Finite Group Databasebeta

← #29575160

Subgroups — #29575160

Order 15616.

966 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839913C211yesmaximal, characteristic
2#21448552C211yesmaximal, characteristic, complemented
3#21445750C211yesmaximal, characteristic
4C2×#16839498C211yesmaximal, characteristic, complemented
5#21443698C211yesmaximal, characteristic, complemented
6#21443662C211yesmaximal, characteristic, complemented
7C61×#1438C211yesmaximal, characteristic
8C22×#11758200—21no—
9C2×#14519756C2211yescharacteristic
10#16839913—22no—
11#16839913C414yescomplemented
12C2×#14519698—21no—
13C2×#14519698—21no—
14C2×#14519698—21no—
15C2×C22⋊#92418C2211yescharacteristic
16C2×C22⋊#92418C2211yescharacteristic
17#16839666—21no—
18#16839659—21no—
19#16839649—21no—
20#16839645—21no—
21#16839635—21no—
22#16839622C2211yescharacteristic
23C4×C22⋊Dic61—21no—
24#16839498—22no—
25C23×D4×C61C2211yescharacteristic
26C22×C22⋊C4×C61—21no—
27C22×C22⋊C4×C61—21no—
28C2×#95×C61C2211yescharacteristic
29C2×#95×C61C2211yescharacteristic
30C22×Dic122D411yescharacteristic
31C2×#11758200—24no—
32C2×#11758200—42no—
33C2×#11758200—42no—
34C22×#92418—21no—
35C22×#92418—21no—
36#14519756—21no—
37#14519756—21no—
38#14519756C2×C412yes—
39#14519756D412yes—
40C2×C4⋊Dic61D411yescharacteristic
41C2×C4⋊Dic61D411yescharacteristic
42C2×C4⋊Dic61D411yescharacteristic
43C2×#11758196—21no—
44C2×#11758196—21no—
45C2×#11758196—21no—
46C2×C22⋊Dic61—21no—
47C2×C22⋊Dic61—21no—
48C2×C4×Dic61—21no—
49C2×C4×Dic61—21no—
50#14519698—24no—
51#14519698—42no—
52#14519698—42no—
53C22⋊#92418—21no—
54C22⋊#92418—21no—
55C22⋊#92418—21no—
56C22⋊#92418C2×C412yes—
57#14519684—21no—
58#14519684—21no—
59#14519684—21no—
60#14519684—21no—
61#14519684—21no—
62C25×C61—21no—
63C22×D4×C61—21no—
64C22×D4×C61—21no—
65C22×D4×C61—21no—
66C22×D4×C61—21no—
67C22×D4×C61—21no—
68C22×D4×C61—42no—
69C22×D4×C61—42no—
70C22×D4×C61C2×C412yes—
71C23×C4×C61—21no—
72C23×C4×C61D411yescharacteristic
73C23×C4×C61D411yescharacteristic
74C23×C4×C61C2311yescharacteristic
75C2×C22⋊C4×C61—42no—
76C2×C22⋊C4×C61—42no—
77C2×C22⋊C4×C61—42no—
78C2×C22⋊C4×C61—42no—
79C2×C22⋊C4×C61—42no—
80C2×C22⋊C4×C61—42no—
81#95×C61—21no—
82#95×C61—21no—
83#95×C61—21no—
84#95×C61—21no—
85C24×C61—22no—
86C24×C61—22no—
87C24×C61—22no—
88C24×C61—41no—
89C24×C61—41no—
90C24×C61—41no—
91C24×C61—41no—
92C24×C61—41no—
93C24×C61—41no—
94C24×C61—41no—
95C24×C61—41no—
96C24×C61—41no—
97C24×C61—41no—
98C24×C61—41no—
99C24×C61—41no—
100C24×C61C2×D411yescharacteristic
101C2×D4×C61—22no—
102C2×D4×C61—22no—
103C2×D4×C61—22no—
104C2×D4×C61—22no—
105C2×D4×C61—22no—
106C2×D4×C61—22no—
107C2×D4×C61—41no—
108C2×D4×C61—41no—
109C2×D4×C61—41no—
110C2×D4×C61—41no—
111C2×D4×C61—44no—
112C2×D4×C61—44no—
113C2×D4×C61—44no—
114C2×D4×C61—44no—
115C2×D4×C61—41no—
116C2×D4×C61—41no—
117C22×C4×C61—21no—
118C22×C4×C61—21no—
119C22×C4×C61—22no—
120C22×C4×C61—21no—
121C22×C4×C61—21no—
122C22×C4×C61—21no—
123C22×C4×C61—41no—
124C22×C4×C61—41no—
125C22×C4×C61—41no—
126C22×C4×C61—41no—
127C22×C4×C61—41no—
128C22×C4×C61—41no—
129C22×C4×C61—41no—
130C22×C4×C61—41no—
131C22×C4×C61—41no—
132C22×C4×C61—41no—
133C22×C4×C61—41no—
134C22×C4×C61—41no—
135C22×C4×C61SD1612yescomplemented
