Finite Group Databasebeta

← D3×#5116 #11866791

Subgroups — D3×#5116 #11866791

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
1C22×C3×D3×C8C211yesmaximal, characteristic
2D3×#924C212yesmaximal
3C2×D3×Dic12C211yesmaximal, characteristic, complemented
4#10592815C211yesmaximal, characteristic, complemented
5C3×#5116C211yesmaximal, characteristic, complemented
6#10591187C212yesmaximal, complemented
7#10590852C211yesmaximal, characteristic, complemented
8#10590851C211yesmaximal, characteristic, complemented
9#10590848C212yesmaximal, complemented
10D3×#818C211yesmaximal, characteristic, complemented
11D3×#816C212yesmaximal, complemented
12C2×#5116—31nomaximal
13D3×#467—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C2×D3×Dic6C2212yes—
16C22×C32×C8C2211yescharacteristic
17#64133C2212yes—
18C2×#3746C2211yescharacteristic, complemented
19C3×#924C2212yes—
20C22×C3×C3⋊C8C2211yescharacteristic
21C2×C3×Dic12C2211yescharacteristic, complemented
22C2×C3×D3×C8—24no—
23C2×C3×D3×C8C2211yescharacteristic
24C2×C3×D3×C8C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic
27D3×#217—22no—
28#63964—22no—
29D3×C4⋊Dic3C2212yes—
30D3×Dic3⋊C4—22no—
31#63857C2212yes—
32#63856C2212yes—
33#63851—22no—
34C2×#3719C2212yescomplemented
35D3×Dic12—24no—
36#63645C2211yescharacteristic, complemented
37#63643C2212yescomplemented
38C3×#818C2211yescharacteristic, complemented
39C3×#816C2212yescomplemented
40#63575C2212yescomplemented
41#63567C2212yescomplemented
42#63566C2212yescomplemented
43C23×C3×C8—31no—
44C2×#924—32no—
45C2×D3×Q16—31no—
46C22×Dic12—31no—
47C22×D3×C8D311yescharacteristic
48D3×C22⋊Q8—32no—
49C3×#467—31no—
50#5188—31no—
51#5116—31no—
52#5116—31no—
53#5116—32no—
54#5116—31no—
55#5116—31no—
56#5116—32no—
57#5116—61no—
58#5116D311yescharacteristic, direct product factor
59C2×#818—31no—
60C2×#816—32no—
61#5051—32no—
62#4887—31no—
63D3×#107—31no—
64#4813—32no—
65D3×#103—32no—
66C23×C3×D3D411yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C2×#634C2312yes—
69C22×C3×Dic3D411yescharacteristic
70C2×C3×C4×D3—22no—
71C2×C3×C4×D3—22no—
72C2×C3×C4×D3D411yescharacteristic
73C2×C3×C4×D3D411yescharacteristic
74C2×C3×C4×D3C2311yescharacteristic
75C2×C3×C4×D3C2311yescharacteristic
76C2×C3×Dic6C2312yes—
77C2×#627—22no—
78C2×D3×Dic3—22no—
79C2×D3×Dic3—22no—
80D3×Dic6—24no—
81D3×Dic6—24no—
82C2×C32×C8—22no—
83C2×C32×C8C2311yescharacteristic
84C2×C32×C8C2311yescharacteristic
85#3757—22no—
86C4⋊(C3⋊Dic3)C2312yes—
87#3750—22no—
88#3746—22no—
89C3×#217—22no—
90C3×C4⋊Dic3C2312yes—
91C3×Dic3⋊C4—22no—
92C2×C3×C3⋊C8—22no—
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95C3×Dic12—22no—
