Finite Group Databasebeta

← #35291950

Subgroups — #35291950

Order 21248.

190 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 39 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#24905414C211yesmaximal, characteristic, complemented
2#24905374C211yesmaximal, characteristic, complemented
3C83×#2050C211yesmaximal, characteristic
4#19127758—21no—
5#19127483—21no—
6#575×C83C411yescharacteristic
7#423×C83C2211yescharacteristic
8C2×#104×C83—21no—
9#413×C83—21no—
10#338×C83C411yescharacteristic
11#14581732—41no—
12C4⋊(C83⋊C8)—41no—
13C22⋊(C83⋊C8)—22no—
14#14581703—41no—
15C2×#41×C83—21no—
16#137×C83—41no—
17AGL(1,ℤ/8)×C83—41no—
18#135×C83—41no—
19C2×M16×C83—21no—
20C2×M16×C83C2×C411yescharacteristic
21C2×M16×C83D411yescharacteristic
22C2×C42×C83D411yescharacteristic
23C4⋊C8×C83—41no—
24#104×C83—41no—
25#104×C83—41no—
26#101×C83—41no—
27#100×C83—41no—
28C2×C83⋊C8—42no—
29C83⋊C16—81no—
30#41×C83—41no—
31#41×C83—41no—
32#41×C83—41no—
33#41×C83—41no—
34C2×Q8×C83—21no—
35C2×D4×C83—21no—
36C2×D4×C83—41no—
37C22×C4×C83—21no—
38C22×C4×C83—41no—
39C22×C4×C83C22⋊C411yescharacteristic
40Q16×C83—41no—
41SD16×C83—42no—
42D8×C83—41no—
43M16×C83—41no—
44M16×C83—41no—
45M16×C83—41no—
46M16×C83—41no—
47C2×C8×C83—21no—
48C2×C8×C83—21no—
49C2×C8×C83—41no—
50C42×C83—21no—
51C42×C83D811yescharacteristic
52C42×C83SD1611yescharacteristic
53C23×C83—41no—
54C23×C83#10411yescharacteristic
55Q8×C83—41no—
56Q8×C83—41no—
57D4×C83—41no—
58D4×C83—41no—
59D4×C83—81no—
60D4×C83—81no—
61C2×C4×C83—21no—
62C2×C4×C83—21no—
63C2×C4×C83—21no—
64C2×C4×C83—21no—
65C2×C4×C83—41no—
66C2×C4×C83—81no—
67C2×C4×C83—81no—
68C2×C4×C83—81no—
69C2×C4×C83#9911yescharacteristic
70C2×C4×C83#10211yescharacteristic
71C8×C83—41no—
72C8×C83—41no—
73C8×C83—81no—
74C83⋊C8—82no—
75C22×C83—21no—
76C22×C83—41no—
77C22×C83—81no—
78C22×C83—161no—
79C22×C83#32711yescharacteristic
80C4×C83—21no—
81C4×C83—41no—
82C4×C83—41no—
83C4×C83—81no—
84C4×C83AΣL(1,𝔽16)11yescharacteristic
85C4×C83#35511yescharacteristic
86#7415—831nomaximal, Sylow
87C2×C83—21no—
88C2×C83—41no—
89C2×C83—161no—
90C2×C83#134511yescharacteristic
91#2050D8311yescharacteristic
92#1327—831no—
93#1307—831no—
94C83#741511yescharacteristic, complemented, Sylow
95#575Dic8311yescharacteristic
96#432—1661no—
97#423C2×D8311yescharacteristic
98C2×#104—21no—
99#413—21no—
100#349—1661no—
101#338Dic8311yescharacteristic
102C2×#41—21no—
103#137—41no—
104AGL(1,ℤ/8)—41no—
105#135—41no—
106C2×M16—21no—
107C2×M16C2×Dic8311yescharacteristic
108C2×M16C22⋊D8311yescharacteristic
109C2×C42C22⋊D8311yescharacteristic
110M32—3321no—
111C4⋊C8—41no—
112C4⋊C8—3321no—
113#104—41no—
114#104—41no—
115#101—41no—
116#100—41no—
117C22⋊C8—1662no—
118#97—3321no—
119#41—41no—
120#41—41no—
121#41—41no—
122#41—41no—
123C2×Q8—21no—
124C2×D4—21no—
125C2×D4—41no—
126C22×C4—21no—
127C22×C4—41no—
128C22×C4C22⋊Dic8311yescharacteristic
129Q16—41no—
130SD16—42no—
131D8—41no—
132M16—41no—
133M16—41no—
134M16—41no—
135M16—41no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—41no—
139C2×C8—3322no—
140C42—21no—
141C42#1305057511yescharacteristic
142C42#1305057811yescharacteristic
143C16—6641no—
144C23—41no—
145C23#1458171911yescharacteristic
146Q8—41no—
147Q8—41no—
148D4—41no—
149D4—41no—
150D4—81no—
151D4—81no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—81no—
158C2×C4—81no—
159C2×C4—81no—
160C2×C4#1458170711yescharacteristic
161C2×C4#1458171311yescharacteristic
162C8—41no—
163C8—41no—
164C8—81no—
165C8—6642no—
166C22—21no—
167C22—41no—
168C22—81no—
169C22—161no—
170C22#1912743511yescharacteristic
171C4—21no—
172C4—41no—
173C4—41no—
174C4—81no—
175C4#1912748811yescharacteristic
176C4#1912749811yescharacteristic
177C2—21no—
178C2—41no—
179C2—161no—
180C2#2490546611yescharacteristic
subgroupG/H
centerC2#24905466
commutatorC2×M16×C83C2×C4
Frattini#423C2×D83
FittingC83×#2050C2
socleC2×C83#1345
prime radical#575×C83C4
cosocle#423×C83C22
hypercenter#2050D83
hypocenterC83#7415
LCSG ▷ C2×M16×C83 ▷ C22×C4×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #423 ◁ #2050

Complements

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

NH ≅ G/Ntype
1. #24905414C2semidirect
2. #24905374C2semidirect
94. C83#7415semidirect

Maximal subgroups

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

subgroupindex
#249054142
#249053742
C83×#20502
#741583