Finite Group Databasebeta

← #28499526

Subgroups — #28499526

Order 15104.

340 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 79 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#21429972C211yesmaximal, characteristic
2#21424092C211yesmaximal, characteristic
3#21422124C212yesmaximal
4#21422103C212yesmaximal
5C59×#1467C211yesmaximal, characteristic
6C2×#14273719C411yescharacteristic
7#16837426—21no—
8C2×#14273646—21no—
9#16837341C411yescharacteristic
10#16837341C2211yescharacteristic
11#16837340—21no—
12#16837332C411yescharacteristic
13#16837332C2211yescharacteristic
14#16837321—21no—
15#16837286—21no—
16#16837286—21no—
17#16837270C411yescharacteristic
18#16837171C2212yes—
19C2×C4×Q8×C59C2211yescharacteristic
20C59×#432—21no—
21C59×#324—21no—
22C59×#324C2212yes—
23C2×#11745664—22no—
24#14273719—41no—
25#14273719—41no—
26C2×C4⋊Dic59C2×C411yescharacteristic
27C2×C4⋊Dic59C2×C411yescharacteristic
28C2×Dic59⋊C4—21no—
29C2×Dic59⋊C4—21no—
30C2×Dic59⋊C4—21no—
31C2×Dic59⋊C4—21no—
32C4⋊(C59⋊C8)—41no—
33C4⋊(C59⋊C8)—41no—
34#14273646—42no—
35C59⋊#95—21no—
36C59⋊#95—21no—
37C59⋊#95—21no—
38C59⋊#95—21no—
39C59⋊#95—21no—
40C59⋊#95—21no—
41C59⋊#95—21no—
42C59⋊#95—21no—
43C59⋊#95C2×C411yescharacteristic
44C59⋊#95C2×C411yescharacteristic
45C22×Q8×C59D411yescharacteristic
46C4×Q8×C59—41no—
47C4×Q8×C59—41no—
48C2×C4⋊C4×C59C2×C411yescharacteristic
49C2×C4⋊C4×C59D411yescharacteristic
50C2×C4⋊C4×C59C2311yescharacteristic
51C2×C42×C59C2×C411yescharacteristic
52C2×C42×C59D411yescharacteristic
53C2×C42×C59D411yescharacteristic
54C4⋊C8×C59—41no—
55C22⋊C8×C59—22no—
56#97×C59—41no—
57C2×Q8×C59—21no—
58C2×Q8×C59—21no—
59C2×Q8×C59—41no—
60C2×Q8×C59—41no—
61C22×C4×C59C22⋊C411yescharacteristic
62C22×C4×C59C22⋊C411yescharacteristic
63C22×C4×C59C22⋊C411yescharacteristic
64C22×C4×C59C22⋊C411yescharacteristic
65C22×C4×C59C22×C411yescharacteristic
66C22×C4×C59C2×D411yescharacteristic
67C22×C4×C59C2×D411yescharacteristic
68C22×Dic59—21no—
69C22×Dic59—21no—
70C22×Dic59—21no—
71C22×Dic59—21no—
72C2×C8×C59—42no—
73C4⋊C4×C59—41no—
74C4⋊C4×C59—41no—
75C4⋊C4×C59—41no—
76C42×C59—21no—
77C42×C59—21no—
78C42×C59—21no—
79C42×C59—21no—
80C42×C59—21no—
81C42×C59—21no—
82C4⋊Dic59—41no—
83C4⋊Dic59—41no—
84Dic59⋊C4—42no—
85Dic59⋊C4—42no—
86Dic59⋊C4—41no—
87Dic59⋊C4—41no—
88Dic59⋊C4—41no—
89Dic59⋊C4—41no—
90#11745664—42no—
91#11745664—42no—
92C2×C59⋊C8—42no—
93C23×C59C2×C22⋊C411yescharacteristic
94Q8×C59—42no—
95Q8×C59—42no—
96C2×C4×C59—21no—
97C2×C4×C59—21no—
98C2×C4×C59—21no—
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—41no—
108C2×C4×C59—41no—
109C2×C4×C59—41no—
110C2×C4×C59—41no—
111C2×C4×C59#9911yescharacteristic
112C2×C4×C59#9911yescharacteristic
113C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
114C2×C4×C59#13711yescharacteristic
115C2×Dic59—41no—
116C2×Dic59—41no—
117C2×Dic59—41no—
118C2×Dic59—41no—
119C2×Dic59—42no—
120C2×Dic59—41no—
121C2×Dic59—41no—
122C2×Dic59—41no—
123C2×Dic59—41no—
124C2×Dic59—41no—
125C2×Dic59—41no—
126C8×C59—82no—
127C59⋊C8—82no—
128#11835—591nomaximal, Sylow
129C22×C59—21no—
130C22×C59—21no—
131C22×C59C2×#9911yescharacteristic
132C22×C59#41711yescharacteristic
133C22×C59#42111yescharacteristic
134C4×C59—21no—
135C4×C59—21no—
136C4×C59—21no—
137C4×C59—21no—
138C4×C59—41no—
139C4×C59—41no—
140C4×C59—41no—
141C4×C59—41no—
142C4×C59—41no—
143Dic59—81no—
144Dic59—81no—
145Dic59—81no—
146Dic59—81no—
147#2634—591no—
148#1801—591no—
