Finite Group Databasebeta

← D3×#4656 #11808188

Subgroups — D3×#4656 #11808188

Order 1152.

1907 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×Dic6C211yesmaximal, characteristic
2C2×D3×C4⋊Dic3C212yesmaximal
3C2×D3×Dic3⋊C4C211yesmaximal, characteristic
4#10592355C211yesmaximal, characteristic, complemented
5C3×D3×#95C211yesmaximal, characteristic
6C3×#4656C211yesmaximal, characteristic, complemented
7#10591397C212yesmaximal, complemented
8D3×C3⋊#95C212yesmaximal
9#10591354C211yesmaximal, characteristic, complemented
10#10591346C211yesmaximal, characteristic, complemented
11#10591338C212yesmaximal, complemented
12D3×#395—31nomaximal
13C2×#4656—31nomaximal
14C22×#634C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16C22×C3×C4×D3C2212yes—
17C22×C3×Dic6C2211yescharacteristic
18C22×#627C2212yes—
19C22×D3×Dic3C2211yescharacteristic
20C22×D3×Dic3C2212yes—
21C22×D3×Dic3C2211yescharacteristic
22C2×D3×Dic6—24no—
23C2×D3×Dic6—28no—
24C2×C4⋊(C3⋊Dic3)C2212yes—
25C2×#3750C2211yescharacteristic
26C2×C3×C4⋊Dic3C2212yes—
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×#3724C2211yescharacteristic
29C2×Dic3⋊Dic3C2211yescharacteristic
30C2×Dic3⋊Dic3C2212yes—
31C2×Dic3⋊Dic3C2212yes—
32D3×C4⋊Dic3—28no—
33D3×Dic3⋊C4—24no—
34C32×#95C2211yescharacteristic
35#63658C2212yes—
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38C3×C3⋊#95C2211yescharacteristic
39#63579C2212yes—
40#63579C2212yes—
41C22×D3×Q8—31no—
42C23×Dic6—31no—
43C22×C4⋊Dic3—32no—
44C22×Dic3⋊C4—31no—
45C2×D3×C4⋊C4—31no—
46C2×D3×C4⋊C4—32no—
47C3×#395—31no—
48C2×C3×#95—31no—
49#5230—31no—
50C2×C3⋊#95—32no—
51#4979—32no—
52#4979—31no—
53D3×#95—32no—
54D3×#95D311yescharacteristic
55#4656—31no—
56#4656—32no—
57#4656—31no—
58#4656—31no—
59#4656—31no—
60#4656—32no—
61#4656—32no—
62#4656—61no—
63#4656D311yescharacteristic, direct product factor
64C23×C3×D3C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2312yes—
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3⋊Dic3C2312yes—
69C22×C3⋊Dic3C2311yescharacteristic
70C2×#634—22no—
71C2×#634—24no—
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2311yescharacteristic
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2312yes—
77C2×C3×C4×D3—24no—
78C2×C3×C4×D3—24no—
79C2×C3×C4×D3—24no—
80C2×C3×C4×D3D414yes—
81C2×C3×C4×D3Q818yescomplemented
82C2×C3×Dic6—22no—
83C2×C3×Dic6—24no—
84C2×#627—24no—
85C2×#627—24no—
86C2×#627—24no—
87C2×D3×Dic3—24no—
88C2×D3×Dic3—24no—
89C2×D3×Dic3—22no—
90C2×D3×Dic3—22no—
91C2×D3×Dic3—22no—
92C2×D3×Dic3—24no—
93C2×D3×Dic3D418yes—
94C2×D3×Dic3Q814yescomplemented
95D3×Dic6—232no—
96C4⋊(C3⋊Dic3)—24no—
97#3750—22no—
98C3×C4⋊Dic3—24no—
99C3×Dic3⋊C4—22no—
100#3724—22no—
101Dic3⋊Dic3—24no—
102Dic3⋊Dic3—22no—
103Dic3⋊Dic3—24no—
104C2×#395—91noSylow
105C22×C3×Q8—31no—
