Finite Group Databasebeta

← D3×#4981 #11808341

Subgroups — D3×#4981 #11808341

Order 1152.

1459 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×C4⋊C4C211yesmaximal, characteristic
2C2×D3×C4⋊Dic3C211yesmaximal, characteristic
3C2×D3×Dic3⋊C4C212yesmaximal
4#10592680C211yesmaximal, characteristic, complemented
5C3×#4981C211yesmaximal, characteristic, complemented
6D3×C3⋊#95C212yesmaximal
7D3×C3⋊#95C211yesmaximal, characteristic
8#10591353C211yesmaximal, characteristic, complemented
9#10591342C212yesmaximal, complemented
10#10591339C212yesmaximal, complemented
11#10591214C211yesmaximal, characteristic, complemented
12C2×#4981—31nomaximal
13D3×#398—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C22×D3×Dic3C2212yes—
18C22×D3×Dic3C2212yes—
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×#3750C2212yes—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×Dic3⋊C4C2211yescharacteristic
25C2×C3×Dic3⋊C4C2211yescharacteristic
26C2×C3×Dic3⋊C4C2212yes—
27C3×D3×C4⋊C4—24no—
28C2×#3724C2212yes—
29C2×Dic3⋊Dic3C2212yes—
30C2×Dic3⋊Dic3C2212yes—
31D3×C4⋊Dic3—24no—
32D3×Dic3⋊C4—28no—
33#63658C2212yes—
34#63658C2211yescharacteristic
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2211yescharacteristic
37#63579C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C22×C3×C4⋊C4—31no—
41C22×C4⋊Dic3—31no—
42C22×Dic3⋊C4—32no—
43C2×D3×C4⋊C4—32no—
44C2×D3×C4⋊C4—31no—
45C2×D3×C4⋊C4D311yescharacteristic
46C3×#398—31no—
47C2×C3⋊#95—31no—
48C2×C3⋊#95—32no—
49#4983—31no—
50#4982—32no—
51#4981—31no—
52#4981—31no—
53#4981—31no—
54#4981—32no—
55#4981—32no—
56#4981—31no—
57#4981—61no—
58#4981D311yescharacteristic, direct product factor
59D3×#95—32no—
60D3×#95—31no—
61#4661—31no—
62#4657—32no—
63C23×C3×D3C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C22×C3⋊Dic3C2312yes—
68C22×C3⋊Dic3C2312yes—
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2312yes—
74C2×C3×C4×D3—22no—
75C2×C3×C4×D3—22no—
76C2×C3×C4×D3—24no—
77C2×C3×C4×D3—22no—
78C2×C3×C4×D3—24no—
79C2×C3×C4×D3D414yes—
80C2×C3×C4×D3D414yes—
81C2×D3×Dic3—24no—
82C2×D3×Dic3—24no—
83C2×D3×Dic3—24no—
84C2×D3×Dic3—24no—
85C2×D3×Dic3—24no—
86C2×D3×Dic3Q818yes—
87C32×C4⋊C4—22no—
88C4⋊(C3⋊Dic3)—22no—
89#3750—24no—
90C3×C4⋊Dic3—22no—
91C3×C4⋊Dic3—22no—
92C3×Dic3⋊C4—22no—
93C3×Dic3⋊C4—24no—
94C3×Dic3⋊C4—22no—
95#3724—24no—
96Dic3⋊Dic3—24no—
97Dic3⋊Dic3—24no—
98C2×#398—91noSylow
99C23×C3×C4—31no—
100C23×C3×C4—31no—
101C23×C3×C4—31no—
102C23×Dic3—32no—
103C23×Dic3—32no—
104C22×C4×D3—32no—
105C22×C4×D3—32no—
106C22×C4×D3C2×D311yescharacteristic
