Finite Group Databasebeta

← #11865878

Subgroups — #11865878

Order 1152.

1159 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#908C211yesmaximal, characteristic, complemented
2#10595032C211yesmaximal, characteristic, complemented
3C2×#63898C211yesmaximal, characteristic, complemented
4C2×#63823C211yesmaximal, characteristic, complemented
5#10592817C211yesmaximal, characteristic, complemented
6C3×#5133C211yesmaximal, characteristic, complemented
7#10591087C211yesmaximal, characteristic, complemented
8#10590751C212yesmaximal, complemented
9#10590750C212yesmaximal, complemented
10#10590749C212yesmaximal, complemented
11#10590748C212yesmaximal, complemented
12#83931—31nomaximal
13#78910—31nomaximal
14C2×C3×#235C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C22×C3×D12C2211yescharacteristic
17C22×D3×Dic3—21no—
18C2×C32×M16C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×#3748C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C3×#908—24no—
23C2×C3×D24C2212yes—
24C2×C3×#204C2212yes—
25#63980—21no—
26#63980—21no—
27C2×(C2×D3)⋊Dic3—21no—
28#63914C2211yescharacteristic, complemented
29C4×#625—21no—
30C4×#625—21no—
31#63898—21no—
32#63898—21no—
33#63898C2212yes—
34#63898C2212yes—
35#63873C2211yescharacteristic, complemented
36#63863C2211yescharacteristic, complemented
37#63863C2211yescharacteristic, complemented
38C2×#3715C2212yes—
39#63823—24no—
40C2×#3713C2212yes—
41#63641C2212yescomplemented
42#63641C2212yescomplemented
43C3×#821C2212yescomplemented
44C3×#816C2212yescomplemented
45#63565C2212yescomplemented
46#63562C2212yescomplemented
47C2×C3×AGL(1,ℤ/8)—31no—
48#5832—31no—
49#5832—31no—
50C2×#949—31no—
51C2×D4×Dic3—31no—
52C2×#932—31no—
53C2×#908D311yescharacteristic, complemented
54C2×#893—31no—
55C3×#417—31no—
56#5232—31no—
57#5165—32no—
58#5162—32no—
59#5153—32no—
60#5150—32no—
61#5133D311yescharacteristic, complemented
62#5118—31no—
63#5118—31no—
64#5118—61no—
65#4966—31no—
66#4819—32no—
67#4818—32no—
68#4787—32no—
69#4786—32no—
70C23×C3×D3—21no—
71C22×C32×C4C2311yescharacteristic
72C22×C3⋊Dic3D411yescharacteristic
73C22×C3⋊Dic3D411yescharacteristic
74C2×C3×#67—21no—
75C2×C3×#67—21no—
76C22×C3×Dic3—21no—
77C3×#235—22no—
78C3×#235—22no—
79C3×#235—22no—
80C3×#235—22no—
81C2×C3×D12—21no—
82C2×C3×D12—22no—
83C2×C3×D12D414yescomplemented
84C2×C3×D12C2311yescharacteristic
85C2×C3×D12C2311yescharacteristic
86C2×C3×D12C2312yes—
87C2×C3×C4×D3—21no—
88C2×C3×C4×D3—21no—
89C2×C3×Dic6C2311yescharacteristic
90C2×C3×Dic6C2311yescharacteristic
91C2×#625—21no—
