Finite Group Databasebeta

← #39909264

Subgroups — #39909264

Order 26176.

154 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 67 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×#20266972C211yesmaximal, characteristic, complemented
2#27189676C211yesmaximal, characteristic, complemented
3#27189644C214yesmaximal, complemented
4C2×#41×C409C211yesmaximal, characteristic
5#20266972—21no—
6#20266972C2212yescomplemented
7C2×#15692543—21no—
8C4⋊Dic409—21no—
9C22⋊Dic409—21no—
10C4×Dic409C2212yescomplemented
11#41×C409—21no—
12#41×C409—21no—
13#41×C409C412yescomplemented
14#41×C409C2212yes—
15C2×Q8×C409C411yescharacteristic, complemented
16C2×D4×C409—21no—
17C2×D4×C409C411yescharacteristic, complemented
18C22×C4×C409—21no—
19C22×C4×C409C2211yescharacteristic
20C2×Dic409—22no—
21#15692543—22no—
22C23×C409—21no—
23C23×C409D411yescharacteristic
24Q8×C409—21no—
25Q8×C409C2×C412yes—
26D4×C409—22no—
27D4×C409—22no—
28D4×C409—21no—
29D4×C409C2×C412yes—
30C2×C4×C409—21no—
31C2×C4×C409—22no—
32C2×C4×C409—22no—
33C2×C4×C409C2×C411yescharacteristic
34C2×C4×C409C2×C411yescharacteristic
35C2×C4×C409D411yescharacteristic
36C2×C4×C409D411yescharacteristic
37C2×C4×C409D411yescharacteristic
38C2×C4×C409C2311yescharacteristic
39C22×C409—22no—
40C22×C409—41no—
41C22×C409—42no—
42C22×C409C22⋊C411yescharacteristic
43C22×C409C22⋊C411yescharacteristic
44C22×C409C2×D411yescharacteristic
45C4×C409—22no—
46C4×C409C22⋊C411yescharacteristic
47C4×C409C22⋊C411yescharacteristic
48C4×C409C22×C411yescharacteristic
49C4×C409C2×D411yescharacteristic
50Dic409—42no—
51C2×C409—21no—
52C2×C409—21no—
53C2×C409—21no—
54C2×C409—42no—
55C2×C409C2×C22⋊C411yescharacteristic
56C409#42111yescharacteristic, complemented, Sylow
57#421—4091nomaximal, Sylow
58C2×#41D40911yescharacteristic
59C2×M16—4091no—
60#117—4091no—
61#104—4094no—
62#41—21no—
63#41—21no—
64#41Dic40912yescomplemented
65#41C2×D40912yes—
66C2×Q8Dic40911yescharacteristic, complemented
67C2×D4—21no—
68C2×D4Dic40911yescharacteristic, complemented
69C22×C4—21no—
70C22×C4C2×D40911yescharacteristic
71M16—8181no—
72M16—4092no—
73C2×C8—8181no—
74C4⋊C4—8181no—
75C22⋊C4—8181no—
76C42—4092no—
77C23—21no—
78C23C22⋊D40911yescharacteristic
79Q8—21no—
80Q8C2×Dic40912yes—
81D4—22no—
82D4—22no—
83D4—21no—
84D4C2×Dic40912yes—
85C2×C4—21no—
86C2×C4—22no—
87C2×C4—22no—
88C2×C4—8182no—
89C2×C4C2×Dic40911yescharacteristic
90C2×C4C2×Dic40911yescharacteristic
91C2×C4C22⋊D40911yescharacteristic
92C2×C4C22⋊D40911yescharacteristic
93C2×C4C22⋊D40911yescharacteristic
94C2×C4C22×D40911yescharacteristic
95C8—8182no—
96C22—22no—
97C22—41no—
98C22—42no—
99C22C22⋊Dic40911yescharacteristic
100C22C22⋊Dic40911yescharacteristic
101C22C2×C22⋊D40911yescharacteristic
102C4—22no—
103C4—16362no—
104C4C22⋊Dic40911yescharacteristic
105C4C22⋊Dic40911yescharacteristic
106C4C22×Dic40911yescharacteristic
107C4C2×C22⋊D40911yescharacteristic
108C2—21no—
109C2—21no—
110C2—21no—
111C2—42no—
112C2C2×C22⋊Dic40911yescharacteristic
subgroupG/H
centerC4C2×C22⋊D409
commutatorC4×C409C22×C4
FrattiniC2×C4C22×D409
Fitting, prime radicalC2×#41×C409C2
socleC2×C409C2×C22⋊C4
cosocleC2×C4×C409C23
hypercenterC2×#41D409
hypocenterC409#421
LCSG ▷ C4×C409 ▷ C2×C409 ▷ C409
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#20266972C2semidirect
2. #27189676C2semidirect
3. #27189644C2semidirect
6. #20266972C22semidirect
10. C4×Dic409C22semidirect
13. #41×C409C4semidirect
15. C2×Q8×C409C4semidirect
17. C2×D4×C409C4semidirect
56. C409#421semidirect
64. #41Dic409semidirect
66. C2×Q8Dic409semidirect
68. C2×D4Dic409semidirect

Maximal subgroups

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

subgroupindex
C2×#202669722
#271896762
#271896442
C2×#41×C4092
#421409