Finite Group Databasebeta

← #11863961

Subgroups — #11863961

Order 1152.

2083 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×D12C211yesmaximal, characteristic, complemented
2C2×C3×#908C211yesmaximal, characteristic, complemented
3#10595022C211yesmaximal, characteristic, complemented
4C2×#63825C211yesmaximal, characteristic, complemented
5#10592830C211yesmaximal, characteristic, complemented
6C3×#5126C211yesmaximal, characteristic, complemented
7#10591086C211yesmaximal, characteristic, complemented
8#10590944C214yesmaximal, complemented
9#10590942C214yesmaximal, complemented
10#83944—31nomaximal
11#78637—31nomaximal
12C23×D32—21no—
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C2×C3×#235C2211yescharacteristic, complemented
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#64135C2211yescharacteristic, complemented
24C2×C3×#208C2211yescharacteristic, complemented
25C3×#908—24no—
26C2×C3×D24C2212yescomplemented
27C2×C3×#204C2212yescomplemented
28#63976—21no—
29#63961—21no—
30#63908C2212yescomplemented
31C4×#625—22no—
32#63856C2212yescomplemented
33C2×#3717C2212yescomplemented
34#63825—24no—
35C2×#3714C2212yescomplemented
36#63648C2214yescomplemented
37C3×(C2×D3)⋊C8C2214yescomplemented
38#63563C2214yescomplemented
39C22×D3×D4—31no—
40C23×D12—31no—
41C2×C3×AGL(1,ℤ/8)—31no—
42#5828—31no—
43C2×#949—31no—
44#5791—31no—
45C2×#908—31no—
46C2×#908D311yescharacteristic, complemented
47C3×#407—31no—
48#5215—31no—
49#5169—34no—
50#5156—34no—
51#5131—31no—
52#5131—31no—
53#5131—31no—
54#5131—61no—
55#5126D311yescharacteristic, complemented
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×C4⋊(C3⋊D3)—21no—
66C2×C4⋊(C3⋊D3)—22no—
67C2×C4⋊(C3⋊D3)D414yescomplemented
68C2×C4⋊(C3⋊D3)C2312yes—
69C2×C3×#67—21no—
70C22×C3×Dic3D411yescharacteristic
71C3×#235—22no—
72C3×#235—22no—
73C2×C3×D12—21no—
74C2×C3×D12—22no—
75C2×C3×D12D414yescomplemented
76C2×C3×D12C2312yes—
77C2×C3×D12C2311yescharacteristic, complemented
78C2×C3×C4×D3—22no—
79C2×C3×C4×D3—22no—
80C2×C3×C4×D3—21no—
81C2×C3×C4×D3D412yes—
82C2×C3×C4×D3C2312yes—
83C2×C3×Dic6C2311yescharacteristic, complemented
84C2×#626—28no—
85C2×#626—24no—
86C2×#625—22no—
87D3×D12—216no—
88D3×D12—28no—
89D3×D12—28no—
90C32×M16—22no—
91C2×C32×C8C2312yescomplemented
92#3757—21no—
93C4⋊(C3⋊Dic3)C2312yescomplemented
94C4×C3⋊Dic3—21no—
95C3×#208—22no—
96C2×C3×C3⋊C8C2312yescomplemented
97C3×D24—24no—
98C3×#204—24no—
99#3724—22no—
100(C2×D3)⋊Dic3—22no—
101(C2×D3)⋊Dic3—22no—
102#3717—24no—
103#3714—24no—
104#3003—91noSylow
105C24×D3—61no—
106C24×D3—61no—
107C2×C3×#41—31no—
108C22×C3×D4—31no—
109C23×C3×C4—31no—
110C22×#67—61no—
111C2×D3×D4—34no—
112C2×D3×D4—64no—
113C2×D3×D4—64no—
114C2×D3×D4—62no—
115C2×#235C2×D311yescharacteristic, complemented
116C22×D12—31no—
117C22×D12—31no—
118C22×D12—34no—
119C22×D12—61no—
120C22×D12—64no—
121C22×D12—62no—
122C22×D12—61no—
