Finite Group Databasebeta

← D3×#5040 #11863613

Subgroups — D3×#5040 #11863613

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
2C3×D3×#121C211yesmaximal, characteristic
3C2×D3×#214C212yesmaximal, complemented
4#10592739C211yesmaximal, characteristic, complemented
5C3×#5040C211yesmaximal, characteristic, complemented
6#10591517C212yesmaximal, complemented
7#10591181C211yesmaximal, characteristic, complemented
8#10591171C211yesmaximal, characteristic, complemented
9D3×#830C211yesmaximal, characteristic, complemented
10#10590603C212yesmaximal, complemented
11D3×#810C212yesmaximal, complemented
12C2×#5040—31nomaximal
13D3×#448—31nomaximal
14C22×#634C2211yescharacteristic, complemented
15C2×C3×D3×D4—21no—
16C2×C3×D3×D4C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C22×C3×Dic6C2211yescharacteristic, complemented
19C22×#627—21no—
20C22×D3×Dic3—21no—
21C2×D3×Dic6—21no—
22C2×D3×Dic6—21no—
23C2×D3×Dic6—28no—
24C2×D3×Dic6C2212yes—
25C2×D3×Dic6C2212yescomplemented
26C32×#121C2211yescharacteristic
27C2×#3754C2212yescomplemented
28C3×#939—21no—
29C3×#938C2211yescharacteristic
30C2×C3×#214C2212yescomplemented
31C3×#930C2211yescharacteristic
32C3×#895C2211yescharacteristic
33C3×D3×C4⋊C4C2211yescharacteristic
34C3×#884—21no—
35C3×D3×C22⋊C4—21no—
36D3×#214—28no—
37C2×#3716C2212yescomplemented
38C2×#3715C2212yescomplemented
39C2×D3×C3⋊C8C2212yes—
40#63657C2211yescharacteristic, complemented
41#63637C2212yescomplemented
42C3×#830C2211yescharacteristic, complemented
43C3×#810C2212yescomplemented
44#63567C2212yescomplemented
45#63565C2212yescomplemented
46(C2×D3)⋊(C3⋊C8)C2212yescomplemented
47C22×D3×Q8—31no—
48C23×Dic6—31no—
49C2×C3×#121—31no—
50C22×#214—32no—
51C2×D3×SD16—32no—
52D3×#121D311yescharacteristic
53C3×#448—31no—
54#5227—31no—
55C2×#830—31no—
56#5170—32no—
57#5040—31no—
58#5040—31no—
59#5040—31no—
60#5040—32no—
61#5040—31no—
62#5040—32no—
63#5040—61no—
64#5040D311yescharacteristic, direct product factor
65C2×#810—32no—
66#4806—32no—
67D3×#103—32no—
68#4738—31no—
69D3×C22⋊C8—31no—
70C23×C3×D3—21no—
71C23×C3×D3D411yescharacteristic
72C2×C32×D4—21no—
73C2×C32×D4C2311yescharacteristic
74C22×C32×C4C2311yescharacteristic
75C22×C3⋊Dic3—21no—
76C2×#634—21no—
77C2×#634—24no—
78C2×#634C2312yes—
79C2×C3×#67—21no—
80C2×C3×#67—21no—
81C2×C3×#67—21no—
82C22×C3×Dic3—21no—
83C22×C3×Dic3D411yescharacteristic
84C3×D3×D4—24no—
85C3×D3×D4—44no—
86C2×C3×D12—21no—
87C2×C3×D12C2311yescharacteristic
88C2×C3×C4×D3—24no—
89C2×C3×C4×D3—21no—
90C2×C3×C4×D3D411yescharacteristic
91C2×C3×C4×D3D411yescharacteristic
92C2×C3×C4×D3C2311yescharacteristic
93C2×C3×C4×D3C2311yescharacteristic
94C2×C3×Dic6—21no—
95C2×C3×Dic6—24no—
96C2×C3×Dic6C2312yes—
97C2×#627—28no—
98C2×#627—22no—
99C2×#627—22no—
100C2×D3×Dic3—28no—
101C2×D3×Dic3—22no—
102C2×D3×Dic3—22no—
103D3×Dic6—28no—
104D3×Dic6—28no—
105D3×Dic6—24no—
106D3×Dic6—24no—
107D3×Dic6—24no—
108D3×Dic6D418yescomplemented
109C32×C4⋊C4C2311yescharacteristic
110C32×C22⋊C4—21no—
111#3754—24no—
112C2×C3⋊(C3⋊C8)C2312yes—
113C3×#217—21no—
114C3×#214—24no—
