Finite Group Databasebeta

← D3×#5225 #11857869

Subgroups — D3×#5225 #11857869

Order 1152.

1579 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×Q8C211yesmaximal, characteristic
2D3×#926C211yesmaximal, characteristic
3C2×D3×#208C211yesmaximal, characteristic
4#10592924C211yesmaximal, characteristic, complemented
5C3×#5225C211yesmaximal, characteristic, complemented
6#10591557C214yesmaximal, complemented
7D3×#835C214yesmaximal, complemented
8#10591100C211yesmaximal, characteristic, complemented
9#10591099C211yesmaximal, characteristic, complemented
10C2×#5225—31nomaximal
11D3×#419—31nomaximal
12C22×C32×Q8C2211yescharacteristic
13C2×C3×D3×Q8—24no—
14C2×C3×D3×Q8—21no—
15C2×C3×D3×Q8—21no—
16C2×C3×D3×Q8C418yescomplemented
17C2×C3×D3×Q8C2212yes—
18C2×C3×D3×Q8C2212yes—
19C22×C3×C4×D3—21no—
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×Dic6—21no—
22C22×C3×Dic6C2211yescharacteristic
23#64135C2211yescharacteristic
24C2×#3748C2211yescharacteristic
25C3×#926C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27D3×#217—21no—
28#63955—21no—
29D3×C4⋊Dic3C2212yes—
30C4×D3×Dic3—21no—
31#63855—21no—
32#63841C2212yes—
33C2×#3711C2212yes—
34D3×#208—24no—
35C2×D3×C3⋊C8C2212yes—
36#63662C2214yescomplemented
37C3×#835C2214yescomplemented
38#63566C2214yescomplemented
39#63565C2214yescomplemented
40C23×C3×Q8—31no—
41C22×D3×Q8D311yescharacteristic
42C2×#926—31no—
43C22×#208—31no—
44C2×D3×M16—31no—
45D3×#117—31no—
46C3×#419—31no—
47#5225—31no—
48#5225—31no—
49#5225—31no—
50#5225—31no—
51#5225—34no—
52#5225—61no—
53#5225D311yescharacteristic, direct product factor
54C2×#835—34no—
55#5120—31no—
56#5004—31no—
57#4802—34no—
58D3×#103—34no—
59C23×C3×D3D411yescharacteristic
60C2×C32×Q8—22no—
61C2×C32×Q8—21no—
62C2×C32×Q8C2×C414yescomplemented
63C2×C32×Q8C2312yes—
64C22×C32×C4—21no—
65C22×C32×C4C2311yescharacteristic
66C22×C3×Dic3—21no—
67C22×C3×Dic3D411yescharacteristic
68C3×D3×Q8—28no—
69C3×D3×Q8—28no—
70C3×D3×Q8—24no—
71C3×D3×Q8—24no—
72C3×D3×Q8C2×C418yes—
73C3×D3×Q8C2×C418yescomplemented
74C2×C3×C4×D3—28no—
75C2×C3×C4×D3—22no—
76C2×C3×C4×D3—22no—
77C2×C3×C4×D3C2×C414yes—
78C2×C3×C4×D3D411yescharacteristic
79C2×C3×C4×D3D411yescharacteristic
80C2×C3×C4×D3D414yes—
81C2×C3×C4×D3C2311yescharacteristic
82C2×C3×C4×D3C2311yescharacteristic
83C2×C3×Dic6—21no—
84C2×C3×Dic6—22no—
85C2×C3×Dic6—28no—
86C2×C3×Dic6—22no—
87C2×C3×Dic6—22no—
88C2×C3×Dic6C2×C414yescomplemented
89C2×C3×Dic6C2312yes—
90C2×D3×Dic3—22no—
91#3757—21no—
92C4⋊(C3⋊Dic3)C2312yes—
93C4×C3⋊Dic3—21no—
94#3748—22no—
95C2×C3⋊(C3⋊C8)C2312yes—
96C3×#217—21no—
97C3×C4⋊Dic3C2312yes—
98C3×C4×Dic3—21no—
99C3×#208—22no—
100C2×C3×C3⋊C8C2312yes—
101Dic3⋊Dic3—22no—
102(C2×D3)⋊Dic3—22no—
103Dic32—22no—
104#3711—24no—
105D3×C3⋊C8—24no—
106C2×#419—91noSylow
107C22×C3×Q8—21no—