92C2×#625—21no—
93C2×D3×Dic3—22no—
94C2×D3×Dic3—22no—
95C2×D3×Dic3—44no—
96C32×M16—22no—
97C2×C32×C8C2312yes—
98C4×C3⋊Dic3D411yescharacteristic
99C4×C3⋊Dic3D411yescharacteristic
100C4×C3⋊Dic3C2311yescharacteristic
101C4×C3⋊Dic3C2311yescharacteristic
102#3748—22no—
103C2×C3⋊(C3⋊C8)C2312yes—
104C3×C4⋊Dic3—21no—
105C3×C4⋊Dic3C2312yes—
106C3×D24—24no—
107C3×#204—24no—
108#3724—21no—
109#3724—21no—
110(C2×D3)⋊Dic3—21no—
111(C2×D3)⋊Dic3—21no—
112(C2×D3)⋊Dic3—21no—
113(C2×D3)⋊Dic3—21no—
114(C2×D3)⋊Dic3—22no—
115(C2×D3)⋊Dic3—22no—
116#3715—24no—
117#3713—24no—
118#3036—91noSylow
119C2×C3×#41—31no—
120C2×C3×#41—31no—
121C22×C3×D4—31no—
122C23×Dic3—61no—
123C2×#235C2×D311yescharacteristic
124C2×#235C2×D311yescharacteristic
125C22×D12C2×D311yescharacteristic
126C22×C4×D3—61no—
127C3×AGL(1,ℤ/8)—64no—
128C2×C3×SD16—32no—
129C2×C3×D8—32no—
130C2×C3×M16—21no—
131C2×C3×M16C2×D311yescharacteristic
132C2×C3×M16C2×D311yescharacteristic
133C2×C3×C4⋊C4—31no—
134C2×#217—61no—
135#949—64no—
136#947—31no—
137#947—31no—
138#944—31no—
139#944—31no—
140C2×#215—32no—
141#940—31no—
142#940—31no—
143#939—61no—
144#939—61no—
145#939—61no—
146#939—61no—
147#936—31no—
148#936—31no—
149D4×Dic3—32no—
150D4×Dic3—32no—
151D4×Dic3—61no—
152D4×Dic3—61no—
153C2×#214—32no—
154#932—64no—
155C2×#213—32no—
156C2×#213—32no—
157C4×#67—61no—
158C4×#67—61no—
159C4×#67—61no—
160C4×#67—61no—
161C2×(C2×D3)⋊C4—61no—
162C2×C4⋊Dic3C2×D311yescharacteristic
163C2×C4×Dic3—31no—
164C2×C4×Dic3—31no—
165C2×C4×Dic3—61no—
166C2×#208—31no—
167C2×#208—31no—
168C2×#208—61no—
169#908—24no—
170C2×D24C2×D312yes—
171C2×#204C2×D312yes—
172#893—32no—
173#893—32no—
174#893—61no—
175#893—61no—
176C3×#103—32no—
177C3×#102—32no—
178#835—32no—
179#832—32no—
180#821C2×D312yescomplemented
181#816C2×D312yescomplemented
182Dic3⋊C8—32no—
183Dic3⋊C8—32no—
184Dic3⋊C8—32no—
185Dic3⋊C8—32no—
186Dic3⋊C8—62no—
187Dic3⋊C8—62no—
188#810—32no—
189#809—32no—
190C23×C32C2×D411yescharacteristic
191C22×C3×D3—24no—
192C22×C3×D3—22no—
193C22×C3×D3—21no—
194C22×C3×D3—21no—
195C22×C3×D3—42no—
196C22×C3×D3—42no—
197C2×C32×C4C2×D411yescharacteristic
198C2×C32×C4C2×D412yes—
199C2×C32×C4#4112yes—
200C2×C32×C4C2411yescharacteristic
201C2×C3⋊Dic3—22no—
202C2×C3⋊Dic3—41no—
203C2×C3⋊Dic3C2×D411yescharacteristic
204C2×C3⋊Dic3C2×D411yescharacteristic
205C2×C3⋊Dic3C2×D411yescharacteristic
206C2×C3⋊Dic3C2×D411yescharacteristic
207C3×#67—42no—
208C3×#67—42no—
209C2×C3×Dic3—21no—
210C2×C3×Dic3—21no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—42no—
213C3×D12—24no—
