Finite Group Databasebeta

← #20268060

Subgroups — #20268060

Order 6592.

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

normal subgroups only

This group has 108 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#15693049C211yesmaximal, characteristic, complemented
2#15693047C211yesmaximal, characteristic, complemented
3C2×#13110090C211yesmaximal, characteristic, complemented
4#15693029C211yesmaximal, characteristic, complemented
5#15692956C211yesmaximal, characteristic, complemented
6#15692937C211yesmaximal, characteristic, complemented
7#100×C103C211yesmaximal, characteristic, complemented
8#13110105C2211yescharacteristic
9C2×D412C2211yescharacteristic
10#13110094—21no—
11#13110093—21no—
12D824—21no—
13#13110090—21no—
14#13110090—21no—
15#13110090—21no—
16#13110089C2211yescharacteristic
17#13110088—21no—
18C2×C103⋊C8C2211yescharacteristic
19C8×D103—21no—
20C2×D4×C103C2211yescharacteristic
21M16×C103C2211yescharacteristic
22M16×C103C2211yescharacteristic
23C23×C103—21no—
24C22×D103—21no—
25D4×C103—21no—
26D4×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—41no—
40C22×C103—81no—
41C22×C103#4111yescharacteristic
42C2×D103—21no—
43C2×D103—41no—
44C2×D103—81no—
45C4×C103C2×D411yescharacteristic
46C4×C103C2×D411yescharacteristic
47Dic103—21no—
48C2×C103—21no—
49C2×C103—81no—
50C2×C103#12111yescharacteristic
51D103—41no—
52D103—81no—
53C103#47211yescharacteristic, complemented, Sylow
54#472—1031nomaximal, Sylow
55AGL(1,ℤ/8)—1031no—
56AGL(1,ℤ/8)—1031no—
57C2×D8—1031no—
58#131—1031no—
59#108—1031no—
60#100—1031no—
61#100D10311yescharacteristic, complemented
62#41—1031no—
63C2×D4—1031no—
64C2×D4C2×D10311yescharacteristic
65SD16—2061no—
66SD16—2061no—
67D8—2061no—
68D8—2061no—
69D8—2061no—
70D8—2061no—
71M16—1031no—
72M16—2061no—
73M16C2×D10311yescharacteristic
74M16C2×D10311yescharacteristic
75C2×C8—1031no—
76C2×C8—2061no—
77C23—21no—
78C23—2061no—
79Q8—1031no—
80D4—21no—
81D4—21no—
82D4—1031no—
83D4—2061no—
84D4—2061no—
85D4—2061no—
86C2×C4—2061no—
87C2×C4C22×D10311yescharacteristic
88C8—21no—
89C8—21no—
90C8—1031no—
91C8—1031no—
92C8—2061no—
93C22—41no—
94C22—81no—
95C22—8241no—
96C22—4121no—
97C22—2061no—
98C22#1311010511yescharacteristic
99C4—2061no—
100C4D4×D10311yescharacteristic
101C4D4×D10311yescharacteristic
102C2—21no—
103C2—81no—
104C2—8241no—
105C2—4121no—
106C2#1569299411yescharacteristic
subgroupG/H
centerC2#15692994
commutatorC2×C4×C103C23
FrattiniC2×C4C22×D103
Fitting#100×C103C2
socleC2×C103#121
hypercenter#100D103
hypocenterC103#472
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C2×C4 ◁ #100

Complements

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

NH ≅ G/Ntype
1. #15693049C2semidirect
2. #15693047C2semidirect
3. C2×#13110090C2semidirect
4. #15693029C2semidirect
5. #15692956C2semidirect
6. #15692937C2semidirect
7. #100×C103C2semidirect
53. C103#472semidirect
61. #100D103semidirect