Finite Group Databasebeta

← D3×#4887 #11866787

Subgroups — D3×#4887 #11866787

Order 1152.

1081 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×Dic12C211yesmaximal, characteristic, complemented
2C2×D32×C8C211yesmaximal, characteristic
3D3×#897C212yesmaximal
4#10592586C211yesmaximal, characteristic, complemented
5C3×#4887C211yesmaximal, characteristic, complemented
6C3×D3×#107C211yesmaximal, characteristic, complemented
7#10590857C211yesmaximal, characteristic, complemented
8#10590852C211yesmaximal, characteristic, complemented
9D3×#810C212yesmaximal, complemented
10#10590579C212yesmaximal, complemented
11#10590525C212yesmaximal, complemented
12D3×#467—31nomaximal
13C2×#4887—31nomaximal
14C2×C4×D32C2211yescharacteristic
15C2×D3×Dic6C2212yes—
16C2×#3746C2211yescharacteristic, complemented
17C2×C8×C3⋊D3C2211yescharacteristic
18#64106C2212yes—
19C2×C3×Dic12C2211yescharacteristic, complemented
20C2×C3×D3×C8C2211yescharacteristic
21C2×C3×D3×C8C2211yescharacteristic
22C3×#897C2212yes—
23C3×D3×C4⋊C4C2212yes—
24D3×(C2×D3)⋊C4—22no—
25#63895—22no—
26#63893—22no—
27D3×C4⋊Dic3—22no—
28#63871C2212yes—
29#63857C2212yes—
30C2×#3719C2212yescomplemented
31C2×#3710C2211yescharacteristic
32C2×D3×C3⋊C8C2211yescharacteristic
33C2×D3×C3⋊C8C2211yescharacteristic
34D3×Dic12—24no—
35D32×C8—24no—
36C32×#107C2211yescharacteristic, complemented
37#63637C2212yescomplemented
38C3×#818C2211yescharacteristic, complemented
39C3×#810C2212yescomplemented
40C3×#807C2212yescomplemented
41#63567C2212yescomplemented
42#63565C2212yescomplemented
43C2×D3×Q16—31no—
44C22×Dic12—31no—
45C22×D3×C8—31no—
46C22×D3×C8—31no—
47D3×C22⋊Q8—32no—
48C2×#897—32no—
49C3×#467—31no—
50C2×C3×#107—31no—
51#5188—31no—
52#5116—31no—
53#5051—32no—
54C2×#810—32no—
55#4887—31no—
56#4887—31no—
57#4887—32no—
58#4887—31no—
59#4887—31no—
60#4887—32no—
61#4887—61no—
62#4887D311yescharacteristic, direct product factor
63D3×#107D311yescharacteristic, complemented
64#4813—32no—
65D3×#103—32no—
66C22×D32D411yescharacteristic
67C2×C4×C3⋊D3C2311yescharacteristic
68C2×#634C2312yes—
69C2×C3×C4×D3—22no—
70C2×C3×C4×D3C2311yescharacteristic
71C2×C3×C4×D3C2311yescharacteristic
72C2×C3×Dic6C2312yes—
73C2×#627—22no—
74C2×#624D411yescharacteristic
75C2×D3×Dic3—22no—
76C2×D3×Dic3D411yescharacteristic
77C2×D3×Dic3D411yescharacteristic
78C4×D32—22no—
79C4×D32—22no—
80D3×Dic6—24no—
81D3×Dic6—24no—
82C2×C32×C8C2311yescharacteristic
83C32×C4⋊C4C2312yes—
84#3752—22no—
85C4⋊(C3⋊Dic3)—22no—
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87#3746—22no—
88C8×C3⋊D3—22no—
89C3×(C2×D3)⋊C4—22no—
90C3×C4⋊Dic3—22no—
91C3×C4⋊Dic3C2312yes—
92C3×Dic3⋊C4—22no—
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95C3×Dic12—22no—
96C3×D3×C8—22no—
97C3×D3×C8D414yes—
