Finite Group Databasebeta

← D3×#5044 #11869596

Subgroups — D3×#5044 #11869596

Order 1152.

972 conjugacy classes of subgroups.

The subgroup lattice has 611 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×C22⋊Q8C211yesmaximal, characteristic
2C2×D3×C4⋊Dic3C211yesmaximal, characteristic
3#10592743C211yesmaximal, characteristic, complemented
4C3×#5044C211yesmaximal, characteristic, complemented
5#10591551C212yesmaximal, complemented
6D3×#835C212yesmaximal, complemented
7D3×#830C211yesmaximal, characteristic
8#10591132C211yesmaximal, characteristic, complemented
9#10591103C211yesmaximal, characteristic, complemented
10D3×#807C212yesmaximal, complemented
11#10590440C212yesmaximal, complemented
12C2×#5044—31nomaximal
13D3×#484—31nomaximal
14C2×C3×D3×Q8C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16C22×D3×Dic3—21no—
17C32×C22⋊Q8C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C3×#946C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C3×#924C2211yescharacteristic
22C3×#897C2211yescharacteristic
23C3×#896—21no—
24C3×D3×C4⋊C4—21no—
25C3×D3×C4⋊C4C2211yescharacteristic
26C3×D3×C22⋊C4—21no—
27C3×#878—21no—
28C2×Dic3⋊Dic3—21no—
29D3×C4⋊Dic3—21no—
30D3×C4⋊Dic3—21no—
31D3×C4⋊Dic3C2212yes—
32D3×C4⋊Dic3C2212yes—
33C2×D3×C3⋊C8C2212yes—
34#63662C2212yescomplemented
35#63657C2211yescharacteristic
36#63634C2212yescomplemented
37C3×#835C2212yescomplemented
38C3×#830C2211yescharacteristic
39C3×#807C2212yescomplemented
40#63576C2212yescomplemented
41#63575C2212yescomplemented
42#63566C2212yescomplemented
43#63565C2212yescomplemented
44(C2×D3)⋊(C3⋊C8)C2212yes—
45C2×C3×C22⋊Q8—31no—
46C22×C4⋊Dic3—31no—
47D3×C22⋊Q8D311yescharacteristic
48C2×D3×C4⋊C4—31no—
49C3×#484—31no—
50C2×#835—32no—
51C2×#830—31no—
52#5044—31no—
53#5044—31no—
54#5044—31no—
55#5044—32no—
56#5044—31no—
57#5044—32no—
58#5044—61no—
59#5044D311yescharacteristic, direct product factor
60#4970—31no—
61C2×#807—32no—
62#4884—32no—
63D3×#107—32no—
64#4811—32no—
65D3×#103—32no—
66D3×C22⋊C8—31no—
67#4722—31no—
68C23×C3×D3D411yescharacteristic
69C2×C32×Q8C2311yescharacteristic
70C22×C32×C4C2311yescharacteristic
71C22×C3⋊Dic3—21no—
72C22×C3×Dic3—21no—
73C22×C3×Dic3D411yescharacteristic
74C3×D3×Q8—24no—
75C2×C3×C4×D3—24no—
76C2×C3×C4×D3—21no—
77C2×C3×C4×D3—21no—
78C2×C3×C4×D3D411yescharacteristic
79C2×C3×C4×D3D411yescharacteristic
80C2×C3×C4×D3C2311yescharacteristic
81C2×C3×C4×D3C2311yescharacteristic
82C2×C3×Dic6—21no—
83C2×C3×Dic6C2311yescharacteristic
84C2×D3×Dic3—22no—
85C2×D3×Dic3—22no—
86C2×D3×Dic3—44no—
87C32×C4⋊C4—21no—
88C32×C4⋊C4C2311yescharacteristic
89C32×C22⋊C4—21no—
90C4⋊(C3⋊Dic3)—21no—
91C4⋊(C3⋊Dic3)C2312yes—
92C2×C3⋊(C3⋊C8)C2312yes—
93C3×#217—21no—
94C3×(C2×D3)⋊C4—21no—
95C3×(C2×D3)⋊C4—21no—
