Finite Group Databasebeta

← C3×#25783 #10644390

Subgroups — C3×#25783 #10644390

Order 768.

1774 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×SD16C211yesmaximal, characteristic, complemented
2C2×C3×#496C212yesmaximal, complemented
3C2×C3×#466C211yesmaximal, characteristic, complemented
4C2×C3×#448C211yesmaximal, characteristic, complemented
5C2×C3×#447C211yesmaximal, characteristic, complemented
6C3×#2436C211yesmaximal, characteristic, complemented
7C3×#2433C211yesmaximal, characteristic, complemented
8C3×#2014C212yesmaximal, complemented
9C3×#2012C212yesmaximal, complemented
10C3×#1973C212yesmaximal, complemented
11C3×#1752C211yesmaximal, characteristic, complemented
12#25783C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×Q8C2211yescharacteristic
14C23×C3×D4C2211yescharacteristic
15C22×C3×SD16—28no—
16C22×C3×SD16—24no—
17C22×C3×SD16C2212yes—
18C22×C3×SD16C2212yes—
19C22×C3×SD16C2212yescomplemented
20C22×C3×D8C2212yes—
21C22×C3×D8C2211yescharacteristic, complemented
22C23×C3×C8C2211yescharacteristic
23C2×C3×#127C2212yes—
24C2×C3×#124C2212yescomplemented
25C2×C3×#121C2211yescharacteristic
26C2×C3×#121C2211yescharacteristic
27C2×C3×#120—22no—
28C3×#496—28no—
29C3×#466—24no—
30C3×#448—24no—
31C3×#447—24no—
32C2×C3×#107C2211yescharacteristic, complemented
33C2×C3×#103C2212yescomplemented
34C2×C3×#102C2212yes—
35C2×C3×#102C2211yescharacteristic, complemented
36C2×C3×#102C2211yescharacteristic, complemented
37C2×C3×C22⋊C8C2211yescharacteristic
38C2×C3×#97C2212yescomplemented
39C3×#393—22no—
40C3×#392—22no—
41C3×#391C2212yescomplemented
42C3×#390C2212yes—
43C3×#386—22no—
44C3×C4×C22⋊C4C2211yescharacteristic
45C3×#336C2212yescomplemented
46C23×SD16C2×C311yescharacteristic, complemented
47C2×#496C2×C312yescomplemented
48C2×#466C2×C311yescharacteristic, complemented
49C2×#448C2×C311yescharacteristic, complemented
50C2×#447C2×C311yescharacteristic, complemented
51#2436C2×C311yescharacteristic, complemented
52#2433C2×C311yescharacteristic, complemented
53#2014C2×C312yescomplemented
54#2012C2×C312yescomplemented
55#1973C2×C312yescomplemented
56#1752C2×C311yescharacteristic, complemented
57C25×C3—21no—
58C22×C3×Q8—21no—
59C22×C3×Q8—24no—
60C22×C3×Q8—22no—
61C22×C3×Q8—22no—
62C22×C3×Q8—42no—
63C22×C3×Q8C2312yes—
64C22×C3×D4—24no—
65C22×C3×D4—21no—
66C22×C3×D4—21no—
67C22×C3×D4—22no—
68C22×C3×D4—22no—
69C22×C3×D4—21no—
70C22×C3×D4—24no—
71C22×C3×D4—42no—
72C22×C3×D4C2311yescharacteristic
73C22×C3×D4C2311yescharacteristic
74C22×C3×D4C2312yes—
75C23×C3×C4—21no—
76C23×C3×C4C2311yescharacteristic
77C2×C3×SD16—232no—
78C2×C3×SD16—24no—
79C2×C3×SD16—24no—
80C2×C3×SD16—24no—
81C2×C3×SD16—24no—
82C2×C3×SD16—24no—
83C2×C3×SD16—24no—
84C2×C3×SD16—24no—
