Finite Group Databasebeta

← #11863959

Subgroups — #11863959

Order 1152.

2137 conjugacy classes of subgroups.

The subgroup lattice has 681 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×D12C211yesmaximal, characteristic, complemented
2C2×#64117C211yesmaximal, characteristic, complemented
3#10595023C211yesmaximal, characteristic, complemented
4C2×#63830C211yesmaximal, characteristic, complemented
5C3×#5131C211yesmaximal, characteristic, complemented
6C3×#5126C211yesmaximal, characteristic, complemented
7#10591096C211yesmaximal, characteristic, complemented
8#10590947C214yesmaximal, complemented
9#10590946C214yesmaximal, complemented
10#78926—31nomaximal
11#78637—31nomaximal
12C23×D32—21no—
13C2×#3828C2211yescharacteristic, complemented
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C3×D12C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C22×#626—21no—
18C2×D3×D12—24no—
19C2×D3×D12—24no—
20C2×D3×D12—22no—
21C2×D3×D12C2214yes—
22C2×C32×M16C2211yescharacteristic, complemented
23#64117—24no—
24C2×#3745C2212yescomplemented
25C2×#3744C2212yescomplemented
26C3×#926C2211yescharacteristic, complemented
27C2×C3×#208C2211yescharacteristic, complemented
28#63977—21no—
29#63966—21no—
30#63909C2212yescomplemented
31C4×#626—22no—
32#63857C2212yescomplemented
33#63830—24no—
34C2×#3716C2212yescomplemented
35C2×#3714C2212yescomplemented
36C3×#821C2214yescomplemented
37C3×(C2×D3)⋊C8C2214yescomplemented
38#63564C2214yescomplemented
39C22×D3×D4—31no—
40C23×D12—31no—
41C2×#932—31no—
42#5791—31no—
43C2×#908—31no—
44C2×#908—31no—
45C2×#908—31no—
46C2×#908—61no—
47#5524—31no—
48C3×#418—31no—
49C3×#407—31no—
50#5131—31no—
51#5131D311yescharacteristic, complemented
52#5126D311yescharacteristic, complemented
53#5001—31no—
54#4776—34no—
55#4773—34no—
56#4732—34no—
57#4731—34no—
58C23×C3⋊D3—21no—
59C23×C3×D3—21no—
60C23×C3×D3D411yescharacteristic
61C22×D32—28no—
62C22×D32—24no—
63C22×D32—48no—
64C22×C32×C4C2311yescharacteristic
65C2×#638—21no—
66#3828—22no—
67#3828—22no—
68C2×C4⋊(C3⋊D3)—21no—
69C2×C4⋊(C3⋊D3)—22no—
70C2×C4⋊(C3⋊D3)D414yescomplemented
71C2×C4⋊(C3⋊D3)C2312yes—
72C2×C4⋊(C3⋊D3)C2311yescharacteristic, complemented
73C2×C4×C3⋊D3—21no—
74C2×#634C2311yescharacteristic, complemented
75C22×C3×Dic3D411yescharacteristic
76C2×C3×D12—21no—
77C2×C3×D12—22no—
78C2×C3×D12D414yescomplemented
79C2×C3×D12C2312yes—
80C2×C3×C4×D3—22no—
81C2×C3×C4×D3—22no—
82C2×C3×C4×D3D412yes—
83C2×C3×C4×D3C2312yes—
84C2×#626—28no—
85C2×#626—24no—
