Finite Group Databasebeta

← D3×#5188 #11866785

Subgroups — D3×#5188 #11866785

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×C3×D3×Q16C211yesmaximal, characteristic, complemented
2D3×#946C212yesmaximal
3C2×D32×C8C211yesmaximal, characteristic
4#10592887C211yesmaximal, characteristic, complemented
5C3×#5188C211yesmaximal, characteristic, complemented
6#10591635C212yesmaximal, complemented
7#10591601C212yesmaximal, complemented
8D3×#835C212yesmaximal, complemented
9#10590857C211yesmaximal, characteristic, complemented
10#10590851C211yesmaximal, characteristic, complemented
11D3×#818C211yesmaximal, characteristic, complemented
12C2×#5188—31nomaximal
13D3×#467—31nomaximal
14C2×C3×D3×Q8C2212yes—
15C2×C4×D32C2211yescharacteristic
16C2×C32×Q16C2211yescharacteristic, complemented
17#64155C2212yes—
18C2×C8×C3⋊D3C2211yescharacteristic
19C3×#946C2212yes—
20C2×C3×#216C2212yescomplemented
21C3×D3×Q16—24no—
22C2×C3×Dic12C2211yescharacteristic, complemented
23C2×C3×D3×C8C2211yescharacteristic
24C2×C3×D3×C8C2211yescharacteristic
25D3×(C2×D3)⋊C4—22no—
26D3×C4⋊Dic3C2212yes—
27#63888—22no—
28#63887—22no—
29D3×Dic3⋊C4—22no—
30#63871C2212yes—
31#63856C2212yes—
32C2×#3710C2211yescharacteristic
33C2×D3×C3⋊C8C2211yescharacteristic
34C2×D3×C3⋊C8C2211yescharacteristic
35D32×C8—24no—
36#63662C2212yescomplemented
37#63645C2211yescharacteristic, complemented
38C3×#835C2212yescomplemented
39C3×#818C2211yescharacteristic, complemented
40#63575C2212yescomplemented
41#63566C2212yescomplemented
42#63565C2212yescomplemented
43C22×C3×Q16—31no—
44C2×#946—32no—
45C2×D3×Q16D311yescharacteristic, complemented
46C22×D3×C8—31no—
47C22×D3×C8—31no—
48D3×C22⋊Q8—32no—
49C3×#467—31no—
50C2×#835—32no—
51#5188—31no—
52#5188—31no—
53#5188—32no—
54#5188—31no—
55#5188—32no—
56#5188—31no—
57#5188—61no—
58#5188D311yescharacteristic, direct product factor
59#5116—31no—
60C2×#818—31no—
61#5051—32no—
62#4887—31no—
63D3×#107—31no—
64#4813—32no—
65D3×#103—32no—
66C22×D32D411yescharacteristic
67C2×C32×Q8C2312yes—
68C2×C4×C3⋊D3C2311yescharacteristic
69C3×D3×Q8—24no—
70C3×D3×Q8—24no—
71C2×C3×C4×D3—22no—
72C2×C3×C4×D3C2311yescharacteristic
73C2×C3×C4×D3C2311yescharacteristic
74C2×C3×Dic6—22no—
75C2×C3×Dic6C2312yes—
76C2×#624D411yescharacteristic
77C2×D3×Dic3—22no—
78C2×D3×Dic3D411yescharacteristic
79C2×D3×Dic3D411yescharacteristic
80C4×D32—22no—
81C4×D32—22no—
82C32×Q16—22no—
83C2×C32×C8C2311yescharacteristic
84#3752—22no—
85C4⋊(C3⋊Dic3)C2312yes—
86#3750—22no—
87C2×C3⋊(C3⋊C8)C2311yescharacteristic
88C8×C3⋊D3—22no—
89C3×#216—24no—
90C3×(C2×D3)⋊C4—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—
98#3724—22no—
99Dic3⋊Dic3—22no—
100Dic3⋊Dic3—22no—
101#3722—22no—
102(C2×D3)⋊Dic3—22no—
