Finite Group Databasebeta

← #29648348

Subgroups — #29648348

Order 15616.

1298 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840313C211yesmaximal, characteristic
2#431×D61C211yesmaximal, characteristic, complemented
3#423×D61C211yesmaximal, characteristic, complemented
4#21444495C214yesmaximal, complemented
5#21444491C211yesmaximal, characteristic, complemented
6#21444488C211yesmaximal, characteristic, complemented
7#21444486C211yesmaximal, characteristic, complemented
8#21444467C214yesmaximal, complemented
9C61×#1546C211yesmaximal, characteristic, complemented
10C22×#11758226—21no—
11C2×M16×D61—21no—
12#16840313—21no—
13#16840313—21no—
14#16840313—21no—
15#16840313—21no—
16#16840313C412yes—
17#16840313C412yes—
18#16840313C2212yes—
19#16840313C2212yes—
20C2×#14519774C2211yescharacteristic
21C2×#14519766—21no—
22C2×#14519752—21no—
23C2×#14519752C412yes—
24C2×#14519739—21no—
25C2×#14519739C412yes—
26C2×C42×D61C2211yescharacteristic
27#16839815C2211yescharacteristic
28#16839814C2212yescomplemented
29#16839813—21no—
30#16839812—21no—
31#16839786C2211yescharacteristic
32#16839785—21no—
33#16839784—21no—
34#16839784C2212yescomplemented
35C4⋊C8×D61—21no—
36C4⋊C8×D61C2212yescomplemented
37C4⋊C8×D61C2212yescomplemented
38C22⋊C8×D61—21no—
39C4×C8×D61—21no—
40#16839508C2214yescomplemented
41#16839505C2214yescomplemented
42#16839505C2214yescomplemented
43C2×C4⋊Q8×C61C2211yescharacteristic
44C61×#431C2211yescharacteristic
45C61×#423C2211yescharacteristic
46C61×#332C2214yescomplemented
47C2×#11758226—22no—
48C2×#11758226—22no—
49C2×#11758226—22no—
50C2×#11758226—22no—
51C2×#11758226—44no—
52C2×#11758226—44no—
53C22×D244—22no—
54C22×D244—21no—
55C22×D244—21no—
56C22×D244C2×C412yes—
57C22×C4×D61—22no—
58C22×C4×D61C2×C411yescharacteristic
59C22×C4×D61D411yescharacteristic
60C22×C4×D61D411yescharacteristic
61C2×#11758194—21no—
62C2×#11758189—22no—
63M16×D61—44no—
64C2×C8×D61—22no—
65C2×C8×D61—22no—
66#14519774—21no—
67#14519774—21no—
68#14519774C2×C412yes—
69#14519774C2312yes—
70#14519766—22no—
71#14519766—22no—
72#14519766—22no—
73#14519766—22no—
74#14519752—22no—
75#14519752—22no—
76#14519752—22no—
77#14519752—22no—
78#14519752—22no—
79#14519752—22no—
80#14519752C2×C414yes—
81#14519752C2×C414yes—
82#14519739—22no—
83#14519739—22no—
84#14519739—22no—
85#14519739—22no—
86#14519739—22no—
87#14519739—22no—
88#14519739C2×C414yes—
89#14519739C2×C414yes—
90C2×#11758198—22no—
91C2×#11758198—22no—
92C2×C4×Dic61C2×C411yescharacteristic
93C2×C4×Dic61D411yescharacteristic
94C2×C4×Dic61D411yescharacteristic
95C42×D61C2×C411yescharacteristic
96C42×D61C2×C411yescharacteristic
97C42×D61D411yescharacteristic
98C42×D61D411yescharacteristic
99C42×D61D411yescharacteristic
100C42×D61D411yescharacteristic
101C42×D61C2311yescharacteristic
102C42×D61C2311yescharacteristic
103C4⋊#92418—21no—
104C4⋊#92418C2312yes—
