Finite Group Databasebeta

← #35315374

Subgroups — #35315374

Order 21248.

304 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 79 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#24918044C211yesmaximal, characteristic
2#24909259C211yesmaximal, characteristic
3#24907599C211yesmaximal, characteristic
4#24905482C211yesmaximal, characteristic
5#24905481C211yesmaximal, characteristic
6#24905480C211yesmaximal, characteristic
7C83×#1350C211yesmaximal, characteristic
8#19128253—21no—
9#19128105C411yescharacteristic
10#19128079C411yescharacteristic
11#19128050—21no—
12#19127942C2211yescharacteristic
13#19127940—21no—
14Q16×Dic83C411yescharacteristic
15#19127795C411yescharacteristic
16#19127793—21no—
17#19127724—21no—
18C2×C8×Dic83C2211yescharacteristic
19Dic83⋊C16—21no—
20C22⋊(C83⋊C16)C2211yescharacteristic
21C16×Dic83—21no—
22#19127466C2211yescharacteristic
23#19127465—21no—
24#467×C83C2211yescharacteristic
25C22⋊C16×C83C2211yescharacteristic
26#341×C83C2211yescharacteristic
27C2×Dic332C2×C411yescharacteristic
28C2×#13050580—21no—
29C2×#13050574—21no—
30C22×C83⋊C8D411yescharacteristic
31#14581791—21no—
32#14581790—21no—
33#14581782—41no—
34#14581771—21no—
35#14581769—41no—
36Q8×Dic83—21no—
37#14581757—21no—
38#14581757—41no—
39#14581748—41no—
40C2×C4×Dic83D411yescharacteristic
41C2×C83⋊C16—21no—
42#14581726C2×C411yescharacteristic
43#14581725—21no—
44Dic83⋊C8—41no—
45Dic83⋊C8—41no—
46#14581717—21no—
47#14581716—21no—
48#14581715—21no—
49C8×Dic83C2×C411yescharacteristic
50C8×Dic83C2×C411yescharacteristic
51C8×Dic83D411yescharacteristic
52C8×Dic83D411yescharacteristic
53C2×Q16×C83C2×C411yescharacteristic
54C2×M16×C83—21no—
55C22×C8×C83C2311yescharacteristic
56C22⋊Q8×C83—21no—
57C2×C16×C83—21no—
58#107×C83C2×C411yescharacteristic
59#103×C83—21no—
60C2×Dic166—21no—
61C2×Dic166—41no—
62C22×Dic83SD1611yescharacteristic
63C22×Dic83SD1611yescharacteristic
64Dic332—41no—
65#13050580—42no—
66#13050574—41no—
67#13050574—41no—
68C2×C83⋊C8—41no—
69C2×C83⋊C8—41no—
70C2×C83⋊C8C22⋊C411yescharacteristic
71C2×C83⋊C8C22⋊C411yescharacteristic
72C4⋊Dic83—21no—
73C4⋊Dic83—41no—
74Dic83⋊C4—41no—
75Dic83⋊C4—41no—
76Dic83⋊C4—41no—
77Dic83⋊C4—41no—
78Dic83⋊C4—41no—
79C22⋊Dic83—41no—
80C4×Dic83—41no—
81C4×Dic83—41no—
82C4×Dic83C22⋊C411yescharacteristic
83C4×Dic83C22⋊C411yescharacteristic
84C4×Dic83D811yescharacteristic
85C4×Dic83D811yescharacteristic
86C83⋊C16—41no—
87C2×Q8×C83—21no—
88C22×C4×C83C2×D411yescharacteristic
89Q16×C83—41no—
90M16×C83—41no—
91M16×C83—41no—
92C2×C8×C83—41no—
93C2×C8×C83—41no—
94C2×C8×C83C22×C411yescharacteristic
95C2×C8×C83C2×D411yescharacteristic
96C4⋊C4×C83—21no—
97C4⋊C4×C83—41no—
98C22⋊C4×C83—41no—
99C16×C83—41no—
100C23×C83C2×SD1611yescharacteristic
101Q8×C83—41no—
102Q8×C83—41no—
103C2×C4×C83—21no—
104C2×C4×C83—21no—
105C2×C4×C83—41no—
106C2×C4×C83—41no—
107C2×C4×C83C2×C22⋊C411yescharacteristic
108C2×C4×C83C2×D811yescharacteristic
109C2×Dic83—22no—
110C2×Dic83—22no—
111C2×Dic83—41no—
112C2×Dic83—41no—
113C2×Dic83#10211yescharacteristic
114C2×Dic83#10211yescharacteristic
115C2×Dic83#10211yescharacteristic
116C2×Dic83#10211yescharacteristic
117Dic166—41no—
118Dic166—41no—
119Dic166—82no—
120C8×C83—21no—
121C8×C83—21no—
122C8×C83—81no—
123C83⋊C8—21no—
124C83⋊C8—21no—
125C83⋊C8—81no—
126C22×C83—21no—
127C22×C83—21no—
128C22×C83—21no—
129C22×C83C2×#10211yescharacteristic
130C4×C83—21no—
131C4×C83—81no—
132C4×C83—81no—
133C4×C83#41011yescharacteristic
134C4×C83#42111yescharacteristic
