Finite Group Databasebeta

← #35309183

Subgroups — #35309183

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#24906113C212yesmaximal
3#24905360C212yesmaximal, complemented
4#24905292C211yesmaximal, characteristic, complemented
5C83×#1832C211yesmaximal, characteristic, complemented
6#19128251C2211yescharacteristic
7#19127754C2212yes—
8#19127725C2211yescharacteristic
9C2×#14581720—22no—
10#19127448—22no—
11#19127444—22no—
12C2×C4⋊C8×C83C2212yes—
13#376×C83C2211yescharacteristic
14#336×C83—22no—
15C2×#13050590—21no—
16C2×#13050574—21no—
17#14581792D411yescharacteristic
18#14581789D411yescharacteristic
19#14581780—21no—
20#14581766—22no—
21C4×D332—22no—
22C4⋊(C83⋊C8)—22no—
23C4⋊(C83⋊C8)—22no—
24#14581720—44no—
25C22⋊(C83⋊C8)—22no—
26C4×C83⋊C8—22no—
27C22×C8×C83—22no—
28C2×C42×C83D412yes—
29C2×C42×C83C2311yescharacteristic
30C4⋊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—
43C4⋊Dic83—22no—
44(C2×D83)⋊C4—42no—
45C22×C4×C83—22no—
46C22×C4×C83C2×D411yescharacteristic
47C22×C4×C83#4112yes—
48C2×C8×C83—42no—
49C2×C8×C83—42no—
50C2×C8×C83—42no—
51C42×C83—22no—
52C42×C83—22no—
53C42×C83C2×D411yescharacteristic
54C42×C83#4111yescharacteristic
55C42×C83#4112yes—
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#1832D8311yescharacteristic, complemented
96#1540—832no—
97#1301—832no—
98#1274—831no—
99C83#1062911yescharacteristic, complemented, Sylow
100#532—831no—
101#431—832no—
102#423—831no—
103C2×C4⋊C8C2×D8312yes—
104C2×#104—1662no—
105#376C2×D8311yescharacteristic
106#336—22no—
107#332—1662no—
108#331—1662no—
109C2×#41—1661no—
110C2×M16—1661no—
111C22×C8—22no—
112C4⋊Q8—831no—
113#127—831no—
114#124—1661no—
115#121—1662no—
116C4×D4—1662no—
117C2×C42C22⋊D8312yes—
118C2×C42C22×D8311yescharacteristic
119C4⋊C8—22no—
120C4⋊C8—22no—
121C4⋊C8—1662no—
122C4⋊C8—1662no—
123#104—3324no—
124C22⋊C8—1662no—
125C4×C8—1662no—
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×C22⋊D8311yescharacteristic
136C22×C4#1305059012yes—
137M16—3322no—
138C2×C8—42no—
139C2×C8—42no—
140C2×C8—42no—
141C2×C8—3322no—
142C2×C8—3321no—
143C4⋊C4—1662no—
144C22⋊C4—3322no—
145C42—22no—
146C42—22no—
147C42D4×D8311yescharacteristic
148C42#1305058911yescharacteristic
149C42#1305059112yes—
150C23—3321no—
151C23#1458177511yescharacteristic
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#1458176311yescharacteristic
163C2×C4#1458177712yes—
164C2×C4#1458178111yescharacteristic
165C2×C4#1458178712yes—
166C2×C4#1458181212yes—
167C2×C4#1458181712yes—
168C8—82no—
169C8—6642no—
170C8—6641no—
171C22—22no—
172C22—6641no—
173C22—6642no—
174C22#1912762711yescharacteristic
175C22#1912802512yes—
176C4—22no—
177C4—22no—
178C4—82no—
179C4—6641no—
180C4#1912791312yes—
181C4#1912805811yescharacteristic
182C4#1912806711yescharacteristic
183C2—22no—
184C2—13281no—
185C2#2490887711yescharacteristic
186C2#2490891412yes—
subgroupG/H
centerC2×C4#14581781
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1832C2
socleC22×C83#397
prime radical#19128251C22
hypercenter#1832D83
hypocenterC83#10629
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1832

Complements

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

NH ≅ G/Ntype
3. #24905360C2semidirect
4. #24905292C2semidirect
5. C83×#1832C2semidirect
95. #1832D83semidirect
99. C83#10629semidirect

Maximal subgroups

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

subgroupindex
#249082952
#249061132
#249053602
#249052922
C83×#18322
#1062983