115C3×(C2×D3)⋊C4—21no—
116C3×(C2×D3)⋊C4—21no—
117C3×C4⋊Dic3C2311yescharacteristic
118C3×Dic3⋊C4—21no—
119C2×C3×C3⋊C8C2312yes—
120#3716—24no—
121#3715—24no—
122D3×C3⋊C8—24no—
123C2×#448—91noSylow
124C22×C3×Q8—31no—
125C22×C3×D4—31no—
126C22×C3×D4—61no—
127C23×C3×C4—31no—
128C23×Dic3—61no—
129C2×D3×Q8—32no—
130C2×D3×Q8—32no—
131C2×D3×Q8—68no—
132C2×D3×Q8—61no—
133C2×D3×Q8—61no—
134C2×D3×D4—21no—
135C2×D3×D4C2×D311yescharacteristic
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—
150C3×#121—21no—
151C3×#121—31no—
152C3×#121—31no—
153C3×#121—31no—
154C3×#121—61no—
155C3×#121—61no—
156C3×#121C2×D311yescharacteristic
157C3×#121C2×D311yescharacteristic
158C2×C3×C4⋊C4—31no—
159C2×C3×C22⋊C4—61no—
160C2×#215—32no—
161#939—21no—
162#938C2×D311yescharacteristic
163C2×#214—32no—
164C2×#214—32no—
165C2×#214—32no—
166C2×#214—32no—
167C2×#214—62no—
168C2×#214—68no—
169C2×#214C2×D312yescomplemented
170#930C2×D311yescharacteristic
171C22×C3⋊C8—32no—
172D3×SD16—68no—
173C2×#204—32no—
174C2×D3×C8—32no—
175#895C2×D311yescharacteristic
176D3×C4⋊C4C2×D311yescharacteristic
177#884—21no—
178D3×C22⋊C4—21no—
179C3×#103—32no—
180C3×C22⋊C8—31no—
181#835—32no—
182#830—31no—
183#830—31no—
184#830—32no—
185#830—61no—
186#830C2×D311yescharacteristic, complemented
187(C2×D3)⋊C8—32no—
188#816—32no—
189#810—32no—
190#810—32no—
191#810—32no—
192#810—32no—
193#810—62no—
194#810C2×D312yescomplemented
195C23×C32—21no—
196C23×C32C2×D411yescharacteristic
197C22×C3×D3—22no—
198C22×C3×D3—22no—
199C22×C3×D3—21no—
200C22×C3×D3—42no—
201C22×C3×D3—42no—
202C22×C3×D3—42no—
203C22×C3×D3SD1614yescomplemented
204C22×C3×D3C2×D411yescharacteristic
205C22×C3×D3C2×D411yescharacteristic
206C32×D4—22no—
207C32×D4—42no—
208C2×C32×C4—22no—
209C2×C32×C4—21no—
210C2×C32×C4C2×D411yescharacteristic
211C2×C32×C4C2411yescharacteristic
212C2×C3⋊Dic3—24no—
213C2×C3⋊Dic3—22no—
214#634—24no—
215#634—22no—
216#634C2×D414yescomplemented
217C3×#67—42no—
218C3×#67—42no—
219C3×#67—42no—
220C2×C3×Dic3—24no—
221C2×C3×Dic3—22no—
222C2×C3×Dic3—22no—
223C2×C3×Dic3—21no—
224C2×C3×Dic3C2×D411yescharacteristic
225C2×C3×Dic3C2×D411yescharacteristic
226C3×D12—22no—
227C3×D12—42no—
228C3×C4×D3—22no—
229C3×C4×D3—22no—
230C3×C4×D3—22no—
231C3×C4×D3—42no—
232C3×C4×D3C2×D414yes—
233C3×Dic6—24no—
234C3×Dic6—22no—
235C3×Dic6C2×D414yescomplemented
236#627—28no—
237#627—28no—
238D3×Dic3—28no—
239D3×Dic3—28no—
240C3⋊(C3⋊C8)—22no—
241C3×C3⋊C8—22no—
242C23×Q8—91no—
243C22×SD16—92no—
244C2×#121—31no—
245#448—31no—
246#448—91no—
247#448—92no—
248#448—92no—
249#448—91no—
250#448—91no—
251C2×#103—92no—
252C2×C22⋊C8—91no—
253C24×C3—31no—
254C24×C3—61no—
255C23×D3—21no—
256C23×D3#6711yescharacteristic
257C2×C3×Q8—32no—
258C2×C3×Q8—64no—
259C2×C3×Q8—61no—
260C2×C3×D4—21no—
261C2×C3×D4—21no—
262C2×C3×D4—21no—
263C2×C3×D4—31no—
264C2×C3×D4—41no—
265C2×C3×D4—61no—
266C2×C3×D4—64no—
267C2×C3×D4—61no—
268C2×C3×D4—61no—
269C2×C3×D4—61no—
270C2×C3×D4—124no—
271C2×C3×D4C22×D311yescharacteristic
272C2×C3×D4C22×D311yescharacteristic
273C22×C3×C4—21no—
274C22×C3×C4—31no—