86C2×#626—22no—
87D3×D12—216no—
88D3×D12—28no—
89D3×D12—28no—
90C32×M16—22no—
91C2×C32×C8C2312yescomplemented
92#3745—24no—
93#3744—24no—
94C3×#217—21no—
95C3×C4⋊Dic3C2312yescomplemented
96C3×C4×Dic3—21no—
97C3×#208—22no—
98C2×C3×C3⋊C8C2312yescomplemented
99Dic3⋊Dic3—22no—
100#3722—22no—
101(C2×D3)⋊Dic3—22no—
102#3716—24no—
103#3714—24no—
104#3003—91noSylow
105C24×D3—61no—
106C24×D3—61no—
107C22×C3×D4—31no—
108C23×C3×C4—31no—
109C22×#67—61no—
110C2×D3×D4—34no—
111C2×D3×D4—64no—
112C2×D3×D4—64no—
113C2×D3×D4—62no—
114C2×#235—31no—
115C2×#235—31no—
116C2×#235—61no—
117C22×D12—31no—
118C22×D12—31no—
119C22×D12—34no—
120C22×D12—61no—
121C22×D12—64no—
122C22×D12—62no—
123C22×D12—61no—
124C22×D12—64no—
125C22×D12C2×D311yescharacteristic
126C22×C4×D3C2×D311yescharacteristic
127C2×C3×M16—21no—
128C2×C3×M16—31no—
129C2×C3×M16C2×D311yescharacteristic, complemented
130C2×C3×M16C2×D311yescharacteristic, complemented
131C3×#117—31no—
132#953—61no—
133C2×#214—32no—
134#932—64no—
135C2×#213—32no—
136#930—32no—
137#929—61no—
138C4×#67—62no—
139#926C2×D311yescharacteristic, complemented
140#924—32no—
141C2×#208C2×D311yescharacteristic, complemented
142#908—64no—
143#908—64no—
144#908—68no—
145#908—64no—
146C2×D24—32no—
147C2×D24—32no—
148C2×D24—32no—
149C2×D24—62no—
150C2×#204—32no—
151C2×#204—32no—
152C2×#204—32no—
153C2×#204—62no—
154#897—32no—
155#895—32no—
156#886—61no—
157#882—61no—
158C4×D12—62no—
159C3×#102—34no—
160C3×C22⋊C8—34no—
161#821—34no—
162#821C2×D314yescomplemented
163(C2×D3)⋊C8C2×D314yescomplemented
164#809—34no—
165C23×C32C2×D411yescharacteristic
166C22×C3⋊D3—24no—
167C22×C3⋊D3—22no—
168C22×C3⋊D3—21no—
169C22×C3⋊D3—44no—
170C22×C3×D3—22no—
171C22×C3×D3—24no—
172C22×C3×D3—24no—
173C22×C3×D3—22no—
174C22×C3×D3—44no—
175C22×C3×D3C2×D412yes—
176C2×D32—216no—
177C2×D32—432no—
178C2×D32—48no—
179C2×D32—48no—
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2×D412yes—
182C2×C32×C4C2×D412yes—
183C2×C32×C4C2411yescharacteristic
184#638—42no—
185C2×C3⋊Dic3—21no—
186C4⋊(C3⋊D3)—21no—
187C4⋊(C3⋊D3)—24no—
188C4⋊(C3⋊D3)—22no—
189C4⋊(C3⋊D3)—21no—
190C4⋊(C3⋊D3)C2×D414yes—
191C4×C3⋊D3—42no—
192#634—21no—
193#634—21no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3C2×D412yes—
197C3×D12—24no—
198C3×D12—22no—
199C3×D12C2×D414yes—
200C3×C4×D3—24no—
201C3×C4×D3—22no—
202C3×C4×D3—22no—
203#626—216no—
204#626—44no—
205C32×C8—22no—
206C3×C3⋊C8—22no—
207C23×D4—91no—
208C2×AGL(1,ℤ/8)—91no—
209C2×AGL(1,ℤ/8)—91no—
210#525—91no—
