Finite Group Databasebeta

← #11863960

Subgroups — #11863960

Order 1152.

2083 conjugacy classes of subgroups.

The subgroup lattice has 667 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3802C211yesmaximal, characteristic, complemented
2C2×C3×#908C211yesmaximal, characteristic, complemented
3#10595034C211yesmaximal, characteristic, complemented
4C2×#63823C211yesmaximal, characteristic, complemented
5#10592825C211yesmaximal, characteristic, complemented
6C3×#5131C211yesmaximal, characteristic, complemented
7#10591085C211yesmaximal, characteristic, complemented
8#10590945C214yesmaximal, complemented
9#10590943C214yesmaximal, complemented
10#83944—31nomaximal
11#78926—31nomaximal
12C23×D32—21no—
13C22×C4×C3⋊D3C2211yescharacteristic
14C2×C3×#235C2211yescharacteristic, complemented
15C22×C3×D12C2211yescharacteristic
16C22×C3×D12C2211yescharacteristic
17C22×#625—21no—
18C2×#3802—22no—
19C2×#3802—24no—
20C2×#3802—24no—
21C2×#3802C2214yes—
22C2×C32×M16C2211yescharacteristic, complemented
23C2×#3748C2211yescharacteristic, complemented
24C3×#926C2211yescharacteristic, complemented
25C3×#908—24no—
26C2×C3×D24C2212yescomplemented
27C2×C3×#204C2212yescomplemented
28#63981—21no—
29#63962—21no—
30#63916C2212yescomplemented
31C4×#626—22no—
32#63871C2212yescomplemented
33C2×#3715C2212yescomplemented
34#63823—24no—
35C2×#3713C2212yescomplemented
36#63647C2214yescomplemented
37C3×#821C2214yescomplemented
38#63562C2214yescomplemented
39C22×D3×D4—31no—
40C22×D3×D4—31no—
41C2×C3×AGL(1,ℤ/8)—31no—
42#5828—31no—
43C2×#949—31no—
44C2×#932—31no—
45C2×#908D311yescharacteristic, complemented
46#5524—31no—
47C3×#418—31no—
48#5215—31no—
49#5169—34no—
50#5156—34no—
51#5131D311yescharacteristic, complemented
52#5126—31no—
53#5126—31no—
54#5126—61no—
55#5001—31no—
56#4776—34no—
57#4773—34no—
58C23×C3⋊D3D411yescharacteristic
59C23×C3×D3—21no—
60C23×C3×D3—21no—
61C22×D32—28no—
62C22×D32—24no—
63C22×D32—48no—
64C22×C32×C4C2311yescharacteristic
65C22×C3⋊Dic3D411yescharacteristic
66C2×C4×C3⋊D3—22no—
67C2×C4×C3⋊D3—22no—
68C2×C4×C3⋊D3D412yes—
69C2×C4×C3⋊D3C2312yes—
70C2×C3×#67—21no—
71C3×#235—22no—
72C3×#235—22no—
73C2×C3×D12—21no—
74C2×C3×D12—21no—
75C2×C3×D12—22no—
76C2×C3×D12—22no—
77C2×C3×D12D414yescomplemented
78C2×C3×D12D414yescomplemented
79C2×C3×D12C2312yes—
80C2×C3×D12C2312yes—
81C2×C3×D12C2311yescharacteristic, complemented
82C2×C3×C4×D3—21no—
83C2×C3×Dic6C2311yescharacteristic, complemented
84C2×#626—22no—
