Finite Group Databasebeta

← #35309142

Subgroups — #35309142

Order 21248.

402 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24908256C211yesmaximal, characteristic
2#24907590C211yesmaximal, characteristic, complemented
3#24907464C211yesmaximal, characteristic
4#24907460C211yesmaximal, characteristic
5#24905347C211yesmaximal, characteristic, complemented
6#24905297C211yesmaximal, characteristic, complemented
7C83×#1296C211yesmaximal, characteristic, complemented
8C2×C4×D332C2211yescharacteristic
9C2×C4⋊(C83⋊C8)C2211yescharacteristic
10C2×#14581714—21no—
11C2×#14581712—21no—
12C2×(C2×D83)⋊C8—21no—
13C2×(C2×D83)⋊C8—21no—
14C2×C4×C83⋊C8C2211yescharacteristic
15#19127571C2211yescharacteristic
16#19127464—21no—
17#19127463—21no—
18#19127463—21no—
19#19127463—21no—
20C2×C4⋊C8×C83C2211yescharacteristic
21C2×C4⋊C8×C83C2211yescharacteristic
22#384×C83C2211yescharacteristic
23C22×D332D411yescharacteristic
24C22×C4×D83—21no—
25C22×C83⋊C8—21no—
26C22×C83⋊C8D411yescharacteristic
27C22×C83⋊C8D411yescharacteristic
28C4×D332—21no—
29C4×D332—21no—
30C4×D332—21no—
31C4×D332—21no—
32C2×C4⋊Dic83—21no—
33C2×C4⋊Dic83—21no—
34C2×C4⋊Dic83—21no—
35C2×C4⋊Dic83D411yescharacteristic
36C2×(C2×D83)⋊C4—21no—
37C4⋊(C83⋊C8)—21no—
38C4⋊(C83⋊C8)—21no—
39#14581714—42no—
40#14581712—42no—
41(C2×D83)⋊C8—42no—
42(C2×D83)⋊C8—42no—
43C4×C83⋊C8—21no—
44C4×C83⋊C8—21no—
45C22×C8×C83—21no—
46C22×C8×C83—21no—
47C2×C4⋊C4×C83—21no—
48C2×C4⋊C4×C83—21no—
49C2×C4⋊C4×C83—21no—
50C2×C42×C83C2311yescharacteristic
51C4⋊C8×C83—21no—
52C4⋊C8×C83—21no—
53C4⋊C8×C83—21no—
54C4⋊C8×C83—21no—
55C23×D83—21no—
56C2×D332—21no—
57C2×D332—21no—
58C2×D332—21no—
59C2×D332—21no—
60C2×D332—21no—
61C2×D332D812yes—
62C22×Dic83—21no—
63C22×Dic83—41no—
64C2×C4×D83—41no—
65C2×C4×D83—41no—
66C2×C4×D83—41no—
67C2×C4×D83—41no—
68C2×C4×D83—41no—
69C2×C4×D83—41no—
70C2×C83⋊C8—21no—
71C2×C83⋊C8—21no—
72C2×C83⋊C8—21no—
73C2×C83⋊C8—21no—
74C2×C83⋊C8—21no—
75C2×C83⋊C8—21no—
76C2×C83⋊C8—41no—
77C2×C83⋊C8—41no—
78C2×C83⋊C8—41no—
79C4⋊Dic83—21no—
80C4⋊Dic83—21no—
81C4⋊Dic83—41no—
82C4⋊Dic83—41no—
83C4⋊Dic83—41no—
84C4⋊Dic83—41no—
85C4⋊Dic83—81no—
86(C2×D83)⋊C4—41no—
87(C2×D83)⋊C4—41no—
88C22×C4×C83—41no—
89C22×C4×C83C2×D411yescharacteristic
90C22×C4×C83C2×D411yescharacteristic
91C22×C4×C83#4111yescharacteristic
92C2×C8×C83—41no—
93C2×C8×C83—41no—
94C2×C8×C83—41no—
95C2×C8×C83—41no—
96C2×C8×C83—41no—
97C2×C8×C83—41no—
98C4⋊C4×C83—41no—
99C4⋊C4×C83—41no—
100C4⋊C4×C83—41no—
101C4⋊C4×C83—41no—
102C4⋊C4×C83—81no—
103C42×C83#4111yescharacteristic
104C42×C83#4111yescharacteristic
105C42×C83#4111yescharacteristic
106C42×C83#4111yescharacteristic
107C23×C83#12111yescharacteristic
108C22×D83—22no—
109C22×D83—41no—
110C22×D83—41no—
111C22×D83—41no—
112C22×D83—41no—
113C22×D83—41no—
114C22×D83—41no—
115C2×C4×C83—21no—
116C2×C4×C83—21no—
117C2×C4×C83—81no—
118C2×C4×C83—81no—
119C2×C4×C83—81no—
120C2×C4×C83#12311yescharacteristic
121C2×C4×C83#12311yescharacteristic
122C2×C4×C83#12311yescharacteristic
123C2×C4×C83#12411yescharacteristic
124C2×C4×C83#12611yescharacteristic