103#3710—22no—
104D3×C3⋊C8—22no—
105D3×C3⋊C8—22no—
106C2×#467—91noSylow
107C22×C3×Q8—32no—
108C2×D3×Q8C2×D312yes—
109C22×C4×D3—31no—
110C22×C4×D3—31no—
111C2×C3×Q16—21no—
112C2×C3×Q16—32no—
113C2×C3×Q16—31no—
114C2×C3×Q16—64no—
115C2×C3×Q16C2×D311yescharacteristic, complemented
116C2×C3×Q16C2×D311yescharacteristic, complemented
117C22×C3×C8—31no—
118C22×C3×C8—31no—
119C3×C22⋊Q8—32no—
120#946—32no—
121#946—32no—
122#946—32no—
123#946—32no—
124#946—62no—
125#946—62no—
126#946—62no—
127#946C2×D312yes—
128C2×#216C2×D312yescomplemented
129C2×(C2×D3)⋊C4—62no—
130C2×C4⋊Dic3—32no—
131#924—32no—
132C2×Dic3⋊C4—62no—
133C22×C3⋊C8—31no—
134C22×C3⋊C8—31no—
135D3×Q16—24no—
136C2×Dic12C2×D311yescharacteristic, complemented
137C2×D3×C8—31no—
138C2×D3×C8—31no—
139C2×D3×C8—31no—
140C2×D3×C8—31no—
141C2×D3×C8—31no—
142C2×D3×C8—31no—
143C2×D3×C8—61no—
144C2×D3×C8—64no—
145C2×D3×C8—64no—
146C2×D3×C8C2×D311yescharacteristic
147C2×D3×C8C2×D311yescharacteristic
148#897—32no—
149#896—62no—
150D3×C4⋊C4—32no—
151D3×C4⋊C4—62no—
152D3×C22⋊C4—62no—
153#878—62no—
154C3×#107—31no—
155C3×#103—32no—
156#835—32no—
157#835—32no—
158#835—32no—
159#835—32no—
160#835—62no—
161#835C2×D312yescomplemented
162#818—31no—
163#818—31no—
164#818—32no—
165#818—61no—
166#818C2×D311yescharacteristic, complemented
167#816—32no—
168#810—32no—
169#807—32no—
170C22×C3⋊D3C2×D411yescharacteristic
171C22×C3×D3C2×D411yescharacteristic
172C22×C3×D3C2×D411yescharacteristic
173C2×D32—22no—
174C2×D32—22no—
175C2×D32Q1614yescomplemented
176C32×Q8—22no—
177C32×Q8—22no—
178C2×C32×C4—22no—
179C2×C32×C4C2411yescharacteristic
180C2×C3⋊Dic3—22no—
181C2×C3⋊Dic3C2×D411yescharacteristic
182C4×C3⋊D3—21no—
183C4×C3⋊D3—21no—
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—
195C3×Dic6—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—31no—
205C23×C8—91no—
206C2×C22⋊Q8—92no—
207#467—31no—
208#467—92no—
209#467—91no—
210#467—92no—
211#467—91no—
212#467—91no—
213C2×#107—91no—
214C2×#103—92no—
215C23×D3—31no—
216C23×D3—31no—
217C2×C3×Q8—22no—
218C2×C3×Q8—32no—
219C2×C3×Q8—62no—
220C2×C3×Q8—64no—
221C2×C3×Q8—64no—
222C2×C3×Q8C22×D312yes—
223C2×C3×Q8C22×D312yes—
224C22×C3×C4—31no—
225C22×C3×C4—31no—
226C22×C3×C4—62no—
227C22×Dic3—31no—
228C22×Dic3—31no—
229C22×Dic3—62no—
230D3×Q8—24no—
231D3×Q8—24no—
232C2×C4×D3—22no—
233C2×C4×D3—31no—
234C2×C4×D3—31no—
235C2×C4×D3—31no—
236C2×C4×D3—31no—
237C2×C4×D3—31no—
238C2×C4×D3—31no—
239C2×C4×D3—61no—
240C2×C4×D3—62no—
241C2×C4×D3—62no—
242C2×C4×D3—62no—
243C2×C4×D3—62no—
244C2×C4×D3—62no—
245C2×C4×D3C22×D311yescharacteristic
246C2×C4×D3C22×D311yescharacteristic
247C2×Dic6—22no—
248C2×Dic6C22×D312yes—
249C3×Q16—22no—
250C3×Q16—22no—
251C3×Q16—42no—
252C3×Q16—64no—
