Finite Group Databasebeta

← #35307128

Subgroups — #35307128

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#24918614C212yesmaximal
2#24908440C211yesmaximal, characteristic
3#24906148C212yesmaximal
4#24905296C211yesmaximal, characteristic
5C83×#2862C211yesmaximal, characteristic
6#19128258C2211yescharacteristic
7#19128104—22no—
8#19128053—22no—
9#19128036—24no—
10#19127993—24no—
11#19127754C2212yes—
12#19127725C2211yescharacteristic
13#19127461—22no—
14#19127447—24no—
15C2×C4⋊Q8×C83C2212yes—
16#391×C83—24no—
17#382×C83—22no—
18C43×C83C2211yescharacteristic
19C2×#13050574—21no—
20#14581792D412yes—
21#14581784—21no—
22#14581771—22no—
23C4×Dic166—22no—
24#14581751—21no—
25#14581725—28no—
26C4⋊(C83⋊C8)—22no—
27C4⋊(C83⋊C8)D414yes—
28#14581715—28no—
29C22⋊(C83⋊C8)—22no—
30C4×C83⋊C8—22no—
31C22×Q8×C83—22no—
32C4⋊Q8×C83—22no—
33C4⋊Q8×C83—22no—
34C4⋊Q8×C83—22no—
35C4⋊Q8×C83—22no—
36C2×C4⋊C4×C83—22no—
37C2×C4⋊C4×C83D414yes—
38C2×C42×C83—22no—
39C2×C42×C83D412yes—
40C2×C42×C83C2311yescharacteristic
41#95×C83—28no—
42C2×Dic166—22no—
43#13050574—42no—
44C2×C83⋊C8—24no—
45C2×C83⋊C8—41no—
46C4⋊Dic83—22no—
47C4⋊Dic83—22no—
48Dic83⋊C4—42no—
49C22⋊Dic83—41no—
50C4×Dic83—41no—
51C2×Q8×C83—48no—
52C2×Q8×C83—42no—
53C2×Q8×C83—42no—
54C22×C4×C83—22no—
55C22×C4×C83—24no—
56C22×C4×C83C2×D412yes—
57C22×C4×C83C2×D411yescharacteristic
58C4⋊C4×C83—24no—
59C4⋊C4×C83—24no—
60C4⋊C4×C83—42no—
61C4⋊C4×C83—42no—
62C42×C83—22no—
63C42×C83—44no—
64C42×C83Q1614yes—
65C42×C83C2×D411yescharacteristic
66C42×C83C2×D412yes—
67C42×C83#4111yescharacteristic
68C23×C83#12011yescharacteristic
69Q8×C83—84no—
70Q8×C83—84no—
71C2×C4×C83—24no—
72C2×C4×C83—24no—
73C2×C4×C83—44no—
74C2×C4×C83—48no—
75C2×C4×C83—44no—
76C2×C4×C83#12012yes—
77C2×C4×C83#12111yescharacteristic
78C2×C4×C83#12112yes—
79C2×C4×C83#12711yescharacteristic
80C2×C4×C83C2×Q1612yes—
81C2×C4×C83#13712yes—
82C2×Dic83—42no—
83Dic166—44no—
84C83⋊C8—44no—
85C83⋊C8—81no—
86C22×C83—22no—
87C22×C83#39211yescharacteristic
88C22×C83#45112yes—
89C4×C83—22no—
90C4×C83—44no—
91C4×C83—84no—
92C4×C83#45414yes—
93C4×C83#46212yes—
94C4×C83#49411yescharacteristic
95C4×C83#49711yescharacteristic
96Dic83—82no—
97#10295—831nomaximal, Sylow
98C2×C83—22no—
99C2×C83#200312yes—
100C2×C83#201611yescharacteristic
101#3230—832no—
102#2862D8311yescharacteristic
103#1994—831no—
104#1549—832no—
105#1276—831no—
106C83#1029511yescharacteristic, complemented, Sylow
107#533—831no—
108C2×C4⋊Q8C2×D8312yes—
109#500—1662no—
110#487—1662no—
111#484—1664no—
112#477—1664no—
113#431—832no—
114#423—831no—
115#391—24no—
116#382—22no—
117C43C2×D8311yescharacteristic
118#339—1662no—
119#332—1664no—
120C22×Q8—22no—
121C2×M16—1661no—
122C4⋊Q8—22no—
123C4⋊Q8—22no—
124C4⋊Q8—22no—
125C4⋊Q8—22no—
126C4⋊Q8—832no—
127#125—1661no—
128C22⋊Q8—1662no—
129C4×Q8—1662no—
130#117—1661no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4C22⋊D8314yes—
133C2×C42—22no—
134C2×C42C22⋊D8312yes—
135C2×C42C22×D8311yescharacteristic
136#107—1668no—
137C4⋊C8—834no—
138C4⋊C8—1662no—
139#103—1668no—
140C22⋊C8—1662no—
141C4×C8—1662no—
142#95—28no—
143C2×Q8—48no—
144C2×Q8—42no—
145C2×Q8—42no—
146C2×Q8—1662no—
147C22×C4—22no—
148C22×C4—24no—
149C22×C4C2×C22⋊D8312yes—
150C22×C4C2×C22⋊D8311yescharacteristic
151M16—3322no—
152C2×C8—3321no—
153C2×C8—1664no—
154C4⋊C4—24no—
155C4⋊C4—24no—
156C4⋊C4—42no—
157C4⋊C4—42no—
158C4⋊C4—3322no—
159C4⋊C4—1662no—
160C4⋊C4—1662no—
161C22⋊C4—3321no—
162C42—22no—
163C42—44no—
164C42—3321no—
165C42#1305058014yes—
166C42D4×D8311yescharacteristic
167C42D4×D8312yes—
168C42#1305058911yescharacteristic
169C23#1458176111yescharacteristic
170Q8—84no—
171Q8—84no—
172Q8—3324no—
173C2×C4—24no—
174C2×C4—24no—
175C2×C4—44no—
176C2×C4—48no—
177C2×C4—44no—
178C2×C4—3322no—
179C2×C4#1458176012yes—
180C2×C4#1458176311yescharacteristic
181C2×C4#1458176412yes—
182C2×C4#1458178811yescharacteristic
183C2×C4C2×#1305058012yes—
184C2×C4#1458182312yes—
185C8—3324no—
186C8—6641no—
187C22—22no—
188C22#1912760911yescharacteristic
189C22#1912785712yes—
190C4—22no—
191C4—44no—
192C4—84no—
193C4—6642no—
194C4#1912787314yes—
195C4#1912790812yes—
196C4#1912808011yescharacteristic
197C4#1912809311yescharacteristic
198C2—22no—
199C2#2490848512yes—
200C2#2490856311yescharacteristic
subgroupG/H
centerC22#19127609
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#2862C2
socleC22×C83#392
prime radicalC23×C83#120
hypercenter#2862D83
hypocenterC83#10295
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2862

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
#249186142
#249084402
#249061482
#249052962
C83×#28622
#1029583