125C2×C4×C83#12611yescharacteristic
126C2×C4×C83C2×D811yescharacteristic
127C2×C4×C83#13511yescharacteristic
128C2×C4×C83#13511yescharacteristic
129C2×C4×C83#13511yescharacteristic
130C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C83#13711yescharacteristic
133C2×C4×C83#13711yescharacteristic
134C2×Dic83—41no—
135C2×Dic83—41no—
136C2×Dic83—41no—
137C2×Dic83—81no—
138C2×Dic83—81no—
139C2×Dic83—81no—
140D332—22no—
141D332—22no—
142D332—41no—
143D332—41no—
144C4×D83—81no—
145C4×D83—81no—
146C4×D83—81no—
147C4×D83—81no—
148C8×C83—81no—
149C8×C83—81no—
150C83⋊C8—41no—
151C83⋊C8—41no—
152C83⋊C8—81no—
153C22×C83#39711yescharacteristic
154C22×C83#46311yescharacteristic
155C22×C83#46311yescharacteristic
156C22×C83#46611yescharacteristic
157C22×C83#47011yescharacteristic
158C22×C83#47111yescharacteristic
159C22×C83#47111yescharacteristic
160C2×D83—42no—
161C2×D83—42no—
162C2×D83—42no—
163C2×D83—81no—
164C2×D83—81no—
165C2×D83—81no—
166C2×D83—81no—
167C4×C83—21no—
168C4×C83—21no—
169C4×C83—161no—
170C4×C83#48011yescharacteristic
171C4×C83#48011yescharacteristic
172C4×C83#48211yescharacteristic
173C4×C83#48211yescharacteristic
174C4×C83#48511yescharacteristic
175C4×C83#48511yescharacteristic
176C4×C83#48811yescharacteristic
177C4×C83#49011yescharacteristic
178Dic83—81no—
179Dic83—161no—
180#10621—831nomaximal, Sylow
181C2×C83#168111yescharacteristic
182C2×C83#168111yescharacteristic
183C2×C83#170311yescharacteristic
184C2×C83#170311yescharacteristic
185C2×C83#207311yescharacteristic
186C2×C83#207511yescharacteristic
187C2×C83#207911yescharacteristic
188D83—82no—
189#1954—831no—
190#1834—831no—
191#1802—831no—
192#1802—831no—
193#1296—831no—
194#1296D8311yescharacteristic, complemented
195#1277—831no—
196C83#1062111yescharacteristic, complemented, Sylow
197C2×C4×D4—831no—
198C2×C4⋊C8—831no—
199C2×C4⋊C8C2×D8311yescharacteristic
200C2×C4⋊C8C2×D8311yescharacteristic
201C2×#102—1661no—
202C2×#102—1661no—
203C2×C22⋊C8—1661no—
204C2×C22⋊C8—1661no—
205C2×C4×C8—831no—
206#384—831no—
207#384C2×D8311yescharacteristic
208#340—1661no—
209#340—1661no—
210#340—1661no—
211#340—1661no—
212C22×D4—831no—
213C23×C4—1661no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—831no—
217C22×C8—831no—
218C22×C8—1661no—
219C4×D4—1661no—
220C4×D4—1661no—
221C4×D4—1661no—
222C4×D4—1661no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—831no—
227C2×C4⋊C4—1661no—
228C2×C4⋊C4—1661no—
229C2×C4⋊C4—1661no—
230C2×C22⋊C4—1661no—
231C2×C42C22×D8311yescharacteristic
232C4⋊C8—21no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8—1661no—
237C4⋊C8—1661no—
238#102—3322no—
239#102—3322no—
240C22⋊C8—3322no—
241C22⋊C8—3322no—
242C4×C8—1661no—
243C4×C8—1661no—
244C24—1661no—
245C2×D4—832no—
246C2×D4—1661no—
247C2×D4—1661no—
248C2×D4—1661no—
249C2×D4—1661no—
250C2×D4—1661no—
251C22×C4—41no—
252C22×C4—3321no—
253C22×C4—3321no—
254C22×C4—3321no—
255C22×C4—3321no—
256C22×C4—3321no—
257C22×C4—3321no—
258C22×C4—3321no—
259C22×C4—1661no—
260C22×C4D4×D8311yescharacteristic
261C22×C4D4×D8311yescharacteristic
262C22×C4#1305059011yescharacteristic
