Finite Group Databasebeta

← D3×#4738 #11863617

Subgroups — D3×#4738 #11863617

Order 1152.

1663 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×Dic6C211yesmaximal, characteristic, complemented
2D3×#930C211yesmaximal, characteristic
3C2×D3×#204C212yesmaximal, complemented
4#10592437C211yesmaximal, characteristic, complemented
5C3×#4738C211yesmaximal, characteristic, complemented
6C3×D3×C22⋊C8C211yesmaximal, characteristic, complemented
7#10591181C211yesmaximal, characteristic, complemented
8#10591174C211yesmaximal, characteristic, complemented
9#10590951C212yesmaximal, complemented
10#10590822C212yesmaximal, complemented
11D3×#816C212yesmaximal, complemented
12D3×#448—31nomaximal
13C2×#4738—31nomaximal
14C22×#634C2211yescharacteristic, complemented
15C22×C3×C4×D3C2211yescharacteristic
16C22×C3×Dic6C2211yescharacteristic, complemented
17C2×D3×#67—21no—
18C22×#627—21no—
19C22×D3×Dic3—21no—
20C2×D3×D12C2211yescharacteristic
21C2×D3×Dic6—21no—
22C2×D3×Dic6—21no—
23C2×D3×Dic6—28no—
24C2×D3×Dic6C2212yes—
25C2×D3×Dic6C2212yescomplemented
26#64139C2211yescharacteristic
27C2×#3744C2212yescomplemented
28C3×#930C2211yescharacteristic
29C2×C3×#204C2212yescomplemented
30C2×C3×D3×C8C2212yes—
31#63978—21no—
32D3×(C2×D3)⋊C4—21no—
33#63909C2211yescharacteristic
34#63908C2211yescharacteristic
35#63906—21no—
36D3×C4⋊Dic3C2211yescharacteristic
37C2×#3717C2212yescomplemented
38C2×#3716C2212yescomplemented
39D3×#204—28no—
40C32×C22⋊C8C2211yescharacteristic, complemented
41#63643C2212yescomplemented
42C3×#830C2211yescharacteristic, complemented
43C3×(C2×D3)⋊C8C2212yescomplemented
44C3×#816C2212yescomplemented
45#63567C2212yescomplemented
46#63566C2212yescomplemented
47C22×D3×Q8—31no—
48C23×Dic6—31no—
49C2×#930—31no—
50C2×D3×SD16—32no—
51C22×#204—32no—
52D3×#121—31no—
53C3×#448—31no—
54C2×C3×C22⋊C8—31no—
55#5227—31no—
56#5170—32no—
57C2×#816—32no—
58#5040—31no—
59#4806—32no—
60D3×#103—32no—
61#4738—31no—
62#4738—31no—
63#4738—32no—
64#4738—31no—
65#4738—31no—
66#4738—32no—
67#4738—61no—
68#4738D311yescharacteristic, direct product factor
69D3×C22⋊C8D311yescharacteristic, complemented
70C23×C3×D3D411yescharacteristic
71C22×D32—21no—
72C22×C32×C4C2311yescharacteristic
73C2×#638—21no—
74C22×C3⋊Dic3—21no—
75C2×C4⋊(C3⋊D3)C2311yescharacteristic
76C2×#634—21no—
77C2×#634—24no—
78C2×#634C2312yes—
79C2×C3×#67—21no—
80C22×C3×Dic3—21no—
81C22×C3×Dic3D411yescharacteristic
82C2×C3×D12C2311yescharacteristic