96C3×C4⋊Dic3—21no—
97C3×C4⋊Dic3—21no—
98C3×C4⋊Dic3C2311yescharacteristic
99C3×C4⋊Dic3C2312yes—
100C3×Dic3⋊C4—21no—
101C3×Dic3⋊C4—21no—
102C3×Dic3⋊C4—21no—
103C2×C3×C3⋊C8C2312yes—
104Dic3⋊Dic3—22no—
105Dic3⋊Dic3—22no—
106D3×C3⋊C8—24no—
107C2×#484—91noSylow
108C22×C3×Q8—31no—
109C23×C3×C4—31no—
110C23×Dic3—61no—
111C2×D3×Q8C2×D311yescharacteristic
112C22×C4×D3—61no—
113C22×C4×D3C2×D311yescharacteristic
114C3×C22⋊Q8—21no—
115C3×C22⋊Q8—31no—
116C3×C22⋊Q8—31no—
117C3×C22⋊Q8—31no—
118C3×C22⋊Q8—61no—
119C3×C22⋊Q8—61no—
120C3×C22⋊Q8C2×D311yescharacteristic
121C3×C22⋊Q8C2×D311yescharacteristic
122C2×C3×C4⋊C4—31no—
123C2×C3×C4⋊C4—31no—
124C2×C3×C4⋊C4—61no—
125C2×C3×C22⋊C4—61no—
126#946C2×D311yescharacteristic
127C2×C4⋊Dic3—31no—
128C2×C4⋊Dic3—31no—
129C2×C4⋊Dic3—32no—
130C2×C4⋊Dic3—32no—
131C2×C4⋊Dic3—61no—
132C2×C4⋊Dic3—61no—
133C2×C4⋊Dic3—61no—
134C2×C4⋊Dic3—61no—
135C2×C4⋊Dic3C2×D311yescharacteristic
136#924C2×D311yescharacteristic
137C2×Dic3⋊C4—61no—
138C22×C3⋊C8—32no—
139C2×D3×C8—32no—
140#897C2×D311yescharacteristic
141#896—21no—
142D3×C4⋊C4—21no—
143D3×C4⋊C4—32no—
144D3×C4⋊C4—32no—
145D3×C4⋊C4—61no—
146D3×C4⋊C4—61no—
147D3×C4⋊C4C2×D311yescharacteristic
148D3×C22⋊C4—21no—
149#878—21no—
150C3×#107—32no—
151C3×#103—32no—
152C3×C22⋊C8—31no—
153#835—32no—
154#835—32no—
155#835—32no—
156#835—32no—
157#835—62no—
158#835C2×D312yescomplemented
159#830—31no—
160#830—31no—
161#830—32no—
162#830—61no—
163#830C2×D311yescharacteristic
164(C2×D3)⋊C8—32no—
165#818—32no—
166#816—32no—
167#810—32no—
168#807—32no—
169#807—32no—
170#807—32no—
171#807—32no—
172#807—32no—
173#807—62no—
174#807C2×D312yescomplemented
175C23×C32C2×D411yescharacteristic
176C22×C3×D3—22no—
177C22×C3×D3—22no—
178C22×C3×D3Q1614yes—
179C22×C3×D3C2×D411yescharacteristic
180C22×C3×D3C2×D411yescharacteristic
181C32×Q8—22no—
182C2×C32×C4—22no—
183C2×C32×C4—21no—
184C2×C32×C4—21no—
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2411yescharacteristic
187C2×C3⋊Dic3—22no—
188C2×C3⋊Dic3—42no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—42no—
194C2×C3×Dic3C2×D411yescharacteristic
195C2×C3×Dic3C2×D411yescharacteristic
196C3×C4×D3—22no—
197C3×C4×D3—22no—
198C3×C4×D3—22no—
199C3×C4×D3—42no—
200C3×C4×D3—42no—
201C3×C4×D3#4114yes—
202C3×Dic6—22no—
203C3×Dic6—42no—
204D3×Dic3—44no—
205D3×Dic3—44no—
206C3⋊(C3⋊C8)—22no—
207C3×C3⋊C8—22no—
208C2×C22⋊Q8—31no—
209C22×C4⋊C4—91no—
210#484—31no—
211#484—91no—
212#484—92no—
213#484—92no—
214#484—91no—
215#484—91no—
216C2×#107—92no—
217C2×#103—92no—
218C2×C22⋊C8—91no—
219C24×C3—31no—
220C23×D3#6711yescharacteristic
221C2×C3×Q8—21no—
222C2×C3×Q8—31no—
223C2×C3×Q8—61no—
224C2×C3×Q8—64no—
225C2×C3×Q8C22×D311yescharacteristic
226C2×C3×Q8C22×D311yescharacteristic
227C22×C3×C4—21no—
228C22×C3×C4—31no—
