Finite Group Databasebeta

← #28497783

Subgroups — #28497783

Order 15104.

526 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 93 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#21426681C211yesmaximal, characteristic
2#21422407C212yesmaximal
3#21422026C211yesmaximal, characteristic
4#21422025C212yesmaximal
5C59×#1317C211yesmaximal, characteristic
6C23×Dic118C411yescharacteristic
7C2×#14273683C411yescharacteristic
8C2×#14273683C2211yescharacteristic
9#16837452—22no—
10#16837306—22no—
11#16837306—22no—
12#16837265C411yescharacteristic
13#16837263C411yescharacteristic
14#16837263C2211yescharacteristic
15#16837127—22no—
16#16837126C2212yes—
17C59×#381C2211yescharacteristic
18C59×#323C2212yes—
19C22×Dic118—21no—
20C22×Dic118—21no—
21C22×Dic118—22no—
22C22×Dic118—42no—
23C22×Dic118—42no—
24C22×Dic118C814yescomplemented
25C23×Dic59C2×C411yescharacteristic
26C23×Dic59C2×C411yescharacteristic
27#14273683—42no—
28#14273683—42no—
29C2×Dic59⋊C4—21no—
30C2×Dic59⋊C4D412yes—
31C2×C22⋊Dic59C2×C411yescharacteristic
32C2×C22⋊Dic59C2×C411yescharacteristic
33C2×C4×Dic59—21no—
34C2×C4×Dic59D412yes—
35Dic59⋊C8—42no—
36C22⋊(C59⋊C8)—22no—
37C8×Dic59—42no—
38C59⋊#95—22no—
39C59⋊#95—22no—
40C59⋊#95—22no—
41C23×C4×C59C2×C411yescharacteristic
42C2×C22⋊C4×C59C2×C411yescharacteristic
43C2×C22⋊C4×C59C2311yescharacteristic
44C22⋊C8×C59—22no—
45#95×C59—22no—
46C24×C59C22×C411yescharacteristic
47C22×C4×C59—21no—
48C22×C4×C59—21no—
49C22×C4×C59—21no—
50C22×C4×C59—41no—
51C22×C4×C59—41no—
52C22×C4×C59C2×C812yes—
53C22×C4×C59C2×D412yes—
54C22×Dic59—22no—
55C22×Dic59—22no—
56C22×Dic59—21no—
57C22×Dic59—21no—
58C22×Dic59—21no—
59C22×Dic59—41no—
60C22×Dic59—41no—
61C22×Dic59C22⋊C411yescharacteristic
62C22×Dic59C22⋊C412yes—
63C22×Dic59C22⋊C411yescharacteristic
64C22×Dic59C2×C812yes—
65C22×Dic59C2×C812yes—
66C22×Dic59M1612yes—
67C2×Dic118—24no—
68C2×Dic118—24no—
69C2×Dic118—42no—
70C2×Dic118—42no—
71C2×Dic118—48no—
72C2×Dic118—42no—
73C2×Dic118—42no—
74C2×Dic118—48no—
75C2×C8×C59—42no—
76C22⋊C4×C59—41no—
77C22⋊C4×C59—41no—
78C22⋊Dic59—41no—
79C22⋊Dic59—41no—
80Dic59⋊C4—42no—
81Dic59⋊C4—42no—
82C4×Dic59—22no—
83C4×Dic59—22no—
84C4×Dic59—42no—
85C2×C59⋊C8—42no—
86C23×C59—21no—
87C23×C59—21no—
88C23×C59—42no—
89C23×C59C2×C22⋊C411yescharacteristic
90C23×C59C22×C811yescharacteristic
91C23×C59C2×M1611yescharacteristic
92C2×C4×C59—22no—
93C2×C4×C59—22no—
94C2×C4×C59—42no—
95C2×C4×C59—41no—
96C2×C4×C59—41no—
97C2×C4×C59—42no—
98C2×C4×C59—42no—
99C2×C4×C59—42no—
100C2×C4×C59—41no—
101C2×Dic59—21no—
102C2×Dic59—21no—
103C2×Dic59—24no—
104C2×Dic59—24no—
105C2×Dic59—22no—
106C2×Dic59—22no—
107C2×Dic59—42no—
108C2×Dic59—41no—
109C2×Dic59—41no—
110C2×Dic59—42no—
111C2×Dic59—42no—
112C2×Dic59—42no—
113C2×Dic59—41no—
114C2×Dic59C22⋊C812yes—
115C2×Dic59C22⋊C812yes—
116C2×Dic59#9912yes—
117C2×Dic59#10012yes—
118Dic118—48no—
119Dic118—48no—
120C8×C59—82no—
121C59⋊C8—82no—
122#11428—591nomaximal, Sylow
123C22×C59—22no—
124C22×C59—21no—
125C22×C59—21no—
126C22×C59—41no—
127C22×C59—41no—
128C22×C59—42no—
129C22×C59—42no—
130C22×C59C2×C22⋊C811yescharacteristic
131C22×C59C2×#9911yescharacteristic
132C22×C59C2×#10011yescharacteristic
133C4×C59—42no—
134C4×C59—42no—
135C4×C59—81no—
136Dic59—22no—
137Dic59—42no—
138Dic59—42no—
139Dic59—81no—
140Dic59#32314yes—