211#450—94no—
212#447—94no—
213#418—31no—
214#418—91no—
215#407—31no—
216C24×C3—31no—
217C24×C3—61no—
218C23×D3—21no—
219C23×D3—64no—
220C23×D3—68no—
221C23×D3—68no—
222C23×D3—61no—
223C23×D3—61no—
224C23×D3—64no—
225C23×D3—121no—
226C23×D3—128no—
227C23×D3—128no—
228C23×D3D1211yescharacteristic
229C2×C3×D4—34no—
230C2×C3×D4—32no—
231C2×C3×D4—61no—
232C2×C3×D4—62no—
233C22×C3×C4—21no—
234C22×C3×C4—31no—
235C22×C3×C4—32no—
236C22×C3×C4—32no—
237C22×C3×C4—62no—
238C22×C3×C4—62no—
239C22×C3×C4C22×D311yescharacteristic
240C22×C3×C4C22×D311yescharacteristic
241C2×#67—68no—
242C2×#67—62no—
243C2×#67—61no—
244C2×#67—61no—
245C2×#67—64no—
246C2×#67—121no—
247C22×Dic3D1211yescharacteristic
248D3×D4—68no—
249D3×D4—68no—
250D3×D4—616no—
251#235—64no—
252#235—62no—
253#235—62no—
254#235—62no—
255#235—62no—
256#235—122no—
257C2×D12—21no—
258C2×D12—22no—
259C2×D12—34no—
260C2×D12—34no—
261C2×D12—32no—
262C2×D12—32no—
263C2×D12—31no—
264C2×D12—31no—
265C2×D12—62no—
266C2×D12—61no—
267C2×D12—64no—
268C2×D12—68no—
269C2×D12—616no—
270C2×D12—64no—
271C2×D12—68no—
272C2×D12—62no—
273C2×D12—61no—
274C2×D12—61no—
275C2×D12—62no—
276C2×D12—68no—
277C2×D12—62no—
278C2×D12—121no—
279C2×D12—122no—
280C2×D12D1214yescomplemented
281C2×D12C22×D312yes—
282C2×C4×D3—22no—
283C2×C4×D3—22no—
284C2×C4×D3—61no—
285C2×C4×D3—61no—
286C2×C4×D3—121no—
287C2×C4×D3D1212yes—
288C2×C4×D3C22×D312yes—
289C2×Dic6—31no—
290C2×Dic6—31no—
291C2×Dic6—61no—
292C3×M16—24no—
293C3×M16—22no—
294C3×M16—22no—
295C3×M16—62no—
296C2×C3×C8—22no—
297C2×C3×C8—32no—
298C2×C3×C8C22×D312yescomplemented
299C2×C3×C8C22×D312yescomplemented
300C3×C4⋊C4—32no—
301C3×C22⋊C4—61no—
302C3×C42—61no—
303#217—21no—
304#217—62no—
305#214—64no—
306#213—64no—
307(C2×D3)⋊C4—62no—
308(C2×D3)⋊C4—62no—
309(C2×D3)⋊C4—62no—
310C4⋊Dic3—62no—
311C4⋊Dic3C22×D312yescomplemented
312Dic3⋊C4—62no—
313C4×Dic3—21no—
314#208—22no—
315C2×C3⋊C8C22×D312yescomplemented
316D24—64no—
317D24—64no—
318D24—68no—
319D24—64no—
320#204—64no—
321#204—64no—
322#204—68no—
323#204—64no—
324C22×C32—22no—
325C22×C32#12012yes—
326C22×C32C22×D411yescharacteristic
327C2×C3⋊D3—24no—
328C2×C3⋊D3—41no—
329C2×C3⋊D3—48no—
330C2×C3⋊D3—44no—
331C2×C3⋊D3—42no—
332C2×C3×D3—28no—
333C2×C3×D3—22no—
334C2×C3×D3—22no—
335C2×C3×D3—24no—
336C2×C3×D3—48no—
337C2×C3×D3—44no—
338C2×C3×D3AGL(1,ℤ/8)14yescomplemented
339D32—432no—
340C32×C4#12012yes—
341C32×C4C22×D411yescharacteristic
342C32×C4C22×D411yescharacteristic
343C3⋊Dic3—41no—
344C3×Dic3—22no—
