Finite Group Databasebeta

← #24905486

Subgroups — #24905486

Order 10624.

154 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 35 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#19127637C211yesmaximal, characteristic
2#19127425C211yesmaximal, characteristic
3#342×C83C211yesmaximal, characteristic
4C2×C4⋊Dic83C411yescharacteristic, complemented
5C2×Dic83⋊C4—21no—
6C2×C22⋊Dic83—21no—
7C22⋊(C83⋊C8)—21no—
8C83⋊#95C411yescharacteristic, complemented
9C2×C22⋊C4×C83—21no—
10C2×C22⋊C4×C83C2211yescharacteristic
11C22×Dic83—21no—
12C22×Dic83—21no—
13C2×C83⋊C8—41no—
14C4⋊Dic83—41no—
15Dic83⋊C4—42no—
16C22⋊Dic83—42no—
17C24×C83D411yescharacteristic
18C22×C4×C83—41no—
19C22×C4×C83C2×C411yescharacteristic
20C22×C4×C83D411yescharacteristic
21C22⋊C4×C83—22no—
22C22⋊C4×C83—41no—
23C22⋊C4×C83—41no—
24C23×C83—21no—
25C23×C83—21no—
26C23×C83—41no—
27C23×C83—41no—
28C23×C83C22⋊C411yescharacteristic
29C23×C83SD1611yescharacteristic
30C23×C83Q1611yescharacteristic
31C2×C4×C83—21no—
32C2×C4×C83—21no—
33C2×C4×C83—41no—
34C2×C4×C83—41no—
35C2×C4×C83—42no—
36C2×C4×C83—81no—
37C2×C4×C83—81no—
38C2×Dic83—22no—
39C2×Dic83—41no—
40C2×Dic83—41no—
41C2×Dic83—41no—
42C2×Dic83—41no—
43C2×Dic83—41no—
44C83⋊C8—81no—
45C22×C83—21no—
46C22×C83—21no—
47C22×C83—21no—
48C22×C83—21no—
49C22×C83—41no—
50C22×C83—41no—
51C22×C83—41no—
52C22×C83—41no—
53C22×C83—81no—
54C22×C83#9911yescharacteristic
55C22×C83#10311yescharacteristic
56C22×C83#10411yescharacteristic
57C4×C83—41no—
58C4×C83—41no—
59C4×C83—82no—
60Dic83—42no—
61Dic83—81no—
62C2×C83—21no—
63C2×C83—21no—
64C2×C83—41no—
65C2×C83—41no—
66C2×C83#32811yescharacteristic
67C2×C83#35211yescharacteristic
68C2×C83#35311yescharacteristic
69#1352—831nomaximal, Sylow
70C83#135211yescharacteristic, complemented, Sylow
71#399—831no—
72#342D8311yescharacteristic
73#323—831no—
74C2×C4⋊C4—831no—
75C2×C4⋊C4—1661no—
76C2×C22⋊C4—21no—
77C2×C22⋊C4—1661no—
78C2×C22⋊C4C2×D8311yescharacteristic
79C22⋊C8—1661no—
80#95—831no—
81C24C22⋊D8311yescharacteristic
82C22×C4—41no—
83C22×C4—1661no—
84C22×C4—1661no—
85C22×C4C4×D8311yescharacteristic
86C22×C4D33211yescharacteristic
87C2×C8—3321no—
88C4⋊C4—3321no—
89C4⋊C4—3322no—
90C22⋊C4—22no—
91C22⋊C4—41no—
92C22⋊C4—41no—
93C22⋊C4—3322no—
94C23—21no—
95C23—21no—
96C23—41no—
97C23—41no—
98C23(C2×D83)⋊C411yescharacteristic
99C23#1305057811yescharacteristic
100C23#1305058011yescharacteristic
101C2×C4—21no—
102C2×C4—21no—
103C2×C4—41no—
104C2×C4—41no—
105C2×C4—42no—
106C2×C4—81no—
107C2×C4—81no—
108C2×C4—3321no—
109C2×C4—3321no—
110C2×C4—3321no—
111C2×C4—3321no—
112C2×C4—3321no—
113C2×C4—1662no—
114C8—6641no—
115C22—21no—
116C22—21no—
117C22—21no—
118C22—21no—
119C22—41no—
120C22—41no—
121C22—41no—
122C22—41no—
123C22—81no—
124C22#1458170611yescharacteristic
125C22#1458171511yescharacteristic
126C22#1458172011yescharacteristic
127C4—41no—
128C4—41no—
129C4—82no—
130C4—3322no—
131C4—6641no—
132C2—21no—
133C2—21no—
134C2—41no—
135C2—41no—
136C2#1912743711yescharacteristic
137C2#1912749011yescharacteristic
138C2#1912749311yescharacteristic
subgroupG/H
centerC22#14581706
commutatorC22×C4×C83C2×C4
FrattiniC2×C22⋊C4C2×D83
Fitting#342×C83C2
socleC22×C83#99
prime radicalC24×C83D4
cosocleC2×C22⋊C4×C83C22
hypercenter#342D83
hypocenterC83#1352
LCSG ▷ C22×C4×C83 ▷ C23×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #342

Complements

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

NH ≅ G/Ntype
4. C2×C4⋊Dic83C4semidirect
8. C83⋊#95C4semidirect
70. C83#1352semidirect