106C23×C3×C4—31no—
107C23×C3×C4—32no—
108C23×Dic3—32no—
109C23×Dic3—31no—
110C23×Dic3—31no—
111C2×D3×Q8—68no—
112C2×D3×Q8—64no—
113C22×C4×D3—31no—
114C22×C4×D3—32no—
115C22×C4×D3—31no—
116C22×C4×D3C2×D312yes—
117C22×C4×D3C2×D311yescharacteristic
118C22×Dic6—31no—
119C22×Dic6—31no—
120C22×Dic6—32no—
121C22×Dic6—32no—
122C22×Dic6—61no—
123C22×Dic6—68no—
124C22×Dic6—64no—
125C22×Dic6C2×D311yescharacteristic
126C2×C3×C4⋊C4—31no—
127C2×C3×C4⋊C4—32no—
128C2×C4⋊Dic3—32no—
129C2×C4⋊Dic3—32no—
130C2×C4⋊Dic3—31no—
131C2×C4⋊Dic3—32no—
132C2×C4⋊Dic3—32no—
133C2×C4⋊Dic3—62no—
134C2×C4⋊Dic3—68no—
135C2×C4⋊Dic3C2×D312yes—
136C2×Dic3⋊C4—31no—
137C2×Dic3⋊C4—31no—
138C2×Dic3⋊C4—31no—
139C2×Dic3⋊C4—31no—
140C2×Dic3⋊C4—32no—
141C2×Dic3⋊C4—32no—
142C2×Dic3⋊C4—31no—
143C2×Dic3⋊C4—61no—
144C2×Dic3⋊C4—64no—
145C2×Dic3⋊C4C2×D311yescharacteristic
146D3×C4⋊C4—68no—
147D3×C4⋊C4—64no—
148C3×#95—21no—
149C3×#95—31no—
150C3×#95—32no—
151C3×#95—32no—
152C3×#95C2×D311yescharacteristic
153C3×#95C2×D311yescharacteristic
154C3⋊#95—32no—
155C3⋊#95—32no—
156C3⋊#95—32no—
157C3⋊#95—32no—
158C3⋊#95—32no—
159C3⋊#95—32no—
160C3⋊#95—62no—
161C3⋊#95C2×D312yes—
162C3⋊#95C2×D312yes—
163C3⋊#95C2×D311yescharacteristic
164C23×C32C2411yescharacteristic
165C22×C3×D3C2×D412yes—
166C22×C3×D3C2×D414yes—
167C22×C3×D3C2×Q814yes—
168C22×C3×D3C2×Q812yes—
169C22×C3×D3#4112yes—
170C2×C32×C4—22no—
171C2×C32×C4—22no—
172C2×C32×C4—22no—
173C2×C32×C4C2×D412yes—
174C2×C32×C4C2×Q814yescomplemented
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3—22no—
177C2×C3⋊Dic3—22no—
178C2×C3⋊Dic3—21no—
179C2×C3⋊Dic3—21no—
180C2×C3⋊Dic3—22no—
181C2×C3⋊Dic3C2×D414yes—
182C2×C3⋊Dic3C2×Q812yescomplemented
183#634—28no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3C2×D412yes—
194C2×C3×Dic3C2×D414yes—
195C2×C3×Dic3C2×Q814yescomplemented
196C2×C3×Dic3C2×Q812yescomplemented
197C3×C4×D3—28no—
198C3×C4×D3—216no—
199C3×Dic6—28no—
200#627—216no—
201D3×Dic3—216no—
202D3×Dic3—28no—
203D3×Dic3—44no—
204C23×Q8—91no—
205C22×C4⋊C4—91no—
206C22×C4⋊C4—92no—
207#395—31no—
208#395—92no—
209#395—91no—
210#395—92no—
211#395—91no—
212#395—91no—
213C2×#95—31no—
214C2×#95—92no—
215C24×C3—31no—
216C23×D3C22×D311yescharacteristic
217C2×C3×Q8—64no—
218C2×C3×Q8—62no—
219C22×C3×C4—22no—
220C22×C3×C4—21no—
221C22×C3×C4—32no—
222C22×C3×C4—31no—
223C22×C3×C4—32no—
224C22×C3×C4—31no—
225C22×C3×C4—34no—
226C22×C3×C4—38no—
227C22×C3×C4—31no—
228C22×C3×C4—64no—
229C22×C3×C4—64no—
230C22×C3×C4—64no—
231C22×C3×C4C22×D312yes—
232C22×C3×C4C22×D311yescharacteristic
233C22×C3×C4C22×D311yescharacteristic
234C22×C3×C4C22×D312yes—
235C22×Dic3—31no—
236C22×Dic3—31no—
237C22×Dic3—32no—
238C22×Dic3—32no—
239C22×Dic3—38no—
240C22×Dic3—34no—
241C22×Dic3—31no—
242C22×Dic3—31no—
243C22×Dic3—61no—
244C22×Dic3—62no—
