Finite Group Databasebeta

← #29651060

Subgroups — #29651060

Order 15616.

662 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455873C211yesmaximal, characteristic
2#21454834C211yesmaximal, characteristic, complemented
3#21444721C211yesmaximal, characteristic, complemented
4#21444707C211yesmaximal, characteristic, complemented
5#21444681C211yesmaximal, characteristic, complemented
6#21444676C211yesmaximal, characteristic, complemented
7#21444655C211yesmaximal, characteristic, complemented
8#21444646C211yesmaximal, characteristic, complemented
9#21444641C211yesmaximal, characteristic, complemented
10C8×#11758199C211yesmaximal, characteristic, complemented
11#21444602C211yesmaximal, characteristic, complemented
12#21444288C211yesmaximal, characteristic, complemented
13#21444204C211yesmaximal, characteristic, complemented
14#21444116C211yesmaximal, characteristic, complemented
15C61×#2935C211yesmaximal, characteristic, complemented
16C4×#11758222C2211yescharacteristic
17#16840083C411yescharacteristic
18#16840083C411yescharacteristic
19#16840054C411yescharacteristic
20#16840049C411yescharacteristic
21#16839959C411yescharacteristic
22#16839954C411yescharacteristic
23#16839905C411yescharacteristic
24#16839905C411yescharacteristic
25#16839892C2211yescharacteristic
26#16839892C2211yescharacteristic
27C4×#11758200C2211yescharacteristic
28C4×#11758200C2211yescharacteristic
29C4×#11758199C2211yescharacteristic
30C4×#11758199C2211yescharacteristic
31#16839831—21no—
32#16839831—21no—
33C8×D244C2211yescharacteristic
34C8×D244C2211yescharacteristic
35#16839819C2211yescharacteristic
36#16839817—21no—
37#16839815C2211yescharacteristic
38#16839815C2211yescharacteristic
39#97×D61—21no—
40#16839514C2211yescharacteristic
41#16839514C2211yescharacteristic
42#16839512C2211yescharacteristic
43#16839512C2211yescharacteristic
44#16839492C2211yescharacteristic
45#16839492C2211yescharacteristic
46D4⋊#92418C2211yescharacteristic
47D4⋊#92418C2211yescharacteristic
48D4⋊#92418C2211yescharacteristic
49D4⋊#92418C2211yescharacteristic
50#16839489C2211yescharacteristic
51#16839489C2211yescharacteristic
52#16839484C2211yescharacteristic
53#16839484C2211yescharacteristic
54#16839483C2211yescharacteristic
55C8×#92418C2211yescharacteristic
56C2×#131×C61—21no—
57C61×#532C2211yescharacteristic
58C61×#436C2211yescharacteristic
59C61×#436C2211yescharacteristic
60C61×#435—21no—
61C61×#435—21no—
62C8×D4×C61C2211yescharacteristic
63C8×D4×C61C2211yescharacteristic
64C2×C4⋊C8×C61C2211yescharacteristic
65C61×#408—21no—
66C4×M16×C61C2211yescharacteristic
67C2×#11758222C2×C411yescharacteristic
68C2×#11758200C2×C411yescharacteristic
69C2×#11758200C2×C411yescharacteristic
70C2×#11758199C2×C411yescharacteristic
71C2×#11758199C2×C411yescharacteristic
72C2×C8×D61—21no—
73C2×C8×D61—21no—
74C4×Dic122C2×C411yescharacteristic
75C4×Dic122C2311yescharacteristic
76C4×D244C2×C411yescharacteristic
77C4×D244C2311yescharacteristic
78C4×C22⋊D61—21no—
