Finite Group Databasebeta

← #35308566

Subgroups — #35308566

Order 21248.

342 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 75 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#24906191C212yesmaximal
3#24906077C212yesmaximal
4#24905374C211yesmaximal, characteristic
5C83×#1849C211yesmaximal, characteristic
6#19128258C2212yes—
7#19127987—22no—
8#19127959—22no—
9#19127912—22no—
10#19127758C2212yes—
11#19127449—22no—
12#19127448—22no—
13#19127442—24no—
14C2×#108×C83—22no—
15#423×C83C2211yescharacteristic
16#423×C83C2211yescharacteristic
17C2×#97×C83C2211yescharacteristic
18C2×Dic332—22no—
19#14581792D412yes—
20#14581792D412yes—
21#14581784—22no—
22#14581771—22no—
23#14581771—22no—
24C4×Dic166—22no—
25C4×Dic166—22no—
26#14581751—22no—
27#14581724—22no—
28C4⋊(C83⋊C8)—22no—
29#14581717—24no—
30C22⋊(C83⋊C8)—22no—
31#14581703—22no—
32C2×M16×C83—21no—
33C2×M16×C83D412yes—
34C22×C8×C83—21no—
35C2×C42×C83C2311yescharacteristic
36#108×C83—44no—
37C4⋊C8×C83—22no—
38C4⋊C8×C83—22no—
39#97×C83—21no—
40#97×C83D412yes—
41C2×Dic166—22no—
42C2×Dic166—22no—
43Dic332—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—22no—
60C2×C8×C83—22no—
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—42no—
69C2×C4×C83#12011yescharacteristic
70C2×C4×C83#12111yescharacteristic
71C2×C4×C83#12112yes—
72C2×C4×C83#12312yes—
73C2×Dic83—42no—
74C2×Dic83—42no—
75Dic166—42no—
76Dic166—42no—
77Dic166—82no—
78C8×C83—24no—
79C8×C83—42no—
80C8×C83—81no—
81C83⋊C8—82no—
82C22×C83—22no—
83C22×C83—21no—
84C22×C83#39411yescharacteristic
85C4×C83—22no—
86C4×C83—22no—
87C4×C83—21no—
88C4×C83#45311yescharacteristic
89C4×C83#45611yescharacteristic
90Dic83—82no—
91Dic83—82no—
92#10528—831nomaximal, Sylow
93C2×C83—41no—
94C2×C83#203911yescharacteristic
95C2×C83#204912yes—
96#3255—831no—
97#1849D8311yescharacteristic
98#1559—832no—
99#1531—832no—
100#1307—831no—
101C83#1052811yescharacteristic, complemented, Sylow
102#533—832no—
103#475—1662no—
104#470—1662no—
105#462—1662no—
106#432—832no—
107C2×#108—22no—
108#423C2×D8311yescharacteristic
109#423C2×D8311yescharacteristic
110C2×#97C2×D8311yescharacteristic
111#333—1662no—
112#332—1662no—
113#330—1664no—
114C2×Q16—1662no—
115C2×M16—21no—
116C2×M16C22⋊D8312yes—
117C22×C8—21no—
118C4⋊Q8—832no—
119C4⋊Q8—832no—
120#125—1662no—
121C22⋊Q8—1662no—
122C22⋊Q8—1662no—
123C4×Q8—1662no—
124C4×Q8—1662no—
125#117—1662no—
126C2×C42C22×D8311yescharacteristic
127#108—44no—
128#106—1662no—
129C4⋊C8—22no—
130C4⋊C8—22no—
131C4⋊C8—1662no—
132#103—1664no—
133C22⋊C8—1662no—
134#97—21no—
135#97—1662no—
136#97D33212yes—
137C2×Q8—1662no—
138C2×Q8—1662no—
139C22×C4C2×C22⋊D8311yescharacteristic
140C22×C4#1305059112yes—
141Q16—6642no—
142M16—42no—
143M16—42no—
144C2×C8—22no—
145C2×C8—22no—
146C2×C8—22no—
147C2×C8—22no—
148C2×C8—41no—
149C2×C8—3322no—
150C4⋊C4—3322no—
151C4⋊C4—3322no—
152C4⋊C4—1662no—
153C4⋊C4—1662no—
154C4⋊C4—1662no—
155C4⋊C4—1662no—
156C22⋊C4—3322no—
157C42—3322no—
158C42D4×D8312yes—
159C42C2×D33211yescharacteristic
160C42#1305059011yescharacteristic
161C23#1458178111yescharacteristic
162Q8—3322no—
163Q8—3322no—
164Q8—6642no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—42no—
168C2×C4—3322no—
169C2×C4—3322no—
170C2×C4#1458176011yescharacteristic
171C2×C4#1458176611yescharacteristic
172C2×C4#1458176712yes—
173C2×C4#1458177712yes—
174C8—24no—
175C8—42no—
176C8—81no—
177C8—6642no—
178C22—21no—
179C22—22no—
180C22#1912761811yescharacteristic
181C4—21no—
182C4—22no—
183C4—22no—
184C4—6642no—
185C4—6642no—
186C4#1912786811yescharacteristic
187C4#1912788311yescharacteristic
188C2—41no—
189C2#2490868711yescharacteristic
190C2#2490874512yes—
subgroupG/H
centerC22#19127618
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1849C2
socleC22×C83#394
prime radicalC23×C83#124
hypercenter#1849D83
hypocenterC83#10528
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1849

Complements

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

NH ≅ G/Ntype
101. C83#10528semidirect

Maximal subgroups

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

subgroupindex
#249188572
#249061912
#249060772
#249053742
C83×#18492
#1052883