245C22×Dic3—61no—
246C22×Dic3—62no—
247C22×Dic3—64no—
248C22×Dic3—64no—
249C22×Dic3—62no—
250C22×Dic3—62no—
251C22×Dic3—64no—
252C22×Dic3C22×D311yescharacteristic
253C22×Dic3C22×D312yes—
254C22×Dic3C22×D311yescharacteristic
255C22×Dic3C22×D312yes—
256C22×Dic3C22×D311yescharacteristic
257D3×Q8—632no—
258C2×C4×D3—24no—
259C2×C4×D3—24no—
260C2×C4×D3—24no—
261C2×C4×D3—38no—
262C2×C4×D3—34no—
263C2×C4×D3—62no—
264C2×C4×D3—64no—
265C2×C4×D3—64no—
266C2×C4×D3—62no—
267C2×C4×D3—62no—
268C2×C4×D3—64no—
269C2×C4×D3Dic618yescomplemented
270C2×C4×D3D1214yes—
271C2×Dic6—22no—
272C2×Dic6—24no—
273C2×Dic6—632no—
274C2×Dic6—64no—
275C2×Dic6—64no—
276C2×Dic6—64no—
277C2×Dic6—64no—
278C2×Dic6—64no—
279C2×Dic6—64no—
280C2×Dic6—62no—
281C2×Dic6—62no—
282C2×Dic6—64no—
283C2×Dic6—64no—
284C2×Dic6—124no—
285C2×Dic6—122no—
286C3×C4⋊C4—64no—
287C3×C4⋊C4—62no—
288C4⋊Dic3—24no—
289C4⋊Dic3—64no—
290C4⋊Dic3—64no—
291C4⋊Dic3—64no—
292C4⋊Dic3—62no—
293C4⋊Dic3—64no—
294C4⋊Dic3—124no—
295Dic3⋊C4—22no—
296Dic3⋊C4—64no—
297Dic3⋊C4—64no—
298Dic3⋊C4—62no—
299Dic3⋊C4—62no—
300Dic3⋊C4—62no—
301Dic3⋊C4—62no—
302Dic3⋊C4—62no—
303Dic3⋊C4—122no—
304C22×C32C22×D411yescharacteristic
305C22×C32C22×D412yes—
306C22×C32C22×Q812yes—
307C22×C32C22×Q811yescharacteristic
308C22×C32C2×#4111yescharacteristic
309C2×C3×D3#12014yes—
310C2×C3×D3C22⋊Q818yes—
311C2×C3×D3C22⋊Q814yes—
312C2×C3×D3C4⋊Q814yes—
313C2×C3×D3C4⋊Q818yes—
314C32×C4—22no—
315C32×C4—24no—
316C3⋊Dic3—24no—
317C3⋊Dic3—22no—
318C3⋊Dic3—41no—
319C3×Dic3—24no—
320C3×Dic3—22no—
321C3×Dic3—22no—
322C3×Dic3—24no—
323C3×Dic3—41no—
324C22×Q8—31no—
325C22×Q8—92no—
326C22×Q8—91no—
327C22×Q8—184no—
328C22×Q8—188no—
329C23×C4—31no—
330C23×C4—32no—
331C23×C4—92no—
332C23×C4—91no—
333C23×C4—91no—
334C2×C4⋊C4—31no—
335C2×C4⋊C4—32no—
336C2×C4⋊C4—91no—
337C2×C4⋊C4—91no—
338C2×C4⋊C4—92no—
339C2×C4⋊C4—92no—
340C2×C4⋊C4—91no—
341C2×C4⋊C4—92no—
342C2×C4⋊C4—184no—
343C2×C4⋊C4—188no—
344#95—31no—
345#95—32no—
346#95—32no—
347#95—92no—
348#95—92no—
349#95—92no—
350#95D3211yescharacteristic
351C23×C3—21no—
352C23×C3—34no—
353C23×C3—32no—
354C23×C3—32no—
355C23×C3—34no—
356C23×C3—32no—
357C23×C3C23×D311yescharacteristic
358C23×C3C23×D311yescharacteristic
359C22×D3C2×Dic614yes—
360C22×D3C2×D1212yes—
361C22×D3D3×D414yes—
362C22×D3#23712yes—
363C22×D3D3×Q812yes—
364C3×Q8—68no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—24no—
372C2×C3×C4—22no—
373C2×C3×C4—32no—
374C2×C3×C4—34no—
375C2×C3×C4—32no—
376C2×C3×C4—34no—
377C2×C3×C4—42no—
378C2×C3×C4—42no—
379C2×C3×C4—42no—
380C2×C3×C4—68no—
381C2×C3×C4—616no—
382C2×C3×C4—61no—
383C2×C3×C4—62no—
384C2×C3×C4—62no—
385C2×C3×C4—62no—
386C2×C3×C4—62no—
387C2×C3×C4—61no—
388C2×C3×C4—62no—
389C2×C3×C4—61no—
390C2×C3×C4—62no—
391C2×C3×C4C2×Dic614yescomplemented
392C2×C3×C4C2×D1212yes—