253C3×Q16—62no—
254C2×C3×C8—21no—
255C2×C3×C8—31no—
256C2×C3×C8—34no—
257C2×C3×C8—31no—
258C2×C3×C8—62no—
259C2×C3×C8C22×D311yescharacteristic
260C2×C3×C8C22×D311yescharacteristic
261C3×C4⋊C4—32no—
262C3×C4⋊C4—62no—
263C3×C22⋊C4—62no—
264#217—62no—
265#216—24no—
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—32no—
274C4⋊Dic3—32no—
275C4⋊Dic3—62no—
276C4⋊Dic3—62no—
277C4⋊Dic3—62no—
278C4⋊Dic3C22×D312yes—
279Dic3⋊C4—22no—
280Dic3⋊C4—62no—
281Dic3⋊C4—62no—
282Dic3⋊C4—62no—
283Dic3⋊C4—62no—
284Dic3⋊C4—62no—
285Dic3⋊C4—62no—
286Dic3⋊C4—122no—
287C2×C3⋊C8—31no—
288C2×C3⋊C8—31no—
289C2×C3⋊C8—61no—
290C2×C3⋊C8—62no—
291C2×C3⋊C8—62no—
292C2×C3⋊C8C22×D311yescharacteristic
293C2×C3⋊C8C22×D311yescharacteristic
294Dic12—22no—
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×C8#6714yes—
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—32no—
325C23×C4—91no—
326C2×Q16—32no—
327C2×Q16—31no—
328C2×Q16—64no—
329C2×Q16D3211yescharacteristic, complemented
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—92no—
344C2×C4⋊C4—182no—
345C2×C22⋊C4—182no—
346#107—31no—
347#107—92no—
348#107—91no—
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—22no—
367C3×Q8—22no—
368C3×Q8—22no—
369C3×Q8—22no—
370C3×Q8—42no—
371C3×Q8—42no—
372C3×Q8—62no—
373C3×Q8—62no—
374C3×Q8—124no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—21no—
378C2×C3×C4—31no—
379C2×C3×C4—32no—
380C2×C3×C4—32no—
381C2×C3×C4—31no—
382C2×C3×C4—42no—
383C2×C3×C4—61no—
384C2×C3×C4—61no—
385C2×C3×C4—62no—
386C2×C3×C4—62no—
387C2×C3×C4—124no—
388C2×C3×C4C23×D311yescharacteristic
389C2×C3×C4C23×D311yescharacteristic
390C2×Dic3—22no—
391C2×Dic3—22no—
392C2×Dic3—31no—
393C2×Dic3—31no—
394C2×Dic3—61no—
395C2×Dic3—62no—
396C2×Dic3—62no—
397C2×Dic3—62no—
398C2×Dic3—62no—
399C2×Dic3—122no—
400C2×Dic3—124no—
401C2×Dic3D3×D411yescharacteristic
402C2×Dic3D3×D411yescharacteristic
403C4×D3—21no—
404C4×D3—21no—
405C4×D3—44no—
406C4×D3—62no—
407C4×D3—62no—
408C4×D3—62no—
409C4×D3—61no—
410C4×D3—61no—
411C4×D3—61no—
412C4×D3—61no—
413C4×D3—62no—
414C4×D3—121no—
415C4×D3—121no—
416C4×D3—124no—
417C4×D3#23712yes—
418C4×D3C2×#6712yes—
419Dic6—22no—
420Dic6—22no—
421Dic6—44no—
422C3×C8—22no—
423C3×C8—32no—
424C3×C8—61no—
425C3×C8D3×D412yes—
426C3×C8C2×#6712yes—
427C3⋊C8—21no—
428C3⋊C8—61no—
429C3⋊C8—61no—
430C3⋊C8—121no—
431C3⋊C8C2×#6712yes—
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—62no—
441C2×Q8—64no—
442C2×Q8—64no—
443C2×Q8C2×D3212yes—
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—22no—
455Q16—64no—
456Q16—62no—
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—92no—
470C4⋊C4—182no—
471C4⋊C4—182no—
472C4⋊C4—182no—
473C4⋊C4—182no—
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×D3D3×Q1612yes—
