Finite Group Databasebeta

← #29571838

Subgroups — #29571838

Order 15616.

900 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840359C211yesmaximal, characteristic
2#21446136C211yesmaximal, characteristic
3#21446126C211yesmaximal, characteristic, complemented
4C2×#16839498C211yesmaximal, characteristic, complemented
5C2×#16839495C211yesmaximal, characteristic
6C2×#16839488C211yesmaximal, characteristic, complemented
7C61×#1441C211yesmaximal, characteristic, complemented
8#16840359—22no—
9#16840359—22no—
10#16840359—22no—
11#16840359C414yescomplemented
12C2×#14519772—21no—
13C2×#14519767—21no—
14C2×#14519762—21no—
15C2×#14519760—21no—
16C2×#14519756C2211yescharacteristic
17C2×#14519755—21no—
18C2×#14519751C2211yescharacteristic
19C2×C4×C22⋊D61—21no—
20C2×#14519700—21no—
21C2×#14519697—21no—
22C2×C22⋊#92418C2211yescharacteristic
23C2×C22⋊#92418C2211yescharacteristic
24#16839524—21no—
25#16839524—21no—
26#16839498—22no—
27#16839495—22no—
28#16839488—22no—
29C22×C4⋊C4×C61C2211yescharacteristic
30C22×C4⋊C4×C61C2211yescharacteristic
31C2×#95×C61—21no—
32C2×#95×C61—21no—
33C2×#95×C61C2211yescharacteristic
34C22×Dic122D411yescharacteristic
35C22×D244D411yescharacteristic
36C22×C22⋊D61—21no—
37C22×C4×D61—21no—
38C22×#92418—21no—
39C22×#92418—21no—
40#14519772—24no—
41#14519772—24no—
42#14519767—24no—
43#14519767—24no—
44#14519762—24no—
45#14519762—24no—
46#14519760—24no—
47#14519760—24no—
48#14519756—21no—
49#14519756—21no—
50#14519756C2×C412yes—
51#14519756D412yes—
52#14519755—24no—
53#14519755—24no—
54#14519751—21no—
55#14519751—21no—
56#14519751C2×C412yes—
57#14519751D412yes—
58C4×C22⋊D61—24no—
59C4×C22⋊D61—24no—
60C2×C4⋊Dic61D411yescharacteristic
61C2×C4⋊Dic61D411yescharacteristic
62C2×#11758196—21no—
63C2×#11758196—21no—
64C2×#11758196—21no—
65C2×#11758196—21no—
66C2×C22⋊Dic61—21no—
67C2×#11758198—21no—
68C2×#11758198—21no—
69C2×#11758198—21no—
70C2×#11758198—21no—
71C2×C4×Dic61—21no—
72#14519700—42no—
73#14519697—42no—
74C22⋊#92418—21no—
75C22⋊#92418—21no—
76C22⋊#92418—21no—
77C22⋊#92418—21no—
78C23×C4×C61—21no—
79C23×C4×C61—21no—
80C23×C4×C61D411yescharacteristic
81C23×C4×C61D411yescharacteristic
82C23×C4×C61C2311yescharacteristic
83C2×C4⋊C4×C61—21no—
84C2×C4⋊C4×C61—21no—
85C2×C4⋊C4×C61—21no—
86C2×C4⋊C4×C61—21no—
87C2×C4⋊C4×C61—21no—
88C2×C4⋊C4×C61—21no—
89C2×C4⋊C4×C61—42no—
90C2×C4⋊C4×C61C2×C412yes—
91C2×C4⋊C4×C61D412yes—
92#95×C61—21no—
93#95×C61—21no—
94#95×C61—42no—
95#95×C61—42no—
96C24×C61C2×D411yescharacteristic
97C23×D61—21no—
98C22×C4×C61—21no—
99C22×C4×C61—21no—
100C22×C4×C61—21no—
101C22×C4×C61—21no—
102C22×C4×C61—21no—
103C22×C4×C61—21no—
104C22×C4×C61—21no—
105C22×C4×C61—21no—
106C22×C4×C61—22no—
107C22×C4×C61—22no—
108C22×C4×C61—41no—
109C22×C4×C61—41no—
110C22×C4×C61—41no—
111C22×C4×C61—41no—
112C22×C4×C61—41no—
113C22×C4×C61—41no—
114C22×C4×C61—41no—
115C22×C4×C61—41no—
116C22×C4×C61—41no—
117C22×C4×C61—41no—
118C22×C4×C61—41no—
119C22×C4×C61—41no—
120C22×C4×C61—41no—
121C22×C4×C61—41no—
122C22×C4×C61—41no—
123C22×C4×C61—41no—
124C22×C4×C61C22⋊C412yes—
125C22×C4×C61C22⋊C412yes—
126C22×C4×C61C22×C411yescharacteristic
