Finite Group Databasebeta

← #28501411

Subgroups — #28501411

Order 15104.

532 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 63 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#21425260C211yesmaximal, characteristic
2#21423086C212yesmaximal, complemented
3#21422096C212yesmaximal, complemented
4#21422024C211yesmaximal, characteristic
5C59×#2483C211yesmaximal, characteristic
6#16838028C2211yescharacteristic
7#16837732—22no—
8#16837258—21no—
9#16837169C2211yescharacteristic
10#16837168—21no—
11#16837138—22no—
12#16837126C2212yes—
13C22×C22⋊C4×C59—21no—
14C59×#397—21no—
15C59×#397C2212yes—
16C59×#385—22no—
17C59×#381—22no—
18C59×#379C2211yescharacteristic
19#14273706—22no—
20#14273704—42no—
21C2×C22⋊Dic59—21no—
22C2×C22⋊Dic59—21no—
23C2×C22⋊Dic59—42no—
24#14273658—42no—
25#14273650—42no—
26C22⋊(C59⋊C8)—22no—
27C25×C59D411yescharacteristic
28C23×C4×C59—21no—
29C23×C4×C59—21no—
30C2×C4⋊C4×C59—21no—
31C2×C4⋊C4×C59D412yes—
32C2×C22⋊C4×C59—22no—
33C2×C22⋊C4×C59—22no—
34C2×C22⋊C4×C59—22no—
35C2×C22⋊C4×C59—42no—
36C2×C22⋊C4×C59—42no—
37C2×C22⋊C4×C59D411yescharacteristic
38C2×C22⋊C4×C59C2311yescharacteristic
39#95×C59—21no—
40#95×C59—22no—
41#95×C59—22no—
42#95×C59D412yes—
43C24×C59—21no—
44C24×C59—21no—
45C24×C59—44no—
46C24×C59—41no—
47C24×C59—41no—
48C24×C59SD1612yes—
49C24×C59C2×D411yescharacteristic
50C22×C4×C59—22no—
51C22×C4×C59—21no—
52C22×C4×C59—22no—
53C22×C4×C59—42no—
54C22×C4×C59—42no—
55C22×C4×C59—44no—
56C22×C4×C59—81no—
57C22×C4×C59—81no—
58C22×C4×C59C2×D412yes—
59C22×Dic59—22no—
60C22×Dic59—41no—
61C2×Dic118—22no—
62C4⋊C4×C59—42no—
63C4⋊C4×C59—81no—
64C22⋊C4×C59—41no—
65C22⋊C4×C59—44no—
66C22⋊C4×C59—44no—
67C22⋊C4×C59—42no—
68C22⋊C4×C59—42no—
69C22⋊C4×C59—41no—
70C22⋊Dic59—41no—
71C22⋊Dic59—41no—
72C22⋊Dic59—41no—
73C22⋊Dic59—41no—
74C22⋊Dic59—84no—
75C4⋊Dic59—22no—
76Dic59⋊C4—42no—
77C2×C59⋊C8—42no—
78C23×C59—24no—
79C23×C59—22no—
80C23×C59—21no—
81C23×C59—21no—
82C23×C59—42no—
83C23×C59—44no—
84C23×C59—42no—
85C23×C59—42no—
86C23×C59—44no—
87C23×C59—41no—
88C23×C59—41no—
89C23×C59—44no—
90C23×C59—81no—
91C23×C59—84no—
92C23×C59—82no—
93C23×C59#12011yescharacteristic
94C23×C59C2×SD1611yescharacteristic
95C23×C59AGL(1,ℤ/8)11yescharacteristic
96C2×C4×C59—22no—
97C2×C4×C59—42no—
98C2×C4×C59—42no—
99C2×C4×C59—44no—
100C2×C4×C59—42no—
101C2×C4×C59—42no—
102C2×C4×C59—41no—
103C2×C4×C59—42no—
104C2×C4×C59—42no—
105C2×C4×C59—84no—
106C2×C4×C59—84no—
107C2×Dic59—42no—
108C2×Dic59—82no—
109C2×Dic59—81no—
110C2×Dic59—82no—
111Dic118—82no—
112C59⋊C8—82no—
113#12203—591nomaximal, Sylow
114C22×C59—22no—
115C22×C59—24no—
116C22×C59—21no—
117C22×C59—21no—
118C22×C59—41no—
119C22×C59—41no—
120C22×C59—42no—
121C22×C59—44no—
122C22×C59—44no—
123C22×C59—42no—
124C22×C59—42no—
125C22×C59—44no—
126C22×C59—81no—
127C22×C59—84no—
128C22×C59—82no—
129C22×C59#45011yescharacteristic
130C22×C59#45511yescharacteristic
131C22×C59B(4,𝔽2)11yescharacteristic
132C4×C59—42no—
133C4×C59—81no—
134C4×C59—82no—
135C4×C59—82no—
136Dic59—82no—
137Dic59—161no—
138#2483D5911yescharacteristic
139#2029—591no—
140#1608—592no—
141#1344—592no—
142#1316—591no—
143C2×C59—21no—
144C2×C59—21no—
