Finite Group Databasebeta

← #21422126

Subgroups — #21422126

Order 7552.

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

normal subgroups only

This group has 140 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#16837171C211yesmaximal, characteristic
2#16837128C211yesmaximal, characteristic
3C59×#395C211yesmaximal, characteristic
4C2×#11745664—21no—
5C22⋊(C59⋊C8)—21no—
6C22×Q8×C59C411yescharacteristic
7C2×C4⋊C4×C59—21no—
8C2×C4⋊C4×C59C2211yescharacteristic
9#95×C59—21no—
10#95×C59C411yescharacteristic
11C2×Q8×C59—42no—
12C2×Q8×C59—41no—
13C22×C4×C59—21no—
14C22×C4×C59—21no—
15C22×C4×C59C2×C411yescharacteristic
16C22×C4×C59D411yescharacteristic
17C22×C4×C59D411yescharacteristic
18C4⋊C4×C59—41no—
19C4⋊C4×C59—42no—
20#11745664—22no—
21#11745664—41no—
22C2×C59⋊C8—41no—
23C2×C59⋊C8—41no—
24C23×C59C22⋊C411yescharacteristic
25Q8×C59—42no—
26Q8×C59—42no—
27C2×C4×C59—21no—
28C2×C4×C59—21no—
29C2×C4×C59—22no—
30C2×C4×C59—22no—
31C2×C4×C59—21no—
32C2×C4×C59—21no—
33C2×C4×C59—41no—
34C2×C4×C59—41no—
35C2×C4×C59—41no—
36C2×C4×C59—41no—
37C2×C4×C59—41no—
38C2×C4×C59—41no—
39C2×C4×C59SD1611yescharacteristic
40C2×C4×C59Q1611yescharacteristic
41C59⋊C8—42no—
42C59⋊C8—81no—
43C22×C59—21no—
44C22×C59—21no—
45C22×C59#9911yescharacteristic
46C22×C59#10311yescharacteristic
47C22×C59#10411yescharacteristic
48C4×C59—21no—
49C4×C59—21no—
50C4×C59—42no—
51C4×C59—41no—
52C4×C59—42no—
53C4×C59—41no—
54#1354—591nomaximal, Sylow
55C2×C59—21no—
56C2×C59—21no—
57C2×C59#32811yescharacteristic
58C2×C59AΣL(1,𝔽16)11yescharacteristic
59C2×C59#35611yescharacteristic
60#395D5911yescharacteristic
61#343—591no—
62#324—591no—
63C59#135411yescharacteristic, complemented, Sylow
64C22×Q8Dic5911yescharacteristic
65C2×M16—1181no—
66C2×C4⋊C4—21no—
67C2×C4⋊C4C2×D5911yescharacteristic
68C22⋊C8—1181no—
69#95—21no—
70#95Dic5911yescharacteristic
71C2×Q8—42no—
72C2×Q8—41no—
73C22×C4—21no—
74C22×C4—21no—
75C22×C4C2×Dic5911yescharacteristic
76C22×C4C22⋊D5911yescharacteristic
77C22×C4C22⋊D5911yescharacteristic
78M16—1182no—
79M16—2361no—
80C2×C8—2361no—
81C2×C8—2361no—
82C4⋊C4—41no—
83C4⋊C4—42no—
84C23C22⋊Dic5911yescharacteristic
85Q8—42no—
86Q8—42no—
87C2×C4—21no—
88C2×C4—21no—
89C2×C4—22no—
90C2×C4—22no—
91C2×C4—21no—
92C2×C4—21no—
93C2×C4—41no—
94C2×C4—41no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—41no—
98C2×C4—41no—
99C2×C4#1174567111yescharacteristic
100C2×C4#1174567211yescharacteristic
101C8—4721no—
102C8—2362no—
103C22—21no—
104C22—21no—
105C22#1427364211yescharacteristic
106C22#1427365111yescharacteristic
107C22#1427365411yescharacteristic
108C4—21no—
109C4—21no—
110C4—42no—
111C4—41no—
112C4—42no—
113C4—41no—
114C2—21no—
115C2—21no—
116C2#1683713911yescharacteristic
117C2#1683718911yescharacteristic
118C2#1683720111yescharacteristic
subgroupG/H
centerC22#14273642
commutatorC22×C4×C59C2×C4
FrattiniC2×C4⋊C4C2×D59
FittingC59×#395C2
socleC22×C59#99
hypercenter#395D59
hypocenterC59#1354
LCSG ▷ C22×C4×C59 ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #395

Complements

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

NH ≅ G/Ntype
63. C59#1354semidirect