Finite Group Databasebeta

← #28482192

Subgroups — #28482192

Order 15104.

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

normal subgroups only

This group has 786 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#21426678C211yesmaximal, characteristic
2#21424011C211yesmaximal, characteristic
3C59⋊#1304C214yesmaximal, complemented
4C59×#1781C211yesmaximal, characteristic
5C2×#14273686C412yescomplemented
6C2×#14273642—22no—
7#16837305—22no—
8#16837305—22no—
9#16837258C412yescomplemented
10#16837258C2212yes—
11#16837258C2212yes—
12C23×D4×C59C2211yescharacteristic
13C2×#99×C59—22no—
14C59×#379C2212yes—
15#14273686—44no—
16C2×C4⋊Dic59—22no—
17C2×C22⋊Dic59—22no—
18C2×C22⋊Dic59—24no—
19C2×C22⋊Dic59—22no—
20C2×C22⋊Dic59—22no—
21C2×C22⋊Dic59—24no—
22C2×C22⋊Dic59C2×C414yes—
23C2×C4×Dic59—22no—
24#14273642—44no—
25C25×C59C2×C411yescharacteristic
26C25×C59C2311yescharacteristic
27C22×D4×C59—24no—
28C22×D4×C59—44no—
29C22×D4×C59D412yes—
30C22×D4×C59D412yes—
31C23×C4×C59C2×C411yescharacteristic
32C2×C22⋊C4×C59—22no—
33C2×C22⋊C4×C59—24no—
34#99×C59—44no—
35C24×C59—22no—
36C24×C59—42no—
37C24×C59—42no—
38C24×C59—82no—
39C24×C59—82no—
40C24×C59C22⋊C412yes—
41C24×C59C22×C411yescharacteristic
42C24×C59C2×D411yescharacteristic
43C24×C59C2×D411yescharacteristic
44C24×C59#4114yes—
45C2×D4×C59—24no—
46C2×D4×C59—24no—
47C2×D4×C59—24no—
48C2×D4×C59—24no—
49C2×D4×C59—42no—
50C2×D4×C59—42no—
51C2×D4×C59—416no—
52C22×C4×C59—22no—
53C22×C4×C59—24no—
54C22×C4×C59—42no—
55C22×C4×C59C22⋊C412yes—
56C22×Dic59—24no—
57C22×Dic59—42no—
58C22⋊C4×C59—44no—
59C22⋊C4×C59—84no—
60C22⋊Dic59—44no—
61C22⋊Dic59—44no—
62C22⋊Dic59—82no—
63C22⋊Dic59—82no—
64C22⋊Dic59—84no—
65C22⋊Dic59—84no—
66C4⋊Dic59—44no—
67C4×Dic59—44no—
68C23×C59—22no—
69C23×C59—22no—
70C23×C59—22no—
71C23×C59—22no—
72C23×C59—22no—
73C23×C59—22no—
74C23×C59—42no—
75C23×C59—42no—
76C23×C59—42no—
77C23×C59—44no—
78C23×C59—44no—
79C23×C59—44no—
80C23×C59—44no—
81C23×C59—44no—
82C23×C59—82no—
83C23×C59—82no—
84C23×C59—88no—
85C23×C59—88no—
86C23×C59C2×C22⋊C411yescharacteristic
87C23×C59#11712yes—
88C23×C59#12312yes—
89C23×C59#12312yes—
90D4×C59—48no—
91D4×C59—48no—
92C2×C4×C59—28no—
93C2×C4×C59—22no—
94C2×C4×C59—22no—
95C2×C4×C59—82no—
96C2×C4×C59—84no—
97C2×C4×C59#9914yes—
98C2×Dic59—44no—
99C2×Dic59—44no—
100C2×Dic59—44no—
101C2×Dic59—82no—
102C2×Dic59—84no—
103#8748—591nomaximal, Sylow
104C22×C59—22no—
105C22×C59—22no—
106C22×C59—22no—
107C22×C59—22no—
108C22×C59—24no—
109C22×C59—24no—
110C22×C59—22no—
111C22×C59—22no—
112C22×C59—44no—
113C22×C59—42no—
114C22×C59—44no—
115C22×C59—82no—
116C22×C59—82no—
117C22×C59—82no—
118C22×C59—82no—
119C22×C59—88no—
120C22×C59—88no—
121C22×C59#38111yescharacteristic
122C22×C59C2×#9912yes—
123C4×C59—24no—
124C4×C59—162no—
125Dic59—84no—
126Dic59—162no—
127#2309—591no—
128#1781—591no—
129#1781D5911yescharacteristic
130#1304—594no—
131C2×C59—22no—
132C2×C59—42no—
133C2×C59—42no—
134C2×C59—42no—
135C2×C59—82no—