275C22×C3×C4—31no—
276C22×C3×C4—31no—
277C22×C3×C4—31no—
278C22×C3×C4—31no—
279C22×C3×C4—64no—
280C22×C3×C4—61no—
281C22×C3×C4—61no—
282C22×C3×C4C22×D311yescharacteristic
283C22×C3×C4C22×D311yescharacteristic
284C2×#67—21no—
285C2×#67—21no—
286C2×#67—21no—
287C22×Dic3—21no—
288C22×Dic3—62no—
289C22×Dic3—62no—
290C22×Dic3—68no—
291C22×Dic3—61no—
292C22×Dic3—61no—
293C22×Dic3—121no—
294C22×Dic3#6711yescharacteristic
295D3×Q8—38no—
296D3×Q8—64no—
297D3×Q8—64no—
298D3×Q8—68no—
299D3×Q8—68no—
300D3×Q8—64no—
301D3×D4—24no—
302D3×D4—44no—
303C2×D12—21no—
304C2×D12C22×D311yescharacteristic
305C2×C4×D3—24no—
306C2×C4×D3—21no—
307C2×C4×D3—68no—
308C2×C4×D3—62no—
309C2×C4×D3—62no—
310C2×C4×D3#6711yescharacteristic
311C2×C4×D3#6711yescharacteristic
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—32no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C22⋊C4—21no—
346C3×C22⋊C4—21no—
347C3×C22⋊C4—41no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351#217—21no—
352#215—64no—
353#214—24no—
354#214—64no—
355#214—64no—
356#214—64no—
357#214—64no—
358#214—124no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—21no—
361C4⋊Dic3C22×D311yescharacteristic
362Dic3⋊C4—21no—
363C2×C3⋊C8—32no—
364C2×C3⋊C8—32no—
365C2×C3⋊C8—62no—
366C2×C3⋊C8—64no—
367C2×C3⋊C8C22×D312yes—
368#204—64no—
369D3×C8—64no—
370C22×C32—21no—
371C22×C32—21no—
372C22×C32—41no—
373C22×C32—41no—
374C22×C32—41no—
375C22×C32C2×SD1612yescomplemented
376C22×C32C22×D411yescharacteristic
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—84no—
384C2×C3×D3#12012yes—
385C2×C3×D3C2×SD1612yes—
386C2×C3×D3C2×SD1612yescomplemented
387C2×C3×D3#13712yes—
388C32×C4—21no—
389C32×C4—41no—
390C32×C4C22×D412yes—
391C3⋊Dic3—24no—
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—31no—
405C22×D4—61no—
406C23×C4—31no—
407C23×C4—181no—
408C2×SD16—32no—
409C2×SD16—92no—
410C2×SD16—92no—
411C2×SD16—92no—
412C2×SD16—188no—
413C22×C8—92no—
414#121—31no—
415#121—31no—
416#121—31no—
417#121—61no—
418#121—61no—
419#121D3211yescharacteristic
420C2×C4⋊C4—31no—
421C2×C22⋊C4—61no—
422#103—32no—
423#103—92no—
424#103—92no—
425#103—92no—
426C22⋊C8—31no—
427C22⋊C8—92no—
428C22⋊C8—91no—
429C23×C3—21no—
430C23×C3—21no—
431C23×C3—21no—
432C23×C3—31no—
433C23×C3—34no—
434C23×C3—31no—
435C23×C3—41no—
436C23×C3—62no—
437C23×C3—62no—
438C23×C3—61no—
439C23×C3—122no—
440C23×C3—122no—
441C23×C3—122no—
442C23×C3D3×D411yescharacteristic
443C23×C3C2×#6711yescharacteristic
444C22×D3—22no—
445C22×D3—22no—
446C22×D3—21no—
447C22×D3—42no—
448C22×D3—42no—
449C22×D3—42no—
450C22×D3#21414yescomplemented
451C22×D3C2×#6711yescharacteristic
452C22×D3C2×#6711yescharacteristic
453C3×Q8—34no—
454C3×Q8—64no—
455C3×Q8—62no—
456C3×D4—22no—
457C3×D4—22no—
458C3×D4—42no—
459C3×D4—42no—
460C3×D4—42no—
461C3×D4—62no—
462C3×D4—82no—
463C3×D4—122no—
464C3×D4—122no—
465C3×D4—122no—
466C3×D4—122no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—31no—
474C2×C3×C4—34no—
475C2×C3×C4—31no—
476C2×C3×C4—42no—
477C2×C3×C4—41no—
478C2×C3×C4—62no—
479C2×C3×C4—62no—
480C2×C3×C4—62no—