96C3×D3×C8—22no—
97C3×D3×C8—22no—
98C3×D3×C8—22no—
99C3×D3×C8D414yes—
100#3724—22no—
101Dic3⋊Dic3—22no—
102Dic3⋊Dic3—22no—
103(C2×D3)⋊Dic3—22no—
104(C2×D3)⋊Dic3—22no—
105#3719—24no—
106C2×#467—91noSylow
107C23×C3×C4—31no—
108C2×D3×Q8—32no—
109C22×C4×D3C2×D311yescharacteristic
110C22×Dic6—32no—
111C2×C3×Q16—31no—
112C22×C3×C8—21no—
113C22×C3×C8—31no—
114C22×C3×C8—31no—
115C22×C3×C8—31no—
116C22×C3×C8—31no—
117C22×C3×C8—31no—
118C22×C3×C8—64no—
119C22×C3×C8C2×D311yescharacteristic
120C22×C3×C8C2×D311yescharacteristic
121C3×C22⋊Q8—32no—
122C2×#217—62no—
123#946—32no—
124C2×#216—32no—
125C2×C4⋊Dic3—32no—
126#924—32no—
127#924—32no—
128#924—32no—
129#924—32no—
130#924—62no—
131#924—62no—
132#924—62no—
133#924C2×D312yes—
134C2×Dic3⋊C4—62no—
135C22×C3⋊C8C2×D311yescharacteristic
136D3×Q16—64no—
137C2×Dic12—32no—
138C2×Dic12—31no—
139C2×Dic12—31no—
140C2×Dic12—61no—
141C2×Dic12—64no—
142C2×Dic12C2×D311yescharacteristic, complemented
143C2×D3×C8—24no—
144C2×D3×C8C2×D311yescharacteristic
145C2×D3×C8C2×D311yescharacteristic
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#818—31no—
158#818—31no—
159#818—32no—
160#818—61no—
161#818C2×D311yescharacteristic, complemented
162#816—32no—
163#816—32no—
164#816—32no—
165#816—32no—
166#816—62no—
167#816C2×D312yescomplemented
168#810—32no—
169#807—32no—
170C23×C32C2×D411yescharacteristic
171C22×C3×D3—22no—
172C22×C3×D3—22no—
173C22×C3×D3Q1614yescomplemented
174C22×C3×D3C2×D411yescharacteristic
175C22×C3×D3C2×D411yescharacteristic
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2411yescharacteristic
180C2×C3⋊Dic3—22no—
181C2×C3⋊Dic3—22no—
182#634—22no—
183#634—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3C2×D411yescharacteristic
188C2×C3×Dic3C2×D411yescharacteristic
189C3×C4×D3—22no—
190C3×C4×D3—21no—
191C3×C4×D3—21no—
192C3×C4×D3—22no—
193C3×C4×D3C2×D412yes—
194C3×C4×D3#4112yes—
195C3×Dic6—22no—
196C3×Dic6—22no—
197#627—44no—
198D3×Dic3—44no—
199D3×Dic3—44no—
200C32×C8—21no—
201C32×C8C2×D412yes—
202C3×C3⋊C8—21no—
203C3×C3⋊C8C2×D412yes—
204C22×Q16—91no—
205C23×C8—31no—
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—
215C24×C3—31no—
216C23×D3D1211yescharacteristic
217C2×C3×Q8—32no—
218C22×C3×C4—21no—
219C22×C3×C4—31no—
220C22×C3×C4—31no—
221C22×C3×C4—31no—
222C22×C3×C4—31no—
223C22×C3×C4—31no—
224C22×C3×C4—62no—
225C22×C3×C4—62no—
226C22×C3×C4C22×D311yescharacteristic
227C22×C3×C4C22×D311yescharacteristic
228C22×Dic3—62no—
229C22×Dic3—62no—
230C22×Dic3D1211yescharacteristic
231D3×Q8—64no—
232D3×Q8—64no—
233C2×C4×D3—22no—
234C2×C4×D3—22no—
235C2×C4×D3—62no—
236C2×C4×D3—62no—