393C2×C3×C4D3×D412yes—
394C2×C3×C4D3×Q814yescomplemented
395C2×Dic3—21no—
396C2×Dic3—22no—
397C2×Dic3—22no—
398C2×Dic3—22no—
399C2×Dic3—22no—
400C2×Dic3—22no—
401C2×Dic3—21no—
402C2×Dic3—21no—
403C2×Dic3—22no—
404C2×Dic3—34no—
405C2×Dic3—34no—
406C2×Dic3—32no—
407C2×Dic3—32no—
408C2×Dic3—64no—
409C2×Dic3—62no—
410C2×Dic3—616no—
411C2×Dic3—68no—
412C2×Dic3—61no—
413C2×Dic3—62no—
414C2×Dic3—61no—
415C2×Dic3—62no—
416C2×Dic3—62no—
417C2×Dic3—62no—
418C2×Dic3—61no—
419C2×Dic3—61no—
420C2×Dic3—61no—
421C2×Dic3—61no—
422C2×Dic3—62no—
423C2×Dic3—62no—
424C2×Dic3—121no—
425C2×Dic3—122no—
426C2×Dic3—122no—
427C2×Dic3—121no—
428C2×Dic3—121no—
429C2×Dic3—122no—
430C2×Dic3—124no—
431C2×Dic3C2×Dic614yescomplemented
432C2×Dic3C2×D1212yes—
433C2×Dic3D3×D414yes—
434C2×Dic3D3×Q812yescomplemented
435C4×D3—216no—
436C4×D3—28no—
437C4×D3—616no—
438C4×D3—68no—
439C4×D3—124no—
440Dic6—28no—
441Dic6—616no—
442Dic6—616no—
443Dic6—68no—
444Dic6—68no—
445Dic6—128no—
446C2×C32C2×#12011yescharacteristic
447C2×C32C2×C22⋊Q812yes—
448C2×C32C2×C22⋊Q811yescharacteristic
449C2×C32C2×C4⋊Q811yescharacteristic
450C2×C32C2×C4⋊Q812yes—
451C3×D3#39518yescomplemented
452C24—31no—
453C2×Q8—64no—
454C2×Q8—62no—
455C2×Q8—184no—
456C2×Q8—184no—
457C2×Q8—184no—
458C2×Q8—184no—
459C2×Q8—1832no—
460C2×Q8—182no—
461C22×C4—31no—
462C22×C4—32no—
463C22×C4—31no—
464C22×C4—32no—
465C22×C4—38no—
466C22×C4—34no—
467C22×C4—31no—
468C22×C4—64no—
469C22×C4—64no—
470C22×C4—64no—
471C22×C4—98no—
472C22×C4—94no—
473C22×C4—91no—
474C22×C4—92no—
475C22×C4—91no—
476C22×C4—182no—
477C22×C4—184no—
478C22×C4—184no—
479C22×C4—182no—
480C22×C4—182no—
481C22×C4—184no—
482C22×C4C2×D3212yes—
483C22×C4C2×D3211yescharacteristic
484C4⋊C4—64no—
485C4⋊C4—62no—
486C4⋊C4—184no—
487C4⋊C4—182no—
488C4⋊C4—182no—
489C4⋊C4—184no—
490C4⋊C4—184no—
491C4⋊C4—182no—
492C22×C3—22no—
493C22×C3—21no—
494C22×C3—22no—
495C22×C3—21no—
496C22×C3—21no—
497C22×C3—38no—
498C22×C3—34no—
499C22×C3—34no—
500C22×C3—34no—
501C22×C3—38no—
502C22×C3C22×Dic612yes—
503C22×C3C22×D1211yescharacteristic
504C22×C3C2×D3×D411yescharacteristic
505C22×C3C2×D3×D412yes—
506C22×C3C2×D3×D412yes—
507C22×C3C2×#23711yescharacteristic
508C22×C3C2×D3×Q812yes—
509C22×C3C2×D3×Q811yescharacteristic
510C22×C3C2×D3×Q811yescharacteristic
511C22×C3D3×#4111yescharacteristic
512C2×D3#86914yes—
513C2×D3#87818yes—
514C2×D3#88214yes—
515C2×D3#88818yes—
516C2×D3#89714yes—
517C3×C4—24no—
518C3×C4—22no—
519C3×C4—22no—
520C3×C4—24no—
521C3×C4—42no—
522C3×C4—44no—
523C3×C4—64no—
524C3×C4—62no—
525C3×C4—62no—
526C3×C4—64no—
527C3×C4—121no—
528Dic3—24no—
529Dic3—22no—
530Dic3—24no—
531Dic3—22no—
532Dic3—41no—
533Dic3—64no—
534Dic3—62no—
535Dic3—64no—
536Dic3—62no—
537Dic3—124no—
538Dic3—122no—
539Dic3—121no—
540Dic3—121no—