136C22×C4×C61C22×C411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61#4111yescharacteristic
141C22×C4×C61#4111yescharacteristic
142C22×Dic61—21no—
143C22×Dic61—21no—
144C22×Dic61—21no—
145C22×Dic61—21no—
146C2×Dic122—21no—
147C2×Dic122—41no—
148C2×Dic122—41no—
149C2×Dic122C22⋊C412yescomplemented
150C22⋊C4×C61—48no—
151C22⋊C4×C61—48no—
152C22⋊Dic61—22no—
153C22⋊Dic61—22no—
154C22⋊Dic61—41no—
155C22⋊Dic61—41no—
156#11758200—48no—
157C4⋊Dic61—21no—
158C4⋊Dic61—41no—
159C4⋊Dic61—41no—
160C4⋊Dic61C22⋊C412yescomplemented
161#11758196—22no—
162#11758196—22no—
163#11758196—81no—
164#11758196—81no—
165C4×Dic61—81no—
166C4×Dic61—81no—
167C2×#92418—22no—
168C2×#92418—41no—
169C2×#92418—41no—
170C2×#92418—41no—
171C2×#92418—41no—
172C2×#92418—41no—
173C23×C61—21no—
174C23×C61—21no—
175C23×C61—21no—
176C23×C61—21no—
177C23×C61—24no—
178C23×C61—42no—
179C23×C61—42no—
180C23×C61—42no—
181C23×C61—42no—
182C23×C61—42no—
183C23×C61—42no—
184C23×C61—42no—
185C23×C61—42no—
186C23×C61—42no—
187C23×C61—42no—
188C23×C61—42no—
189C23×C61—42no—
190C23×C61—42no—
191C23×C61—42no—
192C23×C61—42no—
193C23×C61—42no—
194C23×C61—42no—
195C23×C61—42no—
196C23×C61—81no—
197C23×C61—81no—
198C23×C61—81no—
199C23×C61—81no—
200C23×C61—81no—
201C23×C61—81no—
202C23×C61—81no—
203C23×C61—81no—
204C23×C61—81no—
205C23×C61—81no—
206C23×C61—81no—
207C23×C61—81no—
208C23×C61—81no—
209C23×C61—81no—
210C23×C61—81no—
211C23×C61—81no—
212C23×C61C4×D411yescharacteristic
213C23×C61#12011yescharacteristic
214C23×C61#12111yescharacteristic
215C23×C61C2×SD1611yescharacteristic
216C23×C61#13511yescharacteristic
217C23×C61AGL(1,ℤ/8)11yescharacteristic
218C23×C61#13711yescharacteristic
219D4×C61—24no—
220D4×C61—24no—
221D4×C61—42no—
222D4×C61—42no—
223D4×C61—42no—
224D4×C61—42no—
225D4×C61—42no—
226D4×C61—42no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—22no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—42no—
239C2×C4×C61—42no—
240C2×C4×C61—42no—
241C2×C4×C61—42no—
242C2×C4×C61—42no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—81no—
247C2×C4×C61—81no—
248C2×C4×C61—81no—
249C2×C4×C61—81no—
250C2×C4×C61—81no—
251C2×C4×C61—81no—
252C2×C4×C61C2×C22⋊C411yescharacteristic
253C2×C4×C61C4×D411yescharacteristic
254C2×C4×C61#12111yescharacteristic
255C2×C4×C61#12311yescharacteristic
256C2×Dic61—22no—
257C2×Dic61—22no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268Dic122—42no—
269Dic122—81no—
270#92418—42no—
271#92418—81no—
272#9042—611nomaximal, Sylow
273C22×C61—21no—
274C22×C61—21no—
275C22×C61—21no—
276C22×C61—21no—
277C22×C61—21no—
278C22×C61—21no—
279C22×C61—21no—
280C22×C61—21no—
281C22×C61—21no—
282C22×C61—21no—
283C22×C61—21no—
284C22×C61—21no—
285C22×C61—44no—
286C22×C61—44no—
287C22×C61—44no—
288C22×C61—82no—
289C22×C61—82no—
290C22×C61—82no—
291C22×C61—82no—
292C22×C61—82no—
293C22×C61—82no—
294C22×C61—82no—
295C22×C61—82no—
296C22×C61—82no—
297C22×C61—82no—
298C22×C61—82no—
299C22×C61—82no—
300C22×C61#38611yescharacteristic
301C22×C61C4×SD1611yescharacteristic
302C22×C61#44011yescharacteristic
303C22×C61#44811yescharacteristic
304C22×C61#44911yescharacteristic
305C22×C61#45311yescharacteristic
306C22×C61#45411yescharacteristic
