Finite Group Databasebeta

← #35314853

Subgroups — #35314853

Order 21248.

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

normal subgroups only

This group has 320 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#24909263C211yesmaximal, characteristic
3#24907364C211yesmaximal, 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—
17C2×#14581727—21no—
18M16×Dic83—21no—
19C2×C8×Dic83C2211yescharacteristic
20Dic83⋊C16—21no—
21C22⋊(C83⋊C16)C2211yescharacteristic
22#19127476—21no—
23#19127466C2211yescharacteristic
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#14581727—24no—
43#14581726C2×C411yescharacteristic
44#14581725—21no—
45#14581717—21no—
46#14581716—21no—
47#14581715—21no—
48#14581702—41no—
49C8×Dic83—41no—
50C8×Dic83C2×C411yescharacteristic
51C8×Dic83C2×C411yescharacteristic
52C8×Dic83D411yescharacteristic
53C8×Dic83D411yescharacteristic
54C2×Q16×C83C2×C411yescharacteristic
55C2×M16×C83—21no—
56C22×C8×C83C2311yescharacteristic
57C22⋊Q8×C83—21no—
58C2×C16×C83—21no—
59#107×C83C2×C411yescharacteristic
60#103×C83—21no—
61C2×Dic166—21no—
62C2×Dic166—41no—
63C22×Dic83SD1611yescharacteristic
64C22×Dic83SD1611yescharacteristic
65Dic332—41no—
66#13050580—42no—
67#13050574—22no—
68#13050574—41no—
69C2×C83⋊C8—22no—
70C2×C83⋊C8—41no—
71C2×C83⋊C8C22⋊C411yescharacteristic
72C2×C83⋊C8C22⋊C411yescharacteristic
73C4⋊Dic83—21no—
74C4⋊Dic83—41no—
75Dic83⋊C4—41no—
76Dic83⋊C4—41no—
77Dic83⋊C4—41no—
78Dic83⋊C4—41no—
79Dic83⋊C4—41no—
80C22⋊Dic83—41no—
81C4×Dic83—41no—
82C4×Dic83—41no—
83C4×Dic83C22⋊C411yescharacteristic
84C4×Dic83C22⋊C411yescharacteristic
85C4×Dic83D811yescharacteristic
86C4×Dic83D811yescharacteristic
87C83⋊C16—41no—
88C2×Q8×C83—21no—
89C22×C4×C83C2×D411yescharacteristic
90Q16×C83—41no—
91M16×C83—22no—
92M16×C83—41no—
93C2×C8×C83—41no—
94C2×C8×C83—41no—
95C2×C8×C83C22×C411yescharacteristic
96C2×C8×C83C2×D411yescharacteristic
97C4⋊C4×C83—21no—
98C4⋊C4×C83—41no—
99C22⋊C4×C83—41no—
100C16×C83—41no—
101C23×C83C2×SD1611yescharacteristic
102Q8×C83—41no—
103Q8×C83—41no—
104C2×C4×C83—21no—
105C2×C4×C83—21no—
106C2×C4×C83—41no—
107C2×C4×C83—41no—
108C2×C4×C83C2×C22⋊C411yescharacteristic
109C2×C4×C83C2×D811yescharacteristic
110C2×Dic83—22no—
111C2×Dic83—41no—
112C2×Dic83—41no—
113C2×Dic83—41no—
114C2×Dic83#10211yescharacteristic
115C2×Dic83#10211yescharacteristic
116C2×Dic83#10211yescharacteristic
117C2×Dic83#10211yescharacteristic
118Dic166—41no—
119Dic166—41no—
120Dic166—82no—
121C8×C83—21no—
122C8×C83—21no—
123C8×C83—42no—
124C83⋊C8—21no—
125C83⋊C8—42no—
126C83⋊C8#10412yes—
127C22×C83—21no—
128C22×C83—21no—
129C22×C83—21no—
130C22×C83C2×#10211yescharacteristic
131C4×C83—21no—
132C4×C83—81no—
133C4×C83—81no—
134C4×C83#41011yescharacteristic
135C4×C83C2×#10411yescharacteristic
136Dic83—21no—
137Dic83—21no—
138Dic83—21no—
139Dic83—81no—
140Dic83—81no—
141Dic83#36212yes—
142#11752—831nomaximal, Sylow
143C2×C83—41no—
144C2×C83#150211yescharacteristic
145C2×C83#214311yescharacteristic
