Finite Group Databasebeta

← #29663399

Subgroups — #29663399

Order 15616.

628 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457146C211yesmaximal, characteristic, complemented
2#21457139C211yesmaximal, characteristic, complemented
3#21456394C211yesmaximal, characteristic, complemented
4#21454788C211yesmaximal, characteristic, complemented
5#21445362C211yesmaximal, characteristic, complemented
6#21445358C211yesmaximal, characteristic, complemented
7#21445355C211yesmaximal, characteristic, complemented
8#21445351C211yesmaximal, characteristic, complemented
9#21445222C211yesmaximal, characteristic, complemented
10#21445217C211yesmaximal, characteristic, complemented
11#21445178C211yesmaximal, characteristic, complemented
12#21445173C211yesmaximal, characteristic, complemented
13C2×#16839514C211yesmaximal, characteristic, complemented
14#21444515C211yesmaximal, characteristic, complemented
15C61×#1551C211yesmaximal, characteristic, complemented
16#16840312C2211yescharacteristic
17#16840296C2211yescharacteristic
18#16840165C2211yescharacteristic
19#16840138C2211yescharacteristic
20#16840110C2211yescharacteristic
21#16840108C2211yescharacteristic
22#16840063—21no—
23#16840062—21no—
24#16840058C2211yescharacteristic
25#16840054C2211yescharacteristic
26#16840053C2211yescharacteristic
27#16840049C2211yescharacteristic
28#16839998—21no—
29#16839996—21no—
30#16839996—21no—
31#16839996—21no—
32#16839991—21no—
33#16839989—21no—
34#16839978—21no—
35#16839977—21no—
36#16839963C2211yescharacteristic
37#16839959C2211yescharacteristic
38#16839958C2211yescharacteristic
39#16839954C2211yescharacteristic
40#16839889C2211yescharacteristic
41#16839886C2211yescharacteristic
42C4×#11758199—21no—
43C4×#11758199—21no—
44#16839839C2211yescharacteristic
45#16839830—21no—
46#16839827C2211yescharacteristic
47#16839825—21no—
48#16839824—21no—
49C2×C4⋊#92418C2211yescharacteristic
50#16839719—21no—
51C2×C4×#92418C2211yescharacteristic
52#16839514C2211yescharacteristic
53#16839514C2211yescharacteristic
54#16839514C2211yescharacteristic
55#16839514C2211yescharacteristic
56#16839510C2211yescharacteristic
57#16839510C2211yescharacteristic
58#16839505C2211yescharacteristic
59#16839505C2211yescharacteristic
60C61×#532C2211yescharacteristic
61C61×#432C2211yescharacteristic
62C2×C4⋊C8×C61C2211yescharacteristic
63C61×#333C2211yescharacteristic
64C61×#333C2211yescharacteristic
65C61×#331C2211yescharacteristic
66C61×#331C2211yescharacteristic
67C2×#11758222—21no—
68C2×#11758190—21no—
69C2×#11758200—21no—
70C2×D488—21no—
71C2×#11758199—21no—
72C2×#11758199—21no—
73C2×#11758199—21no—
74C2×#11758189—21no—
75C22×#92418—21no—
76C22×#92418D411yescharacteristic
77C22×#92418D411yescharacteristic
78C2×C8×D61—21no—
79#14519777C2311yescharacteristic
80#14519774C2311yescharacteristic
81#14519771—21no—
82#14519769D411yescharacteristic
83#14519765—21no—
84#14519765D411yescharacteristic
85#14519760—21no—
86#14519756D411yescharacteristic
87#14519751—21no—
88#14519751—21no—
89#14519751D411yescharacteristic
90C4×Dic122C2311yescharacteristic
91C4×D244—21no—
92C4×D244—21no—
93C4×D244C2311yescharacteristic
94C4×C22⋊D61—21no—
95#14519734—21no—
96#14519711—21no—
97#14519710—21no—
98#14519710—21no—
99#14519710—21no—
100#14519709—21no—
101#14519708—21no—
102C4⋊#92418—21no—
103C4⋊#92418C2311yescharacteristic
104C4⋊#92418C2311yescharacteristic
105#14519706—21no—
106#14519706—21no—
107#14519702—21no—
108#14519700—21no—
