Finite Group Databasebeta

← #28484005

Subgroups — #28484005

Order 15104.

404 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 107 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#21434606C211yesmaximal, characteristic
2#21422691C211yesmaximal, characteristic
3#21422516C212yesmaximal
4#21421932C212yesmaximal
5C59×#2986C211yesmaximal, characteristic
6#16837959C2211yescharacteristic
7#16837805C412yes—
8#16837801—22no—
9#16837798C412yes—
10#16837438—22no—
11C4×#11745664C2212yes—
12C2×C4×C59⋊C8C2211yescharacteristic
13#16837144—22no—
14#16837132—22no—
15#16837132—22no—
16C59×#533C2211yescharacteristic
17C59×#446—22no—
18C8×Q8×C59—22no—
19C59×#433—22no—
20C59×#431C2212yes—
21C2×#11745664—22no—
22C22×C59⋊C8—21no—
23#14273727C2×C412yes—
24#14273719—21no—
25#14273706—22no—
26C4×Dic118—22no—
27#14273686—21no—
28#14273660—24no—
29#14273658—24no—
30#14273638—22no—
31C4×C59⋊C8—21no—
32C4×C59⋊C8—22no—
33C4×C59⋊C8C2×C411yescharacteristic
34C4×C59⋊C8C2×C411yescharacteristic
35C4⋊Q8×C59C2×C412yes—
36#125×C59D412yes—
37C22⋊Q8×C59—22no—
38C4×Q8×C59—22no—
39#117×C59D412yes—
40C2×C42×C59C2311yescharacteristic
41C4⋊C8×C59—24no—
42C4⋊C8×C59D412yes—
43C4⋊C8×C59D412yes—
44C22⋊C8×C59—22no—
45#97×C59—22no—
46C4×C8×C59—22no—
47C4×C8×C59—22no—
48C2×Q8×C59—22no—
49C22×C4×C59C2×D411yescharacteristic
50C22×C4×C59#4112yes—
51C2×Dic118—22no—
52C2×C8×C59—22no—
53C2×C8×C59—22no—
54C4⋊C4×C59—22no—
55C4⋊C4×C59—24no—
56C4⋊C4×C59C22⋊C414yes—
57C22⋊C4×C59—22no—
58C42×C59—22no—
59C42×C59C22×C411yescharacteristic
60C42×C59C2×D411yescharacteristic
61C42×C59C2×D412yes—
62C22⋊Dic59—41no—
63C4⋊Dic59—22no—
64C4⋊Dic59—22no—
65Dic59⋊C4—42no—
66C4×Dic59—41no—
67#11745664—24no—
68#11745664—42no—
69C2×C59⋊C8—24no—
70C2×C59⋊C8—21no—
71C2×C59⋊C8—21no—
72C2×C59⋊C8—42no—
73C23×C59#12311yescharacteristic
74Q8×C59—42no—
75Q8×C59—42no—
76C2×C4×C59—22no—
77C2×C4×C59—22no—
78C2×C4×C59—22no—
79C2×C4×C59—24no—
80C2×C4×C59C2×C22⋊C411yescharacteristic
81C2×C4×C59C4×D412yes—
82C2×C4×C59#12011yescharacteristic
83C2×C4×C59#12112yes—
84C2×Dic59—42no—
85Dic118—42no—
86Dic118—42no—
87C8×C59—42no—
88C8×C59—42no—
89C59⋊C8—22no—
90C59⋊C8—22no—
91C59⋊C8—44no—
92#9068—591nomaximal, Sylow
93C22×C59—22no—
94C22×C59—21no—
95C22×C59#38611yescharacteristic
96C4×C59—22no—
97C4×C59—21no—
98C4×C59—44no—
99C4×C59#44312yes—
100C4×C59#44412yes—
101C4×C59#45612yes—
102Dic59—82no—
103#3160—591no—
104#2986D5911yescharacteristic
105#1526—591no—
106#1485—592no—
107#1278—592no—
108C2×C59—41no—
109C2×C59#187612yes—
110C2×C59#188611yescharacteristic
111#533—591no—
112#533C2×D5911yescharacteristic
113#500—592no—
114#499—1182no—
115#498—592no—
116#446—22no—
117C8×Q8—22no—
118#433—22no—
119#431C2×D5912yes—
120#427—1182no—
121C4×M16—592no—
122C2×C4×C8—591no—
123#330—1182no—
124Q8⋊C8—1182no—
125Q8⋊C8—1182no—
126C59#906811yescharacteristic, complemented, Sylow
127C2×M16—1182no—
128C22×C8—1181no—
129C4⋊Q8—592no—
130C4⋊Q8C4×D5912yes—
131#125—1181no—
132#125D23612yes—
133C22⋊Q8—22no—
134C22⋊Q8—1182no—
135C4×Q8—22no—
136C4×Q8—1182no—
137#117—1181no—
138#117C22⋊D5912yes—
139C2×C42C22×D5911yescharacteristic
140#107—1184no—
141#106—1184no—
142C4⋊C8—24no—
143C4⋊C8C22⋊D5912yes—
144C4⋊C8C22⋊D5912yes—
145C22⋊C8—22no—
146#97—22no—
147#97—1182no—
148C4×C8—22no—
149C4×C8—22no—
150C4×C8—591no—
151C4×C8—591no—
152C4×C8—1181no—
153C4×C8—1182no—
154C2×Q8—22no—
155C2×Q8—1182no—
156C22×C4#1174568512yes—
157C22×C4C2×C22⋊D5911yescharacteristic
158M16—1184no—
159M16—2362no—
160C2×C8—22no—
161C2×C8—22no—
162C2×C8—1184no—
163C2×C8—1181no—
164C2×C8—1181no—
165C2×C8—2362no—
166C4⋊C4—22no—
167C4⋊C4—24no—
168C4⋊C4—1182no—
169C4⋊C4—1182no—
170C4⋊C4—2362no—
171C4⋊C4(C2×D59)⋊C414yes—
172C22⋊C4—22no—
173C22⋊C4—2361no—
174C42—22no—
175C42—2361no—
176C42C2×C4×D5911yescharacteristic
177C42C2×D23611yescharacteristic
178C42C2×C22⋊D5912yes—
179C23#1427371011yescharacteristic
180Q8—42no—
181Q8—42no—
182Q8—2362no—
183Q8—2362no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—24no—
188C2×C4—2362no—
189C2×C4C2×(C2×D59)⋊C411yescharacteristic
190C2×C4C4×C22⋊D5912yes—
191C2×C4#1427369611yescharacteristic
192C2×C4#1427370112yes—
193C8—42no—
194C8—42no—
195C8—1182no—
196C8—1182no—
197C8—2364no—
198C22—22no—
199C22—21no—
200C22#1683728111yescharacteristic
201C4—22no—
202C4—21no—
203C4—44no—
204C4—4722no—
205C4#1683751712yes—
206C4#1683752212yes—
207C4#1683758512yes—
208C2—41no—
209C2#2142442312yes—
210C2#2142448911yescharacteristic
subgroupG/H
centerC2×C4#14273696
commutatorC42×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#2986C2
socleC22×C59#386
prime radicalC23×C59#123
cosocleC2×C42×C59C23
hypercenter#2986D59
hypocenterC59#9068
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2986

Complements

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

NH ≅ G/Ntype
126. C59#9068semidirect

Maximal subgroups

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

subgroupindex
#214346062
#214226912
#214225162
#214219322
C59×#29862
#906859