Finite Group Databasebeta

← #35308605

Subgroups — #35308605

Order 21248.

342 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 83 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#24918857C211yesmaximal, characteristic
2#24906200C212yesmaximal
3#24905919C212yesmaximal
4C83⋊#1309C211yesmaximal, characteristic
5C83×#1837C211yesmaximal, characteristic
6#19128258C2212yes—
7#19127987—22no—
8#19127959—22no—
9#19127912—22no—
10#19127725C2212yes—
11#19127448—22no—
12#19127446—22no—
13#19127433—24no—
14#423×C83C2211yescharacteristic
15#423×C83C2211yescharacteristic
16C2×C4×C8×C83C2211yescharacteristic
17#341×C83—22no—
18C2×Dic332—22no—
19C2×#13050574—22no—
20#14581792D412yes—
21#14581792D412yes—
22#14581784—22no—
23#14581771—22no—
24#14581771—22no—
25C4×Dic166—22no—
26C4×Dic166—22no—
27#14581751—22no—
28#14581724—22no—
29C4⋊(C83⋊C8)—22no—
30C4⋊(C83⋊C8)—22no—
31#14581717—24no—
32C2×M16×C83—21no—
33C2×M16×C83D412yes—
34C22×C8×C83—21no—
35C2×C42×C83C2311yescharacteristic
36C4⋊C8×C83—22no—
37C4⋊C8×C83—22no—
38C4×C8×C83—21no—
39C4×C8×C83D412yes—
40C2×Dic166—22no—
41C2×Dic166—22no—
42Dic332—82no—
43#13050574—82no—
44C2×C83⋊C8—42no—
45C4⋊Dic83—22no—
46C4⋊Dic83—22no—
47C4⋊Dic83—22no—
48C4⋊Dic83—22no—
49Dic83⋊C4—42no—
50Dic83⋊C4—42no—
51C22⋊Dic83—42no—
52C4×Dic83—42no—
53C22×C4×C83C2×D411yescharacteristic
54C22×C4×C83#4112yes—
55M16×C83—42no—
56M16×C83—42no—
57C2×C8×C83—22no—
58C2×C8×C83—22no—
59C2×C8×C83—41no—
60C2×C8×C83—41no—
61C2×C8×C83—41no—
62C42×C83C2×D412yes—
63C42×C83C2×D411yescharacteristic
64C42×C83#4111yescharacteristic
65C23×C83#12411yescharacteristic
66C2×C4×C83—21no—
67C2×C4×C83—21no—
68C2×C4×C83—22no—
69C2×C4×C83—22no—
70C2×C4×C83#12011yescharacteristic
71C2×C4×C83#12111yescharacteristic
72C2×C4×C83#12112yes—
73C2×C4×C83#12312yes—
74C2×Dic83—42no—
75C2×Dic83—42no—
76Dic166—42no—
77Dic166—42no—
78Dic166—42no—
79Dic166—42no—
80C8×C83—42no—
81C8×C83—42no—
82C8×C83—81no—
83C83⋊C8—82no—
84C22×C83—22no—
85C22×C83—21no—
86C22×C83#39411yescharacteristic
87C4×C83—22no—
88C4×C83—21no—
89C4×C83#45411yescharacteristic
90C4×C83#45511yescharacteristic
91C4×C83#47112yes—
92C4×C83#47312yes—
93Dic83—82no—
94Dic83—82no—
95#10535—831nomaximal, Sylow
96C2×C83—41no—
97C2×C83#204011yescharacteristic
98C2×C83#205212yes—
99#3255—831no—
100#1837D8311yescharacteristic
101#1561—832no—
102#1493—832no—
103#1309—831no—
104C83#1053511yescharacteristic, complemented, Sylow
105#533—832no—
106#475—1662no—
107#470—1662no—
108#462—1662no—
109#423—832no—
110#423C2×D8311yescharacteristic
111#423C2×D8311yescharacteristic
112C2×C4×C8C2×D8311yescharacteristic
113#341—22no—
114#332—1662no—
115#332—1662no—
116Q8⋊C8—1664no—
117C2×Q16—1662no—
118C2×M16—21no—
119C2×M16—1662no—
120C2×M16C22⋊D8312yes—
121C22×C8—21no—
122C4⋊Q8—832no—
123C4⋊Q8—832no—
124#125—1662no—
125C22⋊Q8—1662no—
126C22⋊Q8—1662no—
127C4×Q8—1662no—
128C4×Q8—1662no—
129#117—1662no—
130C2×C42C22×D8311yescharacteristic
131#106—1662no—
132C4⋊C8—22no—
133C4⋊C8—22no—
134C4⋊C8—1662no—
135C4⋊C8—1662no—
136#103—1664no—
137C4×C8—21no—
138C4×C8D33212yes—
139C2×Q8—1662no—
140C2×Q8—1662no—
141C22×C4C2×C22⋊D8311yescharacteristic
142C22×C4#1305059112yes—
143Q16—6642no—
144M16—42no—
145M16—42no—
146M16—6642no—
147C2×C8—22no—
148C2×C8—22no—
149C2×C8—41no—
150C2×C8—41no—
151C2×C8—41no—
152C2×C8—3322no—
153C4⋊C4—3322no—
154C4⋊C4—3322no—
155C4⋊C4—1662no—
156C4⋊C4—1662no—
157C4⋊C4—1662no—
158C4⋊C4—1662no—
159C22⋊C4—3322no—
160C42—3322no—
161C42D4×D8312yes—
162C42C2×D33211yescharacteristic
163C42#1305059011yescharacteristic
164C23#1458178111yescharacteristic
165Q8—3322no—
166Q8—3322no—
167Q8—3322no—
168Q8—3322no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—3322no—
174C2×C4—3322no—
175C2×C4#1458176011yescharacteristic
176C2×C4#1458176611yescharacteristic
177C2×C4#1458176712yes—
178C2×C4#1458177712yes—
179C8—42no—
180C8—42no—
181C8—81no—
182C8—6642no—
183C22—21no—
184C22—22no—
185C22#1912761811yescharacteristic
186C4—21no—
187C4—22no—
188C4—6642no—
189C4—6642no—
190C4#1912787311yescharacteristic
191C4#1912787811yescharacteristic
192C4#1912796512yes—
193C4#1912797712yes—
194C2—41no—
195C2#2490869211yescharacteristic
196C2#2490876412yes—
subgroupG/H
centerC22#19127618
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1837C2
socleC22×C83#394
prime radicalC23×C83#124
hypercenter#1837D83
hypocenterC83#10535
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1837

Complements

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

NH ≅ G/Ntype
104. C83#10535semidirect

Maximal subgroups

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

subgroupindex
#249188572
#249062002
#249059192
C83⋊#13092
C83×#18372
#1053583