79C4×C22⋊D61—21no—
80#14519736C2×C411yescharacteristic
81#14519734—21no—
82C42×D61—21no—
83#14519710C2×C411yescharacteristic
84#14519710C2×C411yescharacteristic
85#14519708C2×C411yescharacteristic
86#14519708C2×C411yescharacteristic
87C4⋊#92418—21no—
88C4⋊#92418C2×C411yescharacteristic
89C4⋊#92418C2×C411yescharacteristic
90C4⋊#92418C2311yescharacteristic
91C4⋊#92418C2311yescharacteristic
92#14519706—21no—
93#14519706—21no—
94#14519700C2×C411yescharacteristic
95#14519700C2×C411yescharacteristic
96#14519698C2×C411yescharacteristic
97#14519698C2×C411yescharacteristic
98#14519698C2×C411yescharacteristic
99#14519698C2×C411yescharacteristic
100#14519697C2×C411yescharacteristic
101#14519697C2×C411yescharacteristic
102C22⋊#92418—21no—
103C22⋊#92418—21no—
104C22⋊#92418C2×C411yescharacteristic
105C22⋊#92418C2×C411yescharacteristic
106#14519689—21no—
107#14519689—21no—
108#14519688—21no—
109#14519687—21no—
110#14519687—21no—
111C4×#92418C2311yescharacteristic
112C4×#92418C2311yescharacteristic
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C2×#41×C61—21no—
116#131×C61—44no—
117C2×M16×C61—21no—
118C2×M16×C61—21no—
119C2×M16×C61D411yescharacteristic
120C2×M16×C61D411yescharacteristic
121C22×C8×C61—21no—
122C22×C8×C61—21no—
123C22×C8×C61—21no—
124C4⋊Q8×C61C2×C411yescharacteristic
125#127×C61C2×C411yescharacteristic
126#124×C61—21no—
127#121×C61—21no—
128#121×C61C2×C411yescharacteristic
129#121×C61C2×C411yescharacteristic
130C4×D4×C61—21no—
131C4×D4×C61C2311yescharacteristic
132C4×D4×C61C2311yescharacteristic
133C2×C42×C61C2311yescharacteristic
134C4⋊C8×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137C22⋊C8×C61—21no—
138C22⋊C8×C61—21no—
139C22⋊C8×C61—21no—
140C22⋊C8×C61—21no—
141#97×C61D411yescharacteristic
142#97×C61D411yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C4×C8×C61C2311yescharacteristic
145#41×C61—42no—
146#41×C61—42no—
147C2×Q8×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61C22×C411yescharacteristic
153C2×D4×C61C22×C411yescharacteristic
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61C22×C411yescharacteristic
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61#4111yescharacteristic
159C2×C22⋊D61—21no—
160#11758222—22no—
161#11758222—41no—
162C2×D244C22×C411yescharacteristic
163C2×C4×D61—21no—
164C2×C4×D61—21no—
165C2×C4×D61—21no—
166C2×Dic122C22×C411yescharacteristic
167M16×C61—22no—
168M16×C61—41no—
169M16×C61—42no—
170M16×C61—42no—
171C2×C8×C61—21no—
172C2×C8×C61—21no—
173C2×C8×C61—42no—
174C2×C8×C61—42no—
175C2×C8×C61—42no—
176C2×C8×C61C2×D411yescharacteristic
177C2×C8×C61C2×D411yescharacteristic
178C2×C8×C61C2×D411yescharacteristic
179C2×C8×C61C2×D411yescharacteristic
180C4⋊C4×C61—21no—
181C4⋊C4×C61C22×C411yescharacteristic
182C4⋊C4×C61C22×C411yescharacteristic
183C22⋊C4×C61—21no—
184C22⋊C4×C61—21no—
185C22⋊C4×C61—21no—
186C22⋊C4×C61—21no—
187C42×C61C22×C411yescharacteristic
188C42×C61C2×D411yescharacteristic
189C42×C61#4111yescharacteristic
