Finite Group Databasebeta

← #35293689

Subgroups — #35293689

Order 21248.

358 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24914413C211yesmaximal, characteristic
2#24909025C211yesmaximal, characteristic
3#24909025C211yesmaximal, characteristic
4#24905287C211yesmaximal, characteristic
5#24905286C211yesmaximal, characteristic
6#24905285C211yesmaximal, characteristic
7C83×#2100C211yesmaximal, characteristic
8C2×#14581782—21no—
9#19127635—21no—
10#19127634—21no—
11#19127632—21no—
12#19127599C2211yescharacteristic
13#19127599C2211yescharacteristic
14#19127596—21no—
15#19127584—21no—
16#19127463—21no—
17#19127463—21no—
18#19127463—21no—
19#19127463—21no—
20#19127456C2211yescharacteristic
21#19127456C2211yescharacteristic
22#389×C83C2211yescharacteristic
23#384×C83C2211yescharacteristic
24#340×C83—21no—
25#340×C83—21no—
26#336×C83C2211yescharacteristic
27C22×C83⋊C8—21no—
28C22×C83⋊C8—21no—
29#14581782—42no—
30#14581782—42no—
31C2×C4⋊Dic83D411yescharacteristic
32C2×C4⋊Dic83D411yescharacteristic
33C2×C4⋊Dic83D411yescharacteristic
34C2×C4⋊Dic83D411yescharacteristic
35C2×Dic83⋊C4—21no—
36C2×Dic83⋊C4—21no—
37C2×Dic83⋊C4—21no—
38C2×Dic83⋊C4—21no—
39C2×Dic83⋊C4—21no—
40C2×Dic83⋊C4—21no—
41C2×C4×Dic83—21no—
42C83⋊#95—21no—
43C83⋊#95—21no—
44C83⋊#95—21no—
45C83⋊#95—21no—
46C83⋊#95—21no—
47C22×C8×C83—21no—
48C2×C4⋊C4×C83—21no—
49C2×C4⋊C4×C83—21no—
50C2×C4⋊C4×C83—21no—
51C2×C4⋊C4×C83—21no—
52C2×C4⋊C4×C83D411yescharacteristic
53C2×C4⋊C4×C83D411yescharacteristic
54C2×C42×C83C2311yescharacteristic
55#95×C83—21no—
56C22×Dic83—21no—
57C22×Dic83—21no—
58C22×Dic83—21no—
59C22×Dic83—21no—
60C2×C83⋊C8—41no—
61C2×C83⋊C8—41no—
62C2×C83⋊C8—41no—
63C2×C83⋊C8—41no—
64C2×C83⋊C8—41no—
65C2×C83⋊C8—41no—
66C4⋊Dic83—21no—
67C4⋊Dic83—21no—
68C4⋊Dic83—41no—
69C4⋊Dic83—41no—
70C4⋊Dic83SD1612yes—
71C4⋊Dic83Q1612yes—
72Dic83⋊C4—42no—
73Dic83⋊C4—42no—
74Dic83⋊C4—42no—
75Dic83⋊C4—41no—
76Dic83⋊C4—41no—
77Dic83⋊C4—41no—
78Dic83⋊C4—41no—
79Dic83⋊C4—81no—
80C4×Dic83—42no—
81C22×C4×C83—21no—
82C22×C4×C83—21no—
83C22×C4×C83—41no—
84C22×C4×C83C2×D411yescharacteristic
85C22×C4×C83C2×D411yescharacteristic
86C22×C4×C83C2×D411yescharacteristic
87C2×C8×C83—41no—
88C2×C8×C83—41no—
89C2×C8×C83—41no—
90C4⋊C4×C83—21no—
91C4⋊C4×C83—21no—
92C4⋊C4×C83—41no—
93C4⋊C4×C83—42no—
94C4⋊C4×C83—42no—
95C4⋊C4×C83—42no—
96C4⋊C4×C83—41no—
97C4⋊C4×C83—41no—
98C42×C83—41no—
99C23×C83#12011yescharacteristic
100C2×C4×C83—21no—
101C2×C4×C83—21no—
102C2×C4×C83—21no—
103C2×C4×C83—21no—
104C2×C4×C83—21no—
105C2×C4×C83—21no—
106C2×C4×C83—41no—
107C2×C4×C83—41no—
108C2×C4×C83—41no—
109C2×C4×C83—41no—
110C2×C4×C83—41no—
111C2×C4×C83—41no—
112C2×C4×C83—81no—
113C2×C4×C83—81no—
114C2×C4×C83—81no—
115C2×C4×C83C2×SD1611yescharacteristic
116C2×C4×C83C2×Q1611yescharacteristic
117C2×C4×C83#13511yescharacteristic
118C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C83#13711yescharacteristic
120C2×C4×C83#13711yescharacteristic
121C2×Dic83—22no—
122C2×Dic83—22no—
123C2×Dic83—41no—
124C2×Dic83—41no—
125C2×Dic83—41no—
126C2×Dic83—41no—
127C2×Dic83—41no—
128C2×Dic83—41no—
129C2×Dic83—41no—
130C2×Dic83—41no—
131C2×Dic83—41no—
132C2×Dic83—41no—
133C8×C83—81no—
134C83⋊C8—81no—
135C83⋊C8—81no—
136C22×C83#45011yescharacteristic
137C22×C83#45111yescharacteristic
138C22×C83#45211yescharacteristic
139C22×C83#45411yescharacteristic
140C22×C83#45411yescharacteristic
141C22×C83#45411yescharacteristic
142C22×C83#45811yescharacteristic
143C4×C83—21no—
144C4×C83—21no—
145C4×C83—21no—
146C4×C83—21no—
147C4×C83—21no—
148C4×C83—21no—
149C4×C83—81no—
150C4×C83—81no—
151C4×C83—161no—
152Dic83—42no—
153Dic83—42no—
154Dic83—81no—
155Dic83—81no—
156#7827—831nomaximal, Sylow
157C2×C83#161511yescharacteristic
