Finite Group Databasebeta

← D3×#5207 #11857364

Subgroups — D3×#5207 #11857364

Order 1152.

2111 conjugacy classes of subgroups.

The subgroup lattice has 619 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C4×D3C211yesmaximal, characteristic
2C2×D3×#208C212yesmaximal, complemented
3#10592906C211yesmaximal, characteristic, complemented
4C3×#5207C211yesmaximal, characteristic, complemented
5#10591154C214yesmaximal, complemented
6D3×#830C214yesmaximal, complemented
7#10591069C212yesmaximal, complemented
8C2×#5207—31nomaximal
9D3×#407—31nomaximal
10C24×C3×D3C411yescharacteristic
11C23×C32×C4C2211yescharacteristic
12C23×C3×Dic3C411yescharacteristic
13C22×C3×C4×D3—28no—
14C22×C3×C4×D3C411yescharacteristic
15C22×C3×C4×D3C412yes—
16C22×C3×C4×D3C411yescharacteristic
17C22×C3×C4×D3C412yes—
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×C4×D3C2212yes—
20C22×C3×C4×D3C2212yes—
21C22×C3×C4×D3C2211yescharacteristic
22C2×#3748C2212yescomplemented
23C2×C3×#208C2212yescomplemented
24C2×#3711C2214yescomplemented
25D3×#208—28no—
26C2×D3×C3⋊C8C2214yescomplemented
27#63657C2214yescomplemented
28C3×#830C2214yescomplemented
29(C2×D3)⋊(C3⋊C8)C2218yescomplemented
30C24×C3×C4—31no—
31C23×C4×D3D311yescharacteristic
32C22×#208—32no—
33C2×D3×M16—32no—
34C3×#407—31no—
35#5207—31no—
36#5207—31no—
37#5207—32no—
38#5207—34no—
39#5207—61no—
40#5207D311yescharacteristic, direct product factor
41C2×#830—34no—
42#5126—32no—
43#4726—34no—
44D3×C22⋊C8—34no—
45C24×C32C2×C411yescharacteristic
46C23×C3×D3—24no—
47C23×C3×D3—28no—
48C23×C3×D3C2×C411yescharacteristic
49C23×C3×D3C2×C412yes—
50C23×C3×D3C2×C411yescharacteristic
51C23×C3×D3C2×C412yes—
52C22×C32×C4—24no—
53C22×C32×C4C2×C411yescharacteristic
54C22×C32×C4C2×C412yes—
55C22×C32×C4C2312yes—
56C22×C32×C4C2311yescharacteristic
57C22×C3×Dic3—24no—
58C22×C3×Dic3C2×C411yescharacteristic
59C22×C3×Dic3C2×C412yes—
60C22×C3×Dic3C2×C412yes—
61C22×C3×Dic3C2×C411yescharacteristic
62C2×C3×C4×D3—24no—
63C2×C3×C4×D3—24no—
64C2×C3×C4×D3—24no—
65C2×C3×C4×D3—28no—
66C2×C3×C4×D3—28no—
67C2×C3×C4×D3—28no—
68C2×C3×C4×D3—28no—
69C2×C3×C4×D3C2×C412yes—
70C2×C3×C4×D3C2×C412yes—
71C2×C3×C4×D3C2×C412yes—
72C2×C3×C4×D3C2×C412yes—
73C2×C3×C4×D3C2×C412yes—
74C2×C3×C4×D3C2×C411yescharacteristic
75C2×C3×C4×D3C2×C411yescharacteristic
76C2×C3×C4×D3D418yes—
77C2×C3×C4×D3C2312yes—
78C2×C3×C4×D3C2311yescharacteristic
79C2×C3×C4×D3C2311yescharacteristic