501C2×D3D3×Q1612yescomplemented
502C2×D3#91912yes—
503C2×D3#93812yes—
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×C4C2×D3×D411yescharacteristic
514C3×C4C2×#23711yescharacteristic
515C3×C4D3×#4111yescharacteristic
516C3×C4C22×#6711yescharacteristic
517Dic3—21no—
518Dic3—42no—
519Dic3—42no—
520Dic3—61no—
521Dic3—61no—
522Dic3—121no—
523Dic3—122no—
524Dic3—122no—
525Dic3—242no—
526Dic3#93812yes—
527C32C2×#46711yescharacteristic, complemented, Sylow
528C23—31no—
529C23—31no—
530C23—94no—
531C23—91no—
532C23—182no—
533C23—182no—
534Q8—22no—
535Q8—22no—
536Q8—62no—
537Q8—62no—
538Q8—124no—
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×#6712yes—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—34no—
566C2×C3—62no—
567C2×C3D3×#12111yescharacteristic
568C2×C3C2×D3×Q1611yescharacteristic
569C2×C3C2×D3×Q1611yescharacteristic
570C2×C3C2×#91911yescharacteristic
571C2×C3D3×#13511yescharacteristic
572C2×C3C2×#93811yescharacteristic
573D3—22no—
574D3—62no—
575D3—62no—
576D3—122no—
577D3#518814yesdirect 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—
596C4D3×#23711yescharacteristic
597C4C2×D3×#6711yescharacteristic
598C3—21no—
599C3D3×#46711yescharacteristic, complemented
600C3C2×#518811yescharacteristic, complemented
601C2—34no—
602C2—62no—
603C2—182no—
604C2D32×Q1611yescharacteristic
605C2D3×#91911yescharacteristic
606C2D3×#93811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC22×D32D4
hypercenterC2×Q16D32
hypocenterC32C2×#467
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×Q16C2semidirect
4. #10592887C2semidirect
5. C3×#5188C2semidirect
6. #10591635C2semidirect
7. #10591601C2semidirect
8. D3×#835C2semidirect
9. #10590857C2semidirect
10. #10590851C2semidirect
11. D3×#818C2semidirect
16. C2×C32×Q16C22semidirect
20. C2×C3×#216C22semidirect
22. C2×C3×Dic12C22semidirect
36. #63662C22semidirect
37. #63645C22semidirect
38. C3×#835C22semidirect
39. C3×#818C22semidirect
40. #63575C22semidirect
41. #63566C22semidirect
42. #63565C22semidirect
45. C2×D3×Q16D3semidirect
58. #5188D3direct (N × H)
115. C2×C3×Q16C2×D3semidirect
116. C2×C3×Q16C2×D3semidirect
128. C2×#216C2×D3semidirect
136. C2×Dic12C2×D3semidirect
161. #835C2×D3semidirect
166. #818C2×D3semidirect
175. C2×D32Q16semidirect
307. C2×C3⋊D3C2×Q16semidirect
312. C2×C3×D3C2×Q16semidirect
329. C2×Q16D32semidirect
437. C3×D3#467semidirect
501. C2×D3D3×Q16semidirect
527. C32C2×#467semidirect
577. D3#5188direct (N × H)
599. C3D3×#467semidirect
600. C3C2×#5188semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×Q162
D3×#9462
C2×D32×C82
#105928872
C3×#51882
#105916352
#105916012
D3×#8352
#105908572
#105908512
D3×#8182
C2×#51883
D3×#4673