Finite Group Databasebeta

← #28489979

Subgroups — #28489979

Order 15104.

552 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C2×#16837766C212yesmaximal
2#21432164C211yesmaximal, characteristic, complemented
3C2×#16837143C212yesmaximal, complemented
4#21421977C211yesmaximal, characteristic, complemented
5C59×#1961C211yesmaximal, characteristic
6C2×#14273719C2212yes—
7#16837766—24no—
8#16837766—24no—
9C2×#14273648—22no—
10C2×#14273648—22no—
11C2×#14273638C2212yes—
12#16837342—22no—
13#16837334—22no—
14#16837332—22no—
15#16837143—24no—
16C2×#127×C59C2211yescharacteristic
17C2×#102×C59—22no—
18C2×#97×C59C2211yescharacteristic
19C59×#382C2211yescharacteristic
20C22×C59⋊C8—22no—
21#14273719—22no—
22#14273719—22no—
23#14273719—22no—
24#14273719—22no—
25C2×C4⋊Dic59—22no—
26C2×C4⋊Dic59D412yes—
27C2×C4⋊Dic59D412yes—
28C2×Dic59⋊C4—22no—
29C2×Dic59⋊C4—22no—
30#14273648—28no—
31#14273648—28no—
32#14273638—22no—
33#14273638D414yes—
34C59⋊#95—24no—
35C59⋊#95—22no—
36C22×D4×C59—22no—
37C22×D4×C59—21no—
38C22×C8×C59—21no—
39#127×C59—22no—
40#127×C59—21no—
41#127×C59D412yes—
42C2×C4⋊C4×C59D412yes—
43C2×C42×C59C2311yescharacteristic
44#102×C59—44no—
45#97×C59—22no—
46#95×C59—22no—
47C24×C59—41no—
48C2×D4×C59—24no—
49C2×D4×C59—22no—
50C2×D4×C59—42no—
51C2×D4×C59—48no—
52C2×D4×C59—42no—
53C2×D4×C59—42no—
54C2×D4×C59—41no—
55C22×C4×C59—22no—
56C22×C4×C59C2×D412yes—
57C22×C4×C59C2×D411yescharacteristic
58C22×Dic59—22no—
59C22×Dic59—22no—
60C2×C8×C59—22no—
61C2×C8×C59—41no—
62C2×C8×C59—41no—
63C4⋊C4×C59—42no—
64C42×C59C2×D411yescharacteristic
65C42×C59C2×D412yes—
66C42×C59#4111yescharacteristic
67C4⋊Dic59—22no—
68C4⋊Dic59—22no—
69C4⋊Dic59—22no—
70C4⋊Dic59—22no—
71C4⋊Dic59—82no—
72Dic59⋊C4—42no—
73Dic59⋊C4—42no—
74Dic59⋊C4—42no—
75Dic59⋊C4—42no—
76C2×C59⋊C8—24no—
77C2×C59⋊C8—44no—
78C23×C59—42no—
79C23×C59—81no—
80C23×C59—84no—
81C23×C59—81no—
82C23×C59#12011yescharacteristic
83D4×C59—48no—
84D4×C59—44no—
85D4×C59—84no—
86D4×C59—82no—
87C2×C4×C59—21no—
88C2×C4×C59—24no—
89C2×C4×C59—21no—
90C2×C4×C59—42no—
91C2×C4×C59—44no—
92C2×C4×C59#12012yes—
93C2×C4×C59#12112yes—
94C2×C4×C59#12111yescharacteristic
95C2×C4×C59#12711yescharacteristic
96C2×Dic59—42no—
97C2×Dic59—42no—
98C2×Dic59—42no—
99C2×Dic59—44no—
100C2×Dic59—42no—
101C8×C59—42no—
102C59⋊C8—44no—
103#10080—591nomaximal, Sylow
104C22×C59—84no—
105C22×C59—82no—
106C22×C59—162no—
107C22×C59—162no—
108C22×C59#39211yescharacteristic
109C22×C59#45311yescharacteristic
110C22×C59#45414yes—
111C22×C59#45411yescharacteristic
112C4×C59—22no—
113C4×C59—22no—
114C4×C59—21no—
115C4×C59—21no—
116C4×C59—82no—
117Dic59—82no—
118Dic59—82no—
119C2×#490—592no—
120#2822—591no—
121#1961D5911yescharacteristic
122C2×#330—592no—
123#1295—591no—
124C2×C59—162no—
125C2×C59#165712yes—
126C2×C59#165812yes—
127C2×C59#200312yes—
