Finite Group Databasebeta

← #20260899

Subgroups — #20260899

Order 6208.

152 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 43 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×#13095511C211yesmaximal, characteristic
2C2×Dic388C211yesmaximal, characteristic, complemented
3C2×#13095500C211yesmaximal, characteristic, complemented
4#15690789C211yesmaximal, characteristic, complemented
5#15690735C211yesmaximal, characteristic, complemented
6#15690732C211yesmaximal, characteristic, complemented
7C22⋊C8×C97C211yesmaximal, characteristic, complemented
8#13095511—22no—
9#13095511—22no—
10C2×Dic194C2211yescharacteristic
11C2×Dic194C2211yescharacteristic
12C2×D388C2211yescharacteristic
13C2×C22⋊D97—21no—
14C2×C4×D97—21no—
15Dic388—22no—
16#13095500—22no—
17C4⋊Dic97C2211yescharacteristic
18#13095490—21no—
19C22⋊Dic97—21no—
20C22×C4×C97C2211yescharacteristic
21C2×C8×C97C2211yescharacteristic
22C2×C8×C97C2211yescharacteristic
23C23×C97D411yescharacteristic
24C22×D97—21no—
25C2×C4×C97—21no—
26C2×C4×C97—21no—
27C2×C4×C97D411yescharacteristic
28C2×C4×C97C2311yescharacteristic
29C22⋊D97—24no—
30C2×Dic97—21no—
31C2×Dic97—21no—
32C2×Dic97—21no—
33D388—21no—
34D388D412yes—
35C4×D97—24no—
36Dic194—21no—
37Dic194—21no—
38Dic194—21no—
39Dic194D412yes—
40C8×C97—21no—
41C8×C97—21no—
42C22×C97—21no—
43C22×C97—21no—
44C22×C97—21no—
45C22×C97C2×D411yescharacteristic
46C2×D97—22no—
47C2×D97—41no—
48C2×D97—41no—
49C4×C97—21no—
50C4×C97C2×D411yescharacteristic
51C4×C97C2×D411yescharacteristic
52Dic97—22no—
53Dic97—41no—
54Dic97—41no—
55C2×C97—41no—
56C2×C97#12011yescharacteristic
57C2×C97#13511yescharacteristic
58C2×C97#13711yescharacteristic
59D97—42no—
60C97#45211yescharacteristic, complemented, Sylow
61#452—971nomaximal, Sylow
62C2×#41—971no—
63C2×Q16—971no—
64C2×SD16—971no—
65C22⋊Q8—971no—
66#103—971no—
67#102—971no—
68C22⋊C8D9711yescharacteristic, complemented
69#41—1942no—
70#41—1942no—
71C2×Q8—971no—
72C2×Q8—971no—
73C2×D4—971no—
74C2×D4—1941no—
75C22×C4—1941no—
76C22×C4C2×D9711yescharacteristic
77Q16—1942no—
78SD16—1942no—
79C2×C8C2×D9711yescharacteristic
80C2×C8C2×D9711yescharacteristic
81C4⋊C4—971no—
82C4⋊C4—1941no—
83C22⋊C4—1941no—
84C23—1941no—
85C23D38811yescharacteristic
86Q8—972no—
87Q8—1941no—
88Q8—1941no—
89Q8—1941no—
90D4—972no—
91D4—1944no—
92D4—1941no—
93C2×C4—21no—
94C2×C4—21no—
95C2×C4—1944no—
96C2×C4—1941no—
97C2×C4—1941no—
98C2×C4—1941no—
99C2×C4D38811yescharacteristic
100C2×C4C22×D9711yescharacteristic
101C8—21no—
102C8—21no—
103C22—21no—
104C22—21no—
105C22—21no—
106C22—3881no—
107C22—3881no—
108C22—1942no—
109C22C2×D38811yescharacteristic
110C4—21no—
111C4—3881no—
112C4—3881no—
113C4—1942no—
114C4D4×D9711yescharacteristic
115C4D4×D9711yescharacteristic
116C2—41no—
117C2—3882no—
118C2#1569078011yescharacteristic
119C2#1569083211yescharacteristic
120C2#1569084311yescharacteristic
subgroupG/H
centerC22C2×D388
commutatorC2×C4×C97C23
FrattiniC2×C4C22×D97
FittingC22⋊C8×C97C2
socleC22×C97C2×D4
hypercenterC22⋊C8D97
hypocenterC97#452
LCSG ▷ C2×C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×Dic388C2semidirect
3. C2×#13095500C2semidirect
4. #15690789C2semidirect
5. #15690735C2semidirect
6. #15690732C2semidirect
7. C22⋊C8×C97C2semidirect
60. C97#452semidirect
68. C22⋊C8D97semidirect