Finite Group Databasebeta

← #28501959

Subgroups — #28501959

Order 15104.

310 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 67 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#21435441C211yesmaximal, characteristic
2#21426294C212yesmaximal
3#21425584C211yesmaximal, characteristic
4#21422109C212yesmaximal
5C59×#1322C211yesmaximal, characteristic
6#16837959—21no—
7#16837698—22no—
8#16837643—21no—
9#16837643C2212yes—
10#16837613—22no—
11C2×#14273661C2211yescharacteristic
12#16837300—21no—
13#16837230—22no—
14#16837207—22no—
15#16837165—21no—
16#16837165C2211yescharacteristic
17C2×C4⋊C8×C59C2211yescharacteristic
18C59×C22⋊C16C2212yes—
19C2×Dic236—21no—
20C2×Dic236D412yes—
21#14273727—21no—
22#14273727—21no—
23#14273719—41no—
24#14273706—22no—
25#14273706—41no—
26C4×Dic118—22no—
27C4×Dic118—41no—
28#14273686—41no—
29C2×C4⋊Dic59—21no—
30C2×C4⋊Dic59—21no—
31C2×Dic59⋊C4—41no—
32#14273661—21no—
33#14273661—22no—
34#14273661D412yes—
35#14273652—22no—
36#14273652—22no—
37C59⋊#95—41no—
38C22×C8×C59D411yescharacteristic
39C22×C8×C59C2311yescharacteristic
40C2×C42×C59D411yescharacteristic
41C2×C16×C59—22no—
42C4⋊C8×C59—22no—
43C22×C4×C59D811yescharacteristic
44C22×C4×C59D811yescharacteristic
45C22×C4×C59C2×D411yescharacteristic
46C22×Dic59—41no—
47C22×Dic59—41no—
48C2×Dic118—22no—
49C2×Dic118—41no—
50C2×C8×C59—21no—
51C2×C8×C59—41no—
52C2×C8×C59—41no—
53C2×C8×C59C2×D412yes—
54C42×C59—21no—
55C42×C59—21no—
56C22⋊Dic59—42no—
57C4⋊Dic59—22no—
58C4⋊Dic59—22no—
59C4⋊Dic59—41no—
60C4⋊Dic59—41no—
61C4⋊Dic59—41no—
62C4⋊Dic59—41no—
63C4⋊Dic59—41no—
64C4⋊Dic59—41no—
65Dic59⋊C4—42no—
66Dic59⋊C4—42no—
67Dic59⋊C4—82no—
68C4×Dic59—42no—
69Dic236—42no—
70Dic236—81no—
71C16×C59—42no—
72C23×C59C2×D811yescharacteristic
73C2×C4×C59—21no—
74C2×C4×C59—21no—
75C2×C4×C59—21no—
76C2×C4×C59—21no—
77C2×C4×C59—21no—
78C2×C4×C59—41no—
79C2×C4×C59SD3212yes—
80C2×C4×C59#12011yescharacteristic
81C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
82C2×Dic59—42no—
83C2×Dic59—42no—
84C2×Dic59—42no—
85C2×Dic59—81no—
86C2×Dic59—81no—
87C2×Dic59—81no—
88C2×Dic59—81no—
89C2×Dic59—81no—
90Dic118—42no—
91Dic118—42no—
92Dic118—82no—
93C8×C59—22no—
94C8×C59—41no—
95#12289—591nomaximal, Sylow
96C22×C59—21no—
97C22×C59—21no—
98C22×C59#44711yescharacteristic
99C22×C59C2×SD3211yescharacteristic
100C22×C59#51011yescharacteristic
101C4×C59—21no—
102C4×C59—22no—
103C4×C59—41no—
104C4×C59#45611yescharacteristic
105C4×C59#45811yescharacteristic
106Dic59—82no—
107Dic59—82no—
108Dic59—82no—
109Dic59—161no—
110#3249—591no—
111#2235—592no—
112#2086—591no—
113#1348—592no—
114#1322D5911yescharacteristic
115C2×C59—21no—
116C2×C59—21no—
117C2×C59#161011yescharacteristic
