Finite Group Databasebeta

← #28499528

Subgroups — #28499528

Order 15104.

286 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 71 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#21434825C211yesmaximal, characteristic
2#21425908C211yesmaximal, characteristic, complemented
3#21422089C211yesmaximal, characteristic, complemented
4#21422086C211yesmaximal, characteristic
5#21422083C211yesmaximal, characteristic, complemented
6#21422080C211yesmaximal, characteristic
7C59×#1841C211yesmaximal, characteristic, complemented
8#16837936—21no—
9#16837804C411yescharacteristic, complemented
10#16837786C411yescharacteristic, complemented
11#16837757—21no—
12#16837660C2211yescharacteristic
13#16837655C2211yescharacteristic
14#16837648—21no—
15#16837515C411yescharacteristic, complemented
16#16837510C411yescharacteristic, complemented
17#16837504—21no—
18#16837223—21no—
19#16837184C2211yescharacteristic
20#16837184C2211yescharacteristic
21#16837180—21no—
22C4×M16×C59C2211yescharacteristic
23C59×#344—21no—
24C59×#339—21no—
25C59×#338C2211yescharacteristic
26C59×H(3,ℤ/4)C2211yescharacteristic
27C2×Dic236C2×C411yescharacteristic
28C2×#11745660—21no—
29C2×D472C2×C411yescharacteristic
30#14273721—41no—
31#14273719—21no—
32#14273715—21no—
33#14273710—41no—
34#14273706—21no—
35#14273701—21no—
36C4×Dic118—21no—
37C4×D236—21no—
38C4×C22⋊D59—41no—
39#14273684—41no—
40#14273667—21no—
41#14273667—21no—
42#14273661—21no—
43#14273659C2×C411yescharacteristic
44#14273659C2×C411yescharacteristic
45#14273652—21no—
46#14273652—21no—
47#14273649—21no—
48#14273649—21no—
49C2×M16×C59—21no—
50C2×M16×C59D411yescharacteristic
51C2×M16×C59C2311yescharacteristic
52#117×C59—21no—
53C2×C42×C59D411yescharacteristic
54#97×C59C2×C411yescharacteristic
55#97×C59D411yescharacteristic
56C4×C8×C59C2×C411yescharacteristic
57C4×C8×C59D411yescharacteristic
58C22×C4×C59—21no—
59C22×C4×C59C2×D411yescharacteristic
60C2×C22⋊D59—41no—
61C2×D236—21no—
62C2×C4×D59—41no—
63C2×Dic118—21no—
64M16×C59—41no—
65M16×C59—41no—
66M16×C59—41no—
67M16×C59—41no—
68C2×C8×C59—41no—
69C2×C8×C59C22⋊C411yescharacteristic
70C2×C8×C59C22⋊C411yescharacteristic
71C2×C8×C59C22×C411yescharacteristic
72C2×C8×C59C2×D411yescharacteristic
73C4⋊C4×C59—41no—
74C22⋊C4×C59—41no—
75C42×C59—21no—
76C42×C59—41no—
77C42×C59C22⋊C411yescharacteristic
78C42×C59C22⋊C411yescharacteristic
79C22⋊Dic59—41no—
80(C2×D59)⋊C4—41no—
81(C2×D59)⋊C4—41no—
82(C2×D59)⋊C4—41no—
83(C2×D59)⋊C4—41no—
84C4⋊Dic59—21no—
85C4⋊Dic59—21no—
86Dic59⋊C4—41no—
87Dic59⋊C4—41no—
88Dic59⋊C4—41no—
89Dic59⋊C4—41no—
90C4×Dic59—41no—
91Dic236—41no—
92D472—41no—
93#11745660—42no—
94C59⋊C16—41no—
95C59⋊C16—41no—
96C23×C59AGL(1,ℤ/8)11yescharacteristic
97C22×D59—41no—
98C2×C4×C59—21no—
99C2×C4×C59—21no—
100C2×C4×C59—21no—
101C2×C4×C59—21no—
102C2×C4×C59—81no—
103C2×C4×C59—81no—
104C2×C4×C59C2×C22⋊C411yescharacteristic
105C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
106C22⋊D59—82no—
107C2×Dic59—41no—
108C2×Dic59—41no—
109C2×Dic59—41no—
110D236—41no—
111D236—41no—
112C4×D59—82no—
113Dic118—41no—
114Dic118—41no—
115C8×C59—21no—
116C8×C59—21no—
117C8×C59—21no—
118C8×C59—21no—
119C8×C59—81no—
120#11836—591nomaximal, Sylow
121C22×C59—21no—
122C22×C59—41no—
123C22×C59#41811yescharacteristic
124C2×D59—81no—
125C2×D59—81no—
126C2×D59—81no—
127C4×C59—21no—
128C4×C59—41no—
129C4×C59—41no—
130C4×C59—161no—
131C4×C59#41011yescharacteristic
132C4×C59#42111yescharacteristic
133Dic59—81no—
134Dic59—81no—
135Dic59—81no—
136#3183—591no—
137#2165—591no—
