Finite Group Databasebeta

← #28486381

Subgroups — #28486381

Order 15104.

448 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 103 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#21433181C211yesmaximal, characteristic
2#21429301C211yesmaximal, characteristic
3#21422814C212yesmaximal
4#21421951C212yesmaximal
5C59×#1467C211yesmaximal, characteristic
6C2×#14273727C2211yescharacteristic
7#16837533—24no—
8#16837459—21no—
9#16837459C2212yes—
10#16837455—21no—
11#16837322—21no—
12#16837322—21no—
13#16837309C412yes—
14#16837300—21no—
15#16837300—21no—
16#16837271C412yes—
17C4×C4⋊Dic59C2211yescharacteristic
18#16837149—24no—
19C2×C4×Q8×C59C2211yescharacteristic
20C59×#432C2212yes—
21C59×#324—21no—
22C59×#324—21no—
23C22×Dic118—21no—
24#14273727—22no—
25#14273727—22no—
26C2×C4⋊Dic59—21no—
27C2×C4⋊Dic59—21no—
28C2×C4⋊Dic59C2×C412yes—
29C2×Dic59⋊C4—22no—
30C2×Dic59⋊C4—22no—
31C2×C4×Dic59C2×C412yes—
32C4⋊(C59⋊C8)—22no—
33C4⋊(C59⋊C8)—22no—
34C4⋊(C59⋊C8)D414yes—
35C22⋊(C59⋊C8)—22no—
36#14273638—22no—
37#14273638—22no—
38C4×C59⋊C8—22no—
39C59⋊#95—22no—
40C59⋊#95—22no—
41C59⋊#95—21no—
42C22×Q8×C59C2×C411yescharacteristic
43C4×Q8×C59—22no—
44C4×Q8×C59—22no—
45C2×C4⋊C4×C59C2×C411yescharacteristic
46C2×C4⋊C4×C59D411yescharacteristic
47C2×C4⋊C4×C59D411yescharacteristic
48C2×C42×C59D411yescharacteristic
49C2×C42×C59D411yescharacteristic
50C2×C42×C59C2311yescharacteristic
51C4⋊C8×C59—22no—
52C22⋊C8×C59—22no—
53#97×C59—22no—
54C2×Q8×C59—22no—
55C2×Q8×C59—22no—
56C2×Q8×C59—41no—
57C22×C4×C59C22⋊C411yescharacteristic
58C22×C4×C59C22⋊C411yescharacteristic
59C22×C4×C59C22⋊C411yescharacteristic
60C22×C4×C59C22⋊C411yescharacteristic
61C22×C4×C59C22×C411yescharacteristic
62C22×C4×C59C2×D411yescharacteristic
63C22×C4×C59C2×D411yescharacteristic
64C22×Dic59—22no—
65C22×Dic59—22no—
66C2×Dic118—42no—
67C2×Dic118—82no—
68C2×C8×C59—42no—
69C4⋊C4×C59—22no—
70C4⋊C4×C59—22no—
71C4⋊C4×C59—22no—
72C42×C59—21no—
73C42×C59—21no—
74C42×C59—21no—
75C42×C59—21no—
76C42×C59C2×D412yes—
77C42×C59#4112yes—
78C4⋊Dic59—24no—
79C4⋊Dic59—24no—
80C4⋊Dic59—41no—
81C4⋊Dic59—41no—
82Dic59⋊C4—82no—
83Dic59⋊C4—82no—
84C4×Dic59—42no—
85C2×C59⋊C8—24no—
86C23×C59C2×C22⋊C411yescharacteristic
87Q8×C59—44no—
88C2×C4×C59—21no—
89C2×C4×C59—21no—
90C2×C4×C59—21no—
91C2×C4×C59—21no—
92C2×C4×C59—22no—
93C2×C4×C59—21no—
94C2×C4×C59—21no—
95C2×C4×C59—21no—
96C2×C4×C59—21no—
97C2×C4×C59—21no—
98C2×C4×C59—41no—
99C2×C4×C59—41no—
100C2×C4×C59—41no—
101C2×C4×C59#10112yes—
102C2×C4×C59C4×D412yes—
103C2×C4×C59#12011yescharacteristic
104C2×C4×C59#12112yes—
105C2×C4×C59#12311yescharacteristic
106C2×Dic59—24no—
107C2×Dic59—42no—
108C2×Dic59—42no—
109C2×Dic59—42no—
110C2×Dic59—42no—
111C2×Dic59—42no—
112Dic118—84no—
113C8×C59—82no—
114C59⋊C8—44no—
115#9454—591nomaximal, Sylow
116C22×C59—21no—
117C22×C59—21no—
118C22×C59#38611yescharacteristic
119C22×C59C2×#10111yescharacteristic
120C22×C59#41311yescharacteristic
121C4×C59—21no—
122C4×C59—22no—
123C4×C59—22no—
124C4×C59—22no—
125C4×C59—41no—
126C4×C59—41no—
127C4×C59—41no—
128C4×C59#45612yes—
129Dic59—44no—
130Dic59—82no—
131#2983—591no—
132#2567—591no—
133#1556—592no—
