Finite Group Databasebeta

← #28498344

Subgroups — #28498344

Order 15104.

350 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 71 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#21429284C211yesmaximal, characteristic
2#21422438C211yesmaximal, characteristic
3#21422418C211yesmaximal, characteristic
4#21422042C211yesmaximal, characteristic
5#21422039C211yesmaximal, characteristic
6#21422039C211yesmaximal, characteristic
7C59×#1325C211yesmaximal, characteristic
8C2×#14273718C411yescharacteristic
9C2×#14273692C2211yescharacteristic
10#16837456—21no—
11#16837452—21no—
12#16837333—21no—
13#16837333—21no—
14#16837308C411yescharacteristic
15#16837307C411yescharacteristic
16#16837288—21no—
17#16837288—21no—
18#16837267C2211yescharacteristic
19C4×Dic59⋊C4C411yescharacteristic
20#16837128C2211yescharacteristic
21#16837128C2211yescharacteristic
22#16837127—21no—
23#16837127—21no—
24C59×#384C2211yescharacteristic
25C59×#324C2211yescharacteristic
26C59×#324C2211yescharacteristic
27C22×Dic118C2×C411yescharacteristic
28#14273718—41no—
29#14273718—41no—
30#14273692—41no—
31#14273692—41no—
32C2×C4⋊Dic59—21no—
33C2×C4⋊Dic59C2×C411yescharacteristic
34C2×Dic59⋊C4—21no—
35C2×Dic59⋊C4—21no—
36C2×Dic59⋊C4D411yescharacteristic
37C2×Dic59⋊C4D411yescharacteristic
38C2×C4×Dic59C2×C411yescharacteristic
39C2×C4×Dic59C2×C411yescharacteristic
40C2×C4×Dic59D411yescharacteristic
41C2×C4×Dic59D411yescharacteristic
42Dic59⋊C8—41no—
43Dic59⋊C8—41no—
44C22⋊(C59⋊C8)—21no—
45C22⋊(C59⋊C8)—21no—
46#14273637—41no—
47C8×Dic59—41no—
48C59⋊#95—21no—
49C59⋊#95—21no—
50C59⋊#95—21no—
51C59⋊#95—21no—
52C59⋊#95—21no—
53C59⋊#95—21no—
54C59⋊#95—21no—
55C2×C4⋊C4×C59—21no—
56C2×C4⋊C4×C59—21no—
57C2×C4⋊C4×C59C2×C411yescharacteristic
58C2×C4⋊C4×C59C2311yescharacteristic
59C2×C42×C59C2×C411yescharacteristic
60C22⋊C8×C59—21no—
61C22⋊C8×C59—21no—
62C22×C4×C59—21no—
63C22×C4×C59—21no—
64C22×C4×C59C22×C411yescharacteristic
65C22×C4×C59C2×D411yescharacteristic
66C22×C4×C59C2×D411yescharacteristic
67C22×Dic59—21no—
68C22×Dic59—21no—
69C22×Dic59C22⋊C411yescharacteristic
70C22×Dic59C22⋊C411yescharacteristic
71C22×Dic59C22⋊C411yescharacteristic
72C22×Dic59C22⋊C411yescharacteristic
73C2×Dic118—21no—
74C2×Dic118—21no—
75C2×Dic118—22no—
76C2×Dic118—41no—
77C2×C8×C59—41no—
78C2×C8×C59—41no—
79C4⋊C4×C59—41no—
80C4⋊C4×C59—42no—
81C4⋊C4×C59—42no—
82C4⋊C4×C59—41no—
83C42×C59—21no—
84C42×C59—21no—
85C4⋊Dic59—41no—
86C4⋊Dic59—41no—
87C4⋊Dic59—41no—
88Dic59⋊C4—41no—
89Dic59⋊C4—41no—
90Dic59⋊C4—42no—
91Dic59⋊C4—42no—
92C4×Dic59—21no—
93C4×Dic59—21no—
94C4×Dic59—21no—
95C4×Dic59—21no—
96C4×Dic59—21no—
97C4×Dic59—21no—
98C4×Dic59—21no—
99C4×Dic59—21no—
100C2×C59⋊C8—41no—
101C2×C59⋊C8—41no—
102C23×C59C2×C22⋊C411yescharacteristic
103C2×C4×C59—21no—
104C2×C4×C59—21no—
105C2×C4×C59—22no—
106C2×C4×C59—21no—
107C2×C4×C59—21no—
108C2×C4×C59—41no—
109C2×C4×C59—41no—
110C2×C4×C59—41no—
111C2×C4×C59—41no—
112C2×C4×C59—41no—
113C2×C4×C59—41no—
114C2×C4×C59—41no—
115C2×C4×C59#13111yescharacteristic
116C2×C4×C59#13111yescharacteristic
117C2×Dic59—21no—
118C2×Dic59—21no—
119C2×Dic59—21no—
120C2×Dic59—21no—
121C2×Dic59—21no—
122C2×Dic59—21no—
123C2×Dic59—41no—
124C2×Dic59—41no—
125C2×Dic59—41no—
126C2×Dic59—41no—
127C2×Dic59—42no—
128C2×Dic59—41no—
129C2×Dic59—41no—
130C2×Dic59#9911yescharacteristic
131C2×Dic59#9911yescharacteristic
132C2×Dic59#10112yes—
133Dic118—42no—
134Dic118—42no—
135C8×C59—81no—
136C8×C59—81no—
137C59⋊C8—81no—
138C59⋊C8—81no—
139#11571—591nomaximal, Sylow
140C22×C59—21no—
141C22×C59—21no—
142C22×C59#40811yescharacteristic
143C22×C59C2×#9911yescharacteristic
144C22×C59C2×#10111yescharacteristic
145C4×C59—21no—
146C4×C59—21no—
147C4×C59—42no—
148C4×C59—41no—