108C22×C3×Q8—38no—
109C22×C3×Q8—32no—
110C22×C3×Q8—32no—
111C22×C3×Q8—31no—
112C22×C3×Q8—61no—
113C22×C3×Q8—64no—
114C22×C3×Q8—61no—
115C22×C3×Q8—61no—
116C22×C3×Q8C2×D311yescharacteristic
117C22×C3×Q8C2×D311yescharacteristic
118C23×C3×C4—31no—
119C23×C3×C4—61no—
120C2×D3×Q8—24no—
121C2×D3×Q8—21no—
122C2×D3×Q8—21no—
123C2×D3×Q8Dic318yescomplemented
124C2×D3×Q8C2×D312yes—
125C2×D3×Q8C2×D312yes—
126C22×C4×D3—21no—
127C22×C4×D3C2×D311yescharacteristic
128C22×Dic6—21no—
129C22×Dic6C2×D311yescharacteristic
130C2×C3×M16—31no—
131C3×#117—31no—
132C2×#217—61no—
133#926—31no—
134#926—31no—
135#926—32no—
136#926—61no—
137#926—61no—
138#926—61no—
139#926C2×D311yescharacteristic
140C2×C4⋊Dic3—32no—
141C2×C4×Dic3—61no—
142C2×#208—31no—
143C2×#208—31no—
144C2×#208—32no—
145C2×#208—61no—
146C2×#208—64no—
147C2×#208C2×D311yescharacteristic
148C22×C3⋊C8—32no—
149D3×M16—64no—
150C2×ΓL(1,𝔽25)—32no—
151C2×D3×C8—32no—
152#892—32no—
153D3×C4⋊C4—32no—
154D3×C22⋊C4—61no—
155#877—61no—
156#872—61no—
157C42×D3—61no—
158C3×#103—34no—
159#835—34no—
160#835—34no—
161#835—34no—
162#835—34no—
163#835—64no—
164#835C2×D314yescomplemented
165#816—34no—
166#810—34no—
167C23×C32C2×D411yescharacteristic
168C22×C3×D3—24no—
169C22×C3×D3C22⋊C414yes—
170C22×C3×D3C2×D411yescharacteristic
171C22×C3×D3C2×D411yescharacteristic
172C32×Q8—24no—
173C32×Q8—22no—
174C32×Q8C22×C414yes—
175C2×C32×C4—24no—
176C2×C32×C4—22no—
177C2×C32×C4C22×C412yes—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2×D412yes—
180C2×C32×C4C2411yescharacteristic
181C2×C3⋊Dic3—22no—
182C2×C3×Dic3—24no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3C22⋊C414yes—
186C2×C3×Dic3C2×D411yescharacteristic
187C2×C3×Dic3C2×D411yescharacteristic
188C3×C4×D3—28no—
189C3×C4×D3—28no—
190C3×C4×D3C22⋊C414yes—
191C3×C4×D3C22⋊C414yes—
192C3×C4×D3C22×C412yes—
193C3×C4×D3C22×C412yes—
194C3×C4×D3C2×D412yes—
195C3×C4×D3C2×D412yes—
196C3×Dic6—24no—
197C3×Dic6—22no—
198C3×Dic6—28no—
199C3×Dic6—28no—
200C3×Dic6C22×C414yes—
201D3×Dic3—44no—
202C3⋊(C3⋊C8)—22no—
203C3×C3⋊C8—22no—
204C23×Q8—31no—
205C22×M16—91no—
206C2×#117—91no—
207#419—31no—
208#419—94no—
209#419—91no—
210#419—91no—
211#419—91no—
212C2×#103—94no—
213C24×C3—31no—
214C23×D3#6711yescharacteristic
215C2×C3×Q8—22no—
216C2×C3×Q8—21no—
217C2×C3×Q8—22no—
218C2×C3×Q8—21no—
219C2×C3×Q8—24no—
220C2×C3×Q8—22no—
221C2×C3×Q8—38no—
222C2×C3×Q8—38no—
223C2×C3×Q8—34no—
224C2×C3×Q8—32no—
225C2×C3×Q8—42no—
226C2×C3×Q8—41no—
227C2×C3×Q8—68no—
228C2×C3×Q8—62no—
229C2×C3×Q8—62no—
230C2×C3×Q8—68no—
231C2×C3×Q8—68no—
232C2×C3×Q8—64no—
233C2×C3×Q8—64no—
234C2×C3×Q8—62no—
235C2×C3×Q8—61no—
236C2×C3×Q8C4×D314yescomplemented
237C2×C3×Q8C2×Dic314yescomplemented
238C2×C3×Q8C22×D312yes—
239C2×C3×Q8C22×D312yes—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—31no—
