Finite Group Databasebeta

← #28499326

Subgroups — #28499326

Order 15104.

378 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 83 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#21429458C211yesmaximal, characteristic
2#21422440C211yesmaximal, characteristic
3#21422125C212yesmaximal
4#21422122C212yesmaximal
5C4×#101×C59C211yesmaximal, characteristic
6C2×C4×Dic118C411yescharacteristic
7#16837459—21no—
8#16837341C411yescharacteristic
9#16837341C2211yescharacteristic
10#16837322C411yescharacteristic
11#16837322C2211yescharacteristic
12#16837309—21no—
13#16837298—21no—
14#16837286—21no—
15#16837286—21no—
16#16837268C411yescharacteristic
17#16837128—21no—
18#16837128C2212yes—
19C2×C4×Q8×C59C2211yescharacteristic
20C2×#101×C59—21no—
21C4×M16×C59—21no—
22C59×#343C2212yes—
23C22×Dic118C2×C411yescharacteristic
24C4×Dic118—41no—
25C4×Dic118—41no—
26C2×C4⋊Dic59—21no—
27C2×C4⋊Dic59C2×C411yescharacteristic
28C2×Dic59⋊C4—21no—
29C2×Dic59⋊C4—21no—
30C2×Dic59⋊C4—21no—
31C2×C4×Dic59—21no—
32C4⋊(C59⋊C8)—41no—
33C22⋊(C59⋊C8)—22no—
34#14273638—41no—
35C59⋊#95—21no—
36C59⋊#95—21no—
37C59⋊#95—21no—
38C59⋊#95—21no—
39C59⋊#95—21no—
40C59⋊#95—21no—
41C59⋊#95—21no—
42C59⋊#95C2×C411yescharacteristic
43C59⋊#95C2×C411yescharacteristic
44C22×Q8×C59D411yescharacteristic
45C2×M16×C59—22no—
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
54#101×C59—24no—
55#97×C59—41no—
56C4×C8×C59—41no—
57C2×Q8×C59—22no—
58C2×Q8×C59—22no—
59C2×Q8×C59—41no—
60C22×C4×C59C22⋊C411yescharacteristic
61C22×C4×C59C22⋊C411yescharacteristic
62C22×C4×C59C22⋊C411yescharacteristic
63C22×C4×C59C22⋊C411yescharacteristic
64C22×C4×C59C22×C411yescharacteristic
65C22×C4×C59C2×D411yescharacteristic
66C22×C4×C59C2×D411yescharacteristic
67C22×Dic59—21no—
68C22×Dic59—21no—
69C22×Dic59—21no—
70C22×Dic59—21no—
71C2×Dic118—41no—
72C2×Dic118—42no—
73M16×C59—24no—
74M16×C59—42no—
75C2×C8×C59—42no—
76C4⋊C4×C59—41no—
77C4⋊C4×C59—41no—
78C4⋊C4×C59—41no—
79C42×C59—21no—
80C42×C59—21no—
81C42×C59—21no—
82C42×C59—21no—
83C42×C59—21no—
84C42×C59—21no—
85C4⋊Dic59—42no—
86C4⋊Dic59—41no—
87Dic59⋊C4—42no—
88Dic59⋊C4—42no—
89Dic59⋊C4—41no—
90Dic59⋊C4—41no—
91C4×Dic59—42no—
92C2×C59⋊C8—42no—
93C23×C59C2×C22⋊C411yescharacteristic
94Q8×C59—44no—
95C2×C4×C59—21no—
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—41no—
106C2×C4×C59—41no—
107C2×C4×C59—41no—
108C2×C4×C59—41no—
109C2×C4×C59#9911yescharacteristic
110C2×C4×C59#9911yescharacteristic
111C2×C4×C59#10412yes—
112C2×C4×C59#13712yes—
113C2×Dic59—22no—
114C2×Dic59—41no—
115C2×Dic59—41no—
116C2×Dic59—41no—
117C2×Dic59—41no—
118C2×Dic59—41no—
119C2×Dic59—41no—
120C2×Dic59—42no—
121C2×Dic59—41no—
122C2×Dic59—41no—
123C2×Dic59—41no—
124Dic118—42no—
125Dic118—42no—
126C8×C59—44no—
127C59⋊C8—82no—
128#11792—591nomaximal, Sylow
129C22×C59—21no—
130C22×C59—21no—
131C22×C59C2×#9911yescharacteristic
132C22×C59#41911yescharacteristic
133C22×C59C2×#10411yescharacteristic
134C4×C59—21no—
135C4×C59—21no—
136C4×C59—22no—
137C4×C59—22no—
138C4×C59—41no—
