Finite Group Databasebeta

← #20260909

Subgroups — #20260909

Order 6208.

146 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 39 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
1#15690857C211yesmaximal, characteristic, complemented
2#15690838C211yesmaximal, characteristic, complemented
3#15690835C211yesmaximal, characteristic, complemented
4#15690798C211yesmaximal, characteristic, complemented
5#15690738C211yesmaximal, characteristic, complemented
6#15690728C211yesmaximal, characteristic, complemented
7#104×C97C211yesmaximal, characteristic, complemented
8#13095511—21no—
9#13095511C2211yescharacteristic
10#13095510—21no—
11#13095510—22no—
12C2×Dic194—21no—
13C2×Dic194C2211yescharacteristic
14Q8×D97—21no—
15C2×D388C2211yescharacteristic
16#13095500—21no—
17#13095498—21no—
18D776—21no—
19#13095496—21no—
20#13095495C2211yescharacteristic
21#13095488—22no—
22#41×C97C2211yescharacteristic
23M16×C97C2211yescharacteristic
24C42×C97C2211yescharacteristic
25C22×D97—21no—
26Q8×C97D411yescharacteristic
27D4×C97—21no—
28D4×C97D411yescharacteristic
29C2×C4×C97—21no—
30C2×C4×C97—21no—
31C2×C4×C97C2311yescharacteristic
32C22⋊D97—22no—
33C22⋊D97—21no—
34C2×Dic97—22no—
35C2×Dic97D412yes—
36D388—21no—
37D388—21no—
38D388D411yescharacteristic
39C4×D97—22no—
40C4×D97—21no—
41Dic194—22no—
42Dic194—21no—
43Dic194—21no—
44Dic194D411yescharacteristic
45C8×C97—21no—
46#11715895—21no—
47C22×C97—21no—
48C22×C97C2×D411yescharacteristic
49C2×D97—21no—
50C2×D97—42no—
51C2×D97—41no—
52C4×C97—21no—
53C4×C97—41no—
54C4×C97C2×D411yescharacteristic
55C4×C97C2×D411yescharacteristic
56Dic97—22no—
57Dic97—21no—
58C2×C97—21no—
59C2×C97—41no—
60C2×C97#12011yescharacteristic
61D97—41no—
62D97—81no—
63C97#45411yescharacteristic, complemented, Sylow
64#454—971nomaximal, Sylow
652−1+4—971no—
66AGL(1,ℤ/8)—971no—
67AGL(1,ℤ/8)—971no—
68#124—971no—
69#104—971no—
70#104D9711yescharacteristic, complemented
71#101—971no—
72#41—971no—
73#41—1941no—
74#41—1942no—
75#41—1941no—
76#41C2×D9711yescharacteristic
77C2×Q8—971no—
78C2×Q8—1941no—
79C2×Q8—1941no—
80C2×D4—971no—
81SD16—1941no—
82SD16—1941no—
83D8—1941no—
84D8—1941no—
85M16—971no—
86M16C2×D9711yescharacteristic
87C22⋊C4—1942no—
88C42C2×D9711yescharacteristic
89C23—1941no—
90Q8—971no—
91Q8—1942no—
92Q8—1941no—
93Q8—1941no—
94Q8D38811yescharacteristic
95D4—21no—
96D4—971no—
97D4—1942no—
98D4—1941no—
99D4—1941no—
100D4—1941no—
101D4D38811yescharacteristic
102C2×C4—21no—
103C2×C4—21no—
104C2×C4—972no—
105C2×C4—1942no—
106C2×C4—1942no—
107C2×C4—1941no—
108C2×C4C22×D9711yescharacteristic
109C8—21no—
110C8—1941no—
111C22—21no—
112C22—3882no—
113C22—3881no—
114C22—1941no—
115C22D4×D9711yescharacteristic
116C4—21no—
117C4—41no—
118C4—1942no—
119C4—1941no—
120C4D4×D9711yescharacteristic
121C4C2×D38811yescharacteristic
122C2—21no—
123C2—41no—
124C2—7761no—
125C2—3881no—
126C2#1569078011yescharacteristic
subgroupG/H
centerC2#15690780
commutatorC2×C4×C97C23
FrattiniC2×C4C22×D97
Fitting#104×C97C2
socleC2×C97#120
hypercenter#104D97
hypocenterC97#454
LCSG ▷ C2×C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
1. #15690857C2semidirect
2. #15690838C2semidirect
3. #15690835C2semidirect
4. #15690798C2semidirect
5. #15690738C2semidirect
6. #15690728C2semidirect
7. #104×C97C2semidirect
63. C97#454semidirect
70. #104D97semidirect