Finite Group Databasebeta

← #35561266

Subgroups — #35561266

Order 21248.

580 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24919866C211yesmaximal, characteristic, complemented
2#24919150C211yesmaximal, characteristic, complemented
3#24909695C211yesmaximal, characteristic, complemented
4#24909666C211yesmaximal, characteristic, complemented
5#24909655C211yesmaximal, characteristic, complemented
6#24909621C211yesmaximal, characteristic, complemented
7#24909559C211yesmaximal, characteristic, complemented
8#24909549C211yesmaximal, characteristic, complemented
9#24909519C211yesmaximal, characteristic, complemented
10#24909388C211yesmaximal, characteristic, complemented
11#24909377C211yesmaximal, characteristic, complemented
12C4×D1328C211yesmaximal, characteristic, complemented
13#24909171C211yesmaximal, characteristic, complemented
14C2×#19127503C211yesmaximal, characteristic, complemented
15D4×C16×C83C211yesmaximal, characteristic, complemented
16C2×#14581814C2211yescharacteristic
17C22×D664C2211yescharacteristic
18#19128397—21no—
19#19128347—21no—
20C2×#14581737C2211yescharacteristic, complemented
21C2×D1328C2211yescharacteristic
22C2×D1328C2211yescharacteristic
23#19128103C2211yescharacteristic, complemented
24#19128085C2211yescharacteristic
25#19128026—21no—
26#19128020—21no—
27#19128002—21no—
28#19127942C2211yescharacteristic
29#19127937C2211yescharacteristic
30#19127937C2211yescharacteristic
31#19127937C2211yescharacteristic, complemented
32#19127917—21no—
33#19127854—21no—
34#19127848—21no—
35C4×D664C2211yescharacteristic
36C4×D664C2211yescharacteristic, complemented
37#19127739C2211yescharacteristic, complemented
38C2×#14581726C2211yescharacteristic
39#19127529C2211yescharacteristic, complemented
40#19127527C2211yescharacteristic, complemented
41#19127527C2211yescharacteristic, complemented
42#19127506C2211yescharacteristic, complemented
43#19127506C2211yescharacteristic, complemented
44#19127506C2211yescharacteristic, complemented
45#19127503C2211yescharacteristic
46#19127503C2211yescharacteristic
47#19127503C2211yescharacteristic
48#19127503C2211yescharacteristic
49#19127503C2211yescharacteristic
50#19127503C2211yescharacteristic
51#19127503C2211yescharacteristic, complemented
52C22×C16×C83C2211yescharacteristic
53C22×C16×C83C2211yescharacteristic, complemented
54C8×D4×C83C2211yescharacteristic
55C4⋊C16×C83C2211yescharacteristic, complemented
56C22⋊C16×C83C2211yescharacteristic
57C22⋊C16×C83C2211yescharacteristic, complemented
58C4×C16×C83C2211yescharacteristic, complemented
59C2×#13050590—21no—
60C22×D332—21no—
61#14581814—22no—
62#14581814—41no—
63C2×Dic332C2311yescharacteristic
64C2×#13050579—21no—
65C2×#13050579—21no—
66C2×D664—22no—
67C2×D664—21no—
68C2×D664—41no—
69C2×D664C2311yescharacteristic
70C2×D664C2311yescharacteristic
71C2×D664C2311yescharacteristic
72#14581787—41no—
73#14581784—21no—
74#14581780—21no—
75#14581777—41no—
76#14581774—41no—
77#14581771—21no—
78#14581766—21no—
79#14581766—21no—
80#14581766—21no—
81#14581765—41no—
82#14581764—41no—
83#14581760—41no—
84C4×D332—21no—
85C4×D332—21no—
86(C22⋊D83)⋊C4—41no—
87#14581751—21no—
88C2×C4⋊Dic83—21no—
89C22⋊C4×D83—41no—
90#14581737—41no—
91D1328—22no—
92D1328—41no—
93#14581726—21no—
94#14581726C2311yescharacteristic
95#14581726C2311yescharacteristic
96#14581726C2311yescharacteristic
97#14581726C2311yescharacteristic
98#14581724—21no—
99#14581724—21no—
100#14581717—21no—
101#14581714—21no—
102#14581714—21no—
103#14581714—21no—
104#14581714—21no—
105#14581714—21no—
106C22×C8×C83C2311yescharacteristic
107C22×C8×C83C2311yescharacteristic
108C4×D4×C83D411yescharacteristic
109C2×C16×C83—41no—
110C2×C16×C83—41no—
111C2×C16×C83C2311yescharacteristic
112C2×C16×C83C2311yescharacteristic
113C2×C16×C83C2311yescharacteristic
114C2×C16×C83C2311yescharacteristic
115C4⋊C8×C83D411yescharacteristic
116C22⋊C8×C83D411yescharacteristic
117C22⋊C8×C83D411yescharacteristic
118C4×C8×C83C2311yescharacteristic
119C23×D83—41no—
120#13050590—42no—
121#13050590—81no—
122C2×Dic166—21no—
123C2×D332—21no—
124C2×D332—21no—
125C2×D332—21no—
126C2×D332—42no—
127C2×D332—41no—
