Finite Group Databasebeta

← #29721510

Subgroups — #29721510

Order 15616.

690 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455637C211yesmaximal, characteristic, complemented
2C4×#14519803C211yesmaximal, characteristic
3#21454484C211yesmaximal, characteristic, complemented
4#21447265C211yesmaximal, characteristic, complemented
5#21447260C211yesmaximal, characteristic, complemented
6#21447112C211yesmaximal, characteristic
7#21447112C211yesmaximal, characteristic
8#21446813C211yesmaximal, characteristic, complemented
9#21446602C211yesmaximal, characteristic, complemented
10#21446597C211yesmaximal, characteristic, complemented
11#21446595C211yesmaximal, characteristic, complemented
12#21446478C211yesmaximal, characteristic, complemented
13#21446478C211yesmaximal, characteristic, complemented
14#21445811C211yesmaximal, characteristic, complemented
15C2×C61×#478C211yesmaximal, characteristic, complemented
16C2×#14519803C2211yescharacteristic
17C4×#11758222C2211yescharacteristic
18#16840066—21no—
19#16840066—21no—
20#16840059—21no—
21#16840059—21no—
22#16839872—21no—
23#16839862—21no—
24C4×#11758200—21no—
25C4×#11758199—21no—
26#16839822—21no—
27#16839822—21no—
28#16839818—21no—
29#16839814—21no—
30C2×#14519713C2211yescharacteristic
31C2×#14519713C2211yescharacteristic
32#16839802C2211yescharacteristic
33#16839802C2211yescharacteristic
34#16839802C2211yescharacteristic
35#16839786C2211yescharacteristic
36#16839786C2211yescharacteristic
37#16839767C2211yescharacteristic
38#16839761C2211yescharacteristic
39#16839761C2211yescharacteristic
40#16839761C2211yescharacteristic
41C2×#14519694C2211yescharacteristic
42C2×#14519694C2211yescharacteristic
43#16839728C2211yescharacteristic
44#16839728C2211yescharacteristic
45#16839717C2211yescharacteristic
46#16839717C2211yescharacteristic
47C4×#11758194C2211yescharacteristic
48#16839531C2211yescharacteristic
49#16839531C2211yescharacteristic
50#16839531C2211yescharacteristic
51#16839531C2211yescharacteristic
52#16839531C2211yescharacteristic
53#16839531C2211yescharacteristic
54#16839527C2211yescharacteristic
55#16839527C2211yescharacteristic
56C2×#125×C61C2211yescharacteristic
57C2×C4×D4×C61C2211yescharacteristic
58C61×#478—21no—
59C61×#478—21no—
60C61×#478—21no—
61C61×#478—21no—
62C2×#107×C61C2211yescharacteristic
63C2×#106×C61C2211yescharacteristic
64C2×C4⋊C8×C61C2211yescharacteristic
65C2×#102×C61C2211yescharacteristic
66C2×#102×C61C2211yescharacteristic
67C2×#11758222C2311yescharacteristic
68#14519803—22no—
69#14519803—22no—
70C2×#11758200—21no—
71C2×#11758199—21no—
72C2×#11758194C2311yescharacteristic
73C2×#11758194C2311yescharacteristic
74C2×#11758194C2311yescharacteristic
75C2×#11758194C2311yescharacteristic
76C2×#11758194C2311yescharacteristic
77C2×#11758194C2311yescharacteristic
78C4×Dic122D411yescharacteristic
79C4×Dic122D411yescharacteristic
80C4×D244D411yescharacteristic
