Finite Group Databasebeta

← #28488798

Subgroups — #28488798

Order 15104.

424 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 127 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#21432459C211yesmaximal, characteristic
2#21423949C211yesmaximal, characteristic
3#21421978C214yesmaximal
4C59×#1745C211yesmaximal, characteristic
5C2×#14273719C412yes—
6C2×C4⋊(C59⋊C8)—21no—
7C2×#14273638C2212yes—
8#16837300—21no—
9#16837300—21no—
10#16837300—21no—
11#16837300—21no—
12#16837272C411yescharacteristic
13#16837272C411yescharacteristic
14#16837268C2212yes—
15#16837157—21no—
16C2×#97×C59C2212yes—
17C43×C59C2211yescharacteristic
18C59×#336—21no—
19C59×#336—21no—
20C22×C59⋊C8—22no—
21#14273719—44no—
22C2×C4⋊Dic59—21no—
23C2×C4⋊Dic59—21no—
24C2×C4⋊Dic59—21no—
25C2×C4⋊Dic59—21no—
26C2×C4⋊Dic59C2×C412yes—
27C2×C4⋊Dic59C2×C412yes—
28C2×Dic59⋊C4—22no—
29C2×Dic59⋊C4—22no—
30C4⋊(C59⋊C8)—24no—
31#14273638—24no—
32C59⋊#95—22no—
33C59⋊#95—22no—
34C22×C8×C59—22no—
35C2×C42×C59C2×C411yescharacteristic
36C2×C42×C59C2×C411yescharacteristic
37C2×C42×C59D411yescharacteristic
38C2×C42×C59D411yescharacteristic
39C2×C42×C59D411yescharacteristic
40C2×C42×C59D411yescharacteristic
41C2×C42×C59C2311yescharacteristic
42#97×C59—22no—
43#97×C59Q814yes—
44C22×C4×C59C22⋊C411yescharacteristic
45C22×C4×C59C22⋊C411yescharacteristic
46C22×C4×C59C22⋊C411yescharacteristic
47C22×C4×C59C22⋊C411yescharacteristic
48C22×C4×C59C22×C411yescharacteristic
49C22×C4×C59C2×D411yescharacteristic
50C22×C4×C59C2×D411yescharacteristic
51C22×Dic59—22no—
52C22×Dic59—22no—
53C2×C8×C59—24no—
54C2×C8×C59—42no—
55C2×C8×C59—42no—
56C42×C59—22no—
57C42×C59—22no—
58C42×C59—22no—
59C42×C59—41no—
60C42×C59—41no—
61C42×C59—41no—
62C42×C59C2×Q812yes—
63C42×C59#4112yes—
64C4⋊Dic59—42no—
65C4⋊Dic59—42no—
66C4⋊Dic59—42no—
67C4⋊Dic59—42no—
68C4⋊Dic59—42no—
69C4⋊Dic59—42no—
70Dic59⋊C4—44no—
71Dic59⋊C4—44no—
72C2×C59⋊C8—24no—
73C2×C59⋊C8—42no—
74C2×C59⋊C8—42no—
75C23×C59C2×C22⋊C411yescharacteristic
76C2×C4×C59—21no—
77C2×C4×C59—21no—
78C2×C4×C59—21no—
79C2×C4×C59—21no—
80C2×C4×C59—21no—
81C2×C4×C59—21no—
82C2×C4×C59—21no—
83C2×C4×C59—21no—
84C2×C4×C59—21no—
85C2×C4×C59—21no—
86C2×C4×C59—21no—
87C2×C4×C59—21no—
88C2×C4×C59—21no—
89C2×C4×C59—21no—
90C2×C4×C59—21no—
91C2×C4×C59#10012yes—
92C2×C4×C59#10112yes—
93C2×C4×C59#10412yes—
94C2×C4×C59C4×Q812yes—
95C2×C4×C59C22⋊Q812yes—
96C2×C4×C59#12411yescharacteristic
97C2×C4×C59C4⋊Q811yescharacteristic
98C2×Dic59—42no—
99C2×Dic59—42no—
100C2×Dic59—42no—
101C2×Dic59—42no—
102C2×Dic59—42no—
103C2×Dic59—42no—
104C8×C59—44no—
105C59⋊C8—44no—
106#9894—591nomaximal, Sylow
107C22×C59#39111yescharacteristic
108C22×C59C2×#10011yescharacteristic
109C22×C59C2×#10111yescharacteristic
110C22×C59C2×#10411yescharacteristic
111C22×C59#42111yescharacteristic
112C22×C59#42111yescharacteristic
113C22×C59#42111yescharacteristic
114C4×C59—21no—
115C4×C59—21no—
116C4×C59—22no—
117C4×C59—22no—
118C4×C59—22no—
119C4×C59—22no—
120C4×C59—22no—
121C4×C59—41no—
122Dic59—82no—
123Dic59—82no—
124#2859—591no—
125#1767—591no—
126#1745D5911yescharacteristic
127#1295—594no—
128C2×C59#152811yescharacteristic
129C2×C59#153011yescharacteristic
130C2×C59#153411yescharacteristic