214C3×D12—21no—
215C3×D12—21no—
216C3×D12—22no—
217C3×D12—21no—
218C3×D12—21no—
219C3×D12C2×D414yes—
220C3×C4×D3—42no—
221C3×C4×D3—42no—
222C3×Dic6—21no—
223C3×Dic6—21no—
224C3×Dic6—21no—
225C3×Dic6—21no—
226#625—42no—
227#625—42no—
228D3×Dic3—44no—
229D3×Dic3—44no—
230C32×C8—22no—
231C3⋊(C3⋊C8)—22no—
232C2×AGL(1,ℤ/8)—31no—
233C2×AGL(1,ℤ/8)—91no—
234#532—91no—
235C2×C4×D4—91no—
236#463—92no—
237#463—92no—
238#461—92no—
239#459—92no—
240#423—91no—
241#417—31no—
242#417—91no—
243C24×C3—61no—
244C23×D3—21no—
245C3×#41—62no—
246C3×#41—62no—
247C3×#41—62no—
248C3×#41—62no—
249C2×C3×Q8—31no—
250C2×C3×Q8—31no—
251C2×C3×D4—34no—
252C2×C3×D4—32no—
253C2×C3×D4—31no—
254C2×C3×D4—31no—
255C2×C3×D4—61no—
256C2×C3×D4—61no—
257C2×C3×D4—62no—
258C2×C3×D4—61no—
259C22×C3×C4—21no—
260C22×C3×C4—61no—
261C22×C3×C4—61no—
262C22×C3×C4—61no—
263C22×C3×C4C22×D311yescharacteristic
264C22×C3×C4C22×D311yescharacteristic
265C2×#67—21no—
266C2×#67—21no—
267C2×#67—61no—
268C2×#67—61no—
269C2×#67—61no—
270C2×#67—61no—
271C22×Dic3—21no—
272C22×Dic3—31no—
273C22×Dic3—31no—
274C22×Dic3—31no—
275C22×Dic3—31no—
276C22×Dic3—61no—
277C22×Dic3—61no—
278C22×Dic3—62no—
279C22×Dic3—62no—
280C22×Dic3—124no—
281#235—22no—
282#235—22no—
283#235—22no—
284#235—22no—
285C2×D12—21no—
286C2×D12—22no—
287C2×D12#6714yescomplemented
288C2×D12C22×D311yescharacteristic
289C2×D12C22×D311yescharacteristic
290C2×D12C22×D312yes—
291C2×C4×D3—21no—
292C2×C4×D3—21no—
293C2×C4×D3—62no—
294C2×C4×D3—62no—
295C2×C4×D3—124no—
296C2×Dic6C22×D311yescharacteristic
297C2×Dic6C22×D311yescharacteristic
298C3×SD16—64no—
299C3×D8—64no—
300C3×M16—22no—
301C3×M16—22no—
302C3×M16—42no—
303C2×C3×C8—22no—
304C2×C3×C8C22×D312yes—
305C2×C3×C8C22×D312yes—
306C3×C4⋊C4—32no—
307C3×C4⋊C4—61no—
308#217—61no—
309#217—61no—
310#217—61no—
311#217—61no—
312#217—62no—
313#217—62no—
314#215—64no—
315#214—64no—
316#213—64no—
317#213—64no—
318(C2×D3)⋊C4—62no—
319(C2×D3)⋊C4—62no—
320(C2×D3)⋊C4—61no—
321(C2×D3)⋊C4—61no—
322(C2×D3)⋊C4—61no—
323(C2×D3)⋊C4—61no—
324C4⋊Dic3—21no—
325C4⋊Dic3C22×D312yes—
326Dic3⋊C4—61no—
327Dic3⋊C4—61no—
328Dic3⋊C4—61no—
329Dic3⋊C4—61no—
330C4×Dic3—31no—
331C4×Dic3—31no—
332C4×Dic3—31no—
333C4×Dic3—31no—
334C4×Dic3—31no—
335C4×Dic3—31no—
336C4×Dic3—31no—
337C4×Dic3—31no—
338C4×Dic3—61no—
339C4×Dic3—61no—
340C4×Dic3—61no—
341C4×Dic3—61no—
342#208—62no—
343#208—62no—
344#208—122no—
345C2×C3⋊C8—32no—
346C2×C3⋊C8—32no—
347C2×C3⋊C8—62no—
348D24—24no—
349#204—24no—
350C22×C32—21no—
351C22×C32—21no—
352C22×C32#12112yes—