109#14519699—21no—
110#14519699—21no—
111#14519699—21no—
112#14519698—21no—
113#14519698—21no—
114#14519698—21no—
115#14519698—21no—
116#14519697—21no—
117#14519697—21no—
118#14519697—21no—
119#14519689—21no—
120#14519689—21no—
121#14519687—21no—
122C4×#92418D411yescharacteristic
123C4×#92418D411yescharacteristic
124C4×#92418C2311yescharacteristic
125C4×#92418C2311yescharacteristic
126C8×Dic61—21no—
127C2×#41×C61—21no—
128C22×C8×C61—21no—
129C4⋊Q8×C61C2311yescharacteristic
130#127×C61C2311yescharacteristic
131#124×C61—21no—
132#121×C61—21no—
133#121×C61—21no—
134C4×D4×C61—21no—
135C4×D4×C61—21no—
136C2×C42×C61C2311yescharacteristic
137C4⋊C8×C61—21no—
138C4⋊C8×C61C2311yescharacteristic
139C4⋊C8×C61C2311yescharacteristic
140C4⋊C8×C61C2311yescharacteristic
141C4⋊C8×C61C2311yescharacteristic
142C22⋊C8×C61—21no—
143#97×C61—21no—
144#41×C61—82no—
145C2×Q8×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—41no—
150C22×C4×C61—41no—
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61#4111yescharacteristic
154C2×C22⋊D61—21no—
155C2×C22⋊D61—41no—
156#11758222—82no—
157C2×D244—21no—
158C2×D244—21no—
159C2×D244—21no—
160C2×D244C2×D411yescharacteristic
161C2×C4×D61—21no—
162C2×C4×D61—41no—
163C2×Dic122—21no—
164C2×Dic122C2×D411yescharacteristic
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—81no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C22⋊C4×C61—41no—
173C22⋊C4×C61—41no—
174C42×C61C2×D411yescharacteristic
175C42×C61C2×D411yescharacteristic
176C42×C61#4111yescharacteristic
177C42×C61C2411yescharacteristic
178C22⋊Dic61—21no—
179#11758200—81no—
180#11758199—42no—
181#11758199—42no—
182#11758199—81no—
183#11758198—21no—
184#11758198—21no—
185#11758198—21no—
186#11758198—21no—
187#11758198—41no—
188#11758198—41no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61C2×D411yescharacteristic
192C4⋊Dic61C2×D411yescharacteristic
193#11758196—21no—
194#11758196—21no—
195#11758196—21no—
196#11758196—21no—
197C4×Dic61—21no—
198C2×#92418—22no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—41no—
202C2×#92418—81no—
203C2×#92418C2×D411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206C2×#92418C2×D411yescharacteristic
207D488—81no—
208#11758190—81no—
209#11758189—42no—
210C8×D61—42no—
211C23×C61—41no—
212C23×C61#12111yescharacteristic
213C22×D61—21no—
214C22×D61—41no—
215Q8×C61—81no—
216D4×C61—41no—
217D4×C61—41no—
218D4×C61—41no—
219D4×C61—41no—
220D4×C61—81no—
221D4×C61—82no—
222C2×C4×C61—22no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—41no—
228C2×C4×C61—82no—
229C2×C4×C61#12111yescharacteristic
230C2×C4×C61#12111yescharacteristic
231C2×C4×C61#12111yescharacteristic
232C2×C4×C61C22×D411yescharacteristic
233C2×C4×C61C22×D411yescharacteristic
234C2×C4×C61C2×#4111yescharacteristic
235C22⋊D61—42no—
236C22⋊D61—82no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—41no—
241D244—21no—
242D244—21no—
243D244—41no—
244D244—41no—
245D244—41no—
246D244—41no—
247D244—81no—
248C4×D61—41no—
249C4×D61—41no—
250C4×D61—82no—
251Dic122—21no—
252Dic122—21no—
253Dic122—81no—
254C8×C61—41no—
255C8×C61—41no—
256C8×C61—41no—
257C8×C61—41no—
258#92418—21no—
259#92418—21no—
260#92418—21no—
261#92418—41no—
262#92418—41no—
263#92418#13512yes—
264#19222—611nomaximal, Sylow
265C22×C61—21no—
266C22×C61—21no—
267C22×C61—81no—
268C22×C61—81no—
269C22×C61—81no—
270C22×C61#47212yes—
271C22×C61C2×#12111yescharacteristic
272C2×D61—41no—
273C2×D61—41no—
274C2×D61—41no—
