Finite Group Databasebeta

← #39909431

Subgroups — #39909431

Order 26176.

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#27189764C211yesmaximal, characteristic
2#27189750C211yesmaximal, characteristic, complemented
3#27189747C211yesmaximal, characteristic, complemented
4#27189717C211yesmaximal, characteristic, complemented
5#27189645C211yesmaximal, characteristic, complemented
6#27189635C211yesmaximal, characteristic, complemented
7#104×C409C211yesmaximal, characteristic, complemented
8#20266988—21no—
9#20266988C2211yescharacteristic
10#20266987—21no—
11#20266987—22no—
12C2×Dic818—21no—
13C2×Dic818C2211yescharacteristic
14C2×Dic818C2211yescharacteristic
15Q8×D409—21no—
16Dic1636—21no—
17#20266978—21no—
18#20266977—21no—
19#20266976—21no—
20#20266972C2211yescharacteristic
21C4⋊Dic409—22no—
22#41×C409C2211yescharacteristic
23M16×C409C2211yescharacteristic
24C42×C409C2211yescharacteristic
25Dic818—22no—
26Dic818—21no—
27Dic818—21no—
28Dic818—21no—
29Dic818—21no—
30Dic818D411yescharacteristic
31D1636D411yescharacteristic
32C22⋊D409—22no—
33C22⋊D409—21no—
34C2×Dic409—22no—
35C2×Dic409—21no—
36C2×Dic409D412yes—
37C4×D409—22no—
38C4×D409—21no—
39#15692543—21no—
40Q8×C409D411yescharacteristic
41D4×C409—21no—
42D4×C409D411yescharacteristic
43C2×C4×C409—21no—
44C2×C4×C409—21no—
45C2×C4×C409C2311yescharacteristic
46C8×C409—21no—
47C22×C409—21no—
48C22×C409C2×D411yescharacteristic
49C2×D409—21no—
50C4×C409—22no—
51C4×C409—21no—
52C4×C409C2×D411yescharacteristic
53C4×C409C2×D411yescharacteristic
54Dic409—21no—
55Dic409—22no—
56Dic409—41no—
57C2×C409—21no—
58C2×C409—41no—
59C2×C409#12011yescharacteristic
60D409—41no—
61C409#45611yescharacteristic, complemented, Sylow
62#456—4091nomaximal, Sylow
632−1+4—4091no—
64#137—4091no—
65#137—4091no—
66C4⋊Q8—4091no—
67#104—4091no—
68#104D40911yescharacteristic, complemented
69#101—4091no—
70#41—8181no—
71#41—8181no—
72#41—8182no—
73#41—4091no—
74#41C2×D40911yescharacteristic
75C2×Q8—8181no—
76C2×Q8—8181no—
77C2×Q8—4091no—
78C2×Q8—4091no—
79Q16—8181no—
80Q16—8181no—
81SD16—8181no—
82SD16—8181no—
83M16—4091no—
84M16C2×D40911yescharacteristic
85C4⋊C4—8182no—
86C42C2×D40911yescharacteristic
87Q8—8182no—
88Q8—8181no—
89Q8—8181no—
90Q8—8181no—
91Q8—8181no—
92Q8—4091no—
93Q8D163611yescharacteristic
94D4—21no—
95D4—8182no—
96D4—8181no—
97D4—4091no—
98D4D163611yescharacteristic
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—8182no—
102C2×C4—8182no—
103C2×C4—8181no—
104C2×C4—8181no—
105C2×C4—4092no—
106C2×C4C22×D40911yescharacteristic
107C8—21no—
108C8—8181no—
109C22—21no—
110C22—8181no—
111C22D4×D40911yescharacteristic
112C4—22no—
113C4—21no—
114C4—8181no—
115C4—8182no—
116C4—16361no—
117C4D4×D40911yescharacteristic
118C4C2×D163611yescharacteristic
119C2—21no—
120C2—41no—
121C2—16361no—
122C2#2718968711yescharacteristic
subgroupG/H
centerC2#27189687
commutator, cosocleC2×C4×C409C23
FrattiniC2×C4C22×D409
Fitting#104×C409C2
socleC2×C409#120
prime radical#27189764C2
hypercenter#104D409
hypocenterC409#456
LCSG ▷ C2×C4×C409 ▷ C2×C409 ▷ C409
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #27189750C2semidirect
3. #27189747C2semidirect
4. #27189717C2semidirect
5. #27189645C2semidirect
6. #27189635C2semidirect
7. #104×C409C2semidirect
61. C409#456semidirect
68. #104D409semidirect

Maximal subgroups

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

subgroupindex
#271897642
#271897502
#271897472
#271897172
#271896452
#271896352
#104×C4092
#456409