141#2310—591no—
142#1458—592no—
143#1317—591no—
144#1317—592no—
145#1317D5911yescharacteristic
146C2×C59—21no—
147C2×C59—21no—
148C2×C59—41no—
149C2×C59—41no—
150C2×C59C2×#32311yescharacteristic
151C2×C59#212312yes—
152C23×Q8—591no—
153C2×#117—591no—
154C2×#117—591no—
155#431—1182no—
156#391—1182no—
157#391—1182no—
158#381—591no—
159#381—591no—
160#381—591no—
161#381C2×D5911yescharacteristic
162#324—1182no—
163#323—592no—
164#323C2×D5912yes—
165C59#1142811yescharacteristic, complemented, Sylow
166C22×Q8—594no—
167C22×Q8—1181no—
168C22×Q8—1181no—
169C22×Q8—1182no—
170C22×Q8—2362no—
171C22×Q8—2362no—
172C23×C4—591no—
173C23×C4—591no—
174C23×C4C4×D5911yescharacteristic
175#117—2362no—
176#117—2362no—
177C2×C4⋊C4—592no—
178C2×C4⋊C4—1181no—
179C2×C22⋊C4—591no—
180C2×C22⋊C4—591no—
181C2×C22⋊C4C4×D5911yescharacteristic
182C2×C22⋊C4C22×D5911yescharacteristic
183C2×C42—592no—
184C2×C42—1181no—
185C4⋊C8—2362no—
186C22⋊C8—22no—
187C22⋊C8—1182no—
188C4×C8—2362no—
189#95—22no—
190#95—1182no—
191#95—1182no—
192#95—1182no—
193C24C2×C4×D5911yescharacteristic
194C2×Q8—1184no—
195C2×Q8—1184no—
196C2×Q8—2362no—
197C2×Q8—2362no—
198C2×Q8—2368no—
199C2×Q8—2368no—
200C2×Q8—2362no—
201C2×Q8—2362no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—41no—
206C22×C4—41no—
207C22×C4—591no—
208C22×C4—591no—
209C22×C4—592no—
210C22×C4—592no—
211C22×C4—592no—
212C22×C4—592no—
213C22×C4—1182no—
214C22×C4—1182no—
215C22×C4—1181no—
216C22×C4—1181no—
217C22×C4—1181no—
218C22×C4—2361no—
219C22×C4—2361no—
220C22×C4C8×D5912yes—
221C22×C4D4×D5912yes—
222C2×C8—42no—
223C2×C8—2362no—
224C4⋊C4—2362no—
225C4⋊C4—2362no—
226C22⋊C4—41no—
227C22⋊C4—41no—
228C22⋊C4—2361no—
229C22⋊C4—2361no—
230C42—1182no—
231C42—1182no—
232C42—2362no—
233C23—21no—
234C23—21no—
235C23—42no—
236C23C22⋊C4×D5911yescharacteristic
237C23C2×C8×D5911yescharacteristic
238C23M16×D5911yescharacteristic
239Q8—2368no—
240Q8—2368no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—42no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—592no—
251C2×C4—592no—
252C2×C4—592no—
253C2×C4—592no—
254C2×C4—1184no—
255C2×C4—1184no—
256C2×C4—1181no—
257C2×C4—1181no—
258C2×C4—1182no—
259C2×C4—1182no—
260C2×C4—2362no—
261C2×C4—2361no—
262C2×C4—2362no—
263C2×C4—2361no—
264C2×C4—2361no—
265C2×C4—2362no—
266C2×C4—2362no—
267C8—82no—
268C8—4722no—
269C22—22no—
270C22—21no—
271C22—21no—
272C22—41no—
273C22—41no—
274C22—42no—
275C22—42no—
276C22C22⋊C8×D5911yescharacteristic
277C22#99×D5911yescharacteristic
278C22#100×D5911yescharacteristic
279C4—42no—
280C4—42no—
281C4—81no—
282C4—594no—
283C4—1182no—
284C4—4721no—
285C4—2362no—
286C4—2362no—
287C2—21no—
288C2—21no—
289C2—41no—
290C2—41no—
291C2#323×D5911yescharacteristic
292C2#2142574812yes—
subgroupG/H
centerC22#99×D59
commutatorC23×C59C22×C8
FrattiniC2×C22⋊C4C22×D59
FittingC59×#1317C2
socleC22×C59C2×#99
prime radicalC24×C59C22×C4
cosocleC2×C22⋊C4×C59C23
hypercenter#1317D59
hypocenterC59#11428
LCSG ▷ C23×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1317

Complements

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

NH ≅ G/Ntype
24. C22×Dic118C8semidirect
165. C59#11428semidirect

Maximal subgroups

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

subgroupindex
#214266812
#214224072
#214220262
#214220252
C59×#13172
#1142859