Finite Group Databasebeta

← #28499583

Subgroups — #28499583

Order 15104.

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

normal subgroups only

This group has 382 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#21429794C211yesmaximal, characteristic
2#21424173C211yesmaximal, characteristic
3#21422121C212yesmaximal
4#21422097C212yesmaximal
5C59×#1458C211yesmaximal, characteristic
6C2×#14273719C411yescharacteristic, complemented
7#16837341C411yescharacteristic, complemented
8#16837338C2211yescharacteristic
9#16837332C411yescharacteristic, complemented
10#16837327C2211yescharacteristic
11#16837297—21no—
12#16837296—21no—
13#16837286—21no—
14#16837275—21no—
15#16837265—21no—
16#16837248C411yescharacteristic, complemented
17#16837169—21no—
18#16837169C2212yes—
19C2×#117×C59C2211yescharacteristic
20C59×#431—21no—
21C59×#324—21no—
22C59×#323C2212yes—
23#14273719—41no—
24#14273719—41no—
25C2×C4⋊Dic59C2×C411yescharacteristic
26C2×C4⋊Dic59C2×C411yescharacteristic
27C2×Dic59⋊C4—21no—
28C2×Dic59⋊C4—21no—
29C2×Dic59⋊C4—21no—
30C2×Dic59⋊C4—21no—
31C2×C22⋊Dic59—21no—
32C2×C22⋊Dic59—21no—
33C2×C22⋊Dic59—22no—
34C2×C4×Dic59—21no—
35C59⋊#95—21no—
36C59⋊#95—21no—
37C59⋊#95—21no—
38C59⋊#95—21no—
39C59⋊#95—21no—
40C59⋊#95—41no—
41C59⋊#95—41no—
42C59⋊#95C2×C411yescharacteristic
43C59⋊#95C2×C411yescharacteristic
44C23×C4×C59D411yescharacteristic
45#117×C59—41no—
46#117×C59—41no—
47C2×C4⋊C4×C59C2×C411yescharacteristic
48C2×C4⋊C4×C59D411yescharacteristic
49C2×C22⋊C4×C59D411yescharacteristic
50C2×C22⋊C4×C59C2311yescharacteristic
51C2×C42×C59C2×C411yescharacteristic
52C2×C42×C59D411yescharacteristic
53C4⋊C8×C59—41no—
54C22⋊C8×C59—22no—
55C4×C8×C59—41no—
56C24×C59C2×D411yescharacteristic
57C22×C4×C59—22no—
58C22×C4×C59—21no—
59C22×C4×C59—21no—
60C22×C4×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×Dic59—21no—
68C22×Dic59—21no—
69C22×Dic59—21no—
70C22×Dic59—21no—
71C22×Dic59—42no—
72C2×C8×C59—42no—
73C4⋊C4×C59—41no—
74C4⋊C4×C59—41no—
75C22⋊C4×C59—41no—
76C22⋊C4×C59—41no—
77C42×C59—21no—
78C42×C59—21no—
79C42×C59—21no—
80C42×C59—21no—
81C22⋊Dic59—42no—
82C22⋊Dic59—42no—
83C22⋊Dic59—42no—
84C22⋊Dic59—42no—
85C4⋊Dic59—41no—
86C4⋊Dic59—41no—
87Dic59⋊C4—42no—
88Dic59⋊C4—42no—
89Dic59⋊C4—42no—
90Dic59⋊C4—41no—
91Dic59⋊C4—41no—
92C4×Dic59—42no—
93C23×C59—21no—
94C23×C59—21no—
95C23×C59—41no—
96C23×C59—41no—
97C23×C59C2×C22⋊C411yescharacteristic
98C23×C59#13512yes—
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—42no—
109C2×C4×C59—42no—
110C2×C4×C59—41no—
111C2×C4×C59—41no—
112C2×C4×C59—41no—
113C2×C4×C59—41no—
114C2×C4×C59#9911yescharacteristic
115C2×C4×C59#9911yescharacteristic
116C2×Dic59—22no—
117C2×Dic59—41no—
118C2×Dic59—41no—
119C2×Dic59—41no—
120C2×Dic59—41no—
121C2×Dic59—41no—
122C2×Dic59—41no—
123C2×Dic59—41no—
124C2×Dic59—41no—
125C2×Dic59—41no—
126C2×Dic59—41no—
127C2×Dic59—41no—
128C2×Dic59—82no—
129C2×Dic59—82no—
130C2×Dic59—82no—
131C8×C59—82no—
132#11846—591nomaximal, Sylow
133C22×C59—21no—
134C22×C59—21no—
135C22×C59—22no—
136C22×C59—42no—
137C22×C59—41no—
138C22×C59—41no—
139C22×C59—81no—
140C22×C59C2×#9911yescharacteristic
141C22×C59#41611yescharacteristic
142C22×C59#42111yescharacteristic
143C4×C59—21no—
144C4×C59—21no—
145C4×C59—41no—
146C4×C59—41no—
147C4×C59—41no—
148C4×C59—41no—
149C4×C59—41no—
150Dic59—42no—
151Dic59—81no—
152Dic59—81no—
153Dic59—81no—
154Dic59—162no—
155#2611—591no—
156#1820—591no—
157#1458D5911yescharacteristic
158#1352—592no—
159#1344—592no—
160C2×C59—21no—
161C2×C59—21no—
162C2×C59—42no—
163C2×C59#151611yescharacteristic
