Finite Group Databasebeta

← #20260955

Subgroups — #20260955

Order 6208.

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

normal subgroups only

This group has 112 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×#13095501C211yesmaximal, characteristic, complemented
2#15690797C211yesmaximal, characteristic
3Q8×Dic97C211yesmaximal, characteristic, complemented
4#15690739C211yesmaximal, characteristic, complemented
5#15690735C211yesmaximal, characteristic, complemented
6#15690731C211yesmaximal, characteristic
7C2×SD16×C97C211yesmaximal, characteristic
8C2×Dic194C2211yescharacteristic
9#13095501—22no—
10C2×#11715895C2211yescharacteristic
11C4⋊Dic97—21no—
12C4⋊Dic97C2211yescharacteristic
13C22⋊Dic97—21no—
14C22⋊Dic97—21no—
15C4×Dic97—21no—
16C4×Dic97C2211yescharacteristic
17C2×Q8×C97C2211yescharacteristic
18C2×D4×C97C2211yescharacteristic
19SD16×C97—22no—
20C2×C8×C97C2211yescharacteristic
21C23×C97—21no—
22Q8×C97—21no—
23Q8×C97D412yes—
24D4×C97—21no—
25D4×C97—21no—
26C2×C4×C97—21no—
27C2×C4×C97C2311yescharacteristic
28C2×Dic97—21no—
29C2×Dic97—21no—
30C2×Dic97D411yescharacteristic
31C2×Dic97D411yescharacteristic
32Dic194—21no—
33Dic194—21no—
34C8×C97—21no—
35#11715895—21no—
36C22×C97—41no—
37C22×C97—41no—
38C22×C97—41no—
39C22×C97C2×D411yescharacteristic
40C4×C97—22no—
41C4×C97C2×D411yescharacteristic
42C4×C97#4111yescharacteristic
43Dic97—21no—
44Dic97—21no—
45Dic97—41no—
46Dic97—41no—
47C2×C97—81no—
48C2×C97#12111yescharacteristic
49C2×C97#13511yescharacteristic
50C2×C97#13711yescharacteristic
51C97#46411yescharacteristic, complemented, Sylow
52#464—971nomaximal, Sylow
53C2×Q16—971no—
54C2×SD16D9711yescharacteristic
55#124—971no—
56C4×Q8—971no—
57C4⋊C8—971no—
58#103—971no—
59#102—971no—
60C2×Q8—971no—
61C2×Q8C2×D9711yescharacteristic
62C2×D4C2×D9711yescharacteristic
63Q16—1942no—
64SD16—22no—
65C2×C8—971no—
66C2×C8C2×D9711yescharacteristic
67C4⋊C4—971no—
68C4⋊C4—1941no—
69C22⋊C4—1941no—
70C22⋊C4—1941no—
71C42—971no—
72C42—1941no—
73C23—21no—
74Q8—21no—
75Q8—1941no—
76Q8—1941no—
77Q8C22⋊D9712yes—
78D4—21no—
79D4—21no—
80C2×C4—21no—
81C2×C4—971no—
82C2×C4—971no—
83C2×C4—1941no—
84C2×C4—1941no—
85C2×C4C22×D9711yescharacteristic
86C8—21no—
87C8—1941no—
88C22—41no—
89C22—41no—
90C22—41no—
91C22D4×D9711yescharacteristic
92C4—22no—
93C4—3881no—
94C4—3881no—
95C4—1941no—
96C4—1941no—
97C4C2×C22⋊D9711yescharacteristic
98C4#1309551011yescharacteristic
99C2—81no—
100C2#1569078211yescharacteristic
101C2#1569083111yescharacteristic
102C2#1569083911yescharacteristic
subgroupG/H
centerC22D4×D97
commutatorC2×C4×C97C23
FrattiniC2×C4C22×D97
FittingC2×SD16×C97C2
socleC22×C97C2×D4
hypercenterC2×SD16D97
hypocenterC97#464
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×#13095501C2semidirect
3. Q8×Dic97C2semidirect
4. #15690739C2semidirect
5. #15690735C2semidirect
51. C97#464semidirect