353C22×C32C22×D411yescharacteristic
354C2×C3×D3—24no—
355C2×C3×D3—48no—
356C2×C3×D3—42no—
357C2×C3×D3—42no—
358C2×C3×D3—41no—
359C2×C3×D3—41no—
360C2×C3×D3—41no—
361C2×C3×D3—41no—
362C2×C3×D3—41no—
363C2×C3×D3—41no—
364C32×C4#12112yes—
365C32×C4C22×D411yescharacteristic
366C32×C4C2×#4111yescharacteristic
367C3⋊Dic3—21no—
368C3⋊Dic3—21no—
369C3⋊Dic3—21no—
370C3⋊Dic3AGL(1,ℤ/8)12yescomplemented
371C3×Dic3—41no—
372C3×Dic3—41no—
373C3×Dic3—42no—
374C2×#41—31no—
375C2×#41—31no—
376C22×D4—31no—
377C23×C4—181no—
378AGL(1,ℤ/8)—64no—
379AGL(1,ℤ/8)—184no—
380C2×SD16—32no—
381C2×SD16—92no—
382C2×D8—32no—
383C2×D8—92no—
384C2×M16—91no—
385C2×M16D3211yescharacteristic
386C4⋊Q8—91no—
387#127—91no—
388#124—91no—
389#124—91no—
390#121—181no—
391#121—181no—
392C4×D4—92no—
393C4×D4—92no—
394C4×D4—181no—
395C4×D4—181no—
396C4×D4—181no—
397C4×D4—181no—
398C2×C4⋊C4—31no—
399C2×C22⋊C4—181no—
400C2×C42—91no—
401C4⋊C8—92no—
402C4⋊C8—92no—
403#103—32no—
404#103—92no—
405#102—32no—
406#102—92no—
407C23×C3—21no—
408C23×C3—64no—
409C23×C3—62no—
410C23×C3—61no—
411C23×C3—61no—
412C23×C3—122no—
413C23×C3—122no—
414C23×C3D3×D411yescharacteristic
415C23×C3D3×D411yescharacteristic
416C22×D3—24no—
417C22×D3—22no—
418C22×D3—21no—
419C22×D3—21no—
420C22×D3—42no—
421C22×D3—42no—
422C3×Q8—61no—
423C3×Q8—61no—
424C3×Q8—61no—
425C3×Q8—61no—
426C3×D4—34no—
427C3×D4—64no—
428C3×D4—62no—
429C3×D4—61no—
430C3×D4—61no—
431C3×D4—61no—
432C3×D4—61no—
433C3×D4—122no—
434C3×D4—122no—
435C2×C3×C4—21no—
436C2×C3×C4—22no—
437C2×C3×C4—21no—
438C2×C3×C4—22no—
439C2×C3×C4—61no—
440C2×C3×C4—61no—
441C2×C3×C4—62no—
442C2×C3×C4—122no—
443C2×C3×C4—122no—
444C2×C3×C4—122no—
445C2×C3×C4#23512yes—
446C2×C3×C4D3×D411yescharacteristic
447C2×C3×C4D3×D411yescharacteristic
448C2×C3×C4D3×D412yes—
449C2×C3×C4#23712yes—
450C2×C3×C4C2×#6712yes—
451C2×C3×C4C23×D311yescharacteristic
452C2×C3×C4C23×D311yescharacteristic
453#67—42no—
454#67—42no—
455#67—122no—
456#67—122no—
457#67—122no—
458#67—122no—
459C2×Dic3—21no—
460C2×Dic3—21no—
461C2×Dic3—22no—
462C2×Dic3—31no—
463C2×Dic3—31no—
464C2×Dic3—31no—
465C2×Dic3—31no—
466C2×Dic3—31no—
467C2×Dic3—31no—
468C2×Dic3—31no—
469C2×Dic3—31no—
470C2×Dic3—42no—
471C2×Dic3—61no—
472C2×Dic3—61no—
473C2×Dic3—61no—
474C2×Dic3—61no—
475C2×Dic3—62no—
476C2×Dic3—62no—
477C2×Dic3—122no—
478C2×Dic3—124no—
479C2×Dic3—124no—
480C2×Dic3—121no—
481C2×Dic3—121no—
482C2×Dic3—122no—
483D12—24no—
484D12—21no—
485D12—21no—
486D12—22no—
487D12—21no—
488D12—21no—
489D12C2×#6714yes—
490C4×D3—42no—
491C4×D3—42no—
492C4×D3—124no—