85C2×#625—28no—
86C2×#625—24no—
87#3802—216no—
88#3802—28no—
89#3802—28no—
90C32×M16—22no—
91C2×C32×C8C2312yescomplemented
92#3748—22no—
93C2×C3⋊(C3⋊C8)C2312yescomplemented
94C3×#217—21no—
95C3×C4⋊Dic3C2312yescomplemented
96C3×C4×Dic3—21no—
97C3×D24—24no—
98C3×#204—24no—
99Dic3⋊Dic3—22no—
100#3722—22no—
101(C2×D3)⋊Dic3—22no—
102#3715—24no—
103#3713—24no—
104#3003—91noSylow
105C24×D3—61no—
106C24×D3—61no—
107C2×C3×#41—31no—
108C22×C3×D4—31no—
109C22×C3×D4—31no—
110C22×#67—61no—
111C22×#67—61no—
112C2×D3×D4—34no—
113C2×D3×D4—34no—
114C2×D3×D4—62no—
115C2×D3×D4—62no—
116C2×D3×D4—64no—
117C2×D3×D4—64no—
118C2×D3×D4—64no—
119C2×D3×D4—64no—
120C2×#235C2×D311yescharacteristic, complemented
121C22×D12C2×D311yescharacteristic
122C22×D12C2×D311yescharacteristic
123C22×C4×D3—31no—
124C22×C4×D3—31no—
125C22×C4×D3—61no—
126C3×AGL(1,ℤ/8)—64no—
127C2×C3×SD16—32no—
128C2×C3×D8—32no—
129C2×C3×M16—21no—
130C2×C3×M16C2×D311yescharacteristic, complemented
131C2×C3×M16C2×D311yescharacteristic, complemented
132C3×#117—31no—
133#949—64no—
134#946—32no—
135C2×#215—32no—
136#938—32no—
137#937—61no—
138#935—61no—
139C2×#214—32no—
140#932—64no—
141C2×#213—32no—
142C2×#213—32no—
143C4×#67—62no—
144#926C2×D311yescharacteristic, complemented
145C2×#208—31no—
146C2×#208—31no—
147C2×#208—61no—
148#908—24no—
149C2×D24C2×D312yescomplemented
150C2×#204C2×D312yescomplemented
151#897—32no—
152#895—32no—
153#886—61no—
154#882—61no—
155C4×D12—62no—
156C3×#102—34no—
157#832—34no—
158#821C2×D314yescomplemented
159(C2×D3)⋊C8—34no—
160(C2×D3)⋊C8—34no—
161(C2×D3)⋊C8—64no—
162#809—34no—
163C23×C32C2×D411yescharacteristic
164C22×C3⋊D3—22no—
165C22×C3⋊D3—24no—
166C22×C3⋊D3C2×D412yes—
167C22×C3×D3—24no—
168C22×C3×D3—24no—
169C22×C3×D3—22no—
170C22×C3×D3—22no—
171C22×C3×D3—21no—
172C22×C3×D3—44no—
173C22×C3×D3—44no—
174C2×D32—216no—
175C2×D32—432no—
176C2×D32—48no—
177C2×D32—48no—
178C2×C32×C4C2×D412yes—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2×D412yes—
181C2×C32×C4C2411yescharacteristic
182C2×C3⋊Dic3—22no—
183C2×C3⋊Dic3C2×D412yes—
184C4×C3⋊D3—24no—
185C4×C3⋊D3—22no—
186C4×C3⋊D3—22no—
187C3×#67—42no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—21no—
190C3×D12—24no—
191C3×D12—24no—
192C3×D12—22no—
193C3×D12—22no—
194C3×D12—21no—
195C3×D12—21no—
196C3×D12C2×D414yes—
197C3×D12C2×D414yes—
198C3×C4×D3—42no—
199C3×Dic6—21no—
200C3×Dic6—21no—
201#626—44no—
202#625—216no—
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—31no—