146C2×C83C2×#36211yescharacteristic
147#3170—831no—
148#2163—831no—
149C4×#108—831no—
150#1350—831no—
151#1350—831no—
152#1350—831no—
153#1350D8311yescharacteristic
154C83#1175211yescharacteristic, complemented, Sylow
155#533—1661no—
156#500—831no—
157#494—831no—
158#487—1661no—
159#467—831no—
160#467—1661no—
161#467C2×D8311yescharacteristic
162C4×Q16—831no—
163C4×Q16—831no—
164C4×Q16—1661no—
165C2×#108—1661no—
166C4×M16—1661no—
167C2×C4×C8—831no—
168C4⋊C16—1661no—
169C22⋊C16—831no—
170C22⋊C16C2×D8311yescharacteristic
171#346—1661no—
172#341—831no—
173#341C2×D8311yescharacteristic
174C2×Q16—831no—
175C2×Q16—1661no—
176C2×Q16C4×D8311yescharacteristic
177C2×M16—21no—
178C2×M16—1661no—
179C22×C8—831no—
180C22×C8C22×D8311yescharacteristic
181C4⋊Q8—1661no—
182C4⋊Q8—1661no—
183#125—3321no—
184C22⋊Q8—21no—
185C22⋊Q8—3321no—
186C22⋊Q8—1661no—
187C4×Q8—3321no—
188C4×Q8—1661no—
189C4×Q8—1661no—
190#117—3321no—
191C2×C42—831no—
192C2×C16—21no—
193C2×C16—1661no—
194#108—1664no—
195#107—831no—
196#107—1661no—
197#107C4×D8311yescharacteristic
198#103—21no—
199#103—1661no—
200#103—1661no—
201#103—1661no—
202#97—3321no—
203C4×C8—3321no—
204C4×C8—831no—
205C4×C8—831no—
206C4×C8—831no—
207C4×C8—831no—
208C2×Q8—21no—
209C2×Q8—3321no—
210C2×Q8—1661no—
211C22×C4—831no—
212C22×C4—831no—
213C22×C4D4×D8311yescharacteristic
214Q16—41no—
215Q16—3321no—
216Q16—3322no—
217M16—22no—
218M16—41no—
219M16—3321no—
220M16—1662no—
221C2×C8—41no—
222C2×C8—41no—
223C2×C8—3321no—
224C2×C8—831no—
225C2×C8—831no—
226C2×C8—1662no—
227C2×C8C2×C4×D8311yescharacteristic
228C2×C8D4×D8311yescharacteristic
229C4⋊C4—21no—
230C4⋊C4—41no—
231C4⋊C4—3321no—
232C4⋊C4—3321no—
233C4⋊C4—3321no—
234C4⋊C4—3321no—
235C4⋊C4—3321no—
236C4⋊C4—3321no—
237C4⋊C4—1661no—
238C22⋊C4—41no—
239C22⋊C4—3321no—
240C42—3321no—
241C42—3321no—
242C42—831no—
243C42—831no—
244C42—831no—
245C42—831no—
246C16—41no—
247C16—3321no—
248C23SD16×D8311yescharacteristic
249Q8—41no—
250Q8—41no—
251Q8—3321no—
252Q8—3321no—
253Q8—6642no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—3321no—
259C2×C4—3321no—
260C2×C4—3321no—
261C2×C4—831no—
262C2×C4—831no—
263C2×C4—831no—
264C2×C4—831no—
265C2×C4—1662no—
266C2×C4C22⋊C4×D8311yescharacteristic
267C2×C4D8×D8311yescharacteristic
268C8—21no—
269C8—21no—
270C8—42no—
271C8—3322no—
272C8—832no—
273C8—1661no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22#102×D8311yescharacteristic
278C4—21no—
279C4—81no—
280C4—81no—
281C4—832no—
282C4—6641no—
283C4—6641no—
284C4—1661no—
285C4—1661no—
286C4—1661no—
287C4#1912767311yescharacteristic
288C4#104×D8311yescharacteristic
289C2—41no—
290C2#2490595611yescharacteristic
291C2#2490918911yescharacteristic
292C2#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#11752
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
154. C83#11752semidirect

Maximal subgroups

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

subgroupindex
#249180442
#249092632
#249073642
#249054822
#249054812
#249054802
C83×#13502
#1175283