Finite Group Databasebeta

← #28475992

Subgroups — #28475992

Order 15104.

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

normal subgroups only

This group has 456 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#21424024C211yesmaximal, characteristic
2#21424014C211yesmaximal, characteristic
3C59×#1785C211yesmaximal, characteristic
4C2×#14273646—21no—
5C2×#14273644—21no—
6C2×#14273642—21no—
7C2×#14273642—21no—
8#16837366C412yescomplemented
9#16837265C412yes—
10C22×#41×C59C2211yescharacteristic
11C2×#101×C59—21no—
12C2×#100×C59—21no—
13C59×#407C412yescomplemented
14C2×#11745664—22no—
15C2×C22⋊Dic59—22no—
16#14273646—42no—
17#14273644—42no—
18#14273642—42no—
19#14273642—42no—
20C22⋊(C59⋊C8)—42no—
21C59⋊#95—42no—
22C2×#41×C59—42no—
23C2×#41×C59—42no—
24C2×#41×C59—42no—
25C22×Q8×C59D411yescharacteristic
26C22×D4×C59D411yescharacteristic
27C22×D4×C59D411yescharacteristic
28C22×D4×C59Q811yescharacteristic
29C23×C4×C59C2×C411yescharacteristic
30C23×C4×C59C2×C411yescharacteristic
31C23×C4×C59C2×C411yescharacteristic
32C2×M16×C59—22no—
33#101×C59—42no—
34#100×C59—42no—
35C22⋊C8×C59—42no—
36C24×C59C22⋊C411yescharacteristic
37C24×C59C4⋊C411yescharacteristic
38C24×C59C4⋊C411yescharacteristic
39#41×C59—416no—
40C2×Q8×C59—22no—
41C2×Q8×C59—22no—
42C2×Q8×C59—41no—
43C2×D4×C59—22no—
44C2×D4×C59—22no—
45C2×D4×C59—22no—
46C2×D4×C59—22no—
47C2×D4×C59—41no—
48C2×D4×C59—41no—
49C2×D4×C59—41no—
50C2×D4×C59—41no—
51C2×D4×C59—41no—
52C22×C4×C59—22no—
53C22×C4×C59—22no—
54C22×C4×C59—22no—
55C22×C4×C59—41no—
56C22×C4×C59—41no—
57C22×C4×C59—41no—
58C22×C4×C59—41no—
59C22×C4×C59—41no—
60C22×C4×C59—41no—
61C22×C4×C59C4211yescharacteristic
62C22×C4×C59C22⋊C411yescharacteristic
63C22×C4×C59C22⋊C411yescharacteristic
64C22×C4×C59C4⋊C411yescharacteristic
65C22×Dic59—42no—
66M16×C59—42no—
67M16×C59—42no—
68C2×C8×C59—42no—
69C22⋊Dic59—42no—
70C22⋊Dic59—42no—
71#11745664—42no—
72#11745664—42no—
73C2×C59⋊C8—42no—
74C23×C59—21no—
75C23×C59—21no—
76C23×C59—21no—
77C23×C59—21no—
78C23×C59—21no—
79C23×C59—21no—
80C23×C59—21no—
81C23×C59—21no—
82C23×C59—81no—
83C23×C59—81no—
84C23×C59—81no—
85C23×C59#9511yescharacteristic
86C23×C59#9912yes—
87Q8×C59—44no—
88D4×C59—44no—
89D4×C59—44no—
90D4×C59—44no—
91C2×C4×C59—21no—
92C2×C4×C59—21no—
93C2×C4×C59—21no—
94C2×C4×C59—21no—
95C2×C4×C59—21no—
96C2×C4×C59—21no—
97C2×C4×C59—21no—
98C2×C4×C59—21no—
99C2×C4×C59—21no—
100C2×C4×C59—21no—
101C2×C4×C59—44no—
102C2×C4×C59—44no—
103C2×C4×C59—44no—
104C2×C4×C59#9912yes—
105C2×C4×C59#9912yes—
106C2×Dic59—82no—
107C2×Dic59—84no—
108C8×C59—82no—
109C59⋊C8—82no—
110#7319—591nomaximal, Sylow
111C22×C59—22no—
112C22×C59—41no—
113C22×C59—42no—
114C22×C59—42no—
115C22×C59—42no—
116C22×C59—41no—
117C22×C59—41no—
118C22×C59—81no—
119C22×C59—81no—
120C22×C59—81no—
121C22×C59—81no—
122C22×C59—81no—
123C22×C59—81no—
124C22×C59#34211yescharacteristic
125C22×C59#34211yescharacteristic
126C22×C59#34211yescharacteristic
127C4×C59—22no—
128C4×C59—22no—
129C4×C59—41no—
130C4×C59—41no—
131Dic59—162no—
132#1785—591no—
133#1785D5911yescharacteristic
