Finite Group Databasebeta

← #28476285

Subgroups — #28476285

Order 15104.

210 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 37 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#21425612C211yesmaximal, characteristic
2#21422032C211yesmaximal, characteristic
3C59×#1297C211yesmaximal, characteristic
4#16837451C411yescharacteristic, complemented
5#16837450—21no—
6#16837366—21no—
7#16837184—21no—
8C59⋊#338C411yescharacteristic, complemented
9C59×#407C2211yescharacteristic
10C4×C22⋊C4×C59—21no—
11C2×#11745664—21no—
12C2×#11745664—21no—
13#14273667—41no—
14#14273663—41no—
15#14273662—42no—
16C22⋊(C59⋊C8)—42no—
17C23×C4×C59D411yescharacteristic
18C2×M16×C59C2×C411yescharacteristic
19C2×M16×C59D411yescharacteristic
20C2×C22⋊C4×C59—41no—
21C2×C42×C59—41no—
22C22⋊C8×C59—41no—
23#95×C59—22no—
24C24×C59SD1611yescharacteristic
25C22×C4×C59—21no—
26C22×C4×C59—21no—
27C22×C4×C59—41no—
28C22×C4×C59—41no—
29C22×C4×C59—42no—
30C22×C4×C59C22⋊C411yescharacteristic
31C22×C4×C59Q1611yescharacteristic
32M16×C59—41no—
33M16×C59—41no—
34C2×C8×C59—21no—
35C2×C8×C59—21no—
36C22⋊C4×C59—44no—
37C42×C59—81no—
38C42×C59—81no—
39#11745664—41no—
40#11745664—41no—
41#11745664—41no—
42#11745664—41no—
43C2×C59⋊C8—22no—
44C2×C59⋊C8—41no—
45C59⋊C16—81no—
46C23×C59—21no—
47C23×C59—42no—
48C23×C59—41no—
49C23×C59#10311yescharacteristic
50C2×C4×C59—21no—
51C2×C4×C59—21no—
52C2×C4×C59—21no—
53C2×C4×C59—41no—
54C2×C4×C59—41no—
55C2×C4×C59—41no—
56C2×C4×C59—44no—
57C2×C4×C59—81no—
58C2×C4×C59—82no—
59C2×C4×C59—82no—
60C2×C4×C59#9911yescharacteristic
61C2×C4×C59#10411yescharacteristic
62C8×C59—41no—
63C8×C59—41no—
64C59⋊C8—42no—
65C59⋊C8—81no—
66#7432—591nomaximal, Sylow
67C22×C59—22no—
68C22×C59—21no—
69C22×C59—41no—
70C22×C59—41no—
71C22×C59—42no—
72C22×C59—41no—
73C22×C59—81no—
74C22×C59#32811yescharacteristic
75C4×C59—21no—
76C4×C59—41no—
77C4×C59—84no—
78C4×C59#35211yescharacteristic
79C4×C59#35311yescharacteristic
80#2091—591no—
81#1320—591no—
82#1297D5911yescharacteristic
83C2×C59—21no—
84C2×C59—42no—
85C2×C59—41no—
86C2×C59#135211yescharacteristic
87#430—591no—
88#430—1181no—
89#407—1181no—
90#407C2×D5911yescharacteristic
91C4×C22⋊C4—21no—
92#349—1181no—
93#338—591no—
94C59#743211yescharacteristic, complemented, Sylow
95C23×C4C22⋊D5911yescharacteristic
96C2×M16—1181no—
97C2×M16—1181no—
98C2×M16C4×D5911yescharacteristic
99C2×M16D23611yescharacteristic
100C2×C22⋊C4—41no—
101C2×C42—41no—
102M32—2361no—
103#108—2361no—
104#108—2362no—
105C22⋊C8—41no—
106C22⋊C8—2362no—
107#95—22no—
108C24#1174567011yescharacteristic
109C22×C4—21no—
110C22×C4—21no—
111C22×C4—41no—
112C22×C4—41no—
113C22×C4—42no—
114C22×C4(C2×D59)⋊C411yescharacteristic
115C22×C4#1174567211yescharacteristic
116M16—41no—
117M16—41no—
118M16—2361no—
119M16—2361no—
120M16—2361no—
121M16—2361no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—1182no—
125C2×C8—2361no—
126C22⋊C4—44no—
127C42—81no—
128C42—81no—
129C16—4721no—
130C23—21no—
131C23—42no—
132C23—41no—
133C23#1427365011yescharacteristic
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—44no—
141C2×C4—81no—
142C2×C4—82no—
143C2×C4—82no—
144C2×C4#1427364111yescharacteristic
145C2×C4#1427365511yescharacteristic
146C8—41no—
147C8—41no—
148C8—4721no—
149C8—2362no—
150C22—22no—
151C22—21no—
152C22—41no—
153C22—41no—
154C22—42no—
155C22—41no—
156C22—81no—
157C22#1683713811yescharacteristic
158C4—21no—
159C4—41no—
160C4—84no—
161C4#1683719111yescharacteristic
162C4#1683719411yescharacteristic
163C2—21no—
164C2—42no—
165C2—41no—
166C2#2142211911yescharacteristic
subgroupG/H
centerC4#16837194
commutatorC2×M16×C59C2×C4
Frattini#407C2×D59
FittingC59×#1297C2
socleC2×C59#1352
prime radicalC24×C59SD16
cosocleC59×#407C22
hypercenter#1297D59
hypocenterC59#7432
LCSG ▷ C2×M16×C59 ▷ C22×C4×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #407 ◁ #1297

Complements

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

NH ≅ G/Ntype
4. #16837451C4semidirect
8. C59⋊#338C4semidirect
94. C59#7432semidirect

Maximal subgroups

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

subgroupindex
#214256122
#214220322
C59×#12972
#743259