139C4×C59—41no—
140C4×C59—41no—
141C4×C59—41no—
142Dic59—42no—
143Dic59—81no—
144Dic59—81no—
145Dic59—81no—
146#2581—591no—
147C4×#101D5911yescharacteristic
148#1467—591no—
149#1354—592no—
150#1353—592no—
151C2×C59—21no—
152C2×C59—21no—
153C2×C59#150811yescharacteristic
154C2×C59#212011yescharacteristic
155C2×C59#213311yescharacteristic
156C2×C4×Q8—591no—
157C2×C4×Q8C2×D5911yescharacteristic
158#432—1181no—
159C2×#101—21no—
160C4×M16—21no—
161#400—591no—
162#400—591no—
163#395—591no—
164#395—591no—
165#391—1181no—
166#389—1181no—
167#387—1181no—
168#387—1181no—
169#382—591no—
170#343C2×D5912yes—
171#324—592no—
172#324—1181no—
173C59#1179211yescharacteristic, complemented, Sylow
174C22×Q8—591no—
175C22×Q8C22⋊D5911yescharacteristic
176C2×M16—22no—
177C4×Q8—41no—
178C4×Q8—41no—
179C4×Q8—2361no—
180C4×Q8—2361no—
181C2×C4⋊C4—591no—
182C2×C4⋊C4—1181no—
183C2×C4⋊C4—1181no—
184C2×C4⋊C4—1181no—
185C2×C4⋊C4—1181no—
186C2×C4⋊C4C4×D5911yescharacteristic
187C2×C4⋊C4D23611yescharacteristic
188C2×C4⋊C4C22×D5911yescharacteristic
189C2×C42—1181no—
190C2×C42C4×D5911yescharacteristic
191C2×C42D23611yescharacteristic
192C2×C42C22⋊D5911yescharacteristic
193C4⋊C8—2361no—
194#101—24no—
195C22⋊C8—1182no—
196#97—41no—
197#97—2361no—
198C4×C8—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—
208C2×Q8—22no—
209C2×Q8—22no—
210C2×Q8—41no—
211C2×Q8—2361no—
212C2×Q8—2362no—
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—24no—
225M16—42no—
226C2×C8—42no—
227C2×C8—2362no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—2361no—
232C4⋊C4—2362no—
233C4⋊C4—2362no—
234C4⋊C4—2361no—
235C4⋊C4—2361no—
236C4⋊C4—2362no—
237C42—21no—
238C42—21no—
239C42—21no—
240C42—21no—
241C42—21no—
242C42—21no—
243C42—2362no—
244C23C2×(C2×D59)⋊C411yescharacteristic
245Q8—44no—
246Q8—2362no—
247Q8—2362no—
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—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—1182no—
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#1427364111yescharacteristic
274C2×C4#1427364111yescharacteristic
275C2×C4#1427365512yes—
276C2×C4#1427375712yes—
277C8—44no—
278C8—4722no—
279C22—21no—
280C22—21no—
281C22C2×#1427364111yescharacteristic
282C22#1683741011yescharacteristic
283C22C2×#1427365511yescharacteristic
284C4—22no—
285C4—22no—
286C4—21no—
287C4—21no—
288C4—41no—
289C4—41no—
290C4—41no—
291C4—41no—
292C4—4721no—
293C4—4721no—
294C4—4721no—
295C4—2362no—
296C2—21no—
297C2—21no—
298C2#2142261511yescharacteristic
299C2#2142573811yescharacteristic
300C2#2142578311yescharacteristic
subgroupG/H
centerC22C2×#14273641
commutatorC22×C4×C59C22×C4
FrattiniC2×C4⋊C4C22×D59
FittingC4×#101×C59C2
socleC22×C59C2×#99
prime radicalC23×C59C2×C22⋊C4
cosocleC2×C4⋊C4×C59C23
hypercenterC4×#101D59
hypocenterC59#11792
LCSG ▷ C22×C4×C59 ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
173. C59#11792semidirect

Maximal subgroups

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

subgroupindex
#214294582
#214224402
#214221252
#214221222
C4×#101×C592
#1179259