275C2×D61—81no—
276C2×D61—81no—
277C2×D61—81no—
278C4×C61—21no—
279C4×C61—21no—
280C4×C61—21no—
281C4×C61—21no—
282C4×C61—81no—
283C4×C61C2×#13511yescharacteristic
284C4×C61#57511yescharacteristic
285C4×C61#57611yescharacteristic
286C4×C61#57811yescharacteristic
287Dic61—41no—
288Dic61—41no—
289Dic61—41no—
290Dic61—81no—
291#3247—611no—
292#3247—611no—
293#3169—611no—
294#2966—611no—
295#1698—611no—
296#1698—611no—
297#1697—611no—
298#1697—611no—
299#1676—611no—
300#1675—611no—
301#1668—611no—
302#1667—611no—
303C2×#335—611no—
304#1551—611no—
305#1551D6111yescharacteristic, complemented
306C2×C61—22no—
307C2×C61—161no—
308C2×C61#303511yescharacteristic
309C2×C61#306111yescharacteristic
310C2×C61C2×#47211yescharacteristic
311D61—81no—
312D61—161no—
313#532—611no—
314#532C2×D6111yescharacteristic
315#529—611no—
316#500—611no—
317#493—611no—
318#486—611no—
319#486—611no—
320#478—1221no—
321#478—1221no—
322#477—611no—
323#477—611no—
324#476—611no—
325#476—611no—
326#466—1221no—
327#466—1221no—
328#466—1221no—
329#466—1221no—
330#465—1221no—
331#465—1221no—
332#463—1221no—
333#463—1221no—
334#460—611no—
335#460—611no—
336#459—611no—
337#459—611no—
338#446—611no—
339C8×Q8—611no—
340C4×D8—1221no—
341C4×D8—1221no—
342#436—611no—
343#435—1221no—
344C8×D4—611no—
345C8×D4—1221no—
346#433—1221no—
347#432C2×D6111yescharacteristic
348C2×C4⋊C8—611no—
349C2×C4⋊C8C2×D6111yescharacteristic
350#405—1221no—
351C2×C4×C8—611no—
352#335—611no—
353#335—611no—
354#335—611no—
355#335—611no—
356#333—611no—
357#333—611no—
358#333C2×D6111yescharacteristic
359#333C2×D6111yescharacteristic
360#331—611no—
361#331—611no—
362#331C2×D6111yescharacteristic
363#331C2×D6111yescharacteristic
364C61#1922211yescharacteristic, complemented, Sylow
365C2×#41—21no—
366C2×#41—1221no—
367C2×SD16—1221no—
368C2×SD16—1221no—
369C2×D8—1221no—
370C2×D8—1221no—
371C2×D8—1221no—
372C2×D8—1221no—
373C2×M16—1221no—
374C22×C8—21no—
375C22×C8—611no—
376C22×C8—611no—
377C22×C8—1221no—
378C22×C8—1221no—
379C4⋊Q8—611no—
380C4⋊Q8C22×D6111yescharacteristic
381#127—611no—
382#127C22×D6111yescharacteristic
383#126—1221no—
384#125—611no—
385#124—21no—
386#124—611no—
387#124—1221no—
388#123—1221no—
389C22⋊Q8—611no—
390#121—21no—
391#121—21no—
392#121—611no—
393#121—1221no—
394#121—1221no—
395C4×Q8—611no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—611no—
399C4×D4—1221no—
400C4×D4—1221no—
401C4×D4—1221no—
402#117—1221no—
403C2×C42C22×D6111yescharacteristic
404#107—1221no—
405#107—1221no—
406#107—1221no—
407#107—1221no—
408#106—1221no—
409#106—1221no—
410C4⋊C8—21no—
411C4⋊C8—611no—
412C4⋊C8—611no—
413C4⋊C8—1221no—
414C4⋊C8—1221no—
415C4⋊C8—1221no—
416C4⋊C8C22×D6111yescharacteristic
417C4⋊C8C22×D6111yescharacteristic
418C4⋊C8C22×D6111yescharacteristic
419C4⋊C8C22×D6111yescharacteristic
420#103—1221no—
421#103—1221no—
422#102—1221no—
423#102—1221no—
424#102—1221no—
425#102—1221no—
426#102—1221no—
427#102—1221no—
428#102—1221no—
429#102—1221no—
430#102—1221no—
431#102—1221no—
432C22⋊C8—21no—
433C22⋊C8—1221no—
434C22⋊C8—1221no—
435#97—21no—
436#97—1221no—
437C4×C8—611no—
438C4×C8—611no—
439C4×C8—611no—
440C4×C8—611no—
441C4×C8—1221no—
442#41—82no—
443#41—4882no—
444C2×Q8—21no—
445C2×Q8—611no—
446C2×Q8—1221no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C2×D4—611no—
452C2×D4—1221no—
453C2×D4—1221no—
454C2×D4—1221no—
455C2×D4—1221no—
456C2×D4—2441no—
457C22×C4—41no—
458C22×C4—1221no—
459C22×C4—2441no—
