Finite Group Databasebeta

← D3×#4943 #11801019

Subgroups — D3×#4943 #11801019

Order 1152.

2397 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D3×Dic3C211yesmaximal, characteristic
2C2×C3×D3×C22⋊C4C211yesmaximal, characteristic
3C2×D3×#217C211yesmaximal, characteristic
4#10592642C211yesmaximal, characteristic, complemented
5C3×#4943C211yesmaximal, characteristic, complemented
6#10591697C211yesmaximal, characteristic, complemented
7#10591696C211yesmaximal, characteristic, complemented
8#10591362C214yesmaximal, complemented
9D3×C3⋊#95C214yesmaximal, complemented
10C2×#4943—31nomaximal
11D3×#381—31nomaximal
12C24×C3×D3C2211yescharacteristic
13C23×C3⋊Dic3C2211yescharacteristic
14C23×C3×Dic3C2211yescharacteristic
15C22×C3×C4×D3C2212yes—
16C22×D3×Dic3—24no—
17C22×D3×Dic3—24no—
18C22×D3×Dic3C418yescomplemented
19C22×D3×Dic3C2212yes—
20C22×D3×Dic3C2212yes—
21C22×D3×Dic3C2212yes—
22C2×C32×C22⋊C4C2211yescharacteristic
23C2×#3757C2211yescharacteristic
24C2×C3×#217C2211yescharacteristic
25C2×C3×#217C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2212yes—
27C3×D3×C22⋊C4—24no—
28D3×#217—24no—
29C2×(C2×D3)⋊Dic3C2212yes—
30#63658C2214yescomplemented
31C3×C3⋊#95C2214yescomplemented
32#63579C2214yescomplemented
33#63579C2214yescomplemented
34C24×Dic3—31no—
35C23×C4×D3—31no—
36C22×C3×C22⋊C4—31no—
37C22×#217—31no—
38C2×D3×C22⋊C4—31no—
39C2×D3×C22⋊C4D311yescharacteristic
40C3×#381—31no—
41#5211—31no—
42C2×C3⋊#95—34no—
43#4943—31no—
44#4943—31no—
45#4943—31no—
46#4943—31no—
47#4943—31no—
48#4943—34no—
49#4943—61no—
50#4943D311yescharacteristic, direct product factor
51#4664—34no—
52D3×#95—34no—
53C24×C32C2311yescharacteristic
54C23×C3×D3—28no—
55C23×C3×D3C2×C414yes—
56C23×C3×D3D414yes—
57C23×C3×D3D414yes—
58C23×C3×D3C2311yescharacteristic
59C23×C3×D3C2311yescharacteristic
60C22×C32×C4C2312yes—
61C22×C3⋊Dic3—22no—
62C22×C3⋊Dic3—22no—
63C22×C3⋊Dic3C2×C414yescomplemented
64C22×C3⋊Dic3C2312yes—
65C22×C3⋊Dic3C2312yes—
66C22×C3×Dic3—22no—
67C22×C3×Dic3—22no—
68C22×C3×Dic3C2×C414yescomplemented
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C2×C3×C4×D3—24no—
73C2×C3×C4×D3—28no—
74C2×D3×Dic3—232no—
75C2×D3×Dic3—24no—
76C2×D3×Dic3—24no—
77C2×D3×Dic3—24no—
78C2×D3×Dic3—24no—
79C2×D3×Dic3—24no—
80C2×D3×Dic3—28no—
81C2×D3×Dic3C2×C418yes—
82C2×D3×Dic3C2×C418yescomplemented
83C32×C22⋊C4—22no—
84#3757—22no—
85C3×#217—22no—
86C3×#217—22no—
87C3×(C2×D3)⋊C4—24no—
88(C2×D3)⋊Dic3—24no—
89C2×#381—91noSylow
90C25×C3—31no—
91C24×D3C2×D311yescharacteristic
92C23×C3×C4—31no—
93C23×C3×C4—32no—
94C23×Dic3—31no—
95C23×Dic3—31no—
96C23×Dic3—38no—
97C23×Dic3—32no—
