Finite Group Databasebeta

← #28491685

Subgroups — #28491685

Order 15104.

640 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 640 conjugacy classes of subgroups — too many to draw. Only its 105 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#21430066C211yesmaximal, characteristic
2#21424032C212yesmaximal
3#21422366C211yesmaximal, characteristic
4#21421976C212yesmaximal
5C59×#1280C211yesmaximal, characteristic
6C23×Dic118C2211yescharacteristic
7C2×#14273652—22no—
8C2×#14273652—22no—
9#16837344—22no—
10#16837336—22no—
11#16837275—22no—
12#16837262C2212yes—
13C2×C59⋊#95—22no—
14C2×C59⋊#95C2211yescharacteristic
15C2×C22⋊C8×C59C2212yes—
16C2×#95×C59C2211yescharacteristic
17C22×Dic118—22no—
18C22×Dic118—22no—
19C22×Dic118—21no—
20C22×Dic118—44no—
21C22×Dic118Q812yes—
22C23×Dic59—21no—
23C23×Dic59—21no—
24C2×C4⋊Dic59D412yes—
25C2×C4⋊Dic59D412yes—
26C2×Dic59⋊C4—22no—
27C2×Dic59⋊C4—22no—
28C2×C22⋊Dic59—22no—
29#14273652—44no—
30#14273652—44no—
31C59⋊#95—22no—
32C59⋊#95—22no—
33C59⋊#95—22no—
34C59⋊#95—22no—
35C59⋊#95—44no—
36C23×C4×C59D412yes—
37C23×C4×C59C2311yescharacteristic
38C22×C8×C59—22no—
39C22⋊C8×C59—22no—
40C22⋊C8×C59—22no—
41#95×C59—22no—
42C24×C59C2×D411yescharacteristic
43C22×C4×C59—22no—
44C22×C4×C59—22no—
45C22×C4×C59—22no—
46C22×C4×C59—42no—
47C22×C4×C59—42no—
48C22×C4×C59—42no—
49C22×C4×C59C2×D412yes—
50C22×C4×C59C2×Q811yescharacteristic
51C22×C4×C59#4112yes—
52C22×C4×C59#4111yescharacteristic
53C22×Dic59—24no—
54C22×Dic59—22no—
55C22×Dic59—22no—
56C22×Dic59—22no—
57C22×Dic59—22no—
58C22×Dic59—42no—
59C22×Dic59—41no—
60C22×Dic59—41no—
61C22×Dic59—42no—
62C22×Dic59—41no—
63C22×Dic59—41no—
64C22×Dic59—42no—
65C2×Dic118—24no—
66C2×Dic118—24no—
67C2×Dic118—24no—
68C2×Dic118—44no—
69C2×Dic118—48no—
70C2×Dic118—44no—
71C2×Dic118—42no—
72C2×Dic118—42no—
73C2×Dic118—42no—
74C2×C8×C59—42no—
75C2×C8×C59—42no—
76C2×C8×C59—42no—
77C22⋊Dic59—42no—
78C22⋊Dic59—42no—
79C4⋊Dic59—42no—
80C4⋊Dic59—42no—
81Dic59⋊C4—82no—
82Dic59⋊C4—82no—
83C23×C59—21no—
84C23×C59—21no—
85C23×C59—22no—
86C23×C59#12011yescharacteristic
87C23×C59C22⋊Q811yescharacteristic
88C23×C59#12411yescharacteristic
89C23×C59#13512yes—
90C23×C59#13712yes—
91C2×C4×C59—22no—
92C2×C4×C59—22no—
93C2×C4×C59—41no—
94C2×C4×C59—42no—
95C2×C4×C59—41no—
96C2×C4×C59—44no—
97C2×C4×C59—42no—
98C2×C4×C59—42no—
99C2×C4×C59—42no—
100C2×C4×C59—82no—
101C2×C4×C59C22⋊Q812yes—
102C2×C4×C59#12412yes—
103C2×Dic59—24no—
104C2×Dic59—42no—
105C2×Dic59—44no—
106C2×Dic59—42no—
107C2×Dic59—44no—
108C2×Dic59—44no—
109C2×Dic59—42no—
110C2×Dic59—42no—
111C2×Dic59—42no—
112C2×Dic59—42no—
113C2×Dic59—42no—
114C2×Dic59—42no—
115C2×Dic59—42no—
116C2×Dic59—82no—
117C2×Dic59—81no—
118C2×Dic59—81no—
119Dic118—28no—
120Dic118—44no—
121Dic118—44no—
122Dic118—44no—
123C8×C59—82no—
124#10345—591nomaximal, Sylow
125C22×C59—22no—
126C22×C59—22no—
127C22×C59—22no—
128C22×C59—22no—
129C22×C59—21no—
130C22×C59—21no—
131C22×C59—21no—
132C22×C59—21no—
133C22×C59#39311yescharacteristic
134C22×C59#45212yes—
135C22×C59#45511yescharacteristic
136C22×C59#45611yescharacteristic
137C22×C59B(4,𝔽2)12yes—
138C22×C59#47912yes—
139C22×C59#48811yescharacteristic
140C22×C59#49111yescharacteristic
141C4×C59—22no—
142C4×C59—22no—
143C4×C59—82no—
144Dic59—44no—
145Dic59—82no—
146Dic59—82no—
147Dic59—82no—
148#2646—591no—
149#1787—592no—
150#1446—591no—
151#1294—592no—
152#1280D5911yescharacteristic
153C2×C59—21no—
154C2×C59—22no—
