Finite Group Databasebeta

← D3×#4850 #11868444

Subgroups — D3×#4850 #11868444

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
1D3×#869C211yesmaximal, characteristic
2C4×D3×Dic6C211yesmaximal, characteristic
3#10592549C211yesmaximal, characteristic, complemented
4C3×#4850C211yesmaximal, characteristic, complemented
5C3×D3×C4⋊C8C211yesmaximal, characteristic
6#10590805C212yesmaximal, complemented
7#10590804C212yesmaximal, complemented
8D3×#818C212yesmaximal
9D3×#816C212yesmaximal
10#10590284C211yesmaximal, characteristic, complemented
11#10590283C211yesmaximal, characteristic, complemented
12D3×#477—31nomaximal
13C2×#4850—31nomaximal
14C2×D3×Dic6—21no—
15C2×D3×Dic6C2211yescharacteristic
16#64078C2211yescharacteristic
17C4×#634C2211yescharacteristic
18C2×C3×D3×C8C2212yes—
19C3×C42×D3C2211yescharacteristic
20C3×#869C2211yescharacteristic
21C3×C4×Dic6C2211yescharacteristic
22#63918—21no—
23#63918C2212yes—
24C4×#627—21no—
25D3×C4⋊Dic3—21no—
26D3×C4⋊Dic3C2211yescharacteristic
27D3×C4⋊Dic3C2212yes—
28D3×Dic3⋊C4—21no—
29C4×D3×Dic3—21no—
30#63866—21no—
31#63844C2211yescharacteristic
32Dic3×Dic6C2211yescharacteristic
33#63837—21no—
34C32×C4⋊C8C2211yescharacteristic
35#63645C2212yes—
36#63643C2212yes—
37C3×#818C2212yes—
38C3×#816C2212yes—
39C3×Dic3⋊C8C2212yes—
40C3×C4⋊(C3⋊C8)C2211yescharacteristic
41#63575C2212yes—
42#63575C2212yes—
43#63567C2212yes—
44#63566C2212yes—
45D3×C4⋊Q8—31no—
46C4×D3×Q8—31no—
47C2×#869—31no—
48C2×C4×Dic6—31no—
49C3×#477—31no—
50C2×C3×C4⋊C8—31no—
51C2×#818—32no—
52C2×#816—32no—
53#5091—31no—
54#5021—31no—
55D3×#107—32no—
56#4875—32no—
57#4850—31no—
58#4850—31no—
59#4850—31no—
60#4850—31no—
61#4850—32no—
62#4850—32no—
63#4850—61no—
64#4850D311yescharacteristic, direct product factor
65D3×C4⋊C8D311yescharacteristic
66D3×#103—32no—
67#4793—32no—
68C2×#634—21no—
69C2×#634C2311yescharacteristic
70C2×C3×C4×D3D411yescharacteristic
71C2×C3×C4×D3D411yescharacteristic
72C2×C3×C4×D3C2311yescharacteristic
73C2×C3×Dic6—21no—
74C2×C3×Dic6C2311yescharacteristic
75C2×#627—21no—
76C2×#627—22no—
77C2×D3×Dic3—21no—
78C2×D3×Dic3—22no—
79C2×D3×Dic3—21no—
80D3×Dic6—22no—
81D3×Dic6—44no—
82D3×Dic6Q814yescomplemented
83C2×C32×C8C2312yes—
84C32×C42C2311yescharacteristic
85C4⋊(C3⋊Dic3)—21no—
86C4⋊(C3⋊Dic3)C2311yescharacteristic
87C4⋊(C3⋊Dic3)C2312yes—
88#3750—21no—
89C4×C3⋊Dic3—21no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3C2312yes—
92C3×C4⋊Dic3C2311yescharacteristic
93C3×Dic3⋊C4—21no—
94C3×C4×Dic3—21no—
95C3×C4×Dic3D411yescharacteristic