135Dic83—21no—
136Dic83—21no—
137Dic83—81no—
138Dic83—81no—
139Dic83#35912yes—
140Dic83#36212yes—
141#11863—831nomaximal, Sylow
142C2×C83—41no—
143C2×C83#151711yescharacteristic
144C2×C83C2×#35911yescharacteristic
145C2×C83C2×#36211yescharacteristic
146#3170—831no—
147#2162—831no—
148#1837—831no—
149#1350—831no—
150#1350—831no—
151#1350—831no—
152#1350D8311yescharacteristic
153C83#1186311yescharacteristic, complemented, Sylow
154#533—1661no—
155#500—831no—
156#494—831no—
157#487—1661no—
158#467—831no—
159#467—1661no—
160#467C2×D8311yescharacteristic
161C4×Q16—831no—
162C4×Q16—831no—
163C4×Q16—1661no—
164#423—1661no—
165C2×C4×C8—831no—
166C4⋊C16—1661no—
167C22⋊C16—831no—
168C22⋊C16C2×D8311yescharacteristic
169C4×C16—1661no—
170#341—831no—
171#341—1661no—
172#341C2×D8311yescharacteristic
173C2×Q16—831no—
174C2×Q16—1661no—
175C2×Q16C4×D8311yescharacteristic
176C2×M16—21no—
177C2×M16—1661no—
178C22×C8—831no—
179C22×C8C22×D8311yescharacteristic
180C4⋊Q8—1661no—
181C4⋊Q8—1661no—
182#125—3321no—
183C22⋊Q8—21no—
184C22⋊Q8—3321no—
185C22⋊Q8—1661no—
186C4×Q8—3321no—
187C4×Q8—1661no—
188C4×Q8—1661no—
189#117—3321no—
190C2×C42—831no—
191C2×C16—21no—
192C2×C16—1661no—
193#107—831no—
194#107—1661no—
195#107C4×D8311yescharacteristic
196C4⋊C8—3321no—
197C4⋊C8—3321no—
198#103—21no—
199#103—1661no—
200#103—1661no—
201#103—1661no—
202C4×C8—831no—
203C4×C8—831no—
204C4×C8—831no—
205C4×C8—831no—
206C2×Q8—21no—
207C2×Q8—3321no—
208C2×Q8—1661no—
209C22×C4—831no—
210C22×C4—831no—
211C22×C4D4×D8311yescharacteristic
212Q16—41no—
213Q16—3321no—
214Q16—3322no—
215M16—41no—
216M16—41no—
217M16—3321no—
218M16—3321no—
219C2×C8—41no—
220C2×C8—41no—
221C2×C8—3321no—
222C2×C8—3321no—
223C2×C8—831no—
224C2×C8—831no—
225C2×C8C2×C4×D8311yescharacteristic
226C2×C8D4×D8311yescharacteristic
227C4⋊C4—21no—
228C4⋊C4—41no—
229C4⋊C4—3321no—
230C4⋊C4—3321no—
231C4⋊C4—3321no—
232C4⋊C4—3321no—
233C4⋊C4—3321no—
234C4⋊C4—3321no—
235C4⋊C4—1661no—
236C22⋊C4—41no—
237C22⋊C4—3321no—
238C42—3321no—
239C42—3321no—
240C42—831no—
241C42—831no—
242C42—831no—
243C42—831no—
244C16—41no—
245C16—3321no—
246C23SD16×D8311yescharacteristic
247Q8—41no—
248Q8—41no—
249Q8—3321no—
250Q8—3321no—
251Q8—6642no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—3321no—
257C2×C4—3321no—
258C2×C4—831no—
259C2×C4—831no—
260C2×C4—831no—
261C2×C4—831no—
262C2×C4—1662no—
263C2×C4—1662no—
264C2×C4C22⋊C4×D8311yescharacteristic
265C2×C4D8×D8311yescharacteristic
266C8—21no—
267C8—21no—
268C8—81no—
269C8—6641no—
270C8—1661no—
271C8—1661no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22#102×D8311yescharacteristic
276C4—21no—
277C4—81no—
278C4—81no—
279C4—832no—
280C4—832no—
281C4—6641no—
282C4—6641no—
283C4—1661no—
284C4—1661no—
285C4#1912767311yescharacteristic
286C4#1912771611yescharacteristic
287C2—41no—
288C2#2490602111yescharacteristic
289C2#359×D8311yescharacteristic
290C2#362×D8311yescharacteristic
subgroupG/H
centerC22#102×D83
commutatorC2×C8×C83C22×C4
FrattiniC22×C8C22×D83
FittingC83×#1350C2
socleC22×C83C2×#102
prime radicalC23×C83C2×SD16
cosocleC22×C8×C83C23
hypercenter#1350D83
hypocenterC83#11863
LCSG ▷ C2×C8×C83 ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1350

Complements

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

NH ≅ G/Ntype
153. C83#11863semidirect

Maximal subgroups

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

subgroupindex
#249180442
#249092592
#249075992
#249054822
#249054812
#249054802
C83×#13502
#1186383