155C2×C59—21no—
156C2×C59#160312yes—
157C2×C59#160612yes—
158C2×C59#202611yescharacteristic
159C2×C59#202811yescharacteristic
160C2×C59#202911yescharacteristic
161C23×Q8—591no—
162C2×#103—1182no—
163C2×#103—1182no—
164C2×C22⋊C8C2×D5912yes—
165#400—1182no—
166#398—1182no—
167#385—1182no—
168#380—592no—
169C2×#95—591no—
170C2×#95—1182no—
171C2×#95C2×D5911yescharacteristic
172C59#1034511yescharacteristic, complemented, Sylow
173C22×Q8—592no—
174C22×Q8—1181no—
175C22×Q8—1182no—
176C22×Q8—1182no—
177C22×Q8—2364no—
178C23×C4—1181no—
179C23×C4—1181no—
180C23×C4D23612yes—
181C23×C4C22×D5911yescharacteristic
182C22×C8—22no—
183C2×C4⋊C4—592no—
184C2×C4⋊C4—592no—
185C2×C4⋊C4—1182no—
186C2×C4⋊C4—1182no—
187C2×C22⋊C4—1182no—
188#103—2364no—
189#103—2364no—
190C22⋊C8—22no—
191C22⋊C8—22no—
192#95—22no—
193#95—1182no—
194#95—1182no—
195#95—1182no—
196#95—1182no—
197#95—2364no—
198C24C2×D23611yescharacteristic
199C2×Q8—1184no—
200C2×Q8—1184no—
201C2×Q8—1184no—
202C2×Q8—2362no—
203C2×Q8—2362no—
204C2×Q8—2364no—
205C2×Q8—2364no—
206C2×Q8—2368no—
207C2×Q8—2362no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—42no—
212C22×C4—42no—
213C22×C4—42no—
214C22×C4—1184no—
215C22×C4—1182no—
216C22×C4—1182no—
217C22×C4—1182no—
218C22×C4—1182no—
219C22×C4—2362no—
220C22×C4—2361no—
221C22×C4—2361no—
222C22×C4—2362no—
223C22×C4—2362no—
224C22×C4—2361no—
225C22×C4—2361no—
226C22×C4#1174568512yes—
227C22×C4D4×D5912yes—
228C22×C4#1174568711yescharacteristic
229C22×C4Q8×D5911yescharacteristic
230C2×C8—42no—
231C2×C8—42no—
232C2×C8—42no—
233C4⋊C4—4722no—
234C4⋊C4—4722no—
235C4⋊C4—2362no—
236C4⋊C4—2362no—
237C22⋊C4—2362no—
238C22⋊C4—2362no—
239C23—21no—
240C23—21no—
241C23—22no—
242C23#1427369711yescharacteristic
243C23#1427370711yescharacteristic
244C23#1427371511yescharacteristic
245C23#1427374912yes—
246C23#1427376012yes—
247Q8—1188no—
248Q8—2364no—
249Q8—2364no—
250Q8—2364no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—42no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—44no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—82no—
261C2×C4—1184no—
262C2×C4—4721no—
263C2×C4—4722no—
264C2×C4—4721no—
265C2×C4—2362no—
266C2×C4—2364no—
267C2×C4—2362no—
268C2×C4—2362no—
269C2×C4—2362no—
270C2×C4—2362no—
271C2×C4—2362no—
272C2×C4—2362no—
273C2×C4—2362no—
274C2×C4—2364no—
275C2×C4—2362no—
276C2×C4—2364no—
277C2×C4#1427370512yes—
278C2×C4#1427371312yes—
279C8—82no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—22no—
288C22#1683731511yescharacteristic
289C22#1683756612yes—
290C22#1683758211yescharacteristic
291C22#1683758711yescharacteristic
292C22#1683759012yes—
293C22#1683771012yes—
294C22#1683775711yescharacteristic
295C22#1683777111yescharacteristic
296C4—22no—
297C4—22no—
298C4—82no—
299C4—4722no—
300C4—4722no—
301C4—4722no—
302C4—2364no—
303C2—21no—
304C2—22no—
305C2—21no—
306C2#2142306112yes—
307C2#2142307812yes—
308C2#2142524811yescharacteristic
309C2#2142525811yescharacteristic
310C2#2142526111yescharacteristic
subgroupG/H
centerC23#14273697
commutator, cosocleC23×C4×C59C23
FrattiniC23×C4C22×D59
FittingC59×#1280C2
socleC23×C59#120
prime radicalC24×C59C2×D4
hypercenter#1280D59
hypocenterC59#10345
LCSG ▷ C23×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
172. C59#10345semidirect

Maximal subgroups

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

subgroupindex
#214300662
#214240322
#214223662
#214219762
C59×#12802
#1034559