Finite Group Databasebeta

← #35291985

Subgroups — #35291985

Order 21248.

214 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 37 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#24908630C211yesmaximal, characteristic
2#24905393C211yesmaximal, characteristic
3C83×#1306C211yesmaximal, characteristic
4#19128327C411yescharacteristic
5#19127564—21no—
6#19127468C411yescharacteristic
7#19127467—21no—
8#19127425—21no—
9#407×C83—21no—
10#381×C83C2211yescharacteristic
11#14581771—41no—
12#14581769—42no—
13C2×C22⋊Dic83—21no—
14C2×C22⋊Dic83—21no—
15C22⋊(C83⋊C8)—41no—
16C83⋊#95—42no—
17C23×C4×C83D411yescharacteristic
18C2×M16×C83—41no—
19C2×C22⋊C4×C83C2×C411yescharacteristic
20C2×C22⋊C4×C83D411yescharacteristic
21C22⋊C8×C83—22no—
22C22⋊C8×C83—41no—
23#95×C83—41no—
24C2×Dic166—41no—
25C22×Dic83—22no—
26C22×Dic83—41no—
27C2×C83⋊C8—81no—
28C4⋊Dic83—41no—
29Dic83⋊C4—42no—
30C22⋊Dic83—41no—
31C22⋊Dic83—41no—
32C22⋊Dic83—41no—
33C22⋊Dic83—41no—
34C24×C83C22⋊C411yescharacteristic
35C22×C4×C83—21no—
36C22×C4×C83—21no—
37C22×C4×C83—21no—
38C22×C4×C83—21no—
39C22×C4×C83—41no—
40C22×C4×C83—41no—
41C22×C4×C83SD1611yescharacteristic
42C22×C4×C83Q1611yescharacteristic
43M16×C83—81no—
44M16×C83—81no—
45C2×C8×C83—42no—
46C22⋊C4×C83—41no—
47C22⋊C4×C83—41no—
48C23×C83—21no—
49C23×C83—21no—
50C23×C83—81no—
51C23×C83#9911yescharacteristic
52C23×C83#10311yescharacteristic
53C23×C83#10411yescharacteristic
54C2×C4×C83—21no—
55C2×C4×C83—21no—
56C2×C4×C83—41no—
57C2×C4×C83—41no—
58C2×C4×C83—41no—
59C2×C4×C83—41no—
60C2×C4×C83—41no—
61C2×C4×C83—41no—
62C2×C4×C83—81no—
63C2×C4×C83—81no—
64C2×C4×C83—81no—
65C2×Dic83—42no—
66C2×Dic83—82no—
67C2×Dic83—81no—
68C2×Dic83—82no—
69Dic166—161no—
70C8×C83—82no—
71C83⋊C8—161no—
72C22×C83—21no—
73C22×C83—21no—
74C22×C83—41no—
75C22×C83—41no—
76C22×C83—41no—
77C22×C83—42no—
78C22×C83—81no—
79C22×C83#32811yescharacteristic
80C22×C83AΣL(1,𝔽16)11yescharacteristic
81C22×C83#35411yescharacteristic
82C4×C83—41no—
83C4×C83—41no—
84C4×C83—81no—
85C4×C83—81no—
86Dic83—82no—
87Dic83—161no—
88#7427—831nomaximal, Sylow
89C2×C83—21no—
90C2×C83—21no—
91C2×C83—21no—
92C2×C83—41no—
93C2×C83—41no—
94C2×C83#135111yescharacteristic
95#2030—831no—
96#1317—831no—
97#1306D8311yescharacteristic
98C83#742711yescharacteristic, complemented, Sylow
99#543—831no—
100#407—21no—
101#381—1661no—
102#381C2×D8311yescharacteristic
103#342—831no—
104#342—1661no—
105#323—1661no—
106C23×C4C22⋊D8311yescharacteristic
107C2×M16—41no—
108C22⋊Q8—3322no—
109C22⋊Q8—3321no—
110C2×C22⋊C4—1661no—
111C2×C22⋊C4—1661no—
112C2×C22⋊C4C4×D8311yescharacteristic
113C2×C22⋊C4D33211yescharacteristic
114C22⋊C8—22no—
115C22⋊C8—41no—
116C22⋊C8—3321no—
117#95—41no—
118#95—3322no—
119C24(C2×D83)⋊C411yescharacteristic
120C2×Q8—3321no—
121C22×C4—21no—
122C22×C4—21no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—41no—
126C22×C4—41no—
127C22×C4—3321no—
128C22×C4—1662no—
129C22×C4#1305057811yescharacteristic
130C22×C4#1305058011yescharacteristic
131M16—81no—
132M16—81no—
133C2×C8—42no—
134C2×C8—6641no—
135C4⋊C4—3322no—
136C4⋊C4—3321no—
137C22⋊C4—41no—
138C22⋊C4—41no—
139C22⋊C4—3321no—
140C22⋊C4—3321no—
141C22⋊C4—3321no—
142C22⋊C4—3321no—
143C23—21no—
144C23—21no—
145C23—81no—
146C23#1458170611yescharacteristic
147C23#1458171511yescharacteristic
148C23#1458172011yescharacteristic
149Q8—13281no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—81no—
159C2×C4—81no—
160C2×C4—81no—
161C2×C4—3322no—
162C2×C4—6641no—
163C2×C4—6642no—
164C2×C4—6642no—
165C8—82no—
166C8—13281no—
167C22—21no—
168C22—21no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22—42no—
173C22—81no—
174C22#1912743711yescharacteristic
175C22#1912748711yescharacteristic
176C22#1912749511yescharacteristic
177C4—41no—
178C4—41no—
179C4—81no—
180C4—81no—
181C4—13281no—
182C4—6642no—
183C2—21no—
184C2—21no—
185C2—21no—
186C2—41no—
187C2—41no—
188C2#2490548311yescharacteristic
subgroupG/H
centerC2#24905483
commutatorC2×C22⋊C4×C83C2×C4
Frattini#381C2×D83
FittingC83×#1306C2
socleC2×C83#1351
prime radicalC24×C83C22⋊C4
cosocle#381×C83C22
hypercenter#1306D83
hypocenterC83#7427
LCSG ▷ C2×C22⋊C4×C83 ▷ C24×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ #381 ◁ #1306

Complements

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

NH ≅ G/Ntype
98. C83#7427semidirect

Maximal subgroups

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

subgroupindex
#249086302
#249053932
C83×#13062
#742783