Finite Group Databasebeta

← #28486229

Subgroups — #28486229

Order 15104.

422 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 95 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#21427277C211yesmaximal, characteristic
3#21422648C212yesmaximal
4#21421962C212yesmaximal
5C59×#1558C211yesmaximal, characteristic
6#16837959C2211yescharacteristic
7#16837770—22no—
8#16837752C414yescomplemented
9#16837411—22no—
10C4×#11745664C2211yescharacteristic
11#16837309—22no—
12#16837288—24no—
13#16837270C2212yes—
14#16837140—24no—
15C2×C4⋊Q8×C59C2211yescharacteristic
16C59×#432C2212yes—
17C59×#333—22no—
18C2×#11745664—21no—
19#14273727C2×C412yes—
20#14273719—21no—
21#14273706—22no—
22C4×Dic118—22no—
23#14273686—21no—
24C2×C4⋊Dic59—22no—
25C2×C4×Dic59—22no—
26#14273651—28no—
27#14273638—21no—
28C4×C59⋊C8C2×C412yes—
29C59⋊#95—24no—
30C59⋊#95—22no—
31C59⋊#95—22no—
32C59⋊#95D414yes—
33C22×Q8×C59D412yes—
34C4⋊Q8×C59—22no—
35C4⋊Q8×C59C2×C412yes—
36C4⋊Q8×C59D412yes—
37C2×C4⋊C4×C59—22no—
38C2×C42×C59C2311yescharacteristic
39C4⋊C8×C59—22no—
40C22⋊C8×C59—22no—
41#97×C59—22no—
42C2×Q8×C59—22no—
43C2×Q8×C59—42no—
44C2×Q8×C59—42no—
45C2×Q8×C59C22⋊C414yes—
46C22×C4×C59—22no—
47C22×C4×C59C2×D411yescharacteristic
48C22×C4×C59C2×D412yes—
49C22×Dic59—24no—
50C2×Dic118—22no—
51C2×C8×C59—42no—
52C4⋊C4×C59—24no—
53C4⋊C4×C59—24no—
54C42×C59C22×C411yescharacteristic
55C42×C59C2×D411yescharacteristic
56C42×C59#4112yes—
57C22⋊Dic59—41no—
58C4⋊Dic59—22no—
59C4⋊Dic59—22no—
60C4⋊Dic59—82no—
61Dic59⋊C4—42no—
62C4×Dic59—41no—
63C4×Dic59—82no—
64#11745664—42no—
65C2×C59⋊C8—22no—
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×C59C2×C22⋊C411yescharacteristic
75C2×C4×C59C4×D412yes—
76C2×C4×C59#12112yes—
77C2×C4×C59#12311yescharacteristic
78C2×Dic59—48no—
79C2×Dic59—42no—
80C2×Dic59—44no—
81Dic118—82no—
82C8×C59—82no—
83C59⋊C8—42no—
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—
93Dic59—84no—
94Dic59—82no—
95#3139—591no—
96#2381—591no—
97#1558D5911yescharacteristic
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#432C2×D5912yes—
108#419—1182no—
109C4×M16—591no—
110#391—1182no—
111#387—1184no—
112#383—592no—
113#333—22no—
114#328—1184no—
115C59#942611yescharacteristic, complemented, Sylow
116C22×Q8D23612yes—
117C2×M16—1181no—
118C4⋊Q8—22no—
119C4⋊Q8—592no—
120C4⋊Q8C4×D5912yes—
121C4⋊Q8C22⋊D5912yes—
122#125—1181no—
123C22⋊Q8—1182no—
124C4×Q8—1182no—
125#117—1181no—
126C2×C4⋊C4—22no—
127C2×C4⋊C4—1182no—
128C2×C42—1182no—
129C2×C42C22×D5911yescharacteristic
130C4⋊C8—22no—
131#103—1188no—
132C22⋊C8—22no—
133#97—22no—
134#97—1181no—
135C4×C8—592no—
136#95—594no—
137#95—1184no—
138#95—1182no—
139#95—1182no—
140C2×Q8—22no—
141C2×Q8—42no—
142C2×Q8—42no—
143C2×Q8—1182no—
144C2×Q8(C2×D59)⋊C414yes—
145C22×C4—22no—
146C22×C4—1184no—
147C22×C4C2×D23611yescharacteristic
148C22×C4D4×D5912yes—
149M16—2362no—
150C2×C8—42no—
151C2×C8—1182no—
152C4⋊C4—24no—
153C4⋊C4—24no—
154C4⋊C4—1182no—
155C4⋊C4—1182no—
156C4⋊C4—4722no—
157C4⋊C4—2362no—
158C22⋊C4—2361no—
159C42—4722no—
160C42—2361no—
161C42C2×C4×D5911yescharacteristic
162C42#1174568712yes—
163C42C2×C22⋊D5911yescharacteristic
164C23#1427369711yescharacteristic
165Q8—44no—
166Q8—82no—
167Q8—4722no—
168C2×C4—22no—
169C2×C4—24no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—2368no—
174C2×C4—2362no—
175C2×C4—2364no—
176C2×C4C2×(C2×D59)⋊C411yescharacteristic
177C2×C4(C22⋊D59)⋊C412yes—
178C2×C4#1427369912yes—
179C2×C4#1427371111yescharacteristic
180C8—82no—
181C8—2362no—
182C22—22no—
183C22#1683727911yescharacteristic
184C22#1683758212yes—
185C4—21no—
186C4—21no—
187C4—22no—
188C4—22no—
189C4—44no—
190C4—4724no—
191C4—4722no—
192C2—22no—
193C2#2142448211yescharacteristic
194C2#2142458812yes—
subgroupG/H
centerC22#16837279
commutatorC42×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1558C2
socleC22×C59#386
prime radicalC23×C59#120
cosocleC2×C42×C59C23
hypercenter#1558D59
hypocenterC59#9426
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1558

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
#214272772
#214226482
#214219622
C59×#15582
#942659