98C23×Dic3—32no—
99C23×Dic3—32no—
100C23×Dic3—61no—
101C23×Dic3—64no—
102C23×Dic3—64no—
103C23×Dic3C2×D311yescharacteristic
104C22×C4×D3—38no—
105C22×C4×D3—32no—
106C22×C4×D3—32no—
107C22×C4×D3—32no—
108C22×C4×D3—64no—
109C22×C4×D3—64no—
110C22×C4×D3C2×D312yes—
111C2×C3×C22⋊C4—21no—
112C2×C3×C22⋊C4—31no—
113C2×C3×C22⋊C4—31no—
114C2×C3×C22⋊C4—32no—
115C2×C3×C22⋊C4—64no—
116C2×C3×C22⋊C4C2×D311yescharacteristic
117C2×C3×C22⋊C4C2×D311yescharacteristic
118C2×#217—31no—
119C2×#217—31no—
120C2×#217—32no—
121C2×#217—61no—
122C2×#217—64no—
123C2×#217C2×D311yescharacteristic
124C2×#217C2×D311yescharacteristic
125C2×(C2×D3)⋊C4—32no—
126C2×(C2×D3)⋊C4C2×D312yes—
127D3×C22⋊C4—24no—
128D3×C22⋊C4—64no—
129C3×#95—34no—
130C3⋊#95—34no—
131C3⋊#95—34no—
132C3⋊#95—34no—
133C3⋊#95—34no—
134C3⋊#95—34no—
135C3⋊#95—34no—
136C3⋊#95—64no—
137C3⋊#95C2×D314yescomplemented
138C23×C32—24no—
139C23×C32C22×C412yes—
140C23×C32C2×D412yes—
141C23×C32C2×D412yes—
142C23×C32C2411yescharacteristic
143C22×C3×D3—24no—
144C22×C3×D3—216no—
145C22×C3×D3—216no—
146C22×C3×D3—216no—
147C22×C3×D3C22⋊C4116yes—
148C22×C3×D3C22×C412yes—
149C22×C3×D3C22×C412yes—
150C22×C3×D3C2×D412yes—
151C22×C3×D3C2×D412yes—
152C22×C3×D3C2×D412yes—
153C22×C3×D3C2×D412yes—
154C22×C3×D3#4118yes—
155C2×C32×C4—22no—
156C2×C32×C4—24no—
157C2×C3⋊Dic3—28no—
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3—22no—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3—24no—
162C2×C3⋊Dic3C22×C414yes—
163C2×C3×Dic3—28no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—24no—
169C2×C3×Dic3—24no—
170C2×C3×Dic3C22×C414yes—
171C3×C4×D3—48no—
172D3×Dic3—216no—
173D3×Dic3—216no—
174D3×Dic3—48no—
175C24×C4—91no—
176C22×C22⋊C4—31no—
177C22×C22⋊C4—91no—
178#381—31no—
179#381—94no—
180#381—91no—
181#381—91no—
182#381—91no—
183C2×#95—94no—
184C24×C3—21no—
185C24×C3—31no—
186C24×C3—34no—
187C24×C3—34no—
188C24×C3—34no—
189C24×C3—31no—
190C24×C3—68no—
191C24×C3C22×D311yescharacteristic
192C24×C3C22×D311yescharacteristic
193C23×D3—28no—
194C23×D3C4×D314yes—
195C23×D3D1214yes—
196C23×D3#6714yes—
197C23×D3C22×D311yescharacteristic
198C23×D3C22×D311yescharacteristic
199C22×C3×C4—22no—
200C22×C3×C4—34no—
201C22×C3×C4—32no—
202C22×C3×C4—32no—
203C22×C3×C4—32no—
204C22×C3×C4—64no—
205C22×C3×C4—68no—
206C22×C3×C4—62no—
207C22×C3×C4—62no—
208C22×C3×C4C22×D312yes—
209C22×C3×C4C22×D312yes—
210C22×Dic3—22no—
211C22×Dic3—22no—
212C22×Dic3—34no—
213C22×Dic3—34no—
214C22×Dic3—32no—
215C22×Dic3—32no—
216C22×Dic3—38no—
217C22×Dic3—38no—
218C22×Dic3—32no—
219C22×Dic3—32no—
220C22×Dic3—62no—
221C22×Dic3—64no—
222C22×Dic3—62no—
