmaximal, characteristic, complemented
5C3×#5153C212yesmaximal, complemented
6C3×Dic3×D8C212yesmaximal, complemented
7C3×#5034C211yesmaximal, characteristic, complemented
8C3×#4766C212yesmaximal, complemented
9C3×#4758C212yesmaximal, complemented
10C3×#4722C211yesmaximal, characteristic, complemented
11C3×#4718C211yesmaximal, characteristic, complemented
12C3×#3105—31nomaximal
13#79989C311yesmaximal, characteristic, direct product factor
14C22×C32×D4C2211yescharacteristic
15C23×C3×Dic3—21no—
16C2×C32×D8C2212yes—
17C32×#121C2211yescharacteristic
18C2×C3×#217—21no—
19C3×#936C2211yescharacteristic, complemented
20C3×#935—21no—
21C3×D4×Dic3—21no—
22C3×D4×Dic3—21no—
23C3×D4×Dic3—21no—
24C3×D4×Dic3C2212yes—
25C3×D4×Dic3C2212yes—
26C3×D4×Dic3C2211yescharacteristic, complemented
27C2×C3×#214C2212yes—
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C3×#924C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C3×#890C2211yescharacteristic, complemented
32C3×#887C2211yescharacteristic, complemented
33C3×#879—21no—
34C3×#877—21no—
35C32×#102C2212yes—
36C32×C22⋊C8C2211yescharacteristic
37C3×#832C2212yes—
38C3×#832C2212yescomplemented
39C3×#830C2211yescharacteristic
40C3×#818C2212yescomplemented
41C3×#816C2212yescomplemented
42C3×Dic3⋊C8C2212yescomplemented
43C3×C8×Dic3C2212yescomplemented
44C3×#808C2212yescomplemented
45C3×#529—31no—
46C2×C3×C4×D4—31no—
47C2×D4×Dic3C2×C311yescharacteristic, complemented
48#5600C2×C311yescharacteristic, complemented
49C3×#484—31no—
50C3×#481—31no—
51C3×#478—32no—
52C3×#463—32no—
53C3×#450—31no—
54C3×#447—21no—
55C3×#447D311yescharacteristic
56C3×#447C2×C311yescharacteristic
57C3×C4×SD16—32no—
58C3×C4×D8—32no—
59C3×#431—31no—
60#5218C2×C311yescharacteristic, complemented
61#5153C2×C312yescomplemented
62Dic3×D8C2×C312yescomplemented
63#5034C2×C311yescharacteristic, complemented
64#4766C2×C312yescomplemented
65#4758C2×C312yescomplemented
66#4722C2×C311yescharacteristic, complemented
67#4718C2×C311yescharacteristic, complemented
68C24×C32—21no—
69C2×C32×D4—24no—
70C2×C32×D4—21no—
71C2×C32×D4—21no—
72C2×C32×D4C2311yescharacteristic
73C2×C32×D4C2312yes—
74C22×C32×C4C2311yescharacteristic
75C22×C3×Dic3—21no—
76C22×C3×Dic3—21no—
77C22×C3×Dic3—22no—
78C22×C3×Dic3—22no—
79C22×C3×Dic3—44no—
80C22×C3×Dic3D411yescharacteristic
81C22×C3×Dic3D411yescharacteristic
82C2×C3×Dic6C2311yescharacteristic
83C32×D8—24no—
84C2×C32×C8C2312yes—
85C32×C4⋊C4C2311yescharacteristic
86C32×C22⋊C4—21no—
87C3×#217—21no—
88C3×#217—21no—
89C3×#217—21no—
90C3×#217—21no—
91C3×#217—22no—
92C3×#217—22no—
93C3×#214—24no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3—21no—
96C3×C4⋊Dic3C2311yescharacteristic
97C3×C4⋊Dic3C2312yes—
98C3×Dic3⋊C4—21no—
99C3×Dic3⋊C4—21no—
100C3×Dic3⋊C4—21no—
101C3×C4×Dic3—21no—
102C3×C4×Dic3D411yescharacteristic
103C3×C4×Dic3D411yescharacteristic
104C3×C4×Dic3C2311yescharacteristic
105C3×C4×Dic3C2311yescharacteristic
106C2×C3×C3⋊C8C2312yes—
