Finite Group Databasebeta

← #49182834

Subgroups — #49182834

Order 37952.

104 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 45 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#34039305C211yesmaximal, characteristic
2#34039293C211yesmaximal, characteristic, complemented
3#34039292C211yesmaximal, characteristic, complemented
4#34039220C211yesmaximal, characteristic, complemented
5#34039213C211yesmaximal, characteristic, complemented
6#34039196C211yesmaximal, characteristic, complemented
7#104×C593C211yesmaximal, characteristic, complemented
8#23748733C2211yescharacteristic
9#23748723C411yescharacteristic, complemented
10#23748721C411yescharacteristic, complemented
11#23748720C411yescharacteristic, complemented
12#23748718C411yescharacteristic, complemented
13#23748717—21no—
14#23748717C2211yescharacteristic
15#23748716—21no—
16C2×#18011654—21no—
17C2×#18011654C2211yescharacteristic
18C2×#18011654C2211yescharacteristic
19C8×D593—21no—
20#41×C593C2211yescharacteristic
21M16×C593C2211yescharacteristic
22C42×C593C2211yescharacteristic
23Dic1186C2×C411yescharacteristic
24D2372C2×C411yescharacteristic
25C22⋊D593—21no—
26C4×D593—21no—
27#18011654—21no—
28#18011654C2×C411yescharacteristic
29#18011654C2×C411yescharacteristic
30#18011654D411yescharacteristic
31#18011654D411yescharacteristic
32Q8×C593C2×C411yescharacteristic
33D4×C593—21no—
34D4×C593C2×C411yescharacteristic
35C2×C4×C593—21no—
36C2×C4×C593—21no—
37C2×C4×C593C2311yescharacteristic
38C8×C593—21no—
39C22×C593—21no—
40C22×C593#4111yescharacteristic
41C2×D593—21no—
42C4×C593—21no—
43C4×C593—41no—
44C4×C593C22×C411yescharacteristic
45C4×C593C2×D411yescharacteristic
46Dic593—21no—
47C2×C593—21no—
48C2×C593—41no—
49C2×C593C4×D411yescharacteristic
50D593—41no—
51C593#44411yescharacteristic, complemented, Sylow
52#444—5931nomaximal, Sylow
53#135—5931no—
54#131—5931no—
55#131—5931no—
56#108—5931no—
57#104—5931no—
58#104D59311yescharacteristic, complemented
59#97—5931no—
60#41—5931no—
61#41C2×D59311yescharacteristic
62Q16—5931no—
63SD16—5931no—
64SD16—5931no—
65D8—5931no—
66M16—5931no—
67M16—11861no—
68M16—11861no—
69M16C2×D59311yescharacteristic
70C2×C8—5931no—
71C2×C8—5931no—
72C2×C8—11861no—
73C2×C8—11861no—
74C42C2×D59311yescharacteristic
75Q8—5931no—
76Q8C4×D59311yescharacteristic
77D4—21no—
78D4—5931no—
79D4—11861no—
80D4C4×D59311yescharacteristic
81C2×C4—21no—
82C2×C4—21no—
83C2×C4—11861no—
84C2×C4C22×D59311yescharacteristic
85C8—21no—
86C8—5931no—
87C8—5931no—
88C8—5931no—
89C8—5931no—
90C8—11861no—
91C22—21no—
92C22—11861no—
93C22#2374873211yescharacteristic
94C4—21no—
95C4—41no—
96C4—11861no—
97C4C2×C4×D59311yescharacteristic
98C4D4×D59311yescharacteristic
99C2—21no—
100C2—41no—
101C2—23721no—
102C2#3403924511yescharacteristic
subgroupG/H
centerC4D4×D593
commutatorC4×C593C22×C4
FrattiniC2×C4C22×D593
Fitting#104×C593C2
socleC2×C593C4×D4
prime radical#34039305C2
cosocleC2×C4×C593C23
hypercenter#104D593
hypocenterC593#444
LCSG ▷ C4×C593 ▷ C2×C593 ▷ C593
UCSC1 ◁ C4 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #34039293C2semidirect
3. #34039292C2semidirect
4. #34039220C2semidirect
5. #34039213C2semidirect
6. #34039196C2semidirect
7. #104×C593C2semidirect
9. #23748723C4semidirect
10. #23748721C4semidirect
11. #23748720C4semidirect
12. #23748718C4semidirect
51. C593#444semidirect
58. #104D593semidirect

Maximal subgroups

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

subgroupindex
#340393052
#340392932
#340392922
#340392202
#340392132
#340391962
#104×C5932
#444593