Finite Group Databasebeta

← #49182677

Subgroups — #49182677

Order 37952.

190 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C22×C4×D593C211yesmaximal, characteristic
2C2×#23748716C212yesmaximal, complemented
3C22⋊#18011654C211yesmaximal, characteristic, complemented
4#34039197C212yesmaximal, complemented
5C22⋊C8×C593C211yesmaximal, characteristic, complemented
6C23×D593C411yescharacteristic
7C22×Dic593C411yescharacteristic
8C2×C4×D593—24no—
9C2×C4×D593C411yescharacteristic
10C2×C4×D593C411yescharacteristic
11C2×C4×D593C2211yescharacteristic
12C2×C4×D593C2211yescharacteristic
13#23748716—24no—
14C2×#18011654C2212yescomplemented
15C22×C4×C593C2211yescharacteristic
16C2×C8×C593C2212yescomplemented
17C22×D593—22no—
18C22×D593—22no—
19C22×D593—22no—
20C22×D593C2×C411yescharacteristic
21C22×D593C2×C411yescharacteristic
22C2×Dic593—22no—
23C2×Dic593C2×C411yescharacteristic
24C2×Dic593C2×C411yescharacteristic
25C4×D593—22no—
26C4×D593—22no—
27C4×D593—22no—
28C4×D593D414yes—
29#18011654—22no—
30C23×C593C2×C411yescharacteristic
31C2×C4×C593—22no—
32C2×C4×C593C2×C411yescharacteristic
33C2×C4×C593C2311yescharacteristic
34C8×C593—22no—
35C22×C593—21no—
36C22×C593—21no—
37C22×C593M1612yescomplemented
38C22×C593C22×C411yescharacteristic
39C2×D593—28no—
40C2×D593—21no—
41C2×D593—21no—
42C2×D593—21no—
43C2×D593—21no—
44C2×D593C22⋊C412yes—
45C2×D593M1612yescomplemented
46C4×C593—21no—
47C4×C593C2×D412yes—
48Dic593—21no—
49Dic593C22⋊C412yes—
50C2×C593—22no—
51C2×C593C2×C22⋊C411yescharacteristic
52C2×C593C2×M1611yescharacteristic
53C2×C593C2×M1611yescharacteristic
54D593—22no—
55D593—22no—
56C593#40711yescharacteristic, complemented, Sylow
57#407—5931nomaximal, Sylow
58C23×C4—5931no—
59C2×M16—5932no—
60C22⋊C8—5931no—
61C22⋊C8—5932no—
62C22⋊C8D59311yescharacteristic, complemented
63C24—5931no—
64C22×C4—5931no—
65C22×C4—5931no—
66C22×C4—5931no—
67C22×C4—5931no—
68C22×C4—5931no—
69C22×C4—11864no—
70C22×C4C2×D59311yescharacteristic
71M16—11864no—
72C2×C8—5932no—
73C2×C8C2×D59312yescomplemented
74C23—5931no—
75C23—5931no—
76C23—11862no—
77C23—11862no—
78C23—11862no—
79C23C4×D59311yescharacteristic
80C2×C4—22no—
81C2×C4—5931no—
82C2×C4—5934no—
83C2×C4—5931no—
84C2×C4—11862no—
85C2×C4—11862no—
86C2×C4—11862no—
87C2×C4—11862no—
88C2×C4C4×D59311yescharacteristic
89C2×C4C22×D59311yescharacteristic
90C8—22no—
91C8—11862no—
92C22—21no—
93C22—21no—
94C22—5932no—
95C22—5932no—
96C22—11868no—
97C22—11861no—
98C22—11861no—
99C22—11861no—
100C22—11861no—
101C22#2374871612yescomplemented
102C22C2×C4×D59311yescharacteristic
103C4—21no—
104C4—5932no—
105C4—11861no—
106C4D4×D59312yes—
107C2—22no—
108C2—11862no—
109C2—11862no—
110C2C22⋊C4×D59311yescharacteristic
111C2M16×D59311yescharacteristic
112C2C2×#2374871611yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D593
commutator, socleC22×C593C22×C4
FittingC22⋊C8×C593C2
prime radicalC23×D593C4
cosocleC2×C4×C593C23
hypercenterC22⋊C8D593
hypocenterC593#407
LCSG ▷ C22×C593 ▷ C593
UCSC1 ◁ C2×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#23748716C2semidirect
3. C22⋊#18011654C2semidirect
4. #34039197C2semidirect
5. C22⋊C8×C593C2semidirect
14. C2×#18011654C22semidirect
16. C2×C8×C593C22semidirect
37. C22×C593M16semidirect
45. C2×D593M16semidirect
56. C593#407semidirect
62. C22⋊C8D593semidirect
73. C2×C8C2×D593semidirect
101. C22#23748716semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D5932
C2×#237487162
C22⋊#180116542
#340391972
C22⋊C8×C5932
#407593