Finite Group Databasebeta

← #35308895

Subgroups — #35308895

Order 21248.

426 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24912499C211yesmaximal, characteristic
2#24908227C211yesmaximal, characteristic
3#24908227C211yesmaximal, characteristic
4#24907590C211yesmaximal, characteristic
5#24905302C211yesmaximal, characteristic
6#24905302C211yesmaximal, characteristic
7C83×#1296C211yesmaximal, characteristic
8C2×#14581783—21no—
9C2×#14581724—21no—
10C2×#14581724—21no—
11C2×C4×C83⋊C8C2211yescharacteristic
12#19127634—22no—
13#19127600—21no—
14#19127597—21no—
15#19127571C2211yescharacteristic
16#19127570—21no—
17C4×C4⋊Dic83C2211yescharacteristic
18C4×C4⋊Dic83C2211yescharacteristic
19#19127464—21no—
20#19127464—21no—
21#19127463—22no—
22C2×C4⋊C8×C83C2211yescharacteristic
23C2×C4⋊C8×C83C2211yescharacteristic
24#384×C83C2211yescharacteristic
25C22×C83⋊C8—21no—
26#14581783—42no—
27#14581783—42no—
28C2×C4⋊Dic83—22no—
29C2×C4⋊Dic83—21no—
30C2×C4⋊Dic83—21no—
31C2×C4⋊Dic83—21no—
32C2×C4⋊Dic83D411yescharacteristic
33C2×C4⋊Dic83D411yescharacteristic
34C2×C4⋊Dic83D411yescharacteristic
35C2×C4⋊Dic83D411yescharacteristic
36C2×Dic83⋊C4—22no—
37C2×Dic83⋊C4—22no—
38C2×C4×Dic83—21no—
39C2×C4×Dic83—21no—
40#14581724—42no—
41#14581724—42no—
42C4×C83⋊C8—21no—
43C4×C83⋊C8Q812yes—
44C83⋊#95—22no—
45C83⋊#95—21no—
46C83⋊#95—21no—
47C22×C8×C83—21no—
48C22×C8×C83—21no—
49C2×C4⋊C4×C83—21no—
50C2×C4⋊C4×C83—21no—
51C2×C4⋊C4×C83D412yes—
52C2×C42×C83C2311yescharacteristic
53C4⋊C8×C83—21no—
54C4⋊C8×C83—21no—
55C4⋊C8×C83Q812yes—
56C4⋊C8×C83Q812yes—
57C22×Dic83—21no—
58C22×Dic83—21no—
59C22×Dic83—21no—
60C22×Dic83—21no—
61C22×Dic83—41no—
62C2×C83⋊C8—22no—
63C2×C83⋊C8—41no—
64C2×C83⋊C8—41no—
65C4⋊Dic83—21no—
66C4⋊Dic83—21no—
67C4⋊Dic83—21no—
68C4⋊Dic83—21no—
69C4⋊Dic83—21no—
70C4⋊Dic83—21no—
71C4⋊Dic83—44no—
72C4⋊Dic83—42no—
73C4⋊Dic83—41no—
74C4⋊Dic83—41no—
75C4⋊Dic83—41no—
76C4⋊Dic83—41no—
77C4⋊Dic83SD1612yes—
78C4⋊Dic83SD1612yes—
79Dic83⋊C4—44no—
80Dic83⋊C4—82no—
81C4×Dic83—41no—
82C4×Dic83—41no—
83C4×Dic83—41no—
84C4×Dic83—41no—
85C22×C4×C83—22no—
86C22×C4×C83C2×D411yescharacteristic
87C22×C4×C83C2×D411yescharacteristic
88C22×C4×C83C2×D411yescharacteristic
89C2×C8×C83—22no—
90C2×C8×C83—22no—
91C2×C8×C83—41no—
92C2×C8×C83—41no—
93C2×C8×C83—41no—
94C2×C8×C83—41no—
95C4⋊C4×C83—42no—
96C4⋊C4×C83—41no—
97C4⋊C4×C83—41no—
98C4⋊C4×C83—41no—
99C4⋊C4×C83—41no—
100C42×C83C2×Q811yescharacteristic
101C42×C83C2×Q811yescharacteristic
102C42×C83C2×Q811yescharacteristic
103C42×C83#4111yescharacteristic
104C23×C83#12011yescharacteristic
105C2×C4×C83—21no—
106C2×C4×C83—21no—
107C2×C4×C83—42no—
108C2×C4×C83—42no—
109C2×C4×C83—42no—
110C2×C4×C83C22⋊Q811yescharacteristic
111C2×C4×C83C22⋊Q811yescharacteristic
112C2×C4×C83C22⋊Q811yescharacteristic
113C2×C4×C83C4⋊Q811yescharacteristic
114C2×C4×C83C4⋊Q811yescharacteristic
