Finite Group Databasebeta

← #39909510

Subgroups — #39909510

Order 26176.

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

normal subgroups only

This group has 104 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#27189747C211yesmaximal, characteristic, complemented
2#27189742C211yesmaximal, characteristic
3C2×#20266977C211yesmaximal, characteristic, complemented
4#27189653C211yesmaximal, characteristic, complemented
5#27189635C211yesmaximal, characteristic, complemented
6#27189633C211yesmaximal, characteristic, complemented
7#131×C409C211yesmaximal, characteristic, complemented
8C2×Dic818C2211yescharacteristic
9C2×D1636C2211yescharacteristic
10#20266978—21no—
11#20266977—21no—
12#20266977—21no—
13#20266976—21no—
14#20266975—21no—
15#20266973—21no—
16#20266972C2211yescharacteristic
17#20266972C2211yescharacteristic
18#41×C409C2211yescharacteristic
19M16×C409—21no—
20M16×C409C2211yescharacteristic
21C2×C8×C409—21no—
22C2×C8×C409C2211yescharacteristic
23C22×D409—21no—
24Dic818—21no—
25Dic818—21no—
26D1636—21no—
27D1636—21no—
28C2×Dic409—21no—
29#15692543—21no—
30#15692543—21no—
31Q8×C409D411yescharacteristic
32D4×C409—21no—
33D4×C409D411yescharacteristic
34C2×C4×C409—21no—
35C2×C4×C409C2311yescharacteristic
36C8×C409—21no—
37C8×C409D411yescharacteristic
38C8×C409D411yescharacteristic
39C22×C409—21no—
40C22×C409#4111yescharacteristic
41C2×D409—41no—
42C2×D409—81no—
43C4×C409—21no—
44C4×C409C2×D411yescharacteristic
45C4×C409C2×D411yescharacteristic
46Dic409—41no—
47C2×C409—21no—
48C2×C409—41no—
49C2×C409#12111yescharacteristic
50D409—81no—
51C409#47111yescharacteristic, complemented, Sylow
52#471—4091nomaximal, Sylow
53#137—4091no—
54AGL(1,ℤ/8)—4091no—
55C2×SD16—4091no—
56#131D40911yescharacteristic, complemented
57#108—4091no—
58#101—4091no—
59#100—4091no—
60#41C2×D40911yescharacteristic
61C2×Q8—4091no—
62C2×D4—4091no—
63Q16—8181no—
64SD16—8181no—
65SD16—8181no—
66SD16—8181no—
67SD16—8181no—
68D8—8181no—
69M16—21no—
70M16—4091no—
71M16—4091no—
72M16C2×D40911yescharacteristic
73C2×C8—21no—
74C2×C8C2×D40911yescharacteristic
75C23—8181no—
76Q8—8181no—
77Q8—8181no—
78Q8D163611yescharacteristic
79D4—21no—
80D4—8181no—
81D4—8181no—
82D4D163611yescharacteristic
83C2×C4—21no—
84C2×C4—8181no—
85C2×C4C22×D40911yescharacteristic
86C8—21no—
87C8—8181no—
88C8—8181no—
89C8C22⋊D40911yescharacteristic
90C8C22⋊D40911yescharacteristic
91C22—21no—
92C22—16361no—
93C22—32721no—
94C22#2026698811yescharacteristic
95C4—21no—
96C4—16361no—
97C4C2×C22⋊D40911yescharacteristic
98C4C2×D163611yescharacteristic
99C2—21no—
100C2—41no—
101C2—32721no—
102C2#2718969111yescharacteristic
subgroupG/H
centerC2#27189691
commutator, cosocleC2×C4×C409C23
FrattiniC2×C4C22×D409
Fitting#131×C409C2
socleC2×C409#121
prime radical#27189742C2
hypercenter#131D409
hypocenterC409#471
LCSG ▷ C2×C4×C409 ▷ C2×C409 ▷ C409
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131

Complements

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

NH ≅ G/Ntype
1. #27189747C2semidirect
3. C2×#20266977C2semidirect
4. #27189653C2semidirect
5. #27189635C2semidirect
6. #27189633C2semidirect
7. #131×C409C2semidirect
51. C409#471semidirect
56. #131D409semidirect

Maximal subgroups

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

subgroupindex
#271897472
#271897422
C2×#202669772
#271896532
#271896352
#271896332
#131×C4092
#471409