212#418—91no—
213#407—91no—
214C24×C3—61no—
215C24×C3—61no—
216C23×D3—21no—
217C23×D3—21no—
218C23×D3—31no—
219C23×D3—31no—
220C23×D3—61no—
221C23×D3—64no—
222C23×D3—64no—
223C23×D3—68no—
224C23×D3—68no—
225C23×D3—128no—
226C23×D3—128no—
227C3×#41—62no—
228C3×#41—62no—
229C2×C3×Q8—31no—
230C2×C3×D4—34no—
231C2×C3×D4—34no—
232C2×C3×D4—32no—
233C2×C3×D4—32no—
234C2×C3×D4—31no—
235C2×C3×D4—61no—
236C2×C3×D4—62no—
237C2×C3×D4—61no—
238C2×C3×D4—61no—
239C2×C3×D4—62no—
240C22×C3×C4—21no—
241C22×C3×C4—61no—
242C22×C3×C4C22×D311yescharacteristic
243C22×C3×C4C22×D311yescharacteristic
244C2×#67—21no—
245C2×#67—62no—
246C2×#67—64no—
247C2×#67—64no—
248C2×#67—68no—
249C2×#67—68no—
250C22×Dic3—31no—
251C22×Dic3—31no—
252C22×Dic3—61no—
253D3×D4—68no—
254D3×D4—68no—
255D3×D4—616no—
256D3×D4—616no—
257D3×D4—68no—
258D3×D4—68no—
259#235—22no—
260#235—22no—
261C2×D12—22no—
262C2×D12—21no—
263C2×D12—21no—
264C2×D12—22no—
265C2×D12—62no—
266C2×D12D1214yescomplemented
267C2×D12#6714yescomplemented
268C2×D12C22×D312yes—
269C2×D12C22×D312yes—
270C2×D12C22×D311yescharacteristic, complemented
271C2×C4×D3—21no—
272C2×C4×D3—32no—
273C2×C4×D3—32no—
274C2×C4×D3—32no—
275C2×C4×D3—32no—
276C2×C4×D3—62no—
277C2×C4×D3—62no—
278C2×C4×D3—62no—
279C2×C4×D3—62no—
280C2×C4×D3—62no—
281C2×C4×D3—62no—
282C2×C4×D3—122no—
283C2×C4×D3—122no—
284C2×Dic6C22×D311yescharacteristic, complemented
285C3×SD16—64no—
286C3×D8—64no—
287C3×M16—22no—
288C3×M16—22no—
289C3×M16—42no—
290C2×C3×C8—22no—
291C2×C3×C8C22×D312yescomplemented
292C2×C3×C8C22×D312yescomplemented
293C3×C4⋊C4—32no—
294C3×C22⋊C4—61no—
295C3×C42—61no—
296#217—21no—
297#217—62no—
298#215—64no—
299#214—64no—
300#213—64no—
301#213—64no—
302(C2×D3)⋊C4—62no—
303(C2×D3)⋊C4—62no—
304(C2×D3)⋊C4—62no—
305C4⋊Dic3—62no—
306C4⋊Dic3C22×D312yescomplemented
307Dic3⋊C4—62no—
308C4×Dic3—21no—
309#208—62no—
310#208—62no—
311#208—122no—
312C2×C3⋊C8—32no—
313C2×C3⋊C8—32no—
314C2×C3⋊C8—62no—
315D24—24no—
316#204—24no—
317C22×C32—22no—
318C22×C32#12012yes—
319C22×C32C22×D411yescharacteristic
320C2×C3⋊D3—28no—
321C2×C3⋊D3—22no—
322C2×C3⋊D3—22no—
323C2×C3⋊D3AGL(1,ℤ/8)14yescomplemented
324C2×C3×D3—24no—
325C2×C3×D3—24no—
326C2×C3×D3—48no—
327C2×C3×D3—48no—
328C2×C3×D3—44no—
329C2×C3×D3—44no—
330C2×C3×D3—41no—
331C2×C3×D3—42no—
332D32—432no—
333C32×C4#12012yes—
334C32×C4C22×D411yescharacteristic
335C32×C4C22×D411yescharacteristic
336C3⋊Dic3—22no—
337C3×Dic3—41no—
338C3×Dic3—42no—