107C22×C4×D3C2×D311yescharacteristic
108C22×C4×D3C2×D311yescharacteristic
109C2×C3×C4⋊C4—21no—
110C2×C3×C4⋊C4—31no—
111C2×C3×C4⋊C4—31no—
112C2×C3×C4⋊C4—32no—
113C2×C3×C4⋊C4—31no—
114C2×C3×C4⋊C4—31no—
115C2×C3×C4⋊C4—64no—
116C2×C3×C4⋊C4C2×D311yescharacteristic
117C2×C3×C4⋊C4C2×D311yescharacteristic
118C2×C4⋊Dic3—31no—
119C2×C4⋊Dic3—31no—
120C2×C4⋊Dic3—32no—
121C2×C4⋊Dic3—32no—
122C2×C4⋊Dic3—61no—
123C2×C4⋊Dic3—64no—
124C2×C4⋊Dic3C2×D311yescharacteristic
125C2×C4⋊Dic3C2×D311yescharacteristic
126C2×Dic3⋊C4—32no—
127C2×Dic3⋊C4—32no—
128C2×Dic3⋊C4—32no—
129C2×Dic3⋊C4—32no—
130C2×Dic3⋊C4—32no—
131C2×Dic3⋊C4—32no—
132C2×Dic3⋊C4—62no—
133C2×Dic3⋊C4—68no—
134C2×Dic3⋊C4C2×D311yescharacteristic
135C2×Dic3⋊C4C2×D311yescharacteristic
136C2×Dic3⋊C4C2×D312yes—
137D3×C4⋊C4—24no—
138D3×C4⋊C4—68no—
139D3×C4⋊C4—64no—
140C3×#95—32no—
141C3×#95—31no—
142C3⋊#95—32no—
143C3⋊#95—31no—
144C3⋊#95—31no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95—32no—
148C3⋊#95—32no—
149C3⋊#95—32no—
150C3⋊#95—32no—
151C3⋊#95—32no—
152C3⋊#95—61no—
153C3⋊#95—62no—
154C3⋊#95C2×D312yes—
155C3⋊#95C2×D311yescharacteristic
156C23×C32C2411yescharacteristic
157C22×C3×D3C2×D412yes—
158C22×C3×D3C2×D412yes—
159C22×C3×D3C2×Q814yes—
160C22×C3×D3#4112yes—
161C22×C3×D3#4114yes—
162C2×C32×C4—21no—
163C2×C32×C4—21no—
164C2×C32×C4—22no—
165C2×C32×C4—21no—
166C2×C32×C4—22no—
167C2×C32×C4C2×D412yes—
168C2×C32×C4C2×D412yes—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3—22no—
172C2×C3⋊Dic3—22no—
173C2×C3⋊Dic3—22no—
174C2×C3⋊Dic3C2×Q814yes—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—21no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3C2×D412yes—
186C2×C3×Dic3C2×D412yes—
187C2×C3×Dic3C2×Q814yes—
188C3×C4×D3—28no—
189C3×C4×D3—28no—
190C3×C4×D3—44no—
191D3×Dic3—216no—
192D3×Dic3—48no—
193C22×C4⋊C4—31no—
194C22×C4⋊C4—92no—
195C22×C4⋊C4—91no—
196#398—31no—
197#398—92no—
198#398—91no—
199#398—92no—
200#398—91no—
201#398—91no—
202C2×#95—91no—
203C2×#95—92no—
204C24×C3—31no—
205C23×D3C22×D311yescharacteristic
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—32no—
210C22×C3×C4—31no—
211C22×C3×C4—31no—
212C22×C3×C4—34no—
213C22×C3×C4—34no—
214C22×C3×C4—31no—
215C22×C3×C4—32no—
216C22×C3×C4—62no—
217C22×C3×C4—62no—
218C22×C3×C4—64no—
219C22×C3×C4—62no—
220C22×C3×C4—64no—
221C22×C3×C4C22×D311yescharacteristic
222C22×C3×C4C22×D311yescharacteristic
223C22×C3×C4C22×D311yescharacteristic
224C22×C3×C4C22×D311yescharacteristic
225C22×C3×C4C22×D311yescharacteristic
226C22×C3×C4C22×D311yescharacteristic
