Finite Group Databasebeta

← #28501485

Subgroups — #28501485

Order 15104.

388 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 59 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#21429761C211yesmaximal, characteristic
2#21423121C212yesmaximal
3#21422119C212yesmaximal
4#21422026C211yesmaximal, characteristic
5C59×#2030C211yesmaximal, characteristic
6#16837735—22no—
7#16837338C2212yes—
8#16837314—21no—
9#16837306—22no—
10#16837289—22no—
11C4×C22⋊Dic59—21no—
12#16837139—22no—
13#16837126C2212yes—
14C59×#543C2211yescharacteristic
15C59×#381—21no—
16C59×#381C2211yescharacteristic
17C59×#342—21no—
18C59×#342C2211yescharacteristic
19C22×Dic118—21no—
20C2×C4⋊Dic59D412yes—
21C2×Dic59⋊C4—22no—
22C2×C22⋊Dic59—22no—
23C2×C4×Dic59—21no—
24C2×C4×Dic59—21no—
25#14273660—42no—
26#14273651—42no—
27C22⋊(C59⋊C8)—22no—
28C59⋊#95—22no—
29C59⋊#95—21no—
30C59⋊#95—22no—
31C59⋊#95D412yes—
32C23×C4×C59D411yescharacteristic
33C22⋊Q8×C59—22no—
34C22⋊Q8×C59—42no—
35C2×C22⋊C4×C59—21no—
36C2×C22⋊C4×C59—21no—
37C2×C22⋊C4×C59D411yescharacteristic
38C2×C22⋊C4×C59C2311yescharacteristic
39#95×C59—22no—
40#95×C59—42no—
41C24×C59C2×D411yescharacteristic
42C2×Q8×C59—22no—
43C22×C4×C59—21no—
44C22×C4×C59—21no—
45C22×C4×C59—21no—
46C22×C4×C59—22no—
47C22×C4×C59—41no—
48C22×C4×C59—41no—
49C22×C4×C59—41no—
50C22×C4×C59Q1612yes—
51C22×C4×C59C2×D412yes—
52C22×Dic59—22no—
53C22×Dic59—22no—
54C2×Dic118—44no—
55C2×Dic118—81no—
56C4⋊C4×C59—22no—
57C4⋊C4×C59—42no—
58C22⋊C4×C59—41no—
59C22⋊C4×C59—41no—
60C22⋊C4×C59—41no—
61C22⋊C4×C59—41no—
62C22⋊C4×C59—41no—
63C22⋊C4×C59—41no—
64C22⋊Dic59—44no—
65C4⋊Dic59—42no—
66Dic59⋊C4—44no—
67C4×Dic59—81no—
68C4×Dic59—81no—
69C2×C59⋊C8—42no—
70C23×C59—21no—
71C23×C59—21no—
72C23×C59—42no—
73C23×C59#12011yescharacteristic
74C23×C59C2×Q1611yescharacteristic
75C23×C59#13711yescharacteristic
76Q8×C59—82no—
77C2×C4×C59—22no—
78C2×C4×C59—22no—
79C2×C4×C59—41no—
80C2×C4×C59—41no—
81C2×C4×C59—42no—
82C2×C4×C59—42no—
83C2×C4×C59—42no—
84C2×C4×C59—41no—
85C2×C4×C59—42no—
86C2×C4×C59—81no—
87C2×C4×C59—82no—
88C2×C4×C59—81no—
89C2×C4×C59—82no—
90C2×Dic59—24no—
91C2×Dic59—42no—
92C2×Dic59—42no—
93C2×Dic59—42no—
94C2×Dic59—42no—
95C2×Dic59—42no—
96Dic118—84no—
97C59⋊C8—82no—
98#12216—591nomaximal, Sylow
99C22×C59—22no—
100C22×C59—21no—
101C22×C59—21no—
102C22×C59—41no—
103C22×C59—41no—
104C22×C59—42no—
105C22×C59—81no—
106C22×C59#45111yescharacteristic
107C22×C59#45511yescharacteristic
108C22×C59B(4,𝔽2)11yescharacteristic
109C4×C59—42no—
110C4×C59—42no—
111C4×C59—81no—
112C4×C59—82no—
113C4×C59—161no—
114Dic59—44no—
115Dic59—82no—
116#2607—591no—
117#2030D5911yescharacteristic
118#1614—592no—
119#1352—592no—
120#1317—591no—
121C2×C59—21no—
