Finite Group Databasebeta

← #28486363

Subgroups — #28486363

Order 15104.

424 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 103 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#21429283C211yesmaximal, characteristic
2#21422722C212yesmaximal
3#21422440C211yesmaximal, characteristic
4#21421951C212yesmaximal
5C59×#2983C211yesmaximal, characteristic
6C2×#14273719C2211yescharacteristic
7#16837459C2212yes—
8#16837335—21no—
9#16837335—21no—
10#16837309C411yescharacteristic
11#16837309C411yescharacteristic
12#16837286—21no—
13#16837286—21no—
14#16837271C411yescharacteristic
15#16837267C411yescharacteristic
16C4×C4⋊Dic59C2211yescharacteristic
17#16837143—24no—
18#16837128—21no—
19#16837128—21no—
20C2×C4×Q8×C59C2211yescharacteristic
21C59×#446—24no—
22C59×#432—21no—
23C59×#432C2212yes—
24C59×#431—21no—
25#14273719—22no—
26#14273719—22no—
27C2×C4⋊Dic59—21no—
28C2×C4⋊Dic59C2×C411yescharacteristic
29C2×C4⋊Dic59C2×C411yescharacteristic
30C2×Dic59⋊C4—21no—
31C2×Dic59⋊C4—21no—
32C2×Dic59⋊C4—21no—
33C2×Dic59⋊C4—21no—
34C2×C4×Dic59C2×C411yescharacteristic
35C2×C4×Dic59C2×C411yescharacteristic
36C4⋊(C59⋊C8)—22no—
37C22⋊(C59⋊C8)—22no—
38#14273638—22no—
39C59⋊#95—21no—
40C59⋊#95—21no—
41C59⋊#95—21no—
42C59⋊#95—21no—
43C59⋊#95—21no—
44C59⋊#95—21no—
45C59⋊#95—21no—
46C22×Q8×C59C2×C411yescharacteristic
47C4×Q8×C59—22no—
48C4×Q8×C59—22no—
49C2×C4⋊C4×C59C2×C411yescharacteristic
50C2×C4⋊C4×C59D411yescharacteristic
51C2×C4⋊C4×C59D411yescharacteristic
52C2×C42×C59D411yescharacteristic
53C2×C42×C59D411yescharacteristic
54C2×C42×C59C2311yescharacteristic
55C4⋊C8×C59—22no—
56C4⋊C8×C59—22no—
57C4⋊C8×C59—22no—
58C22⋊C8×C59—22no—
59#97×C59—22no—
60#97×C59D414yes—
61C4×C8×C59—22no—
62C2×Q8×C59—22no—
63C2×Q8×C59—22no—
64C2×Q8×C59—41no—
65C22×C4×C59C22⋊C411yescharacteristic
66C22×C4×C59C22⋊C411yescharacteristic
67C22×C4×C59C22⋊C411yescharacteristic
68C22×C4×C59C22⋊C411yescharacteristic
69C22×C4×C59C22×C411yescharacteristic
70C22×C4×C59C2×D411yescharacteristic
71C22×C4×C59C2×D411yescharacteristic
72C22×Dic59—21no—
73C22×Dic59—21no—
74C22×Dic59—21no—
75C22×Dic59—21no—
76C2×C8×C59—24no—
77C4⋊C4×C59—22no—
78C4⋊C4×C59—22no—
79C4⋊C4×C59—22no—
80C42×C59—21no—
81C42×C59—21no—
82C42×C59—21no—
83C42×C59—21no—
84C42×C59C2×D412yes—
85C42×C59#4112yes—
86C4⋊Dic59—22no—
87C4⋊Dic59—22no—
88C4⋊Dic59—42no—
89Dic59⋊C4—42no—
90Dic59⋊C4—42no—
91Dic59⋊C4—41no—
92Dic59⋊C4—42no—
93Dic59⋊C4—41no—
94C4×Dic59—41no—
95C4×Dic59—41no—
96C2×C59⋊C8—42no—
97C23×C59C2×C22⋊C411yescharacteristic
98Q8×C59—44no—
99C2×C4×C59—21no—
100C2×C4×C59—21no—
101C2×C4×C59—21no—
102C2×C4×C59—21no—
103C2×C4×C59—21no—
104C2×C4×C59—21no—
105C2×C4×C59—21no—
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#10112yes—
113C2×C4×C59C4×D412yes—
114C2×C4×C59#12011yescharacteristic
115C2×C4×C59#12112yes—
116C2×C4×C59#12311yescharacteristic
117C2×Dic59—22no—
118C2×Dic59—41no—
119C2×Dic59—41no—
120C2×Dic59—41no—
121C2×Dic59—41no—
122C2×Dic59—41no—
123C2×Dic59—41no—
124C2×Dic59—42no—
125C2×Dic59—41no—
126C2×Dic59—41no—
127C2×Dic59—41no—
128C8×C59—44no—
129C59⋊C8—82no—
130#9450—591nomaximal, Sylow
131C22×C59—21no—
132C22×C59—21no—
133C22×C59#38611yescharacteristic
134C22×C59C2×#10111yescharacteristic
135C22×C59#41311yescharacteristic
136C4×C59—22no—
137C4×C59—22no—
138C4×C59—22no—
139C4×C59—21no—
140C4×C59—21no—
141C4×C59—41no—
142C4×C59—41no—
143C4×C59—41no—
144Dic59—42no—
145Dic59—81no—
146Dic59—81no—