149C4×C59—41no—
150C4×C59—81no—
151Dic59—21no—
152Dic59—21no—
153Dic59—22no—
154Dic59—41no—
155Dic59—41no—
156Dic59—81no—
157Dic59—81no—
158#2565—591no—
159#1467—591no—
160#1461—591no—
161#1325—591no—
162#1325D5911yescharacteristic
163#1324—591no—
164#1324—591no—
165C2×C59—21no—
166C2×C59—21no—
167C2×C59#147211yescharacteristic
168C2×C59#212611yescharacteristic
169C2×C59#213311yescharacteristic
170C2×#125—591no—
171C2×C4×Q8—591no—
172#432—1181no—
173#431—1181no—
174#398—1181no—
175#398—1181no—
176#391—591no—
177#391—591no—
178#387—1181no—
179#387—1181no—
180#384C2×D5911yescharacteristic
181#382—591no—
182C4×C4⋊C4—591no—
183#324—591no—
184#324—591no—
185#324—1181no—
186#324—1181no—
187#324C2×D5911yescharacteristic
188#324C2×D5911yescharacteristic
189C59#1157111yescharacteristic, complemented, Sylow
190C22×Q8—591no—
191#125—2361no—
192#125—2361no—
193C4×Q8—2361no—
194C4×Q8—2361no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—591no—
198C2×C4⋊C4—591no—
199C2×C4⋊C4—591no—
200C2×C4⋊C4—1181no—
201C2×C4⋊C4—1181no—
202C2×C4⋊C4—1181no—
203C2×C4⋊C4C4×D5911yescharacteristic
204C2×C4⋊C4C22×D5911yescharacteristic
205C2×C42—591no—
206C2×C42—591no—
207C2×C42—591no—
208C2×C42—591no—
209C2×C42C4×D5911yescharacteristic
210C4⋊C8—2361no—
211C4⋊C8—2361no—
212C22⋊C8—21no—
213C22⋊C8—21no—
214C22⋊C8—1181no—
215C22⋊C8—1181no—
216#97—2361no—
217C4×C8—2361no—
218#95—1181no—
219#95—1181no—
220#95—1181no—
221#95—1181no—
222#95—1181no—
223#95—1181no—
224#95—1181no—
225C2×Q8—1182no—
226C2×Q8—1181no—
227C2×Q8—1181no—
228C2×Q8—2361no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—591no—
232C22×C4—591no—
233C22×C4—591no—
234C22×C4—591no—
235C22×C4—1181no—
236C22×C4—1181no—
237C22×C4C2×C4×D5911yescharacteristic
238C22×C4D4×D5911yescharacteristic
239C22×C4D4×D5911yescharacteristic
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—2361no—
243C2×C8—2361no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—42no—
247C4⋊C4—42no—
248C4⋊C4—2361no—
249C4⋊C4—2361no—
250C4⋊C4—2361no—
251C4⋊C4—2362no—
252C4⋊C4—2361no—
253C4⋊C4—2361no—
254C4⋊C4—2362no—
255C42—21no—
256C42—21no—
257C42—1181no—
258C42—1181no—
259C42—1181no—
260C42—1181no—
261C42—1181no—
262C42—1181no—
263C42—1181no—
264C42—1181no—
265C23C22⋊C4×D5911yescharacteristic
266Q8—2362no—
267Q8—2362no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—592no—
281C2×C4—591no—
282C2×C4—591no—
283C2×C4—1181no—
284C2×C4—1181no—
285C2×C4—1181no—
286C2×C4—1181no—
287C2×C4—1181no—
288C2×C4—1181no—
289C2×C4—2361no—
290C2×C4—2361no—
291C2×C4—2361no—
292C2×C4—2362no—
293C2×C4—2361no—
294C2×C4—2361no—
295C2×C4—2361no—
296C2×C4#1427373311yescharacteristic
297C2×C4#1427373511yescharacteristic
298C8—81no—
299C8—81no—
300C8—4721no—
301C8—4721no—
302C22—21no—
303C22—21no—
304C22#1683736711yescharacteristic
305C22#99×D5911yescharacteristic
306C22#101×D5911yescharacteristic
307C4—21no—
308C4—21no—
309C4—42no—
310C4—41no—
311C4—41no—
312C4—81no—
313C4—1181no—
314C4—1181no—
315C4—1182no—
316C4—4721no—
317C4—4721no—
318C4—2361no—
319C4—2361no—
320C2—21no—
321C2—21no—
322C2#2142245811yescharacteristic
323C2#2142575811yescharacteristic
324C2#2142578411yescharacteristic
subgroupG/H
centerC22#99×D59
commutatorC22×C4×C59C22×C4
FrattiniC2×C4⋊C4C22×D59
FittingC59×#1325C2
socleC22×C59C2×#99
prime radicalC23×C59C2×C22⋊C4
cosocleC2×C4⋊C4×C59C23
hypercenter#1325D59
hypocenterC59#11571
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

Complements

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

NH ≅ G/Ntype
189. C59#11571semidirect

Maximal subgroups

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

subgroupindex
#214292842
#214224382
#214224182
#214220422
#214220392
C59×#13252
#1157159