107#3105—31noSylow
108C22×C3×D4—21no—
109C22×C3×D4C2×D311yescharacteristic
110C22×C3×D4C22×C311yescharacteristic
111C23×C3×C4—61no—
112C23×Dic3—21no—
113C2×C3×SD16—32no—
114C2×C3×D8—22no—
115C2×C3×D8C2×D312yes—
116C2×C3×D8C22×C312yes—
117C3×#126—61no—
118C3×#125—31no—
119C3×#124—31no—
120C3×#123—61no—
121C3×C22⋊Q8—31no—
122C3×#121—21no—
123C3×#121C2×D311yescharacteristic
124C3×#121C22×C311yescharacteristic
125C3×C4×Q8—31no—
126C3×C4×D4—32no—
127C3×C4×D4—32no—
128C3×C4×D4—31no—
129C3×C4×D4—61no—
130C3×C4×D4—61no—
131C3×C4×D4—61no—
132C3×#117—61no—
133C2×C3×C4⋊C4—31no—
134C2×C3×C22⋊C4—61no—
135C2×C3×C42—31no—
136C2×#217—21no—
137#936C22×C311yescharacteristic, complemented
138#935—21no—
139D4×Dic3—21no—
140D4×Dic3—21no—
141D4×Dic3—21no—
142D4×Dic3C22×C312yes—
143D4×Dic3C22×C312yes—
144D4×Dic3C22×C311yescharacteristic, complemented
145C2×#214C22×C312yes—
146C2×C4⋊Dic3C22×C311yescharacteristic
147#924C22×C311yescharacteristic
148C2×C4×Dic3C22×C311yescharacteristic
149#890C22×C311yescharacteristic, complemented
150#887C22×C311yescharacteristic, complemented
151#879—21no—
152#877—21no—
153C3×#107—32no—
154C3×#106—32no—
155C3×C4⋊C8—32no—
156C3×#103—32no—
157C3×#102—22no—
158C3×#102—32no—
159C3×#102—32no—
160C3×#102C2×D312yes—
161C3×#102C22×C312yes—
162C3×C22⋊C8—21no—
163C3×C22⋊C8—31no—
164C3×C22⋊C8C2×D311yescharacteristic
165C3×C22⋊C8C22×C311yescharacteristic
166C3×C4×C8—32no—
167#832C22×C312yes—
168#832C22×C312yescomplemented
169#830C22×C311yescharacteristic
170#818C22×C312yescomplemented
171#816C22×C312yescomplemented
172Dic3⋊C8C22×C312yescomplemented
173C8×Dic3C22×C312yescomplemented
174#808C22×C312yescomplemented
175C23×C32—24no—
176C23×C32—22no—
177C23×C32—21no—
178C23×C32—42no—
179C23×C32—42no—
180C23×C32C2×D411yescharacteristic
181C32×D4—24no—
182C32×D4—22no—
183C32×D4—22no—
184C32×D4—42no—
185C32×D4#4114yes—
186C2×C32×C4—22no—
187C2×C32×C4—21no—
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4C2411yescharacteristic
190C2×C3×Dic3—22no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—44no—
196C2×C3×Dic3—42no—
197C2×C3×Dic3—42no—
198C2×C3×Dic3—44no—
199C2×C3×Dic3C2×D411yescharacteristic
200C2×C3×Dic3C2×D411yescharacteristic
201C2×C3×Dic3C2×D411yescharacteristic
202C2×C3×Dic3C2×D411yescharacteristic
203C3×Dic6—22no—
204C32×C8—22no—
205C3×C3⋊C8—22no—
206#529—31no—
207C2×C4×D4—31no—
208#484—31no—
209#481—31no—
210#478—32no—
211#463—32no—
212#450—31no—
213#447C3×D311yescharacteristic
214C4×SD16—32no—
215C4×D8—32no—
216#431—31no—
217C24×C3—21no—
218C24×C3—21no—
219C24×C3—41no—
220C2×C3×Q8—31no—
221C2×C3×D4—24no—
222C2×C3×D4—24no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—22no—
228C2×C3×D4—21no—
229C2×C3×D4—41no—
230C2×C3×D4—44no—
231C2×C3×D4—41no—
232C2×C3×D4C22×D311yescharacteristic
233C2×C3×D4C22×D312yes—
234C2×C3×D4C23×C311yescharacteristic
235C2×C3×D4C23×C312yes—
236C22×C3×C4—21no—
237C22×C3×C4—31no—
238C22×C3×C4—31no—
239C22×C3×C4—61no—
