Finite Group Databasebeta

← D3×#5020 #11868402

Subgroups — D3×#5020 #11868402

Order 1152.

880 conjugacy classes of subgroups.

The subgroup lattice has 573 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×D3×Q8C211yesmaximal, characteristic
2D3×#869C211yesmaximal, characteristic
3#10592719C211yesmaximal, characteristic, complemented
4C3×#5020C211yesmaximal, characteristic, complemented
5D3×#835C212yesmaximal
6#10591544C212yesmaximal, complemented
7D3×#808C212yesmaximal
8#10590556C212yesmaximal, complemented
9D3×C4⋊(C3⋊C8)C211yesmaximal, characteristic
10#10590301C211yesmaximal, characteristic, complemented
11#10590285C211yesmaximal, characteristic, complemented
12C2×#5020—31nomaximal
13D3×#475—31nomaximal
14C2×C3×D3×Q8C2211yescharacteristic
15C2×D3×Dic6—21no—
16C32×C4×Q8C2211yescharacteristic
17#64078C2211yescharacteristic
18C3×Q8×Dic3C2211yescharacteristic
19C3×D3×C4⋊C4—21no—
20C3×D3×C4⋊C4C2211yescharacteristic
21C3×#887—21no—
22C3×#887C2211yescharacteristic
23C3×C42×D3—21no—
24C3×C42×D3C2211yescharacteristic
25C3×#869C2211yescharacteristic
26C3×C4×Dic6—21no—
27C3×C4×Dic6C2211yescharacteristic
28#63918—21no—
29#63918C2212yes—
30D3×C4⋊Dic3—21no—
31D3×C4⋊Dic3C2212yes—
32#63866—21no—
33C2×D3×C3⋊C8C2212yes—
34#63662C2212yes—
35#63635C2212yes—
36C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
37C3×#835C2212yes—
38C3×#808C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63574C2212yes—
41#63573C2212yes—
42Dic3⋊(C3⋊C8)C2212yes—
43#63566C2212yes—
44#63565C2212yes—
45C2×C3×C4×Q8—31no—
46D3×C4⋊Q8—31no—
47C4×D3×Q8D311yescharacteristic
48C2×#869—31no—
49C3×#475—31no—
50C2×#835—32no—
51#5094—31no—
52#5020—31no—
53#5020—31no—
54#5020—31no—
55#5020—32no—
56#5020—32no—
57#5020—31no—
58#5020—61no—
59#5020D311yescharacteristic, direct product factor
60C2×#808—32no—
61C2×C4⋊(C3⋊C8)—31no—
62D3×#106—32no—
63#4854—32no—
64#4851—31no—
65D3×C4⋊C8—31no—
66D3×#103—32no—
67#4791—32no—
68C2×C32×Q8C2311yescharacteristic
69C2×#634—21no—
70C3×D3×Q8—22no—
71C3×D3×Q8Q814yescomplemented
72C2×C3×C4×D3—21no—
73C2×C3×C4×D3—21no—
74C2×C3×C4×D3D411yescharacteristic
75C2×C3×C4×D3D411yescharacteristic
76C2×C3×C4×D3C2311yescharacteristic
77C2×C3×Dic6—21no—
78C2×C3×Dic6—21no—
79C2×C3×Dic6C2311yescharacteristic
80C2×#627—22no—
81C2×D3×Dic3—22no—
82D3×Dic6—44no—
83C32×C4⋊C4—21no—
84C32×C4⋊C4C2311yescharacteristic
85C32×C42—21no—
86C32×C42C2311yescharacteristic
87C4⋊(C3⋊Dic3)—21no—
88C4⋊(C3⋊Dic3)C2312yes—
89C2×C3⋊(C3⋊C8)C2312yes—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3C2311yescharacteristic
93C3×C4⋊Dic3C2312yes—
94C3×Dic3⋊C4—21no—