481C2×C3×C4—64no—
482C2×C3×C4—62no—
483C2×C3×C4—62no—
484C2×C3×C4—61no—
485C2×C3×C4—122no—
486C2×C3×C4D3×D411yescharacteristic
487C2×C3×C4C2×#6711yescharacteristic
488C2×C3×C4C23×D311yescharacteristic
489C2×C3×C4C23×D311yescharacteristic
490#67—42no—
491#67—42no—
492#67—42no—
493C2×Dic3—24no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—21no—
497C2×Dic3—68no—
498C2×Dic3—68no—
499C2×Dic3—64no—
500C2×Dic3—64no—
501C2×Dic3—62no—
502C2×Dic3—62no—
503C2×Dic3—122no—
504C2×Dic3—124no—
505C2×Dic3C2×#6711yescharacteristic
506C2×Dic3C2×#6711yescharacteristic
507D12—22no—
508D12—42no—
509C4×D3—22no—
510C4×D3—22no—
511C4×D3—22no—
512C4×D3—42no—
513C4×D3—68no—
514C4×D3—68no—
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—62no—
533C3⋊C8—22no—
534C3⋊C8—62no—
535C3⋊C8—62no—
536C3⋊C8—122no—
537C2×C32—22no—
538C2×C32—81no—
539C2×C32C2×#12011yescharacteristic
540C2×C32C22×SD1611yescharacteristic
541C2×C32C2×#13711yescharacteristic
542C3×D3—22no—
543C3×D3—81no—
544C3×D3#44814yescomplemented
545C24—31no—
546C24—61no—
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—21no—
563C2×D4—31no—
564C2×D4—61no—
565C2×D4—64no—
566C2×D4—61no—
567C2×D4—61no—
568C2×D4—61no—
569C2×D4—124no—
570C2×D4C2×D3211yescharacteristic
571C22×C4—31no—
572C22×C4—31no—
573C22×C4—31no—
574C22×C4—31no—
575C22×C4—31no—
576C22×C4—64no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—182no—
580C22×C4—182no—
581C22×C4—188no—
582C22×C4—181no—
583C22×C4C2×D3211yescharacteristic
584SD16—64no—
585SD16—184no—
586SD16—184no—
587SD16—184no—
588C2×C8—32no—
589C2×C8—92no—
590C2×C8—184no—
591C4⋊C4—31no—
592C4⋊C4—61no—
593C4⋊C4C2×D3211yescharacteristic
594C22⋊C4—21no—
595C22⋊C4—61no—
596C22⋊C4—61no—
597C22⋊C4—61no—
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—41no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—68no—
617C22×C3—61no—
618C22×C3—61no—
619C22×C3—81no—
620C22×C3—81no—
621C22×C3—81no—
622C22×C3—121no—
623C22×C3—121no—
624C22×C3—121no—
625C22×C3—244no—
626C22×C3D3×SD1612yescomplemented
627C22×C3C2×#21412yescomplemented
628C22×C3C2×D3×D411yescharacteristic
629C22×C3C22×#6711yescharacteristic
630C2×D3—21no—
631C2×D3—21no—
632C2×D3—28no—
633C2×D3—41no—
634C2×D3—41no—
635C2×D3—41no—
636C2×D3—84no—
637C2×D3C2×#21412yes—
638C2×D3C2×#21412yescomplemented
639C2×D3#93712yes—
640C2×D3#95112yes—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—22no—
644C3×C4—32no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—64no—
649C3×C4—61no—
650C3×C4—81no—
651C3×C4—121no—
652C3×C4C2×D3×D412yes—
653C3×C4C2×D3×D412yes—
654Dic3—21no—
655Dic3—24no—
656Dic3—41no—
657Dic3—64no—
658Dic3—64no—
659Dic3—124no—
660Dic3#93712yes—
661C32C2×#44811yescharacteristic, complemented, Sylow
662C23—21no—
663C23—31no—
664C23—31no—
665C23—34no—
666C23—62no—
667C23—62no—
668C23—61no—
669C23—122no—
670C23—122no—
671C23—122no—
672C23D3×#6711yescharacteristic
673Q8—34no—
674Q8—64no—
675Q8—62no—
676Q8—94no—
677Q8—184no—
678Q8—188no—
679Q8—188no—
680Q8—182no—
681D4—22no—
682D4—42no—
683D4—62no—
684D4—122no—
685D4—122no—