237C2×C4×D3D1211yescharacteristic
238C2×C4×D3D1211yescharacteristic
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—22no—
251C2×C3×C8—22no—
252C2×C3×C8—21no—
253C2×C3×C8—21no—
254C2×C3×C8—31no—
255C2×C3×C8—34no—
256C2×C3×C8—31no—
257C2×C3×C8—42no—
258C2×C3×C8—62no—
259C2×C3×C8—62no—
260C2×C3×C8—62no—
261C2×C3×C8—62no—
262C2×C3×C8C22×D311yescharacteristic
263C2×C3×C8C22×D311yescharacteristic
264C2×C3×C8C22×D311yescharacteristic
265C2×C3×C8C22×D311yescharacteristic
266C3×C4⋊C4—32no—
267C3×C4⋊C4—62no—
268C3×C22⋊C4—62no—
269#217—22no—
270#217—62no—
271#217—62no—
272#217—62no—
273#217—62no—
274#217—122no—
275#216—64no—
276(C2×D3)⋊C4—62no—
277(C2×D3)⋊C4—62no—
278C4⋊Dic3—32no—
279C4⋊Dic3—32no—
280C4⋊Dic3—62no—
281C4⋊Dic3—62no—
282C4⋊Dic3—62no—
283C4⋊Dic3C22×D312yes—
284Dic3⋊C4—22no—
285Dic3⋊C4—62no—
286Dic3⋊C4—62no—
287Dic3⋊C4—62no—
288Dic3⋊C4—62no—
289Dic3⋊C4—62no—
290Dic3⋊C4—62no—
291Dic3⋊C4—122no—
292C2×C3⋊C8—22no—
293C2×C3⋊C8C22×D311yescharacteristic
294C2×C3⋊C8C22×D311yescharacteristic
295Dic12—22no—
296Dic12—64no—
297Dic12—62no—
298Dic12—62no—
299Dic12—122no—
300D3×C8—22no—
301D3×C8—22no—
302D3×C8—22no—
303D3×C8#6714yes—
304C22×C32—21no—
305C22×C32—21no—
306C22×C32C2×Q1612yescomplemented
307C22×C32C22×D411yescharacteristic
308C2×C3×D3—21no—
309C2×C3×D3—21no—
310C2×C3×D3—28no—
311C2×C3×D3#12112yes—
312C2×C3×D3C2×Q1612yes—
313C2×C3×D3C2×Q1612yescomplemented
314C2×C3×D3#13512yes—
315C32×C4—21no—
316C32×C4C22×D411yescharacteristic
317C32×C4C2×#4111yescharacteristic
318C3⋊Dic3—42no—
319C3⋊Dic3—42no—
320C3×Dic3—21no—
321C3×Dic3—42no—
322C3×Dic3—42no—
323C3×Dic3#12112yes—
324C22×Q8—92no—
325C23×C4—31no—
326C2×Q16—31no—
327C2×Q16—92no—
328C2×Q16—91no—
329C2×Q16—184no—
330C22×C8—31no—
331C22×C8—31no—
332C22×C8—31no—
333C22×C8—31no—
334C22×C8—31no—
335C22×C8—64no—
336C22×C8D3211yescharacteristic
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—21no—
354C23×C3—31no—
355C23×C3—34no—
356C23×C3—31no—
357C23×C3—62no—
358C23×C3—62no—
359C23×C3C2×D1211yescharacteristic
360C23×C3D3×D411yescharacteristic
361C22×D3—22no—
362C22×D3—22no—
363C22×D3Dic1214yescomplemented
364C22×D3C2×D1211yescharacteristic
365C22×D3C2×D1211yescharacteristic
366C3×Q8—62no—
367C3×Q8—62no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—31no—
375C2×C3×C4—32no—
376C2×C3×C4—32no—
377C2×C3×C4—31no—
378C2×C3×C4—41no—
379C2×C3×C4—41no—
380C2×C3×C4—62no—
381C2×C3×C4—62no—
382C2×C3×C4—62no—
383C2×C3×C4—61no—
384C2×C3×C4—61no—
385C2×C3×C4—62no—
386C2×C3×C4—62no—
387C2×C3×C4C2×D1211yescharacteristic
388C2×C3×C4D3×D411yescharacteristic
389C2×C3×C4C23×D311yescharacteristic
390C2×C3×C4C23×D311yescharacteristic