307C22×C61B(4,𝔽2)11yescharacteristic
308C22×C61B(4,𝔽2)11yescharacteristic
309C22×C61#46011yescharacteristic
310C22×C61#46411yescharacteristic
311C4×C61—21no—
312C4×C61—21no—
313C4×C61—21no—
314C4×C61—21no—
315C4×C61—42no—
316C4×C61—82no—
317C4×C61—81no—
318Dic61—42no—
319Dic61—42no—
320Dic61—81no—
321Dic61—81no—
322C2×#450—611no—
323#2329—611no—
324#1786—611no—
325C2×#328—611no—
326#1438D6111yescharacteristic
327#1294—611no—
328#1280—611no—
329C2×C61—21no—
330C2×C61—21no—
331C2×C61—21no—
332C2×C61—21no—
333C2×C61—84no—
334C2×C61#159611yescharacteristic
335C2×C61#159711yescharacteristic
336C2×C61#159911yescharacteristic
337C2×C61#160011yescharacteristic
338C2×C61#188011yescharacteristic
339C2×C61#188311yescharacteristic
340C2×C61#188911yescharacteristic
341C23×D4C2×D6111yescharacteristic
342C22×SD16—1221no—
343C2×C22⋊Q8—611no—
344C22×C22⋊C4—21no—
345C22×C22⋊C4—21no—
346#450—614no—
347#450—1222no—
348C2×#102—1221no—
349C2×#102—1221no—
350C2×#102—1221no—
351C2×C22⋊C8—611no—
352C2×C22⋊C8—611no—
353#391—1221no—
354#389—1221no—
355#387—1221no—
356#387—1221no—
357#385—1221no—
358#380—611no—
359C4×C22⋊C4—1221no—
360C2×#95C2×D6111yescharacteristic
361C2×#95C2×D6111yescharacteristic
362#328—1222no—
363C61#904211yescharacteristic, complemented, Sylow
364C25—21no—
365C22×Q8—611no—
366C22×D4—21no—
367C22×D4—21no—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4—21no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4C4×D6112yes—
374C23×C4—21no—
375C23×C4C22⋊D6111yescharacteristic
376C23×C4C22⋊D6111yescharacteristic
377C23×C4C22×D6111yescharacteristic
378C2×SD16—1224no—
379C2×SD16—2442no—
380C2×SD16—2442no—
381C22×C8—1221no—
382C22×C8—1221no—
383C22⋊Q8—612no—
384C22⋊Q8—612no—
385C22⋊Q8—1221no—
386C22⋊Q8—1221no—
387C2×C4⋊C4—611no—
388C2×C4⋊C4—611no—
389C2×C4⋊C4—611no—
390C2×C4⋊C4—1221no—
391C2×C4⋊C4—1221no—
392C2×C4⋊C4—1221no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—1221no—
400C2×C22⋊C4—1221no—
401C2×C42—1221no—
402C2×C42—1221no—
403#102—1224no—
404#102—2442no—
405#102—2442no—
406C22⋊C8—612no—
407C22⋊C8—1221no—
408C22⋊C8—1221no—
409C22⋊C8—1221no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—1221no—
415#95—1221no—
416#95—1221no—
417#95—1221no—
418#95—1221no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—41no—
423C24—41no—
424C24—41no—
425C24—41no—
426C24—41no—
427C24—41no—
428C24—41no—
429C24—41no—
430C24—41no—
431C24—41no—
432C24—41no—
433C24—41no—
434C24C2×C22⋊D6111yescharacteristic
435C2×Q8—612no—
436C2×Q8—1221no—
437C2×Q8—2441no—
438C2×Q8—2441no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—44no—
450C2×D4—44no—
451C2×D4—44no—
452C2×D4—44no—
453C2×D4—41no—
454C2×D4—41no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—1221no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4—1221no—
477C22×C4#1175820012yescomplemented
478C22×C4C2×C4×D6111yescharacteristic
479C22×C4#1175822211yescharacteristic
480C22×C4D4×D6111yescharacteristic
481C22×C4D4×D6111yescharacteristic
482C22×C4D4×D6111yescharacteristic
483C22×C4#1175822411yescharacteristic
484SD16—2448no—
485C2×C8—1222no—
486C2×C8—2441no—
487C2×C8—2441no—
488C2×C8—2441no—
489C2×C8—2441no—
490C2×C8—2441no—
491C4⋊C4—612no—
492C4⋊C4—1222no—
493C4⋊C4—1222no—