128C2×C59#200611yescharacteristic
129C2×#127C2×D5911yescharacteristic
130C2×#125—592no—
131#490—1184no—
132#490—1184no—
133C2×#102—22no—
134C2×#102—1182no—
135C2×#102—1182no—
136C2×#97—592no—
137C2×#97C2×D5911yescharacteristic
138#400—1182no—
139#398—1182no—
140#398—1182no—
141#382C2×D5911yescharacteristic
142#330—1184no—
143C59#1008011yescharacteristic, complemented, Sylow
144C22×D4—22no—
145C22×D4—21no—
146C22×C8—21no—
147C22×C8—1182no—
148#127—21no—
149#127—22no—
150#127D23612yes—
151#125—1182no—
152#125—1182no—
153#125—1182no—
154#125—1182no—
155C2×C4⋊C4—592no—
156C2×C4⋊C4—592no—
157C2×C4⋊C4—1182no—
158C2×C4⋊C4—1182no—
159C2×C4⋊C4—1182no—
160C2×C4⋊C4C22⋊D5912yes—
161C2×C42C22×D5911yescharacteristic
162#102—44no—
163#102—1188no—
164#102—1188no—
165#97—22no—
166#97—594no—
167#97—1182no—
168#95—22no—
169#95—1184no—
170#95—1182no—
171C24—41no—
172C2×D4—24no—
173C2×D4—22no—
174C2×D4—42no—
175C2×D4—48no—
176C2×D4—42no—
177C2×D4—42no—
178C2×D4—41no—
179C22×C4—22no—
180C22×C4—1182no—
181C22×C4—1182no—
182C22×C4D4×D5912yes—
183C22×C4C2×C22⋊D5911yescharacteristic
184C2×C8—22no—
185C2×C8—41no—
186C2×C8—41no—
187C2×C8—1184no—
188C2×C8—2364no—
189C4⋊C4—42no—
190C4⋊C4—1182no—
191C4⋊C4—1182no—
192C4⋊C4—1182no—
193C4⋊C4—1182no—
194C4⋊C4—4722no—
195C4⋊C4—2362no—
196C4⋊C4—2362no—
197C4⋊C4—2362no—
198C4⋊C4—2362no—
199C42C2×D23611yescharacteristic
200C42#1174568511yescharacteristic
201C42D4×D5912yes—
202C23—42no—
203C23—81no—
204C23—84no—
205C23—81no—
206C23#1427369511yescharacteristic
207D4—48no—
208D4—44no—
209D4—84no—
210D4—82no—
211C2×C4—21no—
212C2×C4—24no—
213C2×C4—21no—
214C2×C4—42no—
215C2×C4—44no—
216C2×C4—2362no—
217C2×C4—2362no—
218C2×C4—2362no—
219C2×C4—2364no—
220C2×C4—2362no—
221C2×C4#1427369712yes—
222C2×C4#1427370012yes—
223C2×C4#1427370111yescharacteristic
224C2×C4#1427372311yescharacteristic
225C8—42no—
226C8—2364no—
227C22—84no—
228C22—82no—
229C22—162no—
230C22—162no—
231C22#1683731111yescharacteristic
232C22#1683756911yescharacteristic
233C22#1683757314yes—
234C22#1683757411yescharacteristic
235C4—22no—
236C4—22no—
237C4—21no—
238C4—21no—
239C4—82no—
240C4—4722no—
241C4—4722no—
242C2—162no—
243C2#2142339212yes—
244C2#2142339712yes—
245C2#2142511912yes—
246C2#2142513711yescharacteristic
subgroupG/H
centerC23#14273695
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1961C2
socleC23×C59#120
prime radicalC2×#127×C59C22
hypercenter#1961D59
hypocenterC59#10080
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1961

Complements

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

NH ≅ G/Ntype
2. #21432164C2semidirect
3. C2×#16837143C2semidirect
4. #21421977C2semidirect
143. C59#10080semidirect

Maximal subgroups

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

subgroupindex
C2×#168377662
#214321642
C2×#168371432
#214219772
C59×#19612
#1008059