Finite Group Databasebeta

← #28476296

Subgroups — #28476296

Order 15104.

224 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 41 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#21425629C211yesmaximal, characteristic
2#21422221C211yesmaximal, characteristic
3C59×#1318C211yesmaximal, characteristic
4C2×#14273658—21no—
5C2×#14273648—21no—
6C2×#14273642—21no—
7#16837272C411yescharacteristic, complemented
8#16837157C411yescharacteristic, complemented
9C59×#390C2211yescharacteristic
10C59×#324—21no—
11C22×C59⋊C8—21no—
12C2×C4⋊Dic59—21no—
13C2×C4⋊Dic59—41no—
14C2×C22⋊Dic59—41no—
15#14273658—42no—
16#14273648—42no—
17#14273642—22no—
18#14273642—41no—
19C22×D4×C59D411yescharacteristic
20C2×C4⋊C4×C59D411yescharacteristic
21C2×C22⋊C4×C59—41no—
22C2×C42×C59C2×C411yescharacteristic
23C22⋊C8×C59—41no—
24C24×C59—21no—
25C2×D4×C59—21no—
26C2×D4×C59—41no—
27C2×D4×C59—41no—
28C2×D4×C59SD1611yescharacteristic
29C2×D4×C59Q1611yescharacteristic
30C22×C4×C59—21no—
31C22×C4×C59—21no—
32C22×C4×C59C22⋊C411yescharacteristic
33C22×Dic59—41no—
34C22×Dic59—81no—
35C2×C8×C59—81no—
36C4⋊C4×C59—41no—
37C22⋊C4×C59—82no—
38C42×C59—41no—
39C22⋊Dic59—42no—
40C22⋊Dic59—81no—
41C4⋊Dic59—41no—
42C4⋊Dic59—41no—
43C4⋊Dic59—82no—
44C2×C59⋊C8—22no—
45C2×C59⋊C8—41no—
46C2×C59⋊C8—41no—
47C23×C59—21no—
48C23×C59—21no—
49C23×C59—41no—
50C23×C59—41no—
51C23×C59—81no—
52C23×C59—81no—
53C23×C59#9911yescharacteristic
54D4×C59—41no—
55D4×C59—41no—
56D4×C59—81no—
57C2×C4×C59—21no—
58C2×C4×C59—21no—
59C2×C4×C59—22no—
60C2×C4×C59—41no—
61C2×C4×C59—41no—
62C2×C4×C59—41no—
63C2×C4×C59—81no—
64C2×C4×C59#10311yescharacteristic
65C2×C4×C59#10411yescharacteristic
66C2×Dic59—82no—
67C2×Dic59—82no—
68C2×Dic59—81no—
69C2×Dic59—161no—
70C2×Dic59—161no—
71C8×C59—161no—
72C59⋊C8—42no—
73#7435—591nomaximal, Sylow
74C22×C59—21no—
75C22×C59—21no—
76C22×C59—41no—
77C22×C59—41no—
78C22×C59—81no—
79C22×C59—81no—
80C22×C59—81no—
81C22×C59—81no—
82C22×C59—161no—
83C22×C59#32811yescharacteristic
84C22×C59#35211yescharacteristic
85C22×C59#35311yescharacteristic
86C4×C59—21no—
87C4×C59—21no—
88C4×C59—42no—
89C4×C59—81no—
90Dic59—162no—
91Dic59—161no—
92#2094—591no—
93#1393—591no—
94#1318D5911yescharacteristic
95C2×C59—21no—
96C2×C59—21no—
97C2×C59—81no—
98C2×C59—81no—
99C2×C59#135211yescharacteristic
100C2×C59#140611yescharacteristic
101C2×C59#140911yescharacteristic
102C2×#106—1181no—
103C2×#102—1181no—
104C2×#99—1181no—
105#390C2×D5911yescharacteristic
106#384—591no—
107#336—591no—
108#324—21no—
109C59#743511yescharacteristic, complemented, Sylow
110C22×D4D23611yescharacteristic
111C22×C8—1181no—
112C2×C4⋊C4—1181no—
113C2×C4⋊C4—2361no—
114C2×C4⋊C4C22⋊D5911yescharacteristic
115C2×C22⋊C4—41no—
116C2×C22⋊C4—2361no—
117C2×C42C4×D5911yescharacteristic
118#106—2362no—
119#102—2362no—
120#99—1182no—
121#99—2361no—
122C22⋊C8—41no—
123C24—21no—
124C2×D4—21no—
125C2×D4—41no—
126C2×D4—41no—
127C2×D4#1174566011yescharacteristic
128C2×D4Dic23611yescharacteristic
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—4721no—
132C22×C4—2361no—
133C22×C4(C2×D59)⋊C411yescharacteristic
134C2×C8—81no—
135C2×C8—1182no—
136C2×C8—2361no—
137C2×C8—2361no—
138C4⋊C4—41no—
139C4⋊C4—4722no—
140C4⋊C4—2361no—
141C4⋊C4—2361no—
142C22⋊C4—82no—
143C22⋊C4—4721no—
144C22⋊C4—2362no—
145C42—41no—
146C23—21no—
147C23—21no—
148C23—41no—
149C23—41no—
150C23—81no—
151C23—81no—
152C23#1427364111yescharacteristic
153D4—41no—
154D4—41no—
155D4—81no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—81no—
163C2×C4—9441no—
164C2×C4—9441no—
165C2×C4—4722no—
166C2×C4—4722no—
167C2×C4—4721no—
168C2×C4#1427365211yescharacteristic
169C2×C4#1427365311yescharacteristic
170C8—161no—
171C8—2362no—
172C22—21no—
173C22—21no—
174C22—41no—
175C22—41no—
176C22—81no—
177C22—81no—
178C22—81no—
179C22—81no—
180C22—161no—
181C22#1683714011yescharacteristic
182C22#1683719311yescharacteristic
183C22#1683719411yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—81no—
188C4—9442no—
189C4—9441no—
190C2—21no—
191C2—21no—
192C2—81no—
193C2—81no—
194C2#2142212111yescharacteristic
195C2#2142225411yescharacteristic
196C2#2142226011yescharacteristic
subgroupG/H
centerC22#16837194
commutatorC2×C42×C59C2×C4
Frattini#390C2×D59
FittingC59×#1318C2
socleC22×C59#353
prime radicalC22×D4×C59D4
cosocleC59×#390C22
hypercenter#1318D59
hypocenterC59#7435
LCSG ▷ C2×C42×C59 ▷ C22×C4×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #390 ◁ #1318

Complements

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

NH ≅ G/Ntype
7. #16837272C4semidirect
8. #16837157C4semidirect
109. C59#7435semidirect

Maximal subgroups

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

subgroupindex
#214256292
#214222212
C59×#13182
#743559