244C22×C3×C4—34no—
245C22×C3×C4—34no—
246C22×C3×C4—31no—
247C22×C3×C4—31no—
248C22×C3×C4—31no—
249C22×C3×C4—31no—
250C22×C3×C4—41no—
251C22×C3×C4—68no—
252C22×C3×C4—62no—
253C22×C3×C4—62no—
254C22×C3×C4—61no—
255C22×C3×C4C22×D311yescharacteristic
256C22×C3×C4C22×D311yescharacteristic
257C22×Dic3—21no—
258C22×Dic3—62no—
259C22×Dic3#6711yescharacteristic
260D3×Q8—28no—
261D3×Q8—28no—
262D3×Q8—24no—
263D3×Q8—24no—
264D3×Q8C2×Dic318yes—
265D3×Q8C2×Dic318yescomplemented
266C2×C4×D3—28no—
267C2×C4×D3—22no—
268C2×C4×D3—22no—
269C2×C4×D3—62no—
270C2×C4×D3C2×Dic314yes—
271C2×C4×D3#6711yescharacteristic
272C2×C4×D3#6711yescharacteristic
273C2×C4×D3#6714yes—
274C2×C4×D3C22×D311yescharacteristic
275C2×C4×D3C22×D311yescharacteristic
276C2×Dic6—21no—
277C2×Dic6—22no—
278C2×Dic6—28no—
279C2×Dic6—22no—
280C2×Dic6—22no—
281C2×Dic6C2×Dic314yescomplemented
282C2×Dic6C22×D312yes—
283C3×M16—62no—
284C2×C3×C8—32no—
285C3×C4⋊C4—32no—
286C3×C22⋊C4—61no—
287C3×C42—61no—
288#217—21no—
289#217—62no—
290#217—61no—
291#217—61no—
292#217—121no—
293(C2×D3)⋊C4—62no—
294C4⋊Dic3—32no—
295C4⋊Dic3—32no—
296C4⋊Dic3—62no—
297C4⋊Dic3—62no—
298C4⋊Dic3C22×D312yes—
299Dic3⋊C4—62no—
300C4×Dic3—21no—
301C4×Dic3—62no—
302C4×Dic3—61no—
303C4×Dic3—61no—
304C4×Dic3—62no—
305C4×Dic3—121no—
306#208—22no—
307#208—64no—
308#208—62no—
309#208—62no—
310#208—122no—
311C2×C3⋊C8—32no—
312C2×C3⋊C8—32no—
313C2×C3⋊C8—62no—
314C2×C3⋊C8—64no—
315C2×C3⋊C8C22×D312yes—
316ΓL(1,𝔽25)—64no—
317D3×C8—64no—
318C22×C32—22no—
319C22×C32C2×C22⋊C412yes—
320C22×C32C22×D411yescharacteristic
321C2×C3×D3—22no—
322C2×C3×D3—28no—
323C2×C3×D3C2×C22⋊C412yes—
324C2×C3×D3C2×C22⋊C412yes—
325C2×C3×D3#13714yes—
326C32×C4—24no—
327C32×C4C2×C22⋊C412yes—
328C32×C4C23×C411yescharacteristic
329C32×C4C22×D411yescharacteristic
330C3⋊Dic3—42no—
331C3×Dic3—24no—
332C3×Dic3—42no—
333C3×Dic3C2×C22⋊C412yes—
334C3×Dic3C2×C22⋊C412yes—
335C22×Q8—38no—
336C22×Q8—32no—
337C22×Q8—32no—
338C22×Q8—31no—
339C22×Q8—61no—
340C22×Q8—61no—
341C22×Q8—61no—
342C22×Q8—64no—
343C22×Q8D3211yescharacteristic
344C23×C4—31no—
345C23×C4—61no—
346C2×M16—31no—
347C2×M16—92no—
348C2×M16—91no—
349C2×M16—184no—
350C22×C8—92no—
351#117—31no—
352#117—92no—
353#117—91no—
354#117—181no—
355#117—181no—
356C2×C4⋊C4—92no—
357C2×C22⋊C4—181no—
358C2×C42—181no—
359#103—34no—
360#103—94no—
361#103—94no—
362#103—94no—
363C23×C3—21no—
364C23×C3—31no—
365C23×C3—34no—
366C23×C3—31no—
367C23×C3—64no—
368C23×C3D3×D411yescharacteristic
369C23×C3C2×#6711yescharacteristic
370C22×D3—24no—
371C22×D3#21714yes—
372C22×D3C2×#6711yescharacteristic
373C22×D3C2×#6711yescharacteristic
374C3×Q8—24no—
375C3×Q8—24no—
376C3×Q8—22no—
377C3×Q8—22no—
378C3×Q8—24no—
379C3×Q8—34no—
380C3×Q8—42no—
381C3×Q8—44no—
382C3×Q8—68no—