227C22×Dic3—32no—
228C22×Dic3—32no—
229C22×Dic3—38no—
230C22×Dic3—32no—
231C22×Dic3—32no—
232C22×Dic3—62no—
233C22×Dic3—62no—
234C22×Dic3—64no—
235C22×Dic3—64no—
236C22×Dic3—64no—
237C22×Dic3—64no—
238C22×Dic3—64no—
239C22×Dic3C22×D311yescharacteristic
240C22×Dic3C22×D312yes—
241C22×Dic3C22×D311yescharacteristic
242C22×Dic3C22×D312yes—
243C22×Dic3C22×D311yescharacteristic
244C2×C4×D3—22no—
245C2×C4×D3—24no—
246C2×C4×D3—22no—
247C2×C4×D3—24no—
248C2×C4×D3—22no—
249C2×C4×D3—38no—
250C2×C4×D3—64no—
251C2×C4×D3—64no—
252C2×C4×D3—64no—
253C2×C4×D3—64no—
254C2×C4×D3—64no—
255C2×C4×D3D1214yes—
256C2×C4×D3#6714yes—
257C3×C4⋊C4—22no—
258C3×C4⋊C4—22no—
259C3×C4⋊C4—42no—
260C3×C4⋊C4—62no—
261C3×C4⋊C4—62no—
262C3×C4⋊C4—64no—
263C3×C4⋊C4—62no—
264C3×C4⋊C4—62no—
265C4⋊Dic3—22no—
266C4⋊Dic3—22no—
267C4⋊Dic3—64no—
268C4⋊Dic3—62no—
269C4⋊Dic3—62no—
270C4⋊Dic3—64no—
271C4⋊Dic3—122no—
272Dic3⋊C4—24no—
273Dic3⋊C4—22no—
274Dic3⋊C4—22no—
275Dic3⋊C4—64no—
276Dic3⋊C4—64no—
277Dic3⋊C4—64no—
278Dic3⋊C4—64no—
279Dic3⋊C4—64no—
280Dic3⋊C4—64no—
281Dic3⋊C4—124no—
282C22×C32C22×D411yescharacteristic
283C22×C32C22×D411yescharacteristic
284C22×C32C22×Q812yes—
285C22×C32C2×#4111yescharacteristic
286C22×C32C2×#4112yes—
287C2×C3×D3#12114yes—
288C2×C3×D3C22⋊Q818yes—
289C2×C3×D3#12314yes—
290C2×C3×D3#12518yes—
291C2×C3×D3C4⋊Q814yes—
292C32×C4—22no—
293C32×C4—22no—
294C32×C4—41no—
295C3⋊Dic3—24no—
296C3⋊Dic3—42no—
297C3×Dic3—22no—
298C3×Dic3—24no—
299C3×Dic3—22no—
300C3×Dic3—42no—
301C3×Dic3—41no—
302C23×C4—31no—
303C23×C4—31no—
304C23×C4—31no—
305C23×C4—92no—
306C23×C4—92no—
307C2×C4⋊C4—31no—
308C2×C4⋊C4—31no—
309C2×C4⋊C4—31no—
310C2×C4⋊C4—32no—
311C2×C4⋊C4—31no—
312C2×C4⋊C4—64no—
313C2×C4⋊C4—92no—
314C2×C4⋊C4—92no—
315C2×C4⋊C4—92no—
316C2×C4⋊C4—92no—
317C2×C4⋊C4—91no—
318C2×C4⋊C4—188no—
319C2×C4⋊C4—184no—
320C2×C4⋊C4D3211yescharacteristic
321#95—31no—
322#95—32no—
323#95—92no—
324#95—92no—
325#95—92no—
326#95—91no—
327#95—92no—
328C23×C3—21no—
329C23×C3—32no—
330C23×C3—32no—
331C23×C3—34no—
332C23×C3—32no—
333C23×C3—34no—
334C23×C3C23×D311yescharacteristic
335C23×C3C23×D311yescharacteristic
336C22×D3C2×D1212yes—
337C22×D3#23512yes—
338C22×D3#23714yes—
339C22×D3D3×Q814yes—
340C22×D3C2×#6712yes—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—22no—
344C2×C3×C4—21no—
345C2×C3×C4—22no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4—21no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—32no—
354C2×C3×C4—32no—
355C2×C3×C4—34no—
356C2×C3×C4—41no—
357C2×C3×C4—41no—
358C2×C3×C4—42no—
359C2×C3×C4—41no—