190C42×C61C2411yescharacteristic
191C22⋊Dic61—21no—
192#11758200—41no—
193#11758200—41no—
194#11758199—22no—
195#11758199—22no—
196#11758198—21no—
197#11758198—21no—
198C4⋊Dic61C22×C411yescharacteristic
199C4⋊Dic61C22×C411yescharacteristic
200#11758196—21no—
201#11758196—21no—
202C4×Dic61—21no—
203C4×Dic61—21no—
204C4×Dic61—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418C22×C411yescharacteristic
210C2×#92418C22×C411yescharacteristic
211C2×#92418C22×C411yescharacteristic
212C2×#92418C22×C411yescharacteristic
213C8×D61—42no—
214C8×D61—42no—
215C23×C61—21no—
216C23×C61—21no—
217C23×C61C4×D411yescharacteristic
218C22×D61—21no—
219Q8×C61—42no—
220D4×C61—21no—
221D4×C61—21no—
222D4×C61—21no—
223D4×C61—21no—
224D4×C61—42no—
225D4×C61—42no—
226D4×C61—42no—
227D4×C61—81no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61C4×D411yescharacteristic
240C2×C4×C61C4×D411yescharacteristic
241C2×C4×C61C4×D411yescharacteristic
242C2×C4×C61C23×C411yescharacteristic
243C2×C4×C61C22×D411yescharacteristic
244C2×C4×C61C2×#4111yescharacteristic
245C22⋊D61—42no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249D244—21no—
250D244#13112yescomplemented
251C4×D61—42no—
252C4×D61—41no—
253C4×D61—41no—
254C4×D61—81no—
255Dic122—21no—
256Dic122—21no—
257C8×C61—21no—
258C8×C61—21no—
259C8×C61—21no—
260C8×C61—41no—
261C8×C61—41no—
262C8×C61AGL(1,ℤ/8)12yes—
263#92418—21no—
264#92418—21no—
265#92418—21no—
266#92418—21no—
267#92418—41no—
268#92418—41no—
269#92418—41no—
270#92418—41no—
271#18007—611nomaximal, Sylow
272C22×C61—21no—
273C22×C61—21no—
274C22×C61—21no—
275C22×C61—41no—
276C22×C61—41no—
277C22×C61—41no—
278C22×C61—41no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61C2×C4×D411yescharacteristic
282C2×D61—22no—
283C2×D61—41no—
284C2×D61—41no—
285C4×C61—21no—
286C4×C61—21no—
287C4×C61—21no—
288C4×C61—21no—
289C4×C61—41no—
290C4×C61—41no—
291C4×C61C2×#13111yescharacteristic
292C4×C61#56811yescharacteristic
293C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
294C4×C61#57511yescharacteristic
295Dic61—41no—
296Dic61—41no—
297Dic61—41no—
298#3106—611no—
299#2970—611no—
300#2935D6111yescharacteristic, complemented
301#1592—611no—
302#1590—611no—
303#1586—611no—
304#1585—611no—
305#1582—611no—
306#1581—611no—
307#1580—611no—
308C8×D8—611no—
309#1573—611no—
310#1496—611no—
311#1477—611no—
312#1453—611no—
313C2×C61—41no—
314C2×C61—81no—
315C2×C61—81no—
316C2×C61#293311yescharacteristic
317C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
318C2×C61#295711yescharacteristic
319D61—42no—
320C2×#131—21no—
321#532C2×D6111yescharacteristic
322C4×#41—611no—
323#482—611no—
324#482—611no—
325#477—611no—
326#476—611no—
327#460—611no—
328#459—611no—
329#449—611no—
330#449—611no—
331#446—611no—
332#446—611no—
333C4×SD16—611no—
334C4×SD16—611no—
335C4×D8—611no—
336C4×D8—611no—
337#436C2×D6111yescharacteristic
338#436C2×D6111yescharacteristic
339#435—21no—
340#435—21no—
341#435—1221no—
