Finite Group Databasebeta

← #35315258

Subgroups — #35315258

Order 21248.

280 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 71 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#24918208C211yesmaximal, characteristic
2#24907612C211yesmaximal, characteristic
3#24905458C212yesmaximal
4#24905452C212yesmaximal
5C83×#2165C211yesmaximal, characteristic
6#19128258—21no—
7#19128099C411yescharacteristic, complemented
8#19128081C411yescharacteristic, complemented
9#19128052—21no—
10#19127959—21no—
11#19127959C2212yes—
12#19127809—21no—
13#19127809C412yescomplemented
14#19127472—21no—
15#19127461—21no—
16C83⋊#338C2211yescharacteristic
17#19127458C2211yescharacteristic
18C4×M16×C83C2211yescharacteristic
19#364×C83—21no—
20#349×C83C2212yes—
21#347×C83—21no—
22C2×Dic332—21no—
23C2×Dic332C2×C412yes—
24C2×#13050574—21no—
25#14581792—21no—
26#14581792—21no—
27#14581784—41no—
28#14581771—22no—
29#14581771—41no—
30C4×Dic166—22no—
31C4×Dic166—41no—
32#14581751—21no—
33#14581751—41no—
34#14581724—21no—
35#14581724C2×C412yes—
36#14581717—22no—
37#14581717—22no—
38C2×M16×C83D411yescharacteristic
39C2×M16×C83C2311yescharacteristic
40C2×C42×C83D411yescharacteristic
41M32×C83—22no—
42#97×C83C2×C411yescharacteristic
43#97×C83D411yescharacteristic
44C4×C8×C83C2×C411yescharacteristic
45C4×C8×C83D411yescharacteristic
46C2×Dic166—22no—
47C2×Dic166—41no—
48Dic332—42no—
49Dic332—42no—
50#13050574—41no—
51#13050574—41no—
52C2×C83⋊C8—41no—
53C4⋊Dic83—22no—
54C4⋊Dic83—41no—
55C4⋊Dic83—41no—
56C4⋊Dic83—41no—
57C4⋊Dic83—41no—
58Dic83⋊C4—42no—
59Dic83⋊C4—42no—
60C22⋊Dic83—42no—
61C22⋊Dic83—41no—
62C4×Dic83—42no—
63C4×Dic83—41no—
64C22×C4×C83—21no—
65C22×C4×C83C2×D411yescharacteristic
66M16×C83—41no—
67M16×C83—41no—
68C2×C8×C83C22⋊C411yescharacteristic
69C2×C8×C83C22⋊C411yescharacteristic
70C2×C8×C83C22×C411yescharacteristic
71C2×C8×C83C2×D411yescharacteristic
72C42×C83—21no—
73C42×C83C22⋊C411yescharacteristic
74C42×C83C22⋊C411yescharacteristic
75C16×C83—42no—
76C23×C83AGL(1,ℤ/8)11yescharacteristic
77C2×C4×C83—21no—
78C2×C4×C83—21no—
79C2×C4×C83—21no—
80C2×C4×C83—21no—
81C2×C4×C83—42no—
82C2×C4×C83C2×C22⋊C411yescharacteristic
83C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
84C2×Dic83—42no—
85C2×Dic83—42no—
86C2×Dic83—81no—
87Dic166—42no—
88Dic166—42no—
89Dic166—82no—
90C8×C83—21no—
91C8×C83—21no—
92C8×C83—21no—
93C8×C83—21no—
94C83⋊C8—81no—
95C22×C83—21no—
96C22×C83—41no—
97C22×C83#41811yescharacteristic
98C4×C83—22no—
99C4×C83—21no—
100C4×C83—41no—
101C4×C83#41011yescharacteristic
102C4×C83#42111yescharacteristic
103Dic83—82no—
104Dic83—82no—
105Dic83—161no—
106#11838—831nomaximal, Sylow
107C2×C83—21no—
108C2×C83—41no—
109C2×C83#151411yescharacteristic
110#3185—831no—
111#2165D8311yescharacteristic