134#1782—591no—
135C2×C59—21no—
136C2×C59—21no—
137C2×C59—21no—
138C2×C59—42no—
139C2×C59—81no—
140C2×C59—81no—
141C2×C59#130411yescharacteristic
142C22×#41C2×D5911yescharacteristic
143C2×#101—21no—
144C2×#101—1181no—
145C2×#100—21no—
146C2×#100—1181no—
147C2×#99—1181no—
148C2×#99—1181no—
149#407—592no—
150#407Dic5912yescomplemented
151#381—592no—
152C59#731911yescharacteristic, complemented, Sylow
153C2×#41—42no—
154C2×#41—42no—
155C2×#41—42no—
156C22×Q8C22⋊D5911yescharacteristic
157C22×D4Dic11811yescharacteristic
158C22×D4D23611yescharacteristic
159C22×D4C22⋊D5911yescharacteristic
160C23×C4C4×D5911yescharacteristic
161C23×C4C4×D5911yescharacteristic
162C23×C4C2×Dic5911yescharacteristic
163C2×M16—22no—
164C2×M16—1182no—
165C2×C22⋊C4—1182no—
166#101—42no—
167#101—2362no—
168#100—42no—
169#100—2362no—
170#99—2362no—
171#99—2362no—
172C22⋊C8—42no—
173C22⋊C8—2362no—
174#95—2362no—
175C24Dic59⋊C411yescharacteristic
176C24C4⋊Dic5911yescharacteristic
177C24(C2×D59)⋊C411yescharacteristic
178#41—416no—
179C2×Q8—22no—
180C2×Q8—22no—
181C2×Q8—41no—
182C2×D4—22no—
183C2×D4—22no—
184C2×D4—22no—
185C2×D4—22no—
186C2×D4—41no—
187C2×D4—41no—
188C2×D4—41no—
189C2×D4—41no—
190C2×D4—41no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—41no—
200C22×C4—2362no—
201C22×C4C4×Dic5911yescharacteristic
202C22×C4Dic59⋊C411yescharacteristic
203C22×C4(C2×D59)⋊C411yescharacteristic
204C22×C4C22⋊Dic5911yescharacteristic
205M16—42no—
206M16—42no—
207M16—2362no—
208M16—2362no—
209C2×C8—42no—
210C2×C8—2362no—
211C22⋊C4—2362no—
212C22⋊C4—2362no—
213C23—21no—
214C23—21no—
215C23—21no—
216C23—21no—
217C23—21no—
218C23—21no—
219C23—21no—
220C23—21no—
221C23—81no—
222C23—81no—
223C23—81no—
224C23C59⋊#9511yescharacteristic
225C23#1427364112yes—
226Q8—44no—
227D4—44no—
228D4—44no—
229D4—44no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—44no—
241C2×C4—44no—
242C2×C4—44no—
243C2×C4—4722no—
244C2×C4—4724no—
245C2×C4#1427364112yes—
246C2×C4#1427364212yes—
247C8—82no—
248C8—4722no—
249C22—22no—
250C22—41no—
251C22—42no—
252C22—42no—
253C22—42no—
254C22—41no—
255C22—41no—
256C22—81no—
257C22—81no—
258C22—81no—
259C22—81no—
260C22—81no—
261C22—81no—
262C22#1683716811yescharacteristic
263C22#1683716811yescharacteristic
264C22#1683716911yescharacteristic
265C4—22no—
266C4—22no—
267C4—41no—
268C4—41no—
269C4—9442no—
270C2—21no—
271C2—21no—
272C2—21no—
273C2—42no—
274C2—81no—
275C2—81no—
276C2C59⋊#130411yescharacteristic
subgroupG/H
centerC2C59⋊#1304
commutatorC22×C4×C59C42
FrattiniC22×#41C2×D59
FittingC59×#1785C2
socleC2×C59#1304
prime radical, cosocleC22×#41×C59C22
hypercenter#1785D59
hypocenterC59#7319
LCSG ▷ C22×C4×C59 ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C23 ◁ C22×#41 ◁ #1785

Complements

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

NH ≅ G/Ntype
8. #16837366C4semidirect
13. C59×#407C4semidirect
150. #407Dic59semidirect
152. C59#7319semidirect

Maximal subgroups

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

subgroupindex
#214240242
#214240142
C59×#17852
#731959