493C4×D3—124no—
494Dic6—21no—
495Dic6—21no—
496Dic6—21no—
497Dic6—21no—
498C3×C8—22no—
499C3×C8—22no—
500C3×C8—42no—
501C3⋊C8—62no—
502C3⋊C8—62no—
503C3⋊C8—122no—
504C2×C32—22no—
505C2×C32C2×#12111yescharacteristic
506C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
507C2×C32#57511yescharacteristic
508C3×D3—44no—
509C3×D3—81no—
510C3×D3—81no—
511C24—61no—
512#41—62no—
513#41—62no—
514#41—62no—
515#41—62no—
516C2×Q8—31no—
517C2×Q8—31no—
518C2×D4—32no—
519C2×D4—31no—
520C2×D4—31no—
521C2×D4—34no—
522C2×D4—61no—
523C2×D4—61no—
524C2×D4—62no—
525C2×D4—61no—
526C2×D4—181no—
527C2×D4—181no—
528C22×C4—61no—
529C22×C4—61no—
530C22×C4—61no—
531C22×C4—91no—
532C22×C4—91no—
533C22×C4—182no—
534C22×C4—182no—
535C22×C4—364no—
536C22×C4C2×D3211yescharacteristic
537SD16—64no—
538SD16—184no—
539D8—64no—
540D8—184no—
541M16—22no—
542M16—182no—
543C2×C8—92no—
544C2×C8C2×D3212yes—
545C4⋊C4—32no—
546C4⋊C4—61no—
547C4⋊C4—181no—
548C4⋊C4—181no—
549C22⋊C4—182no—
550C22⋊C4—182no—
551C22⋊C4—181no—
552C22⋊C4—181no—
553C22⋊C4—181no—
554C22⋊C4—181no—
555C42—91no—
556C42—91no—
557C42—91no—
558C42—91no—
559C22×C3—21no—
560C22×C3—21no—
561C22×C3—21no—
562C22×C3—21no—
563C22×C3—21no—
564C22×C3—22no—
565C22×C3—41no—
566C22×C3—41no—
567C22×C3—64no—
568C22×C3—128no—
569C22×C3—122no—
570C22×C3—122no—
571C22×C3—121no—
572C22×C3—121no—
573C22×C3—121no—
574C22×C3—121no—
575C22×C3—121no—
576C22×C3—121no—
577C22×C3#88412yes—
578C22×C3#93912yes—
579C22×C3C2×D3×D411yescharacteristic
580C22×C3C2×D3×D411yescharacteristic
581C2×D3—24no—
582C2×D3—48no—
583C2×D3—42no—
584C2×D3—42no—
585C2×D3—41no—
586C2×D3—41no—
587C2×D3—41no—
588C2×D3—41no—
589C2×D3—41no—
590C2×D3—41no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—22no—
594C3×C4—121no—
595C3×C4—122no—
596C3×C4—121no—
597C3×C4#88412yes—
598C3×C4#93912yes—
599C3×C4C2×#23511yescharacteristic
600C3×C4C2×D3×D411yescharacteristic
601C3×C4C2×#23711yescharacteristic
602C3×C4C22×#6711yescharacteristic
603Dic3—32no—
604Dic3—32no—
605Dic3—41no—
606Dic3—42no—
607Dic3—41no—
608Dic3—62no—
609Dic3—62no—
610Dic3—61no—
611Dic3—61no—
612Dic3—61no—
613Dic3—61no—
614Dic3—61no—
615Dic3—61no—
616Dic3—121no—
617Dic3—121no—
618C32#303611yescharacteristic, complemented, Sylow
619C23—62no—
620C23—64no—
621C23—61no—
622C23—61no—
623C23—122no—
624C23—122no—
625C23#380211yescharacteristic
626Q8—61no—
627Q8—61no—
628Q8—61no—
629Q8—61no—
630D4—34no—
631D4—62no—
632D4—61no—
633D4—61no—
634D4—61no—
635D4—61no—
636D4—64no—
637D4—122no—
638D4—122no—
639D4—362no—
640D4—362no—