83C2×C3×C4×D3—24no—
84C2×C3×C4×D3D411yescharacteristic
85C2×C3×C4×D3D411yescharacteristic
86C2×C3×C4×D3C2311yescharacteristic
87C2×C3×C4×D3C2311yescharacteristic
88C2×C3×Dic6—21no—
89C2×C3×Dic6—24no—
90C2×C3×Dic6C2312yes—
91D3×#67—44no—
92C2×#627—28no—
93C2×#627—22no—
94C2×#627—22no—
95C2×#626—21no—
96C2×#626—21no—
97C2×#625—21no—
98C2×D3×Dic3—28no—
99C2×D3×Dic3—22no—
100C2×D3×Dic3—22no—
101C2×D3×Dic3—21no—
102D3×D12—24no—
103D3×Dic6—28no—
104D3×Dic6—28no—
105D3×Dic6—24no—
106D3×Dic6—24no—
107D3×Dic6—24no—
108D3×Dic6D418yescomplemented
109C2×C32×C8C2312yes—
110#3752—21no—
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112#3744—24no—
113C3×(C2×D3)⋊C4—21no—
114C3×C4⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊C8C2312yes—
116C3×#204—24no—
117C3×D3×C8—24no—
118Dic3⋊Dic3—21no—
119#3722—21no—
120(C2×D3)⋊Dic3—21no—
121#3717—24no—
122#3716—24no—
123C2×#448—91noSylow
124C22×C3×Q8—31no—
125C23×C3×C4—31no—
126C22×#67—61no—
127C23×Dic3—61no—
128C2×D3×Q8—32no—
129C2×D3×Q8—32no—
130C2×D3×Q8—68no—
131C2×D3×Q8—61no—
132C2×D3×Q8—61no—
133C2×D3×D4—31no—
134C2×D3×D4—61no—
135C22×D12—31no—
136C22×C4×D3—61no—
137C22×C4×D3C2×D311yescharacteristic
138C22×Dic6—32no—
139C22×Dic6—31no—
140C22×Dic6—31no—
141C22×Dic6—32no—
142C22×Dic6—61no—
143C22×Dic6—68no—
144C22×Dic6—61no—
145C22×Dic6—61no—
146C22×Dic6—61no—
147C22×Dic6—61no—
148C22×Dic6C2×D311yescharacteristic, complemented
149C2×C3×SD16—32no—
150C22×C3×C8—32no—
151C3×#121—31no—
152C2×#215—32no—
153#939—61no—
154#938—31no—
155C2×#214—32no—
156#930—31no—
157#930—31no—
158#930—31no—
159#930—31no—
160#930—61no—
161#930—61no—
162#930—61no—
163#930C2×D311yescharacteristic
164C2×(C2×D3)⋊C4—61no—
165C2×C4⋊Dic3—31no—
166D3×SD16—68no—
167C2×#204—32no—
168C2×#204—32no—
169C2×#204—32no—
170C2×#204—32no—
171C2×#204—62no—
172C2×#204—68no—
173C2×#204C2×D312yescomplemented
174C2×D3×C8C2×D312yes—
175#895—31no—
176D3×C4⋊C4—31no—
177#884—61no—
178D3×C22⋊C4—61no—
179C3×#103—32no—
180C3×C22⋊C8—21no—
181C3×C22⋊C8—31no—
182C3×C22⋊C8—32no—
183C3×C22⋊C8C2×D311yescharacteristic, complemented
184C3×C22⋊C8C2×D311yescharacteristic, complemented
185#835—32no—
186#830C2×D311yescharacteristic, complemented
187(C2×D3)⋊C8C2×D312yescomplemented
188#816—32no—
189#816—32no—
190#816—32no—
191#816—32no—
192#816—62no—
193#816C2×D312yescomplemented
194#810—32no—
195C23×C32C2×D411yescharacteristic
196C22×C3⋊D3—21no—
197C22×C3×D3—22no—
198C22×C3×D3—22no—