105C4⋊#92418C2312yes—
106#14519706—22no—
107#14519706—22no—
108#14519706—22no—
109C22⋊#92418—21no—
110#14519689—22no—
111C4×#92418—21no—
112C8×Dic61—22no—
113C22×Q8×C61—21no—
114C2×M16×C61—21no—
115C4⋊Q8×C61—21no—
116C4⋊Q8×C61—21no—
117C4⋊Q8×C61C2×C412yes—
118C4⋊Q8×C61C2312yes—
119C2×C4⋊C4×C61—21no—
120C2×C4⋊C4×C61C2×C412yes—
121C2×C42×C61C2311yescharacteristic
122C4⋊C8×C61—21no—
123C4⋊C8×C61C2312yes—
124C4⋊C8×C61C2312yes—
125C22⋊C8×C61—21no—
126C4×C8×C61—21no—
127C23×D61—22no—
128C23×D61C22⋊C411yescharacteristic
129C2×Q8×C61—22no—
130C2×Q8×C61—22no—
131C2×Q8×C61—42no—
132C2×Q8×C61—42no—
133C22×C4×C61—22no—
134C22×C4×C61C22×C411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×Dic61C22⋊C411yescharacteristic
138C22×Dic61C22⋊C411yescharacteristic
139C22×Dic61C22⋊C411yescharacteristic
140#11758226—48no—
141#11758226—48no—
142#11758226—44no—
143#11758226—44no—
144#11758226—44no—
145#11758226—44no—
146C2×D244—24no—
147C2×D244—24no—
148C2×D244—22no—
149C2×D244—22no—
150C2×D244—22no—
151C2×D244—22no—
152C2×D244—22no—
153C2×D244—44no—
154C2×D244—48no—
155C2×D244—42no—
156C2×D244—42no—
157C2×D244—44no—
158C2×D244C22×C414yes—
159C2×C4×D61—24no—
160C2×C4×D61—24no—
161C2×C4×D61—42no—
162C2×C4×D61—42no—
163C2×C4×D61—48no—
164C2×C4×D61C22⋊C411yescharacteristic
165C2×C4×D61C22⋊C411yescharacteristic
166C2×C4×D61C22⋊C411yescharacteristic
167C2×C4×D61C22⋊C411yescharacteristic
168C2×C4×D61C22⋊C411yescharacteristic
169C2×C4×D61C22⋊C411yescharacteristic
170C2×C4×D61D814yes—
171C2×C4×D61SD1614yes—
172C2×C4×D61C22×C411yescharacteristic
173C2×C4×D61C22×C411yescharacteristic
174C2×C4×D61C2×D411yescharacteristic
175C2×C4×D61C2×D411yescharacteristic
176C2×C4×D61C2×D411yescharacteristic
177C2×C4×D61C2×D411yescharacteristic
178M16×C61—42no—
179C2×C8×C61—22no—
180C2×C8×C61—22no—
181C4⋊C4×C61—22no—
182C4⋊C4×C61—22no—
183C4⋊C4×C61—22no—
184C4⋊C4×C61C22×C414yes—
185C42×C61C22×C411yescharacteristic
186C42×C61C2×D411yescharacteristic
187C42×C61C2×D411yescharacteristic
188C42×C61C2411yescharacteristic
189#11758198—24no—
190#11758198—24no—
191#11758198—24no—
192#11758198—24no—
193C4×Dic61C22⋊C411yescharacteristic
194C4×Dic61C22⋊C411yescharacteristic
195C4×Dic61C22⋊C411yescharacteristic
196C4×Dic61C22⋊C411yescharacteristic
197C4×Dic61C22⋊C411yescharacteristic
198C4×Dic61C22⋊C411yescharacteristic
199C4×Dic61C22×C411yescharacteristic
200C4×Dic61C22×C411yescharacteristic
201C4×Dic61C2×D411yescharacteristic
202C4×Dic61C2×D411yescharacteristic
203C4×Dic61C2×D411yescharacteristic
204C4×Dic61C2×D411yescharacteristic
205#11758194—42no—
206C2×#92418—22no—
207C2×#92418—22no—
208#11758189—44no—
209C8×D61—44no—
210C8×D61—44no—
211C23×C61C2×C22⋊C411yescharacteristic
212C22×D61—24no—
213C22×D61—41no—
214C22×D61—41no—
215C22×D61—44no—
216C22×D61—44no—
217C22×D61—44no—
218C22×D61#10214yes—
219C22×D61C2×C22⋊C411yescharacteristic