96C3×C4×Dic3D411yescharacteristic
97C3×C4×Dic3C2311yescharacteristic
98C2×C3×C3⋊C8C2312yes—
99C3×D3×C8—24no—
100#3724—21no—
101Dic3⋊Dic3—21no—
102Dic3⋊Dic3—21no—
103Dic3⋊Dic3—22no—
104Dic3⋊Dic3—22no—
105Dic32—21no—
106Dic32—21no—
107C2×#477—91noSylow
108C2×D3×Q8—31no—
109C2×D3×Q8—61no—
110C22×Dic6—31no—
111C22×Dic6—61no—
112C22×C3×C8—32no—
113C3×C4⋊Q8—31no—
114C3×C4×Q8—31no—
115C2×C3×C42—31no—
116Q8×Dic3—31no—
117#944—61no—
118C2×C4⋊Dic3—31no—
119C2×C4⋊Dic3—32no—
120C2×C4⋊Dic3—61no—
121C2×Dic3⋊C4—61no—
122C2×C4×Dic3—61no—
123C2×D3×C8C2×D312yes—
124D3×C4⋊C4—31no—
125D3×C4⋊C4—32no—
126D3×C4⋊C4—61no—
127D3×C4⋊C4—61no—
128#888—32no—
129#888—61no—
130#887—31no—
131#887—61no—
132C42×D3—61no—
133C42×D3C2×D311yescharacteristic
134#869—31no—
135#869—31no—
136#869—32no—
137#869—61no—
138#869—61no—
139#869—61no—
140#869C2×D311yescharacteristic
141C4×Dic6—31no—
142C4×Dic6—31no—
143C4×Dic6—31no—
144C4×Dic6—31no—
145C4×Dic6—61no—
146C4×Dic6—61no—
147C4×Dic6—61no—
148C4×Dic6—61no—
149C4×Dic6C2×D311yescharacteristic
150C3×#107—32no—
151C3×C4⋊C8—21no—
152C3×C4⋊C8—32no—
153C3×C4⋊C8—31no—
154C3×C4⋊C8C2×D311yescharacteristic
155C3×C4⋊C8C2×D311yescharacteristic
156C3×#103—32no—
157#835—32no—
158#818—32no—
159#818—32no—
160#818—32no—
161#818—32no—
162#818—62no—
163#818C2×D312yes—
164#816—32no—
165#816—32no—
166#816—32no—
167#816—32no—
168#816—62no—
169#816C2×D312yes—
170Dic3⋊C8C2×D312yes—
171#810—32no—
172#807—32no—
173#807—32no—
174C4⋊(C3⋊C8)C2×D311yescharacteristic
175C22×C3×D3C2×D411yescharacteristic
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2411yescharacteristic
179C2×C3⋊Dic3—21no—
180C2×C3⋊Dic3—21no—
181C2×C3⋊Dic3—22no—
182#634—21no—
183#634—42no—
184#634C2×Q812yescomplemented
185C2×C3×Dic3—21no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3C2×D411yescharacteristic
189C2×C3×Dic3C2×D411yescharacteristic
190C2×C3×Dic3C2×D411yescharacteristic
191C3×C4×D3—22no—
192C3×C4×D3Q1614yes—
193C3×C4×D3C2×Q812yes—
194C3×C4×D3#4112yes—
195C3×Dic6—21no—
196C3×Dic6—42no—
197C3×Dic6C2×Q812yescomplemented
198#627—24no—
199#627—44no—
200D3×Dic3—24no—
201D3×Dic3—44no—
202D3×Dic3—42no—
203C32×C8—22no—
204C3×C3⋊C8—22no—
205C2×C4⋊Q8—91no—
206C2×C4×Q8—91no—
207#477—31no—
208#477—92no—
209#477—92no—
210#477—91no—
211#477—91no—
212#477—91no—
213C2×#107—92no—
214C2×C4⋊C8—31no—
215C2×#103—92no—
216C2×C3×Q8—31no—
217C2×C3×Q8—61no—
218C22×C3×C4—31no—
219C22×C3×C4—31no—
220C22×C3×C4—31no—
221C22×Dic3—61no—
222C22×Dic3—61no—
223C22×Dic3—62no—
224D3×Q8—34no—
225D3×Q8—62no—
