Finite Group Databasebeta

← #28498333

Subgroups — #28498333

Order 15104.

394 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 87 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#21429081C211yesmaximal, characteristic
2#21422420C211yesmaximal, characteristic
3#21422029C214yesmaximal
4C59×#1467C211yesmaximal, characteristic
5C2×#14273727C411yescharacteristic
6C2×#14273725C412yes—
7#16837455—21no—
8#16837332—21no—
9#16837332—21no—
10#16837307C2212yes—
11#16837300—21no—
12#16837300—21no—
13C4×C4⋊Dic59C411yescharacteristic
14#16837128—21no—
15#16837128C2212yes—
16C2×C4×Q8×C59C2211yescharacteristic
17C59×#432—21no—
18C59×#324—21no—
19C59×#324C2212yes—
20C22×Dic118C2×C412yes—
21#14273727—41no—
22#14273727—41no—
23#14273725—44no—
24C2×C4⋊Dic59—21no—
25C2×C4⋊Dic59—21no—
26C2×C4⋊Dic59—21no—
27C2×Dic59⋊C4—22no—
28C2×Dic59⋊C4—22no—
29C2×C4×Dic59C2×C412yes—
30C4⋊(C59⋊C8)—41no—
31C22⋊(C59⋊C8)—22no—
32C4×C59⋊C8—41no—
33C59⋊#95—21no—
34C59⋊#95—22no—
35C59⋊#95—22no—
36C22×Q8×C59C2×C411yescharacteristic
37C4×Q8×C59—41no—
38C4×Q8×C59—41no—
39C2×C4⋊C4×C59D411yescharacteristic
40C2×C4⋊C4×C59D411yescharacteristic
41C2×C4⋊C4×C59C2311yescharacteristic
42C2×C42×C59C2×C411yescharacteristic
43C2×C42×C59D411yescharacteristic
44C2×C42×C59D411yescharacteristic
45C4⋊C8×C59—41no—
46C22⋊C8×C59—22no—
47#97×C59—41no—
48C2×Q8×C59—22no—
49C2×Q8×C59—22no—
50C2×Q8×C59—41no—
51C22×C4×C59C22⋊C411yescharacteristic
52C22×C4×C59C22⋊C411yescharacteristic
53C22×C4×C59C22⋊C411yescharacteristic
54C22×C4×C59C22⋊C411yescharacteristic
55C22×C4×C59C22×C411yescharacteristic
56C22×C4×C59C2×D411yescharacteristic
57C22×C4×C59C2×D411yescharacteristic
58C22×Dic59—22no—
59C22×Dic59—22no—
60C2×Dic118—24no—
61C2×Dic118—42no—
62C2×Dic118—42no—
63C2×C8×C59—42no—
64C4⋊C4×C59—41no—
65C4⋊C4×C59—41no—
66C4⋊C4×C59—41no—
67C42×C59—21no—
68C42×C59—21no—
69C42×C59—21no—
70C42×C59—21no—
71C42×C59—21no—
72C42×C59—21no—
73C4⋊Dic59—24no—
74C4⋊Dic59—42no—
75C4⋊Dic59—41no—
76C4⋊Dic59—41no—
77Dic59⋊C4—44no—
78Dic59⋊C4—44no—
79C4×Dic59—42no—
80C2×C59⋊C8—42no—
81C23×C59C2×C22⋊C411yescharacteristic
82Q8×C59—44no—
83C2×C4×C59—21no—
84C2×C4×C59—21no—
85C2×C4×C59—21no—
86C2×C4×C59—21no—
87C2×C4×C59—22no—
88C2×C4×C59—21no—
89C2×C4×C59—21no—
90C2×C4×C59—21no—
91C2×C4×C59—21no—
92C2×C4×C59—21no—
93C2×C4×C59—21no—
94C2×C4×C59—41no—
95C2×C4×C59—41no—
96C2×C4×C59—41no—
97C2×C4×C59#9911yescharacteristic
98C2×C4×C59#9911yescharacteristic
99C2×C4×C59#10012yes—
100C2×C4×C59#13112yes—
101C2×Dic59—24no—
102C2×Dic59—42no—
103C2×Dic59—42no—
104C2×Dic59—42no—
105C2×Dic59—42no—
106C2×Dic59—42no—
107Dic118—84no—
108C8×C59—82no—
109C59⋊C8—82no—
110#11568—591nomaximal, Sylow
111C22×C59—21no—
112C22×C59—21no—
113C22×C59#40811yescharacteristic
114C22×C59C2×#9911yescharacteristic
115C22×C59C2×#10011yescharacteristic
116C4×C59—21no—
117C4×C59—22no—
118C4×C59—22no—
119C4×C59—41no—
120C4×C59—41no—
121C4×C59—41no—
122C4×C59—41no—
123C4×C59#35612yes—
124Dic59—44no—
125Dic59—82no—
126#2546—591no—
127#1467D5911yescharacteristic
128#1461—591no—