383C3×Q8—68no—
384C3×Q8—64no—
385C3×Q8—62no—
386C3×Q8C2×C4×D314yes—
387C3×Q8C22×Dic314yes—
388C2×C3×C4—24no—
389C2×C3×C4—24no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—21no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—21no—
396C2×C3×C4—34no—
397C2×C3×C4—31no—
398C2×C3×C4—31no—
399C2×C3×C4—34no—
400C2×C3×C4—34no—
401C2×C3×C4—32no—
402C2×C3×C4—32no—
403C2×C3×C4—32no—
404C2×C3×C4—32no—
405C2×C3×C4—42no—
406C2×C3×C4—44no—
407C2×C3×C4—68no—
408C2×C3×C4—68no—
409C2×C3×C4—64no—
410C2×C3×C4—62no—
411C2×C3×C4—62no—
412C2×C3×C4C2×C4×D312yes—
413C2×C3×C4D3×D411yescharacteristic
414C2×C3×C4D3×D412yes—
415C2×C3×C4C22×Dic312yes—
416C2×C3×C4C2×#6711yescharacteristic
417C2×C3×C4C2×#6712yes—
418C2×C3×C4C23×D311yescharacteristic
419C2×C3×C4C23×D311yescharacteristic
420C2×Dic3—24no—
421C2×Dic3—22no—
422C2×Dic3—22no—
423C2×Dic3—62no—
424C2×Dic3—62no—
425C2×Dic3—122no—
426C2×Dic3—124no—
427C2×Dic3#21714yes—
428C2×Dic3C2×#6711yescharacteristic
429C2×Dic3C2×#6711yescharacteristic
430C4×D3—28no—
431C4×D3—28no—
432C4×D3—124no—
433C4×D3#21714yes—
434C4×D3#21714yes—
435C4×D3C22×Dic312yes—
436C4×D3C22×Dic312yes—
437C4×D3C2×#6712yes—
438C4×D3C2×#6712yes—
439Dic6—24no—
440Dic6—22no—
441Dic6—28no—
442Dic6—28no—
443Dic6C22×Dic314yes—
444C3×C8—62no—
445C3⋊C8—22no—
446C3⋊C8—62no—
447C3⋊C8—62no—
448C3⋊C8—122no—
449C2×C32—22no—
450C2×C32C22×C22⋊C411yescharacteristic
451C2×C32C2×#13712yes—
452C3×D3—22no—
453C3×D3#41914yescomplemented
454C24—31no—
455C2×Q8—21no—
456C2×Q8—22no—
457C2×Q8—38no—
458C2×Q8—38no—
459C2×Q8—32no—
460C2×Q8—34no—
461C2×Q8—62no—
462C2×Q8—62no—
463C2×Q8—68no—
464C2×Q8—64no—
465C2×Q8—64no—
466C2×Q8—68no—
467C2×Q8—68no—
468C2×Q8—61no—
469C2×Q8—62no—
470C2×Q8D3×Dic314yescomplemented
471C2×Q8C2×D3212yes—
472C22×C4—21no—
473C22×C4—31no—
474C22×C4—31no—
475C22×C4—31no—
476C22×C4—34no—
477C22×C4—31no—
478C22×C4—31no—
479C22×C4—34no—
480C22×C4—62no—
481C22×C4—62no—
482C22×C4—68no—
483C22×C4—61no—
484C22×C4—182no—
485C22×C4C2×D3211yescharacteristic
486M16—62no—
487M16—184no—
488M16—182no—
489C2×C8—32no—
490C2×C8—92no—
491C2×C8—184no—
492C4⋊C4—32no—
493C4⋊C4—92no—
494C4⋊C4—182no—
495C22⋊C4—61no—
496C22⋊C4—182no—
497C22⋊C4—181no—
498C42—61no—
499C42—182no—
500C42—181no—
501C22×C3—22no—
502C22×C3—22no—
503C22×C3—21no—
504C22×C3—22no—
505C22×C3—32no—
506C22×C3—34no—
507C22×C3—32no—
508C22×C3—42no—
509C22×C3—68no—
510C22×C3—62no—
511C22×C3D3×C22⋊C412yes—
512C22×C3C2×#21712yes—
513C22×C3C2×D3×D411yescharacteristic
514C22×C3C22×#6711yescharacteristic
515C2×D3—22no—
516C2×D3—28no—
517C2×D3#94214yes—
518C2×D3C2×#21712yes—
519C2×D3C2×#21712yes—
520C3×C4—24no—
521C3×C4—24no—
522C3×C4—21no—
523C3×C4—21no—
524C3×C4—22no—
525C3×C4—32no—
526C3×C4—32no—
527C3×C4—44no—
528C3×C4—64no—
529C3×C4—122no—
530C3×C4D3×C22⋊C412yes—