342#435—1221no—
343C8×D4—611no—
344C8×D4—611no—
345C8×D4C2×D6111yescharacteristic
346C8×D4C2×D6111yescharacteristic
347#432—611no—
348#432—1221no—
349#431—611no—
350#431—611no—
351C2×C4⋊C8C2×D6111yescharacteristic
352#408—21no—
353C4×M16C2×D6111yescharacteristic
354C2×#97—1221no—
355#335—611no—
356#335—611no—
357#334—611no—
358#334—611no—
359Q8⋊C8—611no—
360Q8⋊C8—611no—
361D4⋊C8—611no—
362D4⋊C8—611no—
363D4⋊C8—611no—
364D4⋊C8—611no—
365D4⋊C8—611no—
366D4⋊C8—611no—
367#322—611no—
368#322—611no—
369#322—611no—
370C82—611no—
371C61#1800711yescharacteristic, complemented, Sylow
372C2×#41—21no—
373C2×#41—611no—
374C2×SD16—611no—
375C2×SD16—611no—
376C2×D8—611no—
377C2×D8—611no—
378#131—44no—
379C2×M16—21no—
380C2×M16—21no—
381C2×M16C22⋊D6111yescharacteristic
382C2×M16C22⋊D6111yescharacteristic
383C22×C8—21no—
384C22×C8—21no—
385C22×C8—21no—
386C22×C8—1221no—
387C22×C8—1221no—
388C4⋊Q8C4×D6111yescharacteristic
389#127C4×D6111yescharacteristic
390#124—21no—
391#121—21no—
392#121C4×D6111yescharacteristic
393#121C4×D6111yescharacteristic
394C4×Q8—611no—
395C4×Q8—611no—
396C4×D4—21no—
397C4×D4—611no—
398C4×D4—611no—
399C4×D4—1221no—
400C4×D4—1221no—
401C4×D4C22×D6111yescharacteristic
402C4×D4C22×D6111yescharacteristic
403#117—611no—
404#117—1221no—
405C2×C42—1221no—
406C2×C42C22×D6111yescharacteristic
407#107—611no—
408#107—611no—
409#106—611no—
410#106—611no—
411C4⋊C8—21no—
412C4⋊C8—611no—
413C4⋊C8—611no—
414C4⋊C8—611no—
415C4⋊C8—611no—
416C4⋊C8—1221no—
417C4⋊C8—1221no—
418C4⋊C8—1221no—
419C4⋊C8C22×D6111yescharacteristic
420C4⋊C8C22×D6111yescharacteristic
421#103—611no—
422#103—611no—
423#102—611no—
424#102—611no—
425#102—611no—
426#102—611no—
427#102—611no—
428#102—611no—
429C22⋊C8—21no—
430C22⋊C8—21no—
431C22⋊C8—21no—
432C22⋊C8—21no—
433C22⋊C8—611no—
434C22⋊C8—611no—
435C22⋊C8—1221no—
436C22⋊C8—1221no—
437C22⋊C8—1221no—
438C22⋊C8—1221no—
439#97—1221no—
440#97—1221no—
441#97—1221no—
442#97C22⋊D6111yescharacteristic
443#97C22⋊D6111yescharacteristic
444C4×C8—611no—
445C4×C8—611no—
446C4×C8—611no—
447C4×C8—611no—
448C4×C8C22×D6111yescharacteristic
449C4×C8C22×D6111yescharacteristic
450#41—42no—
451#41—42no—
452#41—1222no—
453#41—2441no—
454C2×Q8—21no—
455C2×Q8—611no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—611no—
461C2×D4—1221no—
462C2×D4C2×C4×D6111yescharacteristic
463C2×D4C2×C4×D6111yescharacteristic
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—1221no—
467C22×C4—1221no—
468C22×C4—1221no—
469C22×C4C2×C4×D6111yescharacteristic
470C22×C4#1175822211yescharacteristic
471C22×C4C2×C22⋊D6111yescharacteristic
472SD16—2441no—
473SD16—2441no—
474D8—1222no—
475D8—1222no—
476M16—22no—
477M16—41no—
478M16—42no—
479M16—42no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—42no—
483C2×C8—42no—
484C2×C8—42no—
485C2×C8—611no—
486C2×C8—611no—
487C2×C8—611no—
488C2×C8—611no—
489C2×C8—1221no—
490C2×C8—1221no—
491C2×C8—1221no—
492C2×C8—1221no—
493C2×C8—2442no—
494C2×C8—2442no—