95C3×Dic3⋊C4—21no—
96C3×Dic3⋊C4—21no—
97C3×C4×Dic3—21no—
98C3×C4×Dic3—21no—
99C3×C4×Dic3—21no—
100C3×C4×Dic3D411yescharacteristic
101C3×C4×Dic3D411yescharacteristic
102C3×C4×Dic3C2311yescharacteristic
103C2×C3×C3⋊C8C2312yes—
104Dic3⋊Dic3—22no—
105Dic3⋊Dic3—22no—
106D3×C3⋊C8—24no—
107C2×#475—91noSylow
108C22×C3×Q8—31no—
109C2×D3×Q8—61no—
110C2×D3×Q8C2×D311yescharacteristic
111C22×Dic6—61no—
112C3×C4⋊Q8—31no—
113C3×C4×Q8—21no—
114C3×C4×Q8—31no—
115C3×C4×Q8—31no—
116C3×C4×Q8—31no—
117C3×C4×Q8—61no—
118C3×C4×Q8—61no—
119C3×C4×Q8C2×D311yescharacteristic
120C3×C4×Q8C2×D311yescharacteristic
121C2×C3×C4⋊C4—31no—
122C2×C3×C4⋊C4—61no—
123C2×C3×C42—31no—
124C2×C3×C42—61no—
125Q8×Dic3C2×D311yescharacteristic
126#944—61no—
127C2×C4⋊Dic3—32no—
128C2×C4⋊Dic3—61no—
129C22×C3⋊C8—32no—
130C2×D3×C8—32no—
131D3×C4⋊C4—21no—
132D3×C4⋊C4—32no—
133D3×C4⋊C4—61no—
134D3×C4⋊C4C2×D311yescharacteristic
135#888—32no—
136#888—61no—
137#887—21no—
138#887C2×D311yescharacteristic
139C42×D3—21no—
140C42×D3C2×D311yescharacteristic
141#869—31no—
142#869—31no—
143#869—32no—
144#869—61no—
145#869—61no—
146#869—61no—
147#869C2×D311yescharacteristic
148C4×Dic6—21no—
149C4×Dic6C2×D311yescharacteristic
150C3×#106—32no—
151C3×C4⋊C8—31no—
152C3×#103—32no—
153#835—32no—
154#835—32no—
155#835—32no—
156#835—32no—
157#835—62no—
158#835C2×D312yes—
159#817—32no—
160#816—32no—
161Dic3⋊C8—32no—
162#810—32no—
163#808—32no—
164#808—32no—
165#808—32no—
166#808—32no—
167#808—32no—
168#808—62no—
169#808C2×D312yes—
170C4⋊(C3⋊C8)—31no—
171C4⋊(C3⋊C8)—31no—
172C4⋊(C3⋊C8)—32no—
173C4⋊(C3⋊C8)—61no—
174C4⋊(C3⋊C8)C2×D311yescharacteristic
175C22×C3×D3C2×D411yescharacteristic
176C32×Q8—21no—
177C32×Q8C2×Q812yescomplemented
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2411yescharacteristic
183C2×C3⋊Dic3—22no—
184#634—42no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3C2×D411yescharacteristic
189C2×C3×Dic3C2×D411yescharacteristic
190C2×C3×Dic3C2×D411yescharacteristic
191C3×C4×D3—24no—
192C3×C4×D3—22no—
193C3×C4×D3—42no—
194C3×C4×D3SD1614yes—
195C3×C4×D3C2×Q812yes—
196C3×C4×D3#4112yes—
197C3×Dic6—21no—
198C3×Dic6—24no—
199C3×Dic6—42no—
200C3×Dic6C2×Q812yescomplemented
201#627—44no—
202D3×Dic3—44no—
203C3⋊(C3⋊C8)—22no—
204C3×C3⋊C8—22no—
205C2×C4⋊Q8—91no—
206C2×C4×Q8—31no—
207#475—31no—
208#475—92no—
209#475—91no—
210#475—92no—
211#475—91no—
212#475—91no—
213C2×#106—92no—
214C2×C4⋊C8—91no—
215C2×#103—92no—
216C2×C3×Q8—21no—
217C2×C3×Q8—34no—
218C2×C3×Q8—31no—
219C2×C3×Q8—61no—
220C2×C3×Q8—62no—
221C2×C3×Q8—61no—
222C2×C3×Q8C22×D311yescharacteristic
