Finite Group Databasebeta

← #35309184

Subgroups — #35309184

Order 21248.

310 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 85 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#24908295C211yesmaximal, characteristic
2#24907583C211yesmaximal, characteristic, complemented
3#24906110C212yesmaximal
4#24905359C212yesmaximal, complemented
5C83×#1274C211yesmaximal, characteristic, complemented
6#19128251C2211yescharacteristic
7#19127725C2211yescharacteristic
8C2×C4⋊(C83⋊C8)C2212yes—
9C2×#14581720—22no—
10#19127456—22no—
11#19127446—22no—
12#19127444—22no—
13#431×C83C2212yes—
14#376×C83C2211yescharacteristic
15C2×#13050590—21no—
16C2×#13050574—21no—
17C22×C83⋊C8—22no—
18#14581792D411yescharacteristic
19#14581789D411yescharacteristic
20#14581780—21no—
21#14581766—22no—
22C4×D332—22no—
23C4⋊(C83⋊C8)—22no—
24C4⋊(C83⋊C8)—22no—
25C4⋊(C83⋊C8)—22no—
26#14581720—44no—
27C2×C42×C83D412yes—
28C2×C42×C83C2311yescharacteristic
29C4⋊C8×C83—22no—
30C22⋊C8×C83—22no—
31C4×C8×C83—22no—
32#95×C83—22no—
33#13050590—42no—
34#13050590—42no—
35C2×Dic166—21no—
36C2×D332—21no—
37C2×D332—22no—
38C2×C22⋊D83—41no—
39C2×C4×D83—41no—
40#13050574—42no—
41C2×C83⋊C8—42no—
42C2×C83⋊C8—41no—
43C2×C83⋊C8—42no—
44C2×C83⋊C8—42no—
45C4⋊Dic83—22no—
46(C2×D83)⋊C4—42no—
47C22×C4×C83—22no—
48C22×C4×C83C2×D411yescharacteristic
49C22×C4×C83#4112yes—
50C2×C8×C83—42no—
51C42×C83—22no—
52C42×C83—22no—
53C42×C83C2×D411yescharacteristic
54C42×C83#4112yes—
55C42×C83#4111yescharacteristic
56C23×C83#12311yescharacteristic
57C22×D83—41no—
58C2×C4×C83—42no—
59C2×C4×C83—44no—
60C2×C4×C83—42no—
61C2×C4×C83#12111yescharacteristic
62C2×C4×C83#12312yes—
63C2×C4×C83#12411yescharacteristic
64C2×C4×C83#12612yes—
65C2×C4×C83#13512yes—
66C2×C4×C83AGL(1,ℤ/8)12yes—
67C22⋊D83—82no—
68C2×Dic83—41no—
69D332—42no—
70D332—82no—
71C4×D83—81no—
72C4×D83—81no—
73Dic166—42no—
74C8×C83—82no—
75C83⋊C8—82no—
76C83⋊C8—81no—
77C22×C83—22no—
78C22×C83#39711yescharacteristic
79C22×C83#48212yes—
80C2×D83—81no—
81C2×D83—82no—
82C4×C83—22no—
83C4×C83—22no—
84C4×C83—82no—
85C4×C83#46312yes—
86C4×C83#48811yescharacteristic
87C4×C83#49011yescharacteristic
88Dic83—81no—
89#10629—831nomaximal, Sylow
90C2×C83—22no—
91C2×C83#207311yescharacteristic
92C2×C83#208012yes—
93D83—161no—
94#1963—831no—
95#1832—831no—
96#1540—832no—
97#1301—832no—
98#1274D8311yescharacteristic, complemented
99C83#1062911yescharacteristic, complemented, Sylow
100#532—831no—
101#431C2×D8312yes—
102#423—831no—
103C2×C4⋊C8—832no—
104C2×#104—1662no—
105#376C2×D8311yescharacteristic
106#336—1662no—
107#332—1662no—
108#331—1662no—
109C2×#41—1661no—
110C2×M16—1661no—
111C22×C8—1662no—
112C4⋊Q8—831no—
113#127—831no—
114#124—1661no—
115#121—1662no—
116C4×D4—1662no—
117C2×C42D33212yes—
118C2×C42C22×D8311yescharacteristic
119C4⋊C8—22no—
120C4⋊C8—1662no—
121C4⋊C8—1662no—
122C4⋊C8—1662no—
123#104—3324no—
124C22⋊C8—22no—
125C4×C8—22no—
126#95—22no—
127#41—3322no—
128#41—3322no—
129C2×Q8—1661no—
130C2×D4—3321no—
131C2×D4—1661no—
132C2×D4—1662no—
133C22×C4—22no—
134C22×C4—3321no—
135C22×C4C2×D33211yescharacteristic
136C22×C4#1305058912yes—
137M16—3322no—
138C2×C8—42no—
139C2×C8—3322no—
140C2×C8—3321no—
141C2×C8—3322no—
142C2×C8—3322no—
143C4⋊C4—1662no—
144C22⋊C4—3322no—
145C42—22no—
146C42—22no—
147C42D4×D8311yescharacteristic
148C42#1305059012yes—
149C42#1305059111yescharacteristic
150C23—3321no—
151C23#1458177611yescharacteristic
152Q8—3322no—
153D4—3322no—
154D4—6642no—
155D4—6642no—
156C2×C4—42no—
157C2×C4—44no—
158C2×C4—42no—
159C2×C4—3321no—
160C2×C4—6641no—
161C2×C4—6641no—
162C2×C4#1458176711yescharacteristic
163C2×C4#1458177412yes—
164C2×C4#1458178011yescharacteristic
165C2×C4#1458178712yes—
166C2×C4#1458181412yes—
167C2×C4#1458182012yes—
168C8—82no—
169C8—6641no—
170C8—6642no—
171C22—22no—
172C22—6641no—
173C22—6642no—
174C22#1912762811yescharacteristic
175C22#1912802612yes—
176C4—22no—
177C4—22no—
178C4—82no—
179C4—6641no—
180C4#1912791712yes—
181C4#1912805611yescharacteristic
182C4#1912806611yescharacteristic
183C2—22no—
184C2—13281no—
185C2#2490887811yescharacteristic
186C2#2490891512yes—
subgroupG/H
centerC2×C4#14581780
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1274C2
socleC22×C83#397
prime radical#19128251C22
hypercenter#1274D83
hypocenterC83#10629
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1274

Complements

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

NH ≅ G/Ntype
2. #24907583C2semidirect
4. #24905359C2semidirect
5. C83×#1274C2semidirect
98. #1274D83semidirect
99. C83#10629semidirect

Maximal subgroups

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

subgroupindex
#249082952
#249075832
#249061102
#249053592
C83×#12742
#1062983