Finite Group Databasebeta

← #20268057

Subgroups — #20268057

Order 6592.

104 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 35 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#15693052C211yesmaximal, characteristic, complemented
2#15693049C211yesmaximal, characteristic
3C2×#13110092C211yesmaximal, characteristic, complemented
4#15693029C211yesmaximal, characteristic, complemented
5#15692956C211yesmaximal, characteristic, complemented
6#15692937C211yesmaximal, characteristic, complemented
7#101×C103C211yesmaximal, characteristic, complemented
8#13110105C2211yescharacteristic
9C2×D412C2211yescharacteristic
10#13110095—21no—
11#13110094—21no—
12#13110092—21no—
13#13110092—21no—
14#13110092—21no—
15D824—21no—
16#13110089C2211yescharacteristic
17#13110088—21no—
18C2×C103⋊C8C2211yescharacteristic
19C8×D103—21no—
20C2×Q8×C103C2211yescharacteristic
21M16×C103C2211yescharacteristic
22M16×C103C2211yescharacteristic
23C22×D103—21no—
24Q8×C103—21no—
25Q8×C103—21no—
26C2×C4×C103—21no—
27C2×C4×C103C2311yescharacteristic
28C22⋊D103—21no—
29D412—21no—
30D412—21no—
31D412D411yescharacteristic
32C4×D103—21no—
33Dic206D411yescharacteristic
34C8×C103—21no—
35C8×C103—21no—
36C103⋊C8—21no—
37C103⋊C8D411yescharacteristic
38C103⋊C8D411yescharacteristic
39C22×C103#4111yescharacteristic
40C2×D103—21no—
41C2×D103—41no—
42C2×D103—81no—
43C4×C103—41no—
44C4×C103C2×D411yescharacteristic
45C4×C103C2×D411yescharacteristic
46Dic103—21no—
47C2×C103—21no—
48C2×C103#12111yescharacteristic
49D103—41no—
50D103—81no—
51C103#47111yescharacteristic, complemented, Sylow
52#471—1031nomaximal, Sylow
53#137—1031no—
54AGL(1,ℤ/8)—1031no—
55C2×SD16—1031no—
56#131—1031no—
57#108—1031no—
58#101D10311yescharacteristic, complemented
59#100—1031no—
60#41—1031no—
61C2×Q8C2×D10311yescharacteristic
62C2×D4—1031no—
63Q16—2061no—
64SD16—2061no—
65SD16—2061no—
66SD16—2061no—
67SD16—2061no—
68D8—2061no—
69M16—1031no—
70M16—2061no—
71M16C2×D10311yescharacteristic
72M16C2×D10311yescharacteristic
73C2×C8—1031no—
74C2×C8—2061no—
75C23—2061no—
76Q8—21no—
77Q8—21no—
78Q8—1031no—
79D4—1031no—
80D4—2061no—
81D4—2061no—
82D4—2061no—
83C2×C4—21no—
84C2×C4—2061no—
85C2×C4C22×D10311yescharacteristic
86C8—21no—
87C8—21no—
88C8—1031no—
89C8—1031no—
90C8—2061no—
91C22—8241no—
92C22—4121no—
93C22—2061no—
94C22#1311010511yescharacteristic
95C4—41no—
96C4—2061no—
97C4D4×D10311yescharacteristic
98C4D4×D10311yescharacteristic
99C2—21no—
100C2—8241no—
101C2—4121no—
102C2#1569299411yescharacteristic
subgroupG/H
centerC2#15692994
commutatorC2×C4×C103C23
FrattiniC2×C4C22×D103
Fitting#101×C103C2
socleC2×C103#121
hypercenter#101D103
hypocenterC103#471
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C2×C4 ◁ #101

Complements

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

NH ≅ G/Ntype
1. #15693052C2semidirect
3. C2×#13110092C2semidirect
4. #15693029C2semidirect
5. #15692956C2semidirect
6. #15692937C2semidirect
7. #101×C103C2semidirect
51. C103#471semidirect
58. #101D103semidirect