158C2×C83#161611yescharacteristic
159C2×C83#161711yescharacteristic
160C2×C83#163511yescharacteristic
161C2×C83#163611yescharacteristic
162C2×C83#163711yescharacteristic
163C2×C83#165811yescharacteristic
164#2726—831no—
165#2100—831no—
166#2100—831no—
167#2100D8311yescharacteristic
168#1271—831no—
169#1271—831no—
170#1271—831no—
171C83#782711yescharacteristic, complemented, Sylow
172C2×#125—1661no—
173#398—1661no—
174#398—1661no—
175#398—1661no—
176#389—831no—
177#389—831no—
178#389—1661no—
179#389C2×D8311yescharacteristic
180#387—1661no—
181#384C2×D8311yescharacteristic
182#340—21no—
183#340—21no—
184#340—1661no—
185#340—1661no—
186#340—1661no—
187#340—1661no—
188#336—831no—
189#336—831no—
190#336C2×D8311yescharacteristic
191C22×C8—21no—
192C22×C8—1661no—
193C22×C8—1661no—
194#125—3322no—
195#125—3322no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—831no—
201C2×C4⋊C4—831no—
202C2×C4⋊C4—831no—
203C2×C4⋊C4—831no—
204C2×C4⋊C4—1661no—
205C2×C4⋊C4—1661no—
206C2×C4⋊C4—1661no—
207C2×C4⋊C4—1661no—
208C2×C4⋊C4—1661no—
209C2×C4⋊C4—1661no—
210C2×C4⋊C4C22⋊D8311yescharacteristic
211C2×C4⋊C4C22⋊D8311yescharacteristic
212C2×C42—1661no—
213C2×C42C22×D8311yescharacteristic
214#95—21no—
215#95—1661no—
216#95—1661no—
217#95—1661no—
218#95—1661no—
219#95—1661no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—41no—
223C22×C4—1661no—
224C22×C4—1661no—
225C22×C4—1661no—
226C22×C4—1661no—
227C22×C4D4×D8311yescharacteristic
228C22×C4D4×D8311yescharacteristic
229C22×C4C2×C22⋊D8311yescharacteristic
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—3321no—
234C2×C8—3321no—
235C2×C8—3321no—
236C2×C8—3321no—
237C2×C8—3321no—
238C2×C8—3321no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—41no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—3321no—
248C4⋊C4—3321no—
249C4⋊C4—3322no—
250C4⋊C4—3322no—
251C4⋊C4—3322no—
252C4⋊C4—3321no—
253C4⋊C4—3321no—
254C4⋊C4—3321no—
255C4⋊C4—3321no—
256C4⋊C4—832no—
257C4⋊C4—832no—
258C4⋊C4—6641no—
259C4⋊C4—1661no—
260C4⋊C4—1661no—
261C42—41no—
262C42—3322no—
263C23#1458176011yescharacteristic
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—3321no—
280C2×C4—3321no—
281C2×C4—3321no—
282C2×C4—3321no—
283C2×C4—3321no—
284C2×C4—3321no—
285C2×C4—3321no—
286C2×C4—3321no—
287C2×C4—3321no—
288C2×C4—3321no—
289C2×C4—1662no—
290C2×C4—1662no—
291C2×C4SD16×D8311yescharacteristic
292C2×C4Q16×D8311yescharacteristic
293C2×C4#1458181211yescharacteristic
294C2×C4#1458181911yescharacteristic
295C2×C4#1458182311yescharacteristic
296C2×C4#1458182411yescharacteristic
297C8—81no—
298C8—6641no—
299C8—6641no—
300C22#1912785011yescharacteristic
301C22#1912785511yescharacteristic
302C22#1912786111yescharacteristic
303C22#1912787211yescharacteristic
304C22#1912787211yescharacteristic
305C22#1912787311yescharacteristic
306C22#1912789011yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—81no—
314C4—81no—
315C4—161no—
316C4—3322no—
317C4—3322no—
318C4—6641no—
319C4—6641no—
320C2#2490649211yescharacteristic
321C2#2490649811yescharacteristic
322C2#2490650311yescharacteristic
323C2#2490661311yescharacteristic
324C2#2490661911yescharacteristic
325C2#2490662511yescharacteristic
326C2#2490676411yescharacteristic
subgroupG/H
centerC23#14581760
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#2100C2
socle, prime radicalC23×C83#120
hypercenter#2100D83
hypocenterC83#7827
LCSG ▷ C2×C42×C83 ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2100

Complements

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

NH ≅ G/Ntype
171. C83#7827semidirect

Maximal subgroups

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

subgroupindex
#249144132
#249090252
#249052872
#249052862
#249052852
C83×#21002
#782783