128C2×D332—81no—
129C2×C22⋊D83—41no—
130C2×C22⋊D83—41no—
131C2×C22⋊D83—41no—
132C2×C22⋊D83—41no—
133C22×Dic83—41no—
134C2×C4×D83—41no—
135C2×C4×D83—41no—
136C2×C4×D83—41no—
137Dic332—21no—
138Dic332—21no—
139#13050579—42no—
140#13050579—81no—
141D664—21no—
142D664—21no—
143D664—21no—
144D664—21no—
145D664—21no—
146D664—42no—
147D664#4112yes—
148C4⋊Dic83—21no—
149C4⋊Dic83—21no—
150C4⋊Dic83—21no—
151C4⋊Dic83—21no—
152C4⋊Dic83—41no—
153Dic83⋊C4—41no—
154Dic83⋊C4—41no—
155Dic83⋊C4—41no—
156C22⋊Dic83—41no—
157C22⋊Dic83—41no—
158(C2×D83)⋊C4—41no—
159(C2×D83)⋊C4—41no—
160(C2×D83)⋊C4—41no—
161(C2×D83)⋊C4—41no—
162(C2×D83)⋊C4—41no—
163(C2×D83)⋊C4—41no—
164(C2×D83)⋊C4—41no—
165C4×Dic83—41no—
166C2×D4×C83D811yescharacteristic
167C22×C4×C83C2×D411yescharacteristic
168C22×C4×C83C2×D411yescharacteristic
169C2×C8×C83—21no—
170C2×C8×C83—21no—
171C2×C8×C83—21no—
172C2×C8×C83—21no—
173C2×C8×C83C2×D411yescharacteristic
174C2×C8×C83C2×D411yescharacteristic
175C2×C8×C83C2×D411yescharacteristic
176C2×C8×C83C2411yescharacteristic
177C4⋊C4×C83D811yescharacteristic
178C22⋊C4×C83D811yescharacteristic
179C22⋊C4×C83D811yescharacteristic
180C42×C83C2×D411yescharacteristic
181C16×C83—21no—
182C16×C83—21no—
183C16×C83—21no—
184C16×C83—21no—
185C23×C83C2×D811yescharacteristic
186C23×C83C2×D811yescharacteristic
187C22×D83—41no—
188C22×D83—41no—
189C22×D83—41no—
190C22×D83—82no—
191C22×D83—82no—
192C22×D83—161no—
193D4×C83—22no—
194C2×C4×C83—21no—
195C2×C4×C83—21no—
196C2×C4×C83—21no—
197C2×C4×C83—21no—
198C2×C4×C83C2×D811yescharacteristic
199C2×C4×C83C2×D811yescharacteristic
200C2×C4×C83C2×D811yescharacteristic
201C2×C4×C83C2×D811yescharacteristic
202C2×C4×C83C22×D411yescharacteristic
203C22⋊D83—82no—
204C22⋊D83—82no—
205C22⋊D83—161no—
206C22⋊D83—161no—
207C2×Dic83—41no—
208C2×Dic83—41no—
209C2×Dic83—41no—
210C2×Dic83—41no—
211C2×Dic83—41no—
212C2×Dic83—161no—
213D332—22no—
214D332—41no—
215D332—41no—
216D332—41no—
217D332—41no—
218D332—41no—
219D332—82no—
220C4×D83—82no—
221C4×D83—161no—
222C4×D83—161no—
223Dic166—41no—
224Dic166—41no—
225C8×C83—21no—
226C8×C83—21no—
227C8×C83—21no—
228C8×C83C2×#4111yescharacteristic
229C8×C83H(5,𝔽2)11yescharacteristic
230C22×C83—21no—
231C22×C83—21no—
232C22×C83—21no—
233C22×C83—21no—
234C22×C83—21no—
235C22×C83#50812yes—
236C22×C83C22×D811yescharacteristic
237C2×D83—42no—
238C2×D83—81no—
239C2×D83—81no—
240C2×D83—81no—
241C2×D83—81no—
242C2×D83—81no—
243C2×D83—81no—
244C2×D83—81no—
245C2×D83—81no—
246C2×D83—164no—
247C4×C83—21no—
248C4×C83—21no—
249C4×C83—21no—
250C4×C83—21no—
251C4×C83#54611yescharacteristic
252C4×C83#57711yescharacteristic
253Dic83—81no—
254Dic83—81no—
255Dic83—81no—
256Dic83—81no—
257Dic83—81no—
258#33864—831nomaximal, Sylow
259C2×C83—22no—
260C2×C83—41no—
261C2×C83#329411yescharacteristic
262C2×C83C2×#50811yescharacteristic
263C2×C83#341511yescharacteristic
264D83—82no—
265D83—161no—
266D83—161no—
267#3339—831no—
268#3280—831no—
269#2242—831no—
270#2236—831no—
271#2234—831no—
272#2228—831no—
273#2217—831no—
274#2215—831no—
275#2210—831no—
276#2186—831no—
277#2184—831no—
278C4×D16—831no—
279D4×C16D8311yescharacteristic, complemented
280#2138—831no—
281C2×#357—831no—
282C83#3386411yescharacteristic, complemented, Sylow
283C2×#135—831no—
284C22×D8—831no—
285#553—1661no—
286#546—1661no—
287C2×SD32—831no—
288C2×D16—831no—
289C2×D16—831no—
290C22×C16C2×D8311yescharacteristic
291C22×C16C2×D8311yescharacteristic, complemented
292#499—831no—
293#495—831no—
294#482—1661no—
295#481—1661no—
296#478—1661no—
297#467—831no—
298#466—831no—
299#466—831no—
300#466—831no—
301#463—1661no—
302#450—1661no—
303#449—1661no—
304C4×D8—831no—
305C4×D8—831no—
306C8×D4C2×D8311yescharacteristic
307#427—831no—
308C2×#107—831no—
309#367—831no—
310#366—831no—
311#366—831no—
312C4⋊C16C2×D8311yescharacteristic, complemented
313#358—831no—
314#358—831no—
315#358—831no—
316#357—831no—
317#357—831no—
318#357—831no—
319#357—831no—
320#357—831no—
321#357—831no—
322#357—831no—
323C22⋊C16C2×D8311yescharacteristic
324C22⋊C16C2×D8311yescharacteristic, complemented
325C4×C16C2×D8311yescharacteristic, complemented
326C2×#41—1661no—
327C22×D4—1661no—
