Finite Group Databasebeta

← D3×#5120 #11857871

Subgroups — D3×#5120 #11857871

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×D3×Dic6C211yesmaximal, characteristic
2C2×C3×D3×M16C211yesmaximal, characteristic
3D3×#926C211yesmaximal, characteristic
4#10592819C211yesmaximal, characteristic, complemented
5C3×#5120C211yesmaximal, characteristic, complemented
6#10591107C211yesmaximal, characteristic, complemented
7#10591100C211yesmaximal, characteristic, complemented
8#10590948C214yesmaximal, complemented
9D3×#816C214yesmaximal, complemented
10C2×#5120—31nomaximal
11D3×#419—31nomaximal
12C22×#634C2211yescharacteristic
13C22×C3×C4×D3C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C22×#627—21no—
16C22×D3×Dic3—21no—
17C2×D3×Dic6—21no—
18C2×D3×Dic6—21no—
19C2×D3×Dic6—24no—
20C2×D3×Dic6C418yescomplemented
21C2×D3×Dic6C2212yes—
22C2×D3×Dic6C2212yes—
23C2×C32×M16C2211yescharacteristic
24#64135C2211yescharacteristic
25C3×#926C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27C3×D3×M16—24no—
28C2×C3×ΓL(1,𝔽25)C2212yes—
29C2×C3×D3×C8C2212yes—
30D3×#217—21no—
31#63955—21no—
32D3×C4⋊Dic3C2212yes—
33C4×D3×Dic3—21no—
34#63855—21no—
35#63841C2212yes—
36#63643C2214yescomplemented
37C3×#816C2214yescomplemented
38#63567C2214yescomplemented
39#63566C2214yescomplemented
40C22×D3×Q8—31no—
41C23×Dic6—31no—
42C22×C3×M16—31no—
43C2×#926—31no—
44C2×D3×M16D311yescharacteristic
45D3×#117—31no—
46C3×#419—31no—
47#5225—31no—
48#5120—31no—
49#5120—31no—
50#5120—31no—
51#5120—31no—
52#5120—34no—
53#5120—61no—
54#5120D311yescharacteristic, direct product factor
55C2×#816—34no—
56#5004—31no—
57#4802—34no—
58D3×#103—34no—
59C23×C3×D3D411yescharacteristic
60C22×C32×C4C2311yescharacteristic
61C22×C3⋊Dic3—21no—
62C2×#634—21no—
63C2×#634—22no—
64C2×#634C2×C414yescomplemented
65C2×#634C2312yes—
66C22×C3×Dic3—21no—
67C22×C3×Dic3D411yescharacteristic
68C2×C3×C4×D3C2×C414yes—
69C2×C3×C4×D3D411yescharacteristic
70C2×C3×C4×D3D411yescharacteristic
71C2×C3×C4×D3D414yes—
72C2×C3×C4×D3C2311yescharacteristic
73C2×C3×C4×D3C2311yescharacteristic
74C2×C3×Dic6—21no—
75C2×C3×Dic6—22no—
76C2×C3×Dic6C2×C414yescomplemented
77C2×C3×Dic6C2312yes—
78C2×#627—28no—
79C2×#627—22no—
80C2×#627—22no—
81C2×D3×Dic3—28no—
82C2×D3×Dic3—22no—
83C2×D3×Dic3—22no—
84C2×D3×Dic3—22no—
85D3×Dic6—28no—
86D3×Dic6—28no—
87D3×Dic6—24no—
88D3×Dic6—24no—
89D3×Dic6C2×C418yes—
90D3×Dic6C2×C418yescomplemented
91C32×M16—22no—
92C2×C32×C8C2312yes—
93#3757—21no—
94C4⋊(C3⋊Dic3)C2312yes—
95C4×C3⋊Dic3—21no—
96C3×#217—21no—
97C3×C4⋊Dic3C2312yes—
