Finite Group Databasebeta

← #34091813

Subgroups — #34091813

Order 19904.

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#23755728C211yesmaximal, characteristic
2#23755716C211yesmaximal, characteristic, complemented
3#23755715C211yesmaximal, characteristic, complemented
4#23755643C211yesmaximal, characteristic, complemented
5#23755636C211yesmaximal, characteristic, complemented
6#23755619C211yesmaximal, characteristic, complemented
7#104×C311C211yesmaximal, characteristic, complemented
8#19097315C2211yescharacteristic
9#19097305C411yescharacteristic, complemented
10#19097303C411yescharacteristic, complemented
11#19097302C411yescharacteristic, complemented
12#19097300C411yescharacteristic, complemented
13#19097299—21no—
14#19097299C2211yescharacteristic
15#19097298—21no—
16C2×C311⋊C8—21no—
17C2×C311⋊C8C2211yescharacteristic
18C2×C311⋊C8C2211yescharacteristic
19C8×D311—21no—
20#41×C311C2211yescharacteristic
21M16×C311C2211yescharacteristic
22C42×C311C2211yescharacteristic
23Dic622C2×C411yescharacteristic
24D1244C2×C411yescharacteristic
25C22⋊D311—21no—
26C4×D311—21no—
27C311⋊C8—21no—
28C311⋊C8C2×C411yescharacteristic
29C311⋊C8C2×C411yescharacteristic
30C311⋊C8D411yescharacteristic
31C311⋊C8D411yescharacteristic
32Q8×C311C2×C411yescharacteristic
33D4×C311—21no—
34D4×C311C2×C411yescharacteristic
35C2×C4×C311—21no—
36C2×C4×C311—21no—
37C2×C4×C311C2311yescharacteristic
38C8×C311—21no—
39C22×C311—21no—
40C22×C311#4111yescharacteristic
41C2×D311—21no—
42C4×C311—21no—
43C4×C311—41no—
44C4×C311C22×C411yescharacteristic
45C4×C311C2×D411yescharacteristic
46Dic311—21no—
47C2×C311—21no—
48C2×C311—41no—
49C2×C311C4×D411yescharacteristic
50D311—41no—
51C311#44411yescharacteristic, complemented, Sylow
52#444—3111nomaximal, Sylow
53#135—3111no—
54#131—3111no—
55#131—3111no—
56#108—3111no—
57#104—3111no—
58#104D31111yescharacteristic, complemented
59#97—3111no—
60#41—3111no—
61#41C2×D31111yescharacteristic
62Q16—3111no—
63SD16—3111no—
64SD16—3111no—
65D8—3111no—
66M16—3111no—
67M16—6221no—
68M16—6221no—
69M16C2×D31111yescharacteristic
70C2×C8—3111no—
71C2×C8—3111no—
72C2×C8—6221no—
73C2×C8—6221no—
74C42C2×D31111yescharacteristic
75Q8—3111no—
76Q8C4×D31111yescharacteristic
77D4—21no—
78D4—3111no—
79D4—6221no—
80D4C4×D31111yescharacteristic
81C2×C4—21no—
82C2×C4—21no—
83C2×C4—6221no—
84C2×C4C22×D31111yescharacteristic
85C8—21no—
86C8—3111no—
87C8—3111no—
88C8—3111no—
89C8—3111no—
90C8—6221no—
91C22—21no—
92C22—6221no—
93C22#1909731411yescharacteristic
94C4—21no—
95C4—41no—
96C4—6221no—
97C4C2×C4×D31111yescharacteristic
98C4D4×D31111yescharacteristic
99C2—21no—
100C2—41no—
101C2—12441no—
102C2(C22⋊D311)⋊C411yescharacteristic
subgroupG/H
centerC4D4×D311
commutatorC4×C311C22×C4
FrattiniC2×C4C22×D311
Fitting#104×C311C2
socleC2×C311C4×D4
prime radical#23755728C2
cosocleC2×C4×C311C23
hypercenter#104D311
hypocenterC311#444
LCSG ▷ C4×C311 ▷ C2×C311 ▷ C311
UCSC1 ◁ C4 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #23755716C2semidirect
3. #23755715C2semidirect
4. #23755643C2semidirect
5. #23755636C2semidirect
6. #23755619C2semidirect
7. #104×C311C2semidirect
9. #19097305C4semidirect
10. #19097303C4semidirect
11. #19097302C4semidirect
12. #19097300C4semidirect
51. C311#444semidirect
58. #104D311semidirect

Maximal subgroups

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

subgroupindex
#237557282
#237557162
#237557152
#237556432
#237556362
#237556192
#104×C3112
#444311