Finite Group Databasebeta

← #21425992

Subgroups — #21425992

Order 7552.

154 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 53 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#16837838C211yesmaximal, characteristic
2#16837525C211yesmaximal, characteristic, complemented
3#16837224C211yesmaximal, characteristic, complemented
4#16837215C211yesmaximal, characteristic, complemented
5#16837211C211yesmaximal, characteristic, complemented
6#16837180C211yesmaximal, characteristic, complemented
7C59×#442C211yesmaximal, characteristic, complemented
8#14273749C2211yescharacteristic
9#14273733—21no—
10#14273671C412yescomplemented
11#14273668C412yescomplemented
12#14273667C2211yescharacteristic
13#14273667C2211yescharacteristic
14#14273663C2211yescharacteristic
15#14273655—21no—
16C2×D8×C59C2211yescharacteristic
17C4×D4×C59—21no—
18#106×C59C2211yescharacteristic
19#102×C59—21no—
20#97×C59C2211yescharacteristic
21C2×D4×C59—21no—
22C22×C4×C59—41no—
23#11745685—21no—
24D8×C59—21no—
25D8×C59C2×C412yes—
26C2×C8×C59D411yescharacteristic
27C2×C8×C59C2311yescharacteristic
28C4⋊C4×C59—21no—
29C22⋊C4×C59—41no—
30C42×C59D411yescharacteristic
31#11745664—21no—
32Dic236C2×C411yescharacteristic, complemented
33D472C2×C411yescharacteristic, complemented
34#11745660—21no—
35#11745659—41no—
36C8×D59—41no—
37C59⋊C16—21no—
38C59⋊C16C2×C412yescomplemented
39C23×C59—41no—
40D4×C59—22no—
41D4×C59—41no—
42C2×C4×C59—21no—
43C2×C4×C59—41no—
44C2×C4×C59—82no—
45C2×C4×C59C2×D411yescharacteristic
46C22⋊D59—41no—
47D236—21no—
48C4×D59—41no—
49Dic118—21no—
50C8×C59—21no—
51C8×C59C22×C411yescharacteristic
52C8×C59#4111yescharacteristic
53C59⋊C8—41no—
54C22×C59—42no—
55C22×C59—81no—
56C22×C59—81no—
57C22×C59AGL(1,ℤ/8)11yescharacteristic
58C2×D59—41no—
59C4×C59—41no—
60C4×C59—81no—
61C4×C59C4×D411yescharacteristic
62C4×C59AGL(1,ℤ/8)11yescharacteristic
63Dic59—41no—
64AGL(1,ℤ/16)—591nomaximal, Sylow
65C2×C59—21no—
66C2×C59—82no—
67C2×C59#44211yescharacteristic
68D59—81no—
69#509—591no—
70#444—591no—
71#442D5911yescharacteristic, complemented
72#365—591no—
73#361—591no—
74#360—591no—
75#347—591no—
76C59AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
77#135—591no—
78C2×D8C2×D5911yescharacteristic
79#131—1181no—
80C4×D4—21no—
81SD32—592no—
82D16—592no—
83M32—591no—
84M32—591no—
85#108—591no—
86#106C2×D5911yescharacteristic
87#104—1181no—
88#102—21no—
89#97C2×D5911yescharacteristic
90#41—1181no—
91C2×D4—21no—
92C22×C4—41no—
93Q16—591no—
94SD16—1181no—
95D8—21no—
96D8—591no—
97D8C4×D5912yes—
98M16—1181no—
99M16—2361no—
100C2×C8—2361no—
101C2×C8C22⋊D5911yescharacteristic
102C2×C8C22×D5911yescharacteristic
103C4⋊C4—21no—
104C22⋊C4—41no—
105C42C22⋊D5911yescharacteristic
106C16—592no—
107C16—1181no—
108C23—41no—
109Q8—1181no—
110D4—22no—
111D4—41no—
112D4—1181no—
113D4—2361no—
114C2×C4—21no—
115C2×C4—41no—
116C2×C4—82no—
117C2×C4—2361no—
118C2×C4C2×C22⋊D5911yescharacteristic
119C8—21no—
120C8—2361no—
121C8C2×C4×D5911yescharacteristic
122C8#1174568511yescharacteristic
123C22—42no—
124C22—81no—
125C22—81no—
126C22—2361no—
127C22#1427375311yescharacteristic
128C4—41no—
129C4—81no—
130C4—2361no—
131C4C4×C22⋊D5911yescharacteristic
132C4#1427375211yescharacteristic
133C2—21no—
134C2—82no—
135C2—4721no—
136C2#1683751211yescharacteristic
subgroupG/H
centerC2#16837512
commutatorC8×C59C22×C4
FrattiniC2×C8C22×D59
FittingC59×#442C2
socleC2×C59#442
hypercenter#442D59
hypocenterC59AGL(1,ℤ/16)
LCSG ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #442

Complements

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

NH ≅ G/Ntype
2. #16837525C2semidirect
3. #16837224C2semidirect
4. #16837215C2semidirect
5. #16837211C2semidirect
6. #16837180C2semidirect
7. C59×#442C2semidirect
10. #14273671C4semidirect
11. #14273668C4semidirect
32. Dic236C2×C4semidirect
33. D472C2×C4semidirect
38. C59⋊C16C2×C4semidirect
71. #442D59semidirect
76. C59AGL(1,ℤ/16)semidirect