Finite Group Databasebeta

← #28477990

Subgroups — #28477990

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#21431128C211yesmaximal, characteristic
2#21425660C212yesmaximal
3#21425634C211yesmaximal, characteristic
4#21421918C212yesmaximal
5C59×#1272C211yesmaximal, characteristic
6C2×#14273725—21no—
7C2×#14273660—21no—
8C2×#14273651—21no—
9#16837332—21no—
10#16837323—22no—
11#16837300C2212yes—
12#16837287—22no—
13#16837272C2211yescharacteristic
14#16837165—22no—
15#16837165—22no—
16#16837157C2211yescharacteristic
17C59×#391C2211yescharacteristic
18C59×#336C2212yes—
19C22×Dic118—21no—
20C22×C59⋊C8—21no—
21#14273725—42no—
22#14273725—42no—
23C2×C4⋊Dic59—21no—
24C2×C4⋊Dic59—22no—
25C2×C4⋊Dic59—21no—
26C2×C4⋊Dic59D412yes—
27C2×C4⋊Dic59D412yes—
28C2×Dic59⋊C4—22no—
29C2×Dic59⋊C4—22no—
30C2×C4×Dic59—21no—
31#14273660—42no—
32#14273651—42no—
33C59⋊#95—21no—
34C59⋊#95—22no—
35C59⋊#95—22no—
36C22×Q8×C59D411yescharacteristic
37C22×C8×C59—22no—
38C2×C4⋊C4×C59D411yescharacteristic
39C2×C42×C59C2311yescharacteristic
40#95×C59—22no—
41C2×Q8×C59—21no—
42C2×Q8×C59—41no—
43C2×Q8×C59—41no—
44C2×Q8×C59SD1612yes—
45C22×C4×C59—21no—
46C22×C4×C59—21no—
47C22×C4×C59C2×D411yescharacteristic
48C22×C4×C59C2×D412yes—
49C22×Dic59—22no—
50C22×Dic59—22no—
51C22×Dic59—41no—
52C2×Dic118—42no—
53C2×Dic118—81no—
54C2×Dic118—81no—
55C2×C8×C59—42no—
56C2×C8×C59—42no—
57C2×C8×C59—42no—
58C4⋊C4×C59—41no—
59C42×C59—41no—
60C4⋊Dic59—22no—
61C4⋊Dic59—42no—
62C4⋊Dic59—41no—
63C4⋊Dic59—41no—
64C4⋊Dic59—44no—
65C4⋊Dic59—81no—
66C4⋊Dic59Q1614yes—
67Dic59⋊C4—44no—
68Dic59⋊C4—42no—
69Dic59⋊C4—42no—
70C4×Dic59—42no—
71C2×C59⋊C8—22no—
72C2×C59⋊C8—41no—
73C2×C59⋊C8—41no—
74C23×C59#12011yescharacteristic
75Q8×C59—42no—
76Q8×C59—81no—
77C2×C4×C59—21no—
78C2×C4×C59—22no—
79C2×C4×C59—21no—
80C2×C4×C59—22no—
81C2×C4×C59—22no—
82C2×C4×C59—41no—
83C2×C4×C59—41no—
84C2×C4×C59—41no—
85C2×C4×C59—42no—
86C2×C4×C59C2×SD1611yescharacteristic
87C2×C4×C59C2×Q1612yes—
88C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
89C2×C4×C59#13712yes—
90C2×Dic59—24no—
91C2×Dic59—42no—
92C2×Dic59—42no—
93C2×Dic59—42no—
94C2×Dic59—42no—
95C2×Dic59—42no—
96C2×Dic59—81no—
97C2×Dic59—82no—
98Dic118—84no—
99C8×C59—82no—
100C59⋊C8—42no—
101#7829—591nomaximal, Sylow
102C22×C59#45011yescharacteristic
103C22×C59#45112yes—
104C22×C59#45311yescharacteristic
105C22×C59#45412yes—
106C22×C59#45811yescharacteristic
107C4×C59—21no—
108C4×C59—21no—
109C4×C59—22no—
110C4×C59—22no—
111C4×C59—42no—
112C4×C59—81no—
113Dic59—44no—
114Dic59—82no—
115Dic59—161no—
116#2734—591no—
117#2100—592no—
118#2095—591no—
119#1272D5911yescharacteristic
120#1271—592no—
121C2×C59#161311yescharacteristic