80#3748—24no—
81C2×C3⋊(C3⋊C8)C2314yescomplemented
82C3×#208—24no—
83C2×C3×C3⋊C8C2314yescomplemented
84#3711—28no—
85D3×C3⋊C8—28no—
86C2×#407—91noSylow
87C25×C3—31no—
88C24×D3Dic311yescharacteristic
89C23×C3×C4—21no—
90C23×C3×C4—31no—
91C23×C3×C4—31no—
92C23×C3×C4—31no—
93C23×C3×C4—32no—
94C23×C3×C4—32no—
95C23×C3×C4—31no—
96C23×C3×C4—32no—
97C23×C3×C4—32no—
98C23×C3×C4—31no—
99C23×C3×C4—68no—
100C23×C3×C4C2×D311yescharacteristic
101C23×C3×C4C2×D311yescharacteristic
102C23×Dic3Dic311yescharacteristic
103C22×C4×D3—28no—
104C22×C4×D3Dic311yescharacteristic
105C22×C4×D3Dic311yescharacteristic
106C22×C4×D3Dic312yes—
107C22×C4×D3Dic312yes—
108C22×C4×D3C2×D311yescharacteristic
109C22×C4×D3C2×D312yes—
110C22×C4×D3C2×D312yes—
111C22×C4×D3C2×D311yescharacteristic
112C2×C3×M16—32no—
113C2×#208—32no—
114C2×#208—32no—
115C2×#208—34no—
116C2×#208—62no—
117C2×#208—68no—
118C2×#208C2×D312yescomplemented
119C22×C3⋊C8—34no—
120D3×M16—68no—
121C2×ΓL(1,𝔽25)—34no—
122C2×D3×C8—34no—
123C3×C22⋊C8—34no—
124#830—34no—
125#830—34no—
126#830—38no—
127#830—64no—
128#830C2×D314yescomplemented
129(C2×D3)⋊C8—38no—
130C23×C32—22no—
131C23×C32—24no—
132C23×C32C22×C411yescharacteristic
133C23×C32C22×C412yes—
134C22×C3×D3—232no—
135C22×C3×D3—22no—
136C22×C3×D3—24no—
137C22×C3×D3—24no—
138C22×C3×D3—24no—
139C22×C3×D3—24no—
140C22×C3×D3—24no—
141C22×C3×D3—24no—
142C22×C3×D3—24no—
143C22×C3×D3C22⋊C414yes—
144C22×C3×D3M1618yescomplemented
145C22×C3×D3C22×C411yescharacteristic
146C22×C3×D3C22×C412yes—
147C22×C3×D3C22×C411yescharacteristic
148C2×C32×C4—22no—
149C2×C32×C4—24no—
150C2×C32×C4—24no—
151C2×C32×C4C22×C412yes—
152C2×C32×C4C22×C411yescharacteristic
153C2×C32×C4C2×D414yes—
154C2×C32×C4C2411yescharacteristic
155C2×C3×Dic3—22no—
156C2×C3×Dic3—24no—
157C2×C3×Dic3—24no—
158C2×C3×Dic3C22⋊C414yes—
159C2×C3×Dic3C22×C412yes—
160C2×C3×Dic3C22×C411yescharacteristic
161C2×C3×Dic3C22×C411yescharacteristic
162C3×C4×D3—24no—
163C3×C4×D3—24no—
164C3×C4×D3—24no—
165C3×C4×D3—24no—
166C3×C4×D3—24no—
167C3×C4×D3—24no—
168C3×C4×D3C22⋊C414yes—
169C3×C4×D3C22⋊C414yes—
170C3×C4×D3C2×D414yes—
171C3×C4×D3C2×D414yes—
172C3⋊(C3⋊C8)—24no—
173C3×C3⋊C8—24no—
174C24×C4—31no—
175C22×M16—92no—
176#407—31no—
177#407—94no—
178#407—92no—
179#407—91no—
180C2×C22⋊C8—94no—
181C24×C3—21no—
182C24×C3—31no—
183C24×C3—32no—
184C24×C3—32no—
185C24×C3—31no—
186C24×C3—68no—
187C24×C3—64no—
188C24×C3C4×D311yescharacteristic