223C2×C3×Q8C22×D311yescharacteristic
224C22×C3×C4—31no—
225C22×C3×C4—31no—
226C22×C3×C4—31no—
227C22×C3×C4—61no—
228C22×C3×C4—61no—
229C22×Dic3—62no—
230D3×Q8—22no—
231D3×Q8—124no—
232D3×Q8Dic614yescomplemented
233C2×C4×D3—21no—
234C2×C4×D3—21no—
235C2×C4×D3—62no—
236C2×C4×D3#6711yescharacteristic
237C2×C4×D3#6711yescharacteristic
238C2×C4×D3C22×D311yescharacteristic
239C2×Dic6—21no—
240C2×Dic6—21no—
241C2×Dic6—62no—
242C2×Dic6—61no—
243C2×Dic6—61no—
244C2×Dic6—62no—
245C2×Dic6—121no—
246C2×Dic6—124no—
247C2×Dic6C22×D311yescharacteristic
248C2×C3×C8—32no—
249C3×C4⋊C4—21no—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—21no—
252C3×C4⋊C4—31no—
253C3×C4⋊C4—32no—
254C3×C4⋊C4—41no—
255C3×C4⋊C4—61no—
256C3×C4⋊C4—61no—
257C3×C4⋊C4—61no—
258C3×C4⋊C4—61no—
259C3×C4⋊C4—61no—
260C3×C4⋊C4C22×D311yescharacteristic
261C3×C4⋊C4C22×D311yescharacteristic
262C3×C42—21no—
263C3×C42—21no—
264C3×C42—21no—
265C3×C42—31no—
266C3×C42—31no—
267C3×C42—31no—
268C3×C42—41no—
269C3×C42—61no—
270C3×C42—61no—
271C3×C42—61no—
272C3×C42C22×D311yescharacteristic
273C3×C42C22×D311yescharacteristic
274C4⋊Dic3—21no—
275C4⋊Dic3—21no—
276C4⋊Dic3—32no—
277C4⋊Dic3—32no—
278C4⋊Dic3—62no—
279C4⋊Dic3—62no—
280C4⋊Dic3—62no—
281C4⋊Dic3—61no—
282C4⋊Dic3—61no—
283C4⋊Dic3—121no—
284C4⋊Dic3C22×D311yescharacteristic
285C4⋊Dic3C22×D312yes—
286Dic3⋊C4—21no—
287Dic3⋊C4—21no—
288Dic3⋊C4—21no—
289Dic3⋊C4—62no—
290Dic3⋊C4—62no—
291C4×Dic3—21no—
292C4×Dic3—21no—
293C4×Dic3—21no—
294C4×Dic3#6711yescharacteristic
295C4×Dic3#6711yescharacteristic
296C4×Dic3C22×D311yescharacteristic
297C2×C3⋊C8—32no—
298C2×C3⋊C8—32no—
299C2×C3⋊C8—62no—
300C2×C3⋊C8—64no—
301C2×C3⋊C8C22×D312yes—
302D3×C8—64no—
303C22×C32C22×D411yescharacteristic
304C2×C3×D3C22⋊Q812yes—
305C2×C3×D3C2×SD1612yes—
306C2×C3×D3#13712yes—
307C32×C4—22no—
308C32×C4—21no—
309C32×C4—41no—
310C32×C4C2×SD1612yes—
311C32×C4C22×Q811yescharacteristic
312C32×C4C2×#4111yescharacteristic
313C3⋊Dic3—42no—
314C3×Dic3—22no—
315C3×Dic3—21no—
316C3×Dic3—42no—
317C3×Dic3—41no—
318C3×Dic3C22⋊Q812yes—
319C3×Dic3C2×SD1612yes—
320C22×Q8—31no—
321C22×Q8—181no—
322C22×C8—92no—
323C4⋊Q8—31no—
324C4⋊Q8—92no—
325C4⋊Q8—91no—
326C4⋊Q8—181no—
327C4⋊Q8—181no—
328C4×Q8—31no—
329C4×Q8—31no—
330C4×Q8—31no—
331C4×Q8—61no—
332C4×Q8—61no—
333C4×Q8D3211yescharacteristic
334C2×C4⋊C4—31no—
335C2×C4⋊C4—61no—
336C2×C4⋊C4—92no—
337C2×C4⋊C4—181no—
338C2×C42—31no—
339C2×C42—61no—
340#106—32no—
341#106—92no—
342#106—92no—
343#106—92no—
344C4⋊C8—31no—
345C4⋊C8—92no—
346C4⋊C8—91no—
347#103—32no—
348#103—92no—
349#103—92no—
350#103—92no—
351C23×C3—31no—
