Finite Group Databasebeta

← D97⋊#330 #27157185

Subgroups — D97⋊#330 #27157185

Order 12416.

232 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 64 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#20261694C212yesmaximal
2#20261592C214yesmaximal, complemented
3#125×D97C211yesmaximal, characteristic
4C2×#13095519—22no—
5#15690865—22no—
6#15690865C2214yes—
7#15690802C411yescharacteristic
8#15690801C2212yes—
9#15690800—22no—
10C4⋊C4×D97—22no—
11C4⋊C4×D97C412yes—
12C42×D97C2211yescharacteristic
13#125×C97C411yescharacteristic
14#13095519—28no—
15C2×#11715897—24no—
16C2×C4×D97—22no—
17C2×C4×D97C2×C411yescharacteristic
18C2×C4×D97D412yes—
19C4⋊Dic97—22no—
20C4⋊Dic97C2×C412yes—
21#13095490—22no—
22#13095490—22no—
23#13095490—22no—
24C4×Dic97D412yes—
25C4×Dic97C2311yescharacteristic
26C4⋊C4×C97—22no—
27C4⋊C4×C97C2×C412yes—
28C42×C97C2×C411yescharacteristic
29C22×D97C22⋊C411yescharacteristic
30C2×C4×C97—22no—
31C2×C4×C97C22⋊C412yes—
32C2×C4×C97C22×C411yescharacteristic
33C2×Dic97—22no—
34C2×Dic97C22⋊C411yescharacteristic
35C2×Dic97C2×D412yes—
36C4×D97—22no—
37C4×D97—24no—
38C4×D97—44no—
39#11715897—28no—
40C22×C97C2×C22⋊C411yescharacteristic
41C2×D97#10112yes—
42C2×D97#10414yes—
43C4×C97—21no—
44C4×C97—22no—
45C4×C97—42no—
46Dic97—21no—
47Dic97—22no—
48Dic97—42no—
49C2×C97C2×#10111yescharacteristic
50C2×C97C2×#10412yes—
51D97#33014yescomplemented
52C2×#330—971nomaximal, Sylow
53C97C2×#33011yescharacteristic, complemented, Sylow
54C2×#125—971no—
55C2×#97—972no—
56#330—974no—
57C22×C8—1942no—
58#125—972no—
59#125—971no—
60#125—1942no—
61#125#8760411yescharacteristic
62C2×C4⋊C4—972no—
63C2×C4⋊C4—1942no—
64C2×C42—971no—
65#97—974no—
66#97—1942no—
67C22×C4—972no—
68C22×C4—971no—
69C22×C4—1942no—
70C2×C8—1944no—
71C2×C8—1948no—
72C4⋊C4—22no—
73C4⋊C4—972no—
74C4⋊C4—1942no—
75C4⋊C4—1942no—
76C4⋊C4—1942no—
77C4⋊C4—1942no—
78C4⋊C4C2×#8760412yes—
79C42—972no—
80C42—971no—
81C42C2×#8760411yescharacteristic
82C23—971no—
83C2×C4—22no—
84C2×C4—972no—
85C2×C4—971no—
86C2×C4—3884no—
87C2×C4—1944no—
88C2×C4—1942no—
89C2×C4—1942no—
90C2×C4C22⋊#8760412yes—
91C2×C4C22×#8760411yescharacteristic
92C8—1948no—
93C22—972no—
94C22—974no—
95C22C2×C22⋊#8760411yescharacteristic
96C4—21no—
97C4—22no—
98C4—42no—
99C4—3882no—
100C4—1941no—
101C4—1942no—
102C2—974no—
103C2D97⋊#10111yescharacteristic
104C2D97⋊#10412yes—
subgroupG/H
centerC22C2×C22⋊#87604
commutatorC2×C4×C97C22×C4
FrattiniC2×C4C22×#87604
Fitting#125×C97C4
socleC22×C97C2×C22⋊C4
prime radicalC22×D97C22⋊C4
cosocleC4×Dic97C23
hypercenter#125#87604
hypocenterC97C2×#330
LCSG ▷ C2×C4×C97 ▷ C22×C97 ▷ C97
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
2. #20261592C2semidirect
51. D97#330semidirect
53. C97C2×#330semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202616942
#202615922
#125×D972
C2×#33097