145C2×C59—41no—
146C2×C59—44no—
147C2×C59—41no—
148C2×C59#160111yescharacteristic
149C2×C59#219712yes—
150#543—591no—
151C22×C22⋊C4—21no—
152#483—1182no—
153#397—21no—
154#397C2×D5912yes—
155#385—22no—
156#381—22no—
157#379—1181no—
158#379C2×D5911yescharacteristic
159#342—591no—
160#342—1181no—
161#328—1182no—
162#323—592no—
163C59#1220311yescharacteristic, complemented, Sylow
164C25C22⋊D5911yescharacteristic
165C23×C4—21no—
166C23×C4—21no—
167C22⋊Q8—1182no—
168C22⋊Q8—2362no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4C22⋊D5912yes—
171C2×C22⋊C4—22no—
172C2×C22⋊C4—22no—
173C2×C22⋊C4—22no—
174C2×C22⋊C4—42no—
175C2×C22⋊C4—42no—
176C2×C22⋊C4—1181no—
177C2×C22⋊C4—1181no—
178C2×C22⋊C4—2362no—
179C2×C22⋊C4C22⋊D5911yescharacteristic
180C2×C22⋊C4C22×D5911yescharacteristic
181#106—2362no—
182#103—2362no—
183C22⋊C8—1182no—
184#95—21no—
185#95—22no—
186#95—22no—
187#95C22⋊D5912yes—
188C24—21no—
189C24—21no—
190C24—41no—
191C24—44no—
192C24—41no—
193C24#1174567012yes—
194C24C2×C22⋊D5911yescharacteristic
195C2×Q8—1182no—
196C22×C4—22no—
197C22×C4—21no—
198C22×C4—22no—
199C22×C4—42no—
200C22×C4—42no—
201C22×C4—44no—
202C22×C4—81no—
203C22×C4—81no—
204C22×C4—1182no—
205C22×C4—2361no—
206C22×C4C2×C22⋊D5912yes—
207C2×C8—2362no—
208C4⋊C4—42no—
209C4⋊C4—81no—
210C4⋊C4—1182no—
211C4⋊C4—2362no—
212C22⋊C4—41no—
213C22⋊C4—44no—
214C22⋊C4—44no—
215C22⋊C4—42no—
216C22⋊C4—42no—
217C22⋊C4—41no—
218C22⋊C4—4724no—
219C22⋊C4—2361no—
220C22⋊C4—2361no—
221C22⋊C4—2361no—
222C22⋊C4—2361no—
223C23—24no—
224C23—22no—
225C23—21no—
226C23—21no—
227C23—42no—
228C23—44no—
229C23—42no—
230C23—42no—
231C23—44no—
232C23—41no—
233C23—41no—
234C23—44no—
235C23—81no—
236C23—84no—
237C23—82no—
238C23#1427369611yescharacteristic
239C23C2×#1174567011yescharacteristic
240C23#1427375311yescharacteristic
241Q8—4722no—
242C2×C4—22no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—44no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—84no—
252C2×C4—84no—
253C2×C4—4721no—
254C2×C4—4722no—
255C2×C4—4722no—
256C2×C4—2362no—
257C8—4722no—
258C22—22no—
259C22—24no—
260C22—21no—
261C22—21no—
262C22—41no—
263C22—41no—
264C22—42no—
265C22—44no—
266C22—44no—
267C22—42no—
268C22—44no—
269C22—42no—
270C22—81no—
271C22—84no—
272C22—82no—
273C22#1683755311yescharacteristic
274C22#1683758011yescharacteristic
275C22#1683758911yescharacteristic
276C4—42no—
277C4—82no—
278C4—81no—
279C4—82no—
280C4—9441no—
281C4—4722no—
282C2—21no—
283C2—21no—
284C2—41no—
285C2—44no—
286C2—41no—
287C2#2142304811yescharacteristic
288C2#2142608612yes—
subgroupG/H
centerC22#16837589
commutator, cosocleC2×C22⋊C4×C59C23
FrattiniC2×C22⋊C4C22×D59
FittingC59×#2483C2
socleC22×C59B(4,𝔽2)
prime radicalC25×C59D4
hypercenter#2483D59
hypocenterC59#12203
LCSG ▷ C2×C22⋊C4×C59 ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2483

Complements

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

NH ≅ G/Ntype
2. #21423086C2semidirect
3. #21422096C2semidirect
163. C59#12203semidirect

Maximal subgroups

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

subgroupindex
#214252602
#214230862
#214220962
#214220242
C59×#24832
#1220359