Finite Group Databasebeta

← #20260895

Subgroups — #20260895

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×#13095501C211yesmaximal, characteristic, complemented
3C2×#13095498C211yesmaximal, characteristic, complemented
4#15690733C211yesmaximal, characteristic, complemented
5#15690730C211yesmaximal, characteristic, complemented
6C22⋊#11715895C211yesmaximal, characteristic, complemented
7C22⋊Q8×C97C211yesmaximal, characteristic, complemented
8#13095511—22no—
9#13095511—22no—
10C2×Dic194C2211yescharacteristic
11C2×D388C2211yescharacteristic
12C2×C22⋊D97—21no—
13C2×C4×D97—21no—
14#13095501—22no—
15#13095498—22no—
16C2×#11715895C2211yescharacteristic
17C2×#11715895C2211yescharacteristic
18C2×Q8×C97C2211yescharacteristic
19C22×C4×C97C2211yescharacteristic
20C4⋊C4×C97—21no—
21C4⋊C4×C97C2211yescharacteristic
22C22⋊C4×C97—21no—
23C23×C97D411yescharacteristic
24C22×D97—21no—
25Q8×C97—21no—
26Q8×C97—21no—
27C2×C4×C97—21no—
28C2×C4×C97—21no—
29C2×C4×C97—21no—
30C2×C4×C97—21no—
31C2×C4×C97D411yescharacteristic
32C2×C4×C97C2311yescharacteristic
33C22⋊D97—24no—
34C2×Dic97—21no—
35D388—21no—
36D388D412yes—
37C4×D97—24no—
38Dic194—21no—
39Dic194D412yes—
40#11715895—21no—
41#11715895—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×C97—41no—
51C4×C97—41no—
52C4×C97C2×D411yescharacteristic
53C4×C97C2×D411yescharacteristic
54Dic97—22no—
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⋊Q8D9711yescharacteristic, complemented
66#103—971no—
67#102—971no—
68C22⋊C8—971no—
69#41—1942no—
70#41—1942no—
71C2×Q8—971no—
72C2×Q8C2×D9711yescharacteristic
73C2×D4—971no—
74C2×D4—1941no—
75C22×C4—1941no—
76C22×C4C2×D9711yescharacteristic
77Q16—1942no—
78SD16—1942no—
79C2×C8—971no—
80C2×C8—971no—
81C4⋊C4—21no—
82C4⋊C4C2×D9711yescharacteristic
83C22⋊C4—21no—
84C23—1941no—
85C23C22⋊D9711yescharacteristic
86Q8—21no—
87Q8—21no—
88Q8—972no—
89Q8—1941no—
90D4—972no—
91D4—1944no—
92D4—1941no—
93C2×C4—21no—
94C2×C4—21no—
95C2×C4—21no—
96C2×C4—21no—
97C2×C4—1944no—
98C2×C4—1941no—
99C2×C4C22⋊D9711yescharacteristic
100C2×C4C22×D9711yescharacteristic
101C8—1941no—
102C8—1941no—
103C22—21no—
104C22—21no—
105C22—21no—
106C22—3881no—
107C22—3881no—
108C22—1942no—
109C22C2×C22⋊D9711yescharacteristic
110C4—21no—
111C4—41no—
112C4—41no—
113C4—1942no—
114C4D4×D9711yescharacteristic
115C4D4×D9711yescharacteristic
116C2—41no—
117C2—3882no—
118C2#1569077811yescharacteristic
119C2#1569083011yescharacteristic
120C2#1569084111yescharacteristic
subgroupG/H
centerC22C2×C22⋊D97
commutatorC2×C4×C97C23
FrattiniC2×C4C22×D97
FittingC22⋊Q8×C97C2
socleC22×C97C2×D4
hypercenterC22⋊Q8D97
hypocenterC97#452
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
2. C2×#13095501C2semidirect
3. C2×#13095498C2semidirect
4. #15690733C2semidirect
5. #15690730C2semidirect
6. C22⋊#11715895C2semidirect
7. C22⋊Q8×C97C2semidirect
60. C97#452semidirect
65. C22⋊Q8D97semidirect