Finite Group Databasebeta

← #28486231

Subgroups — #28486231

Order 15104.

422 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 99 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#21434476C211yesmaximal, characteristic
2#21422822C211yesmaximal, characteristic
3#21422646C212yesmaximal
4#21421960C212yesmaximal
5C59×#2381C211yesmaximal, characteristic
6#16837959C2211yescharacteristic
7#16837770—22no—
8#16837752C414yescomplemented
9#16837459C2212yes—
10#16837411—22no—
11C4×#11745664C2211yescharacteristic
12#16837151—22no—
13#16837138—24no—
14C2×C4⋊Q8×C59C2211yescharacteristic
15C59×#391—22no—
16C59×#387—24no—
17C59×#383C2212yes—
18C2×#11745664—21no—
19#14273727C2×C412yes—
20#14273719—21no—
21#14273706—22no—
22C4×Dic118—22no—
23#14273686—21no—
24C4⋊(C59⋊C8)—22no—
25#14273651—28no—
26C22⋊(C59⋊C8)—22no—
27#14273638—21no—
28#14273638—22no—
29C4×C59⋊C8C2×C412yes—
30C22×Q8×C59D412yes—
31C4⋊Q8×C59—22no—
32C4⋊Q8×C59C2×C412yes—
33C4⋊Q8×C59D412yes—
34C2×C4⋊C4×C59—22no—
35C2×C4⋊C4×C59—22no—
36C2×C42×C59—22no—
37C2×C42×C59C2311yescharacteristic
38#95×C59—24no—
39#95×C59—22no—
40#95×C59—22no—
41#95×C59D414yes—
42C2×Q8×C59—22no—
43C2×Q8×C59—42no—
44C2×Q8×C59—42no—
45C2×Q8×C59C22⋊C414yes—
46C22×C4×C59—22no—
47C22×C4×C59—24no—
48C22×C4×C59C2×D411yescharacteristic
49C22×C4×C59C2×D412yes—
50C2×Dic118—22no—
51C4⋊C4×C59—24no—
52C4⋊C4×C59—24no—
53C4⋊C4×C59—82no—
54C42×C59—82no—
55C42×C59C22×C411yescharacteristic
56C42×C59C2×D411yescharacteristic
57C42×C59#4112yes—
58C22⋊Dic59—41no—
59C4⋊Dic59—22no—
60C4⋊Dic59—22no—
61Dic59⋊C4—42no—
62C4×Dic59—41no—
63#11745664—42no—
64C2×C59⋊C8—22no—
65C2×C59⋊C8—42no—
66C23×C59#12011yescharacteristic
67Q8×C59—44no—
68Q8×C59—82no—
69C2×C4×C59—22no—
70C2×C4×C59—24no—
71C2×C4×C59—42no—
72C2×C4×C59—42no—
73C2×C4×C59—42no—
74C2×C4×C59—48no—
75C2×C4×C59—44no—
76C2×C4×C59C2×C22⋊C411yescharacteristic
77C2×C4×C59C4×D412yes—
78C2×C4×C59#12112yes—
79C2×C4×C59#12311yescharacteristic
80C2×Dic59—42no—
81Dic118—82no—
82C59⋊C8—42no—
83C59⋊C8—82no—
84#9426—591nomaximal, Sylow
85C22×C59—22no—
86C22×C59#38611yescharacteristic
87C22×C59#45512yes—
88C4×C59—21no—
89C4×C59—21no—
90C4×C59—22no—
91C4×C59—22no—
92C4×C59—44no—
93C4×C59—84no—
94Dic59—82no—
95#3139—591no—
96#2381D5911yescharacteristic
97#1558—591no—
98#1515—592no—
99#1288—592no—
100C2×C59—22no—
101C2×C59#188511yescharacteristic
102C2×C59#190512yes—
103#533—591no—
104C2×C4⋊Q8C2×D5911yescharacteristic
105#491—1182no—
106#487—594no—
107#432—592no—
108#419—1182no—
109C4×M16—591no—
110#391—22no—
111#387—24no—
112#383C2×D5912yes—
113#333—1182no—
114#328—1184no—
115C59#942611yescharacteristic, complemented, Sylow
116C22×Q8C22⋊D5912yes—
117C2×M16—1181no—
118C4⋊Q8—22no—
119C4⋊Q8—592no—
120C4⋊Q8C4×D5912yes—
121C4⋊Q8D23612yes—
122#125—1181no—
123C22⋊Q8—1182no—
124C4×Q8—1182no—
125#117—1181no—
126C2×C4⋊C4—22no—
127C2×C4⋊C4—22no—
128C2×C42—22no—
129C2×C42C22×D5911yescharacteristic
130C4⋊C8—1182no—
131#103—1188no—
132C22⋊C8—1182no—
133#97—1181no—
134#97—1182no—
135C4×C8—592no—
136#95—24no—
137#95—22no—
138#95—22no—
139#95C22⋊D5914yes—
140C2×Q8—22no—
141C2×Q8—42no—
142C2×Q8—42no—
143C2×Q8—1182no—
144C2×Q8(C2×D59)⋊C414yes—
145C22×C4—22no—
146C22×C4—24no—
147C22×C4C2×C22⋊D5911yescharacteristic
148C22×C4C2×C22⋊D5912yes—
149M16—2362no—
150C2×C8—1182no—
151C2×C8—2362no—
152C4⋊C4—24no—
153C4⋊C4—24no—
154C4⋊C4—82no—
155C4⋊C4—1182no—
156C4⋊C4—1182no—
157C4⋊C4—2362no—
158C22⋊C4—2361no—
159C42—82no—
160C42—2361no—
161C42C2×C4×D5911yescharacteristic
162C42C2×D23611yescharacteristic
163C42#1174568512yes—
164C23#1427369611yescharacteristic
165Q8—44no—
166Q8—82no—
167Q8—4722no—
168C2×C4—22no—
169C2×C4—24no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—48no—
174C2×C4—44no—
175C2×C4—2362no—
176C2×C4C2×(C2×D59)⋊C411yescharacteristic
177C2×C4C4×C22⋊D5912yes—
178C2×C4#1427370112yes—
179C2×C4#1427371011yescharacteristic
180C8—4722no—
181C8—2362no—
182C22—22no—
183C22#1683728111yescharacteristic
184C22#1683758012yes—
185C4—21no—
186C4—21no—
187C4—22no—
188C4—22no—
189C4—44no—
190C4—84no—
191C4—4722no—
192C2—22no—
193C2#2142448411yescharacteristic
194C2#2142459012yes—
subgroupG/H
centerC22#16837281
commutatorC42×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#2381C2
socleC22×C59#386
prime radicalC23×C59#120
cosocleC2×C42×C59C23
hypercenter#2381D59
hypocenterC59#9426
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2381

Complements

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

NH ≅ G/Ntype
8. #16837752C4semidirect
115. C59#9426semidirect

Maximal subgroups

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

subgroupindex
#214344762
#214228222
#214226462
#214219602
C59×#23812
#942659