Finite Group Databasebeta

← D3×#4849 #11865637

Subgroups — D3×#4849 #11865637

Order 1152.

1014 conjugacy classes of subgroups.

The subgroup lattice has 607 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×Dic12C212yesmaximal
2D3×#869C211yesmaximal, characteristic
3C4×D3×Dic6C211yesmaximal, characteristic
4#10592548C211yesmaximal, characteristic, complemented
5C3×#4849C211yesmaximal, characteristic, complemented
6C3×D3×C4⋊C8C211yesmaximal, characteristic
7#10590808C212yesmaximal, complemented
8#10590800C212yesmaximal, complemented
9D3×#816C212yesmaximal
10#10590388C211yesmaximal, characteristic, complemented
11#10590385C211yesmaximal, characteristic, complemented
12D3×#462—31nomaximal
13C2×#4849—31nomaximal
14C2×D3×Dic6C2212yes—
15C2×D3×Dic6C2211yescharacteristic
16C2×#3746C2212yes—
17#64078C2211yescharacteristic
18C4×#634C2211yescharacteristic
19C2×C3×Dic12C2212yes—
20C2×C3×D3×C8C2212yes—
21C3×C42×D3C2211yescharacteristic
22C3×#869C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24#63918—21no—
25#63918—21no—
26C4×#627—21no—
27D3×C4⋊Dic3—21no—
28D3×C4⋊Dic3—21no—
29D3×C4⋊Dic3C2211yescharacteristic
30D3×Dic3⋊C4—21no—
31C4×D3×Dic3—21no—
32#63866C2212yes—
33#63844C2211yescharacteristic
34Dic3×Dic6C2211yescharacteristic
35#63837—21no—
36C2×#3719C2212yes—
37C2×#3719C2212yes—
38D3×Dic12—28no—
39C32×C4⋊C8C2211yescharacteristic
40#63643C2212yes—
41C3×#816C2212yes—
42C3×Dic3⋊C8C2212yes—
43C3×C4⋊(C3⋊C8)C2211yescharacteristic
44#63567C2212yes—
45#63566C2212yes—
46C2×D3×Q16—32no—
47C22×Dic12—32no—
48D3×C4⋊Q8—31no—
49C4×D3×Q8—31no—
50C2×#869—31no—
51C2×C4×Dic6—31no—
52C3×#462—31no—
53C2×C3×C4⋊C8—31no—
54#5182—32no—
55C2×#816—32no—
56#5090—31no—
57#5031—31no—
58#4849—32no—
59#4849—31no—
60#4849—31no—
61#4849—31no—
62#4849—31no—
63#4849—32no—
64#4849—61no—
65#4849D311yescharacteristic, direct product factor
66D3×C4⋊C8D311yescharacteristic
67D3×#103—32no—
68#4795—32no—
69C2×#634C2312yes—
70C2×#634C2311yescharacteristic
71C2×C3×C4×D3D411yescharacteristic
72C2×C3×C4×D3D411yescharacteristic
73C2×C3×C4×D3C2311yescharacteristic
74C2×C3×Dic6C2312yes—
75C2×C3×Dic6C2311yescharacteristic
76C2×#627—21no—
77C2×#627—22no—
78C2×D3×Dic3—21no—
79C2×D3×Dic3—22no—
80C2×D3×Dic3—21no—
81D3×Dic6—22no—
82D3×Dic6—24no—
83D3×Dic6—24no—
84D3×Dic6D414yes—
85C2×C32×C8C2312yes—
86C32×C42C2311yescharacteristic
87C4⋊(C3⋊Dic3)—21no—
88C4⋊(C3⋊Dic3)—21no—
89C4⋊(C3⋊Dic3)C2311yescharacteristic
90#3750—21no—
91C4×C3⋊Dic3—21no—
92#3746—24no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3C2311yescharacteristic
96C3×Dic3⋊C4—21no—
97C3×C4×Dic3—21no—
98C3×C4×Dic3D411yescharacteristic
99C3×C4×Dic3D411yescharacteristic
