Finite Group Databasebeta

← #28486521

Subgroups — #28486521

Order 15104.

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

normal subgroups only

This group has 518 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#21428383C211yesmaximal, characteristic
2#21426699C211yesmaximal, characteristic
3#21424193C212yesmaximal
4#21421950C212yesmaximal
5C59×#1463C211yesmaximal, characteristic
6C2×#14273686C2211yescharacteristic
7#16837341C412yescomplemented
8#16837332C412yescomplemented
9#16837288—24no—
10#16837283—22no—
11#16837275—21no—
12#16837265—21no—
13#16837265—21no—
14#16837265C2211yescharacteristic
15#16837262—21no—
16C4×C22⋊Dic59C2212yes—
17#16837163—24no—
18C22×C4⋊C4×C59C2211yescharacteristic
19C59×#407C2212yes—
20C59×#324—22no—
21#14273686—22no—
22#14273686—22no—
23C2×C4⋊Dic59—22no—
24C2×C4⋊Dic59C2×C411yescharacteristic
25C2×C4⋊Dic59C2×C411yescharacteristic
26C2×Dic59⋊C4—22no—
27C2×C22⋊Dic59—22no—
28C2×C22⋊Dic59—21no—
29C2×C22⋊Dic59—21no—
30C2×C4×Dic59—21no—
31C2×C4×Dic59D414yes—
32C59⋊#95—22no—
33C59⋊#95—24no—
34C59⋊#95—22no—
35C59⋊#95—22no—
36C59⋊#95—22no—
37C59⋊#95—22no—
38C59⋊#95—21no—
39C59⋊#95C2×C412yes—
40C23×C4×C59D411yescharacteristic
41C23×C4×C59D411yescharacteristic
42C23×C4×C59C2311yescharacteristic
43C2×M16×C59—22no—
44C2×C4⋊C4×C59—22no—
45C2×C4⋊C4×C59—22no—
46C2×C4⋊C4×C59C2×C412yes—
47C2×C4⋊C4×C59D412yes—
48C22⋊C8×C59—22no—
49C22⋊C8×C59—22no—
50C24×C59C2×D411yescharacteristic
51C22×C4×C59—21no—
52C22×C4×C59—21no—
53C22×C4×C59—21no—
54C22×C4×C59—21no—
55C22×C4×C59—42no—
56C22×C4×C59—42no—
57C22×C4×C59—42no—
58C22×C4×C59C22⋊C412yes—
59C22×C4×C59C22⋊C412yes—
60C22×C4×C59C22×C411yescharacteristic
61C22×C4×C59C2×D412yes—
62C22×C4×C59C2×D411yescharacteristic
63C22×C4×C59#4112yes—
64C22×Dic59—22no—
65C22×Dic59—21no—
66C22×Dic59—21no—
67C22×Dic59—24no—
68M16×C59—44no—
69C2×C8×C59—42no—
70C4⋊C4×C59—24no—
71C4⋊C4×C59—24no—
72C22⋊Dic59—44no—
73C22⋊Dic59—42no—
74C22⋊Dic59—41no—
75C22⋊Dic59—41no—
76C4⋊Dic59—22no—
77C4⋊Dic59—22no—
78C4⋊Dic59—82no—
79Dic59⋊C4—44no—
80C4×Dic59—42no—
81C4×Dic59—44no—
82C23×C59—22no—
83C23×C59—22no—
84C23×C59—41no—
85C23×C59C2×C22⋊C411yescharacteristic
86C23×C59#12011yescharacteristic
87C23×C59#12311yescharacteristic
88C2×C4×C59—24no—
89C2×C4×C59—22no—
90C2×C4×C59—22no—
91C2×C4×C59—22no—
92C2×C4×C59—22no—
93C2×C4×C59—41no—
94C2×C4×C59—41no—
95C2×C4×C59—42no—
96C2×C4×C59—42no—
97C2×C4×C59—42no—
98C2×C4×C59—42no—
99C2×C4×C59—42no—
100C2×C4×C59—81no—
101C2×C4×C59C4×D412yes—
102C2×C4×C59#12112yes—
103C2×Dic59—42no—
104C2×Dic59—44no—
105C2×Dic59—42no—
106C2×Dic59—44no—
107C2×Dic59—42no—
108C2×Dic59—41no—
109C2×Dic59—41no—
110C2×Dic59—42no—
111C2×Dic59—42no—
112C2×Dic59—44no—
113C8×C59—82no—
114#9482—591nomaximal, Sylow
115C22×C59—21no—
116C22×C59—21no—
117C22×C59—21no—
118C22×C59—21no—
119C22×C59—21no—
120C22×C59—21no—
121C22×C59—21no—
122C22×C59—44no—
123C22×C59#38611yescharacteristic
124C22×C59#42112yes—
125C22×C59#45812yes—
126C4×C59—22no—
127C4×C59—22no—
128C4×C59—42no—
129C4×C59—42no—
130Dic59—84no—
131Dic59—82no—
132Dic59—81no—
133Dic59—81no—
134#2484—591no—
135#2313—591no—
136#1826—592no—