131C2×C59#153611yescharacteristic
132C2×C59#198611yescharacteristic
133C2×C59#199511yescharacteristic
134C2×C59#199711yescharacteristic
135C2×#125—592no—
136C2×C4⋊C8—1181no—
137C2×#97—592no—
138C2×#97C2×D5912yes—
139#389—1181no—
140#389—1181no—
141#389—1181no—
142#389—1181no—
143#384—591no—
144#384—591no—
145#382—592no—
146C43C2×D5911yescharacteristic
147#336—21no—
148#336—21no—
149#336—1181no—
150C59#989411yescharacteristic, complemented, Sylow
151C22×C8—22no—
152C22×C8—1182no—
153#125—2364no—
154C2×C4⋊C4—592no—
155C2×C4⋊C4—592no—
156C2×C4⋊C4—1182no—
157C2×C4⋊C4—1182no—
158C2×C4⋊C4—1181no—
159C2×C4⋊C4—1181no—
160C2×C4⋊C4—1181no—
161C2×C4⋊C4—1181no—
162C2×C42C4×D5911yescharacteristic
163C2×C42C4×D5911yescharacteristic
164C2×C42D23611yescharacteristic
165C2×C42D23611yescharacteristic
166C2×C42C22⋊D5911yescharacteristic
167C2×C42C22⋊D5911yescharacteristic
168C2×C42C22×D5911yescharacteristic
169C4⋊C8—1184no—
170#97—22no—
171#97—1184no—
172#97Dic11814yes—
173#95—1182no—
174#95—1182no—
175C22×C4—1182no—
176C22×C4—1182no—
177C22×C4(C2×D59)⋊C411yescharacteristic
178C22×C4(C2×D59)⋊C411yescharacteristic
179C22×C4(C2×D59)⋊C411yescharacteristic
180C22×C4(C2×D59)⋊C411yescharacteristic
181C22×C4C2×C4×D5911yescharacteristic
182C22×C4C2×D23611yescharacteristic
183C22×C4C2×C22⋊D5911yescharacteristic
184C2×C8—24no—
185C2×C8—42no—
186C2×C8—42no—
187C2×C8—1184no—
188C2×C8—2362no—
189C2×C8—2362no—
190C4⋊C4—2362no—
191C4⋊C4—2362no—
192C4⋊C4—2364no—
193C4⋊C4—2362no—
194C4⋊C4—2362no—
195C4⋊C4—2362no—
196C4⋊C4—2364no—
197C4⋊C4—2362no—
198C42—22no—
199C42—22no—
200C42—22no—
201C42—41no—
202C42—41no—
203C42—41no—
204C42C2×Dic11812yes—
205C42#1174568512yes—
206C23C2×(C2×D59)⋊C411yescharacteristic
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—2362no—
223C2×C4—2362no—
224C2×C4—2362no—
225C2×C4—2362no—
226C2×C4—2362no—
227C2×C4—2362no—
228C2×C4#1427364312yes—
229C2×C4#1427364512yes—
230C2×C4#1427365312yes—
231C2×C4C4×Dic11812yes—
232C2×C4#1427370612yes—
233C2×C4#1427371511yescharacteristic
234C2×C4#1427372711yescharacteristic
235C8—44no—
236C8—2364no—
237C22#1683730811yescharacteristic
238C22C2×#1427364311yescharacteristic
239C22C2×#1427364511yescharacteristic
240C22C2×#1427365311yescharacteristic
241C22#1683741811yescharacteristic
242C22#1683742011yescharacteristic
243C22#1683742011yescharacteristic
244C4—22no—
245C4—22no—
246C4—22no—
247C4—21no—
248C4—21no—
249C4—22no—
250C4—22no—
251C4—41no—
252C4—4722no—
253C4—4722no—
254C2#2142269911yescharacteristic
255C2#2142270811yescharacteristic
256C2#2142272211yescharacteristic
257C2#2142273011yescharacteristic
258C2#2142504011yescharacteristic
259C2#2142507711yescharacteristic
260C2#2142508511yescharacteristic
subgroupG/H
centerC23C2×(C2×D59)⋊C4
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1745C2
socle, prime radicalC23×C59C2×C22⋊C4
cosocleC2×C42×C59C23
hypercenter#1745D59
hypocenterC59#9894
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C43 ◁ #1745

Complements

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

NH ≅ G/Ntype
150. C59#9894semidirect

Maximal subgroups

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

subgroupindex
#214324592
#214239492
#214219782
C59×#17452
#989459