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61C2×D411yescharacteristic
132C2×C22⋊D61—22no—
133C2×C22⋊D61—22no—
134C2×C22⋊D61—41no—
135C2×C22⋊D61—41no—
136C2×C22⋊D61—41no—
137C2×C22⋊D61—41no—
138C22×Dic61—21no—
139C22×Dic61—21no—
140C22×Dic61—21no—
141C2×D244—21no—
142C2×D244—41no—
143C2×D244—41no—
144C2×D244C22⋊C412yes—
145C2×C4×D61—24no—
146C2×C4×D61—81no—
147C2×C4×D61—81no—
148C2×Dic122—21no—
149C2×Dic122—41no—
150C2×Dic122—41no—
151C2×Dic122C22⋊C412yes—
152C4⋊C4×C61—22no—
153C4⋊C4×C61—22no—
154C4⋊C4×C61—22no—
155C4⋊C4×C61—22no—
156C4⋊C4×C61—22no—
157C4⋊C4×C61—22no—
158C4⋊C4×C61—41no—
159C4⋊C4×C61—41no—
160C22⋊Dic61—22no—
161C22⋊Dic61—22no—
162#11758198—24no—
163#11758198—24no—
164#11758198—24no—
165#11758198—22no—
166#11758198—22no—
167C4⋊Dic61—21no—
168C4⋊Dic61—21no—
169C4⋊Dic61C22⋊C412yes—
170C4⋊Dic61C22⋊C412yes—
171#11758196—24no—
172#11758196—24no—
173#11758196—24no—
174#11758196—22no—
175#11758196—22no—
176C4×Dic61—24no—
177C2×#92418—41no—
178C2×#92418—41no—
179C2×#92418—41no—
180C2×#92418—41no—
181C2×#92418—41no—
182C2×#92418—41no—
183C23×C61—21no—
184C23×C61—21no—
185C23×C61—21no—
186C23×C61—21no—
187C23×C61C2×C22⋊C411yescharacteristic
188C23×C61#12011yescharacteristic
189C23×C61#12011yescharacteristic
190C23×C61#13511yescharacteristic
191C23×C61#13511yescharacteristic
192C23×C61AGL(1,ℤ/8)11yescharacteristic
193C23×C61#13711yescharacteristic
194C22×D61—22no—
195C22×D61—41no—
196C22×D61—41no—
197C22×D61—41no—
198C22×D61—41no—
199C22×D61—41no—
200C22×D61—41no—
201C2×C4×C61—21no—
202C2×C4×C61—21no—
203C2×C4×C61—21no—
204C2×C4×C61—21no—
205C2×C4×C61—22no—
206C2×C4×C61—22no—
207C2×C4×C61—22no—
208C2×C4×C61—22no—
209C2×C4×C61—41no—
210C2×C4×C61—41no—
211C2×C4×C61—41no—
212C2×C4×C61—41no—
213C2×C4×C61—41no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61—42no—
220C2×C4×C61—42no—
221C2×C4×C61—42no—
222C2×C4×C61—42no—
223C2×C4×C61—42no—
224C2×C4×C61—42no—
225C2×C4×C61—42no—
226C2×C4×C61—81no—
227C2×C4×C61—81no—
228C2×C4×C61—81no—
229C2×C4×C61—81no—
230C2×C4×C61—81no—
231C2×C4×C61—81no—
232C2×C4×C61—81no—
233C2×C4×C61—81no—
234C2×C4×C61—81no—
235C2×C4×C61C2×C22⋊C411yescharacteristic
236C2×C4×C61C2×C22⋊C411yescharacteristic
237C2×C4×C61#12011yescharacteristic
238C2×C4×C61#12011yescharacteristic
239C22⋊D61—42no—
240C22⋊D61—42no—
241C22⋊D61—42no—
242C22⋊D61—42no—
243C2×Dic61—22no—
244C2×Dic61—22no—
245C2×Dic61—22no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252D244—42no—
253D244—81no—
254C4×D61—84no—
255Dic122—42no—
256Dic122—81no—
257#92418—81no—
258#92418—81no—
259#8407—611nomaximal, Sylow
260C22×C61—21no—
261C22×C61—21no—
262C22×C61—21no—
263C22×C61—21no—
264C22×C61—21no—
265C22×C61—21no—
266C22×C61—21no—
267C22×C61—21no—
268C22×C61—21no—
269C22×C61—21no—
270C22×C61—21no—
271C22×C61—21no—
272C22×C61#37911yescharacteristic
273C22×C61#41611yescharacteristic
274C22×C61#41711yescharacteristic
275C22×C61#44911yescharacteristic
276C22×C61#44911yescharacteristic
277C22×C61#45211yescharacteristic
278C22×C61#45211yescharacteristic
279C22×C61#45411yescharacteristic
280C22×C61#45611yescharacteristic
281C22×C61B(4,𝔽2)11yescharacteristic
282C22×C61#45811yescharacteristic
283C2×D61—42no—
