Finite Group Databasebeta

← #28489350

Subgroups — #28489350

Order 15104.

502 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 81 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#21434040C212yesmaximal
2#21424171C211yesmaximal, characteristic
3#21422629C212yesmaximal
4#21422004C211yesmaximal, characteristic
5C59×#2817C211yesmaximal, characteristic
6C2×#14273686C2211yescharacteristic
7#16837740—24no—
8#16837735—22no—
9#16837730—22no—
10#16837442—22no—
11#16837411—22no—
12#16837366C2212yes—
13#16837265C2211yescharacteristic
14#16837168—22no—
15#16837139—24no—
16C2×C22⋊Q8×C59C2212yes—
17C59×#400—22no—
18C59×#397—22no—
19C59×#395—22no—
20C59×#381C2211yescharacteristic
21C2×#11745664—22no—
22#14273686—22no—
23#14273686—22no—
24C2×C4⋊Dic59D412yes—
25C2×C22⋊Dic59—21no—
26C2×C22⋊Dic59—21no—
27C2×C4×Dic59—21no—
28#14273660—24no—
29#14273658—24no—
30#14273651—24no—
31#14273651—24no—
32C22⋊(C59⋊C8)—22no—
33C22⋊(C59⋊C8)D414yes—
34C59⋊#95—22no—
35C22×Q8×C59D412yes—
36C23×C4×C59C2311yescharacteristic
37C22⋊Q8×C59—22no—
38C22⋊Q8×C59—22no—
39C22⋊Q8×C59—22no—
40C22⋊Q8×C59—22no—
41C2×C4⋊C4×C59—22no—
42C2×C4⋊C4×C59—22no—
43C2×C4⋊C4×C59D412yes—
44C2×C22⋊C4×C59—22no—
45C2×C22⋊C4×C59D412yes—
46#95×C59—24no—
47#95×C59—22no—
48#95×C59—22no—
49C24×C59C2×D411yescharacteristic
50C2×Q8×C59—22no—
51C2×Q8×C59—22no—
52C2×Q8×C59—44no—
53C22×C4×C59—22no—
54C22×C4×C59—22no—
55C22×C4×C59—22no—
56C22×C4×C59—42no—
57C22×C4×C59C2×D412yes—
58C22×C4×C59C2×D411yescharacteristic
59C22×C4×C59C2×D412yes—
60C22×C4×C59#4111yescharacteristic
61C22×Dic59—22no—
62C22×Dic59—41no—
63C4⋊C4×C59—22no—
64C4⋊C4×C59—22no—
65C4⋊C4×C59—42no—
66C4⋊C4×C59—42no—
67C4⋊C4×C59—82no—
68C22⋊C4×C59—42no—
69C22⋊C4×C59—42no—
70C22⋊C4×C59—42no—
71C22⋊Dic59—41no—
72C22⋊Dic59—41no—
73C22⋊Dic59—42no—
74C4⋊Dic59—22no—
75C4⋊Dic59—22no—
76C4×Dic59—42no—
77#11745664—44no—
78C2×C59⋊C8—24no—
79C23×C59—22no—
80C23×C59—42no—
81C23×C59#12011yescharacteristic
82C23×C59#12111yescharacteristic
83C23×C59#12711yescharacteristic
84Q8×C59—44no—
85Q8×C59—82no—
86C2×C4×C59—24no—
87C2×C4×C59—41no—
88C2×C4×C59—42no—
89C2×C4×C59—41no—
90C2×C4×C59—44no—
91C2×C4×C59—44no—
92C2×C4×C59—42no—
93C2×C4×C59—42no—
94C2×C4×C59—42no—
95C2×C4×C59—44no—
96C2×C4×C59#12012yes—
97C2×C4×C59#12112yes—
98C2×Dic59—42no—
99C2×Dic59—82no—
100C2×Dic59—81no—
101C2×Dic59—82no—
102C59⋊C8—44no—
103#9985—591nomaximal, Sylow
104C22×C59—22no—
105C22×C59—22no—
106C22×C59—22no—
107C22×C59—21no—
108C22×C59—21no—
109C22×C59—82no—
110C22×C59#39211yescharacteristic
111C22×C59#45812yes—
112C4×C59—22no—
113C4×C59—22no—
114C4×C59—82no—
115C4×C59—82no—
116C4×C59—82no—
117Dic59—82no—
118Dic59—161no—
119#3095—592no—
120#2817D5911yescharacteristic
121#1820—591no—
122#1511—592no—
123#1306—591no—
124C2×C59—22no—
125C2×C59—41no—