98Dic3⋊Dic3—22no—
99Dic3⋊Dic3—22no—
100#3722—22no—
101(C2×D3)⋊Dic3—22no—
102#3719—24no—
103#3710—22no—
104D3×C3⋊C8—22no—
105D3×C3⋊C8—22no—
106C2×#467—91noSylow
107C2×D3×Q8—32no—
108C22×C4×D3—31no—
109C22×C4×D3—31no—
110C22×Dic6—32no—
111C2×C3×Q16—31no—
112C22×C3×C8—31no—
113C22×C3×C8—31no—
114C3×C22⋊Q8—32no—
115C2×C3×C4⋊C4—32no—
116#946—32no—
117C2×#216—32no—
118C2×(C2×D3)⋊C4—62no—
119C2×C4⋊Dic3—62no—
120#924—32no—
121C22×C3⋊C8—31no—
122C22×C3⋊C8—31no—
123D3×Q16—64no—
124C2×Dic12—32no—
125C2×Dic12—31no—
126C2×Dic12—31no—
127C2×Dic12—61no—
128C2×Dic12—64no—
129C2×Dic12C2×D311yescharacteristic, complemented
130C2×D3×C8—31no—
131C2×D3×C8—31no—
132C2×D3×C8—31no—
133C2×D3×C8—31no—
134C2×D3×C8—31no—
135C2×D3×C8—31no—
136C2×D3×C8—61no—
137C2×D3×C8—64no—
138C2×D3×C8—64no—
139C2×D3×C8C2×D311yescharacteristic
140C2×D3×C8C2×D311yescharacteristic
141#897—32no—
142#897—32no—
143#897—32no—
144#897—32no—
145#897—62no—
146#897—62no—
147#897—62no—
148#897C2×D312yes—
149#896—62no—
150D3×C4⋊C4—62no—
151D3×C4⋊C4C2×D312yes—
152D3×C22⋊C4—62no—
153#878—62no—
154C3×#107—21no—
155C3×#107—31no—
156C3×#107—32no—
157C3×#107C2×D311yescharacteristic, complemented
158C3×#107C2×D311yescharacteristic, complemented
159C3×#103—32no—
160#835—32no—
161#818C2×D311yescharacteristic, complemented
162#816—32no—
163#810—32no—
164#810—32no—
165#810—32no—
166#810—32no—
167#810—62no—
168#810C2×D312yescomplemented
169#807C2×D312yescomplemented
170C22×C3⋊D3C2×D411yescharacteristic
171C22×C3×D3C2×D411yescharacteristic
172C22×C3×D3C2×D411yescharacteristic
173C2×D32—22no—
174C2×D32—22no—
175C2×D32Q1614yescomplemented
176C2×C32×C4—22no—
177C2×C32×C4C2411yescharacteristic
178C2×C3⋊Dic3—22no—
179C2×C3⋊Dic3C2×D411yescharacteristic
180C4×C3⋊D3—21no—
181C4×C3⋊D3—21no—
182#634—22no—
183#634—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3C2×D411yescharacteristic
187C2×C3×Dic3C2×D411yescharacteristic
188C3×C4×D3—21no—
189C3×C4×D3—21no—
190C3×C4×D3—44no—
191C3×C4×D3C2×D412yes—
192C3×C4×D3#4112yes—
193C3×Dic6—22no—
194C3×Dic6—22no—
195#627—44no—
196#624—22no—
197D3×Dic3—22no—
198D3×Dic3—22no—
199D3×Dic3—44no—
200C32×C8C2×D412yes—
201C3⋊(C3⋊C8)—21no—
202C3×C3⋊C8—21no—
203C3×C3⋊C8C2×D412yes—
204C22×Q16—91no—
205C23×C8—91no—
206C2×C22⋊Q8—92no—
207#467—31no—
208#467—92no—
209#467—92no—
210#467—91no—
211#467—91no—
212#467—91no—
213C2×#107—31no—
214C2×#103—92no—
215C23×D3—31no—
216C23×D3—31no—
217C2×C3×Q8—32no—
218C22×C3×C4—31no—
219C22×C3×C4—31no—
220C22×C3×C4—62no—
221C22×Dic3—31no—
222C22×Dic3—31no—
223C22×Dic3—62no—
224D3×Q8—64no—
225D3×Q8—64no—
226C2×C4×D3—22no—
227C2×C4×D3—31no—
228C2×C4×D3—31no—
229C2×C4×D3—31no—
230C2×C4×D3—31no—
231C2×C4×D3—31no—
232C2×C4×D3—31no—
233C2×C4×D3—61no—
234C2×C4×D3—62no—
235C2×C4×D3—62no—
236C2×C4×D3—62no—