391C2×Dic3—22no—
392C2×Dic3—22no—
393C2×Dic3—22no—
394C2×Dic3—62no—
395C2×Dic3—62no—
396C2×Dic3—62no—
397C2×Dic3—62no—
398C2×Dic3—122no—
399C2×Dic3—122no—
400C2×Dic3—124no—
401C2×Dic3—124no—
402C2×Dic3C2×D1211yescharacteristic
403C2×Dic3C2×D1211yescharacteristic
404C4×D3—22no—
405C4×D3—21no—
406C4×D3—21no—
407C4×D3—22no—
408C4×D3—124no—
409C4×D3—124no—
410C4×D3#23512yes—
411C4×D3C2×#6712yes—
412Dic6—22no—
413Dic6—22no—
414Dic6—62no—
415Dic6—62no—
416Dic6—62no—
417Dic6—62no—
418Dic6—122no—
419Dic6—122no—
420Dic6—124no—
421Dic6—124no—
422C3×C8—21no—
423C3×C8—21no—
424C3×C8—22no—
425C3×C8—32no—
426C3×C8—41no—
427C3×C8—61no—
428C3×C8D3×D412yes—
429C3×C8C2×#6712yes—
430C3⋊C8—21no—
431C3⋊C8C2×#6712yes—
432C2×C32—22no—
433C2×C32C2×#12111yescharacteristic
434C2×C32C22×Q1611yescharacteristic
435C2×C32C2×#13511yescharacteristic
436C3×D3—22no—
437C3×D3#46714yescomplemented
438C24—31no—
439C2×Q8—32no—
440C2×Q8—92no—
441C2×Q8—182no—
442C2×Q8—184no—
443C2×Q8—184no—
444C22×C4—31no—
445C22×C4—31no—
446C22×C4—31no—
447C22×C4—31no—
448C22×C4—31no—
449C22×C4—62no—
450C22×C4—62no—
451C22×C4—182no—
452C22×C4—182no—
453C22×C4C2×D3211yescharacteristic
454Q16—62no—
455Q16—184no—
456Q16—182no—
457C2×C8—22no—
458C2×C8—31no—
459C2×C8—34no—
460C2×C8—31no—
461C2×C8—62no—
462C2×C8—62no—
463C2×C8—62no—
464C2×C8—62no—
465C2×C8C2×D3211yescharacteristic
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—21no—
480C22×C3—21no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—22no—
484C22×C3—32no—
485C22×C3—32no—
486C22×C3—32no—
487C22×C3—32no—
488C22×C3—41no—
489C22×C3—41no—
490C22×C3—68no—
491C22×C3—61no—
492C22×C3—61no—
493C22×C3C2×Dic1212yescomplemented
494C22×C3D3×Q1612yescomplemented
495C22×C3C22×D1211yescharacteristic
496C22×C3C2×D3×D411yescharacteristic
497C2×D3—21no—
498C2×D3—21no—
499C2×D3—28no—
500C2×D3#90412yes—
501C2×D3C2×Dic1212yes—
502C2×D3C2×Dic1212yescomplemented
503C2×D3#93012yes—
504C3×C4—21no—
505C3×C4—21no—
506C3×C4—21no—
507C3×C4—21no—
508C3×C4—32no—
509C3×C4—41no—
510C3×C4—61no—
511C3×C4—122no—
512C3×C4—122no—
513C3×C4C2×#23511yescharacteristic
514C3×C4C2×D3×D411yescharacteristic
515C3×C4D3×#4111yescharacteristic
516C3×C4C22×#6711yescharacteristic
517Dic3—21no—
518Dic3—42no—
519Dic3—42no—
520Dic3—122no—
521Dic3—122no—
522Dic3—122no—
523Dic3—122no—
524Dic3—242no—
525Dic3—242no—
526Dic3#93012yes—
527C32C2×#46711yescharacteristic, complemented, Sylow
528C23—31no—
529C23—31no—
530C23—34no—
531C23—62no—
532C23—62no—
533C23D3×D1211yescharacteristic
534Q8—62no—
535Q8—62no—
536Q8—182no—
537Q8—182no—
538Q8—364no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—31no—
