Finite Group Databasebeta

← #28498184

Subgroups — #28498184

Order 15104.

376 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 75 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#21426813C211yesmaximal, characteristic
2#21422438C212yesmaximal
3#21422040C211yesmaximal, characteristic
4#21422029C212yesmaximal
5C59×#1324C211yesmaximal, characteristic
6C2×#14273727C411yescharacteristic
7C2×#14273692C411yescharacteristic
8C2×#14273692C2211yescharacteristic
9#16837456—22no—
10#16837307C411yescharacteristic
11#16837307C2211yescharacteristic
12#16837285—22no—
13#16837285—22no—
14#16837248C411yescharacteristic
15#16837128C2212yes—
16#16837127—22no—
17C59×#382C2211yescharacteristic
18C59×#324C2212yes—
19C22×Dic118C2×C411yescharacteristic
20C22×Dic118C2×C411yescharacteristic
21#14273727—22no—
22#14273727—22no—
23#14273692—42no—
24#14273692—42no—
25C2×C4⋊Dic59—22no—
26C2×Dic59⋊C4—21no—
27C2×Dic59⋊C4D412yes—
28C2×C4×Dic59—21no—
29C2×C4×Dic59C2×C411yescharacteristic
30C2×C4×Dic59C2×C411yescharacteristic
31C2×C4×Dic59D412yes—
32Dic59⋊C8—42no—
33C22⋊(C59⋊C8)—22no—
34#14273637—42no—
35C59⋊#95—22no—
36C59⋊#95—21no—
37C59⋊#95—21no—
38C59⋊#95—22no—
39C2×C4⋊C4×C59C2×C411yescharacteristic
40C2×C4⋊C4×C59C2311yescharacteristic
41C2×C42×C59C2×C411yescharacteristic
42C22⋊C8×C59—22no—
43#95×C59—22no—
44C22×C4×C59—21no—
45C22×C4×C59—21no—
46C22×C4×C59C22×C411yescharacteristic
47C22×C4×C59C2×D412yes—
48C22×Dic59—21no—
49C22×Dic59—21no—
50C22×Dic59C22⋊C412yes—
51C22×Dic59C22⋊C411yescharacteristic
52C22×Dic59C22⋊C411yescharacteristic
53C2×Dic118—21no—
54C2×Dic118—21no—
55C2×Dic118—21no—
56C2×Dic118—41no—
57C2×Dic118—41no—
58C2×Dic118—41no—
59C2×Dic118—41no—
60C2×Dic118M1612yes—
61C2×C8×C59—42no—
62C4⋊C4×C59—41no—
63C4⋊C4×C59—41no—
64C42×C59—21no—
65C42×C59M1612yes—
66C4⋊Dic59—28no—
67Dic59⋊C4—42no—
68Dic59⋊C4—42no—
69C4×Dic59—22no—
70C4×Dic59—22no—
71C4×Dic59—22no—
72C4×Dic59—42no—
73C4×Dic59—41no—
74C2×C59⋊C8—42no—
75C23×C59C2×C22⋊C411yescharacteristic
76C2×C4×C59—21no—
77C2×C4×C59—21no—
78C2×C4×C59—22no—
79C2×C4×C59—22no—
80C2×C4×C59—41no—
81C2×C4×C59—41no—
82C2×C4×C59—42no—
83C2×C4×C59—42no—
84C2×C4×C59—41no—
85C2×C4×C59C2×M1611yescharacteristic
86C2×C4×C59C2×M1611yescharacteristic
87C2×Dic59—22no—
88C2×Dic59—22no—
89C2×Dic59—21no—
90C2×Dic59—22no—
91C2×Dic59—22no—
92C2×Dic59—41no—
93C2×Dic59—41no—
94C2×Dic59—41no—
95C2×Dic59—41no—
96C2×Dic59—41no—
97C2×Dic59—41no—
98C2×Dic59—41no—
99C2×Dic59#9912yes—
100Dic118—42no—
101Dic118—42no—
102Dic118—42no—
103Dic118—42no—
104C8×C59—82no—
105C59⋊C8—82no—
106#11536—591nomaximal, Sylow
107C22×C59—21no—
108C22×C59—21no—
109C22×C59#40711yescharacteristic
110C22×C59C2×#9911yescharacteristic
111C22×C59#41311yescharacteristic
112C4×C59—21no—
113C4×C59—21no—
114C4×C59—42no—
115C4×C59—42no—
116C4×C59—81no—
117Dic59—22no—
118Dic59—41no—
119Dic59—42no—
120Dic59—42no—
121Dic59—81no—