164C2×C59#212311yescharacteristic
165C2×C59#212611yescharacteristic
166C2×#125—591no—
167C2×#117C2×D5911yescharacteristic
168#431—21no—
169#400—591no—
170#399—591no—
171#398—591no—
172#397—591no—
173#389—1181no—
174#388—1181no—
175#387—1181no—
176#385—1181no—
177#381—1181no—
178#376—591no—
179#342—592no—
180#342—1181no—
181#324—21no—
182#323C2×D5912yes—
183C59#1184611yescharacteristic, complemented, Sylow
184C23×C4D23611yescharacteristic
185#125—2361no—
186#125—2361no—
187#117—41no—
188#117—41no—
189C2×C4⋊C4—591no—
190C2×C4⋊C4—591no—
191C2×C4⋊C4—1181no—
192C2×C4⋊C4—1181no—
193C2×C4⋊C4—1181no—
194C2×C4⋊C4—1181no—
195C2×C4⋊C4C4×D5911yescharacteristic
196C2×C4⋊C4C22⋊D5911yescharacteristic
197C2×C22⋊C4—1181no—
198C2×C22⋊C4—1181no—
199C2×C22⋊C4—1182no—
200C2×C22⋊C4D23611yescharacteristic
201C2×C22⋊C4C22×D5911yescharacteristic
202C2×C42—1181no—
203C2×C42C4×D5911yescharacteristic
204C2×C42C22⋊D5911yescharacteristic
205C4⋊C8—41no—
206C22⋊C8—22no—
207C4×C8—41no—
208#95—591no—
209#95—591no—
210#95—1181no—
211#95—1181no—
212#95—1181no—
213#95—1181no—
214#95—1181no—
215#95—2361no—
216#95—2361no—
217C24C2×D23611yescharacteristic
218C22×C4—22no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—41no—
222C22×C4—1181no—
223C22×C4—1181no—
224C22×C4—1181no—
225C22×C4—1181no—
226C22×C4—2362no—
227C22×C4(C2×D59)⋊C411yescharacteristic
228C22×C4(C2×D59)⋊C411yescharacteristic
229C22×C4(C2×D59)⋊C411yescharacteristic
230C22×C4(C2×D59)⋊C411yescharacteristic
231C22×C4C2×C4×D5911yescharacteristic
232C22×C4C2×C22⋊D5911yescharacteristic
233C2×C8—42no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—2361no—
237C4⋊C4—2361no—
238C4⋊C4—2362no—
239C4⋊C4—2362no—
240C4⋊C4—2362no—
241C4⋊C4—2361no—
242C4⋊C4—2361no—
243C22⋊C4—41no—
244C22⋊C4—41no—
245C22⋊C4—2362no—
246C22⋊C4—2362no—
247C22⋊C4—2362no—
248C22⋊C4—2362no—
249C42—21no—
250C42—21no—
251C42—21no—
252C42—21no—
253C42—2362no—
254C23—21no—
255C23—21no—
256C23—41no—
257C23—41no—
258C23C2×(C2×D59)⋊C411yescharacteristic
259C23#1427374912yes—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—1182no—
276C2×C4—4722no—
277C2×C4—4722no—
278C2×C4—4722no—
279C2×C4—2361no—
280C2×C4—2361no—
281C2×C4—2361no—
282C2×C4—2361no—
283C2×C4—2361no—
284C2×C4—2361no—
285C2×C4—2361no—
286C2×C4—2361no—
287C2×C4—2361no—
288C2×C4—2361no—
289C2×C4—2361no—
290C2×C4#1427364111yescharacteristic
291C2×C4#1427364111yescharacteristic
292C8—82no—
293C22—21no—
294C22—21no—
295C22—22no—
296C22—42no—
297C22—41no—
298C22—41no—
299C22—81no—
300C22C2×#1427364111yescharacteristic
301C22#1683739911yescharacteristic
302C22#1683741811yescharacteristic
303C4—21no—
304C4—21no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—9442no—
311C4—4721no—
312C4—4721no—
313C4—4721no—
314C4—2362no—
315C2—21no—
316C2—21no—
317C2—42no—
318C2#2142265311yescharacteristic
319C2#2142575111yescharacteristic
320C2#2142575911yescharacteristic
subgroupG/H
centerC22C2×#14273641
commutatorC22×C4×C59C22×C4
FrattiniC2×C22⋊C4C22×D59
FittingC59×#1458C2
socleC22×C59C2×#99
prime radicalC24×C59C2×D4
cosocleC2×C22⋊C4×C59C23
hypercenter#1458D59
hypocenterC59#11846
LCSG ▷ C22×C4×C59 ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1458

Complements

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

NH ≅ G/Ntype
6. C2×#14273719C4semidirect
7. #16837341C4semidirect
9. #16837332C4semidirect
16. #16837248C4semidirect
183. C59#11846semidirect

Maximal subgroups

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

subgroupindex
#214297942
#214241732
#214221212
#214220972
C59×#14582
#1184659