360C2×C3×C4—42no—
361C2×C3×C4—68no—
362C2×C3×C4—68no—
363C2×C3×C4—62no—
364C2×C3×C4—61no—
365C2×C3×C4—62no—
366C2×C3×C4—61no—
367C2×C3×C4—62no—
368C2×C3×C4—62no—
369C2×C3×C4—62no—
370C2×C3×C4—61no—
371C2×C3×C4—62no—
372C2×C3×C4—62no—
373C2×C3×C4—124no—
374C2×C3×C4C2×D1212yes—
375C2×C3×C4D3×D412yes—
376C2×C3×C4D3×D412yes—
377C2×C3×C4C2×#6712yes—
378C2×Dic3—21no—
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—22no—
382C2×Dic3—21no—
383C2×Dic3—22no—
384C2×Dic3—22no—
385C2×Dic3—22no—
386C2×Dic3—22no—
387C2×Dic3—21no—
388C2×Dic3—34no—
389C2×Dic3—34no—
390C2×Dic3—64no—
391C2×Dic3—616no—
392C2×Dic3—62no—
393C2×Dic3—62no—
394C2×Dic3—62no—
395C2×Dic3—62no—
396C2×Dic3—62no—
397C2×Dic3—62no—
398C2×Dic3—62no—
399C2×Dic3—62no—
400C2×Dic3—62no—
401C2×Dic3—62no—
402C2×Dic3—122no—
403C2×Dic3—122no—
404C2×Dic3—122no—
405C2×Dic3—122no—
406C2×Dic3—122no—
407C2×Dic3—128no—
408C2×Dic3C2×D1212yes—
409C2×Dic3D3×Q814yes—
410C2×Dic3C2×#6712yes—
411C4×D3—28no—
412C4×D3—28no—
413C4×D3—44no—
414C4×D3—616no—
415C4×D3—128no—
416C2×C32C2×#12111yescharacteristic
417C2×C32C2×C22⋊Q812yes—
418C2×C32C2×#12311yescharacteristic
419C2×C32C2×#12512yes—
420C2×C32C2×C4⋊Q811yescharacteristic
421C3×D3#39818yescomplemented
422C24—31no—
423C22×C4—32no—
424C22×C4—31no—
425C22×C4—31no—
426C22×C4—34no—
427C22×C4—34no—
428C22×C4—32no—
429C22×C4—31no—
430C22×C4—62no—
431C22×C4—62no—
432C22×C4—64no—
433C22×C4—62no—
434C22×C4—64no—
435C22×C4—98no—
436C22×C4—92no—
437C22×C4—92no—
438C22×C4—184no—
439C22×C4—184no—
440C22×C4—184no—
441C22×C4—184no—
442C22×C4—184no—
443C22×C4C2×D3211yescharacteristic
444C22×C4C2×D3211yescharacteristic
445C22×C4C2×D3211yescharacteristic
446C4⋊C4—22no—
447C4⋊C4—62no—
448C4⋊C4—62no—
449C4⋊C4—64no—
450C4⋊C4—62no—
451C4⋊C4—62no—
452C4⋊C4—184no—
453C4⋊C4—184no—
454C4⋊C4—184no—
455C4⋊C4—184no—
456C4⋊C4—182no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—22no—
460C22×C3—22no—
461C22×C3—21no—
462C22×C3—34no—
463C22×C3—38no—
464C22×C3—34no—
465C22×C3—34no—
466C22×C3—38no—
467C22×C3C22×D1211yescharacteristic
468C22×C3C2×#23511yescharacteristic
469C22×C3C2×D3×D411yescharacteristic
470C22×C3C2×D3×D411yescharacteristic
471C22×C3C2×#23712yes—
472C22×C3C2×D3×Q812yes—
473C22×C3C2×D3×Q812yes—
474C22×C3D3×#4111yescharacteristic
475C22×C3D3×#4112yes—
476C22×C3C22×#6711yescharacteristic
477C2×D3#88918yes—
478C2×D3#89718yes—
479C2×D3#93014yes—
480C2×D3#93514yes—
481C2×D3#94414yes—
482C3×C4—22no—
483C3×C4—22no—
484C3×C4—22no—
485C3×C4—22no—
486C3×C4—42no—
487C3×C4—42no—
488C3×C4—41no—