118C2×C59#218511yescharacteristic
119C2×C59#219111yescharacteristic
120#533—1181no—
121#477—1182no—
122#467—592no—
123#467—1181no—
124#462—1182no—
125C2×#107—591no—
126C2×C4⋊C8C2×D5911yescharacteristic
127#389—1181no—
128#367—1182no—
129#358—1182no—
130C22⋊C16C2×D5912yes—
131#340—591no—
132#340—1181no—
133C59#1228911yescharacteristic, complemented, Sylow
134C2×Q16—592no—
135C2×Q16—1181no—
136C22×C8D23611yescharacteristic
137C22×C8C22×D5911yescharacteristic
138C4⋊Q8—1181no—
139C4⋊Q8—1181no—
140#125—2361no—
141C22⋊Q8—1182no—
142C22⋊Q8—2361no—
143C4×Q8—1182no—
144C4×Q8—2361no—
145#117—2361no—
146C2×C4⋊C4—1181no—
147C2×C4⋊C4—1181no—
148C2×C4⋊C4—2361no—
149C2×C42D23611yescharacteristic
150C2×C16—22no—
151#107—592no—
152#107—1181no—
153#107—1182no—
154C4⋊C8—22no—
155#103—1182no—
156#103—1182no—
157#95—2361no—
158C2×Q8—1182no—
159C2×Q8—2361no—
160C22×C4—2361no—
161C22×C4—2361no—
162C22×C4D47211yescharacteristic
163C22×C4D47211yescharacteristic
164C22×C4C2×D23611yescharacteristic
165Q16—4721no—
166Q16—2362no—
167C2×C8—21no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8D4×D5912yes—
171C4⋊C4—1182no—
172C4⋊C4—1182no—
173C4⋊C4—4722no—
174C4⋊C4—2361no—
175C4⋊C4—2361no—
176C4⋊C4—2361no—
177C4⋊C4—2362no—
178C4⋊C4—2361no—
179C4⋊C4—2361no—
180C4⋊C4—2361no—
181C4⋊C4—2362no—
182C22⋊C4—2362no—
183C42—21no—
184C42—21no—
185C42—2362no—
186C16—42no—
187C23C2×D47211yescharacteristic
188Q8—4722no—
189Q8—2362no—
190Q8—2362no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—4721no—
198C2×C4—4721no—
199C2×C4—4721no—
200C2×C4—4721no—
201C2×C4—4721no—
202C2×C4—2362no—
203C2×C4—2362no—
204C2×C4—2362no—
205C2×C4#1427367212yes—
206C2×C4#1427369711yescharacteristic
207C2×C4#1427375511yescharacteristic
208C8—22no—
209C8—41no—
210C22—21no—
211C22—21no—
212C22#1683753811yescharacteristic
213C22C2×#1427367211yescharacteristic
214C22#1683784511yescharacteristic
215C4—22no—
216C4—21no—
217C4—41no—
218C4—9441no—
219C4—4722no—
220C4—4722no—
221C4—4722no—
222C4#1683758711yescharacteristic
223C4#1683759311yescharacteristic
224C2—21no—
225C2—21no—
226C2#2142310111yescharacteristic
227C2#2142601511yescharacteristic
228C2#2142604911yescharacteristic
subgroupG/H
centerC22#16837538
commutator, cosocleC22×C8×C59C23
FrattiniC22×C8C22×D59
FittingC59×#1322C2
socleC22×C59#447
prime radicalC23×C59C2×D8
hypercenter#1322D59
hypocenterC59#12289
LCSG ▷ C22×C8×C59 ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #1322

Complements

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

NH ≅ G/Ntype
133. C59#12289semidirect

Maximal subgroups

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

subgroupindex
#214354412
#214262942
#214255842
#214221092
C59×#13222
#1228959