226D3×Q8—124no—
227C2×C4×D3—61no—
228C2×C4×D3—61no—
229C2×C4×D3—62no—
230C2×C4×D3D1211yescharacteristic
231C2×C4×D3D1211yescharacteristic
232C2×C4×D3C22×D311yescharacteristic
233C2×Dic6—21no—
234C2×Dic6—31no—
235C2×Dic6—31no—
236C2×Dic6—34no—
237C2×Dic6—61no—
238C2×Dic6—62no—
239C2×Dic6—61no—
240C2×Dic6—61no—
241C2×Dic6—62no—
242C2×Dic6—61no—
243C2×Dic6—61no—
244C2×Dic6—62no—
245C2×Dic6—121no—
246C2×Dic6—124no—
247C2×Dic6C22×D311yescharacteristic
248C2×C3×C8—22no—
249C2×C3×C8—32no—
250C2×C3×C8—64no—
251C2×C3×C8C22×D312yes—
252C2×C3×C8C22×D312yes—
253C3×C4⋊C4—31no—
254C3×C4⋊C4—32no—
255C3×C4⋊C4—61no—
256C3×C4⋊C4—61no—
257C3×C42—21no—
258C3×C42—31no—
259C3×C42—31no—
260C3×C42—31no—
261C3×C42—61no—
262C3×C42C22×D311yescharacteristic
263C3×C42C22×D311yescharacteristic
264C4⋊Dic3—21no—
265C4⋊Dic3—31no—
266C4⋊Dic3—32no—
267C4⋊Dic3—32no—
268C4⋊Dic3—31no—
269C4⋊Dic3—62no—
270C4⋊Dic3—61no—
271C4⋊Dic3—61no—
272C4⋊Dic3—62no—
273C4⋊Dic3—62no—
274C4⋊Dic3—61no—
275C4⋊Dic3—61no—
276C4⋊Dic3—61no—
277C4⋊Dic3—121no—
278C4⋊Dic3C22×D312yes—
279C4⋊Dic3C22×D311yescharacteristic
280Dic3⋊C4—21no—
281Dic3⋊C4—61no—
282Dic3⋊C4—61no—
283Dic3⋊C4—61no—
284Dic3⋊C4—61no—
285Dic3⋊C4—61no—
286Dic3⋊C4—61no—
287Dic3⋊C4—62no—
288Dic3⋊C4—62no—
289Dic3⋊C4—121no—
290C4×Dic3—21no—
291C4×Dic3—61no—
292C4×Dic3—61no—
293C4×Dic3—61no—
294C4×Dic3—61no—
295C4×Dic3—61no—
296C4×Dic3—61no—
297C4×Dic3—121no—
298C4×Dic3D1211yescharacteristic
299C4×Dic3D1211yescharacteristic
300C4×Dic3C22×D311yescharacteristic
301C2×C3⋊C8C22×D312yes—
302D3×C8—24no—
303C22×C32C22×D411yescharacteristic
304C2×C3×D3C22⋊Q812yes—
305C2×C3×D3C2×Q1612yes—
306C2×C3×D3AGL(1,ℤ/8)12yes—
307C32×C4—21no—
308C32×C4C2×Q1612yes—
309C32×C4C22×Q811yescharacteristic
310C32×C4C2×#4111yescharacteristic
311C3⋊Dic3—22no—
312C3⋊Dic3—42no—
313C3⋊Dic3—41no—
314C3×Dic3—22no—
315C3×Dic3—21no—
316C3×Dic3—42no—
317C3×Dic3—41no—
318C3×Dic3C22⋊Q812yes—
319C3×Dic3C2×Q1612yes—
320C22×Q8—91no—
321C22×Q8—181no—
322C22×C8—32no—
323C4⋊Q8—31no—
324C4⋊Q8—92no—
325C4⋊Q8—91no—
326C4⋊Q8—181no—
327C4⋊Q8—181no—
328C4×Q8—31no—
329C4×Q8—91no—
330C4×Q8—91no—
331C4×Q8—91no—
332C4×Q8—181no—
333C4×Q8—181no—
334C2×C4⋊C4—91no—
335C2×C4⋊C4—92no—
336C2×C4⋊C4—181no—
337C2×C4⋊C4—181no—
338C2×C42—31no—
339C2×C42—181no—
340#107—32no—
341#107—92no—
342#107—92no—
343#107—92no—
344C4⋊C8—32no—
345C4⋊C8—31no—
346C4⋊C8D3211yescharacteristic
347#103—32no—
348#103—92no—
349#103—92no—
350#103—92no—
351C23×C3—31no—
352C22×D3C2×D1211yescharacteristic
353C3×Q8—32no—
354C3×Q8—61no—