531C3×C4C2×#21712yes—
532C3×C4C22×C4×D311yescharacteristic
533C3×C4C2×D3×D411yescharacteristic
534C3×C4C23×Dic311yescharacteristic
535C3×C4C22×#6711yescharacteristic
536Dic3—24no—
537Dic3—42no—
538Dic3—122no—
539Dic3—122no—
540Dic3—242no—
541Dic3C2×#21712yes—
542Dic3C2×#21712yes—
543C32C2×#41911yescharacteristic, complemented, Sylow
544C23—31no—
545C23—31no—
546C23—34no—
547C23—64no—
548C23D3×#6711yescharacteristic
549Q8—22no—
550Q8—24no—
551Q8—34no—
552Q8—68no—
553Q8—68no—
554Q8—62no—
555Q8—64no—
556Q8C2×D3×Dic314yes—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—31no—
560C2×C4—31no—
561C2×C4—34no—
562C2×C4—32no—
563C2×C4—32no—
564C2×C4—32no—
565C2×C4—32no—
566C2×C4—34no—
567C2×C4—34no—
568C2×C4—68no—
569C2×C4—68no—
570C2×C4—62no—
571C2×C4—64no—
572C2×C4—62no—
573C2×C4—182no—
574C2×C4—364no—
575C2×C4C2×D3×Dic312yes—
576C2×C4D3×#6712yes—
577C2×C4D3×#6711yescharacteristic
578C2×C4C22×D3211yescharacteristic
579C8—62no—
580C8—182no—
581C2×C3—22no—
582C2×C3—22no—
583C2×C3—21no—
584C2×C3—22no—
585C2×C3—34no—
586C2×C3—42no—
587C2×C3—62no—
588C2×C3C2×D3×C22⋊C411yescharacteristic
589C2×C3D3×#13712yes—
590C2×C3C2×#94212yes—
591C2×C3C22×#21711yescharacteristic
592D3—22no—
593D3#522514yesdirect product factor
594C22—22no—
595C22—32no—
596C22—34no—
597C22—32no—
598C22—68no—
599C22—62no—
600C22D3×#21712yes—
601C22C2×D3×#6711yescharacteristic
602C4—24no—
603C4—32no—
604C4—32no—
605C4—64no—
606C4—122no—
607C4—362no—
608C4D3×#21712yes—
609C4C22×D3×Dic311yescharacteristic
610C4C2×D3×#6711yescharacteristic
611C3—21no—
612C3D3×#41911yescharacteristic, complemented
613C3C2×#522511yescharacteristic, complemented
614C2—22no—
615C2—34no—
616C2—62no—
617C2D3×#94212yes—
618C2C2×D3×#21711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalC23×C3×D3D4
cosocleC2×C32×C4C24
hypercenterC22×Q8D32
hypocenterC32C2×#419
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
4. #10592924C2semidirect
5. C3×#5225C2semidirect
6. #10591557C2semidirect
7. D3×#835C2semidirect
8. #10591100C2semidirect
9. #10591099C2semidirect
16. C2×C3×D3×Q8C4semidirect
36. #63662C22semidirect
37. C3×#835C22semidirect
38. #63566C22semidirect
39. #63565C22semidirect
53. #5225D3direct (N × H)
62. C2×C32×Q8C2×C4semidirect
73. C3×D3×Q8C2×C4semidirect
88. C2×C3×Dic6C2×C4semidirect
123. C2×D3×Q8Dic3semidirect
164. #835C2×D3semidirect
236. C2×C3×Q8C4×D3semidirect
237. C2×C3×Q8C2×Dic3semidirect
265. D3×Q8C2×Dic3semidirect
281. C2×Dic6C2×Dic3semidirect
453. C3×D3#419semidirect
470. C2×Q8D3×Dic3semidirect
543. C32C2×#419semidirect
593. D3#5225direct (N × H)
612. C3D3×#419semidirect
613. C3C2×#5225semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×Q82
D3×#9262
C2×D3×#2082
#105929242
C3×#52252
#105915572
D3×#8352
#105911002
#105910992
C2×#52253
D3×#4193