Finite Group Databasebeta

← #20260911

Subgroups — #20260911

Order 6208.

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

normal subgroups only

This group has 152 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#15690856C211yesmaximal, characteristic
2#15690841C211yesmaximal, characteristic, complemented
3#15690799C211yesmaximal, characteristic, complemented
4#15690737C211yesmaximal, characteristic, complemented
5#15690736C211yesmaximal, characteristic, complemented
6#15690726C211yesmaximal, characteristic, complemented
7#137×C97C211yesmaximal, characteristic, complemented
8#13095512—21no—
9#13095511—21no—
10#13095511C2211yescharacteristic
11C2×D388—21no—
12C2×D388C2211yescharacteristic
13D4×D97—22no—
14D4×D97—21no—
15#13095501—21no—
16#13095498—21no—
17#13095495C2211yescharacteristic, complemented
18#13095488—22no—
19C4×Dic97C2211yescharacteristic, complemented
20#41×C97C2211yescharacteristic
21C2×Q8×C97C2211yescharacteristic, complemented
22Q16×C97—21no—
23SD16×C97—21no—
24M16×C97C2211yescharacteristic, complemented
25C22×D97—22no—
26C22×D97D412yes—
27Q8×C97—21no—
28Q8×C97—21no—
29Q8×C97D411yescharacteristic
30D4×C97—21no—
31D4×C97D411yescharacteristic
32C2×C4×C97—21no—
33C2×C4×C97—21no—
34C2×C4×C97C2311yescharacteristic
35C22⋊D97—22no—
36C22⋊D97—21no—
37C2×Dic97—21no—
38D388—22no—
39D388—21no—
40D388—21no—
41D388D411yescharacteristic
42C4×D97—22no—
43C4×D97—21no—
44Dic194D411yescharacteristic
45C8×C97—21no—
46#11715895—21no—
47C22×C97—21no—
48C22×C97C2×D411yescharacteristic
49C2×D97—22no—
50C2×D97—21no—
51C2×D97—42no—
52C2×D97—82no—
53C4×C97—21no—
54C4×C97—41no—
55C4×C97C2×D411yescharacteristic
56C4×C97C2×D411yescharacteristic
57Dic97—21no—
58Dic97—41no—
59C2×C97—21no—
60C2×C97—41no—
61C2×C97#12011yescharacteristic
62D97—42no—
63D97—41no—
64C97#45511yescharacteristic, complemented, Sylow
65#455—971nomaximal, Sylow
66H(5,𝔽2)—971no—
67#137—971no—
68#137D9711yescharacteristic, complemented
69#124—971no—
70#104—971no—
71#104—971no—
72#100—971no—
73#41—971no—
74#41—1941no—
75#41—1941no—
76#41C2×D9711yescharacteristic
77C2×Q8C2×D9711yescharacteristic, complemented
78C2×D4—971no—
79C2×D4—1941no—
80C2×D4—1942no—
81C2×D4—1941no—
82Q16—21no—
83Q16—1941no—
84SD16—21no—
85SD16—1941no—
86M16—971no—
87M16C2×D9711yescharacteristic, complemented
88C22⋊C4—1942no—
89C42—971no—
90C23—972no—
91C23—1942no—
92Q8—21no—
93Q8—21no—
94Q8—971no—
95Q8C22⋊D9711yescharacteristic
96D4—21no—
97D4—971no—
98D4—1942no—
99D4—1942no—
100D4—1941no—
101D4—1941no—
102D4—1941no—
103D4C22⋊D9711yescharacteristic
104C2×C4—21no—
105C2×C4—21no—
106C2×C4—1942no—
107C2×C4—1941no—
108C2×C4—1941no—
109C2×C4C22×D9711yescharacteristic
110C8—21no—
111C8—1941no—
112C22—21no—
113C22—7762no—
114C22—3882no—
115C22—1941no—
116C22—1942no—
117C22D4×D9711yescharacteristic
118C4—21no—
119C4—41no—
120C4—3881no—
121C4—1941no—
122C4D4×D9711yescharacteristic
123C4C2×C22⋊D9711yescharacteristic
124C2—21no—
125C2—41no—
126C2—3881no—
127C2—3882no—
128C2#1569077811yescharacteristic
subgroupG/H
centerC2#15690778
commutatorC2×C4×C97C23
FrattiniC2×C4C22×D97
Fitting#137×C97C2
socleC2×C97#120
hypercenter#137D97
hypocenterC97#455
LCSG ▷ C2×C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
2. #15690841C2semidirect
3. #15690799C2semidirect
4. #15690737C2semidirect
5. #15690736C2semidirect
6. #15690726C2semidirect
7. #137×C97C2semidirect
17. #13095495C22semidirect
19. C4×Dic97C22semidirect
21. C2×Q8×C97C22semidirect
24. M16×C97C22semidirect
64. C97#455semidirect
68. #137D97semidirect
77. C2×Q8C2×D97semidirect
87. M16C2×D97semidirect