240C22×C3×C4—62no—
241C22×C3×C4—62no—
242C22×C3×C4—61no—
243C22×C3×C4—124no—
244C22×C3×C4C22×D311yescharacteristic
245C22×C3×C4C23×C311yescharacteristic
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3—22no—
249C22×Dic3—22no—
250C22×Dic3—44no—
251C22×Dic3C3×D411yescharacteristic
252C22×Dic3C3×D411yescharacteristic
253C2×Dic6C23×C311yescharacteristic
254C3×SD16—64no—
255C3×D8—24no—
256C3×D8—24no—
257C3×D8—44no—
258C2×C3×C8—22no—
259C2×C3×C8—32no—
260C2×C3×C8C22×D312yes—
261C2×C3×C8C23×C312yes—
262C3×C4⋊C4—21no—
263C3×C4⋊C4—31no—
264C3×C4⋊C4—32no—
265C3×C4⋊C4—61no—
266C3×C4⋊C4—61no—
267C3×C4⋊C4—61no—
268C3×C4⋊C4—61no—
269C3×C4⋊C4—61no—
270C3×C4⋊C4C22×D311yescharacteristic
271C3×C4⋊C4C23×C311yescharacteristic
272C3×C22⋊C4—21no—
273C3×C22⋊C4—21no—
274C3×C22⋊C4—41no—
275C3×C22⋊C4—62no—
276C3×C22⋊C4—62no—
277C3×C22⋊C4—61no—
278C3×C22⋊C4—61no—
279C3×C22⋊C4—61no—
280C3×C22⋊C4—61no—
281C3×C42—31no—
282C3×C42—31no—
283C3×C42—31no—
284C3×C42—31no—
285C3×C42—61no—
286#217—21no—
287#217—21no—
288#217—21no—
289#217—21no—
290#217—22no—
291#217—22no—
292#214—24no—
293C4⋊Dic3—21no—
294C4⋊Dic3—21no—
295C4⋊Dic3C23×C312yes—
296C4⋊Dic3C23×C311yescharacteristic
297Dic3⋊C4—21no—
298Dic3⋊C4—21no—
299Dic3⋊C4—21no—
300C4×Dic3—21no—
301C4×Dic3C3×D411yescharacteristic
302C4×Dic3C3×D411yescharacteristic
303C4×Dic3C23×C311yescharacteristic
304C4×Dic3C23×C311yescharacteristic
305C2×C3⋊C8C23×C312yes—
306C22×C32—21no—
307C22×C32—21no—
308C22×C32—24no—
309C22×C32—48no—
310C22×C32—42no—
311C22×C32—42no—
312C22×C32—41no—
313C22×C32—41no—
314C22×C32—41no—
315C22×C32#13512yes—
316C22×C32C22×D411yescharacteristic
317C32×C4—21no—
318C32×C4—41no—
319C32×C4C2×#4112yes—
320C3×Dic3—21no—
321C3×Dic3—21no—
322C3×Dic3—21no—
323C3×Dic3—41no—
324C3×Dic3—41no—
325C3×Dic3—42no—
326C3×Dic3AGL(1,ℤ/8)12yes—
327C22×D4C2×C3×D311yescharacteristic
328C23×C4—61no—
329C2×SD16—32no—
330C2×D8C2×C3×D312yes—
331#126—61no—
332#125—31no—
333#124—31no—
334#123—61no—
335C22⋊Q8—31no—
336#121C2×C3×D311yescharacteristic
337C4×Q8—31no—
338C4×D4—32no—
339C4×D4—32no—
340C4×D4—31no—
341C4×D4—61no—
342C4×D4—61no—
343C4×D4—61no—
344#117—61no—
345C2×C4⋊C4—31no—
346C2×C22⋊C4—61no—
347C2×C42—31no—
348#107—32no—
349#106—32no—
350C4⋊C8—32no—
351#103—32no—
352#102—32no—
353#102—32no—
354#102C2×C3×D312yes—
355C22⋊C8—31no—
356C22⋊C8C2×C3×D311yescharacteristic
357C4×C8—32no—
358C23×C3—24no—
359C23×C3—24no—
360C23×C3—22no—
361C23×C3—22no—
362C23×C3—21no—
363C23×C3—21no—
364C23×C3—21no—
365C23×C3—42no—
366C23×C3—41no—
367C23×C3—44no—
368C23×C3—42no—
369C23×C3—42no—
370C23×C3—42no—
371C23×C3—42no—
372C23×C3—82no—
373C23×C3—82no—
374C23×C3D3×D411yescharacteristic
375C23×C3C2×C3×D411yescharacteristic
376C3×Q8—62no—
377C3×D4—24no—
378C3×D4—24no—
379C3×D4—22no—
380C3×D4—22no—
381C3×D4—22no—
382C3×D4—22no—
383C3×D4—24no—
384C3×D4—42no—
385C3×D4—42no—
386C3×D4—44no—
387C3×D4—42no—
388C3×D4—42no—
389C3×D4—82no—
390C3×D4#23714yes—