199C22×C3×D3—21no—
200C22×C3×D3SD1614yescomplemented
201C22×C3×D3C2×D411yescharacteristic
202C22×C3×D3C2×D411yescharacteristic
203C2×D32—42no—
204C2×D32—42no—
205C2×D32—42no—
206C2×C32×C4—22no—
207C2×C32×C4C2×D411yescharacteristic
208C2×C32×C4C2411yescharacteristic
209#638—42no—
210C2×C3⋊Dic3—24no—
211C2×C3⋊Dic3—22no—
212C2×C3⋊Dic3—21no—
213C4⋊(C3⋊D3)—22no—
214#634—24no—
215#634—22no—
216#634C2×D414yescomplemented
217C3×#67—42no—
218C2×C3×Dic3—24no—
219C2×C3×Dic3—22no—
220C2×C3×Dic3—22no—
221C2×C3×Dic3—21no—
222C2×C3×Dic3C2×D411yescharacteristic
223C2×C3×Dic3C2×D411yescharacteristic
224C3×D12—22no—
225C3×C4×D3—22no—
226C3×C4×D3—22no—
227C3×C4×D3—22no—
228C3×C4×D3C2×D414yes—
229C3×Dic6—24no—
230C3×Dic6—22no—
231C3×Dic6C2×D414yescomplemented
232#627—28no—
233#627—28no—
234#626—42no—
235#626—42no—
236#625—42no—
237D3×Dic3—28no—
238D3×Dic3—28no—
239D3×Dic3—42no—
240C32×C8—22no—
241C3×C3⋊C8—22no—
242C23×Q8—91no—
243C22×SD16—92no—
244C2×#121—91no—
245#448—31no—
246#448—92no—
247#448—91no—
248#448—92no—
249#448—91no—
250#448—91no—
251C2×#103—92no—
252C2×C22⋊C8—31no—
253C24×C3—31no—
254C23×D3—61no—
255C23×D3—61no—
256C23×D3D1211yescharacteristic
257C2×C3×Q8—32no—
258C2×C3×Q8—64no—
259C2×C3×Q8—61no—
260C2×C3×D4—31no—
261C2×C3×D4—61no—
262C22×C3×C4—21no—
263C22×C3×C4—31no—
264C22×C3×C4—31no—
265C22×C3×C4—31no—
266C22×C3×C4—31no—
267C22×C3×C4—31no—
268C22×C3×C4—64no—
269C22×C3×C4—61no—
270C22×C3×C4C22×D311yescharacteristic
271C22×C3×C4C22×D311yescharacteristic
272C2×#67—21no—
273C2×#67—61no—
274C2×#67—61no—
275C2×#67—61no—
276C2×#67—61no—
277C2×#67—61no—
278C2×#67—61no—
279C2×#67—121no—
280C2×#67—124no—
281C22×Dic3—21no—
282C22×Dic3—62no—
283C22×Dic3—62no—
284C22×Dic3—68no—
285C22×Dic3—61no—
286C22×Dic3—61no—
287C22×Dic3—61no—
288C22×Dic3—121no—
289C22×Dic3D1211yescharacteristic
290D3×Q8—38no—
291D3×Q8—64no—
292D3×Q8—64no—
293D3×Q8—68no—
294D3×Q8—68no—
295D3×Q8—64no—
296D3×D4—64no—
297D3×D4—124no—
298C2×D12—31no—
299C2×D12—31no—
300C2×D12—61no—
301C2×D12—64no—
302C2×D12—61no—
303C2×D12—61no—
304C2×D12C22×D311yescharacteristic
305C2×C4×D3—24no—
306C2×C4×D3—68no—
307C2×C4×D3—62no—
308C2×C4×D3—62no—
309C2×C4×D3—61no—
310C2×C4×D3D1211yescharacteristic
311C2×C4×D3D1211yescharacteristic
312C2×C4×D3C22×D311yescharacteristic
313C2×C4×D3C22×D311yescharacteristic
314C2×Dic6—21no—
315C2×Dic6—24no—
316C2×Dic6—32no—
317C2×Dic6—32no—
318C2×Dic6—38no—
319C2×Dic6—62no—
320C2×Dic6—64no—
321C2×Dic6—64no—
