Finite Group Databasebeta

← #35307451

Subgroups — #35307451

Order 21248.

536 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24912498C211yesmaximal, characteristic, complemented
2#24908390C211yesmaximal, characteristic
3#24908389C211yesmaximal, characteristic
4#24908269C211yesmaximal, characteristic
5#24905347C211yesmaximal, characteristic, complemented
6#24905303C211yesmaximal, characteristic, complemented
7C83×#1279C211yesmaximal, characteristic, complemented
8C2×#14581789C2211yescharacteristic
9C2×#14581784—21no—
10C2×C4⋊(C83⋊C8)C2211yescharacteristic
11C2×#14581714—21no—
12C2×#14581714—21no—
13C2×#14581714—22no—
14C2×#14581712—21no—
15C2×#14581712—21no—
16#19127635—22no—
17#19127599—21no—
18#19127597—21no—
19#19127571C2211yescharacteristic
20#19127570—21no—
21C4×C4⋊Dic83C2211yescharacteristic
22C2×C4⋊C8×C83C2211yescharacteristic
23C2×C4×C8×C83C2211yescharacteristic
24C4×C4⋊C4×C83C2211yescharacteristic
25C22×D332—21no—
26C22×D332—21no—
27C22×D332—21no—
28C22×C83⋊C8—21no—
29#14581789—21no—
30#14581789—21no—
31#14581789—21no—
32#14581789Q812yes—
33#14581784—42no—
34#14581784—42no—
35C2×C4⋊Dic83—21no—
36C2×C4⋊Dic83—21no—
37C2×C4⋊Dic83D411yescharacteristic
38C2×C4⋊Dic83D411yescharacteristic
39C2×C4⋊Dic83D412yes—
40C2×Dic83⋊C4—22no—
41C2×Dic83⋊C4—22no—
42C2×Dic83⋊C4—22no—
43C2×C4×Dic83—21no—
44C4⋊(C83⋊C8)—21no—
45C4⋊(C83⋊C8)—21no—
46#14581714—44no—
47#14581714—42no—
48#14581714—42no—
49#14581712—42no—
50#14581712—42no—
51C83⋊#95—22no—
52C83⋊#95—21no—
53C22×C8×C83—21no—
54C22×C8×C83—21no—
55C2×C4⋊C4×C83D411yescharacteristic
56C2×C4⋊C4×C83D411yescharacteristic
57C2×C42×C83—21no—
58C2×C42×C83C2311yescharacteristic
59C4⋊C8×C83—21no—
60C4⋊C8×C83—21no—
61C4×C8×C83—21no—
62C4×C8×C83—21no—
63#95×C83—21no—
64C23×D83—41no—
65C2×D332—22no—
66C2×D332—22no—
67C2×D332—22no—
68C2×D332—42no—
69C2×D332—42no—
70C2×D332—41no—
71C2×D332—41no—
72C2×D332—41no—
73C2×D332—41no—
74C2×D332—41no—
75C2×D332—41no—
76C2×D332—41no—
77C2×D332—41no—
78C2×D332—41no—
79C2×D332—41no—
80C2×D332—41no—
81C22×Dic83—21no—
82C22×Dic83—21no—
83C22×Dic83—22no—
84C2×C83⋊C8—41no—
85C2×C83⋊C8—41no—
86C2×C83⋊C8—41no—
87C4⋊Dic83—21no—
88C4⋊Dic83—21no—
89C4⋊Dic83—41no—
90C4⋊Dic83—41no—
91C4⋊Dic83—41no—
92C4⋊Dic83—41no—
93C4⋊Dic83—42no—
94C4⋊Dic83D812yes—
95C4⋊Dic83SD1612yes—
96Dic83⋊C4—44no—
97Dic83⋊C4—44no—
98Dic83⋊C4—82no—
99C4×Dic83—41no—
100C4×Dic83—41no—
101C22×C4×C83—21no—
102C22×C4×C83—21no—
103C22×C4×C83C2×D411yescharacteristic
104C22×C4×C83C2×D411yescharacteristic
105C22×C4×C83C2×D411yescharacteristic
106C2×C8×C83—22no—
107C2×C8×C83—41no—
108C2×C8×C83—41no—
109C2×C8×C83—41no—
110C2×C8×C83—41no—
111C2×C8×C83—41no—
112C4⋊C4×C83—21no—
113C4⋊C4×C83—21no—
114C4⋊C4×C83—21no—
115C4⋊C4×C83—21no—
116C42×C83—41no—
117C42×C83—41no—
118C42×C83C2×Q811yescharacteristic
119C42×C83#4111yescharacteristic
120C42×C83#4111yescharacteristic
121C42×C83#4111yescharacteristic
122C23×C83#12011yescharacteristic
123C22×D83—42no—
124C22×D83—81no—
125C22×D83—81no—
126C22×D83—81no—
127C22×D83—81no—
128C22×D83—81no—
129C22×D83—81no—
130C2×C4×C83—21no—
131C2×C4×C83—21no—
132C2×C4×C83—41no—
133C2×C4×C83—41no—
134C2×C4×C83—41no—
135C2×C4×C83—41no—
136C2×C4×C83—41no—
137C2×C4×C83—41no—
138C2×C4×C83C22⋊Q811yescharacteristic
139C2×C4×C83C22⋊Q811yescharacteristic
140C2×C4×C83C22⋊Q811yescharacteristic