147Dic59—81no—
148#2983D5911yescharacteristic
149#2565—591no—
150#1534—592no—
151#1467—591no—
152#1285—592no—
153C2×C59—21no—
154C2×C59—21no—
155C2×C59#188411yescharacteristic
156C2×C59#190111yescharacteristic
157C2×C59#191211yescharacteristic
158C2×#125—591no—
159C2×C4×Q8C2×D5911yescharacteristic
160#446—24no—
161#432—21no—
162#432—592no—
163#432C2×D5912yes—
164#431—21no—
165#398—1181no—
166#398—1181no—
167#391—591no—
168#391—591no—
169#387—1181no—
170#387—1181no—
171#384—591no—
172#382—591no—
173C4×C4⋊C4—591no—
174#330—1184no—
175#324—1181no—
176#324—1181no—
177C59#945011yescharacteristic, complemented, Sylow
178C22×Q8C4×D5911yescharacteristic
179#125—1182no—
180#125—1182no—
181C4×Q8—22no—
182C4×Q8—22no—
183C2×C4⋊C4—591no—
184C2×C4⋊C4—591no—
185C2×C4⋊C4—1181no—
186C2×C4⋊C4—1181no—
187C2×C4⋊C4—1181no—
188C2×C4⋊C4—1181no—
189C2×C4⋊C4—1181no—
190C2×C4⋊C4C4×D5911yescharacteristic
191C2×C4⋊C4D23611yescharacteristic
192C2×C4⋊C4D23611yescharacteristic
193C2×C42—591no—
194C2×C42—591no—
195C2×C42C22⋊D5911yescharacteristic
196C2×C42C22⋊D5911yescharacteristic
197C2×C42C22×D5911yescharacteristic
198C4⋊C8—22no—
199C4⋊C8—22no—
200C4⋊C8—22no—
201C4⋊C8—1182no—
202C22⋊C8—22no—
203C22⋊C8—1182no—
204#97—22no—
205#97—1182no—
206#97C22⋊D5914yes—
207C4×C8—22no—
208#95—1181no—
209#95—1181no—
210#95—1181no—
211#95—1181no—
212#95—1181no—
213#95—1181no—
214#95—1181no—
215C2×Q8—22no—
216C2×Q8—22no—
217C2×Q8—41no—
218C22×C4—1181no—
219C22×C4—1181no—
220C22×C4—1181no—
221C22×C4—1181no—
222C22×C4(C2×D59)⋊C411yescharacteristic
223C22×C4(C2×D59)⋊C411yescharacteristic
224C22×C4(C2×D59)⋊C411yescharacteristic
225C22×C4(C2×D59)⋊C411yescharacteristic
226C22×C4C2×C4×D5911yescharacteristic
227C22×C4C2×D23611yescharacteristic
228C22×C4C2×C22⋊D5911yescharacteristic
229C2×C8—24no—
230C2×C8—2362no—
231C4⋊C4—22no—
232C4⋊C4—22no—
233C4⋊C4—22no—
234C4⋊C4—1182no—
235C4⋊C4—1182no—
236C4⋊C4—2362no—
237C4⋊C4—2362no—
238C4⋊C4—2362no—
239C4⋊C4—2361no—
240C4⋊C4—2362no—
241C4⋊C4—2361no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—2361no—
247C42—2361no—
248C42#1174568512yes—
249C42C2×C22⋊D5912yes—
250C23C2×(C2×D59)⋊C411yescharacteristic
251Q8—44no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—1182no—
266C2×C4—2361no—
267C2×C4—2361no—
268C2×C4—2361no—
269C2×C4—2361no—
270C2×C4—2362no—
271C2×C4—2361no—
272C2×C4—2361no—
273C2×C4—2361no—
274C2×C4—2361no—
275C2×C4—2361no—
276C2×C4#1427364512yes—
277C2×C4C4×C22⋊D5912yes—
278C2×C4#1427369611yescharacteristic
279C2×C4#1427370112yes—
280C2×C4#1427371011yescharacteristic
281C8—44no—
282C8—4722no—
283C22—21no—
284C22—21no—
285C22#1683728111yescharacteristic
286C22C2×#1427364511yescharacteristic
287C22#1683738411yescharacteristic
288C4—22no—
289C4—22no—
290C4—22no—
291C4—21no—
292C4—21no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—4721no—
297C4—4721no—
298C4—4721no—
299C4—2362no—
300C2—21no—
301C2—21no—
302C2#2142447911yescharacteristic
303C2#2142456411yescharacteristic
304C2#2142463311yescharacteristic
subgroupG/H
centerC22#16837281
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#2983C2
socleC22×C59#386
prime radicalC23×C59C2×C22⋊C4
cosocleC2×C42×C59C23
hypercenter#2983D59
hypocenterC59#9450
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
177. C59#9450semidirect

Maximal subgroups

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

subgroupindex
#214292832
#214227222
#214224402
#214219512
C59×#29832
#945059