Finite Group Databasebeta

← #21422045

Subgroups — #21422045

Order 7552.

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

normal subgroups only

This group has 158 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#16837274C211yesmaximal, characteristic
2#16837126C211yesmaximal, characteristic
3C59×#323C211yesmaximal, characteristic
4C23×Dic59C411yescharacteristic
5C2×Dic59⋊C4—21no—
6C2×C22⋊Dic59C411yescharacteristic
7C22⋊(C59⋊C8)—21no—
8C59⋊#95—21no—
9C2×C22⋊C4×C59C2211yescharacteristic
10C22⋊C8×C59—21no—
11C24×C59C2×C411yescharacteristic
12C22×C4×C59D411yescharacteristic
13C22×C4×C59D411yescharacteristic
14C22×Dic59—21no—
15C22×Dic59—21no—
16C22×Dic59—42no—
17C22×Dic59—41no—
18C2×C8×C59—41no—
19C22⋊C4×C59—41no—
20C22⋊Dic59—21no—
21C22⋊Dic59C812yescomplemented
22Dic59⋊C4—42no—
23C2×C59⋊C8—41no—
24C23×C59—21no—
25C23×C59—21no—
26C23×C59—41no—
27C23×C59—41no—
28C23×C59C22⋊C411yescharacteristic
29C23×C59C2×C811yescharacteristic
30C23×C59M1611yescharacteristic
31C2×C4×C59—21no—
32C2×C4×C59—21no—
33C2×C4×C59—41no—
34C2×C4×C59—41no—
35C2×Dic59—22no—
36C2×Dic59—22no—
37C2×Dic59—41no—
38C2×Dic59—41no—
39C2×Dic59—41no—
40C2×Dic59—42no—
41C2×Dic59—41no—
42C2×Dic59—42no—
43C8×C59—81no—
44C59⋊C8—81no—
45C22×C59—21no—
46C22×C59—21no—
47C22×C59—21no—
48C22×C59—21no—
49C22×C59—41no—
50C22×C59—41no—
51C22×C59—42no—
52C22×C59—41no—
53C22×C59—41no—
54C22×C59C22⋊C811yescharacteristic
55C22×C59#9911yescharacteristic
56C22×C59#10111yescharacteristic
57C4×C59—41no—
58C4×C59—41no—
59Dic59—42no—
60Dic59—42no—
61#1326—591nomaximal, Sylow
62C2×C59—21no—
63C2×C59—21no—
64C2×C59—41no—
65C2×C59—41no—
66C2×C59#32411yescharacteristic
67C2×C59AΣL(1,𝔽16)11yescharacteristic
68C2×C59#35211yescharacteristic
69#385—591no—
70#323—591no—
71#323D5911yescharacteristic
72C59#132611yescharacteristic, complemented, Sylow
73C23×C4—591no—
74C2×C4⋊C4—1181no—
75C2×C22⋊C4—591no—
76C2×C22⋊C4C2×D5911yescharacteristic
77C22⋊C8—21no—
78C22⋊C8—1181no—
79#95—1181no—
80C24C4×D5911yescharacteristic
81C22×C4—1181no—
82C22×C4—1181no—
83C22×C4—2362no—
84C22×C4—2361no—
85C22×C4D23611yescharacteristic
86C22×C4C22⋊D5911yescharacteristic
87C2×C8—41no—
88C2×C8—2361no—
89C4⋊C4—2362no—
90C22⋊C4—41no—
91C22⋊C4—592no—
92C22⋊C4—1181no—
93C23—21no—
94C23—21no—
95C23—41no—
96C23—41no—
97C23C8×D5911yescharacteristic
98C23#1174565911yescharacteristic
99C23(C2×D59)⋊C411yescharacteristic
100C2×C4—21no—
101C2×C4—21no—
102C2×C4—41no—
103C2×C4—41no—
104C2×C4—1182no—
105C2×C4—1182no—
106C2×C4—2361no—
107C2×C4—2361no—
108C2×C4—2361no—
109C2×C4—2362no—
110C2×C4—2361no—
111C2×C4—2362no—
112C8—81no—
113C8—4721no—
114C22—21no—
115C22—21no—
116C22—21no—
117C22—21no—
118C22—41no—
119C22—41no—
120C22—42no—
121C22—41no—
122C22—41no—
123C22(C2×D59)⋊C811yescharacteristic
124C22#1427364111yescharacteristic
125C22#1427364511yescharacteristic
126C4—41no—
127C4—41no—
128C4—2362no—
129C4—2362no—
130C2—21no—
131C2—21no—
132C2—41no—
133C2—41no—
134C2#1683712711yescharacteristic
135C2#1683719011yescharacteristic
136C2#1683719111yescharacteristic
subgroupG/H
centerC22#14273641
commutatorC23×C59C2×C8
FrattiniC2×C22⋊C4C2×D59
FittingC59×#323C2
socleC22×C59#99
hypercenter#323D59
hypocenterC59#1326
LCSG ▷ C23×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #323

Complements

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

NH ≅ G/Ntype
21. C22⋊Dic59C8semidirect
72. C59#1326semidirect