141C2×C4×C83#12411yescharacteristic
142C2×C4×C83#12411yescharacteristic
143C2×C4×C83#12411yescharacteristic
144C2×C4×C83C2×D811yescharacteristic
145C2×C4×C83C2×SD1611yescharacteristic
146C2×C4×C83#13511yescharacteristic
147C2×C4×C83#13511yescharacteristic
148C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C83#13711yescharacteristic
152C2×Dic83—22no—
153C2×Dic83—22no—
154C2×Dic83—41no—
155C2×Dic83—41no—
156C2×Dic83—41no—
157C2×Dic83—41no—
158C2×Dic83—42no—
159C2×Dic83—42no—
160C2×Dic83—42no—
161D332—44no—
162D332—42no—
163D332—42no—
164D332—42no—
165D332—42no—
166D332—82no—
167D332—81no—
168D332—81no—
169D332—81no—
170D332—81no—
171C8×C83—42no—
172C8×C83—81no—
173C83⋊C8—81no—
174C22×C83#39311yescharacteristic
175C22×C83#44711yescharacteristic
176C22×C83#44811yescharacteristic
177C22×C83#44911yescharacteristic
178C22×C83#44911yescharacteristic
179C22×C83#45311yescharacteristic
180C22×C83#45411yescharacteristic
181C2×D83—82no—
182C2×D83—82no—
183C2×D83—82no—
184C2×D83—161no—
185C2×D83—161no—
186C2×D83—161no—
187C2×D83—161no—
188C4×C83—21no—
189C4×C83—21no—
190C4×C83—81no—
191C4×C83—81no—
192C4×C83#47411yescharacteristic
193C4×C83#47611yescharacteristic
194C4×C83#47811yescharacteristic
195C4×C83#47811yescharacteristic
196C4×C83#48611yescharacteristic
197C4×C83#48811yescharacteristic
198C4×C83#48911yescharacteristic
199C4×C83#49011yescharacteristic
200Dic83—42no—
201Dic83—42no—
202Dic83—82no—
203#10354—831nomaximal, Sylow
204C2×C83#162111yescharacteristic
205C2×C83#162211yescharacteristic
206C2×C83#162511yescharacteristic
207C2×C83#162611yescharacteristic
208C2×C83#202311yescharacteristic
209C2×C83#202511yescharacteristic
210C2×C83#202711yescharacteristic
211D83—162no—
212#2552—831no—
213#1982—831no—
214#1982—831no—
215#1957—831no—
216#1296—831no—
217#1279—831no—
218#1279D8311yescharacteristic, complemented
219C83#1035411yescharacteristic, complemented, Sylow
220C2×#127—831no—
221C2×#125—1661no—
222C2×C4⋊C8—831no—
223C2×C4⋊C8C2×D8311yescharacteristic
224C2×#102—1662no—
225C2×#102—1661no—
226C2×#102—1661no—
227C2×#102—1661no—
228C2×#102—1661no—
229C2×C4×C8C2×D8311yescharacteristic
230#398—1662no—
231#389—1661no—
232#389—1661no—
233#384—831no—
234#384—1661no—
235C4×C4⋊C4—831no—
236C4×C4⋊C4C2×D8311yescharacteristic
237C22×D4—1661no—
238C22×D4—1661no—
239C22×D4—1661no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—1661no—
243#127—832no—
244#127—1661no—
245#127—1661no—
246#127—1661no—
247#125—3322no—
248#125—3322no—
249C2×C4⋊C4—832no—
250C2×C4⋊C4—831no—
251C2×C4⋊C4—831no—
252C2×C4⋊C4—1662no—
253C2×C4⋊C4—1662no—
254C2×C4⋊C4—1661no—
255C2×C4⋊C4—1661no—
256C2×C4⋊C4—1662no—
257C2×C4⋊C4D33211yescharacteristic
258C2×C4⋊C4D33211yescharacteristic
259C2×C42—21no—
260C2×C42—1661no—
261C2×C42C22×D8311yescharacteristic
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—1661no—
265C4⋊C8—1661no—
266#102—3322no—
267#102—3322no—
268#102—3324no—
269#102—3322no—
270#102—3322no—
271C4×C8—21no—
272C4×C8—21no—
273#95—21no—
274#95—1662no—
275#95—1661no—
276C24—3321no—
277C2×D4—3322no—
278C2×D4—3322no—
279C2×D4—3321no—
280C2×D4—3321no—
281C2×D4—3321no—
282C2×D4—3321no—
283C2×D4—3321no—
284C2×D4—3321no—
285C2×D4—3321no—
286C2×D4—3321no—
287C2×D4—3321no—
288C2×D4—3321no—
289C2×D4—3321no—
290C2×D4—1662no—
291C2×D4—1662no—