220C22×D61C2×C22⋊C411yescharacteristic
221Q8×C61—42no—
222Q8×C61—42no—
223Q8×C61—44no—
224C2×C4×C61—22no—
225C2×C4×C61—22no—
226C2×C4×C61—24no—
227C2×C4×C61—44no—
228C2×C4×C61C2×C22⋊C411yescharacteristic
229C2×C4×C61C2×C22⋊C411yescharacteristic
230C2×C4×C61C2×C22⋊C411yescharacteristic
231C2×C4×C61C2×D812yes—
232C2×C4×C61C2×SD1612yes—
233C2×C4×C61C23×C411yescharacteristic
234C2×C4×C61C22×D411yescharacteristic
235C2×C4×C61C22×D411yescharacteristic
236C2×Dic61—41no—
237C2×Dic61—41no—
238C2×Dic61#10214yes—
239C2×Dic61C2×C22⋊C411yescharacteristic
240C2×Dic61C2×C22⋊C411yescharacteristic
241C2×Dic61C2×C22⋊C411yescharacteristic
242C2×Dic61C2×C22⋊C411yescharacteristic
243C2×Dic61C2×C22⋊C411yescharacteristic
244C2×Dic61C2×C22⋊C411yescharacteristic
245D244—44no—
246D244—44no—
247D244—48no—
248D244—48no—
249D244—42no—
250D244—42no—
251D244—44no—
252D244—44no—
253D244—44no—
254C4×D61—22no—
255C4×D61—22no—
256C4×D61—22no—
257C4×D61—22no—
258C4×D61—41no—
259C4×D61—41no—
260C4×D61—41no—
261C4×D61—41no—
262C4×D61—48no—
263C4×D61—48no—
264C4×D61#10214yes—
265C4×D61#10214yes—
266C4×D61C2×D812yes—
267C4×D61C2×D812yes—
268C4×D61C2×SD1612yes—
269C4×D61C2×SD1612yes—
270C8×C61—42no—
271C8×C61—42no—
272#92418—42no—
273#92418—42no—
274#17704—611nomaximal, Sylow
275C22×C61—21no—
276C22×C61—21no—
277C22×C61C2×#10212yes—
278C22×C61C22×C22⋊C411yescharacteristic
279C2×D61—21no—
280C2×D61—21no—
281C2×D61—21no—
282C2×D61—21no—
283C2×D61—44no—
284C2×D61—44no—
285C2×D61—44no—
286C2×D61—44no—
287C2×D61—88no—
288C2×D61C2×#10212yes—
289C2×D61C2×#10212yes—
290C4×C61—21no—
291C4×C61—21no—
292C4×C61—44no—
293C4×C61#41312yes—
294C4×C61C2×#10212yes—
295C4×C61C22×D811yescharacteristic
296C4×C61C22×SD1611yescharacteristic
297C4×C61#57512yes—
298Dic61—21no—
299Dic61—21no—
300Dic61—21no—
301Dic61—21no—
302Dic61C2×#10212yes—
303Dic61C2×#10212yes—
304C2×#532—611no—
305C2×#431—611no—
306C2×#423—611no—
307#1547—614no—
308#1546—611no—
309#1546D6111yescharacteristic, complemented
310#1545—611no—
311#1545—611no—
312#1540—614no—
313C2×C61—22no—
314C2×C61C2×#41311yescharacteristic
315C2×C61C22×#10211yescharacteristic
316C2×C61#289611yescharacteristic
317D61—22no—
318D61—22no—
319D61—84no—
320C22×#41—1221no—
321C22×M16—1221no—
322#532—612no—
323#532—612no—
324#532—612no—
325#532—612no—
326#532—1221no—
327#532—1221no—
328#532—1221no—
329#532—1221no—
330C2×C4⋊Q8C2×D6111yescharacteristic
331C2×#127—611no—
332C2×#124—1221no—
333C2×#121—612no—
334C2×#121—1221no—
335C2×C4×D4—612no—
336C2×C4×D4—1221no—
337C22×C42—611no—
338#431—611no—
339#431—612no—
340#431—1221no—
341#431—1221no—
342#431C2×D6111yescharacteristic
343#423—611no—
344#423—612no—
345#423—1221no—
346#423—1221no—
347#423C2×D6111yescharacteristic
348C2×C4⋊C8—612no—
349C2×C4⋊C8—612no—
350C2×C4⋊C8—1221no—
351C2×C22⋊C8—1221no—
352C2×C4×C8—1221no—
353#332—614no—