122#2327—591no—
123#1467—592no—
124#1324—591no—
125#1324D5911yescharacteristic
126#1319—592no—
127C2×C59—21no—
128C2×C59—21no—
129C2×C59#146511yescharacteristic
130C2×C59#212911yescharacteristic
131C2×C59#213311yescharacteristic
132C2×C4⋊Q8—591no—
133C2×C4×Q8—591no—
134C2×C4×Q8—591no—
135#432—1182no—
136#391—591no—
137#391—591no—
138#387—1182no—
139#387—1182no—
140#382C2×D5911yescharacteristic
141#376—591no—
142#324—592no—
143#324—1182no—
144#324C2×D5912yes—
145C59#1153611yescharacteristic, complemented, Sylow
146C22×Q8—591no—
147C22×Q8—591no—
148C4⋊Q8—1182no—
149C4⋊Q8—1182no—
150C4×Q8—2362no—
151C4×Q8—2362no—
152C2×C4⋊C4—592no—
153C2×C4⋊C4—1182no—
154C2×C4⋊C4—1181no—
155C2×C4⋊C4C4×D5911yescharacteristic
156C2×C4⋊C4C22×D5911yescharacteristic
157C2×C42—591no—
158C2×C42—592no—
159C2×C42—591no—
160C2×C42—1181no—
161C2×C42C4×D5911yescharacteristic
162C4⋊C8—2362no—
163C22⋊C8—22no—
164C22⋊C8—1182no—
165#97—2362no—
166#95—22no—
167#95—1181no—
168#95—1181no—
169#95—1182no—
170#95—1182no—
171C2×Q8—592no—
172C2×Q8—1181no—
173C2×Q8—1181no—
174C2×Q8—1181no—
175C2×Q8—2361no—
176C2×Q8—2361no—
177C2×Q8—2361no—
178C2×Q8—2361no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—591no—
182C22×C4—592no—
183C22×C4—591no—
184C22×C4—1181no—
185C22×C4—1181no—
186C22×C4C2×C4×D5911yescharacteristic
187C22×C4D4×D5912yes—
188C2×C8—42no—
189C2×C8—2362no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—1188no—
193C4⋊C4—2362no—
194C4⋊C4—2362no—
195C42—21no—
196C42—1182no—
197C42—1182no—
198C42—1182no—
199C42—2361no—
200C42—2362no—
201C42#1174565912yes—
202C23C22⋊C4×D5911yescharacteristic
203Q8—2362no—
204Q8—2362no—
205Q8—2362no—
206Q8—2362no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—41no—
216C2×C4—592no—
217C2×C4—1182no—
218C2×C4—1182no—
219C2×C4—1182no—
220C2×C4—1181no—
221C2×C4—1182no—
222C2×C4—2361no—
223C2×C4—2361no—
224C2×C4—2361no—
225C2×C4—2361no—
226C2×C4—2361no—
227C2×C4—2361no—
228C2×C4—2361no—
229C2×C4M16×D5911yescharacteristic
230C2×C4C2×#1174565911yescharacteristic
231C8—82no—
232C8—4722no—
233C22—21no—
234C22—21no—
235C22#1683736411yescharacteristic
236C22#99×D5911yescharacteristic
237C22#1683738511yescharacteristic
238C4—21no—
239C4—21no—
240C4—42no—
241C4—42no—
242C4—81no—
243C4—1182no—
244C4—4721no—
245C4—2362no—
246C4—2362no—
247C4—2361no—
248C2—21no—
249C2—21no—
250C2#2142243311yescharacteristic
251C2#2142576911yescharacteristic
252C2#2142578211yescharacteristic
subgroupG/H
centerC22#99×D59
commutatorC22×C4×C59C22×C4
FrattiniC2×C4⋊C4C22×D59
FittingC59×#1324C2
socleC22×C59C2×#99
prime radicalC23×C59C2×C22⋊C4
cosocleC2×C4⋊C4×C59C23
hypercenter#1324D59
hypocenterC59#11536
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
145. C59#11536semidirect

Maximal subgroups

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

subgroupindex
#214268132
#214224382
#214220402
#214220292
C59×#13242
#1153659