345C3×Dic3—42no—
346C25—181no—
347C2×#41—91no—
348C22×D4—31no—
349C22×D4—94no—
350C22×D4—91no—
351C22×D4—182no—
352C22×D4—181no—
353C22×D4—184no—
354C22×D4—184no—
355C23×C4—31no—
356AGL(1,ℤ/8)—184no—
357AGL(1,ℤ/8)—184no—
358C2×SD16—92no—
359C2×SD16—92no—
360C2×D8—92no—
361C2×D8—92no—
362C2×M16—31no—
363C2×M16D3211yescharacteristic, complemented
364#123—181no—
365C22⋊Q8—92no—
366#121—92no—
367#120—181no—
368C4×D4—182no—
369#117—31no—
370#102—34no—
371#102—94no—
372C22⋊C8—34no—
373C23×C3—21no—
374C23×C3—32no—
375C23×C3—64no—
376C23×C3—62no—
377C23×C3—64no—
378C23×C3—62no—
379C23×C3—124no—
380C23×C3C2×D1211yescharacteristic
381C23×C3D3×D411yescharacteristic
382C22×D3—22no—
383C22×D3—24no—
384C22×D3—24no—
385C22×D3—22no—
386C22×D3—44no—
387C22×D3—616no—
388C22×D3—616no—
389C22×D3—64no—
390C22×D3—64no—
391C22×D3—62no—
392C22×D3—62no—
393C22×D3—61no—
394C22×D3—61no—
395C22×D3—121no—
396C22×D3—122no—
397C22×D3—124no—
398C22×D3—1232no—
399C22×D3—128no—
400C22×D3—128no—
401C22×D3—1232no—
402C22×D3—128no—
403C22×D3—124no—
404C22×D3—124no—
405C22×D3—128no—
406C22×D3—244no—
407C22×D3C2×D1212yes—
408C3×D4—34no—
409C3×D4—64no—
410C3×D4—62no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—32no—
416C2×C3×C4—62no—
417C2×C3×C4—64no—
418C2×C3×C4—62no—
419C2×C3×C4—62no—
420C2×C3×C4—62no—
421C2×C3×C4C2×D1211yescharacteristic
422C2×C3×C4C2×D1212yes—
423C2×C3×C4D3×D411yescharacteristic
424C2×C3×C4D3×D412yes—
425C2×C3×C4D3×D412yes—
426C2×C3×C4D3×D412yes—
427C2×C3×C4C23×D311yescharacteristic
428C2×C3×C4C23×D311yescharacteristic
429#67—616no—
430#67—124no—
431#67—124no—
432#67—122no—
433#67—122no—
434C2×Dic3—22no—
435C2×Dic3—22no—
436C2×Dic3—61no—
437C2×Dic3—61no—
438C2×Dic3—121no—
439C2×Dic3C2×D1212yes—
440D12—24no—
441D12—22no—
442D12—34no—
443D12—34no—
444D12—64no—
445D12—62no—
446D12—616no—
447D12—64no—
448D12—64no—
449D12—62no—
450D12—61no—
451D12—62no—
452D12—61no—
453D12—61no—
454D12—61no—
455D12—122no—
456D12—124no—
457D12—121no—
458D12—124no—
459D12C2×D1214yes—
460C4×D3—24no—
461C4×D3—22no—
462C4×D3—22no—
463C4×D3—124no—
464C4×D3—122no—
465C4×D3—122no—
466Dic6—62no—
467Dic6—61no—
468Dic6—61no—
469Dic6—61no—
470Dic6—61no—
471Dic6—121no—
472C3×C8—24no—
473C3×C8—22no—
474C3×C8—22no—
475C3×C8—62no—
476C3⋊C8—22no—
477C2×C32—22no—
478C2×C32C2×#12011yescharacteristic
479C2×C32C2×AGL(1,ℤ/8)12yes—
480C3⋊D3—44no—
481C3⋊D3—81no—
482C3×D3—24no—
483C3×D3—44no—
484C24—31no—
485C24—61no—
486C24—184no—
487C24—188no—
488C24—181no—
489C24—368no—