100C3×C4×Dic3C2311yescharacteristic
101C2×C3×C3⋊C8C2312yes—
102C3×Dic12—24no—
103C3×D3×C8—24no—
104#3724—21no—
105Dic3⋊Dic3—21no—
106Dic3⋊Dic3—21no—
107Dic3⋊Dic3—22no—
108Dic3⋊Dic3—22no—
109Dic32—21no—
110Dic32—21no—
111#3719—24no—
112#3719—24no—
113C2×#462—91noSylow
114C2×D3×Q8—31no—
115C2×D3×Q8—32no—
116C22×Dic6—31no—
117C22×Dic6—32no—
118C2×C3×Q16—32no—
119C22×C3×C8—32no—
120C3×C4⋊Q8—31no—
121C3×C4×Q8—31no—
122C2×C3×C42—31no—
123Q8×Dic3—31no—
124#944—32no—
125C2×#216—32no—
126C2×#216—32no—
127C2×C4⋊Dic3—31no—
128C2×C4⋊Dic3—61no—
129C2×C4⋊Dic3—61no—
130C2×Dic3⋊C4—61no—
131C2×C4×Dic3—61no—
132D3×Q16—68no—
133C2×Dic12—32no—
134C2×Dic12—32no—
135C2×Dic12—32no—
136C2×Dic12—32no—
137C2×Dic12—62no—
138C2×Dic12—68no—
139C2×Dic12C2×D312yes—
140C2×D3×C8C2×D312yes—
141D3×C4⋊C4—31no—
142D3×C4⋊C4—61no—
143D3×C4⋊C4—61no—
144D3×C4⋊C4—61no—
145#888—61no—
146#888—61no—
147#887—31no—
148#887—61no—
149C42×D3—61no—
150C42×D3C2×D311yescharacteristic
151#869—32no—
152#869—31no—
153#869—31no—
154#869—61no—
155#869—61no—
156#869—61no—
157#869C2×D311yescharacteristic
158C4×Dic6—31no—
159C4×Dic6—31no—
160C4×Dic6—31no—
161C4×Dic6—31no—
162C4×Dic6—61no—
163C4×Dic6—61no—
164C4×Dic6—61no—
165C4×Dic6—61no—
166C4×Dic6C2×D311yescharacteristic
167C3×C4⋊C8—21no—
168C3×C4⋊C8—32no—
169C3×C4⋊C8—31no—
170C3×C4⋊C8C2×D311yescharacteristic
171C3×C4⋊C8C2×D311yescharacteristic
172C3×#103—32no—
173#835—32no—
174#816—32no—
175#816—32no—
176#816—32no—
177#816—32no—
178#816—62no—
179#816C2×D312yes—
180Dic3⋊C8C2×D312yes—
181#810—32no—
182C4⋊(C3⋊C8)C2×D311yescharacteristic
183C22×C3×D3C2×D411yescharacteristic
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2411yescharacteristic
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—22no—
190#634—21no—
191#634—22no—
192#634—22no—
193#634C2×D412yes—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3C2×D411yescharacteristic
198C2×C3×Dic3C2×D411yescharacteristic
199C2×C3×Dic3C2×D411yescharacteristic
200C3×C4×D3—22no—
201C3×C4×D3Q1614yescomplemented
202C3×C4×D3C2×D412yes—
203C3×C4×D3#4112yes—
204C3×Dic6—21no—
205C3×Dic6—22no—
206C3×Dic6—22no—
207C3×Dic6C2×D412yes—
208#627—24no—
209#627—44no—
210D3×Dic3—24no—
211D3×Dic3—44no—
212D3×Dic3—42no—
213C32×C8—22no—
214C3×C3⋊C8—22no—
215C22×Q16—92no—
216C2×C4⋊Q8—91no—
217C2×C4×Q8—91no—
218#462—31no—
219#462—92no—
220#462—91no—
221#462—91no—
222#462—92no—
223#462—91no—
224C2×C4⋊C8—31no—
225C2×#103—92no—
226C2×C3×Q8—31no—
227C2×C3×Q8—32no—
228C22×C3×C4—31no—
229C22×C3×C4—31no—
230C22×C3×C4—31no—
231C22×Dic3—61no—
232C22×Dic3—61no—
233C22×Dic3—62no—
234D3×Q8—34no—
235D3×Q8—62no—
236D3×Q8—64no—
237D3×Q8—64no—
238C2×C4×D3—61no—