223C22×Dic3—632no—
224C22×Dic3—64no—
225C22×Dic3—64no—
226C22×Dic3—64no—
227C22×Dic3—64no—
228C22×Dic3—64no—
229C22×Dic3—68no—
230C22×Dic3—62no—
231C22×Dic3—62no—
232C22×Dic3—62no—
233C22×Dic3—62no—
234C22×Dic3—122no—
235C22×Dic3—122no—
236C22×Dic3C4×D314yescomplemented
237C22×Dic3C22×D312yes—
238C22×Dic3C22×D312yes—
239C22×Dic3C22×D312yes—
240C2×C4×D3—28no—
241C2×C4×D3—24no—
242C2×C4×D3—38no—
243C2×C4×D3—38no—
244C2×C4×D3—632no—
245C2×C4×D3—64no—
246C2×C4×D3—64no—
247C2×C4×D3—64no—
248C2×C4×D3—64no—
249C2×C4×D3—64no—
250C2×C4×D3—68no—
251C3×C22⋊C4—22no—
252C3×C22⋊C4—22no—
253C3×C22⋊C4—42no—
254C3×C22⋊C4—64no—
255C3×C22⋊C4—62no—
256C3×C22⋊C4—62no—
257#217—22no—
258#217—22no—
259#217—64no—
260#217—62no—
261#217—62no—
262#217—122no—
263(C2×D3)⋊C4—24no—
264(C2×D3)⋊C4—64no—
265C22×C32—24no—
266C22×C32—24no—
267C22×C32—24no—
268C22×C32C2×C22⋊C414yes—
269C22×C32C23×C411yescharacteristic
270C22×C32C22×D411yescharacteristic
271C22×C32C22×D411yescharacteristic
272C22×C32C2×#4114yes—
273C2×C3×D3—24no—
274C2×C3×D3—24no—
275C2×C3×D3—24no—
276C2×C3×D3—232no—
277C2×C3×D3C2×C22⋊C414yes—
278C2×C3×D3C2×C22⋊C414yes—
279C2×C3×D3#11718yes—
280C2×C3×D3#12318yes—
281C2×C3×D3#12318yes—
282C32×C4—42no—
283C3⋊Dic3—24no—
284C3⋊Dic3—42no—
285C3×Dic3—24no—
286C3×Dic3—42no—
287C3×Dic3—42no—
288C25—31no—
289C23×C4—31no—
290C23×C4—32no—
291C23×C4—92no—
292C23×C4—92no—
293C23×C4—98no—
294C23×C4—92no—
295C23×C4—91no—
296C23×C4—184no—
297C23×C4—184no—
298C2×C22⋊C4—31no—
299C2×C22⋊C4—31no—
300C2×C22⋊C4—32no—
301C2×C22⋊C4—64no—
302C2×C22⋊C4—92no—
303C2×C22⋊C4—91no—
304C2×C22⋊C4—184no—
305C2×C22⋊C4D3211yescharacteristic
306#95—34no—
307#95—94no—
308#95—94no—
309#95—94no—
310C23×C3—24no—
311C23×C3—24no—
312C23×C3—21no—
313C23×C3—22no—
314C23×C3—22no—
315C23×C3—22no—
316C23×C3—32no—
317C23×C3—32no—
318C23×C3—32no—
319C23×C3—38no—
320C23×C3—316no—
321C23×C3—32no—
322C23×C3—32no—
323C23×C3—32no—
324C23×C3—44no—
325C23×C3—616no—
326C23×C3—616no—
327C23×C3—616no—
328C23×C3—64no—
329C23×C3C2×C4×D312yes—
330C23×C3C2×C4×D312yes—
331C23×C3C2×D1212yes—
332C23×C3D3×D412yes—
333C23×C3D3×D412yes—
334C23×C3C2×#6712yes—
335C23×C3C23×D311yescharacteristic
336C23×C3C23×D311yescharacteristic
337C22×D3—24no—
338C22×D3—216no—
339C22×D3—216no—
340C22×D3—216no—
341C22×D3(C2×D3)⋊C4116yes—
342C22×D3C2×C4×D312yes—
343C22×D3C2×C4×D312yes—
344C22×D3C2×D1212yes—
345C22×D3C2×D1212yes—
346C22×D3#23718yes—
347C22×D3C2×#6712yes—
348C22×D3C2×#6712yes—
349C2×C3×C4—22no—
350C2×C3×C4—24no—
351C2×C3×C4—24no—
352C2×C3×C4—22no—
353C2×C3×C4—34no—
354C2×C3×C4—42no—
355C2×C3×C4—44no—
356C2×C3×C4—68no—