129#1319—594no—
130C2×C59—21no—
131C2×C59—21no—
132C2×C59#147111yescharacteristic
133C2×C59#212911yescharacteristic
134C2×C59C2×#35611yescharacteristic
135C2×C4⋊Q8—592no—
136C2×C4⋊Q8—591no—
137C2×C4×Q8C2×D5911yescharacteristic
138#432—21no—
139#431—1181no—
140#398—1181no—
141#398—1181no—
142#391—592no—
143#389—1181no—
144#389—1181no—
145C4×C4⋊C4—591no—
146#324—21no—
147#324—592no—
148#324—1181no—
149#324C2×D5912yes—
150C59#1156811yescharacteristic, complemented, Sylow
151C22×Q8—592no—
152C22×Q8C4×D5911yescharacteristic
153C4⋊Q8—2361no—
154C4⋊Q8—2361no—
155C4⋊Q8—2364no—
156C4×Q8—41no—
157C4×Q8—41no—
158C2×C4⋊C4—1181no—
159C2×C4⋊C4—1182no—
160C2×C4⋊C4—1182no—
161C2×C4⋊C4—1181no—
162C2×C4⋊C4—1181no—
163C2×C4⋊C4D23611yescharacteristic
164C2×C4⋊C4C22⋊D5911yescharacteristic
165C2×C4⋊C4C22×D5911yescharacteristic
166C2×C42—592no—
167C2×C42C4×D5911yescharacteristic
168C2×C42D23611yescharacteristic
169C2×C42C22⋊D5911yescharacteristic
170C4⋊C8—41no—
171C4⋊C8—2361no—
172C22⋊C8—22no—
173C22⋊C8—1182no—
174#97—41no—
175C4×C8—2361no—
176#95—1181no—
177#95—1182no—
178#95—1182no—
179C2×Q8—22no—
180C2×Q8—22no—
181C2×Q8—41no—
182C2×Q8—1184no—
183C2×Q8—2362no—
184C2×Q8—2362no—
185C22×C4—1182no—
186C22×C4—1182no—
187C22×C4(C2×D59)⋊C411yescharacteristic
188C22×C4(C2×D59)⋊C411yescharacteristic
189C22×C4(C2×D59)⋊C411yescharacteristic
190C22×C4(C2×D59)⋊C411yescharacteristic
191C22×C4C2×C4×D5911yescharacteristic
192C22×C4C2×D23611yescharacteristic
193C22×C4C2×C22⋊D5911yescharacteristic
194C2×C8—42no—
195C2×C8—2362no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—1184no—
200C4⋊C4—2364no—
201C4⋊C4—2362no—
202C4⋊C4—2361no—
203C4⋊C4—2361no—
204C4⋊C4—2364no—
205C42—21no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—2362no—
212C23C2×(C2×D59)⋊C411yescharacteristic
213Q8—44no—
214Q8—4724no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—1184no—
230C2×C4—2362no—
231C2×C4—2362no—
232C2×C4—2362no—
233C2×C4—2362no—
234C2×C4—2362no—
235C2×C4#1427364111yescharacteristic
236C2×C4#1427364111yescharacteristic
237C2×C4#1427364312yes—
238C2×C4#1427373512yes—
239C8—82no—
240C8—4722no—
241C22—21no—
242C22—21no—
243C22#1683737011yescharacteristic
244C22C2×#1427364111yescharacteristic
245C22C2×#1427364311yescharacteristic
246C4—21no—
247C4—22no—
248C4—22no—
249C4—41no—
250C4—41no—
251C4—41no—
252C4—41no—
253C4—4722no—
254C4—2364no—
255C4#1683720012yes—
256C2—21no—
257C2—21no—
258C2#2142245711yescharacteristic
259C2#2142577011yescharacteristic
260C2C2×#1683720011yescharacteristic
subgroupG/H
centerC22C2×#14273641
commutatorC22×C4×C59C22×C4
FrattiniC2×C4⋊C4C22×D59
FittingC59×#1467C2
socleC22×C59C2×#99
prime radicalC23×C59C2×C22⋊C4
cosocleC2×C4⋊C4×C59C23
hypercenter#1467D59
hypocenterC59#11568
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

Complements

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

NH ≅ G/Ntype
150. C59#11568semidirect

Maximal subgroups

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

subgroupindex
#214290812
#214224202
#214220292
C59×#14672
#1156859