115C2×C4×C83C4⋊Q811yescharacteristic
116C2×C4×C83C2×SD1611yescharacteristic
117C2×C4×C83C2×SD1611yescharacteristic
118C2×C4×C83#13511yescharacteristic
119C2×C4×C83#13511yescharacteristic
120C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C83#13711yescharacteristic
123C2×C4×C83#13711yescharacteristic
124C2×Dic83—22no—
125C2×Dic83—22no—
126C2×Dic83—41no—
127C2×Dic83—41no—
128C2×Dic83—41no—
129C2×Dic83—41no—
130C2×Dic83—41no—
131C2×Dic83—41no—
132C2×Dic83—41no—
133C2×Dic83—41no—
134C2×Dic83—41no—
135C2×Dic83—41no—
136C2×Dic83—81no—
137C2×Dic83—81no—
138C2×Dic83—81no—
139C8×C83—42no—
140C8×C83—42no—
141C83⋊C8—42no—
142C22×C83#39511yescharacteristic
143C22×C83#44811yescharacteristic
144C22×C83#44911yescharacteristic
145C22×C83#45011yescharacteristic
146C22×C83#45211yescharacteristic
147C22×C83#45411yescharacteristic
148C22×C83#45511yescharacteristic
149C4×C83—21no—
150C4×C83—21no—
151C4×C83—82no—
152C4×C83#47511yescharacteristic
153C4×C83#47611yescharacteristic
154C4×C83#47811yescharacteristic
155C4×C83#47911yescharacteristic
156C4×C83#49811yescharacteristic
157C4×C83#49911yescharacteristic
158C4×C83#50111yescharacteristic
159C4×C83#50111yescharacteristic
160Dic83—42no—
161Dic83—42no—
162Dic83—81no—
163Dic83—81no—
164Dic83—161no—
165#10582—831nomaximal, Sylow
166C2×C83#162611yescharacteristic
167C2×C83#163511yescharacteristic
168C2×C83#164211yescharacteristic
169C2×C83#164311yescharacteristic
170C2×C83#205811yescharacteristic
171C2×C83#205911yescharacteristic
172C2×C83#206111yescharacteristic
173#2552—831no—
174#1948—831no—
175#1948—831no—
176#1834—831no—
177#1296D8311yescharacteristic
178#1279—831no—
179#1279—831no—
180C83#1058211yescharacteristic, complemented, Sylow
181C2×#125—1661no—
182C2×#106—1661no—
183C2×#106—1661no—
184C2×C4⋊C8C2×D8311yescharacteristic
185C2×C4⋊C8C2×D8311yescharacteristic
186C2×C4×C8—831no—
187#398—1662no—
188#389—1661no—
189#389—1661no—
190#384—831no—
191#384—1661no—
192#384C2×D8311yescharacteristic
193C4×C4⋊C4—831no—
194C4×C4⋊C4—831no—
195#340—1661no—
196#340—1661no—
197#340—1662no—
198C22×C8—21no—
199C22×C8—21no—
200C22×C8—1661no—
201#125—3322no—
202#125—3322no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—831no—
206C2×C4⋊C4—831no—
207C2×C4⋊C4—831no—
208C2×C4⋊C4—831no—
209C2×C4⋊C4—1662no—
210C2×C4⋊C4—1662no—
211C2×C4⋊C4—1661no—
212C2×C4⋊C4—1661no—
213C2×C4⋊C4—1661no—
214C2×C4⋊C4—1662no—
215C2×C4⋊C4D33212yes—
216C2×C42—1661no—
217C2×C42—1661no—
218C2×C42C22×D8311yescharacteristic
219#106—3322no—
220#106—3322no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8Dic16612yes—
224C4⋊C8Dic16612yes—
225C4×C8—832no—
226C4×C8—1661no—
227#95—1662no—
228#95—1661no—
229#95—1661no—
230C22×C4—22no—
231C22×C4—3321no—
232C22×C4—1661no—
233C22×C4—1661no—
234C22×C4—1661no—
235C22×C4—1661no—
236C22×C4D4×D8311yescharacteristic
237C22×C4D4×D8311yescharacteristic