123C22×D12—64no—
124C22×D12C2×D311yescharacteristic
125C22×C4×D3C2×D311yescharacteristic
126C3×AGL(1,ℤ/8)—64no—
127C2×C3×SD16—32no—
128C2×C3×D8—32no—
129C2×C3×M16—21no—
130C2×C3×M16—31no—
131C2×C3×M16C2×D311yescharacteristic, complemented
132C2×C3×M16C2×D311yescharacteristic, complemented
133#953—61no—
134#949—64no—
135#946—32no—
136C2×#215—32no—
137#938—32no—
138#937—61no—
139#935—61no—
140C2×#213—32no—
141#930—32no—
142#929—61no—
143C4×#67—62no—
144C4×#67—62no—
145#926—31no—
146#926—31no—
147#926—61no—
148#924—32no—
149C2×#208C2×D311yescharacteristic, complemented
150#908—24no—
151#908—64no—
152C2×D24—32no—
153C2×D24C2×D312yescomplemented
154C2×#204—32no—
155C2×#204C2×D312yescomplemented
156C3×C22⋊C8—34no—
157#832—34no—
158#821—34no—
159#821—34no—
160#821—34no—
161#821—64no—
162(C2×D3)⋊C8C2×D314yescomplemented
163C23×C32C2×D411yescharacteristic
164C22×C3⋊D3—24no—
165C22×C3⋊D3—22no—
166C22×C3⋊D3—44no—
167C22×C3×D3—22no—
168C22×C3×D3—24no—
169C22×C3×D3—24no—
170C22×C3×D3—22no—
171C22×C3×D3—21no—
172C22×C3×D3—44no—
173C22×C3×D3C2×D412yes—
174C2×D32—216no—
175C2×D32—432no—
176C2×D32—48no—
177C2×D32—48no—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2×D412yes—
180C2×C32×C4C2×D412yes—
181C2×C32×C4C2411yescharacteristic
182C2×C3⋊Dic3—22no—
183C4⋊(C3⋊D3)—24no—
184C4⋊(C3⋊D3)—22no—
185C4⋊(C3⋊D3)C2×D414yes—
186C3×#67—42no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3C2×D412yes—
190C3×D12—24no—
191C3×D12—22no—
192C3×D12—21no—
193C3×D12—21no—
194C3×D12C2×D414yes—
195C3×C4×D3—24no—
196C3×C4×D3—22no—
197C3×C4×D3—22no—
198C3×C4×D3—42no—
199C3×Dic6—21no—
200C3×Dic6—21no—
201#626—216no—
202#625—44no—
203C32×C8—22no—
204C3×C3⋊C8—22no—
205C23×D4—91no—
206C2×AGL(1,ℤ/8)—31no—
207C2×AGL(1,ℤ/8)—91no—
208#525—91no—
209#450—94no—
210#447—94no—
211#418—91no—
212#418—91no—
213#407—31no—
214C24×C3—31no—
215C24×C3—61no—
216C23×D3—21no—
217C23×D3—64no—
218C23×D3—68no—
219C23×D3—68no—
220C23×D3—61no—
221C23×D3—61no—
222C23×D3—64no—
223C23×D3—121no—
224C23×D3—128no—
225C23×D3—128no—
226C23×D3D1211yescharacteristic
227C3×#41—62no—
228C3×#41—62no—
229C2×C3×Q8—31no—
230C2×C3×D4—34no—
231C2×C3×D4—32no—
232C2×C3×D4—31no—
233C2×C3×D4—61no—
234C2×C3×D4—61no—
235C2×C3×D4—62no—
236C22×C3×C4—21no—
237C22×C3×C4—31no—
238C22×C3×C4—32no—
239C22×C3×C4—32no—
240C22×C3×C4—62no—
241C22×C3×C4—62no—
242C22×C3×C4—61no—
243C22×C3×C4C22×D311yescharacteristic
244C22×C3×C4C22×D311yescharacteristic
245C2×#67—21no—
246C2×#67—68no—
247C2×#67—62no—
248C2×#67—62no—
249C2×#67—64no—
250C22×Dic3D1211yescharacteristic
251D3×D4—68no—
252D3×D4—68no—
253D3×D4—616no—
254#235—22no—
255#235—22no—
256C2×D12—21no—
257C2×D12—22no—
258C2×D12—34no—
259C2×D12—34no—
260C2×D12—32no—
261C2×D12—32no—
262C2×D12—62no—
263C2×D12—64no—
264C2×D12—68no—
265C2×D12—616no—
266C2×D12—64no—
267C2×D12—68no—
268C2×D12—61no—
269C2×D12—61no—
270C2×D12—62no—
271C2×D12—62no—