489C3×C4—41no—
490C3×C4—62no—
491C3×C4—64no—
492C3×C4—62no—
493C3×C4—81no—
494C3×C4—121no—
495C3×C4—122no—
496Dic3—22no—
497Dic3—22no—
498Dic3—24no—
499Dic3—41no—
500Dic3—42no—
501Dic3—64no—
502Dic3—64no—
503Dic3—124no—
504Dic3—122no—
505Dic3—122no—
506Dic3—242no—
507C32C2×#39811yescharacteristic, complemented, Sylow
508C23—32no—
509C23—32no—
510C23—34no—
511C23—34no—
512C23—32no—
513C23C22×D3211yescharacteristic
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—32no—
520C2×C4—34no—
521C2×C4—32no—
522C2×C4—68no—
523C2×C4—68no—
524C2×C4—62no—
525C2×C4—61no—
526C2×C4—62no—
527C2×C4—62no—
528C2×C4—61no—
529C2×C4—62no—
530C2×C4—62no—
531C2×C4—62no—
532C2×C4—61no—
533C2×C4—62no—
534C2×C4—94no—
535C2×C4—124no—
536C2×C4—1816no—
537C2×C4—182no—
538C2×C4—182no—
539C2×C4—182no—
540C2×C4—182no—
541C2×C4—182no—
542C2×C4—368no—
543C2×C4D3×D1212yes—
544C2×C4D3×#6712yes—
545C2×C3—21no—
546C2×C3—22no—
547C2×C3—21no—
548C2×C3—22no—
549C2×C3—21no—
550C2×C3—38no—
551C2×C3C2×#88912yes—
552C2×C3C2×#89712yes—
553C2×C3D3×#12111yescharacteristic
554C2×C3D3×C22⋊Q812yes—
555C2×C3D3×#12311yescharacteristic
556C2×C3D3×#12512yes—
557C2×C3D3×C4⋊Q811yescharacteristic
558C2×C3C2×#93011yescharacteristic
559C2×C3C2×#93511yescharacteristic
560C2×C3C2×#94411yescharacteristic
561D3#498118yesdirect product factor
562C22—34no—
563C22—38no—
564C22—34no—
565C22—38no—
566C22—34no—
567C22C2×D3×D1211yescharacteristic
568C22D3×#23511yescharacteristic
569C22D3×#23712yes—
570C22D32×Q812yes—
571C22C2×D3×#6711yescharacteristic
572C4—22no—
573C4—22no—
574C4—41no—
575C4—64no—
576C4—62no—
577C4—62no—
578C4—121no—
579C4—122no—
580C4—184no—
581C4—362no—
582C3—21no—
583C3D3×#39811yescharacteristic, complemented
584C3C2×#498111yescharacteristic, complemented
585C2—38no—
586C2D3×#88912yes—
587C2D3×#89712yes—
588C2D3×#93011yescharacteristic
589C2D3×#93511yescharacteristic
590C2D3×#94411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC23×C3×D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#398
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #10592680C2semidirect
5. C3×#4981C2semidirect
8. #10591353C2semidirect
9. #10591342C2semidirect
10. #10591339C2semidirect
11. #10591214C2semidirect
58. #4981D3direct (N × H)
421. C3×D3#398semidirect
507. C32C2×#398semidirect
561. D3#4981direct (N × H)
583. C3D3×#398semidirect
584. C3C2×#4981semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×C4⋊C42
C2×D3×C4⋊Dic32
C2×D3×Dic3⋊C42
#105926802
C3×#49812
D3×C3⋊#952
#105913532
#105913422
#105913392
#105912142
C2×#49813
D3×#3983