Finite Group Databasebeta

← #28486391

Subgroups — #28486391

Order 15104.

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

normal subgroups only

This group has 432 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#21429308C211yesmaximal, characteristic
3#21422812C212yesmaximal
4#21421951C212yesmaximal
5C59×#1467C211yesmaximal, characteristic
6C2×#14273727C2211yescharacteristic
7#16837533—24no—
8#16837459—21no—
9#16837459C2212yes—
10#16837455—21no—
11#16837341—21no—
12#16837341—21no—
13#16837309C412yes—
14#16837308—21no—
15#16837308—21no—
16#16837267C412yes—
17C4×C4⋊Dic59C2211yescharacteristic
18#16837147—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×C4×Dic59C2×C412yes—
30C4⋊(C59⋊C8)—22no—
31C4⋊(C59⋊C8)—22no—
32C4⋊(C59⋊C8)D414yes—
33C22⋊(C59⋊C8)—22no—
34#14273638—22no—
35#14273638—22no—
36C4×C59⋊C8—22no—
37C59⋊#95—22no—
38C59⋊#95—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—44no—
67C2×Dic118—41no—
68C2×Dic118—41no—
69C2×C8×C59—42no—
70C4⋊C4×C59—22no—
71C4⋊C4×C59—22no—
72C4⋊C4×C59—22no—
73C42×C59—21no—
74C42×C59—21no—
75C42×C59—21no—
76C42×C59—21no—
77C42×C59C2×D412yes—
78C42×C59#4112yes—
79C4⋊Dic59—24no—
80C4⋊Dic59—42no—
81C4⋊Dic59—42no—
82C4×Dic59—42no—
83C2×C59⋊C8—24no—
84C23×C59C2×C22⋊C411yescharacteristic
85Q8×C59—44no—
86C2×C4×C59—21no—
87C2×C4×C59—21no—
88C2×C4×C59—21no—
89C2×C4×C59—21no—
90C2×C4×C59—22no—
91C2×C4×C59—21no—
92C2×C4×C59—21no—
93C2×C4×C59—21no—
94C2×C4×C59—21no—
95C2×C4×C59—21no—
96C2×C4×C59—41no—
97C2×C4×C59—41no—
98C2×C4×C59—41no—
99C2×C4×C59#10112yes—
100C2×C4×C59C4×D412yes—
101C2×C4×C59#12011yescharacteristic
102C2×C4×C59#12112yes—
103C2×C4×C59#12311yescharacteristic
104C2×Dic59—42no—
105C2×Dic59—44no—
106C2×Dic59—42no—
107C2×Dic59—42no—
108C2×Dic59—42no—
109Dic118—82no—
110Dic118—82no—
111C8×C59—82no—
112C59⋊C8—44no—
113#9456—591nomaximal, Sylow
114C22×C59—21no—
115C22×C59—21no—
116C22×C59#38611yescharacteristic
117C22×C59C2×#10111yescharacteristic
118C22×C59#41311yescharacteristic
119C4×C59—21no—
120C4×C59—22no—
121C4×C59—22no—
122C4×C59—22no—
123C4×C59—41no—
124C4×C59—41no—
125C4×C59—41no—
126C4×C59#45412yes—
127Dic59—82no—
128Dic59—82no—
129#2983—591no—
130#2568—591no—
131#1556—592no—
132#1467D5911yescharacteristic
133#1285—592no—
134C2×C59—21no—
135C2×C59—21no—
136C2×C59#188811yescharacteristic
137C2×C59#190111yescharacteristic
138C2×C59#190911yescharacteristic
139C2×C4⋊Q8—591no—
140C2×C4×Q8C2×D5911yescharacteristic
141#446—1184no—
142#432—592no—
143#432—1181no—
144#432C2×D5912yes—
145#431—1181no—
146#400—1181no—
147#400—1181no—
148#391—592no—
149#391—1181no—
150#391—1181no—
151#382—592no—
152C4×C4⋊C4—591no—
153#332—1184no—
154#324—21no—
155#324—21no—
156C59#945611yescharacteristic, complemented, Sylow
157C22×Q8—1181no—
158C22×Q8C4×D5911yescharacteristic
159C4⋊Q8—1182no—
160C4⋊Q8—1182no—
161C4×Q8—22no—
162C4×Q8—22no—
163C2×C4⋊C4—592no—
164C2×C4⋊C4—1181no—
165C2×C4⋊C4—1181no—
166C2×C4⋊C4C4×D5911yescharacteristic
167C2×C4⋊C4C22⋊D5911yescharacteristic
168C2×C4⋊C4C22⋊D5911yescharacteristic
169C2×C42—592no—
170C2×C42D23611yescharacteristic
171C2×C42D23611yescharacteristic
172C2×C42C22×D5911yescharacteristic
173C4⋊C8—22no—
174C4⋊C8—594no—
175C4⋊C8—1182no—
176C4⋊C8—1182no—
177C22⋊C8—22no—
178C22⋊C8—1182no—
179#97—22no—
180#97—1182no—
181#97—1182no—
182C4×C8—1182no—
183#95—1182no—
184#95—1182no—
185#95—1182no—
186#95—1182no—
187#95—1181no—
188C2×Q8—22no—
189C2×Q8—22no—
190C2×Q8—41no—
191C2×Q8—2364no—
192C2×Q8—2361no—
193C2×Q8—2361no—
194C22×C4—1182no—
195C22×C4—1182no—
196C22×C4(C2×D59)⋊C411yescharacteristic
197C22×C4(C2×D59)⋊C411yescharacteristic
198C22×C4(C2×D59)⋊C411yescharacteristic
199C22×C4(C2×D59)⋊C411yescharacteristic
200C22×C4C2×C4×D5911yescharacteristic
201C22×C4C2×D23611yescharacteristic
202C22×C4C2×C22⋊D5911yescharacteristic
203C2×C8—42no—
204C2×C8—1184no—
205C4⋊C4—22no—
206C4⋊C4—22no—
207C4⋊C4—22no—
208C4⋊C4—1184no—
209C4⋊C4—2362no—
210C4⋊C4—2362no—
211C42—21no—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—2362no—
216C42D4×D5912yes—
217C42#1174568712yes—
218C23C2×(C2×D59)⋊C411yescharacteristic
219Q8—44no—
220Q8—4722no—
221Q8—4722no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—2362no—
236C2×C4—2362no—
237C2×C4—2364no—
238C2×C4—2362no—
239C2×C4—2362no—
240C2×C4#1427364512yes—
241C2×C4(C22⋊D59)⋊C412yes—
242C2×C4#1427369711yescharacteristic
243C2×C4#1427369912yes—
244C2×C4#1427371111yescharacteristic
245C8—82no—
246C8—2364no—
247C22—21no—
248C22—21no—
249C22#1683727911yescharacteristic
250C22C2×#1427364511yescharacteristic
251C22#1683738411yescharacteristic
252C4—21no—
253C4—22no—
254C4—22no—
255C4—22no—
256C4—41no—
257C4—41no—
258C4—41no—
259C4—4722no—
260C4—4722no—
261C4#1683757712yes—
262C2—21no—
263C2—21no—
264C2#2142449711yescharacteristic
265C2#2142456211yescharacteristic
266C2#2142461611yescharacteristic
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#9456
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
156. C59#9456semidirect

Maximal subgroups

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

subgroupindex
#214331812
#214293082
#214228122
#214219512
C59×#14672
#945659