229C22×C3×C4—31no—
230C22×C3×C4—31no—
231C22×C3×C4—31no—
232C22×C3×C4—31no—
233C22×C3×C4—64no—
234C22×C3×C4—61no—
235C22×C3×C4—61no—
236C22×C3×C4—61no—
237C22×C3×C4C22×D311yescharacteristic
238C22×C3×C4C22×D311yescharacteristic
239C22×Dic3—21no—
240C22×Dic3—62no—
241C22×Dic3—62no—
242C22×Dic3—61no—
243C22×Dic3—61no—
244C22×Dic3—121no—
245C22×Dic3—124no—
246C22×Dic3#6711yescharacteristic
247D3×Q8—24no—
248C2×C4×D3—24no—
249C2×C4×D3—21no—
250C2×C4×D3—21no—
251C2×C4×D3—62no—
252C2×C4×D3—62no—
253C2×C4×D3—124no—
254C2×C4×D3#6711yescharacteristic
255C2×C4×D3#6711yescharacteristic
256C2×C4×D3C22×D311yescharacteristic
257C2×C4×D3C22×D311yescharacteristic
258C2×Dic6—21no—
259C2×Dic6C22×D311yescharacteristic
260C2×C3×C8—32no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—21no—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—31no—
265C3×C4⋊C4—32no—
266C3×C4⋊C4—41no—
267C3×C4⋊C4—61no—
268C3×C4⋊C4—61no—
269C3×C4⋊C4—61no—
270C3×C4⋊C4—61no—
271C3×C4⋊C4—61no—
272C3×C4⋊C4C22×D311yescharacteristic
273C3×C4⋊C4C22×D311yescharacteristic
274C3×C22⋊C4—21no—
275C3×C22⋊C4—21no—
276C3×C22⋊C4—41no—
277C3×C22⋊C4—61no—
278C3×C22⋊C4—61no—
279C3×C22⋊C4—61no—
280#217—21no—
281(C2×D3)⋊C4—21no—
282(C2×D3)⋊C4—21no—
283C4⋊Dic3—21no—
284C4⋊Dic3—21no—
285C4⋊Dic3—32no—
286C4⋊Dic3—32no—
287C4⋊Dic3—62no—
288C4⋊Dic3—62no—
289C4⋊Dic3—62no—
290C4⋊Dic3—61no—
291C4⋊Dic3—61no—
292C4⋊Dic3—121no—
293C4⋊Dic3C22×D311yescharacteristic
294C4⋊Dic3C22×D312yes—
295Dic3⋊C4—21no—
296Dic3⋊C4—21no—
297Dic3⋊C4—21no—
298Dic3⋊C4—62no—
299Dic3⋊C4—62no—
300C2×C3⋊C8—32no—
301C2×C3⋊C8—32no—
302C2×C3⋊C8—62no—
303C2×C3⋊C8—64no—
304C2×C3⋊C8C22×D312yes—
305D3×C8—64no—
306C22×C32—21no—
307C22×C32—21no—
308C22×C32C2×Q1612yes—
309C22×C32C22×D411yescharacteristic
310C2×C3×D3—21no—
311C2×C3×D3—21no—
312C2×C3×D3—28no—
313C2×C3×D3#12312yes—
314C2×C3×D3C2×Q1612yes—
315C2×C3×D3C2×Q1612yes—
316C2×C3×D3AGL(1,ℤ/8)12yes—
317C32×C4—21no—
318C32×C4—41no—
319C32×C4—41no—
320C32×C4C2×#4112yes—
321C3⋊Dic3—42no—
322C3×Dic3—21no—
323C3×Dic3—41no—
324C3×Dic3—42no—
325C3×Dic3—41no—
326C3×Dic3#12312yes—
327C22×Q8—31no—
328C23×C4—31no—
329C23×C4—181no—
330C22×C8—92no—
331C22⋊Q8—31no—
332C22⋊Q8—31no—
333C22⋊Q8—31no—
334C22⋊Q8—61no—
335C22⋊Q8—61no—
336C22⋊Q8D3211yescharacteristic
337C2×C4⋊C4—31no—
338C2×C4⋊C4—31no—
339C2×C4⋊C4—61no—
340C2×C4⋊C4—92no—
341C2×C4⋊C4—92no—
342C2×C4⋊C4—91no—
343C2×C4⋊C4—181no—
344C2×C4⋊C4—181no—
345C2×C4⋊C4—181no—
346C2×C22⋊C4—61no—
347#107—32no—
348#107—92no—
349#107—92no—
350#107—92no—
351#103—32no—
352#103—92no—
353#103—92no—
354#103—92no—
355C22⋊C8—31no—
356C22⋊C8—92no—
357C22⋊C8—91no—
358C23×C3—21no—
359C23×C3—31no—
360C23×C3—34no—
361C23×C3—31no—
362C23×C3—62no—
363C23×C3—62no—
364C23×C3D3×D411yescharacteristic