391C3×D4C3×#4114yes—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—31no—
399C2×C3×C4—31no—
400C2×C3×C4—31no—
401C2×C3×C4—31no—
402C2×C3×C4—42no—
403C2×C3×C4—41no—
404C2×C3×C4—62no—
405C2×C3×C4—62no—
406C2×C3×C4—61no—
407C2×C3×C4—61no—
408C2×C3×C4—62no—
409C2×C3×C4—122no—
410C2×C3×C4—124no—
411C2×C3×C4—124no—
412C2×C3×C4—122no—
413C2×C3×C4D3×D411yescharacteristic
414C2×C3×C4C2×C3×D411yescharacteristic
415C2×C3×C4C23×D311yescharacteristic
416C2×C3×C4C24×C311yescharacteristic
417C2×Dic3—22no—
418C2×Dic3—22no—
419C2×Dic3—21no—
420C2×Dic3—21no—
421C2×Dic3—22no—
422C2×Dic3—44no—
423C2×Dic3—42no—
424C2×Dic3—42no—
425C2×Dic3—44no—
426C2×Dic3C2×C3×D411yescharacteristic
427C2×Dic3C2×C3×D411yescharacteristic
428C2×Dic3C2×C3×D411yescharacteristic
429C2×Dic3C2×C3×D411yescharacteristic
430Dic6—22no—
431C3×C8—22no—
432C3×C8—22no—
433C3×C8—42no—
434C3×C8—62no—
435C3⋊C8—22no—
436C2×C32—22no—
437C2×C32—44no—
438C2×C32—81no—
439C2×C32#52511yescharacteristic
440C2×C32C2×#13511yescharacteristic
441C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
442C24—21no—
443C2×Q8—31no—
444C2×D4—24no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4C22×C3×D311yescharacteristic
448C2×D4C22×C3×D312yes—
449C22×C4—31no—
450C22×C4—31no—
451C22×C4—61no—
452C22×C4—62no—
453C22×C4—62no—
454C22×C4—61no—
455C22×C4—124no—
456C22×C4C22×C3×D311yescharacteristic
457SD16—64no—
458D8—24no—
459C2×C8—32no—
460C2×C8C22×C3×D312yes—
461C4⋊C4—31no—
462C4⋊C4—32no—
463C4⋊C4—61no—
464C4⋊C4—61no—
465C4⋊C4—61no—
466C4⋊C4—61no—
467C4⋊C4—61no—
468C4⋊C4C22×C3×D311yescharacteristic
469C22⋊C4—21no—
470C22⋊C4—62no—
471C22⋊C4—62no—
472C22⋊C4—61no—
473C22⋊C4—61no—
474C22⋊C4—61no—
475C22⋊C4—61no—
476C42—31no—
477C42—31no—
478C42—31no—
479C42—31no—
480C42—61no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—24no—
486C22×C3—24no—
487C22×C3—22no—
488C22×C3—21no—
489C22×C3—41no—
490C22×C3—41no—
491C22×C3—44no—
492C22×C3—48no—
493C22×C3—48no—
494C22×C3—42no—
495C22×C3—42no—
496C22×C3—42no—
497C22×C3—42no—
498C22×C3—41no—
499C22×C3—41no—
500C22×C3—41no—
501C22×C3—41no—
502C22×C3—41no—
503C22×C3—41no—
504C22×C3—82no—
505C22×C3—82no—
506C22×C3—81no—
507C22×C3—81no—
508C22×C3—81no—
509C22×C3—88no—
510C22×C3#91212yes—
511C22×C3C3×#13512yes—
512C22×C3C2×D3×D411yescharacteristic
513C22×C3C22×C3×D411yescharacteristic
514C3×C4—21no—
515C3×C4—21no—
516C3×C4—22no—
517C3×C4—32no—
518C3×C4—41no—
519C3×C4—41no—
520C3×C4—41no—
521C3×C4—61no—
522C3×C4—61no—
523C3×C4—61no—
524C3×C4—81no—
525C3×C4—122no—
526C3×C4—121no—
527C3×C4—121no—
528C3×C4C2×#23712yes—
529C3×C4C2×C3×#4112yes—
530Dic3—21no—
531Dic3—21no—
532Dic3—21no—
533Dic3—42no—
534Dic3—41no—
535Dic3—41no—
536Dic3C3×AGL(1,ℤ/8)12yes—
537C32#310511yescharacteristic, complemented, Sylow
538C23—24no—
539C23—22no—
540C23—21no—
541C23—42no—
542C23—42no—
543C23C3×D3×D411yescharacteristic
544Q8—62no—
545D4—24no—
546D4—22no—
547D4—22no—
548D4—42no—