339C25—181no—
340C2×#41—31no—
341C22×D4—31no—
342C22×D4—31no—
343C22×D4—94no—
344C22×D4—182no—
345C22×D4—181no—
346C22×D4—184no—
347C22×D4—184no—
348C23×C4—91no—
349AGL(1,ℤ/8)—64no—
350AGL(1,ℤ/8)—184no—
351C2×SD16—32no—
352C2×SD16—92no—
353C2×D8—32no—
354C2×D8—92no—
355C2×M16—91no—
356C2×M16D3211yescharacteristic, complemented
357#123—181no—
358C22⋊Q8—92no—
359#121—92no—
360#120—181no—
361C4×D4—182no—
362#117—31no—
363#102—34no—
364#102—94no—
365C22⋊C8—94no—
366C23×C3—21no—
367C23×C3—64no—
368C23×C3—64no—
369C23×C3—62no—
370C23×C3—62no—
371C23×C3—61no—
372C23×C3—124no—
373C23×C3—124no—
374C23×C3D3×D411yescharacteristic
375C23×C3D3×D411yescharacteristic
376C22×D3—24no—
377C22×D3—24no—
378C22×D3—22no—
379C22×D3—22no—
380C22×D3—21no—
381C22×D3—32no—
382C22×D3—32no—
383C22×D3—44no—
384C22×D3—44no—
385C22×D3—62no—
386C22×D3—616no—
387C22×D3—616no—
388C22×D3—64no—
389C22×D3—64no—
390C22×D3—62no—
391C22×D3—62no—
392C22×D3—124no—
393C22×D3—122no—
394C22×D3—128no—
395C22×D3—128no—
396C22×D3—1232no—
397C22×D3—1232no—
398C22×D3—128no—
399C22×D3—128no—
400C3×Q8—61no—
401C3×Q8—61no—
402C3×D4—34no—
403C3×D4—34no—
404C3×D4—64no—
405C3×D4—64no—
406C3×D4—62no—
407C3×D4—61no—
408C3×D4—61no—
409C3×D4—62no—
410C3×D4—122no—
411C2×C3×C4—21no—
412C2×C3×C4—22no—
413C2×C3×C4—21no—
414C2×C3×C4—22no—
415C2×C3×C4—61no—
416C2×C3×C4—62no—
417C2×C3×C4—122no—
418C2×C3×C4C2×D1212yes—
419C2×C3×C4D3×D412yes—
420C2×C3×C4D3×D411yescharacteristic
421C2×C3×C4D3×D411yescharacteristic
422C2×C3×C4D3×D412yes—
423C2×C3×C4C2×#6712yes—
424C2×C3×C4C23×D311yescharacteristic
425C2×C3×C4C23×D311yescharacteristic
426#67—42no—
427#67—616no—
428#67—616no—
429#67—124no—
430C2×Dic3—22no—
431C2×Dic3—21no—
432C2×Dic3—32no—
433C2×Dic3—32no—
434C2×Dic3—62no—
435C2×Dic3—62no—
436C2×Dic3—62no—
437C2×Dic3—122no—
438D12—24no—
439D12—24no—
440D12—22no—
441D12—22no—
442D12—21no—
443D12—21no—
444D12—124no—
445D12C2×D1214yes—
446D12C2×#6714yes—
447C4×D3—42no—
448C4×D3—64no—
449C4×D3—64no—
450C4×D3—62no—
451C4×D3—62no—
452C4×D3—62no—
453C4×D3—62no—
454C4×D3—122no—
455C4×D3—122no—
456C4×D3—124no—
457Dic6—21no—
458Dic6—21no—
459C3×C8—22no—
460C3×C8—22no—
461C3×C8—42no—
462C3⋊C8—62no—
463C3⋊C8—62no—
464C3⋊C8—122no—
465C2×C32—22no—
466C2×C32C2×#12011yescharacteristic
467C2×C32C2×AGL(1,ℤ/8)12yes—
468C3⋊D3—24no—
469C3×D3—44no—
470C3×D3—44no—
471C3×D3—81no—
472C24—61no—
473C24—61no—
474C24—91no—
475C24—184no—
476C24—188no—
477C24—368no—
478#41—62no—