494C4⋊C4—1221no—
495C4⋊C4—4881no—
496C4⋊C4—4881no—
497C4⋊C4—2441no—
498C4⋊C4—2441no—
499C22⋊C4—48no—
500C22⋊C4—48no—
501C22⋊C4—1222no—
502C22⋊C4—1222no—
503C22⋊C4—2441no—
504C22⋊C4—2441no—
505C42—4881no—
506C42—4881no—
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23—24no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—81no—
531C23—81no—
532C23—81no—
533C23—81no—
534C23—81no—
535C23—81no—
536C23—81no—
537C23—81no—
538C23—81no—
539C23—81no—
540C23—81no—
541C23—81no—
542C23—81no—
543C23—81no—
544C23—81no—
545C23—81no—
546C23C4×C22⋊D6111yescharacteristic
547C23#1451974511yescharacteristic
548C23#1451974811yescharacteristic
549C23C2×#1175820011yescharacteristic
550C23#1451979711yescharacteristic
551C23#1451980311yescharacteristic
552C23#1451980711yescharacteristic
553Q8—4881no—
554Q8—2442no—
555D4—24no—
556D4—24no—
557D4—42no—
558D4—42no—
559D4—42no—
560D4—42no—
561D4—42no—
562D4—42no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—81no—
583C2×C4—81no—
584C2×C4—81no—
585C2×C4—81no—
586C2×C4—81no—
587C2×C4—81no—
588C2×C4—1222no—
589C2×C4—1222no—
590C2×C4—2441no—
591C2×C4—2441no—
592C2×C4—2441no—
593C2×C4—2441no—
594C2×C4—2441no—
595C2×C4—2441no—
596C2×C4—2441no—
597C2×C4—2441no—
598C2×C4—2441no—
599C2×C4—2441no—
600C2×C4C22⋊C4×D6111yescharacteristic
601C2×C4#1451973711yescharacteristic
602C2×C4#1451975011yescharacteristic
603C2×C4#1451975911yescharacteristic
604C8—4881no—
605C8—2442no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—44no—
619C22—44no—
620C22—44no—
621C22—82no—
622C22—82no—
623C22—82no—
624C22—82no—
625C22—82no—
626C22—82no—
627C22—82no—
628C22—82no—
629C22—82no—
630C22—82no—
631C22—82no—
632C22—82no—
633C22#1683963811yescharacteristic
634C22C4×#1175820011yescharacteristic
635C22#1683986211yescharacteristic
636C22#1683990011yescharacteristic
637C22#1683990511yescharacteristic
638C22#1683992911yescharacteristic
639C22#1683993411yescharacteristic
640C22#1683994811yescharacteristic
641C22#1683994811yescharacteristic
642C22#1683995911yescharacteristic
643C22#1683998111yescharacteristic
644C4—21no—
645C4—21no—
646C4—21no—
647C4—21no—
648C4—42no—
649C4—82no—
650C4—81no—
651C4—4881no—
652C4—4881no—
653C4—2442no—
654C4—2442no—
655C2—21no—
656C2—21no—
657C2—21no—
658C2—21no—
659C2—84no—
660C2#2144474111yescharacteristic
661C2#2144474611yescharacteristic
662C2#2144475811yescharacteristic
663C2#2144476311yescharacteristic
664C2#2144617711yescharacteristic
665C2#2144619811yescharacteristic
666C2#2144622411yescharacteristic
subgroupG/H
centerC23#14519745
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1438C2
socleC23×C61#120
prime radicalC23×D4×C61C22
cosocleC23×C4×C61C23
hypercenter#1438D61
hypocenterC61#9042
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. #21448552C2semidirect
4. C2×#16839498C2semidirect
5. #21443698C2semidirect
6. #21443662C2semidirect
11. #16839913C4semidirect
135. C22×C4×C61SD16semidirect
149. C2×Dic122C22⋊C4semidirect
160. C4⋊Dic61C22⋊C4semidirect
363. C61#9042semidirect
477. C22×C4#11758200semidirect

Maximal subgroups

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

subgroupindex
C2×#168399132
#214485522
#214457502
C2×#168394982
#214436982
#214436622
C61×#14382
#904261