Finite Group Databasebeta

← #20261106

Subgroups — #20261106

Order 6208.

142 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 47 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×#13095500C211yesmaximal, characteristic, complemented
2C2×#13095499C211yesmaximal, characteristic, complemented
3C2×#13095498C211yesmaximal, characteristic, complemented
4#15690808C211yesmaximal, characteristic, complemented
5#15690806C211yesmaximal, characteristic
6C8×Dic97C211yesmaximal, characteristic, complemented
7C2×SD16×C97C211yesmaximal, characteristic, complemented
8C2×Dic194C2211yescharacteristic
9C2×D388C2211yescharacteristic
10C2×C22⋊D97—22no—
11#13095500—22no—
12#13095499—22no—
13#13095498—22no—
14C2×#11715895C2211yescharacteristic
15#13095490—22no—
16C4×Dic97C2211yescharacteristic
17C2×Q8×C97C2211yescharacteristic
18C2×D4×C97C2211yescharacteristic
19SD16×C97—22no—
20C2×C8×C97C2211yescharacteristic
21C23×C97—21no—
22C22×D97—21no—
23Q8×C97—21no—
24Q8×C97—21no—
25D4×C97—21no—
26D4×C97—21no—
27C2×C4×C97—21no—
28C2×C4×C97C2311yescharacteristic
29C22⋊D97—44no—
30C2×Dic97—21no—
31C2×Dic97D412yes—
32D388—21no—
33D388—21no—
34Dic194—21no—
35Dic194—21no—
36C8×C97D412yescomplemented
37#11715895D412yescomplemented
38C22×C97—41no—
39C22×C97—42no—
40C22×C97C2×D411yescharacteristic
41C2×D97—41no—
42C2×D97—42no—
43C4×C97—41no—
44C4×C97C2×D411yescharacteristic
45C4×C97C2×D411yescharacteristic
46Dic97—41no—
47Dic97SD1614yescomplemented
48C2×C97—81no—
49C2×C97#12711yescharacteristic
50C2×C97C2×SD1612yes—
51D97—81no—
52C97#49211yescharacteristic, complemented, Sylow
53#492—971nomaximal, Sylow
54C2×SD16—971no—
55C2×SD16—971no—
56C2×SD16—971no—
57C2×SD16D9711yescharacteristic, complemented
58C4⋊Q8—971no—
59#127—971no—
60C4×C8—971no—
61C2×Q8—971no—
62C2×Q8C2×D9711yescharacteristic
63C2×D4—971no—
64C2×D4—1942no—
65C2×D4C2×D9711yescharacteristic
66SD16—22no—
67SD16—1942no—
68SD16—1942no—
69SD16—1942no—
70C2×C8—971no—
71C2×C8C2×D9711yescharacteristic
72C4⋊C4—1942no—
73C42—971no—
74C23—21no—
75C23—1941no—
76Q8—21no—
77Q8—21no—
78Q8—1941no—
79Q8—1941no—
80D4—21no—
81D4—21no—
82D4—3884no—
83D4—1941no—
84D4—1941no—
85C2×C4—21no—
86C2×C4—972no—
87C2×C4—1941no—
88C2×C4C22×D9711yescharacteristic
89C8—972no—
90C8C22⋊D9712yescomplemented
91C22—41no—
92C22—42no—
93C22—3881no—
94C22—3882no—
95C22D4×D9711yescharacteristic
96C4—41no—
97C4—974no—
98C4—3881no—
99C4D4×D9711yescharacteristic
100C4C2×C22⋊D9711yescharacteristic
101C2—81no—
102C2—7761no—
103C2#1569080611yescharacteristic
104C2SD16×D9712yes—
subgroupG/H
centerC22D4×D97
commutatorC2×C4×C97C23
FrattiniC2×C4C22×D97
FittingC2×SD16×C97C2
socleC22×C97C2×D4
hypercenterC2×SD16D97
hypocenterC97#492
LCSG ▷ C2×C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#13095500C2semidirect
2. C2×#13095499C2semidirect
3. C2×#13095498C2semidirect
4. #15690808C2semidirect
6. C8×Dic97C2semidirect
7. C2×SD16×C97C2semidirect
36. C8×C97D4semidirect
37. #11715895D4semidirect
47. Dic97SD16semidirect
52. C97#492semidirect
57. C2×SD16D97semidirect
90. C8C22⋊D97semidirect