272C2×D12—68no—
273C2×D12—121no—
274C2×D12—122no—
275C2×D12#6714yescomplemented
276C2×D12C22×D312yes—
277C2×D12C22×D311yescharacteristic, complemented
278C2×C4×D3—22no—
279C2×C4×D3—22no—
280C2×C4×D3—21no—
281C2×C4×D3D1212yes—
282C2×C4×D3C22×D312yes—
283C2×Dic6C22×D311yescharacteristic, complemented
284C3×SD16—64no—
285C3×D8—64no—
286C3×M16—22no—
287C3×M16—22no—
288C3×M16—42no—
289C3×M16—62no—
290C2×C3×C8—22no—
291C2×C3×C8—32no—
292C2×C3×C8C22×D312yescomplemented
293C2×C3×C8C22×D312yescomplemented
294#217—62no—
295#217—61no—
296#217—61no—
297#217—62no—
298#217—121no—
299#215—64no—
300#213—64no—
301(C2×D3)⋊C4—62no—
302(C2×D3)⋊C4—62no—
303C4⋊Dic3—32no—
304C4⋊Dic3—32no—
305C4⋊Dic3—62no—
306Dic3⋊C4—62no—
307Dic3⋊C4—62no—
308C4×Dic3—61no—
309C4×Dic3—61no—
310C4×Dic3—121no—
311#208—22no—
312C2×C3⋊C8C22×D312yescomplemented
313D24—24no—
314D24—64no—
315#204—24no—
316#204—64no—
317C22×C32—22no—
318C22×C32#12012yes—
319C22×C32C22×D411yescharacteristic
320C2×C3⋊D3—24no—
321C2×C3⋊D3—48no—
322C2×C3⋊D3—44no—
323C2×C3×D3—28no—
324C2×C3×D3—22no—
325C2×C3×D3—22no—
326C2×C3×D3—24no—
327C2×C3×D3—48no—
328C2×C3×D3—44no—
329C2×C3×D3—41no—
330C2×C3×D3—42no—
331C2×C3×D3AGL(1,ℤ/8)14yescomplemented
332D32—432no—
333C32×C4#12012yes—
334C32×C4C22×D411yescharacteristic
335C32×C4C22×D411yescharacteristic
336C3⋊Dic3—42no—
337C3×Dic3—22no—
338C3×Dic3—41no—
339C25—181no—
340C2×#41—31no—
341C22×D4—31no—
342C22×D4—94no—
343C22×D4—91no—
344C22×D4—182no—
345C22×D4—181no—
346C22×D4—184no—
347C22×D4—184no—
348C23×C4—31no—
349AGL(1,ℤ/8)—64no—
350AGL(1,ℤ/8)—184no—
351C2×SD16—32no—
352C2×SD16—92no—
353C2×D8—32no—
354C2×D8—92no—
355C2×M16—31no—
356C2×M16D3211yescharacteristic, complemented
357#123—181no—
358C22⋊Q8—92no—
359#121—92no—
360#120—181no—
361C4×D4—182no—
362#117—91no—
363#102—94no—
364#102—94no—
365C22⋊C8—34no—
366C23×C3—21no—
367C23×C3—32no—
368C23×C3—64no—
369C23×C3—62no—
370C23×C3—64no—
371C23×C3—62no—
372C23×C3—61no—
373C23×C3—124no—
374C23×C3C2×D1211yescharacteristic
375C23×C3D3×D411yescharacteristic
376C22×D3—22no—
377C22×D3—24no—
378C22×D3—24no—
379C22×D3—22no—
380C22×D3—21no—
381C22×D3—44no—
382C22×D3—616no—
383C22×D3—616no—
384C22×D3—64no—
385C22×D3—64no—
386C22×D3—62no—
387C22×D3—62no—
388C22×D3—122no—
389C22×D3—124no—
390C22×D3—1232no—
391C22×D3—128no—
392C22×D3—128no—
393C22×D3—1232no—
394C22×D3—128no—
395C22×D3—124no—
396C22×D3—124no—
397C22×D3—128no—
398C22×D3—244no—
399C22×D3C2×D1212yes—
400C3×Q8—61no—
401C3×Q8—61no—
402C3×D4—34no—
403C3×D4—64no—
404C3×D4—62no—
405C3×D4—61no—
406C3×D4—61no—
407C3×D4—122no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—32no—
413C2×C3×C4—62no—
414C2×C3×C4—64no—
415C2×C3×C4—62no—
416C2×C3×C4—62no—
417C2×C3×C4—61no—
418C2×C3×C4—122no—
419C2×C3×C4C2×D1211yescharacteristic
420C2×C3×C4D3×D411yescharacteristic
421C2×C3×C4D3×D412yes—
422C2×C3×C4D3×D412yes—
423C2×C3×C4D3×D412yes—