542C2×C4—32no—
543C2×C4—32no—
544C2×C4—31no—
545C2×C4—62no—
546C2×C4—62no—
547C2×C4—62no—
548C2×C4—61no—
549C2×C4—61no—
550C2×C4—62no—
551C2×C4—62no—
552C2×C4—182no—
553C2×C4—182no—
554C2×C4—364no—
555C2×C4—364no—
556C2×C4D3×D1211yescharacteristic
557C2×C4C22×D3211yescharacteristic
558C8—21no—
559C8—32no—
560C8—61no—
561C8D3×#6712yes—
562C2×C3—22no—
563C2×C3—22no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—21no—
567C2×C3—34no—
568C2×C3—42no—
569C2×C3—62no—
570C2×C3D3×#12111yescharacteristic
571C2×C3C2×#90411yescharacteristic
572C2×C3C22×Dic1211yescharacteristic
573C2×C3C2×D3×Q1611yescharacteristic
574C2×C3D3×#13511yescharacteristic
575C2×C3C2×#93011yescharacteristic
576D3—22no—
577D3#511614yesdirect product factor
578C22—21no—
579C22—21no—
580C22—32no—
581C22—32no—
582C22—32no—
583C22—32no—
584C22—68no—
585C22—61no—
586C22—61no—
587C22D3×Dic1212yescomplemented
588C22C2×D3×D1211yescharacteristic
589C4—21no—
590C4—32no—
591C4—61no—
592C4—122no—
593C4—122no—
594C4—362no—
595C4—362no—
596C4D3×#23511yescharacteristic
597C4C2×D3×#6711yescharacteristic
598C3—21no—
599C3D3×#46711yescharacteristic, complemented
600C3C2×#511611yescharacteristic, complemented
601C2—22no—
602C2—34no—
603C2—62no—
604C2D3×#90411yescharacteristic
605C2C2×D3×Dic1211yescharacteristic
606C2D3×#93011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radicalC23×C3×D3D4
hypercenterC22×C8D32
hypocenterC32C2×#467
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
3. C2×D3×Dic12C2semidirect
4. #10592815C2semidirect
5. C3×#5116C2semidirect
6. #10591187C2semidirect
7. #10590852C2semidirect
8. #10590851C2semidirect
9. #10590848C2semidirect
10. D3×#818C2semidirect
11. D3×#816C2semidirect
18. C2×#3746C22semidirect
21. C2×C3×Dic12C22semidirect
34. C2×#3719C22semidirect
36. #63645C22semidirect
37. #63643C22semidirect
38. C3×#818C22semidirect
39. C3×#816C22semidirect
40. #63575C22semidirect
41. #63567C22semidirect
42. #63566C22semidirect
58. #5116D3direct (N × H)
142. C2×Dic12C2×D3semidirect
161. #818C2×D3semidirect
167. #816C2×D3semidirect
173. C22×C3×D3Q16semidirect
306. C22×C32C2×Q16semidirect
313. C2×C3×D3C2×Q16semidirect
363. C22×D3Dic12semidirect
437. C3×D3#467semidirect
493. C22×C3C2×Dic12semidirect
494. C22×C3D3×Q16semidirect
502. C2×D3C2×Dic12semidirect
527. C32C2×#467semidirect
577. D3#5116direct (N × H)
587. C22D3×Dic12semidirect
599. C3D3×#467semidirect
600. C3C2×#5116semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×C82
D3×#9242
C2×D3×Dic122
#105928152
C3×#51162
#105911872
#105908522
#105908512
#105908482
D3×#8182
D3×#8162
C2×#51163
D3×#4673