Finite Group Databasebeta

← #35325319

Subgroups — #35325319

Order 21248.

154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 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#24909741C211yesmaximal, characteristic, complemented
2#24909343C211yesmaximal, characteristic
3#24905670C211yesmaximal, characteristic, complemented
4#24905660C211yesmaximal, characteristic, complemented
5#24905651C211yesmaximal, characteristic
6#24905649C211yesmaximal, characteristic
7C83×#1426C211yesmaximal, characteristic, complemented
8#19128133C2211yescharacteristic
9#19128102—21no—
10#19127817—21no—
11#19127535C2211yescharacteristic
12#19127529C2211yescharacteristic
13#19127526—21no—
14#19127507—21no—
15C16×Dic83C2211yescharacteristic
16M64×C83C2211yescharacteristic
17#368×C83C2211yescharacteristic
18#367×C83C2211yescharacteristic
19#14581814—21no—
20#14581800—41no—
21#14581783—41no—
22Dic664Q811yescharacteristic
23#14581737—21no—
24D1328Q811yescharacteristic
25C2×C83⋊C16D411yescharacteristic
26#14581726—21no—
27#14581723—41no—
28#14581718—41no—
29C8×Dic83D411yescharacteristic
30C83⋊C32—21no—
31C2×C16×C83C2311yescharacteristic
32#108×C83—21no—
33#107×C83—21no—
34C32×C83—21no—
35#13050590—41no—
36Dic332—21no—
37#13050579—41no—
38D664—21no—
39#13050573—81no—
40C2×C83⋊C8D811yescharacteristic
41C8×D83—81no—
42C4⋊Dic83—41no—
43C4⋊Dic83—81no—
44Dic83⋊C4—81no—
45C4×Dic83D811yescharacteristic
46C83⋊C16—21no—
47M16×C83—41no—
48C2×C8×C83C2×D411yescharacteristic
49C4⋊C4×C83—41no—
50C16×C83C2×Q811yescharacteristic
51C16×C83#4111yescharacteristic
52C2×C4×C83—81no—
53C2×C4×C83C2×D811yescharacteristic
54C22⋊D83—81no—
55C2×Dic83—21no—
56C2×Dic83—81no—
57D332—41no—
58C4×D83—81no—
59Dic166—41no—
60C8×C83—81no—
61C8×C83C22⋊Q811yescharacteristic
62C8×C83#13711yescharacteristic
63C83⋊C8SD3211yescharacteristic
64C83⋊C8SD3211yescharacteristic
65C22×C83#50911yescharacteristic
66C2×D83—81no—
67C4×C83—161no—
68C4×C83#47411yescharacteristic
69C4×C83C2×SD3211yescharacteristic
70Dic83—41no—
71Dic83—81no—
72Dic83—161no—
73#13709—831nomaximal, Sylow
74C2×C83—21no—
75C2×C83#222611yescharacteristic
76D83—161no—
77#2253—831no—
78#2178—831no—
79#1426—831no—
80#1426D8311yescharacteristic, complemented
81#1422—831no—
82#1418—831no—
83#1418—831no—
84C83#1370911yescharacteristic, complemented, Sylow
85#508—831no—
86#499—1661no—
87#443—1661no—
88M64—831no—
89M64C2×D8311yescharacteristic
90#368C2×D8311yescharacteristic
91#367—831no—
92#367C2×D8311yescharacteristic
93#366—1661no—
94#359—1661no—
95C4×C16—831no—
96#135—1661no—
97#131—3321no—
98#125—3321no—
99Q32—831no—
100SD32—1661no—
101D16—831no—
102C2×C16—831no—
103C2×C16C22×D8311yescharacteristic
104#108—21no—
105#107—21no—
106#107—1661no—
107#106—3321no—
108#104—3321no—
109C4×C8—831no—
110C32—21no—
111C32—1661no—
112#41—3321no—
113Q16—1661no—
114SD16—3321no—
115D8—1661no—
116M16—41no—
117M16—6641no—
118C2×C8—831no—
119C2×C8—6641no—
120C2×C8D4×D8311yescharacteristic
121C4⋊C4—41no—
122C4⋊C4—3321no—
123C4⋊C4—6641no—
124C4⋊C4—6641no—
125C42—831no—
126C16—1661no—
127C16Q8×D8311yescharacteristic
128C16#1305059011yescharacteristic
129Q8—3321no—
130D4—3321no—
131D4—6641no—
132C2×C4—81no—
133C2×C4—6641no—
134C2×C4—6641no—
135C2×C4—1661no—
136C2×C4D8×D8311yescharacteristic
137C8—81no—
138C8—831no—
139C8—831no—
140C8#1458177011yescharacteristic
141C8#1458182411yescharacteristic
142C22—6641no—
143C22#1912813811yescharacteristic
144C4—161no—
145C4—13281no—
146C4—3321no—
147C4—6641no—
148C4#1912798011yescharacteristic
149C4SD32×D8311yescharacteristic
150C2—21no—
151C2—13281no—
152C2#2490960911yescharacteristic
subgroupG/H
centerC2#24909609
commutator, cosocleC2×C16×C83C23
FrattiniC2×C16C22×D83
FittingC83×#1426C2
socleC2×C83#2226
prime radical#19128133C22
hypercenter#1426D83
hypocenterC83#13709
LCSG ▷ C2×C16×C83 ▷ C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1426

Complements

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

NH ≅ G/Ntype
1. #24909741C2semidirect
3. #24905670C2semidirect
4. #24905660C2semidirect
7. C83×#1426C2semidirect
80. #1426D83semidirect
84. C83#13709semidirect

Maximal subgroups

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

subgroupindex
#249097412
#249093432
#249056702
#249056602
#249056512
#249056492
C83×#14262
#1370983