424C2×C3×C4C2×#6712yes—
425C2×C3×C4C23×D311yescharacteristic
426C2×C3×C4C23×D311yescharacteristic
427#67—42no—
428#67—616no—
429#67—124no—
430#67—124no—
431C2×Dic3—22no—
432C2×Dic3—21no—
433C2×Dic3—62no—
434C2×Dic3—62no—
435C2×Dic3—122no—
436C2×Dic3C2×D1212yes—
437D12—24no—
438D12—22no—
439D12—21no—
440D12—21no—
441D12—34no—
442D12—34no—
443D12—64no—
444D12—616no—
445D12—64no—
446D12—64no—
447D12—62no—
448D12—62no—
449D12—122no—
450D12—124no—
451D12C2×#6714yes—
452C4×D3—24no—
453C4×D3—22no—
454C4×D3—22no—
455C4×D3—42no—
456Dic6—21no—
457Dic6—21no—
458C3×C8—22no—
459C3×C8—22no—
460C3×C8—42no—
461C3×C8—62no—
462C3⋊C8—22no—
463C2×C32—22no—
464C2×C32C2×#12011yescharacteristic
465C2×C32C2×AGL(1,ℤ/8)12yes—
466C3⋊D3—44no—
467C3×D3—24no—
468C3×D3—44no—
469C3×D3—81no—
470C24—31no—
471C24—61no—
472C24—184no—
473C24—188no—
474C24—181no—
475C24—368no—
476#41—62no—
477#41—62no—
478C2×Q8—31no—
479C2×D4—32no—
480C2×D4—31no—
481C2×D4—34no—
482C2×D4—61no—
483C2×D4—61no—
484C2×D4—62no—
485C2×D4—92no—
486C2×D4—94no—
487C2×D4—184no—
488C2×D4—188no—
489C2×D4—188no—
490C2×D4—1816no—
491C2×D4—188no—
492C2×D4—182no—
493C2×D4—181no—
494C2×D4—182no—
495C22×C4—31no—
496C22×C4—32no—
497C22×C4—32no—
498C22×C4—62no—
499C22×C4—62no—
500C22×C4—61no—
501C22×C4C2×D3211yescharacteristic
502SD16—64no—
503SD16—184no—
504D8—64no—
505D8—184no—
506M16—22no—
507M16—62no—
508C2×C8—32no—
509C2×C8C2×D3212yescomplemented
510C4⋊C4—92no—
511C4⋊C4—182no—
512C22⋊C4—182no—
513C22⋊C4—182no—
514C22⋊C4—181no—
515C42—181no—
516C22×C3—22no—
517C22×C3—22no—
518C22×C3—21no—
519C22×C3—22no—
520C22×C3—34no—
521C22×C3—42no—
522C22×C3—68no—
523C22×C3—62no—
524C22×C3—62no—
525C22×C3—64no—
526C22×C3—128no—
527C22×C3—124no—
528C22×C3—121no—
529C22×C3—122no—
530C22×C3#88212yes—
531C22×C3#93712yes—
532C22×C3C22×D1211yescharacteristic
533C22×C3C2×D3×D411yescharacteristic
534C2×D3—28no—
535C2×D3—22no—
536C2×D3—22no—
537C2×D3—24no—
538C2×D3—48no—
539C2×D3—44no—
540C2×D3—42no—
541C2×D3—41no—
542C2×D3—64no—
543C2×D3—64no—
544C2×D3—124no—
545C2×D3—1232no—
546C2×D3—1232no—
547C2×D3—128no—
548C2×D3—128no—
549C2×D3—124no—
550C2×D3—124no—
551C2×D3—244no—
552C2×D3—248no—
553C2×D3#90814yescomplemented
554C3×C4—21no—
555C3×C4—21no—
556C3×C4—22no—
557C3×C4—62no—
558C3×C4—121no—
559C3×C4#88212yes—
560C3×C4#93712yes—
561C3×C4C2×D3×D411yescharacteristic
562C3×C4C2×D3×D411yescharacteristic
563C3×C4C2×D3×D411yescharacteristic
564C3×C4C22×#6711yescharacteristic
565Dic3—22no—
566Dic3—41no—
567Dic3—122no—
568Dic3—122no—
569Dic3—242no—
570C32#300311yescharacteristic, complemented, Sylow
571C23—32no—
572C23—64no—
573C23—62no—
574C23—62no—
575C23—64no—
576C23—61no—
577C23—124no—
578C23—1816no—
579C23—182no—
580C23—184no—
581C23—364no—
582C23—368no—
583C23—3632no—
584C23—368no—
585C23D3×D1211yescharacteristic
586Q8—61no—
587Q8—61no—
588D4—34no—
589D4—62no—
590D4—61no—
591D4—61no—