490#41—182no—
491#41—182no—
492C2×Q8—91no—
493C2×D4—32no—
494C2×D4—34no—
495C2×D4—61no—
496C2×D4—62no—
497C2×D4—92no—
498C2×D4—91no—
499C2×D4—94no—
500C2×D4—184no—
501C2×D4—188no—
502C2×D4—188no—
503C2×D4—1816no—
504C2×D4—188no—
505C2×D4—182no—
506C2×D4—181no—
507C2×D4—182no—
508C2×D4—181no—
509C22×C4—31no—
510C22×C4—32no—
511C22×C4—32no—
512C22×C4—62no—
513C22×C4—62no—
514C22×C4—181no—
515C22×C4C2×D3211yescharacteristic
516SD16—184no—
517SD16—184no—
518D8—184no—
519D8—184no—
520M16—22no—
521M16—62no—
522C2×C8—32no—
523C2×C8C2×D3212yescomplemented
524C4⋊C4—32no—
525C4⋊C4—182no—
526C22⋊C4—61no—
527C22⋊C4—182no—
528C22⋊C4—182no—
529C42—61no—
530C22×C3—22no—
531C22×C3—22no—
532C22×C3—21no—
533C22×C3—22no—
534C22×C3—34no—
535C22×C3—42no—
536C22×C3—68no—
537C22×C3—62no—
538C22×C3—62no—
539C22×C3—64no—
540C22×C3—128no—
541C22×C3—124no—
542C22×C3#88212yes—
543C22×C3#88212yes—
544C22×C3C22×D1211yescharacteristic
545C22×C3C2×D3×D411yescharacteristic
546C2×D3—28no—
547C2×D3—22no—
548C2×D3—22no—
549C2×D3—24no—
550C2×D3—48no—
551C2×D3—44no—
552C2×D3—64no—
553C2×D3—64no—
554C2×D3—124no—
555C2×D3—1232no—
556C2×D3—1232no—
557C2×D3—128no—
558C2×D3—128no—
559C2×D3—124no—
560C2×D3—124no—
561C2×D3—122no—
562C2×D3—121no—
563C2×D3—121no—
564C2×D3—122no—
565C2×D3—122no—
566C2×D3—244no—
567C2×D3—242no—
568C2×D3—248no—
569C2×D3#90814yescomplemented
570C3×C4—21no—
571C3×C4—21no—
572C3×C4—22no—
573C3×C4—62no—
574C3×C4—122no—
575C3×C4#88212yes—
576C3×C4#88212yes—
577C3×C4C22×D1211yescharacteristic
578C3×C4C2×D3×D411yescharacteristic
579C3×C4C2×D3×D411yescharacteristic
580C3×C4C2×D3×D411yescharacteristic
581Dic3—22no—
582Dic3—42no—
583Dic3—122no—
584Dic3—121no—
585Dic3—121no—
586C32#300311yescharacteristic, complemented, Sylow
587C23—32no—
588C23—64no—
589C23—62no—
590C23—62no—
591C23—64no—
592C23—124no—
593C23—1816no—
594C23—182no—
595C23—184no—
596C23—181no—
597C23—364no—
598C23—368no—
599C23—3632no—
600C23—368no—
601C23D3×D1211yescharacteristic
602Q8—181no—
603Q8—181no—
604D4—34no—
605D4—62no—
606D4—64no—
607D4—94no—
608D4—1816no—
609D4—182no—
610D4—181no—
611D4—181no—
612D4—184no—
613D4—364no—
614D4—362no—
615C2×C4—32no—
616C2×C4—62no—
617C2×C4—62no—
618C2×C4—62no—
619C2×C4—64no—
620C2×C4—62no—
621C2×C4—181no—
622C2×C4—362no—
623C2×C4D3×D1212yes—
624C2×C4D3×D1211yescharacteristic
625C2×C4#381112yes—
626C2×C4C22×D3211yescharacteristic
627C8—22no—
628C8—62no—
629C2×C3—22no—
630C2×C3—22no—
631C2×C3—22no—
632C2×C3—21no—
633C2×C3—42no—
634C2×C3—64no—