357C2×C3×C4—62no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4—64no—
362C2×C3×C4—64no—
363C2×C3×C4—128no—
364C2×Dic3—28no—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—22no—
368C2×Dic3—24no—
369C2×Dic3—24no—
370C2×Dic3—22no—
371C2×Dic3—34no—
372C2×Dic3—34no—
373C2×Dic3—64no—
374C2×Dic3—616no—
375C2×Dic3—616no—
376C2×Dic3—68no—
377C2×Dic3—68no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—62no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—64no—
385C2×Dic3—64no—
386C2×Dic3—122no—
387C2×Dic3—122no—
388C2×Dic3—128no—
389C2×Dic3—122no—
390C2×Dic3—124no—
391C2×Dic3—128no—
392C2×Dic3C2×C4×D314yes—
393C4×D3—48no—
394C4×D3—616no—
395C4×D3—616no—
396C4×D3—128no—
397C2×C32—24no—
398C2×C32C22×C22⋊C411yescharacteristic
399C2×C32C2×#11712yes—
400C2×C32C2×#12312yes—
401C2×C32C2×#12312yes—
402C3×D3—24no—
403C3×D3#38118yescomplemented
404C24—31no—
405C24—31no—
406C24—34no—
407C24—34no—
408C24—34no—
409C24—68no—
410C24C2×D3211yescharacteristic
411C22×C4—32no—
412C22×C4—34no—
413C22×C4—32no—
414C22×C4—32no—
415C22×C4—64no—
416C22×C4—68no—
417C22×C4—62no—
418C22×C4—62no—
419C22×C4—98no—
420C22×C4—98no—
421C22×C4—92no—
422C22×C4—94no—
423C22×C4—92no—
424C22×C4—184no—
425C22×C4—184no—
426C22×C4—184no—
427C22×C4—184no—
428C22×C4—1832no—
429C22×C4—184no—
430C22×C4—188no—
431C22×C4—182no—
432C22×C4—182no—
433C22×C4C2×D3212yes—
434C22⋊C4—22no—
435C22⋊C4—64no—
436C22⋊C4—62no—
437C22⋊C4—62no—
438C22⋊C4—184no—
439C22⋊C4—182no—
440C22×C3—24no—
441C22×C3—24no—
442C22×C3—24no—
443C22×C3—24no—
444C22×C3—24no—
445C22×C3—24no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—24no—
449C22×C3—21no—
450C22×C3—24no—
451C22×C3—38no—
452C22×C3—38no—
453C22×C3—34no—
454C22×C3—38no—
455C22×C3—34no—
456C22×C3—44no—
457C22×C3—44no—
458C22×C3—44no—
459C22×C3—632no—
460C22×C3—64no—
461C22×C3—64no—
462C22×C3—64no—
463C22×C3D3×C22⋊C414yes—
464C22×C3C2×(C2×D3)⋊C414yes—
465C22×C3C22×C4×D311yescharacteristic
466C22×C3C22×C4×D311yescharacteristic
467C22×C3C22×D1211yescharacteristic
468C22×C3C2×D3×D411yescharacteristic
469C22×C3C2×D3×D411yescharacteristic
470C22×C3C2×#23714yes—
471C22×C3D3×#4114yes—
472C22×C3C22×#6711yescharacteristic
473C2×D3—24no—
474C2×D3—24no—
475C2×D3—24no—
476C2×D3—232no—
477C2×D3#87718yes—
478C2×D3#88618yes—
479C2×D3C2×(C2×D3)⋊C414yes—
480C2×D3C2×(C2×D3)⋊C414yes—
481C2×D3#93518yes—
482C3×C4—42no—
483C3×C4—42no—
484C3×C4—64no—
485C3×C4—82no—
486C3×C4—122no—
487C3×C4—122no—
488Dic3—24no—
489Dic3—42no—
490Dic3—42no—
491Dic3—64no—
492Dic3—64no—
493Dic3—124no—
494Dic3—122no—
495Dic3—122no—
496Dic3—242no—
497C32C2×#38111yescharacteristic, complemented, Sylow