239C2×C4×D3—61no—
240C2×C4×D3—62no—
241C2×C4×D3D1211yescharacteristic
242C2×C4×D3D1211yescharacteristic
243C2×C4×D3C22×D311yescharacteristic
244C2×Dic6—31no—
245C2×Dic6—31no—
246C2×Dic6—34no—
247C2×Dic6—32no—
248C2×Dic6—32no—
249C2×Dic6—61no—
250C2×Dic6—62no—
251C2×Dic6—62no—
252C2×Dic6—64no—
253C2×Dic6—64no—
254C2×Dic6—61no—
255C2×Dic6—61no—
256C2×Dic6—62no—
257C2×Dic6—62no—
258C2×Dic6C22×D312yes—
259C2×Dic6C22×D311yescharacteristic
260C3×Q16—64no—
261C2×C3×C8—22no—
262C2×C3×C8—32no—
263C2×C3×C8—64no—
264C2×C3×C8C22×D312yes—
265C2×C3×C8C22×D312yes—
266C3×C4⋊C4—31no—
267C3×C4⋊C4—61no—
268C3×C4⋊C4—61no—
269C3×C4⋊C4—61no—
270C3×C42—21no—
271C3×C42—31no—
272C3×C42—31no—
273C3×C42—31no—
274C3×C42—61no—
275C3×C42C22×D311yescharacteristic
276C3×C42C22×D311yescharacteristic
277#216—64no—
278#216—64no—
279C4⋊Dic3—21no—
280C4⋊Dic3—21no—
281C4⋊Dic3—31no—
282C4⋊Dic3—31no—
283C4⋊Dic3—61no—
284C4⋊Dic3—61no—
285C4⋊Dic3—62no—
286C4⋊Dic3—62no—
287C4⋊Dic3—61no—
288C4⋊Dic3—61no—
289C4⋊Dic3—61no—
290C4⋊Dic3—61no—
291C4⋊Dic3—61no—
292C4⋊Dic3—121no—
293C4⋊Dic3—121no—
294C4⋊Dic3C22×D311yescharacteristic
295Dic3⋊C4—21no—
296Dic3⋊C4—61no—
297Dic3⋊C4—61no—
298Dic3⋊C4—61no—
299Dic3⋊C4—61no—
300Dic3⋊C4—61no—
301Dic3⋊C4—61no—
302Dic3⋊C4—62no—
303Dic3⋊C4—62no—
304Dic3⋊C4—121no—
305C4×Dic3—21no—
306C4×Dic3—61no—
307C4×Dic3—61no—
308C4×Dic3—61no—
309C4×Dic3—61no—
310C4×Dic3—61no—
311C4×Dic3—61no—
312C4×Dic3—121no—
313C4×Dic3D1211yescharacteristic
314C4×Dic3D1211yescharacteristic
315C4×Dic3C22×D311yescharacteristic
316C2×C3⋊C8C22×D312yes—
317Dic12—24no—
318Dic12—64no—
319Dic12—64no—
320Dic12—64no—
321Dic12—64no—
322Dic12—124no—
323D3×C8—24no—
324C22×C32C22×D411yescharacteristic
325C2×C3×D3#12112yes—
326C2×C3×D3C2×Q1612yes—
327C2×C3×D3#13712yes—
328C32×C4—21no—
329C32×C4C2×Q1612yescomplemented
330C32×C4C22×D411yescharacteristic
331C32×C4C2×#4111yescharacteristic
332C3⋊Dic3—22no—
333C3⋊Dic3—42no—
334C3⋊Dic3—41no—
335C3×Dic3—22no—
336C3×Dic3—21no—
337C3×Dic3—42no—
338C3×Dic3—41no—
339C3×Dic3#12112yes—
340C3×Dic3C2×Q1612yescomplemented
341C22×Q8—91no—
342C22×Q8—92no—
343C2×Q16—32no—
344C2×Q16—92no—
345C2×Q16—92no—
346C2×Q16—92no—
347C2×Q16—188no—
348C22×C8—32no—
349C4⋊Q8—31no—
350C4⋊Q8—92no—
351C4⋊Q8—91no—
352C4⋊Q8—181no—
353C4⋊Q8—181no—
354C4×Q8—31no—
355C4×Q8—91no—
356C4×Q8—91no—
357C4×Q8—91no—
358C4×Q8—181no—
359C4×Q8—181no—
360C2×C4⋊C4—91no—
361C2×C4⋊C4—181no—
362C2×C4⋊C4—181no—
363C2×C4⋊C4—181no—
364C2×C42—31no—
365C2×C42—181no—
366C4⋊C8—32no—
367C4⋊C8—31no—
368C4⋊C8D3211yescharacteristic
369#103—32no—
370#103—92no—
371#103—92no—
372#103—92no—
373C23×C3—31no—
374C22×D3C2×D1211yescharacteristic
375C3×Q8—32no—