352C22×D3C2×#6711yescharacteristic
353C3×Q8—21no—
354C3×Q8—21no—
355C3×Q8—22no—
356C3×Q8—32no—
357C3×Q8—41no—
358C3×Q8—64no—
359C3×Q8—61no—
360C3×Q8—122no—
361C3×Q8C2×Dic612yescomplemented
362C3×Q8D3×Q812yescomplemented
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—31no—
371C2×C3×C4—31no—
372C2×C3×C4—34no—
373C2×C3×C4—32no—
374C2×C3×C4—32no—
375C2×C3×C4—31no—
376C2×C3×C4—41no—
377C2×C3×C4—41no—
378C2×C3×C4—62no—
379C2×C3×C4—64no—
380C2×C3×C4—61no—
381C2×C3×C4—61no—
382C2×C3×C4—62no—
383C2×C3×C4—122no—
384C2×C3×C4D3×D411yescharacteristic
385C2×C3×C4D3×D411yescharacteristic
386C2×C3×C4C2×#6711yescharacteristic
387C2×C3×C4C2×#6711yescharacteristic
388C2×C3×C4C23×D311yescharacteristic
389C2×C3×C4C23×D311yescharacteristic
390C2×Dic3—21no—
391C2×Dic3—22no—
392C2×Dic3—21no—
393C2×Dic3—62no—
394C2×Dic3—62no—
395C2×Dic3—122no—
396C2×Dic3—124no—
397C2×Dic3C2×#6711yescharacteristic
398C2×Dic3C2×#6711yescharacteristic
399C2×Dic3C2×#6711yescharacteristic
400C4×D3—24no—
401C4×D3—22no—
402C4×D3—42no—
403C4×D3—124no—
404C4×D3#21514yes—
405C4×D3C2×Dic612yes—
406C4×D3#23512yes—
407Dic6—21no—
408Dic6—24no—
409Dic6—42no—
410Dic6—124no—
411Dic6—122no—
412Dic6—122no—
413Dic6—124no—
414Dic6—242no—
415Dic6C2×Dic612yescomplemented
416C3×C8—62no—
417C3⋊C8—22no—
418C3⋊C8—62no—
419C3⋊C8—62no—
420C3⋊C8—122no—
421C2×C32C2×C22⋊Q811yescharacteristic
422C2×C32C22×SD1611yescharacteristic
423C2×C32C2×#13711yescharacteristic
424C3×D3#47514yescomplemented
425C2×Q8—34no—
426C2×Q8—31no—
427C2×Q8—61no—
428C2×Q8—62no—
429C2×Q8—61no—
430C2×Q8—182no—
431C2×Q8—181no—
432C2×Q8—364no—
433C2×Q8C2×D3211yescharacteristic
434C22×C4—31no—
435C22×C4—31no—
436C22×C4—31no—
437C22×C4—61no—
438C22×C4—61no—
439C22×C4—182no—
440C2×C8—32no—
441C2×C8—92no—
442C2×C8—184no—
443C4⋊C4—21no—
444C4⋊C4—32no—
445C4⋊C4—31no—
446C4⋊C4—61no—
447C4⋊C4—61no—
448C4⋊C4—61no—
449C4⋊C4—61no—
450C4⋊C4—61no—
451C4⋊C4—92no—
452C4⋊C4—182no—
453C4⋊C4—182no—
454C4⋊C4—181no—
455C4⋊C4C2×D3211yescharacteristic
456C42—21no—
457C42—31no—
458C42—31no—
459C42—31no—
460C42—61no—
461C42—61no—
462C42—61no—
463C42C2×D3211yescharacteristic
464C22×C3—21no—
465C22×C3—32no—
466C22×C3—32no—
467C22×C3—32no—
468C22×C3C2×D3×D411yescharacteristic
469C22×C3C22×#6711yescharacteristic
470C2×D3#92412yes—
471C2×D3C2×#21512yes—
472C2×D3#95112yes—
473C3×C4—21no—
474C3×C4—22no—
475C3×C4—21no—
476C3×C4—22no—
477C3×C4—21no—
478C3×C4—21no—
479C3×C4—22no—
480C3×C4—32no—
481C3×C4—32no—
482C3×C4—41no—
483C3×C4—42no—
484C3×C4—41no—
485C3×C4—41no—
486C3×C4—61no—
487C3×C4—62no—
488C3×C4—81no—
489C3×C4—121no—
490C3×C4—122no—