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—3321no—
270C2×C8—3321no—
271C2×C8—3321no—
272C2×C8—1661no—
273C2×C8—1661no—
274C2×C8—1661no—
275C2×C8—1661no—
276C2×C8—1661no—
277C2×C8—1661no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—81no—
283C4⋊C4—3321no—
284C4⋊C4—3321no—
285C4⋊C4—3321no—
286C4⋊C4—3321no—
287C4⋊C4—6641no—
288C4⋊C4—1661no—
289C4⋊C4—1661no—
290C22⋊C4—3321no—
291C22⋊C4—3321no—
292C42#1305058911yescharacteristic
293C42#1305059011yescharacteristic
294C42#1305059011yescharacteristic
295C42#1305059111yescharacteristic
296C23—3321no—
297C23—3321no—
298C23—3321no—
299C23—3321no—
300C23—3321no—
301C23—3321no—
302C23—1662no—
303C23#1458176511yescharacteristic
304D4—3321no—
305D4—3321no—
306D4—1662no—
307D4—1662no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—3321no—
314C2×C4—3321no—
315C2×C4—3321no—
316C2×C4—6641no—
317C2×C4—6641no—
318C2×C4—6641no—
319C2×C4—6641no—
320C2×C4—6641no—
321C2×C4—6641no—
322C2×C4—6641no—
323C2×C4#1458177411yescharacteristic
324C2×C4#1458177711yescharacteristic
325C2×C4#1458177711yescharacteristic
326C2×C4#1458177811yescharacteristic
327C2×C4#1458178611yescharacteristic
328C2×C4#1458178711yescharacteristic
329C2×C4D8×D8311yescharacteristic
330C2×C4#1458181311yescharacteristic
331C2×C4#1458181311yescharacteristic
332C2×C4#1458181511yescharacteristic
333C2×C4#1458181611yescharacteristic
334C2×C4#1458181911yescharacteristic
335C2×C4#1458182111yescharacteristic
336C2×C4#1458182411yescharacteristic
337C8—81no—
338C8—81no—
339C8—3321no—
340C8—3321no—
341C8—6641no—
342C22—3322no—
343C22—3322no—
344C22—3322no—
345C22—6641no—
346C22—6641no—
347C22—6641no—
348C22—6641no—
349C22#1912763011yescharacteristic
350C22#1912791511yescharacteristic
351C22#1912791911yescharacteristic
352C22#1912793611yescharacteristic
353C22#1912795811yescharacteristic
354C22#1912796311yescharacteristic
355C22#1912796711yescharacteristic
356C4—21no—
357C4—21no—
358C4—161no—
359C4—13281no—
360C4—6641no—
361C4#1912801311yescharacteristic
362C4#1912801611yescharacteristic
363C4#1912802711yescharacteristic
364C4#1912802811yescharacteristic
365C4#1912804011yescharacteristic
366C4#1912804511yescharacteristic
367C4#1912805711yescharacteristic
368C4#1912806411yescharacteristic
369C2—6642no—
370C2#2490689911yescharacteristic
371C2#2490690311yescharacteristic
372C2#2490703711yescharacteristic
373C2#2490704111yescharacteristic
374C2#2490888011yescharacteristic
375C2#2490889011yescharacteristic
376C2#2490891211yescharacteristic
subgroupG/H
centerC23#14581765
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1296C2
socleC23×C83#121
prime radicalC22×D332D4
hypercenter#1296D83
hypocenterC83#10621
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
2. #24907590C2semidirect
5. #24905347C2semidirect
6. #24905297C2semidirect
7. C83×#1296C2semidirect
194. #1296D83semidirect
196. C83#10621semidirect

Maximal subgroups

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

subgroupindex
#249082562
#249075902
#249074642
#249074602
#249053472
#249052972
C83×#12962
#1062183