376C3×Q8—61no—
377C3×Q8—62no—
378C3×Q8—62no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—31no—
383C2×C3×C4—31no—
384C2×C3×C4—34no—
385C2×C3×C4—32no—
386C2×C3×C4—32no—
387C2×C3×C4—31no—
388C2×C3×C4—62no—
389C2×C3×C4—61no—
390C2×C3×C4—61no—
391C2×C3×C4—62no—
392C2×C3×C4C2×D1211yescharacteristic
393C2×C3×C4C2×D1211yescharacteristic
394C2×C3×C4D3×D411yescharacteristic
395C2×C3×C4D3×D411yescharacteristic
396C2×C3×C4C23×D311yescharacteristic
397C2×C3×C4C23×D311yescharacteristic
398C2×Dic3—21no—
399C2×Dic3—21no—
400C2×Dic3—22no—
401C2×Dic3—64no—
402C2×Dic3—61no—
403C2×Dic3—61no—
404C2×Dic3—61no—
405C2×Dic3—62no—
406C2×Dic3—61no—
407C2×Dic3—62no—
408C2×Dic3—121no—
409C2×Dic3—121no—
410C2×Dic3—122no—
411C2×Dic3—124no—
412C2×Dic3—122no—
413C2×Dic3C2×D1211yescharacteristic
414C2×Dic3C2×D1211yescharacteristic
415C2×Dic3C2×D1211yescharacteristic
416C4×D3—22no—
417C4×D3—64no—
418C4×D3—124no—
419C4×D3—122no—
420C4×D3Dic1214yescomplemented
421C4×D3D3×D412yes—
422C4×D3#23912yes—
423Dic6—21no—
424Dic6—22no—
425Dic6—22no—
426Dic6—32no—
427Dic6—32no—
428Dic6—62no—
429Dic6—64no—
430Dic6—61no—
431Dic6—61no—
432Dic6—64no—
433Dic6—62no—
434Dic6—62no—
435Dic6—62no—
436Dic6—62no—
437Dic6—121no—
438Dic6—122no—
439Dic6—122no—
440Dic6—124no—
441Dic6—124no—
442Dic6D3×D412yes—
443C3×C8—22no—
444C3×C8—22no—
445C3×C8—42no—
446C3×C8—62no—
447C3⋊C8—22no—
448C2×C32C2×#12111yescharacteristic
449C2×C32C22×Q1611yescharacteristic
450C2×C32C2×#13711yescharacteristic
451C3×D3#46214yescomplemented
452C2×Q8—31no—
453C2×Q8—32no—
454C2×Q8—94no—
455C2×Q8—91no—
456C2×Q8—92no—
457C2×Q8—181no—
458C2×Q8—182no—
459C2×Q8—182no—
460C2×Q8—184no—
461C2×Q8—184no—
462C22×C4—31no—
463C22×C4—31no—
464C22×C4—31no—
465C22×C4—181no—
466C22×C4—181no—
467C22×C4—182no—
468Q16—64no—
469Q16—184no—
470Q16—184no—
471Q16—184no—
472C2×C8—32no—
473C2×C8—64no—
474C2×C8C2×D3212yes—
475C4⋊C4—31no—
476C4⋊C4—61no—
477C4⋊C4—61no—
478C4⋊C4—61no—
479C4⋊C4—91no—
480C4⋊C4—181no—
481C4⋊C4—181no—
482C4⋊C4—181no—
483C4⋊C4—182no—
484C4⋊C4—182no—
485C4⋊C4—181no—
486C4⋊C4—181no—
487C4⋊C4—181no—
488C42—31no—
489C42—31no—
490C42—31no—
491C42—61no—
492C42—181no—
493C42—181no—
494C42—181no—
495C42C2×D3211yescharacteristic
496C22×C3—21no—
497C22×C3—32no—
498C22×C3—32no—
499C22×C3—32no—
500C22×C3C22×D1211yescharacteristic
501C22×C3C2×D3×D411yescharacteristic
502C2×D3#89512yes—
503C2×D3C2×Dic1212yes—
504C2×D3#90912yes—
505C3×C4—21no—
506C3×C4—21no—
507C3×C4—21no—
508C3×C4—22no—
509C3×C4—21no—
510C3×C4—32no—
511C3×C4—32no—
512C3×C4—41no—
513C3×C4—62no—
514C3×C4—61no—
515C3×C4—121no—
516C3×C4—122no—
517C3×C4C2×Dic1212yescomplemented
518C3×C4D3×Q1612yescomplemented