149#1467D5911yescharacteristic
150#1353—592no—
151#1346—592no—
152C2×C59—21no—
153C2×C59—21no—
154C2×C59#151311yescharacteristic
155C2×C59#212311yescharacteristic
156C2×C59#213311yescharacteristic
157C2×#125—591no—
158C2×C4×Q8C2×D5911yescharacteristic
159#432—21no—
160#423—1181no—
161C2×#101—1181no—
162#400—591no—
163#400—591no—
164#400—1181no—
165#398—591no—
166#398—591no—
167#395—1181no—
168#387—1181no—
169#387—1181no—
170#383—591no—
171#343—592no—
172#324—21no—
173#324C2×D5912yes—
174C59#1183511yescharacteristic, complemented, Sylow
175C22×Q8D23611yescharacteristic
176C2×M16—1182no—
177#125—2361no—
178#125—2361no—
179C4×Q8—41no—
180C4×Q8—41no—
181C2×C4⋊C4—591no—
182C2×C4⋊C4—591no—
183C2×C4⋊C4—1181no—
184C2×C4⋊C4—1181no—
185C2×C4⋊C4—1181no—
186C2×C4⋊C4—1181no—
187C2×C4⋊C4C4×D5911yescharacteristic
188C2×C4⋊C4C22⋊D5911yescharacteristic
189C2×C4⋊C4C22×D5911yescharacteristic
190C2×C42C4×D5911yescharacteristic
191C2×C42D23611yescharacteristic
192C2×C42C22⋊D5911yescharacteristic
193C4⋊C8—41no—
194C4⋊C8—2361no—
195C4⋊C8—2361no—
196#101—2362no—
197C22⋊C8—22no—
198#97—41no—
199#95—591no—
200#95—591no—
201#95—1181no—
202#95—1181no—
203#95—1181no—
204#95—1181no—
205#95—1181no—
206#95—1181no—
207#95—1181no—
208#95—1181no—
209C2×Q8—21no—
210C2×Q8—21no—
211C2×Q8—41no—
212C2×Q8—41no—
213C22×C4—1181no—
214C22×C4—1181no—
215C22×C4—1181no—
216C22×C4—1181no—
217C22×C4(C2×D59)⋊C411yescharacteristic
218C22×C4(C2×D59)⋊C411yescharacteristic
219C22×C4(C2×D59)⋊C411yescharacteristic
220C22×C4(C2×D59)⋊C411yescharacteristic
221C22×C4C2×C4×D5911yescharacteristic
222C22×C4C2×D23611yescharacteristic
223C22×C4C2×C22⋊D5911yescharacteristic
224M16—2362no—
225M16—2362no—
226C2×C8—42no—
227C2×C8—2362no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—2361no—
232C4⋊C4—2361no—
233C4⋊C4—2362no—
234C4⋊C4—2362no—
235C4⋊C4—2361no—
236C4⋊C4—2361no—
237C4⋊C4—2361no—
238C4⋊C4—2361no—
239C42—21no—
240C42—21no—
241C42—21no—
242C42—21no—
243C42—21no—
244C42—21no—
245C23C2×(C2×D59)⋊C411yescharacteristic
246Q8—42no—
247Q8—42no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—2361no—
264C2×C4—2361no—
265C2×C4—2361no—
266C2×C4—2361no—
267C2×C4—2362no—
268C2×C4—2361no—
269C2×C4—2361no—
270C2×C4—2361no—
271C2×C4—2361no—
272C2×C4—2361no—
273C2×C4—2361no—
274C2×C4#1427364111yescharacteristic
275C2×C4#1427364111yescharacteristic
276C2×C4#1427375511yescharacteristic
277C2×C4#1427376011yescharacteristic
278C8—82no—
279C8—4722no—
280C22—21no—
281C22—21no—
282C22C2×#1427364111yescharacteristic
283C22#1683740411yescharacteristic
284C22#1683741811yescharacteristic
285C4—21no—
286C4—21no—
287C4—21no—
288C4—21no—
289C4—41no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—41no—
294C4—4721no—
295C4—4721no—
296C4—4721no—
297C4—4721no—
298C2—21no—
299C2—21no—
300C2#2142264011yescharacteristic
301C2#2142574911yescharacteristic
302C2#2142578311yescharacteristic
subgroupG/H
centerC22C2×#14273641
commutatorC22×C4×C59C22×C4
FrattiniC2×C4⋊C4C22×D59
FittingC59×#1467C2
socleC22×C59C2×#99
prime radicalC23×C59C2×C22⋊C4
cosocleC2×C4⋊C4×C59C23
hypercenter#1467D59
hypocenterC59#11835
LCSG ▷ C22×C4×C59 ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

Complements

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

NH ≅ G/Ntype
174. C59#11835semidirect

Maximal subgroups

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

subgroupindex
#214299722
#214240922
#214221242
#214221032
C59×#14672
#1183559