112#1841—831no—
113#1342—832no—
114#1340—832no—
115C83#1183811yescharacteristic, complemented, Sylow
116#533—1661no—
117#498—831no—
118#494—831no—
119#487—1661no—
120#470—832no—
121#470—1661no—
122#441—832no—
123#441—1661no—
124C4×M16C2×D8311yescharacteristic
125#364—21no—
126#349C2×D8312yes—
127#347—21no—
128#344—1661no—
129#339—1661no—
130#338—831no—
131H(3,ℤ/4)—831no—
132C2×Q16—832no—
133C2×Q16—1661no—
134C2×M16—1661no—
135C2×M16D33211yescharacteristic
136C2×M16C22×D8311yescharacteristic
137C4⋊Q8—1661no—
138C4⋊Q8—1661no—
139#125—3321no—
140C22⋊Q8—3321no—
141C22⋊Q8—1662no—
142C4×Q8—3321no—
143C4×Q8—1662no—
144#117—3321no—
145#117—1661no—
146C2×C42D33211yescharacteristic
147M32—22no—
148#106—832no—
149#106—1661no—
150#103—1662no—
151#103—1662no—
152#97C4×D8311yescharacteristic
153#97C22⋊D8311yescharacteristic
154C4×C8C4×D8311yescharacteristic
155C4×C8C22⋊D8311yescharacteristic
156C2×Q8—3321no—
157C2×Q8—1662no—
158C22×C4—21no—
159C22×C4C2×D33211yescharacteristic
160Q16—3322no—
161Q16—3322no—
162M16—41no—
163M16—41no—
164M16—3321no—
165M16—3321no—
166C2×C8—3321no—
167C2×C8(C2×D83)⋊C411yescharacteristic
168C2×C8(C2×D83)⋊C411yescharacteristic
169C2×C8C2×C4×D8311yescharacteristic
170C2×C8C2×C22⋊D8311yescharacteristic
171C4⋊C4—3321no—
172C4⋊C4—3321no—
173C4⋊C4—3321no—
174C4⋊C4—3322no—
175C4⋊C4—3321no—
176C4⋊C4—3322no—
177C4⋊C4—1662no—
178C22⋊C4—3322no—
179C22⋊C4—3321no—
180C42—21no—
181C42—3322no—
182C42—3321no—
183C42(C2×D83)⋊C411yescharacteristic
184C42(C2×D83)⋊C411yescharacteristic
185C16—42no—
186C23#1458182011yescharacteristic
187Q8—3322no—
188Q8—3322no—
189Q8—6642no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—42no—
195C2×C4—3322no—
196C2×C4—3322no—
197C2×C4—6641no—
198C2×C4C2×(C2×D83)⋊C411yescharacteristic
199C2×C4#1458182011yescharacteristic
200C8—21no—
201C8—21no—
202C8—21no—
203C8—21no—
204C8—6641no—
205C22—21no—
206C22—41no—
207C22#1912770711yescharacteristic
208C4—22no—
209C4—21no—
210C4—41no—
211C4—13281no—
212C4—6642no—
213C4—6642no—
214C4#1912767411yescharacteristic
215C4#1912771711yescharacteristic
216C2—21no—
217C2—41no—
218C2#2490601111yescharacteristic
subgroupG/H
centerC2#24906011
commutatorC2×C8×C83C22×C4
FrattiniC2×M16C22×D83
FittingC83×#2165C2
socleC2×C83#1514
prime radicalC23×C83AGL(1,ℤ/8)
cosocleC2×M16×C83C23
hypercenter#2165D83
hypocenterC83#11838
LCSG ▷ C2×C8×C83 ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #2165

Complements

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

NH ≅ G/Ntype
7. #19128099C4semidirect
8. #19128081C4semidirect
13. #19127809C4semidirect
115. C83#11838semidirect

Maximal subgroups

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

subgroupindex
#249182082
#249076122
#249054582
#249054522
C83×#21652
#1183883