81C4×D244D411yescharacteristic
82C4×C22⋊D61—21no—
83C4×C22⋊D61—21no—
84#14519736C2311yescharacteristic
85#14519734—21no—
86C42×D61—21no—
87#14519713—22no—
88#14519713—22no—
89#14519710—21no—
90#14519710—21no—
91#14519710—21no—
92#14519708—21no—
93#14519708—21no—
94#14519708—21no—
95C4⋊#92418—21no—
96C4⋊#92418—21no—
97C4⋊#92418—21no—
98C4⋊#92418—21no—
99#14519700—21no—
100#14519700—21no—
101#14519700—21no—
102#14519698—21no—
103#14519698—21no—
104#14519697—21no—
105#14519697—21no—
106#14519697—21no—
107#14519694—22no—
108#14519694—22no—
109#14519689—21no—
110#14519689—21no—
111#14519689—21no—
112#14519689—21no—
113#14519688—21no—
114#14519687—21no—
115#14519687—21no—
116C4×#92418—21no—
117C8×Dic61—21no—
118C8×Dic61—21no—
119C22×D4×C61C2311yescharacteristic
120C23×C4×C61—21no—
121C22×C8×C61C2311yescharacteristic
122C22×C8×C61C2311yescharacteristic
123#125×C61—21no—
124#125×C61—21no—
125#125×C61—21no—
126#125×C61—21no—
127C4×D4×C61—21no—
128C4×D4×C61—21no—
129C4×D4×C61—21no—
130C4×D4×C61—21no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C22⋊C4×C61—21no—
137C2×C42×C61C2311yescharacteristic
138#107×C61—21no—
139#107×C61—21no—
140#106×C61—21no—
141#106×C61—21no—
142C4⋊C8×C61D411yescharacteristic
143C4⋊C8×C61D411yescharacteristic
144C4⋊C8×C61D411yescharacteristic
145C4⋊C8×C61D411yescharacteristic
146#102×C61—21no—
147#102×C61—21no—
148#102×C61—21no—
149#102×C61—21no—
150C24×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61#4112yes—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—41no—
161C22×C4×C61—41no—
162C22×C4×C61—82no—
163C22×C4×C61#4111yescharacteristic
164C22×C4×C61#4111yescharacteristic
165C22×C4×C61C2411yescharacteristic
166C2×C22⋊D61—21no—
167#11758222—21no—
168#11758222—21no—
169#11758222—21no—
170#11758222—21no—
171C2×D244C2×D411yescharacteristic
172C2×C4×D61—21no—
173C2×C4×D61—21no—
174C2×C4×D61—21no—
175C2×Dic122C2×D411yescharacteristic
176C2×C8×C61—21no—
177C2×C8×C61—21no—
178C2×C8×C61—21no—
179C2×C8×C61—21no—
180C2×C8×C61C2×D411yescharacteristic
181C2×C8×C61C2×D411yescharacteristic
182C2×C8×C61C2×D411yescharacteristic
183C2×C8×C61C2×D411yescharacteristic
184C4⋊C4×C61—21no—
185C4⋊C4×C61—21no—
186C4⋊C4×C61—21no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61—41no—
191C4⋊C4×C61—41no—
192C4⋊C4×C61—41no—
193C4⋊C4×C61—41no—
194C22⋊C4×C61—41no—
195C22⋊C4×C61—41no—
196C42×C61C2×D411yescharacteristic
197C42×C61C2×D411yescharacteristic
198C42×C61C2×D411yescharacteristic
199C42×C61C2×D411yescharacteristic
200C22⋊Dic61—21no—
201#11758200—24no—
202#11758199—24no—
203#11758198—21no—
204#11758198—21no—
205C4⋊Dic61C2×D411yescharacteristic
206C4⋊Dic61C2×D411yescharacteristic
207#11758196—21no—
208#11758196—21no—
209C4×Dic61—21no—
210C4×Dic61—21no—
211C4×Dic61—21no—
212#11758194—21no—
213#11758194—21no—
214#11758194—21no—
215#11758194—21no—
216#11758194—21no—
217#11758194—21no—
218#11758194—21no—
219#11758194—21no—
220#11758194—21no—