498C23—24no—
499C23—32no—
500C23—32no—
501C23—38no—
502C23—32no—
503C23—32no—
504C23—32no—
505C23—32no—
506C23—316no—
507C23—616no—
508C23—616no—
509C23—616no—
510C23—64no—
511C23C4×D3212yes—
512C23D3×D1212yes—
513C23D3×#6712yes—
514C23C22×D3211yescharacteristic
515C2×C4—24no—
516C2×C4—22no—
517C2×C4—34no—
518C2×C4—62no—
519C2×C4—62no—
520C2×C4—68no—
521C2×C4—62no—
522C2×C4—64no—
523C2×C4—64no—
524C2×C4—62no—
525C2×C4—94no—
526C2×C4—128no—
527C2×C4—1816no—
528C2×C4—1816no—
529C2×C4—182no—
530C2×C4—182no—
531C2×C4—188no—
532C2×C4—182no—
533C2×C4—184no—
534C2×C4—368no—
535C2×C3—24no—
536C2×C3—24no—
537C2×C3—22no—
538C2×C3—21no—
539C2×C3—22no—
540C2×C3—22no—
541C2×C3—38no—
542C2×C3—44no—
543C2×C3—64no—
544C2×C3C2×#87712yes—
545C2×C3C2×D3×C22⋊C411yescharacteristic
546C2×C3C2×#88612yes—
547C2×C3D3×#11712yes—
548C2×C3D3×#12312yes—
549C2×C3D3×#12312yes—
550C2×C3C22×(C2×D3)⋊C411yescharacteristic
551C2×C3C2×#93512yes—
552D3—24no—
553D3#494318yesdirect product factor
554C22—24no—
555C22—24no—
556C22—24no—
557C22—38no—
558C22—34no—
559C22—38no—
560C22—38no—
561C22—34no—
562C22—632no—
563C22—64no—
564C22—64no—
565C22—64no—
566C22D3×(C2×D3)⋊C414yes—
567C22C2×C4×D3211yescharacteristic
568C22C2×D3×D1211yescharacteristic
569C22D3×#23714yes—
570C22C2×D3×#6711yescharacteristic
571C4—42no—
572C4—64no—
573C4—122no—
574C4—122no—
575C4—184no—
576C4—362no—
577C3—21no—
578C3D3×#38111yescharacteristic, complemented
579C3C2×#494311yescharacteristic, complemented
580C2—24no—
581C2—38no—
582C2—64no—
583C2D3×#87712yes—
584C2D3×#88612yes—
585C2C2×D3×(C2×D3)⋊C411yescharacteristic
586C2D3×#93512yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC24×C3×D3C22
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#381
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. #10592642C2semidirect
5. C3×#4943C2semidirect
6. #10591697C2semidirect
7. #10591696C2semidirect
8. #10591362C2semidirect
9. D3×C3⋊#95C2semidirect
18. C22×D3×Dic3C4semidirect
30. #63658C22semidirect
31. C3×C3⋊#95C22semidirect
32. #63579C22semidirect
33. #63579C22semidirect
50. #4943D3direct (N × H)
63. C22×C3⋊Dic3C2×C4semidirect
68. C22×C3×Dic3C2×C4semidirect
82. C2×D3×Dic3C2×C4semidirect
137. C3⋊#95C2×D3semidirect
236. C22×Dic3C4×D3semidirect
403. C3×D3#381semidirect
497. C32C2×#381semidirect
553. D3#4943direct (N × H)
578. C3D3×#381semidirect
579. C3C2×#4943semidirect

Maximal subgroups

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

subgroupindex
C23×D3×Dic32
C2×C3×D3×C22⋊C42
C2×D3×#2172
#105926422
C3×#49432
#105916972
#105916962
#105913622
D3×C3⋊#952
C2×#49433
D3×#3813