460C22×C4#1175822211yescharacteristic
461C22×C4D4×D6111yescharacteristic
462C22×C4D4×D6111yescharacteristic
463SD16—4881no—
464SD16—4881no—
465D8—4881no—
466D8—4881no—
467D8—2442no—
468D8—2442no—
469M16—2442no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—81no—
475C2×C8—611no—
476C2×C8—611no—
477C2×C8—611no—
478C2×C8—611no—
479C2×C8—1222no—
480C2×C8—1221no—
481C2×C8—1221no—
482C2×C8—4881no—
483C2×C8—2442no—
484C2×C8—2441no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—611no—
488C4⋊C4—611no—
489C4⋊C4—1221no—
490C4⋊C4—1221no—
491C4⋊C4—1221no—
492C4⋊C4—1221no—
493C4⋊C4—1221no—
494C4⋊C4—1221no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—1221no—
498C22⋊C4—1221no—
499C22⋊C4—1221no—
500C22⋊C4—1221no—
501C22⋊C4—1221no—
502C22⋊C4—2441no—
503C22⋊C4—2441no—
504C42—1221no—
505C42#1175822211yescharacteristic
506C42D4×D6111yescharacteristic
507C42D4×D6111yescharacteristic
508C42C23×D6111yescharacteristic
509C23—41no—
510C23—1221no—
511C23—2441no—
512C23#1451975011yescharacteristic
513Q8—81no—
514Q8—1221no—
515Q8—1221no—
516Q8—4881no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—81no—
522D4—82no—
523D4—1221no—
524D4—1221no—
525D4—4881no—
526D4—4882no—
527D4—2442no—
528D4—2441no—
529D4—2441no—
530D4—2441no—
531D4—2441no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—82no—
539C2×C4—1221no—
540C2×C4—1221no—
541C2×C4—1221no—
542C2×C4—4882no—
543C2×C4—2441no—
544C2×C4—2441no—
545C2×C4—2441no—
546C2×C4#1451975011yescharacteristic
547C2×C4#1451975011yescharacteristic
548C2×C4#1451975011yescharacteristic
549C2×C4C2×D4×D6111yescharacteristic
550C2×C4C2×D4×D6111yescharacteristic
551C2×C4C2×#1175822211yescharacteristic
552C8—41no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—612no—
557C8—1221no—
558C8—1221no—
559C8—1221no—
560C8—2441no—
561C8—2441no—
562C22—21no—
563C22—21no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22—4881no—
568C22—4881no—
569C22—4881no—
570C22—2441no—
571C22—2441no—
572C22—2441no—
573C22#1684003112yes—
574C22C2×#1451975011yescharacteristic
575C4—21no—
576C4—21no—
577C4—21no—
578C4—21no—
579C4—81no—
580C4—4881no—
581C4—2441no—
582C4—2441no—
583C4—2441no—
584C4#135×D6111yescharacteristic
585C4#1684055911yescharacteristic
586C4#1684056611yescharacteristic
587C4#1684057811yescharacteristic
588C2—22no—
589C2—161no—
590C2—9761no—
591C2—4881no—
592C2#2145527211yescharacteristic
593C2#2145548811yescharacteristic
594C2C2×#1684003111yescharacteristic
subgroupG/H
centerC22C2×#14519750
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1551C2
socleC22×C61C2×#121
hypercenter#1551D61
hypocenterC61#19222
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1551

Complements

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

NH ≅ G/Ntype
1. #21457146C2semidirect
2. #21457139C2semidirect
3. #21456394C2semidirect
4. #21454788C2semidirect
5. #21445362C2semidirect
6. #21445358C2semidirect
7. #21445355C2semidirect
8. #21445351C2semidirect
9. #21445222C2semidirect
10. #21445217C2semidirect
11. #21445178C2semidirect
12. #21445173C2semidirect
13. C2×#16839514C2semidirect
14. #21444515C2semidirect
15. C61×#1551C2semidirect
305. #1551D61semidirect
364. C61#19222semidirect

Maximal subgroups

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

subgroupindex
#214571462
#214571392
#214563942
#214547882
#214453622
#214453582
#214453552
#214453512
#214452222
#214452172
#214451782
#214451732
C2×#168395142
#214445152
C61×#15512
#1922261