686D4—122no—
687D4—122no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—31no—
691C2×C4—34no—
692C2×C4—31no—
693C2×C4—62no—
694C2×C4—62no—
695C2×C4—62no—
696C2×C4—64no—
697C2×C4—62no—
698C2×C4—62no—
699C2×C4—61no—
700C2×C4—122no—
701C2×C4—188no—
702C2×C4—188no—
703C2×C4—184no—
704C2×C4—182no—
705C2×C4D3×#6711yescharacteristic
706C2×C4C22×D3211yescharacteristic
707C8—62no—
708C8—182no—
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—81no—
718C2×C3—81no—
719C2×C3—161no—
720C2×C3—241no—
721C2×C3D3×#12011yescharacteristic
722C2×C3C2×D3×SD1611yescharacteristic
723C2×C3D3×#13711yescharacteristic
724C2×C3C22×#21411yescharacteristic
725C2×C3C2×#93711yescharacteristic
726C2×C3C2×#95111yescharacteristic
727D3—22no—
728D3—81no—
729D3#504014yesdirect product factor
730C22—21no—
731C22—21no—
732C22—32no—
733C22—32no—
734C22—32no—
735C22—32no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—68no—
740C22—61no—
741C22—61no—
742C22—121no—
743C22—121no—
744C22—121no—
745C22—244no—
746C22D3×#21412yescomplemented
747C22C2×D3×#6711yescharacteristic
748C4—21no—
749C4—32no—
750C4—41no—
751C4—61no—
752C4—64no—
753C4—121no—
754C4—184no—
755C4D32×D412yes—
756C3—21no—
757C3D3×#44811yescharacteristic, complemented
758C3C2×#504011yescharacteristic, complemented
759C2—22no—
760C2—34no—
761C2—62no—
762C2—81no—
763C2—241no—
764C2C2×D3×#21411yescharacteristic
765C2D3×#93711yescharacteristic
766C2D3×#95111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
prime radicalC3×D3×#121C2
hypercenter#121D32
hypocenterC32C2×#448
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C22×D3×Dic6C2semidirect
3. C2×D3×#214C2semidirect
4. #10592739C2semidirect
5. C3×#5040C2semidirect
6. #10591517C2semidirect
7. #10591181C2semidirect
8. #10591171C2semidirect
9. D3×#830C2semidirect
10. #10590603C2semidirect
11. D3×#810C2semidirect
14. C22×#634C22semidirect
18. C22×C3×Dic6C22semidirect
25. C2×D3×Dic6C22semidirect
27. C2×#3754C22semidirect
30. C2×C3×#214C22semidirect
37. C2×#3716C22semidirect
38. C2×#3715C22semidirect
40. #63657C22semidirect
41. #63637C22semidirect
42. C3×#830C22semidirect
43. C3×#810C22semidirect
44. #63567C22semidirect
45. #63565C22semidirect
46. (C2×D3)⋊(C3⋊C8)C22semidirect
64. #5040D3direct (N × H)
108. D3×Dic6D4semidirect
148. C22×Dic6C2×D3semidirect
169. C2×#214C2×D3semidirect
186. #830C2×D3semidirect
194. #810C2×D3semidirect
203. C22×C3×D3SD16semidirect
216. #634C2×D4semidirect
235. C3×Dic6C2×D4semidirect
375. C22×C32C2×SD16semidirect
386. C2×C3×D3C2×SD16semidirect
450. C22×D3#214semidirect
531. Dic6D3×D4semidirect
544. C3×D3#448semidirect
626. C22×C3D3×SD16semidirect
627. C22×C3C2×#214semidirect
638. C2×D3C2×#214semidirect
661. C32C2×#448semidirect
729. D3#5040direct (N × H)
746. C22D3×#214semidirect
757. C3D3×#448semidirect
758. C3C2×#5040semidirect

Maximal subgroups

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

subgroupindex
C22×D3×Dic62
C3×D3×#1212
C2×D3×#2142
#105927392
C3×#50402
#105915172
#105911812
#105911712
D3×#8302
#105906032
D3×#8102
C2×#50403
D3×#4483