641C2×C4—62no—
642C2×C4—61no—
643C2×C4—61no—
644C2×C4—91no—
645C2×C4—91no—
646C2×C4—91no—
647C2×C4—91no—
648C2×C4—122no—
649C2×C4—122no—
650C2×C4—122no—
651C2×C4—182no—
652C2×C4—364no—
653C2×C4—364no—
654C2×C4—361no—
655C2×C4#379512yes—
656C2×C4#380211yescharacteristic
657C2×C4D3×#6712yes—
658C2×C4C22×D3211yescharacteristic
659C8—22no—
660C8—182no—
661C2×C3—22no—
662C2×C3—22no—
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—42no—
667C2×C3—124no—
668C2×C3—241no—
669C2×C3—241no—
670C2×C3C2×#88411yescharacteristic
671C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
672C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
673C2×C3#577311yescharacteristic
674C2×C3#577711yescharacteristic
675C2×C3C2×#93911yescharacteristic
676D3—44no—
677D3—81no—
678D3—81no—
679C22—21no—
680C22—21no—
681C22—64no—
682C22—128no—
683C22—122no—
684C22—122no—
685C22—121no—
686C22—121no—
687C22—121no—
688C22—121no—
689C22—121no—
690C22—121no—
691C22#6388512yes—
692C22C2×#380211yescharacteristic
693C4—92no—
694C4—121no—
695C4—121no—
696C4—122no—
697C4—181no—
698C4—181no—
699C4—181no—
700C4#6388512yes—
701C4C2×#379511yescharacteristic
702C4C2×D3×#6711yescharacteristic
703C3—21no—
704C3#7891011yescharacteristic, complemented
705C3#8393111yescharacteristic, complemented
706C2—22no—
707C2—124no—
708C2—241no—
709C2—241no—
710C2#1059471611yescharacteristic
711C2#1059471811yescharacteristic
712C2C2×#6388511yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
hypercenterC2×M16D32
hypocenterC32#3036
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. C2×C3×#908C2semidirect
2. #10595032C2semidirect
3. C2×#63898C2semidirect
4. C2×#63823C2semidirect
5. #10592817C2semidirect
6. C3×#5133C2semidirect
7. #10591087C2semidirect
8. #10590751C2semidirect
9. #10590750C2semidirect
10. #10590749C2semidirect
11. #10590748C2semidirect
28. #63914C22semidirect
35. #63873C22semidirect
36. #63863C22semidirect
37. #63863C22semidirect
41. #63641C22semidirect
42. #63641C22semidirect
43. C3×#821C22semidirect
44. C3×#816C22semidirect
45. #63565C22semidirect
46. #63562C22semidirect
53. C2×#908D3semidirect
61. #5133D3semidirect
83. C2×C3×D12D4semidirect
180. #821C2×D3semidirect
181. #816C2×D3semidirect
287. C2×D12#67semidirect
370. C3⋊Dic3AGL(1,ℤ/8)semidirect
618. C32#3036semidirect
704. C3#78910semidirect
705. C3#83931semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9082
#105950322
C2×#638982
C2×#638232
#105928172
C3×#51332
#105910872
#105907512
#105907502
#105907492
#105907482
#839313
#789103