Finite Group Databasebeta

← #28486501

Subgroups — #28486501

Order 15104.

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

normal subgroups only

This group has 610 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#21428383C211yesmaximal, characteristic
2#21426453C211yesmaximal, characteristic
3#21424193C212yesmaximal
4#21421950C212yesmaximal
5C59×#1463C211yesmaximal, characteristic
6C2×#14273686—21no—
7C2×#14273686C2211yescharacteristic
8#16837341C412yescomplemented
9#16837332C412yescomplemented
10#16837283—22no—
11#16837275—21no—
12#16837265—21no—
13#16837265C2211yescharacteristic
14C4⋊C4×Dic59—24no—
15C4×C22⋊Dic59—21no—
16C4×C22⋊Dic59C2212yes—
17#16837163—24no—
18C22×C4⋊C4×C59C2211yescharacteristic
19C59×#407C2212yes—
20C59×#324—22no—
21#14273686—28no—
22#14273686—22no—
23#14273686—22no—
24C2×C4⋊Dic59—22no—
25C2×C4⋊Dic59C2×C411yescharacteristic
26C2×C4⋊Dic59C2×C411yescharacteristic
27C2×Dic59⋊C4—22no—
28C2×C22⋊Dic59—22no—
29C2×C22⋊Dic59—21no—
30C2×C22⋊Dic59—21no—
31C2×C4×Dic59—22no—
32C2×C4×Dic59—21no—
33C2×C4×Dic59—22no—
34C2×C4×Dic59D414yes—
35C59⋊#95—22no—
36C59⋊#95—22no—
37C59⋊#95—22no—
38C59⋊#95—22no—
39C59⋊#95—22no—
40C59⋊#95—21no—
41C59⋊#95C2×C412yes—
42C23×C4×C59D411yescharacteristic
43C23×C4×C59D411yescharacteristic
44C23×C4×C59C2311yescharacteristic
45C2×M16×C59—22no—
46C2×C4⋊C4×C59—22no—
47C2×C4⋊C4×C59—22no—
48C2×C4⋊C4×C59C2×C412yes—
49C2×C4⋊C4×C59D412yes—
50C22⋊C8×C59—22no—
51C22⋊C8×C59—22no—
52C24×C59C2×D411yescharacteristic
53C22×C4×C59—21no—
54C22×C4×C59—21no—
55C22×C4×C59—24no—
56C22×C4×C59—21no—
57C22×C4×C59—21no—
58C22×C4×C59—42no—
59C22×C4×C59—42no—
60C22×C4×C59C22⋊C412yes—
61C22×C4×C59C22⋊C412yes—
62C22×C4×C59C22×C411yescharacteristic
63C22×C4×C59C2×D412yes—
64C22×C4×C59C2×D411yescharacteristic
65C22×C4×C59#4112yes—
66C22×Dic59—24no—
67C22×Dic59—22no—
68C22×Dic59—21no—
69C22×Dic59—21no—
70M16×C59—44no—
71C2×C8×C59—42no—
72C4⋊C4×C59—24no—
73C4⋊C4×C59—24no—
74C22⋊Dic59—28no—
75C22⋊Dic59—42no—
76C22⋊Dic59—41no—
77C22⋊Dic59—41no—
78C4⋊Dic59—28no—
79C4⋊Dic59—22no—
80C4⋊Dic59—22no—
81Dic59⋊C4—44no—
82C4×Dic59—28no—
83C4×Dic59—42no—
84C4×Dic59—44no—
85C4×Dic59—82no—
86C23×C59—22no—
87C23×C59—22no—
88C23×C59—41no—
89C23×C59C2×C22⋊C411yescharacteristic
90C23×C59#12011yescharacteristic
91C23×C59#12311yescharacteristic
92C2×C4×C59—22no—
93C2×C4×C59—22no—
94C2×C4×C59—24no—
95C2×C4×C59—22no—
96C2×C4×C59—22no—
97C2×C4×C59—24no—
98C2×C4×C59—22no—
99C2×C4×C59—41no—
100C2×C4×C59—41no—
101C2×C4×C59—42no—
102C2×C4×C59—42no—
103C2×C4×C59—42no—
104C2×C4×C59—81no—
105C2×C4×C59#10414yes—
106C2×C4×C59C4×D412yes—
107C2×C4×C59#12112yes—
108C2×Dic59—28no—
109C2×Dic59—44no—
110C2×Dic59—44no—
111C2×Dic59—42no—
112C2×Dic59—42no—
113C2×Dic59—42no—
114C2×Dic59—41no—
115C2×Dic59—41no—
116C2×Dic59—42no—
117C2×Dic59—42no—
118C8×C59—82no—
119#9478—591nomaximal, Sylow
120C22×C59—21no—
121C22×C59—21no—
122C22×C59—21no—
123C22×C59—21no—
124C22×C59—21no—
125C22×C59—21no—
126C22×C59—21no—
127C22×C59—44no—
128C22×C59#38611yescharacteristic
129C22×C59C2×#10412yes—
130C22×C59#45812yes—
131C4×C59—22no—
132C4×C59—22no—
133C4×C59—24no—
134C4×C59—42no—
135Dic59—48no—
136Dic59—82no—