322C2×Dic6—68no—
323C2×Dic6—68no—
324C2×Dic6—64no—
325C2×Dic6—64no—
326C2×Dic6—62no—
327C2×Dic6—62no—
328C2×Dic6—68no—
329C2×Dic6—68no—
330C2×Dic6—61no—
331C2×Dic6—61no—
332C2×Dic6—62no—
333C2×Dic6—62no—
334C2×Dic6—64no—
335C2×Dic6—124no—
336C2×Dic6—121no—
337C2×Dic6C22×D312yes—
338C3×SD16—64no—
339C2×C3×C8—22no—
340C2×C3×C8—32no—
341C2×C3×C8—64no—
342C2×C3×C8C22×D312yes—
343C2×C3×C8C22×D312yes—
344C3×C4⋊C4—31no—
345C3×C22⋊C4—61no—
346#217—61no—
347#215—64no—
348#214—64no—
349(C2×D3)⋊C4—21no—
350(C2×D3)⋊C4—61no—
351(C2×D3)⋊C4—61no—
352(C2×D3)⋊C4—61no—
353(C2×D3)⋊C4—61no—
354(C2×D3)⋊C4—61no—
355(C2×D3)⋊C4—121no—
356C4⋊Dic3—31no—
357C4⋊Dic3—31no—
358C4⋊Dic3—61no—
359C4⋊Dic3—61no—
360C4⋊Dic3C22×D311yescharacteristic
361Dic3⋊C4—61no—
362C2×C3⋊C8C22×D312yes—
363#204—24no—
364#204—64no—
365#204—64no—
366#204—64no—
367#204—64no—
368#204—124no—
369D3×C8—24no—
370C22×C32—21no—
371C22×C32—21no—
372C22×C32C2×SD1612yescomplemented
373C22×C32C22×D411yescharacteristic
374C2×C3⋊D3—41no—
375C2×C3⋊D3—41no—
376C2×C3⋊D3—41no—
377C2×C3×D3—21no—
378C2×C3×D3—21no—
379C2×C3×D3—28no—
380C2×C3×D3—41no—
381C2×C3×D3—41no—
382C2×C3×D3—41no—
383C2×C3×D3#12012yes—
384C2×C3×D3C2×SD1612yes—
385C2×C3×D3C2×SD1612yescomplemented
386C2×C3×D3#13712yes—
387D32—84no—
388C32×C4—21no—
389C32×C4C22×D412yes—
390C3⋊Dic3—24no—
391C3⋊Dic3—41no—
392C3×Dic3—24no—
393C3×Dic3—21no—
394C3×Dic3—41no—
395C3×Dic3#12012yes—
396C22×Q8—31no—
397C22×Q8—92no—
398C22×Q8—92no—
399C22×Q8—91no—
400C22×Q8—181no—
401C22×Q8—181no—
402C22×Q8—181no—
403C22×Q8—188no—
404C22×D4—91no—
405C22×D4—181no—
406C23×C4—31no—
407C23×C4—181no—
408C2×SD16—32no—
409C2×SD16—92no—
410C2×SD16—92no—
411C2×SD16—92no—
412C2×SD16—188no—
413C22×C8—32no—
414#121—31no—
415#121—91no—
416#121—91no—
417#121—91no—
418#121—181no—
419#121—181no—
420C2×C4⋊C4—91no—
421C2×C22⋊C4—181no—
422#103—32no—
423#103—92no—
424#103—92no—
425#103—92no—
426C22⋊C8—31no—
427C22⋊C8—32no—
428C22⋊C8D3211yescharacteristic, complemented
429C23×C3—21no—
430C23×C3—31no—
431C23×C3—34no—
432C23×C3—31no—
433C23×C3—62no—
434C23×C3—62no—
435C23×C3—61no—
436C23×C3C2×D1211yescharacteristic
437C23×C3D3×D411yescharacteristic
438C22×D3—22no—
439C22×D3—22no—
440C22×D3—21no—
441C22×D3—61no—
442C22×D3—61no—
443C22×D3—121no—
444C22×D3—122no—
445C22×D3—122no—
446C22×D3—122no—
447C22×D3—122no—
448C22×D3—122no—
449C22×D3—122no—
450C22×D3#20414yescomplemented
451C22×D3C2×D1211yescharacteristic