237C2×C4×D3—62no—
238C2×C4×D3—62no—
239C2×C4×D3C22×D311yescharacteristic
240C2×C4×D3C22×D311yescharacteristic
241C2×Dic6—32no—
242C2×Dic6—32no—
243C2×Dic6—62no—
244C2×Dic6—64no—
245C2×Dic6—64no—
246C2×Dic6—62no—
247C2×Dic6—62no—
248C2×Dic6C22×D312yes—
249C3×Q16—62no—
250C2×C3×C8—21no—
251C2×C3×C8—31no—
252C2×C3×C8—34no—
253C2×C3×C8—31no—
254C2×C3×C8—62no—
255C2×C3×C8C22×D311yescharacteristic
256C2×C3×C8C22×D311yescharacteristic
257C3×C4⋊C4—22no—
258C3×C4⋊C4—32no—
259C3×C4⋊C4—62no—
260C3×C4⋊C4—62no—
261C3×C4⋊C4C22×D312yes—
262C3×C4⋊C4C22×D312yes—
263C3×C22⋊C4—62no—
264#217—62no—
265#216—64no—
266(C2×D3)⋊C4—22no—
267(C2×D3)⋊C4—62no—
268(C2×D3)⋊C4—62no—
269(C2×D3)⋊C4—62no—
270(C2×D3)⋊C4—62no—
271(C2×D3)⋊C4—62no—
272(C2×D3)⋊C4—122no—
273C4⋊Dic3—22no—
274C4⋊Dic3—62no—
275C4⋊Dic3—62no—
276C4⋊Dic3—62no—
277C4⋊Dic3—62no—
278C4⋊Dic3—122no—
279C4⋊Dic3C22×D312yes—
280Dic3⋊C4—22no—
281Dic3⋊C4—62no—
282Dic3⋊C4—62no—
283C2×C3⋊C8—31no—
284C2×C3⋊C8—31no—
285C2×C3⋊C8—61no—
286C2×C3⋊C8—62no—
287C2×C3⋊C8—62no—
288C2×C3⋊C8C22×D311yescharacteristic
289C2×C3⋊C8C22×D311yescharacteristic
290Dic12—22no—
291Dic12—64no—
292Dic12—62no—
293Dic12—62no—
294Dic12—122no—
295D3×C8—22no—
296D3×C8—62no—
297D3×C8—62no—
298D3×C8—62no—
299D3×C8—62no—
300D3×C8—62no—
301D3×C8—62no—
302D3×C8—122no—
303D3×C8D1214yes—
304C22×C32C22×D411yescharacteristic
305C2×C3⋊D3—21no—
306C2×C3⋊D3—21no—
307C2×C3⋊D3C2×Q1612yescomplemented
308C2×C3×D3—21no—
309C2×C3×D3—21no—
310C2×C3×D3#12112yes—
311C2×C3×D3C2×Q1612yes—
312C2×C3×D3C2×Q1612yescomplemented
313C2×C3×D3#13512yes—
314D32—28no—
315C32×C4—42no—
316C32×C4C22×D411yescharacteristic
317C32×C4C2×#4111yescharacteristic
318C3⋊Dic3—21no—
319C3⋊Dic3—42no—
320C3×Dic3—21no—
321C3×Dic3—42no—
322C3×Dic3—42no—
323C3×Dic3#12112yes—
324C22×Q8—92no—
325C23×C4—91no—
326C2×Q16—31no—
327C2×Q16—92no—
328C2×Q16—91no—
329C2×Q16—184no—
330C22×C8—31no—
331C22×C8—31no—
332C22×C8—91no—
333C22×C8—91no—
334C22×C8—91no—
335C22×C8—91no—
336C22×C8—184no—
337C22⋊Q8—32no—
338C22⋊Q8—92no—
339C22⋊Q8—92no—
340C22⋊Q8—92no—
341C22⋊Q8—182no—
342C22⋊Q8—182no—
343C2×C4⋊C4—32no—
344C2×C4⋊C4—182no—
345C2×C22⋊C4—182no—
346#107—31no—
347#107—32no—
348#107D3211yescharacteristic, complemented
349#103—32no—
350#103—92no—
351#103—92no—
352#103—92no—
353C23×C3—31no—
354C23×C3—31no—
355C22×D3—31no—
356C22×D3—31no—
357C22×D3—34no—
358C22×D3—34no—
359C22×D3—61no—
360C22×D3—62no—
361C22×D3—62no—
362C22×D3—62no—
363C22×D3—62no—
364C22×D3D3×D411yescharacteristic
365C22×D3D3×D411yescharacteristic
366C3×Q8—62no—
367C3×Q8—62no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—21no—
371C2×C3×C4—31no—
372C2×C3×C4—32no—
373C2×C3×C4—32no—
374C2×C3×C4—31no—
375C2×C3×C4—42no—
376C2×C3×C4—61no—
377C2×C3×C4—61no—
378C2×C3×C4—62no—
379C2×C3×C4—62no—