592D4—64no—
593D4—94no—
594D4—122no—
595D4—1816no—
596D4—182no—
597D4—184no—
598D4—364no—
599C2×C4—32no—
600C2×C4—62no—
601C2×C4—62no—
602C2×C4—62no—
603C2×C4—64no—
604C2×C4—61no—
605C2×C4—122no—
606C2×C4—182no—
607C2×C4D3×D1211yescharacteristic
608C2×C4#380212yes—
609C2×C4D3×#6712yes—
610C2×C4C22×D3211yescharacteristic
611C8—22no—
612C8—62no—
613C2×C3—22no—
614C2×C3—22no—
615C2×C3—22no—
616C2×C3—21no—
617C2×C3—42no—
618C2×C3—64no—
619C2×C3—124no—
620C2×C3—241no—
621C2×C3C2×#88211yescharacteristic
622C2×C3C2×#90812yes—
623C2×C3D3×AGL(1,ℤ/8)12yes—
624C2×C3C2×#93711yescharacteristic
625D3—24no—
626D3—44no—
627D3—81no—
628D3—124no—
629D3—124no—
630D3—244no—
631C22—22no—
632C22—34no—
633C22—68no—
634C22—62no—
635C22—62no—
636C22—64no—
637C22—128no—
638C22—124no—
639C22—122no—
640C22—121no—
641C22—184no—
642C22—368no—
643C22—3632no—
644C22—364no—
645C22#6392212yes—
646C22C2×D3×D1211yescharacteristic
647C4—62no—
648C4—121no—
649C4—362no—
650C4#6392212yes—
651C4C2×#380211yescharacteristic
652C4C2×D3×#6711yescharacteristic
653C3—21no—
654C3#7863711yescharacteristic, complemented
655C3#8394411yescharacteristic, complemented
656C2—22no—
657C2—64no—
658C2—124no—
659C2—241no—
660C2—364no—
661C2D3×#90812yes—
662C2C2×#6392211yescharacteristic
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×C3×#908C2semidirect
3. #10595022C2semidirect
4. C2×#63825C2semidirect
5. #10592830C2semidirect
6. C3×#5126C2semidirect
7. #10591086C2semidirect
8. #10590944C2semidirect
9. #10590942C2semidirect
14. C2×C3×#235C22semidirect
22. C2×C32×M16C22semidirect
23. #64135C22semidirect
24. C2×C3×#208C22semidirect
26. C2×C3×D24C22semidirect
27. C2×C3×#204C22semidirect
30. #63908C22semidirect
32. #63856C22semidirect
33. C2×#3717C22semidirect
35. C2×#3714C22semidirect
36. #63648C22semidirect
37. C3×(C2×D3)⋊C8C22semidirect
38. #63563C22semidirect
46. C2×#908D3semidirect
55. #5126D3semidirect
67. C2×C4⋊(C3⋊D3)D4semidirect
75. C2×C3×D12D4semidirect
77. C2×C3×D12C23semidirect
83. C2×C3×Dic6C23semidirect
91. C2×C32×C8C23semidirect
93. C4⋊(C3⋊Dic3)C23semidirect
96. C2×C3×C3⋊C8C23semidirect
115. C2×#235C2×D3semidirect
131. C2×C3×M16C2×D3semidirect
132. C2×C3×M16C2×D3semidirect
149. C2×#208C2×D3semidirect
153. C2×D24C2×D3semidirect
155. C2×#204C2×D3semidirect
162. (C2×D3)⋊C8C2×D3semidirect
275. C2×D12#67semidirect
277. C2×D12C22×D3semidirect
283. C2×Dic6C22×D3semidirect
292. C2×C3×C8C22×D3semidirect
293. C2×C3×C8C22×D3semidirect
312. C2×C3⋊C8C22×D3semidirect
331. C2×C3×D3AGL(1,ℤ/8)semidirect
356. C2×M16D32semidirect
509. C2×C8C2×D32semidirect
553. C2×D3#908semidirect
570. C32#3003semidirect
654. C3#78637semidirect
655. C3#83944semidirect

Maximal subgroups

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

subgroupindex
C22×D3×D122
C2×C3×#9082
#105950222
C2×#638252
#105928302
C3×#51262
#105910862
#105909442
#105909422
#839443
#786373