Finite Group Databasebeta

← #21425882

Subgroups — #21425882

Order 7552.

156 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 85 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
1C2×#14273667C211yesmaximal, characteristic
2#16837440C211yesmaximal, characteristic
3#16837229C212yesmaximal, complemented
4#16837227C212yesmaximal, complemented
5C2×#107×C59C211yesmaximal, characteristic
6#14273686—21no—
7#14273667C414yescomplemented
8C2×C59⋊C16C2212yes—
9#14273661C2211yescharacteristic
10#14273661C2211yescharacteristic
11#14273659—21no—
12C22×C8×C59C2211yescharacteristic
13C2×C4⋊C4×C59—21no—
14#107×C59—21no—
15#107×C59C2212yes—
16C22×C4×C59—41no—
17C22×C4×C59D411yescharacteristic
18C2×C8×C59C2×C412yes—
19C2×C8×C59D411yescharacteristic
20C2×C8×C59Q812yes—
21C2×C8×C59C2311yescharacteristic
22C4⋊C4×C59—22no—
23C4⋊C4×C59—41no—
24C22⋊Dic59—41no—
25C4⋊Dic59—21no—
26C4⋊Dic59—21no—
27C4×Dic59—41no—
28C59⋊C16C2×C414yescomplemented
29C23×C59D811yescharacteristic
30C2×C4×C59—42no—
31C2×C4×C59—82no—
32C2×C4×C59C4⋊C412yes—
33C2×C4×C59D811yescharacteristic
34C2×C4×C59Q1612yes—
35C2×C4×C59C2×D411yescharacteristic
36C2×Dic59—41no—
37C2×Dic59—41no—
38C8×C59C4⋊C412yes—
39C8×C59C22×C411yescharacteristic
40C8×C59C2×Q811yescharacteristic
41C22×C59—21no—
42C22×C59—21no—
43C22×C59#10712yes—
44C22×C59C2×D811yescharacteristic
45C4×C59—82no—
46C4×C59#10712yes—
47C4×C59C2×C4⋊C411yescharacteristic
48C4×C59C2×Q1611yescharacteristic
49Dic59—81no—
50Dic59—81no—
51#2159—591nomaximal, Sylow
52C2×C59—22no—
53C2×C59C2×#10711yescharacteristic
54C2×C59#50911yescharacteristic
55C2×C59#51011yescharacteristic
56C2×M32—591no—
57#427—591no—
58C2×#107D5911yescharacteristic
59#367—592no—
60#366—592no—
61C59#215911yescharacteristic, complemented, Sylow
62C22×C8C2×D5911yescharacteristic
63#117—1181no—
64C2×C4⋊C4—21no—
65M32—594no—
66C2×C16—592no—
67#107—21no—
68#107—591no—
69#107—591no—
70#107C2×D5912yes—
71#106—1181no—
72C22×C4—41no—
73C22×C4C22⋊D5911yescharacteristic
74C2×C8Dic11812yes—
75C2×C8C4×D5912yes—
76C2×C8C22⋊D5911yescharacteristic
77C2×C8C22×D5911yescharacteristic
78C4⋊C4—22no—
79C4⋊C4—41no—
80C4⋊C4—1181no—
81C4⋊C4—1181no—
82C22⋊C4—2361no—
83C42—2361no—
84C16—594no—
85C23#1174566911yescharacteristic
86C2×C4—42no—
87C2×C4—82no—
88C2×C4—2361no—
89C2×C4—2361no—
90C2×C4Dic59⋊C412yes—
91C2×C4#1174566911yescharacteristic
92C2×C4#1174567212yes—
93C2×C4C2×C22⋊D5911yescharacteristic
94C8Dic59⋊C412yes—
95C8C2×Dic11811yescharacteristic
96C8C2×C4×D5911yescharacteristic
97C22—21no—
98C22—21no—
99C22#1427366012yes—
100C22C2×#1174566911yescharacteristic
101C4—82no—
102C4—4721no—
103C4—4721no—
104C4#1427366012yes—
105C4C2×Dic59⋊C411yescharacteristic
106C4C2×#1174567211yescharacteristic
107C2—22no—
108C2C2×#1427366011yescharacteristic
109C2#1683783811yescharacteristic
110C2#1683784311yescharacteristic
subgroupG/H
centerC22C2×#11745669
commutatorC8×C59C22×C4
FrattiniC2×C8C22×D59
FittingC2×#107×C59C2
socleC22×C59C2×D8
hypercenterC2×#107D59
hypocenterC59#2159
LCSG ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
3. #16837229C2semidirect
4. #16837227C2semidirect
7. #14273667C4semidirect
28. C59⋊C16C2×C4semidirect
61. C59#2159semidirect