Finite Group Databasebeta

← #28476556

Subgroups — #28476556

Order 15104.

156 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 25 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#21423722C211yesmaximal, characteristic
2#21422259C211yesmaximal, characteristic
3C59×#1408C211yesmaximal, characteristic
4#16837800C411yescharacteristic, complemented
5#16837774—21no—
6#16837748—21no—
7#16837195—21no—
8#16837123C411yescharacteristic, complemented
9C59×#493C2211yescharacteristic
10C59×#353—21no—
11C2×#11745670—42no—
12#14273727—21no—
13#14273659—41no—
14#14273648—42no—
15#14273642—41no—
16C4×C59⋊C8—21no—
17C2×D8×C59—41no—
18#127×C59D411yescharacteristic
19#127×C59D411yescharacteristic
20#99×C59—41no—
21C4×C8×C59C2×C411yescharacteristic
22C2×D4×C59—21no—
23C2×D4×C59—21no—
24C2×D4×C59—41no—
25C2×D4×C59—41no—
26C2×Dic118—41no—
27D8×C59—82no—
28C2×C8×C59—21no—
29C22⋊C4×C59—81no—
30C42×C59C22⋊C411yescharacteristic
31C22⋊Dic59—81no—
32#11745670—84no—
33C4⋊Dic59—41no—
34C4⋊Dic59—41no—
35C2×C59⋊C8—22no—
36C23×C59—41no—
37C23×C59—41no—
38D4×C59—81no—
39D4×C59—81no—
40D4×C59—82no—
41D4×C59—82no—
42C2×C4×C59—21no—
43C2×C4×C59—161no—
44C2×C4×C59#9911yescharacteristic
45C2×Dic59—81no—
46C2×Dic59—161no—
47Dic118—82no—
48C8×C59—22no—
49C59⋊C8—42no—
50#7533—591nomaximal, Sylow
51C22×C59—81no—
52C22×C59—81no—
53C22×C59—161no—
54C22×C59—161no—
55C22×C59#35311yescharacteristic
56C4×C59—22no—
57C4×C59—21no—
58C4×C59—321no—
59Dic59—161no—
60Dic59—321no—
61#1715—591no—
62#1408—591no—
63#1408D5911yescharacteristic
64C2×C59—21no—
65C2×C59—161no—
66C2×C59—161no—
67C2×C59#140911yescharacteristic
68#498—591no—
69#493C2×D5911yescharacteristic
70#492—1181no—
71#486—1181no—
72#353—21no—
73#353—1181no—
74#322—591no—
75C59#753311yescharacteristic, complemented, Sylow
76C2×SD16—2362no—
77C2×D8—41no—
78C4⋊Q8—1181no—
79#127D23611yescharacteristic
80#127C22⋊D5911yescharacteristic
81#106—2361no—
82#102—2362no—
83#99—41no—
84#99—2361no—
85C4×C8—1181no—
86C4×C8C4×D5911yescharacteristic
87C2×Q8—2361no—
88C2×D4—21no—
89C2×D4—21no—
90C2×D4—41no—
91C2×D4—41no—
92SD16—4724no—
93D8—82no—
94C2×C8—21no—
95C2×C8—1182no—
96C4⋊C4—2361no—
97C4⋊C4—2361no—
98C22⋊C4—81no—
99C22⋊C4—4721no—
100C42(C2×D59)⋊C411yescharacteristic
101C23—41no—
102C23—41no—
103Q8—4722no—
104D4—81no—
105D4—81no—
106D4—82no—
107D4—82no—
108C2×C4—21no—
109C2×C4—161no—
110C2×C4—9441no—
111C2×C4—4721no—
112C2×C4#1427364111yescharacteristic
113C8—22no—
114C8—2362no—
115C22—81no—
116C22—81no—
117C22—161no—
118C22—161no—
119C22#1683719411yescharacteristic
120C4—22no—
121C4—21no—
122C4—321no—
123C4—18881no—
124C4—9441no—
125C2—21no—
126C2—161no—
127C2—161no—
128C2#2142226011yescharacteristic
subgroupG/H
centerC2#21422260
commutatorC4×C8×C59C2×C4
Frattini#493C2×D59
FittingC59×#1408C2
socleC2×C59#1409
prime radical, cosocleC59×#493C22
hypercenter#1408D59
hypocenterC59#7533
LCSG ▷ C4×C8×C59 ▷ C42×C59 ▷ C2×C4×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #493 ◁ #1408

Complements

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

NH ≅ G/Ntype
4. #16837800C4semidirect
8. #16837123C4semidirect
75. C59#7533semidirect

Maximal subgroups

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

subgroupindex
#214237222
#214222592
C59×#14082
#753359