452C22×D3C2×D1211yescharacteristic
453C3×Q8—34no—
454C3×Q8—64no—
455C3×Q8—62no—
456C3×D4—62no—
457C3×D4—122no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—31no—
463C2×C3×C4—34no—
464C2×C3×C4—31no—
465C2×C3×C4—42no—
466C2×C3×C4—62no—
467C2×C3×C4—62no—
468C2×C3×C4—62no—
469C2×C3×C4—64no—
470C2×C3×C4—62no—
471C2×C3×C4—62no—
472C2×C3×C4—61no—
473C2×C3×C4C2×D1211yescharacteristic
474C2×C3×C4D3×D411yescharacteristic
475C2×C3×C4C23×D311yescharacteristic
476C2×C3×C4C23×D311yescharacteristic
477#67—42no—
478#67—122no—
479#67—122no—
480#67—122no—
481#67—122no—
482#67—122no—
483#67—122no—
484#67—242no—
485C2×Dic3—24no—
486C2×Dic3—22no—
487C2×Dic3—22no—
488C2×Dic3—21no—
489C2×Dic3—68no—
490C2×Dic3—68no—
491C2×Dic3—64no—
492C2×Dic3—64no—
493C2×Dic3—62no—
494C2×Dic3—62no—
495C2×Dic3—61no—
496C2×Dic3—61no—
497C2×Dic3—122no—
498C2×Dic3—124no—
499C2×Dic3—121no—
500C2×Dic3—122no—
501C2×Dic3C2×D1211yescharacteristic
502C2×Dic3C2×D1211yescharacteristic
503D12—22no—
504D12—62no—
505D12—62no—
506D12—122no—
507D12—122no—
508D12—122no—
509C4×D3—22no—
510C4×D3—22no—
511C4×D3—22no—
512C4×D3—68no—
513C4×D3—68no—
514C4×D3—122no—
515C4×D3D3×D414yes—
516Dic6—24no—
517Dic6—22no—
518Dic6—34no—
519Dic6—34no—
520Dic6—64no—
521Dic6—68no—
522Dic6—68no—
523Dic6—68no—
524Dic6—64no—
525Dic6—64no—
526Dic6—62no—
527Dic6—62no—
528Dic6—68no—
529Dic6—122no—
530Dic6—124no—
531Dic6D3×D414yescomplemented
532C3×C8—22no—
533C3×C8—22no—
534C3×C8—42no—
535C3×C8—62no—
536C3⋊C8—22no—
537C2×C32—22no—
538C2×C32C2×#12011yescharacteristic
539C2×C32C22×SD1611yescharacteristic
540C2×C32C2×#13711yescharacteristic
541C3⋊D3—81no—
542C3×D3—22no—
543C3×D3—81no—
544C3×D3#44814yescomplemented
545C24—31no—
546C24—181no—
547C2×Q8—32no—
548C2×Q8—64no—
549C2×Q8—61no—
550C2×Q8—98no—
551C2×Q8—92no—
552C2×Q8—184no—
553C2×Q8—182no—
554C2×Q8—182no—
555C2×Q8—184no—
556C2×Q8—188no—
557C2×Q8—184no—
558C2×Q8—184no—
559C2×Q8—188no—
560C2×Q8—188no—
561C2×Q8—181no—
562C2×D4—31no—
563C2×D4—61no—
564C2×D4—91no—
565C2×D4—184no—
566C2×D4—181no—
567C2×D4—181no—
568C2×D4—181no—
569C2×D4—181no—
570C2×D4—364no—
571C22×C4—31no—
572C22×C4—31no—
573C22×C4—31no—
574C22×C4—31no—
575C22×C4—31no—
576C22×C4—64no—
577C22×C4—61no—
578C22×C4—182no—
579C22×C4—182no—
580C22×C4—188no—
581C22×C4—181no—
582C22×C4—181no—
583C22×C4C2×D3211yescharacteristic
584SD16—64no—
585SD16—184no—
586SD16—184no—
587SD16—184no—
588C2×C8—32no—
589C2×C8—64no—
590C2×C8C2×D3212yes—
591C4⋊C4—31no—