98C3×C4×Dic3—21no—
99C3×#208—22no—
100C2×C3×C3⋊C8C2312yes—
101C3×ΓL(1,𝔽25)—24no—
102C3×D3×C8—24no—
103Dic3⋊Dic3—22no—
104(C2×D3)⋊Dic3—22no—
105Dic32—22no—
106C2×#419—91noSylow
107C22×C3×Q8—31no—
108C23×C3×C4—31no—
109C23×Dic3—61no—
110C2×D3×Q8—38no—
111C2×D3×Q8—32no—
112C2×D3×Q8—32no—
113C2×D3×Q8—61no—
114C2×D3×Q8—61no—
115C2×D3×Q8—64no—
116C22×C4×D3—61no—
117C22×C4×D3C2×D311yescharacteristic
118C22×Dic6—31no—
119C22×Dic6—31no—
120C22×Dic6—38no—
121C22×Dic6—32no—
122C22×Dic6—32no—
123C22×Dic6—61no—
124C22×Dic6—61no—
125C22×Dic6—61no—
126C22×Dic6—64no—
127C22×Dic6—61no—
128C22×Dic6—61no—
129C22×Dic6C2×D311yescharacteristic
130C2×C3×M16—21no—
131C2×C3×M16—31no—
132C2×C3×M16—32no—
133C2×C3×M16—64no—
134C2×C3×M16C2×D311yescharacteristic
135C2×C3×M16C2×D311yescharacteristic
136C22×C3×C8—32no—
137C3×#117—31no—
138C2×#217—61no—
139#926—31no—
140#926—31no—
141#926—32no—
142#926—61no—
143#926—61no—
144#926—61no—
145#926C2×D311yescharacteristic
146C2×C4⋊Dic3—32no—
147C2×C4×Dic3—61no—
148C2×#208C2×D311yescharacteristic
149D3×M16—24no—
150C2×ΓL(1,𝔽25)C2×D312yes—
151C2×D3×C8C2×D312yes—
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#816—34no—
161#816—34no—
162#816—34no—
163#816—34no—
164#816—64no—
165#816C2×D314yescomplemented
166#810—34no—
167C23×C32C2×D411yescharacteristic
168C22×C3×D3—24no—
169C22×C3×D3C22⋊C414yes—
170C22×C3×D3C2×D411yescharacteristic
171C22×C3×D3C2×D411yescharacteristic
172C2×C32×C4C22×C412yes—
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2×D412yes—
175C2×C32×C4C2411yescharacteristic
176C2×C3⋊Dic3—24no—
177C2×C3⋊Dic3—22no—
178C2×C3⋊Dic3—22no—
179#634—24no—
180#634—22no—
181#634C22×C414yes—
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×D3C22⋊C414yes—
189C3×C4×D3C22⋊C414yes—
190C3×C4×D3C22×C412yes—
191C3×C4×D3C22×C412yes—
192C3×C4×D3C2×D412yes—
193C3×C4×D3C2×D412yes—
194C3×Dic6—24no—
195C3×Dic6—22no—
196C3×Dic6C22×C414yes—
197#627—28no—
198#627—28no—
199D3×Dic3—28no—
200D3×Dic3—28no—
201D3×Dic3—44no—
202C32×C8—22no—
203C3×C3⋊C8—22no—
204C23×Q8—91no—
205C22×M16—31no—
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×D3D1211yescharacteristic
215C2×C3×Q8—34no—
216C2×C3×Q8—32no—
217C2×C3×Q8—61no—
218C2×C3×Q8—62no—
219C22×C3×C4—21no—
220C22×C3×C4—31no—
221C22×C3×C4—34no—
222C22×C3×C4—31no—
223C22×C3×C4—31no—
224C22×C3×C4—34no—
225C22×C3×C4—31no—
226C22×C3×C4—31no—
227C22×C3×C4—61no—
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C22×Dic3—21no—
231C22×Dic3—68no—
232C22×Dic3—62no—
233C22×Dic3—62no—
234C22×Dic3—62no—
235C22×Dic3—61no—