85C2×C3×SD16—42no—
86C2×C3×SD16D418yescomplemented
87C2×C3×D8—24no—
88C2×C3×D8—24no—
89C2×C3×D8—22no—
90C2×C3×D8—24no—
91C2×C3×D8—42no—
92C22×C3×C8—24no—
93C22×C3×C8D414yescomplemented
94C22×C3×C8C2311yescharacteristic
95C22×C3×C8C2312yes—
96C22×C3×C8C2311yescharacteristic
97C3×#127—24no—
98C3×#127—42no—
99C3×#124—24no—
100C3×#124—42no—
101C3×#121—22no—
102C3×#121—22no—
103C3×#121—22no—
104C3×#121—22no—
105C3×#120—48no—
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C22⋊C4—24no—
109C2×C3×C22⋊C4—24no—
110C2×C3×C22⋊C4—21no—
111C2×C3×C22⋊C4—21no—
112C2×C3×C22⋊C4D412yes—
113C2×C3×C42C2312yes—
114C3×#107—22no—
115C3×#103—24no—
116C3×#102—24no—
117C3×#102—22no—
118C3×#102—22no—
119C3×C22⋊C8D414yescomplemented
120C3×#97—24no—
121C3×#95—24no—
122C3×#95D412yes—
123C23×Q8C22×C311yescharacteristic
124C23×D4C22×C311yescharacteristic
125C22×SD16—28no—
126C22×SD16—24no—
127C22×SD16C22×C312yes—
128C22×SD16C22×C312yes—
129C22×SD16C22×C312yescomplemented
130C22×D8C22×C312yes—
131C22×D8C22×C311yescharacteristic, complemented
132C23×C8C22×C311yescharacteristic
133C2×#127C22×C312yes—
134C2×#124C22×C312yescomplemented
135C2×#121C22×C311yescharacteristic
136C2×#121C22×C311yescharacteristic
137C2×#120—22no—
138#496—28no—
139#466—24no—
140#448—24no—
141#447—24no—
142C2×#107C22×C311yescharacteristic, complemented
143C2×#103C22×C312yescomplemented
144C2×#102C22×C312yes—
145C2×#102C22×C311yescharacteristic, complemented
146C2×#102C22×C311yescharacteristic, complemented
147C2×C22⋊C8C22×C311yescharacteristic
148C2×#97C22×C312yescomplemented
149#393—22no—
150#392—22no—
151#391C22×C312yescomplemented
152#390C22×C312yes—
153#386—22no—
154C4×C22⋊C4C22×C311yescharacteristic
155#336C22×C312yescomplemented
156C24×C3—22no—
157C24×C3—21no—
158C24×C3—21no—
159C24×C3—44no—
160C24×C3—42no—
161C24×C3—44no—
162C24×C3—82no—
163C24×C3C2×D411yescharacteristic
164C2×C3×Q8—22no—
165C2×C3×Q8—28no—
166C2×C3×Q8—22no—
167C2×C3×Q8—22no—
168C2×C3×Q8—22no—
169C2×C3×Q8—22no—
170C2×C3×Q8—44no—
171C2×C3×Q8—48no—
172C2×C3×Q8—44no—
173C2×C3×Q8—42no—
174C2×C3×Q8C2×D414yes—
175C2×C3×D4—28no—
176C2×C3×D4—22no—
177C2×C3×D4—22no—
178C2×C3×D4—22no—
179C2×C3×D4—21no—
180C2×C3×D4—21no—
181C2×C3×D4—21no—
182C2×C3×D4—21no—
183C2×C3×D4—22no—
184C2×C3×D4—22no—
185C2×C3×D4—22no—
186C2×C3×D4—22no—
187C2×C3×D4—22no—
188C2×C3×D4—22no—
189C2×C3×D4—48no—
190C2×C3×D4—44no—
191C2×C3×D4—44no—
192C2×C3×D4—48no—
193C2×C3×D4—48no—
194C2×C3×D4—42no—
195C2×C3×D4—42no—
196C2×C3×D4—44no—
197C2×C3×D4—44no—
198C2×C3×D4—42no—
199C2×C3×D4—84no—
200C2×C3×D4C2×D414yes—
201C22×C3×C4—22no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—44no—
207C22×C3×C4—42no—
208C22×C3×C4C2×D414yes—
209C22×C3×C4C2×D411yescharacteristic