354#332C2×D6114yescomplemented
355#331—614no—
356#331—614no—
357C61#1770411yescharacteristic, complemented, Sylow
358C2×#41—1222no—
359C2×#41—1222no—
360C2×#41—1222no—
361C2×#41—1222no—
362C2×#41—2444no—
363C2×#41—2444no—
364C22×Q8—21no—
365C22×D4—612no—
366C22×D4—1222no—
367C22×D4—1221no—
368C22×D4—1221no—
369C23×C4—611no—
370C23×C4—611no—
371C23×C4—611no—
372C23×C4—1222no—
373C2×M16—21no—
374C2×M16—1222no—
375C2×M16—1221no—
376C2×M16—2444no—
377C22×C8—1222no—
378C22×C8—1222no—
379C4⋊Q8—21no—
380C4⋊Q8—21no—
381C4⋊Q8C4×D6112yes—
382C4⋊Q8C22×D6112yes—
383#127—612no—
384#127—612no—
385#127—1221no—
386#127—1221no—
387#124—1222no—
388#124—1222no—
389#124—1222no—
390#124—1222no—
391#121—614no—
392#121—614no—
393#121—1222no—
394#121—1222no—
395#121—1222no—
396#121—1222no—
397#121—1222no—
398#121—1222no—
399C4×D4—614no—
400C4×D4—614no—
401C4×D4—1222no—
402C4×D4—1222no—
403C4×D4—1222no—
404C4×D4—1222no—
405C4×D4—1222no—
406C4×D4—1222no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4C4×D6112yes—
409C2×C22⋊C4—1222no—
410C2×C22⋊C4—1222no—
411C2×C42—611no—
412C2×C42—611no—
413C2×C42—611no—
414C2×C42—611no—
415C2×C42—611no—
416C2×C42—611no—
417C2×C42—611no—
418C2×C42—611no—
419C2×C42—611no—
420C2×C42—611no—
421C2×C42—611no—
422C2×C42C22×D6111yescharacteristic
423C4⋊C8—21no—
424C4⋊C8—612no—
425C4⋊C8—612no—
426C4⋊C8—1222no—
427C4⋊C8—1222no—
428C4⋊C8—1222no—
429C4⋊C8—1221no—
430C4⋊C8C22×D6112yes—
431C4⋊C8C22×D6112yes—
432C22⋊C8—21no—
433C22⋊C8—1222no—
434C22⋊C8—1221no—
435C4×C8—21no—
436C4×C8—1222no—
437C4×C8—1221no—
438C24—611no—
439C24—1222no—
440#41—2448no—
441#41—2448no—
442#41—2444no—
443#41—2444no—
444#41—2444no—
445#41—2444no—
446C2×Q8—22no—
447C2×Q8—22no—
448C2×Q8—42no—
449C2×Q8—42no—
450C2×D4—614no—
451C2×D4—1224no—
452C2×D4—1224no—
453C2×D4—1222no—
454C2×D4—1222no—
455C2×D4—1222no—
456C2×D4—1222no—
457C2×D4—1222no—
458C2×D4—2444no—
459C2×D4—2444no—
460C2×D4—2448no—
461C2×D4—2442no—
462C2×D4—2442no—
463C22×C4—22no—
464C22×C4—611no—
465C22×C4—611no—
466C22×C4—611no—
467C22×C4—611no—
468C22×C4—611no—
469C22×C4—614no—
470C22×C4—614no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—611no—
478C22×C4—611no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—1224no—
482C22×C4—1224no—
483C22×C4—2442no—
484C22×C4—2442no—
485C22×C4—2448no—
486C22×C4C2×C4×D6111yescharacteristic
487C22×C4D4×D6111yescharacteristic
488C22×C4D4×D6111yescharacteristic
489M16—42no—
490M16—2444no—
491M16—2442no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—1222no—
495C2×C8—1222no—
496C2×C8—2444no—
497C2×C8—2444no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4C2×C4×D6114yes—
502C22⋊C4—1224no—
503C22⋊C4—1224no—
504C22⋊C4—1224no—
505C22⋊C4—1224no—
506C42—611no—
507C42—611no—
508C42—611no—
509C42—611no—
510C42—611no—
511C42—611no—
512C42—611no—
513C42—611no—
514C42—611no—
515C42—611no—
516C42—611no—