221#11758194—21no—
222#11758194—21no—
223#11758194#4112yes—
224C2×#92418—21no—
225C2×#92418—21no—
226C2×#92418—21no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C23×C61—22no—
231C23×C61—41no—
232C23×C61—41no—
233C23×C61—81no—
234C23×C61—81no—
235C23×C61C2×#4111yescharacteristic
236C22×D61—21no—
237D4×C61—22no—
238D4×C61—22no—
239D4×C61—41no—
240D4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—82no—
247C2×C4×C61—82no—
248C2×C4×C61—81no—
249C2×C4×C61—81no—
250C2×C4×C61—81no—
251C2×C4×C61#12111yescharacteristic
252C2×C4×C61#12111yescharacteristic
253C2×C4×C61#12111yescharacteristic
254C2×C4×C61#12111yescharacteristic
255C2×C4×C61C22×D411yescharacteristic
256C2×C4×C61C22×D411yescharacteristic
257C2×C4×C61C2×#4111yescharacteristic
258C2×C4×C61C2×#4111yescharacteristic
259C2×C4×C612−1+411yescharacteristic
260C2×C4×C612−1+411yescharacteristic
261C22⋊D61—41no—
262C22⋊D61—41no—
263C2×Dic61—21no—
264C2×Dic61—21no—
265C2×Dic61—21no—
266D244—21no—
267D244—21no—
268C4×D61—42no—
269C4×D61—41no—
270C4×D61—41no—
271C4×D61—81no—
272Dic122—21no—
273Dic122—21no—
274C8×C61—21no—
275C8×C61—21no—
276C8×C61—21no—
277C8×C61—21no—
278#92418—22no—
279#92418—41no—
280#92418—41no—
281#92418—41no—
282#92418—41no—
283#92418—41no—
284#24724—611nomaximal, Sylow
285C22×C61—21no—
286C22×C61—21no—
287C22×C61—42no—
288C22×C61—82no—
289C22×C61—82no—
290C22×C61—81no—
291C22×C61—81no—
292C22×C61C2×#12111yescharacteristic
293C22×C61#55211yescharacteristic
294C22×C61#55611yescharacteristic
295C2×D61—41no—
296C2×D61—41no—
297C2×D61—41no—
298C4×C61—21no—
299C4×C61—21no—
300C4×C61—21no—
301C4×C61—21no—
302C4×C61—81no—
303C4×C61—81no—
304C4×C61—81no—
305C4×C61#52511yescharacteristic
306C4×C61#53611yescharacteristic
307C4×C61#54711yescharacteristic
308C4×C61#54811yescharacteristic
309Dic61—41no—
310Dic61—41no—
311Dic61—41no—
312#3080—611no—
313C2×#478D6111yescharacteristic, complemented
314C4×AGL(1,ℤ/8)—611no—
315#2925—611no—
316#2079—611no—
317#2078—611no—
318#2051—611no—
319#2051—611no—
320#1998—611no—
321#1952—611no—
322#1951—611no—
323#1950—611no—
324#1931—611no—
325#1931—611no—
326#1800—611no—
327C2×C61—21no—
328C2×C61—21no—
329C2×C61—82no—
330C2×C61#241511yescharacteristic
331C2×C61#306711yescharacteristic
332C2×C61#306811yescharacteristic
333D61—81no—
334C2×AGL(1,ℤ/8)—611no—
335C2×#125C2×D6111yescharacteristic
336C4×#41—611no—
337C2×C4×D4C2×D6111yescharacteristic
338#479—1221no—
339#479—1221no—
340#478—21no—
341#478—21no—
342#478—21no—
343#478—21no—
344#478—1221no—
345#478—1221no—
346#442—1221no—
347#440—1221no—
348C4×SD16—1221no—
349C4×D8—1221no—
350#433—1221no—
351#433—1221no—
352#432—1221no—
353#431—1221no—
354C2×#108—611no—
355C2×#108—611no—
356#428—611no—
357#428—611no—
358#428—611no—
359C2×#107C2×D6111yescharacteristic
360C2×#106C2×D6111yescharacteristic
361#423—611no—
362#423—611no—
363C2×C4⋊C8C2×D6111yescharacteristic
364#418—611no—
365#417—611no—
366#417—611no—
