Finite Group Databasebeta

← #28501620

Subgroups — #28501620

Order 15104.

334 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 59 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#21425446C211yesmaximal, characteristic
2#21423103C211yesmaximal, characteristic
3#21423069C211yesmaximal, characteristic
4#21422126C211yesmaximal, characteristic
5#21422102C211yesmaximal, characteristic
6#21422040C211yesmaximal, characteristic
7C59×#2789C211yesmaximal, characteristic
8#16838033C2211yescharacteristic
9#16837732—21no—
10#16837558—21no—
11#16837442—21no—
12#16837171C2211yescharacteristic
13#16837162—21no—
14#16837138—21no—
15#16837138—21no—
16#16837128C2211yescharacteristic
17#16837128C2211yescharacteristic
18C59×#401—21no—
19C59×#400—21no—
20C59×#398C2211yescharacteristic
21C59×#395C2211yescharacteristic
22C59×#391—21no—
23C59×#387—21no—
24C59×#387—21no—
25C59×#387—21no—
26C59×#382C2211yescharacteristic
27C2×#11745672—41no—
28C2×#11745664—21no—
29#14273726—41no—
30#14273718—41no—
31#14273706—21no—
32#14273706—21no—
33#14273686—21no—
34#14273660—41no—
35#14273658—41no—
36#14273658—41no—
37#14273651—41no—
38#14273650—41no—
39C22⋊(C59⋊C8)—21no—
40C22⋊(C59⋊C8)—21no—
41C22×Q8×C59D411yescharacteristic
42C2×C4⋊C4×C59—21no—
43C2×C4⋊C4×C59—21no—
44C2×C4⋊C4×C59—21no—
45C2×C4⋊C4×C59D411yescharacteristic
46C2×C4⋊C4×C59D411yescharacteristic
47C2×C4⋊C4×C59C2311yescharacteristic
48C2×C42×C59—21no—
49C2×C42×C59D411yescharacteristic
50#95×C59—21no—
51#95×C59—21no—
52#95×C59—21no—
53#95×C59—21no—
54#95×C59—21no—
55#95×C59—21no—
56#95×C59—21no—
57#95×C59—21no—
58#95×C59—21no—
59#95×C59—21no—
60#95×C59D411yescharacteristic
61#95×C59D411yescharacteristic
62C2×Q8×C59—42no—
63C2×Q8×C59—41no—
64C22×C4×C59—21no—
65C22×C4×C59—21no—
66C22×C4×C59—21no—
67C22×C4×C59—21no—
68C22×C4×C59—21no—
69C22×C4×C59—21no—
70C22×C4×C59C2×D411yescharacteristic
71C22×C4×C59C2×D411yescharacteristic
72C22×C4×C59C2×D411yescharacteristic
73C2×Dic118—21no—
74C2×Dic118—21no—
75C4⋊C4×C59—41no—
76C4⋊C4×C59—42no—
77C4⋊C4×C59—42no—
78C4⋊C4×C59—41no—
79C4⋊C4×C59—41no—
80C4⋊C4×C59—41no—
81C4⋊C4×C59—41no—
82C42×C59—21no—
83C42×C59—21no—
84C42×C59—81no—
85C22⋊Dic59—41no—
86#11745672—82no—
87C4⋊Dic59—21no—
88C4⋊Dic59—21no—
89C4⋊Dic59—21no—
90C4⋊Dic59—21no—
91Dic59⋊C4—41no—
92Dic59⋊C4—41no—
93C4×Dic59—41no—
94#11745664—22no—
95#11745664—41no—
96C2×C59⋊C8—41no—
97C2×C59⋊C8—41no—
98C2×C59⋊C8—41no—
99C23×C59#12011yescharacteristic
100Q8×C59—42no—
101Q8×C59—81no—
102C2×C4×C59—21no—
103C2×C4×C59—21no—
104C2×C4×C59—22no—
105C2×C4×C59—21no—
106C2×C4×C59—21no—
107C2×C4×C59—41no—
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—41no—
116C2×C4×C59—41no—
117C2×C4×C59—42no—
118C2×C4×C59—41no—
119C2×C4×C59—41no—
120C2×C4×C59—41no—
121C2×C4×C59—41no—
122C2×C4×C59—41no—
123C2×C4×C59—41no—
124C2×C4×C59—41no—
125C2×C4×C59#13511yescharacteristic
126C2×C4×C59#13711yescharacteristic
127C2×Dic59—41no—
128C2×Dic59—41no—
129Dic118—81no—
130Dic118—81no—
131C59⋊C8—42no—
132C59⋊C8—81no—
133C59⋊C8—81no—
134#12237—591nomaximal, Sylow
135C22×C59—21no—
136C22×C59—21no—
137C22×C59#45211yescharacteristic
138C22×C59#45611yescharacteristic
139C22×C59B(4,𝔽2)11yescharacteristic
140C4×C59—21no—
141C4×C59—21no—
142C4×C59—41no—
143C4×C59—41no—