238C22×C4C2×D33211yescharacteristic
239C2×C8—22no—
240C2×C8—22no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—3321no—
246C2×C8—3321no—
247C2×C8—1662no—
248C4⋊C4—42no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—3322no—
254C4⋊C4—3324no—
255C4⋊C4—3324no—
256C4⋊C4—3321no—
257C4⋊C4—3321no—
258C4⋊C4—3321no—
259C4⋊C4—3321no—
260C4⋊C4—832no—
261C4⋊C4—832no—
262C4⋊C4—6642no—
263C4⋊C4—1661no—
264C4⋊C4—1661no—
265C4⋊C4—1661no—
266C4⋊C4—1661no—
267C4⋊C4—1661no—
268C4⋊C4—1661no—
269C42—3321no—
270C42—3321no—
271C42—3321no—
272C42—3321no—
273C42Q8×D8311yescharacteristic
274C42C2×Dic16611yescharacteristic
275C42C2×Dic16611yescharacteristic
276C42#1305058911yescharacteristic
277C23#1458176211yescharacteristic
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—3321no—
284C2×C4—3321no—
285C2×C4—3321no—
286C2×C4—3321no—
287C2×C4—3321no—
288C2×C4—3321no—
289C2×C4—3321no—
290C2×C4—3321no—
291C2×C4—3321no—
292C2×C4—3321no—
293C2×C4—6641no—
294C2×C4—6641no—
295C2×C4—6641no—
296C2×C4—1662no—
297C2×C4—1662no—
298C2×C4#1458176911yescharacteristic
299C2×C4#1458176911yescharacteristic
300C2×C4#1458177211yescharacteristic
301C2×C4#1458179111yescharacteristic
302C2×C4#1458179111yescharacteristic
303C2×C4#1458179211yescharacteristic
304C2×C4SD16×D8311yescharacteristic
305C2×C4SD16×D8311yescharacteristic
306C2×C4#1458181311yescharacteristic
307C2×C4#1458181311yescharacteristic
308C2×C4#1458181611yescharacteristic
309C2×C4#1458181611yescharacteristic
310C2×C4#1458182411yescharacteristic
311C2×C4#1458182411yescharacteristic
312C8—42no—
313C8—42no—
314C8—3322no—
315C22#1912762211yescharacteristic
316C22#1912784111yescharacteristic
317C22#1912784711yescharacteristic
318C22#1912785311yescharacteristic
319C22#1912786611yescharacteristic
320C22#1912787611yescharacteristic
321C22#1912788111yescharacteristic
322C4—21no—
323C4—21no—
324C4—82no—
325C4—13281no—
326C4—3322no—
327C4—3322no—
328C4—6641no—
329C4—6641no—
330C4#1912798411yescharacteristic
331C4#1912798911yescharacteristic
332C4#1912800311yescharacteristic
333C4#1912800611yescharacteristic
334C4#1912809811yescharacteristic
335C4#1912810111yescharacteristic
336C4#1912810911yescharacteristic
337C4#1912810911yescharacteristic
338C2#2490656011yescharacteristic
339C2#2490661511yescharacteristic
340C2#2490666411yescharacteristic
341C2#2490667111yescharacteristic
342C2#2490879511yescharacteristic
343C2#2490880011yescharacteristic
344C2#2490881411yescharacteristic
subgroupG/H
centerC23#14581762
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1296C2
socle, prime radicalC23×C83#120
hypercenter#1296D83
hypocenterC83#10582
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
180. C83#10582semidirect

Maximal subgroups

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

subgroupindex
#249124992
#249082272
#249075902
#249053022
C83×#12962
#1058283