355C3×Q8—122no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—31no—
360C2×C3×C4—31no—
361C2×C3×C4—34no—
362C2×C3×C4—32no—
363C2×C3×C4—32no—
364C2×C3×C4—31no—
365C2×C3×C4—62no—
366C2×C3×C4—61no—
367C2×C3×C4—61no—
368C2×C3×C4—62no—
369C2×C3×C4C2×D1211yescharacteristic
370C2×C3×C4C2×D1211yescharacteristic
371C2×C3×C4D3×D411yescharacteristic
372C2×C3×C4D3×D411yescharacteristic
373C2×C3×C4C23×D311yescharacteristic
374C2×C3×C4C23×D311yescharacteristic
375C2×Dic3—21no—
376C2×Dic3—21no—
377C2×Dic3—22no—
378C2×Dic3—64no—
379C2×Dic3—61no—
380C2×Dic3—61no—
381C2×Dic3—61no—
382C2×Dic3—62no—
383C2×Dic3—61no—
384C2×Dic3—62no—
385C2×Dic3—121no—
386C2×Dic3—121no—
387C2×Dic3—122no—
388C2×Dic3—124no—
389C2×Dic3—122no—
390C2×Dic3C2×D1211yescharacteristic
391C2×Dic3C2×D1211yescharacteristic
392C2×Dic3C2×D1211yescharacteristic
393C4×D3—22no—
394C4×D3—64no—
395C4×D3—122no—
396C4×D3—124no—
397C4×D3Dic1214yes—
398C4×D3#23712yes—
399C4×D3D3×Q812yes—
400Dic6—21no—
401Dic6—32no—
402Dic6—32no—
403Dic6—42no—
404Dic6—62no—
405Dic6—64no—
406Dic6—61no—
407Dic6—61no—
408Dic6—64no—
409Dic6—121no—
410Dic6—124no—
411Dic6—124no—
412Dic6—122no—
413Dic6—122no—
414Dic6—242no—
415Dic6D3×Q812yescomplemented
416C3×C8—22no—
417C3×C8—22no—
418C3×C8—42no—
419C3×C8—62no—
420C3⋊C8—22no—
421C2×C32C2×C22⋊Q811yescharacteristic
422C2×C32C22×Q1611yescharacteristic
423C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
424C3×D3#47714yescomplemented
425C2×Q8—31no—
426C2×Q8—61no—
427C2×Q8—94no—
428C2×Q8—91no—
429C2×Q8—181no—
430C2×Q8—182no—
431C2×Q8—182no—
432C2×Q8—181no—
433C2×Q8—364no—
434C22×C4—31no—
435C22×C4—31no—
436C22×C4—31no—
437C22×C4—181no—
438C22×C4—181no—
439C22×C4—182no—
440C2×C8—32no—
441C2×C8—64no—
442C2×C8C2×D3212yes—
443C4⋊C4—32no—
444C4⋊C4—31no—
445C4⋊C4—61no—
446C4⋊C4—61no—
447C4⋊C4—92no—
448C4⋊C4—91no—
449C4⋊C4—181no—
450C4⋊C4—182no—
451C4⋊C4—181no—
452C4⋊C4—181no—
453C4⋊C4—182no—
454C4⋊C4—181no—
455C4⋊C4—181no—
456C42—31no—
457C42—31no—
458C42—31no—
459C42—61no—
460C42—181no—
461C42—181no—
462C42—181no—
463C42C2×D3211yescharacteristic
464C22×C3—21no—
465C22×C3—32no—
466C22×C3—32no—
467C22×C3—32no—
468C22×C3C22×D1211yescharacteristic
469C22×C3C2×D3×D411yescharacteristic
470C2×D3#89712yes—
471C2×D3C2×Dic1212yes—
472C2×D3#90812yes—
473C3×C4—21no—
474C3×C4—21no—
475C3×C4—22no—
476C3×C4—21no—
477C3×C4—21no—
478C3×C4—32no—
479C3×C4—32no—
480C3×C4—41no—
481C3×C4—62no—
482C3×C4—61no—
483C3×C4—122no—
484C3×C4—121no—
485C3×C4C2×Dic1212yes—
486C3×C4D3×Q1612yes—
