Finite Group Databasebeta

← #35307142

Subgroups — #35307142

Order 21248.

528 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 113 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#24918413C212yesmaximal
2#24915841C211yesmaximal, characteristic
3#24908440C211yesmaximal, characteristic
4#24906143C212yesmaximal
5C83×#1276C211yesmaximal, characteristic
6#19128258C2211yescharacteristic
7C2×#14581792C2212yes—
8#19128081—22no—
9#19128052—22no—
10#19127912—24no—
11#19127859—24no—
12#19127725C2211yescharacteristic
13#19127607—24no—
14#19127567—22no—
15#19127461—22no—
16#19127449—24no—
17#431×C83C2212yes—
18C43×C83C2211yescharacteristic
19C22×Dic166D414yes—
20C2×Dic332—28no—
21C2×#13050574—21no—
22#14581792—22no—
23#14581792—22no—
24#14581792—22no—
25#14581792—22no—
26#14581792D412yes—
27#14581784—21no—
28#14581771—22no—
29C4×Dic166—22no—
30#14581751—21no—
31C2×C4⋊Dic83—22no—
32C2×C4⋊Dic83—22no—
33C4⋊(C83⋊C8)—22no—
34#14581717—28no—
35C83⋊#95—28no—
36C2×C42×C83—22no—
37C2×C42×C83D412yes—
38C2×C42×C83C2311yescharacteristic
39C4⋊C8×C83D414yes—
40C22⋊C8×C83—22no—
41C4×C8×C83—22no—
42C2×Dic166—22no—
43C2×Dic166—24no—
44C2×Dic166—24no—
45C2×Dic166—48no—
46C22×Dic83—24no—
47Dic332—88no—
48#13050574—42no—
49C2×C83⋊C8—41no—
50C4⋊Dic83—22no—
51C4⋊Dic83—22no—
52C4⋊Dic83—42no—
53C4⋊Dic83—42no—
54C4⋊Dic83—42no—
55C4⋊Dic83—42no—
56Dic83⋊C4—42no—
57C22⋊Dic83—41no—
58C4×Dic83—41no—
59C22×C4×C83—22no—
60C22×C4×C83C2×D412yes—
61C22×C4×C83C2×D411yescharacteristic
62C2×C8×C83—24no—
63C42×C83—22no—
64C42×C83—44no—
65C42×C83Q1614yescomplemented
66C42×C83C2×D411yescharacteristic
67C42×C83C2×D412yes—
68C42×C83#4111yescharacteristic
69C23×C83#12011yescharacteristic
70C2×C4×C83—24no—
71C2×C4×C83—24no—
72C2×C4×C83—44no—
73C2×C4×C83#12012yes—
74C2×C4×C83#12112yes—
75C2×C4×C83#12111yescharacteristic
76C2×C4×C83#12711yescharacteristic
77C2×C4×C83C2×Q1612yes—
78C2×C4×C83#13712yes—
79C2×Dic83—48no—
80C2×Dic83—42no—
81C2×Dic83—44no—
82Dic166—44no—
83Dic166—48no—
84Dic166—84no—
85C8×C83—44no—
86C83⋊C8—81no—
87C22×C83—22no—
88C22×C83#39211yescharacteristic
89C22×C83#45112yes—
90C4×C83—22no—
91C4×C83—44no—
92C4×C83#45514yes—
93C4×C83#46212yes—
94C4×C83#49411yescharacteristic
95C4×C83#49711yescharacteristic
96Dic83—84no—
97Dic83—82no—
98#10297—831nomaximal, Sylow
99C2×C83—22no—
100C2×C83#200412yes—
101C2×C83#201611yescharacteristic
102#3209—832no—
103#2862—831no—
104#1994—831no—
105#1548—832no—
106#1276D8311yescharacteristic
107C83#1029711yescharacteristic, complemented, Sylow
108#533—831no—
109C2×C4⋊Q8—832no—
110#494—1662no—
111#487—1662no—
112#462—1664no—
113#451—1664no—
114#431C2×D8312yes—
115#423—831no—
116#391—1664no—
117#382—1662no—
118C43C2×D8311yescharacteristic
119#339—1662no—
120#333—1664no—
121C22×Q8—834no—
122C2×Q16—1668no—
123C2×M16—1661no—
124C4⋊Q8—832no—
125C4⋊Q8—1662no—
126C4⋊Q8—1662no—
127C4⋊Q8—1662no—
128C4⋊Q8—1662no—
129#125—1661no—
130C22⋊Q8—1662no—
131C4×Q8—1662no—
132#117—1661no—
133C2×C4⋊C4—1662no—
134C2×C4⋊C4—1662no—
135C2×C42—22no—
136C2×C42D33212yes—
137C2×C42C22×D8311yescharacteristic
138C4⋊C8—1662no—
139C4⋊C8D33214yes—
140#103—1668no—
141C22⋊C8—22no—
142C4×C8—22no—
143#95—1668no—
144C2×Q8—3328no—
145C2×Q8—1664no—
146C2×Q8—1662no—
147C2×Q8—1664no—
148C22×C4—22no—
149C22×C4—1664no—
150C22×C4D4×D8312yes—
151C22×C4C2×D33211yescharacteristic
152Q16—6648no—
153M16—3322no—
154C2×C8—24no—
155C2×C8—3321no—
156C4⋊C4—3322no—
157C4⋊C4—3322no—
158C4⋊C4—3322no—
159C4⋊C4—3322no—
160C4⋊C4—3322no—
161C4⋊C4—1662no—
162C4⋊C4—1662no—
163C22⋊C4—3321no—
164C42—22no—
165C42—44no—
166C42—3321no—
167C42Dic33214yescomplemented
168C42D4×D8311yescharacteristic
169C42C2×D33212yes—
170C42#1305059111yescharacteristic
171C23#1458176211yescharacteristic
172Q8—3324no—
173Q8—3328no—
174Q8—6644no—
175C2×C4—24no—
176C2×C4—24no—
177C2×C4—44no—
178C2×C4—3328no—
179C2×C4—3322no—
180C2×C4—3324no—
181C2×C4#1458176212yes—
182C2×C4#1458176712yes—
183C2×C4#1458176711yescharacteristic
184C2×C4#1458178911yescharacteristic
185C2×C4C2×Dic33212yes—
186C2×C4#1458182512yes—
187C8—44no—
188C8—6641no—
189C22—22no—
190C22#1912761111yescharacteristic
191C22#1912785912yes—
192C4—22no—
193C4—44no—
194C4—6644no—
195C4—6642no—
196C4#1912788014yes—
197C4#1912791212yes—
198C4#1912808111yescharacteristic
199C4#1912809511yescharacteristic
200C2—22no—
201C2#2490849512yes—
202C2#2490856511yescharacteristic
subgroupG/H
centerC22#19127611
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1276C2
socleC22×C83#392
prime radicalC23×C83#120
hypercenter#1276D83
hypocenterC83#10297
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
65. C42×C83Q16semidirect
107. C83#10297semidirect
167. C42Dic332semidirect

Maximal subgroups

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

subgroupindex
#249184132
#249158412
#249084402
#249061432
C83×#12762
#1029783