549D4C3×#23714yes—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—31no—
553C2×C4—31no—
554C2×C4—31no—
555C2×C4—31no—
556C2×C4—62no—
557C2×C4—62no—
558C2×C4—61no—
559C2×C4—61no—
560C2×C4—62no—
561C2×C4—124no—
562C2×C4—122no—
563C2×C4—124no—
564C2×C4—122no—
565C2×C4C3×D3×D411yescharacteristic
566C2×C4C23×C3×D311yescharacteristic
567C8—22no—
568C8—62no—
569C2×C3—22no—
570C2×C3—22no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—42no—
575C2×C3—44no—
576C2×C3—44no—
577C2×C3—84no—
578C2×C3—81no—
579C2×C3—81no—
580C2×C3—161no—
581C2×C3#558611yescharacteristic
582C2×C3C2×#91211yescharacteristic
583C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
584C2×C3C3×#52511yescharacteristic
585C2×C3C2×C3×#13511yescharacteristic
586C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
587C22—21no—
588C22—21no—
589C22—24no—
590C22—48no—
591C22—42no—
592C22—42no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22C3×#91212yes—
597C22C2×C3×D3×D411yescharacteristic
598C4—21no—
599C4—32no—
600C4—41no—
601C4—61no—
602C4—61no—
603C4—61no—
604C4—122no—
605C4—121no—
606C4—121no—
607C4C2×C3×#23712yes—
608C3—21no—
609C3#7998911yescharacteristic, direct product factor
610C3C3×#310511yescharacteristic, complemented
611C2—22no—
612C2—44no—
613C2—81no—
614C2C3×#558611yescharacteristic
615C2C2×C3×#91211yescharacteristic
616C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
Fitting, prime radicalC32×#447C2
socleC22×C32C22×D4
hypercenterC3×#447D3
hypocenterC3C3×#3105
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#447

Complements

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

NH ≅ G/Ntype
1. C2×C3×D4×Dic3C2semidirect
2. C3×#5600C2semidirect
4. C3×#5218C2semidirect
5. C3×#5153C2semidirect
6. C3×Dic3×D8C2semidirect
7. C3×#5034C2semidirect
8. C3×#4766C2semidirect
9. C3×#4758C2semidirect
10. C3×#4722C2semidirect
11. C3×#4718C2semidirect
13. #79989C3direct (N × H)
19. C3×#936C22semidirect
26. C3×D4×Dic3C22semidirect
31. C3×#890C22semidirect
32. C3×#887C22semidirect
38. C3×#832C22semidirect
40. C3×#818C22semidirect
41. C3×#816C22semidirect
42. C3×Dic3⋊C8C22semidirect
43. C3×C8×Dic3C22semidirect
44. C3×#808C22semidirect
47. C2×D4×Dic3C2×C3semidirect
48. #5600C2×C3semidirect
60. #5218C2×C3semidirect
61. #5153C2×C3semidirect
62. Dic3×D8C2×C3semidirect
63. #5034C2×C3semidirect
64. #4766C2×C3semidirect
65. #4758C2×C3semidirect
66. #4722C2×C3semidirect
67. #4718C2×C3semidirect
137. #936C22×C3semidirect
144. D4×Dic3C22×C3semidirect
149. #890C22×C3semidirect
150. #887C22×C3semidirect
168. #832C22×C3semidirect
170. #818C22×C3semidirect
171. #816C22×C3semidirect
172. Dic3⋊C8C22×C3semidirect
173. C8×Dic3C22×C3semidirect
174. #808C22×C3semidirect
537. C32#3105semidirect
609. C3#79989direct (N × H)
610. C3C3×#3105semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×Dic32
C3×#56002
C32×#4472
C3×#52182
C3×#51532
C3×Dic3×D82
C3×#50342
C3×#47662
C3×#47582
C3×#47222
C3×#47182
C3×#31053
#799893