635C2×C3—124no—
636C2×C3C2×#88211yescharacteristic
637C2×C3C2×#88211yescharacteristic
638C2×C3C2×#90812yes—
639C2×C3D3×AGL(1,ℤ/8)12yes—
640D3—24no—
641D3—44no—
642D3—124no—
643D3—124no—
644D3—244no—
645D3—242no—
646D3—241no—
647D3—241no—
648C22—22no—
649C22—34no—
650C22—68no—
651C22—62no—
652C22—62no—
653C22—64no—
654C22—128no—
655C22—124no—
656C22—184no—
657C22—368no—
658C22—3632no—
659C22—364no—
660C22—362no—
661C22—361no—
662C22#6392312yes—
663C22C2×D3×D1211yescharacteristic
664C4—62no—
665C4—122no—
666C4—361no—
667C4#6392312yes—
668C4C2×D3×D1211yescharacteristic
669C4C2×#381111yescharacteristic
670C3—21no—
671C3#7863711yescharacteristic, complemented
672C3#7892611yescharacteristic, complemented
673C2—22no—
674C2—64no—
675C2—124no—
676C2—364no—
677C2—721no—
678C2D3×#90812yes—
679C2C2×#6392311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
hypercenterC2×M16D32
hypocenterC32#3003
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C22×D3×D12C2semidirect
2. C2×#64117C2semidirect
3. #10595023C2semidirect
4. C2×#63830C2semidirect
5. C3×#5131C2semidirect
6. C3×#5126C2semidirect
7. #10591096C2semidirect
8. #10590947C2semidirect
9. #10590946C2semidirect
13. C2×#3828C22semidirect
22. C2×C32×M16C22semidirect
24. C2×#3745C22semidirect
25. C2×#3744C22semidirect
26. C3×#926C22semidirect
27. C2×C3×#208C22semidirect
30. #63909C22semidirect
32. #63857C22semidirect
34. C2×#3716C22semidirect
35. C2×#3714C22semidirect
36. C3×#821C22semidirect
37. C3×(C2×D3)⋊C8C22semidirect
38. #63564C22semidirect
51. #5131D3semidirect
52. #5126D3semidirect
70. C2×C4⋊(C3⋊D3)D4semidirect
72. C2×C4⋊(C3⋊D3)C23semidirect
74. C2×#634C23semidirect
78. C2×C3×D12D4semidirect
91. C2×C32×C8C23semidirect
95. C3×C4⋊Dic3C23semidirect
98. C2×C3×C3⋊C8C23semidirect
129. C2×C3×M16C2×D3semidirect
130. C2×C3×M16C2×D3semidirect
139. #926C2×D3semidirect
141. C2×#208C2×D3semidirect
162. #821C2×D3semidirect
163. (C2×D3)⋊C8C2×D3semidirect
280. C2×D12D12semidirect
298. C2×C3×C8C22×D3semidirect
299. C2×C3×C8C22×D3semidirect
311. C4⋊Dic3C22×D3semidirect
315. C2×C3⋊C8C22×D3semidirect
338. C2×C3×D3AGL(1,ℤ/8)semidirect
363. C2×M16D32semidirect
523. C2×C8C2×D32semidirect
569. C2×D3#908semidirect
586. C32#3003semidirect
671. C3#78637semidirect
672. C3#78926semidirect

Maximal subgroups

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

subgroupindex
C22×D3×D122
C2×#641172
#105950232
C2×#638302
C3×#51312
C3×#51262
#105910962
#105909472
#105909462
#789263
#786373