Finite Group Databasebeta

← #28498131

Subgroups — #28498131

Order 15104.

288 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 75 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#21432741C211yesmaximal, characteristic
2#21425908C211yesmaximal, characteristic, complemented
3#21422048C212yesmaximal, complemented
4#21422033C212yesmaximal
5C59×#2165C211yesmaximal, characteristic, complemented
6C4×#11745685C411yescharacteristic
7#16837464—21no—
8#16837464—21no—
9#16837453—21no—
10#16837453—21no—
11#16837430C411yescharacteristic
12#16837430C2211yescharacteristic
13#16837370C411yescharacteristic
14#16837370C2211yescharacteristic
15C2×C4×C59⋊C8C411yescharacteristic
16#16837223—21no—
17#16837184C2212yes—
18#16837180—21no—
19C4×M16×C59C2211yescharacteristic
20C59×#364—21no—
21C59×#349C2212yes—
22C59×#347—21no—
23C2×#11745685C2×C411yescharacteristic
24C22×C59⋊C8C2×C411yescharacteristic
25C22×C59⋊C8C2×C411yescharacteristic
26C4×Dic118—21no—
27C4×D236—21no—
28C4×C22⋊D59—22no—
29#14273686C2×C411yescharacteristic
30#14273684—21no—
31C42×D59—21no—
32#14273667—22no—
33Dic59⋊C8—21no—
34Dic59⋊C8—21no—
35Dic59⋊C8—21no—
36Dic59⋊C8—21no—
37(C2×D59)⋊C8—21no—
38(C2×D59)⋊C8—21no—
39(C2×D59)⋊C8—21no—
40(C2×D59)⋊C8—21no—
41C4×C59⋊C8—21no—
42C4×C59⋊C8—21no—
43C2×M16×C59C2×C411yescharacteristic
44C2×M16×C59C2311yescharacteristic
45C2×C42×C59C2×C411yescharacteristic
46M32×C59—22no—
47#97×C59D411yescharacteristic
48#97×C59D411yescharacteristic
49C4×C8×C59D411yescharacteristic
50C4×C8×C59D411yescharacteristic
51C22×C4×C59—21no—
52C22×C4×C59C22×C411yescharacteristic
53C2×C22⋊D59—21no—
54#11745685—41no—
55#11745685—41no—
56C2×D236M1611yescharacteristic
57C2×C4×D59—22no—
58C2×C4×D59—21no—
59C2×Dic118M1611yescharacteristic
60M16×C59—41no—
61M16×C59—41no—
62C2×C8×C59C22⋊C411yescharacteristic
63C2×C8×C59C22⋊C411yescharacteristic
64C2×C8×C59C2×D411yescharacteristic
65C2×C8×C59C2×D411yescharacteristic
66C42×C59—21no—
67C42×C59C22⋊C411yescharacteristic
68C42×C59C22⋊C411yescharacteristic
69C22⋊Dic59M1612yes—
70(C2×D59)⋊C4—22no—
71C4⋊Dic59—21no—
72Dic59⋊C4—22no—
73C4×Dic59—22no—
74C4×Dic59—21no—
75C2×C59⋊C8—21no—
76C2×C59⋊C8—21no—
77C2×C59⋊C8—41no—
78C2×C59⋊C8—41no—
79C16×C59—42no—
80C59⋊C16—42no—
81C23×C59C2×M1611yescharacteristic
82C22×D59—21no—
83C2×C4×C59—21no—
84C2×C4×C59—21no—
85C2×C4×C59—21no—
86C2×C4×C59—21no—
87C2×C4×C59—42no—
88C2×C4×C59C2×C22⋊C411yescharacteristic
89C2×C4×C59C2×M1611yescharacteristic
90C22⋊D59—42no—
91C2×Dic59—21no—
92C2×Dic59—22no—
93D236—41no—
94C4×D59—44no—
95C4×D59—41no—
96C4×D59—41no—
97Dic118—41no—
98C8×C59—21no—
99C8×C59—21no—
100C8×C59—21no—
101C8×C59—21no—
102C59⋊C8—41no—
103C59⋊C8—41no—
104#11524—591nomaximal, Sylow
105C22×C59—21no—
106C22×C59—41no—
107C22×C59#40711yescharacteristic
108C2×D59—42no—
109C2×D59—41no—
110C4×C59—22no—
111C4×C59—21no—
112C4×C59—41no—
113C4×C59#41011yescharacteristic
114C4×C59#41311yescharacteristic
115Dic59—42no—
116Dic59—41no—
117#2922—591no—
118#2165—591no—
119#2165D5911yescharacteristic, complemented