365C23×C3C2×#6711yescharacteristic
366C22×D3—22no—
367C22×D3—22no—
368C22×D3#21614yes—
369C22×D3C2×#6711yescharacteristic
370C22×D3C2×#6711yescharacteristic
371C3×Q8—22no—
372C3×Q8—22no—
373C3×Q8—42no—
374C3×Q8—62no—
375C3×Q8—122no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—31no—
385C2×C3×C4—34no—
386C2×C3×C4—31no—
387C2×C3×C4—42no—
388C2×C3×C4—41no—
389C2×C3×C4—41no—
390C2×C3×C4—62no—
391C2×C3×C4—62no—
392C2×C3×C4—62no—
393C2×C3×C4—62no—
394C2×C3×C4—61no—
395C2×C3×C4—61no—
396C2×C3×C4—62no—
397C2×C3×C4—122no—
398C2×C3×C4—122no—
399C2×C3×C4—122no—
400C2×C3×C4D3×D411yescharacteristic
401C2×C3×C4C2×#6711yescharacteristic
402C2×C3×C4C23×D311yescharacteristic
403C2×C3×C4C23×D311yescharacteristic
404C2×Dic3—22no—
405C2×Dic3—22no—
406C2×Dic3—21no—
407C2×Dic3—21no—
408C2×Dic3—42no—
409C2×Dic3—62no—
410C2×Dic3—62no—
411C2×Dic3—122no—
412C2×Dic3—124no—
413C2×Dic3—124no—
414C2×Dic3—122no—
415C2×Dic3—122no—
416C2×Dic3—242no—
417C2×Dic3C2×#6711yescharacteristic
418C2×Dic3C2×#6711yescharacteristic
419C4×D3—22no—
420C4×D3—22no—
421C4×D3—22no—
422C4×D3—42no—
423C4×D3—42no—
424C4×D3—124no—
425C4×D3—124no—
426C4×D3#23714yes—
427Dic6—22no—
428Dic6—42no—
429C3×C8—62no—
430C3⋊C8—22no—
431C3⋊C8—62no—
432C3⋊C8—62no—
433C3⋊C8—122no—
434C2×C32—22no—
435C2×C32C2×#12311yescharacteristic
436C2×C32C22×Q1611yescharacteristic
437C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
438C3×D3—22no—
439C3×D3#48414yescomplemented
440C24—31no—
441C2×Q8—31no—
442C2×Q8—61no—
443C2×Q8—64no—
444C2×Q8C2×D3211yescharacteristic
445C22×C4—31no—
446C22×C4—31no—
447C22×C4—31no—
448C22×C4—31no—
449C22×C4—31no—
450C22×C4—64no—
451C22×C4—61no—
452C22×C4—61no—
453C22×C4—61no—
454C22×C4—182no—
455C22×C4—182no—
456C22×C4—181no—
457C22×C4—364no—
458C22×C4C2×D3211yescharacteristic
459C2×C8—32no—
460C2×C8—92no—
461C2×C8—184no—
462C4⋊C4—21no—
463C4⋊C4—32no—
464C4⋊C4—31no—
465C4⋊C4—61no—
466C4⋊C4—61no—
467C4⋊C4—61no—
468C4⋊C4—61no—
469C4⋊C4—61no—
470C4⋊C4—92no—
471C4⋊C4—182no—
472C4⋊C4—182no—
473C4⋊C4—181no—
474C4⋊C4C2×D3211yescharacteristic
475C22⋊C4—21no—
476C22⋊C4—61no—
477C22⋊C4—61no—
478C22⋊C4—61no—
479C22×C3—21no—
480C22×C3—21no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—22no—
485C22×C3—32no—
486C22×C3—32no—
487C22×C3—32no—
488C22×C3—32no—
489C22×C3—41no—
490C22×C3—41no—
491C22×C3—68no—
492C22×C3—61no—
493C22×C3—61no—
494C22×C3D3×Q1612yes—
495C22×C3C2×#21612yes—
496C22×C3C2×D3×D411yescharacteristic
497C22×C3C22×#6711yescharacteristic
498C2×D3—21no—
499C2×D3—21no—
500C2×D3—28no—
501C2×D3#93512yes—
502C2×D3C2×#21612yes—
503C2×D3C2×#21612yes—
504C2×D3#94912yes—
505C3×C4—21no—
506C3×C4—21no—
507C3×C4—22no—
508C3×C4—32no—
509C3×C4—41no—
510C3×C4—41no—
511C3×C4—41no—
512C3×C4—41no—
513C3×C4—41no—