144C4×C59—42no—
145C4×C59—81no—
146C4×C59—81no—
147C4×C59—81no—
148C4×C59—81no—
149C4×C59—81no—
150Dic59—81no—
151Dic59—81no—
152#2789D5911yescharacteristic
153#2061—591no—
154#1611—591no—
155#1605—591no—
156#1354—591no—
157#1346—591no—
158#1324—591no—
159C2×C59—21no—
160C2×C59—21no—
161C2×C59#160311yescharacteristic
162C2×C59#219711yescharacteristic
163C2×C59#220311yescharacteristic
164#544—591no—
165#483—1181no—
166#451—1181no—
167#428—1181no—
168#401—21no—
169#400—21no—
170#398C2×D5911yescharacteristic
171#395C2×D5911yescharacteristic
172#391—21no—
173#387—21no—
174#387—21no—
175#387—21no—
176#382C2×D5911yescharacteristic
177#343—591no—
178#339—1181no—
179#328—1181no—
180#328—1181no—
181#324—591no—
182#324—591no—
183C59#1223711yescharacteristic, complemented, Sylow
184C22×Q8C22⋊D5911yescharacteristic
185C2×Q16—2361no—
186C2×M16—1181no—
187C4⋊Q8—2361no—
188#125—2361no—
189C22⋊Q8—1181no—
190C22⋊Q8—1181no—
191#117—1181no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4C22⋊D5911yescharacteristic
196C2×C4⋊C4C22⋊D5911yescharacteristic
197C2×C4⋊C4C22×D5911yescharacteristic
198C2×C42—21no—
199C2×C42C22⋊D5911yescharacteristic
200#107—2361no—
201#106—2361no—
202#106—2361no—
203#103—2361no—
204#103—2361no—
205C22⋊C8—1181no—
206C22⋊C8—1181no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95C22⋊D5911yescharacteristic
218#95C22⋊D5911yescharacteristic
219C2×Q8—42no—
220C2×Q8—41no—
221C2×Q8—1181no—
222C2×Q8—1181no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4C2×C22⋊D5911yescharacteristic
230C22×C4C2×C22⋊D5911yescharacteristic
231C22×C4C2×C22⋊D5911yescharacteristic
232Q16—4722no—
233M16—1182no—
234M16—2361no—
235C2×C8—2361no—
236C2×C8—2361no—
237C2×C8—2361no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—42no—
242C4⋊C4—42no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—1181no—
246C4⋊C4—1181no—
247C4⋊C4—1181no—
248C4⋊C4—1181no—
249C4⋊C4—2361no—
250C4⋊C4—2361no—
251C22⋊C4—2361no—
252C42—21no—
253C42—21no—
254C42—81no—
255C42—2361no—
256C23#1427369611yescharacteristic
257Q8—42no—
258Q8—81no—
259Q8—4721no—
260Q8—4721no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—2361no—
285C2×C4—2361no—
286C2×C4#1427374711yescharacteristic
287C2×C4#1427375711yescharacteristic
288C8—4721no—
289C8—4721no—
290C8—2362no—
291C22—21no—
292C22—21no—
293C22#1683756411yescharacteristic
294C22#1683758511yescharacteristic
295C22#1683758911yescharacteristic
296C4—21no—
297C4—21no—
298C4—41no—
299C4—41no—
300C4—42no—
301C4—81no—
302C4—81no—
303C4—81no—
304C4—81no—
305C4—81no—
306C4—4721no—
307C4—4721no—
308C2—21no—
309C2—21no—
310C2#2142305911yescharacteristic
311C2#2142608611yescharacteristic
312C2#2142611711yescharacteristic
subgroupG/H
centerC22#16837589
commutator, cosocleC2×C4⋊C4×C59C23
FrattiniC2×C4⋊C4C22×D59
FittingC59×#2789C2
socleC22×C59B(4,𝔽2)
prime radicalC23×C59#120
hypercenter#2789D59
hypocenterC59#12237
LCSG ▷ C2×C4⋊C4×C59 ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2789

Complements

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

NH ≅ G/Ntype
183. C59#12237semidirect

Maximal subgroups

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

subgroupindex
#214254462
#214231032
#214230692
#214221262
#214221022
#214220402
C59×#27892
#1223759