Finite Group Databasebeta

← #20260983

Subgroups — #20260983

Order 6208.

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

normal subgroups only

This group has 120 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×#13095498C211yesmaximal, characteristic, complemented
2C2×#13095495C211yesmaximal, characteristic, complemented
3#15690784C211yesmaximal, characteristic
4#15690743C211yesmaximal, characteristic, complemented
5#15690734C211yesmaximal, characteristic, complemented
6#15690730C211yesmaximal, characteristic, complemented
7C22⋊Q8×C97C211yesmaximal, characteristic, complemented
8C2×D388C2211yescharacteristic
9C2×C22⋊D97—21no—
10#13095498—22no—
11#13095495—22no—
12C2×#11715895C2211yescharacteristic
13C2×#11715895C2211yescharacteristic
14C4⋊Dic97C2211yescharacteristic
15#13095488—21no—
16C2×Q8×C97C2211yescharacteristic
17C22×C4×C97C2211yescharacteristic
18C4⋊C4×C97—21no—
19C4⋊C4×C97C2211yescharacteristic
20C22⋊C4×C97—21no—
21C23×C97D411yescharacteristic
22C22×D97—21no—
23Q8×C97—21no—
24Q8×C97—21no—
25C2×C4×C97—21no—
26C2×C4×C97—21no—
27C2×C4×C97—21no—
28C2×C4×C97—21no—
29C2×C4×C97D411yescharacteristic
30C2×C4×C97C2311yescharacteristic
31C22⋊D97—42no—
32C2×Dic97—21no—
33D388—21no—
34D388—21no—
35#11715895—21no—
36#11715895D412yescomplemented
37C22×C97—21no—
38C22×C97—21no—
39C22×C97—21no—
40C22×C97C2×D411yescharacteristic
41C2×D97—41no—
42C2×D97—41no—
43C2×D97—41no—
44C4×C97—21no—
45C4×C97—41no—
46C4×C97—41no—
47C4×C97C2×D411yescharacteristic
48C4×C97#4111yescharacteristic
49Dic97—41no—
50C2×C97—41no—
51C2×C97#12111yescharacteristic
52C2×C97AGL(1,ℤ/8)11yescharacteristic
53C2×C97#13711yescharacteristic
54D97—81no—
55C97#46811yescharacteristic, complemented, Sylow
56#468—971nomaximal, Sylow
57C2×SD16—971no—
58C2×M16—971no—
59C22⋊Q8D9711yescharacteristic, complemented
60#121—971no—
61#107—971no—
62#103—971no—
63#102—971no—
64C2×Q8C2×D9711yescharacteristic
65C2×D4—971no—
66C2×D4—1941no—
67C22×C4C2×D9711yescharacteristic
68SD16—1942no—
69M16—1942no—
70C2×C8—971no—
71C2×C8—971no—
72C4⋊C4—21no—
73C4⋊C4—971no—
74C4⋊C4C2×D9711yescharacteristic
75C22⋊C4—21no—
76C22⋊C4—1941no—
77C23—1941no—
78C23C22⋊D9711yescharacteristic
79Q8—21no—
80Q8—21no—
81D4—3882no—
82D4—1941no—
83D4—1941no—
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—1941no—
89C2×C4C22⋊D9711yescharacteristic
90C2×C4C22×D9711yescharacteristic
91C8—972no—
92C8—1941no—
93C22—21no—
94C22—21no—
95C22—21no—
96C22—3881no—
97C22—3881no—
98C22—3881no—
99C22C2×C22⋊D9711yescharacteristic
100C4—21no—
101C4—41no—
102C4—41no—
103C4—3881no—
104C4D4×D9711yescharacteristic
105C4#1309551011yescharacteristic
106C2—41no—
107C2—7761no—
108C2#1569078211yescharacteristic
109C2#1569083511yescharacteristic
110C2#1569084111yescharacteristic
subgroupG/H
centerC22C2×C22⋊D97
commutatorC2×C4×C97C23
FrattiniC2×C4C22×D97
FittingC22⋊Q8×C97C2
socleC22×C97C2×D4
hypercenterC22⋊Q8D97
hypocenterC97#468
LCSG ▷ C2×C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#13095498C2semidirect
2. C2×#13095495C2semidirect
4. #15690743C2semidirect
5. #15690734C2semidirect
6. #15690730C2semidirect
7. C22⋊Q8×C97C2semidirect
36. #11715895D4semidirect
55. C97#468semidirect
59. C22⋊Q8D97semidirect