495C2×C8C2×C22⋊D6111yescharacteristic
496C2×C8C2×C22⋊D6111yescharacteristic
497C2×C8C2×C22⋊D6111yescharacteristic
498C2×C8C2×C22⋊D6111yescharacteristic
499C4⋊C4—21no—
500C4⋊C4—611no—
501C4⋊C4—611no—
502C4⋊C4—1221no—
503C4⋊C4—1221no—
504C4⋊C4C2×C4×D6111yescharacteristic
505C4⋊C4C2×C4×D6111yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—1221no—
511C22⋊C4—1221no—
512C22⋊C4—1221no—
513C42—1221no—
514C42—1221no—
515C42—1221no—
516C42C2×C4×D6111yescharacteristic
517C42#1175822211yescharacteristic
518C42C2×C22⋊D6111yescharacteristic
519C42C23×D6111yescharacteristic
520C23—21no—
521C23—21no—
522C23—1221no—
523C23C4×C22⋊D6111yescharacteristic
524Q8—42no—
525Q8—1221no—
526Q8—1221no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—21no—
531D4—42no—
532D4—42no—
533D4—42no—
534D4—81no—
535D4—612no—
536D4—1221no—
537D4—2442no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—1221no—
550C2×C4—1221no—
551C2×C4—1221no—
552C2×C4—4881no—
553C2×C4—2442no—
554C2×C4—2441no—
555C2×C4—2441no—
556C2×C4C4×C22⋊D6111yescharacteristic
557C2×C4C4×C22⋊D6111yescharacteristic
558C2×C4C4×C22⋊D6111yescharacteristic
559C2×C4C22×C4×D6111yescharacteristic
560C2×C4C22×C22⋊D6111yescharacteristic
561C2×C4C2×#1175822211yescharacteristic
562C8—21no—
563C8—21no—
564C8—21no—
565C8—41no—
566C8—41no—
567C8—1221no—
568C8—1221no—
569C8—1221no—
570C8—1221no—
571C8—2441no—
572C8—2441no—
573C8—2441no—
574C8—2441no—
575C8#1451980312yes—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—1222no—
586C22—2441no—
587C22—2441no—
588C22C2×C4×C22⋊D6111yescharacteristic
589C4—21no—
590C4—21no—
591C4—21no—
592C4—21no—
593C4—41no—
594C4—41no—
595C4—2441no—
596C4—2441no—
597C4—2441no—
598C4#131×D6111yescharacteristic
599C4#1684052711yescharacteristic
600C4C2×#1451980311yescharacteristic
601C4#1684056011yescharacteristic
602C2—41no—
603C2—81no—
604C2—81no—
605C2—2442no—
606C2#2145454111yescharacteristic
607C2C4×#1451980311yescharacteristic
608C2#2145473411yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#2935C2
socleC22×C61C2×C4×D4
prime radical#21455873C2
cosocleC42×C61C24
hypercenter#2935D61
hypocenterC61#18007
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2935

Complements

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

NH ≅ G/Ntype
2. #21454834C2semidirect
3. #21444721C2semidirect
4. #21444707C2semidirect
5. #21444681C2semidirect
6. #21444676C2semidirect
7. #21444655C2semidirect
8. #21444646C2semidirect
9. #21444641C2semidirect
10. C8×#11758199C2semidirect
11. #21444602C2semidirect
12. #21444288C2semidirect
13. #21444204C2semidirect
14. #21444116C2semidirect
15. C61×#2935C2semidirect
250. D244#131semidirect
300. #2935D61semidirect
371. C61#18007semidirect

Maximal subgroups

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

subgroupindex
#214558732
#214548342
#214447212
#214447072
#214446812
#214446762
#214446552
#214446462
#214446412
C8×#117581992
#214446022
#214442882
#214442042
#214441162
C61×#29352
#1800761