189C24×C3C2×Dic311yescharacteristic
190C23×D3—28no—
191C23×D3—24no—
192C23×D3C2×Dic312yes—
193C23×D3C2×Dic311yescharacteristic
194C23×D3C2×Dic312yes—
195C23×D3C2×Dic311yescharacteristic
196C22×C3×C4—24no—
197C22×C3×C4—24no—
198C22×C3×C4—22no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—22no—
202C22×C3×C4—31no—
203C22×C3×C4—31no—
204C22×C3×C4—31no—
205C22×C3×C4—38no—
206C22×C3×C4—31no—
207C22×C3×C4—31no—
208C22×C3×C4—32no—
209C22×C3×C4—32no—
210C22×C3×C4—31no—
211C22×C3×C4—32no—
212C22×C3×C4—32no—
213C22×C3×C4—32no—
214C22×C3×C4—32no—
215C22×C3×C4—32no—
216C22×C3×C4—32no—
217C22×C3×C4—44no—
218C22×C3×C4—64no—
219C22×C3×C4—68no—
220C22×C3×C4—68no—
221C22×C3×C4—68no—
222C22×C3×C4—68no—
223C22×C3×C4—64no—
224C22×C3×C4—64no—
225C22×C3×C4—64no—
226C22×C3×C4C4×D311yescharacteristic
227C22×C3×C4C4×D312yes—
228C22×C3×C4C2×Dic311yescharacteristic
229C22×C3×C4C2×Dic312yes—
230C22×C3×C4C22×D312yes—
231C22×C3×C4C22×D312yes—
232C22×C3×C4C22×D311yescharacteristic
233C22×C3×C4C22×D311yescharacteristic
234C22×Dic3—24no—
235C22×Dic3C2×Dic311yescharacteristic
236C22×Dic3C2×Dic312yes—
237C22×Dic3C2×Dic312yes—
238C22×Dic3C2×Dic311yescharacteristic
239C2×C4×D3—24no—
240C2×C4×D3—24no—
241C2×C4×D3—24no—
242C2×C4×D3—28no—
243C2×C4×D3—28no—
244C2×C4×D3—28no—
245C2×C4×D3—28no—
246C2×C4×D3C2×Dic312yes—
247C2×C4×D3C2×Dic312yes—
248C2×C4×D3C2×Dic312yes—
249C2×C4×D3C2×Dic312yes—
250C2×C4×D3C2×Dic312yes—
251C2×C4×D3C2×Dic311yescharacteristic
252C2×C4×D3C2×Dic311yescharacteristic
253C2×C4×D3#6718yes—
254C2×C4×D3C22×D312yes—
255C2×C4×D3C22×D311yescharacteristic
256C2×C4×D3C22×D311yescharacteristic
257C3×M16—64no—
258C2×C3×C8—34no—
259#208—24no—
260#208—68no—
261#208—64no—
262#208—64no—
263#208—124no—
264C2×C3⋊C8—34no—
265C2×C3⋊C8—34no—
266C2×C3⋊C8—64no—
267C2×C3⋊C8—68no—
268C2×C3⋊C8C22×D314yescomplemented
269ΓL(1,𝔽25)—68no—
270D3×C8—68no—
271C22×C32—28no—
272C22×C32—22no—
273C22×C32—22no—
274C22×C32—22no—
275C22×C32C2×C22⋊C412yes—
276C22×C32C2×M1614yescomplemented
277C22×C32C23×C411yescharacteristic
278C2×C3×D3—216no—
279C2×C3×D3—28no—
280C2×C3×D3—22no—
281C2×C3×D3—22no—
282C2×C3×D3—22no—
283C2×C3×D3—28no—
284C2×C3×D3—216no—
285C2×C3×D3C2×C22⋊C412yes—
286C2×C3×D3C2×C22⋊C412yes—
287C2×C3×D3C2×M1614yes—
288C2×C3×D3C2×M1614yescomplemented
289C32×C4—22no—
290C32×C4C2×C22⋊C412yes—
291C32×C4C22×D412yes—
292C3×Dic3—22no—
293C3×Dic3C2×C22⋊C412yes—
294C3×Dic3C2×C22⋊C412yes—
295C25—31no—
