Finite Group Databasebeta

← #28476530

Subgroups — #28476530

Order 15104.

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

normal subgroups only

This group has 158 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#21423388C211yesmaximal, characteristic
2#21422267C211yesmaximal, characteristic, complemented
3C59×#1355C211yesmaximal, characteristic, complemented
4#16838150C411yescharacteristic, complemented
5#16837789—21no—
6#16837195—21no—
7#16837144C411yescharacteristic, complemented
8#16837141—21no—
9C59×#490C2211yescharacteristic
10C59×#347—21no—
11C2×#11745670—41no—
12C2×#11745669—41no—
13#14273715—21no—
14#14273712—41no—
15#14273705—41no—
16#14273702—41no—
17#14273642—41no—
18#14273638—21no—
19#127×C59D411yescharacteristic
20#125×C59C2×C411yescharacteristic
21M32×C59—41no—
22#102×C59—41no—
23#97×C59D411yescharacteristic
24C2×D4×C59—21no—
25C2×D4×C59—41no—
26C2×D236—21no—
27C2×D236—41no—
28C2×C4×D59—41no—
29C2×Dic118—21no—
30C2×C8×C59—21no—
31C4⋊C4×C59—21no—
32C4⋊C4×C59—41no—
33C42×C59C22⋊C411yescharacteristic
34C22⋊Dic59—81no—
35#11745670—82no—
36#11745669—82no—
37(C2×D59)⋊C4—41no—
38(C2×D59)⋊C4—41no—
39(C2×D59)⋊C4—41no—
40Dic59⋊C4—41no—
41C2×C59⋊C8—41no—
42C16×C59—42no—
43C23×C59—41no—
44C22×D59—41no—
45D4×C59—81no—
46D4×C59—81no—
47D4×C59—81no—
48C2×C4×C59—21no—
49C2×C4×C59—41no—
50C2×C4×C59#9911yescharacteristic
51C2×Dic59—41no—
52C2×Dic59—161no—
53D236—81no—
54D236—161no—
55C4×D59—161no—
56Dic118—81no—
57C8×C59—41no—
58C59⋊C8—42no—
59#7523—591nomaximal, Sylow
60C22×C59—81no—
61C22×C59—161no—
62C22×C59AΣL(1,𝔽16)11yescharacteristic
63C2×D59—81no—
64C2×D59—81no—
65C2×D59—81no—
66C4×C59—21no—
67C4×C59—41no—
68C4×C59—81no—
69Dic59—81no—
70Dic59—321no—
71#1656—591no—
72#1412—591no—
73#1355D5911yescharacteristic, complemented
74C2×C59—21no—
75C2×C59—161no—
76C2×C59#140411yescharacteristic
77D59—161no—
78#562—591no—
79#496—1181no—
80#490C2×D5911yescharacteristic
81#353—1181no—
82#347—21no—
83#330—591no—
84#329—1181no—
85C59#752311yescharacteristic, complemented, Sylow
86C2×SD16—2361no—
87C2×D8—2361no—
88#127D23611yescharacteristic
89#125C4×D5911yescharacteristic
90#124—1181no—
91#123—2361no—
92C22⋊Q8—2361no—
93#121—2361no—
94M32—41no—
95#102—41no—
96#99—2361no—
97#97—1181no—
98#97C22⋊D5911yescharacteristic
99C2×Q8—1181no—
100C2×D4—21no—
101C2×D4—41no—
102C2×D4—1181no—
103C2×D4—2361no—
104C22×C4—2361no—
105SD16—4722no—
106D8—4722no—
107C2×C8—21no—
108C2×C8—2361no—
109C4⋊C4—21no—
110C4⋊C4—41no—
111C4⋊C4—2361no—
112C22⋊C4—4721no—
113C22⋊C4—2361no—
114C22⋊C4—2361no—
115C22⋊C4—2361no—
116C42(C2×D59)⋊C411yescharacteristic
117C16—42no—
118C23—41no—
119C23—2361no—
120Q8—4721no—
121D4—81no—
122D4—81no—
123D4—81no—
124D4—9441no—
125D4—4721no—
126C2×C4—21no—
127C2×C4—41no—
128C2×C4—9441no—
129C2×C4—9441no—
130C2×C4—2361no—
131C2×C4#1427364111yescharacteristic
132C8—41no—
133C8—2362no—
134C22—81no—
135C22—161no—
136C22—4721no—
137C22—4721no—
138C22—4721no—
139C22#1683719011yescharacteristic
140C4—21no—
141C4—41no—
142C4—81no—
143C4—18881no—
144C4—4721no—
145C2—21no—
146C2—161no—
147C2—9441no—
148C2#2142224811yescharacteristic
subgroupG/H
centerC2#21422248
commutator#125×C59C2×C4
Frattini#490C2×D59
FittingC59×#1355C2
socleC2×C59#1404
prime radical#21423388C2
cosocleC59×#490C22
hypercenter#1355D59
hypocenterC59#7523
LCSG ▷ #125×C59 ▷ C42×C59 ▷ C2×C4×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #490 ◁ #1355

Complements

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

NH ≅ G/Ntype
2. #21422267C2semidirect
3. C59×#1355C2semidirect
4. #16838150C4semidirect
7. #16837144C4semidirect
73. #1355D59semidirect
85. C59#7523semidirect

Maximal subgroups

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

subgroupindex
#214233882
#214222672
C59×#13552
#752359