519C3×C4C2×D3×D411yescharacteristic
520C3×C4C2×D3×D411yescharacteristic
521C3×C4C2×#23911yescharacteristic
522C3×C4D3×#4111yescharacteristic
523Dic3—21no—
524Dic3—22no—
525Dic3—41no—
526Dic3—42no—
527Dic3—62no—
528Dic3—62no—
529Dic3—122no—
530Dic3—121no—
531Dic3—122no—
532Dic3—121no—
533Dic3—122no—
534Dic3—242no—
535Dic3—241no—
536Dic3#89512yes—
537Dic3C2×Dic1212yescomplemented
538C32C2×#46211yescharacteristic, complemented, Sylow
539C23—31no—
540Q8—32no—
541Q8—61no—
542Q8—62no—
543Q8—62no—
544Q8—92no—
545Q8—184no—
546Q8—181no—
547Q8—182no—
548Q8—182no—
549Q8—364no—
550C2×C4—31no—
551C2×C4—31no—
552C2×C4—32no—
553C2×C4—34no—
554C2×C4—32no—
555C2×C4—31no—
556C2×C4—62no—
557C2×C4—61no—
558C2×C4—61no—
559C2×C4—62no—
560C2×C4—184no—
561C2×C4—181no—
562C2×C4—181no—
563C2×C4—182no—
564C2×C4—364no—
565C2×C4—362no—
566C2×C4D3×D1211yescharacteristic
567C2×C4D3×D1211yescharacteristic
568C2×C4C22×D3211yescharacteristic
569C8—22no—
570C8—62no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—34no—
575C2×C3C2×#89511yescharacteristic
576C2×C3D3×#12111yescharacteristic
577C2×C3C22×Dic1211yescharacteristic
578C2×C3C2×#90911yescharacteristic
579C2×C3C2×D3×Q1611yescharacteristic
580C2×C3D3×#13711yescharacteristic
581D3#484914yesdirect product factor
582C22—32no—
583C22—32no—
584C22—32no—
585C22C2×D3×D1211yescharacteristic
586C4—21no—
587C4—32no—
588C4—32no—
589C4—62no—
590C4—61no—
591C4—122no—
592C4—121no—
593C4—182no—
594C4—362no—
595C4—361no—
596C4D3×Dic1212yescomplemented
597C4D32×D411yescharacteristic
598C4D3×#23911yescharacteristic
599C3—21no—
600C3C2×#484911yescharacteristic, complemented
601C3D3×#46211yescharacteristic, complemented
602C2—34no—
603C2D3×#89511yescharacteristic
604C2C2×D3×Dic1211yescharacteristic
605C2D3×#90911yescharacteristic
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×#462
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
4. #10592548C2semidirect
5. C3×#4849C2semidirect
7. #10590808C2semidirect
8. #10590800C2semidirect
10. #10590388C2semidirect
11. #10590385C2semidirect
65. #4849D3direct (N × H)
201. C3×C4×D3Q16semidirect
329. C32×C4C2×Q16semidirect
340. C3×Dic3C2×Q16semidirect
420. C4×D3Dic12semidirect
451. C3×D3#462semidirect
517. C3×C4C2×Dic12semidirect
518. C3×C4D3×Q16semidirect
537. Dic3C2×Dic12semidirect
538. C32C2×#462semidirect
581. D3#4849direct (N × H)
596. C4D3×Dic12semidirect
600. C3C2×#4849semidirect
601. C3D3×#462semidirect

Maximal subgroups

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

subgroupindex
C2×D3×Dic122
D3×#8692
C4×D3×Dic62
#105925482
C3×#48492
C3×D3×C4⋊C82
#105908082
#105908002
D3×#8162
#105903882
#105903852
D3×#4623
C2×#48493