296C23×C4—31no—
297C23×C4—31no—
298C23×C4—31no—
299C23×C4—32no—
300C23×C4—32no—
301C23×C4—31no—
302C23×C4—32no—
303C23×C4—32no—
304C23×C4—31no—
305C23×C4—68no—
306C23×C4D3211yescharacteristic
307C2×M16—32no—
308C2×M16—94no—
309C2×M16—92no—
310C2×M16—188no—
311C22×C8—94no—
312C22⋊C8—34no—
313C22⋊C8—98no—
314C22⋊C8—94no—
315C23×C3—22no—
316C23×C3—24no—
317C23×C3—24no—
318C23×C3—22no—
319C23×C3—22no—
320C23×C3—21no—
321C23×C3—31no—
322C23×C3—34no—
323C23×C3—38no—
324C23×C3—31no—
325C23×C3—32no—
326C23×C3—42no—
327C23×C3—44no—
328C23×C3—64no—
329C23×C3—64no—
330C23×C3—64no—
331C23×C3—64no—
332C23×C3—64no—
333C23×C3—64no—
334C23×C3—632no—
335C23×C3—62no—
336C23×C3—64no—
337C23×C3C2×C4×D311yescharacteristic
338C23×C3C2×C4×D312yes—
339C23×C3C22×Dic312yes—
340C23×C3C22×Dic311yescharacteristic
341C22×D3—232no—
342C22×D3—24no—
343C22×D3—22no—
344C22×D3—24no—
345C22×D3—24no—
346C22×D3—24no—
347C22×D3—24no—
348C22×D3—24no—
349C22×D3—24no—
350C22×D3#20818yescomplemented
351C22×D3#21714yes—
352C22×D3C22×Dic312yes—
353C22×D3C22×Dic311yescharacteristic
354C22×D3C22×Dic311yescharacteristic
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—24no—
358C2×C3×C4—24no—
359C2×C3×C4—24no—
360C2×C3×C4—24no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—22no—
364C2×C3×C4—24no—
365C2×C3×C4—34no—
366C2×C3×C4—31no—
367C2×C3×C4—31no—
368C2×C3×C4—34no—
369C2×C3×C4—34no—
370C2×C3×C4—34no—
371C2×C3×C4—34no—
372C2×C3×C4—32no—
373C2×C3×C4—44no—
374C2×C3×C4—44no—
375C2×C3×C4—42no—
376C2×C3×C4—64no—
377C2×C3×C4—64no—
378C2×C3×C4—64no—
379C2×C3×C4—64no—
380C2×C3×C4—64no—
381C2×C3×C4—64no—
382C2×C3×C4—62no—
383C2×C3×C4—64no—
384C2×C3×C4—64no—
385C2×C3×C4C2×C4×D312yes—
386C2×C3×C4C2×C4×D311yescharacteristic
387C2×C3×C4D3×D414yes—
388C2×C3×C4C22×Dic312yes—
389C2×C3×C4C22×Dic311yescharacteristic
390C2×C3×C4C2×#6714yes—
391C2×C3×C4C23×D311yescharacteristic
392C2×C3×C4C23×D311yescharacteristic
393C2×Dic3—22no—
394C2×Dic3—24no—
395C2×Dic3—24no—
396C2×Dic3#21714yes—
397C2×Dic3C22×Dic312yes—
398C2×Dic3C22×Dic311yescharacteristic
399C2×Dic3C22×Dic311yescharacteristic
400C4×D3—24no—
401C4×D3—24no—
402C4×D3—24no—
403C4×D3—24no—
404C4×D3—24no—
405C4×D3—24no—
406C4×D3#21714yes—
407C4×D3#21714yes—
408C4×D3C2×#6714yes—
409C4×D3C2×#6714yes—
410C3×C8—64no—
411C3⋊C8—24no—
412C3⋊C8—64no—
413C3⋊C8—64no—
414C3⋊C8—124no—
415C2×C32—22no—
416C2×C32—24no—
417C2×C32C22×C22⋊C411yescharacteristic
418C2×C32C22×M1612yes—