284C2×D61—42no—
285C2×D61—42no—
286C2×D61—81no—
287C2×D61—81no—
288C2×D61—81no—
289C2×D61—81no—
290C4×C61—21no—
291C4×C61—21no—
292C4×C61—21no—
293C4×C61—21no—
294C4×C61—42no—
295C4×C61—42no—
296C4×C61—82no—
297C4×C61—82no—
298Dic61—42no—
299Dic61—42no—
300Dic61—42no—
301C2×#539—611no—
302#1874—611no—
303#1872—611no—
304C2×#328—611no—
305C2×#327—611no—
306C2×#324—611no—
307#1441D6111yescharacteristic, complemented
308C2×C61—21no—
309C2×C61—21no—
310C2×C61—21no—
311C2×C61—21no—
312C2×C61#159711yescharacteristic
313C2×C61#160311yescharacteristic
314C2×C61#160911yescharacteristic
315C2×C61#161511yescharacteristic
316C2×C61#178811yescharacteristic
317C2×C61#179011yescharacteristic
318C2×C61#179311yescharacteristic
319D61—82no—
320#539—614no—
321#539—1222no—
322#539—1222no—
323#539—1222no—
324C2×#126—1221no—
325C2×#125—1221no—
326C2×#123—1221no—
327C2×#123—1221no—
328C2×C22⋊Q8—611no—
329C2×C22⋊Q8—1221no—
330C2×#121—611no—
331C2×C4×D4—1221no—
332C22×C4⋊C4C2×D6111yescharacteristic
333C22×C4⋊C4C2×D6111yescharacteristic
334C2×#103—1221no—
335C2×#102—1221no—
336C2×C22⋊C8—611no—
337C2×C22⋊C8—611no—
338C2×#95—21no—
339C2×#95—21no—
340C2×#95C2×D6111yescharacteristic
341#340—1221no—
342#340—1221no—
343#328—1222no—
344#327—1222no—
345#324—1222no—
346C61#840711yescharacteristic, complemented, Sylow
347C22×Q8—611no—
348C22×D4—611no—
349C22×D4—1221no—
350C23×C4—21no—
351C23×C4—21no—
352C23×C4—1221no—
353C23×C4C22⋊D6111yescharacteristic
354C23×C4C22⋊D6111yescharacteristic
355C23×C4C22×D6111yescharacteristic
356C22×C8—1221no—
357C22×C8—1221no—
358#126—1224no—
359#126—1224no—
360#125—1224no—
361#125—1224no—
362#123—1224no—
363#123—1224no—
364#123—1224no—
365#123—1224no—
366C22⋊Q8—612no—
367C22⋊Q8—612no—
368C22⋊Q8—1224no—
369C22⋊Q8—1224no—
370C22⋊Q8—1221no—
371C22⋊Q8—1221no—
372#121—612no—
373#121—612no—
374#121—1221no—
375#121—1221no—
376C4×D4—1224no—
377C4×D4—1224no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—42no—
385C2×C4⋊C4—611no—
386C2×C4⋊C4—611no—
387C2×C4⋊C4—1221no—
388C2×C4⋊C4—1221no—
389C2×C4⋊C4—1221no—
390C2×C4⋊C4—1221no—
391C2×C4⋊C4C4×D6112yes—
392C2×C4⋊C4D24412yes—
393C2×C22⋊C4—1221no—
394C2×C22⋊C4—1221no—
395C2×C22⋊C4—1221no—
396C2×C22⋊C4—1221no—
397C2×C22⋊C4—1221no—
398C2×C42—1221no—
399#103—2442no—
400#102—2442no—
401C22⋊C8—1221no—
402C22⋊C8—1221no—
403C22⋊C8—1221no—
404C22⋊C8—1221no—
405#95—21no—
406#95—21no—
407#95—42no—
408#95—42no—
409C24—1221no—
410C24C2×C22⋊D6111yescharacteristic
411C2×Q8—612no—
412C2×Q8—1221no—
413C2×Q8—2441no—
414C2×Q8—2441no—
415C2×D4—612no—
416C2×D4—1222no—
417C2×D4—1222no—
418C2×D4—1221no—
419C2×D4—2441no—
420C2×D4—2441no—
421C2×D4—2441no—
422C2×D4—2441no—
423C2×D4—2441no—
424C2×D4—2441no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—1224no—
452C22×C4—1221no—
453C22×C4—1221no—
454C22×C4—1221no—
455C22×C4—4881no—
456C22×C4—4881no—
457C22×C4#1175819812yes—
458C22×C4#1175819812yes—
459C22×C4C2×C4×D6111yescharacteristic
460C22×C4C2×D24411yescharacteristic
461C22×C4D4×D6111yescharacteristic
462C22×C4D4×D6111yescharacteristic
463C22×C4D4×D6111yescharacteristic
464C22×C4D4×D6111yescharacteristic
465C2×C8—2441no—
466C2×C8—2441no—
467C2×C8—2441no—