236C22×Dic3—61no—
237C22×Dic3—121no—
238C22×Dic3D1211yescharacteristic
239D3×Q8—38no—
240D3×Q8—38no—
241D3×Q8—68no—
242D3×Q8—68no—
243D3×Q8—64no—
244D3×Q8—64no—
245C2×C4×D3—68no—
246C2×C4×D3—62no—
247C2×C4×D3—62no—
248C2×C4×D3—62no—
249C2×C4×D3C4×D314yes—
250C2×C4×D3D1211yescharacteristic
251C2×C4×D3D1211yescharacteristic
252C2×C4×D3#6714yes—
253C2×C4×D3C22×D311yescharacteristic
254C2×C4×D3C22×D311yescharacteristic
255C2×Dic6—21no—
256C2×Dic6—22no—
257C2×Dic6—34no—
258C2×Dic6—34no—
259C2×Dic6—32no—
260C2×Dic6—32no—
261C2×Dic6—38no—
262C2×Dic6—38no—
263C2×Dic6—62no—
264C2×Dic6—64no—
265C2×Dic6—68no—
266C2×Dic6—68no—
267C2×Dic6—64no—
268C2×Dic6—64no—
269C2×Dic6—68no—
270C2×Dic6—62no—
271C2×Dic6—62no—
272C2×Dic6—61no—
273C2×Dic6—61no—
274C2×Dic6—62no—
275C2×Dic6—62no—
276C2×Dic6—68no—
277C2×Dic6—62no—
278C2×Dic6—62no—
279C2×Dic6—121no—
280C2×Dic6—122no—
281C2×Dic6C4×D314yescomplemented
282C2×Dic6C22×D312yes—
283C3×M16—22no—
284C3×M16—22no—
285C3×M16—42no—
286C3×M16—64no—
287C3×M16—62no—
288C2×C3×C8—22no—
289C2×C3×C8—32no—
290C2×C3×C8—64no—
291C2×C3×C8C22×D312yes—
292C2×C3×C8C22×D312yes—
293C3×C4⋊C4—32no—
294C3×C22⋊C4—61no—
295C3×C42—61no—
296#217—21no—
297#217—62no—
298#217—61no—
299#217—61no—
300#217—121no—
301(C2×D3)⋊C4—62no—
302C4⋊Dic3—32no—
303C4⋊Dic3—32no—
304C4⋊Dic3—62no—
305C4⋊Dic3—62no—
306C4⋊Dic3C22×D312yes—
307Dic3⋊C4—62no—
308C4×Dic3—21no—
309C4×Dic3—62no—
310C4×Dic3—61no—
311C4×Dic3—61no—
312C4×Dic3—62no—
313C4×Dic3—121no—
314#208—22no—
315C2×C3⋊C8C22×D312yes—
316ΓL(1,𝔽25)—24no—
317D3×C8—24no—
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×C4C2×C22⋊C412yes—
327C32×C4C23×C411yescharacteristic
328C32×C4C22×D411yescharacteristic
329C3⋊Dic3—24no—
330C3⋊Dic3—42no—
331C3×Dic3—24no—
332C3×Dic3—42no—
333C3×Dic3C2×C22⋊C412yes—
334C3×Dic3C2×C22⋊C412yes—
335C22×Q8—31no—
336C22×Q8—92no—
337C22×Q8—92no—
338C22×Q8—98no—
339C22×Q8—91no—
340C22×Q8—181no—
341C22×Q8—181no—
342C22×Q8—181no—
343C22×Q8—184no—
344C23×C4—31no—
345C23×C4—181no—
346C2×M16—31no—
347C2×M16—32no—
348C2×M16—64no—
349C2×M16D3211yescharacteristic
350C22×C8—32no—
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×C3C2×D1211yescharacteristic
369C23×C3D3×D411yescharacteristic
370C22×D3—24no—
371C22×D3(C2×D3)⋊C414yes—
372C22×D3C2×D1211yescharacteristic
373C22×D3C2×D1211yescharacteristic
374C3×Q8—34no—
375C3×Q8—64no—
376C3×Q8—62no—
377C2×C3×C4—21no—
378C2×C3×C4—22no—
379C2×C3×C4—21no—
380C2×C3×C4—22no—
381C2×C3×C4—34no—
382C2×C3×C4—31no—
383C2×C3×C4—31no—
384C2×C3×C4—34no—
385C2×C3×C4—34no—
386C2×C3×C4—32no—