138#1841D5911yescharacteristic, complemented
139#1342—591no—
140#1341—591no—
141#1340—591no—
142#1339—591no—
143C2×C59—21no—
144C2×C59—41no—
145C2×C59#151411yescharacteristic
146D59—161no—
147#529—1181no—
148#499—591no—
149#495—591no—
150#488—1181no—
151#470—591no—
152#469—591no—
153#468—1181no—
154#442—591no—
155#441—591no—
156#440—1181no—
157C4×M16C2×D5911yescharacteristic
158#364—1181no—
159#349—591no—
160#349—591no—
161#347—1181no—
162#344—21no—
163#339—21no—
164#338C2×D5911yescharacteristic
165H(3,ℤ/4)C2×D5911yescharacteristic
166C59#1183611yescharacteristic, complemented, Sylow
167C2×Q16—591no—
168C2×SD16—1181no—
169C2×D8—591no—
170C2×M16—21no—
171C2×M16C22⋊D5911yescharacteristic
172C2×M16C22×D5911yescharacteristic
173#126—2361no—
174#125—1181no—
175#124—1181no—
176#123—2361no—
177C22⋊Q8—1181no—
178#121—1181no—
179C4×Q8—1181no—
180C4×D4—1181no—
181C4×D4—2361no—
182#117—21no—
183#117—2361no—
184C2×C42C22⋊D5911yescharacteristic
185M32—1181no—
186M32—1181no—
187#107—1181no—
188#106—591no—
189#106—591no—
190#103—1181no—
191#103—1181no—
192#102—1181no—
193#102—1181no—
194#97C4×D5911yescharacteristic
195#97D23611yescharacteristic
196C4×C8C4×D5911yescharacteristic
197C4×C8D23611yescharacteristic
198C2×Q8—1181no—
199C2×D4—1181no—
200C2×D4—2361no—
201C22×C4—21no—
202C22×C4—2361no—
203C22×C4C2×C22⋊D5911yescharacteristic
204Q16—2361no—
205SD16—2362no—
206D8—2361no—
207M16—41no—
208M16—41no—
209M16—41no—
210M16—41no—
211C2×C8—41no—
212C2×C8(C2×D59)⋊C411yescharacteristic
213C2×C8(C2×D59)⋊C411yescharacteristic
214C2×C8C2×C4×D5911yescharacteristic
215C2×C8C2×D23611yescharacteristic
216C4⋊C4—41no—
217C4⋊C4—1181no—
218C4⋊C4—1181no—
219C4⋊C4—2361no—
220C4⋊C4—2361no—
221C4⋊C4—2361no—
222C4⋊C4—2361no—
223C22⋊C4—41no—
224C22⋊C4—2361no—
225C22⋊C4—2361no—
226C22⋊C4—2361no—
227C22⋊C4—2361no—
228C22⋊C4—2361no—
229C42—21no—
230C42—41no—
231C42—2361no—
232C42(C2×D59)⋊C411yescharacteristic
233C42(C2×D59)⋊C411yescharacteristic
234C16—2361no—
235C16—2361no—
236C23—2361no—
237C23#1427375211yescharacteristic
238Q8—2361no—
239Q8—2361no—
240D4—4722no—
241D4—2361no—
242D4—2361no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—81no—
248C2×C4—81no—
249C2×C4—4722no—
250C2×C4—2361no—
251C2×C4—2361no—
252C2×C4—2361no—
253C2×C4C2×(C2×D59)⋊C411yescharacteristic
254C2×C4#1427375211yescharacteristic
255C8—21no—
256C8—21no—
257C8—21no—
258C8—21no—
259C8—81no—
260C22—21no—
261C22—41no—
262C22—4721no—
263C22—4721no—
264C22—4721no—
265C22#1683740611yescharacteristic
266C4—21no—
267C4—41no—
268C4—41no—
269C4—161no—
270C4—4721no—
271C4—4721no—
272C4—4721no—
273C4#1683737511yescharacteristic
274C4#1683742011yescharacteristic
275C2—21no—
276C2—41no—
277C2—9441no—
278C2#2142264211yescharacteristic
subgroupG/H
centerC2#21422642
commutatorC2×C8×C59C22×C4
FrattiniC2×M16C22×D59
FittingC59×#1841C2
socleC2×C59#1514
prime radical#16837655C22
cosocleC2×M16×C59C23
hypercenter#1841D59
hypocenterC59#11836
LCSG ▷ C2×C8×C59 ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #1841

Complements

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

NH ≅ G/Ntype
2. #21425908C2semidirect
3. #21422089C2semidirect
5. #21422083C2semidirect
7. C59×#1841C2semidirect
9. #16837804C4semidirect
10. #16837786C4semidirect
15. #16837515C4semidirect
16. #16837510C4semidirect
138. #1841D59semidirect
166. C59#11836semidirect

Maximal subgroups

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

subgroupindex
#214348252
#214259082
#214220892
#214220862
#214220832
#214220802
C59×#18412
#1183659