Finite Group Databasebeta

← #35291949

Subgroups — #35291949

Order 21248.

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

normal subgroups only

This group has 190 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#24908750C211yesmaximal, characteristic
2#24905414C211yesmaximal, characteristic, complemented
3C83×#1307C211yesmaximal, characteristic, complemented
4#19128501C411yescharacteristic
5C2×#14581720—21no—
6#19127683—21no—
7#19127483—21no—
8C83⋊#338C411yescharacteristic
9#432×C83—21no—
10#423×C83C2211yescharacteristic
11C2×#13050590—21no—
12#14581825—41no—
13#14581820—41no—
14#14581814—41no—
15C2×#13050574—21no—
16#14581732—41no—
17#14581720—41no—
18#14581720—41no—
19#14581710—41no—
20#14581708—41no—
21C2×M16×C83C2×C411yescharacteristic
22C2×M16×C83D411yescharacteristic
23C2×C42×C83D411yescharacteristic
24C4⋊C8×C83—41no—
25C4⋊C8×C83—41no—
26C22⋊C8×C83—22no—
27#97×C83—41no—
28#13050590—41no—
29#13050590—41no—
30#13050590—41no—
31#13050590—41no—
32C2×Dic166—21no—
33C2×D332—21no—
34C2×C22⋊D83—41no—
35C2×C4×D83—41no—
36Dic332—41no—
37#13050579—42no—
38D664—41no—
39#13050574—41no—
40#13050574—41no—
41C2×C83⋊C8—41no—
42C83⋊C16—81no—
43C22×C4×C83—21no—
44C22×C4×C83C22⋊C411yescharacteristic
45M16×C83—41no—
46M16×C83—41no—
47C2×C8×C83—21no—
48C2×C8×C83—21no—
49C2×C8×C83—42no—
50C42×C83—21no—
51C42×C83D811yescharacteristic
52C42×C83SD1611yescharacteristic
53C23×C83#10411yescharacteristic
54C22×D83—41no—
55C2×C4×C83—21no—
56C2×C4×C83—21no—
57C2×C4×C83—21no—
58C2×C4×C83—21no—
59C2×C4×C83—81no—
60C2×C4×C83#9911yescharacteristic
61C2×C4×C83#10211yescharacteristic
62C22⋊D83—81no—
63C22⋊D83—81no—
64C2×Dic83—41no—
65D332—41no—
66D332—41no—
67C4×D83—81no—
68C4×D83—81no—
69Dic166—41no—
70Dic166—41no—
71C8×C83—41no—
72C8×C83—41no—
73C8×C83—82no—
74C83⋊C8—81no—
75C22×C83—21no—
76C22×C83—41no—
77C22×C83#32711yescharacteristic
78C2×D83—81no—
79C2×D83—161no—
80C4×C83—21no—
81C4×C83—41no—
82C4×C83—41no—
83C4×C83AΣL(1,𝔽16)11yescharacteristic
84C4×C83#35511yescharacteristic
85Dic83—81no—
86#7415—831nomaximal, Sylow
87C2×C83—21no—
88C2×C83—41no—
89C2×C83#134511yescharacteristic
90D83—161no—
91#2050—831no—
92#1327—831no—
93#1307D8311yescharacteristic, complemented
94C83#741511yescharacteristic, complemented, Sylow
95#575—831no—
96#432—21no—
97#423C2×D8311yescharacteristic
98C2×#104—1661no—
99#413—1661no—
100#349—1661no—
101#338—831no—
102C2×#41—1661no—
103#137—3321no—
104AGL(1,ℤ/8)—3321no—
105#135—3321no—
106C2×M16—1661no—
107C2×M16C4×D8311yescharacteristic
108C2×M16D33211yescharacteristic
109C2×C42C22⋊D8311yescharacteristic
110M32—3321no—
111C4⋊C8—41no—
112C4⋊C8—41no—
113#104—3321no—
114#104—3321no—
115#101—3321no—
116#100—3321no—
117C22⋊C8—22no—
118#97—41no—
119#41—3321no—
120#41—3321no—
121#41—3321no—
122#41—3321no—
123C2×Q8—1661no—
124C2×D4—3321no—
125C2×D4—1661no—
126C22×C4—21no—
127C22×C4—3321no—
128C22×C4(C2×D83)⋊C411yescharacteristic
129Q16—3321no—
130SD16—3322no—
131D8—3321no—
132M16—41no—
133M16—41no—
134M16—3321no—
135M16—3321no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—42no—
139C2×C8—3321no—
140C42—21no—
141C42#1305057511yescharacteristic
142C42#1305057711yescharacteristic
143C16—6641no—
144C23—3321no—
145C23#1458172011yescharacteristic
146Q8—3321no—
147Q8—3321no—
148D4—3321no—
149D4—3321no—
150D4—6641no—
151D4—6641no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—81no—
157C2×C4—3321no—
158C2×C4—6641no—
159C2×C4—6641no—
160C2×C4#1458170611yescharacteristic
161C2×C4#1458171211yescharacteristic
162C8—41no—
163C8—41no—
164C8—82no—
165C8—6641no—
166C22—21no—
167C22—41no—
168C22—13281no—
169C22—6641no—
170C22#1912743411yescharacteristic
171C4—21no—
172C4—41no—
173C4—41no—
174C4—6641no—
175C4#1912748911yescharacteristic
176C4#1912749711yescharacteristic
177C2—21no—
178C2—41no—
179C2—13281no—
180C2#2490546511yescharacteristic
subgroupG/H
centerC2#24905465
commutatorC2×M16×C83C2×C4
Frattini#423C2×D83
FittingC83×#1307C2
socleC2×C83#1345
prime radical#19128501C4
cosocle#423×C83C22
hypercenter#1307D83
hypocenterC83#7415
LCSG ▷ C2×M16×C83 ▷ C22×C4×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #423 ◁ #1307

Complements

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

NH ≅ G/Ntype
2. #24905414C2semidirect
3. C83×#1307C2semidirect
93. #1307D83semidirect
94. C83#7415semidirect

Maximal subgroups

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

subgroupindex
#249087502
#249054142
C83×#13072
#741583