328#135—3321no—
329#135—1662no—
330C2×Q16—831no—
331C2×SD16—1661no—
332C2×SD16—1661no—
333C2×D8—3321no—
334C2×D8—831no—
335C2×D8—831no—
336C2×D8—831no—
337C2×D8—1662no—
338C2×D8—1661no—
339C22×C8C22×D8311yescharacteristic
340C22×C8C22×D8311yescharacteristic
341#126—3321no—
342#125—1661no—
343#124—1661no—
344#123—3321no—
345#123—3321no—
346C22⋊Q8—1661no—
347#121—3321no—
348#121—3321no—
349#121—1661no—
350#121—1661no—
351#121—1661no—
352#120—3321no—
353C4×D4—3321no—
354C4×D4—1661no—
355C4×D4—1661no—
356C4×D4D33211yescharacteristic
357#117—1661no—
358C2×C4⋊C4—1661no—
359C2×C22⋊C4—3321no—
360SD32—3321no—
361D16—3321no—
362D16—1662no—
363C2×C16—41no—
364C2×C16—41no—
365C2×C16C22×D8311yescharacteristic
366C2×C16C22×D8311yescharacteristic
367C2×C16C22×D8311yescharacteristic
368C2×C16C22×D8311yescharacteristic
369#107—831no—
370#107—831no—
371#107—831no—
372#107—831no—
373#107—1661no—
374#106—1661no—
375#106—1661no—
376C4⋊C8D33211yescharacteristic
377#103—1661no—
378#102—1661no—
379#102—1661no—
380#102—1661no—
381#102—1661no—
382#102—1661no—
383C22⋊C8D33211yescharacteristic
384C22⋊C8D33211yescharacteristic
385C4×C8C22×D8311yescharacteristic
386C24—3321no—
387#41—3322no—
388#41—6641no—
389C2×Q8—1661no—
390C2×D4—3322no—
391C2×D4—3321no—
392C2×D4—3321no—
393C2×D4—3321no—
394C2×D4—3321no—
395C2×D4—3321no—
396C2×D4—6641no—
397C2×D4—1661no—
398C2×D4—1661no—
399C2×D4—1661no—
400C2×D4D66411yescharacteristic
401C22×C4—3321no—
402C22×C4—3321no—
403C22×C4—3321no—
404C22×C4—3321no—
405C22×C4C2×D33211yescharacteristic
406C22×C4C2×D33211yescharacteristic
407Q16—1661no—
408Q16—1661no—
409SD16—3322no—
410SD16—6641no—
411D8—3322no—
412D8—832no—
413D8—1661no—
414D8—1661no—
415D8—1661no—
416D8—1661no—
417D8—1661no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—21no—
422C2×C8C2×D33211yescharacteristic
423C2×C8C2×D33211yescharacteristic
424C2×C8C2×D33211yescharacteristic
425C2×C8C23×D8311yescharacteristic
426C4⋊C4—3321no—
427C4⋊C4—3321no—
428C4⋊C4—3321no—
429C4⋊C4—3321no—
430C4⋊C4—1661no—
431C4⋊C4—1661no—
432C4⋊C4—1661no—
433C4⋊C4—1661no—
434C4⋊C4D66411yescharacteristic
435C22⋊C4—3321no—
436C22⋊C4—3321no—
437C22⋊C4—3321no—
438C22⋊C4—3321no—
439C22⋊C4—3321no—
440C22⋊C4—3321no—
441C22⋊C4—3321no—
442C22⋊C4—3321no—
443C22⋊C4—3321no—
444C22⋊C4D66411yescharacteristic
445C22⋊C4D66411yescharacteristic
446C42—3321no—
447C42C2×D33211yescharacteristic
448C16—21no—
449C16—21no—
450C16—21no—
451C16—21no—
452C23—13281no—
453C23—3321no—
454C23—3321no—
455C23—3321no—
456C23—6642no—
457C23—6642no—
458C23C2×D66411yescharacteristic
459C23C2×D66411yescharacteristic
460Q8—3321no—
461Q8—3321no—
462D4—22no—
463D4—13281no—
464D4—13281no—
465D4—3321no—
466D4—3321no—
467D4—3321no—
468D4—3321no—
469D4—3321no—
470D4—6642no—
471D4—6642no—
472D4—6642no—
473D4—1662no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—13281no—
479C2×C4—13281no—
480C2×C4—13281no—
481C2×C4—3321no—
482C2×C4—3321no—
483C2×C4—3321no—
484C2×C4—3321no—
485C2×C4—3321no—
486C2×C4—6642no—
487C2×C4C2×D66411yescharacteristic
488C2×C4C2×D66411yescharacteristic
489C2×C4C2×D66411yescharacteristic
490C2×C4C2×D66411yescharacteristic
491C2×C4C22×D33211yescharacteristic
492C8—21no—
493C8—21no—
494C8—21no—
495C8#41×D8311yescharacteristic
496C8#1458183711yescharacteristic
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—13284no—
503C22—3322no—
504C22—6641no—
505C22—6641no—
506C22—6641no—
507C22—6641no—
508C22—6641no—
509C22—6641no—
510C22—6641no—
511C22—6641no—
512C22#1912813312yes—
513C22C22×D66411yescharacteristic
514C4—21no—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—6641no—
519C4—6641no—
520C4—6641no—
521C4—6641no—
522C4—6641no—
523C4#1912834611yescharacteristic
524C4#1912851311yescharacteristic
525C2—22no—
526C2—41no—
527C2—13281no—
528C2—13281no—
529C2—6642no—
530C2#2491927711yescharacteristic
531C2C2×#1912813311yescharacteristic
532C2#2492060411yescharacteristic
subgroupG/H
centerC22C22×D664
commutator, cosocleC2×C8×C83C24
FrattiniC2×C8C23×D83
FittingD4×C16×C83C2
socleC22×C83C22×D8
hypercenterD4×C16D83
hypocenterC83#33864
LCSG ▷ C2×C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ D4×C16