137#1463D5911yescharacteristic
138#1284—592no—
139C2×C59—22no—
140C2×C59—22no—
141C2×C59—41no—
142C2×C59#189011yescharacteristic
143C2×C59#189711yescharacteristic
144C2×C59#191211yescharacteristic
145C2×#117—591no—
146C22×C4⋊C4C2×D5911yescharacteristic
147#407C2×D5912yes—
148#400—592no—
149#398—592no—
150#387—1184no—
151#387—1182no—
152#385—1181no—
153#381—591no—
154#381—1181no—
155#381—1181no—
156#380—1181no—
157C4×C22⋊C4—592no—
158#339—1184no—
159#324—22no—
160C59#948211yescharacteristic, complemented, Sylow
161C23×C4D23611yescharacteristic
162C23×C4D23611yescharacteristic
163C23×C4C22×D5911yescharacteristic
164C2×M16—22no—
165#117—1182no—
166#117—1182no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—591no—
170C2×C4⋊C4—591no—
171C2×C4⋊C4—1182no—
172C2×C4⋊C4—1182no—
173C2×C4⋊C4C4×D5912yes—
174C2×C4⋊C4C22⋊D5912yes—
175C2×C22⋊C4—1181no—
176C2×C22⋊C4—1182no—
177C2×C22⋊C4—1181no—
178C2×C42—594no—
179C2×C42—1181no—
180C22⋊C8—22no—
181C22⋊C8—22no—
182#95—592no—
183#95—1182no—
184#95—1184no—
185#95—1182no—
186#95—1182no—
187#95—1182no—
188#95—1182no—
189#95—1181no—
190C24C2×D23611yescharacteristic
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—42no—
196C22×C4—42no—
197C22×C4—42no—
198C22×C4—1182no—
199C22×C4—1181no—
200C22×C4—1181no—
201C22×C4—1184no—
202C22×C4(C2×D59)⋊C412yes—
203C22×C4(C2×D59)⋊C412yes—
204C22×C4C2×C4×D5911yescharacteristic
205C22×C4D4×D5912yes—
206C22×C4#1174568712yes—
207C22×C4C2×C22⋊D5911yescharacteristic
208M16—44no—
209C2×C8—42no—
210C4⋊C4—24no—
211C4⋊C4—24no—
212C4⋊C4—1182no—
213C4⋊C4—1182no—
214C4⋊C4—4722no—
215C4⋊C4—2364no—
216C22⋊C4—2364no—
217C22⋊C4—2362no—
218C22⋊C4—2361no—
219C22⋊C4—2361no—
220C42—2364no—
221C42—2362no—
222C23—22no—
223C23—22no—
224C23—41no—
225C23C2×(C2×D59)⋊C411yescharacteristic
226C23#1427369711yescharacteristic
227C23#1427371111yescharacteristic
228C2×C4—24no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—41no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—81no—
241C2×C4—2362no—
242C2×C4—2364no—
243C2×C4—2362no—
244C2×C4—2364no—
245C2×C4—2362no—
246C2×C4—2362no—
247C2×C4—2362no—
248C2×C4—2361no—
249C2×C4—2361no—
250C2×C4—2364no—
251C2×C4(C22⋊D59)⋊C412yes—
252C2×C4#1427369912yes—
253C8—82no—
254C22—21no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—44no—
262C22#1683727911yescharacteristic
263C22#1683741812yes—
264C22#1683759312yes—
265C4—22no—
266C4—22no—
267C4—42no—
268C4—42no—
269C4—4724no—
270C4—4722no—
271C4—4721no—
272C4—4721no—
273C2—22no—
274C2—22no—
275C2—41no—
276C2#2142450711yescharacteristic
277C2#2142454211yescharacteristic
278C2#2142463111yescharacteristic
subgroupG/H
centerC22#16837279
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
FittingC59×#1463C2
socleC22×C59#386
prime radicalC24×C59C2×D4
cosocleC23×C4×C59C23
hypercenter#1463D59
hypocenterC59#9482
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
7. #16837341C4semidirect
8. #16837332C4semidirect
160. C59#9482semidirect

Maximal subgroups

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

subgroupindex
#214283832
#214266992
#214241932
#214219502
C59×#14632
#948259