210C22×C3×C4C2×D412yes—
211C22×C3×C4C2×D412yes—
212C22×C3×C4C2411yescharacteristic
213C3×SD16—216no—
214C3×SD16—216no—
215C3×SD16—48no—
216C3×D8—48no—
217C3×D8—44no—
218C2×C3×C8—22no—
219C2×C3×C8—22no—
220C2×C3×C8—22no—
221C2×C3×C8—28no—
222C2×C3×C8C2×D414yes—
223C2×C3×C8C2×D412yes—
224C2×C3×C8C2×D414yes—
225C2×C3×C8C2×D412yes—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—21no—
230C3×C22⋊C4—24no—
231C3×C22⋊C4—48no—
232C3×C22⋊C4—48no—
233C3×C22⋊C4—42no—
234C3×C22⋊C4—42no—
235C3×C42—22no—
236C3×C42—22no—
237C25—21no—
238C22×Q8—21no—
239C22×Q8—24no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—42no—
243C22×Q8C23×C312yes—
244C22×D4—24no—
245C22×D4—21no—
246C22×D4—21no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—21no—
250C22×D4—24no—
251C22×D4—42no—
252C22×D4C23×C311yescharacteristic
253C22×D4C23×C311yescharacteristic
254C22×D4C23×C312yes—
255C23×C4—21no—
256C23×C4C23×C311yescharacteristic
257C2×SD16—232no—
258C2×SD16—24no—
259C2×SD16—24no—
260C2×SD16—24no—
261C2×SD16—24no—
262C2×SD16—24no—
263C2×SD16—24no—
264C2×SD16—24no—
265C2×SD16—42no—
266C2×SD16C3×D418yescomplemented
267C2×D8—24no—
268C2×D8—24no—
269C2×D8—22no—
270C2×D8—24no—
271C2×D8—42no—
272C22×C8—24no—
273C22×C8C3×D414yescomplemented
274C22×C8C23×C311yescharacteristic
275C22×C8C23×C312yes—
276C22×C8C23×C311yescharacteristic
277#127—24no—
278#127—42no—
279#124—24no—
280#124—42no—
281#121—22no—
282#121—22no—
283#121—22no—
284#121—22no—
285#120—48no—
286C2×C4⋊C4C23×C311yescharacteristic
287C2×C4⋊C4C23×C311yescharacteristic
288C2×C22⋊C4—24no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—24no—
292C2×C22⋊C4C3×D412yes—
293C2×C42C23×C312yes—
294#107—22no—
295#103—24no—
296#102—24no—
297#102—22no—
298#102—22no—
299C22⋊C8C3×D414yescomplemented
300#97—24no—
301#95—24no—
302#95C3×D412yes—
303C23×C3—22no—
304C23×C3—22no—
305C23×C3—24no—
306C23×C3—48no—
307C23×C3—42no—
308C23×C3—42no—
309C23×C3—44no—
310C23×C3—44no—
311C23×C3—41no—
312C23×C3—41no—
313C23×C3—42no—
314C23×C3—42no—
315C23×C3—42no—
316C23×C3—42no—
317C23×C3—42no—
318C23×C3—42no—
319C23×C3—816no—
320C23×C3—84no—
321C23×C3—84no—
322C23×C3#12712yes—
323C23×C3AGL(1,ℤ/8)14yes—
324C23×C3C22×D411yescharacteristic
325C3×Q8—24no—
326C3×Q8—24no—
327C3×Q8—48no—
328C3×Q8—42no—
329C3×Q8—42no—
330C3×D4—24no—
331C3×D4—24no—
332C3×D4—48no—
333C3×D4—41no—
334C3×D4—41no—
335C3×D4—42no—
336C3×D4—41no—
337C3×D4—41no—
338C3×D4—42no—
339C3×D4—42no—
340C3×D4—42no—
341C3×D4—816no—
342C3×D4—84no—
343C3×D4—84no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—24no—
348C2×C3×C4—24no—
349C2×C3×C4—24no—
350C2×C3×C4—24no—
351C2×C3×C4—24no—
352C2×C3×C4—48no—
353C2×C3×C4—42no—
354C2×C3×C4—42no—
355C2×C3×C4—41no—
