Finite Group Databasebeta

← #28499089

Subgroups — #28499089

Order 15104.

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

normal subgroups only

This group has 358 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#21429972C211yesmaximal, characteristic
2C4×#14273646C211yesmaximal, characteristic
3#21422124C212yesmaximal
4#21422103C212yesmaximal
5C59×#1461C211yesmaximal, characteristic
6C2×#14273719C411yescharacteristic
7C2×#14273646—21no—
8C4×#11745664—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×#431—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—
32#14273646—24no—
33#14273638—41no—
34C4×C59⋊C8—41no—
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—
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×C8×C59—42no—
72C4⋊C4×C59—41no—
73C4⋊C4×C59—41no—
74C4⋊C4×C59—41no—
75C42×C59—21no—
76C42×C59—21no—
77C42×C59—21no—
78C42×C59—21no—
79C42×C59—21no—
80C42×C59—21no—
81C4⋊Dic59—41no—
82C4⋊Dic59—41no—
83Dic59⋊C4—42no—
84Dic59⋊C4—41no—
85Dic59⋊C4—41no—
86Dic59⋊C4—42no—
87Dic59⋊C4—42no—
88#11745664—24no—
89#11745664—42no—
90C2×C59⋊C8—42no—
91C23×C59C2×C22⋊C411yescharacteristic
92Q8×C59—44no—
93C2×C4×C59—21no—
94C2×C4×C59—21no—
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—41no—
104C2×C4×C59—41no—
105C2×C4×C59—41no—
106C2×C4×C59—41no—
107C2×C4×C59#9911yescharacteristic
108C2×C4×C59#9911yescharacteristic
109C2×C4×C59#10412yes—
110C2×C4×C59#13512yes—
111C2×Dic59—41no—
112C2×Dic59—41no—
113C2×Dic59—41no—
114C2×Dic59—41no—
115C2×Dic59—42no—
116C2×Dic59—41no—
117C2×Dic59—41no—
118C2×Dic59—41no—
119C2×Dic59—41no—
120C2×Dic59—41no—
121C2×Dic59—41no—
122C8×C59—82no—
123C59⋊C8—44no—
124#11740—591nomaximal, Sylow
125C22×C59—21no—
126C22×C59—21no—
127C22×C59C2×#9911yescharacteristic
128C22×C59#41611yescharacteristic
129C22×C59C2×#10411yescharacteristic
130C4×C59—21no—
131C4×C59—21no—
132C4×C59—22no—
133C4×C59—22no—
134C4×C59—41no—
135C4×C59—41no—
136C4×C59—41no—
137C4×C59—41no—
138Dic59—81no—
139Dic59—81no—
140Dic59—81no—
141Dic59—81no—
142#2634—591no—
143C4×#101—591no—
144#1461D5911yescharacteristic
145#1353—592no—
146#1346—592no—
147C2×C59—21no—
148C2×C59—21no—
149C2×C59#150111yescharacteristic
150C2×C59#212311yescharacteristic
151C2×C59#213311yescharacteristic
152C2×#125—591no—
153C2×C4×Q8C2×D5911yescharacteristic
154#431—21no—
155C2×#101—1181no—
156C4×M16—1181no—
157#400—591no—
158#400—591no—
159#400—1181no—
160#398—591no—
161#398—591no—
162#395—1181no—
163#387—1181no—
164#387—1181no—
165#383—591no—
166#343—592no—
167#324—21no—
168#324C2×D5912yes—
169C59#1174011yescharacteristic, complemented, Sylow
170C22×Q8D23611yescharacteristic
171C2×M16—1182no—
172#125—2361no—
173#125—2361no—
174C4×Q8—41no—
175C4×Q8—41no—
176C2×C4⋊C4—591no—
177C2×C4⋊C4—591no—
178C2×C4⋊C4—1181no—
179C2×C4⋊C4—1181no—
180C2×C4⋊C4—1181no—
181C2×C4⋊C4—1181no—
182C2×C4⋊C4C4×D5911yescharacteristic
183C2×C4⋊C4C22⋊D5911yescharacteristic
184C2×C4⋊C4C22×D5911yescharacteristic
185C2×C42C4×D5911yescharacteristic
186C2×C42D23611yescharacteristic
187C2×C42C22⋊D5911yescharacteristic
188C4⋊C8—41no—
189#101—1184no—
190C22⋊C8—22no—
191#97—2361no—
192C4×C8—41no—
193C4×C8—2361no—
194#95—591no—
195#95—591no—
196#95—1181no—
197#95—1181no—
198#95—1181no—
199#95—1181no—
200#95—1181no—
201#95—1181no—
202#95—1181no—
203#95—1181no—
204C2×Q8—22no—
205C2×Q8—22no—
206C2×Q8—41no—
207C22×C4—1181no—
208C22×C4—1181no—
209C22×C4—1181no—
210C22×C4—1181no—
211C22×C4(C2×D59)⋊C411yescharacteristic
212C22×C4(C2×D59)⋊C411yescharacteristic
213C22×C4(C2×D59)⋊C411yescharacteristic
214C22×C4(C2×D59)⋊C411yescharacteristic
215C22×C4C2×C4×D5911yescharacteristic
216C22×C4C2×D23611yescharacteristic
217C22×C4C2×C22⋊D5911yescharacteristic
218M16—1184no—
219M16—2362no—
220C2×C8—42no—
221C2×C8—2362no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—2361no—
226C4⋊C4—2361no—
227C4⋊C4—2362no—
228C4⋊C4—2361no—
229C4⋊C4—2361no—
230C4⋊C4—2362no—
231C4⋊C4—2362no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—21no—
236C42—21no—
237C42—21no—
238C23C2×(C2×D59)⋊C411yescharacteristic
239Q8—44no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—2361no—
255C2×C4—2361no—
256C2×C4—2361no—
257C2×C4—2361no—
258C2×C4—2362no—
259C2×C4—2361no—
260C2×C4—2361no—
261C2×C4—2361no—
262C2×C4—2361no—
263C2×C4—2361no—
264C2×C4—2361no—
265C2×C4#1427364111yescharacteristic
266C2×C4#1427364111yescharacteristic
267C2×C4#1427365312yes—
268C2×C4#1427374912yes—
269C8—82no—
270C8—2364no—
271C22—21no—
272C22—21no—
273C22C2×#1427364111yescharacteristic
274C22#1683739911yescharacteristic
275C22C2×#1427365311yescharacteristic
276C4—21no—
277C4—21no—
278C4—22no—
279C4—22no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—41no—
284C4—4721no—
285C4—4721no—
286C4—4721no—
287C4—4721no—
288C2—21no—
289C2—21no—
290C2#2142258811yescharacteristic
291C2#2142574911yescharacteristic
292C2#2142578311yescharacteristic
subgroupG/H
centerC22C2×#14273641
commutatorC22×C4×C59C22×C4
FrattiniC2×C4⋊C4C22×D59
FittingC59×#1461C2
socleC22×C59C2×#99
prime radicalC23×C59C2×C22⋊C4
cosocleC2×C4⋊C4×C59C23
hypercenter#1461D59
hypocenterC59#11740
LCSG ▷ C22×C4×C59 ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1461

Complements

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

NH ≅ G/Ntype
169. C59#11740semidirect

Maximal subgroups

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

subgroupindex
#214299722
C4×#142736462
#214221242
#214221032
C59×#14612
#1174059