Finite Group Databasebeta

← #35292249

Subgroups — #35292249

Order 21248.

138 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 25 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#24906784C211yesmaximal, characteristic
2#24905498C211yesmaximal, characteristic, complemented
3C83×#1413C211yesmaximal, characteristic, complemented
4#19128449C411yescharacteristic
5#19128063—21no—
6#19127479—21no—
7#19127443C411yescharacteristic
8#19127440—21no—
9#491×C83C2211yescharacteristic
10#356×C83—21no—
11#14581780—21no—
12#14581777—41no—
13#14581770—41no—
14#14581767—41no—
15#14581732—41no—
16#14581715—41no—
17#14581712—41no—
18#14581703—21no—
19C4⋊Q8×C83D411yescharacteristic
20#125×C83C2×C411yescharacteristic
21#103×C83—41no—
22#101×C83—41no—
23#97×C83D411yescharacteristic
24C2×Dic166—21no—
25C2×D332—21no—
26C2×D332—41no—
27C2×C4×D83—41no—
28C2×C83⋊C8—41no—
29Dic83⋊C4—41no—
30(C2×D83)⋊C4—41no—
31(C2×D83)⋊C4—41no—
32(C2×D83)⋊C4—41no—
33C83⋊C16—42no—
34C2×Q8×C83—21no—
35M16×C83—81no—
36C2×C8×C83—21no—
37C4⋊C4×C83—21no—
38C4⋊C4×C83—41no—
39C4⋊C4×C83—41no—
40C42×C83C22⋊C411yescharacteristic
41C22×D83—41no—
42Q8×C83—81no—
43C2×C4×C83—21no—
44C2×C4×C83—41no—
45C2×C4×C83—41no—
46C2×C4×C83#9911yescharacteristic
47C2×Dic83—41no—
48D332—81no—
49D332—161no—
50C4×D83—161no—
51Dic166—81no—
52C8×C83—41no—
53C8×C83—161no—
54C83⋊C8—81no—
55C22×C83AΣL(1,𝔽16)11yescharacteristic
56C2×D83—81no—
57C2×D83—81no—
58C2×D83—81no—
59C4×C83—21no—
60C4×C83—41no—
61C4×C83—81no—
62C4×C83—81no—
63Dic83—81no—
64#7525—831nomaximal, Sylow
65C2×C83—21no—
66C2×C83#140411yescharacteristic
67D83—161no—
68#1662—831no—
69#1413D8311yescharacteristic, complemented
70#1356—831no—
71C83#752511yescharacteristic, complemented, Sylow
72#562—831no—
73#491C2×D8311yescharacteristic
74#489—1661no—
75#356—21no—
76#347—1661no—
77#330—831no—
78#329—1661no—
79C4⋊Q8C22⋊D8311yescharacteristic
80#125C4×D8311yescharacteristic
81#124—1661no—
82#123—3321no—
83C22⋊Q8—3321no—
84#121—3321no—
85M32—3321no—
86#103—41no—
87#103—3321no—
88#102—3321no—
89#101—41no—
90#97—1661no—
91#97D33211yescharacteristic
92C2×Q8—21no—
93C2×Q8—1661no—
94C2×D4—3321no—
95C2×D4—1661no—
96C22×C4—3321no—
97M16—81no—
98C2×C8—21no—
99C2×C8—3321no—
100C4⋊C4—21no—
101C4⋊C4—41no—
102C4⋊C4—41no—
103C4⋊C4—3321no—
104C22⋊C4—3321no—
105C22⋊C4—3321no—
106C22⋊C4—3321no—
107C42(C2×D83)⋊C411yescharacteristic
108C16—3322no—
109C23—3321no—
110Q8—81no—
111Q8—6641no—
112D4—13281no—
113D4—6641no—
114C2×C4—21no—
115C2×C4—41no—
116C2×C4—41no—
117C2×C4—13281no—
118C2×C4—3321no—
119C2×C4#1458170611yescharacteristic
120C8—41no—
121C8—161no—
122C8—6641no—
123C22—6641no—
124C22—6641no—
125C22—6641no—
126C22#1912748711yescharacteristic
127C4—21no—
128C4—41no—
129C4—81no—
130C4—81no—
131C4—6641no—
132C2—21no—
133C2—13281no—
134C2#2490561311yescharacteristic
subgroupG/H
centerC2#24905613
commutator#125×C83C2×C4
Frattini#491C2×D83
FittingC83×#1413C2
socleC2×C83#1404
prime radical#19128449C4
cosocle#491×C83C22
hypercenter#1413D83
hypocenterC83#7525
LCSG ▷ #125×C83 ▷ C42×C83 ▷ C2×C4×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #491 ◁ #1413

Complements

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

NH ≅ G/Ntype
2. #24905498C2semidirect
3. C83×#1413C2semidirect
69. #1413D83semidirect
71. C83#7525semidirect

Maximal subgroups

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

subgroupindex
#249067842
#249054982
C83×#14132
#752583