136C2×C59#181911yescharacteristic
137C2×C59#182812yes—
138C23×D4C2×D5911yescharacteristic
139C2×#117—592no—
140C2×#99—22no—
141C2×#99—1182no—
142#390—1182no—
143#390—1182no—
144#379—592no—
145#379—592no—
146#379—592no—
147#379C2×D5912yes—
148C59#874811yescharacteristic, complemented, Sylow
149C25C4×D5911yescharacteristic
150C25C22×D5911yescharacteristic
151C22×D4—24no—
152C22×D4—44no—
153C22×D4D23612yes—
154C22×D4C22⋊D5912yes—
155C23×C4C4×D5911yescharacteristic
156#117—2364no—
157C2×C4⋊C4—1182no—
158C2×C22⋊C4—22no—
159C2×C22⋊C4—24no—
160C2×C22⋊C4—594no—
161C2×C22⋊C4—1184no—
162C2×C22⋊C4—1182no—
163C2×C22⋊C4—1182no—
164C2×C22⋊C4—1184no—
165C2×C22⋊C4—1182no—
166C2×C42—1182no—
167#99—44no—
168#99—2364no—
169C24—22no—
170C24—42no—
171C24—42no—
172C24—82no—
173C24—82no—
174C24(C2×D59)⋊C412yes—
175C24C2×C4×D5911yescharacteristic
176C24C2×D23611yescharacteristic
177C24#1174568714yes—
178C24C2×C22⋊D5911yescharacteristic
179C2×D4—24no—
180C2×D4—24no—
181C2×D4—24no—
182C2×D4—24no—
183C2×D4—42no—
184C2×D4—42no—
185C2×D4—416no—
186C22×C4—22no—
187C22×C4—24no—
188C22×C4—42no—
189C22×C4—1184no—
190C22×C4—2362no—
191C22×C4(C2×D59)⋊C412yes—
192C4⋊C4—2364no—
193C22⋊C4—44no—
194C22⋊C4—84no—
195C22⋊C4—4724no—
196C22⋊C4—4722no—
197C22⋊C4—4722no—
198C22⋊C4—4724no—
199C22⋊C4—2364no—
200C22⋊C4—2364no—
201C42—2364no—
202C23—22no—
203C23—22no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23—22no—
208C23—42no—
209C23—44no—
210C23—42no—
211C23—44no—
212C23—42no—
213C23—44no—
214C23—44no—
215C23—44no—
216C23—82no—
217C23—82no—
218C23—88no—
219C23—88no—
220C23C2×(C2×D59)⋊C411yescharacteristic
221C23#1427368312yes—
222C23#1427370812yes—
223C23#1427371112yes—
224D4—48no—
225D4—48no—
226C2×C4—28no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—82no—
230C2×C4—84no—
231C2×C4—4724no—
232C2×C4—4722no—
233C2×C4—2364no—
234C2×C4—2364no—
235C2×C4—2364no—
236C2×C4#1427364114yes—
237C22—22no—
238C22—22no—
239C22—22no—
240C22—22no—
241C22—24no—
242C22—24no—
243C22—22no—
244C22—22no—
245C22—44no—
246C22—42no—
247C22—44no—
248C22—82no—
249C22—82no—
250C22—82no—
251C22—82no—
252C22—88no—
253C22—88no—
254C22#1683726311yescharacteristic
255C22C2×#1427364112yes—
256C4—24no—
257C4—162no—
258C4—9442no—
259C4—4724no—
260C2—22no—
261C2—42no—
262C2—42no—
263C2—42no—
264C2—82no—
265C2#2142416811yescharacteristic
266C2#2142420212yes—
subgroupG/H
centerC22#16837263
commutatorC24×C59C22×C4
FrattiniC25C22×D59
FittingC59×#1781C2
socleC22×C59#381
prime radicalC23×D4×C59C22
cosocleC25×C59C23
hypercenter#1781D59
hypocenterC59#8748
LCSG ▷ C24×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C25 ◁ #1781

Complements

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

NH ≅ G/Ntype
3. C59⋊#1304C2semidirect
5. C2×#14273686C4semidirect
9. #16837258C4semidirect
148. C59#8748semidirect

Maximal subgroups

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

subgroupindex
#214266782
#214240112
C59⋊#13042
C59×#17812
#874859