380C2×C3×C4—124no—
381C2×C3×C4C23×D311yescharacteristic
382C2×C3×C4C23×D311yescharacteristic
383C2×Dic3—22no—
384C2×Dic3—22no—
385C2×Dic3—31no—
386C2×Dic3—31no—
387C2×Dic3—61no—
388C2×Dic3—62no—
389C2×Dic3—62no—
390C2×Dic3—62no—
391C2×Dic3—62no—
392C2×Dic3—122no—
393C2×Dic3—124no—
394C2×Dic3D3×D411yescharacteristic
395C2×Dic3D3×D411yescharacteristic
396C4×D3—21no—
397C4×D3—21no—
398C4×D3—44no—
399C4×D3—62no—
400C4×D3—62no—
401C4×D3—62no—
402C4×D3—61no—
403C4×D3—61no—
404C4×D3—61no—
405C4×D3—61no—
406C4×D3—62no—
407C4×D3—121no—
408C4×D3—121no—
409C4×D3—124no—
410C4×D3C2×D1212yes—
411C4×D3#23912yes—
412Dic6—22no—
413Dic6—22no—
414Dic6—62no—
415Dic6—62no—
416Dic6—62no—
417Dic6—62no—
418Dic6—122no—
419Dic6—122no—
420Dic6—124no—
421Dic6—124no—
422C3×C8—22no—
423C3×C8—32no—
424C3×C8—61no—
425C3×C8C2×D1212yes—
426C3×C8D3×D412yes—
427C3⋊C8—21no—
428C3⋊C8—61no—
429C3⋊C8—61no—
430C3⋊C8—121no—
431C3⋊C8C2×D1212yes—
432C2×C32C2×#12111yescharacteristic
433C2×C32C22×Q1611yescharacteristic
434C2×C32C2×#13511yescharacteristic
435C3⋊D3—22no—
436C3×D3—22no—
437C3×D3#46714yescomplemented
438C24—91no—
439C2×Q8—32no—
440C2×Q8—92no—
441C2×Q8—182no—
442C2×Q8—184no—
443C2×Q8—184no—
444C22×C4—31no—
445C22×C4—31no—
446C22×C4—62no—
447C22×C4—91no—
448C22×C4—91no—
449C22×C4—91no—
450C22×C4—91no—
451C22×C4—182no—
452C22×C4—182no—
453C22×C4—182no—
454Q16—62no—
455Q16—184no—
456Q16—182no—
457C2×C8—31no—
458C2×C8—34no—
459C2×C8—31no—
460C2×C8—62no—
461C2×C8—91no—
462C2×C8—182no—
463C2×C8—182no—
464C2×C8—182no—
465C2×C8—182no—
466C2×C8C2×D3211yescharacteristic
467C4⋊C4—32no—
468C4⋊C4—62no—
469C4⋊C4—62no—
470C4⋊C4—182no—
471C4⋊C4—182no—
472C4⋊C4—182no—
473C4⋊C4C2×D3212yes—
474C22⋊C4—62no—
475C22⋊C4—182no—
476C22⋊C4—182no—
477C22⋊C4—182no—
478C22×C3—21no—
479C22×C3—32no—
480C22×C3—32no—
481C22×C3—32no—
482C22×C3—32no—
483C22×C3—61no—
484C22×C3—61no—
485C22×C3C2×D3×D411yescharacteristic
486C22×C3C2×D3×D411yescharacteristic
487C2×D3—21no—
488C2×D3—21no—
489C2×D3—32no—
490C2×D3—32no—
491C2×D3—62no—
492C2×D3—68no—
493C2×D3—61no—
494C2×D3—61no—
495C2×D3—61no—
496C2×D3—61no—
497C2×D3—68no—
498C2×D3—121no—
499C2×D3—121no—
500C2×D3#89512yes—
501C2×D3#91212yes—
502C2×D3D3×Q1612yes—
503C2×D3D3×Q1612yescomplemented
504C3×C4—21no—
505C3×C4—21no—
506C3×C4—32no—
507C3×C4—42no—
508C3×C4—42no—
509C3×C4—61no—
510C3×C4—82no—
511C3×C4—122no—
512C3×C4—122no—
513C3×C4C22×D1211yescharacteristic
514C3×C4C2×D3×D411yescharacteristic
515C3×C4C2×#23911yescharacteristic
516C3×C4D3×#4111yescharacteristic
517Dic3—21no—
518Dic3—42no—
519Dic3—42no—
520Dic3—61no—
521Dic3—61no—
522Dic3—121no—
523Dic3—122no—
524Dic3—122no—
525Dic3—242no—
526Dic3#89512yes—
527C32C2×#46711yescharacteristic, complemented, Sylow
528C23—31no—
529C23—31no—
530C23—94no—
