Finite Group Databasebeta

← #28476563

Subgroups — #28476563

Order 15104.

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

normal subgroups only

This group has 138 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#21423695C211yesmaximal, characteristic
2#21422263C211yesmaximal, characteristic
3C59×#1409C211yesmaximal, characteristic
4#16837800C411yescharacteristic, complemented
5#16837754—21no—
6#16837748—21no—
7#16837201—21no—
8C8×C59⋊C8C411yescharacteristic, complemented
9C59×#492C2211yescharacteristic
10C59×#353—21no—
11#14273727—21no—
12#14273659—41no—
13#14273650—42no—
14#14273648—42no—
15#14273646—41no—
16C4×C59⋊C8—21no—
17C2×SD16×C59—41no—
18C4⋊Q8×C59D411yescharacteristic
19#127×C59D411yescharacteristic
20#99×C59—41no—
21C4×C8×C59C2×C411yescharacteristic
22C2×Q8×C59—21no—
23C2×D4×C59—21no—
24C2×D4×C59—41no—
25C2×Dic118—41no—
26SD16×C59—82no—
27C2×C8×C59—21no—
28C4⋊C4×C59—41no—
29C22⋊C4×C59—81no—
30C42×C59C22⋊C411yescharacteristic
31C4⋊Dic59—41no—
32C4⋊Dic59—41no—
33#11745664—81no—
34C2×C59⋊C8—22no—
35C23×C59—41no—
36Q8×C59—81no—
37D4×C59—81no—
38D4×C59—82no—
39C2×C4×C59—21no—
40C2×C4×C59—41no—
41C2×C4×C59—161no—
42C2×C4×C59#9911yescharacteristic
43C2×Dic59—81no—
44Dic118—82no—
45C8×C59—22no—
46C59⋊C8—42no—
47C59⋊C8—161no—
48#7536—591nomaximal, Sylow
49C22×C59—81no—
50C22×C59—161no—
51C22×C59#35311yescharacteristic
52C4×C59—22no—
53C4×C59—21no—
54C4×C59—81no—
55C4×C59—321no—
56Dic59—161no—
57#1708—591no—
58#1410—591no—
59#1409D5911yescharacteristic
60C2×C59—21no—
61C2×C59—161no—
62C2×C59#140911yescharacteristic
63#498—591no—
64#492C2×D5911yescharacteristic
65#487—1181no—
66#486—1181no—
67#356—1181no—
68#353—21no—
69C82—591no—
70C59#753611yescharacteristic, complemented, Sylow
71C2×SD16—41no—
72C4⋊Q8—1181no—
73C4⋊Q8D23611yescharacteristic
74#127C22⋊D5911yescharacteristic
75#106—2361no—
76#103—2362no—
77#102—2362no—
78#101—2361no—
79#99—41no—
80C4×C8—1181no—
81C4×C8C4×D5911yescharacteristic
82C2×Q8—21no—
83C2×Q8—2361no—
84C2×D4—21no—
85C2×D4—41no—
86SD16—82no—
87M16—4721no—
88C2×C8—21no—
89C2×C8—1182no—
90C4⋊C4—41no—
91C4⋊C4—2361no—
92C4⋊C4—2361no—
93C22⋊C4—81no—
94C42(C2×D59)⋊C411yescharacteristic
95C23—41no—
96Q8—81no—
97Q8—4722no—
98D4—81no—
99D4—82no—
100C2×C4—21no—
101C2×C4—41no—
102C2×C4—161no—
103C2×C4—4721no—
104C2×C4#1427364111yescharacteristic
105C8—22no—
106C8—9441no—
107C8—2362no—
108C22—81no—
109C22—161no—
110C22#1683719411yescharacteristic
111C4—22no—
112C4—21no—
113C4—81no—
114C4—321no—
115C4—9441no—
116C2—21no—
117C2—161no—
118C2#2142226011yescharacteristic
subgroupG/H
centerC2#21422260
commutatorC4×C8×C59C2×C4
Frattini#492C2×D59
FittingC59×#1409C2
socleC2×C59#1409
prime radical#127×C59D4
cosocleC59×#492C22
hypercenter#1409D59
hypocenterC59#7536
LCSG ▷ C4×C8×C59 ▷ C42×C59 ▷ C2×C4×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #492 ◁ #1409

Complements

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

NH ≅ G/Ntype
4. #16837800C4semidirect
8. C8×C59⋊C8C4semidirect
70. C59#7536semidirect

Maximal subgroups

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

subgroupindex
#214236952
#214222632
C59×#14092
#753659