Finite Group Databasebeta

← #35307130

Subgroups — #35307130

Order 21248.

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

normal subgroups only

This group has 504 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#24918616C212yesmaximal
2#24915841C211yesmaximal, characteristic
3#24908440C211yesmaximal, characteristic
4#24906147C212yesmaximal
5C83×#1276C211yesmaximal, characteristic
6#19128258C2211yescharacteristic
7C2×#14581792C2212yes—
8#19128106—22no—
9#19128052—22no—
10#19128037—24no—
11#19127997—24no—
12#19127725C2211yescharacteristic
13#19127607—24no—
14#19127567—22no—
15#19127461—22no—
16#19127448—24no—
17#431×C83C2212yes—
18C43×C83C2211yescharacteristic
19C22×Dic166—22no—
20C2×#13050574—21no—
21#14581792—22no—
22#14581792—22no—
23#14581792—22no—
24#14581792—22no—
25#14581792D412yes—
26#14581784—21no—
27#14581771—22no—
28C4×Dic166—22no—
29#14581751—21no—
30C2×C4⋊Dic83—22no—
31C2×C4⋊Dic83D414yes—
32#14581726—28no—
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—48no—
44C2×Dic166—42no—
45C2×Dic166—42no—
46C22×Dic83—24no—
47#13050574—42no—
48C2×C83⋊C8—41no—
49C4⋊Dic83—22no—
50C4⋊Dic83—24no—
51C4⋊Dic83—22no—
52C4⋊Dic83—24no—
53C4⋊Dic83—42no—
54C4⋊Dic83—42no—
55Dic83⋊C4—42no—
56C22⋊Dic83—41no—
57C4×Dic83—41no—
58C22×C4×C83—22no—
59C22×C4×C83C2×D412yes—
60C22×C4×C83C2×D411yescharacteristic
61C2×C8×C83—24no—
62C42×C83—22no—
63C42×C83—44no—
64C42×C83Q1614yes—
65C42×C83C2×D411yescharacteristic
66C42×C83C2×D412yes—
67C42×C83#4111yescharacteristic
68C23×C83#12011yescharacteristic
69C2×C4×C83—24no—
70C2×C4×C83—24no—
71C2×C4×C83—44no—
72C2×C4×C83#12012yes—
73C2×C4×C83#12112yes—
74C2×C4×C83#12111yescharacteristic
75C2×C4×C83#12711yescharacteristic
76C2×C4×C83C2×Q1612yes—
77C2×C4×C83#13712yes—
78C2×Dic83—48no—
79C2×Dic83—42no—
80C2×Dic83—44no—
81Dic166—44no—
82Dic166—84no—
83Dic166—84no—
84C8×C83—44no—
85C83⋊C8—81no—
86C22×C83—22no—
87C22×C83#39211yescharacteristic
88C22×C83#45112yes—
89C4×C83—22no—
90C4×C83—44no—
91C4×C83#45414yes—
92C4×C83#46212yes—
93C4×C83#49411yescharacteristic
94C4×C83#49711yescharacteristic
95Dic83—82no—
96Dic83—84no—
97#10295—831nomaximal, Sylow
98C2×C83—22no—
99C2×C83#200312yes—
100C2×C83#201611yescharacteristic
101#3230—832no—
102#2862—831no—
103#1994—831no—
104#1549—832no—
105#1276D8311yescharacteristic
106C83#1029511yescharacteristic, complemented, Sylow
107#533—831no—
108C2×C4⋊Q8—832no—
109#500—1662no—
110#487—1662no—
111#484—1664no—
112#477—1664no—
113#431C2×D8312yes—
114#423—831no—
115#391—1664no—
116#382—1662no—
117C43C2×D8311yescharacteristic
118#339—1662no—
119#332—1664no—
120C22×Q8—1662no—
121C2×M16—1661no—
122C4⋊Q8—832no—
123C4⋊Q8—1662no—
124C4⋊Q8—1662no—
125C4⋊Q8—1662no—
126C4⋊Q8—1662no—
127#125—1661no—
128C22⋊Q8—1662no—
129C4×Q8—1662no—
130#117—1661no—
131C2×C4⋊C4—834no—
132C2×C4⋊C4—1662no—
133C2×C42—22no—
134C2×C42D33212yes—
135C2×C42C22×D8311yescharacteristic
136#107—1668no—
137C4⋊C8—1662no—
138C4⋊C8D33214yes—
139#103—1668no—
140C22⋊C8—22no—
141C4×C8—22no—
142#95—1668no—
143C2×Q8—3328no—
144C2×Q8—3322no—
145C2×Q8—3322no—
146C2×Q8—1662no—
147C22×C4—22no—
148C22×C4—1664no—
149C22×C4D4×D8312yes—
150C22×C4C2×D33211yescharacteristic
151M16—3322no—
152C2×C8—24no—
153C2×C8—3321no—
154C4⋊C4—3322no—
155C4⋊C4—3322no—
156C4⋊C4—3322no—
157C4⋊C4—1664no—
158C4⋊C4—1662no—
159C4⋊C4—1664no—
160C4⋊C4—1662no—
161C22⋊C4—3321no—
162C42—22no—
163C42—44no—
164C42—3321no—
165C42Dic33214yes—
166C42D4×D8311yescharacteristic
167C42C2×D33212yes—
168C42#1305059111yescharacteristic
169C23#1458176211yescharacteristic
170Q8—3324no—
171Q8—6644no—
172Q8—6644no—
173C2×C4—24no—
174C2×C4—24no—
175C2×C4—44no—
176C2×C4—3328no—
177C2×C4—3322no—
178C2×C4—3324no—
179C2×C4#1458176212yes—
180C2×C4#1458176712yes—
181C2×C4#1458176711yescharacteristic
182C2×C4#1458178911yescharacteristic
183C2×C4C2×Dic33212yes—
184C2×C4#1458182512yes—
185C8—44no—
186C8—6641no—
187C22—22no—
188C22#1912761111yescharacteristic
189C22#1912785912yes—
190C4—22no—
191C4—44no—
192C4—6644no—
193C4—6642no—
194C4#1912787514yes—
195C4#1912791212yes—
196C4#1912808111yescharacteristic
197C4#1912809511yescharacteristic
198C2—22no—
199C2#2490848812yes—
200C2#2490856511yescharacteristic
subgroupG/H
centerC22#19127611
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1276C2
socleC22×C83#392
prime radicalC23×C83#120
hypercenter#1276D83
hypocenterC83#10295
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
106. C83#10295semidirect

Maximal subgroups

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

subgroupindex
#249186162
#249158412
#249084402
#249061472
C83×#12762
#1029583