487C3×C4C2×#23711yescharacteristic
488C3×C4C2×D3×Q811yescharacteristic
489C3×C4C2×D3×Q811yescharacteristic
490C3×C4D3×#4111yescharacteristic
491Dic3—21no—
492Dic3—22no—
493Dic3—42no—
494Dic3—41no—
495Dic3—62no—
496Dic3—62no—
497Dic3—122no—
498Dic3—122no—
499Dic3—121no—
500Dic3—122no—
501Dic3—121no—
502Dic3—242no—
503Dic3—241no—
504Dic3#89712yes—
505Dic3C2×Dic1212yes—
506C32C2×#47711yescharacteristic, complemented, Sylow
507C23—31no—
508Q8—32no—
509Q8—61no—
510Q8—92no—
511Q8—122no—
512Q8—184no—
513Q8—181no—
514Q8—362no—
515Q8—364no—
516C2×C4—31no—
517C2×C4—31no—
518C2×C4—34no—
519C2×C4—32no—
520C2×C4—32no—
521C2×C4—31no—
522C2×C4—62no—
523C2×C4—61no—
524C2×C4—61no—
525C2×C4—62no—
526C2×C4—184no—
527C2×C4—181no—
528C2×C4—181no—
529C2×C4—182no—
530C2×C4—364no—
531C2×C4—362no—
532C2×C4D3×D1211yescharacteristic
533C2×C4D3×D1211yescharacteristic
534C2×C4C22×D3211yescharacteristic
535C8—22no—
536C8—62no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—34no—
541C2×C3C2×#89711yescharacteristic
542C2×C3D3×C22⋊Q811yescharacteristic
543C2×C3C22×Dic1211yescharacteristic
544C2×C3C2×#90811yescharacteristic
545C2×C3C2×D3×Q1611yescharacteristic
546C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
547D3#485014yesdirect product factor
548C22—32no—
549C22—32no—
550C22—32no—
551C22C2×D3×D1211yescharacteristic
552C4—21no—
553C4—32no—
554C4—32no—
555C4—62no—
556C4—61no—
557C4—122no—
558C4—121no—
559C4—182no—
560C4—362no—
561C4—361no—
562C4D3×Dic1212yes—
563C4D3×#23711yescharacteristic
564C4D32×Q811yescharacteristic
565C3—21no—
566C3C2×#485011yescharacteristic, complemented
567C3D3×#47711yescharacteristic, complemented
568C2—34no—
569C2D3×#89711yescharacteristic
570C2C2×D3×Dic1211yescharacteristic
571C2D3×#90811yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC4⋊C8D32
hypocenterC32C2×#477
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
3. #10592549C2semidirect
4. C3×#4850C2semidirect
6. #10590805C2semidirect
7. #10590804C2semidirect
10. #10590284C2semidirect
11. #10590283C2semidirect
64. #4850D3direct (N × H)
82. D3×Dic6Q8semidirect
184. #634C2×Q8semidirect
197. C3×Dic6C2×Q8semidirect
415. Dic6D3×Q8semidirect
424. C3×D3#477semidirect
506. C32C2×#477semidirect
547. D3#4850direct (N × H)
566. C3C2×#4850semidirect
567. C3D3×#477semidirect

Maximal subgroups

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

subgroupindex
D3×#8692
C4×D3×Dic62
#105925492
C3×#48502
C3×D3×C4⋊C82
#105908052
#105908042
D3×#8182
D3×#8162
#105902842
#105902832
D3×#4773
C2×#48503