367#417—611no—
368C2×#102C2×D6111yescharacteristic
369C2×#102C2×D6111yescharacteristic
370C2×#100—611no—
371C2×#100—611no—
372#408—611no—
373#408—611no—
374#405—611no—
375#405—611no—
376C4×M16—611no—
377#343—611no—
378#343—611no—
379#343—611no—
380#343—611no—
381#343—611no—
382#343—611no—
383#341—611no—
384#341—611no—
385C61#2472411yescharacteristic, complemented, Sylow
386C2×#41—611no—
387C22×D4C22×D6111yescharacteristic
388C23×C4—21no—
389AGL(1,ℤ/8)—1222no—
390AGL(1,ℤ/8)—1222no—
391C2×SD16—1221no—
392C2×D8—1221no—
393C2×M16—611no—
394C2×M16—611no—
395C2×M16—611no—
396C2×M16—611no—
397C2×M16—611no—
398C2×M16—611no—
399C22×C8C22×D6111yescharacteristic
400C22×C8C22×D6111yescharacteristic
401#125—21no—
402#125—21no—
403#125—21no—
404#125—21no—
405C4×Q8—611no—
406C4×Q8—611no—
407C4×D4—21no—
408C4×D4—21no—
409C4×D4—21no—
410C4×D4—21no—
411C4×D4—611no—
412C4×D4—611no—
413C4×D4—1221no—
414C4×D4—1221no—
415#117—611no—
416#117—1221no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4C22×D6111yescharacteristic
420C2×C4⋊C4C22×D6111yescharacteristic
421C2×C4⋊C4C22×D6111yescharacteristic
422C2×C22⋊C4—21no—
423C2×C42—1221no—
424C2×C42C22×D6111yescharacteristic
425#108—1222no—
426#108—1222no—
427#107—21no—
428#107—21no—
429#107—1221no—
430#107—1221no—
431#107—1221no—
432#106—21no—
433#106—21no—
434#106—1221no—
435#106—1221no—
436#106—1221no—
437C4⋊C8—1221no—
438C4⋊C8—1221no—
439C4⋊C8—1221no—
440C4⋊C8—1221no—
441C4⋊C8C22⋊D6111yescharacteristic
442C4⋊C8C22⋊D6111yescharacteristic
443C4⋊C8C22⋊D6111yescharacteristic
444C4⋊C8C22⋊D6111yescharacteristic
445#103—1221no—
446#103—1221no—
447#103—1221no—
448#102—21no—
449#102—21no—
450#102—21no—
451#102—21no—
452#102—1221no—
453#102—1221no—
454#102—1221no—
455#102—1221no—
456#102—1221no—
457#100—1222no—
458#100—1222no—
459C22⋊C8—1221no—
460C22⋊C8—1221no—
461C22⋊C8—1221no—
462C22⋊C8—1221no—
463#97—1221no—
464#97—1221no—
465#97—1221no—
466C4×C8—1221no—
467C4×C8—1221no—
468C4×C8—1221no—
469C24—21no—
470#41—1221no—
471#41—1221no—
472#41—1221no—
473#41—1221no—
474C2×Q8—611no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—611no—
481C2×D4—1221no—
482C2×D4#1175822612yes—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—82no—
489C22×C4—1221no—
490C22×C4—1221no—
491C22×C4—1221no—
492C22×C4#1175822411yescharacteristic
493C22×C4#1175822411yescharacteristic
494C22×C4C23×D6111yescharacteristic
495SD16—1224no—
496D8—1224no—
497M16—612no—
498M16—1221no—
499M16—1221no—
500M16—1221no—
501M16—1221no—
502M16—1221no—
503M16—1221no—
504M16—1221no—
505M16—1221no—
506M16—1221no—
507M16—1221no—
508M16—1221no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—1221no—
514C2×C8—1221no—
515C2×C8—1221no—
516C2×C8—1221no—
517C2×C8—1221no—
518C2×C8—1221no—
519C2×C8C2×C22⋊D6111yescharacteristic
520C2×C8C2×C22⋊D6111yescharacteristic
521C2×C8C2×C22⋊D6111yescharacteristic
522C2×C8C2×C22⋊D6111yescharacteristic