387C2×C3×C4—32no—
388C2×C3×C4—32no—
389C2×C3×C4—32no—
390C2×C3×C4—64no—
391C2×C3×C4—62no—
392C2×C3×C4—62no—
393C2×C3×C4C2×C4×D312yes—
394C2×C3×C4C2×C4×D312yes—
395C2×C3×C4C2×D1211yescharacteristic
396C2×C3×C4D3×D411yescharacteristic
397C2×C3×C4D3×D412yes—
398C2×C3×C4C2×#6712yes—
399C2×C3×C4C23×D311yescharacteristic
400C2×C3×C4C23×D311yescharacteristic
401C2×Dic3—24no—
402C2×Dic3—22no—
403C2×Dic3—22no—
404C2×Dic3—68no—
405C2×Dic3—68no—
406C2×Dic3—64no—
407C2×Dic3—64no—
408C2×Dic3—62no—
409C2×Dic3—62no—
410C2×Dic3—62no—
411C2×Dic3—62no—
412C2×Dic3—122no—
413C2×Dic3—124no—
414C2×Dic3—122no—
415C2×Dic3—124no—
416C2×Dic3(C2×D3)⋊C414yes—
417C2×Dic3C2×D1211yescharacteristic
418C2×Dic3C2×D1211yescharacteristic
419C4×D3—68no—
420C4×D3—68no—
421C4×D3—124no—
422C4×D3(C2×D3)⋊C414yes—
423C4×D3(C2×D3)⋊C414yes—
424C4×D3C2×C4×D312yes—
425C4×D3C2×C4×D312yes—
426C4×D3C2×#6712yes—
427C4×D3C2×#6712yes—
428Dic6—24no—
429Dic6—22no—
430Dic6—34no—
431Dic6—34no—
432Dic6—64no—
433Dic6—68no—
434Dic6—68no—
435Dic6—64no—
436Dic6—64no—
437Dic6—62no—
438Dic6—62no—
439Dic6—68no—
440Dic6—68no—
441Dic6—122no—
442Dic6—124no—
443Dic6C2×C4×D314yes—
444C3×C8—22no—
445C3×C8—22no—
446C3×C8—42no—
447C3×C8—62no—
448C3⋊C8—22no—
449C2×C32—22no—
450C2×C32C22×C22⋊C411yescharacteristic
451C2×C32C2×#13712yes—
452C3×D3—22no—
453C3×D3#41914yescomplemented
454C24—31no—
455C2×Q8—32no—
456C2×Q8—34no—
457C2×Q8—61no—
458C2×Q8—62no—
459C2×Q8—98no—
460C2×Q8—98no—
461C2×Q8—92no—
462C2×Q8—94no—
463C2×Q8—182no—
464C2×Q8—182no—
465C2×Q8—188no—
466C2×Q8—184no—
467C2×Q8—184no—
468C2×Q8—188no—
469C2×Q8—188no—
470C2×Q8—181no—
471C2×Q8—182no—
472C22×C4—31no—
473C22×C4—31no—
474C22×C4—31no—
475C22×C4—34no—
476C22×C4—31no—
477C22×C4—31no—
478C22×C4—34no—
479C22×C4—61no—
480C22×C4—182no—
481C22×C4—182no—
482C22×C4—188no—
483C22×C4—182no—
484C22×C4—181no—
485C22×C4C2×D3211yescharacteristic
486M16—22no—
487M16—64no—
488M16—62no—
489C2×C8—32no—
490C2×C8—64no—
491C2×C8C2×D3212yes—
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×(C2×D3)⋊C412yes—
513C22×C3C22×D1211yescharacteristic
514C22×C3C2×D3×D411yescharacteristic
515C2×D3—22no—
516C2×D3—28no—
517C2×D3#90914yes—
518C2×D3C2×(C2×D3)⋊C412yes—
519C2×D3C2×(C2×D3)⋊C412yes—
520C3×C4—21no—
521C3×C4—21no—
522C3×C4—22no—
523C3×C4—32no—
524C3×C4—32no—
525C3×C4—64no—
526C3×C4—122no—
527C3×C4D3×C22⋊C412yes—
528C3×C4C2×(C2×D3)⋊C412yes—
529C3×C4C22×C4×D311yescharacteristic
530C3×C4C22×C4×D311yescharacteristic
531C3×C4C2×D3×D411yescharacteristic
532C3×C4C22×#6711yescharacteristic
533Dic3—24no—