292C2×D4—1662no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—1662no—
296C22×C4—1661no—
297C22×C4—1661no—
298C22×C4D4×D8311yescharacteristic
299C22×C4D4×D8311yescharacteristic
300C22×C4C2×D33211yescharacteristic
301C2×C8—22no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—3321no—
308C2×C8—3321no—
309C2×C8—3321no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—3322no—
315C4⋊C4—3324no—
316C4⋊C4—3324no—
317C4⋊C4—3321no—
318C4⋊C4—3321no—
319C4⋊C4—3321no—
320C4⋊C4—3321no—
321C4⋊C4—832no—
322C4⋊C4—832no—
323C4⋊C4—6642no—
324C4⋊C4—1661no—
325C4⋊C4—1661no—
326C42—41no—
327C42—41no—
328C42—3321no—
329C42—3321no—
330C42Q8×D8311yescharacteristic
331C42#1305058911yescharacteristic
332C42#1305059011yescharacteristic
333C42#1305059011yescharacteristic
334C23—3322no—
335C23—6641no—
336C23—6641no—
337C23—6641no—
338C23—6641no—
339C23—6641no—
340C23—6641no—
341C23#1458176211yescharacteristic
342D4—3324no—
343D4—3322no—
344D4—3322no—
345D4—3322no—
346D4—3322no—
347D4—6642no—
348D4—6641no—
349D4—6641no—
350D4—6641no—
351D4—6641no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—3321no—
361C2×C4—3321no—
362C2×C4—3321no—
363C2×C4—3321no—
364C2×C4—3322no—
365C2×C4—3322no—
366C2×C4—3322no—
367C2×C4—1662no—
368C2×C4—1662no—
369C2×C4#1458177011yescharacteristic
370C2×C4#1458177011yescharacteristic
371C2×C4#1458177211yescharacteristic
372C2×C4#1458177811yescharacteristic
373C2×C4#1458177811yescharacteristic
374C2×C4#1458178011yescharacteristic
375C2×C4D8×D8311yescharacteristic
376C2×C4SD16×D8311yescharacteristic
377C2×C4#1458181411yescharacteristic
378C2×C4#1458181411yescharacteristic
379C2×C4#1458181911yescharacteristic
380C2×C4#1458182011yescharacteristic
381C2×C4#1458182011yescharacteristic
382C2×C4#1458182411yescharacteristic
383C8—42no—
384C8—81no—
385C8—6641no—
386C22—13281no—
387C22—13281no—
388C22—13281no—
389C22—13281no—
390C22—6642no—
391C22—6642no—
392C22—6642no—
393C22#1912761411yescharacteristic
394C22#1912783611yescharacteristic
395C22#1912784111yescharacteristic
396C22#1912784811yescharacteristic
397C22#1912784811yescharacteristic
398C22#1912787011yescharacteristic
399C22#1912787511yescharacteristic
400C4—21no—
401C4—21no—
402C4—81no—
403C4—81no—
404C4—3322no—
405C4—3322no—
406C4—6642no—
407C4#1912798011yescharacteristic
408C4#1912799011yescharacteristic
409C4#1912800211yescharacteristic
410C4#1912800211yescharacteristic
411C4#1912804611yescharacteristic
412C4#1912805611yescharacteristic
413C4#1912806211yescharacteristic
414C4#1912806611yescharacteristic
415C2—13282no—
416C2#2490653111yescharacteristic
417C2#2490653811yescharacteristic
418C2#2490655511yescharacteristic
419C2#2490656111yescharacteristic
420C2#2490859811yescharacteristic
421C2#2490861011yescharacteristic
422C2#2490861811yescharacteristic
subgroupG/H
centerC23#14581762
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1279C2
socleC23×C83#120
prime radicalC2×#14581789C22
hypercenter#1279D83
hypocenterC83#10354
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
1. #24912498C2semidirect
5. #24905347C2semidirect
6. #24905303C2semidirect
7. C83×#1279C2semidirect
218. #1279D83semidirect
219. C83#10354semidirect

Maximal subgroups

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

subgroupindex
#249124982
#249083902
#249083892
#249082692
#249053472
#249053032
C83×#12792
#1035483