122C2×C59#161712yes—
123C2×C59#163311yescharacteristic
124C2×C59#163712yes—
125C2×C59#165711yescharacteristic
126C2×C4⋊Q8—1181no—
127C2×#107—1181no—
128C2×#103—1181no—
129#398—1181no—
130#395—1182no—
131#391C2×D5911yescharacteristic
132#389—592no—
133#387—1182no—
134#384—591no—
135#340—1182no—
136#340—1182no—
137#336—591no—
138#336C2×D5912yes—
139C59#782911yescharacteristic, complemented, Sylow
140C22×Q8—1181no—
141C22×Q8D23611yescharacteristic
142C22×C8—22no—
143C22×C8—1181no—
144C4⋊Q8—2362no—
145C4⋊Q8—2362no—
146C2×C4⋊C4—592no—
147C2×C4⋊C4—592no—
148C2×C4⋊C4—1181no—
149C2×C4⋊C4—1182no—
150C2×C4⋊C4—1182no—
151C2×C4⋊C4—1181no—
152C2×C4⋊C4—1182no—
153C2×C4⋊C4D23611yescharacteristic
154C2×C42—1181no—
155C2×C42C22×D5911yescharacteristic
156#107—2362no—
157#103—2362no—
158#95—22no—
159#95—1181no—
160#95—1182no—
161#95—1182no—
162C2×Q8—21no—
163C2×Q8—41no—
164C2×Q8—41no—
165C2×Q8—4721no—
166C2×Q8—4721no—
167C2×Q8—2362no—
168C2×Q8#1174566012yes—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—1182no—
172C22×C4—1182no—
173C22×C4—2361no—
174C22×C4C2×D23611yescharacteristic
175C22×C4D4×D5912yes—
176C2×C8—42no—
177C2×C8—42no—
178C2×C8—42no—
179C2×C8—1182no—
180C2×C8—2361no—
181C2×C8—2361no—
182C4⋊C4—41no—
183C4⋊C4—594no—
184C4⋊C4—1182no—
185C4⋊C4—4721no—
186C4⋊C4—2361no—
187C4⋊C4—2361no—
188C4⋊C4—2364no—
189C4⋊C4—2362no—
190C4⋊C4—2364no—
191C4⋊C4—2362no—
192C4⋊C4—2362no—
193C42—41no—
194C42—2362no—
195C23#1427369711yescharacteristic
196Q8—42no—
197Q8—81no—
198Q8—4724no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—42no—
208C2×C4—1184no—
209C2×C4—4721no—
210C2×C4—4722no—
211C2×C4—2362no—
212C2×C4—2362no—
213C2×C4—2362no—
214C2×C4—2362no—
215C2×C4—2362no—
216C2×C4C2×#1174566011yescharacteristic
217C2×C4Q16×D5912yes—
218C2×C4#1427375511yescharacteristic
219C2×C4#1427375612yes—
220C8—82no—
221C8—2362no—
222C22#1683755511yescharacteristic
223C22#1683755912yes—
224C22#1683757211yescharacteristic
225C22#1683757612yes—
226C22#1683759311yescharacteristic
227C4—21no—
228C4—21no—
229C4—22no—
230C4—22no—
231C4—42no—
232C4—81no—
233C4—9441no—
234C4—4722no—
235C4—2364no—
236C2#2142311811yescharacteristic
237C2#2142313912yes—
238C2#2142323711yescharacteristic
239C2#2142326312yes—
240C2#2142339511yescharacteristic
subgroupG/H
centerC23#14273697
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1272C2
socle, prime radicalC23×C59#120
hypercenter#1272D59
hypocenterC59#7829
LCSG ▷ C2×C42×C59 ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
139. C59#7829semidirect

Maximal subgroups

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

subgroupindex
#214311282
#214256602
#214256342
#214219182
C59×#12722
#782959