419C3×D3—22no—
420C3×D3—24no—
421C3×D3#40714yescomplemented
422C24—32no—
423C24—31no—
424C24—32no—
425C24—31no—
426C24—64no—
427C24—68no—
428C24D3×Dic311yescharacteristic
429C22×C4—24no—
430C22×C4—31no—
431C22×C4—31no—
432C22×C4—31no—
433C22×C4—31no—
434C22×C4—31no—
435C22×C4—38no—
436C22×C4—32no—
437C22×C4—32no—
438C22×C4—31no—
439C22×C4—32no—
440C22×C4—32no—
441C22×C4—32no—
442C22×C4—32no—
443C22×C4—32no—
444C22×C4—32no—
445C22×C4—64no—
446C22×C4—68no—
447C22×C4—68no—
448C22×C4—68no—
449C22×C4—68no—
450C22×C4—64no—
451C22×C4—64no—
452C22×C4—64no—
453C22×C4D3×Dic311yescharacteristic
454C22×C4D3×Dic312yes—
455C22×C4C2×D3212yes—
456C22×C4C2×D3211yescharacteristic
457M16—64no—
458M16—188no—
459M16—184no—
460C2×C8—34no—
461C2×C8—94no—
462C2×C8—188no—
463C22×C3—28no—
464C22×C3—28no—
465C22×C3—22no—
466C22×C3—22no—
467C22×C3—22no—
468C22×C3—22no—
469C22×C3—22no—
470C22×C3—22no—
471C22×C3—21no—
472C22×C3—24no—
473C22×C3—22no—
474C22×C3—32no—
475C22×C3—34no—
476C22×C3—32no—
477C22×C3—34no—
478C22×C3—42no—
479C22×C3—42no—
480C22×C3—42no—
481C22×C3—48no—
482C22×C3—68no—
483C22×C3—616no—
484C22×C3—68no—
485C22×C3—616no—
486C22×C3—62no—
487C22×C3—62no—
488C22×C3—62no—
489C22×C3D3×C22⋊C412yes—
490C22×C3D3×M1614yescomplemented
491C22×C3C2×#20814yescomplemented
492C22×C3C2×#21712yes—
493C22×C3C22×C4×D311yescharacteristic
494C22×C3C23×Dic311yescharacteristic
495C2×D3—28no—
496C2×D3—216no—
497C2×D3—22no—
498C2×D3—22no—
499C2×D3—22no—
500C2×D3—216no—
501C2×D3—28no—
502C2×D3C2×#20814yes—
503C2×D3C2×#20814yescomplemented
504C2×D3C2×#21712yes—
505C2×D3C2×#21712yes—
506C3×C4—22no—
507C3×C4—22no—
508C3×C4—22no—
509C3×C4—22no—
510C3×C4—32no—
511C3×C4—32no—
512C3×C4—42no—
513C3×C4—62no—
514C3×C4D3×C22⋊C412yes—
515C3×C4C2×#21712yes—
516C3×C4C2×D3×D412yes—
517C3×C4C22×#6712yes—
518Dic3—22no—
519Dic3C2×#21712yes—
520Dic3C2×#21712yes—
521C32C2×#40711yescharacteristic, complemented, Sylow
522C23—24no—
523C23—22no—
524C23—31no—
525C23—31no—
526C23—32no—
527C23—38no—
528C23—34no—
529C23—64no—
530C23—64no—
531C23—64no—
532C23—64no—
533C23—64no—
534C23—64no—
535C23—632no—
536C23—64no—
537C23—62no—
538C23C2×D3×Dic312yes—
539C23C2×D3×Dic311yescharacteristic
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—31no—
544C2×C4—31no—
545C2×C4—34no—
546C2×C4—34no—
547C2×C4—34no—
548C2×C4—34no—
549C2×C4—34no—
550C2×C4—32no—
551C2×C4—64no—
552C2×C4—64no—
553C2×C4—64no—
554C2×C4—64no—
