Finite Group Databasebeta

← #14580497

Subgroups — #14580497

Order 2624.

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×#10620310C211yesmaximal, characteristic
2C2×#10620284C211yesmaximal, characteristic, complemented
3#13050140C211yesmaximal, characteristic, complemented
4#13050088C211yesmaximal, characteristic, complemented
5#13050086C211yesmaximal, characteristic, complemented
6#13050076C211yesmaximal, characteristic, complemented
7C2×Q16×C41C211yesmaximal, characteristic, complemented
8C2×Q8×C41C2211yescharacteristic
9C2×Q8×C41C2211yescharacteristic
10#10620310—22no—
11#10620310—22no—
12C2×D164—21no—
13C2×D164C2211yescharacteristic
14C2×C4×D41—21no—
15C2×C4×D41C2211yescharacteristic
16Q16×C41—22no—
17C2×C8×C41C2211yescharacteristic
18#10620284—22no—
19#10620281—21no—
20C4⋊Dic41C2211yescharacteristic
21#10620279—21no—
22C2×#66491C2211yescharacteristic
23C22×D41—21no—
24C22×D41D411yescharacteristic
25Q8×C41—21no—
26Q8×C41—21no—
27Q8×C41—21no—
28Q8×C41D412yes—
29C2×C4×C41—21no—
30C2×C4×C41—21no—
31C2×C4×C41C2311yescharacteristic
32C2×Dic41—21no—
33C2×Dic41D411yescharacteristic
34D164—24no—
35D164—21no—
36D164D412yes—
37C4×D41—24no—
38C4×D41—21no—
39C4×D41—21no—
40C8×C41—21no—
41#66491—21no—
42C22×C41C2×D411yescharacteristic
43C2×D41—21no—
44C2×D41—22no—
45C2×D41—21no—
46C2×D41—21no—
47C2×D41—41no—
48C2×D41—41no—
49C4×C41—22no—
50C4×C41—41no—
51C4×C41C2×D411yescharacteristic
52C4×C41C2×D411yescharacteristic
53Dic41—21no—
54Dic41—41no—
55C2×C41#12011yescharacteristic
56C2×C41#13511yescharacteristic
57C2×C41#13711yescharacteristic
58D41—41no—
59D41—42no—
60#452—411nomaximal, Sylow
61C41#45211yescharacteristic, complemented, Sylow
62C2×#41—411no—
63C2×Q16D4111yescharacteristic, complemented
64C2×SD16—411no—
65C22⋊Q8—411no—
66#103—411no—
67#102—411no—
68C22⋊C8—411no—
69#41—822no—
70#41—822no—
71C2×Q8C2×D4111yescharacteristic
72C2×Q8C2×D4111yescharacteristic
73C2×D4—411no—
74C2×D4—821no—
75C22×C4—411no—
76C22×C4—821no—
77Q16—22no—
78SD16—822no—
79C2×C8—411no—
80C2×C8C2×D4111yescharacteristic
81C4⋊C4—411no—
82C4⋊C4—821no—
83C22⋊C4—821no—
84C23—411no—
85C23—821no—
86Q8—21no—
87Q8—21no—
88Q8—21no—
89Q8C22⋊D4112yes—
90D4—412no—
91D4—824no—
92D4—821no—
93C2×C4—21no—
94C2×C4—21no—
95C2×C4—411no—
96C2×C4—824no—
97C2×C4—821no—
98C2×C4—821no—
99C2×C4—821no—
100C2×C4C22×D4111yescharacteristic
101C8—21no—
102C8—821no—
103C22—822no—
104C22—821no—
105C22—821no—
106C22—821no—
107C22—1641no—
108C22—1641no—
109C22D4×D4111yescharacteristic
110C4—22no—
111C4—41no—
112C4—821no—
113C4—1641no—
114C4D4×D4111yescharacteristic
115C4C2×C22⋊D4111yescharacteristic
116C2—1641no—
117C2—1642no—
118C2#1305013211yescharacteristic
119C2#1305018711yescharacteristic
120C2#1305019611yescharacteristic
subgroupG/H
centerC22D4×D41
commutator, cosocleC2×C4×C41C23
FrattiniC2×C4C22×D41
FittingC2×Q16×C41C2
socleC22×C41C2×D4
prime radicalC2×#10620310C2
hypercenterC2×Q16D41
hypocenterC41#452
LCSG ▷ C2×C4×C41 ▷ C2×C41 ▷ C41
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
2. C2×#10620284C2semidirect
3. #13050140C2semidirect
4. #13050088C2semidirect
5. #13050086C2semidirect
6. #13050076C2semidirect
7. C2×Q16×C41C2semidirect
61. C41#452semidirect
63. C2×Q16D41semidirect

Maximal subgroups

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

subgroupindex
C2×#106203102
C2×#106202842
#130501402
#130500882
#130500862
#130500762
C2×Q16×C412
#45241