Complements

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

NH ≅ G/Ntype
1. #24919866C2semidirect
2. #24919150C2semidirect
3. #24909695C2semidirect
4. #24909666C2semidirect
5. #24909655C2semidirect
6. #24909621C2semidirect
7. #24909559C2semidirect
8. #24909549C2semidirect
9. #24909519C2semidirect
10. #24909388C2semidirect
11. #24909377C2semidirect
12. C4×D1328C2semidirect
13. #24909171C2semidirect
14. C2×#19127503C2semidirect
15. D4×C16×C83C2semidirect
20. C2×#14581737C22semidirect
23. #19128103C22semidirect
31. #19127937C22semidirect
36. C4×D664C22semidirect
37. #19127739C22semidirect
39. #19127529C22semidirect
40. #19127527C22semidirect
41. #19127527C22semidirect
42. #19127506C22semidirect
43. #19127506C22semidirect
44. #19127506C22semidirect
51. #19127503C22semidirect
53. C22×C16×C83C22semidirect
55. C4⋊C16×C83C22semidirect
57. C22⋊C16×C83C22semidirect
58. C4×C16×C83C22semidirect
279. D4×C16D83semidirect
282. C83#33864semidirect
291. C22×C16C2×D83semidirect
312. C4⋊C16C2×D83semidirect
324. C22⋊C16C2×D83semidirect
325. C4×C16C2×D83semidirect

Maximal subgroups

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

subgroupindex
#249198662
#249191502
#249096952
#249096662
#249096552
#249096212
#249095592
#249095492
#249095192
#249093882
#249093772
C4×D13282
#249091712
C2×#191275032
D4×C16×C832
#3386483