120#1328—592no—
121#1321—592no—
122C2×C59—21no—
123C2×C59—41no—
124C2×C59#146411yescharacteristic
125D59—81no—
126C4×#41—591no—
127#433—1181no—
128#433—1181no—
129#431—1181no—
130#431—1181no—
131#424—591no—
132#424—591no—
133#408—591no—
134#408—591no—
135C4×M16C2×D5911yescharacteristic
136C2×C4×C8—591no—
137#364—21no—
138#364—1181no—
139#349—592no—
140#349C2×D5912yes—
141#347—21no—
142#347—1181no—
143C59#1152411yescharacteristic, complemented, Sylow
144C2×#41—591no—
145C2×M16C4×D5911yescharacteristic
146C2×M16C22×D5911yescharacteristic
147C22×C8—591no—
148C22×C8—591no—
149C4×Q8—1181no—
150C4×D4—1181no—
151C4×D4—1182no—
152#117—591no—
153#117—1181no—
154C2×C42—1181no—
155C2×C42C4×D5911yescharacteristic
156M32—22no—
157M32—1182no—
158C4⋊C8—1181no—
159C4⋊C8—1181no—
160C4⋊C8—1181no—
161C4⋊C8—1181no—
162C22⋊C8—1181no—
163C22⋊C8—1181no—
164C22⋊C8—1181no—
165C22⋊C8—1181no—
166#97D23611yescharacteristic
167#97C22⋊D5911yescharacteristic
168C4×C8—1181no—
169C4×C8—1181no—
170C4×C8D23611yescharacteristic
171C4×C8C22⋊D5911yescharacteristic
172#41—2361no—
173#41—2361no—
174C2×Q8—591no—
175C2×D4—591no—
176C2×D4—1181no—
177C22×C4—21no—
178C22×C4—1182no—
179C22×C4—1181no—
180C22×C4C2×C4×D5911yescharacteristic
181M16—41no—
182M16—41no—
183C2×C8—1181no—
184C2×C8—1181no—
185C2×C8—2361no—
186C2×C8—2361no—
187C2×C8(C2×D59)⋊C411yescharacteristic
188C2×C8(C2×D59)⋊C411yescharacteristic
189C2×C8C2×D23611yescharacteristic
190C2×C8C2×C22⋊D5911yescharacteristic
191C4⋊C4—1182no—
192C4⋊C4—1181no—
193C22⋊C4—592no—
194C22⋊C4—1182no—
195C42—21no—
196C42—1182no—
197C42—1181no—
198C42(C2×D59)⋊C411yescharacteristic
199C42(C2×D59)⋊C411yescharacteristic
200C16—42no—
201C16—2362no—
202C23—1181no—
203C23M16×D5911yescharacteristic
204Q8—2361no—
205D4—2361no—
206D4—2362no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—42no—
212C2×C4—1182no—
213C2×C4—1181no—
214C2×C4—2364no—
215C2×C4—2361no—
216C2×C4—2361no—
217C2×C4C2×(C2×D59)⋊C411yescharacteristic
218C2×C4M16×D5911yescharacteristic
219C8—21no—
220C8—21no—
221C8—21no—
222C8—21no—
223C8—2361no—
224C8—2361no—
225C22—21no—
226C22—41no—
227C22—2362no—
228C22—2361no—
229C22#1683736511yescharacteristic
230C4—22no—
231C4—21no—
232C4—41no—
233C4—2362no—
234C4—2361no—
235C4#1683737511yescharacteristic
236C4#1683738411yescharacteristic
237C2—21no—
238C2—41no—
239C2—4721no—
240C2#2142242811yescharacteristic
subgroupG/H
centerC4#16837375
commutatorC22×C4×C59C22×C4
FrattiniC2×M16C22×D59
FittingC59×#2165C2
socleC2×C59#1464
prime radicalC2×#11745685C2×C4
cosocleC2×M16×C59C23
hypercenter#2165D59
hypocenterC59#11524
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ C42 ◁ C4×M16 ◁ #2165

Complements

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

NH ≅ G/Ntype
2. #21425908C2semidirect
3. #21422048C2semidirect
5. C59×#2165C2semidirect
119. #2165D59semidirect
143. C59#11524semidirect

Maximal subgroups

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

subgroupindex
#214327412
#214259082
#214220482
#214220332
C59×#21652
#1152459