541Dic3—241no—
542C32C2×#39511yescharacteristic, complemented, Sylow
543C23—34no—
544C23—32no—
545C23—34no—
546C23—32no—
547C23—32no—
548C23C22×D3211yescharacteristic
549Q8—68no—
550Q8—188no—
551Q8—1816no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—34no—
556C2×C4—32no—
557C2×C4—34no—
558C2×C4—32no—
559C2×C4—68no—
560C2×C4—616no—
561C2×C4—61no—
562C2×C4—62no—
563C2×C4—62no—
564C2×C4—62no—
565C2×C4—62no—
566C2×C4—62no—
567C2×C4—61no—
568C2×C4—61no—
569C2×C4—62no—
570C2×C4—94no—
571C2×C4—92no—
572C2×C4—1816no—
573C2×C4—188no—
574C2×C4—181no—
575C2×C4—182no—
576C2×C4—182no—
577C2×C4—181no—
578C2×C4—181no—
579C2×C4—182no—
580C2×C4—364no—
581C2×C4D3×Dic614yescomplemented
582C2×C4D3×D1212yes—
583C2×C3—22no—
584C2×C3—22no—
585C2×C3—21no—
586C2×C3—21no—
587C2×C3—21no—
588C2×C3—38no—
589C2×C3C2×#86911yescharacteristic
590C2×C3C2×#87812yes—
591C2×C3C2×#88211yescharacteristic
592C2×C3C2×#88812yes—
593C2×C3C2×#89711yescharacteristic
594C2×C3D3×#12011yescharacteristic
595C2×C3D3×C22⋊Q812yes—
596C2×C3D3×C22⋊Q811yescharacteristic
597C2×C3D3×C4⋊Q812yes—
598C2×C3D3×C4⋊Q811yescharacteristic
599D3#465618yesdirect product factor
600C22—38no—
601C22—38no—
602C22—34no—
603C22—34no—
604C22—34no—
605C22C2×D3×Dic612yes—
606C22C2×D3×D1211yescharacteristic
607C22D32×D412yes—
608C22D3×#23711yescharacteristic
609C22D32×Q811yescharacteristic
610C4—24no—
611C4—22no—
612C4—64no—
613C4—62no—
614C4—62no—
615C4—64no—
616C4—121no—
617C4—182no—
618C4—184no—
619C4—361no—
620C3—21no—
621C3C2×#465611yescharacteristic, complemented
622C3D3×#39511yescharacteristic, complemented
623C2—38no—
624C2D3×#86911yescharacteristic
625C2D3×#87812yes—
626C2D3×#88211yescharacteristic
627C2D3×#88812yes—
628C2D3×#89711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC23×C3×D3C23
hypercenter#95D32
hypocenterC32C2×#395
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
4. #10592355C2semidirect
6. C3×#4656C2semidirect
7. #10591397C2semidirect
9. #10591354C2semidirect
10. #10591346C2semidirect
11. #10591338C2semidirect
63. #4656D3direct (N × H)
81. C2×C3×C4×D3Q8semidirect
94. C2×D3×Dic3Q8semidirect
174. C2×C32×C4C2×Q8semidirect
182. C2×C3⋊Dic3C2×Q8semidirect
195. C2×C3×Dic3C2×Q8semidirect
196. C2×C3×Dic3C2×Q8semidirect
269. C2×C4×D3Dic6semidirect
391. C2×C3×C4C2×Dic6semidirect
394. C2×C3×C4D3×Q8semidirect
431. C2×Dic3C2×Dic6semidirect
434. C2×Dic3D3×Q8semidirect
451. C3×D3#395semidirect
542. C32C2×#395semidirect
581. C2×C4D3×Dic6semidirect
599. D3#4656direct (N × H)
621. C3C2×#4656semidirect
622. C3D3×#395semidirect

Maximal subgroups

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

subgroupindex
C22×D3×Dic62
C2×D3×C4⋊Dic32
C2×D3×Dic3⋊C42
#105923552
C3×D3×#952
C3×#46562
#105913972
D3×C3⋊#952
#105913542
#105913462
#105913382
D3×#3953
C2×#46563