Finite Group Databasebeta

← #28476536

Subgroups — #28476536

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#21423417C211yesmaximal, characteristic
2#21422269C211yesmaximal, characteristic, complemented
3C59×#1356C211yesmaximal, characteristic, complemented
4#16838150C411yescharacteristic
5#16837764—21no—
6#16837201—21no—
7#16837144C411yescharacteristic
8#16837141—21no—
9C59×#491C2211yescharacteristic
10C59×#347—21no—
11#14273715—21no—
12#14273712—41no—
13#14273705—41no—
14#14273702—41no—
15#14273650—41no—
16#14273647—41no—
17#14273646—41no—
18#14273638—21no—
19C4⋊Q8×C59D411yescharacteristic
20#125×C59C2×C411yescharacteristic
21M32×C59—41no—
22#103×C59—41no—
23#97×C59D411yescharacteristic
24C2×Q8×C59—21no—
25C2×D236—21no—
26C2×D236—41no—
27C2×C4×D59—41no—
28C2×Dic118—21no—
29C2×C8×C59—21no—
30C4⋊C4×C59—21no—
31C4⋊C4×C59—41no—
32C4⋊C4×C59—41no—
33C42×C59C22⋊C411yescharacteristic
34(C2×D59)⋊C4—41no—
35(C2×D59)⋊C4—41no—
36(C2×D59)⋊C4—41no—
37Dic59⋊C4—41no—
38#11745664—81no—
39C2×C59⋊C8—41no—
40C16×C59—42no—
41C22×D59—41no—
42Q8×C59—81no—
43C2×C4×C59—21no—
44C2×C4×C59—41no—
45C2×C4×C59—41no—
46C2×C4×C59#9911yescharacteristic
47C2×Dic59—41no—
48D236—81no—
49D236—161no—
50C4×D59—161no—
51Dic118—81no—
52C8×C59—41no—
53C59⋊C8—81no—
54C59⋊C8—161no—
55#7525—591nomaximal, Sylow
56C22×C59AΣL(1,𝔽16)11yescharacteristic
57C2×D59—81no—
58C2×D59—81no—
59C2×D59—81no—
60C4×C59—21no—
61C4×C59—41no—
62C4×C59—81no—
63C4×C59—81no—
64Dic59—81no—
65#1662—591no—
66#1413—591no—
67#1356D5911yescharacteristic, complemented
68C2×C59—21no—
69C2×C59#140411yescharacteristic
70D59—161no—
71#562—591no—
72#491C2×D5911yescharacteristic
73#489—1181no—
74#356—1181no—
75#347—21no—
76#330—591no—
77#329—1181no—
78C59#752511yescharacteristic, complemented, Sylow
79C4⋊Q8D23611yescharacteristic
80#125C4×D5911yescharacteristic
81#124—1181no—
82#123—2361no—
83C22⋊Q8—2361no—
84#121—2361no—
85M32—41no—
86#103—41no—
87#103—2361no—
88#102—2361no—
89#101—2361no—
90#97—1181no—
91#97C22⋊D5911yescharacteristic
92C2×Q8—21no—
93C2×Q8—1181no—
94C2×D4—1181no—
95C2×D4—2361no—
96C22×C4—2361no—
97M16—4721no—
98C2×C8—21no—
99C2×C8—2361no—
100C4⋊C4—21no—
101C4⋊C4—41no—
102C4⋊C4—41no—
103C4⋊C4—2361no—
104C22⋊C4—2361no—
105C22⋊C4—2361no—
106C22⋊C4—2361no—
107C42(C2×D59)⋊C411yescharacteristic
108C16—42no—
109C23—2361no—
110Q8—81no—
111Q8—4721no—
112D4—9441no—
113D4—4721no—
114C2×C4—21no—
115C2×C4—41no—
116C2×C4—41no—
117C2×C4—9441no—
118C2×C4—2361no—
119C2×C4#1427364111yescharacteristic
120C8—41no—
121C8—9441no—
122C8—4721no—
123C22—4721no—
124C22—4721no—
125C22—4721no—
126C22#1683719011yescharacteristic
127C4—21no—
128C4—41no—
129C4—81no—
130C4—81no—
131C4—4721no—
132C2—21no—
133C2—9441no—
134C2#2142224811yescharacteristic
subgroupG/H
centerC2#21422248
commutator#125×C59C2×C4
Frattini#491C2×D59
FittingC59×#1356C2
socleC2×C59#1404
prime radical#16838150C4
cosocleC59×#491C22
hypercenter#1356D59
hypocenterC59#7525
LCSG ▷ #125×C59 ▷ C42×C59 ▷ C2×C4×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #491 ◁ #1356

Complements

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

NH ≅ G/Ntype
2. #21422269C2semidirect
3. C59×#1356C2semidirect
67. #1356D59semidirect
78. C59#7525semidirect

Maximal subgroups

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

subgroupindex
#214234172
#214222692
C59×#13562
#752559