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—41no—
532C4⋊C4—41no—
533C4⋊C4—611no—
534C4⋊C4—611no—
535C4⋊C4—1221no—
536C4⋊C4—1221no—
537C22⋊C4—41no—
538C22⋊C4—41no—
539C22⋊C4—1221no—
540C22⋊C4—1221no—
541C22⋊C4—1221no—
542C42—1221no—
543C42—1221no—
544C42—1221no—
545C42D4×D6111yescharacteristic
546C42D4×D6111yescharacteristic
547C42C2×C22⋊D6111yescharacteristic
548C42C2×C22⋊D6111yescharacteristic
549C23—22no—
550C23—41no—
551C23—41no—
552C23—81no—
553C23—81no—
554C23—1221no—
555C23C2×#1175822411yescharacteristic
556Q8—1221no—
557Q8—1221no—
558D4—22no—
559D4—22no—
560D4—41no—
561D4—41no—
562D4—1221no—
563D4—1221no—
564D4—2441no—
565D4—2441no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—82no—
572C2×C4—82no—
573C2×C4—81no—
574C2×C4—81no—
575C2×C4—81no—
576C2×C4—1221no—
577C2×C4—1221no—
578C2×C4—1221no—
579C2×C4—4881no—
580C2×C4—2442no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4#1451974811yescharacteristic
584C2×C4#1451974811yescharacteristic
585C2×C4#1451974811yescharacteristic
586C2×C4#1451974811yescharacteristic
587C2×C4C2×D4×D6111yescharacteristic
588C2×C4C22×C22⋊D6111yescharacteristic
589C2×C4#41×D6111yescharacteristic
590C2×C4C2×#1175822611yescharacteristic
591C2×C4#1451982411yescharacteristic
592C2×C4#1451982511yescharacteristic
593C8—21no—
594C8—21no—
595C8—21no—
596C8—21no—
597C8—1222no—
598C8—2441no—
599C8—2441no—
600C8—2441no—
601C8—2441no—
602C8—2441no—
603C22—21no—
604C22—21no—
605C22—42no—
606C22—82no—
607C22—82no—
608C22—81no—
609C22—81no—
610C22—2441no—
611C22—2441no—
612C22—2441no—
613C22C2×#1451974811yescharacteristic
614C22#1684045411yescharacteristic
615C22#1684048311yescharacteristic
616C4—21no—
617C4—21no—
618C4—21no—
619C4—21no—
620C4—81no—
621C4—81no—
622C4—81no—
623C4—2441no—
624C4—2441no—
625C4—2441no—
626C4#1684027511yescharacteristic
627C4#1684033511yescharacteristic
628C4#1684041111yescharacteristic
629C4#1684042311yescharacteristic
630C2—21no—
631C2—21no—
632C2—82no—
633C2—4881no—
634C2#2144924411yescharacteristic
635C2#2145553511yescharacteristic
636C2#2145554311yescharacteristic
subgroupG/H
centerC22C2×#14519748
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#478C2
socleC22×C61C2×#121
prime radicalC2×#14519803C22
hypercenterC2×#478D61
hypocenterC61#24724
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. #21455637C2semidirect
3. #21454484C2semidirect
4. #21447265C2semidirect
5. #21447260C2semidirect
8. #21446813C2semidirect
9. #21446602C2semidirect
10. #21446597C2semidirect
11. #21446595C2semidirect
12. #21446478C2semidirect
13. #21446478C2semidirect
14. #21445811C2semidirect
15. C2×C61×#478C2semidirect
313. C2×#478D61semidirect
385. C61#24724semidirect

Maximal subgroups

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

subgroupindex
#214556372
C4×#145198032
#214544842
#214472652
#214472602
#214471122
#214468132
#214466022
#214465972
#214465952
#214464782
#214458112
C2×C61×#4782
#2472461