479#41—62no—
480C2×Q8—31no—
481C2×D4—32no—
482C2×D4—32no—
483C2×D4—31no—
484C2×D4—34no—
485C2×D4—34no—
486C2×D4—61no—
487C2×D4—62no—
488C2×D4—61no—
489C2×D4—61no—
490C2×D4—62no—
491C2×D4—182no—
492C2×D4—184no—
493C2×D4—188no—
494C2×D4—188no—
495C2×D4—1816no—
496C2×D4—188no—
497C22×C4—61no—
498C22×C4—91no—
499C22×C4—92no—
500C22×C4—92no—
501C22×C4—182no—
502C22×C4—182no—
503C22×C4C2×D3211yescharacteristic
504SD16—64no—
505SD16—184no—
506D8—64no—
507D8—184no—
508M16—22no—
509M16—182no—
510C2×C8—92no—
511C2×C8C2×D3212yescomplemented
512C4⋊C4—32no—
513C4⋊C4—182no—
514C22⋊C4—61no—
515C22⋊C4—182no—
516C22⋊C4—182no—
517C42—61no—
518C22×C3—22no—
519C22×C3—22no—
520C22×C3—21no—
521C22×C3—22no—
522C22×C3—42no—
523C22×C3—64no—
524C22×C3—64no—
525C22×C3—128no—
526C22×C3—128no—
527C22×C3—124no—
528C22×C3—124no—
529C22×C3—121no—
530C22×C3—122no—
531C22×C3#88212yes—
532C22×C3#93712yes—
533C22×C3C2×D3×D411yescharacteristic
534C22×C3C2×D3×D411yescharacteristic
535C2×D3—24no—
536C2×D3—24no—
537C2×D3—34no—
538C2×D3—34no—
539C2×D3—48no—
540C2×D3—48no—
541C2×D3—44no—
542C2×D3—44no—
543C2×D3—42no—
544C2×D3—41no—
545C2×D3—64no—
546C2×D3—68no—
547C2×D3—68no—
548C2×D3—62no—
549C2×D3—62no—
550C2×D3—62no—
551C2×D3—62no—
552C2×D3—122no—
553C2×D3—122no—
554C2×D3—128no—
555C2×D3—1232no—
556C2×D3—1232no—
557C3×C4—21no—
558C3×C4—21no—
559C3×C4—22no—
560C3×C4—121no—
561C3×C4—122no—
562C3×C4#88212yes—
563C3×C4#93712yes—
564C3×C4C22×D1211yescharacteristic
565C3×C4C2×D3×D411yescharacteristic
566C3×C4C2×D3×D411yescharacteristic
567C3×C4C22×#6711yescharacteristic
568Dic3—42no—
569Dic3—41no—
570Dic3—62no—
571Dic3—62no—
572Dic3—122no—
573C32#300311yescharacteristic, complemented, Sylow
574C23—62no—
575C23—62no—
576C23—64no—
577C23—64no—
578C23—61no—
579C23—92no—
580C23—124no—
581C23—124no—
582C23—184no—
583C23—1816no—
584C23—182no—
585C23—368no—
586C23—3632no—
587C23—368no—
588C23#380211yescharacteristic
589Q8—61no—
590Q8—61no—
591D4—34no—
592D4—34no—
593D4—62no—
594D4—61no—
595D4—62no—
596D4—61no—
597D4—64no—
598D4—64no—
599D4—122no—
600D4—1816no—
601D4—364no—
602C2×C4—62no—
603C2×C4—61no—
604C2×C4—92no—
605C2×C4—122no—
606C2×C4—182no—
607C2×C4—182no—
608C2×C4—182no—
609C2×C4—184no—
610C2×C4D3×D1212yes—
611C2×C4#380211yescharacteristic
612C2×C4D3×#6712yes—
613C2×C4C22×D3211yescharacteristic
614C8—22no—
615C8—182no—
616C2×C3—22no—
617C2×C3—22no—
618C2×C3—22no—
619C2×C3—21no—
620C2×C3—42no—
621C2×C3—124no—
622C2×C3—124no—
