Finite Group Databasebeta

← #28476524

Subgroups — #28476524

Order 15104.

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

normal subgroups only

This group has 148 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#21423239C211yesmaximal, characteristic
2#21422265C211yesmaximal, characteristic, complemented
3C59×#1358C211yesmaximal, characteristic, complemented
4#16838118C411yescharacteristic
5#16837689—21no—
6#16837201—21no—
7#16837151C411yescharacteristic
8#16837131—21no—
9C59×#494C2211yescharacteristic
10C59×#364—21no—
11#14273716—41no—
12#14273702—41no—
13C4×D236—21no—
14#14273685—41no—
15#14273658—41no—
16C4⋊(C59⋊C8)—21no—
17#14273647—41no—
18#14273646—41no—
19C2×Q16×C59—41no—
20C4⋊Q8×C59C2×C411yescharacteristic
21C4⋊Q8×C59D411yescharacteristic
22M32×C59—41no—
23C4×C8×C59D411yescharacteristic
24C2×Q8×C59—21no—
25C2×Q8×C59—21no—
26C2×D236—21no—
27C2×D236—41no—
28C2×C4×D59—41no—
29Q16×C59—81no—
30Q16×C59—81no—
31C2×C8×C59—21no—
32C4⋊C4×C59—41no—
33C4⋊C4×C59—41no—
34C42×C59C22⋊C411yescharacteristic
35(C2×D59)⋊C4—42no—
36(C2×D59)⋊C4—41no—
37C4⋊Dic59—21no—
38C4×Dic59—41no—
39#11745664—81no—
40C2×C59⋊C8—41no—
41C16×C59—81no—
42C22×D59—41no—
43Q8×C59—81no—
44Q8×C59—81no—
45C2×C4×C59—21no—
46C2×C4×C59—41no—
47C2×C4×C59—41no—
48C2×C4×C59#9911yescharacteristic
49C2×Dic59—41no—
50D236—41no—
51D236—41no—
52D236—161no—
53C4×D59—81no—
54C4×D59—81no—
55C8×C59—21no—
56C8×C59—21no—
57C59⋊C8—81no—
58C59⋊C8—161no—
59#7521—591nomaximal, Sylow
60C22×C59AΣL(1,𝔽16)11yescharacteristic
61C2×D59—81no—
62C2×D59—81no—
63C2×D59—81no—
64C4×C59—21no—
65C4×C59—21no—
66C4×C59—21no—
67C4×C59—81no—
68C4×C59—81no—
69Dic59—81no—
70#1634—591no—
71#1411—591no—
72#1358D5911yescharacteristic, complemented
73C2×C59—21no—
74C2×C59#140211yescharacteristic
75D59—161no—
76#555—591no—
77#494C2×D5911yescharacteristic
78#476—1181no—
79#364—21no—
80#356—1181no—
81#333—591no—
82D4⋊C8—1181no—
83C59#752111yescharacteristic, complemented, Sylow
84C2×Q16—41no—
85C4⋊Q8C4×D5911yescharacteristic
86C4⋊Q8D23611yescharacteristic
87#124—2361no—
88#121—2361no—
89C4×D4—1181no—
90#117—2361no—
91M32—41no—
92#106—2361no—
93C4⋊C8—1181no—
94#102—2361no—
95#101—2361no—
96C4×C8C22⋊D5911yescharacteristic
97C2×Q8—21no—
98C2×Q8—21no—
99C2×D4—1181no—
100C2×D4—2361no—
101C22×C4—2361no—
102Q16—81no—
103Q16—81no—
104M16—4721no—
105C2×C8—21no—
106C2×C8—2361no—
107C4⋊C4—41no—
108C4⋊C4—41no—
109C4⋊C4—1181no—
110C22⋊C4—2362no—
111C22⋊C4—2361no—
112C42—2361no—
113C42(C2×D59)⋊C411yescharacteristic
114C16—81no—
115C23—2361no—
116Q8—81no—
117Q8—81no—
118D4—9441no—
119D4—2361no—
120D4—2361no—
121C2×C4—21no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4—4721no—
125C2×C4—4721no—
126C2×C4—2361no—
127C2×C4#1427364111yescharacteristic
128C8—21no—
129C8—21no—
130C8—9441no—
131C8—4721no—
132C22—4721no—
133C22—4721no—
134C22—4721no—
135C22#1683719011yescharacteristic
136C4—21no—
137C4—21no—
138C4—21no—
139C4—81no—
140C4—81no—
141C4—4721no—
142C2—21no—
143C2—9441no—
144C2#2142224211yescharacteristic
subgroupG/H
centerC2#21422242
commutatorC4⋊Q8×C59C2×C4
Frattini#494C2×D59
FittingC59×#1358C2
socleC2×C59#1402
prime radical#16838118C4
cosocleC59×#494C22
hypercenter#1358D59
hypocenterC59#7521
LCSG ▷ C4⋊Q8×C59 ▷ C42×C59 ▷ C2×C4×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #494 ◁ #1358

Complements

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

NH ≅ G/Ntype
2. #21422265C2semidirect
3. C59×#1358C2semidirect
72. #1358D59semidirect
83. C59#7521semidirect

Maximal subgroups

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

subgroupindex
#214232392
#214222652
C59×#13582
#752159