356C2×C3×C4—41no—
357C2×C3×C4—42no—
358C2×C3×C4—42no—
359C2×C3×C4#12712yes—
360C2×C3×C4C22×D411yescharacteristic
361C2×C3×C4C22×D412yes—
362C2×C3×C4C22×D411yescharacteristic
363C2×C3×C4H(5,𝔽2)12yes—
364C3×C8—22no—
365C3×C8—24no—
366C3×C8#12014yescomplemented
367C24—22no—
368C24—21no—
369C24—21no—
370C24—44no—
371C24—42no—
372C24—44no—
373C24—82no—
374C24C2×C3×D411yescharacteristic
375C2×Q8—22no—
376C2×Q8—28no—
377C2×Q8—22no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—44no—
382C2×Q8—48no—
383C2×Q8—44no—
384C2×Q8—42no—
385C2×Q8C2×C3×D414yes—
386C2×D4—28no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—48no—
401C2×D4—44no—
402C2×D4—44no—
403C2×D4—48no—
404C2×D4—48no—
405C2×D4—42no—
406C2×D4—42no—
407C2×D4—44no—
408C2×D4—44no—
409C2×D4—42no—
410C2×D4—84no—
411C2×D4C2×C3×D414yes—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—44no—
418C22×C4—42no—
419C22×C4C2×C3×D414yes—
420C22×C4C2×C3×D411yescharacteristic
421C22×C4C2×C3×D412yes—
422C22×C4C2×C3×D412yes—
423C22×C4C24×C311yescharacteristic
424SD16—216no—
425SD16—216no—
426SD16—48no—
427D8—48no—
428D8—44no—
429C2×C8—22no—
430C2×C8—22no—
431C2×C8—22no—
432C2×C8—28no—
433C2×C8C2×C3×D414yes—
434C2×C8C2×C3×D412yes—
435C2×C8C2×C3×D414yes—
436C2×C8C2×C3×D412yes—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C22⋊C4—24no—
442C22⋊C4—48no—
443C22⋊C4—48no—
444C22⋊C4—42no—
445C22⋊C4—42no—
446C42—22no—
447C42—22no—
448C22×C3—22no—
449C22×C3—22no—
450C22×C3—28no—
451C22×C3—44no—
452C22×C3—48no—
453C22×C3—816no—
454C22×C3—82no—
455C22×C3—82no—
456C22×C3—84no—
457C22×C3—81no—
458C22×C3—81no—
459C22×C3—81no—
460C22×C3—81no—
461C22×C3—81no—
462C22×C3—81no—
463C22×C3—84no—
464C22×C3—84no—
465C22×C3#49614yescomplemented
466C22×C3C2×#12711yescharacteristic
467C22×C3D4212yes—
468C22×C3C2×AGL(1,ℤ/8)12yes—
469C22×C3#57712yes—
470C3×C4—22no—
471C3×C4—44no—
472C3×C4—44no—
473C3×C4—81no—
474C3×C4—81no—
475C3×C4C2×#12011yescharacteristic
476C3×C4#53511yescharacteristic
477C3×C4D4212yes—
478C23—22no—
479C23—22no—
480C23—24no—
481C23—48no—
482C23—44no—
483C23—44no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—41no—
491C23—41no—
492C23—42no—
493C23—42no—
494C23—816no—
495C23—84no—
496C23—84no—
497C23C3×#12712yes—
498C23C3×AGL(1,ℤ/8)14yes—
499C23C22×C3×D411yescharacteristic
500Q8—24no—
501Q8—24no—
502Q8—48no—
503Q8—42no—
504Q8—42no—
505D4—24no—
506D4—24no—
507D4—48no—
508D4—41no—
509D4—41no—
510D4—42no—
511D4—41no—
512D4—41no—
513D4—42no—
514D4—42no—
515D4—42no—
516D4—816no—
517D4—84no—
518D4—84no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—48no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4C3×#12712yes—
535C2×C4C22×C3×D411yescharacteristic
536C2×C4C22×C3×D412yes—
537C2×C4C22×C3×D411yescharacteristic