531C23—91no—
532C23—182no—
533C23—182no—
534Q8—62no—
535Q8—62no—
536Q8—182no—
537Q8—182no—
538Q8—364no—
539C2×C4—22no—
540C2×C4—31no—
541C2×C4—32no—
542C2×C4—32no—
543C2×C4—31no—
544C2×C4—61no—
545C2×C4—61no—
546C2×C4—62no—
547C2×C4—62no—
548C2×C4—91no—
549C2×C4—124no—
550C2×C4—182no—
551C2×C4—182no—
552C2×C4—182no—
553C2×C4—181no—
554C2×C4—181no—
555C2×C4—182no—
556C2×C4—364no—
557C2×C4C22×D3211yescharacteristic
558C8—32no—
559C8—61no—
560C8—181no—
561C8D3×D1212yes—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—34no—
566C2×C3—62no—
567C2×C3C2×#89511yescharacteristic
568C2×C3D3×#12111yescharacteristic
569C2×C3C2×#91211yescharacteristic
570C2×C3C2×D3×Q1611yescharacteristic
571C2×C3C2×D3×Q1611yescharacteristic
572C2×C3D3×#13511yescharacteristic
573D3—22no—
574D3—62no—
575D3—62no—
576D3—122no—
577D3#488714yesdirect product factor
578C22—32no—
579C22—32no—
580C22—32no—
581C22—32no—
582C22—61no—
583C22—61no—
584C22—92no—
585C22—188no—
586C22—181no—
587C22—181no—
588C22D32×D411yescharacteristic
589C4—32no—
590C4—42no—
591C4—61no—
592C4—122no—
593C4—122no—
594C4—181no—
595C4—362no—
596C4C2×D3×D1211yescharacteristic
597C4D3×#23911yescharacteristic
598C3—21no—
599C3C2×#488711yescharacteristic, complemented
600C3D3×#46711yescharacteristic, complemented
601C2—34no—
602C2—62no—
603C2—182no—
604C2D3×#89511yescharacteristic
605C2D3×#91211yescharacteristic
606C2D32×Q1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radicalC22×D32D4
hypercenter#107D32
hypocenterC32C2×#467
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
1. C2×D3×Dic12C2semidirect
4. #10592586C2semidirect
5. C3×#4887C2semidirect
6. C3×D3×#107C2semidirect
7. #10590857C2semidirect
8. #10590852C2semidirect
9. D3×#810C2semidirect
10. #10590579C2semidirect
11. #10590525C2semidirect
16. C2×#3746C22semidirect
19. C2×C3×Dic12C22semidirect
30. C2×#3719C22semidirect
36. C32×#107C22semidirect
37. #63637C22semidirect
38. C3×#818C22semidirect
39. C3×#810C22semidirect
40. C3×#807C22semidirect
41. #63567C22semidirect
42. #63565C22semidirect
62. #4887D3direct (N × H)
63. D3×#107D3semidirect
129. C2×Dic12C2×D3semidirect
157. C3×#107C2×D3semidirect
158. C3×#107C2×D3semidirect
161. #818C2×D3semidirect
168. #810C2×D3semidirect
169. #807C2×D3semidirect
175. C2×D32Q16semidirect
307. C2×C3⋊D3C2×Q16semidirect
312. C2×C3×D3C2×Q16semidirect
348. #107D32semidirect
437. C3×D3#467semidirect
503. C2×D3D3×Q16semidirect
527. C32C2×#467semidirect
577. D3#4887direct (N × H)
599. C3C2×#4887semidirect
600. C3D3×#467semidirect

Maximal subgroups

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

subgroupindex
C2×D3×Dic122
C2×D32×C82
D3×#8972
#105925862
C3×#48872
C3×D3×#1072
#105908572
#105908522
D3×#8102
#105905792
#105905252
D3×#4673
C2×#48873