Finite Group Databasebeta

← #20260889

Subgroups — #20260889

Order 6208.

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

normal subgroups only

This group has 148 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
1C2×Q8×D97C211yesmaximal, characteristic
2C2×#13095501C211yesmaximal, characteristic, complemented
3#15690786C211yesmaximal, characteristic
4#15690735C211yesmaximal, characteristic, complemented
5#15690734C211yesmaximal, characteristic, complemented
6#15690722C211yesmaximal, characteristic
7C2×Q16×C97C211yesmaximal, characteristic, complemented
8C2×Dic194—21no—
9C2×Dic194C2211yescharacteristic
10Q8×D97—22no—
11Q8×D97—22no—
12C2×C4×D97—21no—
13C2×C4×D97C2211yescharacteristic
14#13095501—22no—
15C2×#11715895C2211yescharacteristic
16C4⋊Dic97C2211yescharacteristic
17#13095490—21no—
18#13095488—21no—
19C2×Q8×C97C2211yescharacteristic
20C2×Q8×C97C2211yescharacteristic
21Q16×C97—22no—
22C2×C8×C97C2211yescharacteristic
23C22×D97D411yescharacteristic
24Q8×C97—21no—
25Q8×C97—21no—
26Q8×C97—21no—
27Q8×C97D412yes—
28C2×C4×C97—21no—
29C2×C4×C97—21no—
30C2×C4×C97C2311yescharacteristic
31C2×Dic97—21no—
32C2×Dic97—21no—
33C2×Dic97D411yescharacteristic
34C4×D97—24no—
35C4×D97—21no—
36C4×D97—21no—
37Dic194—24no—
38Dic194—21no—
39Dic194D412yes—
40C8×C97—21no—
41#11715895—21no—
42C22×C97C2×D411yescharacteristic
43C2×D97—21no—
44C2×D97—21no—
45C2×D97Q1612yescomplemented
46C4×C97—22no—
47C4×C97—41no—
48C4×C97C2×D411yescharacteristic
49C4×C97C2×D411yescharacteristic
50Dic97—21no—
51Dic97—22no—
52Dic97—41no—
53C2×C97#12011yescharacteristic
54C2×C97C2×Q1611yescharacteristic
55C2×C97#13711yescharacteristic
56D97—22no—
57C97#45111yescharacteristic, complemented, Sylow
58#451—971nomaximal, Sylow
59C22×Q8—971no—
60C2×Q16—971no—
61C2×Q16D9711yescharacteristic, complemented
62C22⋊Q8—971no—
63#103—971no—
64#103—971no—
65C22⋊C8—971no—
66C2×Q8—971no—
67C2×Q8—1941no—
68C2×Q8—1942no—
69C2×Q8—1942no—
70C2×Q8C2×D9711yescharacteristic
71C2×Q8C2×D9711yescharacteristic
72C22×C4—971no—
73C22×C4—1941no—
74Q16—22no—
75Q16—1942no—
76C2×C8—971no—
77C2×C8C2×D9711yescharacteristic
78C4⋊C4—971no—
79C4⋊C4—1941no—
80C22⋊C4—1941no—
81C23—971no—
82Q8—21no—
83Q8—21no—
84Q8—21no—
85Q8—972no—
86Q8—1944no—
87Q8—1941no—
88Q8C22⋊D9712yes—
89C2×C4—21no—
90C2×C4—21no—
91C2×C4—971no—
92C2×C4—1944no—
93C2×C4—1941no—
94C2×C4—1941no—
95C2×C4—1941no—
96C2×C4—1941no—
97C2×C4C22×D9711yescharacteristic
98C8—21no—
99C8—1941no—
100C22—972no—
101C22—1941no—
102C22—1941no—
103C22D4×D9711yescharacteristic
104C4—22no—
105C4—41no—
106C4—3881no—
107C4—1941no—
108C4—1942no—
109C4D4×D9711yescharacteristic
110C4C2×C22⋊D9711yescharacteristic
111C2—1942no—
112C2#1569077811yescharacteristic
113C2Q16×D9711yescharacteristic
114C2#1569084211yescharacteristic
subgroupG/H
centerC22D4×D97
commutatorC2×C4×C97C23
FrattiniC2×C4C22×D97
FittingC2×Q16×C97C2
socleC22×C97C2×D4
hypercenterC2×Q16D97
hypocenterC97#451
LCSG ▷ C2×C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
2. C2×#13095501C2semidirect
4. #15690735C2semidirect
5. #15690734C2semidirect
7. C2×Q16×C97C2semidirect
45. C2×D97Q16semidirect
57. C97#451semidirect
61. C2×Q16D97semidirect