Finite Group Databasebeta

← #35307154

Subgroups — #35307154

Order 21248.

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

normal subgroups only

This group has 576 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#24918609C212yesmaximal
2#24915861C211yesmaximal, characteristic
3#24908440C211yesmaximal, characteristic
4#24906134C212yesmaximal
5C83×#1276C211yesmaximal, characteristic
6#19128258C2211yescharacteristic
7C2×#14581792—22no—
8C2×#14581792C2212yes—
9#19128099—22no—
10#19128052—22no—
11#19128032—24no—
12#19127987—24no—
13#19127725C2211yescharacteristic
14#19127571—24no—
15#19127461—22no—
16#19127446—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#14581792—44no—
26#14581792—44no—
27#14581792D412yes—
28#14581784—21no—
29#14581771—22no—
30C4×Dic166—22no—
31#14581751—21no—
32C2×C4⋊Dic83—28no—
33C2×C4⋊Dic83—22no—
34C2×C4⋊Dic83D414yes—
35#14581724—28no—
36C4⋊(C83⋊C8)—22no—
37#14581717—28no—
38C2×C42×C83—22no—
39C2×C42×C83D412yes—
40C2×C42×C83C2311yescharacteristic
41C4⋊C8×C83D414yes—
42C22⋊C8×C83—22no—
43C4×C8×C83—22no—
44C2×Dic166—22no—
45C2×Dic166—42no—
46C2×Dic166—42no—
47C2×Dic166—44no—
48C2×Dic166—44no—
49C22×Dic83—24no—
50#13050574—42no—
51C2×C83⋊C8—41no—
52C4⋊Dic83—22no—
53C4⋊Dic83—24no—
54C4⋊Dic83—22no—
55C4⋊Dic83—24no—
56C4⋊Dic83—416no—
57C4⋊Dic83—42no—
58C4⋊Dic83—42no—
59Dic83⋊C4—42no—
60C22⋊Dic83—41no—
61C4×Dic83—41no—
62C22×C4×C83—22no—
63C22×C4×C83C2×D412yes—
64C22×C4×C83C2×D411yescharacteristic
65C2×C8×C83—24no—
66C42×C83—28no—
67C42×C83—22no—
68C42×C83SD1614yes—
69C42×C83C2×D411yescharacteristic
70C42×C83C2×D412yes—
71C42×C83#4111yescharacteristic
72C23×C83#12011yescharacteristic
73C2×C4×C83—28no—
74C2×C4×C83—24no—
75C2×C4×C83—24no—
76C2×C4×C83#12012yes—
77C2×C4×C83#12112yes—
78C2×C4×C83#12111yescharacteristic
79C2×C4×C83#12711yescharacteristic
80C2×C4×C83C2×SD1612yes—
81C2×C4×C83AGL(1,ℤ/8)12yes—
82C2×Dic83—42no—
83C2×Dic83—44no—
84C2×Dic83—48no—
85Dic166—44no—
86Dic166—84no—
87Dic166—82no—
88Dic166—82no—
89C8×C83—44no—
90C83⋊C8—81no—
91C22×C83—22no—
92C22×C83#39211yescharacteristic
93C22×C83#45012yes—
94C4×C83—28no—
95C4×C83—22no—
96C4×C83#45614yes—
97C4×C83#46012yes—
98C4×C83#49211yescharacteristic
99C4×C83#49611yescharacteristic
100Dic83—82no—
101Dic83—84no—
102#10299—831nomaximal, Sylow
103C2×C83—22no—
104C2×C83#200512yes—
105C2×C83#201411yescharacteristic
106#3229—832no—
107#2868—831no—
108#1994—831no—
109#1546—832no—
110#1276D8311yescharacteristic
111C83#1029911yescharacteristic, complemented, Sylow
112#533—831no—
113C2×C4⋊Q8—832no—
114C2×C4⋊Q8—1662no—
115#498—1662no—
116#487—1662no—
117#483—1664no—
118#475—1664no—
119#431C2×D8312yes—
120#423—831no—
121#384—1664no—
122C43C2×D8311yescharacteristic
123#339—1662no—
124#332—1664no—
125C22×Q8—1662no—
126C2×M16—1661no—
127C4⋊Q8—3324no—
128C4⋊Q8—3324no—
129C4⋊Q8—832no—
130C4⋊Q8—1662no—
131C4⋊Q8—1662no—
132C4⋊Q8—1662no—
133C4⋊Q8—1662no—
134#125—1661no—
135C22⋊Q8—1662no—
136C4×Q8—1662no—
137#117—1661no—
138C2×C4⋊C4—834no—
139C2×C4⋊C4—1668no—
140C2×C4⋊C4—1662no—
141C2×C42—22no—
142C2×C42D33212yes—
143C2×C42C22×D8311yescharacteristic
144#106—1668no—
145C4⋊C8—1662no—
146C4⋊C8D33214yes—
147#103—1668no—
148C22⋊C8—22no—
149C4×C8—22no—
150C2×Q8—3322no—
151C2×Q8—3322no—
152C2×Q8—3324no—
153C2×Q8—3324no—
154C2×Q8—1662no—
155C22×C4—22no—
156C22×C4—1664no—
157C22×C4D4×D8312yes—
158C22×C4C2×D33211yescharacteristic
159M16—3322no—
160C2×C8—24no—
161C2×C8—3321no—
162C4⋊C4—33216no—
163C4⋊C4—3322no—
164C4⋊C4—3322no—
165C4⋊C4—3322no—
166C4⋊C4—1664no—
167C4⋊C4—1662no—
168C4⋊C4—1664no—
169C4⋊C4—1662no—
170C22⋊C4—3321no—
171C42—28no—
172C42—22no—
173C42—3321no—
174C42#1305057914yes—
175C42D4×D8311yescharacteristic
176C42C2×D33212yes—
177C42#1305059111yescharacteristic
178C23#1458176211yescharacteristic
179Q8—3324no—
180Q8—6642no—
181Q8—6642no—
182Q8—6644no—
183C2×C4—28no—
184C2×C4—24no—
185C2×C4—24no—
186C2×C4—3328no—
187C2×C4—3322no—
188C2×C4—3324no—
189C2×C4#1458176212yes—
190C2×C4#1458176712yes—
191C2×C4#1458176711yescharacteristic
192C2×C4#1458178911yescharacteristic
193C2×C4C2×#1305057912yes—
194C2×C4#1458182012yes—
195C8—44no—
196C8—6641no—
197C22—22no—
198C22#1912761111yescharacteristic
199C22#1912785412yes—
200C4—28no—
201C4—22no—
202C4—6644no—
203C4—6642no—
204C4#1912788514yes—
205C4#1912790212yes—
206C4#1912807411yescharacteristic
207C4#1912809011yescharacteristic
208C2—22no—
209C2#2490850212yes—
210C2#2490855311yescharacteristic
subgroupG/H
centerC22#19127611
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1276C2
socleC22×C83#392
prime radicalC23×C83#120
hypercenter#1276D83
hypocenterC83#10299
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
111. C83#10299semidirect

Maximal subgroups

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

subgroupindex
#249186092
#249158612
#249084402
#249061342
C83×#12762
#1029983