491C3×C4D3×SD1612yes—
492C3×C4C2×#21512yes—
493C3×C4C22×Dic611yescharacteristic
494C3×C4C2×#23511yescharacteristic
495C3×C4C2×D3×Q811yescharacteristic
496C3×C4D3×#4111yescharacteristic
497Dic3—22no—
498Dic3—21no—
499Dic3—42no—
500Dic3—41no—
501Dic3—122no—
502Dic3—122no—
503Dic3—242no—
504Dic3#92412yes—
505Dic3C2×#21512yes—
506C32C2×#47511yescharacteristic, complemented, Sylow
507C23—31no—
508Q8—21no—
509Q8—32no—
510Q8—64no—
511Q8—61no—
512Q8—122no—
513Q8—364no—
514Q8—362no—
515Q8D3×Dic612yescomplemented
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—31no—
519C2×C4—31no—
520C2×C4—32no—
521C2×C4—32no—
522C2×C4—34no—
523C2×C4—31no—
524C2×C4—62no—
525C2×C4—64no—
526C2×C4—61no—
527C2×C4—61no—
528C2×C4—62no—
529C2×C4—122no—
530C2×C4—182no—
531C2×C4—364no—
532C2×C4D3×#6711yescharacteristic
533C2×C4D3×#6711yescharacteristic
534C2×C4C22×D3211yescharacteristic
535C8—62no—
536C8—182no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—34no—
541C2×C3D3×C22⋊Q811yescharacteristic
542C2×C3C2×D3×SD1611yescharacteristic
543C2×C3D3×#13711yescharacteristic
544C2×C3C2×#92411yescharacteristic
545C2×C3C22×#21511yescharacteristic
546C2×C3C2×#95111yescharacteristic
547D3#502014yesdirect product factor
548C22—32no—
549C22—32no—
550C22—32no—
551C22C2×D3×#6711yescharacteristic
552C4—22no—
553C4—21no—
554C4—32no—
555C4—32no—
556C4—41no—
557C4—62no—
558C4—61no—
559C4—121no—
560C4—122no—
561C4—362no—
562C4D3×#21512yes—
563C4C2×D3×Dic611yescharacteristic
564C4D3×#23511yescharacteristic
565C3—21no—
566C3D3×#47511yescharacteristic, complemented
567C3C2×#502011yescharacteristic, complemented
568C2—34no—
569C2D3×#92411yescharacteristic
570C2C2×D3×#21511yescharacteristic
571C2D3×#95111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC4×Q8D32
hypocenterC32C2×#475
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
3. #10592719C2semidirect
4. C3×#5020C2semidirect
6. #10591544C2semidirect
8. #10590556C2semidirect
10. #10590301C2semidirect
11. #10590285C2semidirect
59. #5020D3direct (N × H)
71. C3×D3×Q8Q8semidirect
177. C32×Q8C2×Q8semidirect
200. C3×Dic6C2×Q8semidirect
232. D3×Q8Dic6semidirect
361. C3×Q8C2×Dic6semidirect
362. C3×Q8D3×Q8semidirect
415. Dic6C2×Dic6semidirect
424. C3×D3#475semidirect
506. C32C2×#475semidirect
515. Q8D3×Dic6semidirect
547. D3#5020direct (N × H)
566. C3D3×#475semidirect
567. C3C2×#5020semidirect

Maximal subgroups

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

subgroupindex
C3×C4×D3×Q82
D3×#8692
#105927192
C3×#50202
D3×#8352
#105915442
D3×#8082
#105905562
D3×C4⋊(C3⋊C8)2
#105903012
#105902852
C2×#50203
D3×#4753