592C4⋊C4—91no—
593C4⋊C4—181no—
594C22⋊C4—61no—
595C22⋊C4—181no—
596C22⋊C4—181no—
597C22⋊C4—181no—
598C22×C3—21no—
599C22×C3—21no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—22no—
604C22×C3—32no—
605C22×C3—32no—
606C22×C3—32no—
607C22×C3—32no—
608C22×C3—41no—
609C22×C3—41no—
610C22×C3—68no—
611C22×C3—61no—
612C22×C3—61no—
613C22×C3—121no—
614C22×C3—121no—
615C22×C3—121no—
616C22×C3C2×#20412yescomplemented
617C22×C3D3×SD1612yescomplemented
618C22×C3C22×D1211yescharacteristic
619C22×C3C2×D3×D411yescharacteristic
620C2×D3—21no—
621C2×D3—21no—
622C2×D3—28no—
623C2×D3—41no—
624C2×D3—41no—
625C2×D3—41no—
626C2×D3—121no—
627C2×D3—121no—
628C2×D3—121no—
629C2×D3—121no—
630C2×D3—121no—
631C2×D3—121no—
632C2×D3—241no—
633C2×D3—241no—
634C2×D3—241no—
635C2×D3—244no—
636C2×D3—244no—
637C2×D3#88212yes—
638C2×D3C2×#20412yes—
639C2×D3C2×#20412yescomplemented
640C2×D3#90912yes—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—22no—
644C3×C4—32no—
645C3×C4—41no—
646C3×C4—64no—
647C3×C4—61no—
648C3×C4—121no—
649C3×C4C2×D3×D412yes—
650C3×C4C2×D3×D412yes—
651Dic3—21no—
652Dic3—24no—
653Dic3—41no—
654Dic3—64no—
655Dic3—64no—
656Dic3—124no—
657Dic3—121no—
658Dic3—121no—
659Dic3—241no—
660Dic3#88212yes—
661C32C2×#44811yescharacteristic, complemented, Sylow
662C23—31no—
663C23—31no—
664C23—34no—
665C23—62no—
666C23—62no—
667C23—61no—
668C23—181no—
669C23—362no—
670C23—362no—
671C23—362no—
672C23D3×D1211yescharacteristic
673Q8—34no—
674Q8—64no—
675Q8—62no—
676Q8—94no—
677Q8—184no—
678Q8—188no—
679Q8—188no—
680Q8—182no—
681D4—62no—
682D4—122no—
683D4—182no—
684D4—362no—
685D4—362no—
686D4—362no—
687D4—362no—
688C2×C4—22no—
689C2×C4—31no—
690C2×C4—34no—
691C2×C4—31no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—62no—
695C2×C4—64no—
696C2×C4—62no—
697C2×C4—62no—
698C2×C4—61no—
699C2×C4—188no—
700C2×C4—188no—
701C2×C4—184no—
702C2×C4—182no—
703C2×C4—181no—
704C2×C4—362no—
705C2×C4D3×D1211yescharacteristic
706C2×C4C22×D3211yescharacteristic
707C8—22no—
708C8—62no—
709C2×C3—22no—
710C2×C3—22no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—34no—
715C2×C3—42no—
716C2×C3—62no—
717C2×C3—241no—
718C2×C3C2×#88211yescharacteristic
719C2×C3D3×#12011yescharacteristic
720C2×C3C22×#20411yescharacteristic
721C2×C3C2×#90911yescharacteristic
722C2×C3C2×D3×SD1611yescharacteristic
723C2×C3D3×#13711yescharacteristic
724D3—22no—
725D3—81no—
726D3—241no—
727D3—241no—
728D3—481no—