514C3×C4—61no—
515C3×C4—81no—
516C3×C4—81no—
517C3×C4—121no—
518C3×C4—121no—
519C3×C4—122no—
520C3×C4C2×#23712yes—
521C3×C4D3×#4112yes—
522Dic3—21no—
523Dic3—42no—
524Dic3—41no—
525Dic3—41no—
526Dic3—122no—
527Dic3—122no—
528Dic3—242no—
529Dic3#93512yes—
530C32C2×#48411yescharacteristic, complemented, Sylow
531C23—31no—
532C23—31no—
533C23—34no—
534C23—62no—
535C23—62no—
536C23D3×#6711yescharacteristic
537Q8—22no—
538Q8—62no—
539Q8—122no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—31no—
544C2×C4—34no—
545C2×C4—31no—
546C2×C4—62no—
547C2×C4—62no—
548C2×C4—62no—
549C2×C4—62no—
550C2×C4—61no—
551C2×C4—61no—
552C2×C4—62no—
553C2×C4—122no—
554C2×C4—122no—
555C2×C4—122no—
556C2×C4—182no—
557C2×C4—364no—
558C2×C4—364no—
559C2×C4—362no—
560C2×C4D3×#6711yescharacteristic
561C2×C4C22×D3211yescharacteristic
562C8—62no—
563C8—182no—
564C2×C3—22no—
565C2×C3—22no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—34no—
570C2×C3—42no—
571C2×C3—62no—
572C2×C3D3×#12311yescharacteristic
573C2×C3C2×D3×Q1611yescharacteristic
574C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
575C2×C3C2×#93511yescharacteristic
576C2×C3C22×#21611yescharacteristic
577C2×C3C2×#94911yescharacteristic
578D3—22no—
579D3#504414yesdirect product factor
580C22—21no—
581C22—21no—
582C22—32no—
583C22—32no—
584C22—32no—
585C22—32no—
586C22—68no—
587C22—61no—
588C22—61no—
589C22D3×#21612yes—
590C22C2×D3×#6711yescharacteristic
591C4—21no—
592C4—32no—
593C4—41no—
594C4—41no—
595C4—61no—
596C4—121no—
597C4—122no—
598C4—121no—
599C4—362no—
600C4D3×#23712yes—
601C3—21no—
602C3D3×#48411yescharacteristic, complemented
603C3C2×#504411yescharacteristic, complemented
604C2—22no—
605C2—34no—
606C2—62no—
607C2D3×#93511yescharacteristic
608C2C2×D3×#21611yescharacteristic
609C2D3×#94911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radicalC23×C3×D3D4
hypercenterC22⋊Q8D32
hypocenterC32C2×#484
LCSG ▷ C2×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
3. #10592743C2semidirect
4. C3×#5044C2semidirect
5. #10591551C2semidirect
6. D3×#835C2semidirect
8. #10591132C2semidirect
9. #10591103C2semidirect
10. D3×#807C2semidirect
11. #10590440C2semidirect
34. #63662C22semidirect
36. #63634C22semidirect
37. C3×#835C22semidirect
39. C3×#807C22semidirect
40. #63576C22semidirect
41. #63575C22semidirect
42. #63566C22semidirect
43. #63565C22semidirect
59. #5044D3direct (N × H)
158. #835C2×D3semidirect
174. #807C2×D3semidirect
439. C3×D3#484semidirect
530. C32C2×#484semidirect
579. D3#5044direct (N × H)
602. C3D3×#484semidirect
603. C3C2×#5044semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C22⋊Q82
C2×D3×C4⋊Dic32
#105927432
C3×#50442
#105915512
D3×#8352
D3×#8302
#105911322
#105911032
D3×#8072
#105904402
C2×#50443
D3×#4843