517C42—611no—
518C42C2×C4×D6111yescharacteristic
519C42D4×D6111yescharacteristic
520C42D4×D6111yescharacteristic
521C42C23×D6111yescharacteristic
522C23—611no—
523C23—611no—
524C23—614no—
525C23—1224no—
526C23—2441no—
527C23—2441no—
528C23—2444no—
529C23—2444no—
530C23—2444no—
531C23C22⋊C4×D6111yescharacteristic
532Q8—44no—
533Q8—42no—
534Q8—42no—
535D4—2444no—
536D4—2444no—
537D4—2448no—
538D4—2448no—
539D4—2444no—
540D4—2444no—
541D4—2442no—
542D4—2442no—
543D4—2444no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—44no—
548C2×C4—611no—
549C2×C4—611no—
550C2×C4—614no—
551C2×C4—614no—
552C2×C4—614no—
553C2×C4—612no—
554C2×C4—612no—
555C2×C4—612no—
556C2×C4—612no—
557C2×C4—611no—
558C2×C4—611no—
559C2×C4—611no—
560C2×C4—611no—
561C2×C4—1222no—
562C2×C4—1222no—
563C2×C4—1222no—
564C2×C4—1222no—
565C2×C4—2441no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2448no—
570C2×C4—2448no—
571C2×C4—2441no—
572C2×C4—2441no—
573C2×C4C22⋊C4×D6111yescharacteristic
574C2×C4C22⋊C4×D6111yescharacteristic
575C2×C4C22⋊C4×D6111yescharacteristic
576C2×C4D8×D6112yes—
577C2×C4SD16×D6112yes—
578C2×C4C22×C4×D6111yescharacteristic
579C2×C4C2×D4×D6111yescharacteristic
580C2×C4C2×D4×D6111yescharacteristic
581C8—42no—
582C8—42no—
583C8—2442no—
584C8—2442no—
585C22—21no—
586C22—21no—
587C22—612no—
588C22—612no—
589C22—1221no—
590C22—1221no—
591C22—1221no—
592C22—1221no—
593C22—4888no—
594C22—2444no—
595C22—2444no—
596C22—2444no—
597C22—2444no—
598C22#102×D6112yes—
599C22C2×C22⋊C4×D6111yescharacteristic
600C4—21no—
601C4—21no—
602C4—44no—
603C4—612no—
604C4—612no—
605C4—1221no—
606C4—1221no—
607C4—1221no—
608C4—1221no—
609C4#1683974512yes—
610C4#102×D6112yes—
611C4C2×D8×D6111yescharacteristic
612C4C2×SD16×D6111yescharacteristic
613C4#1684056112yes—
614C2—22no—
615C2—1222no—
616C2—1222no—
617C2—4884no—
618C2C2×#1683974511yescharacteristic
619C2C2×#102×D6111yescharacteristic
620C2#2145433711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1546C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840313C2
cosocleC42×C61C24
hypercenter#1546D61
hypocenterC61#17704
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
2. #431×D61C2semidirect
3. #423×D61C2semidirect
4. #21444495C2semidirect
5. #21444491C2semidirect
6. #21444488C2semidirect
7. #21444486C2semidirect
8. #21444467C2semidirect
9. C61×#1546C2semidirect
28. #16839814C22semidirect
34. #16839784C22semidirect
36. C4⋊C8×D61C22semidirect
37. C4⋊C8×D61C22semidirect
40. #16839508C22semidirect
41. #16839505C22semidirect
42. #16839505C22semidirect
46. C61×#332C22semidirect
309. #1546D61semidirect
354. #332C2×D61semidirect
357. C61#17704semidirect

Maximal subgroups

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

subgroupindex
C2×#168403132
#431×D612
#423×D612
#214444952
#214444912
#214444882
#214444862
#214444672
C61×#15462
#1770461