Finite Group Databasebeta

← #20260916

Subgroups — #20260916

Order 6208.

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

normal subgroups only

This group has 142 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
2#15690841C211yesmaximal, characteristic, complemented
3#15690808C211yesmaximal, characteristic, complemented
4#15690737C211yesmaximal, characteristic, complemented
5#15690736C211yesmaximal, characteristic, complemented
6#15690728C211yesmaximal, characteristic, complemented
7#137×C97C211yesmaximal, characteristic, complemented
8#13095511—21no—
9#13095511C2211yescharacteristic
10#13095510—21no—
11#13095510—22no—
12C2×Dic194—21no—
13C2×Dic194C2211yescharacteristic
14Q8×D97—21no—
15#13095501—21no—
16#13095498—21no—
17#13095495C2211yescharacteristic
18#13095490—22no—
19C4×Dic97C2211yescharacteristic
20#41×C97C2211yescharacteristic
21C2×Q8×C97C2211yescharacteristic
22Q16×C97—21no—
23SD16×C97—21no—
24M16×C97C2211yescharacteristic
25Q8×C97—21no—
26Q8×C97—21no—
27Q8×C97D411yescharacteristic
28D4×C97—21no—
29D4×C97D411yescharacteristic
30C2×C4×C97—21no—
31C2×C4×C97—21no—
32C2×C4×C97C2311yescharacteristic
33C22⋊D97—22no—
34C22⋊D97—21no—
35C2×Dic97—22no—
36C2×Dic97—21no—
37C2×Dic97D412yes—
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—
50C4×C97—21no—
51C4×C97—41no—
52C4×C97C2×D411yescharacteristic
53C4×C97C2×D411yescharacteristic
54Dic97—22no—
55Dic97—22no—
56Dic97—21no—
57C2×C97—21no—
58C2×C97—41no—
59C2×C97#12011yescharacteristic
60D97—41no—
61C97#45611yescharacteristic, complemented, Sylow
62#456—971nomaximal, Sylow
632−1+4—971no—
64#137—971no—
65#137D9711yescharacteristic, complemented
66C4⋊Q8—971no—
67#104—971no—
68#104—971no—
69#101—971no—
70#41—971no—
71#41—1941no—
72#41—1942no—
73#41—1941no—
74#41C2×D9711yescharacteristic
75C2×Q8—971no—
76C2×Q8—1941no—
77C2×Q8—1941no—
78C2×Q8C2×D9711yescharacteristic
79Q16—21no—
80Q16—1941no—
81SD16—21no—
82SD16—1941no—
83M16—971no—
84M16C2×D9711yescharacteristic
85C4⋊C4—1942no—
86C42—971no—
87Q8—21no—
88Q8—21no—
89Q8—971no—
90Q8—1942no—
91Q8—1941no—
92Q8—1941no—
93Q8C22⋊D9711yescharacteristic
94D4—21no—
95D4—971no—
96D4—1942no—
97D4—1941no—
98D4C22⋊D9711yescharacteristic
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—972no—
102C2×C4—1942no—
103C2×C4—1942no—
104C2×C4—1941no—
105C2×C4—1941no—
106C2×C4C22×D9711yescharacteristic
107C8—21no—
108C8—1941no—
109C22—21no—
110C22—1941no—
111C22D4×D9711yescharacteristic
112C4—21no—
113C4—41no—
114C4—1942no—
115C4—1942no—
116C4—1941no—
117C4D4×D9711yescharacteristic
118C4C2×C22⋊D9711yescharacteristic
119C2—21no—
120C2—41no—
121C2—3881no—
122C2#1569077811yescharacteristic
subgroupG/H
centerC2#15690778
commutatorC2×C4×C97C23
FrattiniC2×C4C22×D97
Fitting#137×C97C2
socleC2×C97#120
hypercenter#137D97
hypocenterC97#456
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. #15690808C2semidirect
4. #15690737C2semidirect
5. #15690736C2semidirect
6. #15690728C2semidirect
7. #137×C97C2semidirect
61. C97#456semidirect
65. #137D97semidirect