137Dic59—81no—
138Dic59—81no—
139#2484—591no—
140#2274—591no—
141#1826—592no—
142#1463D5911yescharacteristic
143#1284—592no—
144C2×C59—22no—
145C2×C59—22no—
146C2×C59—41no—
147C2×C59#189011yescharacteristic
148C2×C59#189611yescharacteristic
149C2×C59#191211yescharacteristic
150C2×#117—591no—
151C2×#117—1181no—
152C22×C4⋊C4C2×D5911yescharacteristic
153#407C2×D5912yes—
154#400—592no—
155#398—592no—
156#387—1182no—
157#385—1181no—
158#381—591no—
159#381—1181no—
160C4×C4⋊C4—1184no—
161C4×C22⋊C4—592no—
162C4×C22⋊C4—1181no—
163#339—1184no—
164#324—22no—
165C59#947811yescharacteristic, complemented, Sylow
166C23×C4D23611yescharacteristic
167C23×C4D23611yescharacteristic
168C23×C4C22×D5911yescharacteristic
169C2×M16—22no—
170#117—1188no—
171#117—1182no—
172#117—1182no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—591no—
176C2×C4⋊C4—591no—
177C2×C4⋊C4—1182no—
178C2×C4⋊C4—1182no—
179C2×C4⋊C4C4×D5912yes—
180C2×C4⋊C4C22⋊D5912yes—
181C2×C22⋊C4—1182no—
182C2×C22⋊C4—1181no—
183C2×C22⋊C4—1181no—
184C2×C42—594no—
185C2×C42—1182no—
186C2×C42—1182no—
187C2×C42—1181no—
188C22⋊C8—22no—
189C22⋊C8—22no—
190#95—592no—
191#95—1182no—
192#95—1182no—
193#95—1182no—
194#95—1182no—
195#95—1182no—
196#95—1181no—
197C24C2×D23611yescharacteristic
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—24no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4—1184no—
206C22×C4—1182no—
207C22×C4—1181no—
208C22×C4—1181no—
209C22×C4(C2×D59)⋊C412yes—
210C22×C4(C2×D59)⋊C412yes—
211C22×C4C2×C4×D5911yescharacteristic
212C22×C4D4×D5912yes—
213C22×C4#1174568712yes—
214C22×C4C2×C22⋊D5911yescharacteristic
215M16—44no—
216C2×C8—42no—
217C4⋊C4—24no—
218C4⋊C4—24no—
219C4⋊C4—1188no—
220C4⋊C4—1182no—
221C4⋊C4—1182no—
222C4⋊C4—2364no—
223C22⋊C4—1188no—
224C22⋊C4—2362no—
225C22⋊C4—2361no—
226C22⋊C4—2361no—
227C42—1188no—
228C42—4722no—
229C42—2364no—
230C42—2362no—
231C23—22no—
232C23—22no—
233C23—41no—
234C23C2×(C2×D59)⋊C411yescharacteristic
235C23#1427369711yescharacteristic
236C23#1427371111yescharacteristic
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—24no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—24no—
243C2×C4—22no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—81no—
250C2×C4—1188no—
251C2×C4—2362no—
252C2×C4—2362no—
253C2×C4—2362no—
254C2×C4—2362no—
255C2×C4—2362no—
256C2×C4—2361no—
257C2×C4—2361no—
258C2×C4—2364no—
259C2×C4—2364no—
260C2×C4#1427365314yes—
261C2×C4(C22⋊D59)⋊C412yes—
262C2×C4#1427369912yes—
263C8—82no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—44no—
272C22#1683727911yescharacteristic
273C22C2×#1427365312yes—
274C22#1683759312yes—
275C4—22no—
276C4—22no—
277C4—24no—
278C4—42no—
279C4—4722no—
280C4—4721no—
281C4—4721no—
282C4—2368no—
283C2—22no—
284C2—22no—
285C2—41no—
286C2#2142450711yescharacteristic
287C2#2142453711yescharacteristic
288C2#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#9478
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
8. #16837341C4semidirect
9. #16837332C4semidirect
165. C59#9478semidirect

Maximal subgroups

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

subgroupindex
#214283832
#214264532
#214241932
#214219502
C59×#14632
#947859