126C2×C59—41no—
127C2×C59#200912yes—
128C2×C59#202211yescharacteristic
129C2×C22⋊Q8C2×D5912yes—
130C2×#117—591no—
131#485—1184no—
132#484—1182no—
133#483—1182no—
134#428—1182no—
135#419—1182no—
136#407—592no—
137#400—22no—
138#397—22no—
139#395—22no—
140#381—591no—
141#381C2×D5911yescharacteristic
142#342—1182no—
143#328—1184no—
144C59#998511yescharacteristic, complemented, Sylow
145C22×Q8C22⋊D5912yes—
146C23×C4C22×D5911yescharacteristic
147C2×M16—1182no—
148C22⋊Q8—22no—
149C22⋊Q8—22no—
150C22⋊Q8—22no—
151C22⋊Q8—22no—
152#117—1182no—
153#117—1182no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—592no—
157C2×C4⋊C4C22⋊D5912yes—
158C2×C22⋊C4—22no—
159C2×C22⋊C4—1181no—
160C2×C22⋊C4—1181no—
161C2×C22⋊C4C22⋊D5912yes—
162C2×C42—1181no—
163#107—1184no—
164#106—1184no—
165#103—1184no—
166#103—1184no—
167C22⋊C8—594no—
168C22⋊C8—1182no—
169#95—24no—
170#95—22no—
171#95—22no—
172#95—1182no—
173C24C2×C22⋊D5911yescharacteristic
174C2×Q8—22no—
175C2×Q8—22no—
176C2×Q8—44no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—22no—
180C22×C4—42no—
181C22×C4—1182no—
182C22×C4—2361no—
183C22×C4D4×D5911yescharacteristic
184C22×C4D4×D5912yes—
185C22×C4#1174568711yescharacteristic
186C22×C4C2×C22⋊D5912yes—
187M16—2364no—
188C2×C8—1184no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—42no—
192C4⋊C4—42no—
193C4⋊C4—82no—
194C4⋊C4—1182no—
195C4⋊C4—1182no—
196C22⋊C4—42no—
197C22⋊C4—42no—
198C22⋊C4—42no—
199C22⋊C4—2362no—
200C22⋊C4—2361no—
201C22⋊C4—2361no—
202C42—2362no—
203C23—22no—
204C23—42no—
205C23#1427369611yescharacteristic
206C23#1427369811yescharacteristic
207C23#1427372311yescharacteristic
208Q8—44no—
209Q8—82no—
210C2×C4—24no—
211C2×C4—41no—
212C2×C4—42no—
213C2×C4—41no—
214C2×C4—44no—
215C2×C4—44no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—44no—
220C2×C4—4721no—
221C2×C4—4722no—
222C2×C4—4722no—
223C2×C4—2362no—
224C2×C4#1427369512yes—
225C2×C4#1427369912yes—
226C8—2364no—
227C22—22no—
228C22—22no—
229C22—22no—
230C22—21no—
231C22—21no—
232C22—82no—
233C22#1683731011yescharacteristic
234C22#1683759212yes—
235C4—22no—
236C4—22no—
237C4—82no—
238C4—82no—
239C4—82no—
240C4—9441no—
241C4—4722no—
242C2—22no—
243C2—41no—
244C2—41no—
245C2#2142515612yes—
246C2#2142522511yescharacteristic
subgroupG/H
centerC22#16837310
commutator, cosocleC23×C4×C59C23
FrattiniC23×C4C22×D59
FittingC59×#2817C2
socleC22×C59#392
prime radicalC24×C59C2×D4
hypercenter#2817D59
hypocenterC59#9985
LCSG ▷ C23×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2817

Complements

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

NH ≅ G/Ntype
144. C59#9985semidirect

Maximal subgroups

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

subgroupindex
#214340402
#214241712
#214226292
#214220042
C59×#28172
#998559