555C2×C4—64no—
556C2×C4—64no—
557C2×C4—62no—
558C2×C4—64no—
559C2×C4—64no—
560C2×C4C2×D3×Dic312yes—
561C2×C4C2×D3×Dic311yescharacteristic
562C2×C4D3×#6714yes—
563C2×C4C22×D3211yescharacteristic
564C8—64no—
565C8—184no—
566C2×C3—22no—
567C2×C3—24no—
568C2×C3—24no—
569C2×C3—22no—
570C2×C3—21no—
571C2×C3—22no—
572C2×C3—34no—
573C2×C3—44no—
574C2×C3—42no—
575C2×C3—62no—
576C2×C3—64no—
577C2×C3C2×D3×C22⋊C411yescharacteristic
578C2×C3C2×D3×M1612yes—
579C2×C3C22×#20812yes—
580C2×C3C22×#21711yescharacteristic
581D3—24no—
582D3—22no—
583D3#520714yesdirect product factor
584C22—28no—
585C22—22no—
586C22—22no—
587C22—22no—
588C22—32no—
589C22—34no—
590C22—32no—
591C22—34no—
592C22—616no—
593C22—68no—
594C22—616no—
595C22—68no—
596C22—62no—
597C22—62no—
598C22—62no—
599C22D3×#20814yescomplemented
600C22D3×#21712yes—
601C22C22×D3×Dic311yescharacteristic
602C4—22no—
603C4—32no—
604C4—32no—
605C4—62no—
606C4D3×#21712yes—
607C4C2×D3×#6712yes—
608C3—21no—
609C3D3×#40711yescharacteristic, complemented
610C3C2×#520711yescharacteristic, complemented
611C2—24no—
612C2—22no—
613C2—34no—
614C2—62no—
615C2—64no—
616C2C2×D3×#20812yes—
617C2C2×D3×#21711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC23×C32×C4C22
prime radicalC24×C3×D3C4
cosocleC2×C32×C4C24
hypercenterC23×C4D32
hypocenterC32C2×#407
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×D3×#208C2semidirect
3. #10592906C2semidirect
4. C3×#5207C2semidirect
5. #10591154C2semidirect
6. D3×#830C2semidirect
7. #10591069C2semidirect
22. C2×#3748C22semidirect
23. C2×C3×#208C22semidirect
24. C2×#3711C22semidirect
26. C2×D3×C3⋊C8C22semidirect
27. #63657C22semidirect
28. C3×#830C22semidirect
29. (C2×D3)⋊(C3⋊C8)C22semidirect
40. #5207D3direct (N × H)
81. C2×C3⋊(C3⋊C8)C23semidirect
83. C2×C3×C3⋊C8C23semidirect
118. C2×#208C2×D3semidirect
128. #830C2×D3semidirect
144. C22×C3×D3M16semidirect
268. C2×C3⋊C8C22×D3semidirect
276. C22×C32C2×M16semidirect
288. C2×C3×D3C2×M16semidirect
350. C22×D3#208semidirect
421. C3×D3#407semidirect
490. C22×C3D3×M16semidirect
491. C22×C3C2×#208semidirect
503. C2×D3C2×#208semidirect
521. C32C2×#407semidirect
583. D3#5207direct (N × H)
599. C22D3×#208semidirect
609. C3D3×#407semidirect
610. C3C2×#5207semidirect

Maximal subgroups

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

subgroupindex
C23×C3×C4×D32
C2×D3×#2082
#105929062
C3×#52072
#105911542
D3×#8302
#105910692
C2×#52073
D3×#4073