Finite Group Databasebeta

← #28476562

Subgroups — #28476562

Order 15104.

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

normal subgroups only

This group has 150 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#21423682C211yesmaximal, characteristic
2#21422261C211yesmaximal, characteristic
3C59×#1410C211yesmaximal, characteristic
4#16837800C411yescharacteristic, complemented
5#16837798—21no—
6#16837774—21no—
7#16837195—21no—
8C8×C59⋊C8C411yescharacteristic, complemented
9C59×#492C2211yescharacteristic
10C59×#356—21no—
11C2×#11745670—42no—
12#14273727—21no—
13#14273659—41no—
14#14273658—42no—
15#14273642—41no—
16C4×C59⋊C8—21no—
17C2×SD16×C59—41no—
18C4⋊Q8×C59D411yescharacteristic
19#127×C59D411yescharacteristic
20#101×C59—41no—
21C4×C8×C59C2×C411yescharacteristic
22C2×Q8×C59—21no—
23C2×D4×C59—21no—
24C2×D4×C59—41no—
25C2×Dic118—41no—
26SD16×C59—82no—
27M16×C59—81no—
28C2×C8×C59—21no—
29C4⋊C4×C59—41no—
30C42×C59C22⋊C411yescharacteristic
31C22⋊Dic59—81no—
32#11745670—84no—
33C4⋊Dic59—41no—
34C4⋊Dic59—41no—
35C2×C59⋊C8—22no—
36C23×C59—41no—
37Q8×C59—81no—
38D4×C59—81no—
39D4×C59—82no—
40C2×C4×C59—21no—
41C2×C4×C59—41no—
42C2×C4×C59#9911yescharacteristic
43C2×Dic59—81no—
44C2×Dic59—161no—
45Dic118—82no—
46C8×C59—22no—
47C8×C59—161no—
48C59⋊C8—24no—
49#7535—591nomaximal, Sylow
50C22×C59—81no—
51C22×C59—161no—
52C22×C59#35311yescharacteristic
53C4×C59—22no—
54C4×C59—21no—
55C4×C59—81no—
56Dic59—161no—
57Dic59—321no—
58#1705—591no—
59#1410D5911yescharacteristic
60#1409—591no—
61C2×C59—21no—
62C2×C59—161no—
63C2×C59#140911yescharacteristic
64#498—591no—
65#498—1181no—
66#492—1181no—
67#492C2×D5911yescharacteristic
68#356—21no—
69#353—1181no—
70C82—591no—
71C59#753511yescharacteristic, complemented, Sylow
72C2×SD16—41no—
73C2×SD16—2362no—
74C4⋊Q8—1181no—
75C4⋊Q8C22⋊D5911yescharacteristic
76#127D23611yescharacteristic
77#106—2362no—
78#106—2361no—
79#101—41no—
80#99—2361no—
81C4×C8—1181no—
82C4×C8C4×D5911yescharacteristic
83C2×Q8—21no—
84C2×Q8—2361no—
85C2×D4—21no—
86C2×D4—41no—
87SD16—82no—
88SD16—4724no—
89M16—81no—
90C2×C8—21no—
91C2×C8—1182no—
92C4⋊C4—41no—
93C4⋊C4—2361no—
94C4⋊C4—2361no—
95C22⋊C4—4721no—
96C42(C2×D59)⋊C411yescharacteristic
97C23—41no—
98Q8—81no—
99Q8—4722no—
100D4—81no—
101D4—82no—
102C2×C4—21no—
103C2×C4—41no—
104C2×C4—9441no—
105C2×C4—4721no—
106C2×C4#1427364111yescharacteristic
107C8—22no—
108C8—161no—
109C8—1184no—
110C22—81no—
111C22—161no—
112C22#1683719411yescharacteristic
113C4—22no—
114C4—21no—
115C4—81no—
116C4—18881no—
117C4—9441no—
118C2—21no—
119C2—161no—
120C2#2142226011yescharacteristic
subgroupG/H
centerC2#21422260
commutatorC4×C8×C59C2×C4
Frattini#492C2×D59
FittingC59×#1410C2
socleC2×C59#1409
prime radical#127×C59D4
cosocleC59×#492C22
hypercenter#1410D59
hypocenterC59#7535
LCSG ▷ C4×C8×C59 ▷ C42×C59 ▷ C2×C4×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #492 ◁ #1410

Complements

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

NH ≅ G/Ntype
4. #16837800C4semidirect
8. C8×C59⋊C8C4semidirect
71. C59#7535semidirect

Maximal subgroups

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

subgroupindex
#214236822
#214222612
C59×#14102
#753559