534Dic3—42no—
535Dic3—64no—
536Dic3—64no—
537Dic3—124no—
538Dic3—122no—
539Dic3—122no—
540Dic3—242no—
541Dic3C2×(C2×D3)⋊C412yes—
542Dic3C2×(C2×D3)⋊C412yes—
543C32C2×#41911yescharacteristic, complemented, Sylow
544C23—31no—
545C23—31no—
546C23—34no—
547C23—64no—
548C23D3×D1211yescharacteristic
549Q8—34no—
550Q8—62no—
551Q8—64no—
552Q8—94no—
553Q8—188no—
554Q8—188no—
555Q8—182no—
556Q8—184no—
557C2×C4—31no—
558C2×C4—31no—
559C2×C4—34no—
560C2×C4—32no—
561C2×C4—32no—
562C2×C4—32no—
563C2×C4—32no—
564C2×C4—34no—
565C2×C4—34no—
566C2×C4—62no—
567C2×C4—64no—
568C2×C4—62no—
569C2×C4—188no—
570C2×C4—188no—
571C2×C4—182no—
572C2×C4—184no—
573C2×C4—182no—
574C2×C4—364no—
575C2×C4C4×D3212yes—
576C2×C4D3×D1211yescharacteristic
577C2×C4D3×#6712yes—
578C2×C4C22×D3211yescharacteristic
579C8—22no—
580C8—62no—
581C2×C3—22no—
582C2×C3—22no—
583C2×C3—22no—
584C2×C3—21no—
585C2×C3—34no—
586C2×C3—42no—
587C2×C3—62no—
588C2×C3C2×D3×C22⋊C411yescharacteristic
589C2×C3C2×#90912yes—
590C2×C3D3×#13712yes—
591C2×C3C22×(C2×D3)⋊C411yescharacteristic
592D3—22no—
593D3#512014yesdirect product factor
594C22—22no—
595C22—34no—
596C22—32no—
597C22—32no—
598C22—68no—
599C22—62no—
600C22D3×(C2×D3)⋊C412yes—
601C22C2×D3×D1211yescharacteristic
602C4—32no—
603C4—32no—
604C4—64no—
605C4—122no—
606C4—184no—
607C4—362no—
608C4D3×(C2×D3)⋊C412yes—
609C4C2×C4×D3211yescharacteristic
610C4C2×D3×#6711yescharacteristic
611C3—21no—
612C3D3×#41911yescharacteristic, complemented
613C3C2×#512011yescharacteristic, complemented
614C2—22no—
615C2—34no—
616C2—62no—
617C2D3×#90912yes—
618C2C2×D3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC23×C3×D3D4
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32C2×#419
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
4. #10592819C2semidirect
5. C3×#5120C2semidirect
6. #10591107C2semidirect
7. #10591100C2semidirect
8. #10590948C2semidirect
9. D3×#816C2semidirect
20. C2×D3×Dic6C4semidirect
36. #63643C22semidirect
37. C3×#816C22semidirect
38. #63567C22semidirect
39. #63566C22semidirect
54. #5120D3direct (N × H)
64. C2×#634C2×C4semidirect
76. C2×C3×Dic6C2×C4semidirect
90. D3×Dic6C2×C4semidirect
165. #816C2×D3semidirect
281. C2×Dic6C4×D3semidirect
453. C3×D3#419semidirect
543. C32C2×#419semidirect
593. D3#5120direct (N × H)
612. C3D3×#419semidirect
613. C3C2×#5120semidirect

Maximal subgroups

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

subgroupindex
C22×D3×Dic62
C2×C3×D3×M162
D3×#9262
#105928192
C3×#51202
#105911072
#105911002
#105909482
D3×#8162
C2×#51203
D3×#4193