538C2×C4C3×H(5,𝔽2)12yes—
539C8—22no—
540C8—24no—
541C8C3×#12014yescomplemented
542C2×C3—24no—
543C2×C3—84no—
544C2×C3—161no—
545C2×C3—161no—
546C2×C3#243311yescharacteristic
547C2×C3C2×#49611yescharacteristic
548C2×C3#315411yescharacteristic
549C2×C3#326514yes—
550C22—22no—
551C22—22no—
552C22—28no—
553C22—44no—
554C22—48no—
555C22—816no—
556C22—82no—
557C22—82no—
558C22—84no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—84no—
566C22—84no—
567C22C3×#49614yescomplemented
568C22C2×C3×#12711yescharacteristic
569C22C3×D4212yes—
570C22C2×C3×AGL(1,ℤ/8)12yes—
571C22C3×#57712yes—
572C4—22no—
573C4—44no—
574C4—44no—
575C4—81no—
576C4—81no—
577C4C2×C3×#12011yescharacteristic
578C4C3×#53511yescharacteristic
579C4C3×D4212yes—
580C3#2578311yescharacteristic, direct product factor, Sylow
581C2—24no—
582C2—84no—
583C2—161no—
584C2—161no—
585C2C3×#243311yescharacteristic
586C2C2×C3×#49611yescharacteristic
587C2C3×#315411yescharacteristic
588C2C3×#326514yes—
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×C4×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×C3×SD16C2semidirect
2. C2×C3×#496C2semidirect
3. C2×C3×#466C2semidirect
4. C2×C3×#448C2semidirect
5. C2×C3×#447C2semidirect
6. C3×#2436C2semidirect
7. C3×#2433C2semidirect
8. C3×#2014C2semidirect
9. C3×#2012C2semidirect
10. C3×#1973C2semidirect
11. C3×#1752C2semidirect
12. #25783C3direct (N × H)
19. C22×C3×SD16C22semidirect
21. C22×C3×D8C22semidirect
24. C2×C3×#124C22semidirect
32. C2×C3×#107C22semidirect
33. C2×C3×#103C22semidirect
35. C2×C3×#102C22semidirect
36. C2×C3×#102C22semidirect
38. C2×C3×#97C22semidirect
41. C3×#391C22semidirect
45. C3×#336C22semidirect
46. C23×SD16C2×C3semidirect
47. C2×#496C2×C3semidirect
48. C2×#466C2×C3semidirect
49. C2×#448C2×C3semidirect
50. C2×#447C2×C3semidirect
51. #2436C2×C3semidirect
52. #2433C2×C3semidirect
53. #2014C2×C3semidirect
54. #2012C2×C3semidirect
55. #1973C2×C3semidirect
56. #1752C2×C3semidirect
86. C2×C3×SD16D4semidirect
93. C22×C3×C8D4semidirect
119. C3×C22⋊C8D4semidirect
129. C22×SD16C22×C3semidirect
131. C22×D8C22×C3semidirect
134. C2×#124C22×C3semidirect
142. C2×#107C22×C3semidirect
143. C2×#103C22×C3semidirect
145. C2×#102C22×C3semidirect
146. C2×#102C22×C3semidirect
148. C2×#97C22×C3semidirect
151. #391C22×C3semidirect
155. #336C22×C3semidirect
266. C2×SD16C3×D4semidirect
273. C22×C8C3×D4semidirect
299. C22⋊C8C3×D4semidirect
366. C3×C8#120semidirect
465. C22×C3#496semidirect
541. C8C3×#120semidirect
567. C22C3×#496semidirect
580. C3#25783direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×SD162
C2×C3×#4962
C2×C3×#4662
C2×C3×#4482
C2×C3×#4472
C3×#24362
C3×#24332
C3×#20142
C3×#20122
C3×#19732
C3×#17522
#257833