623C2×C3—241no—
624C2×C3C2×#88211yescharacteristic
625C2×C3D3×AGL(1,ℤ/8)12yes—
626C2×C3D3×AGL(1,ℤ/8)12yes—
627C2×C3C2×#93711yescharacteristic
628D3—44no—
629D3—44no—
630D3—64no—
631D3—64no—
632D3—81no—
633D3—124no—
634C22—22no—
635C22—64no—
636C22—64no—
637C22—94no—
638C22—128no—
639C22—128no—
640C22—124no—
641C22—124no—
642C22—122no—
643C22—121no—
644C22—188no—
645C22—182no—
646C22—182no—
647C22—3632no—
648C22#6392212yes—
649C22C2×#380211yescharacteristic
650C4—122no—
651C4—121no—
652C4—182no—
653C4#6392212yes—
654C4C2×D3×D1211yescharacteristic
655C4C2×D3×#6711yescharacteristic
656C3—21no—
657C3#7892611yescharacteristic, complemented
658C3#8394411yescharacteristic, complemented
659C2—22no—
660C2—124no—
661C2—124no—
662C2—184no—
663C2—241no—
664C2#1059471612yes—
665C2C2×#6392211yescharacteristic
subgroupG/H
centerC22C2×#3802
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×#3802C2semidirect
2. C2×C3×#908C2semidirect
3. #10595034C2semidirect
4. C2×#63823C2semidirect
5. #10592825C2semidirect
6. C3×#5131C2semidirect
7. #10591085C2semidirect
8. #10590945C2semidirect
9. #10590943C2semidirect
14. C2×C3×#235C22semidirect
22. C2×C32×M16C22semidirect
23. C2×#3748C22semidirect
24. C3×#926C22semidirect
26. C2×C3×D24C22semidirect
27. C2×C3×#204C22semidirect
30. #63916C22semidirect
32. #63871C22semidirect
33. C2×#3715C22semidirect
35. C2×#3713C22semidirect
36. #63647C22semidirect
37. C3×#821C22semidirect
38. #63562C22semidirect
45. C2×#908D3semidirect
51. #5131D3semidirect
77. C2×C3×D12D4semidirect
78. C2×C3×D12D4semidirect
81. C2×C3×D12C23semidirect
83. C2×C3×Dic6C23semidirect
91. C2×C32×C8C23semidirect
93. C2×C3⋊(C3⋊C8)C23semidirect
95. C3×C4⋊Dic3C23semidirect
120. C2×#235C2×D3semidirect
130. C2×C3×M16C2×D3semidirect
131. C2×C3×M16C2×D3semidirect
144. #926C2×D3semidirect
149. C2×D24C2×D3semidirect
150. C2×#204C2×D3semidirect
158. #821C2×D3semidirect
266. C2×D12D12semidirect
267. C2×D12#67semidirect
270. C2×D12C22×D3semidirect
284. C2×Dic6C22×D3semidirect
291. C2×C3×C8C22×D3semidirect
292. C2×C3×C8C22×D3semidirect
306. C4⋊Dic3C22×D3semidirect
323. C2×C3⋊D3AGL(1,ℤ/8)semidirect
356. C2×M16D32semidirect
511. C2×C8C2×D32semidirect
573. C32#3003semidirect
657. C3#78926semidirect
658. C3#83944semidirect

Maximal subgroups

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

subgroupindex
C22×#38022
C2×C3×#9082
#105950342
C2×#638232
#105928252
C3×#51312
#105910852
#105909452
#105909432
#839443
#789263