468C2×C8—2441no—
469C2×C8—2441no—
470C2×C8—2441no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—612no—
480C4⋊C4—612no—
481C4⋊C4—1224no—
482C4⋊C4—1224no—
483C4⋊C4—1224no—
484C4⋊C4—1222no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—1222no—
488C22⋊C4—1224no—
489C22⋊C4—1224no—
490C22⋊C4—1224no—
491C22⋊C4—1222no—
492C22⋊C4—1222no—
493C22⋊C4—1222no—
494C22⋊C4—1222no—
495C42—1224no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—1222no—
501C23—2441no—
502C23—2441no—
503C23—2441no—
504C23—2441no—
505C23—2441no—
506C23—2441no—
507C23C2×#1175819811yescharacteristic
508C23#1451974511yescharacteristic
509C23#1451974511yescharacteristic
510C23#1451979711yescharacteristic
511C23#1451979711yescharacteristic
512C23#1451980311yescharacteristic
513C23#1451980811yescharacteristic
514Q8—4881no—
515Q8—2442no—
516D4—4881no—
517D4—2442no—
518D4—2442no—
519D4—2442no—
520D4—2442no—
521D4—2442no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—81no—
548C2×C4—81no—
549C2×C4—81no—
550C2×C4—81no—
551C2×C4—81no—
552C2×C4—81no—
553C2×C4—81no—
554C2×C4—81no—
555C2×C4—81no—
556C2×C4—1222no—
557C2×C4—1222no—
558C2×C4—1222no—
559C2×C4—4884no—
560C2×C4—2441no—
561C2×C4—2441no—
562C2×C4—2441no—
563C2×C4—2441no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4C22⋊C4×D6111yescharacteristic
567C2×C4C22⋊C4×D6111yescharacteristic
568C2×C4#1451974711yescharacteristic
569C2×C4#1451974711yescharacteristic
570C8—4881no—
571C8—4881no—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—4881no—
585C22—4881no—
586C22—4881no—
587C22—4881no—
588C22—2442no—
589C22—2442no—
590C22—2442no—
591C22#1683961711yescharacteristic
592C22#1683975611yescharacteristic
593C22#1683976111yescharacteristic
594C22#1683990511yescharacteristic
595C22#1683990511yescharacteristic
596C22#1683992211yescharacteristic
597C22#1683992211yescharacteristic
598C22#1683993411yescharacteristic
599C22#1683994411yescharacteristic
600C22#1683994811yescharacteristic
601C22#1683995111yescharacteristic
602C4—21no—
603C4—21no—
604C4—21no—
605C4—21no—
606C4—42no—
607C4—42no—
608C4—82no—
609C4—82no—
610C4—2442no—
611C4—2442no—
612C4—2442no—
613C2—21no—
614C2—21no—
615C2—21no—
616C2—21no—
617C2—4882no—
618C2#2144474611yescharacteristic
619C2#2144478011yescharacteristic
620C2#2144481411yescharacteristic
621C2#2144484811yescharacteristic
622C2#2144575711yescharacteristic
623C2#2144576611yescharacteristic
624C2#2144577711yescharacteristic
subgroupG/H
centerC23#14519745
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1441C2
socleC23×C61#120
prime radicalC2×#14519751C22
cosocleC23×C4×C61C23
hypercenter#1441D61
hypocenterC61#8407
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1441

Complements

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

NH ≅ G/Ntype
3. #21446126C2semidirect
4. C2×#16839498C2semidirect
6. C2×#16839488C2semidirect
7. C61×#1441C2semidirect
11. #16840359C4semidirect
307. #1441D61semidirect
346. C61#8407semidirect

Maximal subgroups

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

subgroupindex
C2×#168403592
#214461362
#214461262
C2×#168394982
C2×#168394952
C2×#168394882
C61×#14412
#840761