122C2×C59—21no—
123C2×C59—41no—
124C2×C59—41no—
125C2×C59#160211yescharacteristic
126C2×C59#219812yes—
127#543C2×D5911yescharacteristic
128#484—1182no—
129#399—592no—
130#393—1181no—
131#391—1182no—
132#387—1182no—
133#381—21no—
134#381C2×D5911yescharacteristic
135C4×C22⋊C4—1181no—
136#342—21no—
137#342C2×D5911yescharacteristic
138#328—1182no—
139#323—592no—
140C59#1221611yescharacteristic, complemented, Sylow
141C22×Q8—1181no—
142C23×C4C22⋊D5911yescharacteristic
143C22⋊Q8—22no—
144C22⋊Q8—42no—
145C2×C4⋊C4—592no—
146C2×C4⋊C4—1182no—
147C2×C22⋊C4—21no—
148C2×C22⋊C4—21no—
149C2×C22⋊C4—1182no—
150C2×C22⋊C4C22⋊D5911yescharacteristic
151C2×C22⋊C4C22×D5911yescharacteristic
152C2×C42—1181no—
153C2×C42—1181no—
154#107—2362no—
155#103—2362no—
156C22⋊C8—1182no—
157#95—22no—
158#95—42no—
159#95—592no—
160#95—1182no—
161#95—1181no—
162#95—1182no—
163C24C2×C22⋊D5911yescharacteristic
164C2×Q8—22no—
165C2×Q8—4721no—
166C2×Q8—2364no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—22no—
171C22×C4—41no—
172C22×C4—41no—
173C22×C4—41no—
174C22×C4—1182no—
175C22×C4—1182no—
176C22×C4#1174567212yes—
177C22×C4D4×D5912yes—
178C2×C8—2362no—
179C4⋊C4—22no—
180C4⋊C4—42no—
181C4⋊C4—2362no—
182C4⋊C4—2364no—
183C22⋊C4—41no—
184C22⋊C4—41no—
185C22⋊C4—41no—
186C22⋊C4—41no—
187C22⋊C4—41no—
188C22⋊C4—41no—
189C22⋊C4—2364no—
190C42—4721no—
191C42—4721no—
192C23—21no—
193C23—21no—
194C23—42no—
195C23#1427369511yescharacteristic
196C23C2×#1174567211yescharacteristic
197C23#1427375711yescharacteristic
198Q8—82no—
199Q8—4724no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—81no—
210C2×C4—82no—
211C2×C4—81no—
212C2×C4—82no—
213C2×C4—1184no—
214C2×C4—2362no—
215C2×C4—2362no—
216C2×C4—2362no—
217C2×C4—2362no—
218C2×C4—2362no—
219C8—4722no—
220C22—22no—
221C22—21no—
222C22—21no—
223C22—41no—
224C22—41no—
225C22—42no—
226C22—81no—
227C22#1683755711yescharacteristic
228C22#1683757911yescharacteristic
229C22#1683758811yescharacteristic
230C4—42no—
231C4—42no—
232C4—81no—
233C4—82no—
234C4—161no—
235C4—4722no—
236C4—2364no—
237C2—21no—
238C2—21no—
239C2—41no—
240C2—41no—
241C2#2142305211yescharacteristic
242C2#2142609012yes—
subgroupG/H
centerC22#16837588
commutator, cosocleC2×C22⋊C4×C59C23
FrattiniC2×C22⋊C4C22×D59
FittingC59×#2030C2
socleC22×C59B(4,𝔽2)
prime radicalC24×C59C2×D4
hypercenter#2030D59
hypocenterC59#12216
LCSG ▷ C2×C22⋊C4×C59 ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2030

Complements

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

NH ≅ G/Ntype
140. C59#12216semidirect

Maximal subgroups

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

subgroupindex
#214297612
#214231212
#214221192
#214220262
C59×#20302
#1221659