Finite Group Databasebeta

← #37559665

Subgroups — #37559665

Order 23872.

120 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 41 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×#20238593C211yesmaximal, characteristic, complemented
2#26045768C211yesmaximal, characteristic, complemented
3#26045763C211yesmaximal, characteristic
4#26045726C211yesmaximal, characteristic, complemented
5#26045716C211yesmaximal, characteristic, complemented
6#26045713C211yesmaximal, characteristic, complemented
7C2×SD16×C373C211yesmaximal, characteristic, complemented
8C2×C22⋊D373—21no—
9C2×C4×D373C2211yescharacteristic
10#20238593—22no—
11C2×#15688412C2211yescharacteristic
12C4⋊Dic373C2211yescharacteristic
13C4⋊Dic373C2211yescharacteristic
14#20238589—21no—
15C22⋊Dic373—21no—
16#20238587—21no—
17C2×Q8×C373C2211yescharacteristic
18C2×D4×C373C2211yescharacteristic
19SD16×C373—22no—
20C2×C8×C373C2211yescharacteristic
21C22×D373D411yescharacteristic
22C22⋊D373—42no—
23C2×Dic373—21no—
24C2×Dic373—21no—
25C2×Dic373D411yescharacteristic
26C4×D373—21no—
27C4×D373—21no—
28#15688412—21no—
29C23×C373—21no—
30Q8×C373—21no—
31Q8×C373—21no—
32D4×C373—21no—
33D4×C373—21no—
34C2×C4×C373—21no—
35C2×C4×C373C2311yescharacteristic
36C8×C373D412yescomplemented
37C22×C373—41no—
38C22×C373—41no—
39C22×C373—41no—
40C22×C373C2×D411yescharacteristic
41C2×D373—21no—
42C2×D373—21no—
43C2×D373—21no—
44C4×C373—41no—
45C4×C373C2×D411yescharacteristic
46C4×C373#4111yescharacteristic
47Dic373—21no—
48Dic373—41no—
49Dic373—41no—
50C2×C373—81no—
51C2×C373#12111yescharacteristic
52C2×C373AGL(1,ℤ/8)11yescharacteristic
53C2×C373#13711yescharacteristic
54D373—41no—
55C373#46811yescharacteristic, complemented, Sylow
56#468—3731nomaximal, Sylow
57C2×SD16D37311yescharacteristic, complemented
58C2×M16—3731no—
59C22⋊Q8—3731no—
60#121—3731no—
61#107—3731no—
62#103—3731no—
63#102—3731no—
64C2×Q8C2×D37311yescharacteristic
65C2×D4—7461no—
66C2×D4C2×D37311yescharacteristic
67C22×C4—3731no—
68SD16—22no—
69M16—7462no—
70C2×C8—3731no—
71C2×C8C2×D37311yescharacteristic
72C4⋊C4—3731no—
73C4⋊C4—3731no—
74C4⋊C4—7461no—
75C22⋊C4—7461no—
76C22⋊C4—7461no—
77C23—21no—
78C23—3731no—
79Q8—21no—
80Q8—21no—
81D4—21no—
82D4—21no—
83D4—14922no—
84C2×C4—21no—
85C2×C4—3731no—
86C2×C4—7461no—
87C2×C4—7461no—
88C2×C4—7461no—
89C2×C4—7461no—
90C2×C4C22×D37311yescharacteristic
91C8—7461no—
92C8C22⋊D37312yescomplemented
93C22—41no—
94C22—41no—
95C22—41no—
96C22—7461no—
97C22—7461no—
98C22—7461no—
99C22D4×D37311yescharacteristic
100C4—41no—
101C4—14921no—
102C4—14921no—
103C4—7461no—
104C4C2×C22⋊D37311yescharacteristic
105C4#2023860911yescharacteristic
106C2—81no—
107C2—14921no—
108C2#2604576311yescharacteristic
109C2#2604581911yescharacteristic
110C2#2604582111yescharacteristic
subgroupG/H
centerC22D4×D373
commutator, cosocleC2×C4×C373C23
FrattiniC2×C4C22×D373
FittingC2×SD16×C373C2
socleC22×C373C2×D4
prime radical#26045763C2
hypercenterC2×SD16D373
hypocenterC373#468
LCSG ▷ C2×C4×C373 ▷ C2×C373 ▷ C373
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#20238593C2semidirect
2. #26045768C2semidirect
4. #26045726C2semidirect
5. #26045716C2semidirect
6. #26045713C2semidirect
7. C2×SD16×C373C2semidirect
36. C8×C373D4semidirect
55. C373#468semidirect
57. C2×SD16D373semidirect
92. C8C22⋊D373semidirect

Maximal subgroups

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

subgroupindex
C2×#202385932
#260457682
#260457632
#260457262
#260457162
#260457132
C2×SD16×C3732
#468373