134#1467D5911yescharacteristic
135#1285—592no—
136C2×C59—21no—
137C2×C59—21no—
138C2×C59#188611yescharacteristic
139C2×C59#190111yescharacteristic
140C2×C59#191011yescharacteristic
141C2×C4⋊Q8—591no—
142C2×C4×Q8C2×D5911yescharacteristic
143#446—1184no—
144#432—592no—
145#432—1181no—
146#432C2×D5912yes—
147#431—1181no—
148#395—1181no—
149#395—1181no—
150#391—592no—
151#389—1181no—
152#389—1181no—
153#384—592no—
154C4×C4⋊C4—591no—
155#332—1184no—
156#324—21no—
157#324—21no—
158C59#945411yescharacteristic, complemented, Sylow
159C22×Q8—1181no—
160C22×Q8C4×D5911yescharacteristic
161C4⋊Q8—1182no—
162C4⋊Q8—1182no—
163C4×Q8—22no—
164C4×Q8—22no—
165C2×C4⋊C4—592no—
166C2×C4⋊C4—1181no—
167C2×C4⋊C4—1182no—
168C2×C4⋊C4—1182no—
169C2×C4⋊C4—1181no—
170C2×C4⋊C4C4×D5911yescharacteristic
171C2×C4⋊C4C22⋊D5911yescharacteristic
172C2×C4⋊C4C22⋊D5911yescharacteristic
173C2×C42—592no—
174C2×C42D23611yescharacteristic
175C2×C42D23611yescharacteristic
176C2×C42C22×D5911yescharacteristic
177C4⋊C8—22no—
178C4⋊C8—594no—
179C4⋊C8—1182no—
180C4⋊C8—1182no—
181C22⋊C8—22no—
182C22⋊C8—1182no—
183#97—22no—
184#97—1182no—
185#97—1182no—
186C4×C8—1182no—
187#95—1182no—
188#95—1182no—
189#95—1181no—
190C2×Q8—22no—
191C2×Q8—22no—
192C2×Q8—41no—
193C2×Q8—4722no—
194C2×Q8—2362no—
195C22×C4—1182no—
196C22×C4—1182no—
197C22×C4(C2×D59)⋊C411yescharacteristic
198C22×C4(C2×D59)⋊C411yescharacteristic
199C22×C4(C2×D59)⋊C411yescharacteristic
200C22×C4(C2×D59)⋊C411yescharacteristic
201C22×C4C2×C4×D5911yescharacteristic
202C22×C4C2×D23611yescharacteristic
203C22×C4C2×C22⋊D5911yescharacteristic
204C2×C8—42no—
205C2×C8—1184no—
206C4⋊C4—22no—
207C4⋊C4—22no—
208C4⋊C4—22no—
209C4⋊C4—1184no—
210C4⋊C4—1184no—
211C4⋊C4—4722no—
212C4⋊C4—4722no—
213C4⋊C4—2361no—
214C4⋊C4—2361no—
215C42—21no—
216C42—21no—
217C42—21no—
218C42—21no—
219C42—2362no—
220C42D4×D5912yes—
221C42#1174568712yes—
222C23C2×(C2×D59)⋊C411yescharacteristic
223Q8—44no—
224Q8—4724no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—1184no—
239C2×C4—2362no—
240C2×C4—2362no—
241C2×C4—2362no—
242C2×C4—2362no—
243C2×C4—2362no—
244C2×C4#1427364512yes—
245C2×C4(C22⋊D59)⋊C412yes—
246C2×C4#1427369711yescharacteristic
247C2×C4#1427369912yes—
248C2×C4#1427371111yescharacteristic
249C8—82no—
250C8—2364no—
251C22—21no—
252C22—21no—
253C22#1683727911yescharacteristic
254C22C2×#1427364511yescharacteristic
255C22#1683738411yescharacteristic
256C4—21no—
257C4—22no—
258C4—22no—
259C4—22no—
260C4—41no—
261C4—41no—
262C4—41no—
263C4—4722no—
264C4—2364no—
265C4#1683758712yes—
266C2—21no—
267C2—21no—
268C2#2142448711yescharacteristic
269C2#2142456211yescharacteristic
270C2#2142462111yescharacteristic
subgroupG/H
centerC22#16837279
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1467C2
socleC22×C59#386
prime radicalC23×C59C2×C22⋊C4
cosocleC2×C42×C59C23
hypercenter#1467D59
hypocenterC59#9454
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

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

NH ≅ G/Ntype
158. C59#9454semidirect

Maximal subgroups

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

subgroupindex
#214331812
#214293012
#214228142
#214219512
C59×#14672
#945459