729D3#473814yesdirect product factor
730C22—21no—
731C22—21no—
732C22—32no—
733C22—32no—
734C22—32no—
735C22—32no—
736C22—68no—
737C22—61no—
738C22—61no—
739C22—121no—
740C22—121no—
741C22—121no—
742C22—361no—
743C22—361no—
744C22—361no—
745C22—724no—
746C22D3×#20412yescomplemented
747C22C2×D3×D1211yescharacteristic
748C4—21no—
749C4—32no—
750C4—61no—
751C4—64no—
752C4—121no—
753C4—184no—
754C4—361no—
755C4D32×D412yes—
756C3—21no—
757C3C2×#473811yescharacteristic, complemented
758C3D3×#44811yescharacteristic, complemented
759C2—22no—
760C2—34no—
761C2—62no—
762C2—241no—
763C2—721no—
764C2D3×#88211yescharacteristic
765C2C2×D3×#20411yescharacteristic
766C2D3×#90911yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radicalD3×#930C2
hypercenterC22⋊C8D32
hypocenterC32C2×#448
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
1. C22×D3×Dic6C2semidirect
3. C2×D3×#204C2semidirect
4. #10592437C2semidirect
5. C3×#4738C2semidirect
6. C3×D3×C22⋊C8C2semidirect
7. #10591181C2semidirect
8. #10591174C2semidirect
9. #10590951C2semidirect
10. #10590822C2semidirect
11. D3×#816C2semidirect
14. C22×#634C22semidirect
16. C22×C3×Dic6C22semidirect
25. C2×D3×Dic6C22semidirect
27. C2×#3744C22semidirect
29. C2×C3×#204C22semidirect
37. C2×#3717C22semidirect
38. C2×#3716C22semidirect
40. C32×C22⋊C8C22semidirect
41. #63643C22semidirect
42. C3×#830C22semidirect
43. C3×(C2×D3)⋊C8C22semidirect
44. C3×#816C22semidirect
45. #63567C22semidirect
46. #63566C22semidirect
68. #4738D3direct (N × H)
69. D3×C22⋊C8D3semidirect
108. D3×Dic6D4semidirect
148. C22×Dic6C2×D3semidirect
173. C2×#204C2×D3semidirect
183. C3×C22⋊C8C2×D3semidirect
184. C3×C22⋊C8C2×D3semidirect
186. #830C2×D3semidirect
187. (C2×D3)⋊C8C2×D3semidirect
193. #816C2×D3semidirect
200. C22×C3×D3SD16semidirect
216. #634C2×D4semidirect
231. C3×Dic6C2×D4semidirect
372. C22×C32C2×SD16semidirect
385. C2×C3×D3C2×SD16semidirect
428. C22⋊C8D32semidirect
450. C22×D3#204semidirect
531. Dic6D3×D4semidirect
544. C3×D3#448semidirect
616. C22×C3C2×#204semidirect
617. C22×C3D3×SD16semidirect
639. C2×D3C2×#204semidirect
661. C32C2×#448semidirect
729. D3#4738direct (N × H)
746. C22D3×#204semidirect
757. C3C2×#4738semidirect
758. C3D3×#448semidirect

Maximal subgroups

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

subgroupindex
C22×D3×Dic62
D3×#9302
C2×D3×#2042
#105924372
C3×#47382
C3×D3×C22⋊C82
#105911812
#105911742
#105909512
#105908222
D3×#8162
D3×#4483
C2×#47383