Finite Group Databasebeta

← #20260872

Subgroups — #20260872

Order 6208.

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

normal subgroups only

This group has 158 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, complemented
2C2×#13095499C211yesmaximal, characteristic, complemented
3#15690781C211yesmaximal, characteristic
4#15690735C211yesmaximal, characteristic, complemented
5#15690734C211yesmaximal, characteristic, complemented
6#15690722C211yesmaximal, characteristic, complemented
7C2×SD16×C97C211yesmaximal, characteristic, complemented
8C2×Dic194—21no—
9C2×Dic194C2211yescharacteristic
10Q8×D97—22no—
11Q8×D97—22no—
12C2×C22⋊D97—21no—
13C2×C4×D97—21no—
14C2×C4×D97C2211yescharacteristic
15#13095499—22no—
16C2×#11715895C2211yescharacteristic
17C4⋊Dic97C2211yescharacteristic
18C22⋊Dic97—21no—
19C2×Q8×C97C2211yescharacteristic
20C2×D4×C97C2211yescharacteristic
21SD16×C97—22no—
22C2×C8×C97C2211yescharacteristic
23C23×C97—21no—
24C22×D97D411yescharacteristic
25Q8×C97—21no—
26Q8×C97D412yescomplemented
27D4×C97—21no—
28D4×C97—21no—
29C2×C4×C97—21no—
30C2×C4×C97C2311yescharacteristic
31C22⋊D97—42no—
32C2×Dic97—21no—
33C2×Dic97—21no—
34C2×Dic97D411yescharacteristic
35C4×D97—24no—
36C4×D97—21no—
37C4×D97—21no—
38Dic194—24no—
39Dic194—21no—
40Dic194D412yescomplemented
41C8×C97—21no—
42#11715895—21no—
43C22×C97—41no—
44C22×C97—41no—
45C22×C97—41no—
46C22×C97C2×D411yescharacteristic
47C2×D97—21no—
48C2×D97—21no—
49C2×D97SD1612yescomplemented
50C4×C97—22no—
51C4×C97C2×D411yescharacteristic
52C4×C97C2×D411yescharacteristic
53Dic97—21no—
54Dic97—22no—
55Dic97—41no—
56C2×C97—81no—
57C2×C97#12011yescharacteristic
58C2×C97C2×SD1611yescharacteristic
59C2×C97#13711yescharacteristic
60D97—22no—
61C97#44811yescharacteristic, complemented, Sylow
62#448—971nomaximal, Sylow
63C22×Q8—971no—
64C2×SD16—971no—
65C2×SD16D9711yescharacteristic, complemented
66#121—971no—
67#103—971no—
68#103—971no—
69C22⋊C8—971no—
70C2×Q8—971no—
71C2×Q8—1941no—
72C2×Q8—1942no—
73C2×Q8—1942no—
74C2×Q8C2×D9711yescharacteristic
75C2×D4—1941no—
76C2×D4C2×D9711yescharacteristic
77C22×C4—971no—
78C22×C4—1941no—
79SD16—22no—
80SD16—1942no—
81C2×C8—971no—
82C2×C8C2×D9711yescharacteristic
83C4⋊C4—971no—
84C22⋊C4—1941no—
85C23—21no—
86C23—971no—
87Q8—21no—
88Q8—972no—
89Q8—1944no—
90Q8—1941no—
91Q8C22⋊D9712yescomplemented
92D4—21no—
93D4—21no—
94D4—3882no—
95C2×C4—21no—
96C2×C4—971no—
97C2×C4—1944no—
98C2×C4—1941no—
99C2×C4—1941no—
100C2×C4—1941no—
101C2×C4—1941no—
102C2×C4C22×D9711yescharacteristic
103C8—21no—
104C8—1941no—
105C22—41no—
106C22—41no—
107C22—41no—
108C22—972no—
109C22—1941no—
110C22—1941no—
111C22D4×D9711yescharacteristic
112C4—22no—
113C4—3881no—
114C4—1941no—
115C4—1942no—
116C4D4×D9711yescharacteristic
117C4C2×C22⋊D9711yescharacteristic
118C2—81no—
119C2—1942no—
120C2#1569077811yescharacteristic
121C2SD16×D9711yescharacteristic
122C2#1569083911yescharacteristic
subgroupG/H
centerC22D4×D97
commutatorC2×C4×C97C23
FrattiniC2×C4C22×D97
FittingC2×SD16×C97C2
socleC22×C97C2×D4
hypercenterC2×SD16D97
hypocenterC97#448
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×Q8×D97C2semidirect
2. C2×#13095499C2semidirect
4. #15690735C2semidirect
5. #15690734C2semidirect
6. #15690722C2semidirect
7. C2×SD16×C97C2semidirect
26. Q8×C97D4semidirect
40. Dic194D4semidirect
49. C2×D97SD16semidirect
61. C97#448semidirect
65. C2×SD16D97semidirect
91. Q8C22⋊D97semidirect