Finite Group Databasebeta

← #28482219

Subgroups — #28482219

Order 15104.

398 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 91 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#21426699C211yesmaximal, characteristic
2#21424176C211yesmaximal, characteristic
3#21422005C214yesmaximal
4C59×#1821C211yesmaximal, characteristic
5#16837366C2212yes—
6#16837288—22no—
7#16837288—22no—
8#16837265C2212yes—
9#16837262C412yes—
10C4×C22⋊Dic59C412yes—
11#16837171—22no—
12C22×C4⋊C4×C59C2211yescharacteristic
13C59×#407C2212yes—
14C59×#343—22no—
15C2×#11745664—22no—
16C2×C4⋊Dic59—22no—
17C2×C22⋊Dic59C2×C414yes—
18C2×C4×Dic59—22no—
19C22⋊(C59⋊C8)—24no—
20C59⋊#95—22no—
21C59⋊#95—22no—
22C59⋊#95—22no—
23C59⋊#95—22no—
24C23×C4×C59C2×C411yescharacteristic
25C23×C4×C59C2×C411yescharacteristic
26C23×C4×C59C2311yescharacteristic
27C2×M16×C59—22no—
28C2×C4⋊C4×C59—24no—
29C2×C4⋊C4×C59D412yes—
30C2×C4⋊C4×C59D412yes—
31C22⋊C8×C59—24no—
32C24×C59C22×C411yescharacteristic
33C22×C4×C59—22no—
34C22×C4×C59—22no—
35C22×C4×C59—42no—
36C22×C4×C59—81no—
37C22×C4×C59—81no—
38C22×C4×C59C22⋊C412yes—
39C22×C4×C59C22⋊C412yes—
40C22×C4×C59C2×D411yescharacteristic
41C22×C4×C59C2×D411yescharacteristic
42C22×C4×C59#4114yes—
43C22×Dic59—24no—
44M16×C59—44no—
45C2×C8×C59—42no—
46C4⋊C4×C59—24no—
47C4⋊C4×C59—24no—
48C22⋊Dic59—44no—
49C4⋊Dic59—82no—
50C4×Dic59—82no—
51#11745664—44no—
52C2×C59⋊C8—42no—
53C23×C59—22no—
54C23×C59—41no—
55C23×C59—41no—
56C23×C59C2×C22⋊C411yescharacteristic
57C23×C59#11712yes—
58C2×C4×C59—22no—
59C2×C4×C59—22no—
60C2×C4×C59—22no—
61C2×C4×C59—22no—
62C2×C4×C59—44no—
63C2×C4×C59—42no—
64C2×C4×C59—42no—
65C2×C4×C59—82no—
66C2×C4×C59—82no—
67C2×C4×C59#12312yes—
68C2×C4×C59#12312yes—
69C2×Dic59—44no—
70C2×Dic59—44no—
71C2×Dic59—44no—
72C8×C59—82no—
73C59⋊C8—82no—
74#8755—591nomaximal, Sylow
75C22×C59—21no—
76C22×C59—21no—
77C22×C59—22no—
78C22×C59—22no—
79C22×C59—22no—
80C22×C59—44no—
81C22×C59#38111yescharacteristic
82C22×C59#41012yes—
83C4×C59—22no—
84C4×C59—22no—
85C4×C59—42no—
86C4×C59—42no—
87Dic59—84no—
88#2313—591no—
89#1821—591no—
90#1821D5911yescharacteristic
91#1306—594no—
92C2×C59—22no—
93C2×C59—42no—
94C2×C59#182011yescharacteristic
95C2×C59#182911yescharacteristic
96C2×C59#183011yescharacteristic
97C22×C4⋊C4C2×D5911yescharacteristic
98#407—592no—
99#407C2×D5912yes—
100#387—1182no—
101#387—1182no—
102#381—592no—
103#380—592no—
104C4×C22⋊C4—592no—
105#343—22no—
106#343—1182no—
107C59#875511yescharacteristic, complemented, Sylow
108C23×C4C4×D5911yescharacteristic
109C23×C4C4×D5911yescharacteristic
110C23×C4C22×D5911yescharacteristic
111C2×M16—22no—
112C2×M16—1182no—
113C2×C4⋊C4—24no—
114C2×C4⋊C4—1182no—
115C2×C4⋊C4D23612yes—
116C2×C4⋊C4C22⋊D5912yes—
117C2×C22⋊C4—594no—
118C2×C42—1182no—
119C22⋊C8—24no—
120C22⋊C8—1184no—
121#95—1182no—
122#95—1182no—
123#95—1182no—
124#95—1182no—
125C24C2×C4×D5911yescharacteristic
126C22×C4—22no—
127C22×C4—22no—
128C22×C4—42no—
129C22×C4—81no—
130C22×C4—81no—
131C22×C4—1184no—
132C22×C4(C2×D59)⋊C412yes—
133C22×C4(C2×D59)⋊C412yes—
134C22×C4C2×D23611yescharacteristic
135C22×C4#1174568714yes—
136C22×C4C2×C22⋊D5911yescharacteristic
137M16—44no—
138M16—2364no—
139C2×C8—42no—
140C2×C8—2362no—
141C4⋊C4—24no—
142C4⋊C4—24no—
143C4⋊C4—4722no—
144C22⋊C4—2364no—
145C42—4722no—
146C23—22no—
147C23—41no—
148C23—41no—
149C23C2×(C2×D59)⋊C411yescharacteristic
150C23#1427368312yes—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—44no—
156C2×C4—42no—
157C2×C4—42no—
158C2×C4—82no—
159C2×C4—82no—
160C2×C4—2364no—
161C2×C4—2364no—
162C2×C4—2364no—
163C2×C4#1427370812yes—
164C2×C4#1427371112yes—
165C8—82no—
166C8—4722no—
167C22—21no—
168C22—21no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—44no—
173C22#1683726311yescharacteristic
174C22#1683737512yes—
175C4—22no—
176C4—22no—
177C4—42no—
178C4—42no—
179C4—4724no—
180C2—22no—
181C2—42no—
182C2#2142417111yescharacteristic
183C2#2142420511yescharacteristic
184C2#2142420811yescharacteristic
subgroupG/H
centerC22#16837263
commutator, prime radicalC24×C59C22×C4
FrattiniC23×C4C22×D59
FittingC59×#1821C2
socleC22×C59#381
cosocleC23×C4×C59C23
hypercenter#1821D59
hypocenterC59#8755
LCSG ▷ C24×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
107. C59#8755semidirect

Maximal subgroups

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

subgroupindex
#214266992
#214241762
#214220052
C59×#18212
#875559